Where ds is the length of the element.
Hence the flux through dS is qdw.
According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).
This therefore expresses the secondary disturbance at a distance r and in a direction making an angle cp with OZ (the direction of primary vibration) due to the element dS of the wave-front.
If, instead of supposing the motion at dS to be that of the primary wave, and to be zero elsewhere, we suppose the force operative over the element dS of the lamina to be that corresponding to the primary wave, and to vanish elsewhere, we obtain a secondary wave following quite a different law.
B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.
Then let a small, very short cylinder be described of which dS is a section, and the generating lines are normal to the surface.
The cylinder is of volume u dt dS, so that the product of this and expression (9) must give the number of impacts between the area dS and molecules of the kind under consideration within the interval dt.
Taking co-ordinates in the plane of the screen with the centre of the wave as origin, let us represent M by, n, and P (where dS is situated) by x, y, z.
Construct a small cylinder inside the gas, having dS as base and edges such that the projections of each on the coordinate axes are udt, vdt, wdt.