Among these was Synesius, of a noble pagan family, who cultivated philosophy and the mathematics with the utmost ardour, and who had been one of her most intimate friends and followers. On account of his learning, talents, and open disposition, he was universally esteemed, and he had been employed with great success on public occasions of importance. The church at Ptolemais at length wished to have him for their bishop. After much reluctance he accepted the office, but on condition that they should not require him to acknowledge the resurrection of the dead, which he doubted. The people having consented to allow him this indulgence, he suffered himself to be baptized, and became their bishop. He was confirmed by the orthodox patriarch Theophilus, the predecessor of Cyril, to whose jurisdiction Ptolemais belonged; and he afterwards renounced his errors, and declared himself convinced of the truth of the resurrection. This learned man showed his gratitude to Hypatia, by the honourable mention which he made of her in some letters that are still preserved among his writings.
In his fifteenth letter, he tells Hypatia that he was so unfortunate, or found himself so ill, that he wished to use a hydroscopium, and he requests that she would cause one to be constructed for him. “It is a cylindrical tube,” adds he, “of the size of a reed or pipe. A line is drawn upon it lengthwise, which is intersected by others, and these point out the weight of water. At the end of the tube is a cone, the base of which is joined to that of the tube, so that they have both only one base. This part of the instrument is called baryllion. If it be placed in water, it remains in a perpendicular direction, so that one can discover by it the weight of the fluid.”
Petavius, who published the works of Synesius in the year 1640, acknowledges in his annotations, that this passage he did not understand. An old scholiast, he says, who had added some illegible words, seemed to think that it referred to a water-clock; but this he considers improbable, as a clepsydra was not immersed in water, but filled with it. He conjectures, therefore, that it may allude to some such instrument as that which Vitruvius calls chorobates. The latter however was employed for leveling; and it appears that Synesius, who complains of the bad state of his health, could not think of leveling. Besides, no part of the description in Vitruvius agrees with that which is given in so clear a manner by Synesius.
Petau published his edition of the works of this philosopher in the time of Peter de Fermat, conseiller au parlement de Toulouse, a man of great learning, who was an excellent mathematician, and well-acquainted with antiquities and the works of the ancients. We have by the latter a commentary upon some obscure passages of Athenæus, annotations on the writings of Theon of Smyrna, and emendations from a manuscript to the Stratagemata of Polyænus, which may be found also in his Miscellanies. Mursinna, in his edition of the same author, has added them to the end of the preface. As Fermat was often consulted respecting difficult passages of the ancients, he could not be unacquainted with that in the new edition of Synesius. He drew up an explanation of it, and gave it to a friend who was then about to publish a French translation of Bened. Castelli’s book, Della Misura dell’Acque Correnti, and who caused it to be printed along with that work. Fermat died in the year 1665. After his death his son published some of his writings under the title of Varia Opera Mathematica[414]; and in this collection is inserted his short treatise on the hydroscopium, from which I have extracted the following explanation.
It is impossible, says he, that the hydroscopium could be the level or chorobates of Vitruvius, for the lines on the latter were perpendicular to the horizon, whereas the lines on the former were parallel to it. The hydroscopium was undoubtedly a hydrometer of the simplest construction. The tube may be made of copper, and open at the top; but at the other end, which, when used, is the lowest, it must terminate with a cone, the base of which is soldered to that of the tube. Lengthwise, along the tube, are drawn two lines, which are intersected by others, and the more numerous these divisions are, the instrument will be so much more correct. When placed in water, it sinks to a certain depth, which will be marked by the cross lines, and which will be greater in proportion to the lightness of the water. A figure, which is added, illustrates this explanation more than was necessary. When a common friend of Fermat and Petavius showed it to the latter, he considered it to be so just, that he wished to have an opportunity of introducing it in a new edition.
