502 



allowable, since the fourth differences are supposed to be constant. 

 Hence the effect of the complete motion, consisting of one forward 

 and one backward motion, is to make all the numbers advance one 

 stage ; and therefore by continuing to turn the handle the numbers 

 u *+i> u x +2> u x+3 & c -> will b e calculated in succession. According 

 as these numbers are calculated they are impressed, by the action of 

 the machine itself, on a plate of lead, by means of steel punches, while 

 a numerator at the same time impresses beside them the values of 

 the argument x. These plates are afterwards taken out, and stamped 

 on an easily fusible alloy just on the point of solidifying, and thus 

 are obtained stereotype plates of the calculated results, fit for 

 printing from. 



In retaining a given number of decimals, it is usual to add one to 

 the last figure if the first digit left out be 5 or a higher number. 

 This is effected in the machine in the simplest possible manner, 

 namely by placing the cog which occasions the carriages from the 

 ninth to the eighth place in the highest tier in such a position that 

 the carriage takes place when the ninth wheel changes from 4 to 5, 

 instead of from 9 to 0. 



The principle of the machine is not of course dependent upon the 

 circumstance that the radix of the scale of notation commonly em- 

 ployed has the particular value 10; and it would be as easy to con- 

 struct a machine adapted to the senary or duodenary as to the denary 

 scale. Not only so, but the machine actually constructed admits 

 of being changed very readily from the denary to the senary scale, 

 or rather to a mixture of the denary and senary scales, which is 

 required in tabulating degrees, minutes, and seconds. For this 

 purpose it is sufficient to take off the ordinary figure- wheels from 

 those spindles which are to count by sixes, and put on spare wheels 

 which are provided, adapted to the senary scale. 



The machine works with the greatest freedom and smoothness. 

 The parts move with the utmost facility, in fact, quite loosely. On 

 this account no amount of dust which it would reasonably be 

 expected to receive in any moderate time seems likely to interfere 

 with its action. Besides, it can easily be taken to pieces and 

 examined, if need be. Those motions which are not the direct con- 

 sequences of the revolution of the handle acting through a train of 

 rigid bodies are performed in consequence of gravity, no springs 



