6 11. A. Newton — Relation of the Orbits of 



Table showing the distances from the earth's quit, to the absolute quit of a 

 meteoroid for different distances from the earth's quit to the relative quit of the 

 meteoroid. 



Distance from Q to relative quit. 



30 c 



60 



90 



120 



150 



180 



Distance from Q 



to absolute quit. 



w=l-414. 



w=l-244. 



9°*3 



6°-3 



22-1 



15'8 



45-0 



36'5 



82-1 



75-8 



129-3 



126-3 



180-0 



180-0 



In the following constructions the maximum velocity of the 

 meteoroid has been used. When the meteoroid's relative quit 

 is known as a point the absolute quit is at once constructed. 

 If, however, we have an area within which the relative quit is 

 probably located we may mark off with equal facility points on 

 the boundaries of the area within which the absolute quit is 

 probably located. If the former area is a circle the latter will 

 be an oval. The center of the circle does not correspond ex- 

 actly to the center of the oval, but by applying a correction to 

 the table the center of the oval absolute-quit area can be 

 directly constructed from the center of the circular relative- 

 quit area. 



In figure 1 I have given in a single diagram constructed on 

 a stereographic projection, the results for 116 stone-falls. The 

 best determinations which the accounts admit of for the mete- 

 or's direction were first made out. Then the center of the 

 probable quit area in each case was assumed to be the actual 

 quit, When only the quarter of the heavens from which the 

 stones came is stated the center of probable area was taken 20° 

 above the horizon. Interpreted thus, the stars in figure 1 rep- 

 resent the places of the 116 absolute quits relatively to the 

 place of the sun, S, and to that of the earth's quit and goal, 

 Q and G. 



Let us denote any one of these quits (or stars), by the letter 

 q. The elements of the orbit in which the corresponding stone 

 was formerly moving can be easily obtained from the projec- 

 tion. The earth's longitude on the day of fall is the longitude 

 of the node. The angle <^SQ is the inclination of the orbit to 

 the ecliptic, and its amount is at once read off on the projec- 

 tion. The orbit has been assumed to have been a parabola. 

 Hence, twice the complement of ^S was the angular distance 

 of the stone from its perihelion. If qS> 90°, the perihelion 

 had not been reached ; if ^S < 90, the perihelion, had been 

 passed. The perihelion distance was Sin 2 ^S. If, however, it be 

 assumed that the orbit was a long ellipse of given major axis, 

 the place of the absolute quit, q, moves somewhat nearer to Q 



