Prof. E. Bouty's Studies on Magnetism. 191 



Beyond 10 millims. for the thickest needle, and 6 millims. for 

 the thinnest, the characteristic points are, theoretically and prac- 

 tically, confused with the asymptote. 



The agreement of calculation and experiment is very remark- 

 able for the needles which are not too short in proportion to 

 their diameter. It was for this case only that Green established 

 the formula which we are engaged in verifying. For extremely- 

 short needles, in all the experiments the observed are invariably 

 greater than the calculated numbers. The absolute differences 

 are, it is true, very small ; but they exceed the limit of errors of 

 observation, and as much more as the diameter of the needles is 

 more considerable. Nevertheless they are not sufficiently great 

 to permit us to seek empirically the form of the correction which 

 would have to be added to the formula to make it perfectly 

 accurate. 



2. Needles of different diameters. — For needles of different 

 diameters Green's formula admits of other verifications. The 

 angular coefficient C, of the asymptote, has to be proportional to 

 the square of the diameter of the needles, and the abscissa at the 

 origin, D, proportional to their diameter. 



It is easy to attach a physical meaning to the quantities C 

 and D. Let us consider two needles of the same diameter, suf- 

 ficiently long for their characteristic points to place themselves 

 sensibly on the asymptote. Their magnetic moments y and y' 

 are represented by the corresponding ordinates of the asymptote ; 

 that is to say, we have 



y=C(*-D)A 



y' = C(a^-D)J W 



On the other hand, we know, from Coulomb, that in long needles 

 the distance of the poles from the extremities is constant, what- 

 ever the length may be. Let P be that distance, and fx the quan- 

 tity of magnetism of each pole (also constant) ; we have 



The systems (3) and (4) are incompatible, unless we have at 

 the same time C = /£ and D=2P; so that the semiabscissa at 

 the origin of the asymptote is equal to the distance of the needle's 

 pole from the corresponding extremity, and the angular coeffi- 

 cient of the same right line is equal to the quantity of magnetism 

 of each pole. 



Thus, in the case of long cylindrical needles of different dia- 

 meters, Green's formula expresses the proportionality of the 

 power of the poles to the square of the diameter, and the pro- 



