The Complete Mathematical and General Navigation Tables

motion of the iniaginary or mean Sun; and thence down to the golden number. Besides unfolding a considerable portion of the Ephemeris, they clear up a number of curious and important points relative to the motions of the earth, which have hitherto escaped the notice of mere theoretical writers on Navigation and Nautical Astronomy.

The Introductory Problems, which begin at page 341, are solved in such an explanatory manner as to exhibit the most direct and practicable modes of applying the various elements in the Ephemeris to the important purposes for which they are designed. And, in every problem that seemed to require a specific illustration, a summary of its theory is introduced; so as to convey to the mind of the reader the most familiar idea of the spherical principles upon which the consequent practical rule is founded. ·

The problem for finding the longitude by means of a chronometer, manifests the unquestionable reason (page 453) why a timekeeper regulated on shore, or at an observatory, and then taken on board a ship, never answers the expectations of a navigator at sea; and it shows a rational cause why the rate of a chronometer should always be determined on board the ship to which it belongs, and never on shore. Aware of the difficulty of removing an old prejudice, or of doing away with a mistaken custom of long standing, I have therefore entered into all the details of the argument, and intentionally sacrificed conciseness to clearness of expression, so as to demonstrate, in the most ample manner, the easy practicability of establishing the error and the rate of a chronometer on board a ship, after it has been duly fixed in its berth, or resting-place.

In the practical part of the Lunar Observations, the peculiarities attendant on the phases of Venus, accordingly as she may be situated in the heavens as an evening or a morning star, are pointed out in the most perspicuous manner (page 517), for the purpose of preventing those who are not much versed in physical Astronomy from falling into a mistake in observing an angular distance between her enlightened limb and that of the moon.

Certain parts of the original work have been omitted :—as thus, finding that "the Method for determining the Longitude on shore by means of an Altitude of the Moon,"-though strictly correct in principle, was not likely to be of much practical utility, on account of the extreme degree of precision with which the observation should be made; I have, therefore, struck it out, and substituted in its stead (but not in the same part of the Volume) a more generally useful and prac

ticable problem; which shows the method of deducing the longitude from the transit of the moon's enlightened limb over the meridian of an observer. And, as the operation is remarkably simple and concise, it will be found useful to maritime surveyors, and to all others who are in possession of transit instruments and timekeepers.

With the view of perfecting the Astronomical part of the work, and of leaving nothing undone that could possibly conduce to the advancement of Navigation; a problem is therefore given (page 536), which shows how the longitude is to be deduced from an occultation of a fixed star or planet by the moon, or from an eclipse of the sun. In this problem the apparently mysterious doctrine of the occultations is unveiled and laid open to the view of the reader ;-familiar terms are substituted for the mystical abstruseness of analytical expressions; and thus the whole of that hitherto occult and highly interesting science is brought down to the standard of ordinary capacities, and reduced to the comprehension of every person who understands the use of the Trigonometrical Tables. And, as the formula which I have laid down renders the calculation extremely simple and free from restrictive cases, there are good grounds for hoping that the infallible method of finding the longitude by the occultations of the fixed stars &c., will soon become as general throughout the Royal Navy as the Lunar Observations are at present.

The Volume in question is concluded with a series of useful Problems; the last of which exposes the absurdity of supposing the earth to be at rest, and the heavenly bodies in motion revolving round it.

The Second Volume did not admit of many alterations, and but very few corrections.-At page 611 three new Tables have been introduced; these are of vast importance in problems relating to the longitude :-the principles upon which those Tables are constructed, and the uses for which they are intended, will be found in the Explanatory Articles, between pages 336 and 340 of the First Volume.-To the Tables is subjoined an Appendix, showing the method of finding the ratio which the circumference of the circle bears to its diameter ;-the method of deducing the natural sines from the circle ;—and, the method of performing the celebrated operation called "Tetragonism," or the squaring of the circle.-As this new and highly improved Edition is drawn up in such a manner as to combine theory with an extensive practical knowledge of all nautical subjects,-the latter being the result of thirty years' experience in the Royal Naval Service of Her Majesty,-it is therefore particularly adapted to meet the wants and the wishes of

Naval Men, and of all others whose early entrance into the great Maritime World may have prevented their making much progress in the sublime science of Astronomy. Hence, in presenting this Work to the Sons of the Ocean and to the public in general, I feel a degree of confidence that it will prove, on every occasion, to be a complete MasterKey, which unfolds, explains, and turns to direct application every elementary expression that has any relation to the sciences of Navigation and Nautical Astronomy.

Her Majesty's Ship Pique,
January, 1838.

THOMAS KERIGAN.

THE FIRST EDITION of this Work was honoured with the immediate patronage of His late Majesty, who held the office of Lord High Admiral at the period of its publication; and it was dedicated, by permission, to the Right Honourable the Lords Commissioners of the Admiralty, who had executed that high office during its progress through the press.

In addition to this testimony of their approbation, their Lordships were pleased to contribute the sum of one hundred guineas for ten copies of the work.

The Elder Brethren of the Honourable Trinity Corporation contributed one hundred pounds for five copies, and

The Court of Directors of the Honourable East India Company contributed one hundred guineas for ten copies.

The Honourable the Commissioners of the Navy, the Honourable the Commissioners for Victualling the Navy, the Directors of Greenwich Hospital, the Committee of Lloyd's, the Royal Naval Club, the British Library, Jersey, and upwards of two hundred Officers of The Royal Navy, and others, likewise honoured the First Edition of the I work with their names as Subscribers.

Books