414 



Mr Wilson, On Convection of Heat. 



When x is large 



K ° (x) = \/Tx e ~ 



so that for very large values of r 



8x + 2 ! (8x)* 



3 2 .5 2 

 3 ! (8#) ; 



+ 



e = 



usp , . 



Qe^ {x - r) 

 2 Juspirkr 



For very small values of r 



-Q 



•zai**'**™-) 



If instead of a line source of heat we have a very fine wire 

 heated by an electric current, then, provided the wire is so thin 

 that it produces no appreciable disturbance of the moving 

 medium outside the region where 



'■S^""). 



it is easy to see that the solution obtained for the line source 

 will be very approximately true for the distribution of temperature 

 due to the wire except very near the wire. 



The heat given out by such a wire can be calculated from its 

 electrical resistance and the current flowing through it so that 

 Q can be determined. If then the rise of temperature at some 

 point in a known position with respect to the wire were deter- 

 mined, the equation 



U ~27rk 6 K ° [ 2k ) 

 would enable k for the moving medium to be estimated. The 



quantity ~- can easily be made very large, so that the approxi- 

 mate formula 







Q 5(-r) 



2 Jirspkur 



could be used to determine k in this way. Thus, if two fine plati- 

 num wires were stretched parallel to each other, one along the axis 

 of z and the other at x = a, y = 0, and the rise of temperature of 

 the second, due to passing a current through the first, were deter- 

 mined, k could be got by means of the equation 



Q 



since x — r = 0, when y 



6 = 



2 s/irspkua 



- and x is positive. 



