470 PROFESSOR KNOTT ON THE STRAINS PRODUCED IN IRON, 



The quantities tabulated under SV and Bv' are the means of the readings obtained 

 on application and withdrawal of the magnetizing force. In the majority of cases, the 

 sum SV + Bv is not very different from Bv', a result which gives a check on the 

 accuracy of the experiment. 



§ 8. The Dilatations in Iron and Steel Tubes (Bored). — From the volume and 

 length changes, in the manner described in § 3, the dilatations S, X, ju,, v , ll', v' were 

 calculated, and are entered in the appropriate columns in Table VII. A selection of 

 the results is given graphically in the second and fourth rows of Plate II. 



There is a tendency for the dilatations m and v to be of opposite sign from X — that is 

 to say, they are, as a rule, negative when X is positive, and positive when X is negative. 

 The curves obtained by plotting the dilatations in terms of the magnetic fields are, with 

 one exception, remarkably smooth, and in no way reflect the peculiar features of the 

 Bv and Bv' curves, from which they have been derived by a purely arithmetical process. 

 Compare, for example, the groups of curves for A V., A VI., B V., and B VI. The 

 grouping of the X, /j., v curves is broadly the same in all ; and yet, at first sight, nothing 

 is more striking than the differences between the Bv and Bv' curves for V. and VI. The 

 reason for this is not far to seek. The ratios Bv/v and Bv'/v' become for the thinner 

 walled tubes distinctly smaller than X, so that the calculated values of m and fx' are 

 more affected by the peculiarities of X than by those of (X + 2m) and (X + 2//). 



One interesting feature in regard to the relative magnitudes of m and v is that they, 

 so to speak, change places in the transition from Tube A V. to A VI., and from B VI. 

 to B VII. In other words, we find, on plotting the curves, that the m curves lie below 

 the corresponding v curves up to A V. and B VI., and that thereafter the ll curves lie 

 above the v curves. In this respect the coiled tubes discussed in next paragraph are 

 comparable to A VII. and B VII. This result seems to be one that could hardly have 

 been expected. A gradual convergence to equality might more reasonably have been 

 looked for, as the tube was taken thinner and thinner. The interchange of m and v in 

 regard to magnitude is, however, characteristic of both the nickel and the iron, and 

 must have some fundamental significance. 



The results for the other iron tubes given in Tables VIII. and IX. are very similar 

 to those for the A and B series. In these tables an average value for B is assumed, 

 so that the values of v, //, and v' are, at the best, tentative. It is, however, noteworthy 

 that the large Tubes 3, 5, 7, VII., and 9, and V. to VIII'. should give results, broadly 

 speaking, identical with those obtained from the shorter and narrower tubes of the A 

 and B series. It is instructive to note how comparatively little the values of the j 

 transverse and radial dilatations are affected by the sign of the change of volume j 

 of bore. As already pointed out, the longitudinal dilatation X has a preponderating 

 influence upon the character of the other dilatations. To express it otherwise, the ratio ' 

 X + 2m, which was the particular object of study in the first paper, is subject to relatively 

 great changes of values, simply because it is the difference of two ratios, X and - 2m, j 

 of which sometimes one and sometimes the other is the greater. Thus, the ' 



