26 



SOLAR DIURNAL VARIATION 



The hours of no semi-annual change are 6 A. M. and 7 P. M. ; the greatest changes 

 take place about 2 A. M. and 4 P. M., with a range of .000370 and .000328 parts 

 of the force respectively. 



The turning epochs are found from the variations at the hours 6 A. M. and 7 

 P. M. The following numbers are the differences from the respective annual means. 



For 20 h the sign has been changed. 



All expressed in units of the sixth place of decimals. 



The values in the last column are represented by the formula : 



A a = 0.000075 sin (6 + 280) + 0.000025 sin (26 + 131) 



6 counting from January 1st. The change of sign occurs about April 4th and about 

 September 12th, on the average, therefore, the change takes place about three days 

 after the equinoxes. 



ANALYSIS OF THE SOLAR-DIURNAL VARIATION OF THE TOTAL FORCE. 



In the following expressions of the solar-diurnal variation of the total force, is 

 counted from midnight at the rate of 15 an hour ; a positive sign indicates increase 

 of total force, a negative sign the reverse. The coefficients are expressed in parts 

 of the force. The formulas are deduced directly from Table VIII. 



For January ,A f = 0.000139 sin (8 + 318O 14') + 0.000157 sin (28+ 37 57') + 0.000020 sin (38 + 217) 



For February A, = 0.000215 sin (8 + 276 00') + 0.000143 sin (28 + 41 01') + 0.000060 sin (38 + 96) 



For March A r = 0.000148 sin (8 + 284 00') + 0.000106 sin (28 + 31 27') + 0.000014 sin (38 + 242) 



For April A, = 0.000283 sin (8 + 270 27') + 0.000084 sin (28 + 342 03') + 0.000042 sin (38 + 74) 



For May A, = 0.000383 sin (8 + 264 08') + 0.000084 sin (28 + 325 13') + 0.000062 sin (38 + 108) 



For June A ( = 0.000470 sin (9 + 266 26') + 0.000108 sin (28 + 2 57') + 0.000016 tin (38 + 96) 



For July A f = 0.000513 sin (8 + 265 24') + 0.000103 sin (28 + 344 53') +0.000036 sin (38 + 126) 



For August A f = 0.000500 sin (8 + 259 41') + 0.000109 sin (28 + 29 29') + 0.000025 sin (38 + 193) 

 For September A r = 0.000405 in (8 + 252 37') + 0.000097 sin (28 + 15 05') + 0.000010 sin (39 + 163) 



For October A, = 0.000170 sin (fl + 307 00') + 0.000084 sin (29 + 45 35') + 0.000033 sin (38 + 44) 



For November A f = 0.000122 sin (8+266 37') +.0.000074 sin (28+ 68 28') + 0.000010 sin (39 + 119) 



For December A, = 0.000136 sin (9 + 317 52') + 0.000112 sin (28+ 46 38') + 0.000017 sin (38 + 234) 



The months from April to September are counted as summer months ; those from 

 October to March as winter months. 



For Summer A, = 0.000426 sin (8 + 262 51') + 0.000095 sin (28 + 358 00') + 0.000026 sin (33 + 114) 

 For Winter A r = 0.000146 sin (8 + 292 00') + 0.000110 sin (28 + 43 20') + 0.000007 sin (39 + 1 1 !i ) 

 For Year A, = 0.000277 sin (8 + 270 45') + 0.000095 sin (28 + 22 29') + 0.000018 sin (38 + 115) 



