J. M. Schaeberle—Lateral Astronomical Refraction. 469 
Now the term r,—r, being due to the difference in the density 
of the atmosphere at the two stations, the layers of the same 
density will not be parallel to the horizon. The equivalent 
inclination of the layers of equal pressure, for a uniform tem- 
perature, will depend upon the term eet adh, while the 
0 
sure, will depend upon the term ¢(c,—7,)=Jh’. ese layers 
and meridian planes will then be respectively, 
Al ' , 
> sin ¥, cil sin’, and a cos ¥, coe P. 
Hence the complete expressions for 4a and dz will become 
a fOr; An’ . ° ! 
4a= a (5 sin Y +57 sin (180° + ¥ )) cos z sec 0 
Ama cos YW + ls cos (180° + v')) sec? z, 
.If D and D’ are expressed in miles, 4h and 4h’ must also be | 
expressed in the same unit. As the adjacent lines on 
maps differ by 0°10 inch for the isobars, and by 10° F. for the 
isotherms, we have* 
O10. ,_. 9°59 
dh= = 512 Ah! = — 
Now let 6 denote the inclination of the axis of rotation of a 
meridian instrument, then if for 6 we substitute 
ra > sin WY oat sin (180° + vy) 
5°12. 
D by 
and use this value in the reduction of the observations, the 
corrections to the times of transit, for meridian refraction In 
right ascension, will be wholly allowed for. 
* If still greater accuracy is desired, the mean of the two given pressures 
should be used in place of 29°6. 
