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Signetics 2650 & 2636 programming/2650 processor

The 2650 was first released by Signetics in 1975. These video game consoles use the 2650A, a redesigned version that was smaller, cheaper to manufacture and had improved operating margins. The 2650A was released in 1977. A later version, the 2650B, had a few design changes and additional features, but we aren't concerned with those here. The 2650 was fabricated in NMOS, was TTL compatible, and its many control signals made it simple to interface to. It was described by Adam Osborne as being a very minicomputer-like device having been closely based on the IBM 1130. It has a number of distinguishing features:

 * 32k byte address range, organised as four 8k byte pages.
 * Variable-length instructions of 1, 2 or 3 bytes.
 * Single bit I/O path (flag and sense pins).
 * Multiple addressing modes including indirect and indexed.
 * Vectored interrupt.
 * Eight-level return address stack.
 * Seven 8-bit registers.
 * Two program status bytes.
 * Powerful instruction set.

Registers
The 2650 has seven general purpose 8-bit registers. R0 is always available, whereas there are two banks of R1, R2 and R3 which are selected by the RS bit in the Program Status Word.

Program Status Word
The Program Status Word (PSW) is a special purpose register that contains status and control bits. It is divided into two bytes, the Program Status Upper (PSU) and Program Status Lower (PSL). The PSW bits may be tested, loaded, stored, preset or cleared using the instructions tpsu, tpsl, lpsu, lpsl, spsu, spsl, ppsu, ppsl, cpsu or cpsl.

Reset
When a Reset pulse is applied to the 2650A, program execution is forced to begin at memory address 0. The only other thing we know for sure about the state of the processor after reset is that the Interrupt Inhibit bit in the Program Status Word is cleared. As we very much don’t want spontaneous interrupts to happen, one of the first things our program should do is set it to disable them until we ready for them. The “Signetics 2650 Initialization Application Memo” also suggests that we may set the Stack Pointer to zero, and that we should set the Register Select bit to a known state.

The With Carry bit and the Compare bit may be set to whatever condition you will need them in first. In a simple program which has them in the same state throughout, this is a straightforward decision. In more complex programs it is generally best to set them to the most used condition initially, and then switch them back and forth whenever the opposite condition is needed. If the With Carry bit is on, then the Carry bit should be initialised appropriately before the first arithmetic instruction. Otherwise there is no need to initialise Carry or any of the other bits (Condition Code, Interdigit Carry, or Overflow).

Interrupts
Certain events occurring in the PVI cause it to signal the 2650 that it needs attention by setting the $\overline{interrupt}$ line low. If the Interrupt Inhibit bit in the Program Status Word is not set, (in other words interrupts are enabled), the processor will finish the current instruction and then set the Interrupt Inhibit bit. The PVI then outputs its interrupt vector, 3, to the data bus and the processor executes a ZBSR (branch to subroutine on page zero) to address $0003.

When the interrupt service subroutine has finished, it should be exited with either a RETC or RETE instruction. The latter will re-enable interrupts.

Instruction set
All mnemonics in the 2650A instruction set are 3 or 4 characters long. The first two or three characters specify the operation, and if present, a final character indicates an addressing mode to use (see the next section, Addressing modes for more detail). Assembly code for the 2650 generally looks something like this:

loop:  lodi,r0 $20          ; load r0 from the byte immediately following, $20 stra,r0 $1F40	    ; store r0 in the absolute address $1F40 eorz   r0           ; exclusive-or r0 with itself bctr,un loop        ; branch relative, unconditionally, to address specified by 'loop'

There are 34 basic instructions:

Addressing modes
The Signetics 2650 has four main addressing modes: Register, Immediate, Relative and Absolute. In addition Indirect and Indexing may be combined with some of these.

Register addressing
All register-to-register instructions are 1 byte in length and use R0 as the first operand, while the other can be any of R0, R1, R2, R3. lodz   r3          ; load r0 from r3        addz    r2          ; r0 = r0 + r2        lodz    r0          ; not very useful! eorz   r0          ; exclusive-or r0 with itself ; very useful! A one byte instruction for r0 = 0

Immediate addressing
In immediate addressing the first operand, which can be any register, is specified next to the instruction; followed by the value of the other operand, which implicitly must be a constant. All immediate addressing instructions are two bytes in length. lodi,r2 $20       ; r2 = 32 subi,r0 8	  ; r0 = r0 - 8 iori,r1 %00100000 ; set bit5 of r1        comi,r3 15         ; compare r0 to 15

Absolute addressing
In absolute addressing the first operand, which can be any register(but see exception in Indexed addressing below), is specified next to the instruction. The second argument designates the absolute address of the memory location where the other operand is located.

Relative addressing
In relative addressing the first operand, which can be any register, is specified next to the instruction. The second argument designates a memory location where the other operand is located. This second argument is a relative displacement from the current address and can be any value from -64 to +63. In practice we don't specify this value as a number. It generally takes the form of a label and the assembler does the calculation for us. If the label is too far away the assembler will generate an error message. Relative addressing is also used in branch instructions to jump to a memory location close by. lodr,r2 number    ; r2 = 42 bctr,un next      ; branch to next number: db     42         ; define a data byte = 42 next:  addi,r2 53

Indexed addressing
When indexed addressing is used, the effective address is calculated by adding the contents of the specified index register to the address field. The addition uses the value in the index register as an 8-bit positive number. lodi,r2 5 loda,r0 $1F00,r2   ; r0 = contents of address $1F05 Note that the first argument is always r0. Some assemblers may allow this to be omitted from the code, but for the sake of readability it should be included if possible.

Two other options allow for the index register to be auto-decremented or auto-incremented before it is added to the base address: lodi,r2 5 loda,r0 $1F00,r2+   ; r0 = contents of address $1F06 lodi,r3 $A6 loda,r0 $1000,r3-   ; r0 = contents of address $10A5

Indexing may only be used with absolute addressing. It may not be used with branch instructions, but two special instructions exist for this purpose. They are BXA (branch indexed, absolute) and BSXA (branch to subroutine indexed, absolute). Auto-increment and auto-decrement cannot be used with them, and register R3 must be specified as the index register.

Indirect addressing
Indirect addressing means that the argument address of an instruction is not specified by the instruction itself, but rather the argument address will be found in the two bytes pointed to by the instruction. The indirect addressing mode is indicated by an asterisk. pointer dw $0F00           ; in most cases this would be an address in RAM, i.e. a variable .....       loda,r1 *pointer    ; r1 = contents of $0F00 Indirection may be used with relative addressing as well, but since code in these consoles is operating out of ROM, and RAM addresses are generally too far away for a relative address, there is no apparent use. One exception does occur when space for code is at a premium: :bar  equ     $1F0E 0000 066A    :      lodi,r2 $6A 0002 CE1F0E  :      stra,r2 bar 0005 0D1F0E  :foo   loda,r1 bar 0008 0BFC    :      lodr,r3 *foo+1   ; load r3 indirectly from $0006, i.e. $1F0E The last two instructions both load a register from bar, but the last instruction only uses two bytes rather than three.

Indexed Indirect addressing
When indexing and indirect are used together, the value of the index register is added to the indirect address, not to the value in the address field of the instruction.


