68 MOLECULAR MOTION AND ITS ENERGY 34 



measured by the momentum which is transferred in unit 

 time across unit area, we must conclude that the pressure 

 exerted by the gas in the direction of its motion is greater 

 than p by pa 2 in consequence of the flow, and so rises to 

 p + pa 2 = p(%7rW + a 2 ). 



This increment of the pressure in the direction of the flow 

 makes itself perceptible as stress when a surface is put in 

 the way of the flowing stream of gas. 



An equally great stress results between the surface and 

 the gas when the gas is at rest and the surface is moved 

 with velocity a against the gas in the direction of its normal. 

 The force which then results and tends to stop the motion 

 is felt as resistance, and the resistance of a gas is therefore 

 also determined by the formula 



P Fa 2 , 



which expresses the law that the resistance increases pro- 

 portionally to the square of the velocity. 



That this law holds not only for the resistance in a 

 liquid, but also for the motion of a body in air, has already 

 been proved by Newton and Hawksbee 1 by means of 

 experiments on falling bodies; it has lately been found 

 also for other gases by Cailletet and Colardeau 2 by 

 means of observations on the gases in flow. A rernarkable 

 confirmation of the formula deduced for gaseous resistance 

 arises from an observation made by Him, 3 from which 

 too Him himself thought he must conclude that the kinetic 

 theory of gases is wrong. He found in fact that the 

 resistance does not alter with the temperature if the 

 density is kept unchanged. With this fact the theoretical 

 formula is in perfect agreement, as it does not contain the 

 molecular velocity G, but only that of the flow a. 



The range of applicability of Newton's formula is 

 however dependent on definite limits for the value of the 



1 Newton, Principia, bk. ii. prop. 40; Hawksbee, Physico-mecJmn. 

 Experiments, London 1709; Musschenbroek, Tentamina Exper. in Acad. 

 del Cimento, Lugd. 1731, pt. ii. p. 118. 



2 Comptes rendus, cxvii. 1893, p. 145. 



3 Mem. de VAcad. de Belgique, xiii. 1882. 



