25 inches, bung diameter, corresponding log. = 2.795880 Content in wine gallons 1.491362 54.52 common log.= 1.736582 Remark.-Should the bung diameter not come within the limits of the second part of the Table; that is, should it be under 10 or above 50 inches, then twice the common log. corresponding thereto will express the log. of the said bung diameter, with which proceed as before: hence, the rule becomes universal for all circular-headed casks, be the size ever so great or ever so trivial. This subject will be revived in a subsequent page of the present work. TABLE LVIII. Latitudes and Longitudes of the principal Sea-Ports, Islands, Capes, &c. &c., with the Time of High Water at the Full and Change of the Moon at all Places where it is known. In drawing up this Table, the greatest pains have been taken to render it not only the most accurate, but also the most extensive of any now extant. Perfect accuracy, however, is not to be expected in a Table which principally depends on the observations made, at different periods, by the navigators of most civilized nations; because, in those periods, or at the time when a very considerable portion of the latitudes and longitudes were established, the nautical instruments and tables employed in their determination were far from being in that highly-improved state in which they are found at present: besides, it is a fact well known to the generality of nautical persons, that if two or more navigators be directed to ascertain the position of any particular place, they will, in most cases, differ four or five miles in the latitude, and perhaps thrice as many in the longitude. In constructing all the other Tables in this work, there were fixed data to work upon, with certain means of detecting and exterminating errors; but, in this, there were no determinate means of ensuring the desired degree of accuracy, except in those positions where chance or professional duties happened, from time to time, to conduct the author. Hence, although every possible degree of attention has been paid in consulting the most approved works of the present day, and in collating this with the best modern Tables; yet the mariner must not expect to find it perfectly free from blemishes; though, doubtless, he will find it considerably less so than any with which he may have been hitherto acquainted. Since this Table is not intended for general geographical purposes, the positions of places inland, which do not concern the navigator, have, with one or two exceptions, been purposely omitted: hence, the latitudes and longitudes are limited to maritime places. These are so arranged as to exhibit to the mariner the whole line of coast along which he may chance to sail, or on which he may be employed, agreeably to the manner in which it unfolds to his view on a Mercator's chart. This mode of arrangement is evidently much better adapted to nautical purposes than the alphabetical mode. With the view of keeping up the identity of the Table with the line of coast laid down on particular charts, a few positions have been inserted a second time. This, it is presumed, if not conducive to good, will not, at least, be productive of any evil, since the repetition is so very trivial as not to embrace, in the whole, more than ten or twelve positions. The time of high water, at the full and change of the moon, is given at all places where it is known. This, it is hoped, will be found not a little convenient, since it does away with the necessity of consulting a separate Table for that particular purpose. In order to render this Table still more complete, an alphabetical reference has been annexed, which will very essentially contribute towards assisting the mariner in readily finding out most of the principal coasts and islands contained in that Table, ་ The page which immediately follows the alphabetical reference to Table LVIII. contains the form of a Transit Table, and the next page a variety of numbers with their corresponding logarithms, &c., which may, perhaps, be found useful on many occasions. At the foot of these numbers there is a small Table, showing the absolute time at which the hour and minute hands of a well-regulated watch or clock should exactly be in conjunction, and also in opposition, in every revolution. Having thus completed the Description and Use of the Tables contained in this work, it now remains to show their application to the different elements connected with the sciences of navigation and nautical astronomy. In doing this, since the author's design carries him no farther than that of giving an ample illustration of the various purposes to which they may be applied; the reader must not, therefore, expect to find the elementary part of the sciences treated of. Hence, in this part of the work, the author will endeavour to confine himself to such Problems and subject matters as may appear to be most interesting and useful to nautical persons, without entering into particulars or the minutiae of the sciences, and thus swelling the work to an unnecessary size;-a thing which he most anxiously wishes to avoid. 156 A CONCISE SYSTEM OF DECIMAL ARITHMETIC. ALTHOUGH, from what has been said in the last paragraph, it may appear somewhat irregular, and even contrary to the general tenor of this work, to introduce any subject therein that does not come immediately under the cognizance of logarithms; yet, since the reader may be desirous of having some little acquaintance with the nature of decimal fractions previously to his entering on the logarithmical computations, the following concise system is given for that purpose.-It has been deemed advisable to touch upon this subject for two cogent reasons ;-first, because a short account of decimals may be acceptable to the mariner whose early entrance on a sea life prevents him from going through a regular course of scholastic education on shore; and, second, that he may have directly under his view all that is essentially necessary to be known in the practically useful branches of science, without being under the necessity of consulting any other author for the purpose of assisting him in the comprehension of the different subjects contained in this work. DECIMAL FRACTIONS, A decimal fraction signifies the artificial manner of setting down and expressing natural vulgar fractions as if they were whole numbers. A decimal fraction has always for its denominator an unit (1,) with as many ciphers annexed to it as there are places in the numerator; and it is generally expressed by setting down the numerator only, with a point before it, on the left hand; thus, is .5; is .75; 85 is .025; Tobbo is .00114, του &c. &c. :-hence the numerator must always consist of as many figures as there are ciphers in the denominator. 75 A mixed number is made up of a whole number and a decimal fraction, the one being separated from the other by a point; thus 5.75 is the same as 5, or 0. Ciphers on the right hand of decimals do not increase their value; for .5.50.500.5000, &c., are decimal fractions of the same value, each being equal to, or -But when ciphers are placed on the left hand of a decimal they decrease its value in a tenfold proportion;-thus, .5 is % or 5 tenths; but .05 is only 1 or 5 hundredths; .005 is only 100 or 5 thousandths, and so on :-hence it is evident that in decimals as well as in whole numbers, the value of the place of the figure increases towards the left hand, and decreases towards the right, each being in the same tenfold proportion. ADDITION OF DECIMALS. Addition of decimals is performed in the same way as addition of whole numbers, observing to place the numbers right; that is, all the decimal points under each other, units under units, tenths under tenths, hundredths under hundredths, &c.; taking care to point off from the total or sum as many places for decimals as there are in the line containing the greatest number of decimal places. Subtraction of decimals is likewise performed the same way as in whole numbers; observing to place the numbers right; that is, the decimal points under each other, units under units, tenths under tenths, hundredths under hundredths, &c. &c. Multiplication of decimals is also performed the same way as in whole numbers; observing to cut off as many decimal places in the product as there are decimal places in both factors; that is, in the multiplicand and multiplier. Example 1. Example 2. Note. If a decimal fraction be multiplied by a decimal fraction the product will be less than either the multiplicand or the multiplier.-And if any number either whole or mixed, be multiplied by a decimal fraction, the product will be always less than the multiplicand, as in example 1 ;-hence if a decimal fraction be multiplied by itself, its value will decrease in the proportion of its multiple :—thus, Division of decimals is performed in the same manner as in whole numbers; observing to point off as many decimal places in the quo |