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User talk:Tom Dobbie aka Edmond Dantes

By human reckoning this is Nov 4th 2021, and, well, this is interesting - and, I am pleased for the new possibilities.

The name on my birth certificate says Thomas William Dobbie, but like my aka Edmond Dantes I was buried by criminals in authority to silence me for their personal gain.... The story is 12 years of torture, and 18 years previous to that when I was only being abused... but, my whole life before that has been magnificent....

So, I escaped the Chateau d'if and like Solzhenitsyn, I choose to switch on lights in the darkness for I have children to rescue, and so so many more.

Let me catch my breath, and more will be made clear...

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Tom Dobbie aka Edmond Dantes


text:
User talk:Fhatanimunzhelele

Grade 8 History Notes Term 2 The Scramble for Africa

Causes for the Scramble for Africa:

-During the late 19th century,, European countries were fighting against each other to be the most richest and powerful nation -Citizens became proud of their country's achievement and they were willing to go to war to fight for their country -This pride and devotion to one's country is called nationalism
 * Growth for nationalism

-Africa I rich in raw materials, Europeans wanted to have a direct control over the raw materials of Africa
 * Search for raw materials

-When Europeans soldiers came to Afric,many of them died due to being bitten by malaria-caring mosquitoes -In the 19th century it was discovered that Quinine was an effective treatment for malaria. -As a result Europeans were able to settle in Africa
 * The discovery of Quinine

title: User talk:Fhatanimunzhelele


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Marxism, Communism, and Socialism/Origins of Marxism/

Kautsky traces the roots of Marxism to German Philosophy, British Classical Economics, and French Socialism. Thus, it is best to look at these components in layman's English.

As a note, it is best to say Dialecticians rather than German philosophers influenced Marx and Engels. Hegel is the major player in both cases; he was "the most encyclopedic" of the dialecticians, and German philosophy "culminated" in the Hegelian System[1].

Dialectics

But what is "dialectics"? It is, more or less, a form of logic. It began with the Ancient Greeks as the logic. Literally, dialectic corresponds to "discourse" since the Greek dialectic was simply a discourse between a "pro" and "con" position on an issue.

Hegel changed this, for Hegel had created the "Modern" dialectic. This note will be a step-by-step explanation of his method, so it may be a longer section than the others. Hegel believed the starting point is the immediately given experience at a particular historical juncture. This immediate experience is not "apprehended". Thought must proceed from that which is initially given onwards.

Yet what is "initially given"? This brief moment is when Hegel, a philosopher who is an idealist, is empirical. Or, in other words, this is when Hegel looks at reality (empiricism) rather than only thinking about it.

The goal is not to "create" the world out of pure thought processes, but to reconstruct the "intelligibility" (ability to apprehend by intellect only) of the world. This requires us to assign the fundamental categories that capture that intelligibility.

Hegel writes: "In order that this science (i.e. Hegel's own theory) may come into existence, we must have the progression from the individual and particular to the universal - an activity which is a reaction on the given material of empiricism in order to bring about its reconstruction. The demand of a priori knowledge, which seems to imply that the Idea should construct from itself, is thus a reconstruction only ... In consciousness it then adopts the attitude of having cut away the bridge from behind it; it appears to be free to launch forth in its ether only, and to develop without resistance to this medium; but it is another matter to attain to this ether and to development of it."

Now, what exactly is a "category"? Hegel explains that a category articulates a structure with two poles, a pole of unity and a pole of differences. From this general notion of a category we can go on to derive three general types of categorial structures.

In one, the moment of unity is stressed, with the moment of differences implicit. In another the moment of difference is emphasised, with the moment of unity now being only implicit (or in other words the nature of the moment of unity is left undeveloped). In a third both unity and differences are made explicit together, both are developed.

Another way of speaking of the connections is the concept of dialectical contradiction. Hegel's views on contradiction have been controversial (to say the least). In terms of categories, what he means is fairly straightforward. If a category is a principle that unifies a manifold, then if a category exhibits only the moment of unity, then there is a "contradiction" between what is inherently qua is category (unifier of a manifold) and what it is explicitly (moment of unity alone). Overcoming the contradiction requires the initial category to be negated (in the sense that a second category must be formulated that makes the moment of difference explicit). Yet when this is done the moment of difference will be emphasised at the cost of having the moment of unity implicit. This means there is another contradiction. To overcome this the second category needs to be replaced with a category in which both poles, unity and difference, are each made explicit simultaneously.

Hegel is well aware of what contradiction and negation mean in formal logic. He was following a tradition since Plato of using "contradiction" and "negation" as logical operators. The logic is dialectical logic.

British Classical Economics

Classical Economics is a vast school of economic thought which will not be entirely discussed here. Instead, only David Ricardo and Adam Smith will be reviewed.

Adam Smith had argued that value could not have originated in utility. He presented the counterpoint: if utility was the basis of value, how is it that water (which we need to live) is of no value compared to diamonds (which have no use at all)? He came to the conclusion that the labor used to make the commodity determines the value in exchange.

As a general matter, Smith thought, the amount of labor required to produce the goods would determine the rate at which they could be exchanged for one another, though he mentioned some exceptions. If the supply of goods could not be increased by labor, then their value would be determined by their scarcity, and not by the labor embodied in them. Old master paintings would be a case in point -- no more could be produced, since all the old masters were dead, so the price of these paintings could rise to any height without calling forth a competing supply of new production. Monopoly would be another exception. The monopoly would be able to keep the good scarce, preventing any competing new production. The general idea seems to have been the people can always choose to produce for themselves rather than obtaining goods and services in exchange for others. If they must give up more labor to get the good by exchange, then they would produce for themselves instead.

Basically, the work of Adam Smith that is relevant to Marxism is summed up to a single proposition: Exchange Value must depend on something common to all goods; embodied labor is the one common factor on which exchange value depends.

Ricardo essentially reformed the Labor Theory of Value so value wasn't "entirely" based on labor, although a large portion of value is. He theorized about the influence of machinery affecting value. Ricardo saved the labor theory of value from a serious objection. The objection had to do with land and rent. On the one hand, land rent seems to be a cost of production -- shouldn't the "natural price" of an agricultural product depend on the rent of land? On the other hand, labor will be more productive on land that is more fertile. Crops grown on fertile land will cost less labor. Does that mean it has less value?

I'll skip the math and come to Ricardo's conclusions. It is the labor required for production on marginal land (the next unit of land) that determines the normal price or value of agricultural products. And the surplus of production on more fertile land is "absorbed" by rent. Landowners don't have to do anything to earn this rent -- they get it automatically as a result of the competition for fertile land.

Ricardo fortified the Labor Theory of Value from most criticisms. There were three main vulnarable points: absolutely scarce goods, international trade, and monopoly. Marx played with these, which will be discussed later.

French Socialism

French Socialism can be summed up as the rejection of capitalism. All sorts of outlandish ideas have been associated with French socialism (e.g. polygamy, etc.).

French socialism is only one name of the concepts. Marx referred to them as utopian socialism. Marx grounded his theory in scientific materialism (i.e. beyond physical reality there is nothing), and thus criticized the Utopian socialists for not having a basis in reality for their theories.

The utopian socialists explained that "somehow" everything will fit together into an ideal society. Of course they never bothered to investigate how socialism would come about. They wrote instead of what socialism is.

