192 Mr. J. Bridge on a Calculating Apparatus 



F Gr (fig. 3) is a frame which is movable along the board. 

 It carries a number of glass slides, a, b, c, d, &c. (figs. 1 and 

 2), movable on it in the direction of their length. These are 

 made opaque except at the middle, where an aperture is left 

 (fig. 4) large enough to show two adjacent digits on the 

 tablets. 



g (fig. 1) is a fixed ridge of hard wood with notches at equal 

 intervals; and g' (fig. 3) is a corresponding groove in the 

 frame, p, p are pins going down through the frame so that 

 their lower ends, which are rounded, fall into the notches of g. 

 By the help of a little pressure from the finger on one of them 

 they serve to fix the frame at any of the positions it ought to 

 take — namely, so that each slide is half over one tablet and 

 half over the next (fig. 4). 



2. Multiplication. — Suppose 74628394 to be the multipli- 

 cand and 4736 the multiplier. Fig. 2 shows the arrangement 

 required. Tablets headed with the digits of the multiplicand 

 are set up in direct order on the board, the first filling the 

 space to 1 of the scale S S ; and the slides a, b, c, d are set 

 to the lines corresponding to the digits 4, 7, 3, 6 respectively 

 of the multiplier. 



The frame is then moved step by step from right to left. 

 At each step the sum of all the digits seen through the aper- 

 tures is taken, its units' figure recorded and its tens' figure 

 carried. When F arrives opposite on the scale the whole 

 product will have been recorded. 



3. This will be seen without explanation ; but for the sake 

 of what is to follow, the process may be compared with the 

 arranged details of the product. 



1 



2 

 3 

 4 



Let the sum of each pair of adjacent digits be called an ele- 

 ment, each vertical series of elements a column, and each hori- 

 zontal series a row. The columns will then correspond to the 

 places on the scale S S, or of the digits of the multiplicand; 

 and the rows will correspond to the places of the digits of the 

 multiplier, row 1 to 1st digit, and so on. The position of an 

 element in the product may be described by indicating its 

 column and its row, and its rank is the sum of the numbers 

 indicating its column and its row. Thus the element (6, 3) 

 is that which is found in column 6 and row 3, and its rank is 







1 



2 



3 



4 



5 



6 



7 



8 



2 



81 



62 



40 



83 



21 



23 



61 



6 



4 



92 



84 



21 



45 



62 



16 



32 



8 



2 



11 



21 



80 



62 



40 



92 



71 



2 



4 



22 



43 



61 



24 



81 



85 



42 



4 



