While he whom Toil has braced, or manly play, As light as air each limb, each thought as clear as day. O who can speak the vigorous joys of health! 28. SAINT AUGUSTINE. Augustine was born at Thagaste, a town in Numidia, in the year 354. He was a judicious divine, and the most voluminous writer of all the Fathers. He died in 430, at the age of 77. 29.-JOHN BAPTIST BEHEADED. This day was formerly denominated Festum Collectionis Sancti Johannis Baptista; or, the feast of gathering up St. John the Baptist's relics; but afterwards, by corruption, Festum Decollationis, the festival in remembrance of his being beheaded. His nativity is celebrated on the 24th of June, which see. *31. 1422.-HENRY VI BEGAN TO REIgn. He was chaste, pious, compassionate, and charitable; and so inoffensive, that the bishop, who was his confessor for ten years, declares, that in all that time he had never committed any sin that required penance or rebuke. In a word, he would have adorned a cloister, though he disgraced a crown; and was rather respectable for those vices he wanted, than for those virtues he possessed. He founded the colleges of Eton and Windsor, and King's College in Cambridge, for the reception of those scholars who had begun their studies at Eton.-Smollett. Astronomical Occurrences In AUGUST 1817. The Sun enters Virgo at 28 m. past 10 in the morning of the 23d of this month, and the days then begin to decrease with greater rapidity than they have done since the Sun entered Cancer; as will appear evident from the following TABLE Of the Sun's Rising and Setting for every fifth Day of the Month. Friday, Wednesday, Monday, Saturday, Thursday, Tuesday, Sunday, Aug. 1st, Sun rises 20 m. after 4. Sets 40 m. after 7 28 4 32 7 6th, 36 7 • 45 7 54 2 12 21st, 26th, 11th, 16th, 21st, 26th, 31st, TABLE For every fifth Day of the Month. m. 5. August 1st, to the time by the dial add 5 57 6th, 5 33 4 54 2 56 38 10 24 15 6 58 48 The Equation of Time, or quantity to be added to the time marked by a good sun-dial, also decreases from the beginning of the month, till it become nothing at the end of it; as appears from the following Table. From that time it increases till it attain its annual maximum, on the 3d of November, when it is 16 m. 16.1 s. 1 0 The Moon commences her last quarter at 51 m. U past 2 in the morning of the 5th of August. The change takes place at 7 in the morning of the 13th. She enters her first quarter at 50 m. after 4 in the afternoon of the 19th; and she is full at 36 m. past 7 in the evening of the 26th. The Moon may likewise be seen to pass the meridian at the following times in the course of the present month. August 22d, at 40m. after 8 in the evening 9 • 23d, 39 10 28 11 The Moon and Mars will be in conjunction at 58 m. past 9 on the evening of the 5th; and she will also be in conjunction with the star in Libra at 27 m. past 6 in the evening of the 18th. a Mercury will be in conjunction with the star marked in Leo on the 10th, when the star will be 68' south of the planet. Jupiter and the star marked ẞ in Scorpio will also be in conjunction on the 10th; and the star will then be 23' north of the planet. Mercury will be in his superior conjunction at past 2 in the morning of the 2d. Jupiter will be in quadrature at past 5 on the evening of the 25th. Saturn will be in opposition at 8 in the morning of the 26th; and Mars will be in quadrature at 30 m. after midnight of the 28th. There will only be one eclipse of Jupiter's satellites visible this month. The first satellite will be eclipsed on the 12th; and the emersion will take place at 31 m. after 8 in the evening. ON THE CALCULATION OF ECLIPSES. AMONG the various phenomena of the heavens there are none which have awakened so much curiosity, excited such interest, or caused such universal terror, as eclipses; nor are there any of the calculations of the astronomer which has excited so much astonishment in the minds of the unlearned in all ages, as those by which he is enabled to predict them with such undeviating accuracy. In treating of eclipses, the observations may be conveniently arranged under three distinct heads: a description of the general phenomena which they present; a determination of the circumstances under which they can take place; and the method of predicting them. On the first of these heads we have already treated in the popular view of eclipses given in our former volumes; viz. vol. i, p. 181; and vol. ii, p. 179 and seq. We have also indicated our intention (T.T. 1815, p. 227) to explain the other two; and shall now endeavour to redeem that pledge.. The first subjects which present themselves to be determined in this research, are the lengths of the conical shadows projected behind the Earth and the Moon, in order to ascertain whether the former extends to the orbit of the Moon, and the latter to that of the Earth. On the Lengths of the Shadows projected by the Earth and Moon. To render this inquiry as simple as possible, it will be necessary to consider the Earth as a spherical body, and not to take into the account the slight effects of its atmosphere. Upon these principles, let S (in the following fig. 7) be the centre of the Sun, E that of the Earth, M AB a right line forming a tangent to the Earth and the Sun, and which forms the limit of the real sha dow. SE will be the axis of the conical shadow, and EC the length it is required to determine. This can be done when the angle ECB, at the vertex of the cone, is known. Now, by the principles of geometry, this angle is easily found to be equal to the semidiameter of the Sun minus his horizontal parallax, which has been stated, in the preceding article on that subject, to be equal to 8".78, for the Earth's mean distance from the Sun. From this it is easy to find the length of the shadow CE; for in the triangle CBE right angled at B, the angle C and the side EB, which is the radius of the Earth, are both known; and, therefore, as sin C: rad. (1) ::r: T CE, where r denotes the radius BE of the Earth. If we put D for the apparent diameter of the Sun, and p for his horizontal parallax, we shall have, from what is above stated, CE= From sin (3D — p)' this it is evident, both from an inspection of the figure and the nature of the preceding formula, that the value of CE, the length of the conical shadow, must vary with the apparent diameter of the Sun, and consequently with his distance from the Earth, being greatest when his distance is greatest, and the contrary. Now the apparent diameter of the Sun is, when 1955".567 In perigee At his mean distance ጥ sina C 1922 .713 1 D 2 1 Draw FE parallel to CB, and put the angle ECB SEE=c: SP SA-EB then we shall have the sin c = = SE SE sin p, where D is the apparent diameter of the Sun, and p its horizontal parallax. Then, since the arcs are so small, they may be substituted for their sines without sensible error, and we have c = {D — p, as above stated. = = = sin |