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Academy accords accuracy admit adopted affirms Annals anomaly appears Arbury Hill assumed astronomical attraction azimuths Baron calculation cause character circumstances Clifton compared compression computation conclusion conducted confirmation consider correct corresponding deduced degree Delambre determining deviation distance Don Rodriguez doubt Dunnose earth effect elements employed England English equal equator error estimate examination expressed extent extremity fact figure formed former France French give given Greenwich Gregory hypothesis inference irregularities Italy latitude least length less Major mathematicians matter means measurement ment meridian method Mudge naturally nearly never object oblateness observations occasion operations opinion perfect Philosophical Transactions position present probable prove published question readers reason reduced remarks respect Royal Society says seconds seen sides spheroid stars station supposed surface taken Thomson tion toises triangles volumes whole

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Página 48 - Society answerable, for the certainty of the facts, or propriety of the reasonings, contained in the several Papers so published, - which must still rest on the credit or judgment of their respective Authors.

Página 39 - Cavendish has since considered this matter more minutely, and having mathematically investigated several rules for finding the attraction of the inequalities of the Earth, has, upon probable suppositions of the distance and height of the Allegany mountains from the degree measured, and the depth and declivity of the Atlantic ocean, computed what alteration might be produced in the length of the degree, from the attraction of the said hills, and the defect of attraction of the Atlantic; and finds...

Página 8 - U u reduces all angles to the plane of the horizon, and with such a degree of correctness, that the error in the sum of the three angles of any triangle is scarcely, in any instance, found to exceed three seconds of a degree, and in general not more than a small fraction of a second. Accordingly the geodetical observations were conducted with a degree of exactness, which hardly can be exceeded ; and even if we suppose for a moment, that the chains made use of in the measurement of the bases may not...

Página 39 - ... by these causes. He has also found, by similar calculations, that the degrees measured in Italy, and at the Cape of Good Hope, may be very sensibly affected by the attraction of hills, and defect of the attraction in the Mediterranean Sea and Indian Ocean.

Página 63 - To •which are added some farther observations on the rectification of the hyperbola : among which the great advantage of descending series over ascending series in many cases is clearly shown; and several methods are given for computing the constant quantity by which those series differ from each other. By the Rev. John Hellins, BDFRS, and Vicar of Potter's Pury in Northamptonshire.

Página 4 - ... which we do not know the relation to our own, in fact give us very little assistance in learning either the figure or dimensions of our globe. It was not till the revival of science in Europe that the two great philosophers, HUYGHENS and NEWTON, first engaged in the consideration of this question, and reduced to the known laws of mechanics, the principles on which the figure of the earth should be determined. They demonstrated that the rotatory motion should occasion differences in the force...

Página 7 - These new measures were found to confirm, in a remarkable manner, the general results of those which had preceded, and gave very nearly the same proportion for the eccentricity and other dimensions of the globe, so that there would not have remained the smallest doubt respecting the figure of the earth being flattened at the poles, had there not been a fourth measurement performed in England at the same time as that undertaken in Lapland, the results of which were entirely the reverse. This measurement,...

Página 8 - ... 54 60884, The singularity of these results excites a suspicion of some incorrectness in the observations themselves, or in the method of calculating from them. The author has not informed us in his Memoir, what were the formulae which he employed in the computations of the meridian ; but one sees, by the arrangement of his materials, that he made use of the method of the perpendiculars without regard to the convergence of the meridians ; and although this method is not rigorously exact, it can...

Página 9 - ... arrangement of his materials, that he made use of the method of the perpendiculars without regard to the convergence of the meridians ; and although this method is not rigorously exact, it can make but a very few fathoms more in the total arc, and will have very little effect on the magnitude of each degree. It is therefore a more probable supposition, that, if any errors exist, they have occurred in the astronomical observations. But it is scarcely possible to determine the amount of the errors,...

Página 35 - Nevertheless, the results deduced by the author, from this measure alone, would lead to the supposition that the earth, instead of being flattened at the poles, is in fact more elevated at that part than at the equator, or at least, that its surface is not that of a regular solid.