72 



DISCUSSION OF THE I X F I. F K N (' K OK T II K MOON 



(A.) 



+1.5 

 +1.0 

 +0.5 



a 







0.5 



LuXAR-DlCRXAL VARIATION OF THE HORIZONTAL FORCE IN Sl'MMKK AM) \V INTER. 



I 1 1 r~ 



2.0 



\ 



0" 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 h 

 U. C. (Western hour angles of the moon.) L. C. (Eastern hour angles of the rnoou.) U. C. 



-- summer deflection. 

 - ...... winter deflection. 



If there is any marked difference in the lunar diurnal variation in the summer 

 and winter season, the summer range is slightly greater than the winter range; as 

 to the epoch, there is no doubt that in winter the lunar maxima and minima are 

 earlier than in summer. It is a remarkable fact that we have found the same fea- 

 tures in the lunar effect on the declination, viz., a greater amplitude in summer and 

 an earlier occurrence of the maxima and minima in winter; the amount of the 

 shifting of the two curves appears to be nearly the same. From the ten year series 

 of observations at Prague (1840-49) Mr. Karl Kreil found a larger lunar effect in 

 the summer months than in the winter months. 



Recurring to the final values of the lunar-diurnal variation of the horizontal force, 

 as given in Table VIII., they can be represented by the usual Bcsselian form of 

 periodic functions. 



The angle 6 counts from the moon's upper culmination westward at the rate of 

 15 to an hour; a + sign indicated greater, a sign, less force than the average 

 normal. The observed values are represented by the following expression: 

 HZ = 0.01 + 0.40 ain (6 + 13 29') + 0.60 sin (26 + 38 43') + 0.155 sin (3 6 



+ 244 31'). 



The three coefficients arc expressed in scale divisions; if expressed in parts of the 

 horizontal force the equation may be written as follows: (M signifies millionth parts 

 of the force.) 



MM M M 



// c = _ ().3f> + U.60 sin (0 + 13.o) + 21.90 .sin (2 + 38. 7) + 5.64 sin (3 + 



If expressed in absolute measure and if n = number of hours after the upper cul- 

 mination, it may be written 



MM M M 



1.5 + 61.0 ain (15 n + 13.5) + 91.5 ain (30 n + 39) + 23.6 sin (45 n + 



244.5.) 



