570 PROFESSOR TAIT ON MIRAGE. 
be regarded as constant throughout. Here J. THomson’s formula* is imme- 
diately and usefully applicable. For, if 0,,—0,, be the angles the ray makes 
with the horizon just after entering and just before escaping, we have 
WWE ot dp 
are a gg? 
where ¢ is the length of the vessel. But, if 6;,—0;, be its directions before 
entering and after escaping, we have approximately, 
O,=10,, 0,=pb,. 
Thus the whole change of direction is 
6! +0; = — i, 
depending only on the rate of change, not on the value, of the refractive index. 
Parallel rays, passing nearly horizontally through such a vessel, will all be bent 
in the direction in which the refractive index increases :-—but that which passes 
through the stratum of most rapid change of index will be the most bent, so 
that the illuninated portion of a sufficiently distant screen on which the rays 
fall will be terminated by a spectral band of which the violet is outermost. 
Measurements of the position of this band, from day to day, from hour to hour, 
or even (in some cases) from minute to minute, will give an extremely accurate 
mode of measuring the rate of diffusion. To interpret their indications, 
however, a determination must be made of the law which connects the 
refractive index of a mixture of the two fluids with the relative proportions 
in which they are mixed. And it may not always, or even usually, be the case 
that the stratum of greatest rapidity of change of refractive index is necessarily 
coincident with that of most rapid diffusion. From the former, however, the 
latter can always be found; and, so long as the original layers of the fluids 
remain in part unaltered by the diffusion, the knowledge of the plane and rate 
of greatest diffusion is sufficient for the complete determination of the other 
circumstances. I believe that many important questions connected with 
diffusion may be speedily and accurately investigated by this very simple 
method. I propose to give a detailed account of it, with experimental results, 
to the Society on a future occasion. 
* B. A. Report, 1870. Tomson finds by a simple process, for the curvature of a ray in a non- 
homogeneous medium, the expression 
where m is measured towards the centre of curvature. The result is seen to follow immediately from 
the corpuscular theory (in which =v) by multiplying both sides by py, for it is thus found to be merely 
the equation of acceleration of a corpuscle in the direction perpendicular to its path. It is really in- 
volved in Prop. I. of Wottaston’s paper (Phil. Trans., 1800). 
