LU.VAE ECLIPSES.] 



ASTRONOMY. 



977 



= 1819* -9 and C P, to the hourly motion of the moon in 

 declination minus hourly motion of the sun in declina- 



Fig. 128. 





tion, or 14' 48* '1; the point P being placed above C, as 

 the moon was moving northward. Join O P and draw 

 parallel to it through G the line N G H, which represents 

 the path of the moon, and on N H let fall the perpen- 

 dicular C K. At 14h. 10m. 29s. -6 the moon was at G. 

 To find its position at 14h. we make the proportion : 

 As i^im. : 10m. 29s. "6 : : O P : G X. The position of 

 the moon's centre at 14h. is set at X, and its position at 

 ]6h., 15h., <tc , may be laid down in the same manner 

 by adding the distance OP. Subdividing those into 

 sixty parts, the beginning, end, and middle of the eclipse 

 will be ascertained, answering to the times when the 

 moon's centre is at E, H, and K. 



The calculation of the eclipse may be performed accu- 

 rately as follows : In the right-angfed triangle O C P we 

 have C O = 1819 r 9 and C I' = 888" 1, then C P : R : : 

 C O : tan C P O. 



CO- 1810' -9 = 3-2000475 

 888* ! = 2-9484619 



C P O = 63 off 16* = 0-3115856 log. tan. 

 Sin. CPO:R::CO:OP. 



CO = 3-2600475 

 Kin. CPO = 9-9536150 



O P = 2025" -0 = 3-3064325 



The angle C P O = angle C G K, G K and O P being 

 parallel. The angle C G E = 116 W 44* ; the side C G 

 -863* -7, and the line C E=3642*-2. The angles C E G 

 and the side E G of the triangle C E G are found 

 thus: 



C E : sin. C G E : : C G : sin. C E G. 

 Comp. CE = 6-4386362 

 Sin. CGE = 9-!C.::<;i:,o 



C E G = 12 18' 1 8* Sin. 9 -3286141 

 Therefore the angle E C G = 51 40' 58". 



Sin. C G E : C E : : sin. E C G : E G. 

 Comp. sin. C G E = 0-0463850 

 CE= 3-5613638 

 Sin. EGG = 9-8946428 



EG = 3179*7 = 3-5023916 

 To Determine the Time of Describing EG. 

 As OP : Hi. : : EG ( = 3179s. -7) : lh. 34m. 12s. -8, 

 which, subtracted from the time of opposition in right 

 ascension, or 19h. l?m. 55s. -6 (Greenwich time), gives 

 the time of the beginning of the eclipse, or first contact 

 with shadow, at 17h. 43m. 42s. -8. The middle of the 

 eclipse is found by the triangle C G K similar to C P O, 

 in which the angles and hypothenuse are given to find 

 CKaudKG. 



R : CG : :sin.CGK : CK : : cos. CG K : G K. 

 Sin. CGK = 9-9536150 Cos. C G K = 9-6420319 

 CG= 2-9363029 CG= 2-9363629 



C K = 776" 



VOL. I. 



2-2 -8899779 



378*-8=2 -5783948 



To Determine the Time of Describing G K. 

 2)25": lh. : : 378" -8 : 673s. -4 = llm. 13s. -4, which, 

 added to the Greenwich mean time of opposition, 

 gives 19h. 29m. 9s. for the middle of the eclipse. The 

 duration of the eclipse will consequently be 3h. 30m. 

 52s. '4, and the end 21h. 14m. 35s. -2 Greenwich mean 

 time. The magnitude of the eclipse is found by 

 subtracting C K = 12' 56" "2 from C R = 44' 23* -4, 

 whence K R = 31' 27*-2 ; to which adding the 

 moon's semi-diameter, we obtain R L = 47' 46* O. 

 Dividing this by the moon's diameter, or 32' 37" '6, 

 the magnitude of the eclipse = 1 "464 on the northern 

 limb. 



The beginning and end of total darkness is found 

 as follows : With the radius of the earth's shadow, 

 or C B diminished by the moon's semi-diameter, or 

 44' 23" -4 16' 18" -8 =28' 4" -6, or 1684" -6, describe 

 a circle about the centre C cutting H N in the points 

 S and T, which will represent the points of beginning 

 and end of total darkness. 



In the triangle C G S, C G = R63 7, C S = 1684-6, 

 and the angle C G S = 11C 0' 44". Hence C S : sin. C US 

 : : C G : sin. C S G. 



Comp. CS = 67735032 



Sin. C G S = 9 9536150 



CG = 29363629 



C S G=27 26' 12". Sin. = 9 6634811 

 And the angle S C G = 36 33' 4". 



Sin. C G S : C S : : sin. S C G : S G. 

 Conip. sin. C G S = 0-0463850 

 C S = 3 2264968 

 Sin. S C G = 9 7749107 



G 8 = 11163 = 30477925 



2*o Determine the Time of Describing G S. 

 2025-0 : lh. : : 1116 3 : 1984-0= 33m. 4s. -6, which 

 being subtracted from 19h. 17m. 55s. -6, gives 18h. 44m. 

 51s. for the time of disappearance or beginning of total 

 darkness. The duration of total darkness is therefore 

 lh. 28m. 36s., and the time of the end of total darkness 

 or reappearance = 20h. 13m. 27s., the middle of the 

 eclipse occurring at 19h. 29m. 9s. 



The semi-diameter of the penumbra is equal to the 

 semi-diameter of the shadow -f- the sun's diameter, or 

 44' 23" -4 + 32' 15-8 = 76' 39"' 2. Let the circle ARE 

 represent, in this case, the limits of the penumbra, then 

 C E = 76' 39" "2 + 16' 18" 8=92' 58" -0. In the triangle 

 CGE, the angle CGE=116 0' 44". CG=863'7 and 

 CE = 5578"-0. 



C E : Sin. C G E : : C G : sin. C E G. 

 Comp. log. CE = 6-2535215 

 bin. CG K = 9-9536150 

 CG = 2-9363629 



C E G=7 59- 56" Sin. = 9-1434994 

 And angle E GG=55 59' 20". 



Sin. C G E : C E : : sin. E C G : E G. 

 Comp. sin. C E G = 0463850 

 C E = 3 7464785 

 Sin. E C G = 9-9185174 



EG=5144" -9 = 3-7113809 



As 2025 : 1. h. : : 5144 9 : 2h. 32m. 26s. -5, which gives 

 the time of describing E G. This subtracted from 19h. 

 17m. 53s. -6, gives 16h. 45m. 29s. -1 for the time of first 

 contact with the penumbra ; and the whole duration being 

 5h. 27m. 19s. -8, we get the time of ending, 22h. 12m. 

 48s. '9 for the last contact with the penumbra. 



An eclipse of the moon can only be seen at those parts 

 of the earth where the moon is above the horizon, as well 

 as the shadow of the earth, or at least a portion of this 

 shadow. As this can only take place when the sun is 

 below the horizon, it is only during the night that 

 eclipses of the moon are visible. It may happen, how- 

 ever, that the eclipses may be seen for a few moments 

 before the setting of the sun, or after its rising. This is 

 due to the refraction of the atmosphere, which, when 



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