CONCERNING THE POWER.
§ 1. The power or force which the Dannemora fire- and air-machine possesses is equal to a weight of 21575 skålpund or 53 skeppund, 18 lispund , 15 skålpund victualie-weight, and this power is derived from the weight of the atmosphere, which presses in all directions and on all sides of all bodies existing on this earth. (Considering the many thousands of years the world has existed, it is much to be wondered that the weight of the air was not realised until the time of the great Galileo, in spite of the fact that man has not been able to live without this fluid matter for a single moment. The impulse to this important discovery was given by a gardener in Florence, who noticed that the water in his pump did not rise more than 28 feet; Torricelli later on compared the weight of the air with a column of mercury 29 inches high; but the burgermaster of Magdeburg, Otto von Guerike, made most wonderful experiments with the air-pump, that he had invented, in the presence of the diet of Regensburg, when amongst other experiments he proved that six pair of horses were unable to separate his two hemispheres, 18 inches in diameter. This ought not, however, to be considered incredible when one realises that the air was pressing on these half-globes with a weight equal to 53 skeppund 15 lispund victualie-weight. All this and much more of a novel and strange interest can be learned from his Experimenta Nova Magdeburgica).
§ 2. For although the air, which surrounds our globe, is so subtle, that we are unable to see it with our naked eyes, or the very best of microscopes; and a cubic inch of air is about 1000 times lighter than a similar inch of water, (See Tractaten om Hydrostastika Wågbalken, Stockholm, printed 1728.) in spite of all this, and because the air is fluid matter, which stands comparatively high above the earth, it will be found to press in the same way as other fluid matter does, and this in proportion to the vertical height and base. Consequently it will be found that the power of the fire-machine varies with the diameter or piston-area of the cylinder, and is in every way equal to the weight of a column or pillar of mercury, which has a base equal to the area of the piston and a height of 29 inches, which again is equal to a water-column with the same base and a height of 34 feet, because mercury is 14 times heavier than water. From this it follows that our earth, with all the things upon it, experiences a pressure from the air to the same extent as if our globe were surrounded or covered all over by a layer of water 34 feet high. (A pillar of water 34 feet high and of the same base as the area of the piston of the Dannemora fire-machine, viz., 1018 2/7 square inches, weighs 21,575 skålpund and 53 skeppund 18 lispund 1 5 skålpund victualie weight, which therefore constitutes the power of the machine).
§ 3. To what extent the air presses upon a vessel which is void of air may be better conceived by the following simile: imagine a door without a lock or latch, and on the inside of that door three strong men who are pressing their shoulders with all their might against the said door, and outside the same door also three men of equal strength in the same position:-For whatever length of time these men now tried their strength against each other, no change would be visible in the position of the door, nor could it be opened; should however one of the men outside the door be removed-it does not matter by what means-the door would then be thrown immediately open by the strength of one of the strong men who are inside the door; Again, should i withdraw two men from the outside of the door, then the door would be opened by a force equal to the strength of two men; And should 1 furthermore be able to remove all the three men from the outside, then the door would fly open with a force equal to the strength of all the three said men pressing upon the same;-Now this is exactly what takes place with regard to the weight and pressure of the air: for as long as the air in a vessel remains in its natural state, this air will--by the expanding force which is equal to the weight of the whole atmosphere (those versed in natural science have proved by many experiments that the elasticity or the expanding force of the air is equal to the weight of the air)--press upon all the inner parts of the vessel with a weight equal to the weight of the air outside, or--applied to our fire-machine,--when the air below the piston is in its natural state, the pressure of this quantity, however small, will always equalise the pressure of the whole atmosphere against the bottom, thus balancing the pressure of the whole atmosphere above the piston; but in case this air below the piston should get weakened, then the air above the piston will press in proportion to the diminishing capacity of resistance of the inner air; and as the piston is attached by a chain to one end of the big beam, this beam will at the same time be pressed down whilst the other end will be able to lift a weight equal to this power.
§ 4. The weight and the power of the fire-machine may also be represented by two heavy weights of 40 and 20 skeppund respectively; attached to either end of a scale-beam, in which case, as a matter of course, the weight of 40 skeppund will quickly pull the other weight of 20 skeppund up in the air for the simple reason that 40 skeppund possess a greater power of approaching the centre of the earth than 20 skeppund.
§ 5. As however those who are not very well acquainted with natural science fail to realise with what a miraculous power the air is able to press upon all things, existing on this globe, (when lecturing on natural science in the House of Lords at Stockholm, 1727 and 1728, I demonstrated and established the weight and wonderful power of expansion and elasticity of the air in a series of experiments) thinking that this element, taken cubic inch for cubic inch, is altogether too light in comparison with other kinds of fluid matter, I will--for their sake and benefit--endeavour to explain the appaerent difference by a simple example.
§ 6. Suppose I put into one scale of a balance one cubic inch or die of lead, and pile into the other scale dice of cork of an equal size, one upon the other, until an equilibrium is achieved or the dice of cork are balancing the die of lead. It will now be evident to every reader that the piled up dice of cork not only rest and press, one upon the other, but also that the lowermost is supporting and carrying the whole weight of all the others put together, from which follows that the lowermost--whatever its own weight may be--must necessarily press the scale down just as much as it is being pressed by the weight of the other dice.
