to the Longitudinal Expansion in Rods of Spring Steel. 35 

 from which follow, 



I shall indicate, by prefixing a S, the changes which the magni- 

 tudes in question experience by the weights P being suspended 

 at B' and B" ; we have then 



Vs 2 



6V 2 -oV' 2 = jp 



W.-W.- 



2?ls 

 L ' 



from which is obtained 



L~ 1+ l + 2<9~~ Sa' 2 -oV' 2 2/' ' ■ ■ W 



If the weights P are suspended in D' and D n instead of at B' 

 and B", the same equations prevail, provided —/is substituted 

 for/. 



It must now be shown how Sa f 2 , 6V' 2 , 8/3 ! ^ 8/3" 2 are found 

 from the readings of the scale. For this purpose I shall take 

 into account the directions of the normals to the mirrors directed 

 downwards, and designate them by n 1 and n u . For the sake of 

 shortness I will set 



cos (nff ) = a', cos (n'r)) = /3', cos (n'f ) = 7', 



cos (n"D = a", cos (A) = 0", cos (»"£) = 7". 



In fig. 6, let f be the visual axis of the first telescope, Of 

 and Orj be two lines drawn in the plane of the scale parallel to 

 the f axis and the 77 axis; let the point £be the intersection of 

 the visual line with the plane of the mirror, N be the intersection 

 of the normal to the mirror drawn from the point f with the 

 plane of the scale, and let S be the point of the scale the image 

 of which lies in the visual line. The coordinates of the point f, 

 in reference to the f , 77, f axes, I designate by a', b f , d, those of 

 the point S by X', Y', ; those of the point N by A', B', 0. We 

 have then 



A'-fl'=-N£.a', 



B'-&'=-N£./3', 

 D2 



