#### Background

English chemist William Hyde Wollaston was the original inventor of the Scale of Chemical Equivalents, as is explained on the back of the scale. Scientists Lewis C. Beck and Joseph Henry redesigned the scale in order to make it more effective.

The redesigned scale, with Hydrogen as the “radix of unity,” became an extremely useful tool in the teaching of chemistry, specifically by helping to identify the proportions of the constituents of a compound of known weight. As was explained in a letter from Lewis Beck to Joseph Henry, “‘Suppose we have 100 parts of Carbonate of Lime & we wish to know how much acid & base it contains. Move the Slide so that 100 on it shall be directly opposite to Carb. Lime. The number opposite Lime will be 56 & opposite Carbonic acid 44. = to 100. Now if we wish to decompose this with any of the acids we can instantly ascertain the amount of each necessary to effect this object as of Liquid Sulphuric acid 98 parts % the result will be crystallized Sulphate of Lime 172 parts.'” Carbonate of Lime, also known as calcium carbonate, is one part Calcium, one part Carbon, and three parts Oxygen and has a molar mass of 100.0869 g/mol.

WOLLASTON’S SCALE

Wollaston introduced the original scale of chemical equivalents in his paper entitled “A Synoptic Scale of Chemical Equivalents.” He explained, “The scale, which I am about to describe, is designed to answer at one view all these questions, with reference to most of the salts contained in the table, not merely expressing numerically the proportions by which the desired answers may be calculated, but directly indicating the actual weights of the several ingredients, contained in any assumed weight of the salt under consideration, and also the actual quantities of several reagents that may be used, and of the precipitates that would be obtained by each.” Wollaston based the numbers on his scale off of Richter’s measurements, specifically due to the accuracy of his law of permanent proportions

#### Inscription

**DESCRIPTION AND USE**

**Of the Scale**

The scale of Chemical Equivalents, the invention of which is due to Dr. Wollaston, is an instrument stamped with the accuracy and ingenuity of its author; and which has contributed, in an eminent degree, to facilitate the general study and practice of Chemistry. The present scale differs from the original one, in the assumption of Hydrogen, as the radix or unity. Two principal advantages arise from assuming this substance as the unit.

1. We avoid fractional quantities, and the whole scale, when the slider is properly placed, becomes a table of atomic weights.

2. These atomic numbers exhibit for the most part, in reference to hydrogen, the specific gravity of gasses and other chemical substances supposed to be in æriform state, and also the combining ratios of their weights under the same volume.

MATHEMATICAL CONSTRUCTION

It will be observed that the slider of the scale is graduated into divisions and sub-divisions continually decreasing in length, from 8 at the top to 330 near the bottom. These divisions correspond in relative lengths to the differences of the logarythms of the numbers placed opposite them. The were protracted by assuming a convenient length to unity,and transferring from a scale of equal parts to the distances corresponding to the differences of the logs of the several numbers on the slider. Thus the distance between 8 and 9, or between 10 and 20, is a linear representation of the excess of the log of the latter over that of the former of these numbers.

Now since the division of numbers is performed by taking the difference of their logs, and since the several divisions on the scale represent the difference of the logs, of the numbers placed opposite them, it follows, that the distance between any two numbers will be equal to the distance between any other two that give the same quotient by division. But numbers which give the same quotient have the same ratio to each other, therefore equality of ratio on the scale is expressed by equality of distance.

Thus if one leg of a pair of compasses be placed at 8 and the other opened to 16, and the instrument be transferred as a measure to any other part of the scale, its extremities will be found to rest only on numbers that have the same ratio as those from which it was transferred; as 10 and 20, 30 and 60. &c.

But the same thing may be performed by placing marks on the fixed part of the scale to represent particular openings of the compass, and by merely moving the slider past these, the several numbers which have the same ratios will be indicated. Thus, marks at oxygen and sulphur on the fixed part correspond, when the slider is in a proper position, to 8 and 16. Now if the slider be moved so that 10 is at the upper mark, the lower will be opposite 20, &c. as in the above case.

CHEMICAL EXPLANATION

The application of the logametric scale to Chemistry is founded on the most important fact in this science; which is, that all bodies whether simple or compound, that enter into Chemical combination, always unite in weights or in multiples of weights that have the same constant ratio to each other. And as these relative weighs have the same effect in forming neutral compounds and in producing other chemical changes they are called chemical equivalents, and may be expressed in numbers referable to a common standard taken as unity. On this scale the least combining quantity of hydrogen is taken as the unit; and as eight times as much oxygen by eight enters into combination with hydrogen to form the chemical compound water, oxygen will be expressed by 8, and water by 9. If, therefore, the slider be so placed that 8 near the top of it coincides with the upper oxygen, the whole scale becomes a synopsical table of these chemical…

(the original scale is cut off here, but the Joseph Henry Papers Volume I contains the rest)

…equivalents, having hydrogen as its radix. Thus 16 is the equivalent for Sulphur, 17 for Ammonia, 24 for Sodium, 70 for Barium, 110 for Silver, &c. &c. These substances were placed opposite the respective numbers on the slider as they have been determined by Thompson, Brande, and other approved authors.

In order to diminish the length of the scale and render it more portable, it commences with oxygen 8, instead of hydrogen 1, and 10 atoms of hydrogen are placed opposite 10 on the slider For the same reason 2 carbon, the atomic weight of the atom of which is 6, is placed opposite 12.

Again, as water and oxygen enter into combination in several definate proportions, 2 oxygen is placed opposite 16, 2 water opposite 18; 2 ox. opposite 24; 3 water opposite 27, &c, &c.