in longitude Horary motion of Sun in longitude Horary motion of Moon in latitude

As the tract of this e

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incipally confined to Europe, er, namely nk that an accurate delineatise co Sematish of the penumbra, engraved pon a map of that quarter of the world, would not be uninteresting to many curious persons, who could then see, at one view, the progress of the greatest eclipse we shall have in these parts, for many years to THOMAS SQUIRE.

come.

Epping, Dec. 30, 1812.

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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

SIR.

I SHALL once more, with your pere mission, occupy a small portion of your valuable Magazine, with a few observations 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 physico mechanical 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. iii. Prop. x. has, as it appears to me, fallen into more than one error. For, first he lays it down as a

ture VB, at the point of contact, is at

right angles to it; and then (by Mecha

nics) 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 IL, 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,

into half its thickness, that is, GLX FE XEG. But, with the same respectful deference as before, I again contend, that the sum of this resistance is equal to GLX FEX EG+ LG X area of semiarch; for, as the weight of the whole arch and covering must act upon the inside faces of the two piers, the weight of the semi-arch must act upon the inside face of one; and, this being admitted, I shall refer to Example the second, in the same proposition, and compare results.

By the admeasurements, as there set down, the distance of the centre of gravity from D, or DN, is 33.58 feet, which answers to the tangent of 33° 15' of the curve D A nearly, and consequently the other tangent in the direc. tion of the initial pressure being the same from the point of contact at B to N, the whole quantity of the curve to be considered as an arch, is 66° 30'. But the whole curve, from the apparent angle of abutment at A to D, is 77° 20′, and 77° 20′ — 66° 30′ 10° 50′, a portion of the curve, which cannot be properly considered as part of the arch, in determining the thickness of the piers.

809,

It will be found by calculation, that the distance between the apparent and virtual angle of abutment, will be equal to 2.24 feet; therefore the height of the pier to calculate from, will be 18+2.24 20 24, and N M 40—2′24—37.76, Nm. MA 16'42, and area = remaining the same. Then, from those data, and the whole height of the pier 64, its thickness may be deduced, and it will be found to be 6912 feet, little more than half the thickness of Dr. Hutton's pier, which is 13.67 feet. Notwithstanding, the efficacious force of the arch is greater by our method than by 809 × 16:42 his: for by our's it is 37.76 20.24 7120 432, and by his 809X 16.42

40

-X 18-5976.

X

Such opposite differences in cause and effect almost staggers belief, and, upon merely a superficial view of the subject, Teluses its assent, to what I conceive to have been made sufficiently clear; and those doubts will be further strengthened when we recollect that the second edition of Dr. Hutton's work was published after a lapse of twenty-nine years, from the publication of the first; and at a time when the Commons of the United Kingdom had applied to him for his opinion upon the subject. This, together with

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his well-known abilities as a mathema tician, would have induced me also to think I was wrong, were I not convinced, both by theory and practice, that I am right. But we are now both before a discerning public, and it is for them to decide.

Here, Mr. Editor, I shall close this subject, and likewise our correspondence, for the present, as I know of nothing more that appears to me very reprehen sible, or likely to mislead my brother bridge-builders in their pursuit to attain knowledge in their profession. But, if time and other circumstances will permit, I intend in another shape to furnish them with every information I am capable of affording them, both in theory and practice. And now, with thanks for the indulgence I have received from you, I conclude.

JAMES PARRY, Bridge-builder. Bridgewater, Dec. 24, 1812.

To the

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asdf the Monthly Magazine.

too much gratified with the al is 5' 1 ng account of the Honour9° 1' 18 Cavendish, in your Num be in latituer last, to be inclined to few 16647". ith it; but there is one stnesient at chat memoir which is cal culated to make a wrong impression, and which a desire to do justice to my excellent friend, Dr. Hutton, induces me to correct. The assertion to which I advert is, that, at the top of column 2, page 421, where the deterinination of the mean density of the earth is ascribed to Dr. Maskelyne, and no mention whatever is made of Dr. Hutton, though he was undoubtedly the first person who ascer tained that point. Had Dr. Maskelyne been living, I am persuaded that distinguished astronomer, and truly atniable man, would not have suffered so mistaken an assertion to pass without correction: but, as he has passed to other regions, and higher employments, and as Dr. Hutton is, I believe, too much engaged in other concerns at present to enforce his own claims, perhaps you will indulge me with the insertion of the following hasty sketch of the leading proceedings relative to the matter in question.

