﻿32 Mr. S. Newcomb on Hansen's Theory of the 



and it is therefore found that the radiation-coefficient for metals 

 is about five- or sixfold smaller than that for a blackened sur- 

 face. Stewart and Tait observed that the aluminium disk with 

 a pure metallic surface radiated about one-fourth the heat of a 

 blackened one. 



Breslau, September 11, 1868. 



V. On Hansen's Theory of the Physical Constitution of the Moon. 

 By Simon Newcomb*. 



THE great reputation of the author has given extensive cur- 

 rency to the hypothesis put forth by Professor Hansen 

 some years since, that the centre of gravity of the moon is con- 

 siderably further removed from us than the centre of figure. 

 The consequences of this hypothesis are developed in an elabo- 

 rate mathematical memoir to be found in the twenty-fourth 

 volume of the Memoirs of the Royal Astronomical Society. But 

 the reception of the doctrine seems to have been based rather on 

 faith in its author than on any critical examination of its logical 

 foundation f. Such an examination it is proposed to give it. 

 An indispensable preliminary to this examination is a clear un- 

 derstanding of what the basis of the doctrine is. Let us then 

 consider these three propositions : — 



(1) The moon revolves on her axis with a uniform motion 

 equal to her mean motion around the earth. 



(2) Her motion around the earth is not uniform, but she is 

 sometimes ahead of and sometimes behind her mean place, owing 

 both to the elliptic inequality of her motions and to perturbations. 



(3) Suppose her centre of gravity to be further removed from 

 us than her centre of figure, and so placed that, when the moon 

 is in her mean position in her orbit, the line joining these cen- 

 tres passes through the centre of the earth. 



Let us also conceive that these two centres are visible to an 

 observer on the earth. Then a consideration of the geometrical 

 arrangements of the problem will make it clear that when the 

 moon is ahead of her mean place the observer will see the two 

 centres separated, the one nearest him being further advanced 

 in the orbit ; while, when the moon is behind her mean place, 



* From Silliman's American Journal for November 1868. 



t In this connexion it is curious to notice that on page 83 of his memoir 

 Hansen appears as the first of the independent modern discoverers of Cag- 

 aoli's theorem of spherical trigonometry — 



cos a cos & cos C+ sin a sin 6= cos A cos B cos c+ sin A sin B. 



This was about three years before the above formula was published as new 

 by Mr. Cayley, and geometrically demonstrated by Professor Airy, in the 

 Philosophical Magazine. 



