NATURE 



[Jan. 27, I i 



frictionless. Let the pit be a metre square at its upper 

 end, and let it be excavated quite down to the sun's centre, 

 everywhere of square horizontal section, and tapering 

 uniformly to a point at the centre. Let the weight be 

 simply the excavated matter of the sun's mass, with merely 

 a little clearance space between it and the four sides of 

 the pit, and a kilometre or so cut off the lower pointed 

 end to allow space for its descent. The mass of this 

 weight is 326 x 10'' tons. Its heaviness, three-quarters of 

 the heaviness of an equal mass at the sun's surface, is 

 244 X 10" tons solar surface-heaviness. Now a horse- 

 power is 270 metre-tons, terrestrial surface-heaviness, per 

 hour ; or 10 metre-tons, solar surface-heaviness, per hour. 

 To do 78,000 horse-power, or 780,000 metre-tons, solar 

 surface-heaviness, per hour, our weight must therefore 

 descend at the rate of i metre in 313 hours, or about 28 

 metres per year. 



To advance another step, still through impracticable 

 mechanism, towards the practical method by which the 

 sun's heat is produced, let the thread of the screw be of 

 uniformly decreasing steepness from the surface down- 

 wards, so that the Velocity of the weight, as it is allowed 

 to descend by the turning of the screw, shall be in simple 

 proportion to distance from the sun's centre. This will 

 involve a uniform condensation of the material of the 

 weight ; but a condensation so exceedingly small in the 

 course even of tens of thousands of years, that, whatever 

 be the supposed character, metal or stone, of the weight, 

 the elastic reaction against the condensation will be utterly 

 imperceptible in comparison with the gravitational forces 

 with which we are concerned. The work done per metre 

 of descent of the top end of the weight will be just four- 

 fifths of what it was when the thread of the screw was 

 uniform. Thus, to do the 78,000 horse-power of work, the 

 top end of the weight must descend at the rate of 35 

 metres per year : or 70 kilometres, which is one one- 

 hundredth per cent. (1/10,000) of the sun's radius, per 

 2000 years. 



Now let the whole surface of our cool solid sun be 

 divided into squares, for example as nearly as may be of 

 I square metre area each, and let the whole mass of 

 the sun be divided into long inverted pyramids or pointed 

 rods, each 700,000 kilometres long, with their points 

 meeting at the centre. Let each be mounted on a screw, 

 as already described for the long tapering weight which 

 we first considered ; and let the paddle at the top end of 

 each screw-shaft revolve in a fluid, not now confined to a 

 vat, but covering the whole surface of the sun to a depth 

 of a few metres or kilometres. Arrange the viscosity of 

 the fluid and the size of each paddle so as to let the 

 paddle turn just so fast as to allow the top end of each 

 pointed rod to descend at the rate of 35 metres per year. 

 The whole fluid will, by the work which the paddles do in 

 it, be made incandescent, and it will give out heat and 

 light to Just about the same amount as is actually done by 

 the sun. If the fluid be a few thousand kilometres deep 

 over the paddles, it would be impossible, by any of the 

 appliances of solar physics, to see the difterence between 

 our model mechanical sun and the true sun. 



Now, to do away with the last vestige of impracticable 

 mechanism, in which the heavinesses of all parts of each 

 long rod are supported on the thread of an ideal screw 

 cut on a vertical shaft of ideal matter, absolutely hard 

 and absolutely frictionless : first, go back a step to our 

 supposition of Just one such rod and screw working in a 

 single pit excavated down to the centre of the sun, and 

 let us suppose all the rest of the sun's mass to be rigid 

 and absolutely impervious to heat. Warm up the matter 

 of the pyramidal rod to such a temperature that its mate- 

 rial melts and experiences enough of Sir Humphrey 

 Davy's " repulsive motion " to keep it balanced as a fluid, 

 without either sinking or rising from the position in which 

 it was held by the thread of the screw. When the matter 

 is thus held up without the screw, take away the screw 



or let it melt in its place. We should thus have a pit from 

 the. sun's surface to his centre, of a square metre area at 

 the surface, full of incandescent fluid, which we may sup- 

 pose to be of the actual ingredients of the solar substance. 

 This fluid, having at the first instant the temperature with 

 which the paddle left it, would at the first instant continue 

 radiating heat just as it did when the paddle was kept 

 moving ; but it would quickly become much cooler at its 

 surface, and to a distance of a few metres down. Con- 

 vection-currents, with their irregular whirls, would carry 

 the cooled fluid down from the surface, and bring up 

 hotter fluid from below, but this mixing could not go on 

 through a depth of very many metres to a sufficient 

 degree to keep up anything approaching to the high tem- 

 perature maintained by the paddle; and after a few hours 

 or days, solidification would commence at the surface. If 

 the solidified matter floats on the fluid at the same tem- 

 perature below it, the crust would simply thicken as ice 

 on a lake thickens in frosty weather ; but if, as is more 

 probable, solid matter, of such ingredients as the sun 

 is composed of, sinks in the liquid when both are at the 

 melting temperature of the substance, thin films of the 

 upper crust would fall in, and continue falling in, until, for 

 several metres downwards, the whole mass of mixed solid 

 and fluid becomes stiff enough (like the stiffness of paste 

 or of mortar) to prevent the frozen film from falling down 

 from the surface. The surface film would then quickly 

 thicken, and in the course of a few hours or days become 

 less than red-hot on its upper surface. The whole pit full 

 of fluid would go on cooling with extreme slowness until, 

 after possibly about a million million million years or so, 

 it would be all at the same temperature as the space to 

 which its upper end radiates. 



Now, let precisely what we have been considering be 

 done for every one of our pyramidal rods, with, however, 

 in the first place, thin partitions of matter impervious to 

 heat separating every pit from its four surrounding neigh- 

 bours. Precisely the same series of events as we have 

 been considering will take place in every one of the 

 pits. 



Suppose the whole complex mass to be rotating at the 

 rate of once round in 25 days. 



Now at the mstant when the paddle stops let 

 all the partitions be annulled, so that there shall 

 be perfect freedom for convection-currents to flow 

 unresisted in any direction, except so far as resisted 

 by the viscosity of the fluid, and leave the piece of matter, 

 which we may now call the .Sun, to himself. He will 

 immediately begin showing all the phenomena known in 

 solar physics. Of course the observer might have to 

 wait a few years for sunspots, and a few quarter-centuries 

 to discover periods of sunspots, but they would, I think 

 I may say probably, all be there just as they are ; because 

 I think we may feel that it is most probable that all these 

 actions are due to the sun's own mass and not to external 

 influences of any kind. It is, however, quite possible, 

 and indeed many who know most of the subject think it 

 probable, that some of the chief phenomena due to sun- 

 spots arise from influxes of meteoric matter circling round 

 the sun. The energy of chemical combination is as 

 nothing compared with the gravitational energy of shrink- 

 age, to which the sun's activity is almost wholly due, but 

 chemical combinations and dissociations may, as urged 

 by Lockyer, be thoroughly potent determining influences 

 on some of the features of non-uniformity of the brightness 

 in the grand phenomena of sunspots, hydrogen flames, and 

 corona, which make the province of solar physics. But 

 these are questions belonging to a very splendid branch 

 of solar science with which we are not occupied this 

 evening. 



What concerns us at present may be summarised in 

 two propositions : — 



(i) Gigantic convection-currents throughout the sun's 

 liquid mass are continually maintained by fluid, slightly 



