CHAPTER III. 



THE ELASTICS OF SMALL BODIES. 



27. Introductory method. At the request of Professor W. G. Cady, who 

 was in need of Young's modulus in case of certain crystals used in experiments 

 in which he is interested, the endeavor was made to adapt the above : inter- 

 ferometer for measuring small angles with an auxiliary mirror for this pur- 

 pose. The project seems feasible and apparently simple in execution when 

 the method of end-thrust indicated in figure 27 is used. 

 Here F is a rigid metallic bar subjected to the force couple 

 P,P', carrying the coplanar mirrors m,m' and capable of ro- <J- 

 tating slightly in a horizontal plane. The mirrors m and m' 

 receive the corresponding rays a, b of the interferometer. 

 The couple P,P' is resisted by the resilience of the rods r,r' 

 to be tested, as these push respectively against the ends of 

 the bar F and against the rigid abutments A and A' of the apparatus. If 

 the couple P,P' changes, the bar F rotates correspondingly and the com- 

 ponent rays a, b of the interferometer will register the amount of rotation by 

 the methods given in Chapter I. Thus, if E is the traction modulus, I the 

 elongation of each rod of length L and right section A under the force P, 



AP/A 





2, 





E = 



Ae/L 



A being a differential symbol. If the distance apart of the rays a, b is 2R 

 and that of the force couple is zK ', 



2 RAa = AN cos i 



if the bar F rotates over an angle Aa, in consequence of the increment AP of 

 thrust, and if AN is the displacement of micrometer mirror (angle of 

 incidence is i), needed to restore the interference fringes to their original 

 position. But 



A/ - R'Aa = R' nearly ; 



2R 



so that after reduction 



2 LR AP 



~AR' cos i AN 



Since* = 45, E=2\/2 (L/A}(R/R'}(AP/AN} 



The method will not of course be very exact, because for rods less than 

 an inch long the quantities involved, particularly AN, are so small. Any 

 flexures or slight dislocations of parts of the apparatus are of relatively great 



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