text:
Can a company pay a net salary?

I have been approached by a start-up which said that the monthly salary I would earn is a net salary, with no taxes to report on my side, because all taxes are paid and reported by the company.

A company must pay company taxes, but can a company enter into the personal taxes domain and provide tax-free money? I'm not speaking about not paying taxes, but shifting the tax burden from the worker to the company, so that the employee doesn't ever need to report any income at all from this employer.

Legislation is Singapore but it would be interesting to know whether this is possible in any other jurisdiction.

• There are countries were personal taxes can be paid by the company. More info there: en.wikipedia.org/wiki/Withholding_tax – superjedi Sep 21 '14 at 15:13
• While I've often thought it would be nice if the government and my employer could work out the payments without my having to file a form (since realistically that money was never "mine" anyway), in practice that wouldn't work. There are too many other numbers -- deductable expenses, hobby income, investment income, medical expenses not covered by the company's insurance, and so on -- which have to go into calculating the final number. Even if you trust your employer to keep all of that info private, telling them would be no less work than telling the government directly. – keshlam Sep 21 '14 at 15:41
• In Italy it's quite usual, for instance. – o0'. Sep 21 '14 at 22:20
• @keshlam Actually in a lot of countries everything is done that way. In the UK for example PAYE takes your tax off you as the salary is paid, the same is done for bank interest. You only need to do a tax return if you have another source of income. – Tim B Sep 22 '14 at 9:37
• Other countries simply don't have all these deducatables and things like investment income are done entirely seperately to salary. – JamesRyan Sep 22 '14 at 10:53

In Singapore, this is sufficiently common that the Singapore IRS has a page on their website dedicated to informing employers of how to properly pay this under Responsibilites of an Employer.

Specifically, tax paid by employer is taxable income for the employee (as it's really the employee's responsibility), so they must pay tax for that tax. A tax-on-tax is computed for the tax paid, which also would be owed by the employer if they were paying the full tax rate for the employee.

As a clarification, this is not the employer being truly responsible for the employee's income; this is the employer compensating the employee further to offset their taxable income. This is effectively a fringe benefit, although it may be particularly useful in countries where either tax evasion is common (and thus an employer must compete with employers willing to pay under the table) or where employers are competing with others in nearby countries with lower tax rates. It is not the same thing as the employer making your income nontaxable, though, and has implications for your tax filing.

Significantly, it is likely that if you have additional income beyond income from that employer, it is likely to be taxed at your highest tax rate, as the employer will likely calculate the tax due based on their income being the only income you have in that year.

*Edit based on emphasis in question: I'm not from Singapore nor am I a lawyer, but based on my reading of the IRAS website, it looks like you do not have to file if you have no other source of income, because they have a No-Filing Service which takes income information from your employer automatically and generates a tax bill, which presumably would be fully paid in your case. This only aplies if you have no other sources of income, however; you still have to file if you have other sources of income since your employer would not know about them.

If you are eligible for this service, you should get a letter informing you as such. They also have a tool to check your filing status on their website.

• This sounds to me like "grossing up" the benefit of not having to pay taxes. – Peter K. Sep 21 '14 at 23:08
• This is common in European countries as well. You should be able to adjust the tax as filed by the employer up and down on your final return, depending on your specific circumstances. For instance, if they put you in too high a bracket while you qualify for reduced rates for whatever reason, it's likely that you'd be getting money back at tax season. – Lilienthal Sep 22 '14 at 11:25
• @Hal I don't see any evidence of that being true. As far as I can tell, Canada is like the US: employers deduct from your paycheck (a form of Withholding), and send it on for you, but it's your money they're taking out (ie, your salary is $80k, they withhold$20k and send it on, so your net pay is $60k). The treatment the asker is interested in is different: when the company pays you your full income (ie, whatever you discussed in your salary letter), PLUS pays what you would be liable for in terms of income tax (assuming this is your only, or first, source of income). – Joe Sep 22 '14 at 16:11 • How is this anything other than arguing semantics though? 'We will pay you 80K (pre-tax)' or 'You'll receive 60K (post-tax)' has no meaningful difference to me, as long as the company clearly states what number(s) they're providing to prospective employees. It seems to me like both the question and answers here are conflating two distinct issues: whether companies are free to provide gross or net pay figures, and how income tax withholding works in Singapore. – Lilienthal Sep 23 '14 at 8:55 • Because the original question was about those semantics. – Joe Sep 23 '14 at 12:12 If a country had a genuine completely flat income tax system, then it wouldn't matter who paid the tax since it doesn't depend on the employee's other income. Since not many countries run this, it doesn't really make sense for the employee to "take the burden" of the tax, as opposed to merely doing the administration and paying the (probable) amount of tax at payroll, leaving the employee to use their personal tax calculation to correct the payment if necessary. Your prospective employer is probably saying that your tax calculation in Singapore is so simple they can do it for you. They may or may not need to know a lot of information about you in order to do this calculation, depending what the Singapore tax authorities say. If you're not a Singapore national, they may or may not be relying on bilateral tax agreements with your country to assert that you won't have to pay any further tax on the income in your own country. It's possible they're merely asserting that you won't owe anything else in Singapore, and in fact you will have taxes to report (even if it's just reporting to your home tax authority that you've already paid the tax). Still, for a foreign worker a guarantee you won't have to deal with the local tax authority is a good thing to have even if that's all it is. Since there doesn't appear to be any specific allowance for "tax free money" in the Singapore tax system, it looks like what you have here is "just" the employer agreeing to do something that will normally result in the correct tax being paid in your behalf. This isn't uncommon, but it's also not exactly what you asked for. And in particular if you have two jobs in Singapore then they can't both be doing this, since tax is not flat. The example calculation includes varying tax rates for the first X amount of income that (I assume without checking) are per person, not per employment. Joe's answer has the link. In practice in the UK (for example), there are plenty of UK nationals working in the UK who don't need to do a full tax return and whose tax is collected entirely at source (between PAYE and deductions on bank interest and suchlike). In this sense the employer is required by law to take the responsibility for doing the admin and making the tax payments to HMRC. Note that a UK employer doesn't need to know your circumstances in detail to make the correct payroll deductions: all they need is a so-called "tax code", which is calculated by HMRC and communicated to the employer, and which basically encodes how much they can pay you at zero rate before the various tax rate tiers kick in. That's all the employer needs to know here for the typical employee: they don't need to know precisely what credits and liabilities resulted in the figure. However, these employers still don't offer empoyees a net salary (that is, they don't take on the tax burden), because different employees will have different tax codes, which the employer would in effect be cancelling out by offering to pay two people the same net salary regardless of their individual circumstances. The indications seem to be that the same applies in Singapore: this offer is really a net salary subject to certain assumptions (the main one being that you have no other tax liabilities in Singapore). If you're a Singapore millionaire taking that job for fun, you might find that the employer doesn't/can't take on your non-standard tax liability on this marginal income. Everyone pays their personal income tax with funds from their employer; some of it through withholding, and the rest through the balance due at the time of filing. All that is happening here is that the company is calculating your personal tax return for you, and fiddling retroactively with the gross salary to yield a specific after-tax salary. One problem is that there is a lot of information I put in my return to earn deductions, that I would not care to tell my employer. The system would also appear to be contrary to public policy. Governments create tax deductions to give a larger income to those with socially acceptable expenses: health care, dependents, etc. The system you describe would give employees with such deductions a lower gross salary. • You explain the regular way, where you report a (now slightly higher) salary and pay taxes. But, as I said, can they make it so tax-free that you don't even have to report it? – jujenis Sep 21 '14 at 14:17 • Not in the US, certainly. – keshlam Sep 21 '14 at 15:36 • @jujenis See my answer; this isn't what the employer is doing, even if it's how they're explaining it to you. Offsetting your taxes is not the same as actually removing the obligation to pay. – Joe Sep 21 '14 at 22:41 • The company is not calculating your personal taxes. It's calculating income tax on the wage they pay you based on standard applicable rates. An employee still files his deductions separately. – Lilienthal Sep 22 '14 at 11:27 In Canada, the majority of your taxes are remitted by the employer on your behalf after the employer deducts the calculated amount from your pay. Then when you file your income tax return you pay (or get reimbursed) the difference stemming from your particular social situation. Note that this is optional. The employer has to pay its own part of some deductions, but the employee can opt out from getting the standard amount of income tax deducted at source. It is his responsibility alone to pay for his taxes. So in this context, it's entirely possible to advertise an approximate net salary. Most of the accounting over here is done by way of accounting software, and those that support payroll go through a testing and acceptance phase for each revision to the tax tables, so the amount calculated is usually pretty exact (I got reimbursed 120$ last year).

• This isn't what the asker is talking about; they're talking about the employer paying their taxes, not withholding. – Joe Sep 22 '14 at 3:02
• What the OP describes seems to me to be exactly the same as income tax withholding though. – Lilienthal Sep 22 '14 at 11:33
• @Lilienthal Except the company is paying above and beyond his listed salary, which introduces a couple of separate issues (namely tax on tax, and an implicit raise if taxes go up). – Joe Sep 22 '14 at 12:38
• @Joe So this is peculiar to Singapore where not all of the income tax due is withheld automatically, but employers can choose to do this withholding themselves resulting in an administrative advantage for the employee (and the implicit raise)? – Lilienthal Sep 22 '14 at 12:44
• @Joe I don't see how. What is listed is mostly a convention. – Relaxed Sep 24 '14 at 7:08

In Sri Lanka, this is the normal practice. We, employees are free from the burden of paying tax for the income we get as a salary. Because that part is been taken care of by the company/employer.

• This implies that there's nothing (or very little) that would create more tax due, or reduce your tax after the fact. e.g. mortgage interest, donations, etc. – JoeTaxpayer Sep 23 '14 at 12:17

Just a real-world counterpoint, in the UK, we negotiate the "before tax" salary as some number of pounds per period of time. Out of this amount, income tax is typically deducted and this calculation is quoted on the payslip. (Like most of the rest of the world.)

However, there's another grade of income tax called "Employer’s National Insurance". This is calculated just like the other forms of income tax, paid by the employer directly, but the employee never sees this on their payslip and it is not part of the negotiated salary.

https://www.gov.uk/national-insurance-rates-letters/contribution-rates

So say you're an employer and you've budgeted £1000/month for a potential employee's salary. You'd have to offer that person £878.73/month salary to bring the amount you'd actually be paying to the £1000 you've budgeted.

Why they do this, I have no idea.
https://politics.stackexchange.com/questions/4917/what-is-the-rationale-for-employers-national-insurance-in-the-uk

• It's a way to hide the tax. In the UK even a basic rate taxpayer effectively pays 40%, higher rate is 60%. They hide that though by saying its 20% (or 40%) tax, 10% national insurance and not even telling you about the 10% employer's national insurance. – Tim B Sep 22 '14 at 9:40
• Mostly the difference between employer's and employee's contributions is how it impacted wages at the time it was introduced and how it interacts with minimum wage regulations. In some countries (e.g. France) both are actually listed on pay slips even though the distinction still exists. – Relaxed Sep 22 '14 at 17:02

Many countries have employers report their employees' salaries and withhold some money for income tax purposes (it's called “pay as you earn”, “withholding taxes” or taxing “at the source”). Often the system is designed in such a way that most people actually pay too much and can get money back at the end of the year. In that case, the salary you receive can certainly be considered a “net salary”.

