52 



NATURE 



[June i6, i 



from E Q towards either pole, the declination of a 

 heavenly body (corresponding to latitude on the earth) is 

 measured, and from the first point of Aries (the celestial 

 meridian passing through which is the prime meridian 

 of the heavens) right ascension is measured round east- 

 ward, instead of east and west, as longitude on the earth. 



Now let the reader imagine his eye to be at C, that 

 the earth is a transparent sphere, and that it and its 

 atmosphere are absolutely free from refrangibility, then 

 every point in the celestial meridian would be seen through 

 its prototype on the surface of the earth, and any and 

 every angle at C, measures the same arc of the celestial 

 meridian, and of the one on the surface of the earth. 

 Now, what is true here holds good for every other 

 meridian— every other great circle of the celestial con- 

 cave, and the one that has the same plane on the earth's 

 surface. 



The latitude of a place is the arc of a meridian, inter- 

 cepted between the place and the equator, consequently 

 ^ O is the latitude of O ; but ^ O and E z are both measured 

 by the angle ^CO, and EZ = PR, each being the com- 

 plement of P z, which accounts for one of the best-known 

 rules in nautical astronomy, viz. that the altitude of the 

 pole = the latitude of the place ; so that if there was a 

 star at P, its altitude would give the latitude without any 

 further computation. Let s, s', &c., be the positions of 

 stars on the meridian. But very little consideration will 

 make it clear that if the observer can measure one of the 

 arcs S R, S^R, s%, or S^H, and at the same time get the 

 star's declination from the Nautical Almanac, it is a 

 mere question of addition and subtraction of arcs to ob- 

 tain the latitude. P S is the complement of the declina- 

 tion, and PS + SR = ES'-ZSl = ES^-f-ZS2 = ZS^-ES^ 

 = EZ, the latitude of O. This is known as finding the 

 latitude by the meridian altitude. It gives one line 

 parallel to the equator, on which the ship must be 

 situated. To fix her position on it, we must get another 

 line to cross it, which passes through the position of the 

 vessel, when, manifestly, she must be at the point of inter- 

 section. The nearer the cross is to right angles the 

 better. To do this we must find the time, and thence by 

 comparison with the time at the prime meridian (Green- 

 wich is now accepted by most nations as the prime 

 meridian), the meridian on which the ship is situated. 

 Neglecting minor differences and irregularities, the sun 

 appears to revolve round the earth in twenty-four hours, 

 or at the rate of is'^ in an hour. Now if we find that 

 it is 9 a.m. at the ship, when it is noon at Greenwich, the 

 ship must be in longitude 45° W. If, on the other hand, 

 the chronometer showed 5 a.m. the vessel would be in 

 longitude 60° E. The Greenwich time may be calculated 

 from a lunar observation, which the perfection of the 

 modern chronometer and the shortening of voyages have 

 driven out of the field. To get the time at ship, we have 

 recourse to spherical trigonometry, or rules and tables 

 based on it, to calculate the hour angle. The sun's 

 westerly hour angle is the apparent time at place (A.T.P.), 

 which is converted into mean time (M.T.P.) by applying 

 the equation of time, which, like declination, «&c., is sup- 

 plied by the Nautical Almanac. If the body observed is 

 a star, we get the M.T.P. by adding to the hour angle 

 the star's right ascension, and subtracting that of the 

 mean sun, which is a transposition of the well-known 

 and useful equation, >l<'s hour-angle = M.T.P. -I- mean 0's 

 R.A. - >|<'s R.A. which we use for time azimuths, and for 

 finding when a body will cross the meridian, for when 

 hour angle = o 



M.T.P. = >|<'s R.A. - mean 0's R.A. 



Now, just as the simplest way of getting the latitude is 

 by a body on the meridian, so the best way of calculating 

 the time for longitude is by using the altitude of the sun 

 or a star on the prime vertical {i.e. the vertical circle 

 passing through the E. and W. points of the horizon). If, 



NO. 1494, VOL. 58] 



by means of this altitude, or any other way, we could tell 

 the exact instant that the body was on the prime vertical, 

 there being a right angle in the triangle A P z (Fig. j), we 

 could calculate the time by right-angled spherics from 

 any two of the three sides, colatitude, polar distance and 

 zenith distance, or their complements latitude, declina- 

 tion and altitude. But in practice, whilst it is easy to 

 get the meridian altitude, it is impossible to be sure of 

 getting the altitude exactly on the prime vertical. It is, 

 however, comparatively easy to observe a body near 

 enough to the prime vertical to be very favourably 

 situated for finding the time by oblique spherics (or 

 formula deduced from it), and thence the longitude ; and 

 this, combined with the meridian altitude, is perhaps the 

 simplest and most favourable method of fixing the posi- 

 tion at sea. However desirable, it is by no means neces- 

 sary that the body be near the prime vertical, though, 

 generally speaking, the further it is removed from it, the 

 less favourable the conditions, till at last the triangle 

 becomes an impossible one. 



Every particular star is, at every instant of time, in the 

 zenith of some spot on the surface of the earth. At any 

 given instant of time, let z, in the accompanying figure, 



Fig. 2. 



be this spot, as it would be seen from the zenith ; 

 then the concentric circles represent circles of equal 

 altitude on the earth's surface, i.e. everywhere on 

 the outermost circle the star will be on the horizon 

 (neglecting refraction, &c.). On all places in the next 

 circle the altitude will be 22|^°, on the next 45°, &c. ; and, 

 of course, there may be an infinite number of imaginary 

 circles between the spot under the star and the outer 

 circle, which brings it on the horizon. Now, it is evident 

 that at whatever point on any of the above circles an 

 observer may be situated, a tangent to the circle at that 

 point will be at right angles to the bearing of the body ; 

 but a small portion of the circle may be represented by 

 a similar portion of the tangent, and it is evident 

 that the larger the circle (which is equivalent to the 

 smaller the altitude), the longer the portion of its cir- 

 cumference that may with impunity be treated as a 

 straight line. This straight line is known as " a line ox 

 position." The line of position obtained from a meridian 

 altitude differs from all others in this, that the ship is not 

 only on the circle of equal altitude, but on its vertex,^ 

 and the tangent may be assumed as of infinite length. 



1 Compare figure in paper on " Navigation," (p. 104) illustrating composite 

 sailing, where, however, the circles that touch the parallel are great circles. 



