Several curious and in some respects useful consequences might be deduced from these experiments and theorems. M. Bettancourt shews 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 injection. 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 expensive, whose vapour may be so much stronger than that of water, with the same 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 asserts, 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 superior to what is obtained from the steam of water. Another use of these researches suggested by M. Bettancourt is, to measure the height of mountains by means of a thermometer immersed in boiling water; which he thinks may be done 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 somie 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 accurate. His chief error consists in having assumed the force of vapour from water of 32° (Fahrenheit) to be nothing; which makes his numbers essentially 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 elasticity.

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 spirit and that from water; and inferred the same with regard to the vapour from other fluids. But, on pursuing the subject, he concluded that this principle was not true, either with respect to spirit of wine or any other liquid. His experiments upon six different liquids agree in establishing as a general law, "That the variation of the force of vapour from all liquids is "the same for the same variation of temperature, reckoning from vapour of any given force: thus, assuming a force

66

"equal to thirty inches, of mercury as the standard, it being the "force of vapour from any liquid boiling in the open air, we "find aqueous vapour loses half its force by a diminution of 30 "degrees of temperature: so 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 decrement 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."

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The experiments on which this conclusion rests, are related in the fifth volume of the Manchester Memoirs; they may also be seen in the 6th volume of the New Series of Mr. Nicholson's Journal. Mr. Dalton has calculated a table of the force of vapour of water from the temperature of 40° below zero of Fahrenheit, 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 measuring unit, that the small differences in the results of the English and the Spanish philosopher may be the more readily traced.

If x denote the degrees of heat measured on Fahrenheit's thermometer from 212°, the ordinary boiling point of water, and f be the force of compression measured in inches of mercury,

then, to express the elasticity of the steam generated from water, we have this logarithmic formula: viz.

Log. ƒ = log. 30 + 45 log. (1·250-015-4).

45

Hence when r is known, we may find f, which measures both the compression on the surface of the water, and the elastic force of the steam. The above theorem will serve to estimate the force of steam generated from any other liquid, provided it be reckoned from the ordinary boiling point of the respective liquid, when the barometer stands at 30 inches.

66. There remains for us to consider another kind of mover of machinery, which is ANIMAL EXERTION, and which is of so 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 besides 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 advanced 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 second; 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 asserts, that a man can raise of water or any other weight about 550 lbs., or one hogshead (weight of the vessel 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 solid 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 83 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 state 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 two 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 10 hours a day he will raise a weight of 30lbs. 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 can more easily draw up 70lbs. 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 150lbs. to 200 or 250 lbs. according to their strength. A man cannot well draw more than 70 lbs. or 80lbs. horizontally: and he cannot thrust with a greater force acting horizontally at the height of his shoulders than 27 or 30 lbs. But one of the most advantageous ways in which a man can exert his force is to sit and pull towards him nearly horizontally, as in the action of rowing.

69. M. Coulomb communicated to the French National Institute the results of various experiments on the quantity of action which men can afford by their daily work, according to the different manners in which they employ their strength. In the first place he examined the quantity of action which men can produce when, during a day, they mount a set of steps or stairs, either with or without a burthen. He found that the quantity of action of a man who mounts without a burthen, having only his own body to raise, is double that of a man loaded with a weight of 68 kilogrammes, or 223 lbs. averdupois*, both continuing at work for a day. Hence it appears how much, with equal fatigue and time, the total or absolute effort may obtain different values by varying the combinations of effort and velocity.

But the word effect here denotes the total quantity of labour employed to raise, not only the burthen, but the man himself; and, as Coulomb observes, what is of the greatest importance to consider is the useful effect, that is to say, the total effect, deducting the value which represents the transference of the weight of the man's body. This total effect is the greatest possible when the man ascends without a burthen; but the useful effect is then nothing: it is also nothing if the man be so much loaded as to be scarcely capable of moving and conse

* The kilogramme is = 22966 grs. = 3.28 lbs. averd.

quently there exists between these two limits a value of the load such that the useful effect is a maximum. M. Coulomb supposes that the loss of quantity of action is proportional to the load (an hypothesis which experience confirms), whence he obtains an equation which, treated according to the rules of maxima and minima, gives 53 kilogrammes (1734 lbs. averd.) for the weight with which the man ought to be loaded, in order to produce during one day, by ascending stairs, the greatest useful effect: the quantity of action which results from this determination has for its value 56 kilogrammes (1833 lbs. averd.) raised through one kilometer, or nearly 1094 yards. But this method of working is attended with a loss of three-fourths of the total action of men, and consequently costs four times as much as work in which, after having mounted a set of steps without any burthen, the man should suffer himself to fall by any means, so as to raise a weight nearly equal to that of his own body.

From an examination of the work of men walking on a horizontal path, with or without a load, M. Coulomb concludes that the greatest quantity of action takes place when the men walk being loaded: and is to that of men walking under a load of 58 kilogrammes (1904 lbs. averd.) nearly as 7 to 4. The weight which a man ought to carry in order to produce the greatest useful effect, namely, that effect in which the quantity of action relative to the carrying his own weight is deducted from the total effect, is 50-4 kilogrammes, or 165.3 lbs. averdupois.

There is a particular case which always obtains with respect to burthens carried in towns, viz. that in which the men, after having carried their load, return unloaded for a new burthen. The weight they should carry in this case, to produce the greatest effect, is 61.25 kilogrammes (200-7 lbs. averd.). The quantity of useful action in this case compared with that of a man who walks freely and without a load is nearly as 1 to 5, or, in other words, he employs to pure loss of his power. By causing a man to mount a set of steps freely and without burthen, his quantity of action is at least double of what he affords in any other method of employing his strength.

When men labour in cultivating the ground, the whole quantity afforded by one during a day amounts to 100 kilogrammes elevated to one kilometer, that is, 328 lbs. raised 1094 yards. M. Coulomb comparing this work with that of men employed to carry burthens up an ascent of steps, or at the pile-engine, finds a loss of about part only of the quantity of action which may be neglected in researches of this kind.

In estimating mean results we should not determine from