1879.] 



the Capillary Phenomena of Jets. 



91 



the vertical plane, by causing the coalescence of drops which come into 

 contact. When the projection is nearly vertical, the whole scattering 

 is due to collisions, and is destroyed by electricity. If the resolution 

 into drops is regularised by vibrations of suitable frequency, the 

 principal drops follow the same path, and unless the projection is 

 nearly vertical, there are no collisions, as explained in my former 

 paper. It sometimes happens that the spherules are projected laterally 

 in a distinct stream, making a considerable angle with the main stream. 

 This is the result of collisions between the spherules and the principal 

 drops. I believe that the former are often reflected backwards and 

 forwards several times, until at last they escape laterally. Occasionally 

 the principal drops themselves collide in a regular manner, and ulti- 

 mately escape in a double stream. In all cases the behaviour under 

 electrical influence is a criterion of the occurrence of collisions. The 

 principal phenomena are easily observed directly, with the aid of 

 instantaneous illumination. 



Appendix I. 



The subject of this appendix is the mathematical investigation of 

 the motion of frictionless fluid under the action of capillary force, the 

 configuration of the fluid differing infinitely little from that of equi- 

 librium in the form of an infinite circular cylinder. 



Taking the axis of the cylinder as axis of z, and polar co-ordinate r,9 

 in the perpendicular plane, we may express the form of the surface at 

 any time t by the equation 



r=a +f(6,z) (11), 



in which / (0,z) is always a small quantity. By Fouriers' theorem, 

 the arbitrary function / may be expanded in a series of terms of the 

 type an cos 716 cos hz ; and, as we shall see in the course of the in- 

 vestigation, each of these terms may be considered independently of 

 the others. The summation extends to all positive values of and to 

 all positive integral values of n, zero included. 



During the motion the quantity a Q does not remain absolutely con- 

 stant, and must be determined by the condition that the inclosed 

 volume is invariable. Now for the surface. 



r=a + & n cos n0 cos hz (12), 



we find 



volume=i /7r 2 ^t?2=/(7ra 2 +i^ rt 2 co$?'kz)dz=z(7ra 2 + i-x ) i) ; 



so that, if a denote the radius of the section of the undisturbed 

 cylinder, 



7ra~ = Tra ( f + j7ra rt 2 , 



