AND VELOCITY OF METEORS. 85 



of the different meteors. Now this difference of direction amounts to more 

 than 10° on the average (according to Erman) from the mean direction, and 

 cannot, for the maximum, be less than 25°. This difference of direction may- 

 arise 



1. From the difference in their elliptic orbits about the sun. 



2. From their mutual action. 



3. From the earth's attraction. 



1. Supposing, with Erman, the breadth of the ring to be 2°, the difference 

 arising from the first cause cannot be more than 1° from the mean direction. 



2. The deviations arising from their mutual attractions must be trifling; 

 they cannot, for instance, be supposed greater than they would be if all the 

 meteors but the disturbed one, which we may be considering, were combined 

 into one planet, about which this disturbed one moved as a satellite. Now if 

 we consider that the variation in the moon's absolute direction from the earth's 

 is only about 2°, we shall have no hesitation in neglecting this second cause of 

 disturbance. 



The difference in direction arising from the first two causes is absolute, and 

 may be somewhat magnified when converted into relative direction, but not 

 much, unless the relative velocity v' is very small. There is also a difference 

 of absolute velocity, which will produce a difference of relative direction of 

 about the same order of magnitude with that arising from the difference of ab- 

 solute direction. 



3. The observed difference of direction must then be chiefly referred to the 

 principal disturbing cause, the earth ; and the following method of calculation 

 is sufficiently accurate for the present case. Let 



v' — the relative velocity of the meteors at the moment of entering the 

 sphere of the earth's influence, which sphere we may, for this cal- 

 culation, suppose to be infinite, 

 ^ = the angular deflection of the meteor's relative motion, 

 then no other meteor will be so much deflected as the one which just grazes 

 the surface of the earth; and for this meteor we have 



v'^ R 



cosec. 4) = 1 -f- 



m 



III' f ^ 1 \ 



= — [cosec. ^ — 1) 



VIII. — w 



