COUNTING & COUNTING MACHINES.

Progress, Volume I, Issue II, 1 September 1906, Page 315

COUNTING & COUNTING MACHINES.

By J. Watkin Kinniburgh

SECOND PAPER. In iB6O, a simple and clever contrivance was used by Jardme Henry for use m the construction of joint life annuities, of which I give an illustration. I quote from Mr. Henry's paper on the principle of this device :—": — " Let A B C be a right angle triangle of which A B is the base and A C the hypothenuse, and from any point D in A C let fall D E perpendicular to A B ; then from the similar triangles A D E, A C B, we haye — DE:AE:.BC:AB AEx B C and D E = A B " Now if A B be taken as equal to 1, 10, 100, 1000, or 10,000, we may say, disregarding the decimal point, that DE = AExßC.'* The instrument used consisted of a brass rightangle triangle with two legs equal, each 75 inches long, and each of the three sides divided into 10,000 parts. There was also a movable table similarly graduated, which slid along the triangle, and could be fixed by a clamp where required parallel to B C. The annuity values constructed with this instrument were worked at the rate of 400 per hour, and were generally correct to the third place of decimals.

to get a quotient of five. In the Millionaire only one turn of the handle is necessary for any single figure, so that in the former machine to multiply a number by 5646354 would require 33 turns of the handle ; in the latter only 7 turns would be necessary. To estimate the full importance of this fact, I must explain that the Arithmometer, worked at full speed by one operator, and the results of multiplication of, say, six figures by five, being written down by an assistant, will do the work of five first-class computers. The Millionaire, used on a similar operation, would do the work of ten. The results could be read off by the operator as quickly as they could be written down by his assistant taking the whole day through. In short, multiplication and division can be worked as quickly as addition or subtraction. In reporting on this machine recently, I expressed my doubts as to whether the working parts would stand the strain for any length of time, and I am still dubious on this point. If it is constructed on sound mechanical principles, and its workmanship is equal to that of the Arithmometer, it may continue to do its work for years. In that case it must I imagine, eventually supersede every other machine for arithmetical work. One of these machines is, I understand, now being used by the Australian Mutual Provident Society at its head office in Sydney. Of machines specially designed for addition there are a large number on the market, but except where there are large operations and constant work for those skilled in their manipulation, they

pression that keys i or 2 would, and there is consequently a tendency not to press the high key down sufficiently, the consequence being that sometimes a number less than 9 will be registered, f This objection is altogether removed in Burroughs' machine, where the keys all require the same force to depress them, no matter what figure they represent. The Burroughs' machine, I must point out, is much more expensive than the Comptograph. The prospectus of an adding machine lately put on the market by the makers of the Brunsviga has been received by a gentleman in Wellington, who has kindly drawn my attention thereto. It is apparently much similar to the Burroughs' machine, and according to the prospectus does exactly the same work and almost in the same manner. Its English name is the Addograph, a very suggestive and suitable title. I must mention that in all the three last-mentioned machines provision is made by simple adjustment to enable them to perform the addition of money columns, and I have no doubt that once they get a footing in mercantile houses they will soon be almost as generally used as the typewriter. Not many years ago a citizen of Wellington — Mr. Poynter — designed a very ingenious adding machine, of which he showed me the working model, and it seems a pity that circumstances prevented him from perfecting so useful a machine. I believe that Mr. Poynter was the first to devise a differential gear that was quickly convertible from decimal to money columns, or vice versa. Hitherto I have dealt with purely mechanical

oon A coincides with 3on B. In both cases there is a constant difference of 3. " If the scale B be reversed and inverted, and arranged as shown, it will be seen that the sum is constant and equal to 7. At the same time it follows that the difference between 7 and any number on B is given opposite to that number on A. " If the logarithms of simple numbers are considered, and if the divisions on A and B are taken as decimal values up to 1.00, a logarithmic scale may be constructed. The common logarithms of numbers are .—. — log. 1 = 0.000, log. 2 = 0.30r, log. 3 .= 0.477, etc. These values may then be marked off on A and B as shown in the figure. Taking A and B in the position shown, where 1 on B coincides with 2 on A, it will be seen that now each number on A has twice the value of the coinciding number on B — that is, the operation of multiplication by 2 has been performed. At the same time, also, the value of each number on B is one-half of the value of the coinciding number on A." The engineer's slide rule varies from 8 to 10 inches in length, and may be carried in the pocket. It is especially designed for the use of engineers, surveyors, and kindred professions, and generally bears on its faces tables of constants m every-day use. It has two slides at least, and although a simple instrument, it has the appearance of intricacy. The divisions on such a rule being necessarily very small, it is not adapted for a long series of computations. The general utility of the logarithmic scale is limited by its workable length ; hence other forms have been devised. Hannyngton's improvement consists of a series of fixed rules of equal length, arranged one below the other, and graduated in such manner that the values towards the end of the topmost scale are repeated at the beginning of the second scale,

values. ,-,v;Any list of machines and scales in use must necessarily be incomplete, the march of invention always keeping pace with the times. I have not attempted to give even a nearly complete list, but those dealt with m the latter parts of these papers comprise, I think, the most used. Every year brings forward some new device, and every year the use of counting machines increases. What the typewriter has become to the correspondent, the author, and the journalist, so, before many years have passed, will the mechanical computer become to all engaged m finance, banking, and mercantile calculations. The great drawback hitherto to the employment of these machines in British commercial houses is the want of a uniform system of expressing weights, measures and currency m decimals. This reform, which has now been advocated for over 200 years, is bound to come m the near future, and with its advent a new field of occupation will be opened up, and computing-machine experts will vie m numbers with those of the typewriter.

