Part 12

The construction of a boiler, on which if a figure is placed, shaped as if in the act of blowing, the figure shall blow on the coals and thus the boiler be heated: moreover, if an open spout project near the mouth of the boiler, nothing shall flow from it until we have first poured cold water into a cup; and the cold water shall not mix with the hot until it passes to the bottom of the vessel, while water extremely hot flows from the spout. The shape of the boiler having been determined at pleasure, in that part of it intended to hold the water a small chamber, perfectly air-tight, is intercepted between two perpendicular partitions. With this chamber a tube, one of those which pass under the coals, communicates near the bottom, one end of the tube being closed that no water may enter it from the boiler: the other tubes lead into the chamber where the water is. Thus when the coals are ignited they will generate vapour through that tube which leads into the small chamber. This vapour is carried along a tube which pierces the surface of the boiler, and through the mouth of the figure on to the coals, (for the figure must be bent so as to blow downwards;) and as vapour is always being generated, the figure is always blowing. The vapour is generated from the fire, and, if we pour a very small quantity of water into the small chamber, we shall produce more vapour, and the figure, blowing with great violence, will heat the boiler still higher: just as in the case of cauldrons exposed to fire we see smoke ascending from the water. The figure should be moveable by means of a double sliding tube, to allow of our pouring in the small quantity of water: and, at the same time, by means of this tube, whenever we do not require the figure to blow on the coals, we can turn it round in the opposite direction. On the surface place a small cup from which a tube leads to the bottom of the boiler, that when cold water is poured in, it may pass through to the bottom. In order that the boiler may admit of being filled when water is poured in, and, at the same time, that the water may not boil over and run out, let another pipe communicate with the cup on its inner surface, to avoid offending the sight. We will now expose to view the construction of the boiler. Set up a hollow cylinder (fig. 74), of which A B is the under surface, and C D the upper; and construct another hollow cylinder, with the same axis as the former, of which E F is the under surface, and G H the upper. On the outer edges of the cylinders let plates be fastened, so as to keep the cylinders together and cover the edges. In the cylinder E F G H place the tubes, O K, L X, M N, of which L X perforates the cylinder on one side only at X, while the other two are bored quite through at each end, and their orifices either way open into the space between the cylinders. Into the space intercepted between the two cylinders let down the partitions E G, H F, intercepting the chamber G H E F, into which the tube described above, perforated at one side only, penetrates. Place on the surface, that is on G H, a small tube having the figure attached to, and communicating with, it; the figure must be perforated throughout, and incline downwards so as to look towards the coals. That the figure may cease blowing whenever we like, let the tube on which it sits be fitted tightly into the other, so that, when we turn it round in the opposite direction, the figure will no longer blow on the coals but away from the boiler. We shall also find this sliding tube useful for pouring water into the chamber G F E H, for, after raising the figure from the tube on which it is placed, we can pour the water through, and thus more vapour will be passed along into the figure. On the surface H C let a cup, R S, be placed; communicating with the interior, and having a tube at its extremity reaching down to the bottom of the boiler with the exception of a passage for water. When we desire to let the hot water out, we must pour in cold through R S; this will pass through the tube which communicates with the cup into the chamber of the warm water, which will ascend and flow out through the spout near the neck, for the cold water which has been introduced will not yet have mingled with the warm below. As often as this is repeated we shall obtain warm water for the cold we throw in. In order that we may know when the boiler will bubble up, the chasmatium is contrived, perforated throughout, and placed on the neck, a hole having been made in the surface: it is furnished with a small tube which looks towards the cup R S, that, when the warm water ascends, it may be carried into the cup. Such is the construction of the boiler. If we prefer not to cut off the chamber F G E H through the whole length, but only for a portion of it, the partitions are made to reach half-way, and another is placed upon them, admitting through it a tube which extends up to the figure. When the fire is kindled there will be a rush of vapour from the small chamber, into which water will be poured as before.

75. A Steam-Boiler from which either a hot Blast may be driven into the Fire, a Blackbird made to sing, or a Triton to blow a Horn.

