SOLAR ECLIPSES.] 



ASTRONOMY. 



031 



from the point T (which is situated exactly between S 

 and 12) on the line perpendicular to C M, we obtain the 

 extremities of the longest axis of the ellipse, or the 

 points at which Greenwich will appear at 6 A.M. and 6 

 P M. At the times of the equinoxes these hours will be 

 projected at the edges of the disc (as they are almost so in 

 the present instance), but at all the other times of the 

 ycur they will be more or less distant. 



In order to obtain the position of Greenwich at any 

 other hour of the day, we take, with a radius equal to 

 T 6, the sine of 15, or one hour of time, which is set off 

 on each side of the point T. The sines of 30, 45, 60, 

 75 may be obtained and set off in the same way. 

 Through these points draw lines parallel to C M. With 

 a radius equal to S T take the sines of 75, 60, 45, 30, 15, 

 which are marked off on each side of the line T 6 respec- 

 tively at the points 15, 30, 45, <tc., as before. By 

 drawing an elliptic curve through those points, the 

 several positions of Greenwich at each hour of the day 

 from sunrise to sunset are readily obtained ; and by con- 

 tinuing it on the opposite side, its position (here repre- 

 sented by the dotted line) is represented during the 

 night. The points at which the ellipse touches the circle 

 A D B show the time of sunrising and sunsetting. It 

 will be seen that the ellipse will be more open near the 

 time of the solstices, and more eccentric near the equi- 

 nozeo (as is the case iii the present instance). The 

 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, represent 

 the position of Greenwich at those hours, which are 

 I from noon towards the right. If the sun's decli- 

 nation had been north, the diurnal path of Greenwich 

 would be on the lower or dotted portion of the ellipse. 

 If possible, the figure should be constructed on such a 

 cale that the hours might be divided into minutes with 

 lufficient certainty. 



Having represented the position of Greenwich at the 

 various hours of the day, as they appear to a spectator 

 nn the sun, the next thing to be done is to draw the 

 moon's apparent path across the earth's disc. From the 

 same scale of equal parts used in the radius C B, measure 

 off an interval equal to the moon's latitude, or 37' 43" ; 

 and, an the moon's latitude is north, make it equal to 

 C G, above the ecliptic A B. Take in the same scale, 

 C O, equal to 31' 49*, and apply it on the line C B, from 

 C to O. This quantity represents the hourly motion of 

 the moon from the sun in longitude. Draw O R perpen- 

 dicular to C B, and make it equal to 3' 9", the hourly 

 motion of the moon in latitude ; and as the moon is 

 moving northwards, set it above the line C B. The line 

 C R, joining the points C and R, represents the relative 

 hourly motion of the sun and moon ; and parallel to this 

 line draw the orbit of the moon, or L G N, on which, by 

 means of the hourly motion C R, we 

 can mark the position of the moon 

 from hour to hour ; and as the mo- 

 ment of new moon at Greenwich is 

 at three minutes past noon of ap- 

 parent time, the position of the moon 

 at apparent noon is found by taking 

 the proportion of 60m. : 3m. : : the 

 distance C R, to the distance G XII., 

 which is measured to the left of the 

 point G, and shows the position of 

 the moon at twelve o'clock, or noon. 

 By taking the line C R in the com- 

 passes, the other hours may be marked 

 off which represent the places of the 

 moon at those times. If the scale 

 be made sufficiently large, those spaces 

 may be subdivided into sixty parts 

 or minutes. 



In order to find the times at which 

 the eclipse is greatest, those times 

 must be found on the path of the 



pectator, and the path of the moou, j 



which are marked with the same 



times, and which are at the least distance from each 

 other. The times which best correspond to those 

 conditions in the present case are those of 12h. 



52m., or 52 minutes past noon of apparent time. The 

 appearance of the moon at any hour may be shown by 

 taking its semi-diameter to the adopted scale of equal 

 parts and which in this instance=15' 54"~6 and with 

 this radius to describe a circle whose centre is the point 

 where the moon's centre is at the given time. The 

 position of the disc of the sun at the same moment may 

 be represented in the same manner, by taking a radius 

 equal to the semi-diameter of the sun =16' 6"' 5, and 

 describing a circle taking the same time on the path of 

 the spectator for a centre. The relative positions given 

 in the diagram are those at which the eclipse are greatest, 

 when the magnitude of the eclipse = 0'976, on the 

 northern limb, the sun's diameter being 1 '000 ; and as the 

 moon's semi-diameter is less than that of the sun, the 

 eclipse will be annular and partial. The sun's centre 

 must be invisible over all that portion of the earth, re- 

 presented as being covered by the moon's disc, and 

 throughout a much larger area some portion of the sun's 

 disc will be obscured. The extent of this area will be 

 found by describing a circle with the same centre, and 

 whose radius is equal to the sum of the semi-diameters 

 of the sun and moon, measured on the adopted scale. 



In order to determine the times of the beginning and 

 end of the eclipse, we take from the scale of equal parts 

 a distance equal to the sum of the semi-diameters of the 

 sun and moon=32'l"'l, and beginning nearL, place one 

 foot of the compasses on the moon's path, and the other 

 on the path of the spectator, and shift them backwards 

 and forwards until the same times are found on the two 

 paths, which are this distance apart. This will give the 

 time of the beginning of the eclipse, which in the pre- 

 sent case is lib. 32m. A.M., apparent time. In the same 

 manner find the corresponding times on the other side of 

 the moon's path, and the end of the eclipse will be de- 

 termined, which in the present case is 2h. 9m. P.M., of 

 apparent time. We thus determine : 



Apparrat Time. Mean Time. 



llh. 32m. A.M. llh. 41m. A.M. 

 Oh. 62m. P.M. Ih. 1m. P.M. 

 2h. 9m. P.M. 2h. 18m. P.M. 

 When this projection is made on a sufficient scale, and 

 carefully finished, it will give the above times accurately 

 to one or two minutes, and furnish a useful chart of the 

 various phases of the eclipse. By drawing different 

 parallels of latitude, we can determine the phases of the 

 eclipse for any place. The results are obtained in appa- 

 rent time, because both the moon's path and the path of 

 the spectator correspond to apparent time. 



PROJECTION BF RIGHT ASCENSIONS AND DECLINATIONS. 

 Instead of employing longitudes and latitudes in the 

 projection of a solar eclipse, we may make use of right 

 Fig. Ml. 



Beginning of Eclipse 

 Greatest Obscuration 

 End of Eclipse 



20 o 10 



ascensions and declinations ; and as tliose are the ele- 

 ments given in the Nautic-il Almatiac for these pheno- 

 mena, it may be convenient to append' an example for 



