118 B. A. Gould—Algebraic Expression of the 
and yearly results are thus made numerically accordant; but 
at a sacrifice of real accuracy. The corrections thus applied 
have the effect of belatening the minimum in the spring half of 
the year and anticipating it in autumn. For it cannot seri- 
ously be maintained that the influence of an increase or de- 
crease of the sun’s declination continues through the night- 
hours as through the day. This influence is necessarily inter- 
mittent ; in dealing with annual variations, we cannot use.hours 
as the independent variables; although here also the numerical 
changes are small, and although their influence disappears from 
the daily means and from determinations based upon them, yet 
whatever effect they may have goes to produce distortion and 
error in the resultant curve of diurnal variation. In this very 
case of May at Tiflis, the observations themselves give 4" 473 
for the mean epoch of minimum, instead of 4% 50™5, which 
results after they have been modified by this reduction for an- 
nual variation, or of 5" 0™ as deduced graphically by Dr. Wild. 
This modification has a still greater effect upon the time of 
mean maximum, for it changes this epoch from its true value 
14" 18™-8 to 14" 28™ or to 14" 32™ if we accept the graphical 
result. 
But, leaving this relatively unimportant question, the most 
striking fact to be noted in the example now considered is that 
the form of the diurnal curve, in the vicinity of its maximum, 
is such that, while the minimum temperature—4°°60, as given 
by only three variable terms, corresponds to an epoch 4” 176, 
yet the analogous value—4°-76, deduced from the full series of 
twelve terms, and only 0°:16 lower, corresponds to the epoch 
4® 50"-5, more than half an bour later. That obtained graph- 
ically and given as the correct one by Dr. Wild, is, as above 
mentioned, 5® 0". 
The accomplished physicist, whose views we reluctantly op- 
pose, maintains that his method gives the epoch with accuracy 
to within 2™. With reference to this we will only remark that 
careful trials, plotting the observations with the utmost care 
upon the scale employed by Dr. Wild, show that the graphical 
method could give any value from 4% 48™ to 5" 12" according 
to the taste or fancy of the draughtsman. Tracing the curve 
as it results from the formula, its true form may be recognized. 
If graphical processes are to be trusted in such cases, they 
must be based upon more frequent observations :—half-hourly, 
at least, in case the result is to represent the actual mean epoe 
within eight or ten minutes. How inordinately the resu tant 
epoch would be affected by the, certainly not improbable, error 
of a few hundredths of a degree in the mean observed tempera- 
ture, either for 4" or for 5%, is manifest. It may not be amiss 
to add that the mean discordance between the observed and 
