Radial and Axial Components of Magnetic Force. 197 



The cases for which 



?' < T and S > r > T, 

 and S > r > T and S > r' > T, 



respectively, do not need separate investigation. The results, though 

 long and cumbrous, can easily bo written down from the foregoing. 



The accompanying tables were originally calculated by means of the 

 formulae : 



--* 



s = 6 sin + - 1 / 1 sin 3 0, 

 



^= - 5 sin 20 + ^ sin' 2 sin 20, 



. 5 = - 15 sin + l{i-- sin ;J - -^1^- sin 5 0, 



!i = - -V sin 2 + i|^- sin 2 sin 2 - ^ sin 4 sin 2 0, 

 ^0 



^ = -28sin0+189sin 3 0-^^sin 5 + ^ ( ;^sin 7 0. 

 The results were finally checked by means of the relation 



using for this purpose the table of P calculated by Messrs. Holland, 

 Jones, and Lamb, and published by Professor Perry in the ' Phil. Mag./ 

 vol. 32, 1891. This is not a complete check on the fourth figure in my 

 tables, but no disagreement larger than OOOCM has been passed over 

 without examination, and that only in the higher values of dPJdO. It 

 is therefore hoped that the tables may be found accurate as a whole, 

 though it is perhaps scarcely to be expected but that some errors have 

 escaped detection. 



With the aid of Perry's tables and those now given the magnetic 

 force at any point inside a coil may be found numerically by means of 

 the formulse in the body of the paper. For points outside the coil a 