Another construction of the same kind is employed to produce the sound of a trumpet and the note of a blackbird. A boiler is made (fig. 75), of the same kind as the last, of which all the tubes in the base are bored through at each end, and near the surface there is a tube Q E, into which another tube K L is closely fitted, extending into the chamber for warm air, and moveable about the pin K L. This tube is perforated by three holes, M, N, X, and similarly three holes are bored in Q E opposite the holes M, N, X. Near X, an aperture is made in a support which receives a tube fitting closely into X and surmounted by the figure, as was described in the last paragraph: and from M and N two tubes extend, M O, N P, bent at their upper extremities; these tubes pierce through the surface of the boiler, into which they are carefully soldered. Through the apertures other tubes pass, fitting tightly into the tubes P and O. On one of these tubes is placed the figure of a sparrow, hollow within so as to receive water: the tube on which the bird sits is bent, and provided with a tuning-pipe, such as are made to produce notes, and the curved part of it passes as far as the water contained in the sparrow, so that, when the sound of the pipe reaches the water, the note of a blackbird is produced. In like manner the tube N P has another tube fitting closely into it, on which is placed a figure shaped like a triton with a trumpet in its mouth: the tube on which the triton is placed is moreover furnished with the mouthpiece and bell as usual, and when the vapour reaches these and enters them it will give out the sound of a trumpet. We must discover by trial when the holes in K L are opposite the tubes M O and N P, and when to X on which the figure is placed. Having learnt this, we must make corresponding marks on the pin K L, that the trumpet may sound, or the figure blow, or the blackbird’s note be produced, at our pleasure. The arrangements about the cup and the ascent of the warm water are to be made according to the previous description.

76. An Altar Organ blown by manual Labour.

The construction of a hydraulic organ. Let A B C D (fig. 76), be a small altar of bronze containing water. In the water invert a hollow hemisphere, called a pnigeus, E F G H, which will allow of the passage of the water at the bottom. From the top of this and communicating with it let two tubes ascend above the altar; one of them, G K L M, bent without the altar and communicating with a box, N X O P, inverted, and having its inner surface made perfectly level to fit a piston. Into this box let the piston R S be accurately fitted, that no air may enter by its side; and to the piston attach a rod, T U, of great strength. Again, attach to the piston rod another rod, U Q, moving about a pin at U, and also working like the beam of a lever on the upright rod W Y, which must be well secured. On the inverted bottom of the box N X O P let another smaller box, Z, rest, communicating with N X O P and closed by a lid above: in the lid is a hole through which the air will enter the box. Place a thin plate under the hole in the lid to close it, upheld by means of four pins passing through holes in the plate, and furnished with heads so that the plate cannot fall off: such a plate is called a valve. Again, let another tube, F I, ascend from F G, communicating with a transverse tube, A´ B´, on which rest the pipes A, A, A, communicating with the tube, and having at the lower extremities small boxes, like those used for money; these boxes communicate with the pipes, and their orifices B, B, B, must be open. Across these orifices let perforated lids slide, so that, when the lids are pushed home, the holes in them coincide with the holes in the pipes, but, when the lids are drawn outwards, the connexion is broken and the pipes are closed. Now, if the transverse beam U Q be depressed at Q, the piston R S will rise and force out the air in the box N X O P; the air will close the aperture in the small box Z by means of the valve described above, and pass along the tube M L K G into the hemisphere: again it will pass out of the hemisphere along the tube F I into the transverse tube A´ B´, and out of the transverse tube into the pipes, if the apertures in the pipes and in the lids coincide, that is, if the lids, either all, or some of them, have been pushed home.

In order that, when we wish any of the pipes to sound, the corresponding holes may be opened, and closed again when we wish the sound to cease, we may employ the following contrivance. Imagine one of the boxes at the extremities of the pipes, C D, to be isolated, D being its orifice, E the communicating pipe, R S the lid fitted to it, and G the hole in the lid not coinciding with the pipe E. Take three jointed bars F H, H M, M M^2, of which the bar F H is attached to the lid S F, while the whole moves about a pin at M^3. Now, if we depress, with the hand, the extremity M^2 towards D the orifice of the box, we shall push the lid inwards, and, when it is in, the aperture in it will coincide with that in the tube. That, when we withdraw the hand, the lid may be spontaneously drawn out and close the communication, the following means may be employed. Underneath the boxes let a rod, M^4 M^5, run, equal and parallel to the tube A´ B´, and fix to this slips of horn, elastic and curved, of which M^6, lying opposite C D, is one. A string, fastened to the extremity of the slip of horn, is carried round the extremity H, so that, when the lid is pushed out, the string is tightened; if, therefore, we depress the extremity M^2 and drive the lid inwards, the string will forcibly pull the piece of horn and straighten it, but, when the hand is withdrawn, the horn will return again to its original position and draw away the lid from the orifice, so as to destroy the correspondence between the holes. This contrivance having been applied to the box of each pipe, when we require any of the pipes to sound we must depress the corresponding key with the fingers; and when we require any of the sounds to cease, remove the fingers, whereupon the lids will be drawn out and the pipes will cease to sound.

