16 



HOMING AND RELATED ACTIVITIES OF BIRDS. 



EVIDENCE AGAINST HACHET-SOUPLET'S THEORY BASED UPON 

 MATHEMATICAL CONSIDERATIONS. 



The evidence we offer below militates against any theory of return over 

 long distances at sea based upon vision. It immediately discredits Hachet- 

 Souplet's theory of "direct perception of the goal" (as applied to the terns). 



The distance at which an object is visible at sea is expressed approximately 

 by the formula d = 1 .3 1 7 \/x in feet, where d is the distance of the ob j ect in statute 

 miles and x the height of the object above the earth's surface in feet. The 

 altitude obtained by this formula is, for shorter distances, approximately that 

 obtained by calculating the tangent to the arc of the distance and correcting 

 for the mean refraction at the horizon (36' 29"), but for great distances the 

 value obtained is somewhat too great. However, for our problem this error 

 is negligible. 



TABLE 1. 



The second column of table 1 gives the height at which a bird must fly in 

 order that its eye may meet with rays reflected from an object at sea-level at 

 the distance indicated in the first column, provided that the bird is stimu- 

 lated only by light waves ranging from 400 /JL/JL to 700 juyu in length. The 

 lighthouse upon Loggerhead Key is 151 feet in height. The third column of 

 the table gives the height at which a bird must fly in order to see the upper 10 

 feet of the light tower at the distances given. Even upon the assumption 

 that the birds have absolute visual acuity, it is evident that they can not fly 

 high enough to be guided by light reflected from the goal for more than a 

 small fraction of the distance through which they find their way back. But 

 the limitations of acuity are probably even greater than those imposed by 

 the curvature of the earth. For man two points of light are not distinguishable 

 unless they are separated by at least 30" of arc. Hence for a coast-line to be 



