152 Transactions. — Miscellaneous. 



sistauce and molecular exchange act as resistances to planetary motion and 

 are both maximum at perihelion, thereby decreasing aphelion distance and 

 rendering the orbit more circular. 



Gaseous Adhesion. 



When a body is moving forward in a gas, the gas adheres and produces 

 retardation. If the body be revolving this retardation is unequal and the 

 body is deflected. The well-known fact that if a projectile revolves on any 

 other axis than its own direction it is deflected, is an illustration of this 

 action, and it is to make the ball move in its true path that a gun is rifled. 

 It has been shown in the paper " On the general problem of stellar 

 collision"* that all the bodies developed by "partial impact" tend to 

 revolve in the same direction ; in order, therefore, to ascertain the effect of 

 this gaseous adhesion on the path of a planet revolving in a nebula we have 

 especially to consider the case of a body revolving in the same direction as 

 its orbit, and on an axis perpendicular to its plane. 



Problem 3. To ascertain the influence of gaseous adhesion on a rotat- 

 ing planet revolving in a nebula. — Let the arrows in fig. 6 represent the 

 general direction of motion. Let a b represent the planet rotating in the 

 direction of its arrow ; it is evident that a particle at a is tending to move 

 forward faster than a particle at b, for if the path of b were an epycycle, as 

 it might be, it is evident that for an instant it would be at rest ; hence 

 gaseous resistance is stronger at a than at b, hence a is retarded more than 

 b, and the direction the body will tend to take is towards c. In other words, 

 gaseous adhesion acting on a planet revolving on an axis perpendicular to 

 its ecliptic in the same direction as its orbit tends to straighten the curve. 



From the above problem it is evident that on the first return when it 

 meets the nebula it tends to increase perihelion distance and alter apsides, 

 as shown by the dotted ellipse fig. 6. After the first return, were the nebula 

 uniform, it would tend to make a larger ellipse, that is increase its average 

 distance from the centre, thus the potential energy of the planet would be 

 increased, and this increase is done at the expense of the planet's rotation. 

 It might be supposed that this would be a very small matter, but it must be 

 remembered that all the time the body is contracting from a more or less 

 dense gaseous to a liquid state the whole of this potential energy will be 

 converted into rotation, thus the total effect may be very considerable, but 

 as this action will be chiefly at perihelion it will tend materially to alter the 

 eccentricity. It must be clearly understood that it is the differential 

 resistance on the sides of the planet towards and away from the sun that is 

 discussed in this paragraph ; its general retarding action was studied in the 

 last problem. 



* " Trans. N.Z. Inst.," Vol. Xn., Art. XIV. 



