from a Body cooled by a Stream of Fluid. 601 



the cylinder, and therefore the assumption that it is constant 

 is not permissible. For example, if the radius of one wire is 

 a hundred times that of another, the average heat per square 

 centimetre of surface which is carried off per second by the 

 liquid from the small wire is ten times greater than from the 

 large wire. We also see that if we quadruple the velocity 

 of the flow of the liquid, the temperature of the wire being 

 maintained constant, the convection of heat is doubled, and 

 if the convection of heat is constant the difference of tem- 

 perature between the wire and the liquid is halved. 



6. Cylinder' with Elliptic Section. 



Let the direction of the current be at right angles to the 

 axis of the cylinder, and let it make an angle a. with the 

 major axis of the elliptic section which we take as the axis 

 ofX. If 



Z = cos a and m = sin a, 



we easily find from the formulae given in Lamb's ' Hydro- 

 dynamics' (p. 70, 3rd ed.) that 



j3=lb\/— fe-'sinf+fo 



V a — b 



/a + b „ y , 

 + nia\/ - — -, e n cos £ -+- my, 



where 



A'=c sin f cosh rj, y~c cos £ sinh 17, and c= V'a 2 — & 2 . 



On the surface of the cylinder we have 



a = c cosh 77, b = c sinh 77, 



and thus at these points 



# = asin£, and y = b cos f. 



At points, therefore, on the surface of the cylinder, 



7 b , a , 



6 — 1- x+lx + m T y + mi/i 

 a 



