1826.] Copper and other Substances during Rotation, 257 



particle in the copper urges the needle from the magnetic meri- 

 dian yvith. a force varying as "- ^r^^^^M^ y which law would arise 



from the magnetism in the needle developing the magnetism in 

 the particles of copper, so that its intensity would vary as 



7rr-r^f and this magnetism again acting on the poles of the 

 needle with a force varying as .-r^^- Supposing this to be the 



case, if X is, the distance of a lamina of copper from the plane of 

 the needle, s the arc of a circle in this lamina at the distance r 

 from the axis of rotation, R the radius of the copper cylinder, 

 t its thickness, c the distance of its upper surface from the 

 needle, and a the distance of the pole of the needle from its 

 centre : then the whole force with which the cylinder urges the 

 needle will be proportional to 



r d s dr dz 



fffx 



Although this may be integrable, the integral would be in so 

 complicated a form, that it would be very ill suited for compa- 

 rison with the results obtained from observation ; but if we 

 consider only the annulus of the copper immediately under the 

 pole of the needle, which will be the most efficient part, we may 

 readily make this comparison. For calling ^ the deviation, we 



should have sin. 9 = / -^ x const, or sin. 5 = (^-^ — . ^ ^S \ 

 X const; and consequently •-. '—^ — = const. 



C5 "" (7+1)3 



From my experiments t being 1, 1 should obtain the following 



, ty sin. 6 



values of ; . — 



(c + 0^ 



U'M i 



C3 (C + if 



3-5 r 39' 2-33161 



^^Sr^V'" 3 14 2-6341 I 



dw ,:.'i.g;ST} 5 10 2-6409 >Mean 2-505 



v.s^'*ruy 



abft^ 2'.0 14 10 2-8144 | 



■''"'"'^ " 1-5 29 20 2-1040J 



'Although there is a considerable difference in the numbers, 

 especially the last, yet as the parts whose action is not consi- 

 dered have here the greatest effect, and all the observations are 

 liable to errors arising from the difficulty of making the copper 

 revolve with the same velocity in all cases, I think the agreement 

 New Sericii, v ol. x ii . s 



