THE AID OF THE ACHROMATIC FRINGES. 69 



By direct comparison the following values were found: 



480 405 460 cm. 

 io 5 AAf=i45 165 125 i55 cm. 

 io 4 Xratio= 32 34 31 34 



The mean value is AAV Ae = 0.003 2 8, or A<?/AA r = 305. The variable Ae> is 

 thus over 300 times larger than AN. 



The cyclic experiments with the steel rods previously used showed a lack 

 of coincidence of the ascending and descending graphs which must here be 

 spurious. I obtained, for instance, 



AP=i 2 3 4 5 4 3 2 i kg. 

 io 3 Ae = o 90 170 250 330 275 190 no o cm. 



As the ascending graph is fairly regular, the apparent modulus may be found 

 from it. Three such series gave mean values of A<?, from which AN, A/, and E 

 were computed as follows : 



io 3 A<?/AP = S5 81 86 cm. /kg. 



io 5 AAYAP = 28.i 27.0 28.4 cm. /kg. 



io 5 A//AP=i4.6 14.0 14.8 cm./kg. 



io~ 10 E= 0.35 0.36 0.34 



To find A/, the elongation of each rod, the equation 



R f AN cost 



A/= - - =0.52 AN 



R 2 



suffices, since R'/R=i.^ and 1 = 45. The values of E = 97.8/1 A A r /AP) 

 are of the same low order, scarcely one-fifth of the true value already found ; 

 i. e., they merely indicate the deficient rigidity of the apparatus. 



In the last series of triplets made under different circumstances by aid of 

 A?, the mean values were 



Mean load 15 25 35 45kg. 



MeanXicT 12 0.28 0.35 0.46 0.51 



a steady progression, with remarkable consistency throughout; but it would 

 require a load of 20 to 25 kg. to reach the true modulus for steel. So also E 

 increases in successive triplets to a limit; as, for instance, at the loads 4 to 5 kg., 



EXicf 12 = o.4o, 0.49, 0.54, 0.52 



39. Summary. It has been found that a spurious displacement of 3 to 6 

 fringes per kilogram of the load, apparently within the apparatus, has not 

 only not been overcome in the above form of construction, but the cause of 

 this residual discrepancy could not be definitely ascertained. Very slight 

 flexures or torsions of the bar F (fig. 28) by the stresses would account for it; 

 but in such a case the slit-images should lose coincidence, and this has not 

 been typically the case. A slight rotation of the whole apparatus around 



