92 MR. tt. TOMLINSON ON THE INFLUENCE OF STRESS 
We learn from Table XII. that the ratios of consecutive times become more and 
more constant as the load on the wire is made larger and larger, and therefore that the 
velocities of increase of resistance for small equal increments of resistance form a 
geometrical progression. 
In order to make the mean values of the common ratios comparable with each other, 
the common ratios calculated for equal increments of resistance of T per cent, are 
recorded in the last column ; the calculation was effected by raising the observed ratio 
in the last column but one to the power obtained by dividing T by the percentage 
values of the equal increments of resistance given in the fourth column. For example, 
with a load of 1448 kilogs. per square centimetre, the common ratio of the geometrical 
progression found by the times taken for the load to increase the resistance by suc¬ 
cessive percentage amounts of ‘0314 was found to be 1'35, therefore the ratio which 
would have ensued, if the times taken to increase through T per cent, had been 
i_ 
observed, would have been 1‘35'°3 14 or 2‘572. 
Again, the loads in kilogrammes per square centimetre given in the third column 
are calculated from the resistances given in the first column in the following manner : 
let S x and be the sections of the wire before and after stretching, and let the 
J> l g 
corresponding resistances be R 1 , Ph, and the lengths l x and L; then, — 2 =pxA, 
-til /i 
provided that there be no change in the specific resistance of the metal; also 
Z 1 XS 1 =kxS 2 , or provided that the stretching does not alter the density. But 
we shall see that neither the density nor the specific resistance is altered by stretch¬ 
ing to any extent sufficient to introduce any appreciable error, therefore we have 
S, 
or 
S 2 =SjX a/^ Thus the 
V Jtln 
within a sufficiently close approximation jp 
section S x having been determined, it is easy to ascertain the section after any amount 
of stretching. For example, the section of the wire last used was before stretching 
'0183 square centim., and the resistances before and after the stretching were 1056 
and 1'080 respectively, therefore the section of the wire after stretching would be 
nearly '0183 X A / \ , Jt and the actual load on the wire being 9'75 measures of water 
J V 1-080 
. „ ... ill ,. ... 9-75x5'825 /l(J80 
or 9’7a X 5'825 kilogs., the load per square centimetre would be -hdgT— X 'y 
kilogs. =1570 kilogs. In nil cases the resistances recorded in the first column are 
the means between the resistances observed at the commencement and end of the 
times during which the velocities of increase were noted, and the wire was allowed 
to run down for some time (about 20 minutes) before the observations of the velocities 
of increase commenced. 
It is, moreover, evident from the last column in the table that the common ratio of 
the geometrical progression becomes less and less as the load becomes larger and 
