1894.] upon the Dimensions and Volume of Iron Rings. 



97 



units. With this he found a contraction in the length of the pipe of 

 7 ten-millionths, a result which agrees very well with that obtained 

 by myself for the same small magnetising force. 



As was shown in my last paper, the effects along the lines of mag- 

 netisation are very different in the two rings. The annealed ring 

 (Ring I) begins to contract circumferentially with the smallest 

 forces, and continues to contract with the large ones ; while the 

 hardened ring expands with small forces and contracts with large 

 ones. These effects are indicated in the figure by the dotted curves. 



By combining the results of the old and of the new experiments we 

 can ascertain the nature of the changes produced by magnetisation 

 in the volumes of the rings. 



If k = elongation (+ or ) along the lines of magnetisation, 



I = elongation ( + or ) transversely to the lines of magnetisa- 

 tion, 



then the increment or decrement of volume when the ring is mag- 

 netised is approximately* k + 2L 



FIG. 3. 



From the two sets of curves in fig. 1 corresponding values of k and 

 Z can be found, and thence the changes of volume may be deduced. 

 These are given in Table II and fig. 3, which show that the volume 

 of the annealed ring is rather suddenly diminished by a small mag- 

 netising force, passes a minimum under a force of about 50 units, 



* Neglecting P and products of k and I. 

 VOL. LVI. H 



