Dr. Everett on a new Proportion-Table. 351 



figures are written, radiating outwards in all directions like the 

 signatures to a round-robin — an arrangement which prevents the 

 eye from gathering them in easily at one view, and renders it 

 necessary, after the first and second terms of a "proportion have 

 been brought into coincidence, to turn the instrument bodily 

 into a different position before the third and fourth terms can be 

 found. This necessity for handling the instrument after it has 

 been set, demands a certain amount of stiffness in the turning of 

 the moveable circle, to prevent unintentional displacement, while, 

 on the other hand, too much stiffness retards the operation of 

 setting ; and between these two extremes, with the swelling and 

 shrinking of materials to increase the difficulty, the true mean 

 of convenient working is not often attained. 



The new arrangement which we have now to describe is free 

 from these disadvantages, and at the same time permits of a 

 much greater enlargement of scale. Its distinguishing feature 

 consists in breaking up each of the two pieces which constitute a 

 sliding-rule into a number of equal parts, and arranging these 

 consecutively in tabular fashion in parallel columns, the columns 

 on one of the two pieces being visible through openings cut be- 

 tween the columns of the other. 



The arrangement of the columns is as follows. One of the 

 two pieces, that to which we shall give the name B, contains an 

 even number of columns, which, if placed in one continuous line 

 in the order of their succession, would form a logarithmic scale 

 in duplicate, like one of the scales of the ordinary sliding-rule. 



The other piece, which we shall call A, contains only half as 

 many columns, but these are of double the length. They must 

 be so arranged that the numbers in any one column are conse- 

 cutive, and that the lower half of any column is precisely similar 

 to the upper part of that which follows it. 



In one of these two pieces (it is theoretically indifferent which) 

 openings are cut between the columns, and the arrangement is 

 complete. 



It will be observed from this description that the piece called 

 A is twice as high as B, but only half as wide. When one piece 

 is laid upon the other, the portion common to both is a rectangle 

 whose area is half that of either of the pieces \ and this rectangle 

 contains on each of the two pieces a complete series of numbers 

 — that is to say, a series proceeding gradually from a certain num- 

 ber up to another ten times as great. All the numbers on one 

 piece have the same ratio to those which stand opposite them on 

 the other; so that we have thus a complete Table of proportional 

 numbers for the particular ratio corresponding to the position in 

 which the pieces have been laid ; and this ratio can be made 

 anything we please. It is of course necessary that the pieces be 



