CHEAT BRITAIN 



GREAT CIRCLE 



381 



K!i M. .!. .11 trade, 1868. 



i, \f.. 1874. 



II I. blllr Ixx.k. 



Karr. vital statistics, 1837-78. 



1898-84. 

 rood, prioMftwigwi, 1746. 



:l an. I ir.. ii, i 

 Fowick, iron ami steel, l.vu. 



IXfH, IMI',. 



. litiaucittl enxayii, 1880-80. 

 rt, lankily. 1&0. 

 .M-r, nificoinlu^v. 1859. 



r. sin piling. 1S80. 



i statistics, 1759. 

 ii 1807. 



-i, Brit manufac., 1715. 

 k, Irish .. 1879. 



IMS, medical Static., I SIM. 



'i, statist, of Ireland. 1862. 



liel. meteorology. 1S61. 

 Hull, 1'n.f., coalfields, 1881. 

 Humphreys, vilal statist., 1883. 

 Hunt, mining industries, 1882. 

 Jeans, iron and steel, 1888. 

 Jeula, shipping, 1874. 

 JevoiiM, prices, &c., 1865. 

 Jones, national wealth, 1844. 



Livergne, Brit. griciilt., lsi3. 

 Uwea, ,, .. 1880. 



Levi, ooinnierce, 1870. 

 Lowe, agriculture, 1822. 

 Malwon. indiiHt. charU, 1882. 

 M'Culloch, Brit, umpire, 1837. 

 .. diet, of com., 18(10. 

 MThewon, hint, of com., inor,. 

 M'yuc.-n. llritisli empire. 1860. 

 Mann, cotton trade, 1800. 

 Miirshiill, .1 1. .-,! .,i -tat, 1833. 

 Martin, colonies, 1889. 



Mori-Ail, emu ive, 1828. 



Mulliall.dict. of statist. 1886. 

 \e\y march &T(M>ke,|)riceH, 1867. 

 <>-!, , vital HtatixtiCH, 1882. 

 I'algravi', local taxes, 1871. 

 1'ariirll, liuaiices, 1827. 

 I'orter, progress of nation, 1860. 

 Itcdiiriive, factories, 1876. 

 Rogers, Thorold, agricul., 1888. 

 Seeley, geography, 1SM. 

 Statesman's Year-book,1864,&c. 

 Valpy, commerce, 1853. 

 Williams, railways, 1879. 

 Yeats, commerce, 1872. 

 Young, agriculture, 1780-1808. 



Great Circle or Tangent Sailing. In 



order to have a clear idea of the advantages or great 

 circle sailing it is necessary to rememlier that the 

 shortest distance between two places on the earth's 

 surface is along an arc of a great circle (see 

 SniKKE); for instance, the shortest distance be- 

 tween two places in the same latitude is not along 

 the parallel of latitude, but along an arc of a circle 

 whose plane would pass through the two places and 

 the centre of the earth. The object, then, of great 

 circle sailing is to determine what the course of a 

 *hip must be in order that it may coincide with a 

 great circle of the earth, and thus render the dis- 

 tance sailed over the least possible. This problem 

 may be solved in various ways. The handiest 

 practical solution is to stretch a string over a 

 terrestrial globe quite tight between the ports 

 of departure and arrival. The string will lie 

 on the great circle required. A few spots on 

 the track of the string should be transferred to 

 the ordinary navigating (i.e. Mercator's) chart, 

 a free curve should be drawn through these 

 transferred spots, and the ship should be kept as 

 close to that curve as possible. The solution by 

 computation is simply the calculation of sides and 

 angles in a spherical triangle. The method by 

 computation will be understood from the accom- 

 panying diagram, where ns are the poles of the 



earth, we the equator : ntcse represents a meridian 

 which passes through the place p, nxvs another 

 meridian through the place x, and pxm a portion of 

 a great circle ; let p be the place sailed from, and 

 the place sailed to, then px is the great circle 

 track, and it is required to determine the length of 

 px (called the distance), and the angles npx, //<//, 



which are equal to the first and lout true courne*. 

 TM .l.-ti-nniin- these we have throe things given : 

 /", til-- co-latitute of x ; np, the co- latitude of p; 

 and the an^li- /////, whirli, measured along ve, 

 gives the (inference of longitude. The problem 

 tli us lici-DineH a simple case of spherical trigo- 

 nometry, the way of solving which will be found 

 in any of the ordinary treatises on the subject of 

 Spherical Trigonometry. 



Next, several longitudes on the route, nay at 5" 

 intervals, are chosen, and the co- latitudes of the 

 spots on the great circle which corresjKmd to these 

 assumed longitude* are calculated. The latitude 

 and longitude of these spots on the great circle 

 In-ill^ now obtained, the courses and distances from 

 one to the other in succession can be found by tlie 

 ordinary processes of navigation. The work is 

 somewhat shortened by finding that particular 

 spot on the entire great circle which lies farthest 

 from the equator. It is called the vertex, and Is 

 easily found by the property that the meridian 

 running through it is at right angles to the great 

 circle at that spot. To avoid these, or some of 

 these somewhat troublesome calculations, charts 

 have been constructed on projections different 

 from that of Mercator. On one of these, called 

 the Gnomonic Projection, all the great circles 

 are straight lines ; on another, all the great 

 circles are true circles. It has also been suggested 

 that the ports of departure and arrival being 

 given, and the vertex (described above) having 

 been found, and all three having been marked on 

 a Mercator's chart, a true circle drawn through 

 these three spots will be near enough to the great 

 circle for practical purposes. A modification of 

 this approximate method is useful in the run 

 between the Cape of Good Hope and Australia, on 

 which the great circle route goes too far into the 

 southern ice-region. If a spot of highest safe south 

 latitude be here substituted for the latitude of 

 the vertex, a circle drawn through the places of 

 departure, of arrival, and of the substituted safe 

 vertex will give what is called a composite great 

 circle. 



From the theory of great circle sailing the follow- 

 ing most prominent features are at once deduced : 

 A ship sailing on a great circle makes direct for 

 her port, ana crosses the meridians at an angle 

 which is always varying, whereas, by other sail- 

 ings, the ship crosses all meridians at the same 

 angle, or, in nautical phrase, her head is kept 

 on the same point of the compass, and she 

 never steers for the port direct till it is in 

 sight, except in the two cases where the ordinary 

 track lies ( 1 ) on a meridian, or ( 2 ) on the equator. 

 As Mercator's Chart (see MAP) is the one 

 used by navigators, and on it the course by the ordi- 

 nary sailings is laid down as a straigftt line, it 

 follows, from the previous observations, that the 

 great circle track must be represented by a curve, 

 and a little consideration win show that the latter 

 must always lie in a higher latitude than the 

 former. If the track is in the northern hemisphere 

 it trends towards the north pole ; if in the southern 

 hemisphere it trends towards the south pole. This 

 explains how a curve-line on the Mercator's chart 

 represents a shorter track between two places than 

 a straight line does ; for the difference or latitude is 

 the same for both tracks, and the great circle has 

 the advantage of the shorter degrees of longitude 

 measured on the higher circles of latitude, dm 

 sequentlv, the higher the latitude is the more do 

 the tracks differ, especially if the two places are 

 nearly on the same parallel. The point of maxi- 

 mum separation, as it mav be called, is that 

 point in the great circle which is farthest from the 

 rhumb-line on Mercator's chart. Since the errors 

 of dead -reckoning, or even of dead-reckoning 