Mersenne, on the other hand, entertains some doubt[415] respecting this instrument, though he does not mention Fermat, with whom he was well-acquainted; for in the dispute which the latter had with Descartes, Mersenne was the bearer of the letters that passed between them, as we learn from the Life of Descartes, by Baillet. His objections however are of little weight. Why should Synesius, asks Mersenne, consider himself unfortunate, because he had not a hydrometer? It may be here replied, that he was in an infirm state, and that the physicians seem to have ordered him to drink no water but what was pure and light. We know that in former times, when so many artificial liquors were not in use, people were accustomed, more than at present, to good water. We read in the works of the ancient physicians, such as Galen and Celsus, directions how to examine the lightness and purity of water. He might have tried it, says Mersenne, with a common balance. He indeed might, but not so conveniently. That Synesius was in a bad state of health is apparent from several of his letters; otherwise one might say that in a letter many expressions may be only jocular, respecting some circumstance known to the friend to whom one writes; and that every expression is not to be taken according to its literal meaning. One might confess also, without weakening a received explanation, not to know what Synesius alludes to in the first line of his letter. But even if we allow that the instrument was not a hydrometer, but a water-clock, or a level; it may be asked how the want of these could make him unfortunate? Mersenne thinks further, that the cone, added to the end of the tube, would have been unnecessary in a hydrometer; but it serves to keep the instrument with more ease in a perpendicular direction in the water. Such is the opinion of H. Klugel, whom I shall soon have occasion to quote.
For the explanation of Fermat one may produce a still stronger testimony, with which he seems not to have been acquainted. It can be proved that this instrument was used in the next, or at least in the sixth century. Of that period, we have a Latin poem on weights and measures, which contains a very just description of a hydrometer. The author, in manuscripts, is called sometimes Priscianus, and sometimes Rhemnius Fannius Palæmon; but we know, from grounds which do not belong to this subject, that the former was his real name. Two persons of that name are known at present. The one, Theodore Priscian, was a physician, and lived in the time of the emperor Valentinian, towards the end of the fourth century. As more physicians have written on weights and measures, with which it is indispensably necessary they should be acquainted, one might conjecture that this Priscian was the author of the above poem. The rest of his writings, however, still preserved, are in so coarse and heavy a style, that one can scarcely ascribe to him a work which is far from being ill-written; especially as it is nowhere said that he was a poet. With much more probability may we consider as the author the well-known grammarian Priscian, who died about the year 528.
This poem has been often printed, and not unfrequently at the end of Q. Sereni Samonici De Medicina Præcepta. The best edition is that inserted by Wernsdorf in the fifth part of the first volume of his Poetæ Minores, where an account may be found of the other editions.
Be the author who he may, this much is evident, that he was acquainted with the hydrometer of Synesius, and has described it in a very clear manner.
“Fluids,” says he, “are different in weight, as may be proved by the specific gravity of oil and honey compared with that of pure water;” and the given proportion agrees almost with that found by modern experiments. “This,” adds he, “may be discovered by an instrument,” which he thus describes:—“It consists of a thin metallic cylinder made of silver or copper, about as large as the joint of a reed between two knots, to the end of which is added a cone. This cone makes the lower end so heavy, that the instrument, without sinking or floating on the surface, remains suspended perpendicularly in the water. Lengthwise, upon the cylinder, is drawn a line, which is divided by cross lines into as many parts as are equal to the weight of the instrument in scripla. If placed in light fluids, more of the divisions will be covered than when put into heavy fluids; or it sinks deeper into those which are light than into those which are heavy. This difference of gravity may be found also,” continues he, “by filling vessels of equal size with the fluids and weighing them; for the heavier must then weigh most; but when one takes an equal weight of two fluids, the lighter will occupy more space than the heavier. If twenty-one divisions of the instrument are covered in water, and twenty-four in oil, and if one take twenty-four scripla of water, twenty-one scripla of oil only can be contained in the space occupied by the water.” Such is the manner in which Professor Klugel has conjectured the meaning of the author from hydrostatic principles; though neither he nor Wernsdorf has ventured to give a literal translation of the words which ought to convey this explanation. But however obscure they may be, it evidently appears that they allude to a hydrometer.