Definite Proportions. 3 
the remaining 49 acids, making, together, 149 experiments. 
Without the knowledge of the law under consideration, to 
ascertain the same facts it would be necessary to find, by ex- 
periment, how much of each of the 100 bases it required to 
saturate each of the 50 acids, implying 5000 experiments. 
Now, 149 : 5000: 1 : 33553; ; that is, the labour is reduced 
more than 33 times, and we have the great advantage of the 
accuracy of numerical ratios, instead of experiments, which, 
when they become so numerous, are apt to be more or less 
imperfect. In illustrating this subject to the learner, I have 
found an advantage in placing before him a row of spheres, — 
like marbles, to represent acids, and another row of cubes, 
like dice-blocks, to represent bases. It will then be obvious 
how much less labour is implied in applying first, all the 
cubes to one of the spheres, and, secondly, one of the cubes 
to all the spheres, than in going through the entire process of 
applying each cube, successively, to all the spheres. 
Proposition 3. The respective quantities of any number - 
_ of acids, required to saturate a given quantity of any base, 
are always in the same ratio to each other, to what base soever 
they be applied. In this proposition, the same relation is de- 
clared to exist between the acids, with respect to their respec- 
tive powers of saturating any base, as was de d, in ee. 
position 2d, to exist between the bases, with regard to their 
respective powers of saturating any acid: and the illustra- 
tions in this case, are similar to those of the other. 
The respective quantities of several bodies which produce 
the same effects in combination, are called chemical equiva- 
lenis. 'Thus, in the example given under Proposition 2, two 
parts of soda and three of potash are equivalents, because 
one saturates just as much acid as the other. This fact may 
be generalized ; and it is a most interesting and curious fact, 
that the ratios between the weights of all bodies, that are ca- 
pable of entering into chemical combination, whether simple 
or compound, are constant, and may be accurately expressed 
by numbers, being all referred to a common standard of 
unity. Thus, by inspecting a table of chemical equivalents, 
we may perceive that the numbers 1, 2, 3 and 4, are attached 
to the substances A, B, C and D, respectively; signifying 
that when A and B are found in combination with each oth- 
er, the quantity of A is one half that of B. In like manner, 
it is one third that of C, and one fourth that of D. t 
number 2, which is the representative number of B, imports 
