38 



DISPLACEMENT INTERFEROMETRY BY 



where a is the coefficient of expansion, k the bulk modulus, r and r z the 

 internal and external radius of the steel tube of length /. Hence 



(4) aM = 



and equation (i) becomes 



(5) 



a 



Jpc 



or 

 (6) 



c = 



a'd 



a' 



Hence c may be found from observations of A/ and A/>, provided a.' and p, a, 

 and j3 are sufficiently known. 



23. Measurement of the pressure coefficient /3. For this purpose the tube 

 TT, figure 40, is placed in a water-jacket of constant temperature, and /3 

 found directly. Experiments of this kind were contributed with some detail 

 in an earlier paper.* The method then used consisted in finding /3 from the 

 displacement of the spectrum ellipses under known conditions; but the present 

 method o[ the contact lever and achromatic fringes may be considered prefer- 

 able, particularly if the tube contains water (as a conducting medium for 

 pressure), for which the thermal discrepancy is small. 



Moreover since A?? is primarily aimed at, /3 should be made as small as pos- 

 sible. This may be done by selecting relatively thick- walled tubes of small 

 external diameter. A few data are here desirable. Using an ocular microm- 

 eter plate i cm. long with scale-parts of o.oi cm. each and fringes of moderate 

 size (i or 2 scale-parts in width) we may write as in the preceding paper, 



(7) 



where Le is the displacement of the achromatic fringe on the ocular scale cor- 

 responding to the elongation A/. 



Hence for steel tubes (& = i.8Xio 12 ) the following data apply, /3 being 

 reckoned per atmosphere : 



24. Measurement of the thermal expansion, a. For this purpose the tube 

 TT (fig. 40) is to be clean and empty, the nozzle p removed, and a long- 

 stemmed thermometer passed from end to end of the tube, through the end p, 

 as in figure 37. Externally the tube is surrounded by a coil of wire for electric 

 heating and appropriately jacketed. Measurements made in this way with 



Carnegie Inst. Wash. Pub. No. 249, pp. 84-94, I 9 I 7- 