This may not seem like a bad idea, but to Marx it was a grievous error. Marx explained his theory with historical materialism, which is our next topic.


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Marxism, Communism, and Socialism/Historical Materialism/

"[People] make their own history, but they do not make it as they please; they do not make it under self-selected circumstances, but under circumstances existing already, given and transmitted from the past. The tradition of all dead generations weighs like an nightmare on the brains of the living."[2]

In the beginning, according to Historical Materialism, is material reality. A particular group of humans, living in a specific part of the world, with a unique history, a particular technology, etc. It is Marx's idea that those specific details produce a certain kind of society with certain kinds of classes, certain relationships between them. Those relationships, in turn, generate ideas, religions, cultures, etc.

So we have an "orderly" explanation of human society: material conditions leading to technology leading to classes leading to culture. It was Marx's observation that there were "regularities" over long periods of time in this process. (He called them "laws" because that was the custom in 19th century European science.) He saw the evolution of human society in these "regularities" or "stages" (taken from the Wikipedia article) This is the "Ladder of Marxism".

1. Primitive communism. Human society organised in traditional tribe structures, typified by shared production and consumption of the entire social product. As no permanent surplus product is produced, there is also no possibility of a ruling class coming into existence. As this mode of production lacks differentiation into classes, it is said to be classless. Paleolithic and Neolithic tools, pre- and early-agricultural production, and rigorous ritualised social control are the typifying productive forces of this mode of production.

2. The asiatic mode of production. This is a controversial contribution to Marxist theory, initially used to explain pre-slave and pre-feudal large earthwork constructions in China, India, the Euphrates and Nile river valleys (and named on this basis of the primary evidence coming from greater "Asia"). The asiatic mode of production is said to be the initial form of class society, where a small group extracts social surplus through violence aimed at settled or unsettled band communities within a domain. Exploited labour is extracted as forced corvee labour during a slack period of the year (allowing for monumental construction such as the pyramids, ziggurats, ancient Indian communal baths or the Chinese Great Wall). Exploited labour is also extracted in the form of goods directly seized from the exploited communities. The primary property form of this mode is the direct religious possession of communities (villages, bands, hamlets) and all those within them. The ruling class of this society is generally a semi-theocratic aristocracy which claims to be the incarnation of gods on earth. The forces of production associated with this society include basic agricultural techniques, massive construction and storage of goods for social benefit (grainaries).

3. The slave mode of production. It is similar to the asiatic mode, but differentiated in that the form of property is the direct possession of individual human beings. Additionally, the ruling class usually avoids the more outlandish claims of being the direct incarnation of a god, and prefers to be the decendants of gods, or seeks other justifications for its rule. Ancient Greek and Roman societies are the most typical examples of this mode. The forces of production associated with this mode include advanced (two field) agriculture, the extensive use of animals in agriculture, and advanced trade networks.

4. The feudal mode of production. It is usually typified by high feudalism in Western Europe. The primary form of property is the possession of land in reciprocal contract relations: the possession of human beings as peasants or serfs is dependent upon their being entailed upon the land. Exploitation occurs through reciprocated contract (though ultimately resting on the threat of forced extractions). The ruling class is usually a nobility or aristocracy. The primary forces of production include highly complex agriculture (two, three field, lucerne fallowing and manuring) with the addition of non-human and non-animal power devices (clockwork, wind-mills) and the intensification of specialisation in the crafts--craftsmen exclusively producing one specialised class of product.

5. The capitalist mode of production. It is usually associated with modern industrial societies. The primary form of property is the possession of objects and services through state guaranteed contract. The primary form of exploitation is wage labour (see Das Kapital, wage slavery and exploitation). The ruling class is the bourgeoisie, which exploits the proletariat. The key forces of production include the factory system, mechanised powered production, Taylorism, robotisation, bureaucracy and the modern state.

6. The socialist mode of production. Since this mode of production has not yet come into effect, its exact nature remains debatable. Some theorists argue that prefiguring forms of socialism can be seen in voluntary workers' cooperatives, strike committees, labour unions, soviets and revolutions. The socialist mode of production is meant to be a society based on workers' control of all production, with a property form equating consumption with productive labour. The key forces of production are similar to those in capitalism, but changed in their nature due to workers' control and collective management. Additionally, the merging of mental and manual labour is meant to increase the level of productivity and quality of the productive forces. The primary ruling class of this mode is meant to be the working class. The primary form of exploitation is meant to be self-exploitation - in other words, the exploitation of some people by others (the "exploitation of man by man") is meant to be abolished.

7. The communist mode of production. Since it refers to the far future, it is a highly debated theoretical construct. Some theorists argue that prefiguring forms of communism can be seen in communes and other collective living experiments. Communism is meant to be a classless society, with the management of things replacing the management of people. Particular productive forces are not described, but are assumed to be more or less within the reach of any contemporary capitalist society. Despite the imminent potential of communism, some economic theorists have hypothesised that communism is more than a thousand years away from full implementation.

These are not rigid and impenetrable categories. There were capitalists in Ancient Greece and Egypt, and elements of feudalism exist today with American Corporations.

The Marxist hypothesis is that while the ultimate cause for such changes lies in technological innovation, the means by which one social order supplants another is that of class struggle. Nomads had to physically defeat savages; early despots had to defeat nomad barbarians; feudal lords had to defeat the despots; and capitalists had to defeat the feudal lords. These were not simply military struggles; they also took place in the realm of ideas. For example, new religions were invented to "justify" the rise of a new kind of ruling class. New "moralities", new "legal" concepts, new "philosophies", followed. If this "metahistory" is more or less correct, asked Marx, what happens next? Is capitalism the "end of history", or will there be another new social order?

We know the answer that Marx gave, of course. Possibly he noticed the curious trajectory that was followed: primitive equality to proto-classes to centralized despotism, then mini-despots, then a lot of mini-despots, then...advanced equality? More likely, I must admit, he probably used Hegalian dialectics to arrive at the same conclusion (Hegalian philosophy was very fashionable in Marx's youth and exerted a lasting influence on the way he approached matters).

Technologically advanced equality, which he called communism, would be the next "stage" of human history, and one in which classes would no longer exist at all. Moreover, like all the others, it would come into existence through class struggle with the old ruling class. To Marx, it seemed inevitable that capitalism, left to itself, would become more and more openly despotic (and with fewer and fewer significant despots) and, because of its own economic constraints, would generate crisis after crisis threatening a return to barbarism or savagry unless overthrown...by all those who were not capitalists, the working class.


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Marxism, Communism, and Socialism/Marxist Economics/

On Commodities
Commodities is to capitalism as elements are to chemistry. It is very important in capitalism. (Economics, Marx and Engels argued, is the science of capitalism).

The commodity has two values: one if its usefulness, fulfilling a need, it's called a use-value; the other "expresses" the use-value in relations to each other, called the exchange-value. Use-value is concerned with "quality"(or the character of different sorts of commodities), and exchange-value is concerned with "quantity".

Here's where Marx's translation gets warped: every commodity has both forms of value. If we take away value, we are left with labor. But since we screwed around with the value, we screw around with the labor also.

Value is affected directly by labor. Marx cites the example of power-looms which decreased the labor necessary to weave by half, in effect the value of the linen decreased by half also.

