by M. Struve.

count of it, published at the East India Company's
expense in 1847.
The heats and the rains, the
dull opake atmosphere of the Doab, with its bound-
less and densely-wooded flats, the jungle fever and
the wild animals, were natural impediments enough.
But Colonel Everest, whose conscientious anxiety
reached almost a nervous pitch, seems not to have
been satisfied with any one instrument which the
mechanicians of London could produce; but to
have metamorphosed most of them, partly with his
own hands, partly by native aid. It says much for
his ability in this respect, that the results appear
entitled to compete with all the most exquisite of the
kind in Europe. His bases, for instance, about 7
miles in length, when checked by intermediate trian-
gulation above 400 miles in extent, differed in one
instance by 4, in another by 7 inches from the pri-
mary measurement. The whole extent of Lambton's
and Colonel Everest's operations includes a continu-
ous arc of 21° 21' (1477 miles), by far the greatest
at that time executed.

(252.) It is indeed only rivalled in this respect by a vast Russian arc operation very lately executed in Russia and other northern countries of Europe, by which an arc of 25° 20', extending from the banks of the Danube to the shores of the Arctic Sea, near the North Cape, has been measured under the general superintendence and direction of that able astronomer M. Struve, whose meritorious labours in other departments of astronomy will be specified in a succeeding section. The results are still incomplete, though the operations in the field were happily concluded just in time to prevent their total frustration by the unhappy war in which Russia has since engaged.

(253.) The arcs of India and of Russia include a space Its extent. from Lat. 8° to Lat. 71°, with the exception of only about sixteen degrees, and are unquestionably the most important which exist for the determination of the earth's figure. When to them we add the French arc of 12° 22' in a medium latitude, it will scarcely be necessary to take into account any other, at least for the Northern Hemisphere.

(254.)

(255.) Details of the Russo

The following brief details of the Russian arc are taken from the provisional report of M. Struve (1852). The southern extremity of the Russo-Scandinavian

is Ismaïl on the Danube (Lat. 45° 20′), the northScandina ern extremity is Fuglenaes on the island of Qualoe vian Arc. in Finnmarken (Lat. 70° 40′). The interval from Tornea to Fuglenaes (4°49′) was measured by Swedish and Norwegian engineers; all the remainder by those of Russia, and, in particular, by M. Von Tenner, who, with M. Struve, has since 1816 directed the whole operation. The whole line is remarkably free from considerable inequalities of ground, and from mountain ranges, so that local attractions are probably inconsiderable. On the other hand, extensive forests ex

1

tending over dead flats have, in the southern part of the arc (as in India), occasioned great difficulties, and compelled the erection of numerous temporary structures to overlook the country. In the north the extraordinary refractions have, as usual, created some difficulties. Ten different base lines, all at a small height above the sea, form part of the operations. It is a very satisfactory circumstance, that by the care of M. Struve and Mr Airy, the standards of length used in the Indian and Russian arcs have been directly compared.

(256.) General result as to the Earth's

ments.

The calculation of the figure of the earth from the completed Russian arc, in combination with others, has not yet been made, but it is believed that it will indicate an ellipticity somewhat greater than ellipticity that generally received. The results obtained by Co- from geolonel Everest, on the other hand, by comparing his desy; are with those of Europe, give generally small ellipticities, that is under. The French and Indian arcs, for instance, give Now Mr Airy had deduced 20 years ago from the best existing observations; Bessel, a few years later, obtained the almost identical result of; and Schmidt of år. The determinations by means of the pendulum are and from somewhat larger. The extensive observations of Co- pendulum lonel Sabine and Captain Foster concur in giving experian ellipticity of; but the French experiments by Duperrey and Freycinet lead to a result considerably greater. The discrepancy between the geodetical and pendulum results may of course be a real one depending on local variations of density. The astronomical determination from the lunar inequalities, which might be expected to concur with the results of the pendulum, gives (as we have seen in the chapter on Physical Astronomy, Art. 63) at a mean. I regret that my limits do not permit me to speak of the measure of degrees of longitude or arcs of parallel, as another test of the earth's figure. The results, however, cannot compete in point of certainty with those from arcs of the meridian. It may be satisfactory to add, that the British arc of parallel from Greenwich to Valentia (west coast of Ireland) sensibly accords with the earth's figure obtained independently.

3 5

(257.)

British arc of parallel.

