492^ 



PROFESSOR FORBES ON THE DIMINUTION OF TEMPERATURE WITH 



If we consider only the first two terms, which amounts to supposing the 

 curves to become the common curve of sines, the position of maximum or mini- 

 mum difference of temperature is easily found, and its relation to the elements 

 exhibited. 



The value of x (or the horary angle), which will make a + 6 sin(j:' + e) in Eq. (3) 

 a maximum, is evidently 



a;^ + c = 90°; or2;, = 90-c. 

 1 BcosC-B'cosC 



Whence 



tan x^ = 



tanc BsinC-B'sinC 



In the figure, let OPQRS represent the curve at the lower station, and 

 0' P' Q! R' S' at the higher ; if we place the origin of the time at 0, C wiU vanish, 



and C will denote the acceleration or retardation of the epoch for the tempera- 

 ture curve at the colder, compared to that at the warmer station. Thus the 

 above expression for the time x^ of the maximum difference of temperature be- 

 comes 



"Tl/ _ _ ^ i^r T> 



(6) 



B'cosC'-B 



tan X, = — ^ --. _ - 

 B' sin C 



When C'=0, or, when there is no difference of epoch, ,r^=90, and the maxima 

 of the three curves coincide. 



As C increases positively, that is, as 0' falls to the left hand of (which is 

 the case in the diurnal curve), tan x^ being negative (for whilst B 7^ B', as we 

 have assumed it to be, the numerator is essentially negative), x^ lies somewhere 

 between 90° and 180°. It never, however, reaches the latter value, its greatest 

 excursion being determined by the condition 



cosC 



B' I r>2 TQ/2 



--g- ; and therefore, tan x^= — J — ^ — 



When C becomes equal to + 180°, x, has resumed its value of 90°. This cor- 

 responds to a coincidence of the minimum of one curve with the maximum of 

 the other, when b in Eq. (4) has its greatest value, which of course is B + B', 

 whilst its least value when C = is B — B'. 



