EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 39 



They are about equally clear in all positions. A displacement at the mirror 

 N of about 4 cm. per meter, i.e., 0.04 radian, equivalent to a rotation of 2.3 of 

 the reflected ray, or a rotation of 1.15 for the grating, was within the scope 

 of the interferometer and the tests were made within this limit. It is far in 

 excess of anything required in the horizontal pendulum. No doubt if the 

 mirror N had been wider, the ellipses could have been retained for larger angles 

 of rotation of the grating, though they would in such a case travel several 

 times through the spectrum. The micrometer at M would have to be used. 

 If long columns of glass are to be inserted in either beam (GM or GN) the 

 concave mirror is not available, since the direct slit images will then have 

 different focal positions. The rays issue from the plane-parallel column, 

 parallel to this focal direction, but from a virtual focus nearer the concave 

 mirrors. Hence, if the column is placed in the beam GM, the beam GN will, 

 as a rule, have to be correspondingly shortened. The algebraic relations are 

 complicated. 



22. Observations with the interferometer. The horizontal pendulum with 

 which the following observations were made had the following constants, M 

 being the total mass of the fixed parts, m the attached mass, h the distance 

 of the center of gravity from the axis, R the distance of the vertical line of 

 light on the grating (also mean distance of m and of FR) from the axis, <f> the 

 inclination of the axis : M = i , 2 50 grams ; m = 2 2 7 grams ; h = 80 cm. ; R = 1 1 1 .3 

 cm. The observed periods (primes refer to the loaded pendulum) for M and 

 M-\-m were 7=18.48 seconds; 7' = i8.87 seconds. Thus 1 = 85.1 cm.; 



<p=a/d = o. 01081 radian = o.62 



and // = 7, 3 94 cm.; L = 8, 488 cm.; #' = 7, 834 cm.; ^ = 8,853 cm. 



Since 6 = AN/2R when AAf is the mean displacement for the horizontal 

 deflection (0) of the pendulum, 



a= io J X4.86AAf radians. 



Thus, if AAf = io- 4 cm., a= io- s second of arc, or the change of a per vanish- 

 ing interference ring (A7V=io~ 6 X3o) is 0.000310 second of arc. Since 7 

 may easily be increased over 3 times, this limit may be reduced to a = .000030" 

 per ring. 



Similarly, the forces at distance R from the axis of the horizontal pendulum 



are 



m R^ 

 + M h 



Thus if AAf=io- 4 cm., F' R = o.oo$4 dyne or about 0.0016 dyne per vanishing 

 interference ring, in case of the pendulam loaded with the disk m. 



In the graph which follows an example is given of a series of observations 

 made for 6 and a, and no further explanation will be needed. Since 

 a =(pQ o.oio80, a need not be recorded. 



