OF ARTS AND SCIENCES: FEBRUARY 8, 1S70. 201 



Six Hundred and seventeenth Meeting. 



February 8, 1870. — Monthly Meeting. 



The President in the chair. 



The President called the attention of the Academy to the 

 recent decease of Overbeck, at Rome, of the Foreign Honorary 

 Members. 



Dr. E. H. Clark made a communication on the results of 

 an analysis of one thousand cases of disease in general practice, 

 as to the curative action of drugs. 



Dr. Bowditch made a communication, illustrated by a chart, 

 on the apparent connection of cloudy days and mortality from 

 consumption, for the period from 1811 to 1857, and in this 

 vicinity. 



Two papers by Mr. G. W. Hill were presented at the meet- 

 ing of December 11, 1869. 



The following problem seems to possess some interest, and I have 

 not, in my reading, met with any discussion of it : — 



To determine the elements of the orbit of a planet or satellite, 

 which moves in a circle in the plane of the ecliptic, from three obser- 

 vations of its direction from the earth, made at equal intervals of time ; 

 the positions of the earth and the central body at these times being 

 known, but the sum of the masses of the central body and the planet 

 or satellite being unknown. 

 Or, geometrically stated, — 



In a plane, given a point as centre and three straight lines, required 

 to describe a circle, so that the arcs intercepted between the first and 

 second, and the second and third, lines may be equal. 



Let generally R denote the distance of the central body from the 

 earth ; 

 " " L its longitude as seen from the earth ; 



" " r the radius of the orbit of the planet ; 



" " A its longitude as seen from the earth ; 



" " x i ts longitude as seen from the central body. 



Moreover, employ the subscripts (_-,) , ( ) , ( x ) , to denote the special 

 values of the above quantities, which have place respectively at the 

 three times of observation in their order. 

 VOL. VIII. 2fi 