Depending on the tax system, individuals might need to file a separate tax returns to report any other income (investments, rents, whatever) or benefit from tax incentives but it can also be optional. If you live in such a country and your situation is simple enough that there are no applicable deductibles, you might simply choose to forgo it and let your employer take care of everything.


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# The Times from London, Greater London, England · Page 5

Publication:
Location:
London, Greater London, England
Issue Date:
Wednesday, November 17, 1915
Page:
Page 5

THE TIMES. WEDNESDAY. NOVEMHETi 17. 191K A SURVEY OF CIVIC ECONOMY. SAVING OX PUBLIC SERVICES. REPORTS FROM THE COUNTRY. UVn I he need of private and public economy wi rr Jz.xl it bocame obvious that the munici- n M would have to set their house in order M v. -aid with few exceptions they have taken t J'- l with the matter. For years past jjt in all parts of the country had been "steadily. partly of course because of B..w datu jin osed by Parliament on the j.-jnirtpalitK partly on account of elaborate n-cvetiient and clearance ftcbemeo and it jin-iord if there was little chance of any halt uA.nut some drastic action from the centre. 'w itii the beginning of the war. however the f icti rhanged. The Local Government Board l known that a rigorous control of all local rulUure was a national doty. Freed r. ib'- anxieties of the November elections. r t of the municipalities appointed special retrenchment committee to BOO how their could bo reduced and we pubtisb thin reports from many of the large muni- which show how the tendency to is progrrtwing. c. Throughout thn war the Finance Conf the City Ubonnl LAA Ujcn preaching m nr l the various spen ding commitlne ii it e tiraated that a taring of about 3OOOO I b. fffurt -d' in the pn-wnt half-year. lntendr d ii.rri- have bn-n deferred and expenditure -i vt iinproTeinaatJi and other public work Hut for the war the work of laying d urn th' thrd pipe w fawTeajing tke supply of t r from VTales woofd bare been carried out at n oUn-Jd font of afcoot 6I.OOO.MM. jnvnrw.H. XThtn war broke out Edinburgh f n t uncil utoT-ped all except mnnnenU.rve i.t.ifa i nditon\ tbn only capital outlay being -.r E.-W -lectrie hgktug Italian wkich TU i' rn' T lurewiary. 1 current expenditure a sora iiv -vinas ved on Urwta and everaj thousand m iuUK licking d oth r department Em- v iJiaMBff have the dillejTnoe in their Army cwd up to them which mean an annual .p.niture of 27.000. The rates hare been r- a -d by one r -mry u tLe pound and but for to .mpJoyes by 3d. Inquine are T. m u -J to how expenditure can be further Corporation have born effecting j. -e D"nir in a quiet way. Although street ians "M rrctncted to 80 per cent only within 'It ciinUh half of the street lamps hare been u-i.it f' r 'mnnUu to nave the consumption of coal. r niumnpal d partments ara withhal fi&g con- 'r -v s ks to be abte to carry on with short ctafls. j. v prnT o- -J to oipen l wort on the extension Kj ai- for tV raunjapal bwldinffj. mi- MiniKi aethntx hare been -rut down I- Lti1' now rrgwded as tie irreducible minhaom -nt iU pnbue kealth. No capital x- i i atur i" l 3 -anl rked upon and for certain I wtuc indiipr DB W orh M clerical wUiiT in Uie Town Hall and the train ways women I. l i i f-mplor'J u tii the pUors of men who l.lv rlr t. i.t Ailuwanr.ii to CorporaUon i-m- wli'i tiiv ruliabd involve an expenditure r.ulv Hs'i.ow" Work h b n stopped on the at I iundhay. and very little "u truet cU-inuiff or in th Tho ror ratkm w s /unoog the flrrt Vi not- Uic nr v ity or rrdnrcd expenditure .I'miig-tSK- woi w.d vrr initiated a tfsiaa .f .iiwim r pitl -jp--nditure waa topped nd -.rdii l 'K nTB.- Ting chrm Wer put in kK'Tjnr. hitjtii.nu. have also been eCected m mnnircp d ijai1iJK nU. i wi i-Tix. Tk V rporation H now lijiiuirJi it sob-ermmiM -s in carefully invo tjr iihi ry i tnvit A asr 'rtin wSat economics is t. v lh t in Hri iirm T wli.-r. T.T xil'l. a/id it U bnlioTed r iuo- ita expenditure H. Tli fV rf t tion d ruled to postpone r litur.- ponM. nd haa given fj"i- r ro JJ nirn1 t oil down ordinary wmiitiirt Vi sfiiilc -wii-rs u arriTed at -i- i. r. ir ff N fh. r. jit malpamation of the 'Is T'IMI Urp outlay u bejcg incurred on T tnmway rr\ires. For the fir t the -.ir'm 1 ttu- Trr-u IUK been obtatmxL and i1 wjar u Ui S.KXJHI payiaent will ke pcetponed i. -f \b wjn. llu-iv u liUle pro p t tn u. -ai tanr i of any fc TEg which will Intod I j r. Uatil if liny n urtion of the rates. 'RUSSIA'S DAY. Till HOSPITAL IN PETROGRAD. 'V ujn. -.if the Anflo-Kuvian Hospital one f the appeal of lluhfiia'i Day to\-n -.nd from I &djr Hibyl Orey. who r- -MM Uicni iu IVuvRrad a report of the n ni uic f..r its a vommodati n there. r i n -d.d utate of the city the use 1 I''IIB.-I .f the j Uoe of the Grand Dnke -iMn f tho Tsar. U u in the principal i 'f"irrJ jii.st p oRite the palace of the T Krn n M. li w not prwwible to hoasrt the O ur-i'ital staff there but at a ehort dU 4\ th. mf-mlHTS of a club hare handed over T rrnt frn orw floor of their bnfldlng. The pr pmiot thr paliKe-for hospital tw is pro- f rapdh but it enUiU very considerable UN and m addition Uw pric -a of fuel and .ni.- ri w lifh m Vtn r d t ha V the re ia MI L. a b ivy dmin on the resoureea of the llospitaj rationu al will have to be 4 J out of the f uada. i .r.f'im ton cn be obtained from th lion i .n. us. Vi- ona- tr t London H.W and -'Tpji Iu nt uu.n or to Me r Haring Hr "in.Kv.t.- K.C. Chexitwa should be croB-d i-uing Hrt and Cx Limited Cmf rt h. "t to Ldy Owui Kiilippa 7 atone-.W. TUT CFXSOR AGAIX. m formed that a young lady writing recently j'in io in a pre incr of war in Germany d. tn informing him of her father's inU-ntioi i- hnmll party to shoot pheasanU on his tl.at ffttlH-r has great dtiiculty in getting TV valuable piece of military information leii by tto DEATH OF PROFESSOR MELDOLA. WORK IN COAL-TAR DYES. We regret to announce the death of Professor Raphael Meldola which occurred yesterday at the age of 66 at his home in Brunswick-square. Professor Meldola was one of the comparatively few chemists in this country who had actual practical experience in the manufacture of coal-tar colours. After attending the Royal School of Mines he entered the colour factory of Messrs. Williams Thomas and Domer at Brentford and after remaining there for about' two years became a member of tho teach ing staff in the Royal College of Science South Kensington where for u time he was private assistant to Sir Edward Frank land in the research laboratory. He next became Assistant to Sir Norman Lockyer in the Solar Physics Laboratory with the object of gaining experience in astronomical and spectroncopic work and in 1876 ho WAS in charge of a Government expedition which was sent to the Nicobar LjUnda to observe tho i total eclipse of the sun. On boa return he received an appointment in the colour works j of Mfertrs. Brooke Simpson and Spilkr at Hackney Wick and daring the eight years ho pent there be made some hnprrtant inventions or discoveri in connexion with coal-tar dycu. He left this position in 18S5 to become Pro- foGM r of Chemistry in Finabury Technical CoDejru but though he thus severed any j official connexion with the coal-tar colour j industry lio always mfcintauv-d hi. intt-roB't i in t. Even t that time he fore-1 aw the decadence of that industry in this country unless ite methods were reformed. Ue always refused to admit that factors such an industrial alcohol and our patent laws were the cause of ita decay and stodfantry proclaimed that chnmical research was the prime- factor in its development and that its decline in this country dated from the time j that Continental manufacturers allied themselves with pure science and British manu- j fACturers neglected such aid. So recently OH the beginning of this year in connexion with the British Dyes Company of the advisory' council of which he waa appointed chairman last July he protested strongly in a. letter to The Times acainst the subordination of science to business in an industry in which science ehould govern the directorate. He was also an authority on photographic j chemistry and in 1901 published a book on th Chemical Synthesis of Vital Products. OuUude chemistry he had an interest in biological mirations. Ho wan editor and trans lator of Weismann's Studies in the Theory of Dofcccnt in 1882-83 and served as president of tho Entomological Society in 1895-97 and one of his hobbies was the study of mimicry in butterflies. Among tha honours he received were th presidencies of the Chemical Society the Society of Chemical Industry the Society of j yers and Colourista and tho Institute of rhemistry. He became a Fellow of the Royal Society in 1886 and in 1913 was awarded ita 11 3avy ftledal. In 1910 he was Herbert Spencer Lecturer at Oxford University from which he' received the honorary degree of IXSc. j The funeral will be at the Jewish Cemetery at Golders Green to-morrow at 1L MR. C. M. GREXFELL. The death took place in London on Monday of Sharks llolyneux Qrenf ell late Lieutenant 10th Liussars. I i He was the son of the late C. W. flrenfell. M.P. i and married in 1S87 tho lion. M&bel Mills sister of tho present Lord Uillingdon and leaves one daughter ftylvia who tnamod Captain Arthur Watts- Itaiscll. Mr. Grenfell wus a noted nder in hia youth winning the Kadir Cup in India. lie took part in Egyptian campaign of IK&Vand 1886. MRS. PANKHDRST'S MEETING CANCELLED. REFUSAL TO LET THE HALL. The managing couxil of the Royal Albert Hall aare refused to allow the meeting organized by the WJSJMJ. to demand the loyal and rigorous conduct of the war to take place there to-morrow. Mrs. I Fankhnmt waa announced as the chairman aid Lord Wllloaghby de Broke Mr. Annan Bryce M.P. and Mrs. Annie Kermey were to hare spoken. In a letter cooTeying this decision the s-crttary pointed out tkat the hail was Jet for a great patriotic meeting but that In the opinion of the council a j mcetiag of the character stated in the circular kUer could not be d ocnbed as patnotic. This letter which was