350 
PHYSIOLOGY: W. F. HAMILTON 
Proc. N. a. S. 
It has been proved that: (1) If (1.1) and (1.2) are differential equations 
which define the same system of paths then the functions and A j^, 
are related by the equations 
— A^p = ip^p = b^ipp + (4.3) 
in which (p^ is a vector. (2) If (1.1) are the differential equations of a sys- 
tem of paths and (p^ is any covariant vector then there exists a second set 
of differential equations (1.2) for the same system of paths, the functions 
A„'^ being defined by (4.3). 
The formula (3.7) reduces to that obtained by Kisenhart on page 235 of 
this volume in the case when 5 is a function of t alone. This makes it 
evident that his work must be taken as referring to a geometry in which 
there is an element of distance ds defined by means of functions of position. 
In this sense his theorem on page 235 will be found not to be in contradic- 
tion with the theorem (2) above. 
A DIRECT METHOD OF TESTING COLOR VISION IN 
LOWER ANIMALS 
By W. F. Hamilton 
De^partment of Physiology, Yai^e University 
Communicated, October 26, 1922 
1. When spectral lights of different wave-lengths are directed on the 
photoreceptors of lower organisms, their reactions show that one of the 
two lights is, physiologically, the more effective. Even when the unequal 
distribution of energy in the spectrum is equated for, there still remains a 
difference in the physiological effectiveness of the stimuli. (Laurens and 
Hooker.^) This difference must be dependent upon wave-length. 
But it is also evident to the colorblind eye (Koenig^). We cannot there- 
fore argue that the differential response on the part of the organism is 
proof of color division. 
Researches which have approached the question of color vision in lower 
organisms by means of conditioned behavior have not been done with pure 
spectral lights. Even when pure spectral lights are used, the difference 
in brightness must be equalized, not, however, in accordance with the 
luminosity curve of the human eye, but with that of the organisms whose 
color vision is to be tested. Obviously it is difficult to obtain a luminosity 
curve free from extraneous factors from the reactions of organisms suffi- 
ciently complex and intelligent to exhibit conditioned behavior. 
