This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ... series convergent else any conclusions, as to the values of h's, deduced from them are not legitimately established. The number of conditions, necessary to insure stability, of course increases with the number of bodies composing the system. In all cases, the constant annexed to the integral of living forces in relative motion must be negative. It is needless to say that in the solar system this condition is fulfilled. Certain popular writers have got it that incommensurability of mean motions is a sine qua non of stability but I am not aware that this has been asserted by any geometer or astronomer of note. This mistake doubtless arose from noticing that the near approach of mean motions to commensurability produces inequalities having large coefficients through the division by the small mean motion of the argument. But it will not do to assume that these coefficients increase beyond every limit when the mean motion of the argument diminishes without limit, or that when this vanishes, there are terms in the planetary elements proportional to the time. Let us illustrate this point more at length. If a is the mean distance of one of the planets, and 6 an argument whose mean motion nearly or altogether vanishes then, so far as this argument is concerned, we may have the equation do. w = Asme. If the mean motion of 6 is supposed to vanish, the integral of this equation is often written a = a0 A sin 6. t, a0 being the value of a at the origin of time. But, although this treatment is allowable when we wish to find the value of a for small values of t, it will not answer when the object is to discover whether a is a periodic function of t or not. For it has been assumed that A is constant, whereas it is a function, not only of a, ..."
About George William Hill
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Author  :  George William Hill 
Publisher  :  Theclassics.Us 
Data Published  :  12 September 2013 
ISBN  :  1230859268 
EAN  :  9781230859262 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  78 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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