A. MATHEMATICS AND ASTRONOMY. 9 



The spectroscope, then, has demonstrated the present exist- 

 ence of immense nebulous masses, such as that from which 

 Laplace supposed the solar system to have been derived. It 

 has shown, moreover, a progressive change in their physical 

 structure, in accordance with the views of the same astrono- 

 mer. In short, the evidence afforded by spectrum analysis 

 in favor of the nebular hypothesis is cumulative, and of itself 

 sufficient to give this celebrated theory a high degree of 

 probability. 4 D, September, 1871, 155. 



DETERMINATION OF THE MASS OF THE MOON BY TIDAL 



OBSERVATIONS. 



At the meeting of the National Academy of Sciences on 

 the 19th of April, 1871, Mr. William Ferrel, of the United 

 States Coast Survey, gave an account of his discussion of 

 tidal observations with reference to determining the mass of 

 the moon. He used in this investigation a series of observa- 

 tions made for the Coast Survey during nineteen years a 

 full lunar cycle at Boston, Massachusetts, and a similar 

 series of observations made at Brest, France, from 1812 to 

 1831 inclusive. 



Without going into the mathematical form of the investi- 

 gation, he endeavored to show that the moon's mass must be 

 mainly inferred from the ratio which the spring and neap 

 tides bear to the constant or average tides. This ratio, how- 

 ever, does not depend entirely upon the moon's mass, but 

 varies greatly for different ports, the heights and times of the 

 tide being modified by local circumstances ; and, consequent- 

 ly, the tides have not been hitherto considered an available 

 means for determining: the mass of the moon. 



In addition to the constant, to be determined by observa- 

 tion, introduced into the conditions by Laplace for determin- 

 ing the moon's mass, Mr. Ferrel has introduced another, de- 

 pending upon friction. Hence, there being three unknown 

 quantities to be determined, including the moon's mass, he 

 uses the condition depending upon the moon's parallax in 

 addition to the two used by Laplace. Without the introduc- 

 tion of this additional constant and the additional condition 

 for eliminating it, Laplace's conditions for the determination 

 of the moon's mass entirely fail when applied to the Boston 

 tides. 



A2 



