A Source Book in Greek Science

Author: Hero of Alexandria

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The Principles of Pneumatics and Some Demonstrations

Hero of Alexandria, Pneumatics I, Introduction; II. 11.1 Translation of J. G. Greenwood


The investigation of the properties of Atmospheric Air having been deemed worthy of close attention by the ancient philosophers and mechanists, the former deducing them theoretically, the latter from the action of sensible bodies, we also have thought proper to arrange in order what has been handed down by former writers, and to add thereto our own discoveries: a task from which much advantage will result to those who shall hereafter devote themselves to the study of mathematics. We are further led to write this work from the consideration that it is fitting that the treatment of this subject should correspond with the method given by us in our treatise, in four books, on water-clocks. For, by the union of air, earth, fire, and water, and the concurrence of three, or four, elementary principles, various combinations are effected, some of which supply the most pressing wants of human life, while others produce amazement and alarm.

But, before proceeding to our proper subject, we must treat of the vacuum.1 Some2 assert that there is absolutely no vacuum; others that, while no continuous vacuum is exhibited in nature, it is to be found distributed in minute portions through air, water, fire, and all other substances: and this latter opinion, which we will presently demonstrate to be true from sensible phenomena, we adopt. Vessels which seem to most men empty are not empty, as they suppose, but full of air. Now the air, as those who have treated of physics are agreed, is composed of particles minute and light, and for the most part invisible. If, then, we pour water into an apparently empty vessel, air will leave the vessel proportioned in quantity to the water which enters it. This may be seen from the following experiment. Let the vessel which seems to be empty be inverted, and, being carefully kept upright, pressed down into water; the water will not enter it even though it be entirely immersed: so that it is manifest that the air, being matter, and having itself filled all the space in the vessel, does not allow the water to enter. Now, if we bore the bottom of the vessel, the water will enter through the mouth, but the air will escape through the hole. Again, if, before perforating the bottom, we raise the vessel vertically, and turn it up, we shall find the inner surface of the vessel entirely free from moisture, exactly as it was before immersion. Hence it must be assumed that the air is matter. The air when set in motion becomes wind (for wind is nothing else but air in motion), and if, when the bottom of the vessel has been pierced and the water is entering, we place the hand over the hole, we shall feel the wind escaping from the vessel; and this is nothing else but the air which is being driven out by the water. It is not then to be supposed that there exists in nature a distinct and continuous vacuum, but that it is distributed in small measures through air and liquid and all other bodies.1 Adamant2 alone might be thought not to partake of this quality, as it does not admit of fusion or fracture, and, when beaten against anvils or hammers, buries itself in them entire. This peculiarity however is due to its excessive density: for the particles of fire, being coarser than the void spaces in the stone, do not pass through them, but only touch the outer surface; consequently, as they do not penetrate into this, as into other substances, no heat results. The particles of the air are in contact with each other, yet they do not fit closely in every part, but void spaces are left between them, as in the sands on the sea shore: the grains of sand must be imagined to correspond to the particles of air, and the air between the grains of sand to the void spaces between the particles of air. Hence, when any force is applied to it, the air is compressed, and, contrary to its nature, falls into the vacant spaces from the pressure exerted on its particles: but when the force is withdrawn, the air returns again to its former position from the elasticity of its particles, as is the case with horn shavings and sponge, which, when compressed and set free again, return to the same position and exhibit the same bulk. Similarly, if from the application of force the particles of air be divided and a vacuum be produced larger than is natural, the particles unite again afterwards; for bodies will have a rapid motion through a vacuum, where there is nothing to obstruct or repel them, until they are in contact. Thus, if a light vessel with a narrow mouth be taken and applied to the lips, and the air be sucked out and discharged, the vessel will be suspended from the lips, the vacuum drawing the flesh towards it that the exhausted space may be filled. It is manifest from this that there was a continuous vacuum in the vessel. The same may be shown by means of the egg-shaped cups used by physicians, which are of glass, and have narrow mouths. When they wish to fill these with liquid, after sucking out the contained air, they place the finger on the vessel’s mouth and invert them into the liquid; then, the finger being withdrawn, the water is drawn up into the exhausted space, though the upward motion is against its nature. Very similar is the operation of cupping-glasses, which, when applied to the body, not only do not fall though of considerable weight, but even draw the contiguous matter toward them through the apertures of the body. The explanation is that the fire placed in them consumes and rarefies the air they contain, just as other substances, water, air or earth, are consumed and pass over into more subtle substances. . . .1

When, therefore, the air in the cupping-glasses, being in like manner consumed and rarefied by fire, issues through the pores in the sides of the glass, the space within is exhausted and draws towards it the matter adjacent, of whatever kind it may be. But, if the cupping-glass be slightly raised, the air will enter the exhausted space and no more matter will be drawn up.

