Navigation and Nautical Astronomy

AND

NAUTICAL ASTRONOMY.

PART II.

CONTAINING

THE INVESTIGATIONS AND PROOFS OF THE PRINCIPAL RULES
AND CORRECTIONS.

With practical Examples.

BY H. W. JEANS, F.R.A.S.

ROYAL NAVAL COLLEGE, PORTSMOUTH;

Author of a Work on "Plane and Spherical Trigonometry;" "Handbook of the Stars;"
"Problems in Astronomy, Navigation, &c. with Solutions:" formerly Mathematical
Master in the Royal Military Academy, Woolwich; and an Examiner of Officers in the
Merchant-Service in Nautical Astronomy, &c.

Designed for Beginners and for advanced Students.

LONDON:

LONGMAN, BROWN, GREEN, AND LONGMANS.
1859.

184. C. 19.

OTHE

LONDON:

PRINTED BY ROBSON, LEVEY, AND FRANKLYN, Great New Street and Fetter Lane.

BODLE

PREFACE.

THE First Part of this Work, consisting of practical rules in Navigation and Nautical Astronomy, with a series of examples under each rule, was originally drawn up for the use of beginners, and as introductory to some of the larger works on the subject; but recent additions render it complete in itself, and it will now be found to contain ample directions for the guidance of the practical navigator. The rules are adapted to any of the standard Nautical Tables now in use, such as Norie's, Raper's, or Riddle's; but as the collection of tables published by Dr. Inman* is almost uni

* This venerable and most useful public servant died on the 8th of the present month, at his residence at Southsea, near Portsmouth, at the advanced age of eighty-three years. The Reverend James Inman, D.D., was upwards of thirty years Professor of Mathematics at the Naval College. He was the oldest of Cambridge senior wranglers, and long possessed a just celebrity in naval circles for his application of science to navigation and ship-building. He laboured very many years unobtrusively but zealously in his country's service. He sailed round the world, having been appointed to the expedition under Flinders, as astronomer; was wrecked with him; and returning to Europe in the fleet of East-India ships under the command of Commodore Dance, was present in that celebrated action in which a fleet of merchantmen repulsed the French Admiral Linois. While professor of mathematics at the Royal Naval College, he reduced to system the previously ill-arranged methods of navigation, and published several valuable works on the subject; but he was best known by his having been the first person in the country who built ships on scientific principles. Dr. Inman's translation of Chapman, with his valuable annotations, is the textbook on which all subsequent writers have proceeded. His pupils,* a long list of distinguished naval officers, will remember him as a type of the highminded scholar,-of the loyal, the truthful, and independent man.

* One of the earliest, Lieutenant Henry Raper, author of a well-known work on Navigation, died a few weeks before his old preceptor. Lieutenant Raper was a distinguished and able writer on various subjects connected with naval science. The table of the positions of places on the surface of the earth contained in his Navigation is the best and most extensive compilation of the kind.

versally adopted in the Royal Navy, these tables have in most cases been used in working out the examples. The present volume, Part II., may be considered as the scientific part of the subject, consisting of the analytical investigations and proofs of the principal rules and corrections in Navigation and Nautical Astronomy. The author trusts that the plan followed by him in this Part, namely to exhibit a geometrical figure or diagram of each problem, then to give the analytical investigation from which the rule is derived, followed by a numerical example worked out to show the application of the formula, together with more than 200 examples for practice dispersed throughout the volume, will render the book useful to beginners (for whom, in fact, it is chiefly intended), as well as deserving the attention of more advanced students, and increasing the confidence of the practical navigator. The author's wish was to exclude from the present work every problem requiring a mathematical knowledge beyond algebra and trigonometry; he has, however, been induced to depart from this, in one or two instances, at the request of several Naval Instructors, who thought that it would render the work more useful to introduce the problems for finding the longitude by an occultation, and for determining the spheroidal figure of the earth from actual measurements on its surface. Part II., it is hoped, will enable the naval student to comprehend without difficulty the principal rules in Nautical Astronomy; and this he will more readily do, if he has previously made himself acquainted with the author's volume of Astronomical Problems, which work may be looked upon as introductory to the more important subject of Nautical Astronomy, explained and illustrated at large in the present volume.

ROYAL NAVAL COLLEGE,

Feb. 28, 1859.

CONTENTS.

The student is recommended to confine his attention at first to the problems and
articles not marked with an asterisk (*).