The Physical Basis of Probability. 433 
The nature of the reaction between pure aqueous hydric 
sulphate and zinc is shown by our experiments to be of a very 
complicated character. Thus, from 58*77 to 79*62 there are 
two temperatures corresponding to every strength : and 
between strength 54*47 and 57'77 at least, there are four 
temperatures corresponding to every strength. 
The law of relation of temperature to chemical change has 
hitherto been very little investigated. Hood and Warder, 
after some trial experiments, have regarded chemical effect 
as proportional to the square of the temperature. Our own 
representation places temperature on the footing of a chemical 
reagent. 
Our work has had exclusive reference to the beginning of 
a chemical reaction ; its object has been to find the initial line 
of no chemical change. There is, however, obviously a ter- 
minal zero-line, similarly obtainable, and related to the condi- 
tions existing at the close of a reaction. Between these two 
lines lies the surface, on which would occur all possible events 
in the actual process of change. 
It is our intention to resume this investigation. 
LXII. The Physical Basis of Probability. By F. Y. Edge- 
WOETH, M.A., Lecturer on Logic at King's College, London*. 
AKEMAKKABLE analogy has been drawn by Donkinf 
between the behaviour of a material particle tending to 
equilibrium under the influence of attractive centres of various 
force, and the determination of the judgment to the "weighted 
mean " of several observations. The essential feature of the 
analogy is, according to the view of the present writer, the 
circumstance that mental as well as mechanical equilibrium is 
represented by a sum of squares. The expression 
g x {sB x — xf + g 2 (x 2 - xf + g 3 (x 2 - ssf + &c. 
represents (twice) the potential energy of a dynamical system 
consisting of centres, at the points x 1} x 2 , &c. along a line, of 
attractive force proportioned to the simple distance multiplied 
by gi, g 2 , &c. respectively. The same expression represents 
the disadvantage incurred by taking x as the real point from 
which the observations x 1} x 2 , &c. of weights respectively g 1} 
g 2 , &c. have diverged. But the representation in the latter 
case is not so faithful as in the former. The simple sum of 
squares is not the measure, but only the criterion, of the 
psychical quantity; decreasing as it decreases, and becoming 
* Communicated by the Author. 
t Ashmol. Soc. Trans. 1844 ; Liouville, Journ. Math. xv. (1850). 
Phil. Mag. S. 5. Vol. 16. No. 102. Dec. Ib83. 2 H 