They, then, who assert that there is absolutely no vacuum may invent many arguments on this subject, and perhaps seem to discourse most plausibly though they offer no tangible proof. If, however, it be shewn by an appeal to sensible phenomena that there is such a thing as a continuous vacuum, but artificially produced; that a vacuum exists also naturally, but scattered in minute portions; and that by compression bodies fill up these scattered vacua, those who bring forward such plausible arguments in this matter will no longer be able to make good their ground.

Provide a spherical vessel, of the thickness of metal plate so as not to be easily crushed, containing about 8 cotylae [2 quarts].2 When this has been tightly closed on every side, pierce a hole in it, and insert a siphon, or slender tube, of bronze, so as not to touch the part diametrically opposite to the point of perforation, that a passage may be left for water. The other end of the siphon must project about 3 fingers’ breadth [2 inches]2 above the globe, and the circumference of the aperture through which the siphon is inserted must be closed with tin applied both to the siphon and to the outer surface of the globe, so that when it is desired to breathe through the siphon no air may possibly escape from the vessel. Let us watch the result. The globe, like other vessels commonly said to be empty, contains air, and as this air fills all the space within it and presses uniformly against the inner surface of the vessel, if there is no vacuum, as some suppose, we can neither introduce water nor more air, unless the air contained before make way for it; and if by the application of force we make the attempt, the vessel, being full, will burst sooner than admit it. For the particles of air cannot be condensed, as there must in that case be interstices between them, by compression into which their bulk may become less; but this is not credible if there is no vacuum: nor again, as the particles press against one another throughout their whole surface and likewise against the sides of the vessel, can they be pushed away so as to make room if there is no vacuum. Thus in no way can anything from without be introduced into the globe unless some portion of the previously contained air escape; if, that is to say, the whole space is closely and uniformly filled, as the objectors suppose. And yet, if any one, inserting the siphon in his mouth, shall blow into the globe, he will introduce much wind without any of the previously contained air giving way. And, this being the uniform result, it is clearly shown that a condensation takes place of the particles contained in the globe into the interspersed vacua. The condensation however is effected artificially by the forcible introduction of air. Now if, after blowing into the vessel, we bring the hand close to the mouth, and quickly cover the siphon with the finger, the air remains the whole time pent up in the globe; and on the removal of the finger the introduced air will rush out again with a loud noise, being thrust out, as we stated, by the expansion of the original air which takes place from its elasticity. Again, if we draw out the air in the globe by suction through the siphon, it will follow abundantly, though no other substance take its place in the vessel, as has been said in the case of the egg. By this experiment it is completely proved that an accumulation of vacuum goes on in the globe; for the particles of air left behind cannot grow larger in the interval so as to occupy the space left by the particles driven out. For if they increase in magnitude when no foreign substance can be added, it must be supposed that this increase arises from expansion, which is equivalent to a re-arrangement of the particles through the production of a vacuum. But it is maintained that there is no vacuum; the particles therefore will not become larger, for it is not possible to imagine for them any other mode of increase. It is clear, then, from what has been said that certain void spaces are interspersed between the particles of the air, into which, when force is applied, they fall contrary to their natural action.

The air contained in the vessel in water does not undergo much compression, for the compressing force is not considerable, seeing that water, in its own nature, possesses neither weight nor power of excessive pressure.1 Whence it is that, though divers to the bottom of the sea support an immense weight of water on their backs, respiration is not compelled by the water, though the air contained in their nostrils is extremely little. It is worth while here to examine what reason is given why those who dive deep, supporting on their backs an immense weight of water, are not crushed. Some say that it is because water is of uniform weight: but these give no reason why divers are not crushed by the water above. The true reason may be shown as follows: Let us imagine the column of liquid which is directly over the surface of the object under pressure (in immediate contact with which the water is) to be a body of the same weight and form as the superincumbent liquid, and that this is so placed in the water that its under surface coincides with the surface of the body pressed, resting upon it in the same manner as the previously superincumbent liquid, with which it exactly corresponds. It is clear, then, that this body does not project above the liquid in which it is immersed, and will not sink beneath its surface. For Archimedes has shewn, in his work On Floating Bodies, that bodies of equal weight with any liquid, when immersed in it, will neither project above nor sink beneath its surface:1 therefore they will not exert pressure on objects beneath.2 Again, such a body, if all objects which exert pressure from above be removed, remains in the same place; how then can a body which has no tendency downward exert pressure? Similarly, the liquid displaced by the body will not exert pressure on objects beneath; for, as regards rest and motion, the body in question does not3 differ from the liquid which occupies the same space.

