46 



DISCUSSION OF THE VERTICAL COMPONENT 



At 5| A. M. and 7 P. M. there is no change in the diurnal variation throughout 

 the year ; at the hours 2 A. M. and 4 P. M. the change is a maximum, viz : range 

 equal 0.000403 parts and 0.000333 parts of the force, or equal 0.00517 and 0.00427 

 when expressed in absolute measure. 



The turning epochs of the annual inequality as found from the hours 2 A. M. 

 and 4 P. M. are derived from the following table, in which the numbers are 

 expressed in parts of the force ; the numbers in the last column were obtained by 

 changing the sign of the afternoon difference before taking the mean. 



The figures in the last column are represented by the equation 



A a = : + 0.000260 sin (0 + 86) + 0.000031 sin (20 + 180) 



the angle counting from January 1st at the rate of 30 a month. According to 

 this expression the transition of the inequality from a positive to a negative value, 

 and vice versa, takes place in the first quarter of April and October, or about 17 

 days after the equinoxes. The retardation of the phenomenon in the declination, 

 horizontal and vertical force is, therefore, 10, 22, and 17 days respectively, or 16 

 "days on the average. 



Analysis of the Solar-Diurnal Variation of the Vertical Force. For greater 

 facility of the investigation, and for purposes of comparison, the numbers of Table 

 I. have been expressed analytically. The angle counts from midnight at the rate 

 of 15 an hour. 



For January, A. = 714 d .2 + 4.8 sin ( e + 134 09') + 5.5 sin (2 + 224 22') 



+ 0.8 sin (30 + 61) 

 For February, A, = 712 d .O + 7.5 sin (9 + 91 47') + 5.1 sin (20 + 226 22') 



+ 1.6 sin (SO + 273) 

 For March, A. = 703 d .6 + 5.5 sin ( e + 98 24') + 3.6 sin (29 + 220 22') 



+ 0.7 sin (36 + 95) 

 For April, A, = 701 d .3 + 10.5 sin ( + 89 12') + 2.2 sin (20 + 175 59') 



+ 1.3 sin (30 + 232) 

 For May, A. = 693 d .5 + 13.1 sin (0 + 85 17') + 1.9 sin (20 + 144 31') 



+ 1.8 sin (30 + 278) 

 For June, A, = C89 d .O + 15.8 sin (6 + 81 22') + 3.1 sin (20 + 193 56') 



+ 0.4 sin (39 + 210) 



