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A NOTE CONCERNING THE PHYSICAL SIGNIFICANCE OF 
THE MEAN DIURNAL CURVE OF TEMPERATURE. 
By J. R. Sutton, ScD., F.R.S.S.Af. 
(Read July 17, 1912.) 
The hourly average temperatures for the different months, or for the 
year, are sometimes subjected to elaborate processes of analysis for the 
purpose of eliciting, if possible, some relation bearing upon the enigma 
of the semi-diurnal oscillation of the barometer. But have these hourly 
averages any great scientific value ? Is the mean diurnal curve of tem- 
perature, for example, that to which each daily curve tends to conform ? 
Or, further, is the method of least squares applicable in the sense that the 
average value of all the observations is the most probable value ? The 
original object of the present brief investigation was to test this point. 
It is of course true that for any hour in any period, say a month, 
the sum of the squares of the deviations from the arithmetic mean tem- 
perature of that hour and month will be a minimum. For let T be the 
arithmetical mean temperature for any given hour of a month ; t^, t^, t^, 
. . . the individual temperatures for that hour for each day of the month ; 
P the " most probable value " of the set of daily temperatures. 
Then— 
S = (P - t^)^ +(F — + . . . = a minimum. 
c/S 
.-. = 2nF - 2(t, + + + . . .) ^ 0. 
.-. V = {t, + + + . . .)/n = T. 
This assumes, however, that each individual temperature is under 
some sort of compulsion to approximate to the mean value. There is no 
such compulsion, for the mean temperature curve of any assigned month 
in one year may be materially different from the mean temperature curve 
of that same month in any other year. 
Any attempt to test the value of the arithmetic mean temperature in 
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