472 PROFESSOR KNOTT ON THE STRAINS PRODUCED IN IRON, 



of 500, does not exceed "2 x 10"°. In the calculation of the radial dilatations (i/) the 

 cubical dilatation has been assumed to be zero. If, as is highly probable, the cubical 

 dilatation is positive, the values for v' will be slightly greater. There is, however, no 

 pronounced difference between the values of /*' and v', such as exists in the case of the 

 coiled nickel tubes. 



For the sake of easy comparison the Bv' curves for C I. and C II. are shown on Plate 

 II., drawn to the same reference point and axes as the curves giving the volume changes 

 for A V. They are the dotted curves, and are characterised by a maximum in Field 25, 

 followed by a minimum in Field 120 or 130. They thus bear a certain resemblance to 

 the Bv' curve for A I., in which, however, the early maximum is not strongly marked. 



The maximum elongation occurs in both cases about Field 60, a distinctly higher 

 value than what is usually obtained with wires. 



The broad distinction between the results for the bored and coiled tubes is the 

 comparatively large distortion experienced by the latter in strong magnetic fields. 



§ 10. General Conclusions. — It remains to give a general summary of the 

 results, with special reference to the characteristics of the strains which accompany the 

 magnetization of iron, nickel, and cobalt tubes. In a broad sense, the results for any 

 one metal are much the same, whatever the dimensions of the tube may have happened 

 to be. The changes in the values of the various dilatations, cubical or linear, as we 

 pass from tube to tube of the same metal, are, for the most part, of secondary importance, 

 and seem to belong to the same category of phenomena as the influence of form upon 

 the susceptibility. 



Of all the quantities measured, the changes of volume of bore and the changes of 

 external volume of the plugged tube obey what, in certain cases, appear to be most 

 capricious rules. But as soon as we calculate the strain coefficients, we see at once the 

 reason for this apparent capriciousness. The strain coefficients themselves have, as already 

 mentioned, very similar values in all the tubes of one metal ; but as the longitudinal 

 elongation (X) usually differs in sign from the transverse elongation (m), the ratio (X + 2/x) 

 is arithmetically a difference of two numbers not very different in value. Sometimes 

 the one term predominates, sometimes the other. Thus the A and B tubes Nos. V. and 

 VI. are very similar as regards their dilatations (Table VII.), but there is at first sight 

 a marked dissimilarity as regards their volume changes, Bv and Bv' (Table VI.). 



In my former paper I found great difficulty in interpreting the apparently 

 capricious results obtained there. This difficulty now in great measure disappears, and 

 the interest is transferred from the measured volume changes to the dilatations to which 

 they lead. 



As a general rule, the elongation in the direction of the magnetizing force is 

 the most important. Mr Bid well * has made us familiar with the laws of its variation 

 in iron, nickel, and cobalt; and the values obtained by me are in full accord with his. 

 The steady manner in which the maximum elongation point shifts into lower fields 



* Phil. Trans., Series A., vol. 179, 1888. 



