558 



angle for instance, if there is such), we have q=o, and therefore au 

 elevation of temperature amounting to 



v 



41X^9. 



If, for instance, the absolute temperature, 9, of the air at a distance 

 from the solid be 287 (that is 55 on the Fahr. scale), for which the 

 velocity of sound is 1115 per second, the elevation of temperature at 

 a pole, or at any point of no relative motion, will be, in degrees 

 Centigrade, 



/V\a / V V 



58-8 x(-J, or 58-8 x^), 



the velocity V being reckoned in feet per second. If, for instance, 

 the velocity of the body through the air be 88 feet per second (60 

 miles an hour), the elevation of temperature at the points of no 

 relative motion is '36, or rather more than y of a degree Centi- 

 grade. 



To find the greatest depression of temperature in any case, it is 

 necessary to take the form of the body into account. If this be 

 spherical, the absolute velocity of the fluid backwards across the 

 equator will be half the velocity of the ball forwards ; or the relative 

 velocity (q) of the fluid across the equator will be ^ of the velocity 

 of the solid. Hence the depression of temperature at the equator of 

 a sphere moving slowly through the air will be just -| of the ele- 

 vation of temperature at each pole. It is obvious from this that a 

 spheroid of revolution, moving in the direction of its axis, would 

 experience at its equator a depression of temperature, greater if it be 

 an oblate spheroid, or less if it be a prolate spheroid, than of 

 the elevation of temperature at each pole. 



It must be borne in mind, that, besides the limitation to velocities 

 of the body small in comparison with the velocity of sound, these 

 conclusions involve the supposition that the relative motions of the dif- 

 ferent parts of the air are unresisted by mutual friction, a supposition 

 which is not even approximately true in most cases that can come 

 under observation. Even in the case of a ball pendulum vibrating 

 in air, Professor Stokes* finds that the motion is seriously influenced 



* " On the Effect of the Internal Friction of Fluids on the Motion of Pen- 

 dulums," read to the Cambridge Philosophical Society, Dec. 9, 1850, and pub- 

 lisbed in vol. ix. part 2 of their Transactions. 