Now, this is just what takes place with the air; for on all the air-grains or particles nearest to us or to the earth, rest and press all the upper ones, as far as the atmosphere extends above the surface of our globe, and just as the dice of cork may balance the die of lead, so also is the air balancing the mercury in our barometers; and just as a pillar of mercury, 29 inches high and 1018 2/7 inches in square, weighs 21575 skålpund, so the weight of the atmosphere is pressing the piston down at every stroke of the machine with a weight of 53 skeppund, 18 lispund, 15 skålpund, because the area of the piston contains 1018 2/7 square inches.
§ 7. That most learned Englishman, Fellow of the Royal Society of England, Doctor Halley, has determined by calculations founded on a similar way of reasoning, the differences in the height of mercury in a tube, at different heights, and, vice versa, depths of the atmosphere: e.g. in the deep mines; assuming that the heights of the atmoshpere increase in an arithmetical proportion and the density of the air decreases in a geometrical proportion. In this way he has been able to determine, with the aid of the Torricelli's tube alone, the actual height of the highest mountains, and the depth of the deepest mines.
The height of the atmosphere in English miles Diminishing density of the air 7 Miles up in the air 4 times thinner 14 " " " " " " " " " 16 " " " " " " " 21 " " " " " " " " " 64 " " " " " " " 28 " " " " " " " " " 256 " " " " " " 35 " " " " " " " " " 1024 " " " " " " 42 " " " " " " " " " 4096 " " " " " " The height of the mercury corresponding to the heights of the atmosphere can easily be calculated by means of this table, if 30 inches of mercury is divided by the grades of the expansion of the air, from which follows that the mercury in a barometer 42 English miles above the earth would stand a trifle higher than 1/100 part of an English inch.
§ 8. All this and innumerable other experiments prove in a way, clear as the sun, that every particle of air possesses an expanding force which equals, at the surface of the earth, the whole weight of the atmosphere.
§ 9. The praiseworthy Englishman Robert Boyle has also proved by experiments that one cubic inch of air is able, in a heated state, to fill a space of 15000 cubic inches and to press against the surrounding air with the same force as if this space had been filled with air in its natural state, which I presume many will consider incredible. For the sake of convincing the readers I will relate an experiment which can be easily undertaken without any costly and elaborate apparatus. Take an ox bladder and leave it in a small quantity of air; close the bladder tightly at the neck so that not a particle of the enclosed air will be able to escape; expose the bladder to the fire of an ordinary fireplace. Now it will be seen that the enclosed air expands and swells to such an extent, that the bladder becomes quite distended and and packed. But if the same bladder is removed from the fire and put upon a stone-floor or in cold water, it will be found that it quickly regains it former shape, the air inside the bladder is now becoming condensed and reduced to a state in which it does not occupy a larger space than before it was first exposed to the fire, but if the bladder is allowed to remain before the fire for a longer time, so that the air gets still more expanded by the heat, the bladder is bound to burst with a report. This experiment proves not only that the air obtains an incredible expanding force by the heat, but that the air, as soon as it is cooled down, shrinks back again to its former volume.
>From this remarkable quality of the air of expanding when heated is derived the power or effect of the fire-machine. For the steam, which is allowed to pass into the cylinder, is nothing but moist air, heated to a high degree, every particle of air being surrounded by an incomparably thin membrane or coat of water, very much like a bladder.
§ 10. This highly rarefied or expanding hot air drives out speedily all the cold air, existing under the piston, through the snifting valve as soon as it gets into the cylinder, which event takes place with a terrible sputtering noise that generally frightens those onlookers and visitors, who have never witnessed a fire-machine when being started.
§ 11. I have said that the hot air (many will wonder from where all this hot air is derived which the machine seems to demand when it is in constant motion. For those it will be useful to learn that all water contains an un-measurable quantity of air, which can easily be proved by allowing water to stand under the receiver of an air pump) or steam drives the cold air out of the cylinder, but it must also be understood that the cold air helps itself to get out ever so much quicker through the valve as well as between the cylinder and piston, so that the cold water, which is turned on the piston from above, stands, as it were, and boils, because the cold air is also quickly heated by the steam and consequenstly requires a much larger space than it is able to find in the cylinder; as soon as the cold air is thus driven out, which is easily noticed, the communication with the boiler is again closed and the injection-valve opened, which causes a jet of water of one kanna or more--in accordance with the vauum wanted or the weights of the water-columns in the pumps and the friction.
The cold water which jets against the bottom of the piston and falls back as a heavy rain, cools the highly rarefied air and robs it of all its expanding force, thus causing the weight of the atmosphere to bear upon the piston of the machine with a force equal to a weight of 53 skeppund, 18 lispund, 15 skålpund, whilst the weight of the water-columns in the pumps down in the mine, which is 37 fathoms deep, is only 20 skeppund, 16 lispund, 5 skå lpund, which proves that only half of the power of the machine has been used.
§ 12. It is also equally obvious that once the mine becomes 70 fathoms deeper, or altogether 107 fathoms deep, the machine will still be powerful enough to draw water out of such a depth and keep all the so called Solwerbergs mines clear from water, only the pumps will have to be reduced to 6 or 7 inches in diameter instead of the existing 9 inches.