The water is poured into the altar that the superabundant air, (I mean, of course, that which is thrust out of the box and forces the water upwards,) may be confined in the hemisphere, so that the pipes which are free to sound may always have a supply. The piston R S, when raised, drives the air out of the box into the hemisphere, as has been explained; and when depressed, opens the valve in the small box Z. By this means the box is filled with air from without, which the piston, when forced up again, will again drive into the hemisphere. It would be better that the rod T U should move about a pivot at T also, by means of a single [loop,] R, which may be fitted into the bottom of the piston, and through which the pivot must pass, that the piston may not be drawn aside, but rise and fall vertically.

77. An Altar Organ blown by the agency of a Wind-mill.

The construction of an organ from which, when the wind blows, the sound of a flute shall be produced. Let A, A, A, (fig. 77), be the pipes, B C the transverse tube communicating with them, D E the vertical tube, and E F another transverse tube leading from D E into a box G H, the inner surface of which is made level to fit a piston. Into this box fit the piston K L, which is capable of descending into it freely. To the piston attach a rod, M N, and to this another, N X, working on the rod P R. At N let there be a pin moving readily, and to the extremity X fasten a small plate, X O, near which a rod, S, is to be placed, moving on iron pivots placed in a frame which admits of being shifted. To the rod S attach two small wheels, U and Q, of which U is furnished with pegs placed close to the plate X O, and Q with broad arms like the sails of a wind-mill. When all of these arms, urged by the wind, drive round the wheel Q, the rod S will be driven round, so that the wheel U and the pegs attached to it will strike the plate X O at intervals and raise the piston; when the peg recedes, the piston, descending, will force out the air in the box G H into the tubes and pipes, and produce the sound. We may always move the frame which contains the rod S towards the prevailing wind, that the revolution may be more rapid and uniform.

78. An Automaton, the head of which continues attached to the body, after a knife has entered the neck at one side, passed completely through it, and out at the other; the animal will drink immediately after the operation.

An animal shall be made to drink while it is being severed in two. In the mouth of the animal (fig. 78), let there be a tube, A B, and in the neck another, C D, passing along through one of the outer feet. Between these tubes let a male cylinder, E F, pass, to which are attached toothed bars, G and H. Above G place a portion of a toothed wheel, K, and, in like manner, beneath H a portion of a toothed wheel, L. Over all let there be a wheel, M, the inner rim of which is thicker than the outer; and let sections be cut out of this wheel by the three circles M, N and X, so that the interval between each division may be equal to the radius of the wheel. Let the rim or felly be likewise divided by the circles, so that the circumference of the wheel will no longer be a circle. Having made an incision, O P, in the upper part of the neck, and severed the head within the incision, make in it a circular cavity broader below than above, as it were a female tube shaped like an axe, which will contain two sides of the hexagon inscribed in the circle. Let this cavity be R S, in which the entire rim M N X will revolve in such a manner that, before one division disappears, the beginning of the next will succeed, and similarly with the third: so that, if a pin be inserted through the wheel, the wheel will revolve, and the head of the animal adhere to the neck. Now, if a knife is passed down through the incision O P, it will enter one of the clefts of the wheel M, and confine it in the circular cavity; and, descending lower, it will touch the projecting tooth of the part K of the wheel, which, being forced downwards, will fit its teeth into those of the bar G, and the bar being pushed back will bring the cylinder out of the tube A B. The knife, passing through the intervening space, will still descend and fall upon the projecting tooth of the part L of the wheel; and this, being forced downwards, and fitting its teeth into the toothed bar H, will drive the cylinder out of C D and fit it into A B. This cylinder is an interior tube fitted into the two tubes, that, namely, in the mouth of the animal, and that reaching from the incision in the neck to the hinder foot. When the knife has passed quite through the neck, and the tube E F has touched both A B and C D, let water be offered to the animal, and a pair of sliding tubes, placed under the herdsman, be turned round. When the herdsman revolves, the water above will flow downwards along the tube C D E F A B, and the current of air caused by the stream of water will attract the water offered to the mouth of the animal. Of course the sliding tubes are so arranged that, as the herdsman turns round, the holes in them coincide.