In connection with the subject of the pendulum (258.) treated in the earlier part of this section, I shall here M. Foucault's penmention a very remarkable experimental observation dulum excommunicated to the Paris Academy of Sciences, on periment, the 3d February 1851, by M. Léon Foucault, to whom we also owe some ingenious experiments on the velocity of light. It is not indeed connected with the determination of the earth's figure, but it has a connection with astronomy, inasmuch as it affords the most remarkable and direct proof of the earth's rotation round its axis.

(259.) Suppose a considerable weight suspended by a wire demonof regular elasticity from a fixed point or stand constrating the 'nected firmly with the ground; and let us first imaEarth's rotation. gine the place of the experiment to be exactly over the North Pole. Let the wire pendulum be swung so as to coincide with the plane of the meridian of London. As the earth rotates, the wire and the ball must evidently rotate too. But the motion of the mass originally impressed parallel to a given plane will continue in that plane, and consequently the plane of motion will coincide in the course of 12 hours with every meridian in succession, and the apparent rotation will be entirely completed in a uniform manner in 24 hours. In any other latitude than 90°, but greater than 0°, a continuous and regular apparent change of motion must also occur, since a meridian of the globe does not preserve its parallelism during diurnal motion, excepting only at the equator; consequently, at all points of the earth's surface, except at the equator, the plane of motion of the pendulum will vary uniformly in azimuth-quicker, however, in high than in low latitudes. To find this velocity, it is only necessary to decompose the rotation of the earth round its axis into two, one of which (which is alone effective) is round the vertical of the place of observation. The apparent angular motion is thus proportional to the sine of the angle of latitude. Thus, in an hour, it is 15° x sine lat.

Encke. Periodic Comets.

to be at

tended

M. Foucault's experiment was made, in the first in- (260.) stance, with a pendulum of steel wire from 03 to 05 Corrections inch in diameter, bearing a ball of 12 pounds weight. todo. It is desirable to make the pendulum vibrate in small arcs, in consequence of the tendency to ellipticity in the vibrations, which is necessarily accompanied by a rotation of the major axis of the ellipse, which might easily be mistaken for the influence of the earth's motion. To take account of this disturbing force, we have only to measure accurately the greater and less axes of the ellipse described. Then a revolution of the apsides (from this cause only) will be performed in a time which will be found by multiplying the time of a double vibration of the pendulum by 8 times the square of the length of the pendulum, divided by 3 times the product of the two axes of the ellipse. This formula is due to Mr Airy. The theory of M. Foucault's beautiful experiment has been verified by numerous experiments in different latitudes.

(262.) PROFESSOR JOHANN FRANZ ENCKE, Director of the Professor Observatory of Berlin, is one of the most eminent physical and practical astronomers of the present day. The author of many valuable observations and important memoirs, he is best known by those which are connected with the motions and theory of Comets. I shall therefore devote this section to an abstract of the progress of this interesting subject, and more particularly of M. Encke's discoveries and speculations. I must premise, however, that, easy and agreeable as it would be to introduce here a detailed essay on Cometary Astronomy, the design and extent of this discourse alike forbid it, and at the cost of some self-denial, I will endeavour to confine myself entirely to what is most new and characteristic in the Cometary history of later years.

whose return was confidently predicted, in firm reliance on the Newtonian Theory of Gravity. Halley's announcement-grounded not on vague analogies, but on laborious computations-that it would reappear early in 1759, was realized almost to the letter; Its return and Clairaut, whose surprising analytical ability often in 1759. left but little to his successors to accomplish, calculated the perturbations with an accuracy which even the present state of physical astronomy has hardly exceeded. Indeed no general method for calculating perturbations in highly elliptic orbits is as yet in use, and though the methods of Clairaut have been superseded by those of Lagrange and Bessel and Leverrier, the summation of the effects by the method of "quadratures" is always used, the periodic time of the comet being divided into short intervals throughout which the elements are considered invariable, and during which the configurations and perturbing effects of the principal planets are computed with much labour.

The chief improvement in the calculation of per- (264.) turbations is the introduction by Lagrange of the celebrated method of the Variation of the elements (44.)

bations

calculated

astronomers.

