from a Body cooled by a Stream of Fluid . 



007 



up and continually bring fresh particles into contact with 

 the surface. In our notation, the formula deduced is 



H = A0 + BaY0, 



where A and B are constants. 



As the first term is small, H is approximately proportional 

 to V. T. E. Stanton *, who has given an experimental 

 verification of Reynolds's theory, finds that H varies as V n 

 where the value of n is a little less than unity. 



E. Gr. Coker t and S. B. Clement have proved that the 

 critical velocity at which stream-line motion changes to eddy 

 motion varies directly as the viscosity of the liquid and 

 inversely as the radius of the tube. 



12. Electric Current required to fuse a Wire. 



Let us suppose that the wire is horizontal with its axis at 

 right angles to the direction of the flow of the liquid in 

 which it is immersed, and let us suppose that the electric 

 current through it is increased very slowly until the wire 

 fuses. Let a be the radius in centimetres of the wire which 

 we suppose to be cylindrical, the current in amperes, 6 the 

 steady temperature corresponding to this current, and p t the 

 volume resistivity of the metal at t° C. When the steady 

 state is attained the heat generated by the current per unit 

 length of the wire per second must equal the heat convected. 

 Hence, by (12), 



0-239CA = 8a/^0 .... (26) 



and thus, 



C = 7-70(%) 1 /2( 5 ^V)V4 a 1 '25 . . . .(27) 



If 6 be the melting temperature of the metal, we see that 

 the fusing current varies as (sakY) 1 *, and also as the l*25th 

 power of the radius of the wire. This latter result is in good 

 agreement with experimental results obtained by Professor 

 Schwartz (I. c. ante). In his experiments the wire was 

 stretched horizontally in air. The current through it was 

 then increased very slowly until the wire melted, the reading 

 on the ammeter in the circuit at this instant giving the 

 fusing current. Before it melted a vertical stream of air 

 was flowing past the wire, the heating of the air by the wire 

 causing this convection current. For wires of small diameter 

 this current would be approximately constant, and so making 



* Phil. Trans, vol. 190, p. 67 (1897). 

 f Phil. Trans, vol. 201, p. 4,5 (1903). 



