80 ANNUAL OF SCIENTIFIC DISCOVERY. 



cylindrical surface of each ring are engraved the ordinary numerals from 

 to 9, one of which, in each position of the ring, appears in front, so that the 

 successive numbers shown in any horizontal row of rings may be read from 

 left to right, as in ordinary writing. The upper row exhibits the number or 

 answer resulting from the calculation to fifteen places of figures, the first 

 eight of which the machine stereotypes. The numbers seen on the second 

 row of rings constitute the first order of differences, also to fifteen places of 

 figures, if that number be required ; and the third, fourth, and fifth rows of 

 rings, in like manner, exhibit the second, third and fourth orders of differ- 

 ences. Any row can be set by hand, so as to present to the eye any number 

 expressed according to the decimal scale of notation ; such as the number 

 987654321056789, the first eight figures of which, if in the uttermost row, 

 would, on being calculated by the machine, be immediately stereotyped But 

 by simply changing a ring in each of two of the vertical columns, the machine 

 can be made to exhibit and to calculate numbers expressed in the mixed 

 senary system of notation, as in that of degrees, minutes, seconds, and deci- 

 mals of a second. Thus, for instance, if the result 874324687356402 were 

 indicated in the upper row of rings, it would be stereotyped 87 degrees, 43 

 minutes, 24'69 seconds. "While this process is going on, the argument 

 proper to each result is at the same time also stereotyped in its proper place ; 

 nothing more being required for that purpose than to set each row of figure 

 rings to differences previously calculated from the proper formula, and to place 

 a strip of sheet lead on the slide of the printing apparatus ; then, by turning 

 the handle (to do which requires no greater power than what is exerted in 

 turning that of a small barrel-organ), the whole table required is calculated 

 and stereomoulded in the lead. By this expression is meant that the strip of 

 lead is made into a beautiful stereotype mould, from which any number of 

 sharp stereotype plates can be produced ready for the working of an ordinary 

 printing press. At the average rate of working the machine, 120 lines per 

 hour of arguments and results are calculated and actually stereotyped, ready 

 for the press. It is found on trial that the machine calculates and stereo- 

 types, without chance of error, two-and-a-half pages of figures in the same 

 time that a skilful compositor would take merely to set up the types for one 

 single page. 



Our readers will, of course, understand that the machine is not self-act- 

 ing. It does not give logarithms, for example, merely for saying, Good 

 machine, we want logarithms. It must be fed both with manual power and 

 with calculation. The seed must be according to the harvest wanted ; men 

 do not grow figs of thistles, even in a calculating machine. But the return 

 is greater than in most harvests ; a very little calculation makes the machine 

 do an enormous quantity of result by help of barrel-organ exercise. But 

 how are errors to be avoided if human fallibility is at the bottom of all '? 

 It is not a matter of course that errors will be avoided ; but casual errors 

 will be avoided. All is right, if the machine is rightly fed ; all is wrong, if 

 it be wrongly fed. Now, error throughout must be detected ; labor and lead 

 therefore may be thrown away, but wrong will never be published for right. 



The tables consist of a complete five-figure set of logarithms, with the 



