AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
219 
In order to be sure that these are the values of which result from the application 
n 
of the equations, it is necessary (since the approximate equations only have been 
used) to see that the squares of c may be neglected. 
Substituting from equation (124) in (96) 
L's 
c — '388 net— 
J ^ 
which for L'=100, N = 100, gives 
and for L'=100, In =450, 
c=*033w 8 ^ 
c = "065n z 
. (133) 
So that the approximations hold, and, as already stated in Art. 30, this consider¬ 
able increase in the value of a with the load constant suggests that the temperature 
of the film was not really 90°. And as this point has been considered in the last 
section the equations of that section may be at once used to determine the law of 
this temperature, after which the values of - may be determined witli precision. 
37. The Rise in Temperature of the Film owing to Friction. 
In order to determine the values of E, A, and B in equations (119) and (120), by 
substituting in these equations corresponding values of N and f for 1/=100, the 
tabular values of f were somewhat rectified by plotting and drawing the curve N, f . 
These corrected values are in the second row, Table III. 
From these values, and the corresponding values of N, it was then found by trial 
that the equations (119) and (120) respectively 
f— P x qj c -(C+E) (T-T,) 
J a x + mL 
f=k{ T„+ET„ 2 } + §(T„) 
c = '0221 
are approximately satisfied for values of T — T x =T m if 
jjb x _’01346 
«* + mx 400 n 
A=‘022308 
£=•0222 
B=-95914 
2 F 2 
> 
(134) 
( 133 ) 
