OP ARTS AND SCIENCES. 32 



Q 



Herschel's observations, as collected and reduced by Zullner, exhibit a 

 still greater divergence from Lambert's formula than those of Zullner 

 himself. Bond also obtained a like result from his own photometric 

 observations. 



It seems, accordingly, to be well worth while to investigate the 

 results of Lambert's hypothesis when applied to a rough body of some 

 kind. As a first step in this direction, Zijlluer's discussion of the 

 phases of a roughened cylinder was apparently judicious, although he 

 seems to have laid too much stress on the analogy between a smooth 

 cylinder and a smooth sphere. But the accidental error in his analysis, 

 which has been noticed above, would have made it difficult to decide, 

 in the absence of further examination, whether any confidence could 

 be placed in his conclusion. The formula obtained in the preceding 

 pages, however, agrees with Zollner's in its most important peculiarity. 

 We find that the phases of a furrowed cylinder, like the observed 

 phases of the Moon, must exhibit a comparatively rapid increase of 

 light towards opposition, and that this increase ends abruptly when 

 opposition is reached, beginning to diminish abruptly as soon as oppo- 

 sition is passed. The great angle of elevation required in the ridges 

 of the cylinder, before its computed phases begin to resemble those of 

 the Moon, makes it probable that other forms of roughness besides 

 that exhibited by the furrowed cylinder are concerned in the problem. 

 But the degree of success attending the investigation proj^osed by 

 ZiJllner is sufficient to encourage further examination. Undoubtedly, 

 however, additional observations are much more important, if not more 

 interesting, than these theoretical reconciliations of Lambert's hypoth- 

 esis with the facts of nature. 



The meteoric theory of the zodiacal light is affected by inquiries 

 into the phases of rough bodies, since it is highly probable that the 

 meteors assumed, to produce the light are of irregular shape and of 

 uneven surface. An important result already obtained is, that minute 

 but abrupt irregularities may be expected materially to modify the 

 phases of the bodies which exhibit them, and that, upon any plausible 

 hypothesis of reflection, such irregularities will tend to produce a 

 relatively great amount of light in the direction opposite to that of the 

 Sun. A few obvious remarks naturally present themselves with re- 

 gard to the probable effects to be expected from different kinds of 

 irregularity in surfaces ; but these effects need some mathematical ex- 

 amination before anything can be said of them sufficiently definite to 

 be useful. 



