220 Prof. G. M. Minchin on the Magnetic 



which, if only terms of the first order were taken account of, 

 the line of force would cut the next circle (of radius T>g) is 

 defined by the value e = 90° 14', which, being corrected by 

 the terms of the second order, becomes 89° 9', and the cor- 

 responding point is q. 



In like manner the points r', s', t f given by terms as far as 

 the first order correspond to values of e equal to 



112° 48' ; 134° 26' ; 165° 41', 

 which are corrected into 



111° 40' ; 133° 13' ; 163° 17', 

 the corresponding points being r, s, t. Thus the line of force 

 which starts from the inner surface of the wire is ^Etpqrst, and 

 it is found to cut the diameter EB in a point v such that Dv 

 is about 1*52 millim. 



The lines of force at points between B and v are incomplete 

 curves which emanate from various points on the surface 

 EHB of the wire between E and B. The line of force at B 

 itself reduces to a mere point. These lines can, of course, be 

 traced by putting m and ir for m and cj> in (60). 



It has been already pointed out that the magnetic effect of 

 a current running in a wire is not the same, at points near 

 the surface of the wire, as if the whole current were con- 

 centrated in an infinitely thin filament running along the 

 central line of the wire, although such is sometimes assumed 

 to be the case. 



Let us, for example, see what the values of <£, or of e, 

 would be in the numerical case just discussed if we assume 

 that c can be put equal to zero, i.e. \ = 0. 



The value of e which corresponds to the circle of radius 

 1*1 millim. (supposing still that we are tracing the line of 

 force which passes through E) is found to be 66° 15' instead 

 of 63° 20' ; the value of e which corresponds to the circle of 

 radius 1*4 is 142° instead of 134° 26', while that which cor- 

 responds to the radius 1*5 is impossible — indicating that, to 

 the first order of small quantities, the line of force does not 

 intersect the circle of radius Dj, but lies within it. Thus 

 there is a notable difference made in the results by assuming 

 that the whole current can be concentrated in a line running 

 through D. 



If a— co , i.e., if the current runs in a straight wire, the 

 conical angle and the constants of the lines of force are the 

 same as if c = 0, and therefore such concentration of a current 

 along the central line of the wire is allowable only when the wire 

 is straight, or when the curve into which it is bent has a very 

 large radius of curvature. 



