to the Longitudinal Expansion in Rods of Spring SteeL 37 



Inconsequence of this, the last equations may be written 



J \ 



In like manner we get 



ft= z£. 



1 2— —..- > 



(6) 



P.= 



P»-0< 



m 



With the aid of these equations expressions for d and c !t can 

 be developed. Let the equation of the plane of the first mirror 

 in reference to the axes of x, y, and z drawn from the point A' be 



x cos (n ! x) + y cos (rJy) + z cos {rlz) — D ! = o ; 



the equation of ^ i same plane in reference to the axes of £, 77, f 

 is then 



(£-iy+fr-7/)/3'+({;-?V-D'=o- 



The point for which f is = a\ rj = V 3 f = c' belongs to this plane ; 

 hence 



from which there follows 



D'+(g'-fly+(V-5')ff 



In my apparatus D 1 and ?/ — &' were a few millimetres, {■' — a f 

 a few centimetres, c* more than two metres ; hence, considering 

 the smallness of ex! and ft, we may write instead of this equation, 



and for a! it is permissible to substitute an approximate value, 

 even if not very near. I set 



?=C-fAA (8) 



in which A is a very small magnitude as compared with C. In 

 consequence of equation (4), I can make 



"- — ge~ (9) 



I then obtain 





