in the e cubic torrid seldom exceeds 300; in stronger earth it becomes 370; and in some fa vourable cases more than 45o, 1. If h = AD, x = AE, 0 = 4 DA G, and S and s represent the specific gravities of the wall and earth, the state of equilibrium is expressed by this equation, x2. S h2. s. tan. 0. Ex. Suppose the wall to be 39.37 feet high, of brick, specific gravity 2000, and the bank of earth specific gravity 1428, and the natural slope 53°; then a, 2000% X 39.37 X 1428 X tan.2 2640, .9.6 feet thickness of wall, The following practical results may be found useful. Values of DG for different materials. Do. of vegetable earth mixed with small gravel Do. of vegetable earth mixed with large gravel. www DG.646 h. DG 414 h. DG.618 h.. Thickness of walls, both faces vertical. 1. Wall brick, 109 lbs. per cubic foot, bank vegetable 3. Wall brick, earth clay well rammed www.n 6. Do. bank clay 7. Bank of earth mixed with large gravel, wall of When the earth of the bank is liable to be much saturated with water the proportional thicknesses of the walls must at least be doubled. 2. For walls with an interior slope, or a slope towards the bank, let where m = .0424 for vegetable or clayey earth, mixed with large gravel; m = .0464 if the earth be mixed with small gravel; m = .1528 for sand; and m.166 for semifluid earths. Ex. Let the height of a wall be 20 feet, and 1 20 of the height for the base of the slope, suppose also the specific gravity of the wall and bank to be 2600 and 1400, and the earth semifluid; then 5 feet, while the thickness of the wall at the bottom will be 6 feet. EASTER, to find it on any year.-(Delambre.) 1. Divide the year proposed by 19 ............... Call remainder a. 2. Divide the same number by 4 Call remainder b. Call remainder e. 5. Divide (2b+ 4 c + 6 d + N) by 7 6. Then Easter day will fall either on (22 +d+e) of March; or on 2. If it give ............ 24 ............ 5 1. If the computation give April 26, substitute the 19th. April 25, substitute the 18th. ECCENTRICITY of a Planet's orbit.-(Woodhouse, Playfair.) centre, found by observation, and put g 570.29578 =h, then bank, let gravel; r sand; or the bank tom In the earth's orbit h is very small, .. eh nearly. The secular diminution = 18". 79, and .. if this diminution continued uniform (which, however, we have not a right to suppose) the earth's orbit would become a circle in about 36300 years. ECHO. That an echo may return one syllable as soon as it is pronounced, the reflecting surface should be 80 or 90 feet distant; for a dissyllablic echo 170 feet, &c. This is upon the supposition that sound proceeds at the rate of 1142 feet per second, and that the ear can distinguish the succes sion of two sounds or syllables, when the interval between them is 1 -th An echo in Woodstock Park repeats 17 syllables by day, and 20 by night. An echo on the north side of Shipley church in Sussex, repeats 21 syllables.(Young's Nat. Phil.) ECLIPSES.-(Woodhouse, Playfair.) 1. Eclipses of the Moon. 1. The length of the earth's shadow varies, according to the distance of the sun and earth, between the limits of 212,896, and 220,238 semidiameters of the earth; its mean length being 216,531. And in general if r be the earth's radius, the apparent semidiameter, and p the horizontal par allax of the sun, the length of the shadow, reckoned from the earth's centre, 2. Hence half the angle subtended at the earth's centre by the section of the shadow, at the distance of the moon, (if P be the horizontal parallax of the moon) is From this formula the apparent diameters of the earth's shadow may be computed for various distances of the sun and moon, as in the following Table. Moon in apogee Apparent diam, of 1o. 15'. 24,3036 at mean distance.............. 1. 23. 2:31 Sun in perigee Cin perigee 1. 30, 40,3164 3. The distance of the centres of the moon and of the earth's shadow, when the moon's disk just touches the shadow (if d = moon's diameter) D 16. 13, we have the mean 2 diameter of the earth's shadow Cor. If P57.1", p =8", 8, and apparent 41. 8",5, which is nearly three apparent diameters of the moon. Hence since the moon in the space of an hour moves over a space nearly equal to its diameter, the moon may be entirely within the shadow, or a total eclipse may endure, about two hours. 4. The apparent diameter of a section of the penumbra at the moon's orbit= And the distance of the moon's centre and of the centre of the shadow, when the moon first enters the penumbra, is D d 5. To find the time, duration, and magnitude of a lunar eclipse. Let m moon's motion in longitude, nmoon's motion in latitude, ssun's (or the shadow's centre's) motion in longitude, time from opposition, e distance of moon and earth's shadow, from which expression may be deduced values of the time, corresponding to any assigned values of c, as in the following instances. (j) To determine the time at which the moon first enters the penumD bra, for c put P+p+ + t has two values, and the second value 2 2 will denote the time at which the moon quits the penumbra. (ii) To determine the time at which the moon enters the umbra, put (iii) To determine the time when the whole disk has just entered the shadow, we must deduct d from the preceding value, and make c=P+ sin.2 0 (jjjj) To find the middle of the eclipse, we have t=— a and in that case the distance of the centres (c) is a cos. 0. (v) The nearest approach of the centres being known, the magnitude of the eclipse is easily ascertained. Thus on the supposition that a cos, d is less than the distance (P+P + ē at which the moon's limb just touches the shadow, some part of the moon's disk is eclipsed; and the portion of the diameter of the eclipsed part is The portion of the diameter of the non-eclipsed part is the moon's apparent diameter d, minus the preceding expression, and therefore is If this expression should be equal nothing, the eclipse would be just a total one. If the expression should be negative, the eclipse may be said to be more than a total one, since the upper boundary of the moon's disk would be below the upper boundary of the section of the shadow. first entering to her finally quitting the shadow or umbra. And if in the |