in 



ASTRONOMY. 



[LUNAR ECLIPSE 



The commencement of the ectipM accordingly took 



pUoa at 7h. 33m. -8 morning, and the end at loli. 39m. 



The distance of the centres corresponding to 



the middle of the eclipse, or \ cos. S3' 8* ; and the 



eclip**! part, or ^- + p + P - X cos. - 21' *, 



(allowing for the effect of atmosphere), or the magnitude 

 of the eclipse, reckoning the uiixm's diameter at 1 

 071. 



In order to determine the time at which the moon 



D 

 entered the penumbra, we assume, rf~P + p+o' + 2~ 



86' 9* -8, whence the two values of t are 2h. 44m. -32 and 

 2h. 58m. -64, which, applied to the time of opposition, 

 Oh. 13m. *6, gives the time of commencement at Oli. 

 l.'uii. -0 a.m., and the time of ending at llh. 07m. 'D a.m. 



GRAPHICAL Cossrm-iTiojr OF A LUNAR ECLIPSE. 

 Instead of calculating the various phases of a lunar 

 eclipse, they may be obtained by the following graphical 

 process, applied to the eclipse of November 13th and 

 14th, 1845. 



At Paris, mean noon of November 13th, the longitude 

 of the sou exceeded that of the moon by 186 20 1" -4. 

 On the 14th, at the same hour, it exceeded it by 

 J71 43' 8* '6. Finding, by interpolation, the instant at 

 which the difference of longitudes was exactly 180", or 

 the moment at which the moon was in opposition, we 

 obtain, November 14th, nt Ih. 4m. 20s. -9 morning. At 

 this time the parallax of the moon was 55' 39* '6 ; that of 

 the sun, 8* -7 ; the semi-diameter of the moon, 15' 10" -1 ; 

 and that of the sun 1C' 12* "3 ; whence, as before, we 

 conclude that the semi-diameter of the shadow of the 

 earth was 39' 36*, or increasing it by -fa = 2415* '6. In 

 addition to this, we find that at Oh. 30m. on the morn- 

 ing of the 14th, the longitude of the sun exceeded that 

 of the moon by 180 16' 33*7 ; and that the latitude of 

 the moon was 25' 57*'C S. At Ih. 30m. of the same 

 morning, the excess of the longitude of the sun was 

 179 47*37*7, and the latitude of the moon 28' 61*-5 S. 

 Let the circle A B C D (Fig. 127) represent the dioien- 



i(t. 127. 



ions of the shadow of the earth at the distance of the 

 moon(smid. - O A - 2415* -6), let E E' be the ecliptic. 

 At Oh. 30m. of the morning of the 14th, the lom,'>tude 

 of the sun surpassed that of the moon by 180 16' 33*7, 

 the longitude of the centre, O, of the shadow, there- 

 fore, only exceeded that of the moon by 993*7. Accord- 

 ing to the scale adopted, set down OF- 993*7. Make 

 >ilar to E E' and mark off FO - 25' 57*-6, 

 which i the latitude of the moon at the time, and O is 

 the position of the centre of the moon at Oh. 30m. morn- 

 ing. In the name manner, take OH- 12' 22* -3. or 

 742*3, and H K - 28' 61*-5, or J731*-6 ; and K will be 

 the position of the centre of the moon at Ih. 30m. morn- 



ing. Draw a right line, M M', through the points G and 

 his line will represent the path of the moon during 

 the eclipse, in reference to the shadow of the earth. The 

 point N is the position of the moon at the moment of 

 opposition, or at Ih. 4m. 20s. 1 9 morn. 



With a radius equal to the sum of the radii of the 

 shadow and of the moon, or 3325*7 describe a circle 

 with the centre O. The circumference will cut the line 

 M M' at two points, L L' ; and it is plain that, if with 

 those two points as centres, we describe two lesser circles 

 with the radius of the moon, or 910*-1, these two circles 

 will touch the circumference of the shadow A B C D, 

 and represent the position of the moon at the beginning 

 and end of the eclipse. If, moreover, the perpendicular, 

 P O, be raised on M M', the point P represents the 

 position of the centre of the moon, at the middle of the 

 eclipse. 



As the moon employs an hour In passing from G to K, 

 we may, by proportion, determine the time it takes in 

 pausing from N to P (if we make the figure large enough) ; 

 and we thus find that it takes 5ui. 41s. in going through 

 this distance, or 5m. 41s. before the opposition, or it U 

 at Oh. 58m. 40s. that the middle of the eclipse happens. 

 In the same manner, we find that the moon should be 

 Ih. 30m. 19s. in passing from P to L' ; and it is therefore 

 at llh. 29m. 21s. of the evening of November 13th that 

 the eclipse commences, and at 2b. 38m. of the morning 

 of the 14th that it ends. The magnitude of the eclipse 

 is found, likewise, by this graphical construction ; and in 

 this case we perceive that it is partial, since at the 

 moment when the centre of the moon is nearest the 

 centre of the shadow, a portion of its disc lies vithimt 

 the latter circle. If we draw the diameter Q S, directed 

 towards the point O, and we take the proportion of this 

 diameter S R, which is in the shadow, and the diameter 

 itself, we find tho magnitude. In the present case this 

 amounts to 0-92, the diameter being 1-00- Should the 

 diameter Q S be within the circle of the shadow, or the 

 eclipse be total, the various phases, it will be seen, can 

 be measured off with equal facility, as in the instance 

 here given. 



Instead of making use of latitudes and longitudes, the 

 right ascensions and declinations of the sun and 

 moon may be employed, as in the following ex- 

 ample of the total eclipse of October 24, 1855 

 (Loomis Ast.) The Greenwich time of opposition 

 in right ascension is I9h. 17m. 55s. '6, or the 

 Washington time = 14h. 10m. 29s. '6, for which 

 time the Nautical Almanac furnishes the fol- 

 lowing data : 



a I * 



Declination of moon . . 11 42 24-3 north. 

 ]>eclination of sun . . . 11 50 48-0 south. 

 _ Moon's horizontal parallax 



(lat.45 ) - 69 390 



Sun's horizontal parallax 8 '6 



Moon's semi-diameter . . 16 188 

 Sun's . . . = 16 7-9 



Moon's hourly motion in 



R. A. ...- 3322-1 

 Sun's - 223-6 



Moon's hourly motion in 



declination ....- 15 40-1 north. 

 Sun's ,, ,, - 052-0 south. 



The semi-diameter of the earth's shadow, or CB 

 (Fig. 128) - 59' 39* -0 + 8* -6 16' 7*'9 - 43'39* 7, 

 to which adding one-sixtieth for refraction, C B 44'23*-4, 

 and the distance of the moon's centre, or C E 60 7 42* '2. 

 Tho hourly motion of the moon from the sun in right 

 ascension is 30' 58* '6, and this reduced to the arc of a 

 great circle by multiplying it by the cosine of the moon's 

 declination - 1819* -9. 



From the centre C (Fig. 128), with the radius C B de- 

 scribe tho circle A R B, or the shadow of the earth. 

 Draw the line A C B to represent a parallel to the equator, 

 and make G perpendicular to it, equal to 14' 23*7, or 

 the sun's declination minus the moon's declination, the 

 point G being taken below C as the centre of the moon 

 is south of the centre of the earth's shadow. Make C O 



