Prof. Ayrton and Mr. Mather on Galvanometers. 375 



marked, for in that time the short-period needle will have 

 moved over the space AB, whilst the long-period needle will 

 have traversed the distance AM'. 

 Again, 



AN=AB(l-cos/3), 



= 6(l-cosj8) (say), 

 and AM = AC(l-cos7), 



= c(l — cosy) (say) ; 

 but c=m\ 



and /3=my, 



,\ AN =6(1 — cos ray), 

 and AM = m% ( 1 — cos y ) . 



AM ?n 2 (l— cos 7) 



AN 1 — cos ray 

 Expanding the cosines we get 



la !± + !ti i 



(i) 



m- 

 AM 



AN TraV ra 4 y 4 ™V \ 

 1 12 f~ + "l6~"" &C -j 



[* |i |6 



2 o 

 Dividing top and bottom by — -^-, we have 



AM 12 + 360 (KC * 



AN ., ra 2 7 2 ?>z 2 7 2 D 



(2) 



This, to the 1 st degree of approximation, is unity, and only 

 differs slightly from unity when ray is considerable, thus 

 confirming the general reasoning above. Taking m equal 2, 

 as in the figure, and 7 equal to J, i. e. 28°* 6, we have 



AM_ 48 5760 



AN" 2l JL 



12 T 360 " 



= 1-06. 

 Consequently the displacements differ by about 6 per cent. 



in a time equal to about one-sixth ( ^— j of the period of the 

 quick-moving instrument. ^ 7r ' 



