August 26, 1929] 



NA TURE 



H7 



ings seems hopeless in any conditions, save possibly 

 in a thunderstorm, when we remember that all the 

 bells and wires are in good electric contact with each 

 other, and in more or less indifferent contact at many 

 places with pipes, walls, &c. Further, only the bell at the 

 end of a row could be rung by electrical attraction to the 

 opposite wall, because the bells swing parallel to the wall 

 on which they are fixed, and considerable force is required 

 to make them move in a direction at right angles to their 

 free swing. 



In the case referred to by Mr. C. L. Tweedale, it might 

 have been worth while to see if the wire attached to the 

 livelv bell he mentions did not come in contact with any 

 other wires at any part of its length. \\'hat makes me 

 suggest this is that in one of my rooms I can tell when 

 the front-door bell is rung by a sympathetic movement of 

 the bell-pull in the room, due to the wires rubbing against 

 each other at some part and the wire to the door bell 

 pulling the wire to the room. 



When one considers the class of workmanship put into 

 bell-hanging, one need not be surprised at the vagaries of 

 the bells. Like plumber work, it is mostly out of sight, 

 and as the woric has often to be done in very imperfect 

 light and under cramped conditions, anything that will 

 work is c#hsidered good enough. John Aitken. 



Ardenlea, Falkirk, August 21. 



FLYING ANIMALS AND FLYING MACHINES. 



T T NTIL quite recently human flight was considered 

 ^ by the mass of mankind as so impracticable 

 that " I can no more do that than fly " was 'a phrase 

 used to denote something not to be accomplished. It 

 is no wonder, then, that the fact that several people 

 (probably some dozens at the present moment) have 

 actually flown should appeal to the popular imagina- 

 tion, and the appeal is especially strong in such a case 

 as M. Bleriot's flight over the English Channel, 

 although there is nothing really more formidable in a 

 flight over water than over land. It may be of some 

 interest to show- briefly how it is that what was 

 formerly looked on as a typical impossibilit}- has now 

 become a matter of ever5'day occurrence. 



It will be a help to take first the case of such 

 aniiTials as have wings, and to see why it is that no 

 creature the height of which approaches even one- 

 quarter that of a inan has been able to fly either in 

 present or former times. In order that the 

 wings may support the body, their movement must 

 generate a downward current of air of which the 

 momentum per unit of time is equivalent to the down- 

 ward momentum which the body and wings would 

 acquire in the same time under the influence of 

 gravity. This does not necessarily involve a large 

 expenditure of work. For instance, when a weight 

 is attached to a parachute and is dropped from a 

 height the speed of descent soon becomes constant, 

 and the work done in the air by the parachute is then 

 just equal to the product of the weight into the dis- 

 tance fallen. The resistance of the parachute is pro- 

 portional to its area, and the speed of descent can 

 be made as small as we please if the area is made 

 large enough. The work, therefore, expended in a 

 given time, that is, the power delivered to the air, is 

 diminished in the same proportion. 



Suppose now that instead of an inanimate weight 

 an animal is suspended from the parachute bv a long 

 rope ladder. When the speed of descent is slow- 

 enough, the animal will have no difficulty in climbing 

 the ladder at such a rate that the centre of gravity 

 of the " system " may remain stationary in the air, 

 and this by an expenditure of work which can be 

 diminished indefinitely by increasing the area of the 

 parachute. 



This case is analogous to the hovering of a bird in 

 NO. 2078, VOL. 81] 



the air without horizontal velocity during the down- 

 stroke of the wings, and as no means are here pro- 

 vided for restoring the wing to its primitive position 

 the time of support is limited. The illustration 

 suffices, how^ever, to show- that the work required in 

 order to maintain a stationary position in the air by 

 means of wings is equal to the worlc required to raise 

 the total weight involved at the same rate as that at 

 which it would fall were no work to be expended. 



Of the total weight supported, namely, the animal 

 and the parachute, the animal only is a source of 

 pow-er. Thus, while in " dynamically similar " com- 

 binations the total weight varies as the cube of the 

 linear dimensions, the supporting area varies as the 

 square, and the living power available varies, not as 

 the total weight, but as the total weight less the 

 weight of the supporting wing. It will be readily 

 seen that if the animal can only deliver a certain 

 amount of pow-er per unit weight of body these con- 

 ditions lead to an absolute limit to the weight of an 

 animal which can sustain itself stationary in the air. 

 For, suppose the total weight is K' = «'„-fK', (the 

 weights, namely, of the animal and the parachute of 

 area s), Wg must vary as .t?, and if the downward 

 velocity is to be constant x must be proportional to -w. 

 From this it can be shown that the greatest weight 

 an animal (incapable of climbing faster than some 

 given speed) can have is 2h' It,c', where b = w'Js' and 

 c=U','js'', 7C'g and s' being known values of wing 

 weight and wing area fulfilling the condition of fall- 

 ing with the required velocity w-hen the total weight 

 is It''. If we take w„' = w'jn, the expression 

 2b' I y' becomes giw'i!". 



As an example, suppose that 30 feet per minute is 

 the limiting velocity at which an animal can continue 

 to climb, and that the area of the parachute which 

 will drop at the appropriate speed when the total 

 weight of parachute and load is i lb. is too square 

 feet, and also that the weight of the parachute alone 

 is J lb., then it appears that no animal could main- 

 tain itself stationary in the air by means of a para- 

 chute the weight of which exceeded §(4)" (or about 

 105 lb.), and the area required for this weight would 

 be more than 1600 square feet. Thus, if no more 

 favourable way of supporting a weight w-as available 

 than- the down stroke of a wing in still air, flight 

 would be impossible for all except the very smallest 

 animals. 



As is well know-n, how-ever, the vertical reaction on 

 a slightly inclined plane moving rapidly in a horizontal 

 direction enormously exceeds that which it would 

 experience in dropping through still air, and although 

 the proportionalities between the weights and the sup- 

 porting area still remain, viz. sxw and 7t',ccj-;, the 

 actual weight which can be supported by a given area 

 increases indefinitely as the horizontal speed in- 

 creases. 



If there w-ere no such thing as air friction, the work 

 expended in supporting a given load might also be 

 reduced indefinitely, for the resistance to the horizontal 

 motion (which, when the inclination of the plane is 

 small, may be regarded as the horizontal component of 

 the normal force) could be diminished indefinitely by 

 decreasing the inclination. 



Air friction, however, fixes a limit beyond which 

 the inclination of the plane to the direction of motion 

 cannot bo advantageously reduced. Experiments have 

 shown that this inclination is about 5°, and that then 

 the ratio of the supporting force to the resistance lies 

 between 5 and 7 (depending partly on the shape of 

 the plane). A knowledge of the best angle of inclina- 

 tion and the ratio of the resistance to the force on the 

 plane at right angles to its path afford means of deter- 

 mining the possible cfticicncy (see " Experiments on 



