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OlST THE INTEGRATED VELOCITY EQUATIONS OF CHEMICAL 
EEACTIONS. 
By J. P. Dalton. 
(From University College, Johannesburg.) 
§ L A Certain Function and its Derivatives. 
The object of this note is to show how the integrals of many velocity 
equations which occur in practice may be written down in terms of a certain 
function of the relative initial concentrations of the reactants, and of its 
derivatives. The function in question is 
1 1-^ 
^G^) = -fri loge X . . . (I) 
where \ is a parameter whose significance will shortly appear. 
Successive derivatives of 4' according to x are given bv the scheme 
{x-l)4^'U) + r+'-i(aO = (-1) -1 r^l ! [(;^),.- ^,.] (2) 
The function and its derivatives become indeterminate at x = 1, but 
definite limits exist as x — - 1 ; for these limits we find 
^W-[lix-l] .... (3) 
and, in general, 
^-1(1) - (-1)-' - . . (4) 
^, i//' and yp" are tabulated in § 5 for values of \ from 01 to 0 9, and for 
certain values of x over the range 1-10. 
§ 2. The Occurrence of the Function ^. 
The velocity equation of a chemical reaction is a differential equation of 
the type 
= k(a-xy {b-,-y (c-x)y (5) 
where a, h, . . . are the initial molecular concentrations of the reactants ; a, 
