Variation of the Rigidity of Pliosplior-Bronze. 425 



uniform cross-section and perfectly straight. It is well known 

 that metal manufactured in sheets is subject to such over- 

 strains, especially when it is rolled at too low a temperature — 

 as is shown by the fact that a perfectly plane sheet of metal 

 may be made convex by a very small force, and cannot be 

 made plane again unless manipulated by skilful hands. That 

 such overstrains existed in the phosphor-bronze strip seems 

 to be proved by the following experiments. 



I thought it possible that if the observed discrepancy was 

 due to such an overstrain it would disappear if the strip was 

 annealed ; and on making a trial found that it did so. The 

 method finally adopted for the purpose of annealing the strip 

 was to place it, after carefully straightening it out, on the 

 plane surface of a brass bar 2 cm. square and 2S cm. long, 

 and then to place on the top of the strip a similar bar of brass, 

 care being taken to keep the strip straight during the 

 operation. The whole was then placed on a tripod and 

 gently heated with a blowpipe-flame. When a suitable 

 temperature was reached, the bar was kept approximately at 

 that temperature for about 10 minutes and then allowed to 

 cool. It was not necessary to wait until the rods had com- 

 pletely cooled and the strip could be taken out when fairly 

 hot. It was then found to be very soft, and the restoring 

 couple per unit angle of twist was now the same for all loads. 

 Fig. 2 curve V. shows the results obtained with one strip. 

 It will be noticed that although the annealing has made the 

 strip softer, yet the restoring couple per unit angle of twist 

 has been substantially increased. In the process of annealing- 

 care must be taken not to make the strip too hot nor to keep 

 it hot too long, as if either is done the strip becomes "short,"' 

 its strength is much diminished, and the restoring couple 

 per unit angle of twist becomes much less. It is difficult to 

 avoid this when using very thin strips; but even in this case 

 the discrepancy was very largely removed, and this alteration 

 was permanent in character. These experiments therefore 

 afford strong proof that the discrepancy is due to an over- 

 strain in the strip. This view was further confirmed by 

 another experiment. It was thought that if the discrepancy 

 was due to such an overstrain, then if it was overstrained in 

 another manner the effect would be altered. It is obvious 

 that it w T ould be better to overstrain it in such a way that the 

 outside layers were treated differently from the interior 

 portions, as the overstrain due to the method of manufacture 

 will be chiefly on the outer layers. Such a method of over- 

 straining is that of wrapping the strip round a narrow 

 cylinder. This method was adopted. When taken off the 

 cylinder it was in the form of a spiral of permanent form, 



