418 Dr. S. Bidwell. On the Changes of [Apr. 11, 



dimensions due to magnetisation, published in 1888, I wrote: "One 

 of the influences tending to produce retraction must certainly be of a 

 purely mechanical nature. Suppose a uniformly magnetised rod to be 

 transversely divided through the middle. The two halves, if placed 

 end to end, will be held together by their mutual attraction, pressing 

 against each other with a certain force per unit of area, which can be 

 measured by the weight necessary to tear one half from the other. 

 The same pressure will exist between any two portions of the rod 

 separated by any possible cross section, and a certain longitudinal 

 contraction of the rod will be the consequence. If, now, the rod, 

 having been first demagnetised, be placed in a vertical position upon a 

 fixed base, and loaded at the upper end with a weight equal to the 

 greatest it could support when magnetised, it will undergo the same 

 contraction as before, the [compressive] stresses being equal in the two 

 cases." It is pointed out that in the latter case the contraction is 

 expressed as a fraction of the original length by P/M, M being 

 Young's modulus, and P the load, both in grammes weight per 

 square centimetre. Assuming the magnetisation to be such that the 

 divided rod can just support a weight of P grammes per square 

 centimetre, it is inferred that the contraction due to the mechanical 

 effect of magnetisation would again be P/M, and it is shown that this 

 accounts for a part only of the observed change of length. In an 

 earlier paper* it was calculated that P, the weight per square centimetre 

 supported in the field H, was equal to (2ttI 2 + HI)/7/, I being the 

 magnetisation, and g the intensity of gravity. This expression (which 

 is equivalent to (B 2 - H 2 )/87n/), is applicable when the magnetic metal 

 is magnetised longitudinally and uniformly by an external field, as was 

 approximately the case in the experiments with which the present 

 paper is concerned, where the wires were placed in the axis of an 

 independent magnetising coil. For the special case in which each half 

 of the divided rod is surrounded by a separate magnetising coil wrapped 

 tightly around it, another term, H 2 /8tt, must be added for the mutual 

 action of the two coils, and we shall have 



Yg = 2irI* + HI + g- 2 = ^I + H) 2 = » : 



. 8tt 8tt 8tt 



Also for a permanent ring-magnet, in which there is no magnetic 

 force H, 



?g = 2ttI 2 = 2tt /Bx2 B ' 



i-J 8tt 



It should be noticed that since, except in very strong fields, H 2 is 

 negligible in comparison with B 2 , the force in the first case considered 



# ' Roy. Soc. Proc.,' vol. 47, p. 486, 1886. 



