So that the weight of the quicksilver in the tube, above that in the bason, is at all times equal to the weight or pressure of the column of atmosphere above it, and of the same base with the tube; and hence the weight of it may at all times be computed; being nearly at the rate of half a pound avoirdupois for every inch of quicksilver in the tube, on every square inch of base; or more exactly it is of a pound on the square inch, for every inch in the altitudeof the quicksilverweighs justlb, or nearly a pound, in the mean temperature of 55° of heat. And consequently, when the barometer stands at 30 inches, or 24 feet high, which is nearly the medium or standard height, the whole pressure of the atmosphere +30 29 -28 27 is equal to 143 pounds, on every square inch of the base; and so in proportion for other heights. OF THE THERMOMETER. 390. THE THERMOMETER is an instrument for measuring the temperature of the air, as to heat and cold. It is found by experience, that all bodies expand by heat, and contract by cold; and hence the degrees of expansion become the measure of the degrees of heat. Fluids are more convenient for this purpose than solids and quicksilver is now most commonly used for it. A very fine glass tube, having a pretty large hollow ball at the bottom, is filled about half way up with quicksilver: the whole being then heated very hot till the quicksilver rise quite to the top, the top is then hermetically sealed, so as perfectly to exclude all communication with the outward air. Then, in cooling, the quicksilver contracts, and consequently its surface descends in the tube, till it come to a certain point, correspondent to the temperature or heat of the air. And when the weather becomes warmer, the quicksilver expands, VOL. II. Hh and 30 and its surface rises in the tube; and <-100 20 like equal degrees are also continued to any extent below the freezing point, and above the boiling point. The divisions are then numbered as follows; namely, at the freezing point is set the number 32, and consequently 212 at the boiling point; and all the other numbers in their order. This division of the scale is commonly called Fahrenheit's. According to this division, 55 is at the mean temperature of the air in this country; and it is in this temperature, and in an atmosphere which sustains a column of 30 inches of quicksilver in the barometer, that all measures and specific gravities are taken, unless when otherwise mentioned; and in this temperature and pressure the relative weights, or specific gravities of air, water, and quicksilver, are as 1 for air, and these also are the weights of a cu 1000 for water, bic foot of each, in avoirdupois ounces, 13600 for mercury; in that state of the barometer and thermometer. For other states of the thermometer, each of these bodies expands or contracts according to the following rate, with each degree of heat, viz. Air about Water about 43 part of its bulk, 1 6 part of its bulk, part of its bulk. ON ON THE MEASUREMENT OF ALTITUDES BY THE 391. FROM the principles laid down in the scholium to prop 76, concerning the measuring of altitudes by the barometer, and the forgoing descriptions of the barometer and thermometer, we may now collect together the precepts for the practice of such measurements, which are as follow: First Observe the height of the barometer at the bottom of any height, or depth, intended to be measured; with the temperature of the quicksilver, by means of a thermometer attached to the barometer, and also the temperature of the air in the shade by a detached thermometer. Secondly. Let the same thing be done also at the top of the said height or depth, and at the same time, or as near the same time as may be. And let those altitudes of barometer be reduced to the same temperature, if it be thought necessary, by correcting either the one or the other, that is, augment the height of the mercury in the colder temperature, or diminish that in the warmer, by its part for every degree of difference of the two. Thirdly Take the difference of the common logarithms of the two heights of the barometer, corrected as above if necessary, cutting off 3 figures next the right hand for decimals, when the log-tables go to 7 figures, or cut off only 2 figures when the tables go to 6 places, and so on; or in general remove the decimal point 4 places more towards the right hand, those on the left hand being fathoms in whole numbers. Fourthly. Correct the number last found for the difference of temperature of the air, as follows; Take half the sum of the two temperatures, for the mean one: and for every degree which this differs from the temperature 31°, take so many times the part of the fathoms above found, and add them if the mean temperature be above 31°, but subtract them if the mean temperature be below 31°; and the sum or difference will be the true altitude in fathoms: or, being multiplied by 6, it will be the altitude in feet. 392. Example 1, Let the state of the barometers and thermometers be as follows; to find the altitude, viz. Barom. Thermom. 393. Exam. 2. To find the altitude, when the state of the barometers and thermometers is as follows, viz. ON THE RESISTANCE OF FLUIDS, WITH THEIR FORCES AND ACTIONS ON BODIES PROPOSITION LXXVIL 394. If any Body Move through a Fluid at Rest, or the Fluia Move against the Body at Rest; the Force or Resistance of the Fluid against the Body, will be as the Square of the Velocity and the Density of the Fluid. That is, Rc dv2. FOR. the force or resistance is as the quantity of matter or particles struck, and the velocity with which they are struck. But the quantity or number of particles struck in any time, are as the velocity and the density of the fluid. Therefore the resistance, or force of the fluid, is as the density and square of the velocity. 395. Corol. 1. The resistance to any plane, is also more or less, as the plane is greater or less; and therefore the resistance on any plane, is as the area of the plane a, the density of the medium, and the square of the velocity. That, is Rα adv2. 396. Corol. 2. If the motion be not perpendicular, but oblique to the plane, or to the face of the body; then the resistance, in the direction of motion, will be diminished in the triplicate ratio of radius to the sine of the angle of inclination of the plane to the direction of the motion, or as the cube of radius to the cube of the sine of that angle. So that Rα adv2s3, putting 1 radius, and 8 a sine of the angle of inclination CAB. For, if AB be the plane, AC the direction of motion, and Bс perpendicular toac; then no more particles meet the plane than what meet the perpendicular BC,and therefore their number is diminished as AB to Bc or as 1 to s. But the force of each par A ticle, striking the plane obliquely in the direction ca, is also diminished as AB to BC, or as I to s; therefore the resistance, which is perpendicular to the face of the plane by art. 52, is as 1 to 82. But again, this resistance in the direction perpendicular to the face of the plane, is to that in the direction AC, by art. 51, as AB to BC, or as 1 to 8. Consequently, on all these accounts, the resistance to the plane when moving perpendicular to its face, is to that when moving obliquely, as 13 to 83, or 1 to s3. That is, the resistance in the direction of the motion, is diminished as I to s3, or in the triplicate ratio of radius to the sine of inclination. PROPOSITION LXXVIII. 397. The Real Resistance to a Plane, by a Fluid acting in a Direction perpendicular to its Face, is equal to the Weight of a Column of the Fluid, whose Base is the Plane, and Altitude equal to that which is due to the Velocity of the Motion, or through which a Heavy Body must fall to acquire that Velocity. THE resistance to the plane moving through a fluid, is the same as the force of the fluid in motion with the same velocity, on the plane at rest But the force of the fluid in motion, is equal to the weight or pressure which generates that motion; and this is equal to the weight or pressure of a column of the fluid, whose base is the area of the plane, and its altitude that which is due to the velocity. 398. Corol. 1. If a denote the area of the plane, v the velocity, n the density or specific gravity of the fluid, and g = 16 fect, or 193 inches. Then the altitude due to 82 the velocity being therefore a X n x 4g be the whole resistance, or motive force R. 22 anv 2 4g . 4.g will 399. Corol. 2. If the direction of motion be not perpendicular to the face of the plane, but oblique to it, in any angle, whose sine is s. Then the resistance to the plane will 400. Corol. 3. Also, if w denote the weight of the body, whose plane face a is resisted by the absolute force R; then and 283 R the retarding force ƒ, or will be f, W 48w 401. Corol. 4. And if the body be a cylinder, whose face |