Variation of the Rigidity of Phosphor-Bronze. 419 



being much greater for a heavy load than for a light one. 

 This discrepancy was noticed during experiments with a 

 vibration magnetometer for which it was necessary to 

 measure the restoring couple per unit angle o£ twist, which, 

 though small, was appreciable, by means of brass bars of the 

 same dimensions as the magnets whose magnetic moments 

 are being measured : and it was found that the rigiditv was 

 much less when the stirrup only was supported than when 

 the brass was held in the stirrup. The discrepancy observed 

 was so large that the following experiments were made to 

 determine the cause of it. 



The experiments were made chiefly with phosphor-bronze 

 strips of the following dimensions : (1) 0*0010 cm. thick, 

 0*022 cm. wide, and 25 cm. long ; and (2) 0*0043 cm. thick, 

 0*48 cm. wide, and 25 cm. long. The dynamical method 

 was used to measure the coefficients of torsion of the strips. 

 One end of the strip was soldered to a piece of brass which 

 was rigidly held in a torsion-head, and the other end was 

 soldered to a light copper stirrup, which supported in a 

 horizontal position circular brass rods of weights varying 

 from *1 gr. to 25 gr. and each about 9 cm. in length. The 

 whole was enclosed in a glass case. When a rod of a given 

 weight had been placed in the stirrup the time of a convenient 

 number of swings was observed. The moments of inertia of 

 the rods and stirrup were then calculated from a knowledge 

 of their measurements and weights. It is easy to see that a 

 knowledge of these and of the time of swing for each of them 

 will give the values of the restoring couple per unit angle of 

 twist. In practice relative values of the restoring couples for 

 the various weights supported were obtained in the following 

 manner : — 



Let t 1 and t 2 be the restoring couples, T 1 and T 2 the times 

 of swing when the first and second rods were respectively 

 placed on the stirrup, and let I Xj I 2 , and I 5 be the moments of 

 inertia of the first and second rods and stirrup respectively. 



Then 

 and 

 Hence 



V Tl 



T 2 = 2,r x /k±l£. 



V T 2 



ti T 2 2 • \1 2 + V 

 Similarly the ratios of r 3 , t 4 . . . r n to r : were determined. 



