measurement of the difference of time required for the two pencils to traverse the circuit would furnish a quantitative test of the entrainement.
But it is not necessary that the path should encircle the globe, for there would still be a difference in time for any position of the circuit.
This difference is given by the formula
where V is the velocity of light, v the velocity of the earth's surface at the element of path ds, and θ the angle between v and ds.
If the circuit he horizontal, and x and y denote distances east and west and north and south respectively, and φ the latitude of the origin, and R the radius of the earth, then for small values of y/R we have approximately
The integral being taken round the circuit the first, term vanishes, and if of the circuit,
The corresponding difference of path for equal times expressed in light-waves of length λ is
Thus, for latitude 45° ; the velocity of light is in the same units, and the length of a light-wave is : which approximate values substituted in the preceding formula give
Thus if the circuit be one kilometre square
The system of interference-fringes produced by the superposition of the two pencils — one of which has traversed the circuit clockwise, and the other counterclockwise — would be shifted through seven-tenths of the distance between the fringes, in the direction corresponding to a retardation of