circulated privately contained a new version of the objects of the meeting. It announced that Anziety conocrning the Gorernmejit's conduct of the nation's affairs durmg the war has been steadily growing for some time past. The betrayal of Serbia has come as a final and tragic proof that neither the honour nor thri interests of tLe nation are safe in the present hands and that in particular the lYime Minister and Sir Edward Grey are unfit for the great and responsible positions they hold. On Monday the text of the letter became known for the first time and from that moment many of those who bad supported the meeting in its original form refused further countenance to it The W.S.P.U. now announce A meeting win be held. The time place and date will be announced later. Ticket-holders are asked to retain their tickeU for a few days until further arrangements hare been made. j Kir John Simon who had not then heard of the cancellation stated In the House of Commons yester day in reply to question as stated in our Parliamentary report tha to attempt to stop such a meeting by Government action would be to gh e it a wholly false importance. At a malintf held at the London Opera House yesterday it aid of tha Cinema Ambulance Fund for purchasing an ambulance convoy for the Hntish lied Cncs Society at a cost of 30,000 Sir George Alexander announced that up to the present the proceeds ol the Cinema Day movement had been over 25,000. Yesterday's performance ia expected to produce about Prepare for the Winter Campaign by fitting Non-Skid Tyres The strongest and most reliable of all Non-Skid Tyres is the Wood Milne Steel Studded The Studs CANNOT Come Loose Milne STEEL-STUPDED NON-SKID ft RES. GUARANTEED 3,500 MILES Fitted Diagonally with Wood-Milne Special All Rubber Non-Skids they form The Ideal Combination g WOOD-MILNE LTD. PRESTON 'l'i" -r r mfort. rnvfn. Telephone 411 s Mturhfoter Av. K.O. 'Grmra Byturninf. London. Theme Oily 4797. s IlIllHTDU I1IUMINOHAM. IIELFXST. DUBLIN GL.VSOOW. s raiutiramniaiiiiiraifflifliDiniM COUNCILS OF EMPIRE. DOMINIONS AFTER THE WAR LORD ROSEBERT'S FORECAST. The Earl of Rosebery M Chancellor of the University of Londonpre8ided yesterday evening at University College when Professor J. H. Morgan gave the first of a senes of five Rhodes Lectures on The Was- and the Political Unitv of the Empire. Before the lecture Lord Rosebery inspected a guard of honour provided by the University O.T.C. LORD ttosEBEBT In a short peech at the close of the lectore said he coold not foBow Protanor Morgan orer the whole of hU territory and domain bnt he would Eke to state his complete agTeement with the theais that th old Bnrvpe as we knew It had disappeared never to irUiia in its present ehapo and that at the conclusion of the war tbe form It would assume would be nothing like the form with which we had bo n familiar- He said I do not know anything more discouraging than the announcement that ha rrcentJy been mada ttwt j the one great State in the world which is so remote aud ao powerful that one mieht think it mirht free itbeif from tbe. hideous and bl idy burden of war I Lnw of Botkiag more duhearteninc than Uie announoouent that the Unlknd Btatea of America U about to embark upon a kage Amada. deatined to be eqnuj or acccod only to our own. TMs means that the burden wtfl centime m afl ether Ti i nii and be inrreaced ezaoUy in proMstion to the Fleet of the U iteJ 8Utea. I confem it ia a diaKearteziing prospect that the United States so great and intclfi- Kent a country so happily remote from European conflict should voluntarily in these days take up a burden which after the w&r will be ibund almost tu have broken our b cks. IifFEiUAL FEOE&VTION. Let me tnll you noraethin about the Imperial Federation League. It was founded by W. E. Fonter I should think more than i yean ago and it did excellent work in the way of drawing together the Coloniea a they were then called and the Mother Onmtry. We had meetings both with the ftolnnisbi and with the home stateeiacn and UM rnvntt wan emmentry fruiUal but at laxt our more impatient Ffnntx be an to urge that we shoukl mbmit a c n titational plan for the Uovernment of the Empire in a drflnit tonn t the jad neat of Uie public Thoae who atrreed. with me were mortally opposed to thu. We did not Uemk it was the rigfat or the privilege of a private soo e y t attempt anythinc BO gigantic and at that time we had a very strong TTnTW M KlrYTt Kjb rvA rtf n f af on- TYfr Ti nmn I A9 k f. sV4 J should come frvra what are now the Dominions and not from tha Mather Country. I am rather disprMed to Uiink that wrUi tho ftux of tine and the ex- periencoa of the war that jndfroent may be revened and that the proposal ehould come from the Mother Country to tax Dominions to come into her councils and share her responsibility aa ragwds h r foreign poLcj- Howevwr that only shows wtit progress the question hi nude. Let me take another instance from my own recollec tion. I was in Canada in 1873 and m Australia in 1681. and I am bound to Kay that in 1873 and 1883 both in Canada and hi Austnvha tke Inpwlal sentiment was a very pale sxwdow of wh t ft is now. I think that if our hotter spirits had been able to influence the Government of thia country and to have prr- vuaded it to invite the Coloum as they were then to come and share the government of the Empire 1 they would have met with some unpleasant rejoinders. There wuu tkis very prime roroUerution in the that the Mother Country waa then 1 providing for the whole defence of the Empire and the inhabitants of the Dominions then much more sparse and poorer than they are now wero extremely reJuetAnt to share the white man's burden and feared that might bo their destiny if they were called upon to take part in the Governmcut of the Empire. REOBa&xizrKO THE EXPIRE. All that has changed. Th v have leaped into the arena of their own accord. 1 upy have fought under I thn Imp-nil flag with a henrorm that has akucfct sur- j pa ed that of oar own sons in tkla war. But Ute I they hare shod on our behalf must in its Coaaequenctft change tha constitution of the Kmj'tre. 1 am not now talking about an ideal licn&e of Commons and proportional representation a dummy whioh I think our friend demolished witk almost t o much care because it is pntcticikUy impo sibks I 4o aot care v.tat form it U going to take. Our Constitution is after all. in tho technical sense a mere ruin. There aeo so many breaches in the walls that there is ample opportunity for rebuilding when we c n find the architect. I cannot doubt that when the arduous efforts of the peace oongreus are over on awful task far sur passing a dozen conferences of Yirxrna which wJl Lc before the PlenipotentiArk of the Great Powers whenever they meet when that ta&k over there will appear higher peaks behind mountain summits. there will appear the almost more gicantic taak of reorganizing the British Empire. We hare not hitherto been very elastic in our constitutional dealing but we shall hare I almost hesitate to i ay woat I am going to say. because I am quoting words of my own we shall have to clean a good deal off our slate before \re begin to wntc the new organization of the Empire upon it. God grant that wisdom and power may be given to our ntaitesmen In that day whenever it may come that th patriotism of our outer Dominions will be shown as much in those bloodi 8 councils as it hss beon in the Oelds of the Dardanelles and Flanders. Cheers. One last word to express my pleasure as a Rhodes trustee to hare heard the first of ibis series of lectures. I hope though I can hardly oxpcct that they will all be equal in merit and charm to that to which we hare just lictcond. It is Mmething to frel .that in the halls of Cniversity College tho gigantic figure of Cecil Rhodes is still prexent to help and inspire the Imperial tradition of which he wag so great an apostle. Chows. irOJ/J.V'S STATUS /.V THE CHURCH. The Biauor pf Sornnv RK presided ycFterd.iy at thf opernn of the Southwark Diocesan Conference. Woman's status in the Chnrch was the subject of a rei ort from the Women's Work Cornmitt A Rtrons opinion waa expressed that th present time demand.-d and presented a favourable opportunity of aecurinx an increased supply of educated women trained for service in the Church. CANON BROWNE in moving the adoption of the report said that if a woman turned to the Church for an opportunity of devoting her services they appoinU-d her to very narrow and suhwrwot ways such a mothers' meetinjrs. distribution of magazines visiting A.- That was not the kind of scope which the talents of liettf-r-fdui'ateil nomen rt-quircd. rl A mischievous by-product of the women's movement was the claim of women to be advanced to the priesthood. Such a claim howler did not emanate t from the deaconrames or those strictly concerned with their ord T. The report was adopt -d and the conference adjourned. LOXDOX DIOCESAN FIXAXCE. The BISHOP of Lowr ov prwridin yesterday orer the Londou Diociwan Conference at which matters of finance only were tliwuhwd said he thuught they hd done well in producing 63,770 dun s the year under the finance scheme. The E t London Church Fund had beeu saved from bankruptcy by it. Mr. EVKIAH HrBBAjin rhairman of the Financ IV ard stated that the um of 168,000 was wanted to meet diocesan requirements for the coming year this being a reductirm of IS per rent oa the-previoua budget figure of 80 00. WELSH MIXERS' WAGES. A meeting of the South WjJcj Coal ConriliAti n Board was held at Caidiff yesterday when LDRU ST. AI.DWT prrAlnd as tnJ'iN-nd'nt chairman ami the ownor" at plj tion for a 5 per cent. redu tmn t in the gcnerul wagi- ri.te chanted. Mr. T. L. Davu ar i' l ttf off for the O THTS. and Mr. A. Onions rrpli.