1*14.] Scale of Chemical Equivalents. 179 



any one ratio, so the sum of any two or three equal spaces represent 

 a double or triple ratio. If 1 be increased three times by the ratio 

 of 1 to 2, it becomes 8, which bears to 1 triple the ratio of 2 to 1. 

 This ratio is therefore rightly represented by A D, which is the 

 triple of A B. 



" The distances of the intermediate numbers 5, 7? If, '1,13, &c. 

 from 1 are likewise made proportional to the ratios which they bear 

 to 1, and are easily laid down by means of a table of logarithms ; 

 for as these arc arithmetic measures of the ratios which all numbers 

 bear to unity, the spaces proportional to them become linear repre- 

 sentations of the same quantities. 



" As the entire spaces A D, A E, represent the ratios of 8 and 

 of If; respectively to 1, so the difference I) E represents the ratio 

 of H and 16, which stand at D and E, to each other. And in the 

 same manner, any other space, k /, represents correctly the ratio of } 

 to i:i; so that the measure of a fraction expressed by quantities that 

 are incommensurate is rendered as obvious to sight as that of any 

 simple multiple. And if a pair of compasses be opened to this 

 interval, and transferred to any other part of the scale, the points 

 of the compassis will be found to test upon numbers bearing the 

 same proportion to each other as those from which the interval was 

 transferred. 



" It is exactly in this manner that the various points in the 

 column of equivalents indicate the several quantities sought in any 

 given position of the slider. The relative distances, at which the 

 articles are placed, represent so many different openings of the 

 compasses rendered permanent and presented to view at once. In 

 the table, which I shall place at the end of this communication, 

 the relation of the various substances enumerated to each ether is 

 expressed by numbers. In the engraved scale of equivalents, the 

 ratios of these numbers arc represented by logometric intervals at 

 which they are placed, their several positions being determined by 

 of their respective numbers on the slider, which is logometri- 

 cally divided. Consequently all the several points in the column of 

 equivalents will indicate numbers in the same due proportions to 



• other, whatever part of the scale may he presented to them. 

 Those who formation may obtain it by inspection j those 



who already possess it may he able to correct the positions of some 

 articles by direct comparison with the !>c-t analyses upon record, in 

 whatever numbers the results of those analyses may happen to be 

 expresse 



u •-' 



