236 



Mr. J. W. Peck on the Steady 



or 



r 2 =— -x + c, 



A-2 



(26) 



where c is a parameter depending upon the temperature of 

 the isothermal considered. We have, therefore, a family of 

 similar coaxial paraboloids of revolution. Their concavities 

 are towards the hot "end, their common axis is the axis of the 

 cylindrical rod, and the distance from focus to vertex (AS) 



is for each —- . 



A2 ^ 



This constant of the family, AS or — , has by (20) the 



A-2 



value . 



aL</2 



or 



vn 



i+ 



8LJ 



(27) 



In the diagram these paraboloidal surfaces are shown to 

 scale for the case of a bismuth rod of 4 cms. radius. Close 

 to the origin this form is deviated from because there 

 A 2 2 6 _Al ' x becomes comparable with \i 2 e~ K * x , and at the origin 

 we have the isothermal surface becoming, of course, a plane. 

 The greater L is for a series of bars of substances under 

 similar thermal conditions the greater is the value of the 

 constant AS, and therefore the paraboloids approach more 

 nearly to the planes of the first approximation. 



=2, L=60, AS 



Isothermals y 2 = — 44r+C. 

 Lines of Flow y = Ae x f 22 . 



11. Z=50. 



In this second approximation the four characteristic lengths 

 are the semi-radius (a/2), the thermal length modulus (L), 

 the distance from focus to vertex of the paraboloidal surface 