The same result can be brought about without the aid of a stream of water in the following manner. Take once more a pedestal perfectly air-tight, A B C D (fig. 79), having a partition across the middle, E F. Let the tube from the mouth of the animal, G H K, lead into the pedestal, and another tube, L M N, pass through the surface A D and the partition E F. In the tube, L M N, perforate a hole, X, just above the partition E F, and let another tube, O P, fit into it closely, having a hole, R, corresponding with the hole X. To the tube O P attach a figure of Pan, or some other figure with a fierce look, and, when the figure is turned towards the animal, it shall not drink, as though frightened; when the figure turns away, it shall drink. Now, if we pour water into the compartment A D E F through a hole, G´, which must afterwards be carefully closed with wax or some other substance, it will be found that, if the holes R and X are made to coincide, the water which was poured in will pass into the compartment E B C F. As A D E F becomes empty, it will attract the air through the mouth of the figure, which will then drink when a cup is presented to it.

APPENDIX.

There are four MSS. of Hero contained in the British Museum. Two belong to the Harleian Collection: they are numbered 5605 and 5589, and are assigned, the first to the fifteenth, the second to the sixteenth century; they are distinguished in the table below by the letters a and b. The others are among the Burney MSS., (108 and 81), and are both assigned to the sixteenth century: they are cited as c and d. Of these MSS. the first and third, (a and c), are by far the most trustworthy: they generally supply the clauses missing in the printed text, and often furnish emendations of passages otherwise corrupt. The other two agree, for the most part, with each other, and with the printed text, both in the omission of numerous clauses and in the grossest errors in individual words. It is thus rendered probable that the defects of the Paris edition are in great measure due, not to the Editors, but to the MS. followed.

In the following table of emendations made in the text of Hero as it appears in the Veterum Mathematicorum Opera, those only have been noticed which appeared curious or important. Many more have been passed over in which the correction was obvious even without the aid of any MS. The references are to the page and line of the Paris edition.

