45o THE POPULAR SCIENCE MONTHLY. 



increase of velocity about the middle of the period when either foot is 

 on the ground. This fact is in harmony with experiments which I 

 have already published. 



I will add, in concluding, that one of the most important results 

 obtained by these researches is, the idea which they give of the varia- 

 bility of the movement of translation of the body during walking and 

 running. 



In another publication I shall show the applications which can 

 be deduced from these studies to the best utilization of the work of 

 animals. 



II. On the Resistance op the Air to the Wings of a Bird 

 during its Flight. I have presented to the Academy of Sciences a 

 memoir which proves that the wings of a bird, during their downward 

 movements, meet with more resistance from the air when the bird 

 has an horizontal motion of progression than when the bird, depress- 

 ing his wings with the same velocity, has no horizontal motion of 

 translation. 



The explanation of this phenomenon appears to me to be as follows : 

 a wing, or any surface whatever, which moves against the air, meets, 

 at the beginning of its motion, a considerable resistance, on account 

 of the inertia of the air, which resists every displacement ; but, little 

 by little, the air yields, and the velocity of its motion gradually in- 

 creases, until it may equal that of the moving surface which displaces 

 it; this phase of motion having been reached, the resistance dimin- 

 ishes. Finally, when the moving body stops, the moving air tends to 

 continue its journey, and it thereby produces before the moving sur- 

 face a true aspiration, or negative pressure. But a bird, which moves 

 horizontally during the depressions of its wings, acts, during succes- 

 sive instants of that depression, on a series of columns of air over which 

 it passes. From each column it meets with that maximum resistance 

 which the inertia of the air presents at the first instants of the action 

 of the wing. Finally, when the wing has reached the lowest point of 

 its depression, it is not over the mass of air which it has just set in mo- 

 tion, because the motion of translation of the bird continually brings 

 it into regions where the air is at rest. All of these conditions are 

 evidently favorable to flight, since they increase the resistance of the 

 air, which alone furnishes to the bird its support, and the reaction to 

 its moving wing. 



To prove the exactness of this theory, I have made certain experi- 

 ments in which a uniform quantity of work was applied to produce the 

 elevation and depression of the wings of an artificial bird. In some 

 experiments the motions of the wings took place while the machine 

 was stationary; they had a great amplitude of motion. In other 

 experiments we gave the artificial bird a motion of translation, and 

 then we observed that the amplitude of the flaps of the wing dimin- 





