of Methods for Observing Small Rotations. 95 



2 3 



c*. When this is the case, c= A> , and b,= w b'. Hence 



( 7 



Comparing this with (7) we find that for equal moments of 

 inertia 



h_ ^936 _ 9.8 



6' _ ~1 _ 7 ' 



In this case, therefore, the mirror has a decided advantage 

 over the interferometer system, i. e. for a given aperture 

 b = b' the moment of inertia of the simple mirror is actually 

 less than that of the two mirrors. When the width of the 

 mirrors is j 1 ^ the aperture, we have 



b_ y/lQ5120 _ 18 



u ~ ~\i 17 



+ 



or the simple mirror still has the advantage. And it is not 

 until the horizontal aperture is over twelve times the height 

 that the interferometer system has any advantage over the 

 mirror of the same effective aperture, as regards the moment 

 of inertia and consequent effect on the time of swing of the 

 suspended mass to which it is ati ached. It is true that a 

 mirror of this length would probably have to be thicker than 

 the two small mirrors B and D ; but the increase in the 

 moment of inertia due to this would be more than counter- 

 balanced by the inertia of the mounting of the two mirrors, 

 of which no account is taken in (8)f. 



In attaining the highest degree of accuracy in the use of 

 the mirror, the German method of reading (telescope and 

 scale) is greatly superior to the English method, chieflv 

 because of the greater fineness of the reference-line (the cross- 

 wire of the telescope, instead of a ruled line on a scale). The 

 mirror ought also to be as nearly optically flat as possible, 

 and the greatest care should be taken in selecting the glass 



* It would be better to have the length twice the height (see paper in 

 'Physical Review' already referred to). But this would make the 

 moment of inertia for a given aperture b' considerably greater. 



t A practical disadvantage of the very narrow mirror that has been 

 pointed out by Boys is that the vertical definition is not sufficiently good 

 to enable the figures on the scale to be read. This, however, could be 

 overcome by making these figures very large, or by using in place of 

 them characters similar to those used on stadia rods. 



