94 Prof. F. L. 0. Wadsworth on the Optical Efficiency 



system is the distance between the centres of the portions B 

 and D*. Hence, for a constant moment of inertia I, the 

 horizontal aperture b (which alona determines resolution) will 

 be greater for the narrow rectangular mirror than for either 

 the circular mirror or the interferometer system. Thus we 

 have for the circular mirror (if thin) 



I= o^ 4 = M^ 4 ' ( 5 ) 



/j, being the mass per unit surface of the plate. For the 

 rectangular mirror, height c, we have similarly 



Ii=j^. (6) 



If the height c is taken as i the breadth (fig. 4) we have 



!i=^^ 4 (7) 



Hence, if the thickness of the mirrors is the same in the two 

 cases, the horizontal apertures will for a constant moment of 

 inertia vary nearly in the proportion of four to three. The 

 resolving powers will therefore (since the resolving power of 

 a circular aperture is about 0*9 that of a rectangular aperture 

 of the same horizontal diameter) be about in the proportion 

 of 10 to 7. 



The moment of inertia of the interferometer system will 

 similarly be (not allowing for the support of the mirrors) 



i 3 =2(l^;+^ / (| / ) 2 ), .... (8) 



b t being the length of each of the interferometer mirrors 

 B and D (fig. 4) and V the distance between the centres. 

 For comparison with the rectangular mirror, assume that the 

 height c is the same as in the case of the mirror, i. e. 



- b= - {b t + b'). The length of each mirror, b n should be for 



practical reasons at least one and one-half times the height 



* If It were only possible to make these two independent surfaces part 

 of the same optical plane (which is not necessary in the case of the 

 interferometer) we might also dispense with the intermediate dotted 

 portion in the ordinary method of mirror reading. In such a case the 

 effectiveness of the mirror method would be quite equal to that of the 

 interferometer method. 



