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THE ABSORPTION OF HEAT IN THE SOLAR ATMOSPHERE.
By W. E. WILSON, M.R.I.A., AND A. A. RAMBAUT,
[Read MAY 9, 1892.]
One of the most interesting questions in Solar Physics which awaits solution is-Does the quantity of heat received by the earth from the sun vary from year to year, or is it a constant ? Assuming that the internal temperature of the sun remains constant, there are yet two factors, variations in which would cause the amount of solar heat received by the earth to vary. These are—the absorption of heat in the solar atmosphere, and the absorption in the earth's atmosphere. It is with the first of these that we propose to deal in this paper. From the accompanying diagram (fig. 1) it will be seen that the amount of absorption at the edge of the disc of the sun must be much larger than at the centre. This fact has long been known as a matter of observation. Professor Henry of Princeton, in 1845, was the first to discover this, and it has since been confirmed by Secchi, Langley, and many others.
These observers all make the amount of heat coming from a point on the edge of the disc about half that coming from the centre. It is also an interesting subject of inquiry, how much of the sun's total heat is absorbed by his atmosphere. Laplace, making certain assumptions, R.I.A. PROC., SER. III., VOL. II.
found that the sun would be 12 times as bright if he was stripped of his atmosphere. Pickering, taking other data, says that the sun without his atmosphere would be 43 times as bright as it is. Langley and some others have investigated this difficult problem, and whatever the true amount may be, one thing is quite certain that the sun's radiation is stopped to a considerable extent by his atmosphere. If the solar atmosphere varies in depth it is plain from the diagram that the ratio of the absorptions at the centre and edge of the disc will vary, and if accurate measures were taken from time to time of these quantities, we could determine whether the depth of the solar atmosphere was constant or variable. It is with reference to the solution of this problem that we bring the following researches to your notice.
In 1884 Mr. Wilson had an apparatus made to carry out some experiments in this direction. It consisted of two small thermo-piles which were coupled up in such a way that as long as the corresponding faces of both continued at the same temperature the galvanometer remained at zero. At first, both piles were placed on the edge of the solar image formed by a large Cassagrain reflecting telescope. When the galvanometer was steady at zero one of the piles was moved into the centre of the disc. The deflection of the galvanometer was noted. The experiment was then repeated again and again, each time reversing the order of the piles. These experiments gave 0·52 as the heat from the limb, that from the centre being 1.00. Mr. Wilson soon came to the conclusion that some more accurate means would have to be devised before any final result could be reached. In 1888 Professor C. V. Boys invented his radio-micrometer. It is an instrument of extraordinary sensibility to radiant heat, and it occurred to Mr. Wilson that it would be an excellent instrument to use in these researches. In the first place it is so sensitive that we can use an enormously large image of the sun and still get plenty of heat to affect the instrument, and secondly it is very prompt and dead beat in its motion. The sensitive surface on which the heat is allowed to fall is only about 2 m.m. square, so that a very small portion of the solar surface can be examined at one time. Using an image of the sun of 80 c.m. in diameter, the instrument only covers the good orth part of the entire disc.
In 1888 Mr. Wilson fitted up a heliostat with silvered mirrors which reflected a small beam of sunlight into a dark room. It was received by a concave mirror of 10 feet focus, and a small convex mirror was placed inside of the focus : this formed a fine image of the sun 80 c.m. in diameter. In the plane of this image the radio-micrometer was set on a heavy slate shelf. A slice of limelight was allowed to fall on the
mirror of the instrument and reflected from that to a scale. The relative position of the various parts of the apparatus is shown in fig. 2.
At first readings were taken with the edge of the sun and centre alternately on the instrument. On account of the very rapid fall in heat near the edge, this plan was not found to give satisfactory results; and at present the best results are got by allowing the image of the sun to transit across the instrument, and by recording the motion of the spot of limelight by means of a falling photographic plate.'
It became evident, from the first photographic curve obtained, that to translate its meaning, corrections would have to be applied for some disturbing causes, such as the damping effect of the air, and the variation in intensity of the source of heat to which the instrument was exposed. Dr. Rambaut has investigated these matters, and below will be found an exposition of the methods he has adopted to surmount the difficulties. What we now propose to do is to take frequent curves of absorption from time to time throughout a sun-spot cycle of 11 years, and thus try to solve the problem-Whether the sun's atmosphere varies in depth in that time. From a comparison of the photographs taken of it in maximum and minimum years, it would appear that the sun's corona varies in form, and also that the spots alter their characters in the same period. Is it not probable that changes are also taking place in the solar atmosphere? If we find that such changes are taking place, as will be shown by the alteration in the ratio of the heat from the limb
1 See British Assoc. Report, Cardiff, 1891 ; Trans. of Section A.
2 C 2
and centre of the disc, we think it will be quite possible, by an investigation of the co-ordinates of these curves, to determine the change in the value of the solar constant.
EXAMINATION OF THE CURVES.
From the nature of the instrument it is clear that the only forces acting on the system are the directive force of the magnet, the force of torsion, and the resistance of the surrounding medium. If we denote the angle of torsion by d, and the difference in temperature between the two ends of the couple by ®, we obtain the following differential equation representing the motion :
in which 2a is the resistance of the medium, bo the torsion, and co the directive force of the magnet.
Also, if K denotes the intensity of the heat falling on the heated end of the couple, we have the equation
For the following method of obtaining this euqation we are indebted to Professor G. F. Fitzgerald :
If we suppose 0, and 0, to be the elevation of temperature of the two ends of the couple above that of the surrounding medium, and if we suppose the couple divided into a number of segments ds, taking into account the resistance of the couple, a Peltier absorption of heat at the hotter, and emission of heat at the colder end, and a Thomson effect at other parts of the wire, we have, for any segment after the first, an equation of the form
in which TC is the Thomson effect, the conduction, på the radiation, and r C2 the heating by resistance. At the ends themselves we have a Peltier, instead of a Thomson, effect; and for the heated end the equation becomes
a = £K - P.C +6 d. i - p8, + rC”, and for the other end
20 = kW + P,C-o a - p@s + rC", in which P, C and P, C represent the Peltier effects at the two ends of the couple. We thus obtain de, dd,
i nie (de, de on the go = kW – (P2 + P.) C+) - P(8. – 6a). We may also assume that the terms and are each to a first approximation proportional to the difference of temperature, so that we obtain
14 = kK - 10 -(P+ Ps) C. The last term here is so small that in an investigation like the present we may neglect it so that we reach the result given in equation (2).
If now we eliminate between equations (1) and (2) we obtain the following linear differential equation of the third order
* + (2a + 1)* + (6 + 2al) als + Pol= ckK. (3) In the method of observation described above the intensity K is a function of the time, so that we obtain the equation
Denoting the roots of the equation x2 + 2ax + b2 = 0 by - m and – n, and remarking that
we obtain the solution of equation (4) in the form