EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 23 



or for the above data 



quantities of the same order as the above. Thus if dx= i cm. (for the rela- 

 tively small distance of scale from mirror, D = goo cm.), v'' = o.35Xio 6 , and it 

 should be easy to measure one-tenth of this expansion. 



The peculiar interest which attaches to this equation for da or any corre- 

 sponding case is the absence of all need of length measurement in the combina- 

 tion. In the right-angled triangle hvb, fig. 15, it is merely the angle 6 which 

 must be given, all the quantities compared being numbers. Of course, the 

 relation of x and a remains, into which the distance of the mirror from the 

 scale will enter. In the complete equation (if da is replaced by a) 



<p may be found directly as shown above. 



If the interferometer is used, x/^D is to be replaced by AAT/2.R so that 



If values of the above order be inserted, i.e., 93 = 0.01 ; AA/" = io~ 4 ; R = io 2 ; tan 

 = 0.25; then </' /3 = 1 2 X io- 10 . In case of the other equation, da = 2^/sin 26, 



In any case, therefore, an expansion of the order of 4Xio~ 10 per vanishing 

 interference ring (AJV = 3/io 5 ) should be measurable. This seems by far the 

 most sensitive arrangement for measuring elongations which has yet been 

 proposed. The full equation in question would be 



da = tan 6 



fdh _ db\ 

 \h" b) 



n 



cos I -; 

 \h 



tdh_dv\ 



v / 



from which any of the above forms follow at once. 



In its bearing on the horizontal pendulum, the above result is fatal. Braces 

 of all types will have to be discarded. The following incidental experiments 

 will bear this out: The brace was heated with a single rapid brush of the 

 Bunsen flame, such as would not have imparted any easily appreciable in- 

 crease of temperature to the massive rod. The times of observation were 

 also recorded, the results being as follows : 



