86 THE INTERFEROMETRY OF 



passing into the hyperbolic patterns. However, a pair of plates of about the 



same thickness (0.7 cm.), but respectively of crown and flint glass, when in- 



serted in the M and N beams, gave good hyperbolas.* It was interesting 



to notice that in the principal focus the n " n 



fringe pattern was nearly circular or a 



roundish elliptic, but the ellipses were not . 



strong. On drawing the ocular out, these 



ellipses underwent continuous deforma- 



tion, passing through horizontal bands 



finally into sharp and strong hyperbolic 



forms. The fringes obtained with the 



differently dispersing plates must therefore be referred to space loci in which, 



on passing along the axis, an elliptic cone becomes linear at the apex and 



symmetrically hyperbolic beyond. Thus in figure 56 the sections of the cone 



at a, b, c show fringes of the form d, e, f. 



43. Observations. Thick steel tube. The seamless steel tube in my pos- 

 session had the following dimensions: Length between mirrors, 160.8 cm.; 

 diameter inside, 0.515 cm.; diameter outside, 1.278 cm. Hence the inside 

 cross-section is 0.208 square cm. and the cross-section of steel 1.075 sq. cm. 

 Such a tube is therefore rather adapted for measuring very high pressures, 

 whereas the following work will not go beyond 1,000 atmospheres; but it 

 was admitted for trial. If the case is treated as simple traction with Young's 

 modulus taken as 2.i4Xio 12 , the elongation should be about i4Xio" 6 

 cm. per atmosphere, equivalent to a little less than half an interference 

 ring. But this is obviously too large, as the tube expands in all directions 

 by internal pressure. The case has been treated by Tait and will presently 

 be referred to. 



The experiments made proceeded with unexpected smoothness from the 

 outset, barring the tremors of the laboratory, which made it difficult to set 

 the ellipses. Comparing the steel gage with a standard Bourdon gage read- 

 ing in steps of 10 atmospheres to 1,000 atmospheres, the first six series of 

 experiments showed an elongation AL of tube per atmosphere of 



io 6 AL = 7.5, 8.0, 7.0, 8.0, 7.0, 7.5 cm. 

 In the last series the individual results were: 



Pressure ............ 100 200 300 400 500 500 400 300 200 100 atmosph. 



Micrometer at ...... 93 87 79 71 65 65 73 81 89 96 cm./io 4 



cm. 



The data for decreasing pressures do not return into the preceding values 

 for increasing pressures for incidental reasons which need not be discussed, 

 but the mean rates are not very different. The discrepancies are probably 

 in the setting of the Bourdon gage. They are not due to temperature here, 



* Later experiments showed that the flint plate was slightly curved. 



