short side, in order to avoid the risk of letting the ship over-run her reckoning. Massey's Frictionless Log is one of the most reliable self-indicating instruments for ascertaining the distance run in a given time. It is towed from the weather counter, and sometimes from an outrigger 8 or 10 feet in length, to keep the log clear of the eddy in wake of the ship, with from 30 to 60 fathoms of patent line. Walker's Taffrail Log is a most complete instrument, and saves a great amount of labour. Lee-way can always be ascertained before hauling in the log by having a graduated arc on the taffrail and a small crutch or fairlead fixed inboard at a distance corresponding to the radius of the arc. The angle which the log-line (when placed in the crutch) makes with the foreand-aft line of the vessel is the lee-way. COMMON LOGARITHMS. Logarithms were invented by John Napier, Baron of Merchiston. They are a series of numbers in arithmetical progression corresponding to another series of numbers in geometrical progression, and are used in order to facilitate processes of numerical calculation. Base Nos. 4 5 6 7 6 - 7 8 1-5-25-125-625-3,125-15,625-78,125-390,625 5 Logs. 0-1 — 2 —- 3 4 - 5 To Multiply-add the logarithms of the numbers together, and find the number to correspond. To Divide-subtract the logarithms of the numbers from one another, and find the number to correspond. Involution, or raising a number to any power,-multiply the logarithm of the number by the index or power required. Evolution, or extracting the root of a number,-divide the logarithm of the number by the index of the root. Every logarithm consists of two parts, the index and the decimal part or mantissa. The index or log proper is supplied by the calculator, and is always one less than the number of integral figures in the number. When the number has no integral figures, the index of the logarithm is one more than the number of cyphers immediately after the decimal place, and has the negative sign (-) placed over it. Required the square root of 9801 Number 9801 Log 2)3-991270 ... Required the square root of 03422 Number 03422... Log 2)2.534280 S. 60 10 W. S. 14 4 W. 8 0 E. Correct the courses for deviation, variation, and leeway, and find the course and distance from the given point, and the latitude and longitude in by inspection. Look for middle latitude as a course, and for departure in a latitude column, then the distance will equal the difference of longitude. Look for difference of latitude and departure to come together, then distance to correspond is distance made good, and course is taken from top or bottom of page to suit. E 58.5 14.1 10.5 = Diff. Lat. 142.2=Dep 14° 12' 00" S. 10 30 N. 1 30 S. Diff. Long. = Long. left, ... ... 179° 38′ W. 2 27 W. Long. in 182 5 W. or from 360 Long. in = 177 55 E. |