TRANSACTIONS OF THE SECTIONS. 41 



On Atmosplierk Bef faction of Inclined Rays, and on the Path of a Level Ray. 

 3y James Thomson, LL.D., Professor of Civil Enciineering in Queen's 

 College, Belfast. 



Many years ago, in considering, from a civil-engineering point of vle-w, the patli 

 of a level or nearly level ray of light through the atmosphere, with special refer- 

 ence to corrections in observations -ndth the levelling-instrument, the author found 

 himself unable to rest satisfied with the views put forward on the subject in books 

 on Practical Geodesy, or in any writings with which he was acq^uainted. The only 

 views which he then met with were to the following efl'ect : — 



The atmosphere was regarded as consisting of an infinite number of infinitely thin 

 horizontal laminae, with a gradual increase of density in passing downwards through 

 these laminse, so that the density in each lamina would differ only in an infinitely 

 small degree from that in the one immediately above it, or from "that in the one 

 immediately below it. It was then inferred that a ray of light, passing obliquely 

 downwards through the laminaj, must, at each successive transition from one lamina 

 into the denser one next below, sufi'er refraction so that its course must make a less 

 angle with a normal to the laminre in the denser lamina than it did with the same 

 normal in the rarer one immediately above, and that the path of the ray must 

 therefore be curved with the concave side downwards. From this reasoning, with- 

 out noticing that its whole foundation, in oblique transition of the light across 

 laminae with gradual change of density in those successive!}' traversed, vanishes in 

 the case of a horizontal ray, authors have tacitly assumed that a ray proceeding 

 through the atmosphere, so as to enter a levelling-instrument horizontally, should 

 be expected to be curved with its underside concave. In one sense such a conclu- 

 sion, in connexion with the mode stated in which it has been inferred, may be 

 partly justified — that is, if the consideration be that a ray coming from a consider- 

 able distance so as to enter an instrument horizontally must have previously been 

 descending obliquely through the nearly spherical level laminre of the air which are 

 rounded in correspondence with the figure of the earth. Rays arriving level at an 

 observer's station from the rising or setting sun afford an instance of what is here 

 referred to, and one in which the light has descended obliquely through the whole 

 depth of the atmosphere. It may readily be admitted, from the usual reasoning 

 cited above, that any such ray will be curved and concave downwards at all parts 

 of its course where it is sensibly descending ; but as the advancing ray gradually 

 approaches to the level position with a gradual diminution down to cessation of 

 oblique descent through the lamina, it might still, so far as that reasoning would 

 indicate, be held an open question whether the curvature of the ray would approach 

 towards zero, or whether it would approach towards a maximum, or generally 

 what might be the condition as to cuv^■ature or straightness of the ray, as the ray 

 comes to be level. 



The author proposed the question in 186.3 to Professor Purser, of Queen's Col- 

 lege, Belfiist ; and Prof. Purser, on the moment, made out an analytical investiga- 

 tion which depended on the proportionality of the sine of the angle of incidence to 

 the sine of the angle of refraction holding good for infinitely thin laminaj differing 

 infinitely little in densit}', and holding good to the extreme case in which the ray 

 becomes parallel to the lamina?. This investigation appeared to the author of the 

 present paper to be consistent with all physical conditions ; and he regarded it as an 

 hypothesis likely to be full}' confirmed by experimental investigations, if at any 

 time experiments bearing on the subject should be found practicable. From direct 

 experiments, however, on the curvature of a ray of light in the atmosphere, no 

 accurate results are to be hoped for, on account of the great and constantly varying 

 disturbances to which the ray is subject, through changes in the distribution of heat 

 and moisture in the air, and movements of its parts among one another, and other 

 varying influences. 



Prof. Purser's investigation, which from the first has been deemed by the author 

 of tlie present paper to be of much interest and value, was to the following eflPect, the 

 question being : — 



la find ic/wthcr a ray of liylit 2)nssi)iy iiijinitcly nearly horizontally throuyh the 

 atniosphire icill he bent with a finite curvature, or not bent at all; and ^vhefher tlte'ciirva- 



