STATIONS NEAR THE NORTHERN BOUNDARY OF OHIO. 257 



case, it must vary with the observer, and with the optical capacity of the 

 instrument used. It would also vary with the different limbs ; since the 

 transit of the first limb exhibits the approach to tangency of the convex 

 side of an arc, that of the second limb of the concave side of the same. 

 Granting the existence of such an equation, it could hardly be the same 

 for each limb; the difference, then, remains constant, with the same ob- 

 server and same instrument, and cannot be eliminated otherwise than 

 by a multiplication of observers and instruments. Whatever be the 

 cause of the error of irradiation, experience has shown that the results 

 of moon-culminations, like those of eclipses of Jupiter's satellites, ap- 

 proach nearer to the truth in proportion as the instruments approach to 

 equality in their optical powers. The method of computing the cor- 

 rection of Burckhardt's semidiameter, from observations of both limbs 

 of the moon, when nearly full, is given by Professor Airy, in the Green- 

 wich Observations for 1836. His method, combined with Encke's 

 formulae, in the Berlin Jahrbuch for 1832, p. 251, may be thus analy- 

 tically expressed. 



S = the correct sidereal time of the moon's semidiameter 



passing the meridian, 

 S' = the computed time, 



2 1 = the observed duration of the transit of the moon's de- 

 fective diameter, 

 a = the sid. time of U. C. of moon's defective limb, 

 A and D = the sun's R. A. and dec, 

 ( S — I) = S' COS. D (1 -h cos. (*-A) ) 



= compliment of duration of transit of moon's defective 

 diameter, 

 i = S — S ' = correction of Burckhardt's semidiameter, 

 m = the increase of the R. A. of the moon's bright limb 



in arc, in a lunar day, 

 X = Burckhardt's constant value of "'""f semidiameter, 



moon's horizontal parallax, 



^ = the moon's horizontal equatorial parallax, 



8 = the moon's true declination, 



„, 360° H- m . 



^ = 360° • ^ ^ ''^- ^ 



