along the line qQ, the angle in the plane of the orbit from perihelion was a little more than twice the complement of qS, and the perihelion distance somewhat less than Sin'qS. But all these quantities are easily computed in terms of the assumed major axis. With a semi-major axis as large as 5 the change in figure 1 would not be so considerable as to modify any conclusions we can deduce from the grouping of the stars. The most noticeable fact revealed by the figure is the clustering of the stars about the point Q. All but 7 of the 116 meteor quits are in the Q hemisphere; that is, had orbits. whose inclinations were less than 90°. One hundred and nine followed the earth, seven met it. Again the two lines STE are drawn to represent circles inclined 35° to the ecliptic. More than two-thirds of the meteor quits lie between these two lines; hence, over two-thirds of the orbits were inclined less than 35° to the ecliptic, the motion being direct. It should be said that this clustering of the points near Q is somewhat exaggerated in the figure by the nature of the stereographic projection. The scale of distances near Q differs from that near the circumference. But this does not affect the distribution between the hemispheres. It has been assumed that certain centers of quit areas were themselves the quits. Can the condensation of the quits near Q have been caused in any way by this assumption? * Or, is it possible that general errors of observation, or inaccuracy of reporting, could have been the cause? To answer this question let us suppose that there had existed a law that led to condensation of the relative quits in any manner whatever. The effect of the errors of observing or reporting, and also the effect of the assumption above stated, would be toward scattering these relative quits over the heavens more equably, and thus masking the law. Then when the relative quits thus unduly scattered are reduced to absolute quits there might be as a result a tendency towards condensation near Q. If, however, we draw the circle TT, enclosing those absolute quits whose relative quits are in the hemisphere next Q, the general tendency of the errors in question would be towards equalizing the number of absolute quits within to those without the circle TT. Now, the number of stars is nearly twice as great within as without the circle. The condensation about Q, shown in figure 1, exists therefore in spite of, and not in consequence of, these errors. With a good deal of confidence do I conclude that these 116 meteors were, as a class and with probably a very few exceptions, before coming into the air following the earth in its orbit about the sun. Another fact of great interest is also shown by the grouping of the points in figure 1. In general these stones did not go 2 in their orbits very near to the sun. Assuming that the orbits were parabolas we have for all the stones whose perihelion distances were less than one-half, Sin'qS <. If there be drawn Sin29S circles, AA, AA, 45° from S and from E, then will all the stones whose absolute quits were in the central zone, APPAAA which is bounded by the circles AA, have perihelion distances greater than one-half and less than unity. Of these there are 103 out of a total of 116. If the same orbits are assumed to have had semi-major axes equal to 5, then the circles AA would have to be drawn a fraction of one degree farther from S and from E to serve as the limiting curve to orbits whose perihelion distances exceed one-half. It appears from figure 1 that these 116 stones were, with a few exceptions, following the earth in their orbit about the sun. This could happen from either one or more of three possible causes : Firstly, that nearly all the stones in the solar system are moving in direct orbits, very few in retrograde orbits;— Or, secondly, that stones moving in retrograde orbits for some reason, as for example their great relative velocity, may not have been able to pass through the air and to reach the ground in solid form ; Or, thirdly, that stones moving in such retrograde orbits, and coming through the air, may be falling while men sleep, or for some like reason may fail to be found. In other words, the effective cause may work above the air, in the air, or below the air. Let us assume, as an hypothesis, that neither of the first two are the true causes. In that case we should have the stones moving in every direction as they cross the earth's orbit. There should be about as many orbits having retrograde motions as direct motions. Hence the absolute quits of all stones coming into and hence, by hypothesis, coming through the air, should be symmetrically distributed in their longitudes relative to the sun. At least there should be as many absolute quits in the G-hemisphere as in the Q-hemisphere (figure 1). Take account now of the earth's motion and locate the relative quits. All these stones whose absolute quits lie outside of the circle TT will have their relative quits in the G-hemisphere. Upon the hypothesis of parabolic orbits and of an equable distribution of the absolute quits over the celestial sphere the number of relative quits in the G-hemisphere should be to those in the Q-hemisphere as 1+cos: 1-cos- or as 17:3. The relative Π 4 Π 4' quits should then be very much more numerous in the G-hemisphere than in the Q-hemisphere. Furthermore, suppose that the heavens visible at a given time and place, are divided by a vertical circle into two halves; and suppose that this vertical circle