Giant brains; or, Machines that think

When we think of counting, we usually think of saying softly to ourselves “one, two, three, four, ···.” This is a good way to find the total of a small group of objects. But when we have a large group of objects or a great many groups of objects to be counted, a much faster way of counting is needed. A very fast way of sorting and counting is punch-card calculating machinery. This is machinery which handles information expressed as holes in cards. Punch-card machines can:

• Sort, count, file, select, and copy information,
• Make comparisons, and choose according to instructions,
• Add, subtract, multiply, and divide,
• List information, and print totals.

For example, in a life insurance company, much routine handling of information about insurance policies is necessary:

All these operations can be done almost automatically by punch-card machines.

ORIGIN AND DEVELOPMENT

When a census of the people of a country is taken, a great quantity of sorting and counting is needed: by village, county, city, and state; by sex; by age; by occupation; etc. In 1886, the census of the people of the United States which had been taken in 1880 was still being sorted and counted. Among the men then studying census problems was a statistician and inventor, Herman Hollerith. He saw that existing methods were so slow that the next census (1890) would not be finished before the following census (1900) would have to be begun. He knew that cards with patterns of holes had been used in weaving patterns in cloth. He realized that the presence or absence of a property, for example employed or unemployed, could be represented by the presence or absence of a hole in a piece of paper. An electrical device could detect the hole, he believed, since it would allow current to flow through, whereas the absence of the hole would stop the current. He experimented with sorting and counting, using punched holes in cards, and with electrical devices to detect the holes and count them. A definite meaning was given to each place in the card where a hole might be punched. Then electrical devices handled the particular information that the punches represented. These devices either counted or added, singly or in various combinations, as might be desired.

More than 50 years of development of punch-card calculating machinery have since then taken place. Several large companies have made quantities of punch-card machines. A great degree of development has taken place in the punch-card machines of International Business Machines Corporation (IBM), and for this reason these machines will be the ones described in this chapter. What is said here, however, may also in many ways apply to punch-card machines made by other manufacturers—Remington-Rand, Powers, Control Instrument, etc.

GENERAL PRINCIPLES

To use punch-card machines, we first convert the original information into patterns of holes in cards. Then we feed the cards into the machines. Electrical impulses read the pattern of holes and convert them into a pattern of timed electrical currents. Actually, the reading of a hole in a column of a punch card is done by a brush of several strands of copper wire pressed against a metal roller (Fig. 1). The machine feeds the card (the bottom edge first, where the 9’s are printed) with very careful timing over the roller; and, when the punched hole is between the brush and the roller, an electrical circuit belonging to that column of the card is completed. The machine responds according to its general design and its wiring for the particular problem: it punches new cards, or it prints new marks, or it puts information into new storage places. Clerks, however, move the cards from one machine to another. They wait on the machines, keep the card feeds full, and empty the card hoppers as they fill up. A human error of putting the wrong block of cards into a machine may from time to time cause a little trouble, especially in sorting. Actually, in a year, billions of punch cards are handled precisely.

The punch card is a masterpiece of engineering and standardization. Its exact thickness matches the knife-blade edges that feed the cards into slots in the machines, and matches the channels whereby these cards travel through the machines. The standard card is 7⅜ inches long and 3¼ inches wide, and it has a standard thickness of 0.0065 inch and other standard properties with respect to stiffness, finish, etc.

The standard IBM punch card of today has 80 columns and 12 positions for punching in each column (Fig. 2). A single punched hole in each of the positions known as 0 to 9 stands for each of the digits 0 to 9 respectively. The remaining 2 single punch positions available in any column are usually called the 11 position and 12 position (though sometimes called the numerical X position and Y position). These two positions do not behave arithmetically as 11 and 12. Actually, in the space between one card and the next card as they are fed through the machines, more positions occur. For example, there may be 4 more: a 10 position preceding the 9, and a 13, a 14, and a 15 position following the 12. The 16 positions in total correspond to a full turn, 360°, of the roller under the brush, and to a complete cycle in the machine; and a single position corresponds to ¹/₁₆ of 360°, or 22½°. In some machines, the total number of positions may be 20. A pair of punches stands for each of the letters of the alphabet, according to the scheme shown.

For example, the word MASON is shown punched in Fig. 3.

