PROCEEDINGS. 123 



the style is opposite the figure to be added, and then the hand on 

 the disc will point to the result. When the hand passes over the 

 space between 9 and 0, a unit is carried to the next higher disc. 

 In like manner the addition of each succeeding digit is effected on 

 its own disc, the units on the unit disc, the tens on the tens, and 

 so on. 



To effect subtraction, the point of the style is placed in the hole 

 opposite the figure to be subtracted, and the disk is moved in the 

 direction 3, 2, 1, until the style is opposite 0. The hand then 

 indicates the result. If in the process the hand passes the space 

 between and 9, a unit will be deducted from the superior disc. 



The instrument enables us also to perform multiplication and 

 division, but not so readily as the larger machines constructed by 

 the Earl. 



Each disc is placed on a tubular spindle carrying — 



1. A flange which lying immediately under the face or lid of the 

 box, keeps the mechanism in its place. The flange is somewhat 

 larger than the disc. 



2. A wheel having ten teeth, and 



3. A " carrying-tooth," to effect the carriages, that is to say, to 

 move the next higher disc one figure forward or backward when 

 passing from 9 to in addition, or from to 9 in subtraction. 

 This " carrying-tooth " is of rather more than twice the radius of 

 the toothed wheel. When therefore it gears and moves the wheel 

 on the next superior disc, it does so at a correspondingly greater 

 speed, and therefore with a proportionate loss of power. This is 

 of no consequence so long as the carrying affects only one or two 

 of the higher discs, but when they all indicate 9, and the carryings 

 has therefore to run through the whole series, a practical difficulty 

 arises. Thus, let the disc indicate 999,999,999, and let 1 be 

 added ; then each disc will have to advance one figure, and since 

 the whole movement forward has to be effected by the movement 

 of the units disc, the force required will be enormously greater 

 than would be sufficient to move the units disc by itself. Each 

 carrying tooth is necessarily in the same plane with the toothed 

 wheel into which it gears ; but in order that the carrying teeth 

 may not interfere with each other, they are arranged in three 

 different planes. Each tubular spindle fits into a pin of the same 

 length fixed in the bottom of the brass box containing the machine. 

 On this pin it revolves freely as required. Each disc is steadied 

 by a grasshopper spring, one end of which is fixed to the box, the 

 other or free end being Y-shaped and falling between two teeth of 

 the above-named toothed wheel. Besides steadying the disc in 

 each of its ten positions, this spring completes the work of carry- 

 ing, for each carrying tooth leaves the wheel into which it gears 

 before it has moved the latter through a full tenth of its circum- 



