All recent discoveries in physics have tended to establish what is now accepted as a fundamental theorem of scientific cosmogony, viz., that the sun and all orbs of which we know anything at all, including our earth itself, are heated bodies, which must in the end succumb to the effects of their constant radiation of heat into the cold wastes of space. Although we have no data by which to determine whether the sun itself has reached that stage of aggregation at which its temperature must be constantly falling, the idea that it has both reached and passed that point in its history seems to be generally prevalent in the scientific world.
It has been established that, so far as we are able to probe it, the temperature of the interior of the earth is very considerable. Prevalent theories as to the past of our globe lead to the conclusion that this internal temperature is sufficient to maintain the central portions of the sphere in a molten condition; and, though this has been energetically disputed, on the ground of its alleged disaccordance with the phenomena of nutation and precision, it remains certain that the internal heat is adequate to maintain the surface at a temperature considerably above that of external space, even in the absence of the sun. But whatever this temperature might be, it is certain
that the conditions under which life is now maintained on the earth are derived from the additions which the solar radiation constantly makes to the intrinsic heat of our planet.
It becomes then a point of the highest interest to ascertain the actual temperature of this great ruler of our system, what its present rate of cooling would be if that temperature were not continually restored, and what means of maintaining that temperature appear to exist. It is with the first of these that we have to do, but it may not be without interest to state here one of the most probable estimates that has been made as to the other two. Ericsson has calculated that, if the contraction which constant radiation of heat must necessarily effect in the sun, should proceed at the rate of one foot of his radius in 3 days and about 34 ½ minutes (3.024 days), the development of heat would equal the radiation from the solar surface, as he determines it. Contraction at this rate would in about 2,000,000 years reduce the sun's diameter by one-tenth. The thermal energy at the sun's surface would, during the whole period, be maintained constant at its present figure, but the diminished size of the solar disc would result in a diminution of the temperature communicated to the earth, at its present distance, by an average of nearly 13° Fah. Although this would involve a notable change in the conditions of life on the earth, and would probably be sufficient to depopulate its arctic regions, the change would not reduce the average temperature of tropical regions to that which at present prevails in Dunedin. This is, of course, all pure speculation, because the data assumed cannot be verified. My object to-night is indeed to show that they are very unreliable. We may, nevertheless, rest content in the conviction that the secular cooling and contraction of the sun, if it should actually be proceeding in the manner which Ericsson assumes, will have no effect on the conditions of life upon the earth within a period utterly beyond our powers of conception; for, though we can express millions of years in numbers, the idea which we form in our minds of such a lapse of time is really of the vaguest description. At any rate, there appears to be every reason to believe that before the earth becomes too cold to be inhabited by beings like ourselves, there will be ample time for “social evolution” to carry our race to that future of perfect development towards which we are taught to believe that it is inevitably tending.
The subject we have in hand excited, not long ago, considerable attention amongst scientific men, on account of the publication by Father Secchi, in his work, “Le Soleil” (Paris, 1870), of his estimate of the solar temperature as not less than 10,000,000° Cent. (say 18,000,000° Fah.) The learned Director of the Roman Observatory, in the calculations by which he arrived at this enormous temperature, rejected the received law of radiation estab
-lished by Dulong and Petit, as a result of their experiments on the rate of cooling of various bodies. A rather smart discussion occurred, in which many eminent men took part, each of whom appears to have retired from the controversy without seeing reason to modify his own opinion, a circumstance which may assure us that we are yet a long way from a sure ground on which to base a definite calculation of the solar temperature.
Attempts have been made by many physicists to determine the radial energy of the sun since the day when Newton first made the calculation by which he estimated that the comet of 1680 was subjected at its perihelion to a temperature of 1,484,000° Fah. As a preliminary to certain considerations which have occurred to my mind during the study of this subject, I must ask you to allow me to describe briefly the methods which have most recently been employed to test the energy of the solar radiation, and the deductions which have been drawn from observations thus conducted.
The method which I have selected for description is that of the thermoheliometer. This instrument, which has been variously fashioned in accordance with the ideas of those who have used it, consists essentially of two concentric cylinders placed within one another. The annular space between these is filled with water or oil maintained at a known constant temperature. At one point a tube passes through both cylinders by means of which a thermometer is introduced into the interior of the smaller one. The bulb of this thermometer is blackened, and the rays of the sun are allowed to fall upon it through the circular opening at one end of the cylinder. The whole apparatus is of course attached to a heliostat, by means of which the axis of the cylinders is kept constantly directed to the face of the sun. The thermometer thus exposed to the sun's rays shows a rapid increase of temperature up to a certain point, after which its indications vary directly with the increasing or decreasing altitude of the sun, so long as the sky remains equably clear. From a multitude of observations taken at different zenith distances of the sun, it is not difficult to calculate what temperature would be indicated by the thermometer if the sun were actually overhead. These measures, at various altitudes of the sun above the horizon, also give us the means of determining the mean absorption of heat by the atmosphere, since the difference between the effective radiation at low altitudes and at noon is caused solely by the difference in the depths of air which the solar rays traverse. The results obtained by different observers with instruments constructed on this principle vary with the amount of precaution taken to secure (1), the steadiness of temperature on the environment; (2), freedom from draughts and other causes which disturbe the indications of the thermometer; and (3), equable heating of the whole mass of the bulb of the instrument by the sun's rays.
