On Lines of no Chemical Change. 429 
crystal owing to the heating-effect of the rays concentrated 
on one side during the measurement of an angle. 
In bringing to a close this paper, of which the latter part 
has been given up to a critical examination of the important 
results obtained by Beckenkamp, we beg to express on behalf 
of the students of crystals our hearty thanks for the series 
of careful observations made by him with the elaborate in- 
strument belonging to the University of Strasburg ; and we 
may add that the labour involved in the interpretation of his 
measurements will only be fully appreciated by those who may 
be attracted by the subject to repeat some of the calculations. 
LXI. On Lines of no Chemical Change. By Edmund J. 
Mills, D.Sc, F.R.S., and William M'D. Mackey*. 
[Plate Vni.] 
MOST of the chemical changes we ordinarily observe are 
examined either in their course or at their termination; 
but although it is clear that they must have a beginning, the 
beginning is extremely difficult as a mental conception, and 
quite inaccessible to direct experiment. 
We have considered it of great interest to determine in cer- 
tain cases the " origin " of chemical change, such origin being 
obviously identifiable in many instances with a line of no 
chemical change. 
The substances selected for reaction were aqueous hydric 
sulphate and zinc, brought in contact under definite conditions. 
Supposing the temperature to remain constant, and hydrogen 
to be evolved from the unrenewed reagents, the gas will, as is 
well known, cease to appear when the hydric sulphate has 
been partially exhausted. If y be the percentage strength of 
the sulphate (H 2 S0 4 ) and x the amount of gas evolved, we 
can express y in terms of x (provided the experimental num- 
bers lie sufficiently near to the origin) by the equation 
y = a + bx + cx 2 , 
where a, b, c are constants to be calculated from three expe- 
riments at least. Then putting x = 0, we obtain the value a 
for y: this value is a point on the line of no chemical change. 
Other points can be similarly obtained at other constant 
temperatures ; and when these are all continuously joined, the 
result is the line of no chemical change for the hydrogen 
reaction as a function of strength and temperature. We have 
always used three experiments and three terms of Taylor's 
* Communicated by the Authors. 
