144 
ON THE PERIODIC AND NON-PERIODIC VARIATIONS 
in which is the temperature on x the required daj’’, A,, the mean temperature of the 
year at the hour required, a=wX30°, n denoting the number of months and parts of 
a month between January 1 5 and a?, and Ai, Ag, Bj, . . . . B 3 , constants derived 
from the values in Table I. by the method of least squares. 
The constants for each of the hours, and for the mean temperature, derived from 
the six years of hourly observation, are as follows ; — 
Table II. 
Constants for the calculation of the Temperature on the several Days and Hours 
from the Mean Monthly Values in six years. 
Toronto 
astrono- 
mical time. 
A„. 
Af. 
Bp 
Ag. 
B ,. 
A3. 
B3. 
A4. 
B4. ; 
Ag. j 
Bo- 
Ae- 
Hours. 
0. 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
49*12 
49- 82 
60-22 
50- 24 
49-88 
49-00 
47- 47 
45-52 
43-89 
42-80 
42- 02 
41-38 
40-87 
40- 27 
3979 
39-37 
39-01 
38- 83 
39- 71 
41- 25 
43- 11 
45- 12 
46- 82 
48- 14 
— 23-38 
— 23-48 
— 23-65 
— 23-87 
—24-23 
— 24-52 
— 24-10 
— 22-54 
-20-95 
— 20-05 
— 19-61 
-19-25 
— 19-02 
— 18-84 
— 18-60 
- 18-38 
— 18-11 
-18-17 
-19-58 
— 21-48 
—22-63 
— 23-05 
— 2.3-20 
— 23-28 
-2-53 
-2-35 
— 2-28 
— 2-21 
— 2-02 
-1-73 
-1-69 
—2-03 
— 2-55 
-2-89 
-2-97 
-3-07 
-2-93 
— 3-03 
— 3-13 
— 3-20 
— 3-28 
— 3-30 
-3-05 
— 2-62 
— 2-60 
-2-59 
-2-63 
— 2-63 
+ 0-60 
+ 0-65 
+ 0-73 
+ 0-85 
+ 1-00 
-1-17 
+ 1-56 
+ 1-46 
+ 0-91 
+ 0-75 
+ 0-72 
+ 0-68 
+ 0-52 
+ 0-52 
+ 0-58 
+ 0-47 
+ 0-50 
+ 0-60 
+ 1-20 
+ 1-21 
+ 0-85 
+ 0-56 
+ 0-50 
+ 0-55 
+ 0-29 
+ 0-31 
+ 0-45 
+ 0-47 
+ 0-46 
+ 0-42 
— 0-03 
— 0-41 
— 0-31 
— 0-29 
— 0-33 
-0-37 
-0-21 
-0-17 
— 0-14 
-0-13 
-0-19 
-0-48 
-1-01 
-0-92 
-0-49 
— 0-13 
+ 0-07 
+ 0-22 
+ 0-62 
+ 0-63 
+ 0-55 
+ 0-59 
+ 0-68 
+ 0-70 
+ 0-48 
+ 0-38 
+ 0-58 
+ 0-69 
+ 0-66 
+ 0-71 
+ 0-68 
+ 0-63 
+ 0-59 
+ 0-59 
+ 0-59 
+ 0-54 
+ 0-65 
+ 0-80 
+ 0-73 
+ 0-69 
+ 0-70 
+ 0-69 
0 
-1-11 
-1-17 
— 1-16 
-1-17 
-1-14 
-1-36 
— 1-43 
-1-10 
-1-09 
— 1-20 
-1-30 
— 1-42 
-1-40 
-1-35 
-1-29 
— 1-35 
-1-41 
— 1-37 
-1-18 
-1-46 
-1-51 
— 1-31 
— 1-20 
-1-17 
+ 0-31 
+ 0-30 
+ 0-36 
+ 0-35 
+ 0-31 
+ 0-20 
+ 0-21 
+ 0-23 
+ 0-15 
+ 0-15 
+ 0-14 
+ 0-11 
+ 0-02 
-0-05 
+ 0-02 
+ 0-14 
+ 0-13 
+ 0-12 
+ 0-31 
+ 0-43 
+ 0-39 
+ 0-34 
+ 0-24 
+ 0-29 
+ 0-54 
+ 0-57 
+ 0-56 
+ 0-60 
+ 0-52 
+ 0-50 
+ 0-57 
+ 0-40 
+ 0-27 
+ 0-30 
+ 0-37 
+ 0-34 
+ 0-17 
+ 0-20 
+ 0-18 
-t-0-11 
+ 0-15 
+ 0-24 
+ 0-38 
+ 0-34 
+ 0-35 
+ 0-50 
+ 0-54 
+ 0-54 
0 
+ 0-25 
+ 0-13 
+ 0-09 
+ 0-15 
+ 0-16 
+ 0-16 
+ 0-27 
+ 0-28 
+ 0-43 
+ 0-51 
+ 0-52 
+ 0-55 
+ 0-51 
+ 0-58 
+ 0-63 
+ 0-65 
+ 0-69 
+ 0-73 
+ 0-79 
+ 0-65 
+ 0-70 
+ 0-53 
+ 0-44 
+ 0-34 
+ 0-44 
+ 0-45 
+ 0-40 
+ 0-47 
+ 0-48 
+ 0‘48 
+ 0-50 
+ 0-46 
+ 0-55 
+ 0-62 
+ 0-60 
+ 0-67 
+ 0-76 
+ 0-81 
+ 0-80 
+ 0-79 
+ 0-75 
+ 0-70 
+ 0-61 
+ 0-66 
l + 0’58 
+ 0-42 
1 + 0-37 
j + 0-40 
+ 0-31 
+ 0-27 
+ 0-29 
+ 0-25 
+ 0-26 
+ 0-35 
+ 0-35 
+ 0-35 
+ 0-35 
+ 0-34 
+ 0-34 
+ 0-30 
+ 0-21 
+ 0-22 
+ 0-25 
+ 0-22 
+ 0-20 
+ 0-17 
+ 0-47 
+ 0-59 
; + 0-53 
1 + 0-45 
+0-39 
1 + 0-32 
Mean of j 
the 24 )> 
hours. J 
44-32 
-21-41 
-2-64 
+ 0-80 
— 0-12 
+ 0-63 
— 1-28 
+ 0-22 
+ 0-38 
+ 0-45 
1 
+ 0-58 j + 0-32 
From the temperatures computed by the formula with the constants in Table II., 
corrections have been obtained to the mean temperature of the day for each of the 
hours of observation throughout the year, to be employed whenever a less onerous 
system than that of hourly or two-hourly (equidistant) observation is adopted, as was 
tl)e case in the second period (also of six years) at Toronto. Table III. exhibits these 
corrections for every hour on every fifth day throughout the year ; the corrections on 
the intermediate days admitting of easy interpolation. The corrections are additive 
when in the larger character, and subtractive when in the smaller. 
