sible, our Cadets and Midshipmen in these interesting researches ; as such higher objects of pursuit not only invigorate their faculties, but inspire them with a taste for the acquirement of professional eminence.
The Explanation of the Tables will, it is hoped, be found full and explicit, especially towards the beginning. The explanations of such tables as follow others, analogous in structure or arguments, may sometimes be less full, as it is presumed that those preceding them are well understood.
Uniformity and simplicity, in the methods of calculation, have been particularly studied, so that, with equal or greater facility, by means of the ordinary tables thus improved, those problems may be solved which frequently require the aid of a variety of subsidiary tables. This advantage has been obtained by annexing to several of the principal tables, differences and proportional parts, and to tables V. and LXXV. especially, double arguments in both arcs and time, by which many problems in Practical Astronomy and Navigation are solved with more facility, and with less chance of error, than when those tables are used which have arguments of arcs only. The trouble of referring to tables LXI. and LXII., to change arcs into time, and the converse, is therefore seldom requisite, though their use is constantly required when the common tables are employed. Hence, also, such tables as those in our usual works on Navigation, entitled Half-elapsed Time, Middle Time, Rising, &c., are unnecessary.
For this second edition, I have been favoured with the remarks of several of our most distinguished mathematicians and practical astronomers, who have testified to me their approbation of the first edition, and I have adopted some of their suggestions. The work has also been carefully revised throughout, many useful additions have been made, and such improvements and corrections introduced as, it is hoped, will render it more perfect, both with regard to accuracy and utility, than any other work of a similar description now before the public.
*The author having again examined his Tables since the preface was written and the stereotype Tables were thrown off, regrets to find that one error has been found in page 16, Log. of 9462-for 5933, read 5983; and another in page 76, Prop. log. of 24′ 59′′for 32504, read 32594.