AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 227 
The values of c, as given by equation (94) are only a first approximation and are too 
large, but the error is not large, even when c=‘5 only amounting to 8 per cent., as is 
shown by comparing equation 104 with 95. 
With these values of c in the equation (154) the values of // have been calculated 
for all values of c up to ’250. At c ='12 these values of are about 5 per cent, 
larger than the experimental values, but they have been carried to c=‘25 in order to 
show that the calculated friction follows in its variations the idiosyncracies of the 
experimental frictions, falling with the load to a certain minimum, and then rising 
again. 
These values of f( carry the comparison of the frictions deduced from the theory 
up to loads of 205 lbs. for all velocities, and up to 363 lbs. for the highest velocity. 
To carry the approximation further use has been made of the more complete inte¬ 
grations of the equations for the case of 
c= ’5. 
These are given by equations (104) and (105). 
As already stated, comparing (104) with (94) it appears that when c=”5 the 
approximate values of c in the Table IY. are about 8 per cent, too large ; that is to 
say, a value c='5 40 in the table would show that the actual value was c=‘5. 
Comparing equation (95), from which the values // have been calculated, with 
equation (105), it appears that when c=‘5 the values of f by (105) are given by 
,, 2-3773 
J 1.37 /1 
This is not, however, quite satisfactory, as that portion of the friction which is due 
to necking does not increase with the load. This portion in // is 
and since n — 1*25, this gives for c=‘5 
/'= 1-585/' 
So that for c='5 
n-1 
n ^ 1 
2-3773 + 1-37Q-1Y 
' ~~ 1-37 n * 
If, therefore, any of the approximate values of c were exactly ‘540, the complete 
value of f would be 1 '585 times the value of //. This does not happen, the nearest 
approximate values of c being ‘578, "520, ‘520, ‘510. Multiplying the corresponding 
values of// by 1‘585, the results are as follows :—• 
2 g 2 
