DIVISION • To divide one number by another, select the logarithms from Table 42 and when properly indexed, subtract the logarithm of the divisor from that of the dividend, adding 10 to the index of the logarithm of the dividend if necessary to make subtraction possible, and the re nainder will be the logarithm of the quotient. Example: Divide 20.01 by 8.7. 20.01 index 1.30125 8.7) 2 0.0,1 ( 2.3 Proof “ – 0.93952 174 Ans. 2.300 = 0.36173 261 261 Example: Divide 7 by 8. index + 10 = 10.84510 , 8)7. (.87 5 Proof - 8. - 0.90309 64 Ans. .875 = 9.94201 8.7 60 s6 40 40 LOGARITHMS FROM TABLE 44 For the solution of many problems in navigation the use of logarithms from Table 44 is necessary and should be thoroughly understood. In this work they are used in the sailings. The degrees begin at the top of the page and run to the right to 45°. From that they run on the bottom to the left to 90° and then on the bottom to the right to 134o. From 135° to 180° they run to the left at the top of the pages. The degree of the angle being located at one side or the other of the page, the miles must be taken from the mile column on the same side. If the degrees are found at the top, the various names must also be read from there and when the degrees are at the bottom of the page the names over the columns must be read from the bottom. If the logarithm wanted is to be corrected for seconds, the logarithm for the lesser mile is taken and then find the seconds in the left-hand mile column. The correction will be found opposite in the column of differences next to that from which the loragithm is taken and is added or subtracted, according to the next logarithm being more or less. Up to and including 4° and other angles on the same pages, the correction columns contain the difference for I'. When the angle falls on those pages, the correction for seconds is found by taking the number directly opposite, dividing it by 60 and then multiply by the number of seconds or reduce the seconds to a decimal part of a mile and by it multiply the number from the correction column. The logarithm is taken for the nearest mile when a correction column is not given. 1. Example: Find the logarithm sine for 35° 25' 28”. 35° 25' sin. 9.76307 cor. + 8 35° 25' 28" =sin. 9.76315 28" 2. Example: Find the logarithm cosine for 125° 54' 42". 125° 54 cos. 9.76817 cor. + 12 125° 54' 42" =cos. 9.76829 42" 3. Example: Find the logarithm cosine for 144° oo 50". 144° oo' cos. 9.90796 cor. + 8 144° 06' 50" =cos. 9.90804 50" 4. Example: Find the logarithm tangent for 54° 20' 54". 54° 20' tang. I4406 54" cor. + 24 54° 20' 54" tang. 14430 5. Example: Find the logarithm tangent for 35° 50' 38". 35° 50' tang. 9.85860 cor. + 17 35° 50' 38" tang. 9.85877 38" 6. Example: Find the logarithm cosine for 54° 27' 40". 54° 27' cos. 9.76448 cor. - 12 54° 27' 40" =cos. 9.76436 40% 7. Example: Find the logarithm cosine 35° 10' 46". 35° 10' cos. 9.91248 cor. - 7 35° 10' 46" =cos. 9.91241 46" 8. Example: Find the logarithm cosine for 86° 28'42". 86° 28' cos. 8.78979 Dif. 1 204 cor. for 42" = 204 X .7 = - 143 42" = X .7 86° 28' 42" =cos. 8.78836 143 = 142.8 or the cor. 142.8 = 204 X 42" DEFINITIONS Compass course is that course steered by the ship's compass. It includes variation and deviation, heeling error, current and leeway, if any. Magnetic course is the course steered by the ship's compass when free from deviation and other influences. True course is the course obtained by applying the variation, deviation and leeway, if any. Leeway is the angle between the ship's keel and the direction being made through the water. Variation is the quantity the north point of the compass is east or west of the true north. It is the earth's effect on the compass and is not the same in all localities. It is always increasing or decreasing. Deviation is the quantity the north point of the compass is east or west of the magnetic north. It is the result of the ship's effect on the compass. It is different for every point of the compass and, therefore, changes every time the course is altered. Compass error is the quantity the north point of the compass is east or west of the true north. If the compass is free of deviation, it will be the same as the variation. · Distance is the number of miles the ship makes on any one course or the number of miles between any two points on the earth's surface. Distance made good is the number of miles a ship is from the point she started regardless of the distance she has sailed. Departure course is the bearing reversed of the fixed object on shore from which a ship takes her departure upon leaving port. The distance is also noted. Wind is air in motion and its direction is named after the point from which it blows. Current is water having progressive motion. Its set is named after the point from which it flows and its drift is expressed in miles either hourly or daily. Difference of latitude is the quantity taken for each corrected course and distance from the latitude column in Tables I or 2, taking care to use the top or bottom according to the course. They are entered in the traverse table in the north column for north courses and in the south column for south courses. It is also the north or south distance between any two points on the earth's surface. Departure is the quantity taken for each corrected course and distance from Tables 1 or 2 and entered in the traverse table in the east column for east courses and in the west column for west courses. It is also the east or west distance between any two points on the earth's surface expressed in true or latitude miles. Latitude is the distance any point on the earth's surface is north or south of the equator, and is expressed in degrees, minutes and seconds. Parallel of latitude is a circle parallel to the equator and equidistant from the north or south poles. The equator is a great circle around the globe equidistant from the poles. From it the degrees of latitude are counted north or south toward the poles. Longitude is the distance any point on the earth's surface is east or west of the meridian of Greenwich measured on the equator and is expressed in degrees, minutes and seconds in this work, but for other purposes in hours, minutes and seconds. A meridian is the arc of a great circle 180° extending from pole to pole, its plane cutting that of the equator at right angles. Meridian of Greenwich is the prime meridian from which longitude is counted east or west. Middle latitude is half the sum of the two latitudes between which a course and distance may be wanted. It is used for converting difference of longitude into departure or departure into difference of longitude, using Table 2. Meridional parts is the distance any point on the earth's surface is north or south of the equator measured on a Mercator chart with a degree of longitude at the equator and is expressed in miles and tenths. Meridional parts are found in Table 3 for any degree or mile of latitude to latitude 79° 59'. Meridional difference is the difference of the meridional parts for the latitudes of any two points on the earth's surface. |