557 



If the fluid be air instead of the ideal "perfect liquid," and if the 

 motion be slow enough to admit of the approximation referred to 

 above, there will be a heating effect on the fore and after parts of 

 the bod}', and a cooling effect on the equatorial zone. If the di- 

 mensions and the thermal conductivity of the body be such that 

 there is no sensible loss on these heating and cooling effects by 

 conduction, the temperature maintained at any point of the surface 

 by the air flowing against it, will be given by the equation 



where denotes the temperature of the air as uninfluenced by the 

 motion, and^ and II denote the same as before*. Hence, using for 

 p its value by the preceding equation, we have 



But if H denote the length of a column of homogeneous atmosphere, 

 of which the weight is equal to the pressure on its perpendicular 

 section, and if g denote the dynamical measure of the force of gravity 

 (32-2 in feet per second of velocity generated per second), we have 



ffpH=U; 



and if we denote by a the velocity of sound in the air, which is equal 

 to V^l'41 X(/H, the expression for the temperature becomes 



According to the supposition on which our approximation depends, 

 that the velocity of the motion is small, that is, as we now see, a 

 small fraction of the velocity of sound, this expression becomes 



t( 



At either the fore or after pole, or generally at every point where 

 the velocity of the air relatively to the solid vanishes (at a re-entrant 



* The temperatures are reckoned according to the absolute thermodynamic 

 scale which we have proposed, and may, to a degree of accuracy correspondent 

 with that of the ordinary " gaseous laws," be taken as temperature Centigrade by 

 the air-thermometer, with 273'7 added in each case. See the author's previous 

 paper "Ou the Thermal Effects of Fluids in Motion," Part II., Philosophical 

 Transactions, 1851, part 2. p. 353. 



2 S2 