-.l for tiu- workmen Beduce l w Kiag price anil elimination in foreign trude were the points on hnh the owners relief. I It m undetvtofKt tt-at statttjrs showed an ar -ratre j r lu -tv n of rd. por ton n pn -c and a fallm off of 4 a million fn In rxpo-t dunr the pervxi under j t j revvw. The workmen cr ttenl that thi advanm i P T oent. on Srpumber fl di l iwt repre nt i all they might have lie.'n rntitU-d to. Ijom' ST. Aunwrf cure ha citing vote for the t irdoction 'n Det-cr.iber 1. The wafi rat therefore j t I becomes 23-81 Jwr i- tt N re the standard. I It w n acrrsi to meet on DeremSor 3 with L rd bt. Aldwyn to flx an equivalent elUn5 prioe to tha minimum wage rate. FIRST SXOirt'AI.L IX LOXDOX. London and tl.e snuth of Hngland has had its first I snowfall nvi. h t-a.-Iur thsn f r many years pa.f. It came in the early hours of yesterday morning though there was a sliRlit and derolU ry fall in North j I Ixindon before 10 p.m. on the previous night and by daybreak yertrrdsy streel and quirc and roofs were covrrrd white to a depth of more than an inch. With the coming of broad dcytight the weather im- i proved nd the alien wow qukkly thawed. 11 EARLIER BANKING. VIEWS ON THREE O'CLOCK CLOSING. After earlier shopping earlier banking. The new arrangement fixing 3 p.m. M the closing hour to which as announced in our City notes yesterday the London banks have1 given their adherence will probably come into force on and after December 1. The arrangement does not apply to country banks which gener ally ppeaking fix their hours according to local needs nor for the present will there be any change in the Clearing Hoiyw hours. It was however stated authoritativelv yesterday that earlier hours at the Clearing House are" likely to follow ad a matter of course when the new schnme is established. The final'details ofji 3 o'clock banking" are expected to be arranged this week. Among bank managers and their stafb inqmrim yesterday showed that the coming change is- greatly i appreciated. The general manager of one of the most important joint stock banks said that everybody j had fallen in very readily with the scheme M being likely to make vrorkmg conditions more comfortable. Jlrreatly with fewer clerks and if anythirg. more business extra working hours for the stalls after the doors had been ekined to tho public have been common in most of the btg bunks. One effect is likely to be an eneouragement to bank customers to observe the golden bnt generally forgotten rule pay in year drafts before the last haU-kour of the day. When the earlier ciostBg schema was first mooted in the rpring. It had a good effect in ttlis direction in the case of one bank at all event Inquiry In one case revealed th fact that a director who had charge of his lira's banking business had when he heard that there was a possibility of the banks clotting at 3 o'clock adopted the plan of com pleting the banking work before coing to lunch. One'possible result of earlier banking is that the Stock Exchange which now closes at J p.m. may open half an hour earlier in the morning. HELP FOR COAST TOWNS. CLAIMS OF THE FISHING COMMUNITY. It is understood that immediate steps are to be taken to relieve the distress among lodging- house keepers and small tradesmen at watering" places and small fishing towns and villages on the east and south -o\st coasts. Tha Government Committee on the Prevention and Rene/ of Civil Distress has approved a scheme for UM alleviation of exceptional cases of distress at those places which it is felt hare a rpedal claim for asststaace. from the funds genermiFly provided by the Canadian Government. A deputation representing north- a t and east coast towns which recently waited on the committee was Informed that the case was recognized as one deserving of Imstetfiat relief and it was agreed that a conference to which representatives of the Sorrth- district should also be invited skould be held to decide on an equitable apportionment of the hind. It was expnWy urged that the claims of fishing towns and villages which had suffered as a result of the taking over by the Government of trawlers and fishing boats should not be overlooked. It is pointed out that the scheme is not one for the assistance of the rating authorities. Up to the present all tke places affected hare boen able to provide the orduury means of subsistence by grants from the National Relief Pund or from special local funds. No provMK n however has hitherto been made to assist the lodging-boose keepers and small traders to pay their rente and it is this the new schema u specially designed to do. DOCKERS AND THE DRINK RESTRICTIONS. DEPUTATION OF PROTEST. The Central Control Board Liquor Traffic receired a deputation yesterday morning from the Dock Wharf. Riverside and/ General Workers' Union. The deputation emphoaizcd the part which the union had played in the prosecution of the war and pro toe ted against the inconvenience c.tuwd by the No-treating Order and against the tbreaten d ira- pnfcition of further restrictions in the London area. They also advocated the establishment of c.inb ens at wt&h good food could be supplied at reasonable Mr. HOBOE M.P. referring to the canteens estab lished through the actirm of the B ard ut Liverpool expreCTrxl the intention of the Board to initiate similar action in Lrndon. LOUD D'ABEBNOH in thanking the deputation for their attendance s.uil that tln-ir rri r wntAtions would receive the most careful f nnsidcratiun and that the Board fully recognized the v.J'iable assistance which they had received from trade unions. He said aowever that Uie Board had obtained from practically all areas authoritative -viden -e of the beneficial results which had followed from their orders and that these rults had been partirijarly notable in the case of tho various jKJrtn. He a.tBured Uie deputation that the Mile obje t of thi' Board was to promote Uie successful prosecution of Uie war and they comd not ignoiv repri'scntationa from tho responeMe for the output of munitions who considered further lestrktions deiir hlf. it waa agreed that with the cooperation of the onion the Board should endeavour to t&ke stefis immediately for tha establishment of cantoena situated at such points in or near the docks an inquiry might show to be mo&t suitable. Dr. Addison Parliamentary Secretary to the Ministry of Munitions rirculat.-d la t ni ht a return showm convictions for drunkenness m the Metropolitan Pohre district for th four eeL"i l eforo and the four weeks after the coming into force of the. N'o Treating Order. Tlas tliow- that the average numb 'r of convictions for the four wtvks hefore the OnUr came into eCctt wa 1 93 uul for tLe four weeks after it became operative 710. THE MAYFLOWER CLl'li. Members of the English Mayflower Club gave an At Home jesttrday in the Harcourt Room Iloasp of Commons to meet the American Ambassador and Lord Bryce. Among those present were Ur Jvrcr AU n. M.I' ipmftdrotl. Mr fiirttj Bno. MJ An W Brlco. M P U i. Tmilmln. K.P Mr bouuo. U I' Hi. Nucl Burton MJ Kr. U t. Price. M.P Mr R. Iloirc. JCP Mi R 4f vl. LP Mr. W Ooota. UJ- Mr Jowrtt. MJ Mr ccUor. MJ1 Mr. Wuno. M.P. cod Sir C'uckUiro. ALLEGED XEWSPAPER WAR CODE. A complaint under the Defeno of U e Realm Act against the proprietors of U Daily Retard and J/oU i Olaopow. to the effec hat between June 9 and September I 115 they u-wd or had tn their posnex- dion or under Uteir control a cipher rode or other means adapted for secretly communicating naval or military mlormation was heard at Glasgow yesterday. Mr. Janu Lumsden editor and Mr. Andrew Forbes managrr of the a\ly Record and Mml both appeared in Court. A plea of Not Guilty was intimateii and tho -anng of the case was tiled for November 19. .4 DOER'S MATRIMOXIAL DIFFILTLTIL'S. At the Crtitral Cnrrurt l Cruirt ymtrrdAf before I the I corder UATKI\H jAroers p Korx. rtudrnt on bail pleaded Guilty to an indictment charging him with bigaoiy. Mr. Cnrns BKXWETT. for the prosecution. ald Uie defend nt was ruafried to his wife on October 7 I I30S and in M rch of last y r they separated. i Early in thr.s year the drfer.fiact met a MM Osvm uid went through tU cr'rm nr of marriage wiUi her I at Vpe Town oa September 0. Mr. R. D. Mem soul iAat after his departure for 1 South Afnea he wrot to hi wife and t-he at otM instrlot'd dtvoree pnvvding which ho thought would hare bnn completed at the time be went through the nrrmosy ct mamaf- at C&r Town. The Rwor-liEn bound the defendant over In his own rrrogniiAncrt in 40 to r nne up for judgment if called upon and directed him to pay the costs of the prosecution. THE COXTEST AT JIERTHTIt. Our CsjdiT C rtTp ndent telegraphs The wnt for the Tarujinvntary ejertinn in Merthyr Bnrnugh was rereirwl yrstrrdsy. Th nominations haro to be abmitt i by Hatardiy nest and Thurid&y. N'nrcmlvr 25 has been pruwionaUy fixed aa the date of polling. NVither Mr. WinMon nor Mr. Stanton has yet held a meeting but it antteips&ed that nnnit the contest starts m earntt it will be hurt and ioUsodv bitUx. FIGHTING CARS. MR. CHURCHILL ON THE WORK OF THE SQUADRONS. Tn one of the Committee rooms of the House of Commons yesterday afternoon a portrait of Mr. Churchill by Mr. John Lavery was pre sented to him by Lieutenant-Commander Wedgwood D.S.O. as a gift from the officers of the Armoured Car Squadrons. Among those present at the ceremony which was quite in formal were Mrs. Churchill Mr. J. King M.P. Mr. Lynch. M.P. Mr. O'Malley M.P. and about a dozen representatives of the Armoured Car Service. -LtEDTEX ANT-Oottx ANDES W EDO WOOD in presenting the portrait said they were there as officers of a force which Mr. Churchill established and which had proved Invaluable. Rarty in September 1914 Mr. CVorefaill. baring set the Boyal Xaral Air Serrice on ita legs determined to establish a land force tn work In cooperation with it and to axsist. according to the intention then held in keeping th remains of Belgimn cli- r of the OVrman hordes. IJy October so great ws the speed and energy which he put into the work tfv armoured cars wsre in the field. They were in Lilli. Dooai. Antwerp and alorg the Scheldt in short wherever there waa fighting. Since then they had been used in South Afnca East Africa West Africa. OaUtpnu and France. In Galtipoh' the gun- also used eparatey and were UD bring nurd in the trcockea. In France under tke Doke of West' they wrre of great u tkj. in the battle of N ure CkapWle and May on on occasion U ry filled a gap In the lines and Bared