North Sea, and entering Germany, not far from the mouth of the Weser, crossing that country to Trieste; thence down the Gulph of Venice, into the Mediterranean Sea; and, passing near Cape Matapan and the Isle of Candia, it leaves the Mediterranean to enter Palestine: passing between Jerusalem and Gaza, it quickly enters Arabia, where it quits the earth, with the setting sun, in latitude 27° 15' N., longitude 46° 9' E. But the penumbra will first touch the earth in latitude 59° 40′ 38′′ N., longitude 91° 5' 5" W. and finally leave it in latitude 3° 20′ 33′′ N., longitude 20° 28′ E. Owing to the great northern latitude of the moon, this eclipse will not extend farther south then latitude 13° 26' S., Jongitude 32° 6' E. But the penumbra will pass far above the earth in the other hemisphere.

At all those places where the digits eclipsed are 11, the obscuration will be as great as where it is central, for the whole of the moon will, in such case, appear upon the disc of the sun. The sun will be central eclipsed on the meridian, in latitude 77° 20′ 43′′ N., longitude 16° 37' 45" W.

The centre of the penumbra will be 2h. 13m. in passing over the earth, and the whole duration of the general eclipse, or the time of the penumbra passing over the disc of the earth, will be rather more than five hours and a quarter.

After giving this outline of the general eclipse, I shall proceed to the calculation of it for the latitude and meridian of Greenwich; but let me premise, that the places of the sun and moon are computed with the greatest care, and from the best astronomical tables. Moreover, as the accuracy of all computations regarding solar eclipses, depends entirely upon the nicety observed in obtaining the parallaxes of the moon, I have been particularly careful on this head; and, not wishing to confide in any auxiliary tables, I have computed the parallaxes from the triangles themselves; for, in the present instance, the conjunction happens so very near the nonagesimal degree, a greater exactness was required, owing to the curvature of the apparent orbit; and I have ascertained no fewer than ten points of the segment of the said orbit, which is described during the time of the visible eclipse at Greenwich, so that the beginning, middle, end, and digits eclipsed, will be found to agree with the best observations to a surprising degree of exactness.

The apparent time of the true conjungtion is September, 7d. 1h. 51m. 27.28., at which time the true longitude of the sun and moon is 5o 14° 47′ 41′′ (happening only 48' 14.6" east of the nonagesimal degree) with the moon's true latitude 44 37.9" N. descending the horary motion of the moon in latitude 2' 41'94" and in longitude from the sun 27' 1'58"; the horizontal parallax of the moon from the sun reduced to the radius vector, for the given latitude is 53′ 40·08". Hence the longitude of the sun and moon at the visible conjunction is 5° 14° 47' 37.8"; and the apparent latitude of the moon 3' 10-73" N. At the time of the greatest obscuration, the angle of the moon's visible way from the sun is 16° 56′ 16′′; and the nearest distance of their centres 3' 2.45". Now the apparent semidiameters of the sun and moon

are

15′ 54.81" and 14' 51.93"; hence the parts deficient are 27' 44:29", and the digits eclipsed 10 27' 30'1" on the sun's upper limb; or 17° 18′ 22′′ to the east of the vertical point of his periphery; at the same time, the longitude of the nonagesimal is 5o 14° 20′ 23.7", and its altitude 39° 1' 18'3"; the parallax of the moon in latitude 41′ 39.72" and longitude 16'647". The moon is on the nonagesimal at 1h. 55m. 14s. or about 2m. 26s. after the time of the greatest obscuration at Greenwich.

1

At the beginning of this eclipse, the apparent latitude of the moon is 12′ 11.3′′ N., and her visible difference of longitude from the sun 28′ 17.27"; the moon's apparent semidiameter is 14' 53.28", and the point of contact of the sun and moon's limbs is 49° 9' 54.3" to the west of the sun's upper limb. But, owing to the moon's decrease in latitude, and the position of the nonagesimal at the time of emersion, the apparent point where the moon's limb quits the sun is 86° 56' 0", to the east of the zenith of his disc when the moon's apparent semidiameter is 14' 49.88"; the apparent latitude of the moon 5′ 20′′ and the difference of longitude 30′ 17′′.

Eclipse of the Sun at Greenwich, September 7th, 1820: apparent time P. M.