There are two factors in labor: labor-power, the degree of power given by labor; and labor-time, how much time is consumed by laboring. The reason why gold is so valuable is because so much labor-time is dedicated to finding it, then labor-power to extract it. For example: Brazil around the 1820s found a rich vein of diamonds. They spent so much labor-power on the diamonds that the combined value within the next three years of the diamonds is as much as Brazil's sugar crops within one year, because the amount of labor dedicated to each respective sector created a balanced value. We determine labor through necessary labor time.

NOTE: Not all things with a use-value is created by labor, e.g. virgin soil, air, etc. A use-value can have no value. Labor is able to create value, but it is also capable of not doing so.

Marx gives the example a coat=20 yards of linen. That would mean that the coat takes 2W labor time, and the 20 yards of linen has 2W labor time. The element that allows us to say 1 coat=20 yards linen is value. Money is a commodity which is used to express value, it could be gold, cattle, etc.

Now it gets tricky... when there is a series of commodities set to be expressed through the means of gold, it is the "money form of value"; for example:

2 ton Iron 20 yards linen 2 coats = 3 ounces gold 1 table x commodity A

This is the "price form". Prices go up because of an increased amount of labor on the commodity, or a decreased amount on the gold. The opposite is true too.

The circulation of commodities and money is a little weird at first, but I'll try to explain it. There is the sale transaction, the commodity-money(C-M), which exchanges a commodity for money. Then there is the purchase transaction, the money-commodity(M-C), which exchanges money for commodity.

What happens is the two form the C-M-C process, the circulation of commodities; or selling in order to purchase. The equation N x P = V x S, or the number of sales(N) at the average price(P) equals the velocity, or number of transactions,(V) multiplied by the money supply(S).

This all assumes that money is not being hoarded, of course. Then money itself is a commodity. Finally, money, if based on a standard, has its standard as the universal money; that is to say, if money is backed by gold, the unvirsal money is gold.

Transformation of Money into Capital
The general formula for the circulation of commodities is C-M-C. The opposite is basically the same for the merchant's point of view: M-C-M. However, there is a profit to be "made". If one buys 1000 yds of linen for $20, then sells it for $25, you exchange $20 for $25. So, it is M-C-M', where M'= M + M. That triangle thingy, for those who don't know, means "the difference between"; in this case it would mean $5 surplus-value.

There is a contradiction, though, that the value is expressed through another commodity of equal value. Yet the exchange was of unequal values! This surplus-value could be used to get more capital. Well, the difference between M' and M would be the percent which prices are affected.

Every human has labor-power. It is the only commodity which they are born with, and forced to sell in capitalism. There is a limit, however, to how much labor-power that can be expended; old age takes its toll. As Marx says: "The price of the labour-power is fixed by the contract, although it is not realised till later, like the rent of a house. The labour-power is sold, although it is only paid for at a later period."


text:
Marxism, Communism, and Socialism/Printable version

 * Origins of Marxism

 * Historical Materialism

 * Marxist Economics


text: Supplemental Guide to Lord of the Flies/Printable version


text:
Voice over IP/ENUM and E146 Technology

The following section is quite technical, as it deals with complicated infrastructure and the integration of VoIP into core internet technologies.

The ENUM protocol (described in RFC document RFC 3761) translates standard telephone number routing (known as E.164, as the ITU defines the standard by which telephone numbers are assigned in the E.164 standard) into an addressing scheme able to route to VoIP (eg. SIP/H323) gateways using DNS technology.

ENUM technology allows VoIP servers to use the DNS infrastructure to query routing paths for terminating voice calls given a phone number.

When a call is initiated to a given phone number, a VoIP gateway capable of ENUM service will query the provided number in DNS to determine whether there is a path other than the PSTN line available to the destination service.

This allows providers to advertise paths via VoIP to services otherwise only available via a VoIP to PSTN gateway.

ENUM records may contain other information in addition to a VoIP gateway address, such as a web URL or e-mail address.

Private vs Public ENUM databases
The public ENUM database is a collection of ENUM records, known as NAPTR RRs in DNS speak, which map telephone numbers to VoIP service gateways. These records are stored in a hierarchical tree beneath the e164.arpa domain.

Records within the e164.arpa domain are delegated to their responsible owner via the E.164 addressing convention. Much like the in-addr.arpa domain, which is used to provide mapping of IP addresses to names, these records are delegated in blocks to the agency responsible for this number assignment.

The agency is then responsible for further smaller delegations where necessary. As a result, it is unlikely that individuals or small businesses will have access to provide ENUM records for their telephone numbers.

It also stands to reason that telephone companies would be hesitant to allow telephone calls destined to their customers to instead terminate over the Internet, as much of a phone company's revenue would be derived from call termination fees, charged to carriers for calls terminating on a company's network.

This is unfortunate for end users. Via the ENUM database, you would have the opportunity to direct VoIP-based calls to terminate over the Internet via your VoIP gateway, rather than via a phone line.

For this reason, several free ENUM databases have been created to allow users to share alternate IP-based paths to their phone numbers. Most ENUM aware gateways will allow additional 'search domains' to be configured, providing access to these unofficial databases.

Whilst configuring a gateway to query these extra domains can dramatically reduce costs by terminating calls over IP, therefore freeing copper lines/voice channels for both the caller and recipient, there is an important factor to consider. If a malicious or unauthenticated entry is added, an attacker can direct calls for a phone number to an arbitrary VoIP gateway.

Consider the example of rival businesses. If Business A were tech-savvy and entered their competitor's number into a public directory, directing calls to their own VoIP gateway, any calls placed via a VoIP gateway configured to query that directory would be directed to Business A's phone, rather than the intended recipient, Business B.

Some of these directories require voice verification of ownership when you register phone numbers. Others do not require verification or have dispute resolution policies which deal with disputes on a case-by-case basis.

Another less serious but still important consideration is the possibility that your information will be harvested from the database, or sold by the database owner. ENUM information may be valuable to advertisers or phone spammers, as it would provide them with a list of valid phone numbers, and allow them to call for free via IP.

VoIP Providers Worldwide
VoIP technology has completely changed how companies interact with their customers. VoIP has scaled so much that now it is being used for residential as well as business purposes. VoIP providers are mainly of two types, Retail VoIP provider and wholesale VoIP provider. There are bunch of VoIP providers online but these are some of the best VoIP providers online.

 * Traverse Telecom
 * Ringcentral
 * Grasshopper

ENUM Trial Registries
Many ENUM trial registries are becoming available. Most of these registries are regional, and often are limited by telephony provider, limited number of trial participants, or a trial fee.

Australian ENUM Trial - Fee applies for registration

Austrian ENUM Trial - Open to Austrian residents, a fee applies for registration.

German ENUM Trial

Japanese ENUM Trial - Open to ETJP contributors since 2003. Currently has 46 members.

Taiwan ENUM Trial

UK ENUM Trial

title: Voice over IP/ENUM and E146 Technology


text:
Voice over IP/VoIP Gateways and PABX Integration

VoIP Gateway Systems
This chapter deals with the complex world of VoIP gateway systems. These systems are responsible for providing some amount of call control and routing from VoIP phone devices.

Each of these systems is responsible for receiving calls from a VoIP handset, ATA or softphone device via a supported VoIP protocol, consulting a dial-plan or other call routing table, and correctly routing the call. Other features made available by some or all of these gateways include:

Authentication - Ensuring that clients have permission to use VoIP resources.

