Parallax and augmentation of semidiameter. 16. Calculate the moon's parallax in right ascension and declination, and her augmented semidiameter, for Providence, when her hour angle is 58° 0′ 18", declination 21° 42′ 52" S., and horizontal parallax 61′ 16′′.2 The latitude of Providence is 41° 49′ 22′′ N. Ans. The parallax in right ascension = 2523′′.2 17. Calculate the moon's parallax in right ascension and declination, and her augmented semidiameter, for Mount Joy Observatory, Portland, when her hour angle is 58° 15' 54", declination, 21° 42′ 52" S., and horizontal parallax 61' 16".2. The latitude of Mount Joy Observatory is 43° 39′ 52′′ N. Ans. The parallax in right ascension 2426′′.0 66 declination = 2864".2 the augmented semidiameter 1003".8 18. Calculate the moon's parallax in right ascension and declination, and her augmented semidiameter, for Mr. Bond's observatory, in Dorchester, when her hour angle is 60° 38' 34", declination 22° 42′ 8′′ N., and horizontal parallax 56' 14".4. The latitude of Mr. Bond's observatory is 42° 19′ 10′′. Ans. The parallax in right ascension 2375".3 declination = 16324.9 the augmented semidiameter = 928".5 Solar eclipse. CHAPTER XII. ECLIPSES. 149. A solar eclipse is an obscuration of the sun, arising from the moon's coming between the sun and the earth; and occurs therefore at the time of new moon. It is central to an observer, when the centre of the moon passes over the sun's centre. It is total, when the moon's apparent disc is larger than the sun's, and totally hides the sun. It is annular, when the moon's apparent disc is smaller than the sun's, but is wholly projected upon the sun's disc. The phase of an eclipse is its state as to magnitude. 150. An occultation of a star or planet is an eclipse of this star or planet by the moon. A transit of Venus or Mercury is an eclipse of the sun by one of these planets. 151. Problem. To find when a solar eclipse will take place. Solution, Let O (fig. 57) be the sun's centre, and 0, the moon's centre at the time of new moon, and let the_latitude of the moon at new moon = 001. When a solar eclipse will happen. Let ON be the ecliptic, and N the moon's node, so that NO, is the moon's path. Let 1 N the inclination of the moon's orbit to the ecliptic; Draw OP perpendicular to the moon's orbit, and if, when the moon arrives at P, the sun arrives at O', the least distance of the centres of sun and moon is nearly equal to O'P. Now the triangle OPO' gives n = ratio of the sun's mean motion divided by the moon's we have = T' nearly, (798) 00' = n X 0 ̧P = n ẞ sin. N. Draw O'B perpendicular to OP, and we have nearly The apparent distance of the centres of the sun and moon is affected by parallax, and the true distance is diminished as much as possible for that observer, who sees the sun and moon in the horizon, and OP vertical, in which case the diminution is equal to the difference of the horizontal parallaxes of the sun and moon. Let, then, we have P = the moon's horizontal parallax, π the sun's horizontal parallax, the least apparent dist. OP — (P — π) - sin.2 N-P+. (800) When a solar eclipse will happen. Now, an eclipse will take place, when this least apparent distance of the centres is less ameters of the sun and moon. than the sum of the semidiThus, let s = the moon's semidiameter, In case of an eclipse, we must have Now, in the last term of (802) we may put for N its mean value, and for its mean value obtained by supposing it equal to the preceding terms, which gives |