494 Supposed Repulsion between Magnetic Lines of Force. 



x axis coincides with F / in the y axis, as in fig. 14, then evi- 

 dently the feet of the ordinates drawn from any point on the 

 hyperbola xy=ff r will he conjugate to one another. This 

 construction gives us a readier means of finding many of the 

 points whose positions have already been discussed. 

 Thus self -conjugate points are at once given by 



x(2h-x)=ff; 



and the points K, K' (§ 15) by 



2hx=ff. 



Again, H being the middle point of FF', if H is the image 

 of G, and J of H, we have 



F / J=^- / =2FK = FG. 



28. From the construction of the preceding section it appears 

 that the lines joining pairs of conjugate points on the two 

 axes touch the hyperbola 



Fig. 14 shows that the conjugate points V, V are equidistant 

 from H, the middle point of FF', and that 



FV = F / V / = FT = x //y v - 



LVI. On the supposed Repulsion between Magnetic Lines of 

 Force. By R. H. M. Bosanquet, St. John's College, 

 Oxford. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



THE idea of a repulsion between magnetic lines of force 

 was derived by Faraday from the repulsion which exists 

 between two magnetic needles placed " side by side with like 

 poles in the same direction " (Exp. Res. vol. iii. p. 419). 



In the deduction of the forces which accompany lines of 

 force, Maxwell reduces them to a tension along the lines of 

 force combined with a pressure in all directions at right angles 

 to them. 



Now it is easy to show experimentally, and indeed it is well 

 known, that rings magnetized by means of a continuous coil 

 uniformly wound round them present no external magnetic 

 action, though they may be the seat of closed circuits of mag- 

 netic lines of force of very great intensity. It is clear that in 

 this case we may suppose the ring divided into a number of 

 separate rings, each containing lines of force, and that such 