1813.]

may be disposed to give a geometrical construction of the same. The semidiameter of the Earth's disc

Sun's declination N. decreasing

Moon's true latitude N.

decreasing

The angle, which relative

50 59 39.5

44 37.9

Horary motion of Sun in longitude

Horary motion of Moon in latitude

29 27.38

2 25 8

2 41.94

I

SIR,

SHALL once more, with your permission, occupy a small portion of your valuable Magazine, with a few ob. servations on a similar subject to what I have heretofore. But the author, from whom I now venture to differ in opinion, is so far my superior in physicomechanical acquirements, that it is with the utmost diffidence I enter upon the task, although, from an attentive examination of the subject, I am persuaded that I have truth to support me; and, being thus supported, I am encouraged to proceed, notwithstanding the great disparity above-mentioned.

Dr. Hutton, in his Principles of Bridges, Sec. ii. Prop. x. has, as it appears to me, fallen into more than one error. For, first he lays it down as a

GEL

D

Now, with all due deference to those superior acquirements, I contend, that Mechanics will not bear him out; for a line, drawn from N to A, will not meet the angle of abutment at right angles to it, which is required it should do by Mechanics; neither will this line be in the line in that direction will be a tangent to direction of the initial pressure, for a the arch, as the line Na. Besides the line NA intersects the curve, and is a chord to part of it above A, instead of a tangent, and consequently can no-where, within the limits of the voussoir, meet a radius of curvature at right angles. But the line Na is a tangent to the curve, and consequently in the direction of the initial pressure, and the radius of curvature VB, at the point of contact, is at right angles to it; and then (by Mechanics) this radius of curvature would be virtually the angle of abutment, which must be transferred, or supposed to be, to the pier at a, where this line intersects the vertical line I L, or face of that pier, and that intersection will be the height of the same to calculate from, as will the vertical distance from thence to the line DN, continued N m, be the measure of the vertical pressure for that purpose; and from those measures, together with the area of the semi-arch 809, the effi cacious force of the arch, to overset the pier, may be obtained by the rules given in that work.

=

Secondly, the whole resistance of the pier is there stated to be only what will arise from the multiplication of its area,

1813.]

rities in attraction, occasioned by pro tuberances and depressions on the surface of a planet, will in some cases be perceptible and appreciable: and hence it has been naturally inferred, that, where mountains are of a favourable magnitude, shape, and position, their attraction may actually be determined by experiment. Newton himself gave the first hint of such an attempt in his "System of the World," (Principia, lib. 3,) where he remarks, “that a mountain of an hemispherical figure, three miles high, and six broad, will not, by its attraction, draw the plumb-line two minutes out of the perpendicular." In truth, the effect of its attraction would not exceed 1' 18".

The first actual attempt to determine the attraction of a mountain, was made by the French academicians, who measured three degrees of the meridian near Quito, in Peru, and who found Chimboraço, a very high mountain in that vicinity, to draw the plumb-line 8" from the vertical, by its attraction. This resuit, however, fell far short of what the ory might lead us to expect; and, therefore, M. Bouquet expressed his wish that the experiment might be repeated in other places, and in more favourable

circumstances.

Nearly forty years after, namely, in the year 1772, 3, and 4, the confirmation that such an experiment properly conducted, would furnish to the theory of the universal and mutual attraction of all matter, was the subject of frequent disquisition among the fellows of the Royal Society of London, at their meetings; and it was at length determined, that an extensive experiment should be undertaken under the superintendence of a person suitably qualified, both for the purpose of ascertaining the effect of the attraction of a hill, and, if possible, of inferring from thence, the mean density of the earth. The first business was to fix upon a hill favourably situated for the purpose. Dr. Maskelyne, in a paper published in the Phil. Transactions for 1775, recommended two places which he thought would be found very convenient; the one, on the coufines of Lancashire and Yorkshire, where, within the compass of twenty miles, are four remarkable hills, Pendle-hill, Pennygant, Ingleborough, and Whernside; the other a valley, two miles broad, between the hills Helwellin and Skiddaw, in Cumberland. It was found, however, on closer examination, that neither of these locahues possessed all the advantages that

7

might be wished; and a committee was in consequence appointed, among whom were Dr. Maskelyne and Dr. Hutton, "to consider of a proper hill on which to try the experiment, and to prepare every thing necessary for carrying the design into execution." Mr. Charles Mason, (well known for his astronomical tables,) and Mr. Smeaton, were among the most active in making the inquiry; and the latter, at length, informed the committee, that, in his opinion, Mount Schehallien, one of the Grampian bills in the north of Scotland, possessed the desired properties in a very eminent degree; "being a very lofty and narrow ridge, very steep, extending a great length east and west, and very narrow from north to south.”

