The following text may have been generated by Optical Character Recognition, with varying degrees of accuracy. Reader beware!

TAE Marine REVIEW THE THEORY AND PRACTICE OF LAKE NAVIGATION BY CLARENCE E. LONG METHOD BY APPROXIMATION, In steaming along the land one can get the distance of a light or object ahead near enough by simply noting some land object marked on the chart, when it comes abeam. For this purpose you need no bearing instrument of any kind. Draw on the chart a line at right angles to the true course steered that will pass through the object on shore. The vessel is then situated somewhere on this line, or was at the time the bearing was taken} but how far from the object is the next ques- tion. You can guess this distance close enough, or by the height of the eye above the water and the height of the object. Whatever the distance you de- termine on prick this off on the bearing line drawn at right angles to the course and find the ship's position. All that is required then is to measure from the © vessel's position to.the light, or other ob- ject, that you desire to pass at a certain distance and pick it out of the tables as explained. Could there be anything more simple than this? We think not. EITHER NAUTICAL OR STATUTE MILES. Note."Do not get the idea that the data contained in the foregoing tables is for nautical miles only, and that to make it correspond to statute miles, the latter 'have to be turned into knots. This has nothing to do with it at all. The theory of it is that triangles that are equiangular are similar, and if they are similar the corresponding sides must be proportional; in other words, if you have a triangle of a certain size, and you construct another triangle either inside or outside of it, having the same angles their correspond- ing sides will be proportional, because tri- angles which are equiangular are simi- lar. Here is another way of explaining iit BOAT MAKING NAUTICAL 'MILES. A boat starts from a certain place, and steers N by E for 100 nautical miles, at the end of her run how far will she be from the meridian passing through the place she started from? Answer. She will be 19.5 miles (nautical). BOAT MAKING STATUTE MILES, A second boat starts from the same place as the one above and steers N by E 100 statute miles, at the end of her run, how far will she be from the same meridian passing through the place started from? Answer. She will be 19.5 statute miles, or the same distance in statute miles that the other boat is in nautical miles; that is, both boats will be the same number, but in their own kind of miles, from the meridian. DOES NOT LOOK IT, BUT IS SO. 'This does not seem possible at first thought, but it is nevertheless a truth, for although the vessel making nautical miles sails a much greater distance than _ the one making statute miles she is leay- ing the meridian by the same proportion that the boat is that is making statute miles. The following diagram will bet- ter explain this. 19.5 Nautical Miles | 19.5 Statute Miles Meridian of Place Starting Point. Another good way to prove this is to lay it off ona chart: Draw a N by E course having its start- ing point coincide at the intersection of some parallel and meridian. Lay off 100 statute miles (or a less number of miles will do) on the line representing the course and then draw another line (east and west) that will be at right angles to -the meridian and that will pass through the ship's place at the end of her run. Measure the length of this line. Next prick off the same number of nautical miles as you have statute miles and lay it off on this course, and draw an east and west line and measure it as before, and if you work correctly you will find them to be the same number, but different kind of miles. The distance run repre- sents the hypotenuse, the meridian the perpendicular; and the east and west line, the base. The reason some men think the dis- tance in a case of this kind corresponds only te nautical miles, is from the fact. that these tables are employed in Traverse Sailing, where each mile (nautical) is equal to a minute of latitude. Of course, if you are sailing statute miles under these conditions you would first turn them into nautical miles. THE REGULAR TABLES. The regular Traverse Tables give dis- tances up to 300 miles, and some of them to 600 miles. Where they 'are employed for dead-reckoning and the various sails ings, this is necessary. . SQUARE ROOT. The square root of a number is one of the two equal factors of that number. ' Thus, 3 is the square root of 9, be- cause 3 multiplied by 3 produces 9; 5 is the square root of 25, Evolution is the process of finding the root of any power of a number. The radical sign is V when prefixed by a number, it indicates that some root of it is to be found. The index of the root is a small figure placed above the radical sign to denote which root is to be found. When no in- dex is written the index 2 is under- stood.® : To extract the square root of any num- ber: Separate the expressions into groups of two figures each by placing a dot over the units' figure and over every alternate figure for the units, thus 121, which is a perfect square, its root being IT, that is) Fl x 1) =e 7) 2d. Take the largest square contained in | the number expressed in the left-hand group out of that number and express its square root as the highest terms of the required root; with the remainder unite next term of the power for a dividend. Thus, in 121, the greatest square of 1 is.1, because 1 X 1 = 1; then bring down the 21 for a dividend. 3d. Multiply the . terms of the root already found by 2, and add a cipher to it for a divisor, by; which divide the dividend and express the quotient as the next term of the root. Thus, 2 X 1 = 2 and a cipher added) makes 20 for a divisor. 4th. See how many times this divisor is contained in the remainder and add this number to the divisor. (Having thus obtained the first two terms of the root, if there are other terms to be found.) -- 5th. Unite with the remainder the next term of-the power for a new divi- dend. 6th. Multiply the terms of the root already found by 2, and apply the rule as in rule 3 and onward. 29