describes that part of the ecliptic which is comprised between this circle and the tropic of Cancer, it is spring with respect to the northern hemisphere, but autumn in the opposite half of the globe. During his passage from this tropic to the equator, it is summer in the northern and winter in the southern hemispheres. But as he now enters again into the opposite hemisphere, their spring and our autumn commence; and these are succeeded by summer in the former case and winter in the latter, which completes the regular gradation. It will, therefore, readily be perceived from the preceding observations, that the duration of light at any place must principally depend upon its situation and the elevation of the Sun; or, in more astronomical language, upon the latitude of the place and the Sun's declination. When these two are known, it will be easy to find the duration of day and night at any given place. If three visual rays be supposed to be drawn from the observer, one to his zenith, another to the body at the instant its centre appears in the horizon, and a third to the pole, they will form a spherical triangle, the three sides of which are known: viz. the distance from the pole to the zenith, which may be denoted by D; the polar distance of the body, which may be represented by ▲; and the zenith distance Z of the body, which is equal to 90° + refraction-parallax. With these data, the horary angle H, which is subtended by the side Z, may be calculated. For the more readily finding of this angle, writers on spherical trigonometry have investigated this formula, viz. sin. H = (sin.{(Z+^—D)sin. ¿(Z+D—A)). sin. A sin. D The angle H, when reduced into time, gives the duration between the instant of the body's rising and that of its passage over the meridian. This is also equal to half the time which it remains above the horizon, and on this account the arc H is denominated, in astronomical language, the semi-diurnal arc. Hence by substituting the values of Z, A, and D in this formula, we shall obtain the value of H, for the time and place corresponding to the values that are substituted, and consequently the duration of the solar day for that time and place becomes immediately known. The arc thus calculated will also answer for any of the other heavenly bodies. To exemplify the use of this formula, and elucidate the mode of computation it requires, that the juvenile reader may be at no loss in its application, we shall select the 22d of June as an example, and find the length of that day at London. The latitude of London being nearly 51° 31', we shall have D = 38° 29'; the Sun's declination on that day is 23° 28', and hence his polar distance = 66° 32′, while his distance from the zenith Z = 90° + 33′ 16′′ —- 9′′ — 90° 33' 7". Then, by substituting these quantities in the preceding formula, we shall have sin&H=√(sing(90°33'′7′′ ́+66°32′—38°29′)sin} (90°33′7′′+38°29′—66°32′) = sin 66°32' x sin 38°29' sin 590 18' 4"X sin 31° 15' 3" sin 66° 32′ x sin 38° 29, this, converted into logarithms, gives sin(9.9344288 +97149880)-(9.9625076+9.7939907) } (19.6494168 — 19·7564983); hence = sin H and therefore H 9.9464592; 62° 8' x 2 = 124° 16′, which is the semi-diurnal arc for the time and place required; and consequently we have the corresponding length of the day equal to If half this time be subtracted from 12 h., it will give the time of the Sun's rising on that day, which reject 1 ing the seconds, is 43 m. after 3; while this half itself will denote the time of his setting, which is therefore at 17 m. past 8. If we take the shortest day at the same place as another example, and reject the seconds for the sake of abridging the calculation, we shall have, gingH=√(sir ́sing (90°33′+113°28′—38°29′)sin (90°33′+38°29′—113°28′)` sin 113028'x sin 38° 29' by expressing this in logarithms, we have, sin H={(9·9965299+9.1317064)-(9.9625076+9.7939907) } and therefore sin } H=9•6858690, and H=29° 1‘x2=58° 2 ; which converted into time, gives 7 h. 44 m. for the length of the shortest day in the latitude of London. It is hardly necessary to remark, that by subtracting the length of the day from 24 h., we shall obtain the corresponding night. The shortest night, for instance, at London, will be 24 h.-16h. 343 m. = 7 h. 251 m.; and the longest equal 24 h. — 7 h. 44 m. 16h. 16m. When we have a table of semi-diurnal arcs already calculated, it is only necessary to enter this table with the latitude of the place and the declination of the heavenly body as arguments, and we immediately obtain half the time which, that body is above the horizon on that day; which subtracted from 12h. when it is for the Sun, gives the time of his rising, while the number itself expresses the time of his setting. But if it be a planet, this time must be subtracted from the hour of its southing, or passing the meridian. Thus, if it were required to ascertain the time of Jupiter's rising at London on the 25th of this month, we have, in the Nautical Almanac, his declination equal to 16° 23′ S., and the time of his passing the meridian is 32m. after 5 in the morning, and the latitude of the place 51° 30′ nearly; then entering the table with these, we find the semi-diurnal arc equal to 4 h. 37m. Therefore, to find the true time of Jupiter's rising and setting, we have Time of rising 0 55 Setting 10 9 And the time of his whole duration above the hori zon on that day is 9 h. 14 m. [To be continued.] The Naturalist's Diary For JUNE 1819. No gradual bloom is wanting, from the bud, As o'er the fabled fountain hanging still ; Nor broad Carnations, nor gay spotted Pinks; With hues on hues, expression cannot paint The breath of Nature, and her endless bloom. THOMSON. INNUMERABLE herbs and flowers now embellish our gardens, gratify our sense of smell, and purify and renovate the atmosphere. The fields of clover (trifolium pratense), which are now in blossom, produce a delightful fragrance. Of this plant there are two. varieties, the white and the purple; from the latter, the bees extract much honey. The bean blossoms also shed a still more exquisite odour. The elder, now in flower, diffuses its Frontiniac scent to the air, which it likewise imparts to wine made in imitation of that from the grapes growing in the neighbourhood of the town of that name in France. The sweet-scented vernal grass (anthoxanthum odoratum), which is the cause of the very delightful scent of hay, flowers in this month, and diffuses its fragrance throughout the country. In the field, in the stack, in the horse-rack, or in the cow-crib, sweet hay is one of the most agreeable of perfumes. About the beginning of this month, the pimpernel (anagallis arvensis), thyme (thymus serpyllum), the bitter sweet nightshade (solanum dulcamara), white bryony, the dog-rose (rosa canina), and the poppy (papaver somniferum), have their flowers full blown. The poppy (says Cowley) is scattered over the fields of corn, that all the needs of man may be easily satisfied, and that bread and sleep may be found together. See some beautiful lines on this subject in T.T. for 1816, p. 180. Among the insects which appear in this month, one of the most interesting is, in its perfect state, the angler's may-fly (ephemera vulgata), which appears about the 4th, and continues nearly a fortnight. It emerges from the water, where it passes its aurelia state, about six in the evening, and dies about eleven at night. There are also the grasshopper (gryllus), the golden-green beetle (scarabæus auratus), various kinds of flies; the cuckoo-spit insect (cicada spumaria), and the stag-beetle (lucanus cervus). The several species of the gad-fly (oestrus bovis-equi-and ovis), the ox, horse, and sheep gad-fly, make their appearance in this month. The fern-owl may be seen, in the evening, among the branches of oaks, in pursuit of its favourite repast, the fern-chaffer (scarabæus solstitialis). The several kinds of corn come into ear and flower during this month, as well as most of the numerous species of grasses. See our last volume, p. 205, for an account of the various kinds of wheat; and p. 150 for a description of the grasses. Gooseberries, currants, and strawberries, now begin to ripen. The hay harvest commences about the end of the month, in the southern and midland parts of the kingdom. About this time, also, birds cease |