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HISTORY OP PHYSICAL ASTRONOMY.

had been made by a native of the British Isles since the days of Mac-laurin. The memoir which contains its original announcement deservesalso to he mentioned, on account of the intimate acquaintance which theauthor of it exhibits with methods of analytical investigation, the use ofwhich had been hitherto confined exclusively to the mathematicians of thecontinent. Mr. Ivory soon afterwards gave another striking proof of histalents by a critical examination of Laplace’s researches relative to theattraction of spheroids of small eccentricity. Having pointed out what heconceived to be certain defects in Laplace’s reasoning, he expounded thepeculiar calculus of that great geometer by a method of his ow r n, remarkablefor its clearness and elegance. The objections urged against Laplace’sdemonstration are now admitted to have originated mainly in a miscon-ception of the author’s meaning; but the memoir of Mr. Ivory has beenuniversally admired as a fine exhibition of analytical skill *. The importantsubject, of the attraction of spheroids has more recently engaged the atten-tion of Plana, Gauss, Poisson , Airy, and other eminent geometers, but nostriking results have been elicited by their researches.

Before proceeding to notice the applications which have been made ofClairaut’s theorem to the determination of the Earth ’s ellipticity, it maynot perhaps he uninteresting to give a brief account of the geodeticoperations which have been carried on in recent times with the view ofattaining the same object by the actual measurement of arcs on theEarth ’s surface.

An arc of the meridian has been measured in the present century byGauss, extending from Gottingen to Altona, and embracing an amplitudeof 2° 0' 57". The latitudes at the two extremities of the arc were deter-mined by means of Ramsden’s famous zenith sector. An arc of stillgreater extent has been measured in Russia by M. Struve. Its northernextremity is situated in Hochland, an island in the Gulf of Finland ; andfrom this point to Jacobstadt , its southern extremity, it embraces anamplitude of 8° 35' 5". One of the peculiarities connected with themeasurement of this arc consisted in the determination of the latitudesby means of the transits of stars across the prime verticalf. Wemay remark that this mode of observation is extensively practised by theGerman astronomers of the present day, for the purpose of ascertainingthe declinations of the stars. The operations of M. Struve were subse-quently connected with those of Von Tenner in the south of the Russianempire, and the whole arc now extends to 8° 2' 28"-91. The geodeticoperations by means of which Bessel j connected the arc of M. Struve, inRussia, with the extensive triangulations of the west and south of Europe ,exhibited in a remarkable degree the power of that illustrious astronomerto sytematize and perfect every subject which bore any relation to hisfavourite science. It may be remarked that in all geodetic operationsmore angles are generally observed, than those which the principles ofgeometry render indispensably necessary to be known for the purposes ofcomputation. This circumstance will manifestly give rise to a number ofrelations between the observed angles, which would be rigorously satisfiedby the latter if they were mathematically accurate. This condition, how-

* Phil. Trans., 1812-22.

t Born at Minden 1784; died at Kdnigsberg 1846. He is generally allowed to bethe greatest astronomer which the present century has hitherto produced.

| The latitudes were also found with the zenith sector, and a mean of both results wasin each case taken for the final determination.