466. J. M. Schaeherle—Lateral Astronomical Refraction. 
Arr. LVI.—Laieral Astronomical Refraction; by 
J. M. SCHAEBERLE. ~ 
IN astronomical investigations where an extreme limit of 
can, in general, be eliminated. 
In the theory of astronomical refraction as given by Laplace, 
Bessel and others, each investigator assumes that the refraction 
always takes place in a vertical plane, and all refraction tables 
in use at the present time are constructed on this hypothesis, 
which therefore, assumes that all layers of atmosphere of the 
same density, over any given locality, are parallel to the horizon. 
That such an assumption is frequently the cause of errors, by no 
means insensible, which can, at most observatories, be removed 
by computation, will now be shown. 
Let us suppose that two observers at points A and B, on the 
same level and separated by the short distance D, observe at the 
same instant, equal temperatures, the barometric pressures how- 
ever being p, ow in order that the pressures over the 
two stations shall be the same, the observer at B must ascend 
through the distance 4h corresponding to a decrease in the pres- 
sure p, equal to p,—p, A line drawn from A to the elevated 
: Py edagocag! 
station will then be the line of equal pressure, and the inclina- 
tion of this line to the horizon will equal tan-*s) which, since 
: : 4h 
this angle will always be small, can be placed equal to D: 
As the differences between the refractions computed for 
inclined and for horizontal strata will always be very small, an 
error in the assumed law of refraction will have little or D0 
effect on these differences; terms of the second order becoming 
sensible only at great zenith distances. The familiar expresso? 
' r=a tan z 
giving nearly the observed mean refractions, and nearly corre- 
sponding to the refractions that would be produced by a homo- 
geneous atmosphere 5°12 miles high, having an index of refrac- 
tion m=1-00028, can for the present purpose be assumed to 
‘represent the observed mean refractions. 
