APPLICABLE TO THE MOTION OF FLUIDS. 393 



By the integration of this equation f is obtained ; whence —■ and 



consequently the density and the pressure at the surface of displacement 

 are known. The question I have been considering is evidently identical 

 with the Problem of the Resistance of the air to a vibrating sphere, of 

 which I have given a solution in my last communication to this Society. 

 But the method there employed, for obtaining the above equation, 

 requires the reasoning I have now gone through to render it complete. 



18. Another inference may be drawn from equation (10) on the 

 supposition that Q = and V is very small. It thus becomes 



Now if r and r' be each infinitely great, the motion is strictly recti- 

 linear, and must be the same at all points of any plane drawn perpendicular 

 to the direction of propagation. But if r and r' be very large but 

 not infinite, and if the motion be vibratory, we may conceive a portion 

 of the fluid of the form of a cylinder to be alone agitated, whilst the 

 rest of the fluid is stationary. The values of r and r' must, however, be 

 infinitely great for points on the surface of the cylinder, and the velocity 

 and condensation there must vanish. If the condensation be symmetrically 

 disposed about the axis of the cylinder, the motion of particles situated 

 on this axis will be rectilinear, but the vibrations of all other particles 

 will be partly longitudinal and partly transversal. A line drawn at 

 a given instant in the direction of the motion of the particles through 

 which it passes will be of a serpentine form, approaching nearer to a 

 straight line as r and r are greater. That r and r' may be large, 

 the diameter of the cylinder must be large compared to the breadth 

 of an undulation. These considerations applied to the Undulatory 

 Theory of Light, will account for the rectilinear propagation of a small 

 cylindrical pencil of light without divergence. 



Cambridge Observatory, 



April 8, 1842. 



