LuDGATE — On a Proposed Analytical Machine. 85 



the index and each of the four slides are respectively 3 + 14, + 14, 7 + 14, 

 and 1 + 14 units (that is 17, 14, 21, and 15 units), so that pointers attached 

 to the four slides, which normally point to zero on the index, will now point 

 respectively to the 17th, 14th, 21st, and 15th divisions of the index. 

 Consulting Table 3, we find that these divisions correspond to the partial 

 products 72, 9, 27, and 18. In the index the partial products are expressed 

 mechanically by movable blades placed at the intervals shown in column 2 

 of the third table. Now, the duration of the first movement of any blade 

 is as the unit figure of the partial product which it represents, so that the 

 movements of the blades concerned in the present case will be as the 

 numbers 2, 9, 7, and 8, which movements are conveyed by the pointers to 

 the mill, causing it to register the number 2978. A carriage near the index 

 now moves one step to effect multiplication by 10, and then the blades 

 partake of a second movement, this time transferring the tens' figures of 

 tlie partial products {i.e. 7, 0, 2, and 1) to the mill, which completes the 

 addition of the units' and tens' figures thus — 



2978 

 7021 



73188 



— the result being the product of the multiplicand b by the first digit of the 

 multiplier a. After this the index makes a rapid reciprocating movement, 

 bringing its slide into contact with the second type of the inner shuttle 

 (which represents the figure 2 in the quantity a), and the process just 

 described is repeated for this and the subsequent figures of the multiplier a 

 until the whole product ab is found. The shuttles are afterwards replaced in 

 the shuttle-boxes, the latter being then rotated until the second shuttles of 

 both boxes are opposite to the shuttle-race. These shuttles are brought to 

 the index, as in the former case, and the product of their Variables 

 (21893 X 823) is obtained, which, being added to the previous product 

 (that product having been purposely retained in the mill), gives the required 

 value of X. It may be mentioned that the position of the decimal point 

 in a product is determined by special mechanism which is independent of 

 both mill and index. 



Most of the movements mentioned above, as well as many others, are 

 derived from a set of cams placed on a common shaft parallel to the 

 driving-shaft ; and all movements so derived are under the control of tlie 

 formula-paper. 



The ordinals in Table 1 are not mathematically important, but refer to 



SCIENT. PBGC, K.D.S. VOL. XII., NO. IX. Q 



