2 DISPLACEMENT INTERFEROMETRY APPLIED TO 



an adaptation of the pin-valve of an oxygen tank, with a good micrometer- 

 screw 5 and stuffing-box n. The head h of the screw is graduated. The 

 barrel b is at right angles to the tube aa! ', which at a joins the capillary tube 

 d, leading to I of figure i . At the end a' there is a cock C which shuts off com- 

 munication with the atmosphere. Thus, when C is closed, pressure is applied 

 directly at A, figure i, by rotating the head h in figure 2. This pressure is at 

 once removed by opening C. 



The apparatus worked surprisingly well. When C is closed and h rotated, 

 the fringes may be placed anywhere in the field about as conveniently as with 

 the micrometer-screw at the mirror of the interferometer. There is, however, 

 one difficulty which I have not thus far been able to remove. When the 

 pressure increments exceed a certain small value, the plates g, g' no longer 

 rise and fall in parallel. The coincidence of images is destroyed and the fringes 

 vanish. There is here a conflict with the capillary forces present at the edges 

 of the disk. I endeavored to improve this by using small plates g, g', 

 anchored near the center of MM' by four loose threads, but the advantage 

 was not marked. Fringes a scale-part in size will not usually be available for 

 more than 50 scale-parts, being sharpest in the middle. This is about half the 

 diameter of field of the ordinary telescope. 



3. Equations and pressure observations. If the cock C, figure 2, is closed 

 and the temperature for brief intervals is considered constant, Boyle's law may 

 be written (ignoring signs of increments) 



__ 



V " V = p "76 



where V is the total volume inclosed, dv the increment at the micrometer-screw 

 hs, and dV the corresponding decrement equivalent to the pressure decrement 

 dp. If a is the area of the piston at g, dV = a dh/2, and if V = aH, H being the 

 corrected depth of the air-space at A, equation (i) becomes 



, . dv dh _dh 



~V~^H~^6 



But dh on the interferometer is equivalent to n fringes of wave-length X, so 

 that dh = n\/2. Hence finally 



(3) ^=y*(-^ + - 



2 \76 2/f 



This equation gives a test of the trustworthiness of the gage. 



In the apparatus used the following constants were found by measurement : 

 F=66.8 cm. 3 , = 29.2 cm. 2 , H = z.2g cm. The pitch of the screw was 0.073 

 cm. and its mean diameter 0.51 cm. Hence, per turn, 6^ = 0.073X0.204 = 

 0.0149 cm. 3 , and ofo/V=io~ 4 X2.23 per turn. The mean wave-length 



being X = 6Xio- 5 cm., equation (3) reduces to ((-^ + -jj\ = 0.0066+0.1092^ 