Call Accounting - Providing tracking of calls via the gateway, including reports and cost controls.

Complex Dialplans - Most dialplans configured on simple devices such as ATAs and softphones only allow for a very straightforward dialplan configuration. Using a VoIP gateway such as Asterisk, factors such as time of day, or even values obtained from external sources can be used to determine which path a call should take.

Hardware Integration - Most gateways provide the ability to interface with physical hardware such as FXS (internal line) and FXO (PSTN line) cards to create a PBX system. They additionally provide the dialplan configuration to determine which calls should route via IP, and which should utilize a card. It is important when selecting gateway software to evaluate which devices they support, and ensure yours is listed. Some devices (for example, Cisco line cards) may require the vendor's specific implementation of VoIP gateway for any support at all.

Internal Numbering - Some gateways offer the ability to provide internal extension numbering for clients, allowing one VoIP device to dial another device registered on your local gateway using a short internal extension number.

When would you use a VoIP gateway?
In which situations would you use a VoIP gateway product?

Generally, if you require an advanced configuration such as advanced call accounting for billing, cost controls, complex dialplans, or the ability to call between extensions, you should implement a gateway solution.

If you are interested in integrating extra hardware such as FXO cards (interfaces to the PSTN) you MUST use a gateway product.

If you are designing VoIP solutions for mid-large size business, or will be requiring IVR (Interactive Voice Response) functionality, you should implement a VoIP gateway.

Asterisk: The open-source PBX
Asterisk is an extremely popular open-source PBX system which runs on BSD, Linux, Mac OS X, and Windows. The project is sponsored by Digium, a PBX hardware manufacturer.

Asterisk has support for ENUM, e911, Caller ID, all call controls such as Forwarding, Conferencing, Hold, Transfer and Call Waiting. Additional features such as Call Monitoring, Call Recording and Privacy Controls also exist.

In addition to the above, Asterisk is able to provide IVR functions, allowing interactive voice prompts, call queuing, and many many advanced call routing features.

In all, Asterisk is a remarkably full featured commercial-grade PBX system available free of charge.

OpenSER
Web page: http://openser.org

OpenSER is a robust and powerful SIP server. Released under GPL, OpenSER is the first free server with integrated TLS, offering secure VoIP communications. It has an architecture designed for scalability and flexibility and high performances.

Main characteristics:

 * SIP proxy/registrar/redirect server (RFC3261)
 * transaction stateful
 * UDP/TCP/TLS support
 * modular architecture
 * scripting configuration file with pseudo-variables
 * authentication, authorization and accounting via database, radius or text files
 * enum support
 * NAT traversal system
 * formatted logging
 * least cost routing
 * Call Processing Language (CPL)
 * MySQL/Postgres/Flat files database backend
 * sever monitoring

SIP Express Router
Web page: http://www.iptel.org/ser

SIP Express Router (SERi) is a high-performance, configurable, free SIP server licensed under the open-source GNU license. It can act as SIP (RFC 3261) registrar, proxy or redirect server. SER can be configured to serve specialized purposes such as load balancing or SIP front-end to application servers, SEMS for example.

SER features:
 * complete support of RFC 3261 functionality,
 * a variety of database backends (mysql, oracle, postgres, radius, text-db),
 * management features (remote management via XML-RPC, load-balancing),
 * NATi traversal, telephony features (LCR, speeddial),
 * multidomain hosting, ENUM, presence, and even more.

SER is additionally enhanced by a variety of additional SIP tools, which provide functionality for management, media processing, CDRi processing, etc.

SER is today default part of numerous operating systems and their distributions: Debian, FreeBSD, Gentoo, NetBSD, OpenBSD, OpenSUSE, Solaris.

SER history spans back to the previous century. SER has been used since 2002 for various different purposes, frequently in the industry by major ISPs/ASPs and by universities to enable VoIPi services. SER's particular strength is its performance (SER runs well even under heavy load caused by large subscriber populations or abnormal operational conditions), flexibility (SER's genuine configuration language and module interface allow high degree of customization) and interoperability (tested and operated against tens of SIP products over the years, including but not limited to (Microsoft, Cisco, Mitel, snom, Pingtel, Siemens, xten, and many others).

Yate - Yet Another Telephony Engine
Yate is a next-generation telephony engine; while currently focused on Voice over Internet Protocol (VoIP), its power lies in its ability to be easily extended. Voice, video, data and instant messaging can all be unified under Yate's flexible routing engine, maximizing communications efficiency and minimizing infrastructure costs for businesses.

Yate can be used as a:

 * VoIP server ****
 * VoIP client
 * VoIP to PSTN gateway
 * PC2Phone and Phone2PC gateway
 * H.323 gatekeeper
 * H.323 multiple endpoint server
 * SIP session border controller
 * SIP router
 * SIP registration server
 * IAX server and client
 * IP Telephony server and client
 * Call center server
 * IVR engine
 * Prepaid and post-paid cards system

YXA
YXA is a SIP server written in the programming language Erlang at Kungliga Tekniska Högskolan and Stockholms universitet. Erlang was developed by Ericsson to program ordinary telephone switches, with the goal of making a programming system fault-tolerant and robust.

This helps YXA to be a robust SIP server/stack capable of serving tens of thousands of users. The project's goal is to make YXA compliant to all RFC standards relevant to SIP.

 * It is RFC3261 compliant SIP-server, capable of everything a generic domain needs:
 * Registrar that keeps track of your users
 * Handles incoming SIP requests to your domain
 * Handles routing of requests from your users to remote domains
 * TCP, UDP and TLS (including SIPS) support
 * Automatically maps e-mail addresses of your users to their SIP addresses, if you have the e-mail addresses in LDAP
 * Handles multiple domains using a single server instance
 * ENUM support for PSTN-bypass whenever possible
 * IPv6 support
 * Forking, both parallel and sequential
 * CPL (RFC3880) support for advanced user-control of events (currently incoming calls only)
 * Modular user database, currently with LDAP, Mnesia, MySQL and text-file backends
 * PSTN destination access control (per user or for anonymous users)


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Voice over IP/Advanced VoIP Configuration

Correctly terminating emergency calls
Particular attention should be given to ensuring that emergency calls on VoIP lines are handled correctly. In some cases, it may not be possible to provide useful or reliable emergency service via VoIP services. In this case, it may be possible to offload emergency calls to a landline service.

If reliable emergency service is not available, the handset or VoIP device should clearly be marked with a warning.

Some VoIP providers allow emergency calls to be routed via their service; however this is only of use if you are within an area covered by the receiving emergency call centre. Additionally, a lack of bandwidth or Internet service or a power loss can lead to loss of emergency service via telephone.

Suggestions for dealing with emergency calls
If a functioning landline handset is nearby, it is advisable to attach a notice to the VoIP device directing emergency calls to the landline. It is much easier for emergency services to assist if they have information on your location which is generally not available via VoIP calls.

Where calls are handled by a gateway administered by yourself or your organisation, and the ability to route certain calls via landline exists, the dialplan for your VoIP gateway should immediately route emergency calls via the landline, and where possible, any active conversations should be dropped if there are not sufficient lines to handle the call.

