1893.] of Observations of Air Temperature and Pressure. 71 



In the summer the time of absolute minimum is between the 

 hours of 3 a.m. and 6 a.m., during which the whole of the components 

 are negative. 



Sunrise in December is about an hour and a half before the time 

 of mean temperature; while in June it is more than four hours 

 earlier. 



Sunset in December is rather more than three hours before the 

 time of mean temperature ; in June it is about half an hour after that 

 time. 



The rationale of some of the empirical rules for obtaining the mean 

 daily temperature from a limited number of observations is supplied 

 by reference to the ha-rmonic expressions for the hourly deviations of 

 temperature from the mean value ; it being borne in mind that the 

 relative magnitude of the fourth component is very small. 



In the first place, it will be seen that by adding together the 

 harmonic expressions for any two hours twelve hours apart, the 

 whole of the odd components disappear, and that the sum is twice 

 the mean value, added to twice the sum of the even components of 

 the selected hours, which are equal. Disregarding the components 

 above the fourth order, if the selected hours are such that the 

 component of the second order is zero, which will be the case at 

 hours corresponding to /* 2 + 45° or ^ + 135°, then half the sum, of the 

 temperatures at the selected hours will be the true daily mean added 

 to the fourth component for the selected hour, which at English 

 stations will never amount to and on the average is less than 



At Greenwich the mean between the observations at a.m. or 

 10J a.m. and the corresponding afternoon hours in January, will 

 differ by less than from the true value, and similar results 

 will be obtained for June by the mean of observations made at 

 3 a.m. or 9 a.m. and the corresponding hours in the afternoon. 



By taking the mean of observations at any four hours, at intervals 

 of six hours, both the odd components and those of the second order 

 will disappear, and the result will only differ from the true mean by 

 the amount of the fourth component for the selected hours. 



As this component disappears when ^4 + 22j° = 0° or 180°, the 

 hours at Greenwich that will give the best result are 2, 8, 14, and 20, 

 or 5, 11, 17, and 23. 



So, if the mean of any three hours at equal intervals of eight 

 hours be taken, the sums of the first, second, and fourth components 

 will disappear, and the result will only differ from the true mean by 

 the amount of the third component for the selected hours, which in 

 no case can be so much as J°, 



By adopting hours when // 3 + 30 = 0° or 180°, the third component 

 disappears, and this result will be obtained at Greenwich by com- 

 bining observations at 3, 11, and 19 honrs, or 7, 15, and 23. 