is at right angles to the plane containing the zenith and the earth's quit and goal. That half of the visible heavens that lies towards the earth's goal may be called the goal-half, the other half may be called the quit-half of the visible heavens. In any given period there should evidently be, under the several hypotheses stated, many more stones coming into the air and reaching the ground directed from the goal-half than there should be directed from the quithalf of the visible heavens. Still further, since this proposition applies to any epoch whatever, we may apply it to 116 periods covering the times of the 116 stone-falls, that is, to the 116 stone-falls themselves. Many more of these should (under the hypotheses stated) have come from the goal-half than from the quit-half of the visible heavens. If, then, the relative quit of each of these 116 stones is supposed to be carried around in azimuth 180°, the altitude being unchanged, the 116 distances from each new place of the quit to the earth's quit for the epoch of the fall should, in the average, be decidedly less than the corresponding 116 distances from the actual relative quits to the earth's quit. This should hold true (under the hypotheses stated) no matter what causes below the air may have occasioned the selection of the 116 epochs. The fact that more persons are abroad in the evening hours from 6 to 10h P. M., than in the corresponding morning hours, 2h to 6h A. M., may well cause that more stones should be secured in the evening than in the morning hours. In the evening hours the earth's quit is above the horizon; in the morning hours the earth's goal. It might easily be that we should for this reason get more stones of direct than of retrograde motions. But the above criterion is entirely independent of any such principle of selection of the epochs. A change of the azimuth of the quits through 180° should cause a larger number of them (under the hypothesis stated) to approach the earth's quit than to recede from it. I have marked off upon the working sheets the position 180° in azimuth from each of 115 relative quits, the altitude being unchanged, and measured the several distances from the earth's quit. (One fall, Nedagolla, was unavailable.) The following is the result. In 44 cases the meteor's quit by the change approaches the earth's quit; in 70 cases it approaches the earth's goal; in one it remains unchanged. That is, instead of a very large majority of the quits moving towards the earth's quit we have nearly two-thirds of them moving the other way. In the reversed position, moreover, we should have had 38 absolute quits in the G-hemisphere instead of 7. These numbers show very decidedly that the hypotheses made above are not true. The principle of selection is not entirely below the air, and the numbers testify so markedly against that hypothesis that I feel warranted in adding that the cause is mainly either above the air, or in the air. Between the first and second causes named the materials used for the present discussion do not furnish a positive critical test. But if, as I believe, the Stannern stone came from the south, we have at least one instance of stones coming into the air with a velocity of nearly, or quite, 45 miles a second and reaching the ground in solid form. About 25 of the quits in figure I imply velocities of not less than 25 miles a second on entering the air. Large velocities do not seem to be entirely fatal to the integrity of the meteorites. I believe that the first cause was the dominant one rather than the second, yet for a crucial test of the two causes, if one can be found, we must look to a class of facts other than those we have been considering. We are now in position to consider the other 94 stone-falls. In figure 2, the construction of which is similar to that of figure 1, the stars mark the zenith points for each time and place of the 94 falls. A grouping is at once noticeable. They are nearly all in the northern hemisphere, since the observing peoples live there. Those stars in the hemisphere of which S is the pole, that is between the two lines PP and PP, are evidently daylight stone falls, since S is above the horizon for each case. These constitute about seven eighths of the whole number. The reason for this predominance is manifest. In the night men see the fireball or the train, whereas in the day the first intimation of the stone-fall is usually the hearing of the detonation two or three minutes after the fireball has disappeared. Hence, daylight stone-falls are those whose directions are less likely to be observed, and these 94 falls are the ones of which the directions are unknown. It will also be seen that there are nearly twice as many in the Q-hemisphere as in the G-hemisphere; that is, there are nearly twice as many that fell when the earth's quit was above the horizon as there were when the earth's goal was above the horizon. In general, the former were afternoon stone-falls, the latter forenoon stone-falls. Now the habits of the urban population have not much to do with these daylight meteors, for the fireballs were not seen. The accounts come from the country, where the stones in general have fallen, and about as many people are there abroad in the forenoon as in the afternoon. If stones came to the ground as often from retrograde as from direct orbits we ought apparently to have had very many more zeniths in the G-hemisphere than in the Q-hemisphere. The contrary being the fact of experience we may rea |