8 



LUNAR EFFECT 



These results, I, II, III, when expressed analytically by means of Bessel's form 

 of periodic functions, and when treated by the method of least squares, are repre- 

 sented by the following equations, in which the moon's hour-angle is reckoned 

 from the upper transit westwards at the rate of 15 to each hour. AC represents 

 the lunar diurnal variation. 



Group I, 1840-'41. A^ = -f O'.OOS + 0'.063 sin. (e + 92) + OM89 sin. (29 + 67) 

 " II, 1842-'43. A C = O'.OOG + O'.OSO sin. (e + 263) + 0'.282 sin. (29 + 63) 

 " III, 1844-M5. A C = O'.OOO + 0'.075 sin. (o + 292) + 0'.219 sin. (29 + 88) 



The numerical results from these equations are presented graphically on the 



following diagram. 



LuNAB-DlDRNAL VARIATION OP THE MAGNETIC DECLINATION. 



Oh. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24>>. 

 U. C. L. C. U. C. 



from 4,900 observations in 1840, '41. 



from 6,715 observations in 1842, '43. 



from 10,029 observations in 1844, '45. 



The curves all agree in their distinctive characters, and show two east and two 

 west deflections in a lunar day, the maxima W. and E. occurring about the upper 

 and lower culminations, and the minima at the intermediate six hours. The total 

 range hardly reaches 0'.5. These results agree generally with those obtained for 

 Toronto and Prague. 



From 8,000 to 10,000 observations seem to be required to bring out the results 

 satisfactorily, and the best results are derived from the use of all the groups. 



The following table contains annual sums of deflections for each hour, and the 

 resulting lunar-diurnal variation from the 21,644 observations available for the 

 purpose : 



