Chemical Equivalent. When an element enters into chemical combination with another element, it does so in a fixed proportion which may be expressed in numbers. This ratio is termed the combining equivalent, combining proportion, equivalent weight, or simply the equivalent of the element. The term atomic weight is also used synonymously by those who accept the atomic theory. The numbers in the annexed table of equivalents (64) were prepared in 1872 for the use of the students of the school of mines of Columbia college, by Prof. Charles F. Chandler. For convenience of reference both the old and the new equivalents are given. (See Atomic THEORY.) The perissads are printed in Italics, and the ar-tiads in Roman. To convert formulas of the old system into the new, double the atoms of the perissads, or halve the atoms of the artiads, and vice versa. Hydrogen is adopted as the unit:

ELEMENTS.

Symbols.

EQUIVALENTS.

Old.

New.

Aluminum.....

Al.

137

27.4

Antimony....

Sb.

122

122

Arsenic........

As.

75

75

Barium.........

Ba.

68.5

137

Bismuth.......

Bi.

210

210

Boron.....

B.

11

11

Bromine....

Br.

80

80

Cadmium........

Cd.

56

112

Coesium.......

C'8.

133

133

Clacium..........

Ca.

20

40

Carbon.....

C.

6

12

Cerium.....

Ce.

45.7

91.4

Chlorine.......

Cl.

35.5

35.5

Chromium.......

Cr.

26.1

52.2

Cobalt.............

Co.

30

60

Columbium....

Cb.

94

94

Copper...

Cu.

31.7

63.4

Didymium....

D.

47.5

95

Erbium..........

E.

563

112.6

Fluorine.......

F.

19

19

Glucinum....

Gl.

4.6

9.2

Gold...........................

Au.

197

197

Hydrogen....

H.

1

1

Indium.......

In.

56.7

113.4

Iodine....

I.

127

127

Iridium.........

Ir.

99

198

Iron.

Fe.

28

56

Lanthanum...

La.

46

92

Lead.....

Pb.

103 5

207

Lithium.......

Li.

7

7

Magnesium.......

Mg.

12

24

Manganese.....................

Mn.

275

55

Mercury....

Hg.

100

200

Molybdenum.....

Mo.

48

96

Nickel.....

Ni.

29

58

Nitrogen.....

N.

14

14

Osmium.......

Os.

100

200

Oxygen.....

0.

8

16

Palladium..

Pd.

53

106

Phosphorus....

P.

31

31

Platinum...

Pt.

98.7

197.4

Potassium.......

k.

39.1

39.1

Rhodium.......

Ro.

52

104

Rubidium.....

Rb.

85.4

85.4

Ruthenium....

Ru.

52

104

Selenium........

Se.

395

79

Silicon.......

Si.

14

28

Silver.....

Ag.

108

108

Sodium........................

Na.

23

23

Strontium......................

Sr.

44

88

Sulphur..........

S.

16

32

Tantalum.....................

Ta.

182

182

Tellurium......................

Te.

64

128

Terbium.....

Tb.

37.7

75.4

Thallium......................

Tl.

204

204

Thorium....

Th.

59.2

118.4

Tin............................

Sn.

59

118

Titanium.......................

Ti.

25

50

Tungsten........

W.

92

184

Uranium.......................

U.

60

120

Vanadium.........

V.

51.3

51.3

Yttrium........

Y.

30.8

61.6

Zinc...........................

Zn.

32.5

65

Zirconium.............

Zr.

44.8

89.6

Each element has its own special combining equivalent, and is incapable of uniting with other elements except in this proportion or some multiple of it. The equivalents of compound bodies are represented by the sums of the equivalent numbers of all the elements which enter into their composition. The weights of the equivalents of the elements are ascertained by determining experimentally how much of each is required to replace the others in their combinations with some well known element, the weight of the equivalent of which has been assumed. Thus, the quantity by weight of each element which unites with one equivalent of oxygen to form a protoxide, analogous to water, is usually considered to represent its equivalent. A knowledge of the exact weights of the equivalents is of the first importance to chemists; all calculations regarding the composition of bodies, as in analysis, or of the quantities of materials to be employed in the manufacture of compounds, being based upon them. As the equivalent numbers express nothing but the relative weights in which the elements unite with each other, it is evident that the weight of any one equivalent may be arbitrarily chosen as a standard to which all the others shall be referred; it is essential only that the relation be strictly observed.

Tables of equivalents are thus constructed, in which the equivalent weight of each of the elements is attached to its name. Several standards have been selected, but only two have ever been generally used. The equivalent weight of hydrogen, being smaller than that of any other element, was regarded as unity by Dalton, who referred all the other equivalents to it. This system has been generally adopted by the chemists of Great Britain and the United States. It possesses the very great advantage that in it the equivalents are represented by small numbers, many of them without fractions, which are convenient in calculations, and can be easily retained by the memory. Another table, in which the equivalent weight of oxygen is assumed to be 100, has been much used on the continent of Europe. It was proposed by Berzelius, mainly it would seem for the purpose of discountenancing a theory advanced by Prout, that all the equivalent numbers are simple multiples of that of hydrogen; superiority was claimed for it on the ground that as oxygen is the most abundant of all the elements, and as the greater number of bodies studied by chemists are compounds of it, calculations would be simplified if its equivalents were regarded as equal to 100; in which case it is only necessary to add 100, 200, 300, etc, to the equivalent weight of the element with which oxygen is combined, in order to ascertain the equivalent weights of its several oxides.

The equivalent of sulphur, a very common element, would also have a simple expression, being equal to 200. But these instances do not at all compensate for the high numbers by which the other equivalents must be represented; numbers which cannot be remembered without great difficulty, and which render even the most common calculations extremely laborious unless logarithms are resorted to. Berzelius, who believed that the equivalent numbers should be regarded as entirely accidental and unconnected with each other, desiring to give them the most accurate expression possible, introduced the custom of attaching to them large decimal fractions; indeed, the power to do this which is afforded by the high numbers of his system has always been claimed as one of its advantages. The accuracy of thus employing several decimals, in cases where the process by which the result has been obtained is liable to errors of considerable magnitude, was long since pointed out by Erdmann, who called attention to the fact that no greater or lesser number of decimals ought to be given than the experiment justifies. All tables of equivalents heretofore published are more or less defective from neglect of this truth.

The equivalent numbers have been thoroughly investigated and revised by Dumas, who has again brought forward and upheld Prout's theory, which, owing to the vigorous opposition of Berzelius, had found but few supporters of late years. Most of the equivalents thus far studied by Dumas are simple multiples of that of hydrogen. To this rule there are, however, several exceptions; among which some are multiples of one half, while others are multiples of one quarter of an equivalent of hydrogen. It is still a subject of discussion whether the equivalents of several of the elements should not be regarded as twice, or that of others as one half of those ordinarily admitted. This change would greatly simplify certain portions of chemical science, and many chemists habitually employ equivalents thus modified.