By the foregoing TABLE, it is readily seen in what ratio the several intensities, furnished by the different methods, stand one to another, that the French annular lamp, for instance, has a maximum power = half that of the mechanical, or that of the camphene, or 5 wax candles, 3 to the lb., that the camphene, at its maximum power, yields an intensity equal to that afforded by 16 ÷ .57, = 28 tallow candles, moulds, 8 to the lb.,-that as the intensity of a six wax candle, 13 in., is .92, and that of an eight mould tallow .57, 57 candles of the former yield an intensity equal to that afforded by 92 of the latter, &c., &c. THE QUANTITY OF MATERIAL consumed in any given time by either of the foregoing methods, in the production of any given intensity of light, is readily ascertained by help of the preceding TABLE. Suppose, for example, an intensity equal to that afforded by 1 camphene paragon lamp at its greatest power, is required, and for three hours, and that it is proposed to produce the same by tallow candles, moulds, 10 to the lb.; the quantity by weight of candles consumed in the production is required, and, consequently, the number of lights that must be used. ILLUSTRATION. Intens. of camph., (16) intensity of candles, (.66): 24 candles, and grs. in 1 h. by 1 candle, (132) X 24 X 3 hours 1 lb. 5 oz. Ans. THE ECONOMY OF USE, as between any two materials, under either their respective forms, or methods of consumption, for the production of equal lights in equal times, and therefore for the production of any intensity, is also, by help of the given TABLE, easily learned, the market price of both being known; and, thereby, the per cent., if any difference exist, in favor of the more economical, or less expensive of the two, may be found. To illustrate :- 1. The price of camphene is 10 cents a pound, and that of sperm oil, 15; the economy of use as between the two for the production of equal lights-equal intensities in equal times, greater or less-the former consumed in the paragon lamp, and the latter in Parker's heating, is desired, and the per cent. in favor of the less expensive. = 10 X 1 10, and 15 X 1.19 17.85; showing the economy to be in favor of the camphene-showing it so to an extent 17.85 - · 10 77, or to an extent 7 cts. 8 mills per 17 cts. 81⁄2 mills an extent, therefore, = 785 1785 17.85 7.85 :: 100 = 44 per cent. Ans. to 2. The price of sperm candles, 4's, is 40 cts. a pound, and the price of tallow, mould 10's, is 11 cts. It is desired to know which of the two, for the production of an intensity nearest obtainable to that afforded by one of the wax, but not less than that of 1 wax, is the less expensive, and to what extent per cent. By casting the eye to the table, it is readily seen that two tallow candles must be employed, the comparative intensity of which = 1.32, and 3.75 X 1.32 = 4.95, is .66 each; therefore, .66 X 2 equivalent weight; consequently = 40 X 2.66 106.4, and 11 X 4.95 = 54.45, and 106.4 54.45 = 51.95. Therefore, 106.4 51.95: 100= =48% per cent. Ans. = Showing that an intensity nearly greater is afforded by the tallow than the wax, and at an expense 49 per cent. less. The same rule of practice is applicable, as between any two methods, for equal or greater or less intensities, as desired. When it is desired to reduce the +°, (degrees above the zero): RULE.-Multiply the degrees Reaumur, by 2.25, and add 32° to the product; the sum will be the degrees Fahrenheit. When it is desired to reduce the -°, (degrees below the zero): — RULE. Multiply the Reaumur by 2.25, and subtract the product from 32°; the difference will be the degrees Fahrenheit. EXAMPLE. — The degrees R. are 40; required the equivalent degrees F. 40 X 2.25 EXAMPLE. 90+32= = 122°. Ans. The degrees below 0, R., are 10; what are the corresponding degrees F.? = 10 X 2.25 22.5, and 32 — 22.5 91°. Ans. = EXAMPLE. The degrees below 0, R., are 16; what point on the scale F. corresponds thereto? 16 X 2.25 = 36, and 32 — 36 = = To reduce the Centigrade to Fahrenheit. Ans. RULE. Multiply the degrees C. by 1.8, and in all other respects proceed as directed for Reaumur, above. NOTE.The zero of Wedgewood's pyrometer is fixed at the temperature of iron red-hot in daylight, 10770 F., and each degree W. equals 1300 F. The instrument is not considered reliable, and is but little used. HORSE POWER. A HORSE-POWER, in machinery, as a measure of force, is estimated equal to the raising of 33000 lbs. over a single pulley one foot a minute, 550 lbs. raised one foot a second,= 1000 lbs. raised 33 feet a minute. ANIMAL POWER. A man of ordinary strength is supposed capable of exerting a force of 30 lbs. for 10 hours in a day, at a velocity of 2 feet a second, 75 lbs. raised 1 foot a second. = 375 lbs. raised The ordinary working power of a horse is calculated at 750 lbs. for 8 hours in a day, at a velocity of 2 feet a second, 1 foot a second, = 5 times the effective power of a man during associated labor, and 4 times