Convection of Heat and Similitude. 695 



Examination of' Formula. 



h=(k6/l)¥(c 2 gl*a0/k 2 ) (4)* 



The form of the function F may be determined experi- 

 mentally by finding its variation with " 0," say, the other 

 quantities remaining constant. Dulong & Petit f, PecletJ, 

 and Compan § have given formulae in which, for the same 

 body, Aacfl 1 * 88 . Hence 



F(c 2 gl*adlk 2 ) = {c 2 gl*a6/k 2 y 233 , 



whence (5) becomes 



Now we may put c — c p p, where c p is the specific heat of 

 unit mass of the fluid, and for air is known to be practically 

 independent of the density " p." Hence, for any given 

 body, if "*," "a," and "g" do not alter, h<Xp m d 1 ' 233 . 

 In excellent agreement with this, Dulong & Petit found 

 for air hacp'^d 1 ' 233 , the pressure "p" being of course 

 proportional to k< p." Further, in one experiment with 

 a very small cooling-chamber, Cqmpan || found Accfl 1 ' 154 . 

 Similar reasoning in this case gives h <x p' 308 6 V154: , and 

 Compan found experimentally h <Xp' 30 as his mean for 

 this series. This is excellent agreement. 



Let us return to the question of models. If, instead 

 of attempting to determine the form of the function in 

 (5), we so choose our models that its value is constant, 



* Equation (4) is present in Boussinesq's paper in the form 



^0'W 3 if lo:(c 2 a9/k-y 1/S , .... (4a) 

 which is seen to be equivalent to (4) for 



&<? I x if \kc?a? '■' when / s. (c^e/h 2 )- 1 3 . 



From this Boussinesq obtains an equivalent of (6), but limited to the 

 same body so that "I" does not occur. He does not further test 

 the equation. 



t Dulong & Petit. See Preston's 'Heat.' 



PSclet. Scf Paulding's translation, 'Practical Laws and Data on 

 tli*' Condensation of Steam in Covered and Bare Pipes.' 0, P. Paulding-. 

 Van Nostrand Co., 190 1. 



§ Compan, Ann. de Chimie et de Physique, xwi. p. 482 (1002). 



|| Compan, loc cit. 



