322 



THE POPULAR EDUCATOR. 



wish to steer true N.E., we add 2J points to the right to find 

 the compass course to be steered, knowing, as we do, that N.E. 

 on the card is really that distance to the left of the true N.E. : 

 thus we steer, by card, E.N.E.^ E. The variation of the needle 

 in any given part of the world is easily found by nautical 

 astronomy. 



But besides the variation of the needle, easily allowed for, 

 there are two grave sources of error in the 

 courses noted on the log-board viz., lee- 

 way and currents. Lee- way is caused by the 

 ship drifting sideways under the pressure of 

 a side wind. Its amount varies greatly with 

 the build of ship, force of wind, etc., and 

 can only be estimated roughly by the angle 

 which the vessel'3 apparent course i.e., the 

 direction in which her head points makes 

 with the real course, as shown by the line 

 of broken water in her " wake." The esti- 

 mated amount is noted on the log-board. 

 Currents are still more troublesome, and no 

 estimate of them can be thoroughly relied 

 on ; an estimate of their force and direction, 

 if any, must, however, be noted on the log- 

 board. Its value depends upon the judgment 

 and experience of the observer. A common 

 mode of estimating currents is to render a 

 boat stationary by lowering a heavy weight from it to i great 

 depth, and seeing how fast, and in what direction, the ship 

 drifts from the boat. But it not unfrequently happens that 

 this test is fallacious, from the boat having dropped its weight 

 Into some under-current, which causes it to move, even if the 

 lurface be quite still. 



Having during twenty-four hours put upon the log-board the 

 materials he can, in his character of practical observer, the 

 navigator next proceeds, as mathematician, to apply the rules 

 to be developed in the ensuing sections. 



II. Definition of terms. 



The earth is assumed, for simplicity's sake, and with sufficient 

 accuracy for purposes of navigation, to be a perfect globe or 

 sphere (strictly it is not so, as it slightly bulges out at the 

 equator, and is flattened at the poles). 



The axis of the earth is the diameter upon which it revolves, 

 an imaginary line passing through the centre (N s in Fig. 2). 

 The points on the surfaco at which this line terminates are 

 called the poles (N, s in the figure). 



A great circle of a sphere is any circle of the same radius as 

 the sphere, and consequently having the same centre as the 

 sphere. Every sphere may bear upon it an infinite number of 

 great circles, cutting each other in all directions, but they 

 clearly must all be of the same size that is, the greatest size 

 which any circle traced upon the sphere can attain. With any 

 other point in the interior of the sphere 

 for a centre, one circle only can be traced 

 upon the surface, which will be smaller than 



the great circle in proportion as its centre ^ B b , I z ^, B 

 is distant from the centre of the sphere. 

 Examination of a terrestrial globe will 

 explain this : the equator and meridians 

 of longitude are all great circles, the 

 parallels of latitude are small circles. 



The equator (E Q) is a great circle sur- 

 rounding the earth exactly midway between the poles. Every 

 point on the equator is therefore equidistant from the north 

 and south pole. 



A meridian, or meridian of longitude, is half the great circle 

 which passes through any given place and the two poles, or, in 

 other words, is an imaginary line drawn north and south through 

 any place, and prolonged to the poles. Such line is called the 

 meridian of the place or spot in question : NXS, NYS, NZS 

 are the meridians of A, B, and c respectively, and of all other 

 places situated on the same north and south lines. 



A parallel of latitude is a " small circle" drawn through any 

 place, encircling the earth parallel io the equator. The farther 

 tho place is from the equator, of course the smaller the circle. 

 P L is the parallel on which A, B, and c are situated. 



The latitude of a place is its distance north or south from the 

 equator, and is measured by the length of that portion of any 

 meridian included between the equator and its parallel of lati- 



tude, or, which is the same thing, by its distance from the 

 equator, measured' along its own meridian. Thus the latitude 

 (north) of B is B Y (or A X or C z), and if we assume B Y to be 

 the sixth part of the meridian N B Y s, which, as a semicircle, 

 contains ISO 3 , we can immediately define its position as 30 

 north latitude. Obviously the meridional arc from the equator to 

 either pole is 90S, or the fourth of a circle ; consequently latitude 

 is never expressed in figures higher than 90. 

