16 ON SHOOTING STAES. 



AVERAGE LENGTH OF THE VISIBLE PART OF METEOR-PATHS. 

 If I be the length of an arc, and b the radius, the angle subtended is measured by 



j. If we consider any number n of arcs, the average of the angles subtended is - l' T . If b is 

 n o 



constant, or is proportional to I, the value of this expression would be equal to the mean 



value of I divided by the mean value of b. Applying this to the meteor-paths, the higher, 



and hence more distant paths, are probably longer than the lower and nearer ones. The value 



of b does uot moreover become very small. Hence we may consider - 1 j- as approximately f-, 



where 7 6 is the mean length and b is the mean distance. We have, then, approximately, 



l 10.04 - „ „„ 



Since the mean of fractions having the same numerator is greater than the numerator 

 divided by the mean of the denominators, we may, however, consider l„ as less than 0.286. 

 The difference from this cause is probaly less than one-tenth of the whole amount, as will be 

 seen by summing the values of j instead of those of b. 



Inasmuch as the value of b is found to be between 140 and 232 kilometres, we have 1° 

 comprised between 39 and 65 kilometres, or between 24 and 40 statute miles, or between 

 21 and 34 geographical miles. The smaller number is without doubt much nearer the truth 

 than the other. 



THE MEAN DURATION OF FLIGHT AND THE MEAN VELOCITY OF THE SHOOTING STAES. 



Mr. Wartmann, of Geneva, gives for the aggregate duration of 368 flights observed 

 during one night in August, 1838, by six observers, 180 a .33, which is S .49 for each flight. 

 The mean of 499 estimates made in August and November last is S .418. The mean of the 

 whole 867 estimates is s . 45. If the durations given by those observers who are accustomed 

 to estimate small intervals of time had alone been taken, the result would have been very 

 nearly the same. Almost all observers agree that the* mean duration of flight is not much, 

 if any, greater than half a second.* 



A mean duration of half a second, and a mean length of path between 39 and 65 kilo- 

 metres, seem to imply a mean velocity between 78 and 130 kilometres per second. The smallest 

 of these velocities (more than 48 miles) is twice and a half the velocity of the earth in its 

 orbit about the sun. This cannot consist with the supposition that the meteoroids all move 

 in closed orbits about the sun. Hence we must accept as highly probable, one, or more, of 

 these three conclusions, viz: 



1st. That the length of track is too long, which seems to involve that the altitudes, on 

 which all the computations are based, are on the whole too large. All the altitudes greater 

 than 150 kilometres might, I think, have been safely rejected. 



*A shortening of the duration of flight toward morning is indicated by theory, and is confirmed by observation. 

 (300) 



