( 543 ) 



The Adjustment of Mean Hourly Values for Diurnal Range. 



The mean hourly values of the different meteorological elements given in this volume 

 are the simple arithmetical means (or sums) of the observations ; but in the tables, 

 which show the departure of each hourly value from the mean for the whole day, a 

 correction has been applied to eliminate any general rise or fall which may take place 

 throughout the whole day, and thus to more nearly show the true diurnal effect inde- 

 pendent of changes of longer period than twenty-four hours. In order to effect this, to 

 the series of average values for each of the twenty-four hours is added one giving the 

 average value for the midnight preceding each day, thus making twenty-five entries in 

 all in the order, — 



Midnight, 1, 2, 3, 4, . . . . 21, 22, 23, miduight. 



The difference between the values at these two midnights gives the amount of the 



general change occurring during the mean day of the month or other period under 



consideration, and fractional parts of the difference are applied to the twenty-four 

 hourly values in the following proportion : — 



Hour .1 2 3 .... 11 12 13 14 .... 22 23 Mdt. 



n .. 23 21 19 .... 3 1 1 3 .... 19 21 23 



Correction, — — — — — — — — — — 



' 46 46 46 46 46 46 46 46 46 46 



the corrections from 1 to 12 being opposite in sign to those from 13 to midnight. If 

 the previous midnight has been higher than the midnight at the end of the day, then 

 the first half of the correction (1 to 12) is — , and the second (13 to midnight) + ; if the 

 previous midnight is the lower of the two, the signs are reversed. Thus whatever is 

 added to or subtracted from any morning hour, an equal amount is subtracted from or 

 added to a corresponding afternoon hour, and the mean value of the whole day is not 

 altered, but the beginning and end of the diurnal curve are brought into agreement and 

 the curve becomes a repeating function. 



To facilitate the carrying out of this, a table has been prepared (p. 545). The 

 numbers in heavy tj^pe at the head of each column represent differences between the 

 two midnight values, and the figures in the column the quantities to be added to or 

 subtracted from each hourly value, the hours being given at the side. Values are given 

 for each difference from 1 to 100, and for successive hundreds to 1000. For example, 

 in the mean hourly values of barometric pressure for a month, suppose that 



The previous midnight is ..... . 29'894 inches 



The midnight at end of day is 29 '862 



The difference between them being .... O032 „ 



Turning to the column headed 32 in the table, we find numbers ranging from 16 to 

 1, which are the corrections, in thousandths of an inch, to be applied to each hourly 



