478 
MR. E. H, C4RIFEITHS ON THE VALUE OF 
where h is the resistance temperature'coefficient of the wire, and ^ is the number of 
degrees that the wire is hotter than the water in contact wuth it. 
Similarly 
M' = M {1 + le^^e] 
where I is the mean coefficient of increase of specific heat of the water and calornneter. 
For the non-electrical supply, we have shown that tr^ = K (p. 438), where t is the 
time of rising 1° C. and r is the rate of revolution of the stirrer, and therefore the 
rise per second is oiven by 
o-=r3/K .(5), 
and 
O..0. 
.( 6 ). 
Scr = Y Sr 
By (6) we can reduce all observations to the standard rate r. 
Equation (1) after introducing terms due to stirring becomes 
that is. 
JR 
M [1 -f Z — d)] ^ — ^} + (cr — p 6*^ — (9 q) M(1 + Z dj — ^) (7); 
. . . (8^1. 
or 
dOy _ 1 — k {6y ^ — 0) 
dt JRM 1 + / (Pj _ p) 
+ o- — p(di - do) 
If we write 
‘li). (f 
for the electrical and non-electrical terms in this expression, 
ddl ^ {d^\ fd_ly 
dt \ dt /e \ dt /o 
(9). 
* Equation (8) may be expressed in the following form— 
deyidt = K + \0y, 
where A is the sum of quantities independent of 0y, and X is the sum of a number of small quantities. 
The range d0y is reckoned from slightly below 0y, say from 0', to slightly above say 0” ; hence if t' 
and t” are the times at 0' and d", we may assign to dOyjdt the value (d'' -- 0') j {t" — t'). 
Strictly speaking, the equations ought to be integrated from t = t', Avhen d^ = d', to t = t", when 
0i — d", but the error introduced by the above method may, provided the ranges are sufficiently small, 
be neglected. 
We have adopted throughout our experiments ranges of from 1° to 1°'5 C. It does not appear prob¬ 
able that increased accuracy would have resulted from the adoption of smaller ranges, for the effect of 
errors in the thermometry is increased as the size of the ranges is diminished, 
