The Nebular Hypothesis of Laplace. 811 



time, tlie entire mass of the nebula would revolve with an 

 angular velocity greater than that which it had in the begin- 

 ning. Thus the progressive condensation of the primitive 

 gaseous matters of the nebula, and their agglomeration about 

 its centre, necessarily produces a continual augmentation in 

 the velocity of the nebula's rotation about its own axis." 



t( A nebula such as we have imagined, animated with a move- 

 ment of rotation about its axis, cannot extend itself in the 

 plane of its equator beyond a certain limit, the position of 

 which depends on the velocity of its motion. Any molecule 

 situated in the plane of the nebula's equator, and participating 

 in its movement, must be subjected at one and the same time 

 to the attraction which the entire mass can exert upon it, and 

 also to the centrifugal force resulting from its rotatory motion. 

 The dimensions of the nebula cannot remain such as would 

 cause the second force to prevail over the first even at any 

 part of its equator, for should this happen, and any molecules 

 be impelled by centrifugal force beyond the control of gravita- 

 tion, they would cease to form part of the nebula, and move 

 off, independently of it, with the velocity that they possessed 

 at the instant of their starting away." 



" The progressive condensations of different portions of the 

 matter forming the nebula would, as we have said, accelerate 

 its rotation, and by consequence give rise to a corresponding 

 augmentation of centrifugal force for any point situated at a 

 given distance from its axis, and thus the limit beyond which 

 the nebula could not extend and cohere would become more 

 and more restricted." 



' c If at a certain epoch, this limit, measured from the centre, 

 terminates at the surface of the nebula, the condensation to 

 which this further cooling will give rise must cause the limit to 

 fall within the surface, and then the outside molecules of the 

 nebula surrounding its equator will be beyond this limit, and 

 consequently this excess of matter beyond that which the 

 nebula can retain by means of its attraction, will cease to be a 

 portion of the mass, and will separate in the form of a ring, 

 rotating in its own plane about its own centre with the velocity 

 which it possessed at the moment of its detachment. It is 

 only about its equator that the nebula can abandon portions of 

 the matter composing it ; for in no other place, except in the 

 plane of this circle, can a molecule be acted upon by the 

 attractive force in the same line as that in which the centrifugal 

 force operates. These two forces compose a resultant force,* 



* For those who are unacquainted with this term as used in mechanics, we 

 may explain its meaning by stating, that if one force impels a ball straight for- 

 ward, and a second force of the same amount impels it exactly across, or at right 

 angles to, the line of the first force, the two forces will combine into a resultant 

 force, sending it in an intermediate direction.. 



