1878.] Mr Hichs, On the motion of two cylinders in a fluid. 227 



(2) Mr W. M. Hicks, M.A., On the motion of two cylinders 

 in a fluid. 



The investigation relates to the motion of two cylinders sur- 

 rounded by fluid ; more particularly in the cases of (1) one cylinder 

 in an infinite fluid bounded by a plane, (2) two cylinders in an 

 infinite fluid and rigidly connected, (3) one cylinder fixed, and 

 (4) both cylinders free to move generally. The first case cor- 

 responds to the motion of two equal cylinders, one moving as the 

 image of the other with respect to -the plane. If the cylinder be 

 projected from contact with the plane in a direction perpendicular 

 to it, the limiting velocity as it moves off to an infinite distance 



is increased in the ratio \/\^ ^j )• If it be projected from 



any point, the future path will have its concavity turned towards 

 the plane, and will turn round and meet the plane or not according 

 as the direction of projection makes an angle with the perpen- 

 dicular to the plane greater or less than a certain angle a, 

 which depends only on the distance of the point from the plane. 

 When the cylinder is projected from contact with the plane the 

 values of a for densities of the cylinder 0, 1, 10, are about 41° 22'; 

 51° 14'; 70" 15' respectively. 



The case where one cylinder is fixed and the other moves in 

 any manner was also discussed. If they are equal and the move- 

 able one is projected away from the centre of the fixed cy Under, 



the limiting velocity is a/(^-— "T"] J x the initial velocity. 



In the former case the ratio was h \/ \~ ^~j — j x relative 



velocity of the cylinder and its image, so that the effect of the 

 constraint is to increase the limiting relative velocity in the two 



cases in the ratio a/[o '^, — .,^ _ ^ ) • If the cylinder be projected 



in any way, it will move as if attracted on the whole by the fixed 

 one, and the path will have its concavity turned towards it and 

 will have two asymptotes, whose distance from the centre of the 



fixed cylinder =./(^ -" j x apsidal distance", where P^ is a 



certain number depending only on this distance. If e.g. they 

 touch when nearest, P^ = l7r^ - 1. If on the contrary both are free 

 to move, and they are projected so that the whole "momentum" 

 of the system is zero, they move as if they repel one another and 



