33i A STUDY OF CORRELATIONS AMONG TERRESTRIAL TEMPERATURES. 



by the spots. The fluctuation of terrestrial temperature was shown to be the greatest 

 in the equatorial regions, and to diminish progressively as the latitude increased to 

 north or south. There were also indications of a non-correspondence between the 

 epochs of maximum and minimum temperatures, and tlie minimum and maximum 

 of spottedness, but the determination of the difference must be considered as weak, in 

 view of the uncertainty of the data and the minuteness of the fluctuation. 



The writer proposes to reinvestigate this question, using both Koppen's data and 

 more recent observations, in order to apply the more rigorous method of equations of 

 condition. We assume only that the mean temperature at the earth's surface fluctu- 

 ates harmonically in a period of 11.13 years. This hypothesis may be represented in 



the general form 



At = X cos fJ^t + y sin fJi^t -\- z (29) 



where /a is to be so taken that the angle ^it shall go through 360° in the given period. 

 Taking the year as the unit of time this gives 



^t. = 32°.35 



The epoch from wliich / is measured is quite arbitrary, because when, after deriving 

 X and y from observations, we reduce tlie expression to a monomial 



At = p sin (^/Mt -\- c) 



the value of ju,<-|-c for a given moment of time will be the same, whatever the chosen 



epoch for f = 0. 



Putting, for brevity, 



a = cos fit ; Ij ^ sin fit 



each observed deviation of temperature, At = r, will give the equation of condition 



((.(• -)- bii + z = r 



These conditional equations being treated by the method of least squares we shall have 



the normal equations 



[aa~\x + [ab'\y + [aclz = [<t>i] 



[«/.].!•+ [l>h]y+ [bc]z= [bn] 



[ac]x + [bc'jy + [cc]z = [en] 



Having found x and y from these equations we may substitute them in (15), and 

 reduce the trigonometric terms to a monomial by computing p and c from 



p cos c = .r 

 p sin c = — y 



The harmonic fluctuations of which we are in search will then be 



At = p cos [fit -\- c) 



