1893.] of Observations of Air Temperature and Pressure. 67 



A n =p + Pi sin (» . 15° + TO + P 2 sin (2 n . 15° + T 2 ), &c. . . (2) . 



In these tables, and the present disenssion, the coefficients of the 

 cosines of the arcs for the several components are designated by the 

 letter p, and those of the sines by the letter q. The amplitude for 

 the several components is designated by P, and the epoch of the 

 first maximum that occurs after midnight is designated by the 

 letter p. 



By the introduction of the epoch of maximum, the connexion of 

 the component with the hour of the day and the sun's place is 

 directly indicated, which for the purpose of these discussions is more 

 convenient than the method usually adopted, of stating the value of 

 the angle T in formula (2). 



Reference is made to difficulties and uncertainties that occasionally 

 arise in computing the mean values of some of these constants. 

 Where there are periodical variations of value which lead to changes 

 of sign, the arithmetical mean will tend to obliterate variations 

 which may, in truth, be strongly marked. Also difficulty at times 

 arises in respect to the epoch of maximum, from uncertainty, in deal- 

 ing both with casual irregularities, and periodical changes, in saying 

 whether the epoch has been thrown forward or backward. 



The absolute magnitudes of the coefficients p and q indicate the 

 amplitude of the component, and their signs the phase, or the epoch 

 of maximum. It will readily be seen that the combinations of 

 coefficients, +p + q; —p + q; —p—q; +p—q, correspond respec- 

 tively to epochs of maximum in the first, second, third, and fourth 

 quadrants of the period of the component ; and the mutual destruc- 

 tion of a series of positive and negative values of p and q in a mean 

 value will therefore only signify that there is no true mean epoch of 

 maximum, and that all positions are alike probable or uncertain. 



The foregoing remarks apply to the whole series of computations ; 

 what follows refers only to the temperature tables, to which the 

 present communication is limited. 



1. Greenwich Temperature. 



The examination of the tables shows that, with very considerable 

 variations of absolute magnitude, there is on the whole very marked 

 consistency in the main characteristics of the components. 



Taking as a test the position of the epoch of maximum, which may 

 be regarded as more directly dependent on the sun's action, and on 

 his position, it will be seen that the values of /x indicate very clearly 

 the closeness of this connexion. 



In all the components a truly periodical variation of the value of pi 

 is apparent, and the period of maximum always travels backwards, 

 that is, it becomes earlier as the year passes from winter to summer,, 



f 2 



