82 G. H. KNIBBS. 



be sufficiently accurate to take the mean of the average 

 daily values for the two contiguous months. The difference 

 between this average value and average value for either 

 month is one half the difference of the given averages. 



Thus reverting to line (2) of the previous table, we have 

 the differences shewn on line (3), and these are the bases 

 of the corrections, which when applied to the values in line 

 (2), give ultimately those of line (4). Excepting the case 

 of leap year there are two terms in the correction for every 

 month but January and December, and one for each of these 

 months. In leap year there are one-term corrections for 

 the months of January, August, October, and December. 



The value of the correction may be found thus : — Let the 

 difference of the daily averages of two successive months 

 be denoted by 2d, the sign being always determined by 

 subtracting the daily average value of the preceding from 

 that of the following month, and let M denote the length 

 of the uniform month. Then if 2d a , and 2d 2 denote the 

 difference-values for the beginning and the end of any month 

 we have for the corrected average value, (v) 

 (5) v = v -j- c' 



v being the crude daily average and c' the correction 

 thereto. Denoting the interval between the end of the 

 uniform and actual months by t, and regarding t as always 

 positive, we shall have for the value of c 

 (6) c = - d j^ for January. 



(6a) c = - dltl ~ d2t for February. 



(6b) c'=-^ for December. 



(6c) c = + dlt] ~L d2t2 for every other month. 



The sign of all the values of d must be carefully attended 

 to. These corrections may be at once deduced from the 

 consideration that if the position either of the beginning 



