ART. V.-On a mode of employing Instantaneous Photography as a means for the Accurate Determination of the Path and Velocity of a Shooting Star, with a view to the Determination of its Orbit; by JONATHAN H. LANE.

A tolerably accurate knowledge of the orbits of those meteors, or shooting stars, which may enter our atmosphere, would be of very high value in the settlement of certain questions as to their origin. Hitherto this knowledge has appeared unattainable by reason of the difficulty of effecting sufficiently precise observations of the meteor in the transient period of its visible flight, especially considering how this difficulty is aggravated on account of retardation of its motion by the resistance of the atmosphere. Recently, however, a method has occurred to me of applying instantaneous photography, so as to show accurately, not only the track of the meteor, but the division of its track into many equal and known fractions of time. If this can be successfully accomplished, we should have the data for ascertaining the velocity of the meteor at each point of the recorded part of its track, and the rate or law of variation of the velocity, and thence, with probably a good degree of accuracy, the velocity it had beyond the limits of the atmosphere, and the like remark may be made concerning the direction of the motion, should that be found subject to change.

The basis of the proposed process, as already intimated, is the extraordinary advances that have been made within a few years in the preparation of the sensitized surfaces of photographic plates, whereby artists are enabled to produce good pictures by an exposure of a very small fraction of a second-so small as to afford a tolerable definition of objects in motion, such as sailing vessels. This holds out encouragement for a hope, at least, that a passing meteor would leave a visible trace on a plate so prepared, or, even if that degree of sensitiveness has not yet been reached, that it will be hereafter. I need therefore make no apology for placing the suggestion on record previous to direct experiment on this point.

In the first place, simple exposure in a camera, at a given station, would give the apparent track of a meteor as seen by the observer at that station, and a pair of such records made in two cameras at two stations, would give the track in absolute space. In the second place, if one of the two cameras were furnished with a mechanism by which equidistant points of time should be marked upon the trace made in that camera, these points could be referred to the real path in space, and if both cameras were in like manner furnished, the two records would, to that extent be a check upon each other, and serve to reduce the limits of probable error. The

device for marking time is an application of the revolving glass prism, very similar to that described in my paper on a visual method of comparing time between distant stations, published in the January number of this Journal.* Immediately in front of the object glass of the camera, a glass prism of small angle and sufficient area to cover the entire aperture, is made to rotate at an accurately measured rate of say twenty-five revolutions per second. The prism may be replaced by an excentric lens, or the object glass itself may revolve on a slightly excentric axis. The consequence will be that the image of a fixed star in any part of the field of view will traverse the circumference of a circle every twenty-fifth of a second, and the image of a shooting star will combine this motion with its motion of translation. If the photographic surface retain a visible impres sion of the looped curve or the waved curve which will thus be produced, then, neglecting for the present the small effects of optical distortion, the line drawn midway between the two straight or regularly curved lines between which the looped or waved curve oscillates, will represent the apparent track of the meteor, and the points where it intersects the looped or waved curve, if they be translated along this middle line through a space equal to the optical displacement of the meteoric image, will show the apparent place occupied by the meteor at points of time separated by the equal intervals of one fiftieth of a second. If the period be made too brief, the impression left by the head of the meteor in one sweep of the looped or waved curve, might possibly be obliterated by the impression of the closely following parts of its train, while the head is traversing the subsequent sweeps of the curve. But there is no reason to anticipate from this cause any difficulty in obtaining a sufficiently short period to determine the law of variation of the velocity or direction.

In the above statement I have supposed only a single camera, but it will probably be impossible in this way to command a sufficient extent of the heavens. A system of many cameras may, however, be formed, so arranged that their several optic axes shall cross in a common point in front of the object glasses. The object glasses may thus be approximated as closely as we can desire, and the several revolving prisms, or excentric lenses, may have a common geared connection, and the backs of the cameras will be readily accessible for the renewal of plates. When the track of a meteor, by reason of its extent or situation, is obtained in parts from different cameras of such a system, it is geometrically impossible, on account of the spherical excess, that the exact interval of one fiftieth of a second between the times

* Vol. xxix, 43.

marked upon the meteor's track, should, in general, be preserved in the transition from one plate to another in all situations of the track, or in other words, that every two adjacent cameras in the system shall be capable of marking, in the manner described, the same common point of time upon the track of a meteor, but the exact difference in time can always be known.

In the execution of such a plan as this, two stations are to be selected at a suitable distance, and a system of cameras established at each, of such range that the two may cover in common a sufficient extent of the upper regions of the atmosphere to afford a fair chance for the occurrence of meteors. Each station will require at least an observer and a photographer. The photographer will renew the plates as often as their surfaces, either from time or exposure, become impaired, and will perform the manipulations required in fixing the impression when taken. The observer, after having made the necessary instrumental adjustments and determinations will be charged with the sole duty of watching for meteors in the region covered by his system of cameras, and at the appearance of a meteor will touch a spring so contrived as to cause the instant unveiling of all the cameras of the system, and on the extinction of the meteor will promptly replace the screen.

