Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/268

Rh 256 NAVIGATION series ; but more than sufficient has been quoted for the purposes of navigation. At the end he adds that the same may be obtained in like manner by taking the versed sines in arithmetical pro portion. The next writer who made his mark upon this problem was Dr E. Halley (Phil. Trans., No. 219, 1695). He states that the tangential proportion between the latitude and the divisions of the meridional line was discovered by chance, and first published by H. Bond, in Norwood s Epitome of Navigation. James Gregory furnished a demonstration in 1668 ; but it was long and tedious. Halley claimed for himself the honour of being the first to give a rule whereby the meridional parts between any two latitudes may be calculated at once by the relation of the logarithmic tangents ; but it is practically the same as that published by Bond. Halley said that Wright s table nowhere exceeded the truth by half a mile. Sir Jonas Moore s system, he said, was nearer the truth, but the difference is not appreciable till beyond navigable waters. A rather curious paper was read before the Royal Society, June 4, 1666, by Nicholas Mercator upon the meridional line ; he pro poses to divide it into the hundred-thousandth part of a minute. Roger Cotes wrote upon the same subject an exhaustive paper in Latin, called &quot; Logometria,&quot; Phil. Trans., No. 338, 1714. He gives an illustrative figure in which the rhumb line crosses the meridians at an angle of 45. His demonstrations by the ratios arrive at similar conclusions to those clearly expressed by Halley. All these rules assume the earth to be truly spherical, instead of spheroidal. For the history of inquiry into the exact figure of the earth, see EARTH. It may be mentioned that a pamphlet on this subject by Murdoch, published in 1741, in which meridional parts are adapted to a (very exaggerated) spheroid, shows that plane charts and the roughly-divided Mercator s charts were still used at that date. Plane charts, indeed are explained even later, as in Robertson s Navigation, 1755. The power of taking observations correctly, either at sea or on shore, was greatly assisted by the invention which bears the name of Pierre Vernier, which was published in Brussels in 1631 (see VERNIER). As Vernier s quadrant was divided into half degrees only, the sector, as he called it, spread over 14 degrees, and that space carried thirty equal divisions, numbered from to 30. As each division of the sector contained 29 minutes of the arc, the vernier could be read to minutes. The verniers now commonly adapted to sextants can be read to 10 seconds. Shortly after the invention it was recommended by Bouguer and Jorge Juan, who describe it in a treatise entitled La Con struction, &c., du quadrant nouveau. About this period Gascoigne applied the telescope to the quadrant (see MICROMETER) ; and Hevelius invented the tangent screw, to give slow and steady motion when near the desired posi tion. In 1635 Henry Gellibrand published his discovery of the change in variation of the needle, which was effected by his comparing the results of his own observations with those of Burrough and Gunter. The latter was his pre decessor at Gresham College. In 1637 Richard Norwood, a sailor, and reader in mathematics, published an account of his most laudable exertions to remove one of the greatest stumbling-blocks in the way of correct navigation, that of not knowing the actual size of a degree or nautical mile, in a pamphlet styled The Seaman s Practices. Norwood ascertained the latitude of a position near the Tower of London in June 1633, and of a place in the centre of York in June 1635, with a sextant of more than 5 feet radius, and, having care fully corrected the declination, refraction, and parallax, made the difference 2 28. He then measured the distance with a chain, taking horizontal angles of all windings, and he made a special table for correcting elevations and depressions. A few places which he was unable to measure he paced. His conclusion was that a degree contained 367,176 English feet; this gives 2040 yards to a nautical mile, only about 12 yards too much. Norwood s works went through numerous editions, and retained their popularity over a hundred years; the last which the writer has seen a good book for the time, free from nonsense is dated 1732. In it he says that, as there is no means of discovering the longitude, a seaman must trust to his reckoning. He recommends the knots on the log-line to be placed 51 feet apart, as the just proportion to a mile when used with the half- minute glass. Dr Hooke read a paper at the Royal Society, in 1666, upon deep-sea sounding by means of a weight which be came detached on striking the bottom, and allowed a float to ascend to the surface, Avhile the time was carefully noted basing his calculations upon performances in known depths. He was on the verge of a great success; he required Sir W. Thomson s piano-wire instead of the float. In the same year a paper was read by Dr Wallis (who had previously published a discourse on tides) showing that the modern theory was not then generally accepted. This was followed by a paper by Sir Robert Moray, who recommended frequent and extended observations, and proposed to form a table which embraced every circum stance that would appear to be desirable even at the present day. Sir Robert also spoke of the irregularities in the tides past the western islands of Scotland. In Phil. Trans., 1683, vol. xiii. No. 143, there is an account of Flamsteed s tide table for London Bridge, which gave each high tide every day in the year. He justly condemns the old almanacs for deriving the moon s age from the epact, and then allowing forty-eight minutes for every day. Brooker was the first to amend this reckoning, but in a rough manner. Henry Philips, well known by his works on navigation, was the first to bring the inequality to a rule, which was found more conformable to experience than was expected ; but Flamsteed made corrections on his rule. The necessity for having correct charts was equalled by the pressing need of obtaining the longitude by some simple and correct means available to seamen ; and we have seen how many plans had already been thought of for this purpose. At one time it was hoped that the longitude might be directly discovered by the variation of the compass; in 1674 Charles II. actually appointed a commission to investigate the pretensions of a scheme of this sort devised by Bond, 1 and the same idea appears as late as 1777 in S. Dunn s Epitome. But the only real way of ascertaining the longitude is by knowing the difference of time at two meridians; and till the invention and perfecting of chronometers this could only be done by finding at two places the apparent time of the same celestial phenomenon. The most obvious phenomena to select were the motions of the moon among the sun and stars, which as we have seen were suggested as a means of finding the longitude by Werner in 1514, and continued to receive attention from later writers. But to make this idea practical it was necessary on the one hand to have better instruments for observation, and on the other to have such a theory of the moon s motions as should enable its place to be predicted with accuracy, and recorded before hand in an almanac. The very principles of such a theory were unknown before Newton s great discovery, when the lunar problem begins to have a chief place in the history of navigation ; the places of stars were derived from various and widely discrepant sources ; and almanacs gave little useful information beyond the declination of the sun, the age of the moon, and the time of high water. 2 Another class of phenomena whose comparative frequency recom mended them for longitude observations, viz., the occulta- tions of Jupiter s satellites, became known through Galileo s discovery of these bodies (1610). Tables for 1 Bond published in 1676 a quarto volume entitled The Longitude Found. 2 Wharton s Angelus Britannicus, 1666-1715, is a fair specimen of the almanacs of the period.