Again, that void spaces exist may be seen from the following considerations: for, if there were not such spaces, neither light, nor heat, nor any other material force could penetrate through water, or air, or any body whatever. How could the rays of the sun, for example, penetrate through water to the bottom of the vessel?4 If there were no pores in the fluid, and the rays thrust the water aside by force, the consequence would be that full vessels would overflow, which however does not take place. Again, if the rays thrust the water aside by force, it would not be found that some were reflected while others penetrated below; but now all those rays that impinge upon the particles of the water are driven back, as it were, and reflected, while those that come in contact with the void spaces, meeting with but few particles, penetrate to the bottom of the vessel. It is clear, too, that void spaces exist in water from this, that, when wine is poured into water, it is seen to spread itself through every part of the water, which it would not do if there were no vacua in the water. Again, one light traverses another; for, when several lamps are lighted, all objects are brilliantly illuminated, the rays passing in every direction through each other. And indeed it is possible to penetrate through bronze, iron, and all other bodies, as is seen in the instance of the marine torpedo.5

That a continuous vacuum can be artificially produced has been shewn by the application of a light vessel to the mouth and by the egg of physicians.1 With regard, then, to the nature of the vacuum, though other proofs exist, we deem those that have been given, and which are founded on sensible phenomena, to be sufficient. It may, therefore, be affirmed in this matter that every body is composed of minute particles, between which are empty spaces less than the particles of the body2 (so that we erroneously say that there is no vacuum except by the application of force, and that every place is full either of air, or water, or some other substance) and, in proportion as any one of these particles recedes, Psome other follows it and fills the vacant space: that there is no continuous vacuum except by the application of some force: and again, that the absolute vacuum is never found, but is produced artificially.

These things having been clearly explained, let us treat of the theorems resulting from the combination of these principles; for, by means of them, many curious and astonishing kinds of motion may be discovered.3

A Ball Rotated by Steam

11. Place a cauldron over a fire: a ball shall revolve on a pivot. A fire is lighted under a cauldron, AB [see figure], containing water, and covered at the mouth by the lid CD: with this the bent tube EFG communicates, the extremity of the tube being fitted into a hollow ball, HK. Opposite to the extremity G place a pivot, LM, resting on the lid CD; and let the ball contain two bent pipes, communicating with it at the opposite extremities of a diameter, and bent in opposite directions, the bends being at right angles and across the lines FG, LM. As the cauldron gets hot it will be found that the steam, entering the ball through EFG, passes out through the bent tubes towards the lid, and causes the ball to revolve, as in the case of the dancing figures.1

Philo of Byzantium, Pneumatics 7, 8 (Schmidt)2

A Thermoscope

7. Fire, too, by its nature is closely connected with air, and for that reason air is drawn along with it.3 This will be proved by what follows.

Take a sphere of lead, hollowed out, so that there is room within, and of moderate size. It should not be too thin, lest it be easily broken; nor should it be too heavy. For our

purposes it should be quite dry.4 Pierce the sphere on top and insert a bent tube reaching almost to the bottom. Place the other end of the same tube in another vessel filled with water. Let this end also, as in the other case, reach almost to the bottom, so that the flow of water may be facilitated.1 Call the sphere A, the tube B, and the vessel C.

I say, then, that if you expose the sphere to the sun, part of the air enclosed in the tube will pass out when the sphere becomes hot. This will be evident because the air will descend from the tube into the water, agitating it and producing a succession of bubbles.

Now if the sphere is put back in the shade, that is, where the sun rays do not reach it, the water will rise and pass through the tube until it descends into the sphere. If you then put the sphere back in the sun the water will return to the vessel; but it will flow back to the sphere once more if you place the sphere in the shade. No matter how many times you repeat the operation the same thing will always happen.

In fact, if you heat the sphere with fire, or even if you pour hot water over it, the result will be the same. And if the sphere is then cooled, water passes from the vessel to the sphere.

Combustion and Air

8. . . . Hence we shall prove that a place cannot be empty of air and of all other bodies as well. For example, pour water into a vessel, A.

