228 NOTE ON THE CONSTANT OF LUNAR PARALLAX. [28 



Also Captain Kater's determination of the length of the seconds' pendulum 



in London is 



39-13929 inches = 3-2616075 feet. 



Hence as the square of the number of vibrations made at a given 

 place in a given time varies inversely as the length of the pendulum, we 

 derive the value above given for P. 



The values of the fundamental elements employed by Hansen are the 

 following : 



^ = 80, 

 m 



A =(5377157 metres, 



7^ = 6370063 



^ = 0-992666 



and 7?! and P, belong to a point the sine of the geocentric latitude of 



. 1 

 which is -p . 



v" 



The corresponding values of R and P for a point the sine of whose 



geographical latitude is -j= are the following : 



V'3 



7^ = 6370126 metres, 

 P = 0-992651 



And the constant term of the sine of the equatorial horizontal parallax 

 may be represented either by 



/ M A* \ h I M A' \* 



/ J.rj_ }. \ / T 1 / \ 77 



(M+mE'Pj y [M+mRfPJ '' 



In my calculation of the factor F, I took into account terms of the order 

 of the square of the Earth's compression. It would otherwise have been 

 useless to distinguish between R-P and R l 'P l or between F and 7^. 



At the time when Hansen's paper appeared in the Astron. Nachr. Bessel's 

 latest determination of the figure and dimensions of the Earth was not 

 available. Hansen employed an earlier determination given by Bessel in 

 Astron. Nachr., Vol. xiv., p. 344, in which the results were affected by an 

 error in the calculation of the French arc of the meridian which was 

 discovered later. 



