Maxima and certain Conditions of Temperature, fyc. 413 



hourly readings for the winter months, November to February, taken 

 at intervals of seven or eight days, and but eight series for J une and 

 July, but so regular is the march of the diurnal variation both of 

 temperature and pressure in this climate, that even these suffice to 

 show the distinctive characters of the curves at both seasons. The 

 observations have been published at length in the first volume of the 

 1 Indian Meteorological Memoirs.'* To eliminate small irregularities, 

 corrected hourly values have been computed from these by means of 

 the harmonic formula. A very exact determination of the critical 

 phases cannot of course be expected from such data, but according to 

 the method of computation adopted, t the epochs of the forenoon 

 pressure maximum and of most rapid heating are as follow at the two 

 seasons : — 



Max. rise temp. Bar. max. 



Winter months. ... 9 h. 38 m. A.M. 9 h. 36 m. A.M. 

 Summer months . . 7 h. 56 m. „ 7 h. 38 m. 



* Op. et vol. cit., p. 94, et seq. 



f Throughout this paper the time of most rapid heating has been determined in 

 the following manner : in general, from the uncorrected means of the observations, 

 which, for the reasons shown by Dr. Bergsma (' Batavia Mag. and Met. Obs.,' vol. 1, 

 p. xvii) and in accordance with my own experience and that of other Indian 

 meteorologists, if the observations are sufficiently extensive, are more trustworthy 

 than the so-called corrected values obtained by computing them from three or four 

 terms of the harmonic formula. 



The instant of most rapid rise of temperature may be ascertained by twice 

 differentiating for the values of t the formula which expresses the temperature 6 as 

 a function of the time t, and putting 



d?d 



m = °- 



The most convenient formula for this purpose is that of the method of differences 

 employed. by Dr. Jelinek for obtaining the approximate times of the maximum and 

 minimum phases of temperature, pressure, &c. On taking the first, second, and 

 third differences of the temperatures at the clock hours, two before and two after 

 the instant of most rapid rise, the hour in which this occurs is shown by the change 

 of algebraical sign of the second order of differences. Denoting that which pre- 

 cedes this change by A 2 , and the differences of the first and third order next follow- 

 ing in order of sequence by A' and A' 3 , the second differentiation of the formula 



, , t (t-1) (t + l) t (t-1) , 

 6 = a + tA\ + A 2 + } - A' 3 + . . . . 



neglecting the higher terms, gives 



d 2 e . , ■ n 



whence 



t = - % 

 A' 3 



which value of t reckons from the clock hour corresponding to A 2 . The epoch thus 

 obtained has an error of a few minutes only, and is quite accurate enough for the 

 present purpose. 



