AND STRAIN ON THE ACTION OF PHYSICAL FORCES. 
93 
larger, and we might expect to find some relation between the decrease of velocity 
of increase of resistance and the difference between the breaking-load and the load 
actually on the wire. A further examination of the results given in Table XII. shows 
that a relation does exist of an extremely simple nature ; in fact, if we denote the 
breaking-load and the actual load on the wire by P and p respectively, the decrease 
per unit of the velocity of increase of resistance is inversely proportional to P —p. 
The value of P was carefully determined by loading pieces of the wire by moderate 
amounts at a time, and allowing each load to remain on the wire some ten minutes 
before each further addition, and measuring the diameter close to the point of breakage 
by means of a wire-gauge graduated to '01 millim. The mean of several trials gave a 
value for P of 2625 kilogs. per square centimetre. 
Now if t 1 , t. 2 , t 3 , &c., are the times taken to increase the resistance by successive 
equal and small amounts, the ratios t. 2 : t 1} t 3 : t 2 , &c., have been proved to be constant 
for the same value of p : let this constant be denoted by r ; then the decrease per 
unit of the velocity of increase of resistance being =y—y-i-y will therefore 
*2 t L V 
r —1 
and accordingly if the above-mentioned relation holds good, - ■— (P— p) should be a 
constant for different values of p. The last column of the table gives the values of r 
v — 1 
for the loads given in the third column, and the values of —-—(P— p) are for the four 
loads there recorded, '000519, '000496, '000484, and '000504, with a mean value of 
•000501. 
The question next arises, will the ratio 
r —1 
be the same for other metals as for 
r x (P— p) 
copper ? for if so we can calculate the breaking-load by merely loading the wire beyond 
the second critical point, and observing the value of r; then, since - / /T) -- -= '000501, 
r x (P —p) 
P =lH 
— l 
r x '000501* 
With a view of ascertaining whether the breaking-load could be thus calculated, a 
series of experiments with different metals was begun, the mode of operating being 
similar to that just described in the case of copper, and the results are shown in the 
next table. In the same table are also given the ratios of the different moduli of 
longitudinal elasticity to the corresponding breaking-loach 
