CHAPTER IV. 



EXPERIMENTS IN GRAVITATION. 



I. GRAVITATIONAL ATTRACTION. 



40. Introduction. The ease with which the rectangular interferometer 

 admits of the measurement of small angles induced me to adapt an apparatus 

 with reference to it, for the measurement of the Newtonian constant. In 

 addition to the usual system suspended in air, I also tested a floating system. 

 Accurate work is scarcely to be expected in this laboratory, where temper- 

 ature variations and the agitation of the room conflict with the condition of 

 its obtainment. But the trial is nevertheless interesting and the final work 

 may be done elsewhere. 



41. Equations. The old bifilar system has more recently been superseded 

 by the quartz fiber of Boys. We should have in systems of the same length 

 L under like torque T per radian in the two cases, the modulus 



= mg IV I L = 7Tr 4 /2L 



where mg is the weight of the needle, II' the spacing (above and below) 

 of the bifilar, n the rigidity, and r the radius of the quartz fiber. If 

 w = 5Xio n , g = g8i, this relation reduces to 



w//' = 8Xio 8 Xr 4 , nearly 



If r = io~ 2 cm., mil' = 8, so that for / = o.i cm. and ^ = 0.5 cm., w=i6o grams 

 would give equivalent elastic efficiency. The bifilar would be superior, as the 

 quartz fiber could not carry this load. Iir= io~ 3 cm., m = o.oi6 grams only 

 could be used in equivalence, quite apart from the torsion coefficient of the 

 silk fiber of the bifilar. Here the quartz fiber would be superior, as so small 

 a load implies a correspondingly small gravitational force. 



In relation to the gravitational experiment, if M is the modulus in either 

 case, we would have in succession 







COS 1 



2R 



AN 



where * = 4S is the angle of incidence and iR the distance apart of beams 

 of light, AN the micrometer displacement of the interferometer, //" the 

 force couple of the torsion balance. Hence 



d 2 cos * 

 Mml" 2R 



t* v,wo * 



v = u - AN 



f* TI r -ill T-> 



If we take the first case (/ = o.i, Z' = o.5, L = 5o) for the bifilar ju = 



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