CHAPTER III. 



THE SUSPENDED PLANE. 



The first instrument, called the Suspended Plane, was devised to illustrate 

 an unfamiliar application of a known principle. I call the application "un- 

 familiar" because distinguished physicists have held, for instance, that a bird 

 (which obviously expends a certain amount of muscular effort in simply hovering 

 in the air) must expend in flight all the effort required for hovering, together 

 with so much additional energy as is required to overcome the resistance of 

 the air to its horizontal motion, so that the energy expended increases with the 

 velocity attained,* while the consideration of the action of the suspended plane 

 indicates, if it do not demonstrate, that the opposite view is the true one, and 

 thus serves as a useful introduction to the demonstrative experiments I have 

 spoken of as coming later. 



* This view of flight received indorsement from a source of the highest authority in a report by Gay-Lussae, 

 Flourens, and Navier, accepted and published by the Institute of France in 1830. [Navier, C. L. M. H. — Ptapport 

 sur un Memoire de ]M. Chabrier concernant les moyens de voyager dans I'air et de s'y diriger, contenent une 

 nouvelle th^orie dea mouvements progressifs. (Commissaires, MM. Gay-Lussac, Flourens, et Navier, rapporteur.) 

 Paris, Mem. Acad. Sci. xi, 1832 (Hist.), pp. 61-118.] The report is drawn up by Navier, to whom the mathe- 

 matical investigation is due. He formulates the diflerential equations of motion for the two cases of hovering 

 and horizontal flight, integrates them in the customary way, assumes approximate values for the constants of 

 the equations, and computes the work expended by an ordinary swallow with the following results: For 

 hovering, the work done per second by the swallow is approximately equal to the work required to raise its own 

 weight eight meters. While in horizontal flight the work done varies as the cube of the velocity, and for 1.5 

 meters per second is equal to 5.95 kilogrammeters per second, or enough to raise its weight 390 metere. This 

 \slifly times as much as that expended in hovering, or in English measures, over 2,.500 foot-jjounds per minute, 

 which is a rate of working greater than a man has when lifting earth with a spade. 



The same computation applies to any larger bird whose weight bears the same ratio to the extent of its 

 wings. In view of these figures Navier suggests that tlwre exints tlie same ratio between the efforts necesssary for simple 

 suspension and for rapid flight as exists for terrestrial animals between the effort required for standing upright and that 

 required for running. [Nous remarquerous la grande difference qui existe entre la force necessaire pour que I'oiseau 

 se soutienne simplement dans I'au-, et celle qu'exige un mouvement rapide. Lorsque la vitesse de ce mouvement 

 est de 15™ par seconde, on trouve que cette derniere force est environ cinquante fois plus grande que la premiere. 

 Ainsi I'eflfort qu'exerce I'oiseau pour se soutenir dans I'air est fort petit comparativement ii I'eflfort qu'il exerce 

 dans le vol. II en coute peut-etre moins de fatigue a I'oiseau pour se soutenir simplement dans I'air, eu egard a 

 la fatigue qu'il est capable de supporter, qu'il ne'en coute a I'homme et aux quadrupedes pour se soutenir debout 

 sur leurs jambes." — Paris, Mem. Acad. Sci. si, 1832 (Hist.), p. 71.] The supposed elegance and validity of 

 Navier's mathematical processes, and especially tlie elaboration with which they were carried out, appears to 

 have obscured the absolutely inadmissible character of these results, and they received the miqualifled adlierence 

 of the remainder of the committee. This report thereupon became a standard authority upon the theory of 

 flight, and continued to be so accepted for many years. 



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