Its pertur- His successors have distinguished themselves chiefly by the praiseworthy minuteness and extent of their by various calculations, which are amongst the most laborious, if not indeed the most laborious, which occur in Physical Astronomy. The computers who calculated the return of Halley's Comet in 1835 were four in number, MM. Damoiseau, Pontecoulant, Lehmann, and Rosenberger. Their memoirs are all considered by competent judges to be excellent, but especially that of Rosenberger, who calculated more fully than the others the perturbations from 1682 to 1759, and who has introduced a theoretical correction of some importance. Some idea of the extent of these calculations may be formed from the fact, that in some parts of the orbit the Elements were made to vary for intervals of only two days. The Comet of Halley was rediscovered at Rome on the 6th August 1835, in the Jesuits' College. The error of Rosenberger's Ephemeris was only seven minutes of are, and the perihelion passage took place on the 16th November (civil reckoning), five days after the predicted time. Bessel states the remarkable fact, that the coincidence of the comet's path with the results of previous calculation is as close as the use of five-place logarithms in computing the perturbations would permit. All this is very creditable to the state of Astronomy; still it is infinitely less remarkable than Clairaut's approximation, only a little less close, made 77 years before. It is a matter of regret that neither in the matter of this comet, nor in any other point of theory connected with Cometary movements, have our countrymen made any considerable advance since the time of Halley.

(265.) Its return in 1835.

At its return in 1835, this Comet was watched until May 1836, and in the course of its long visibility was made the subject of minute and admirable telescopic researches, by Bessel in Europe, and by Sir John Herschel at the Cape of Good Hope. Their observations strictly confirmed a remark of M. Valz, that the Tails of Comets, though evidently generated under the influence of the neighbourhood of the Sun, yet commonly disappear at the period of closest approach. This, at least, was the case with Halley's Comet. The tail began to grow on the 2d October, two months after its discovery, and diminished after the 15th (a month before perihelion). The comet reappeared in the end of January without any vestige of a tail, and then dilated in absolute bulk with incredible quickness. But before its final disappearance, on the 5th May, the tail is supposed to have Its peculiar been reabsorbed into the nucleus, which presented then a uniform circular outline. The evolution of the highly-expansible luminous matter of the tail took place from the nucleus in luminous fan-like jets, directed on the whole towards the Sun, and issuing on the side of the Comet exposed to that body. The jets had a vibratory motion. The tail

features.

com

(directed from the Sun) was formed by the abrupt inflexion of these effluent jets, in a manner resembling electrical repulsion; and Sir John Herschel has not hesitated to ascribe the phenomenon to the bination of a repulsive force as respects the Sun, ("of an energy very far exceeding the gravitating force towards that luminary") with "a peculiar and highly energetic attraction to the nucleus, differing from, and exceptional to, the ordinary power of gravitation." The opinion that polar forces resembling magnetism or electricity are necessary to explain the phenomena of Comets, has been for some time current in Germany, and received, I believe, the countenance of Bessel. That there exist in the movements of these bodies anomalies so great as to render the sufficiency and completeness of the Theory of Gravity suspected by such high authorities, makes the statement of them very important, though I confess a great reluctance to share in the conclusion.

Table of its

returns.

I shall terminate this notice of Halley's Comet (266.) with a table of the dates of its probable perihelion passages, according to M. Laugier and Mr Hind.2 The earlier appearances are deduced from the Chinese Annals :—

The differences in the above periods are attributed tɔ the effects of perturbation. The extreme distance of the Comet's path from the Sun is 35 times the radius of the Earth's orbit, which is only one-sixth part greater than the distance of Neptune, and therefore nearly within the recognized limits of the planetary system.

Comet of Encke.

observa.

tion.

to the orbit of Jupiter), and made the subject by him of a series of investigations altogether peculiar. On this account it bears the name of Encke, instead of that of its discoverer Pons, although M. Encke himself, with unaffected modesty, always describes it as the Comet of Pons.

(268.) Newton gave, in the Principia, his celebrated soCometary lution of the problem of determining a Comet's orbit orbits derived from assumed to be parabolic, from three geocentric places. This solution has been simplified and improved by Lagrange and Boscovich, and also by Olbers. Laplace gave a method for an elliptic orbit, which may represent any number of observations. Gauss, in his Theoria Motús Corporum Celestium, treated the subject with great skill and generality. I am unable to state who first attempted to discriminate an elliptic from a parabolic cometary orbit, or to determine the period in the former from observations at one apparition only. It is evident that such outstanding differences as are irreconcilable with a parabolic orbit, will be most perceptible in the case of comets whose orbits have a tolerably short major axis, or whose period is not very great, and will be materially increased by watching a comet through a considerable part of its orbit, which the assiduous application of telescopes to every part of the heavens has of late years rendered much more frequent than formerly. Amongst others, Bessel, who has signalized himself by a capital performance in this, as in every other department of Astronomy, applied rigorous methods to determine the orbits of the comets of 1807 and 1815; the latter of which will very probably return to its perihelion in 1887. It is undeniable, however, that expert calculators have often been deceived in assigning orbits, even when believed to be of short period, founded upon a single apparition.

