510 C. Barus — Application of the Displacement 



4. Observations with a grating rotating on a fixed vertical 

 axis. — When the opaque mirrors M and JV are identically con- 

 cave and are put on the ordinary interferometer at a distance 

 equal to their radius of curvature from the stationary grating, 

 the latter may he rotated (without translation) as far as the 

 breadth of the opaque mirror JV permits, without readjust- 

 ment. The ellipses are not lost. Inasmuch, however, as 

 different thicknesses of glass are introduced into the rays 

 when the grating is rotated, the ellipses travel horizontally 

 through the spectrum from the red to the violet end or the 

 reverse. They are about equally clear in all positions. A dis- 

 placement at the mirror JV of about 4 centimeters per meter, 

 i. e., *04 radian, is equivalent to 2*3° of reflected ray, or a 

 rotation of 1*15° for the grating, were 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 pendu- 

 lum. No doubt, if the mirror JV 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 GJV) 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 GJV will, as a rule, have to be correspondingly short- 

 ened. The algebraic relations are complicated. 



5. 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 J^ R ) from 

 the axis, <f> the inclination of the axis, H the indicated length 

 and L the vertical pendulum length. M = 1250 grains ; m = 

 227 grams; h = 80 centimeters; JR == 111*3 centimeters. 



The observed periods (primes refer to the loaded pendulum) 

 for M and M + m were 



T= 18*48 seconds T' — 18*87 seconds- 



Thus i = 85*1 cm.; <f> = a / 6 = -01081 rad. = -62°, and 

 R = 7394 cm.; L = 8488 cm.; H! = 7834cm.; L '= 8853 cm. 



Since 6 = AJV/2R when AJV is the mean displacement for 

 the horizontal deflection (6) of the pendulum 



a = 1CT 5 X 4-S6 AlV radians. 



