198 Mr Cookson, The Effect of the Lunar Deflection 



The Effect of the Lunar Deflection of the Vertical on Latitude 

 Observations. By B. Cookson, M.A., Trinity College. 



[Received 30 November 1905.] 



The maximum tide-raising force of the moon on a point of the 

 earth's surface amounts to about 1/8,500,000 of gravity at the 

 point, and the maximum horizontal component of this force is 

 nearly 1/12,000,000. Thus, owing to this force, the plumb line 

 may be deviated through an angle of -^ 10 -6 x cosec 1", that is, 

 0"*017, or say 0"*02. The latitude of a point on the earth's surface 

 is defined by the direction in space of the plumb line at the point, 

 and the question arises whether it might not be possible to detect 

 its deviation by examining some of the large series of observations 

 which have been made in recent years with the zenith telescope. 



Since the latitude is found from the meridional zenith-distances 

 of stars, we require only the southward component of the moon's 

 tide-raising force : its value is 



3 Ma s 

 L = -t -^Tvj { sm 2$ cos 2 8 cos 2h 



— cos 2<j> sin 25 cosh 



+ sin20(l- 3sin 2 S)} (1), 



M = mass of moon, 

 E = mass of earth, 



a -— earth's radius, 

 D = distance between centres of earth and moon, 



<b = latitude of place, 



& = moon's declination, 



h = moon's hour-angle. 



For the present purpose we may take D as constant: we have 

 then three terms, the first with a period of half a lunar day, or 

 nearly 124 hours, the second with a period of one lunar day, and 

 the third depending on the moon's declination. Now suppose 

 that the latitude is found from the observed zenith distances of 



where 



