2 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



The pencil from the collimator strikes the plate of glass G at the end of 

 the horizontal pendulum, the greater part of this, d', being transmitted to 

 the opaque mirror M, the remainder, d, reflected from the opaque mirror N. 

 It is advantageous to have M and N equidistant from G, as nearly as prac- 

 ticable (20 or 30 cm.), and far from the lamp/, to avoid the menace of tem- 

 perature discrepancies. If the mounting is of gas-pipe, water circulation 

 might be used, but this is not necessary. 



In the diagram the pencils d and d' are normally reflected at M and N. 

 On returning d is transmitted and d' reflected, so that the beams reunite and 

 proceed together to the far focus F, 20 or 30 meters distant, where they are 

 caught on a paper or ground-glass screen, or directly observed with the lens. 

 It is particularly necessary that the movable reflector at G be an excellent 

 optical plate, i or more inches square. When the plate at G (which is at 

 the extremity of the horizontal pendulum) rotates over a small angle 6, the 

 reflected rays d" and d'" now diverge in opposed directions from the center 

 C on the face of the opaque mirror N, and pass to the distant foci F" and F'", 

 where they are now at a distance x apart. If the rotation of the horizontal 

 pendulum were 6, the positions of the beams would be exchanged (see F' 

 and F 1V ). In other words, if the pendulum vibrates, the two foci F" and F'" 

 move in opposed directions, passing through each other, when the normal 

 position is instantaneously assumed, irrespective of the amplitude of vibra- 

 tion. It may be noted that a similar adjustment may often with advantage 

 be attached to any ordinary pendulum. 



The mounting of the plate G and the mirrors M, N, etc., is identical with 

 that of the interferometer described in the next section (the plate G is there 

 replaced by a transparent grating) and need not be treated here. Necessarily 

 the collimator and the mirrors M and N are attached to the same pier which 

 carries the horizontal pendulum, to the end of which the mirror G is attached ; 

 but the horizontal pendulum and its case must otherwise be quite independent 

 of the goniometric apparatus. 



2. Equations. It will be convenient to suppose the foci F, F", F'" to lie 

 in the plane of the mirror M, and the two mirrors M and TV to be equidistant, 

 so that d = d f , taken from the plate G as an ideal plane. Let a be the angle 

 between the normal to AT and the direction of the incident pencil; i.e., let a 

 be the angle between the mirrors, made as small and as convenient as prac- 

 ticable. Then if the mirror at G rotates over any angle 6 = b/2, the distance 

 apart x of the foci F" and F'" will be 



( \ rl ^ 2b ( I _L I \ 



cos(a-d) Vcosa+fr^cosfc/ 



This equation may be transformed to 



/ cos 2 b i cos b \ 



(2) * = 40 tan 6 - f H --- -, - rr ) 

 w Vcos 2a+cos 26 2 cos (a o) / 