To increase the versatility of the machines and provide them with instructions, many of them have plugboards (Fig. 4). These are standard interchangeable boards filled with prongs on one side and holes or terminals called hubs on the other side. The side with the prongs connects to the ends of electrical circuits in the punch-card machine, which are brought together in one place for the purpose. On the other side of the board, using plugwires, we can connect the hubs to each other in different ways to produce different results. The single-panel plugboard is 10 inches long and 5¾ inches wide. It contains 660 hubs in front and 660 corresponding prongs in the back. A double-panel plugboard or a triple-panel plugboard applies to some machines. In less time than it takes to describe it, we can take one wired-up plugboard out of a machine and put in a new wired-up plugboard and thus change completely the instructions under which the machine operates. Many of the machines have a number of different switches that we must also change, when going from one kind of problem to another.

The numbers that are stored or sorted in punch-card machines may be of any size up to 80 digits, one in each column of the punch card. In doing arithmetic (adding, subtracting, multiplying, and dividing), however, the largest number of digits is usually 10. Beyond 10 digits, we can work out tricks in many cases.

TYPES OF PUNCH-CARD MACHINES

The chief IBM punch-card machines are: the key punch, the verifier, the sorter, the interpreter, the reproducer, the collator, the multiplying punch, the calculating punch, and the tabulator. Of these 9 machines, the last 6 have plugboards and can do many different operations as a result.

There is a flow of punch cards through each of these machines. The machines differ from each other in the number and relation of the paths of flow, or card channels, and in the number and relation of the momentary stopping places, or card stations, at which cards are read, punched, or otherwise acted on. We can get a good idea of what a machine is from a picture of these card channels.

Key Punch

We use a key punch (Fig. 5) to punch original information into blank cards. In the key punch there is one card channel; it has one entrance, one station, and one exit. At the card station, there are 12 punching dies, one for each position in the card column, and each card column is presented one by one for punching. The numeric keyboard (Fig. 6) for the key punch has 14 keys:

Of course, in using a key punch, we must punch the same kind of information in the same group of columns. For example, if these cards are to contain employees’ social security numbers, we must punch that number always in the same card columns, numbered, say, 15 to 23, or 70 to 78, etc.

Verifier

The verifier is really the same machine as the key punch, but it has dull punching dies moving gently instead of sharp ones moving with force. It turns on a red light and stops when there is no punched hole in the right spot to match with a pressed key.

Sorter

The sorter is a machine for sorting cards, one column at a time (Fig. 7). The sorter has a card channel that forks; it has one entrance, one station, and 13 exits. Each exit corresponds to: one of the 12 punch positions 0 to 9, 11, and 12; or reject, which applies when the column is nowhere punched. It has one card station where a brush reads a single column of the card. We can turn a handle and move the brush to any column.

Interpreter

The interpreter takes in a card, reads its punches, prints on the card the marks indicated by the punches, and stacks the card. We call this process interpreting the card, since it translates the punched holes into printed marks. The interpreter (Fig. 8) has one card channel, with one entrance, 2 card stations, and one exit. What the machine does at the second card station depends on what the machine reads at the first card station and on what we have told the machine by switches and plugboard wiring to do.

Reproducer

The reproducer or reproducing punch can:

The reproducer (Fig. 9) has 2 independent card channels, the cards not mingling in any way, called the reading channel and the punching channel. We can run the machine with only the punching channel working; in fact, IBM equips some models only with the punching channel, particularly for “summary punch” operation. The machine is timed so that, when any card is at the middle station in either channel, then the next preceding card is at the latest station, and the next following card is at the earliest station. At 5 stations, the machine reads a card. At the middle station of the punching channel, the machine punches a card. Using a many-wire cable, we can connect the tabulator to the reproducer and so cause the tabulator to give information electrically to the reproducer. This connection makes possible the “summary punch” operation. Here is an instance with punch-card machines where, in order to transfer information from one machine to another, we are not required to move cards physically from one machine to another.

Collator

The collator is a machine that arranges or collates cards. It is particularly useful in selecting, matching, and merging cards. The collator (Fig. 10) has 2 card channels which join and then fork into 4 channels ending in pockets called Hoppers 1, 2, 3, and 4. The 2 card feeds are called the Primary Feed and the Secondary Feed. Cards from the Primary Feed may fall only into the first and second hoppers. Cards from the Secondary Feed may fall only into the second, third, and fourth hoppers. The collator has 3 stations at which cards may be read.

