φ = angle of deflection. d′ = corrected displacement (linear). r = radius of measurement. D = twice the distance between the mirrors. n = number of revolutions per second. α = inclination of plane of rotation d = deflection as read from micrometer. B = number of beats per second between electric Vt₂ fork and standard Vt₃ Cor = correction for temperature of standard Vt3. V = velocity of light. T = value of one turn of screw. (Table, page 126.) Substituting for d, its value or d×T×sec α (log sec α = .00008), and for D its value 3972.46, and reducing to kilometers, the formulæ become-- dT (3) tan φ = c′ ----; log c′ = .51607 r n (4) V = c ---; log c = .49670 φ D and r are expressed in feet and d′ in millimeters. Vt₃ fork makes 256.070 vibrations per second at 65° Fahr. D = 3972.46 feet. tan α = tangent of angle of inclination of plane of rotation = 0.02 in all but the last twelve observations, in which it was 0.015. log c′ = .51607 (.51603 in last twelve observations.). log c = .49670. The electric fork makes ½(256.070 + B + cor.) vibrations per second, and n is a multiple, submultiple, or simple ratio of this. Observations. Specimen Observation. June 17. sunset. Image good; best in column (4). The columns are sets of readings of the micrometer for the deflected image of slit. 112.81 112.80 112.83 112.74 112.79 81 81 81 76 78 79 78 78 74 74 80 75 74 76 74 79 77 74 76 77 82 79 72 78 81 82 73 76 78 77 76 78 81 79 75 83 79 74 83 82 73 73 76 78 82 ------- ------- ------- ------- ------- Mean = 112.801 112.773 112.769 112.772 112.779 Zero = 0.260 0.260 0.260 0.260 0.260 ------- ------- ------- ------- ------- d = 112.451 112.513 112.509 112.512 112.519 Temp = 77° 77° 77° 77° 77° B = + 1.500 Corr = - .144 ------- + 1.365 256.070 ------- n = 257.426 257.43 257.43 257.43 257.43 r = 28.157 28.157 28.157 28.157 28.157