SUPPLEMENTARY REPORT ON METEOROLOGY. 75 
of the approximations of calculation*, still we find little reason 
to trust implicitly to the results, however ingeniously obtained. 
We have seen (69.) that the effective action of solar radiation 
cannot be expressed simply by the quantity of heat which would 
fall on a square foot of the earth’s surface were the atmosphere 
removed ; but the absorption is very great even in the clearest 
weather, and therefore (even admitting a uniform distribution 
of vapours over the whole year, so that their opacity need not 
be considered as a function of the time) the quantity of solar 
heat depends on the thickness of the atmosphere traversed, and 
is therefore a function both of the hour angle and of the fraction 
ofa year. The integrals, therefore, expressing the discontinu- 
ous quantity of sunshine, are wholly unadapted to the physical 
conditions of the problem. 
106. That 4 cannot thereby be rightly estimated, will appear 
from this consideration: viz. that the whole effect of sunshine 
can only be deduced from the annual range at a given depth (or 
at the surface) by the following reasoning. The winter-action 
of the sun may (it is assumed) be compared a priori with the 
summer-action of the sun, and the excess of the latter action 
determined; but the Effect due to this Excess being observed 
(viz. the annual range), the effect due to either of the constituent 
actions (summer or winter) may be found, which gives the whole 
climateric effect of the sun at any season, and hence its mean 
effect throughout the yeart. Now in applying this principle, 
it is clear that unless the @ priori estimate of the sun’s relative 
radiation in summer and winter be made on correct principles, 
a knowledge of the difference of effect due to the change of the 
cause will not lead to a correct value of the cause. In point of 
fact, a neglect of the absorption due to obliquity (not to mention 
the enormous excess of cloudy weather in the winter half-year) 
will inevitably lead to an under estimate of the proportion which 
the summer radiation bears to the winter radiation, and (as the 
difference between these effects is the quantity known) the value 
* So involved are these expressions, that the author himself has inadvertently 
‘Made use of two identical values of one quantity, this same h, and quoted the 
coincidence as a proof of the accuracy of the formule and observations (p. 
503-4). This he admits in the Supplément, page 72. 
+ This at least is my understanding of the principles of solving the problem. 
The problem which Fourier has proposed (Mém. de I’ Institut, v. 167, &c.) is 
_ amuch simpler and also a less important one, viz. to find the quantity of solar 
heat alternately absorbed and emitted by the earth’s surface in the course of a 
year, which evidently does not include the permanent or mean heat derived 
from the sun, and which is subject to no annual change, but which would be 
dissipated were the sun extinguished. 