IBM can supply additional wiring called the collator counting device. With this we can make the collator count cards as well as compare them. For example, we could put 12 blank cards from the Secondary Feed behind each punched-card from the Primary Feed in order to prepare for some other operation.

Calculating Punch

The calculating punch was introduced in 1946. It is a versatile machine of considerable capacity. It adds, subtracts, multiplies, and divides. It also has a control over a sequence of operations, in some cases up to half a dozen steps.

This machine (Fig. 11) has one card channel with 4 stations called, respectively, control brushes, reading brushes, punch feed, and punching dies. At station 1, there are 20 brushes; we can set these by hand to read any 20 of the 80 card columns. At station 2 there are 80 regular reading brushes. At station 3 the card waits for a part of a second while the machine calculates, and, when that is done, the card is fed into station 4, where it is punched or verified. The multiplying punch is an earlier model of the calculating punch, without the capacity for division.

Tabulator

The tabulator can select and list information from cards. Also, it can total information from groups of cards in counters of the tabulator and can print the totals.

The tabulator (Fig. 12) has one card channel with two stations where cards may be read, called the Upper Brushes and Lower Brushes. When the Lower Brush station is reading one card, the Upper Brush station is reading the next card. The tabulator also has another channel, which is for endless paper (and sometimes separate sheets or cards). This channel has one station; here printing takes place. Unlike the typewriter, the tabulator prints a whole row at a time. It can print up to 88 numerals or letters across the sheet in one stroke. The cards flowing through the card channel and the paper flowing through the paper channel do not have to move in step; in fact, we need many different time relations between them, and the number of rows printed on the paper may have almost any relation to the number of punch cards flowing through the card channel.

At the station where paper is printed, we can put on the machine a mechanism called the automatic carriage. This is like a typewriter carriage, which holds the paper for a typewriter, but we can control the movement of paper through the automatic carriage by plugboard wiring, switch settings, and holes in punch cards. Thus we can arrange for headings, spacing, and feeding of new sheets to be controlled by the information and the instructions, with a great deal of versatility.

HANDLING INFORMATION

We have now described briefly the chief available punch-card machines as of the middle of 1948. The next question is: How do we actually get something done by means of punch cards? Let us go back to the census example, even though it may not be a very typical example, and see what would be done if we wished to compile a census by punch cards.

The first thing we do is plan which columns of the punch card will contain what information about the people being counted. For example, the following might be part of the plan:

Under the heading state, we know that there are 48 states, the District of Columbia, and several territories and possessions—all told, perhaps 60 possibilities. So, 2 punch-card columns are enough: they will allow 100 different sets of punches from 00 to 99 to be put in them. We then assign the code 00 to Maine, 01 to New Hampshire, 02 to Vermont, etc., or we might assign the code 00 to Alabama, 01 to Arizona, 02 to Arkansas, etc.—whichever would be more useful. Under the other headings, we do the same thing: count the possibilities; assign codes. In this case, it will be reasonable to use numeric codes 0 to 9 in each column in all places because we shall have millions of cards to deal with and numeric codes can be sorted faster than alphabetic codes. Alphabetic codes require 2 punched holes in each column, and sorting any column takes 2 operations.

The punch cards are printed with the chosen headings. We set up the codes in charts and give them to clerks. Using key punches and verifiers, they punch up the cards and check them. They work from the original information collected by the census-taker in the field. Since the original information will come in geographically, probably only one geographic code at a time will be needed, and it will be simple to keep track of. As to occupation, however, it may be useful to assign other clerks full-time to examining the original information and specifying the right code for the occupation. Then the clerks who do the punching will have only copying to do.

The great bulk of the work with the census will be sorting, counting, and totaling. The original punch cards will be summarized into larger and larger groups. For example, the cards for all males age 23 last birthday living in the state of Massachusetts are sorted together. This group of cards may be put into a tabulator wired to a summary punch. When the tabulator has counted the last card of this group, the summary punch punches one card, showing the total number in this group. Some time later a card like this will be ready for every state. Then the whole group of state cards may be fed into the tabulator wired to the reproducer acting as summary punch. When totaled, the number of males age 23 last birthday in the United States will be punched into a single card. After more compiling, a card like this will be ready for all males in the United States at each age. Then this group of cards may be fed into the tabulator wired to the summary punch. Each card may be listed by the tabulator on the paper flowing through it, showing the age and the number of males living at that age. At the end of the listing, the tabulator will print the total number of all males in the list, and the summary punch will punch a card containing this total.

