41 G Mr Wilson, On Convection of Heat. 



Substituting this in the differential equation, we get 



d?G n _ spu dCn _ /wttY n - 

 dx> k dec \t J U,l-U ' 



a solution of which is G n — A n e a » x , where 



Consequently, putting p = -£=- 



spu 



M=l \ t J 



is a solution of the differential equation. When # = this becomes 



*=T^sin(«3), 



which can be made to represent any distribution of temperature 

 or sources of heat, on the part of the plane yz between AB and 

 GD, which is a function of y only. 



If y = or y = t, then 6 = 0, so that the solution 



n=\ \ t J 



enables the temperature distribution due to any distribution of 

 temperature or of heat supply along Oy, when the planes AB 

 and GD are kept at temperature zero everywhere, to be deter- 

 mined. 



If a constant term is added to the above expression for 6 it 

 is still a solution of the differential equation. Now of the two 



values of a it is clear that p+\ / ( — ) +p 2 will be the appropriate 



value when x is negative and p — a/ ( -, ) +p 2 when x is positive. 



The solution with a constant term added will therefore represent 

 the temperature due to any distribution of temperature or heat 

 supply along Oy, when the planes AB and GD are maintained at 

 constant temperatures, 1 where x is positive and 2 where x is 

 negative. 



If u = 0, this solution becomes 



n=\ \ t J 