a regiment of caralry which had been left in the air. Oommaoder OliT r Ixx-ker-Imp n had contingent now working with the Bel ruin Army. Mr. CiiVBTHlLL in accepting the gift raid tho Armoured Car Semcc noa j-jtifle t its creation. The\ of the war in the West had not been such as to ive proper scope to engines of that character. They were densed at a time when the right flank of the German adrance was exposed to attacks from the sea-eoaat to work in coBJimcttan with th airplane squadrons which the Ailrurarty aa asked in the beginning of the war to maint\in in France and Piaaden. Where conditions of mancnrrre prerailed and armies wej moving swif Uy to and fro the power and value of the armoured ear would be mestimabU. But very quickly the linrs reached the sea and coo- ditioui of Uvnch warfare supervened which had lasted until the present time. In the. Went therefore where the armies were bigger than the country there was not that scope for'the action of armoured cars that there might De in the Kast where the counter certainly larger than the armies. But in spite of these conditions the can had made themselves so he was assured when he was at Uta Admiralty by many official report extremely useful and ratuaMe and U ever the line should break either in t a farourabie or ao uniarourable diTcUon their use i and value would be even more widely appreciated. i Ue and hia wife would cherish the portrait not alone 1 for ita own sake but as the unexpected gift of those who belonged to a service which h had the honour to 1 raiae. 1 The portrait will be exhibited to-day in the f Groavenor Galleries. A WESSEX FILM. "FAR FROM THE MADDING CROWD. So many authors and dramatista have allowed their work to be filmed for the cinematograph of late that one can hardly be surprised to find that Mr. Thomas Ilardy kas followed the prevailing custom. A film based on Far from the Madding Crowd and produced hr Turner Films Limited was shown pnrately at the West find Cinema yesterday morning. Mr. Hardy can have htue reason to comptaiirof the way in which hi work has been handled. The Haray-esque touches of dialogue cannot be reproduced of conrse but the fihn has succeeded in catching in U happiest way tho atmosphere of Wessex which mirht well hare proved an insurmountable bamer. On feels that the country in wkich the action is laid is really the Westiex of the novel and that the arm the calth the sheep are the genuine ones orer which Gabriel Oak watched with such rare. The acting also is unnsuallr good notably that of Miss Florence Turner as Bath&heba Mr. Campbell Guilan as Sergeant Troy Mr. Malcolm Cbrrry ad Fanner Boldwood and Mr. Henry Edwards as Gabriel. The Early Closing Association has this week opened a oionpaign lor clr ing at 8 p.m. on throe nights. 9 p.m. on Fridays and 10 p.m. on Saturdays in the Walworth and CaraboTwelf-rosds and on to Peckham aldo the New and Old Kent-roads as for as Deptford. News in Briei Twelve members of Uw St. Peter1 TlTertoa ebott have Joined the Army. Damage estimated at between 10,000 and 15,000 WM done by a fire U Eat Dereham. Norfolk early yesterday morning. At the Central Criminal Court resterdty. m a was sentenced to three years' penal erritade tot theft from a pillar-box. At Ashford. Kent yesterday a hairdresser named Cttin was fined tit tor supplying drink to Canadian soldiers and tii tor setting it without a licence. Mr. George Cave. K.C. the new Solicitor-General and one of his Majesty Privy Council was yesterday returned unopposed for the Kingston Division ol Surrey. William Benjimin Reeve. 41 the litber of flv children was executed at Bedford yesterday morning for the murder of his wile at LeighUm Buzxard on July ft. Mr. Frederick Rogers who took a prominent part in organizing toe national campaign for Old-Air Pensions died at his residence at New Cross yesterday aged (0. BirmmghAra Tramways Committee yecterday re ported ttut 800 women were now acting as tramway conductors and that they had far performed their duti satisfactorily. The closing scores yesterday in thft billiard match of 18,000 points up between M. Inman and O. Gray a the Grand Hall. Leicester-square were Gray la play 11.170 Inman. 11.116. Mr. Charles Carew of Warnkombe. Tirerton. wiQ be put forward a candidate for the Ttverton Division In succession to the late Mr. Lionel Walrond who died from daease contracted while oa active service. An action brought at Liverpool yesterdav by Lancashire fanner aeainst the Army Council to determine the price of hay a Ul "d by the plaintiff bom awarded payment at the rate nf 7 5s. pet ton. A second death that of George Henry nillingkMrt 60 metal roller has resulted from the tramway accident at Birmingham on Friday. The inqneat was opened yesterday and adjourned until UM zith last. Sir George Askwith will attend the adjourned sKUng of the Scottish Coal-Trade Conciliation Board at Glasgow on Monday. The Scottish miners' claim on behalf of 90,000 workers is for 9d per day increase. The present wage u fid. per day. Sixteen wagons wrre derailed and the permanent way considerably damaged at Banbury early yesterday morning through a Great Western Railway goods train from 8 wind on to Bordesley running past tha point The fireman was slightly injured. For causing three calm to b slaughtered la contravention of the Maintenance of Live Stock Order 1913 Archibald Holdctock. wholesale butcher was fined 10 at Reading Police Court. It was stated that this was -the lint conviction ia tha United Kingdom under the Order. Mr. William Blane wLoe death tn hi $0th year was announced yesterday rt Windsor was for dearly fiO years in Royal service. One of his sops. Trooper Alfred Blane recently died of wounds received at Galtipoli. Of two other sons serving one is- now home from the front wounded. The London County Council offers about J40 trade scholarships for girls between the ages of VI .J Itt V AM MB VBW.K I 1 O I It 11 f A IP provide free education for two years at trade school approved by the Council with maintenance grant o 8 for UK tint year and 12 for the second year. A wage conference was held ymterday in London between the board of tbe Port of London Authority and representatives of the Dockets' Union. After discussion the board informed the men's leaden thai their application for an increan of 3d. per day in their war bonus w uld be reviewed at a later meeting and the- decision communicated to them. It was stated by a motor-omnibus driver at a Southwark inqntvt yesterday that if the woman who was knoekrd down in the dark had been wearing a light dress instead of a black one he would haw seen her and been able to avoid her. lie added that it would be well if people earned a newspaper or a handkerchief in the darkened streets. A joint conference between the master dyers and bleachers and the bleachers' trade unions on th question of a claim or increased wagrs was. resumed at Manchester yesterday. The official announcement on the result was as follows An agreement hM been reached and notion are to be withdrawn. A ballot will be taken at the works at once. At Burslem yesterday three men were ommon 4 nnder the Protection of Animals Act in respect of a rabbt conning match the prosecution contending S that as the ground was fenced the rabbits wcro -jf- captive animals. The Stipendiary dismissed tbe snmraonva holding that.though the rabbiU could nut I escape they were not actually under control. Catarrh ofDigestive Organs. Angier's Emulsion exercises soothing' lubricating aotifennentative effects through out the entire digestive tract. That is why it is so valuable in affections of the stomach and intestines. It soothes and cleanses tha mucous membrane allays irritation fermentation catarrh olceradon. It restores tona to all the digestive functions and it promotes normal healthy action of the bowels. Pre scribed by the medical profession for twenty- four years it has proved its value in many obscure digestive and bowel disorders. Endorsed by the Medical Profession. A Doctor write 1 advocau 11 bar tun. both by myttlf and u strongly th use of Angier't Emaluoa I coiualunt. Mvtnl very tuccMira in all catei of flataleot dyspepsia. cairi of ihu dcripuoo ia which ictetrioal indigestion and in tbat I Aanier'f EmaUiaa wu tb t roedj. tembia compliant macotn cclitU. Sifntd M.D U-B tc. Free Sample Coupon. AtUrttt. THB ANQICN CMKHIOIML OO Ltrf. NOTICE re HORSE WHISKY The great rise in price of all material and our small margin ol profit owing to the high craaEty we supply compels us to raise the price 3d. per bottle in order to maintain our reputation Price now 4/3 per bottle. Sold by all Wint Merchants. MACKIE CO. DISTILLERS LTD. QUALITY IS MORE IMPORTANT THAN PRICE. l'r lS 5.1 YIXG SER VICES. T E n 'f'd f1.z..J b 'CADle ob\ oas paLw t ir r. till" 1.1 Jt'c.1 I ti..la inl l l r."Tl.-1iI n" itDpo'lNi b l Jn itj" \-euJt'nt f./ 'I.fd tic Witb hO\1 eV'l"r. f.7.:101I d 'lIOO. i al11 al ro' J.jiture n mal d t M1let t f'l tions t bud..ts t'ow 'e b b crait 'io Bho ency tW11J.ie 1 progrn emg. jRf.r.n..ut.- ThI"ou hoa of P" 1.0 IIp''nJing J I t. t f t:30.000 -rlo..f nt rc f 1'N'd ,1t d. d. or d.-n tor inneut t. PIY .vr 's d an .w U.OOG Wl'1U'IU.H.-Wbo.n -u ive dl.'ndit ilI .t. ch 1'1I''r DI lJ1 c .xpendi a.lvf.v" .f'don.u..rta d doI a.nd o.b..r I" I. .tnl ve t 'G' c nt' O' bid- I "ur.a. i---TtI f in a t :4 1.'Ii t. ont .t I" 1.h 1I1. t. wlt j.r l .r" i. 'r T".J IIWlf""I1d wo k I' it tJ1IiJdin l.Jtr" UfJri' f'fl 1.t.A.t L' DOW"-gvdNi .t. 4. wlt.b ex- 1000I in -ml.oorl..d .t lcli Ind1"P'rv..bl. tr.omwaTS. I'n rm kl1-.l t.o 1.\.IIL' \.o.1. .II. C rpor oti.on 11 "l. "d ex .1'1 tu. -'n o 'p'Pti lur.hlll IIl".u rou d W"ur 1. tJD1'1 1 tr t ck ol1llJ3' th. l..r. LI 't.-Th f'orl"ration 0. for 1. nl' C"p'W on,1 1'4.1 'It. "It'll'nng Chf'mt'8 w. mlllllcipool IJ W11J" ii1lr. 'Tt.I-Th. i E'Dgagood. IJ'O 'arPfull inVt'f\t IU. r..ry 'IIJI1. 10 a..n..in .1 I. t..t..1. Th'I. t r .Iut. d..t.fonntnat.l tOo lol'.j' bt Ih.t .to mIWtll" r.a r..dllc 1U4- d"17" I'Jnr""TH..T/r .1'f"'tjoD .1 I..It. -4. 1" j. tI" a f" j"- 'lIjm' ru "W'I.Jr. 1/ r. i. at. .i .4. 11 to r..nt "lDA m&tIon 4 111' 4 flutL. IS 9"tJ. II I IN" I 1ir. L ,4 n o t.L.