ON THE ANNUAL DISTRIBUTION 01? TEMPERATURE 



475 



and autumns warmer. Thus, comparing two sets of quarterly groups, 

 separated by an interval of ten years, we have as follows : 



Winter. Spring. Summer. Autumn. 



1841-'50 25-1 41-0 64-7 46-4 



1861-'68 23-4 40-3 65-6 47-4 



Cliange — 1-V —0-7 +0-9 +1-0 



The old tables of normals being thus manifestly inapplicable to the 

 observations of recent years, I decided to construct new tables, and 

 employed for the purpose the observations of the ten years 1859-'68, 

 collected into monthly means for each of the sis ordinary hours of 

 observation, as shown in Table I. 



TABLE I. 



Monthly Mean Temperatures at Toronto, at each of the six ordinary hours of observation, derived 

 from the ten years 1859 to 1868, inclusive. 



Hour. 



t p. M. 



4 p. M. , 

 10 P. M. 



Midt. . . 



6 A. M. , 



8 A. M. . 



Mean . . 



57-28 

 57-10 

 49 -5C 

 48-06 

 47-45 

 51-62 

 51-84 



Sep. 



Oct. 



51-62 

 50-77 

 44-96 

 44-03 

 42-42 

 -93 45-03 

 -56'46-47 



Nov. 



Dec. 



28-10 

 27-22 

 24-55 

 23-86 

 23-26 

 23-23 

 25-04 



Taking each hour separately, and adopting in the first instance the 

 ordinary hypothesis that the monthly means represent the temperatures 

 proper to the middle days of the respective months, sis formulae were 

 constructed of the form : 



T„ = To+Ti sm(nX30+C,)+T3sin(2nX3d+C2)+&c.&c. Tg cos 6nX30°; 

 the January mean being the temperature corresponding to the 15th 

 of January, regarded as the origin or zero of time ; T„ the temperature 

 at the time (n), the unit of time being the twelfth part of a year; and 



T. 



Te; C, C, 



monthly means. 



The value of these constants are as follows 



C;, constants derived from the twelve 



T. 



T, T, T, T, T, 



C, 



C2 C3 C4 C^ 



The accuracy of the computation of each formula being tested by the 

 reproduction of the twelve monthly means on the substitution of 0, 1, 2, 

 (fee., 11, for (n) ; {he differences (disregarding sign.) between the actual 

 3 



