ASTRONOMY. 203 



It is first proposed that the rate of expansion of the planetary orbits, 

 due to the reaction of the frictional tides raised hy the planets in the 

 Qun, must be very slow compared with that due to the reaction of the 

 tides raised by the sun in the planets. Thus it would be much more 

 nearly correct to treat the sun as a rigid body, and to suppose the 

 l)lanets alone to be subject to frictional tides than the converse. It did 

 not, however, seem exi^edient to attempt to give any numerical solution 

 of the problem thus suggested, which should api^ly to the solar system 

 as a whole. The effect of tidal friction is to convert the rotational 

 momentum of the tidally-disturbed body into orbital momentum of the 

 tide-raising body. Hence, a numerical evaluation of the angular mo- 

 mentum of the various parts of the solar system will atiord the means 

 of forming some idea of the amount of change in the orbits of the sev- 

 eral planets and satellites which have been produced by tidal friction. 

 Such an evaluation is accordingly made in this paper, with as much 

 accuracy as the data permit. 



From the numerical values so found, it is concluded that the orbits 

 of the planets round the sun can hardly have undergone a sensible 

 enlargement from the effects of tidal friction, since those bodies first 

 attained a separate existence. 



Turning to the several subsystems it appears that althougli it is pos- 

 sible that the orbits of the satellites of Mars, Jupiter, and Saturn about 

 their planets may have been considerably enlarged, yet it is certainly 

 not possible to trace the satellites back to an origin almost in contact 

 with the present surfaces of their j^lanets, in the same manner as was 

 done for the case of the moon in the j)revious iiapers. 



The numerical values above referred to exhibit so marked a contrast 

 between the case of the earth with the moon, and that of the other 

 planets with their satellites, that it might, a priori, be concluded as prob- 

 able that the modes of evolution have differed considerably. The con- 

 clusion above stated concerning the satellites of the other planets can- 

 not therefore be regarded as unfavorable to the acceptance of the views 

 maintained in the previous papers. It must, however, be supposed that 

 some imi^ortant cause of change, other than tidal friction, has been con- 

 ceived in the evolution of the solar system and the planetary subsys- 

 tems. According to the nebular hypothesis of Laplace, that cause has 

 been the condensation of the heavenly bodies. Accepting that hypoth- 

 esis the author then proceeds to consider the manner in w^hich contrac- 

 tion and tidal friction are likely to have Avorked together. 



A numerical comparison shows tliat notwithstanding the greater age 

 which the nebular theory assigns to the exterior planets, yet the effects 

 of solar tidal friction in reducing planetary rotation must, in all proba- 

 bility, be considerably less for the remote than for the nearer planets. 

 It is, however, remarkable tliat the number expressive of the rate of 

 retardation of the Martian rotation by solar tidal friction is nearly the 

 same as the similar number for the earth, notwithstanding the greater 



