28] NOTE ON THE CONSTANT OF LUNAR PARALLAX. 229 



Hence the corrections to be applied to the logarithms employed by 

 Hansen in order to make them agree with those employed by me are the 

 following, expressed in units of the 7th decimal : 



Correction. 



M } +9 87 

 m] 



log^j + 25 



log(p) -150 



The correction to be applied to Hansen's value of the logarithm of the 

 constant term in the sine of the parallax is therefore 



25 + -(987-150) = 304 of the same units, 

 o 



And the corresponding correction of the constant term of the sine of the 

 parallax will be 0" - 24, and therefore according to Hansen's preliminary theory, 

 employing rny system of fundamental data, the value of this constant term 

 will be 3422"'26. 



In my independent transformation of Hansen's expression I found the 

 rather more precise value 3422"'264. 



This is less than my own value of the same constant by 0" - 06 nearly, 

 as stated in my paper in the Appendix to the Nautical Almanac for 1856. 



I there intimated my belief that Hansen's definitive theory would pro- 

 bably be found to introduce a correction to his former value of the constant 

 term in question, and this turns out to be the case. 



In Astron. Nachr., Vol. xvn., p. 298, the constant term in w which 

 denotes the perturbations of the natural logarithm of the reciprocal of the 

 radius vector, divided by sin 1", is given as 1345"'281, but in the Intro- 

 duction to Hansen's Lunar Tables this same quantity is given as 1348"'840. 

 Hence, the correction to the former value is 3"'559, and multiplying this 

 by sin 1" and by 3422" we find the corresponding correction of the constant 

 of parallax to be 0"'059, so that this constant becomes 3422"'323, a result 

 which agrees perfectly with my own. 



In this connection it may be worth mentioning that the only periodic 

 term in which I found any difference much exceeding 0"'01 between my 