Mount Schehallien being thus deter mined upon, it became necessary to provide for the expense of the undertaking, and to appoint duly qualified persons to conduct it. As to the expense, it was defrayed out of a surplus remaining from the benefaction of his Majesty, that enabled Dr. Maskelyne to observe the transit of Venus in 1769; and no fitter person could be wished for to superintend the proceedings than Dr. Maskelyne himself, provided he could obtain leave of absence from the Royal Observatory, for a sufficient time to take all the nicer and more delicate observations. "This permission," says the Doctor, "his Majesty was graciously pleased to grant;" and, accordingly, the Astronomer Royal immediately prepared for the operations. He had two assistants, Mr. Reuben Burrow, who had previously been assistant astronomer at Greenwich; and Mr. William Menzies, a land-surveyor in Perthshire. These gentlemen mea. sured all the lines, angles, elevations, sections, &c. which were judged neces sary; and Dr. Maskelyne inade a tew of the nicer astronomical observations, as well as determined the deflection of the plummet from the vertical line, at convenient stations, on both sides of the hill. This business being accomplished, he returned to Greenwich, and prepared the general account of the measurements and observations, which is inserted in the Philosophical Transactions for 1775.

From this memoir, in the Transactions, we learn that the sum of the deflections on both sides, occasioned by the attraction of Schehallien, was 11.6. Dr. Maskelyne adds, "The attraction of the bill, computed in a rough manner, on supposition of its density being equal to

the mean density of the earth, and the force of attraction being inversely as the square of the distances, comes out about double this. Whence it should follow, that the density of the hill is about half the mean density of the earth. But this point cannot be properly settled till the figure and dimensions of the hill have been calculated from the survey, and thence the attraction of the hill, found from the calculation of several separate parts of it, into which it is to be divided, which will be a work of much time and labour." After this, Dr. Maskelyne presents a few general corollaries; but leaves the main difficulty to be surmounted,and the grand and much-looked for result to be presented, either by him. self or some other person, at a future

time.

The person who first effected this, then, is clearly entitled to the principal honour arising from the solution of this intricate and interesting problem. And that this honour is due to Dr. Hutton, and to him alone, is evident from his elaborage paper published in the Philosophical Transactions for 1778. Such of your readers as have not an opportunity of consalting_the_Transactions, will not be displeased to see the Doctor's own account of his labours, as given in the 38th volume of the Philosophical Magazine.

"The next consideration was, whether and how these observations and measurements could be employed, in comparison with the magnitude and effects of the whole globe of the earth, to determine its mean density, in comparison with that of the mountain. This indeed was the grand question, a point of the highest importance to natural philosophy, of novel and of the most delicate and intricate consideration, as well as a work of immense labour. Here were to be calculated, mathematically, the exact magnitude of the hill, its shape and form, in every respect, the position and situation of all its parts, the various elevations and depressions, and the attrac tion on the plummets, by every point and particle in the hill, as well as of the neighbouring mountains on every side of it. Then there was to be calculated, in like manner, the attraction of the whole magnitude and mass of the earth, on the same plummets. Lastly, the proportion of these two computed attractions was to be compared with that of the observed effects on the plummets, viz, the lateral

deviation by the hill in comparison with the perpendicular direction of gravity, which comparison of the computed and observed effects, would give the ratio of the densities, namely, of the bill and the earth.

"The magnitude and novelty of these nice calculations, the requisite portion of science and ingenuity for making them with effect, were such as appalled every mind, and every one shrank from the task; when, at the request of the President and Council of the Society, I undertook the performance; and after incessant labour, during the course of a year, produced the result of the whole, to the entire satisfaction of all the Society. The account of these calculations was published in the Philosophical Transactions for the year 1778, and in volume xiv. of my Abridgment of these Transactions; and, though in a very condensed form, occupied no less than a hundred quarto pages in that work, containing only the results of many thousands of intricate calculations."

Indeed, the ingenuity called into exercise in the course of those computations, and the labour requisite to carry them through, are greater than have been manifested by any one man, since the invention of logarithms, and the computations that were required to ensure the utility of that admirable invention.

The conclusion inferred by Dr. Hut. ton from the complete investigation, was, that the mean density of the whole mass of the earth is to that of the mountain as 9 to 5. Assuming this as the correct ratio, and at the same time assuming the mean density of the hill as agreeing with that of common stone, or being about 21, the doctor by compounding the two ratio's, obtained 44 to 1, for the ratio of the densities of the earth and of rain water; and from the whole made this deduction: "Since then the mean density of the whole earth is about double that of the general matter near the surface, and within our reach, it follows, that there must be somewhere within the earth, towards the more central parts, great quantities of metals, or such like dense matter, to counterbalance the lighter materials, and produce such a considerable mean density."-Phil. Trans. 1778. This notion, then, of the much greater density about the central regions of the earth, or indeed to nearly twothirds of the earth's diameter, was originally the suggestion of Dr. Hutton; M.

Cuvier,