-MIL' PROFESSOB KNOTT ON THE STRAINS PRODUCED IN IRON, 



small numerical increase in the values of the longitudinal elongations (X) as the bore of 

 the tube is increased — that is, as the thickness of the wall is diminished. This is quite 

 in accordance with what might be expected if the elongation depends on the induction 

 rather than on the field. For, as I found by direct experiment in the case of the large 

 tubes, the induction in a given field is smaller in the tube of narrower bore or wider wall. 



The " tangential " elongations (ja) at the inner surface are all positive and much smaller 

 numerically than the longitudinal elongations. They show a tendency, however, to 

 increase with the bore. Because of the comparatively small value (practically zero) of 

 the cubical dilatation, the corresponding "radial" elongations (v) are distinctly larger 

 than the tangential elongations, but show no marked tendency either to diminish or 

 increase as the bore varies. 



On the other hand, the tangential and radial elongations (m', v') at the outer surface 

 behave somewhat in contrary fashion, // increasing, and v' correspondingly decreasing, ns 

 the bore increases. For any given field and tube the four ratios /a, //, v f , v are in order of 

 magnitude, // and v approximating to equality when the bore is narrow, and gradually 

 diverging in value as the bore increases. These relations are well shown in the curves. 



Had it been possible to obtain wider bores without hopelessly damaging the tube, 

 which already showed signs of cracking, it is highly probable that // and v' would 

 again approximate to equality, just as was found to be the case with the like quantities 

 for the iron tube (see below). 



By application of equation (3/ of last paragraph, the ratio /x' was calculated for 

 the large Nickel Tubes 1, 4, 7, and VII. Similar calculations were also made for Tubes 

 I. to VI., the elongation A being assumed to be the same for these as for their final form 

 VII. Although this assumption is not strictly accurate, it is sufficiently near the truth 

 not to lead to any serious error in the calculations of the other ratios. 



The results for the four existing tubes are given in Table III., and are represented 

 graphically in the third row of Plate I. 



An epitome of the results for Tubes I. to VII. forms Table IV., and some of the 

 features are shown graphically in the fourth row of Plate I. 



The volume changes measured are, of course, much larger for these tubes than for the 

 B tubes. Nevertheless, the linear dilatations come out with values practically identical 

 in the two sets. This will appear the more remarkable when the different conditions 

 under which the large and small tubes are magnetized are borne in mind. Each large 

 tube when inserted in the magnetizing coil extended to within a few inches of each 

 end, and could not therefore be magnetized so uniformly as one of the short tubes which 

 lay much more completely within the magnetizing coil. 



One interesting point brought out by the large tubes is the negative value of /x in 

 the tubes of narrowest bore under high magnetizing forces. See, for example, the 

 /x-graphs of No. 1, II. and III. (Plate I.). Also there is an interesting gradation in 

 the effect as the bore increases. Thus the values of m for Nos. 1 and I. arc positive 

 in fields lower than 140 and 180 respectively, and negative in higher. In Tube No. II. 



