NA TURE 



[July i i, 1901 



opinion, definitely less convenient than any good arithmo- 

 meter. 



The comptometer is conveniently available for ordinary com- 

 mercial operations, such as interest and discount, as well as for 

 merely adding up accounts. In the ordinary machine with only 

 decimal notation the last two columns must be retained foi the 

 pence, the next two for the shillings, leaving all the rest for 

 the pounds. However, a special build is now promised with 

 special shilling and pence columns, .so that on this any number 

 of money entries, taken in any order, may be very quickly added 

 up. Nevertheless, the process of dividing by 12 or 20 on the 

 decimal machine, for which it is necessary to strike the keys 

 marked in black 8 and 8 or i, as the case may be, is so rapid 

 that the pence when added up become shillings and pence on the 

 register in a moment, and the shillings, whicli must lie added after 

 the pence, become pounds and .shillings in even less time, and 

 tlie pounds, shillings and pence so obtained are in their proper 

 places. The comptometer arranged for British currency would, 

 however, be the more convenient where the adding up of ac- 

 counts is mo.stly wanted, but it does not seem as if it would meet 

 every case that will arise. For instance, in a large retail busi- 

 ness the number of entries to be checked of this type, 23!^ yards 

 at 7.t. <)\d. a yard, is so great that in one case that I know of 

 a special branch of the office is devoted to this work alone. The 

 cost of this branch amounts to 1000/. a year, and yet, partly in 

 consequence of the amazing quickness of the clerks, but chielly 

 because of our hopeless nun-decimal system, it is not possible 

 with much advantage to employ mechanical means of calculation 

 tn reduce this tax upon the business. Now with a decimal 

 money system the multiplication by 2375 in a machine would 

 be direct and simple enough, but I do not see how this could be 

 dire.ttly effected upon the British currency comptometer. I do 

 not see how multiplication or division by numbers of several 

 digits can be advantageously carried out. 



As a last example of the way in which ingenuity has been 

 exercised in finding a way of making this adding machme per- 

 form other operations, I may refer to the directions for finding 

 a square root. It is not my intention to explain this process 

 here, but simply refer to the artifice. "The simplest way to 

 extract square root on the comptometer is to act on the principle 

 that in the series of odd numbers, I, 3. 5, 7, 9, &c., the square 

 ol the number of terms always equals the sum of all the terms." 

 On this a process of addition is devised, using the red numbers 

 on the keys, which I find, even without much practice, is sur- 

 prisingly lapid for the first three figures, but which, like the 

 ordinary head and pencil way, becomes increasingly cumbersome 

 with a greater number. 



The comptometer is like all arithmometers in that, having 

 found one product of two or more numbers, or having any 

 previous result on the register, any further products of two 

 numbers may be added to or subtracted from this, one at a time, 

 without the necessity of writing down any intermediate result or 

 of separately finding these products ; and then, when this is 

 done, the sums or ditTerences of all the products may be divided 

 by a final number. If a further division is required the compto- 

 meter differs from all arithmometers except Edmondson's in that 

 the result is found on the .same register as the previous dividend, 

 and so it might appear that any number of divisions could be 

 effected. This is not the case, as the quotient occasionally 

 moves up the machine towards the left and so gets out of range, 

 whereas in Edmondson's, as the machine is arranged in a circle, 

 the quotients and dividends may chase each other round the 

 machine without ever coming to a dead stop. In ordinary arith- 

 mometers the quotient gets on to the counter wheels, when 

 nothing more can be done to it unless it is again transferred to 

 the register. 



The operation, therefore, that these machines can perform 

 with the greatest advantage is of the form 



ah ±cd± rf± . . . 



whereas the operation that is most favourable for the use of 

 logarithms is of the form 



a" />••' tabf e . . . 



r' s' tab''' <p . . . 

 fab representing any of the tabulated logarillimic functions. 

 This advantage is so great that formuke are artificially mani- 

 pulated until they are finally rammed into this form and are 

 then said to be adapted to logarithmic computation. Now the 



NO. 1654, VOL. 64] 



advantages of the calculating machines referred to are so great, 

 and they are in so many ways preferable to logarithms where 

 they can be used, that it is just as important to adapt formukv 

 to mechanical computation by putting them where convenient 

 into the first of these two forms. Then, according as they can 

 be put into one or other of the.se forms, machines or logarithms 

 should be used for the purpose of computation, and no attempt 

 should be made to use either for work specially adapted in this 

 way for the other. 