In the center of A let a sort of candle-holder, B, be set up protruding over the water, and let a lighted candle, C, be placed at the top of B. Over C invert vessel D in such a way that its mouth is near the water2 and the candle is in the center of D. A short while after this is done you will see water rise from the lower to the upper vessel. Now this will not happen except for the reason we have indicated, namely, that the air enclosed in vessel D is destroyed by the fire, because air cannot remain in proximity to fire. After the air has been destroyed by the action of the fire, the latter will raise the water in proportion to the quantity of air which is lost. This is similar to what takes place in the case of the tube described above.3 Thus the air in this vessel (D) placed over the candle is destroyed because it is, so to speak, dissolved by the fire. For this reason the water is raised and entering fills the place left by the air, since that place was empty. The figure is appended.4

1 See p. 211, n. 1, above. [Edd.]

2 E.g., Aristotle (see pp. 204 ff.). [Edd.]

1 Hero (or Strato) holds here that there is a void between any two atoms of a material body, but that a complete void between two bodies of gross matter cannot exist naturally, though it can, as the sequel shows, be produced artificially. [Edd.]

2 The reference here is to the diamond. [Edd.]

1 There follow, in the part here omitted, instances of transformation of the elements through intermixture. [Edd.]

2 The figure in brackets is only approximate. [Edd.]

1 The Greek text may mean that water naturally has no weight in water (cf. Aristotle’s view, p. 247), though the translator does not so interpret it. [Edd.]

1 See p. 237. [Edd.]

2 But this is true only because the water exerts buoyant force from below. In other words, this explanation is not essentially different from the other if that be understood to mean that the pressure at any point below the surface is equal in all directions (see pp. 247 f.). [Edd.]

3 The translator supplies this word, as necessary to the sense, though it is not in the manuscripts. The text of W. Schmidt (Leipzig, 1899) may be rendered thus: "for only with regard to rest and motion does the body in question differ from the liquid which occupies the same place." [Edd.]

4 The assumption is that light is corporeal, an assumption that Aristotle sought to refute (see p. 285). [Edd.]

5 The reference is to the conduction by metals of the electric shock of the torpedo (see p. 430). [Edd.]

1 I.e., the cupping glass. [Edd.]

2 It would seem to follow that within a body of gross matter the atoms occupy more space than the void. But wide variations among substances in their weight per unit of volume would be excluded, on this theory, if the atoms differed only in size and shape. [Edd.]

3 There follows the passage on the siphon (see pp. 242 ff.). [Edd.]

1 The passage of the steam is accompanied by a reaction that causes the sphere to rotate in the opposite direction. In a similar device operated by warmed air, not by steam, as here, a disk upon which are placed small figures is made to rotate. It is to this that the "dancing figures" refer. Cf. the action of the modern rotating lawn sprinkler. It may be noted that the translator entitles this chapter "The Steam-Engine." [Edd.]

3 The precise meaning is doubtful. The next selection would seem to indicate that the meaning is that the air is attracted by the fire and destroyed, but here it is the expansion of air that is involved.

4 I.e., "water-proof," as the extant Arabic version indicates.

1 For this purpose the end must always be immersed in water.

2 So both the Latin and the extant Arabic versions. But for the experiment to succeed the mouth must be under the water.

3Pneumatics, ch. 7.

4 Though the idea of destruction of air in combustion is here expressed, there is, of course, no notion of oxidation.

Cf. Galen IV. 487–488 (Kühn): "For clearly we see these [flames], just as living things, swiftly extinguished when they are deprived of air. If a physician’s cupping instrument or any narrow or concave vessel be put over the flames so as to cut off the access of air they are soon snuffed out. Now if we could discover why flames are in these cases extinguished, we should perhaps discover what advantage the heat in animals derives through respiration."


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Chicago: Hero of Alexandria, "Combustion and Air," A Source Book in Greek Science, ed. Schmidt and trans. J. G. Greenwood in A Source Book in Greek Science, ed. Morris R. Cohen and I. E. Drabkin (Cambridge: Harvard University Press, 1948), 248–256. Original Sources, accessed December 6, 2022, http://www.originalsources.com/Document.aspx?DocID=LHQKZEAHKTVPPZN.

MLA: Hero of Alexandria. "Combustion and Air." A Source Book in Greek Science, edited by Schmidt, and translated by J. G. Greenwood, Vol. II, in A Source Book in Greek Science, edited by Morris R. Cohen and I. E. Drabkin, Cambridge, Harvard University Press, 1948, pp. 248–256. Original Sources. 6 Dec. 2022. http://www.originalsources.com/Document.aspx?DocID=LHQKZEAHKTVPPZN.

Harvard: Hero of Alexandria, 'Combustion and Air' in A Source Book in Greek Science, ed. and trans. . cited in 1948, A Source Book in Greek Science, ed. , Harvard University Press, Cambridge, pp.248–256. Original Sources, retrieved 6 December 2022, from http://www.originalsources.com/Document.aspx?DocID=LHQKZEAHKTVPPZN.