the reading secretaryship. And how well Mr. H. discharged the duties of that office may well be. judged by the many excellent translations of foreign communications from the Latin, French, and Italian, languages, printed in the Transactions, in the several following years, till 1784.

In the Transactions of the same year appeared "An Account of the Calculations made from the Survey and Measures taken at Schehallien, in order to ascertain the mean Density of the Earth." The determination of the mean density of the earth was an important problem instituted by the Society; and the survey and measurements, for that purpose, were taken at and about the hill Schehallien, in Perthshire, in the years 1774, 1775, 1776, by the direction, and partly under the inspection, of Dr. MASKELYNE, the Astronomer Royal: after which, the Society confided to Mr. H. the important office of making the calculations, and drawing the proper deductions from them. This was a very laborious work, requiring many thousand calculations, which were completed in the space of one year. It was also of great importance in itself, as affording one of the best proofs of the general attraction of matter; and, besides great accuracy in the calculation, it was necessary the operator should possess no ordinary portion of genius and address to manage so very delicate a business, being in a manner of a quite novel nature. And perhaps the Society could hardly have discovered another person possessing the requisite qualifications in so

eminent

eminent a degree. Indeed the conclusion of this work fully justified the Society's choice, the operation doing equal honour to the Society and to the computor. In the result, Mr. H. found that the mean density of the earth was in proportion to that of the hill Schehallien, as 9 is to 5; so that, whenever the actual density of the hill shall be ascertained, (which it seems consists of a solid mass of the hardest stone,) from thence the real density of the earth, in respect of stone, or of water, will also easily follow.

The year following was given another paper, by Dr. Hutton, intended as a supplement to the foregoing one, containing "Calculations to determine at what Point in the Side of a Hill its Attraction will be the greatest ;" a desideratum very useful in such a problem, as the deviation of the plumb-line, by the attraction of the hill, is but small in any

case.

The next communication, which was in the year 1780, was a very long tract on cubic equations and infinite series; in which the subject of those equations seems to be exhausted.

The next, in the year 1783, was a " Project for a new Division of the Quadrant." This is a project for adopting or calculating new tables of sines, tangents, and secants, to equal parts of the radius, instead of to those of the quadrant; in which way, the numbers in the column of arcs will denote the real lengths of the arcs, instead of the arbitrary division of 60ths, or degrees and minutes.

This was the last of Dr. H.'s communications to the Society; as it seems a stop was put to his usefulness in that way, by what was deemed a cruel act of oppression in the new president, which it seemed grew out of the following circumstan

ces.

The adjudication of the prize-medal to Dr. H.'s paper, before-mentioned, on the force of fired gunpowder, had necessarily produced a considerable intercourse between him and the president, Sir John Pringle, while this learned veteran was drawing up the curious paper containing the speech he was to pronounce on delivering the medal to Dr. H. an intercourse which produced a mutual friendship and confidence, which ended only with the death of Sir John. This circumstance, with that of his not paying sufficient court and attendance on the new president, (a practice at all times hostile to Dr. H.'s natural disposition,) it was alleged, by his friends, produced a jealousy and dislike against him, and at length a determination of removing Dr. H. from his office of foreign secretary. For this purpose, it seems, the president procured a resolution of council, "that it was expedient for the foreign secretary to reside constantly in London.” Dr. H. conceiving himself to have been affronted by this resolution of the council, went to the Society, and resigned his place, in a speech, which, though couched in modest words, and apparently conveying no more than an ordinary resignation, strongly spoke the language of injured merit.

In consequence of these and other alleged circumstances of malversation in his office, the conduct of the president was loudly arraigned by Dr. HORSLEY, and other friends of Dr. HUTTON, in some violent debates; which at length concluded with the resignation of the secretaryship by Mr. Maty, and the secession of a number of the learned members. These proceedings took place in 1784; and accounts of them were given in several pamphlets published at the same time.

Soon after this, viz. in 1786, Dr. H. published a volume of mathematical and philosophical tracts," in 4to, containing a number of curious papers, which would probably have appeared in the volumes of the Philosophical Transactions had notthe foregoing proceedings taken place in the Society. Among these tracts, which are all of them' curious and original, is a long one, of near 200 pages, of great importance to the public utility of the nation. It consists of "New Experiments in Artillery; for determining the Force of fired Gunpowder; the Initial Velocity of Cannon-Balls; the Ranges of Pieces of Cannon at different Elevations; the Resistance of the Air to Projectiles; the Effect of different Lengths of Cannon; and of different Quantities of Powder, &c. &c." These valuable experiments were the result of the employment of the years 1783, 1784, 1785; and the account of them is accompanied with calculations, and followed by deductions of the highest concernBeside

ment.

I 4

Beside these works, the active and patient mind of Dr. H. has produced several other useful and ingenious publications. As, first, in 1781, in a folio volume, "Tables of the Products and Powers of Numbers published by Order of the Commissioners of Longitude." A very curious work, of immense labour and calculation, which, it has been said, was chiefly owing to the industry of his present or second wife, a lady of extraordinary learning, talents, and goodness, who it seems has also assisted him on some other occasions of laborious calculations.

Secondly, in 1785, "Mathematical Tables; containing the common, hyperbolic, and logistic, Logarithms; also Sines, Tangents, Secants, and Versed Sines, both natural and logarithmic; with several other Tables useful in mathematical Calculations to which is prefixed, a large and original History of the Discoveries and Writings relating to those Subjects." A history, which it must have cost many years painful toil in reading different books, and collecting the materials for it, and to describe in detail their contents, the inventions, and improvements, contained in such a number of scarce and curious books, in all languages. A second edition was printed in 1794,

In 1786, "The compendious Measurer; being a brief, yet comprehensive, Treatise on Mensuration and practical Geometry; with an Introduction to decimal and duodecimal Arithmetic; adapted to Practice and the Use of Schools." This is chiefly

an