- 'flAl pa c. tbo. 11. proorpoooct 1. I4inc. 114"1':1 i' "Y. r.-duct.lc.n a PETRO GRAD. "r tor An HOfIJ"it.&l--aDl' J" "f .1 1Jay" I. lAdy 'j l'f'U'c aJ. 11".1 'f 1/ i. 11".1 hI h Tald.Of' f tol tt. T'.tr-'loraJ. i'L.1 oJ'JlOIIite hnl' I hou. It. l ut -11. fr .f proPIm' "act' -for r--r r- iI i r .1. "rt lrad thatrtlwre \'Y 1'PtIOtJn .n at. \1i.j r.I"nr''h"n th I IIi. 'Ioria-stt. LoDd n. R. W. 1 .nt M I. "I. nl'l. t rta I' ,0 t. ro. 1\ that. nU "t. pn..n'r 't 'nf inlC tting r. -c. 1 l'1f' r. Brnn.swick. qua.rc. M ldola l I I rern&inin I I K'ns &lSis Fra.nlclarf h A I I 'nt w I i 8im I e t j eri" dy e Con I I th wayt m it. at fore. I W in' la chtm ca.1 i m8oDU a.ctureno Ives lh l be a.letter I I busi .C8S" auth the Synt.h is ccnt Entornolo a1 butte il'8. j Amon re i\'f'd I Indll try. 'Dy6l'S Che stz I I. I OJ'f'nlelJ. ll 1 M.P..I' J I bel liit d..u ht.er. Hn. the 11'84- Attd I hue or Zed w r" w. 8 't'd I' Kennf' .re vt' df'C .t.ary for" op Jm" ag e I Weh ci W obJ W that- Govf'rnIIV .nt'lI 301' b. th int4' I Pa.l' CuJa.r S J' I I'f"lpottl\ ble J' th bt It. &I1DO m P Tlck "ldf'l'll the J' I for. menl.8 t bo Clf'Uation--staW ted I'ar g \'e wboU 'e. Id I y i" I II 'rr8ocif'ty..t co..tof t30.0 O. Of'Of1PeAt'X Uld"r1 p nt t h 8 t bt n Y ftltf'l'da'a 1. .0. IIfUIlnmnunnnmmmnnllllUDIDD n mmmmnmnnmnmnmmumIHIllmmmllrnmmun nnUD is. \V ood Wood-Milne TIRES. Filt 1'.1. ToI..phon413. L.11'I 'G 'Pht'll.-t'itY47117. 4 l1IJIlnnnmnlnuruilmmnnDllnmmUIUnU1mrnnnnurmunmmml1lJIIltl lmnnumnU nnnullt munumllmnnnIIIUIDI V AR. London. presided or en L 8Ir Ro ber'J' b t. the PfO' tttahapo. tr th oot'n laid- a rt'cl'I' Jy t l eety war. ttiah of tl Inu'd ern euotJ .tion Vattt' en dialJoeut.n ftg p hap ily s th. l e b..t.cks. i t'Xre ent d .r Cokm 8 I t 1 nistli /WI b a 'onRtitution&l Go1'ernm to ju.l..meat mortall thi. to I im .me WI. tbt an nrn-.1 O I an n Wt Do C.'S war. lnti nt ll'Pvel'Po 'd I t e Do t'O fOft nowe 'RJ' I a.DO r in t&nt- 'P'JO J e wJ.t n Intue GoVf' t. t u.ad -d n8 the entment. wit1l1Ome unpl AdaDt m.t..r. the' iAh.a -nts ftOW. I d tioy tht- J REOnoA. O Th.-v h.a. U thf' J' 11.- 1m P"'riaI t. at. t p-.1 0 11' 'e 1f n l..m iDl C .I l mmons fr f'nd d t..o pnoc caUy impo..i inl CoDl'Ut is. in i. rebulJ.1i whn f t &t c' d t th wh t 1uu eo a I onc aw fr s pu dozn onen -k whh wi le bore t 1'let o 6J' Powe t I ove t w apP hl p hin meuntn awmt Uu re wl ap p t II t lr gintc t o 'rgani Briti Epi. h tth vt'r EWic conttioD tel 'e Ihal ha"tI al t hcute t IY .ht I g b qtotina wor ow abl .Vf' deA g of lr w e wte DW Of1Pa tOtt un it Go t W ad pw..r mY b g.n O dy. wh..nc'r my c. tt tbe patotim o ou ot Dmn b .hw r tb LI. oudl hs btt t th Dan li'I Cf On W 11 fJ rl a R" t t te ft t 8r l tU hop c hy' mpec. tLy wil L equa m ad Ju I is t ff h Cnvety CU to Igaoc tn ol Ithol I p hlp ad ire th Imi tat wlh wa.1 gat a a pU C TOJI.Y'S ST.tTlS TIE Te DrSor f Sr'RI rndt y fpr.by thl opIin Suthwak Diofs Conf"lncI 'omn's I1at I hI 'arh 1& Ch. I II1r rm tC Wor"n'lI Worl wa f'X N lht th. Jnl p tf'd fa.urahl opprunit A'llnj in'J'f'1 aupJly 'ural tred Iri t Cuh. nl' p. mong t aopton th. "pr .id tt i I turN oppuity df'.tin b.r 1IC th'yappinl. lwr ver nr' &utf t way. Iuch a mothln' rNtnj. distribufn m&uit vi it- In Tht Wi tt fOI whih I h. t..nt 'uild. m it'ou bY'Iru't wom.n' mO''mf'nt Wf 'omll lvan P u. rrMt. ho. caim. hw..r. fantt' d..Aon. th0 tricly wacmed wth thfr Ordl1. Te Ipor WI adoh- ajof. LO.'DO. DICESAN FIXtoCE. U1'OP L s. pl ing o\ 'r fio..n OnfD lnttf' 'e onl 't" tboultht'j L63. .0 dunRt th IM.t I f n i o.w. 'Ar i p lUl'll 80,800. I I .f I .u ilt "t' t."Ja af'1'lk.ti"n rrdurti"n hrn..rll tI. anW. I" aru..1 OIJOlll-nl I .Ili .timlnu on for" hl 'h I ur. "tOt' d .oIi lj. a 'I' 1".Ju..t1 I r rrir. a 1 f&lltno I. f1'\-j wc rLin"11 1,1'11&1.-1 I I I of I i I" 11 Vp m".r 10 diol M J'f'Prw..Dt AI.f W'Y f' r. l ratt' I bf. .U 't'nt. oJ. 1O'M wi 1 f' .I 1. n th 1 m'kh -i. r ff\ Ll'8 d..ullt r in t mehto-arod att I pron d q l I ehopping--ea.rlior not terd. y. ber n pre nt I Ollrs. I Cl l' ng are nt' of o' r inq'11 J' t. aUy f'r man 'r im nt a. I an. n b t'1f nt"O mea.t emto nI fo n ru p" t. eV1"a III. t il w1 e J'OIII bility clnRi o. optf'll ba.nkin lun h. One' possible b Exch.1D I t. Rt t t'men t aIleviat oa gt'ttt"'O\ 1 b r zrd d ng I te I w Me h rf'.Sf'n t.at J o \Mern 8 oulel ap 1J'I"W 1y fi3 in taki o\'f'ri 1 RA IitaD f' nt 8U b ta 8Iion. n iBt k p"MI t ir desi ned S. Yf'JI ay an. p t war.and JIT'Ot.o incon\.n t'nre d .t.ric' ton. Ad c.\nt..na Y' Ho oE f.1" t-n. .ta act cm n..n1 f'XP initi te D'AJER. os. t I r'1'r.'nt.ati t I'on. i l'r"ti.m. uil 1 .I nllobl. a. t.ani' 1'f' \-f'd a. .1 r o c Il It B ol'J I. Il 'aI' igno thoo.c I'f'I eJ lr"hl" eed imm.di&t. ly 'ant \.dd.i n N-J''t ry f 1a4 niht t h Po 'e 'omi o h" tli Or.l r 1193. U Jf..f Cr. 'JJ. ish 'rday t .l't'- 'Cy DtJ. r. 1W n. .P 'U n. uJmln. 116.1' Ra l'd. ChaJ E. 3U'.4 Df f..noe Qw A t tII u. l ai1y Jl aal t'ff t I. Ita oth r me ns \1' t Dalv M 1J. I ap .a'f'd I .J/A It. .urt Itf'cord..r. OK ocx. :9 n c O'TT. O .p -.ar m t Il Wul1lo'f'Dt .e" .I .h t N ul.h h U\ tltftt i w t I .u m.r.y m.Art C. f" nE 'Or.1J:1\ d. h CniZAD. tsl d I Ct 'inn nr.Mu h 'rcrot. ha 1' .0 bnuu..t /\at 1I.l\la y nf'S t. T" i"1' m1w-r .s. d&t S r. f m. is I t. ahur1. 1hMp. 1 bi td. L i I Am ng in- Ilonnal' Ch hill. Ir. L-nch.3LP. I I -1.IJOvrr.u.CoWX.L"'PEB 'WEDOWOOD nt.- in the mtAhli. In1' uable. 8ept bf'r. r. .nJ on' d..t Tm rati intm. tJn u. -r Scbt'ldt--tn Soc l u.eclllf'paratf'ty tftme e& W. tIa t. NeuTe H. one .I'd "in 'OlrT' l.IO .1. I aca-rt. J..t n i. eng' ht .he sq n1 Admiralt ing W armJ 'I movin q wekl l"NW h lie& "d nt b r for' t.he count. 06t&inI I r n b IDA.ZI o r.zb ext remely tlBef uI f. di T ue widel an4hl I w o beJol1 he to-da FRO I man "the Ay ve eem f hit H t que loud d the a.tmos mJ M 11 ue ne fl't'b. f 5i1 d acti notabl &t b& Farm 'D dot in CIllI1bt rwel1'Nat.s M ew I l11fttt rs b l1l. mAD ten h .u aup qJaA t r. re Ca w t1'da Frect k rs nation Old. r ew I' the aoo IlAtisfact.oril Ora -Gray pia Warnloom t' -lAte oa Uo el Yf'tlttordar b L cuhit'f' U lI1It O und ha wuo .uJ.-I l7 pE' d tb. O 'OI'f" 60. Ri m kwith at..nd.tbt' 'oaJ. 'I'rad. ond. da ilI Sol. df' If'd mo RaUwayl'OOt windO poi.ntll. tiJ'f' be Ul m hIa YNt rday Troo bf' 13& and 16 years oa M h 31. 1118. The acholat'l.hh. pr v'ide t.- -tnde t wi lID& of -'it 1:8 tJ W. 't rf'p ntati..f"I I UlI ton. -'i thf' J' in"J'f' da 11 \t J. 1' J'f''f' -.d 1S b 1- in'1U ttord"t t t l n t. f. r1' blf'Iol" f'n t UD the -r for Yt t4'A'da 'H 1-\n t. .d..f' :1 taken..t a 'ii1 r Yf""t t'\\al .H. Prot. -tf.lOa 0 co ng p Q'ioQ t t. n bJt.a JfIi to anim.aI5. d i t" "r actuaJ..l ,1. I7j .fr fl 1 1 I i Emuls on I .1 J t I t 1 t 4 1t l t' I1. or man :1. 'ftfJ En orsed 'iff. t writel- II 11& u. ,1 .t 111'0111 the useof .enl aucce.hiI tll.leDt \11P"psiz..1 d oa. Em1ill aD the oompJa.itlt-DlOC01J. coli a. M.D. K.B. etc. ANG a-w. 11 SION .Nil ttJC. u.c. P\U in eo.- 1M -d w,1 f. PMb4e 00. Lt Oa..tleh LO. I It 1 n 4n'O OWI'"I 4/ EetaWiaW na. N V V t w n I V et 1 II 1i4iiti4' r.cenJcut icbon-and j jd ha1 thnUt I i I r. va I r i4 1.t I .rtu I rQ.n1r argo crAitkf. rG C ty T Wt 'afl 5sr a V Lu TVLt th pit.1 V T W I fl ut4 c- th nJtur T V 4 Y 3 Id. re ial b1 b a-i iiiM .t w. rt ct4d t it aZ. ZO WIthh5hhD.Z C fl- r.t. V' t4 i r j' 1. th D' r t1.Vflt io I 1iItue LU O V V. V .t.tMI. U'I t i .ur UfliIiy.ti c I V L.uJ.ngVThc necewity fl r YVSI la'g rA I.t T.VO. TnUflUi d1jj1iia un inveetiga- .4&m.t V l. S T4UI .V.V iw.h'y r. pV c &w.nA- I'L'vy.TrIL. -TI. hV 1. 4V'.V 1j--r.- I. 'nrn.t. jjt.1r. ni. y wjr e.-- V5 t. 4 .jf y obta ed. VV eg e. T j' V' 0 t V r- V. frIVV V ir. jt ar'ommodation t. rrvd.d fli. f he V V V LII V' VmTfl..s. 1 &uo rTh ml.eN i V iT prices an I 'etrured i -.T t4 I he th V Vjfl ve Li i 'v'4V.jlUtoIthl. r't.r no Vj.ior-j&-t an I VVPJkVfR Mssr. cro Co. C.ZUIOrts V inr. y. ting cen1J r iT5it.ner 0 V Vk ti i S Vi1 tIt M 1 2 V I im-ent ons j. posi on for 1 a I I I w I t r t 3 I afl 1j5 pat ot c. T man y meetin V Simon-who V give il I 'i tb Li I 11111 /N f I I IV I ofall C A V I 11 Ceiyafert A 'Grama-'Byturninf. I J o on" W Ro KazsT h t r.pe L eemo re th Btat is I nn ODd m i e..vs I exa y peot on -nt I I FED EstTION. nething I Federsl on L.usg ueV. e&Onieti tp rtts bean t i I .DneRt I th tin iteon imnpsii&m tA. mv Vh.f 54. cozi at n i a ani f gment a f tot I s icr r png1 t I I f sa 188 I f f th r me ery S Lii I I t. IrE e t S nu S p. repr sezitation ou 1 C o ot 0 s aU i man cn c if oex'-iut w U Is meet-when is hare-i own- re Uoodkeis Rhod Iectw oUee V 110.11.4 X'S ST1I ITS SOtTTWARK opening str.n the order. a d V 1nan a CVOfl L IrA GUS. mectin Sii a Mn own.r" spphratir'n ensrid S 5 f s are i. avera-e rvluetion t. p tb sve W shove fj-.q.4 selhn i ehr nd V end I 1 t final details f i I i a ii inrnostotthebtg is eucnnra V th the r i ti i or south-enet S nd vil or t th cLam or north-et ot eteee onth euitable i I t protesited th MI.HODt1E th V e rintrit tions dei.1rLhIe. the weikP oiiri 1o pjg FFL 0 WER 0 Akien. vV By M.P. eI M2. Y. efps'i. Jow-I 5tP. SI DE. fla3 ces- on L DI FFICUL TIES. defendant March ceremony y -ro f. j noes 't0'5'P1Ifl Vfl (5flpf Cape f come f A T Correspondent Merih o- r "P. 'LtEtrrENt.-r. MXtNDEa ug orce 1 ts won n gu und aes'ice I they .1 a Belrisn eas swiftly V V b h reporin-ettrcrnely p p btt e gem ne Fl rerioe V a. I elneiri p.m. V I a .4. .4 I a fc 23 .nadi5 23 4 Cvi onJuly6. .ic 4. h Cro s a duties t a. a heinZ V f ts. 5c in .A n .eh 5i V -ear 1 3j 1 wi Vi' 1 J. weaiin .e f'ft V sn. .S 7 is' waea was i.y i iJ t agwemei .t' 4 i.f.i a swnmoned j of 4.4 'i- e.cape.they V t V if V V V .i V .4S. V V V V 4 t h V V V 'V V I my's. a j Vp i0 f mdi .iion comp siet-mucouc ANGIERNULSION V OfsflCbii&S. I1.&I.44.I6. I 2s tll 4 I TH CS4ltO Sa as4 Lands t r V W1 ItM V Itr r mnrTzj WIIITEIIORSE pre marg o r.e price in maiutau V V . . . / \ . . . * < : . ! , < * , . . . - . ' , . . ' - . , . ! ! * , . . . - ; ; " . , , . . * { > . - * . , . - - ) . . ' . , . : : . , ; . < > , , , . , . , . 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# statsmodels.genmod.cov_struct.GlobalOddsRatio¶

