Septembee 10, 1909] 



SCIENCE 



339 



attraction would generate a velocity of nearly 

 seven miles per second in a body falling from an 

 infinite distance into its atmosphere, whether the 

 sun were attracting it or not. The greatest rela- 

 tive velocity will be when the earth and meteor 

 meet, which is 25 + 7 + 18 = 50 miles per second. 

 The least will be when the meteor overtakes the 

 earth, which is 25 + 7 — 18=14 miles per second. 



Now the velocities due to the sun's attrac- 

 tion and to the earth's upon a particle falling 

 to the latter under the action of both can not 

 be added in this simple manner. 



The geometric explanation why the veloc- 

 ities can not be directly added is that when 

 each body is supposed to act alone the times 

 involved in their actions are different, while 

 when they act together these are naturally the 

 same. In the latter case the velocity due the 

 sun hurries the particle through the space 

 faster than the earth's pull alone could and so 

 gives the earth less time to act. 



For the analytical solution of the problem 

 the reader is referred to a paper in the Astro- 

 nomical Journal, No. 601, in which he will find 

 that the speed the earth can impart depends 

 on the mode of approach, that it can never ex- 

 ceed 2.66 miles a second and may fall as low 

 as 0.53 mile. 



We shall now go on to what concerns the 

 hypothesis more directly. The first point we 

 shall mention is found on page 460. In the 

 criticism of the suggestion that " when Saturn 

 extended out to the orbit of the ninth satel- 

 lite, it rotated in the retrograde direction with 

 the period of this body," the book says : 



When the rotation period of the nebulous mass 

 equaled that of its revolution, it filled some space 

 aa that indicated by the dotted curve in Fig. 108. 

 Up to this time the tides generated by the sun had 

 increased its moment of momentum by changing 

 it from a negative quantity to a certain positive 

 quantity. After this time the tides generated by 

 the sun decreased its moment of momentum, for 

 they always retarded the rotation. Therefore, if 

 the theory is true, the greatest moment of mo- 

 mentum in the whole history of the Saturnian 

 system should be found when the day and year of 

 its nebula were equal. 



The fallacies here are two: (1) It is sup- 

 posed that the sun-tides would act solely in the 



Saturnian plane ; whereas they would undoubt- 

 edly turn the system over in the act. (2) The 

 moment of momentum here considered is that 

 of the solar system ; whereas in the generation 

 of satellites it is that of the Saturnian system 

 itself, a totally different matter; so that the 

 supposed destructive proof falls to the ground. 



The next point is on page 480, where we are 

 told with regard to the acceleration of a satel- 

 lite nucleus by a particle m that 



It is found by a mathematical discussion that 

 this always results if the eccentricity of the orbit 

 of m is greater than 



It 



+ 



MB 



where R is the radius of the orbit of the planetary 

 nucleus around the sun, r the radius of the satel- 

 lite nucleus around M, and il the mass of the 

 planetary nucleus expressed in terms of the sun's 

 mass. In the case of the earth and moon the 

 limit comes out 0.035, but in the case of the larger 

 planets and closer satellites it is very much larger. 



Now the determining equation is 



whe 



whence 



ViJ— \ r ~y£r—2 a 



a(I + e) =R — r 



H- 



-231+ ■ 



■^^+a 



or taking terms of the first order only 

 jMB MR 



e = 2' 



approx. 



Comparing this with the printed value we see 

 that a term of the first order has been omitted 

 and one of the second kept. The result is 

 that with Jupiter and his fourth satellite we 

 have 



true value e=r0.86 

 planetesimal value e=1.26 



or actually a hj-perbolic orbit. 



The next point is from pages 478 to 481. 

 The book says, speaking of the effect of par- 

 ticles inside the planet's orbit : 



The satellite nucleus is carried forward by the 

 motion of M, while it moves backward in its 

 revolution around M. The latter is a much slower 

 motion than the former. ... It follows from the 



