EQUIPOTENTIAL SURFACES OF A SOLENOID. 245 



fifty points in one quadrant, which, on account of symmetry, gives 

 about 160 points at which the potential was known round the 

 solenoid. The potential at any other point was then found by 

 interpolation. Points Avhose potential was the same were joined 

 by the curves which seemed best to suit. The spherical harmonies 

 were obtained from a table recently published by Professor Perry* 

 The difference of potential between points lying on one curve and 

 on the next, both inside and ourside, is 2 tt n 7 a X '05. This 

 difference was chosen as a matter of convenience, 2 tt nj a being 

 in all these coils a factor of O. In the three shorter coils the equi- 

 potential curves start with a value zero at the equator, increasing 

 positively and negatively respectively on each side by 2 tt n j a X *05 

 from line to line, both inside and outside. In coil (4), Plate V.. the 

 potential inside is infinite, on account of :: being infinite. Outside 

 the potential of points on the outermost line is 2 tt n j a Y. -2, 

 those for 2 tt nj a X "15, 2 tt nj a X -1, &c., going off the paper. 



As Maxwell points out. there is a discontinuity in the magnetic 

 potential at the plane ends of the solenoids, but the equipotential 

 surface lines inside at the end are connected with those outside at 

 the end, and the curvative is the same for both. 



In some cases it was exceedingly difficult to find curves -which 

 passed nicely through the points Avhich had to be joined together, 

 and the drawing was all done at night. The most palpable error, 

 which, however, is not likely to mislead anyone, is to be found in 

 coil (2), Plate III. The spacing of the lines near the corners of 

 the square representing the solenoid obviously requires altering. 

 The curves bring out very clearly the want of uniformity of the 

 field in the interior of short coils, even the first line from the 

 equatorial in coil (I), Plate II., being sUghtly curved. In the other 

 coils it is uniform for a greater and greater length, as the solenoid 

 becomes longer and longer. In coil (2), Plate III., it is uniform 



for a little less than - on either side of the central line, in coil (3), 

 8 



oa 

 2^ 



end. Since the curves are all drawn to the same scale, the ratio of 

 the distance between any pair of lines in one coil to that of the 

 corresponding pair in all other gives us the ratio of the magnitude 

 of the force in the second coil to that in the first, so that the curves 

 ishow also how very much feebler the force is at the centre of the 

 solenoid for a short coil than for a long one which has the same 

 number of turns per centimetre, the same radius of section, and 

 the same current round the coils. 



* Phil. Mag., ser. 5, Dec, 1891. 



