598 Dr. A. Russell on the Convection of Heat 



velocity V in the direction XO, and that its temperature is 

 zero before it meets the cylinder. 

 In this case we know * that 



ami 



(8) 



where a is the radius of the cylinder and 



9 2 i 2 



r = a? 4- y 2 . 



The equation to the stream-line a , which flows on the 

 surface of the cylinder (fig. 2), is a = 0, and the equations 

 to the two equipotential lines, ft and ft, are 



*(l + J) = ~ 2a and ' T ( 1 + ?) = 



2a 



respectively. These curves cut the cylinder and the stream- 

 line « a ^ angles of 45°. We see therefore that the velocity 

 of the liquid at L and L' must be zero. The velocity at M 

 and M' is 2V. At a great distance away from the cylinder 

 ft and ft practically coincide with the lines 



x = —2a and x = 2a. 



Let us suppose that the temperature flow has become 

 steady and that the temperature of all points on the stream- 

 line a is /(ft). On this stream-line (fig. 2), from /3 = co to 

 /3 = ft, we have 



=:/(/?) =0, 



and on the same stream-line from ft to ft we have 



0=/(/3). 

 It is easy to verify f by differentiation that 



is a solution of (7). Also, when a. is zero, 6 = /(ft. This 

 solution; therefore, i< applicable to our problem. 



* LamVs ' Hydrodynamics,' Third Edition, p. 74. 



t Cf. Boiissinesc[, Application des Potentials, p. 360 (1885). 



