185 EXAMPLE Given Log 6.175407 .175222 next lesser Log diff. of Logs. To the right hand side of 185 place o, and divide by 290, which is the Tab. Diff. in the right-hand column opposite the Log taken out. 290)1850(637 1740 I100 2300 270 Next place the 637 to the right of the 1497, and so get 1497637, the number required. EXAMPLE....Given Log 5.557513 3610 corresponds to 557507 next lesser Log 600 Answer 361005. EXAMPLES FOR PRACTICE. Find the nunibers corresponding to the following Logs : No. No. No. I. 3.601951 7. 4.000000 13. 7.896004 2. 4.637790 8. 4.432656 14. 6.770668 3. 2.438542 9. 15. 6.158365 4. 5.685195 IO. 16. 4.141682 5. 5.296237 II. 17. 2.140780 1.999957 I 2. 18. 5.264794 For Answers, see end of book. MULTIPLICATION BY LOGARITHMS. RULE.—Find the Logs of the two numbers, and add them together. Then find the number corresponding to the sum, the number thus found is the product of the two given numbers. EXAMPLE. Multiply 145.544 by 500 by common Logarithms. 145.544 2.162994; 162863 Diff. 298 44 1. Multiply 20 by 30 by common Logarithms. 144 by 12 240 by 250 165.21 by 5 40000 by 250 108.58! by 500 9. 271.006 by 368.9585 1000000 by 1000 II. 27090.5 by 8 5024 by 240 13 4.3825 by 54 14. 701050 by 200 15. 19735 by 350 16. 13392.9 by 54.39 17. 11028.83 by 393.9 370.52 by 300.25 27000 by 1200 For Answers, see end of book. 12. DIVISION BY LOGARITHMS. RULE.–Find the Logs of the two numbers, then subtract the Log of the divisor from the Log of the dividend. The number corresponding to the difference of these logs is the required quotient. EXAMPLE. Diff. 200 ogo 18,000 338058 +18 initino noo EXAMPLES FOR PRACTICE. by common Logarithms. 2592 by 3.6 4300 by 2150 5 39104 by 9776 28.004 by 14.002 998001 by 99.9 100000 by 2500 9. 3680 by 3680 10. 726030 by 40335 II. 40884.8 by 202 12. 243 by 90 13. 120.95 by 24.19 14. 1930640 by 39.441 15. 6060 by .15 16. 430 by .0215 172.8 by .0012 18. 615 by .03075 i by .005 500 by .I For Answers, see end of book. 17. 9 19. 20. THE DAY'S WORK. THE BEARING OR DEPARTURE COURSE.-Reverse the given bearing, consider the number of points it is from North or from South, and turn them into degrees, then allow the Deviation for the direction of the Ship's head. Easterly Deviation to the Right hand; Westerly Deviation to the Left hand. After which allow the Variation : Easterly Variation to the Right hand; Westerly Variation to the Left hand. The result is considered as a course, and is entered into the Traverse Table. Then take the FIRST COURSE, correct it for leeway (in points) : If on the port tack to the Right hand; If on the starboard tack to the Left hand. After which allow the deviation and the variation by the rule given above. The result is the True Course. If over goo subtract it from 180°, and change N. into S., or S. into N., keeping it E. if E., or W. if W. Proceed in the same manner with the other courses. Then take the CURRENT COURSE, and allow the váriation on it in the usual manner. Note.-The set of the current being generally given correct magnetic, no deviation is required. When all these courses are correctly found, they are entered to the nearest degree into the Traverse Table, then get the distances, and enter them into the Distance Column. Then from Table II. take out the D. Lat. and Dep. for each course and distance, and place them in their respective columns, and so complete the Traverse Table. Add up the N. column, and then the S. column, and subtract the less from the greater; the result is the D. Lat. of the same name as the greater. Add up the E. column and then the W. column, and subtract the less sum from the greater; the result is the Dep. of the same name as the greater. TO FIND THE LATITUDE IN.- Write down the Lat. left, that is the Lat. of the point of land, and below it place the D. Lat. (previously bringing it into degrees, if necessary). Lat. left and D. Lat. same name, add ; Lat. left and D. Lat. contrary names, subtract; The sum or the remainder is the Lat. in of the same name as the greater. TO FIND THE MIDDLE LATITUDE.—Bring down the Lat. left below the Lat. in, and if of the same name add them together; if of different names subtract the less from the greater, and divide the sum or the remainder by 2. This gives the mid. Lat. TO FIND THE DIFFERENCE OF LONGITUDE.—With mid. Lat. as a course in Table II., and with Dep. in D. Lat. column, the number in Dist. column is the D. Long. of the same name as the Dep. Note:—When the Dep. (being too large) cannot be found in the D. Lat. column, divide the Dep. by 2, and proceed as directed above. The result is half the D. Long., which must be multiplied by 2 to obtain the whole D. Long. TO FIND THE LONGITUDE IN.—Write down the Longitude left, and below it place the D. Long. (previously bringing it into degrees if necessary). Long, left and D. Long. same name, add ; Long. left and D. Long. different names, subtract. The sum or remainder is the Longitude in of the same name as the greater. Note.—When the Long. in is greater than 180° subtract from 360°, and call the remainder the Long. in, of an opposite name to the Long. left. TO FIND THE COURSE AND DISTANCE MADE GOOD.These are found from Table II. The course is on the top of the page when D. Lat. in your Traverse Table is greater than the Dep., and on the bottom when less. Then seek in Table II. a page on which your D. Lat. and Dep. correspond (or nearly so) with each other. The Distance is alongside, and the Course on the top or bottom as previously determined. |