46 J. 0. Thompson — Law of Elastic Lengthening. 



The equations giving the relation between elastic lengthen- 

 ing and stretching weight when one begins with zero load are 

 as follows : 



Steel X=34-672P + 0-6498P 2 -0-0525P 3 



Brass .. X=34-924P+0-2386P 2 -f-0-1487P 3 



Silver X=38-907P-j- 0-446 2P 2 — 0-0313P 3 



Copper . X=27-46lP-j-0-2883P 2 4-0-0538P 3 



The specific gravities, cross-sections, and moduli calculated 

 by the above method are given in the following table. 



True 

 Sp. G-r. Cross-section. Modulus. Modulus I. Modulus IT. 



Steel 7-74 0-03263 20050 19430 19230 



Brass ... 8-42 0-0627 10370 9820 9450 



Silver ...10-00 0-0687 8490 8300 8250 



Oopper.. 8-99 0-0641 12890 12620 12420 



In order to show still more clearly the dependence of the 

 modulus on the tension I add two more columns. The next 

 to the last column gives the modulus which one would obtain 

 if only the lengthening caused by the maximum added load 

 were taken into account. The last column, the modulus which 

 would be obtained if only the increase of lengthening caused 

 by the last 02 kg. should be made the basis of calculation. As 

 will be seen, the true modulus of elasticity of the brass wire is 

 nearly 10 per cent greater than the one given in the last 

 column. 



Influence of Contraction of Cross- Section. 



When a wire is stretched so that each unit of length in- 

 creases by d, the cross-section becomes Q (l—2jud) if Q is the 

 original cross-section. Theoretically [i can have in different 

 bodies any value between the limits and -J. Supposing that 

 in the case of steel ^=0-294, as Kirchhoff states, we find that 

 for a weight of 1 kg. <?=35 -8-:- 22700 =0-00 16 and the cross- 

 section is accordingly Q (l — 0*00094). If we wished to refer 

 the modulus of elasticity in this case to this diminished cross- 

 section, the coefficients of our equations would suffer a per- 

 ceptible change. But it is not customary to do this, and we 

 shall refer the modulus to the condition of the unstretched 

 wire. Further it should be noticed that the value of fi is not 

 definitely known ; in fact, there is ground. for believing that 

 in one and the same body it is a variable quantity. 



Larger Wires. 



In order to be perfectly sure that the phenomena which I 

 have described were not confined to fine wires, I made careful 

 measurements with larger wires. The loads placed on these 



