Astronomical observations being made at various places on the surfacc Li' the earth, it was altogether impossible to reduce thern to any common point of reference, such as the centre of the terrestrial spheroid, without a know ledge of tile true form and magnitude of the earth. The exact determination of the moon's place, an element of great importance in the calculation of the longitude, was, more especially, deeply involved in these measurements ; and even the allowance to be made for elevation above the surface of the ocean, in observing the altitudes of ce lestial objects, could not be duly estimated, before the de flection of the terrestrial arch below its tangent had been correctly ascertained.
The earlier navigators seldom had recourse to astro nomical observations for the correction of their reckon ing, unless such as were of the simplest nature. The instruments they employed were too rude in their con struction to be applied to any thing beyond finding the elevation of the polar star, or the mei idian altitude of the sun ; the only observations they required for.a gross approximation to the ship's latitude. The Astrolabe, or Astronomical Ring-, which was nothing but an arch gra duated into degrees and half-degrees, and suspended at a particular part in the circumference, seems to have been onc of the first instruments used, in the infancy of navi gation, for taking the sun's altitude ; and to this was af terwards added the Cross staff; or Arbalete, which was considered better adapted for the measurement of celes tial arches in general. The Astrolabe was recommended for taking observations at sca so early as 1485 ; the Ar balete was introduced at a later period, and is particularly described by John Werner, -of Nuremburgh, as a fit in strument to find the distance of the moon from a fixed star, for the purpose of determining the longitude. The truth is, however, that both these instruments were ex ceedingly imperfect ; neither of them possessing any thing in its construction which adapted it, in the slightest degree, to the peculiar circumstances in which observa tions are usually made at sea. About the year 1600, the Arbalete received a considerable improvement from the celebrated Davis, one of the most enterprising seamen of his day, who gave to the instrument under its new form the appellation of thc Back-staff, on account of the position in which the observer stood with respect to the sun, at the time of making an observation. This instru ment, which is commonly known by the name of Davia's Quadrant, was afterwards still farther improved by Elam stead and Halley, and continued to be almost the only in strument used for taking the altitudes of the celestial bodies at sea until the year 1731, when it was entirely superseded by Hadley's Quadrant, one of the most ad mirable inventions of the last t.entury. By this happy contrivance, which seems to have been first suggested by Newton, celestial observations can be made at sea, nearly with the samc facility as on land, the observer D being but little incommoded by the agitation to which he is exposed from the motion of the vessel. The disco very ol the principle on which Hadley's quadrant is con structed has been ascribed, by some miters, to Thomas Godfrey, of Philadelphia, who contrived a similar instru ment about the year 1731 ; but, if Hadley is to be de prived of the honour of having invented the valuable in strument which bears his name, Godfrey's claims must yield to those of Newton, who proposed an instrument for measuring angles by two rellexions sn early as 1699.
Even before this period, thc ingenious Dr. Hooke seems to have had an idea of an instrument for measuring an gular distances by rellexion, as we find stated in the His tory of the Royal Society, by Sprat and I3irch.
The introduction of Hadley's quadrant may be re garded as forming a most important era in the history of astronomical navigation; that valuable instrument being no less indispensably necessary in this department of the nautical art, than the mariner's compass is to the me tliods of determining a ship's place by her course and distance. At the time when this instrument came into general use, the tables of the sun and moon had been brought to a considerable degree of peifection by the joint labours of the most eminent astronomers in Europe; a circumstance which gave an additional value to the in vention, by furnishing the mariner at the same time with data suited to the perfection of his instrument. The theory of universal gravitation had been confirmed by the nnost delicate observations ; and nothing seemed want ing to render it applicable to the purposes of navigation, but a more complete development of the effects of the simple law, which Newton demonstrated to be the grand 'tiling principle in the whole of the celestial motions. The labours of Flamstead and Halley contributed in no small degree to this end ; but it is to the profound re searches of D'Alembert and Clairaut, of Euler and La place, that thc extreme accuracy of the present lunar tables is chiefly to be ascribed. Guided by the theory of Euler, the celebrated Tobias Mayer made a vast number of observations on the lunar motions, from which Ile drew up, with singular address, a set of tables that were found to correspond much better with the various irregulari ties of the moon's mo:ion, than the deductions of the rnost distinguished analysts, who, following out a loftier and more independent mode of inquiry, had admitted nothing into their investigations except the simple law of universal attraction. Such, indeed, was the accuracy of these tables, that the British government, in 1763, or dered a recompense of 3000/. to be paid to the widow of Mayer, in consideration ol the benefits which navigation had derived rrom the labours of her husband. Several important improvements were afterwards added to them by Dr. Maskelyne and Mr. Mason; and in their present form, as they were published by the Board of Longitude in 1770, they seldom give the moon's place 30" from the truth, whereas the tables of Dr. Halley, which were in use before that period, sometimes gave an error of 7' or 8'. From the year 1789 to the year 1804, they were em ployed, with the new equations of the British astrono mers, in the calculation of the tables of the moon's place, as laid down in the Nautical Almanack; but sub sequently the more correct tables of Burg, and, more lately still, those of Burckhardt, have been adopted in drawing up that useful work.