544 THE ADJUSTMENT OF MEAN HOURLY VALUES. 



value ; those from 1 to 12 being subtractive, and from 13 to midnight additive, as in 

 this instance the midnight at the beginning of the day was the higher of the two. 

 In general, regarding the hourly values as a curve, it is rotated round a point midway 

 between 12 and 13 o'clock, by adding or subtracting at each hour a quantity propor- 

 tional to its distance from this point, until the two ends of the curve coincide, and 

 the two midnight values become equal. Between 1 o'clock and midnight there are 

 46 half hours, 23 of which lie before the central point, 12.30, and 23 after it, the odd 

 numbers from 1 to 23 corresponding to the distance in time of the hours from the 

 central point and forming the numerators of the fractional parts of the whole difference, 

 the denominator of which is 46, the length of the whole period in half hours. 



Any difference between the two midnights may be accidental, and due to the period 

 taken not being sufficiently long to get rid of chance differences, as is probably the 

 case in hourly values of the barometer in this country when taken for periods of less 

 than about one thousand days. But it may be inherent in the data selected, as for 

 instance in the barometric readings at many tropical stations and in Central Asia, 

 where in Spring and Autumn the monthly average values differ by more than a tenth 

 of an inch in successive months. The hourly values in such months exhibit both the 

 diurnal period and a fractional part of this annual change. No matter how many days 

 be taken in successive years, there would still remain a difference between the two 

 midnight values equal to the average rise or fall of the barometer in twenty-four 

 hours at that season, and the true diurnal effect would be masked. A difference 

 between the two midnight values may be regarded as measuring a tilting of the hourly 

 values ; when the midnight value at the beginning of the day is higher than that at 

 the end, the hourly values start too high and end too low, and when the first midnight 

 has the lower value the reverse is the case, and the sole use of the table on the 

 next page is to eliminate this tilting. Any distortion of the values due to changes 

 during a day are not corrected by this process, as for example a sharply marked 

 barometric minimum occurring during one of a few days selected for examination. 

 Such a distortion of the diurnal curve can best be eliminated by taking such a large 

 number of days as to make abnormal readings on any one inappreciable on the mean 

 of the whole. 



