A system of physical chemistry - Index of

WHETHAM'S RULE OF COLLOID COAGULATION 7

The ratios in which these three concentrations stand to one another are—

Ci : C2 : C3 :

= B^

III

B^" : B^"«

L

= I : b'^" : B3».

I

Putting B^" = i/^, the ratios can be written—

I : i/jt- : \lx^.

These represent numbers which indicate relative concentrations **of** equal

coagulating power. Hence the relative coagulating powers Pj, Pg, P3 **of**

equal concentrations **of** these three ions are given by the reciprocal **of**

the above numbers. That is—

,

The value **of** x, which depends upon a number **of** unknown factors

characteristic **of** the colloid considered, cannot be found on a priori

grounds. If we take Linder and Picton's experiments into account and

set jc = 32, we get for the relative coagulating powers **of** univalent,

divalent, and trivalent ions respectively, the values i : 32 : 1024.

It will be seen that these numbers are **of** quite the same order **of** magni-

tude as those observed. Whetham predicted on this basis that the

coagulating power **of** a tetravalent ion on the above colloid should be

a large number, approximately 33000. Recent measurements have

corroborated this result in so far as an extraordinarily large coagulating

power is actually obtained.

The Law **of** Error.— It is a familiar fact in physico-chemical

measurements that repetitions **of** a certain measurement give rise to a

series **of** numbers which are not identical. The variations we speak **of**

as experimental errors. The measurements are as likely to be too high

as too low, that is, the errors are as **of**ten positive as negative, provided

is assumed that

we make a very large number **of** determinations. (It

there is no **system**atic error in the apparatus or in the method **of**

measurement.) The treatment **of** such results so as to obtain the most

probable result, i.e. the most accurate determination, is a further illus-

tration **of** the application **of** the theory **of** probability, somewhat more

complex in nature than that hitherto considered.

Thus, it is possible to construct a probability curve, by means **of**

the probability equation given below, which has been found to agree

closely with the actual results obtained in a series **of** experimental determinations

**of** a given quantity. Examples will be found in a textbook

**of** mathematics, e.g. Mellor's Higher Mathematics. The large

majority **of** the readings will fall very closely together, i.e. they will

not be far removed from the true result, a smaller number **of** readings

will be farther away on either side **of** the true result, and only a very

small number will be much to one side or the other. This distribution

**of** values may be represented by an expression **of** the form—

'