ORIGIN OF THE SOLAR SYSTEM JEANS 157 



the satellites of these planets. For immediately after the birth of 

 any planet, say Jupiter, the original situation repeats itself in minia- 

 ture. Jupiter now plays the part originally assigned to the sun, 

 while either the wandering star or the sun itself, or possibly the com- 

 bination of the two, acts the part of the tide-raising disturber. Again 

 we get the emitted filament, again the formation of condensations, 

 and again, as the ultimate result, a sequence of detached bodies with 

 the most massive in the middle. Since Jupiter, the sun, and the dis- 

 turbing star all move in the same plane — namely, the plane of Jupi- 

 ter's orbit — it follows that Jupiter's satellites, when formed, ought 

 also to move in this plane, as in actual fact they are observed to do. 



So long as we merely discuss the matter in general terms it looks 

 as though the process might go on for generation after generation, 

 each member of a family of satellites producing minor satellites to 

 circle round itself, and so on ad infinitum. Common sense suggests 

 that this can not go on forever; there must be a limit somewhere. 

 Exact calculation confirms the view of common-sense, with the dis- 

 concerting addition, that we are in danger of overstepping the limit 

 if we attempt to account for the whole of the satellites in the solar 

 system in the way just suggested. 



I have already mentioned a mathematical formula which enables 

 us to calculate the masses of the bodies formed out of the condensa- 

 tions in the arms of spiral nebulae. The same formula puts us in a 

 position to calculate the' masses of the planets which ought to be 

 formed from the filament drawn out of the sun. Let us suppose that 

 when the tidal cataclysm took place the sun had a radius equal to 

 that of Neptune's orbit, and therefore a mean density of 5.5X10"". 

 Let us suppose that at the middle parts of the ejected filament the 

 mean density was one-tenth of this, or 5.5X10"^^. Let us further 

 suppose that the temperature of the ejected matter corresponded to a 

 molecular velocity 4X10^, this being about the molecular velocity of 

 hydrogen or oxygen at their ordinary boiling points. Then our 

 formula indicates that the masses of the planets formed out of the 

 middle parts of the filament ought to be about 10^° gm., a mass inter- 

 mediate between those of Jupiter and Saturn. This is satisfactory as 

 showing that there is no numerical difficulty in supposing Jupiter 

 and Saturn to have come into being in the Avay we have imagined. 

 If we like to accept the tidal theory of their birth, we can reverse 

 our calculation and can calculate from their present known masses 

 what must have been the density of the matter from which they were 

 formed. 



Naturally an inverted calculation of this kind is not applicable 

 only to Jupiter and Saturn ; if the tidal hypothesis is correct it must 

 be applicable to all the planets and to all their satellites. For ex- 

 ample, the first five satellites of Saturn all have masses of about 

 20397—25 12 