ARITHMETICAL OPERATIONS

Punch-card machines can perform the arithmetical operations of counting, adding, subtracting, multiplying, dividing, and rounding off.

Counting

Counting can be done by the sorter, the tabulator, and the collator. The tabulator can print the total count. The tabulator and summary punch wired together can put the total count automatically into another punch card. The sorter shows the count in dials.

Adding and Subtracting

Adding and subtracting can be done by the tabulator, the calculating punch, and the multiplying punch. In the calculating and multiplying punches, the sum or difference is usually punched into the same card from which the numbers were first obtained. The tabulator, however, obtains the result first in a counter; from the counter, it can be printed on paper or punched into a blank card with the aid of the summary punch.

Numbers are handled as groups of decimal digits, and the machines mirror the properties of digits in the decimal system. Negative numbers are usually handled as complements (see Supplement 2). For example, if we have in the tabulator a counter with a capacity of six digits, the number-000013 is stored in the counter as the complement 999987. We cannot store in the counter the number +999987, since we cannot distinguish it from-000013. In other words, if a counter is to be used for both positive and negative numbers, its capacity is actually one digit less, since in the last decimal place on the left 0 will mean positive and 9 will mean negative.

Multiplying and Dividing

Multiplying is done in the calculating and multiplying punches. In both cases, the multiplication table is built into the circuits of the machine, and the system of left-hand components and right-hand components is used (see Supplement 2).

Dividing is done in the calculating punch and is carried out in that machine much as in ordinary arithmetic. By means of an estimating circuit the calculating punch guesses what multiple of the divisor will go into the dividend. Then it determines that multiple and tries it.

Rounding Off

Rounding off may be done in 3 punch-card machines, the calculating and multiplying punches, and the tabulator. For example, suppose we have the numbers 49.1476, 68.5327, and we wish to round them off to 2 decimal places. The results will be 49.15 and 68.53. For the first number, we raise the .0076, turning .1476 into .15, since .0076 is more than .005. For the second number, we drop the .0027 since it is less than .005.

Each of these punch-card machines provides what is called a 5 impulse in each machine cycle. When the number is to be rounded off, the 5 impulse is plugged into the first decimal place that is to be dropped, and it is there added. If the figure in the decimal place to be dropped is 0 to 4, the added 5 makes no difference in the last decimal place that is to be kept. But, if the figure in the decimal place to be dropped is 5 to 9, then the added 5 makes a carry into the last decimal place that is to be kept, increasing it by 1, and this is just what is wanted for rounding off.

LOGICAL OPERATIONS

Punch-card machines do many operations of reasoning or logic that do not involve addition, subtraction, multiplication, or division. Just as we can write equations for arithmetical operations, so we can write equations for these logical operations using mathematical logic (see Chapter 9 and Supplement 2). If any reader, however, is not interested in these logical equations, he should skip each paragraph that begins with “in the language of logic,” or a similar phrase.

Translating

Reading and writing are operations perhaps not strictly of reasoning but of translating from one language to another. Basically these operations take in a mark in one language and give out a mark with the same meaning in another language. For example, the interpreter takes in punched holes and gives out printed marks, but the holes and the marks have the same meaning.

The major part of sorting is done by a punch-card sorting machine and can be considered an operation of translating. In sorting a card, the machine takes in a mark in the form of a punched hole on a punch card and specifies a place bearing the same mark where the card is put. The remaining part of sorting is done by human beings. This part consists of picking up blocks of cards from the pockets of the sorter and putting the blocks together in the right sequence.

Comparing

The first operation of reasoning done by punch-card machines is comparing. For an example of comparing in the operation of the tabulator, let us take instructing the machine when to pick up a total and print it. As an illustration, suppose that we are making a table by state, county, and township of the number of persons counted in a census. Suppose that for each township we have one punch card telling the total number of persons. If all the cards are in sequence, then, whenever the county changes, we want a minor total, and, whenever the state changes, we want a major total. What does the machine do?

The tabulator has a mechanism that we shall call a comparer (Fig. 13). A comparer has 2 inputs that may be called Previous and Current and one output that may be called Unequal. The comparer has the property of giving out an impulse if and only if there is a difference between the 2 inputs.