class statsmodels.genmod.cov_struct.GlobalOddsRatio(endog_type)[source]

Estimate the global odds ratio for a GEE with ordinal or nominal data.

Notes

The following data structures are calculated in the class:

‘ibd’ is a list whose i^th element ibd[i] is a sequence of integer pairs (a,b), where endog_li[i][a:b] is the subvector of binary indicators derived from the same ordinal value.

cpp is a dictionary where cpp[group] is a map from cut-point pairs (c,c’) to the indices of all between-subject pairs derived from the given cut points.

References

PJ Heagerty and S Zeger. “Marginal Regression Models for Clustered Ordinal Measurements”. Journal of the American Statistical Association Vol. 91, Issue 435 (1996).

Thomas Lumley. Generalized Estimating Equations for Ordinal Data: A Note on Working Correlation Structures. Biometrics Vol. 52, No. 1 (Mar., 1996), pp. 354-361 http://www.jstor.org/stable/2533173

Methods

 covariance_matrix(expected_value, index) Returns the working covariance or correlation matrix for a given cluster of data. covariance_matrix_solve(expval, index, …) Solves matrix equations of the form covmat * soln = rhs and returns the values of soln, where covmat is the covariance matrix represented by this class. get_eyy(endog_expval, index) Returns a matrix V such that V[i,j] is the joint probability that endog[i] = 1 and endog[j] = 1, based on the marginal probabilities of endog and the global odds ratio current_or. initialize(model) Called by GEE, used by implementations that need additional setup prior to running fit. To obtain the crude (global) odds ratio, first pool all binary indicators corresponding to a given pair of cut points (c,c’), then calculate the odds ratio for this 2x2 table. pooled_odds_ratio(tables) Returns the pooled odds ratio for a list of 2x2 tables. Returns a text summary of the current estimate of the dependence structure. update(params) Update the association parameter values based on the current regression coefficients.


text:
Main Content

# Resolver-to-Digital Converter

Resolver-to-digital converter

• Library:
• Simscape / Electrical / Control / Observers

## Description

The Resolver-to-Digital Converter block models a transducer that converts the angular position or velocity of a rotating shaft to an electrical signal. Resolver-to-digital converters are commonly used in harsh, rugged environments, such as in fully electric vehicles.

The converted signal is proportional to the sine or cosine of the shaft angle.

A resolver sensor has one rotor winding with the exciter sine wave that is AC-coupled to two stator windings. The stator windings, a sine coil and a cosine coil, are mechanically positioned 90-degrees out-of-phase. As the rotor spins, the rotor position angle changes with respect to the stator windings. The resulting amplitude-modulated signals must then be gained, demodulated and post processed to extract angle and velocity information ([1] and [2]).

### Equations

The block uses a phase-locked loop (PLL) to extract the angle and the velocity of the rotating shaft. The error voltage used by the PI controller is obtained as:

`${V}_{e}={V}_{y}{V}_{p}\mathrm{cos}\left(N\theta \right)-{V}_{x}{V}_{p}\mathrm{sin}\left(N\theta \right),$`

where:

• `Vp` is the excitation voltage.

• `Vx` is the `x` voltage for the secondary winding of the resolver.

• `Vy` is the `y` voltage for the secondary winding of the resolver.

• `N` is the number of pole pairs for the resolver.

• `θ` is the angle.

Therefore, the velocity is obtained as:

`$\omega ={K}_{p}{V}_{e}+{K}_{i}\int {V}_{e},$`

and the angle is computed from the velocity using:

`$\frac{d\theta }{dt}=\omega .$`

## Ports

### Input

expand all

Simulink signal that corresponds to the voltage phase angle.

Data Types: `single` | `double`

Simulink signal that corresponds to the `x`-axis voltage.

Data Types: `single` | `double`

Simulink signal that corresponds to the `y`-axis voltage.

Data Types: `single` | `double`

### Output

expand all

Simulink signal that corresponds to the rotational velocity.

Data Types: `single` | `double`

Simulink signal that corresponds to the rotational angle.

Data Types: `single` | `double`

## Parameters

expand all

Number of pole pairs in the attached machine.

Proportional gain for the phase-locked loop filter. This value determines how aggressively the PLL tracks and locks to the phase angle. Increase this value to more closely track step changes in the phase angle.

Integral gain for the phase-locked loop filter. Increase this value to increase the rate at which steady-state error is eliminated in the phase angle. This value also determines how aggressively the PLL tracks and locks to the phase.

Initial estimate of the phase angle. If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

For inherited discrete-time operation, specify `-1`. For discrete-time operation, specify a positive integer. For continuous-time operation, specify `0`.

Note

If this block is in a masked subsystem, or another variant subsystem that allows you to switch between continuous operation or discrete operation, promote the sample time parameter to ensure correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

## References

[1] Santanu Sarma, V.K. Agrawal, Subramanya Udupa. Software-Based Resolver-to-Digital Conversion Using a DSP. IEEE Transactions on Industrial Electronics, 55, 371-379 . February 2008. (https://www.researchgate.net/publication/3219673_Software-Based_Resolver-to-Digital_Conversion_Using_a_DSP)

[2] Ankur Verma, Anand Chellamuthu. Design considerations for resolver-to-digital converters in electric vehicles. Texas Instruments, Analog Applications Journal. 2016.

## Version History

Introduced in R2019b


text:
# GSEB Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths 3 Understanding Quadrilaterals InText Questions

Try These (Page 43)

Question 1 .
Take a regular hexagon as shown in the figure:

1. What is the sum of the measures of its exterior angles x, y, z, p, q, r?

2. Is x = y = z = p = q = r? Why?

3. What is the measure of each?

(i) exterior angle
(ii) interior angle

4. Repeat this activity for the cases of
(i) A regular octagon
(ii) a regular 20-gon
Solution:
1. ∠x + ∠y + ∠z + ∠p + ∠q + ∠r = 360°
[∵ Sum of exterior angles of a polygon = 360°]

2. Since, all the sides of the polygon are equal.
∴ It is a regular hexagon.
So, its interior angles are equal.
x = (180° – a) y = (180° – a)
z = (180° – a) p = (180° – a)
q = (180° – a) r = (180° – a)
∴ x – y = z = p = q = r

3.
(i) ∵ x + y + z + p + q + r = 360°
[∵ sum of exterior angles = 360°] and all these angles are equal.
∴ Measure of each exterior angle
= $$\frac{360^{\circ}}{6}$$ = 60°

(ii) ∵ Exterior angle = 60°
∴ 180° – 60° = Interior angle
or 120°= Interior angle
or Measure of interior angle = 120°

4.
(i) In a regular octagon, number of sides (n) = 8
∴Each exterior angle = $$\frac{360^{\circ}}{8}$$ = 45°
∴Each interior angle = 180° – 45° = 135°

(ii) For a regular 20-gon, the number of sides (n) = 20
∴Each exterior angle = $$\frac{360^{\circ}}{20}$$ = 18°
Thus, each interior angle = 180° – 18° = 162°

Question 2.
Find the number of sides of a regular polygon whose each exterior angle has a measure of 40°?
Solution:
Since, the given polygon is a regular polygon.
∴ Its each exterior angle is equal.
∵ Sum of all the exterior angles = 360°
∴ Number of exterior angles = $$\frac{360^{\circ}}{40^{\circ}}$$ = 9
⇒ Number of sides = 9
Thus, it is a nonagon.

Try These (Page 47)

Question 1.
Take two identical set squares with angles 30° – 60° – 90° and place them adjacently to form a parallelogram as shown in Figure? Does this help to you to verify the above property?

Solution:
The given figure helps us to verify that Opposite sides of a parallelogram are of equal length.

Try These (Page 48)

Question 1.
Take two identical 30° – 60° – 90° set – squares and form a parallelogram as before. Does the figure obtained help you to confirm the above property?
Solution:
Above figure also help us to confirm that: opposite angles of a parallelogram are equal.

Try These (Page 50)

Question 1.
After showing m∠R = m∠N = 70°, can you find m∠I and m∠G by any other method?

Solution:
Yes, without using the property of a parallelogram, we can also find m∠I and m∠G as given below:
∵ m∠R = m∠N = 70° and RG || IN. the transversal RI intersecting them.
∴ m∠R + m∠I = 180°
[Sum of interior opposite angles is 180°]
or 70° + m∠I = 180°
m∠I = 180° – 70° = 110°
Similarly, m∠G = 110°

Question 2.
In the figure. ABCD is a parallelogram. Given that OD = 5 cm and AC is 2 cm less than BD. Find OA?

