180 



ASTRONOMY. 



[SOUK ECLIPSES. 



di*c may ba laid down in a similar way, and its position 

 from hour to hour noted. In order to determine the 

 tune at which the eclipse appears greatest at thu locality, 

 we must find that point in the moon's 

 path and the path of the observer 

 marked with the same times, and 

 which are at the least distance from 

 each other. The beginning or end 

 of the eclipse will be determined by 

 finding those points in the moon's 

 path and in the path of the spectator 

 which an marked with the same 

 times, and whose distance is equal 

 to the sum of the semi-diameters 

 of the sun and moon. As an illus- 

 tration of this method we will choose 

 the solar eclipse which was visible 

 in the British Islands, March 15th, 

 1868 (Figs. 140 and 141), and gene- 

 rally seen throughout the north of 

 Europe. This is the greatest which 

 has occurred or will happen in this 

 country for many years. The times 

 and phases of the eclipse are for 

 the latitude of Greenwich, or 51 

 28' 38". 



By the Nautical Almanac the time 

 of new moon is March 15d. Oh. 12m. Os., mean time, 

 corresponding to March 13d. Oh. 2 '9m. apparent time, 

 the equation of time being 9 '1m. Th following ele- 

 ments are calculated for that epoch ; 



<r / // 



Sun's longitude . . . . 354 38 33 

 Sun's declination . . . .27158 

 Moon's latitude . . . . 37 43 N 

 Moon's hourly motion in longitude . 34 18 

 Sun's hourly motion in longitude . 2 29 

 Moon's hourly motion in latitude . 039 

 Moon's equatorial horizontal paralla^ 5S 15 -2 

 Sun's equatorial horizontal parallax . 00 8 '6 

 Moon's true semi-diameter . . 15 54-6 

 Sun's true semi-diameter . . 16 6 3 



The geocentric latitude, which is found by applying 

 the angle of the vertical (p. 922) to the geographical 

 latitude (and which in this case is 11' 13"), - 51 17' 4. 

 The moon's equatorial horizontal parallax being that 

 which is given by the tables, the horizontal parallax for 

 any other latitude will be found by applying the follow- 

 ing correction : 



the relative positions of the two bodies, will be 57' 59" -4, 

 which is the semi-diameter of the earth as seen from the 

 moon, that of the moon seen from the earth being 

 fig. 110. 



The moon's horizontal parallax for Greenwich will 

 therefore be 68'8"-0; and as the relative positions of 

 the sun and moon will remain the same if the sun be 

 suppoMd to retain a fixed position, and the moon be 

 supposed to be affected with the difference of both their 

 parallaxes, the relative parallax, or that which affecti 



15' 54" -6. The relative sizes of their discs will be in 

 the same proportion if viewed from any distance. 

 With a radius A C (Fig. 140) equal to 57' 69"-4, or if 

 practicable with one of 3,479 parts from any scale of 

 equal parts, describe the semicircle A D B with the 

 centre G, which represents the northern half of the en- 

 lightened part of the globe of the earth viewed from the 

 sun. If the place were in south latitude, the lower half 

 of the earth's disc should be that represented. The line 

 A C B represents the ecliptic, and the perpendicular C D 

 the axis of the ecliptic. Take from a sector, or any 

 other convenient scale, the chord of 23 28' (which is tho 

 obliquity of the ecliptic) to the radius C B, and set it oil" 

 from D to H and in the periphery of the circle, or the 

 angle D H 23 28' may be at once set off. Draw the 

 straight line EH, cutting CD in K. By consi<l>-rin,' 

 Figs. 130, 137, 138, 139, it will be seen that the north 

 pole of tho earth, as viewed from the sun, will constantly 

 appear on this line E K H, E being its position at the 

 autumnal, H at the equinox, and K. at the solstices. It* 

 distance from H at any time will be equal to the versed 

 sine of the sun's longitude, or its distance from K will 

 be the sine of the difference between the sun's longitude 

 and 90 or 270. To the radius E K take the sine of 

 354 38 ; -(5 - 270" - 84 38' 6, and set it off from K to P, 

 the north pole of the earth ; for when the sun's longi- 

 tude is between 270" and 90, the north pole lies to the 

 right of the pole of the ecliptic, and to the left when it 

 is in tlio other six signs. Draw C P, which is tho 

 northern half of the earth's axis, and produce it until it 

 cuts the circle A D B in M. 



In order to draw tha parallel of latitude of Greenwich 

 on the earth's disc as seen from the sun, from sunrise to 

 sunset, the following method may be taken : -If the 

 latitude of the place were exactly equal to tho sun's de- 

 clination, it would be vertical at noon, and the place of 

 observation would be at the centre C. But as the latitude 

 of the place exceeds the sun's declination by 53 24', it 

 must be seen that distance north of the place where the 

 sun is vertical, or when projected on the disc ; this will 

 be the sine of that angle which is set off from C to 1 12, 

 which is the apparent position of Greenwich at noon of 

 March 15. The position of Greenwich at midnight is 

 determined in the same manner by taking C S equal to 

 the sine of 49 10' to the radius A C, and the point S 

 will be its position at midnight. It is easily seen that 

 the line 12 S will be the shortest diameter of tho ellipse 

 into which tho circle of latitude is projected. To deter- 

 mine the length of the longest diameter, as it is not 

 shortened by being viewed obliquely, it will be equal to 

 the diameter of the parallel of latitude, or to the cosine 

 of the co-latitude = 38" 43' ; and setting off this distance 



