26 ON MAGNITUDE [ch. 



contained in the equation V = \^l, a result which happens to be 

 identical with one we had also arrived at in the case of the fish. 

 In the bird's case it has a deeper significance than in the other; 

 because it implies here not merely that the velocity will tend to 

 increase in a certain ratio with the length, but that it must do so 

 as an essential and primary condition of the bird's remaining aloft. 

 It is accordingly of great practical importance in aeronautics, for 

 it shews how a provision of increasing speed must accompany every 

 enlargement of our aeroplanes. If a given machine weighing, say, 

 500 lbs. be stable at 40 miles an hour, then one geometrically 

 similar which weighs, say, a couple of tons must have its speed 

 determined as follows: 



W -.wi-.L^: P :: 8 : 1. 



Therefore L:l::2:l. 



But 72 : ^2 :: Z : I. 



Therefore V : v.: V2 : 1 = 1-414 : 1. 



That is to say, the larger machine must be capable of a speed 

 equal to 1-414 x 40, or about 56| miles per hour. 



It is highly probable, as Lanchester* remarks, that Lilienthal 

 met his untimely death not so much from any intrinsic fault in 

 the design or construction of his machine, but simply because his 

 engine fell somewhat short of the power required to give the 

 speed which was necessary for stability. An arrow is a very 

 imperfectly designed aeroplane, but nevertheless it is evidently 

 capable, to a certain extent and at a high velocity, of acquiring 

 "stability" and hence of actual "flight": the duration and 

 consequent range of its trajectory, as compared with a bullet of 

 similar initial velocity, being correspondingly benefited. When 

 we return to our birds, and again compare the ostrich with the 

 sparrow, we know little or nothing about the speed in flight of 

 the latter, but that of the swift is estimated f to vary from a 

 minimum of 20 to 50 feet or more per second, — say from 14 to 

 35 miles per hour. Let us take the same lower limit as not far 

 from the minimal velocity of the sparrow's flight also ; and it 



* Aerial Flight, vol. 11 (Aerodonetics), 1908, p. 150. 

 f By Lanchester, op. cit. p. 131. 



