AiKi - A2K1 = AiKj - AaKa.
If we arrange a series of m negative ions, Ai, Aa, . . . A^, in a horizontal row, and a series of n positive ions, Bi, B2, . . . B„, in a vertical row, then by combination of these ions mn salts AB can be obtained, as the following scheme shows : —
��Ai A2 . . Bi AiBi A2B1 . . B2 A1K2 A2B.J . .
�A
. A„Bs
� ��B„ AiB„ A2B,. . . . A,^B„
In this scheme we may write in place of each salt AB the numerical value of one of its properties in, for exampJi^, normal solution, and this property is to be regarded as additive if the following relationship exists between the differences —
AiBi - A1B2 = A2B1 - AaBa = . . . x\,J^i - A.„Ba.
Expressed in words, this may be stated thus; The differences between two values which are in the same vertical column and two certain horizontal rows must be the same (within the experimental error) for all the vertical columns if the property in question is additive.
Exactly the same must hold good for the differences 1>etween the horizontal rows and, of course, for any concen- tration, provided this is the same for all the salt solutions. By constructing such a table (the so-called additive scheme) and calculating the differences between the rows and the columns, it is easy to decide whether the particular property of the dissolved salt is additive or not.
According to Valson (/), additive properties can also be expressed by moduli. As an example, we give below the moduli for the specific gravities. Valson chose as his starting
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