his power per day; and as machinery may be supposed to work continually, a trifle less than 23 per cent. per day of a machine horse-power. STEAM. Table exhibiting the expansive force and various conditions of steam under different degrees of temperature. - [An atmosphere is 14 lbs. to the square inch.] NOTE. By the above table it is seen that any given quantity of steam having a temperature of 2120 F., occupies a space, under the ordinary pressure of the atmosphere, 1694 times greater than it occupied when as water in a natural state. It exerts a mechanical force, consequently, 1694 times the weight or force of the atmosphere resting on the bulk from which it was generated, or resting on 1-1694th of the space it occupies. A force, if we consider the volume as so many cubic inches, equal to the raising of 2087 lbs. 12 inches high, by a quantity of steam less than a cubic foot, heated only to the temperature of boiling water, and weighing but 248 grains, and that, too, the product of a single cubic inch of water. The mean pressure of the atmosphere at the earth's surface is equal to the weight of a column of mercury 29.9 inches in height, or to a column of water 33.87 feet in height,=2116.8 lbs. per square foot, or 14.7 lbs. per square inch. Its density above the earth is uniformly less as its altitude is greater, and its extent is not above 50 miles its mean altitude is about 45 miles; at 44 miles it ceases to reflect light. Were it of uniform density throughout, and of that at the surface, its altitude would be but 5 miles. Its weight is to pure water of equal temperature and volume, as 1 to 829. It revolves with the earth, and its average humidity, at 40° of latitude, is 4 grains per cubic foot. Its weight at 60°, b. 30, compared with an equal bulk of pure water at 40°, b. 30, is as 1 to 830.1. The curvature of the earth is 6.99 inches (.5825 foot) in a single statute mile, or 8.05 inches in a geographical mile, and is as the square of the distance for any distance greater or less, or space between two levels; thus, for three statute miles it is 1:32 :: 6.99: 5 feet, nearly. The horizontal refraction is 13. Degrees of longitude are to each other in length, as the cosines of their latitudes. At the equator a degree of longitude is 60 geographical miles in length, at 90° of latitude it is 0; consequently, a degree of longitude at Time is to longitude 4 minutes to a degree, or 5.785 minutes per hundred statute miles-faster, east of any given point; slower, west. The mean velocity of sound at the temperature of 33° is 1100 feet a second. Its velocity is increased a foot a second for every degree above 33°, and decreased a foot a second for every degree below 33°. In water sound passes at the rate of 4708 feet a second. GRAVITATION. A body falling freely from rest, will descend 16 feet in the first second of time, and at the end of that time will have acquired a velocity which will carry it through 484 feet in the next second of time, and so on. = Velocities of falling bodies, therefore, are as the times, the spaces fallen through, as the square of the times, and the space fallen through in each time, as 1, 3, 5, 7, &c., that fallen through in the first space of time. Thus, in 10 seconds, a body will fall 102 × 161⁄2 1608 feet; the velocity which it will have acquired at the end of that time will be 10 X 32 = 321 feet per second, and the space fallen through during the last second will be 19 × 161 = 305 feet. The above is strictly true as regards all bodies one with another, great or small, compact or porous, falling in vacuo; and is sufficiently near the truth for all practical purposes as between all dense bodies falling in atmosphere. Water obeys the same law in its descent, and is estimated as having the same velocity. The time, therefore, in seconds, occupied by a body falling a given distance, is the square root of the quotient obtained by dividing the distance by 16; and the velocity in feet per second, attained at the end of any given time, is the square root of the product of the distance, or space fallen through and 64.333, or 4 times 16; thus, 1608.33 16.083 = 100 10 seconds, and 1608.33 X 64.33: 103463.89 321.66, velocity at end of 10 seconds. = = The momentum or force with which a falling body strikes, is the product of its weight and velocity (the weight multiplied by the square root of the product of the space fallen through and 64.33, or 4 times 16); thus, 100 lbs. falling 50 feet, will strike with a force, 50 X 64.333 = 3216.66 56.71 X 100 = 5671 lbs. An entire revolution of the earth, from west to east, is performed in 23 hours, 56 minutes, and 4 seconds. A solar year = 365 days, 5 hours, 48 minutes, 57 seconds. The area of the earth is nearly 197,000,000 square miles. Its crust is supposed to be about 30 miles in thickness, and its mean density 5 times that of water. About of its area, or 150,000,000 square miles is covered by water. The portions of land in the several |