If the attraction of gravity be exerted, as Newton supposed, not only between the large bodies in the universe, but between the minutest particles, of which those bodies are constituted, it becomes exceedingly probable that the irregula

rities in attraction, occasioned by protuberances 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 bemispherical 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 Chim boraço, a very high mountare in that viciuity, to draw the plumb-le 8" from the vertical, by its attractiontra This result, however, fell far short fewhat the ory might lead us to expect Said, therefore, M. Bouquet expreseonstie wish that the experiment might hree kinated in other places, and in mourable

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 ascertaming 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 confines 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 localines possessed all the advantages that

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 bilis 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 pro vide 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 superin tend the proceedings than Dr. Maske lyne himself, provided he could obtain leave of absence from the Royal Obser vatory, 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 Astrono mer 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 measured all the lines, angles, elevations, sections, &c. which were judged necessary; and Dr. Maskelyne made a few 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 hill, 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 Jabour." 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 himself 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 elaborate paper published in the Philosophical Transactions for 1778. Such of your readers as have not an opportunity of consulting the Transactions, will not be displeased to see the Doctor's own account of his labours, as given in the 88th volume of the Philosophical Magazine.

66 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 deter mine 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 clevations and depressions, and the attraction 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

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ingenuity called into exercise urse of those computations al is 51 bour requisite to carry ther rough, 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 24, 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 ori ginally the suggestion of Dr. Hutton; M.

Cuvier, and many other persons, err in ascribing it to Dr. Maskelyne or to Mr. Cavendish.

I cannot conclude without remarking that, though Dr. Hutton had no reason to doubt the accuracy of his computations, he expressed in the paper, from which I have last quoted, some doubts as to the correctness of the assumption of the density of the hill, and pointed out methods by which that assumption might be corrected. He went farther. Feeling constantly a desire to give the finishing and correcting stroke to these computations, I very well remember hearing him, about nine or ten years ago, urge the learned Mr. Professor Playfair, of Edinburgh, either to make, or to pro. cure and communicate to him, such more accurate observations upon the geological structure of the hill, as would enable him to give the utmost precision to his results, of which they were suscepible. From the information transmitted by Mr. Playfair, the doctor infe.ed that the mean specific gravity of Schehallien is about 2.7 or 2.8, its constituent varieties being reduced to three kinds, the specific gravity of one being 24, of ano ther about 2.75, and some parts as high as 3, and even 3.2. Thus, then, taking 2.75 as the mean, he obtains X 2 2

8. or almost 5, for the mean density of the whole mass of the earth; a result which was first given, I believe, by the doctor himself in part 55 of the New Abridgment of the Philosophical Transactions, published in 1808, and repeated in the re-publication of the whole paper, in the second volume of his 8vo. Tracts.

Professor Playfair has recently gone over all the computations necessary to determine this point, de novo, making use of his own observations as to the mineralogical constitution of the bill; and his results confirm, in a remarkable manner (see Phil. Transac. for 1811) the accuracy of the calculations and deductions made by Dr. Hutton.

I have dwelt longer upon this subject than might otherwise have been neces sary, in order that here, as well as upon other topics, "Honour should be given where honour is due." One of the strongest incitements to men of science is, "the quiet and peaceable possession" of the fame accruing from their inventions and discoveries; and one of the greatest mortifications to which a man of virtue and ingenuity can be subjected, must be to see the result of his learning, MONTHLY MAG. No. 237.

his science, his labours, and investigations, ascribed, however unintentionally, to another.

OLINTHUS GREGORY. Royal Military Academy, Woolwich, Dec. 14, 1812.

To the Editor of the Monthly Magazine.

SIR,

as often afforded to an author assail ed by some bandit of literature, a small space for defence and triumph, to ask the like favour for one, who knows not (exclusive of the advantageous respecta bility, independence, and great circulation, of the Monthly Magazine) where else to apply. I will strictly confine my self to this wretch's discomfiture, and my charge shall be single, clear, and con cise-that, the British Critic's Review (in February 1812, which by chance I heard of) of JOSEPH, a religious Poem, is FALSE.

AM induced, by that liberality which

The work is of considerable extent, and aims to embrace the whole of the Jewish dispensation; the Preface clearly defines the plan; yet the Reviewer, (what an incongruous name, and yet it is the only one he ever dare own,) after a few desultory remarks, quotes part of a short speech, so as to destroy both sense and grammar, and then cries, "Here certainly is no rival to Moses."

Rival to Moses! I suppose then be reckons Milton a successful rival-and Louth likewise of Isaiah-and Klopstock and Cumberland victorious over Matthew, Mark, Luke, and John!

But, in my case, sir, it happens that his quotation is not even the paraphrase of a Mosean passage: it is Joseph's supposed introductory account of himself to Potiphar. Was the critic only ignorant that there is no such scene in the Bible? I know not: the false view of the work, which he immediately adds, cannot so easily be excused.

Afterwards (con

tinues this critic) we find him writing what Moses, without a very extraordi nary gift of prophecy, could not have written; and, it may reasonably be doubted, whether he would if he could." He then quotes three lines, chiefly names of modern missionaries. Now, sir, I beg leave to ask, does not this critique (without further troubling you or your readers) draw the direct inference that I speak in the name of Moses, or of some person of that period, or that I have made a prophetical attempt, or, at least, been guilty of an anachronism? It is

neither