10 ON SHOOTING STARS. 



every clear, moonless night.* He always watched between 11 and 1' o'clock. During 71 

 hours aud 22 minutes he saw 572 shooting stars. Allowing one-fourth of a minute (the period 

 estimated by him) for recording each path, and we have an average of 8 meteors per hour. 

 By what factor we must multiply the number seen by one observer to obtain the whole number 

 visible at the place, we have no observations, that I know of, to determine. It is probable 

 that this multiplier is as large as four, and that 30 is not too large for the mean value of n. 

 This would give the average number of meteors that traverse the atmosphere daily, and that 

 are large enough to be visible to the naked eye if the sun, moon, and clouds would permit, 

 equal to 30x21x10400, or more than seven and a half millions. 



I shall now assume that the phenomenon called a shooting, or falling star is caused by a 

 small body, (probably a solid,) which was originally moving in its own orbit in the solar 

 system, or in space; that this body coming into the atmosphere of the earth elicits light by the 

 loss of velocity, and is usually itself dissipated before reaching the earth's surface. The term 

 meteoroid will be used to denote such a body before it enters the earth's atmosphere. 



NUMBER OF METEOROIDS IN THE SPACE WHICH THE EARTH TRAVERSES. 



Suppose many small bodies to be distributed through an indefinite space, so that there shall 



be n bodies in a cubic unit. Suppose that these bodies have all an uniform velocity of v units 



per second in the same direction. Suppose a large sphere t whose radius is R, and which is 



without attraction, to be at rest in this space. The sphere intercepts in each second as many 



small bodies as are contained in a right cylinder, whose length is v, and whose radius is R, 



that is, - n R 3 v bodies. 



Suppose now that the sphere attracts the small bodies. Let 



the hyberbolic arc MB, figure 3, represent the orbit of one of 



these bodies which just grazes the surface of the sphere at B. 



Let MA be its asymptote, and EA the perpendicular on the 



asymptote from the centre of the sphere, then will the large 



body intercept all the small bodies in a cylinder whose radius is EA. But if v is the 



velocity of the small bodies at a great distance from E, and u x is the velocity at B, 



then will EBx»! = EAxy by the law of conservation of areas. The number of bodies 



v 2 

 intercepted by the sphere is then evidently tt n^xEA 2 , that is, ttjivR 2 -4-. If now v a be the 



velocity which a body would acquire by falling from infinity to the surface of the sphere when 

 acted on only by the attraction of the sphere, then will v 2 -f- v* = vf, by the law of conserva- 

 tion of force. Hence the sphere will meet in each second with iz nv R* | 1 -| — ^ j bodies. 



If the sphere has an uniform motion in any direction, the same reasoning and formulas 

 apply by making v and v l represent velocities relative to the centre of the sphere. 



This reasoning may be extended to several systems of small bodies. Let there be distrib- 

 uted uniformly through the indefinite space in each unit it bodies of one system, n" bodies of 



*Comptes Iieiulus, xiii, 1039. 

 (300) 



