TRANSACTIONS OF SECTION G. 821 



four pounds, and in addition to this is the weight (35 lbs. for a large wild swan), 

 and this weight is only supported by every downstroke of the wings. The rare- 

 faction on the top side of a wing is produced by the suction from the air-currents 

 passing its rigid fore-edge, just as the rarefaction is produced in a funnel by the 

 wind passing over its edge : a difierence in pressure corresponding to 30 lbs. per 

 squai-e foot may occur on windy days. The other important factor in producing 

 a rarefaction on the lee side of a rotating surface is centrifugal force, as explained 

 in the paper. These considerations wiU serve to explain why the area required for 

 an air-propeUer has no connection with the ratio between the specific gravities of air 

 and water, the only means of moving a large quantity of air so as to create a mo- 

 mentum being the rarefaction, or storm centre, in front of the propeller. To create 

 a sufficient rarefaction, the area of an air-propeller ought to be 12-14 times, and 

 the diameter 3-4 times, that of the ordinary water-propeller ; but less than this for 

 large vessels, as a natural consequence of the mathematical laws governing these 

 matters. The losses of a propeller in water are — (1) loss by friction ; (2) loss by 

 throwing out water in wi-ong directions ; (3) loss by blows. Thanks to the perfect 

 elasticity of air, there will only be the two first-named kinds of losses in that 

 medium. If, for instance, equal weights of air and water moving at the same velocity 

 strike a plane, the pressure from the air will be twice that from the water ; and this 

 can also be recognised from the resistance of air, which is about yjo*^ P^'^'* ^^ *^^ 

 resistance of water, although the ratio between their specific gravities is ^l^. An 

 air-propeller is therefore not efficient as a fan, but very efficient as a propeller. 

 If an air-propeller is mounted on a boat and pulled by the power of a man, the 

 boat receives much greater speed than when the same man appUes his force in the 

 same boat furnished with a water-propeller. But this difference between the thrusts 

 which a man can yield with an air-propeller and a screw is, of course, not great. 

 The same winds which are useful for ordinary sails are also a gain for rotating sails ; 

 that is, 75 per cent, of the winds augments the thrust of an air-propeUer, and the 

 energy of the natural wind is taken advantage of when the pitch is changed in 

 accordance with it. When the wind ' straight against ' equals the speed of the points 

 of effort of the rotating sails, the thrust of the air-propeUer is decreased nearly 

 60 per cent,, or just the same as the thrust of gaff" sails is reduced when from having 

 the wind on the beam the course is changed until four points from the wind. Now 

 it happens once a month that a strong wind is actually so straight against the course 

 as to reduce the thrust by 60 per cent, for a propeller with manual power. On a 

 ] ,000-ton ship the speed of the points of eflfort of its air-propeller would be over 

 150' per second, and no hurricane would be able to reduce its thrust by 60 per cent., 

 and 3'5 pomts from the hurricane the thrust of the air-propeller would be greater 

 than in a calm. As compared with this the increased resistance caused bj- the screw 

 is constant. 



Details of experiments on a large scale, as well as of the formula for finding 

 the area and speed of an air-propeller, are gi^en in the paper. 



6. A neio Spliere Planimeter. By Professor H. S. Hele Shaw. 

 See Section A, p. 584. 



W£nNi:si)Ar, September 12. 



The following Papers were read : — 



1. Underground Railway Communication in Great Cities. 

 By Colonel Rowland R. Hazard. 



Perhaps the most important physical problem, growing out of the concentration 

 of great populations in limited areas, is the construction, maintenance, administra- 

 tion, and uses of the public streets. These, absolutely indispensable for purposes 