 The longitude of a place is its distance east 

 or west of some special meridian arbitrarily 

 chosen as a standard of reference, there being 

 no meridional great circle with natural claims 

 to pre-eminence, such as the equator has 

 amongst parallels of latitude. The English 

 reckon the longitude of all places as so many 

 degrees east or west of the meridian of Green- 

 wich (the national observatory) ; the French 

 count from Paris, and so on. The longitude 

 of a place is thus its distance from the 

 meridian of Greemvich (not from Greenwich 

 itself), measured along its own parallel of 

 latitude, or, as some put it, the arc of the 

 equator lying between its own meridian and 

 that of Greenwich. Thus the longitude of 

 B, assuming N 2 s to be the meridian in 

 which Greenwich is situate, is B c west. 

 Assuming B c to be the sixth part of the circle P L (360), we can 

 now defino B'S position exactly ; it is lat. 30 N., long. 60 W. 

 The longitude of Y, or any other place on the meridian NYS, is 

 also 6C W. Seeing that all meridians gradually approach each 

 other towards the poles, it is evident that a degree of longitude 

 (measured as it is upon a circle of uncertain size) varies in length 

 from nearly seventy statute miles at the equator to nothing at 

 the poles ; whereas a degree of latitude, measured always upon a 

 meridian (a great circle), is constant, and is the same as a degree 

 of longitude at the equator. Each degree, of course, contains 

 60 minutes (nautical miles), and each minute 60 seconds. 



The student must guard against the common error of viewing 

 degrees of longitude and latitude as mere measures of length, com- 

 parable only with miles and furlongs. They are also measures of 

 angles; thus, "B is in 30 N. lat." means that B subtends with 

 tho equator an angle of 30 at the centre of the circle of which 

 its meridian forms part (necessarily also the centre of the globe). 

 Regarding the definition of B'S position as 30 lat. N. as simply 

 signifying that it lies 1,800 nautical miles to the north of the 

 equator, the expressions "sine of latitude of B," "cosine 30Iat.," 

 would be unintelligible ; but viewing it as the measure of the 

 angle BOY, they offer no difficulty. Similarly, the 60 of longi- 

 tude between Y and z are the measure of the angle YOZ. (A 

 I knowledge of Trigonometry, as given in this work, as far as the 

 i solution of right-angled triangles, is assumed in the student.) 



The difference of latitude between two 

 places, whether on the same meridian or 

 not, is the arc of a meridian intercepted 

 between their respective parallels of lati- 

 tude. If they are both north or both south 

 of the equator, the difference is found by 

 subtracting the less latitude from the 

 greater; if one has north and the other 

 south latitude, the two must be added to 

 give the difference. Similarly with differ- 

 | ence of longitude : if both east or both west of Greenwich sub- 

 tract the less from the greater ; if one east and the other west, 

 add the two amounts together. Thus the difference of longi- 

 tude between a place 40 W. and another 130 W. is 90; 

 I between a place 40 W. and another 110 E., the difference is 

 | 150. Between the place 130 W. and that 110 E. we do not, 

 I however, describe the difference as 240. Obviously the greatest 

 i possible difference is 180, half the circumference of the globe, 

 so that where the difference amounts by the rule GO over 180, 

 we take the difference between the amount found and 360, 

 the whole circumference of the globe. Thus 360 - 240 = 

 120 = difference between the places named. A little conside- 

 ration will show this to be the proper difference, as the two places 

 are so far from the Greenwich meridian that they begin, so to 

 | say, to approach each other on the other side of the world. 



The horizon, in popular language, is the line formed by the 

 junction in the distance of the sea and sky. Strictly, the 