It is important to find out whether your VoIP provider(s) offer emergency numbers, what areas they are able to cover and whether they are able to provide enhanced emergency services such as e911 initiatives which allow providers to transmit information on subscribers to 911 call centres.

Ensure that emergency calls are routed via the most appropriate gateways in your dial plan.

IVR (Interactive Voice Response) application
IVR applications are automated response units which receive input from the user (traditionally in the form of DTMF) and allow the user to progress along a pre-set interactive path. For example, a menuing system where the IVR may announce Press 1 for Sales, 2 for Marketting and then await user input. Once the user input arrives the IVR unit may patch through the call to another line and/or may provide a pre-recorded message.


text: Voice over IP/Reference

title: Voice over IP/Reference


text: Voice over IP/Printable version

title: Voice over IP/Printable version


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Electric Motors And Generators/Vectors and Fields

The use of vectors and vector fields greatly simplifies the analysis of many electromagnetic (and indeed other) systems. Due to their usefulness, these concepts will be used extensively in this book. For this reason it will be useful to begin with a general treatment of the subject.

Vectors
A vector is a quantitative which has both magnitude, direction and sense. The magnitude represents the vector's size or physical quantity. The direction represents the vector's position with respect to a reference axis. The sense represents the vector's orientation and it is represented by its arrow head. This contrasts with the definition of a scalar which has only magnitude. Examples of scalar quantities include temperature, resistivity, voltage and mass. In comparison, examples of vector quantities would include velocity, force, acceleration and position.

The most familiar and intuitive use of vectors is in the two-dimensional (x, y coordinates) or three-dimensional (x, y and z coordinates) Cartesian coordinate system.

Fields
The term field has a general meaning in mathematics and physics, but here we will be referring only to the special cases of scalar and vector fields. Generally, a field is a region in space where the quantity in question, exist and its influence is being felt. A scalar field is a region of space in which each point is associated with a scalar value. A classic example of a scalar field is a temperature field in a heated block of material.

If some heat source is applied to a cube of a conductive material, such as a metal, the temperature in the block will be highest where the heat source is applied, dropping off as we move away from the source in any direction. At every position inside the block a value could be assigned which is the temperature at this point. These temperature values make up the scalar temperature field in the block. It might be that it is possible to model accurately these values with some mathematical function, but the field itself is simply the variation in the scalar quantity in the space occupied by the block.

A vector field differs from a scalar field in that it has not only a magnitude at every position, but also direction. A good example of a vector field is the velocity of the fluid flow in a winding river of changing width. Clearly at every point in the river, the velocity of the fluid will have a magnitude (the speed) which will be lower where the river is wide, and higher where the river is narrow. However, the flow will also have a direction which changes as the water is forced around the river bends. If we noted the fluid speed and direction everywhere in the river, the result would be a vector field of the fluid flow.

In addition to varying in space, fields can also vary in time. In the first example, if we started with a cold block and then applied the heat source, mapping the temperature field at set time intervals, it would be seen that the values of the temperature at every point would change as the heat conducted throughout the block over time. The result therefore is a scalar field that varies in the three dimensions of space and one of time.


text:
Electric Motors And Generators/Magnetic Field Concepts

Magnetic Field Concepts
An electromagnetic field is a region of space in which electrical charges experience forces. The classical definition of the electromagnetic field is given by the following equation

 * $$\mathbf{F}=q\mathbf{E}+q\mathbf{v}\times\mathbf{B}$$

What this equation states, is that an electrical charge of size $q$ experiences a force when in the presence of an electric field denoted by $E$. Furthermore if the charge is moving, with velocity $v$, it will experience a further force if in the presence of a magnetic field denoted by $B$. Therefore the force on a electric charge defines what the electric and magnetic fields are in a given region of space. Without the presence of a charged particle it could never be known what their magnitudes or directions were.

Further Reading on Magnetism

 * See Magnetic field and Magnetic phenomena and Physics Study Guide/Magnetism and Permanent magnets and Current's magnetic effects and Electromagnetism and Magnetism's units.
 * Wikipedia: Magnet and Wikipedia: Magnetic forces and Wikipedia: Magnetism and Wikipedia: Magnetism's origin

Further Reading on Electric Current

 * See Current and Kirchoff's Current Law (KCL) and Current (Physics) and Relationships: voltage, current and resistance.
 * Wikipedia: Current and Wikipedia: DC and Wikipedia: AC.


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Electric Motors And Generators/AC Motors and Generators

 * See Single-phase motors and generators, and 3-phase motors and generators, and AC basics, and also this.

AC generators
AC generator works on the principle of Faraday's laws electro-magnetics.
 * A very simple AC generator consists of a permanent magnet that rotates inside a coil in such a way that the N-pole and S-pole alternate as seen from the coil. An analog voltmeter (or rather a millivoltmeter?) that has its zero at the middle of the scale is connected to the ends of the coil. As the magnet is rotated the voltmeter moves first one way, then the other way. The speed of rotation determines the number of "cycles per second", called Hertz(Hz). A rotation speed of 3000 revolutions per minute(RPM) produces 50 Hz, and 3600 RPM produce 60 Hz.
 * The rotating permanent magnet can be replaced by another coil that is fed by DC and acts as an electromagnet. Doubling the number of coils will double the number of, what is called "the poles", and then only half the rotation speed is required for a given output frequency.
 * See also Wikipedia: Alternator

AC motors
AC motors are generally divided into two categories, induction and synchronous motors. The most common AC motor is the "Squirrel cage motor", a type of induction motor. These have only one or more coils within which a special kind of mechanical rotor is free to rotate. There is no electrical connection to the rotor from the outside. The general formula to determine the synchronous speed of an induction motor is

$$Speed = \frac{120f}{P}$$

For induction motors, this is a theoretical speed, even though it will never be obtained. The motor will always run slower than synchronous speed with a slip of S. If a motor were to be operated at full synchronous speed, the relative speed of the rotor to the stator would be 0, making it impossible to induce a voltage (Faraday's law) in the rotor windings. This in turn would make the flow of current impossible. Without current no magnetic field can be generated.

Most AC motors require a starter, or method of limiting the inrush current to a reasonable level. Types of motor starting include reactive (capacitor start and inductive start), and electronic (frequency drives and soft start drives). The reactive start method is usually used on fractional horsepower motors, and the electronic method is usually reserved for larger motors (cost of the drives is the main reason for this). Connecting these motors to computers, PLC's (programmable logic controllers), and interfacing with automation systems, is becoming more prevalent.

DC Generators
DC generators are basically AC generators whose output voltage is switched the other way round at the proper moment, so that the direction of the voltage is always in a single direction. But the magnitude of the voltage keeps changing, just as it does in an AC generator, and it can be said that the output of a DC generator is DC plus a "superimposed" AC voltage, called "ripple". Connecting a capacitor across the output terminals reduces that ripple. See also Wikipedia: "Testatika" Electrostatic generators

DC Motors
Direct Current (DC) motors have a "Commutator" that switches the part of the coil that is closest to the poles at the time, more or less similar to the legendary "donkey" that tries to catch the carrots, but never succeeds. See the very simplified commutator shown in blue.

