ference of longitude made good is of a contrary name to the longitude sailed from; then, if the difference of longitude, expressed in degrees, be greater than the longitude left, their difference will be the longitude come to; which will be of a contrary name to that sailed from; because, in this case the ship will have crossed the meridian whence the longitude is reckoned. Again.-When a ship increases her longitude; that is, when the difference of longitude made good, expressed in degrees, is of the same name with the longitude sailed from, their sum will be the longitude come to; but, if this sum exceeds 180 degrees, then, its difference to 360 degrees will express the longitude come to, which will be of a contrary denomination to that sailed from; for, in this case, also, the ship will have crossed the meridian that the longitude was reckoned from : -see Problems, Rules, and Remarks, between pages 211 and 217. Example 2. A ship from the Island of Annabona, in latitude 1:23 S., and longitude 5:34 E., sailed W. N. W. 546 miles; required the latitude and longitude of the place at which she arrived? Meridional difference of lat. = To find the Difference of Longitude, and hence the Longitude come to. Course steered = Diff. of long. = 8:25: W. = 504.6 miles. Logarithm= 2.702922 Hence, the latitude come to is 2:6 N. and the longitude 2:51 W. Example 3. A ship from Pitt's Island, in latitude 2:54 N. and longitude 174:30: E. sailed S. E. by E. E. 760 miles; required the latitude and longitudes of the place at which she arrived? To find the Difference of Longitude, and hence the Longitude come to. 2.554126 Diff. of long. made good =11:10: E. 670 miles. Log. 2.826169 Longitude sailed from = 174.30 E. Hence, the latitude come to is 3:4 S., and the longitude 174:20: west. PROBLEM VII. Given both Latitudes and the Course; to find the Distance Sailed and the Longitude come to. RULE. To the logarithmic secant of the course,* add the logarithm of the difference of latitude; the sum, abating 10 in the index, will be the logarithm of the distance.-Then, The course steered, per compass, is to be reduced to the true course by Problem VI., page 577. To the logarithmic tangent of the course, add the logarithm of the meridional difference of latitude; the sum, abating 10 in the index, will be the logarithm of the difference of longitude; which being applied to the longitude left by addition or subtraction, according as it is increasing or decreasing, the sum or difference will be the longitude come to. Example. A ship, from a place in latitude 3:4: S., and longitude 174:20: W., sailed N. W. by W. W. until she was found, by observation, to be in latitude 2:54 N.; required the distance sailed, and the longitude at which the ship arrived? Lat. sailed from = Merid. parts = 184.1 miles. 174.1 miles. 5:58 358 ms. Merid. diff. lat. 358. 2 miles. . To find the Distance Sailed. 5 points. Log. secant = 10.326613 358 miles. Note.-The three last Problems comprehend all the cases that usually occur in the practical part of Mercator's sailing ;-for the speculative cases, see pages from 236 to 248, inclusive. PROBLEM VIII. To find the Course, Distance, Difference of Latitude, and Difference of Longitude made good upon compound Courses, and also the Bearing and Distance from a Ship to the Place to which she is bound, viz. :To make out a Day's Work at Sea. RULE. Make a Table of any convenient size, and divide it into six columns : -in the first of these place the several courses, taken from the log board (corrected for lee-way, if any, and also for variation), and in the second place their corresponding distances.-The third and fourth columns are to contain the differences of latitude, and, therefore, to be marked N. S. at top; and the fifth and sixth the departures, or meridian distances, which are to be marked at top, also, with the letters E. W.-Now, Enter the general Traverse Table, and take out the difference of latitude and departure answering to each corrected course and distance, and place them in their respective columns :-then, the difference between the sums of the N. and S. columns will be the whole difference of latitude made good, of the same name with the greater; and the difference between the sums of the E. and W. columns will be the whole departure made good, of the same name with the greater term. Remark. The courses, taken from the log board, are to be corrected for variation, and lee-way, if any, in the following manner, viz. If the variation be easterly, it is to be allowed to the right hand of the course steered by compass; but to the left hand if it be westerly.* -And, If the larboard tacks be aboard, the lee-way is to be allowed to the right hand of the course steered by compass; but, to the left hand if the starboard tacks be aboard. To find the Course and Distance made good. From the logarithm of the departure, the index being increased by 10, subtract the logarithm of the difference of latitude; the remainder will be the logarithmic tangent of the course.-Then, To the logarithmic secant of the course, thus found, add the logarithm of the difference of latitude, and the sum, abating 10 in the index, will be the logarithm of the distance. * See Problem VI., page 577. To find the Latitude in, by Account, or Dead Reckoning. If the difference of latitude, and the latitude of the place from which the ship's departure was taken, or the yesterday's latitude, be of the same name; their sum will be the latitude in, by account: but if of contrary names, their difference will be the latitude in, of the same name with the greater term. To find the Difference of Longitude; and thence the Longitude come to. To the logarithmic tangent of the course made good, add the logarithm of the meridional difference of latitude (by observation); the sum, abating 10 in the index, will be the logarithm of the difference of longitude.-Now, if the difference of longitude, and the longitude of the place from which the ship's departure was taken, or the yesterday's longitude, be of the same name; their sum will be the longitude in, by account, when it does not exceed 180 degrees; otherwise it is to be taken from 360 degrees, and the remainder will be the longitude in, of a contrary name to that left:-but, if the difference of longitude, and the longitude left be of contrary names, their difference will be the longitude come to, of the same name with the greater term. To find the Bearing and Distance of the Ship to the Port, or Place to which she is Bound. From the logarithm of the difference of longitude between the ship and the place to which she is bound, the index being increased by 10, subtract the logarithm of the meridional difference of latitude; the remainder will be the logarithmic tangent of the course. Then,—To the logarithmic secant of the course, thus found, add the logarithm of the difference of latitude, and the sum, rejecting radius, will be the logarithm of the distance. Note. The true bearing, or course thus found, may be reduced to the magnetic, or compass course, if necessary, by allowing the value of the variation to the right hand thereof if it be westerly; but, to the left hand, if easterly :—this being the converse of reducing the course steered by compass to the true course.* And this rule comprises the substance of that nautical operation, which is generally termed making out a day's work at sea. * See Problem V., page 576. |