20 



ON SHOOTING STARS. 



To obtain this equation v' has been supposed equal to or greater than v. If v' is less 

 than v there is a maximum value of d, determined by the equation v sin = v', and the radical 

 in the'value of v" changes sign. The same expression for N would, however, be found in this 

 case by proceeding as follows. The number of shooting stars whose relative motion is from 

 the triangle OAB, figure 6, would be equal to the whole number whose absolute motion is 

 from the lune, diminished by those meteors for which d exceeds a certain value OA. The 



amount of this diminution is -j-^ multiplied by the difference of the two values of 1 — cos Oct 



7 2 



obtained by changing the sign of the radical — that is, by 7p-(l 72 sin 2 0)%. Hence, 



n r*' v 2 * 



N = »-5^/ (1— -ssin 2 0) cosOdp, 



where tan 0= cos a sec <p, and <p' is the value of <p when v sin d = v'. Substituting and inte- 

 grating, we have as before, 



No = 5 (l + -7COSfl). 



Let I be the latitude of a place, h the hour angle counting from the time when the point 

 to which the earth is moving is on the meridian, and 8 the declination of that point; then 



cos a — sin I sin 8 + cos I cos d cos //.. 

 The mean value of 8 for the year is zero, and hence for the entire year we may use the 

 equation cos a= cos I cos h, and hence, approximately, 



N =-(H — 7 cos I cos A). 

 2 v' 



If we compute according to this formula the value of N -r n for the several hours of the 



night, for the latitude of New Haven, and that of Paris with the three values v' =v y/H, v' = v, 



and v' — ty, we shall have the following table: 



Table IV. — IIypollictiral distribution of the shooting stars through the hours of the night. 



(310) 



