The Formulæ.
Reading edition
The formulæ employed are—
d′
(1) tan φ = -----
r
2592000″ × D × n
(2) V = -----------------
φ″
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.