382 
PROF. LOUIS YESSOT KING ON THE CONVECTION OF 
It is shown that when the cooling stream is air at ordinary pressure, there exists 
a value of the product Yd (Y expressed in cm./sec. and the diameter d in cm.) given 
by Yd = 0'0187 which discriminates between the twoformulse: when Yd<0’0187 (32) 
is appropriate to the problem, while for Yd>0‘0187 (33) must be employed. In 
practically all cases except for very small wires and extremely low velocities the 
condition Yd>0'0187 is satisfied and equation (33) expresses with sufficient 
accuracy nearly all applications of the formula. 
Section 7. Note on the Interpretation and Application of the Preceding Theory. 
That the expression for the heat-loss from a cylinder cooled by a stream of fluid 
derived in the preceding sections and leading to equation (21) may be identified with 
reality involves many delicate considerations as to the nature of the boundary 
condition over the surface of the cylinder. A comparison with the results of 
experiment described in Section 13 gives strong support to the validity of this formula 
and seems to justify the boundary condition of constant flux by means of which it was 
derived. Looking at the matter from the point of view of the kinetic theory of gases, 
temperature conditions cannot strictly be defined in the immediate neighbourhood of 
the heated cylinder, and it is only at a distance of several free paths when equipartition 
is nearly complete that we may define temperature and that normal thermal conduction 
takes place. The boundary condition of constant flux is one which must look for its 
explanation in the light of the kinetic theory, making use of the precise knowledge 
which is now coming to hand regarding the nature of molecular impacts on solid 
boundaries from recent investigations on the properties of ultra-rarefied gases.( 13 ). 
This aspect of the question must, however, be left over for future discussion. That 
there should exist a discontinuity of temperature between the stream and the cylinder 
at ordinary pressures is not surprising ; this discontinuity was considered possible by 
Poisson and is now known to exist in the case of rarefied gases. ( 14 ) 
The solution of the present problem on the conduction of heat in moving media is 
only a particular case which may be applied to many other problems for which the 
same formal expression of the physical conditions holds ; for instance, the results apply 
mutatis mutandis to the problem of diffusion or evaporation from liquid surfaces into 
streams of gases flowing over them. It must be kept in mind, however, that in each 
type of problem to which this analysis may be applied, the nature of the boundary 
condition must in each case be referred to a comparison with the results of 
experiment. 
( 13 ) A summary of recent work on the subject is given by Knudsen (‘ La Tb4orie du Rayonnement et 
les Quanta,’ Gauthier-Villars, Paris, 1912, p. 133), and more recently by Dunoyer (‘Les Idees. Modern es 
sur la Constitution de la Matibre,’ Gautbier-Villars, Paris, 1913, p. 215 et seq.). 
( 14 ) Kundt and Warburg, ‘ Pogg. Ann.,’ vol. 156, 1875, p. 177; also Smoluchowski, ‘ Wied. Ann.,’ 
64, 1898, p. 101. 
