< 29 4 DE. CHARLES CHREE: SOME PHENOMENA OF 



the inequality would be very peaked in one case and very flat topped in the other. 

 If the range was the same in the two inequalities, the curves would represent the 

 action of forces having the same maximum but widely different mean values, and 

 from some points of view the mean value may possess more importance than the 

 maximum. This is the chief reason for recording in the inequality tables the average 

 of the 24 hourly departures from the mean for the day. In previous papers I have 

 usually recorded not the average departure but the sum of the 24 hourly differences 

 from the mean. The one result is, of course, immediately derivable from the other. 



Table XL gives particulars of the ratio borne by the average departure from the 

 mean to the inequality range. There are two sets of data as in Table X., the first 

 representing arithmetic means of the ratios calculated for the 12 months of the year 

 individually, the second the corresponding values for the seasonal inequalities. For 

 the sake of comparison, results are given for quiet as well as for disturbed days. In 

 the case of D and V the ratio is decidedly higher for the disturbed than for the quiet 

 days. In other words, a comparison based on the range alone would underestimate 

 the forces producing the diurnal inequality on disturbed days, as compared to the 

 corresponding forces on quiet days. In the case of I and H there is little, if any, 

 difference as regards the ratio between quiet and disturbed days. The differences 

 between the values of the ratio answering to all the disturbed days and to the smaller 

 number of more highly disturbed days are too small to rely on. 



Fourier Coefficients. 



18. A diurnal inequality may be analysed in a Fourier series, taking either of the 



equivalent forms 



<*! cos t + b l sin t + a 2 cos 2t + l> 2 sin 2t+ ... , 



Cj sin (t + a^ + Cg sin (2t + a 2 )+ ... , 



where t denotes time reckoned from a.m., 15 being taken as the equivalent of 

 one hour. 



The natural order is to calculate the a and b constants from the hourly inequality 

 values, and then derive the c (amplitude) and a (phase angle) constants from the 



formula 



tan a B = a n /b n> c n = a n /sin = 6 B /cos a n . 



Physical interest attaches mainly to the c and a constants, and especially to those 

 of the first two terms, which represent the 24-hour and 12-hour "waves." 



In the present case there is inevitably an appreciable "accidental" element in the 

 values obtained for individual months, especially in the case of the 8-hour and 6-hour 

 waves, to say nothing, of course, of higher terms which we shall leave out of account. 

 To economise space, the values of the a and b constants are not given here, and values 

 of c and a for individual months are limited to the 24- and 12-hour waves. These are 



