CEKTAIN HARMONIES OF THE SOLAR SYSTEM. 17 



isECTION III. 



APPLICATION OF THEORETICAL CONSIDERATIONS AND THE DEVELOPMENT OF OTHER 



RELATIONS. 



(24) The further discussion of the relations exhibited in Section II. will be 

 aided, and circumlocution, at the same time, avoided, by the introduction of con- 

 siderations having reference to the Nehular Hy;pothesis of Laplace ; and this espe- 

 cially in the exposition of other relations, the investigation of which was prompted 

 by suggestions furnished by the application of this very hypothesis somewhat 

 extended and modified, in a manner now to be specified. 



In the exposition of his hypothesis, its illustrious author supposes the atmos- 

 phere of the rotating Sun to have extended, in ancient times, to the limit (or, when 

 at the furthest, very near to the limit) at which the centrifugal force of rotation 

 must have balanced the force of attraction. 



That afterwards — the atmosphere shrinking from loss of heat —the rotation (for 

 reasons which he specifies) would be accelerated as the atmospheric molecules drew 

 nearer to the centre of the Sun,^ and, that the limit in the plane of the Sun's 

 equator, at which the two forces — 



centripetal andt centrifugal — would ^'g- ^- 



balance one another, would, there- 

 fore, be found further and further in.^ 



That thus successively, at new 

 limits in the plane of the Sim's equa- 

 tor, further and further inward, the 

 centrifugal and centripetal forces 

 would indeed balance one another; insomuch that the tliiii and narroio zmes thus 

 inequilibrio in the plane of the equator (they having no tendency either to fall in or 

 to be thrown off), would themselves be "abandoned" by the atmosphere in its 

 farther shrinkage.^ 



(25) The description then goes on to state that the same equilibrium of forces 

 not existing with respect to the atmospheric molecules situated on the parallels to 



' The loss of heat will not affect the moment of rotation— the turning power— and every mole- 

 cule (because of the shrinkage) having a shorter circuit, will accomplish it in less time. Then also, 

 as shown hereafter, there will be some acceleration of the actual velocilij._ The original phraseology, 

 as it were, anticipates this also, and provides for both. "La rotation doit etre plus prompte, qaand 

 ces molecules se rapprochent du centre du soleil." — Exposition du Syst&me du Monde. Note VI.I- 



» The centrifugal force, in accordance with its law, increasing at a more rapid rate than the 

 attractive force; the centrifugal force (with conservation of areas) varying inversely as the cube of 

 the distance, instead of inversely as the square of the distance, so that, at a distance a little vjithin 

 the atmospheric limit, and at which the attractive force was still somewhat in excess, it would soon 

 happen that a small increase of both forces (from the shrinkage of the material) would result in 

 increasing the centrifugal force so much more rapidly as to exhaust the difference of the two forces, 

 and leave the nebulous material ready to be "abandoned." 



= Very different this, from the supposition of many misinformed persons, that the rings here 

 spoken of were throivn off by an excess of centrifugal force. 

 3 November. 1S74. 



