RESISTANCE OF SUBMERGED PLANES 



389 



frictional resistances form an increasingly large portion of the whole, this 

 law does not hold. Lord Riyleigh, 1 indeed, showed that a rational 

 expression for the normal pressure on the front face of the plane when 

 moving through an infinite mass of fluid is given by 



W a ~ sin 6 



P = 



. r 2 Ibs. 



g ' 4 -f 77 sin 6 

 this neglecting the effect of eddy formation. 



From this we have, if P' = normal pressure on oblique plane, and if 

 P = corresponding pressure on a normal plane, 



, _ (4 + TT) sin 6 _ sin 



' 4 + TT sin 6 ' -56 + -44 sin ff 



As the result of experiment M. Joessels, of the French Navy, deduced 

 an empirical formula of this type, making 



-39 + -61 sin V 

 while Duchemin deduced the relationship 



_ p 2sinfl 



' 1 + sin 2 0' 



The following table shows results experimentally obtained by Colonel 

 Beaufoy and by Stanton, and also some results of experiments by Vince 

 quoted by Rayleigh, together with corresponding values as calculated by 

 the sin 2 # formula, and by those of Rayleigh, of Joessels, and of 

 Duchemin. 



1 " Scientific Papers," I., p. 287. and III., p. 491 ; or see Lamb's "Hydrodynamics," p. 93. 