It niay perhaps lie worth while, by way of example, to mention 

 that in the large number of corrections of the scale readings to 

 bring them to circular measure that I had to make in my ex- 

 periments on the constant of gravitation, I found I could 

 calculate 9- .', 9''+ I 9'' in less time on an arithmometer than was 

 required to look up the angle in the trigonometrical tables. 



A few final observations are desirable bearing on the com- 

 parison of the conqjtometer with arithmometers. 



In the first place the comptometer makes a most aggravating 

 noise, like a typewriter through a megaphone ; but other arith- 

 mometers are noisy, none, however, so bad as this machine. The 

 only silent arithmometer is that beautiful machine invented by 

 Prof. Selling, but this is practically unknown in this country. 



To my mind the comptometer, with its single figure opeta- 

 tions, is not so convenient as the arithmometer for reducing and 

 computing observations in the laboratory. Its success is only 

 rendered possiI)le by the fact that it is a key machine, for key 

 strokes may be so very rapid. The operating numbers on most 

 arithmometers are set by slides and that is relatively slow, the 

 operation, however, by the handle afterwards is vastly more 

 rapid. Selling's arithmometer is, however, a key machine for 

 the setting, while the turning handle is replaced by a sliding 

 movement, one complete slide doing the work of five turns of 

 the handle. Again, the fact that there is no record of the 

 operating figures actually given to the comptometer seems to be, 

 for scientific work, decidedly a drawback. 



On the other hand the construction is .admirable, perfectly 

 adapted to its purpose, and, I should judge, fairly indestructible. 

 I would on this point only make one complaint, which, however, 

 refers to a defect in no respect essential to the machine. I refer 

 to the difficulty of reading the numbers on the register. The 

 figures are elegant, with a great contrast between the thick and 

 the thin parts, and they are upon a polished reflecting wheel 

 face. They are seen through small windows in a polished metal 

 plate. The result is they are not as legible .as they ought to be ; 

 great care has to be taken to get a suitable light, and it is use- 

 less to sit facing a window. The 3's may be confused with the 

 S's, the I's with the 4's, and the o's with the 9's. If block 

 figures were used, and if, further, they were dead white upon a 

 bl.ack ground, or even the reverse, and were not seen through 

 a shining plate, this little defect, which I am surprised to see 

 in the product of an American shop, would be remedied. 



I have m.ade no comparison between the comptometer and 

 the slide rule because a good slide rule, such as Gravet's, cannot 

 be approached in convenience by any mechanism where the 

 limited accuracy of the slide rule is sufficient, nor can wheel- 

 work machines directly find the fourth term in a proportion in 

 which the three other terms are numbers, their squares, or roots, 

 or trigonometrical functions, or the reciprocals of these, nor can 

 they give logarithms at sight. 



The attempts that have been made to increase the .accuracy 

 of the slide rule by increasing its length are not, in my opinion, 

 of much success, because to gain only one more figure ten times 

 the length, at least, is necessary. The rule must then be broken 

 up griiliron fashion, as in General Hannyngton's,' Prof. Everett's 

 and Thatcher's, or wound in a spiral as in Fuller's, or be alto- 

 gether peculiar as Tower's. When an extra figure has been 

 gained in this way the extreme handiness of the slide rule is 

 gone, as it can no longer be carried in the pocket, it takes 

 longer to find the place, and, as a rule, the range is limited to 

 mere simple proportion. Where the accur.acy of i/io per cent, 

 given by a 26 cm. rule, or 1/20 per cent, by a half-metre 

 Clravct rule is not sufficient, I should prefer in general five- 

 figure logarithms or a wheel-machine to an extended slide rule. 

 Whether the wheel-machine should be a comptometer or an 

 arithmometer must depend upon the char.acter of the calculations 

 most often met with. I have attempted in my preceding remarks 

 to give the information necessary to emable any one to judge in 

 his own particular case. C. \'. Boys. 



1 The Slide Rule Extended. E. .iiid F. N. Spoil. 16 Cfi;ring Cros', .-in.f 

 .-^ston and M.-inder, Old Conipton Street, Soho. 