Mr. Waterston used one of these instruments in India, and determined the singular fact that, whatever the temperature of the environment, the difference between it and that of the thermometer exposed to direct solar radiation was always the same. His experiments were made with temperatures varying from 60° Fah. to 220° Fah.
Father Secchi, for the basis of his calculations, adopted the experiments made by M. Soret on Mont Blanc and in other mountainous regions, in order that he might avoid as much as possible the errors introduced into the results by atmospheric influences. He obtained a difference of 29.02 Cent. (= 52.24 Fah.) between the temperature of the thermometer and that of the enceinte.
M. Pouillet appears to have obtained a somewhat higher figure. Mr. Ericsson, whose observations have decidedly been conducted with greater care to avoid disturbing influences, and with more completeness than those of any other observer, arrived at 67.20° Fah., as the effective intensity of solar radiation at aphelion, and 72.68° Fah. for perihelion. The difference between these two temperatures coincides very closely with that which he has calculated as the necessary effect of the nearer approach of the earth to the sun at the latter period of the year.
The figures thus ascertained require correction (1) for the absorption by the earth's atmosphere, which is approximately known; and (2) for that of the sun's absorption, as to which the widest differences of opinion exist. It then remains to determine what the temperature of a body must be which can radiate so large a quantity of heat across the space which divides the sun from the earth. Here, again, irreconcilable differences of opinion exist as to the law of radiation. Pouillet, and with him a number of eminent French physicists, have adopted the law of cooling established by Dulong and Petit. According to this, the radiation increases so much more rapidly than the temperature, that an increase of 600° in temperature multiplies a hundredfold the energy of radiation. Using this law Pouillet fixed the temperature of the sun's surface, or rather that portion of it which is effectively radiated into space, at from 1,461° to 1,761° Cent. (= 2,630 to 3,170 Fah). Vicaive, adopting Secchi's value of the solar radiation, obtains by the same law a temperature of 1,398° Cent., or about 2,520° Fah., and estimates that, when all the necessary corrections have been made, the result must still be less than 3,000° Cent.—say 5,400° Fah.
Both Secchi and Ericsson refuse to accept Dulong's law, and fall back on that of Newton, who assumed that the intensity of radiation from a hotter body to a cooler one must be proportionate to the differences of their temperatures and to the distance between them. The latter element of the calculation is of course treated in the same manner by both parties.Pro-
ceeding in this matter, Ericsson fixes the solar temperature at 4,035,584° Fah.; whilst Father Secchi makes it at least 18,000,000° of the same scale. The widest difference in their treatment of the question lies in their respective estimates of the absorbing power of the sun's atmosphere. I need not stop to consider the arguments they adduce, each in support of his own view. So far as they differ on other points, I have no hesitation in accepting Ericsson's results as the more reliable of the two. As to the influence of the absorbing media in the neighbourhood of the sun, there can be no doubt that it is much better, in the present state of our knowledge, to limit our investigation to a search for the value of the effective radiation, instead of seeking to calculate what actual internal temperature this must indicate.
We find, then, that the basis of all these various calculations of the temperature of the sun is the ascertained difference between the temperature established in a terrestrial object on which the rays of the sun shine directly, and the general temperature of surrounding objects more or less completely screened from those rays. It appears to me that the indications thus trusted to are not satisfactory definitions of the work which the solar rays are actually performing. They fall very far short of this, because what we want to know is not the difference which has thus been measured, but the difference between the actual temperature the sun's rays can create in terrestrial objects, and the temperature at which those objects would rest if the heat radiated from the sun were withdrawn.
The earth itself is a heated body, and a certain temperature would exist at its surface if the solar radiation ceased entirely. This temperature would steadily fall, in consequence of the earth's own radiation into space; but what we need to ascertain is the initial temperature for the moment of withdrawal of the solar heat, if such an event could happen. The difference of this temperature, and the highest which a thermometer will indicate when subjected to the action of a vertical sun on the clearest day, with a corrective introduced for the (approximately known) absorption of the terrestrial atmosphere, is the nearest measure we can obtain of the actual solar radiation. Evidently this quantity will greatly exceed any of those which have hitherto been adopted by physicists.
