216 REPORT— 1895. 



months a few hours before niidnight. To attain certainty iu such a case 

 one would require a very lai'ge number of observations for each month in 

 the year. When the results of several months are grouped together, 

 secondary maxima, unless occurring very nearly at the same hour in each 

 month, are apt to disappear. The smoothness of the mean curve for a 

 year or a half-year is doubtless in part due to the elimination of observa- 

 tional errors by means of the large number of observations included ; but 

 in some cases at least it arises from what may be termed the suicide of 

 secondary phenomena. Mutual extermination of very delicate phenomena 

 may even arise when so short a period as a month is dealt with as a 

 unit. 



If, instead of the inequality of declination, the inequality of the 

 disturbing force perpendicular to the magnetic mei'idian be desired, then 

 the results of Table III. may be converted into C.G.S. measure of force- 

 at the rate of V to 53 x 10-« C.G.S. units. 



In the horizontal force inequality the most conspicuous feature is 

 the minimum occurring from 10 to 11 A.M. In every month there is 

 an unmistakable maximum — especially conspicuous in summer — about 

 .7 P.M. 



In winter there is distinct evidence of a second minimum and maximum 

 during the night and early morning, the maximum being usually the largest 

 in the twenty-four hours. In summer the evidence in favour of a second 

 maximum and minimum appears somewhat uncertain. The i-esults are in 

 general accord with the conclusions for Dublin on p. 184 of Dr. Lloyd's 

 ' Treatise.' 



Harmonic Analysis of Diurnal Inequality. 



§ 9. The diurnal inequality of one of the elements, say the declina- 

 tion, D, can be analysed into a series such as 



s-n ^^t . I • 27r< , 2Trnt , , . 2wnt , ,, . 



^D=ai cos 24 +°i ^m 24 + ' "" ^°^ '947 + °'* ^^^ '2i ' ' ^ ^^ 



or 



9;r , . 9 



cD = Ci cos ;^^(<-r,)-f- . -fc, cos--:J^--(<-T„)-|- (16> 



Here t is the time in hours measured from the first midnight ; w is an 

 integer ; a,„ b,„ c„, -„ are constants, connected by the equations 



c„=v^<MA^ (2> 



04 

 Tn==, — tan-1 (6„/a„) (3) 



In what follows it is arranged that c„ shall always be positive, and so 

 r„ is the time of the first maximum, in an algebraic sense, subsequent to 

 midnight. 



Supposing hourly values of the element known, one has twenty-three- 

 constants at one's disposal ; but here I have contented myself with deter- 

 mining the coefficients of the terms whose periods are respectively 24, 12,, 

 8, and 6 hours. The subsequent terms appear in reality to be very small, 

 and any numerical results one might reach in connection with them 

 would be of doubtful accuracy. 



The following table, V., gives the values of the a, b, c coefficients 