The expense and trouble of this process will certainly be great, but will not be disproportioned to the importance of the object in view. Only let us have a photographic surface that will give a visible trace of the meteor's path, in the face of exposure to the light of the sky during the time of the meteor's visible flight, and then success, as regards the attainments of an accurate record, will be nearly certain, and we should not hesitate at the expense and trouble.

Nor does it seem to me that our success would be much less certain in respect to the reliable determination of the direction and velocity which the meteor had before entering the atmosphere, and consequently of the orbit in which it had moved. A very simple calculation based upon the mechanical theory of heat, leads us to the conclusion that any body of a nature to become readily incandescent by heat, of such a thickness as half an inch, and not possessing a greater power of conducting heat through its mass than any we are acquainted with, must, on entering our atmosphere with planetary velocity, become self luminous by the time that velocity has been reduced by some such fractional part as one thousandth. The vis viva of a body moving with a velocity of twenty miles a second is equivalent to the heat that would raise the temperature of an equal weight of water about 224,000° Fah. With such a velocity, so many times exceeding that of sound, the masses of air lying in the

path of the body must be driven before it, and receive a velocity equal to that of the body, or at least to a large fractional part of it. The mass of air which the body must have encountered in losing the thousandth part of its velocity, will, therefore, be of the order of a thousandth part of that of the body. With the loss of a thousandth part of the velocity, the loss of the body's own vis viva will correspond to the quantity of heat that would raise the temperature of its weight of water 448° Fah. If after making allowance for the motion communicated to the displaced air-approximately one half-and for the quantity of generated heat which this air retains and carries off, we assume that a twentieth part of the above 448° enters into the body itself, and by reason of the rapidity of its production is collected in a superficial coating of a hundreth part of its mass, and give this a specific heat within that of water, we should find an elevation of temperature of 2240° or upwards. The inference we would draw from these considerations seems confirmed by what we know of the great length of the visible flight of meteors, and of the great elevation of the region of atmosphere in which it

occurs.

If, therefore, upon suitable trials made upon the fixed stars, and upon shooting stars themselves, we shall find ourselves in possession of sufficient photographic power, there is no reason why an organized system of observations should not be instituted. If the fact in regard to the retardation of a meteor's motion be as the foregoing considerations lead us to anticipate, the discussion of a collection of such records as we should obtain, of a large number of meteors, will be likely to afford us complete assurance on the subject, by pointing out certain laws of the resistances at different altitudes. A moderate degree of accuracy in the absolute determination of the orbits, except, when they make a near approach to the parabola, will be sufficient to answer all the questions of interest that will be likely to arise upon which a knowledge of the orbits would have any bearing. Whether the November meteors, for instance, move through regions that would identify them with the Zodiacal light, according to the theory of the late Prof. Olmsted, is a question that would receive an absolute determination.

ART. VI.-The True Figure of the Earth.-Notice by Mädler in Prof. Heis' Wochenschrift für Astronomie, Meteorologie und Geographie, No. 51 and 52. Dec. 21 and 28, 1859.*

Essai d'une détermination de la véritable figure de la terro. Par T. F. DE SCHUSt. Petersbourg, 1859.

BERT.

THIS brief but very important paper treats of a question which has engaged mankind for ages, and treats it in such a way as to convince us that an essential step forward has been taken towards its final determination.

It is not intended to recapitulate the history of opinions and notions which antiquity, as well as the middle ages, had formed on this topic so generally interesting, as it does not belong to the plan of the work to be discussed.

Since the establishment of Newton's theory, that the earth is flattened at its poles, and the confirmation of this theoretical result by the first measurements of arcs in the eighteenth century, the chief inquiry has been directed to the magnitude of this compression, or, in other words, the difference between the semimajor and the semi-minor axes of the earth. The attempt was made to determine it by comparing arcs measured in different latitudes, the latitudes of their extremities being astronomically and their extent on the earth geodetically determined. In this manner was obtained, between 1735 and 1746, two arcs, the one in Peru, and the other in Lapland, which could be compared with each other, as well as that previously measured by Cassini in France. The result of the comparison was not satisfactory. Although they proved a comparison, the measures did not agree, and the source of this difference was too obscure to favor the supposition that any nearer approach had been made to the object of research.

In the course of the eighteenth century measures of arcs of the meridian were executed or attempted in France, Austria, Italy and Pennsylvania, at the Cape of Good Hope and other places. Their comparison made it apparent that the compression (), as at first concluded, was too great, and that it must be reduced one half or even more. Yet the uncertainty remained very considerable.

The measurement of arcs was continued in the nineteenth century over greater extents in different parts of the earth and with greater care and accuracy, and the close agreement of these arcs, as it appears from the comparison of their parts, left but little, further to be desired. Perceptibly different values for the compression were nevertheless obtained, as when the most proba

* Translated for the American Journal of Science by CHARLES A. SOHOTT, Assistant, and communicated by Prof. A. D. BACHE, Supt. U. S. Coast Survey.