Solution:
∵ Diagonals of a parallelogram bisect each other.
∴ OD = OB =5 cm
or OB = 5cm
or BD = 5 cm × 2 = 10 cm
∵ AC = BD – 2cm
∴ AC = (10 – 2) cm = 8 cm
0r $$\frac{1}{2}$$ AC = $$\frac{1}{2}$$ × 8 cm = 4cm
or OA = 4 cm.

Try These (Page 56)

Question 1.
A mason has made a concrete slab. He needs it to be rectangular In what different ways can he make sure thai it is rectangular?
Solution:
He can make sure thai it is rectangular using the following different ways:

1. By making opposite sides of equal length.
2. By keeping each angle at the corners as 900.
3. By keeping the diagonals of equal length.
4. By making opposite sides parallel and ensuring one angle as 900 in measure.
5. By making all angles equal and ensuring the measure of one angle as 900.

Question 2.
A square was defined as a rectangle with all sides equal. Can we dfine it as rhombus with equal angles? Explore this idea?
Solution:
Yes, because a rhombus becomes a square if its all angles are equal.

Question 3.
Can a trapezium have all angles equal? Can it have all sides equal? Explain?
Solution:
Yes, if it is a rectangle. It can have all sides equal, when it becomes a square.


text:
# Creating a solved 9x9 Sudoku based on certain rules

The question:

A rectangular fence is a set of 4 cells on a solved sudoku grid with co-ordinates $(i,j)$, $(m,j)$, $(m,n)$ and $(i,n)$. You can visualize this as the 4 corners of a rectangle.

A symmetric rectangular fence is a rectangular fence where opposite corners hold the same value. Meaning $grid(i,j)=grid(m,n)$ and $grid(m,j)=grid(i,n)$

Make a 9x9 completely-filled sudoku that has a minimum number of symmetric rectangular fences.

I have been trying to prove that there exists no 16-hint solvable sudoku. I realized that if there exists a symmetric rectangular fence (as I have termed it), then it becomes necessary to give at least one of the 4 cells as a hint. So, minimizing the number of such occurences would make it possible to create lesser-hint sudoku's and maybe throw some light on why 17 hints are still required.

For puzzlers, the question in section 1 is complete by itself; you need not bother about the rest. You may use a program to find the answer, but there are many, many possibilities, so you will still have to use some logical approach to it.

• +1 cool question. the 4 cells do not need be adjacent, right? hence the use of rectangle, instead of square? – JLee Mar 19 '15 at 16:53
• While I am still mulling this over, I hunted up a paper I read awhile back about Sudoku generation that may be of interest either to you or others working on answers: Sudoku: Bagging a Difficulty Metric & Building Up Puzzles Leone, A., M. D. & Vaswani, P.. – user2322 Mar 20 '15 at 0:43
• @JLee No, they don't have to be adjacent. – ghosts_in_the_code Mar 20 '15 at 10:03

Here's one I just created with zero symmetrical rectangular fences.

• Judging from your first three columns, you started with the same idea as me. +1 for a better-looking answer. – KSmarts Mar 19 '15 at 18:32
• It looks like the same basic idea, but mine was posted first, by around 10 minutes. I was just attempting to create ANY sudoku so that I could analyze it for "symmetrical rectangular fences" and the first one I tried had zero fences. – JLee Mar 19 '15 at 19:14

I just did the easiest construction that I could—I put the numbers 1-9 in order on each row, and then shifted the rows to avoid block or column duplicates. This appears to produce a grid with no "symmetric rectangular fences," but I don't know the minimum number of hints required to solve it.

123 456 789
456 789 123
789 123 456

234 567 891
567 891 234
891 234 567

345 678 912
678 912 345
912 345 678

There's a method described in Sudoku: Bagging a Difficulty Metric & Building Up Puzzles for generating a solved Sudoku board. You take the 12 order three latin squares (using values of 0, 1, and 2). Of these 12, you select 9 with replacement that are placed on a 3x3 board and then a 10th is the 'over board'. Each value is then read as trinary when converting to base 10, and then some specific swaps are done.

Here's where I'm guessing, and I haven't done the full analysis of the resulting board. Unfortunately, I don't have the math background to be able to prove that that such is the case.

I am a programmer though, and so I whipped up a quick bit of code:

#!/usr/bin/perl

use strict;

use List::Util qw(shuffle);

my @squares = shuffle (
[[0,1,2],[1,2,0],[2,0,1]],
[[0,1,2],[2,0,1],[1,2,0]],
[[0,2,1],[1,0,2],[2,1,0]],
[[0,2,1],[2,1,0],[1,0,2]],

[[1,0,2],[0,2,1],[2,1,0]],
[[1,0,2],[2,1,0],[0,2,1]],
[[1,2,0],[0,1,2],[2,0,1]],
[[1,2,0],[2,0,1],[0,1,2]],

[[2,1,0],[0,2,1],[1,0,2]],
[[2,1,0],[1,0,2],[0,2,1]],
[[2,0,1],[0,1,2],[1,2,0]],
[[2,0,1],[1,2,0],[0,1,2]],
);

my @board;
my @final;
my $outer = shift @squares; for my$i (0 .. 2) {
for my $j (0 .. 2) {$board[$i][$j] = shift @squares;

for my $x (0 .. 2) { for my$y (0 .. 2) {
$final[$i * 3 + $x][$j * 3 + $y] = 3 *$outer->[$i][$j] + $board[$i][$j][$x][$y] + 1; } } } } # now, swap R2 & R4; R3 & R7; R6 & R8 for my$i (0 .. 8) {
($final[1][$i], $final[3][$i]) = ($final[3][$i], $final[1][$i]);
($final[2][$i], $final[6][$i]) = ($final[6][$i], $final[2][$i]);
($final[5][$i], $final[7][$i]) = ($final[7][$i], $final[5][$i]);
}

foreach my $r (@final) { foreach my$c (@{$r}) { print "$c ";
}
print "\n";
}

And running it a few times I get:

7 9 8 2 1 3 5 6 4
3 1 2 6 5 4 9 8 7
5 6 4 7 8 9 1 2 3
9 8 7 3 2 1 6 4 5
2 3 1 5 4 6 7 9 8
4 5 6 9 7 8 2 3 1
8 7 9 1 3 2 4 5 6
1 2 3 4 6 5 8 7 9
6 4 5 8 9 7 3 1 2

4 5 6 1 3 2 9 8 7
3 2 1 8 9 7 6 4 5
7 8 9 6 4 5 2 3 1
5 6 4 3 2 1 7 9 8
2 1 3 9 7 8 5 6 4
9 7 8 4 5 6 1 2 3
6 4 5 2 1 3 8 7 9
1 3 2 7 8 9 4 5 6
8 9 7 5 6 4 3 1 2

7 9 8 2 1 3 6 5 4
2 1 3 6 5 4 7 9 8
4 5 6 8 9 7 3 1 2
9 8 7 1 3 2 5 4 6
3 2 1 4 6 5 8 7 9
5 6 4 9 7 8 2 3 1
8 7 9 3 2 1 4 6 5
1 3 2 5 4 6 9 8 7
6 4 5 7 8 9 1 2 3

5 6 4 3 1 2 7 9 8
1 3 2 8 9 7 4 5 6
9 7 8 5 4 6 3 2 1
4 5 6 2 3 1 8 7 9
3 2 1 9 7 8 6 4 5
7 8 9 6 5 4 2 1 3
6 4 5 1 2 3 9 8 7
2 1 3 7 8 9 5 6 4
8 9 7 4 6 5 1 3 2

I'm taking the shortcut of not doing the replacement in my code. There are some properties of these puzzles... if you note, the 7, 8, and 9 are always in the same set of three, as are the 1, 2, 3 and the 4, 5, 6. The fact that its a latin square on the over board too, then makes the swaps such that I believe that the rectangular fence cannot form.

If you have the process only use one latin square, the grid looks like:

1 2 3 4 5 6 7 8 9
7 8 9 1 2 3 4 5 6
4 5 6 7 8 9 1 2 3
3 1 2 6 4 5 9 7 8
9 7 8 3 1 2 6 4 5
6 4 5 9 7 8 3 1 2
2 3 1 5 6 4 8 9 7
8 9 7 2 3 1 5 6 4
5 6 4 8 9 7 2 3 1

This next one (another one grid generation) is one that is probably closest to the other solutions that have been provided and allows a clear picture of the patterns that are formed in this type of generation.

1 2 3 4 5 6 7 8 9
4 5 6 7 8 9 1 2 3
7 8 9 1 2 3 4 5 6
2 3 1 5 6 4 8 9 7
5 6 4 8 9 7 2 3 1
8 9 7 2 3 1 5 6 4
3 1 2 6 4 5 9 7 8
6 4 5 9 7 8 3 1 2
9 7 8 3 1 2 6 4 5

Though, while I am confident that these do not have rectangular fences, and the generation method precludes them, I am not sure that such is the case.

The key part is in order to form a rectangular fence, I need to swap two columns somewhere (either in a single 3x3, or in the over grid):

? A B
? B A
? ? ?

The thing is that this pattern does not happen in any of the latin squares because that would force the third element of the square to be in the same row or column as itself, which is a violation of the definition of the latin square. ... but, as I said, I'm not sure I have a proof there.


text:
# Measurement of angular and momentum distributions of charged particles within and around jets in Pb+Pb and $pp$ collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV with the ATLAS detector

Research output: Contribution to journalArticlepeer-review

## Authors

• ATLAS Collaboration

## Abstract

Studies of the fragmentation of jets into charged particles in heavy-ion collisions can provide information about the mechanism of jet-quenching by the hot and dense QCD matter created in such collisions, the quark-gluon plasma. This paper presents a measurement of the angular distribution of charged particles around the jet axis in $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV Pb+Pb and $pp$ collisions, using the ATLAS detector at the LHC. The Pb+Pb and $pp$ data sets have integrated luminosities of 0.49 nb$^{-1}$ and 25 pb$^{-1}$, respectively. The measurement is performed for jets reconstructed with the anti-$k_{t}$ algorithm with radius parameter $R = 0.4$ and is extended to an angular distance of $r= 0.8$ from the jet axis. Results are presented as a function of Pb+Pb collision centrality and distance from the jet axis for charged particles with transverse momenta in the 1$-$63 GeV range, matched to jets with transverse momenta in the 126$-$316 GeV range and an absolute value of jet rapidity of less than 1.7. Modifications to the measured distributions are quantified by taking a ratio to the measurements in $pp$ collisions. Yields of charged particles with transverse momenta below 4 GeV are observed to be increasingly enhanced as a function of angular distance from the jet axis, reaching a maximum at $r=0.6$. Charged particles with transverse momenta above 4 GeV have an enhanced yield in Pb+Pb collisions in the jet core for angular distances up to $r = 0.05$ from the jet axis, with a suppression at larger distances.

## Bibliographic note

43 pages in total, author list starting page 27, 11 figures and no table, submitted to PRC. All figures including auxiliary material figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2018-03/

## Details

Original language English Phys. Rev. B 100 Published - 2 Dec 2019

## Keywords

• nucl-ex, hep-ex