28. 



NOTE ON THE CONSTANT OF LUNAR PARALLAX. 



[From the Monthly Notices of the Royal Astronomical Society, Vol. XL. (1880).] 



FROM the report of a discussion which took place at a late meeting 

 of the Society, I have reason to believe that an explanation of the ap- 

 parent discrepancy between the value of the constant of parallax given by 

 me in the Appendix to the Nautical Almanac for 1856, and in the Monthly 

 Notices, vol. xiii. p. 263, and the value of the constant found by Hansen 

 in the Introduction to his Lunar Tables, may not be unacceptable to some 

 of our members. 



It will be proper to begin this explanation by recalling to mind that 

 my formula, in the article of the Monthly Notices above referred to, does 

 not represent the parallax itself, but rather the sine of that quantity 

 converted into seconds of arc by dividing by sin 1" or, which is the same 

 thing, by multiplying by the number of seconds in the arc equal to the 

 radius. The employment of the sine of the parallax instead of the parallax 

 itself appears to be desirable both on theoretical as well as practical grounds. 



In the first place, the sine of the parallax, being proportional to the 

 reciprocal of the radius vector, is the quantity given directly by the lunar 

 theory, and, in the next place, it is the same quantity which is wanted 

 in the reduction of lunar observations. 



What I have called the constant of parallax in the papers above 

 referred to is, then, the constant term in the expression for the converted 

 sine of the parallax, supposing the periodic terms to be expressed in cosines 