Since the introduction of the Arithmometer there have been several useful machines brought out for performing the same work. A very good and strong machine is Grant's Hand Organ, an American invention. Another from the same country, the maker's name of which has escaped my memory, is on the principle of the Arithmometer, but circular in form The most useful however, and one which is now running the Arithmometer very closely, is the machine known as the Brunsviga, originally invented by Ohdner, a Russian, and now improved and constructed by Grimme, Natalis and Co., of Brunswick. This machine has some advantages not possessed by its rivals. It is lighter to work and quieter m operation. It has no reversing lever, the handle simply being turned backwards for subtraction or division. The quotient figures are in two colours, red and black, and you may tell at a glance whether a figure is xor - The construction is very clever, and the mechanism is altogether different in design from the Arithmometer. It is also of a very handy size, and being enclosed in a case like a typewriter is easily portable. Several improvements have already been made m this machine since its introduction, and it is now perfectly reliable and very difficult to put out of order. A new machine, the " Millionaire," has quite recently been introduced, which, if it carries out the promises of its prospectus, must soon eclipse all its predecessors. It has somewhat the appearance of the Arithmometer. In the Arithmometer, to multiply by five, five turns of the handle are necessary, and the same number of turns is required

do not appear to take on to any great extent m British countries. I think that this is probably due to our mixed coinage and measures to a great extent, most of these machines until lately having been constructed on the decimal scale. One of the neatest and cheapest machines for casting a single column of figures is known as the Centigraph, of which an illustration is given. It has five keys and is worked by the right hand only. Beginning with the little finger and depressing the key farthest to the right scores i on the dial, the third finger key scores 2, the second 3, and the first 4, while the thumb key scores 5. If you want to express any number above 5, say 8 for instance you press both the thumb key (5) and the second finger key (3). This is very quick and reliable, but as it is limited to one column it is not capable of much faster work, if any, than a fairly expert adder. The Comptometer, a well-known machine, will add up to nine columns at a time, and can easily be understood from an inspection In the hands of an expert it is a very useful machine, and would soon pay for itself 111 the saving of the weary brain work of long and heavy additions. The Comptograph is a further development of the same machine, by which the results can be typed on to paper as often as is desired, either partial or complete totals. A machine of much the same design is al so used. It is known as Burroughs' Registering Accountant. It is of much finer and stronger workmanship, and has many points of superiority over the Comptograph In the latter machine when a high figure like 9 has to be scored the key moves through a much longer distance, and needs twice the de-

appliances, but there is a class of computing devices based upon the logarithmic scale which is perhaps in more general use than machines. I refer to the adaptations of the slide rule, originally introduced by Dr. Roget, and based on Gunter's scale. I cannot improve on the simple description of the principle of the slide rule given m Vol. 11. of Green's Encyclopaedia of Accounting, which reads as follows .—. — "Let two slips of paper be taken and divided equally and similarly into ten parts each. Let one of these be lettered A, and the other B. If these be placed alongside, then corresponding figures will coincide. If, however, B be moved to the right until o on B coincides with 3 on A, it will be seen at once that each figure on A is greater by 3 than the coinciding figure on B. By this means is obtained the addition of 3 to each number on B. At the same time, each figure on B is less by 3 than the figure with which it coincides on A, and thus the subtraction of 3 from each number on Ais obtained. This latter process will be better shown by moving B to the left until

*Journal oi the Institute of Actuaries, Vol. XVI, p. 212. f Since writing the above description the manufacturers have sent me particulars of the later Comptometers, in which this defect has been entirely removed and the machine altogether has been considerably improved ; now it compares favourably with its competitors and is much cheaper than any of them.

and this arrangement is repeated so that the figures practically overlap. The movable part is arranged in the same manner, and if, when the scales are set, a portion of the movable scale projects beyond the fixed scale at one extremity, the result may be read from another part of the rule. Fuller's scale takes the form of a spiral wound around a movable cylinder and a fixed point attached to a second inside cylinder. This adaptation is equal to a fiat slide rule 84 feet long but it is very trying and wearisome to the eyes as they are constantly fixed on a shining surface convex to the plane of sight, and the figures are very small and faintly printed. The same maker furnishes a circular slide rule. Here the length of the rule, though limited by the size of the circumference, is practically endless, the circular form doing away with overlap. The circle, however, could, without great difficulty, be enlarged to such an extent as to enable many of the calculations now usually performed by machines to be done silently and expeditiously by an expert operator. In statistical work the slide rule is specially useful for taking out the percentage of each of a series of items to their total, as the total once set to unity fixes the ratio of each item thereto, and the results can be read off without further trouble beyond due care in placing the decimal point. There is a very clever adaptation of the diagonal scale invented by Mr Poynter, of this city. It is especially suitable for the calculation of fire premiums where the insurance is for odd amounts. The principal advantage of this ready reckoner lies in the fact that it is so scaled that the results may be read either in money or decimal