310 PROCEEDINGS OP THE AMERICAN ACADEMY 



XIII. 



THE PHASES OF THE MOON. 

 By Arthur Searle. 



Presented April 9, 1884. 



During the passage of the Moon through the ordinary course of its 

 phases, the observed variations of the total amount of hght which 

 we receive from it are not readily accounted for by the accepted laws 

 of optics. The Photometrische Untersuchungen of Zollner (Leipzig, 

 1865) contains the results of previous inquiries into this subject, in- 

 cluding those of Zollner himself. Since then, so far as I have learned, 

 no important observations or theories relating to the phases of the 

 Moon have been made public. Additional knowledge of these phases 

 would have some useful applications to other subjects, and in particular 

 to that theory of the zodiacal light which ascribes it to sunliglit re- 

 flected from meteoric matter. From this point of view, an exami- 

 nation of Zollner's conclusions in the work above named, and an 

 attempt to derive some additional inferences from the material collected 

 by him, may be desirable. 



The formula most commonly assumed as an expression of the 

 variation of the total observed light of a distant object, in consequence 

 of its changes of phase, is due to Lambert. The hypotliesis on which 

 it depends is that the light received from equally bright surfaces will 

 be proportional to their apparent areas. In other words, Lambert 

 asserts the quantity of light received from a small distant object to be 

 proportional, other things being equal, to the magnitude of its ortho- 

 graphic projection U2)on a plane perpendicular to the line of sight. 

 The validity of the assertion was rather feebly supported by Lambert 

 himself, and has never been clearly established. Zollner, however, 

 has pointed out some considerations favorable to Lambert's hypothesis ; 

 and it will probably continue to find emplovment, in the want of a 

 more complete investigation of the question to which it relates. 



In addition to this special hypothesis, Lambert accepts the ordinary 

 photometric rule, (which appears to be almost a necessary consequence 

 of the rectilinear transmission of light,) that the actual illumination of 