In the language of the algebra of logic (see Supplement 2 and Chapter 9), let the pieces of information coming into the comparer be a and b, and let the information coming out of the comparer be p. Then the equation of the comparer is:

p = T(a ≠ b)

where “T (···)” is “the truth value of ···” and “···” is a statement, and where the truth value is 1 if true and 0 if false.

In wiring the tabulator so that it can tell when to total, we use the comparer. We feed into it the county from the current card and the county from the previous card. Out of the comparer we get an impulse if and only if these two pieces of information are different. This is just what happens when the county changes. The impulse from the comparer is then used in further wiring of the tabulator: it makes the counter that is busy totaling the number of persons in the county print its total and then clear. In the same way, another comparer, which watches state instead of county, takes care of major totals when the state changes.

Selecting

The next operation of reasoning which punch-card machines can do is selecting. The tabulator, collator, interpreter, reproducer, and calculating punch all may contain mechanisms that can select information. These mechanisms are called selectors.

For example, suppose that we are using the tabulator to make a table showing for each city the number of males and the number of females. In the table we shall have three columns: first, city; second, males; third, females. Suppose that each punch card in columns 30 to 36 shows the total of males or females in a city. Suppose that, if and only if the card is for females, it has an X punch (or 11 punch) in column 79. What do we want to have happen? We want the number in columns 30 to 36 to go into the second column of the table if there is no X in column 79, and we want it to go into the third column of the table if there is an X in column 79. This is just another way of saying that we want the number to go into the males column if it is a number of males, and into the females column if it is a number of females. We make this happen by using a selector.

A selector (Fig. 14) is a mechanism with 2 inputs and 2 outputs. The 2 inputs are called X Pickup and Common. The 2 outputs are called X and No X. The X Pickup, as its name implies, watches for X’s. The Common takes in information. What comes out of X is what goes into Common if and only if an X punch is picked up; otherwise nothing comes out. What comes out of No X is what goes into Common if and only if an X punch is not picked up; otherwise nothing comes out. From the point of view of ordering punch-card equipment, we should note that there are two types of selectors: X selectors or X distributors, which have a selecting capacity of one column—that is, one decimal digit—and class selectors, which ordinarily have a selecting capacity of 10 columns or 10 decimal digits. But we shall disregard this difference here, as we have disregarded most other questions of capacity in multiplication, division, etc.

In the language of logic (see Chapter 9 and Supplement 2), if p, a, b, c are the information in X Pickup, Common, X, and No X, respectively, then the equations for a selector are:

b = a·p

c = a·(1 - p)

Returning now to the table we wish to make, we connect columns 30 to 36 of the punch card to Common. We connect column 79 of the punch card to the X Pickup. We connect the output No X to the males column of the table. We connect the output X to the females column of the table. In this way we make the number in the punch card appear in either one of two places in the table according to whether the number counts males or females.

We might mention several more properties of selectors. A selector can be used in the reverse way, with X Pickup, X, and No X as inputs and Common as output (Fig. 15). What will come out of Common is (1) what goes into input No X if there is no X punch in the column to which input X Pickup is wired, and (2) what goes into input X if there is an X punch in the column to which input X Pickup is wired.

In this case the logical equation for the selector is:

a = bp + c(1 - p)

Also, selectors can be used one after another, so that selecting based on 2 or 3 X punches can be made.

In the language of logic, if p, q, r are the truth values of “there is an X punch in column i, j, k,” respectively, then by means of selectors we can get such a function as:

c = apq + b(1 - q)(1 - r)

Also, a selector may often be energized not only by an X punch but also by a punch 0, 1, 2, ···, 9 and 12. In this case, the selector is equipped with an additional input that can respond to any digit. This input is called the Digit Pickup.

Digit Selector

Something like an ordinary selector is another mechanism called a digit selector (Fig. 16). This has one input, Common, and 12 outputs, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12. This mechanism is often included in the tabulator and may be included in other punch-card machines. For example, suppose that we want to do something if and only if column 62 of a punch card contains a 3 or a 4 or a 9. Then we connect a brush that reads column 62 of the punch card to the Common input of the digit selector. And we connect out from the digit selector jointly from outputs 3, 4, and 9.

