478 Royal Society : — 



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 ^ denote the dynamical measure of the force of gravity 

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



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

 to V 1-41 x^H, the expression for the temperature becomes 



r 1-41 V2— «2-i rfi. 



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 



.=e{n-4ix-^}. 



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 

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

 elevation of temperature amounting to 



•41X2^6. 



If, for instance, the absolute temperature, 0, 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 i-elative motion, will be, in degrees 

 Centigrade, 



58°-8x(-j,or58-8x(-^n5). 



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 i 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 f 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 



tlie air-thermometer, ^Yith 273"-7 added in each case. See the author's previous 

 paper "On tlie Thermal Effects of Fluids in Motion," Part II., Philosophical 

 Transactions, 185 J, part 2. p. 353. 



