14 DISPLACEMENT INTERFEROMETRY BY 



B at d, but passing loosely through a perforation in the middle of C. The 

 end near d of the rod df is threaded (20 threads to the inch) so as to admit of 

 the compression of the spring 5 by aid of the thumb-nut w. S was a precision 

 spring taken from an indicator apparatus and provided (as usual )with two 

 end brass collars. It is essential that the sliding parts of the apparatus work 

 smoothly and with a minimum of friction. Such as exists may be eliminated 

 by tapping b and c before each observation. Thrusts up to 15 to 20 kg. may 

 be easily applied by the thumb-nut w. These stresses act in the direction ar 

 and jd collinearly , and there are no couples endangering the accuracy of the 

 elastic displacements of r. The stress is standardized in terms of the observed 

 rotation of the thumb-nut w. Figure 7 (a) to (d) are details, showing different 

 methods of clutching the rod r. 



Figure 8 shows a similar apparatus in the same notation. Here the spring 

 55 acts by tension and more and more strongly as the thumb-nut w advances/. 

 The apparatus is slightly more complicated but offers certain differences in 

 relation to the friction of parts. 



6. Observations. Hard rubber. As in the preceding paper, if Ax is the 

 longitudinal compression of the rod r is the sheath s, 



1 i ) Ax = (r cos i/b}AN 



where AN is the displacement of the micrometer at ^ = 45 to the rays, b the 

 breadth of the ray parallelogram, and r the effective length of the contact lever. 

 Furthermore, since the modulus E for the length of rod L and section A is 



E=(F/A)/(A X /L) 

 F being the thrust, 



(2) E = F-- 



A r cos iAN 



The ocular micrometer, if used, is to be standardized in terms of AW by direct 

 comparison. 



To graduate the spring 5, the apparatus ABC, figure 7, was detached from 

 the interferometer and the brick B fastened to the edge of a strong flat table 

 with its large face toward A lowermost and horizontal. The rectangle AC was 

 thus vertical, A below C, just clearing the edge of the table. Weights from 

 i to 9 kg. were now hung from A, compressing the spring 5 by measurable 

 amounts. In this way it was found that the stretch 0.7 mm. corresponded to 

 i kg. Since the threads of w were 1.275 mm - apart, it follows that i rotation 

 of the thumb-screw w corresponds to 1.82 kg. or i.78Xio 6 dynes. 



In the interferometer, 6 = 9.3 cm -> r=n.o cm., were directly measured. 



The test-rod r was here of hard rubber, of length ., = 2.47 cm., diameter 

 = 0.377 cm. , and area A = o. 1 1 2 cm 2 . Hence for n turns of the screw w, equa- 

 tion (2) 



(3) E = wXi.78Xio 6 -^-- -^ = 4.69X10-' -, 



0.112 uXo.'jo'jXAN AN 



or if we express AN in io"" : cm., E= io 10 X4-69 T- 



