56 GEOLOGY. 



even thus be wholly disrupted, if the body to which it approached 

 were much superior to it in mass and the approach were very close. 

 Roche long ago demonstrated that the differential attraction of a 

 large body upon a smaller one revolving about it, was competent to 

 disrupt it at an appreciable distance, as previously stated (p. 34). 

 In a body whose elasticity nearly matches its gravity, it is not necessary 

 that the Roche limit should be actually invaded before disruptive 

 phenomena of a high order of intensity and magnitude would take 

 place. A more distant approach would suffice. 



Exceptional protuberances developed on opposite sides by close ap- 

 proach. — According to the well-known tidal principle, these exceptional 

 protuberances would rise from opposite sides, and herein lies the assigned 

 explanation of the prevalence of two diametrically opposite arms in 

 the spiral nebulae. 



The demands on protuberant action not severe. — The present 

 planets and their satellites, all together, amount to about one seven- 

 hundredth part of the mass of the system. Simply to supply the 

 required planetary matter, the protuberances need include but this 

 small fraction of the ancestral sun; but some considerable part of 

 the projected matter must probably have been gathered back into 

 the sun, and some part may possibly have been projected beyond 

 the control of the system. Making allowances for both these factors, 

 the proportion of the sun's mass necessarily involved in the protuber- 

 ances is still very small. Apparently one or two per cent, of the sun's 

 mass would amply suffice. 



The acquisition of rotatory motion. — The protuberances, by hy- 

 pothesis, would be thrust out as the sun and the passing star were 

 swinging about their common center of gravity in curves more or less 

 sharp, and at velocities more or less prodigious, according to their 

 relative distances. That protuberance which was shot from the sun 

 toward the star would be drawn forward by the star in the direction of 

 its movement, with a power inversely proportional to the square of the 

 distance. The protuberance shot in the opposite direction would be 

 attracted by the star also, but owing to its greater and constantly 

 increasing distance, in a very greatly less degree, in accordance with the 

 same law. The sun at an intermediate distance would be attracted 

 in an intermediate degree. With reference to the sun, therefore, the 

 two protuberances would move in opposite directions, and their motions 



