Manchester Memoirs, Vol. xHv. (1899), No. 5. 23 



of (35) reduces to its first term. We conclude that when 

 a screw advances at a sufficiently rapid rate, the energy 

 left behind in the fluid is negligible, so that the whole 

 work done is available for propulsion. The distinction 

 between //'and //, as formerly employed, then disappears. 

 If U denote the rate at which W would have to be 

 lifted ill order to do the work actually performed by the 

 machine, we may now take from (15), as applicable to the 

 rapid flight of an aeroplane, 



U-- 



X/C^) <3.). 



In the case of direct maintenance by a screw rotating 

 about a vertical axis, (31) gives 



-y(i^) (3,). 



It may be interesting to compare the powers required 

 in the two methods, especially as some high authorities 

 have favoured direct maintenance, without the use of an 

 aeroplane, as the more economical. The ratio of the 

 values of U in (36), ii'j) is 



/ fpsma S' 



(3^) 



or, in the case of air, since k:=0024, () = '00!2, 



7(2 sin a. 675) (39). 



Since a may be made small, and S the area of the 

 plane may be a large multiple of S the area swept over 

 by the screw, it would appear that the advantage must lie 

 with the aeroplane, even if the object be mere maintenance, 

 and not a rapid transit from place to place. 



But although the flying machine of the future will, as 

 it appears to me, be on the princijjle of the aeroplane, it 

 cannot be denied that the method of direct maintenance 



