ON THE POSSIBLE DISTURBANCE OF A RANGE-FINDER BY ATMOSPHERIC REFRACTION DUE TO THE MOTION OF THE SHIP WHICH CARRIES IT.
[Transactions of the Optical Society, Vol. xx. pp. 125—129, 1919.]
THE suggestion has been put forward (as I understand by Lt.-Col. A. C. Williams) that the action of a range-finder, adjusted for a quiescent atmosphere, may be liable to disturbance when employed upon a ship in motion, as a result of the variable densities in the air due to such motion and consequent refraction of the light. That this is vera causa must be admitted; but the question arises as to the direction and magnitude of the effect, and whether or not it would be negligible in practice. It is not to be supposed that any precise calculation is feasible for the actual circumstances of a ship; but I have thought that a simplified form of the problem may afford sufficient information to warrant a practical conclusion. For this purpose I take the case of an infinite cylinder moving transversely through an otherwise undisturbed atmosphere, and displacing it in the manner easily specified on the principles of ordinary hydrodynamics. When the motion of the fluid is known, the corresponding pressures and densities follow, and the refraction of the ray of light, travelling from a distance in a direction parallel to the ship's motion, may be calculated as in the case of astronomical and prismatic dispersion or of mirage. It is doubtless the fact that in the rear of the disturbing body the motion differs greatly from that assumed; but in front of it the difference is much less, and not such as to nullify the conclusions that may be drawn. The first step is accordingly to specify the motion, and to determine the square of the total velocity (q) on which depends the reduction of pressure.
The motion of the fluid, due to that of the cylinder of radius c and moving parallel to oc with velocity U, is well known*. The problem may conveniently be reduced to one of "steady motion" by supposing the cylinder to be at rest while the fluid flows past it—a change which can make no
* See Lamb's Hydrodynamics, § 68.e to the line F. According to the interference theory, then, the range of coloration should be from the full red of C to the blue-green of F, and this is just about what is observed. The agreement must be admitted to be a strong argument in favour of the theory. So far as I have seen, so great a range cannot be found in the surface-colour of any dye, even with the aid of polarized light.