132 HENRY A. KOWLAXD 



this more thoroughly numerical results were attempted, and, after 

 weeks of labor, obtained. I give below the last results which, from 

 the precautions taken and the increase of experience, have the greatest 

 weight. 



The magnetizing force of the disc was obtained from the deflection 

 of the astatic needle as follows. Turning the two needles with poles 

 in the same direction and observing the number n of vibrations, and 

 then turning them opposite and finding the number n' of vibrations in 

 that position, we shall find, when the lower needle is the strongest, 



Y -p, w 2 n" 1 n' 2 A w n . 



JL JL 5; jz = *. 72 77 ** I .... (1) 



w 2 + n ' i? + n D 



where X' and X are the forces on the upper and lower needle re- 

 spectively, A the deflection, D the distance of the scale and H the 

 horizontal component of the earth's magnetism. As X' and n' are very 

 small the first term is nearly X X'. The torsion of the silk fibre was 

 too small to affect the result, or at least was almost eliminated by the 

 method of experiment. 



The electricity was in the first experiment distributed nearly uni- 

 formly over the disc with the exception of the opening in the centre 

 and the excess of distribution on the edge. The surface density on 

 either side was 



V y 



a* - 



V - -V being the difference of potential between the disc and the 

 outside plates, /? the thickness of the disc and B the whole distance 

 apart of the outside plates. The excess on the edge was (Maxwell's 

 Electricity, Art. 196, Eq. 18), 



*=*<?- ^ *** "*> ' < 3 > 



where C is the radius of the disc. 



We may calculate the magnetic effect on the supposition that, as in 

 the conducted current, the magnetizing force due to any element of 

 surface is proportional to the quantity of electricity passing that 

 element in a unit of time. The magnetic effect due to the uniform 

 distribution has the greatest effect. With an error of only a small 



