46 



DISCUSSION OF THE VERTICAL COMPONENT 



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

 the year ; at the liours 2 A. M. and 4 P. M. the cliange 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. INI. 

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

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

 changin" the sisn of the afternoon difference before taking the mean. 





2 A. M. 



Differences. 



4 P. M. 



Differences. 



Mean difference. 





0.000. 



0.000. 



0.(100. 



(1.000. 



000. 



.January .... 



+238 



+353 



—092 



—257 



+3(15 



February 











+033 



+148 



+ 198 



+033 



+058 



March . 











+086 



+201 



+ 020 



—145 



+173 



April 











—155 



—040 



+241 



+076 



—058 



May 











^346 



—231 



+313 



+ 148 



—190 



June 











—297 



—182 



+363 



+198 



—190 



July . 











—406 



—291 



+386 



+221 



—256 



August . 











—386 



—271 



+340 



+ 175 



—223 



September 











—304 



—189 



+356 



+191 



—190 



October . 











+066 



+181 



—033 



—198 



+190 



November 











—043 



+072 



—010 



—177 



+125 



December 











+ 139 



+254 



—092 



—257 



+256 



Mean 



—115 1 



+165 



> 





The figures in the last column are represented by the equation 



A„ = + 0.000260 sin (0 + 86°) + 0.000031 sin (2 d + 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 Yertieal Force. — For greater 

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

 I. have been expressed analytically. The angle 6 counts from midnight at the rate 

 of 15° an hour. 



For January, a„ = 714''.2 + 4.8 sm ( 6 + 134° 00') + 5.5 sin (2 9 + 224° 22') 



+ 0.8 sin (39 + 61°) 

 For February, a. = TIS'^.O + t.5 sin (9 + 91° 41') + 5.1 sin (2 9 + 226° 22') 



+ 1.6 sin (39 + 273°) 

 For March, A„ = 703".6 + 5.5 sin (9 + 98° 24') + 3.6 sin (2 9 + 220° 22') 



+ O.T sin (39 + 95°) 

 For April, a„ = lOl-'.S + 10.5 sin (9 + 89° 12') + 2.2 sin (2 9 + 175° 59') 



+ 1.3 sin (39 + 232°) 

 For May, a. = 093'>.5 + 13.1 sin (9 + 85° 17/) + 1.9 sin (2 9 + 144° 31') 



+ 1.8 sin (30 + 278°)' 

 For June, a„ = 689"".0 + 15.8 sin (9 + 87° 22') + 3.1 sin (2 9 + 193° 56') 



+ 0.4 sin (39 + 210°^ 