(269.)

researches

on the comet of

riod 3

years.

M. Encke, however, was more fortunate in the case M. Encke's of the first comet of 1819. Using the methods of Gauss, he showed that an Elliptic Orbit of about 3 years must be admitted, and that the comet had pro1819-pe- bably been already observed in 1786, by Méchain, in 1795 by Miss Herschel,1 and in 1805 by Pons. He investigated with great labour the effects of the planetary perturbations on this body, which, in the case of Jupiter, are occasionally very large, if that planet be in the part of its orbit near the aphelion position of the comet, when it approaches the orbit of Jupiter. The careful calculations of M. Encke for the next return in 1822 were verified by the observations of Sir Thomas Brisbane, at that time fortunately governor of New South Wales, where he had, with characteristic liberality, founded an Observatory. Since then, this body, insignificant in its physical appearance (being to all appearance a small cloud of vapour without a solid nucleus), has been detected in one or

Miss Caro

:

ritions.

Its accele

another part of the world at every revolution:· namely, in 1825, 1828, 1832, 1835, 1838, 1842, Its appa1845, 1848, and 1852; so that the Comet has been observed at fourteen (not all consecutive) returns. The complete establishment of the existence and pe- (270.) riodicity of a comet, quite in the interior of the planet-rated moary system (its greatest distance from the Sun being tion four times the Earth's distance, and its least distance but one-third of the Earth's), was a discovery in itself highly interesting. But something yet remained behind. Professor Encke, in comparing the earlier with the later apparitions of the Comet, detected a gradual acceleration of its movement, which amounted between 1786 and 1838, to 1.8 days, on a period of about 1211 days; being about 2 hours per revolution. Whatever may be the cause of this, the fact is undisputed, even by Bessel, who was indisposed to accept M. Encke's explanation. This fact, it will be observed, is unique in Astronomy. The major axis and periodic times of the planets and satellites have, as we have seen in the chapter on Physical Astronomy, no secular variation. The moon's apparent acceleration has been otherwise accounted for. M. Encke at once, attributed and at an early period, attributed the acceleration of to a resisting methe Comet's mean motion to the effect of a slightly dium. resisting medium, insensible in the case of the planets, partly owing to their incomparably greater density (for this Comet appears to be one of the most loosely aggregated bodies known, being transparent to its very centre); and also, to the circumstance, that the density of the ether or resisting medium is assumed to diminish rapidly at a distance from the Sun. M. Encke supposes it to decrease in density with the square of the distance, and only to affect the Comet sensibly within 25 days preceding or following its perihelion. That the effect of resistance is to accelerate the return of the Comet is evident, by considering that the projectile force becoming gradually extinguished, the Sun's attraction must be more available to pull the body inwards at each revolution, thus shortening the major axis of the ellipse, and diminishing the time.

(271.)

Perturbations of

masses of

In order satisfactorily to arrive at any such conclusion, it was of course necessary to estimate with great accuracy the perturbing effects of the planets Encke's on the Comet's motion; and it is not a little curious comet apand satisfactory, that the movements of this insigni- plied to rectify the ficant erratic body should have occasioned a material rectification of the masses of two of the Planets. Mercury M. Encke very early suspected that the received and Jupimass of Jupiter was too small, a fact clearly established afterwards by Mr Airy; and in 1838 M. Encke showed that the mass of Mercury (which, not having a satellite, was little more than guessed at previously) had been assumed nearly three times too great by Lagrange. The perihelion of the Comet approaches much

VOL. I.

