O F THE DIP. 



19 



The diagram shows the hours of no semi-annual change as follows: 5| A.M.; 

 1 P. M.; 3 P. M., and 7 P. M.; greatest change at 10 A. M., secondary at 6 P. M., 

 with a range of 0/51 and 0/18, respectively. 



The turning epochs are found by the variation at the hour 10 A. M., when the 

 monthly differences from the annual mean are as follows : 



These values are represented by the formula 



A a = 0.'35 sin (6 + 253 38') + 0/10 sin (20 + 328 39') 



the angle 6 counting from January 1st. This formula gives a change of sign for 

 the middle of April and the middle of October, or about 25 days after the equinoxes. 



ANALYSIS OP THE SOLAR-DIURNAL VARIATION OP THE DIP. 



In the following formula? expressing the solar-diurnal variation of the dip for 

 each month, summer, winter, and year, the angle counts from midnight at the 

 rate of 15 an hour ; a positive sign indicates increase of north dip, a negative sign 

 the reverse. The expressions are derived directly from Table IV. 



For January A. = 0.'24sin (9 + 284O 19') + 0/33 sin (28+ 78 15') + 0.'14 sin (39+282O) 

 For February A, = 0.'34 tin (9 + 246O 28') + 0.'30 sin (28 + 75 40') + O.'OS sin (38 + 308O) 

 For March A ( = 0.'40 sin (8 + 251O 24') + 0.'24 tin (29 + 85O 27') + 0.'12 sin (38 + 303O) 

 AJ = 0.155 sin (8 + 2630 10') + 0.'23 sin (28 + 109 36') + O.'IS tin (38 + 330) 

 A, = 0/50 sin (9 + 2710 33') + O.'22'sin (28 + 146O 40') + 0.'14 sin (39 + OO) 

 A ( = 0/53 sin (9 + 2740 37') + 0/2] sin (28 + 109O 03') + 0.'19 sin (38+ 331O) 

 A l = 0.'G4sin (8 + 2750 34') + 0. '24 sin (28 + 131O 08') + 0.'14 sin (38+322O) 



For April 

 For May 

 For June 

 For July 

 For August 



A, = 0.'68 sin (9 + 272O 55') + 0/32 sin (28 + 132O 56') + 0.'24 sin (38 + 331O) 



For September A, = 0/70 sin (8 + 260O 14') + 0/27 sin (28 + 116 49') + 0.'23 sin (38 + 349O) 

 For October A S = 0/41 sin (8 + 256O 31') + 0/27 sin (28 + 101O 19') + O.'ll in (38 + 335O) 

 For November A, = 0/28 sin (8 + 259O 21') + 0/27 sin (29 + 99O 30') + 0/08 stn (38 + 328O) 

 For December A, = 0/20 sin (9 + 258O 09') + 0/37 sin (29 + 77O 45') + 0/12 sin (38 + 258O) 



We have also : 



For Summer A, = 0/60 sin (8 + 269O 37') + 0/25 sin (29 + 125O 02') + 0/18 sin (39 + 335) 

 For Winter A, = 0.'30sin (8+ 260 57') + 0/29 sin (28+ 85O 12') + 0/10 sin (38 + 300O) 

 For Year A, = 0/45 sin (8 + 266O 47') + 0/25 sin (29 + 103O 19') + 0/13 sin (38 + 322O) 



Summer is comprised of the months from April to September; winter of the 

 months from October to March. 



The following comparison of the observed 'and computed values for August shows 

 about average differences ; in general the summer values are a little better repre- 

 sented than the winter values. 



