the Extensibility of Elastic Solids. dS 



limits of perfect elasticity. But it does not seem to have oc- 

 curred to him, nor (singularly enough) to later experimenters, 

 to deduce from the forces required to produce given devia- 

 tions, the specific extensibility, or what Dr. Young calls the 

 viodiilus of elasticity of the body. 



It is essential that the deviation from the rectilinear position 

 of the wire should be ascertained with great nicety, and 

 S'Gravesande's contrivance effects this in a very neat and 

 satisfactory way. A fine steel chain attaches by a hook to 

 the middle point of the extended wire, the other end being 

 secured to the circumference of a nicely-centred wheel. An- 

 other chain attached similarly to the wire of the same wheel 

 has a scale attached to it, a weight placed in which causes the 

 wheel to revolve, and by means of the first chain and hook 

 pulls the wire out of the straight line. A long index fixed to 

 the same axis with the wheel points out the deviation on a 

 much-magnified scale, referred to a divided semicircle of brass. 

 Thus a weight being placed in the scale, the corresponding 

 deviation is instantly shown. 



Let P be the weight in the scale, D the deviation of the 

 wire, s = halfxhe length of the wire between the vices ; it was 

 proved in this communication that 



p=.tP.m(^)'. 



where M is the modulus of elasticity, measured in grains, which 

 is easily reduced to the equivalent length of a similar wire or 

 lamina, according to Dr. Young's definition. This is on the 

 supposition that Hooke's law of elasticity (the extension is as 

 the extending force) is correct; and that law is verified if the 



term M( — 1 be found for the same wire practically to vary 



as the cube of the deviation. The value of M, the modulus, 

 is also at once given by a single observed deviation, the ten- 

 sion being known. 



A small correction in the value of P is to be made for the 

 weight of the wire deflecting it from a straight line. This 

 small correction had not escaped the notice of S'Gravesande 

 when he verified Hooke's law. 



Example. A steel pianoforte wire, tension 50,000 grains 

 = T; 5=25 inches. 



Values of D. Values of P. 2T 5. mC-V. 



•25 inch 1100 grains 1000 100 

 •50 ... 2720 ... 2000 720 

 •75 ... 5400 ... 3000 2400 



