102 B. A. Gould—Algebraic Expression of the 
obtained from accurate numerical calculation by means of the 
formula. 
I am not aware that it has ever been considered desirable to 
base extended humerival coareoes upon o a made 
sired, the influence of the additional observations could, if per- 
ceptible, be introduced into the formula quite as well as into 
the graphical sketch. It may therefore be assumed that the 
form of the diurnal curve, as afforded by hourly observations is 
a sufficient for all the present purposes of scientific in- 
uir 
So much being premised, it may be well briefly to consider, 
even though only in an elementary manner, how an what 
extent the formula in question may find legitimate application. 
Denoting by h the number of hours elapsed since any given 
moment (for which we will, as usual, adopt that of midnight), 
the observed temperature will be represented with absolute pre- 
cision for each one of the twenty-four hours, by the formula 
which, in its most een) and ofeeant form, may be written 
n which a, A, 0, B, ¢ Le ete., are oe bikes can only be 
Ga eclaas by ede an nd s the mean of the twenty- 
four equidistant observations, this sain the “daily mean” as 
defined by the ee usage of physicists. a is perhaps 
needless to add that A should in strictness be made to denote 
hours of true and not of mean time; but this is a iis which 
need not be considered if the length of the interval, for which 
the formula is determined, be either such as to eliminate the 
equation of time from the means of the daily observations, or 
so short that its inclusion may be recognized and allowed for, 
if pene 
meteorology require; for all the errors of observation, not elim- 
_— from the data, would thereby be reproduced, whereas by- 
The curious numerical values upon p. se of Dr. Wild’s “Zemperatur- Verhilt- 
piss des Russischen Reiches” from which it is inferred that the ~~ imate results 
from twenty-four equidistant ponent anes ully represented by a for- 
ect of these errors is quite oo it is true, and amounts to only a very 
few hundredths of a degree; but it is precisely upon these small quantities, much 
fecha FE in magnitude to the unavoidable errors of pact "that the whole 
argument of the author depends. 
