A most important question is suggested by these considerations. The consequences of frightful extravagance are known to us all; we know that such conduct tends to bankruptcy and ruin; and certainly the expenditure of heat by the sun is the most magnificent extravagance of which our knowledge gives us any conception. Accordingly, the important question arises: As to how the consequences of such awful prodigality have been hitherto averted. How is it that the sun is still able to draw on its heat reserve, from year to year, from century to century, from æon to æon, ever squandering two thousand million times as much heat as that which genially warms our temperate regions, as that which draws forth the exuberant vegetation of the tropics or which rages in the desert of Sahara? That is the great problem to which our attention has to be given.
We must first ascertain, with such precision as the circumstances permit, the actual amount of heat which the sun pours forth in its daily radiation. The determination of this quantity has engaged the attention of many investigators, and the interpretation of their results is by no means free from difficulty. It is to be observed that what we are now seeking to ascertain is not exactly a question of temperature, but of something quite different. What we have to measure is a quantity of heat, which is to be expressed in the proper units for quantities of heat. The unit of heat which we shall employ is the quantity of heat necessary to raise one pound of water through one degree Fahrenheit.
The solar constant is the number of units of heat which fall, in one minute, on one square foot of a surface placed at right angles to the sun’s rays, and situated at the mean distance of the earth from the sun. We shall suppose that losses due to atmospheric absorption have been allowed for, so that the result will express the number of units of heat that would be received in one minute on a square foot turned directly to the sun, and at a distance of 93,000,000 miles.
Fig. 14.—The Sun (July 8th, 1892).
(Royal Observatory, Greenwich.)
(From the Royal Astronomical Society Series.)
This is a matter for determination by actual observation and measurement. Theory can do little more than suggest the precautions to be observed and discuss the actual figures which are obtained. There have been many different methods of making the observations, and the results are somewhat various, but the discrepancies are not greater than might be expected in an investigation of such difficulty. The mean value which has been arrived at is fourteen, and the fundamental fact with regard to the solar radiation which we are thus enabled to state is that an area of a square foot exposed at right angles to the solar rays, at a distance of 93 millions of miles, will in each minute receive from the sun as much heat as would raise one pound of water fourteen degrees Fahrenheit.
It follows that the total radiation from the sun must suffice to convey, in each minute, to the surface of a sphere whose radius is 93,000,000 miles, fourteen units of heat per square foot of that surface. This radiation comes from the surface of the sun. It is easily shown that the heat from each square foot on the sun will have to supply an area of 46,000 square feet at the distance of the earth. Hence the number of units of heat emerging each minute from a square foot on the sun’s surface must be about 640,000.
We can best realise what this statement implies by finding the amount of coal which would produce the same quantity of heat. It can be shown that the heat given out by each square foot of the solar surface in one minute will be equivalent to that produced in the combustion of forty-six pounds of coal. If the sun’s heat were sustained by combustion, every part of the sun’s surface as large as the grate of an ordinary furnace would have to be doing at least one hundred times as much heating as the most vigorous stoking could extract from any actual furnace.
The radiation of heat from a single square foot of the solar surface in the course of a year must, therefore, be equivalent to the heat generated in the combustion of 11,000 tons of the best coal. If we estimate the annual coal production of Great Britain at 250,000,000 tons, we find that the total heat which this coal can produce is not greater than the annual emission from a square of the sun’s surface of which each side is fifty yards. All the coal exported from England in a year does not give as much heat as the sun radiates in the same time from every patch on its surface which is as big as a croquet ground.
There is perhaps no greater question in the study of Nature than that which enquires how the sun’s heat is sustained so that the radiation is still dispensed with unstinted liberality. If we are asked how the sun can be fed so as to sustain this expenditure, we have to explain that the sun is not really fed. If, then, it receives no adequate supplies of energy from without, we have to admit that the sun must be getting exhausted.