152 ON THE PERIODIC AND NON-PERIODIC VARIATIONS 
observations were for the most part made on a less perfect system than that of 
twelve or twenty-four equidistant observations in the twenty-four hours. The hours 
of observation during this portion of the series were as follows ; 
January 1841 to June 1842 inclusive; two-hourly equidistant. 
July 1848 to December 1848 inclusive; 2, 3, 4, 9, 10, 11, 17, 19, 21, 22. 
1849. January to December inclusive; 1, 2, 3, 5, 6, 9, 10, 11, 18, 19, 20, 22. 
1850. January to April inclusive; hourly. 
1850. May to June inclusive; 2, 3, 10, 11, 18, 19. 
1850. July and August; hourly. 
1850. September to December inclusive; two-hourly equidistant. 
1851. January to April inclusive ; two-hourly equidistant. 
1851. May to December inclusive; 2, 4, 10, 12, 18, 20. 
1852. January to December inclusive; 2, 4, 10, 12, 18, 20. 
Whenever the observations during these six years were either hourly, or two- 
hourly and equidistant, a mean of the observations simply, without corrections 
applied to any of them, has been taken as the mean temperature of the day. In all 
the other cases corrections taken from Table III. have been applied individually to 
the observations at the hours to which they refer, and the mean temperature of the 
day has been computed from the mean of the observations so corrected. 
Having thus obtained the mean daily temperatures during the second period of six 
years, we have the mean monthly temperatures derived from the twelve years as 
follows ; — 
January . 24-97 April . 41-14 July . . 66-41 October . 44-93 
February. 23-40 May . 5T18 August. . 66-16 November. 36-51 
March. . 30-23 June . 61-05 September 58-02 December. 26-75 
Mean of the whole 44°-23, 
Employing these values, we obtain the formula representing the mean annual variation 
of the temperature at Toronto as follows : — 
4=-l-44°-23 — 2r-81 sin (a-f 81° 27') + l°’06 sin (2a-f 71° 32') 
_ o°-80 sin (3a-|-347° 42') -l-0°-22 sin (4a-l-37° 27') 
-h 0°-88sin (5«-l-50° 41')-l-0°-325 cos 6n, 
a=nx 30° ; n being reckoned as before from January 15th. 
Table IV. (pages 154 to 159 inclusive) exhibits in column 1 the mean temperature 
of every day of the year, computed by the preceding formula ; and in columns 2 to 13, 
under the respective years 1841 to 1852, the differences of the mean temperatures 
actually observed on each day from the mean of the twelve years computed as 
described and shown in column 1. These “ differences” are the non-periodic varia- 
tions of each day, on the assumption that the monthly means of twelve years furnish 
a sufficient basis for the deduction of approximate normal values ; which is certainly 