5 Q

ter.

medium not

more nearly to the orbit of Mercury than the aphelion does to that of Jupiter; consequently at times the perturbations due to the former planet may be very great, and though the gravitating mass of the Comet is utterly unknown, yet since the momentary direction of its motion depends solely on the ratio of the attractive force of the Sun and Mercury, its observed course gives the means of estimating that ratio.1

(272.) The theory of a resisting medium was, on the whole, Theory of well received, especially in England, where some of a resisting our first authorities gave it their adhesion. The then altogether recent establishment of the Undulatory Theory of favourably Light, was thought by many to receive a confirmation received, from this evidence of something material filling the planetary spaces. In Germany the hypothesis of resistance received the complete opposition of Bessel's high authority; who declared that "a hundred other reasons" might be found for the fact of the acceleration, which he admits to be true. Encke, in reply, reduces these 100 possible hypotheses to four, of which we shall mention only one, as seemingly important, namely, the forces exerted with so much intensity within the body of the Comet itself, as indicated by the projection of the tail. But he observes, with great sagacity, that these forces, being apparently usually excited in the line of the radius-vector joining the Comet and the Sun, can hardly be supposed to affect the periodic time. It having also been objected that Halley's Comet shows no trace of acceleration, but, if anything, of the reverse, M. Encke truly says, that its perihelion distance does not lie within the assumed limits of the denser ether.

(273.) Nevertheless, the theory of a resisting medium in and still space is not perhaps very popular, except in England. questioned. Although M. de Humboldt appears to favour it, I understand that the German astronomers in general scarcely regard it as in any degree proved.

(274.)

Yet, if not true, the cardinal fact remains unexplained. The anomalous phenomena of the Tails of Comets, considered by Herschel to be altogether inexplicable by the law of gravity, demand the closest scrutiny; and one can hardly help supposing that the two difficulties may be in close connection. As the Newtonian law is now considered (since the discovery of Neptune, and the latest corrections of the Lunar Tables) to be absolutely sufficient to account for everything connected with planetary motion, the Astronomy of Comets will be looked to with increasing interest, as likely to reveal some laws of nature not otherwise to be detected. In this respect, Professor Encke's labours are likely to be more and more important in their results.

(275.) With reference to this very eminent astronomer, M. Encke we have only to add, that he has for a great many on pertur years been at the head of the Observatory at Berlin, and in that capacity has published an Astronomical Ephemeris of first-rate excellence. It is as a phy

bations.

sical astronomer, however, that he will be principally remembered. Besides his admirable investigations connected with the Comet, he improved the theory of Vesta, and has very lately published a new Method of Computing Perturbations, especially for orbits considerably elliptical. Neptune was discovered at his Observatory, by the assistant astronomer, M. Galle.

and Brela's

Gambart's and Biela's Comet.-JEAN GAMBART, (276.) one of the most promising astronomers in France, died Gambart's of consumption at a comparatively early age, I believe comet. in 1836. He was director of the Observatory at Marseilles, which, notwithstanding its very unfavourable position in the midst of the town, has acquired considerable celebrity as regards the discovery and observation of Comets. Pons, by whom Encke's Comet was found, both in 1805 and 1818, conducted the Observatory; but its mounting was as bad as its situation, and Pons used despairingly to describe his telescope as rather paralytic than parallactic. To this crippled establishment M. Gambart succeeded, and by his skill in managing his defective instruments, and by his patience in sweeping for Comets, he discovered and subsequently computed the orbits of a number of these bodies between 1822 and the period of his death. Gambart was highly esteemed, both by French and foreign Astronomers. Pons also deserves great credit for his extraordinary diligence in the discovery of Comets, and M. Valz, who still directs the Observatory of Marseilles has cultivated this and other branches of the science with success.

Gambart's most remarkable discovery was the pe- (277.) riodicity of the first Comet of 1826, having detected Periodicity that body independently at Marseilles, though it had in 62 years. been observed some days previously in Bohemia, by Biela, an officer in the Austrian service. It is most usually called Biela's Comet, though it might with equal right be termed Gambart's, who assigned its path and predicted its return. Clausen, about the same time with Gambart, assigned it a period of about 7 years; and it was identified with former appearances in 1772 and 1805-6. Its period thus appeared to be 2460 days, or 63 years; its aphelion is a little exterior to Jupiter's orbit, and its perihelion is not much within the Earth's. This Comet's orbit very nearly intersects in one place the orbit of the Earth, so that had the earth been one month forwarder in its annual course in 1832, a collision would have taken place, or at least the Earth would have been enveloped in a cometary haze; for it is difficult to imagine a collision with a body whose tenuity is so excessive, that Sir John Herschel perceived through its entire thickness (estimated at 50,000 miles) stars of the most excessive minuteness (16th or 17th magnitude) as seen by his 20-feet reflector. It is an interesting circumstance, that the first predicted perihelion passage, in 1832, took place within some hours of the time fixed by MM. Santini and Damoiseau,