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 In the preceding investigations, we have followed the method of Maclaurin for points situated in the surface of a spheroid, or within the solid. This method has always been justly admired; but neither its inventor, nor, as far as we know, any other Geometer, has applied it, excepting to spheroids of revolution; and it is here, for the first time, extended to ellipsoids. In regard to points without the surface, we have employed the method first given by Mr Ivory, in the Philosophical Transactions for 1809. The combination of these two methods has enabled us to derive the attractions of an ellipsoid on a point placed anywhere, from the attractions at the poles. Thus, this extremely complicated problem has, by geometrical reasoning of no great difficulty, been reduced to the investigation of the polar attractions, which are the only cases that require a direct computation.

34. Of the attractions of spheroids composed of elliptical shells that vary in their densities and figures according to any law.

When a spheroid is composed of concentric elliptical shells of variable density and figure, we may consider every shell as the difference of two homogeneous spheroids of the same density with the shells, and having their surfaces coinciding with the surfaces of the shell. The attractions of the spheroids being computed by the preceding methods, their difference will be equal to the attractions of the shell; and the integral obtained by summing the attractions of all the shells, will give the attractions of the heterogeneous spheroid. This case, therefore, gives rise to no new difficulties, except what are purely mathematical, and depend upon the law, according to which, the densities and figures of the shells are supposed to vary.

ATTRACTION OF MOUNTAINS. See , in the Encyclopædia, and.  ATWOOD, an Author celebrated for the accuracy of his mathematical and mechanical investigations, and considered as particularly happy in the clearness of his explanations, and the elegance of his experimental illustrations, was born in the early part of the year 1746. He was educated at Westminster school, where he was admitted in 1759. Six years afterwards he was elected off to Trinity College, Cambridge. He took his degree of Bachelor of Arts in 1769, with the rank of third wrangler, Dr Parkinson, of Christ’s College, being senior of the year. This distinction was amply sufficient to give him a claim to further advancement in his own College, on the list of which he stood foremost of his contemporaries; and, in due time, he obtained a fellowship, and was afterwards one of the tutors of the College. He became Master of Arts in 1772; and, in 1776, was elected a Fellow of the Royal Society of London.

The higher branches of the Mathematics had, at this period, been making some important advances at Cambridge, under the auspices of Dr Waring, and many of the younger members of the University became diligent labourers in this extensive field. Mr Atwood chose, for his peculiar department, the illustration of mechanical and experimental philosophy, by elementary investigations and ocular demonstrations of their fundamental truths. He delivered, for several successive years, a course of lectures in the Observatory of Trinity College, which were very generally attended, and greatly admired. In the year 1784, some circumstances occurred which made it desirable for him to discontinue his residence at Cambridge; and soon afterwards Mr Pitt, who had become acquainted with his merits by attending his lectures, bestowed on him a patent office, which required but little of his attendance, in order to have a claim on the employment of his mathematical abilities in a variety of financial calculations, to which he continued to devote a considerable portion of his time and attention throughout the remainder of his life.

The following, we believe, is a correct list of Mr Atwood’s publications:

1. A Description of Experiments to illustrate a Course of Lectures. 8vo. About 1775, or 1776.

2. This work was reprinted with additions, under the title of An Analysis of a Course of Lectures on the Principles of Natural Philosophy. 8vo. Cambr. 1784.

3. A General Theory for the Mensuration of the Angle subtended by two objects, of which one is observed by Rays after two Rejections from plane Surfaces, and the other by Rays coming directly to the Spectator’s Eye. Phil. Trans. 1781, p. 395.

4. A Treatise on the Rectilinear Motion and Rotation of Bodies, with a Description of Original Experiments relative to the Subject. 8vo. Cambr. 1784.

5. Investigations founded on the Theory of Motion, for determining the Times af Vibration of Watch Balances. Phil. Trans. 1794, p. 119.

6. The Construction and Analysts of Geometrical Propositions, determining the positions assumed by homogeneal bodies, which float freely, and at rest, on a fluid’s surface; also Determining the Stability of Ships, and of other Floating Bodies. Phil. Trans. 1796, p. 46.

7. A Disquisition on the Stability of Ships. Phil. Trans. 1798, p. 201.

8. A Review of the Statutes and Ordinances of Assize, which have been established in England from the 4th year of King John, 1202, to the 37th of his present Majesty. 4to, Lond. 1801.

9. A Dissertation on the Construction and Properties of Arches. 4to, Lond. 1801.

10. A Supplement to a Tract entitled a Treatise on the Construction and Properties of Arches, published Rh