58 Mr. C. H. Lees on the 



Where v — excess of temp, at point x at time t over 

 temp, of air which is supposed constant. 

 c= specific heat \ 



p = density >of material of bar. 



k = inner conductivity ) 

 q = area of section. 

 p = perimeter of section. 

 h = outer conductivity. 

 It is deduced on the assumption that c, k, and h, are con- 

 stant and that the isothermal surfaces are planes perpen- 

 dicular to the axis of the bar.* If the restriction as to the 

 constancy of c, k, h be removed, the equation takes the form — 

 Iv I ( lv\ p 



^-st*w- ?**••■ (2) 



where the subscripts denote values of c, k y h, at temp. v~ 

 Now the experiments of Bede, Brystrom, Naccari, and 

 others shew that c v seldom varies more than 10 per cent per 

 ioo° C, and the same holds for k v according to the experi- 

 ments of Forbes, Lorenz, Mitchell, &c. I find, however, that 

 h v often varies 50 to 100 per cent in the same interval. The 

 first step towards a more correct theory seems then to be a 

 determination of the variation of h v . 



A bar of diameter small in proportion to its length, if 

 heated to a constant temperature and then suspended hori- 

 zontally in air to cool, would during cooling be very nearly 



ov 

 of the same temperature throughout We have then ~- = > 



and the equation of temperature is 



lv p 

 - qCv p Tt =-h v v. 



Or writing m for the mass, s for the surface of the bar,, 

 and h v v = hf(v) where // has same meaning as in the note 

 (p. 57), we have 



- mcv-f t = skf(v). (3) 



*Theorie analytique cle la Chaleur, art. 105. 



