of Chemical Eciuivalents. 17 
As the entire spaces AD, AE represent the ratios of 8 and 
of 16 respectively to 1, so the difference DE represents the 
ratio of 8 and 16, which stand at D and E, to each other. And 
in the same manner, any other space kl represents correctly 
the ratio of 7 to 13 ; so that the measure of a fraction ex- 
pressed 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 compasses will 
be found to rest upon numbers bearing the same proportion 
to each other as those from which the interval was trans- 
ferred. 
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 other is expressed by numbers. In the 
engraved scale of equivalents, the ratios of these numbers are 
represented by logometric intervals at which they are placed, 
their several positions being determined by those of their 
respective numbers on the slider, which is logometrically 
divided. Consequently all the several points in the column of 
equivalents will indicate numbers in the same due proportions 
to each other, whatever part of the scale may be presented to 
them. Those who seek information may obtain it by inspec- 
tion; those who already possess it, may be able to correct the 
positions of some articles by direct comparison with the best 
MDCCCXIV. D 
