MAGNETISM AND TWIST IN IRON AND NICKEL. 389 



is greater for smaller values of r. It is positive when (m — a) is positive, as in iron in 

 moderate fields; it is negative when (vs—cr) is negative, as in nickel throughout, and as 

 in iron in high fields. The existence of a maximum twist for some intermediate value 

 of either a or /3 (ft or a remaining constant) will depend upon the particular way in 

 which {zs — cr) depends on the quantities a and /3. Let us suppose, for instance, that a, 

 the circularly magnetising force, is constant, and that /3 is allowed to vary through a 

 large range. This supposition is a near enough approximation to the case of a wire con- 

 veying a steady current, and then longitudinally magnetised. Now, it is clear that even 

 if (ts — a) is constant, there is a maximum value for the twist given by the condition 

 |3 = a. A maximum value of (m — a) for intermediate values of the field is not then a 

 necessary condition for the existence of a maximum twist. Hence, it is not surprising 

 that the field at which the maximum twist occurs should not be the same as the field at 

 which the maximum elongation occurs. The maximum twist may exist without any 

 maximum elongation ; as for example in nickel, in which I have recently obtained a maxi- 

 mum twist about a field of 200 or 300. According to Mr Bidwell's recent experiments 

 (see Nature, July 1888), nickel goes on distinctly contracting in magnetic fields up to 

 750, after which up to 1300 or higher the length remains apparently constant. 



If we look closely at Mr Bidwell's curves of elongation for iron in ascending magnetic 

 fields, we see that at first the curve is concave upwards, then becoming convex it reaches 

 a maximum, after which it proceeds nearly straight in a long slope down to, and finally 

 below, the zero line. For a considerable range of field near the point of inflexion we may 

 regard the elongation as a linear function, of the most general form, of the magnetising 

 force ; and such an assumption gives a maximum twist, or rather the possibility of it, 

 except in the very special case of simple proportionality of the elongation to the magnetic 

 force. 



Let us now test the expression for 6 by a direct numerical calculation, taking for this 

 purpose the numbers given in Table I. for wire No. 1. Here r= '02, a= 11*4, /3=10'5, 

 and we may take {?>*! — o^) to be approximately "000004. With these values, we get 



6 = -00002, 



about 2^ times smaller than the observed value for the wire. 



A similar calculation can very easily be made for nickel. Now the contraction for 

 nickel in magnetic fields is considerably greater than the expansion for iron; and yet the 

 twist numbers given in Table III. are sensibly of the same magnitude as those in Table I. 

 The reason of this, however, is not far to seek. For it will be noticed that the factor 

 a)S/(a 2 -f /3 2 ) is, because of the greater inequality of a and /3, much smaller than in the 

 case of iron. 



At first sight, this may not seem to be a very promising result ; but when all the 

 circumstances of the case are borne in mind, it will, I think, be admitted that the result 

 is really as satisfactory as we could reasonably expect. The calculated twist for the tube 

 is, at any rate, of the same order of quantity as the observed twist for the wire. The 



VOL. XXXV. PART 9. 3 T 



