208 PROCEEDINGS OF SECTION A. 
Analysis respecting the longer distances shows that, for lines 
greater than 30 miles, K may be taken as uniformly equal to -135, 
and for the results above outlined the co-efficient for shorter 
distances will be best represented by the following expression, in 
which D is the distance in miles :— 
K = :135 — -000081 (380 — D)*. 
Examination of some of the results obtained in the United 
States* shows that they exhibit the same need for bringing the 
distance in as a function, or what comes to the same thing, the 
height of the ray above the ground, for it may be assumed to var 
with the distance. It would seem then to be established that the 
practice of using an average value derived from the formula 
R — (ae Ae 
will need modification. It is to be noted that, in the above dis- 
cussion, Struves’ pressure factor » Where B represents the mean 
reading, in English inches, of the barometer at the place of 
observation, by which all co-efficients may be referred to sea level, 
has not been applied, the area covered being nearly enough at the 
one level to enable it to be disregarded without affecting the con- 
clusions. It should be observed too, that the co-efficient deter- 
mined above results, not the mean refraction, but the refraction 
at the usual time of observation, 2 to 4 p.m., when though less 
liable to fluctuation, it is really at one extreme of its daily 
range. 
In the absence of proper topographical surveys which would fix 
the height of the ray above the surface, it is of some importance to 
investigate the general effect of changing distance on the refraction. 
This w {Il be seen when it is remembered that the co-efficient is 
determinable only by the reciprocal observations which are usually 
made only on the longer lines of the survey, and that it is, as a 
rule, needed for application on the shorter lines, which are those 
fixing stations from which no observations have been made. The 
gre eat advance which photographic surveying has recently made 
leads to the hope that it may be usefully applied to obtaining 
such topographical information as is needed for a proper discussion 
of terrestrial refraction, both vertical and lateral. In the course 
of examining the refractions it has been a source of regret that 
the few photographs from each station, which were needed for 
this purpose, were not available. The usefulness of even such an 
approximate topographic survey for affording other information 
will be referred to later. 
Ke—se—— 
*U.S.C. and G. 8. Report for 1876, p. 371. 
