640 



SCIENCE 



[N. S. Vol. XXX. No. 775 



with the planetesimal hypothesis, for the al- 

 leged error occurs in a discussion of the 

 Laplacian theory in connection with the ninth 

 satellite of Saturn. In this, I have used only 

 the universally accepted principle of dynamics 

 that the moment of momentum of any mass 

 about an axis can be changed only by a 

 couple about the same axis. I can not accept 

 the interpretation Dr. Lowell puts on my 

 words, nor admit the correctness of his con- 

 tention. 



The statements which contain the third 

 and fourth alleged errors do, indeed, appear 

 in my discussion of the planetesimal hypothe- 

 sis. They are quoted by Dr. Lowell, one as 

 being " on page 480," and the other as being 

 " from pages 4Y8 to 481." They are, however, 

 not only a part of the same discussion, but are 

 in a single short paragraph on the same page 

 (480). The third alleged error is in a formula 

 occurring at the end of the fourth alleged 

 erroneous statement, and gives the precise 

 condition under which the conclusion reached 

 is true. I suppose it is a part of the new logic 

 to divide what is indivisible by the old logic, 

 to invert the order, to give reference to the 

 specific page of one, and to state simply that 

 the other lies between certain pages; or, the 

 last may be for rhetorical effect, as it avoids 

 the repetition of a page-number, which might 

 become monotonous if given more than once. 



Not being as yet very familiar with the new 

 logic, I will, with Dr. Lowell's permission, 

 treat the statements in the order in which they 

 occur in my book. The point in question is 

 the effect of the collision of meteoric masses 

 upon the dimensions of satellite orbits, par- 

 ticularly in the earlier stages of their develop- 

 ment. By carefully omitting, in his last quo- 

 tation, the sentences in which I have given the 

 conditions under which my conclusions are 

 true, he has made it appear that I have made 

 categorical statements of universal applica- 

 tion, and he has then found examples outside 

 of the conditions clearly specified where my 

 conclusions are not true. He then asserts 

 that this is a " disproof " of the planetesimal 

 hypothesis. 



The associated alleged error is in the form- 



ula expressing the final conditions under which 

 my conclusions are true. Dr. Lowell's friends 

 will regret to learn that he has been over- 

 hasty in criticizing it, considering the weighty 

 conclusion he has hung upon his criticism. 

 In the first place he has not quoted it quite 

 correctly, and in the second place he starts 

 from an erroneous equation himself. Since 

 the linear units are not specified, the elemen- 

 tary principle of homogeneity of units should 

 have shown him that the right member of his 

 first equation is incorrect. Its left member is 

 also inexact, due apparently to an erroneous 

 use of the integrals of the two-body problem. 

 If we let fi, represent the mass of the satellite, 

 his first equation should have been the in- 

 equality 



/ 





■V^ 



'M-^li, 



i/l- 



/F^ 



'A'iJ 



Developing and omitting the negligible terms 

 of higher order, we get precisely the formula 

 given in my book. Consequently I stand by 

 the conclusions reached in my book on this 

 subject when the conditions are satisfied 

 under which I have clearly stated they are 

 true. 



Now of the planetesimal hypothesis itself, 

 which is much more important in the present 

 connection, Dr. Lowell appears really to have 

 a very excellent opinion, barring its tag and 

 signs of parentage. In his " Mars as the 

 Abode of Life " (1908) he says, pp. 3 and 4 : 



So far as thought may peer into the past, the 

 epic of our solar system began with a great 

 catastrophe. Two suns met. ... It is not to be 

 supposed that the two rovers actually struck, the 

 chances being against so head-on an encounter; 

 but the effect was as disastrous. Tides raised in 

 each by the approach tore both to fragments, the 

 ruptured visitant passing on and leaving a dis- 

 membered body behind in lieu of what had been 

 the other. . . . Thus, what had been a sun was 

 left alone, with its wreckage strewn about it. 

 Masses large and small made up its outlying 

 fragments, scattered through space in its vicinity, 

 while a shattered nucleus did it for core. 



On page 6 he says : 



Thus they [the meteorites] proclaim themselves 

 clearly fragments of some greater body. To the 



