SHARP (Abraham)

, an eminent mathematician, mechanist, and astronomer, was descended from an ancient family at Little-Horton, near Bradford, in the West Riding of Yorkshire, where he was born about the year 1651. At a proper age he was put apprentice to a merchant at Manchester; but his genius led him so strongly to the study of mathematics, both theoretical and practical, that he soon became uneasy in that situation of life. By the mutual consent therefore of his master and himself, though not altogether with that of his father, he quitted the business of a merchant. Upon this he removed to Liverpool, where he | gave himself up wholly to the study of mathematics, astronomy, &c; and where, for a subsistance, be opened a school, and taught writing and accounts, &c.

He had not been long at Liverpool when he accidentally fell in company with a merchant or tradesman vifiting that town from London, in whose house it seems the astronomer Mr. Flamsteed then lodged. With the view therefore of becoming acquainted with this eminent man, Mr. Sharp engaged himself with the merchant as a book-keeper. In consequence he soon contracted an intimate acquaintance and friendship with Mr. Flamsteed, by whose interest and recommendation he obtained a more prositable employment in the dockyard at Chatham; where he continued till his friend and patron, knowing his great merit in astronomy and mechanics, called him to his assistance, in contriving, adapting, and fitting up the astronomical apparatus in the Royal Observatory at Greenwich, which had been lately built, namely about the year 1676; Mr. Flamsteed being then 30 years of age, and Mr. Sharp 25.

In this situation he continued to assist Mr. Flamsteed in making observations (with the mural arch, of 80 inches radius, and 140 degrees on the limb, contrived and graduated by Mr. Sharp) on the meridional zenith distances of the fixed stars, sun, moon, and planets, with the times of their transits over the meridian; also the diameters of the sun and moon, and their eclipses, with those of Jupiter's satellites, the variation of the compass, &c. He assisted him also in making a catalogue of near 3000 fixed stars, as to their longitudes and magnitudes, their right ascensions and polar distances, with the variations of the same while they change their longitude by one degree.

But from the fatigue of continually observing the stars at night, in a cold thin air, joined to a weakly constitution, he was reduced to a bad state of health; for the recovery of which he desired leave to retire to his house at Horton; where, as soon as he found himself on the recovery, he began to fit up an observatory of his own; having first made an elegant and curious engine for turning all kinds of work in wood or brass, with a maundril for turning irregular figures, as ovals, roses, wreathed pillars, &c. Beside these, he made himself most of the tools used by joiners, clockmakers, opticians, mathematical instrument-makers, &c. The limbs or arcs of his large equatorial instrument, sextant, quadrant, &c, he graduated with the nicest accuracy, by diagonal divisions into degrees and minutes. The telescopes he made use of were all of his own making, and the lenses ground, figured, and adjusted with his own hands.

It was at this time that he assisted Mr. Flamsteed in calculating most of the tables in the second volume of his Historia Cœlestis, as appears by their letters, to be seen in the hands of Mr. Sharp's friends at Horton. Likewise the curious drawings of the charts of all the constellations visible in our hemisphere, with the still more excellent drawings of the planispheres both of the northern and southern constellations. And though these drawings of the constellations were sent to be engraved at Amsterdam by a masterly hand, yet the originals far exceeded the engravings in point of beauty and elegance: these were published by Mr. Flamsteed, and both copies may be seen at Horton.

The mathematician meets with something extraordinary in Sharp's elaborate treatise of Geometry Improved (in 4 to 1717, signed A. S. Philomath.), 1st, by a large and accurate table of segments of circles, its construction and various uses in the solution of several difficult problems, with compendious tables for finding a true proportional part; and their use in these or any other tables exemplified in making logarithms, or their natural numbers, to 60 places of figures; there being a table of them for all primes to 1100, true to 61 figures. 2d, His concise treatise of Polyedra, or solid bodies of many bases, both the regular ones and others: to which are added twelve new ones, with various methods of forming them, and their exact dimensions in surds, or species, and in numbers: illustrated with a variety of copperplates, neatly engraved by his own hands. Also the models of these polyedra he cut out in box wood with amazing neatness and accuracy. Indeed few or none of the mathematical instrument-makers could exceed him in exactly graduating or neatly engraving any mathematical or astronomical instrument, as may be seen in the equatorial instrument above mentioned, or in his sextant, quadrants and dials of various sorts; also in a curious armillary sphere, which, beside the common properties, has moveable circles &c, for exhibiting and resolving all spherical triangles; also his double sector, with many other instruments, all contrived, graduated and finished, in a most elegant manner, by himself. In short, he possessed at once a remarkably clear head for contriving, and an extraordinary hand for executing, any thing, not only in mechanics, but likewise in drawing, writing, and making the most exact and beautiful schemes or figures in all his calculations and geometrical constructions.

