432 Lord Rayleigh on the Resistance of Fluids. 



derable velocity, and at the edge itself retains the full velocity 

 of the original stream. Nevertheless the amount of error in- 

 volved in the theory referred to is not great, as appears from 

 the result of KirchhofFs calculation of the case of two dimen- 

 sions, from which it follows that the resistance per unit of area 



is -. pu 2 instead of \pu 2 . 



It is worthy of notice that by a slight modification of the 

 conditions of the problem the estimate ^pu 2 may be made ac- 

 curate. For this purpose the lamina is replaced by the bottom 

 of a box-shaped vessel, whose sides project in the direction 

 from which the stream is flowing, and are sufficiently extended 

 to cause approximate quiescence over the whole of the bottom 

 (Plate V. fig. 1). In the absence of friction, the sides 

 themselves do not contribute any thing to the resistance. It 

 appears from this argument that the increase of resistance 

 due to concavity can never exceed a very moderate value. 



Although not very closely connected with the principal sub- 

 ject of this communication, it may be well to state the corre- 

 sponding result in the case of a compressible fluid such as air. 

 If p be the normal pressure in the stream, a the velocity of 

 sound corresponding to the general temperature, 7 the ratio 

 of the two specific heats, ^pu 2 is replaced by 



Po 



{('^D*-'} 



which gives the resistance per unit of area. The compression 

 is supposed (as in the theory of sound) to take place without 

 loss of heat; and the numerical value of 7 is 1*408. 



When u is small in comparison with a, the resistance fol- 

 lows the same law as if the fluid were incompressible ; but in 

 the case of greater velocities the resistance increases more ra- 

 pidly. The resistance to a meteor moving at speeds compa- 

 rable with 20 miles per second must be enormous, as also 

 the rise of temperature due to compression of the air. In 

 fact it seems quite unnecessary to appeal to friction in order 

 to explain the phenomena of light and heat attending the 

 entrance of a meteor into the earth's atmosphere. 



But although the old theory of resistance was not very 

 ■wide of the mark in its application to the case of a lamina 

 against which a stream impinges directly, the same cannot 

 be said of the way in which the influence of obliquity was 

 estimated. It was argued that inasmuch as a lamina moved 

 edgeways through still fluid would create no disturbance (in 

 the absence of friction), such an edgeways motion would pro- 

 duce no alteration in the resistance due to a stream perpendi- 



