24 



University of California Puhlications. [Entomology 



may be illustrated by the diagramatic projection shown in 

 Fig. 6. In an insect viewed from the left side let AB repre- 

 sent the hinge, or axis, about which the wing swings at 

 each stroke, the direction of progression being from B toward A. 

 Let the line CD represent the mean inclination of all parts of 

 the wing during the up stroke, and CD' the same during the 

 down stroke. These lines CD and CD' converge l^ehind, 

 because, as is well known, the more flexible posterior field of 

 the wing yields more to the resistance of the air than the 

 anterior margin and, therefore, lags behind in both upward 

 and downward strokes. Draw from any point O of the line 



AB, perpendiculars OE 

 and OE' to the lines CD 

 and CD'; then the lines 

 OE and OE' represent 

 the direction of the force 

 exerted by the wing dur- 

 ing the up and down 

 strokes respectively. 

 Perpendiculars to the 

 line AB from E and E' 

 (FE and FE') represent 

 the amount of this force 

 which is neutralized by 

 reason of the opposition 

 in direction of the two 

 strokes, and 20F the net 

 resultant force producing forward propulsion. 



A more economical motion would be produced by increasing 

 the obliquity of the lines CD and CD' to the base line, AB; 

 but it would require at the same time a greater rapidity of 

 stroke to maintain the same rate of progression. 



Such motion as that just described requires, in order to 

 accomplish horizontal flight, that the axis of vibration lie 

 somewhat obliquely to overcome the effect of gravity. In the 

 diagram let A'B' represent the actual line of motion. Now, 

 drawing the lines EG and E'H perpendicular to A'B', we have 

 the lifting power that opposes gravity represented by E'H 

 minus EG, and the propelling force OG minus OH. At both 

 the beginning and end of the stroke the two pairs of wings 

 oppose each other, and thus exert no lifting or depressing 



. Diagram illustrating mechanics 

 of flight. 

 •VOB, horizontal line: A'OB', axis of body; CD 

 and CD', mean inclination of wings; EFE', per- 

 pendicular to AB; EG and E'H. perpendiculars 

 to A'B'. 



