440 Mr. K. H. M. Bosanquet on the Horizontal 



effects were measured by the throw of a nearly astatic gal- 

 vanometer, with mirror and scale. A rough preliminary 

 experiment, with approximate value of H, gave 15*1 centim. 

 for 2L from the above formula. A more careful series gave 

 15*5 centim. 



The mean of these measures, 18*6 and 15*5, is 17 nearly, 

 corresponding to A 2 = 145, with which value all the observa- 

 tions were finally reduced. The observations at different 

 distances were, on the whole, better satisfied by this than by 

 any other of the numerous values tried. 



This ratio, ^ of the length, lies between Joule's values, 

 which are from -f to -J of the length. 



The deflection-observations were made with two instru- 

 ments. One has a small brass circle, needle-point suspension, 

 and scale up to 80 centim. on either side. The other has a 

 wooden circle with paper scales divided to 10', silk suspen- 

 sion, and mirror reading. The scales were divided on the 

 lathe, the degrees being ^ inch, which could, after some 

 failures, be accurately done. The circle was turned by trial 

 till the paper scales exactly fitted round it. This is a much 

 more accurate instrument than the other ; but it is a great 

 object to use the smaller instrument. As it is only possible 

 to read to tenths of a degree with this, it is necessary to use 

 larger deflections. But when this is done allowance must be 

 made for their effect, as has been pointed out to me. As I 

 do not know of any discussion of this, I give it here. 



Let R be the force at distance r, then R=-y. Let 2 A be 



the distance of the poles of the deflected needle, /jl their 

 strength, so that 2A//, = m. 

 Forces on poles of needle are 



2Mu 2Mfi 



(r — A sin 6f' (r + A sin 6f 



From these arise a resultant of translation and a couple. 

 Resultant of translation 



2Mm . n f 4 . 5 /A sin 0\* 



'{•+&(*=-7+-}' 



r 



Couple = A cos 6 x numerical sum of forces, 



^2 



1 r n 3.4/A . A 2 , ~| 

 i 1+ TT2(7 sin *) + ---j' 



The resultant of translation may become important if large 

 deflections are used with a silk suspension. I use two 

 magnets applied on opposite sides (Joule), in which case the 