It can hardly prove impossible to determine how much of the average temperature at the surface of the earth is due to the solar heat and how much to the internal heat of the earth. The condition of affairs produced by our long polar winter nights offers us data in one direction. That which obtains in arid equatorial wastes will serve us in the other direction. Even when all the necessary data are collected, the problem will not be easy of solution; but an approximate estimate cannot be beyond the power of our
scientific men, armed with all the knowledge of the laws and character of heat which has already been accumulated. It appears to me that this estimate is the absolutely necessary basis of any such calculations as Secchi, Ericsson, and others have been attempting.
Again, as the basis appears to me yet wanting, so also is it with the methods of working back from it to the desired object–the temperature of the sun, and on this point, also, I ask leave to submit one or two considerations.
We have discarded from our minds the old idea that heat is a distinct unponderable substance, which so many considerations force upon us, that it is only a vibratory motion in what we call ether and in the ultimate molecules of those bodies which display it. Nevertheless, we are a long way from being able to conceive distinctly the character of this motion which we call heat. The discussions which have taken place on this subject of solar temperature and radiation appear to me to be clouded by the old notion of heat as a communicable substance. Not that any such idea was present in the minds of eminent men who have busied themselves with the question. But the want of a terminology in which to express definitely our modern ideas of heat makes itself felt the moment that any discussion of this sort is enterprised. This will remain very much the same until we can cease to speak of heat and define its manifestations as this or that species of molecular action, and we are a very long way yet from this desirable position. When we speak of the effects of solar radiation, we are, after all, only relating the effect this will produce in the body we use as a heat measurer–say in the mercury of a thermometer bulb. We know very well that the sun's rays never, under identical circumstances, communicate such a temperature as we speak of to the atmosphere. We talk of the different powers of absorbing heat possessed by different bodies. The phrase is borrowed from our discarded theories of caloric. We want to know not how hot the mercury becomes, but how many thermal units per second radiated to it are necessary to maintain it at that temperature in spite of the influence of all the surrounding circumstances. Time must be an element in the definition of solar heat-energy, and before we claim that a certain temperature must exist at the surface of the sun, we must learn the relations between what we call radiation of heat and its constant re-development at the radiating surface. All our experiments on this subject have hitherto (with few exceptions) been conducted with bodies which were actually cooling rapidly. If the sun must be put in the category of bodies which are in process of cooling down—and we have as yet no evidence to prove this, or even to negative a contrary supposition–its rate of cooling, as compared with human eras of time, must be infinitesimally slow. For any period over which our experi-
ments can be extended it may be assumed that the heat expended in radiation is simultaneously re-developed in the photosphere of the sun. Before, then, we can say what heat-energy at the surface of the sun, the work its rays do at this distance, implies we have a great deal to learn, and a totally new series of experiments to make.
Other considerations lead us to the same doubt of the reliability of the estimates that have hitherto been made of the solar temperature. What is it that we call a ray of heat from the sun? It is at the earth's surface a vibration of the ether, a series of waves whose lengths may vary somewhat, but is never very different from 1/39,000 part of an inch, travelling at a speed somewhat less than 200,000 miles per second. We have only to draw together as many of them as will pass through an aperture measuring a few square feet, and at the point of their intersection they cause such a commotion as will dissipate into vapour any terrestrial substance whatsoever. But if we let the focal point form in mid air, or in any gas, nothing happens to give us evidence of this storm of molecular motion. Yet, if it were what we call an enormous temperature that existed there and vapourized the granite which we subjected to its action, it must be still present when nothing is presented to its action. Since then these rays emanated from masses of incandescent gas and vapour, the molecular motion, which we call the temperature of the sun, may differ very little from that induced in the molecules of a gas in which a bundle of these rays is concentrated by our lens. The sun's rays, which at once drive asunder the molecules of a solid body until they have assumed vibrations and motions amongst themselves, which define the condition we call vapour, will pass through that vapour itself with scarcely any effect upon it, so far as we have been able to observe their action. Is it necessary to suppose that there is no limit to that molecular agitation we call heat? or that the molecules of the incandescent gases of the photosphere must vibrate a million times more energetically than those which exist at ordinary temperatures on the surface of the earth? Again, we may well ask what meaning do we attach to “increase of temperature?” What is the change in the nature of the vibration we call heat which corresponds to our words hotter and colder? As we at present conceive it, increased temperature means a greater amplitude of vibration in the heated molecule. Must there not be a limit to the excursions of the swinging atom? In that train of vibrations, which we call a ray of heat, we can approximately measure the distance from one wave crest to another, and, so far as we know, the variation in this distance for different temperatures is proportionately very slight indeed. If then the amplitude of vibration, the height of the wave, be continually increased, is it not certain that a point must be reached at
which the magnitude of the excursion of the vibrating particle will be so great as of necessity to alter the wave length, if it be further increased? We need to be a great deal more competent to answer such questions as these before we can assure ourselves that any of our observations yield us the data, or any of our calculations form the logical processes, which will lead us to a definition of the temperature of the sun.
1.“On the cause of the former great Extension of the Glaciers in New Zealand,” by Captain F. W. Hutton. (See Transactions, page 383.)