Usually a commutator has many "segments", as many as there are taps on the coil. Starting a DC motor requires often an external resistor or rheostat to limit the current. The value, in Ohms, of that resistor is reduced in steps as the speed of the motor increases, until finally that resistor is removed from the circuit as the motor reaches close to its final speed. See also Wikipedia: Car starter

Universal
See Wikipedia: Universal motors

Stepper
A stepper motor is a brushless, synchronous electric motor that can divide a full rotation into a large number of steps, for example, 200 steps.

See Robotics: Stepper Motors and Wikipedia: Stepper motor

Electrostatic
See Wikipedia: Electrostatics

Superconducting
See Wikipedia: Applications


text: Electric Motors And Generators/Printable version


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Telescope Making/Thinking About Telescopes

People have been making telescopes for 400 years, and it's no surprise they've built a vocabulary of specialized terms. In this section we'll take a quick look at some of the most important, and provide links to pages that explain them in more depth. Follow those now, or come back and follow them later when you feel the need for more detail.

Refracting Telescopes
The first telescopes were refracting telescopes. In a refracting telescope, light passes through two or more lenses. The right combination of lens shapes brings the light from a small area to focus on the retina of your eye, giving you a magnified image.

A basic problem with a refracting telescope is that different colors of light are bent by different amounts. The red light comes to a focus at a very slightly different point than the blue or green light does. The result is a fringe of rainbow color around bright objects. Camera designers tinker endlessly with lens materials and coatings to avoid this false color problem.

Small inexpensive refracting telescopes can often be found at surplus and used merchandise stores very cheaply. Amateurs can make refracting telescopes. You need a magnifying lens of long focal length, called the objective lens, paired with one of short focal length (the eyepiece). A usable objective lens can be salvaged from many types of equipment that use projection lenses and other optical components.

Refracting Telescope (english)

Reflecting Telescopes
The reflecting telescope is designed around mirrors, not lenses. The light does not pass through a lens and is not refracted. It is simply reflected. Since there is no refraction, all colors of light are affected equally, hence there is no problem of false color.

A reflecting telescope has its own problems. Its mirrors must be shaped precisely, within a fraction of the wavelength of light, in order to avoid distortion. (Historically, the main mirror of the Hubble Space Telescope was improperly curved, due to a failure of communications between the designer and manufacturer. A space shuttle trip had to be made to introduce a compensating lens in the system to clear up the image.)

It is not as hard to shape a perfect mirror as you might think. Our first project, the Newtonian Reflector, requires mirrors, and we will make them. It is really very easy to do because (as you will find), physics is on our side.

Reflecting telescope (english)

Catadioptric telescopes
Catadioptric telescopes are a sort of hybrid. They use both lenses and mirrors to focus the light.

Technical Terms
We need a few technical terms. The first two are focal point and focal length.

The focal length of a lens, or of a curved mirror, is the distance at which it brings incoming light to a focal point, or simply focus. The curvature of the lens or mirror surface determines the focal length. The less the curvature, the longer the focal length.

The greater the focal length, the greater the effective magnification of the image. As a general rule, the greater the focal length, the less the impact of imperfections in the curvature. The less the focal length, the more critical it is to have a perfect curve.


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Telescope Making/Project 1: The Newtonian Reflector

Project 1: The Newtonian Reflector
The Newtonian Reflector Telescope is an extremely simple and efficient design. It consists of two mirrors in a tube. That's all!

The larger, curved mirror directs incoming light to a focus. The smaller, angled mirror shunts the focused light out the side of the tube, where you can place your eye to see the image. In the Newtonian reflector, the smaller mirror is flat, but in a related design, the Cassegrain, it is convex. Read the Wikipedia article on the Newtonian Reflector for its history.

Newtonian Telescope (english)

After we consider how you will use your telescope, we will get deeply into how we choose the exact shapes and sizes of these simple pieces. Then we'll build it!

How Will You Use Your Telescope?
How will you actually use your telescope? Most folks, me included, spent a lot of time dreaming about making the telescope without giving serious thought to how we might use it. I talked about looking at stars and planets—but I also talked about looking at birds and retreating snow fields. Only when I looked through the telescope did I discover some problems. One is, the basic Newtonian telescope makes everything look upside down! Looking at the stars? This is not an issue. Looking at birds or scenery? We have a problem. Fortunately you can buy an inverting eyepiece that will turn things right side up. A second issue with the Newtonian telescope is that it is by design quite powerful. This means you might be looking at a bird's feather detail, not the bird. Third, the telescope is much larger than a pair of binoculars and needs to be supported so you can aim it and hold it steady. I don't want you to stress over this, but you need to consider, what will you do with the telescope?

Telescope Design
The telescope design covers everything from the optics (in our case the two mirrors), the brackets that hold those optics and keep them aligned, and the tube assembly that contains it all. Design also includes the supporting framework that holds the tube and lets you swivel and point it. That piece is called the telescope mount.

So let's say you think that you mainly want to look at planets and stars in the sky. Longer focal length telescopes give higher magnification. That is just how it works: the longer the focal length, the more magnified the image at your eye. Bigger mirrors will gather more light, but two telescopes with different sized mirrors will give the same size image at the focal point, if they have the same focal length (although, since more light is being put into the same size image with a larger mirror, the image in a telescope with a larger mirror will be brighter). Mirrors with a long focal length are somewhat easier to make and more forgiving of error. However, the longer the focal length, the longer the telescope, making it more difficult to move around and to store.

Shorter focal-length telescopes give less magnification, but a wider field of view. The image is a bit smaller but that is rarely an issue when looking through the eyepiece. The mirrors require a bit more work, a different technique, but they are as easy to make as the long ones. A shorter telescope is easier to move, easier to store, easier to set up for use.

There is no right answer here. The telescope you make should be one you are comfortable with and will use. I have made a lot of telescopes in the last few years. My first--I called it the Long Dog--had a truss design that took about five minutes and 10 bolts to set up. The truss poles were six feet long. It was heavy and long and you had had to stand on a ladder to reach the eyepiece, but it gave images that would take your breath away. I got one of my favorite comments while using that telescope. I showed a friend the planet Saturn. It was a perfect night, calm sky, dark, Saturn was high. He looked at the planet and said, "That is so amazing it doesn't look real." That is what we call resolution.

Regardless of the length and size of telescope you choose to make, you will find the information to build it here. I am going to do two mirrors and several mounting ideas for this, the first project of the book. I will grind and polish a shorter focal length mirror and a longer focal length mirror. Whatever you decide on I will cover it here and you will be successful with your first telescope.

Links to new terms and topics for this page:

 * [[Image:Wikipedia-logo.png|20px| ]] Newtonian Telescope (english)

 * [[Image:Wikipedia-logo.png|20px| ]] Truss Telescope Design (english)

The parts of the Telescope
Time to get into the details of design. The following will have some basic math and some pictures to help.

Radius of Curvature
Having considered the physical size of the telescope and the use to which I want to put it, I can now begin to consider the optics. The focal length depends on the choices made while thinking about the telescope. The focal length is set by the shape of the curve in the front of the main mirror. We make that curve by grinding the mirror. The amount of grinding and the depth of the curve are both directly affected by the choices made while thinking about the telescope.

It is the front surface of the mirror that forms the image, so it is the front surface that gets all of our attention. The back of the mirror may get quite beat up during this process. That is OK, as long as we don't crack it or put big chips in it.