In the language of logic, if a is the digit going into Common, and if p is the impulse coming out of the digit selector, then the equation of the mechanism in this case is:

p = T(a = 3, 4, 9)

Sequencer

A fourth operation of reasoning done by punch-card machines is finding that one number is greater than, or equal to, or less than another. This operation is done in the collator and may be called sequencing. For example, suppose that we have a file of punch cards for cities, showing in columns 41 to 48 the number of people. Suppose that we wish to pick out the cards for cities over 125,000 in population. Now the collator has a mechanism that has 2 inputs and 3 outputs (Fig. 17). We may call this mechanism a sequencer, since it can tell the sequence of two numbers. What goes into the Primary input is a number: let us call it a. What goes into Secondary is another number: let us call it b. An impulse comes out of Low Primary if a is less than b. An impulse comes out of Equal if a equals b. An impulse comes out of Low Secondary if a is greater than b.

In the language of logic, if p, q, r are the three indications in Low Primary, Equal, and Low Secondary, then:

p = T(a < b)

q = T(a = b)

r = T(a > b)

Returning to our example, we punch up a card with 125,000 in columns 43 to 48, and we put this card into the Secondary Feed. We take the punch cards for cities and put them into the Primary Feed. In the plugboard, we connect the hubs of the Secondary Brushes (that read the card in the Secondary Feed), columns 43 to 48, to the Secondary input of the Sequencer. We connect the hubs of the Primary Brushes (that read the card in the Primary Feed), columns 41 to 48, to the Primary input of the Sequencer. Then we connect the Low Primary output of the Sequencer to a device that causes the city card being examined to fall into pocket 1. We connect Equal output and Low Secondary output to a device that causes the city card being examined to fall into pocket 2. Then, when the card for any city comes along, the machine compares the number of people in the city with 125,000. If the number is greater than 125,000, the card will fall into pocket 1; otherwise the card will fall into pocket 2. At the end of the run, we shall find in pocket 1 all the cards we want.

NEW DEVELOPMENTS

We may expect to see over the next few years major developments in punch-card machinery. It would seem likely that types of punch-card machines like the following might be constructed:

SPEED

The speed of various operations with present IBM punch-card machines is about as shown in the table.

COST

Punch-card machines may be either rented or purchased from some manufacturers but only rented from others. If we take the cost of a clerk as $120 to $150 a month, the monthly rent of most punch-card machines ranges from ⅒ of the cost of a clerk for the simplest type of machine, such as a key punch, to 3 times the cost of a clerk for a complicated and versatile type of machine, such as a tabulator with many attachments. The rental basis is naturally convenient for many kinds of jobs.

RELIABILITY

The reliability of work with punch cards and punch-card machines is often much better than 99 per cent: in 10,000 operations, failures should be less than 2 or 3. This is, of course, much better than with clerical operations.

There are a number of causes for machine or card failures. Sometimes cards may be warped and may not feed into the machines properly. Or, the air in the room may be very dry, and static electricity may make the cards stick together. Or, the air may be too humid; the cards may swell slightly and may jam in the machine. A punch may get slightly out of true alignment, and punches in the cards may be slightly off. A relay may get dust on its contact points and, from time to time, fail to perform in the right way. Considerable engineering effort has been put into remedying these and other troubles, with much success.

To make sure that we have correct results from human beings working with punch-card machines, we may verify each process. Information that is punched on the key punch may be verified on the verifier. Multiplications done with multiplicand a and multiplier b may be repeated and compared with multiplications done with multiplicand b and multiplier a. Cards that are sorted on the sorter may be put through the collator to make sure that their sequence is correct. It is often good to plan every operation so that we have a proof that the result is right.

It is standard practice to have the machines inspected regularly in order to keep them operating properly. On the average, for every 50 to 75 machines, there will be one full-time service man maintaining them and taking care of calls for repairs. Of course, as with any machinery, some service calls will be a result of the human element; for example, a problem may have been set up wrongly on a machine.

GENERAL USEFULNESS

Punch-card calculations are much faster and more accurate than hand calculations. With punch cards, work is organized so that all cases are handled at the same time in the same way. This process is very different from handling each case separately from start to finish. As soon as the number of cases to be handled is more than a hundred and each item of information is to be used five or more times, punch cards are likely to be advantageous, provided other factors are favorable. Vast quantities of information have been handled very successfully by punch-card machines. Over 30 scientific and engineering laboratories in the United States are doing computation by punch cards. Over a billion punch cards, in fact, are used annually in this country.