of Ediiibiirgh, Session 1882-83. 
129 
Monday, 19^^ March 1883. 
Professor DOUGLAS MACLAGAN, M.D., Vice-President, 
in the Chair. 
The following Communications were read : — • 
1. On the Impossibility of Inverted Images in the Air. 
By Edward Sang. 
It is narrated that a physician, having given cogent reasons to 
show that there could be no recovery, and somewhat disconcerted 
by the return of sound health, yet maintained the cogency of his 
pathological arguments. The present may be a new edition of the 
same story ; however, we shall advance the arguments, and leave it 
to futurity to tell whether there be any patient at all. 
In order that an inverted image of any object be seen in the 
air, it is, in the first place, requisite that the light from that object, 
proceeding obliquely upwards, be bent again down to reach the eye 
of the observer; and, in the second place, that this retrofleetion 
occur in a determinate manner, so that the lights proceeding from 
different parts of the object may arrive in contiguous directions. 
These effects must be produced by the action of the air. The law 
according to which transparent media change the direction of light 
has been well known from direct experiment, and the index of re- 
fraction of air has been carefully measured. 
In proceeding upwards, the light reaches air of gradually decreas- 
ing refractive power, so that the path is curved, the form of the 
curve depending on the law of diminution of the air’s density, and 
also on the earth’s roundness. The manner of the diminution of 
density is imperfectly known, and hence astronomers encounter 
great difficulty in investigating the amount of refraction for the 
stars ; that amount, in fact, being computed from empirical formulm. 
Yet there are relations among the heights, refractive powers and 
directions, very easily investigated ; and, because of its great sim- 
plicity as well as for the sake of those who may not previously have 
looked at the matter or who may have been frightened by the dis- 
play of algebraic symbols, I shall here give the analysis. 
If the air were composed of concentric layers, each, within itself, 
