740 



J. A. BROUN ON THE LUNAR DIURNAL VARIATION OF 



Jan. y = 



— 00233 cos t 



?- 



0-0143 



sin ( 



? + 



•2264 



cos 



20- 



0-0442 



sin 20 



Pro! 



). error 0-018 



Feb. 



— 



•0126 



>> 



— 



•0084 



» 



+ 



•1155 



» 



— 



•0463 



)> 



•011 



Mar. 



— 



•0290 



>) 



— 



•0633 



)> 



+ 



•0676 



)> 



— 



•0788 



j; 





'014 



April 



+ 



•0026 



)> 



— 



•0122 



>■> 



+ 



•0386 



)) 



— 



•0900 



» 





•009 



May 



+ 



•0406 



>> 



— 



•0134 



V 



— 



•0193 



>) 



— 



•0203 



j) 





■013 



June 



— 



•0045 



i> 



— 



•0142 



)) 



— 



•0532 



>> 



— 



•0082 



;; 





•013 



July 



— 



•0128 



» 



+ 



•0318 



J) 



— 



■0827 



7) 



+ 



•0350 



>J 





, -012 



Aug. 



— 



•0001 



» 



— 



■0089 



» 



— 



■0566 



)! 



+ 



•0378 



>> 





•017 



Sept. 



+ 



•0104 



>) 



+ 



•0566 



» 



— 



0358 



» 



+ 



•0511 



)) 





•010 



Oct. 



— 



•0246 



>> 



— 



•0206 



;; 



+ 



0415 



>> 



+ 



•0197 



)) 





•015 



Nov. 



+ 



•0158 



?> 



— 



■0611 



jj 



+ 



0904 



)> 



— 



•0008 



>> 





■014 



Dec. 



+ 



•0355 



>> 



— 



•0324 



;> 



+ 



1740 



» 



+ 



•0303 



» 





•012 



The following are the equivalent equations for the diurnal and semi-diurnal 

 periods, or, 



y = a\ sin (6 + c : ) + a' 2 sin (20 + c 2 ) . 



Jan. y 



Feb. y 



Mar. y 



April y 



May y 



June y 



July y 



Aug. y 



Sept. y 



Oct. y 



Nov. y 



Dec. y 



= 



0273 



sin 



(0 + 



238 



0151 



sin 



(0 + 



236 



0697 



sin 



(0 + 



204 



0126 



sin 



(0 + 



167 



0428 



sin 



(0 + 



108 



0149 



sin 



(0 + 



197 



0343 



sin 



(0 + 



338 



0089 



sin 



(0 + 



180 



0575 



sin 



(0 + 



10 



0321 



sin 



(0 + 



230 



0631 



sin 



(0 + 



165 



0481 



sin 



(0 + 



132 



24) + 



2307 sin (! 



14)+ • 



1244 sin ( 



35)+ ■ 



1038 sin ( 



45) + 



•0980 sin ( 



12) + 



0280 sin ( 



28) + 



0538 sin ( 



3) + 



■0898 sin ( 



3) + 



0681 sin ( 



25) + 



•0624 sin ( 



4) + 



0459 sin ( 



32) + 



0904 sin ( 



18) + 



•1766 sin( 



20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 

 20 + 



101 3) 



111 50) 



139 32) 



156 47) 



223 30) 



261 12) 



292 55) 



303 45) 



324 58) 



64 38) 



90 30) 



80 7) 



15. The conclusions from the observed and calculated variations are as 

 follow (see Plate XXVI.) :— 



1st, The mean lunar diurnal variation consists of a double maximum and 

 minimum of easterly declination in each month of the year. 



2d, In December and January, the maxima occur near the times of the 

 moon's upper and lower passages of the meridian ; while in June, they occur 

 six hours later, the minima then occurring near the time of the two passages of 

 the meridian. 



3d, The change of the law for December and January to that for June and 

 July, does not occur as in the case of the solar diurnal variation, by leaps in 

 the course of single months (those of March and October), but more or less 

 gradually for different maxima and minima. 



16. But the change of hours for the maxima and minima will be better seen 

 in the following table, where the epochs derived from the computed variations,* 

 as well as those deduced from the observed quantities are given. 



* The epochs for the diurnal and semi-diurnal periods are obtained directly from the values of c x 

 and c 2 in the preceding series of formulae ; those for both terms are obtained from the formulas by the 

 equation 



dv 



a = —„ 

 d0 



