1884.] New Spring for Electric and other Instruments. 311 



Or, as a is very large in comparison with b, 



(!+«*•) (18). 



If, as is usual in the case of the springs we employ, the edges of 

 the strip nearly touch one another in two consecutive coils, and the 

 angle of the spiral is 45°, we have the area of the cylinder which the 



metal strip approximately covers, or "^/^"j equal to the area of the 



strip, or 21a, so that 



r_ a/2 



and equations (16), (17), and (18) may be simplified thus — 



^°- 17 ?(^-i) — • (19) - 



(21). 



We have preferred to say that 0, d, and / are respectively propor- 

 tional rather than equal to the expressions on the right hand side, 

 because when the strip is wide in comparison with the radius of the 

 cylinder about which it is bent, the strip receives in addition to the 

 bending and shear strains which we have considered, a lateral bending 

 also, and the exact effect of this we have not yet fully investigated. 



Use of Spring to determine ~. — Before proceeding to a description 



of the various measuring instruments in which we have applied this 

 new form of spring, we may mention one interesting application of it 

 to enable us to determine readily the ratio of the modulus of rigidity, 

 N, to Young's modulus of elasticity, E, for any material. It is w^ell 

 known that the celebrated conclusion of MM. Navier and Poisson 

 from Boscovich's molecular theory requires that the ratio of E to N 

 should be 2'5 for all solids. Professor Stokes showed that this con- 

 clusion was impossible if its authors supposed it to apply to jellies 

 and to india-rubber, and that it was probably untrue in the case of 

 metals ; and Wertheim, Kirch hoff, Thomson, Everett, and others have 

 experimentally shown its untruth in the case of brass, iron, copper, and 

 glass. In pursuance of the present investigation it has struck us that 

 this ratio may be most conveniently determined by the use of our 

 springs from one experiment. 



