Stress and Strain on the Properties of Matter. 



521 



the temporary alteration of length increases in greater proportion than 

 the load, this increase of effect is very much less than is the case 

 when the alteration of resistance is concerned, the difference between 

 the first and last numbers of the third column being only 31 per cent, 

 as compared with the 170 per cent, difference between the first and 

 last numbers of the second column. 



It has been proved that longitudinal traction on the whole causes 

 increase of resistance, but this increase is less than can be accounted 

 for by mere change of dimensions, provided that the temporary stress 

 used be sufficiently small. In the present instance it may be assumed 

 that for any temporary stress not exceeding \ kilo, we shall barely 

 enter into the region where "Hooke'slaw" no longer holds good,* 

 and that up this limit of loading the increase of resistance and of 

 length will, within the limits of errors of observation, be proportional 

 to the load, since, were it otherwise, there could not be the accordance 

 which there is between the value of " Young's modulus " as deter- 

 mined by the statical and dynamical methods. f If, then, we take 

 4*4 divisions of the platinum-iridium wire to represent the temporary 

 increase of resistance produced by a load of \ kilo., we gather that 

 the increase of resistance due to a stress of 1 gram per square centi- 

 metre is 1841 x 10 -12 per unit. In calculating the alteration of 

 resistance per unit, resulting from increase of length, we must take 

 the value of " Young's modulus " obtained by using the statical 

 method, for the alteration of resistance is necessarily determined by 

 this method. If we do so we find that the ratio of the increase of 

 resistance per unit to the increase of length per unit is 0*7813. The 

 mere change of dimensions, however, would cause an increase of 

 resistance of 1 + 25, where is the ratio of lateral contraction to 

 longitudinal extension, and may be taken as equal to 0*2501 ; so that 

 on the whole we have a decrease of the specific resistance per unit, 

 equal to 1-5002 — 0*7813, or 0*7189. With aluminium also it has been 

 shown"]: that there is a decrease of specific resistance per unit ; but 

 this is of small amount, namely, 0*420 for the unannealed, and 0*262 

 for the annealed metal. We may say, then, that though magnesium 

 does not agree with nickel and cobalt in having its resistance 

 decreased — in spite of change of dimensions — it does agree with 

 these metals and with aluminium in having its specific resistance 

 decreased by longitudinal traction of small amount. 



The question next arises, shall we, passing the limit of temporary 

 stress up to which " Hooke's law " holds good, eventually find the 

 decrease of specific resistance changed into increase when the tem- 



* See loc. cit., pp. 12, 13. 



f The temporary elongation produced by i kilo., namely, 2*37 half -millimetres, 

 was employed in calculating the former of the two values. 

 X Loc. cit., p. 52. 



VOL. XXXIX. 2 M 



