552 



PROFESSOR KNOTT ON THE STRAINS PRODUCED IN 



his experiments the magnetisation of the ring must have been fairly uniform through- 

 out — a condition very far from being realised in the case of the tubes. 



Dilatations x 10 7, 











Iron. 









Field 



















I. 



II. 



III. 



IV. 



V. 



VI. 



VII. 



100 



+ 2-1 



+ 3-9 



- -7 



-1-3 



- 1-6 



- -2 



+ M 



200 



-16 



-5-3 



-2-8 



+ 4-6 



+ 9-2 



+ 10-0 



+ 8-4 



300 



-18-1 



-4-6 



+ -2 



+ 6-6 



+ 11-5 



+ 11-8 



+ 9-6 



400 



-22-3 



-6-2 



- -2 



+ 6-7 



+ 11-7 



+ 11-8 



+ 10 



500 



-29-3 



-7-4 



-1-0 



+ 6-2 



Nickel. 



+ 11-7 



+ 12-3 



+ 10-1 



100 



- 29 



- 18 



- 15 



- 9-4 



- 7-4 



- 29-3 



- 31 



200 



-201 



-141 



-126 



- 81-3 



-56-6 



- 91 



- 76-4 



300 



-285 



-191 



-193 



-121 



-81 



-115 



- 93 



400 



-305 



-247 



-218 



-138 



-90 



-122 



-100 



500 



-319 



-253 



-230 



-146 



-94 



-126 



-102 



The dilatations given above are the average dilatations of the material of the tube 

 along the inner surface in its successive states from the quarter-inch bore to the final 

 inch and sixteenth. Let us assume for the moment that the dilatation in a solid bar 

 at any given distance from the axis is to some extent similar to the dilatation that 

 would exist if the bar were bored out to that distance. There is, of course, little doubt 

 that this is a very crude assumption, for a free surface newly formed quite alters the 

 molecular arrangements in the immediate neighbourhood, and with considerably less 

 restraint there will be greater tendency to form new configurations. Nevertheless, it may- 

 be plausibly enough assumed that the dilatations at increasing distances from the axis of 

 a solid bar will follow a law in some respects similar to the law followed by the dilata- 

 tions in the tubes of corresponding bore. In other words, the numbers tabulated above 

 may be regarded as at all events giving a hint as to the condition of strain in the 

 successive cylindrical shells of a solid bar when magnetised. 



With this assumption, then, what is the significance of dilatations varying from 

 centre to circumference in the manner suggested by the values tabulated above ? In 

 the case of the iron, the dilatation in the higher fields is negative near the axis, but 

 changes to positive at a distance from the axis equal to about one-third the external 

 radius. Now a dilatation following such a law must clearly be associated with a strain 

 involving a change of form of the bar as a whole. Either the originally plain sections 

 must become curved, or the cylindrical surface spindle-shaped or hyperboloidal ; or 

 possibly both effects may be present. As soon as part of the bar is removed from the 

 inside, the greater freedom acquired may easily show itself in the greater dilatations 

 obtained. In this way the magnitude of the negative dilatation in the case of Tube 



