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Thus the formula for the vapour of spirit of wine is found as fimple as that for the vapour of water, without ceasing to represent the experiments with all desirable exactness. But more than this, we may retrench one of the variable terms; for in the first degree je locit has no greater value than 0·18, and when x is 2, 3, or any other positive value, this third term may be safely neglected. The equation therefore is reduced to
y=uner +29,5 + Moir; a form much more simple than Bettancourt's original equation, and indeed more simple than Prony's improved equation for the vapour of water.
64. To save the trouble of investigating the strength of the vapour by these formula for every separate case that may occur, we add a table (calculated from these principles) in which the strength of the vapour both of water and of fpirit of wine is shewn for every degree of Reaumur's thermometer up to 110°, or for every 25 degrees of Fahrenheit, from 32 to 280°: the strengths are expressed, not in English or in French inches upon the barometer, but in terms whose unit is the medium pressure of the atmosphere, supposing that medium equivalent to 29.9 English, or 28 French inches of mercury. The preffure upon a square inch in pounds averdupois corresponding to any temperature may be found by multiplying the corresponding number taken from the table by 14:75: and the pressure for any in. termediate degree of Fahrenheit may be found pretty nearly, by proportioning, as is usual in tables of Logarithms, &ce
Several curious and in some respects useful consequences might be deduced from these experiments and theorems. M. Bettancourt Thews for instance, that the effect of steam engines must, in general, be greater in winter than in summer, owing to the different degrees of temperature in the water of inje&tion. And from the greatly superior strength of the vapour of spirit of wine over that of water, he argues that, by trying other fluids, some may be found, not very expenfive, whose vapour may be fo much stronger than that of water, with the fame degree of heat, that it may be substituted instead of water in the boilers of steam engines, to the great saving in the expence of fuel : nay, he even aflerts, that spirit of wine itself might thus be employed in a machine of a particular construction, which, with the same quantity of fuel, and without any increase of expence in other things, shall produce an effect far fuperior to what is obtained from the steam of water. Another use of these researches suggested by M. Bettancourt is, to meafure the height of mountains by means of a thermometer immersed in boiling water; which he thinks may be dorie with a precision equal, if not superior, to that of the barometer. But this, being foreign to our present enquiries, cannot be entered upon here: a comparison of the results of this method with fome deduced from the more customary process may be seen in Dr. Hutton's Dictionary, vol. II. pa, 756, to which such as are desirous of further information on this point are referred.
65. Our ingenious countryman Mr. Dalton, of Manchester, is of opinion that M. Bettancourt's deductions are not quite ac
His chief error confits in having allumed the force of vapour from water of 32° Fahrenheit) to be nothing; which makes his numbers eflentially wrong at that point and in all the lower parts of the scale: and in the higher part, or that which is above 212, the force is determined too much ; owing, as Mr. Dalton apprehends, to a quantity of air, which being disengaged from the water by heat and mixing with the steam, increases the clasticity,
Mr. Dalton's first experiments with spirit of wine led him to adopt the same conclusion as M. Bettancourt, with respect to the constant ratio between the force of the vapour from this fpirit and that from water and inferred the same with regard to the vapoor from other fluids. But, on parsuing the subject, he concluded that this principle was not true, either with refpect to fpirit of wine or any other liquid. His experiments upon fit different liquids agree in establishing as a general law, "That the pariation of the force of vapour froin all liquids is the de fume for the fame variation of temperature, reckoning from vapout " of any given force: thus, affuming a force equal to thirty inches
" of mercury as the ftandard, it being the force of vapour from
any liquid boiling in the open air, we find aqueous vapour e loses half its force by a diminution of 30 degrees of tem* perature: fo does the vapour of any other liquid lose half its « force by diminishing its temperature 30 degrees below that « in which it boils, and the like for any other increment or de
crement of heat. This being the case, it becomes unnecessary
to give distinct tables of the force of vapour from different "* liquids, as one and the same table is sufficient for all."
The experiments on which this conclufion refts, are related in the fifth volume of the Manchester Memoirs : they may also be feen in the 6th volume of the New Series of Mr. Nicholson's Fournal. Mr. Dalton has calculated a table of the force of vapour of water from the temperature of 40° below zero of Fahfenheit, to 325° above it. From this table we have extracted the following; in which we have, as before, reduced the force to the medium pressure of the atmosphere for the meafuring unit, that the small differences in the results of the English and the Spanish philosopher may be the more readily traced.
66. There remains for us to consider another kind of mover of machinery, which is ANIMAL EXERTION, and which is of fo fluctuating a nature that it is not easy to subject it to any estimate. Physical causes must affect both the magnitude and duration of the efforts either of man or beast, and begides this,
the strength of man is considerably influenced by his moral habits. The various combinations of these different causes have occasioned a variety of estimates of animal labour to be adó vanced by different authors.
In the first volume of this work (art. 378.) we stated the average force of a man at rest to be 70 lbs., and his utmost walking velocity when unloaded to be about 6 feet per fecond; and we thence inferred that a man would produce the greatest momentum when drawing 31. lbs. along a horizontal plane with a velocity of 2 feet per second. But this is not the most advantageous way of applying human strength.
67. Dr. Desaguliers afferts, that a man can raise of water or any other weight about 550 lbs., or one hogshead (weight of the veffel included), 10 feet high in a minute: this statement, though he says it will hold good for 6 hours, appears from his own facts to be too high; and is certainly such as could not be continued one day after another. Mr. Smeaton considers this work as the effort of haste or distress; and reports that 6 good English labourers will be required to raise 21141 folid feet of sea water to the height of four feet in four hours: in this case the men will raise a very little more than 6 cubic feet of fresh water each to the height of 10 feet in a minute. Now the hogshead containing about 8t cubic feet, Smeaton's allowance of work proves less than that of Desaguliers in the ratio of 6 to 8 or 3 to 4. And as his good English labourers who can work at this rate are estimated by him to be equal to a double set of common men picked up at random, it seems proper to ftate that, with the probabilities of voluntary interruption, and other incidents, a man's work for several successive days ought not to be valued at more than half a hogshead raised 10 feet high in a minute. Smeaton likewise states, that 2 ordinary horses will do the work in three hours and twenty minutes, which amounts to little more than two hogsheads and a half raised 10 feet high in a minute. So that, if these statements be accurate, one horse will do the work of five men.
68. Mr. Emerson affirms, that a man of ordinary strength turning a roller by the handle can act for a whole day against a resistance equal to 30 pounds weight, and if he works to hours a day he will raise a weight of 30 lbs. through 3 feet in a second of time; or, if the weight be greater, he will raise it to a proportionally less height. If two men work at a windlass or roller, they caif more easily draw up 70 lbs. than one man can 30 lbs.; provided the elbow of one of the handles be at right angles to that of the other. Men used to bear loads, such as porters, will carry from 150 lbs. to 200 or 250 lbs, according to their strength. A man cannot well draw more than 70 lbs.