176 J. D. Everett on Reducing Observations of Temperature. 
yt tt pte pis pig tts tte | 
the expression for half-yearly means will be 
Y=t, +644, —'236¢,4-173¢, ; 
that is, 
Y=A,+ 644 A,sin(c+E,)—236A,sin(3z+-E,)4-173A ,sin(57-+-E,) 
and since ‘236 A, and 173 A, are practically insignificant com- 
pared with ‘644 A,, the two last terms may be neglected. 
For Greenwich, we have 
“644A = 644 12-44—8°01, 
‘236A ,—°236X ‘18= °04, 
‘173A,='173X -20== *03. 
Hence the sum of the two last terms in the expression for Y 
cannot exceed 04+ °03=°07, which is oniy ;1; of 644A, ; and 
the greatest error produced by the omission of these terms in 
comparing two halves of the year cannot be more than about 
+1, of the difference between the greatest and least values of Y. 
It is to be observed that the half-yearly means denoted by Y 
are not limited to means of 6 calendar months, but may belong 
to any 1824 consecutive days. ; 
It thus appears that the values of A,, A,, E, are sufficient to 
determine, with competent accuracy, the mean temperature of 
any half-year, and hence to determine the range as measured by 
the difference between the warmest and coldest halves of the — 
year, a system of measurement which I think is as fair as any 
that can be devised. 
The determination of the precise dates of maximum and min- 
imum is always difficult, whatever met e pursued, owing 
to the slow rate at which temperature changes when near 11s 
imum or minimum. Even the table of daily temperatures 
at Greenwich, though derived from an average of 48 years, leaves 
both these dates doubtful, as a glance will show. It is always 
much easier to determine the dates at which the temperature 18 
equal to the mean of the year, (or at which the curve of temper — 
ature intersects the line of mean annual temperature,) because — 
at and near these dates the temperature changes with its greatest 
rapidity. This remark applies to half-yearly means, as well 38 
to wad temperatures; hence we can determine more prec 
“the 
ture, while the latter de upon the dates at which is 
maximum or minimum. i 
f 
ht 
ates which divide the year into halves whose temperatures 
are each equal to the mean of the year,” than the dates which — 
_ are the centres respectively of the warmest and coldest halves of — 
the year. For the former determination depends upon the dates — 
at which the value of Y is equal to the mean annual ——— ae 
And the above phrase in inverted 
7 + fs se oe 4 warm 
Re ET age = iy oe SER c 
PE ee ee Te Re Sop ale Sy gee A ee sae 
tons 
f 
Apes! Seiad Pedi e Diy 
PE ee NR re 
See Ne oe eee ee 
OP Migs a ee ee EU Le eee 
Pept fe aoe Selb Sem 