The curve in the front of a telescope mirror is called the Radius of Curvature, abbreviated ROC, or sometimes just R. The front of the mirror is a smooth bowl-shaped depression. Imagine a ball, and if you have one handy, look at it while you read this. The ball has some radius, the distance from the center of the ball (an imaginary point inside where you can't see it, but it is there) to the inner surface of the ball. That is the ROC. It defines the ball's size, and the curve of the surface.

Imagine that the ball is reflective inside. Imagine that we place a source of light (a fancy way of saying put a light bulb or a flash light or something that emits light) at the center of the ball. All of the light would reflect back to the light source, at the center. However, if we move the light source away from the center, the point of reflection, or focal point, will also move away from the center in the opposite direction. When the source of light gets really far away from the center of the ball, at infinity, the focal point ends up being about half way between the center of the ball and the surface of the ball. (How far away is "infinity"? Well, figure at least 200 times the ROC.)

Now imagine that we cut off a small slice of the ball, or press the surface of the ball into some soft material, clay or moist dirt. Either way, we have a shallow, smooth, bowl-shaped depression. It would be curved just like the front surface of a telescope mirror.

The surface of the mirror has a uniform curvature that determines its focal length. The mirror is usually circular; it is a circular patch cut from that imaginary ball. It can be any size; ours will be a few inches across. (For comparison, the mirror of the Subaru telescope on Mauna Kea in Hawaii is 8.2 meters, 27 feet.) The radius of the mirror, one-half its diameter, is denoted as r.

 * [[Image:Wikipedia-logo.png|20px| ]] List of Large Telescopes (english)

The Primary Mirror
The depth of the bowl-shaped curve that is ground into the front of the mirror is called the sagitta.

There is a math formula to figure out how deep to make the sagitta to achieve a specific focal length.

The formula relates the ROC and r, which we know to be the radius of the mirror, to S, the sagitta. The formula reads, multiply the radius of the mirror times itself, then divide it by two times the Radius of Curvature. Huh? Well, we can measure the diameter of the mirror with a ruler or tape measure and divide it in half to get the radius of the mirror. If it is eight inches across, the radius is half of that or four inches. But how much is the ROC?

Well, remember how the focal point moves as the light source moves away from the center of the ball. When the light source is at infinity, or a long way away, the focal point is halfway between the center of the ball and the surface of the ball. So the focal length is one half the Radius of Curvature, one half the ROC.

This is when we have to get specific about the telescope: what focal length did you want? Well, how long of a telescope did you want? Lets say you wanted a four-foot telescope. The ROC is twice that length, or eight feet. (If you have made a telescope before, you are fuming right now, because you know the length of the telescope has little to do with the focal length of the mirror. I'll clear it up before I'm done.)

I asked, why am I figuring out the ROC when it is just another way of saying two times the focal length? Why not just use the focal length in the Sagitta formula? Two times the ROC is equal to four times the focal length, so why not use this?

Well, you can. For our purposes as amateurs we can use either and it will be good enough.

So! let's figure out a Sagitta for an eight inch mirror with a focal length of forty eight inches.

Not much, is it? 0.08333 inches, (and those threes go on forever). It is about the thickness of a (U.S.) penny. A ream of paper is pretty close to 2 inches thick. There are 500 sheets in a ream. 250 sheets times 0.08333 is about 21 sheets.

How accurate do you have to be? How close to a four foot telescope do you want? The focal length of the mirror will determine, to some extent, the length of the telescope tube, and for quick consideration you can assume the focal length of the mirror and the telescope tube are the same. But note that In practice the telescope tube will be as much as 25% longer than the actual focal length. If a five-foot telescope sounds too big, you can re-do the formula for a 3-foot focal length, or any other value you want.

We have spent several paragraphs on the primary mirror and I have only shared the basics. Many good books and web pages document the making of the primary mirror. Look at the links at the end of the book. Now we need to consider the second half of the optics, the secondary mirror.

The Secondary Mirror
In the diagram above (and the wikipedia page on Newtonian Telescopes) we see that the telescope gathers and focuses the light, bouncing it back up the tube. Then the optical path is turned 90 degrees and the focus and eyepiece are on the side of the tube. This is accomplished with a flat mirror set at a 45 degree angle in the tube. (It is possible in smaller telescopes to use a type of prism, but a mirror is simpler for use to make and works as well.)

 * [[Image:Wikipedia-logo.png|20px| ]] Roof Prism (english)

How big this secondary mirror should be, its shape, and where it should sit relative to the primary, are functions of the basic measurements of the telescope. In the previous section we used an 8 inch mirror with a 48 inch focal length as an example for our calculations. I will continue to use that example in this section.

Sizing the Tube
Before we can calculate the size and location of the secondary, we need to think about the telescope tube that supports the mirrors. How long should it be? How big in diameter? How far in will the primary mount?

The tube needs to be bigger than the primary mirror; by how much? A safe number is one inch clearance around the mirror. This works out to a tube that is two inches bigger in diameter than the primary mirror. For the 8 inch primary that is our example mirror, the tube would be 10 inches in diameter.

Tube length is determined by the focal length of the primary mirror, plus the space at the end for the primary mirror and the mirror cell—that is, the framework that supports the mirror and holds it perpendicular to the axis of the tube.

The typical primary mirror and cell form a stack about 3 to 4 inches in height. Add that to the focal length and you would have a tube that is long enough (remember, part of the focal length is turned sideways by the secondary mirror). A little extra length, say 3 or 4 more inches, gives a shield that works to block stray local light. Our example mirror has a focal length of 48 inches. Add 4 more for the mirror and cell, and 4 more for blocking light, and we have a tube 56 inches in length, and at least 10 inches in diameter.

 * [[Image:Wikipedia-logo.png|20px| ]] Vignetting (english)

Sizing the Secondary
So, how big shall we make the secondary mirror? Before we can answer we need to consider one more key dimension, the focal offset.

A formula for figuring the size of the secondary is as follows.

In this formula,

 * Os is the focal offset,
 * D is the Diameter of the primary mirror
 * f is focal length of the primary mirror
 * d is the minor axis diameter of the secondary mirror

We multiply the diameter of the primary mirror by the focal offset and divide by the focal length of the primary mirror. This gives us a minimum minor axis. A second rule of thumb is, the secondary should be no bigger than 20 percent of the primary mirror diameter. Given an 8-inch primary, that is 1.6 inches. Purists haggle over these numbers forever. My opinion and experience are, a secondary that is a bit too big is preferable to one that is a bit too small.

Lets look at that formula in operation. I used these values:

$$d = \frac{Os \times D}{fl} = \frac{8 \times 8}{48} = \frac{64}{48} = 1.333$$

The formula yields a size of 1.33 inches. This is a minimum size. You could increase it by 25% and have a better secondary fit. 1.33 x 1.25 = 1.66 inches—which just happens to be at the 20% mark. Pretty cool, huh?

That's it! That is how, beginning with the diameter and focal length of the primary mirror, we decide on the tube diameter and length, and the size of the secondary mirror.

The formulas are important enough that I have included them here on a graphic that will make a 3 x 5 card. Print it out!

These formulas and the considerations that lead to them will guide your second telescope and every telescope you make after that first one. But next you need to teach your hands how to grind and polish a mirror, and that is best learned on simple inexpensive stuff.