Page and | | Line of | | Paris | | edition. | Reading of Paris Text. | Reading adopted. ------------+--------------------------+---------------------------- 147 - 29 | συκίαν a b d. | σικύαν c. 150 - 10 | ἐκφανείας | ἐπιφανείας a b c d. — - 34 | τὴν—διαστολὴν | κατὰ τὴν—διαστολὴν a. 151 - 8 | μυκτῆρσιν d. | μυκτῆρσιν ἀέρος a b c. — - 51 | ὅσας | ὅσαι a b c d. 153 - 6 | βαθύτερον d. | βαρύτερον a b c. — - 23 | στεγνὸν d. | στενὸν a c. 155 - 3 | ἀντέχον a c d. | ἀντέχων b. 156 - 1 | πνυκτικὸς a b. | πνικτικὸς c. | | Commandine reads | | πνευματικὸς. — - 24 | ἀλλὰ τὸ μὴ c. | ἀλλὰ τῷ μὴ a b d. — - 26 | ἀντεπεξίοντος | ἀντὶ τοῦ ἐπεξίοντος a b | | c d. 159 - 17 | τὸ ἐν τῷ ὑγρῷ | τὸ ἐν ἀυτῷ ὑγρὸν a c. | (τὸ εν τῷ ὑγρον b.) | 161 - 2 | ἰσθμὸς | ἠθμὸς. This correction, | | adopted originally on the | | conjecture of Professor | | Malden, is supported by the | | variations of the MSS.; a | | reads ἱθμος, b ἡθμος. In | | like manner elsewhere read | | ἠθμοειδή, &c. for ἰσθμοειδή. — - 20 | ἐκκεκρυήσεται | οὐκ ἐκρυήσεται | (so all the MSS.) | 170 - 30 | ἐκείνοις | ἔκεινον a b c. 172 - 17 | κατέχοντος c. | κατέχοντες a b. — - 18 | ἐὰν δὲ ἄνω ὄντος | ἐὰν δὲ ἀνῶμεν ἔτι ἄνω ὄντος | | a b c. — - 30 | ἴσον, ἐὰν | ὅσον ἐὰν a b c. 173 - 20–24 | This passage is unintelligible as it stands. It should | be read (with a b c) as follows:— | | Ἐγχέωμεν οὖν καὶ εἰς τὴν ΜΝΞΟ βάσιν καὶ εἰς τὸν ΠΡ | κρατῆρα τὸν οἶνον ὥστε πλήρη εἶναι τὸν ΠΡ κρατῆρα, | καὶ τὴν ΜΝΞΟ βάσιν πεπληρῶσθαι ἄχρι τοῦ Η στομίου | τοῦ σωλῆνος· τούτου δὲ γενομένου, καὶ φραγέντος | τοῦ Ε, οὐ διὰ τοῦ ΚΛ σωλῆνος, &c. In the printed | text all the words from τὸν οἶνον to τὸν κρατῆρα | inclusive are omitted; so is the οὐ after φραγέντος. | In the translation the MSS. have been departed from | in reading “as high as the mouth of the tube G H,” | instead of “as high as the mouth G of the tube G H.” | The latter reading is clearly inconsistent with the | argument. 174 - 3 | εἰσχωρεῖ καὶ διὰ τοῦ | εἰσχωρεῖν καὶ διὰ τοῦ Υ | τρήματος | τρήματος a b c. — - 13 | ὁ Κ, ὁ κενὼν | ὁ Κ ἔνων a b c. 177 - 1 | ἀνακεκαμφθέντα ἀγγεῖα | ἀνακεκάμφθω εἰς τὰ ἀγγεῖα | | c. a b have ἀνακεκάμφω. — - 24 | The printed text is here quite unintelligible. | We find (beginning of § 24 in translation) these | words:—ἔστω σμηρισμάτιον ᾧ ἐὰν βουλώμεθα λόγῳ· ἔστω | δὲ τὸ ὕδωρ τοῦ οἴνου διπλάσιον. The opening sentence | should be as follows: Ἀγγείου ὄντος κενοῦ καὶ ἑτέρου | οἶνον ἔχοντος, ὅσον ἐὰν ὕδωρ εἰς τὸ κενὸν ἀγγεῖον | ἐμβάλωμεν, τοσοῦτον διὰ κρουνοῦ ληψόμεθα κεκραμένον | ᾧ ἐὰν βουλώμεθα εἶναι λόγῳ· ἔστω δὲ τὸ ὕδωρ τοῦ οἴνου | διπλάσιον. So a c: b d agree with the text. 180 - 11 | Omit τρίτου with a c: b d agree with the text | in retaining the word, which is unintelligible. 192 - 3 | ἐπιληφθέντα b d. | ἐπειληθέντα c. | | a has ἐπειληφθέντα. 193 - 26 | ἀποδεδεμένοι | ἀποδεδομένοι a b c d. 195 - 7 | ἀποδεδόσθω | ἀποδεδέσθω a b c d. 197 - 6 | ἄνω a b c d. | κάτω, which is given in | | the margin of d, is | | necessary to the sense. 200 - 8 | Read ἐναρμοσθεὶς εἰς τὸ σφαίριον φερέτω εἰς τὴν χώνην, | καὶ ἐμβεβλήσθω εἰς τὸ σφαίριον ὕδωρ. So all the MSS. | In the text all from φερέτω to σφαίριον inclusive is | omitted. — - 14 | After ὑγρὸν add καὶ ἀναπληρώσει τὸν κενωθέντα τόπον. | So a b c. 202 - 20 | The last clause of § 50 (of the translation) is | unintelligible as it stands in the printed text. | For στρέφειν εἰς τὴν χώραν a and c give εἰς τὴν | σφαῖραν. In the translation σφαῖραν is preferred to | χώραν, and εἰς omitted. 205 - 10 } | Clauses of considerable length are missing in the 206 - 10 } | text from the usual cause. They are supplied in 185 - 11 } | the translation. 212 | The arrangement of the three plans for self-acting | lamps has been altered in conformity with a and c; | b and d, agreeing with the printed text. 216 - 26 | ἐκπίπτοντος | εἰσπίπτοντος a. 223 - 7 | ΓΔ (CD) | ΕΖ (EF): this change has | | been made on conjecture. — - 16 | Before ὥστε ἢ has been inserted, without support | from the MSS. The passage is otherwise | self-contradictory. 226 - 23 | διηνοιγμένον a b c d. | διενηνεγμένον? 227 - 21 | This passage is corrupt, but the MSS. give no light. 228 - 8 | ἐκτὸς | ἐντὸς a b c d. — - 41 | ἐν τοῖς αὐλοῖς a b c d.| τοῖς ἐν τοῖς αὐλοῖς? 229 - 30–40 | The reading of the text is evidently corrupt here, | but the MSS. do not supply means for correcting it: μίας | οὔσης may be a corruption of μενούσης; Hero speaks | elsewhere of a περόνη μένουσα. 232 - 14 | The text and all the MSS. read ὑπὸ; nevertheless ὑπὲρ | has been substituted in the translation. If the holes X | and R were beneath the partition, the action of the | tubes would fail.

INDEX.

Air (atmospheric), 1.

Adamant, 2.

Anvil, 2.

Archimedes, 9.

Air-pump (condensing), 23.

Altar, 26, 83.

Apple, 62.

Arrow, 62.

Air-engine, 95.

Bottle, 3.

Bitumen, 5.