The quadrature of the circle was undertaken by him for his own private amusement in the year 1699, deduced from two different series, by which the truth of it was proved to 72 places of figures; as may be seen in the introduction to Sherwin's tables of logarithms; that is, if the diameter of a circle be 1, the circumference will be found equal to 3.1415926535897932 38462643383279502884197169399375105820974944 592307816405, &c. In the same book of Sherwin's may also be seen his ingenious improvements on the making of logarithms, and the constructing of the natural sines, tangents, and secants.

He also calculated the natural and logarithmic sines, tangents, and secants, to every second in the first minute of the quadrant: the laborious investigation of which may probably be seen in the archives of the Royal Society, as they were presented to Mr. Patrick Murdoch for that purpose; exhibiting his very neat and accurate manner of writing and arranging his figures, not to be equalled perhaps by the best penman now living.

The late ingenious Mr. Smeaton says (Philos. Trans. an. 1786, pa. 5, &c):

“In the year 1689, Mr. Flamsteed completed his mural arc at Greenwich; and, in the Prolegomena to his Historia Cœlestis, he makes an ample acknowledgment of the particular assistance, care, and industry of Mr. Abraham Sharp; whom, in the month of August 1688, he brought into the observatory, as his amanuensis and being as Mr. Flamsteed tells us, not | only a very skilful mathematician, but exceedingly expert in mechanical operations, he was principally employed in the construction of the mural arc; which in the compass of 14 months he finished, so greatly to the satisfaction of Mr. Flamsteed, that he speaks of him in the highest terms of praise.

“This celebrated instrument, of which he also gives the figure at the end of the Prolegomena, was of the radius of 6 feet 7 1/2 inches; and, in like manner as the sextant, was furnished both with screw and diagonal divisions, all performed by the accurate hand of Mr. Sharp. But yet, whoever compares the different parts of the table for conversion of the revolutions and parts of the screw belonging to the mural arc into degrees, minutes, and seconds, with each other, at the same distance from the zenith on different sides; and with their halves, quarters, &c, will find as notable a disagreement of the screw-work from the hand divisions, as had appeared before in the work of Mr. Tompion: and hence we may conclude, that the method of Dr. Hook, being executed by two such masterly hands as Tompion and Sharp, and found defective, is in reality not to be depended upon in nice matters.

“From the account of Mr. Flamsteed it appears also, that Mr. Sharp obtained the zenith point of the instrument, or line of collimation, by observation of the zenith stars, with the face of the instrument on the east and on the west side of the wall: and that having made the index stronger (to prevent flexure) than that of the sextant, and thereby heavier, he contrived, by means of pulleys and balancing weights, to relieve the hand that was to move it from a great part of its gravity. Mr. Sharp continued in strict correspondence with Mr. Flamsteed as long as he lived, as appeared by letters of Mr. Flamsteed's found after Mr. Sharp's death; many of which I have seen.

