34 MAXWELL'S LAW 69 



velocity a. If this value is too great, the resulting heat 

 (see 19) cannot be disregarded ; if it is too small, the 

 viscosity of the air (see Chapter VII.) cannot be left out of 

 account. 



In another relation, too, the formula for the resistance 



does not exactly correspond to the results of experiment. 

 Hut ton l and Borda 2 long ago found that the resistance 

 is not exactly proportional to the extent of the surface F of 

 the moved body, and that it depends also on the curvature 

 of the surface. For plane discs which move at right angles 

 to their plane, Schellbach, 3 Gr. Hagen, 4 and Him 5 have 

 shown that the factor F would be more exactly replaced by 

 expressions of the form 



AF n or AF(l + Bq), 



where A, B are constants, n an exponent greater than 1, and 

 q the circumference of the disc. The cause of this deviation 

 is easy to indicate. Part of the air which is pushed in front 

 of the disc turns off sideways, and the resistance is thereby 

 diminished ; the theoretical expression has therefore to be 

 multiplied by a proper fraction A. This fraction, however, 

 depends also on the size of the disc, since the air cannot slide 

 aside so easily in front of a large surface as in front of a 

 smaller ; hence the value of the fraction increases with 

 the area F or with the circumference q of the disc. 



35. Reaction. Cross -pressure 



In a flowing gas there is also, in the direction opposite 

 that of the flow, a change of pressure due to the flow, 

 which is also an increase and not a decrease. To. prove 

 this statement I might merely rely on the mechanical 

 principle that action and reaction, and consequently pressure 

 and counter-pressure, must be always equal. Yet I prefer 



1 Trans. Boy. Soc. Edin. ii. 1790. 2 Mtm. Paris 1763, 1767. 



3 Pogg. Ann. cxliii. 1871, p. 1. 4 Ibid. clii. 1872, p. 95. 



5 M6m. de VAcad. de Belgique, xiii. 1882. 