“I have been the more particular relating to Mr. Sharp, in the business of constructing this mural arc; not only because we may suppose it the first good and valid instrument of the kind, but because I look upon Mr. Sharp to have been the first person that cut accurate and delicate divisions upon astronomical instruments; of which, independent of Mr. Flamsteed's testimony, there still remain considerable proofs: for, after leaving Mr. Flamsteed, and quitting the department above-mentioned, he retired into Yorkshire, to the village of Little Horton, near Bradford, where he ended his days about the year 1743 (should be, in 1742); and where I have seen not only a large and very fine collection of mechanical tools, the principal ones being made with his own hands, but also a great variety of scales and instruments made with them, both in wood and brass, the divisions of which were so exquisite, as would not discredit the first artists of the present times: and I believe there is now remaining a quadrant, of 4 or 5 feet radius, framed of wood, but the limb covered with abrass plate; the subdivisions being done by diagonals, the lines of which are as finely cut as those upon the quadrants at Greenwich. The delicacy of Mr. Sharp's hand will indeed permanently appear from the copper-plates in a quarto book, published in the year 1718, intituled Geometry Improved by A. Sharp, Philomath.” (or rather 1717, by A. S. Philomath.) “whereof not only the geometrical lines upon the plates, but the whole of the engraving of letters and figures, were done by himself, as I was told by a person in the mathematical line, who very frequently attended Mr. Sharp in the latter part of his life. I therefore look upon Mr. Sharp as the first person that brought the affair of hand division to any degree of perfection.”

Mr. Sharp kept up a correspondence by letters with most of the eminent mathematicians and astronomers of his time, as Mr. Flamsteed, Sir Isaac Newton, Dr. Halley, Dr. Wallis, Mr. Hodgson, Mr. Sherwin, &c, the answers to which letters are all written upon the backs, or empty spaces, of the letters he received, in a short-hand of his own contrivance. From a great variety of letters (of which a large chest full remain with his friends) from these and many other celebrated mathematicians, it is evident that Mr. Sharp spared neither pains nor time to promote real science. Indeed, being one of the most accurate and indefatigable computers that ever existed, he was for many years the common resource for Mr. Flamsteed, Sir Jonas Moore, Dr. Halley, and others, in all sorts of troublesome and delicate calculations.

Mr. Sharp continued all his life a bachelor, and spent his time as recluse as a hermit. He was of a middle stature, but very thin, being of a weakly constitution; he was remarkably feeble the last three or four years before he died, which was on the 18th of July 1742, in the 91st year of his age.

In his retirement at Little Horton, he employed four or five rooms or apartments in his house for different purposes, into which none of his family could possibly enter at any time without his permission. He was seldom visited by any persons, except two gentlemen of Bradford, the one a mathematician, and the other an ingenious apothecary: these were admitted, when he chose to be seen by them, by the signal of rubbing a stone against a certain part of the outside wall of the house. He duly attended the dissenting chapel at Bradford, of which he was a member, every Sunday; at which time he took care to be provided with plenty of halfpence, which he very charitably suffered to be taken singly out of his hand, held behind him during his walk to the chapel, by a number of poor people who followed him, without his ever looking back, or asking a single question.

Mr. Sharp was very irregular as to his meals, and remarkably sparing in his diet, which he frequently took in the following manner. A little square hole, something like a window, made a communication between the room where he was usually employed in calculations, and another chamber or room in the house where a servant could enter; and before this hole he had contrived a sliding board: the servant always placed his victuals in this hole, without speaking or making any the least noise; and when he had a little leisure he visited his cupboard to see what it afforded to satisfy his hunger or thirst. But it often happened, that the breakfast, dinner, and supper have remained untouched by him, when the servant has gone to remove what was left—so deeply engaged had he been in calculations.—Cavities might easily be perceived in an old English oak table where he sat to write, by the frequent rubbing and wearing of his elbows.—Gutta cavat lapidem, &c. |

By Mr. Sharp's epitaph it appears that he was related to archbishop Sharp. And Mr. Sharp the eminent surgeon, who it seems has lately retired from business, is the nephew of our author. Another nephew was the father of Mr. Ramsden, the present celebrated instrument maker, who says that his grand uncle Abraham, our author, was some time in his younger days an exciseman; which occupation he quitted on coming to a patrimonial estate of about 200l. a year.

, in Music, a kind of artificial note, or character, thus formed : this being presixed to any note, shews that it is to be sung or played a semitone or half note higher than the natural note is. When a Sharp is placed at the beginning of a stave or movement, it shews that all notes that are found on the same line, or space, throughout, are to be raised half a tone above their natural pitch, unless a natural intervene. When a Sharp occurs accidentally, it only affects as many notes as follow it on the same line or space, without a natural, in the compass of a bar.