This instrument, called in Latin hydrometrum, hygroscopium, hygrobaroscopium, hydroscopium, areometrum, and baryllion, serves to determine the weight or specific gravity of different fluid masses, by the depth to which it sinks in them.

The laws respecting the comparative specific gravity of fluids and solid bodies immersed in them were discovered by Archimedes, when he tried the well-known experiment, by order of Hiero king of Sicily, to find the content of a golden crown, made for that sovereign. Upon these is founded the construction of the hydrometer; and it is not improbable that Archimedes, who was killed in the year 212 before the Christian Æra, was the inventor of it, though no proofs to warrant this conjecture are to be found in the writings of that great man, or in those of any other author.

The oldest mention of the hydrometer occurs in the fifth century, and may be found in the letters of Synesius to Hypatia. Of the lives of these two persons I must here give some anecdotes, as they deserve to be known on account of the singular fate which attended them. Hypatia was the daughter of Theon, a well-known mathematician of Alexandria, some of whose writings are still extant. By her father she was instructed in mathematics, and from other great men, who at that time abounded in Alexandria, she learned the Platonic and Aristotelian philosophy, and acquired such a complete knowledge of these sciences, that she taught them publicly with the greatest applause. She was young and beautiful, had a personable figure, was sprightly and agreeable in conversation, though at the same time modest; and she possessed the most rigid virtue, which was proof against every temptation. She conducted herself with so much propriety towards her lovers, that they never could obtain more than the pleasure of her company and of hearing her discourse; and with this, which they considered as an honour, they were contented. Those who wished to intrude further were dismissed; and she destroyed the appetite of one who would not suffer her to philosophise, by means of some strong preparation, which, as far as I know, remained a secret. She was not baptized, and with all her knowledge, adopted the blind superstition of paganism. Had she been a Christian, and suffered a cruel death from heathen persecution, she would have merited a place in the martyrology of the saints: but the case was reversed; for, by the conduct of the Christians towards her, she became entitled to have her name enrolled in the martyrology of the philosophers.

The patriarch of Alexandria, at the time when she lived, was Cyril, whose family for a hundred years before had produced bishops, who were of more service to their relations than to the church. This prelate was a proud, litigious, vindictive and intolerant man, who thought every thing lawful which he conceived to be for the glory of God; and who, as prosecutor and judge, condemned Nestorius without hearing his defence. In the city of Alexandria, which was then very flourishing on account of its commerce, the emperor allowed greater toleration than he imagined could be justified to the clergy in any other place; and it contained a great many Jews, who carried on an extensive trade, as well as a number of pagan families who were of service to the city, or at least did it no harm. This, in the eyes of Cyril, was not proper; he would have the sheep-fold clean, and the Jews must be banished. Orestes, however, the governor, who was a man of prudence, and better acquainted with the interests of the city, opposed a measure that was likely to be attended with mischief, and he even caused to be condemned to death a Christian profligate, who had done some injury to the Jews. This malefactor was, by the order of Cyril, buried in the church as a martyr; and he immediately collected five hundred monks, who ill-treated Orestes in the streets, and excited an insurrection among the people, who plundered the unfortunate Jews, and expelled them from a city in which they had lived since the time of Alexander the Great.

Cyril, observing one day a great number of horses and servants belonging to persons of the first rank, before a certain house in the city, inquired the cause of their being assembled in that manner. He was informed that the house was the habitation of the celebrated female philosopher Hypatia, who, on account of her extensive learning and eminent talents, was visited not only by people of the highest distinction, but even by the governor himself. This was sufficient to excite the bishop’s jealousy against the unbelieving Hypatia, and he resolved to effect her ruin. As he had instigated the people against the Jews, he in like manner encouraged them to attack Hypatia. They seized her in the street, hurried her to the church, stripped off her clothes, tore her flesh to pieces with potsherds, dragged her mangled limbs about through the city, and at length burned them. This bloody tragedy, which took place in the year 415, could tend only to inspire the heathens with a greater hatred to Christianity, and to make sensible Christians ashamed of the conduct of their brethren. To Cyril, however, it occasioned no shame; on the contrary, he endeavoured to divert the emperor from punishing those who had been guilty of so gross a violation of the principles of justice, and in this he was assisted by his numerous adherents and friends. In some circumstances of this relation historians are not agreed, but they all concur in bestowing praise on Hypatia, whose memory was honoured and preserved by her grateful and affectionate scholars413.

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 Mathematica414; 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 doubt415 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.

This poem was once published together with Celsus De Re Medica, in 1566, by Robert Constantin, who died at an advanced age in 1605, and who added a few, but excellent notes, which have been inserted by Wernsdorf in his edition. This Constantin seems to have known that the instrument of Priscian and the hydroscopium of Synesius were the same; and that they were used for determining the weight of fluids. He explains the use of them very properly; but is mistaken in supposing the cone to have been of wood, though it served to render the lower part of the instrument heavier, as the poet himself says: “cui cono interius modico pars ima gravatur.” I am almost induced to think that interius implies that additional weight was given to the cone by throwing some small heavy bodies into it, through the opening above; and at present grains of leaden shot are employed for that purpose. It appears therefore that the honour of having first given a good explanation of the before-quoted passage of Synesius belongs rather to Constantin than to Fermat; but I can readily believe that the latter was not acquainted with the observations made on it by the former. Before I conclude the history of this instrument among the ancients, I shall add two remarks further. It is evidently wrong when one, with Muschenbroek and others, whose opinion I adopted before I engaged in this research, considers Hypatia as the inventress of the hydrometer. It was known at her time, and was made at Alexandria; but it seems not to have been very common, as Synesius wrote to Hypatia to procure him one, and even thought it necessary to give her a description of it.

Those are mistaken likewise, who say that this instrument was called also baryllium. That word, as far as I have been able to learn, occurs only in Synesius, who expressly tells us that the small heavy cone alone was meant by it. In the same manner has it been understood by Constantin. In the Dictionary of Basle it is said to be hydroscopii pars; and in Stephen’s Dictionary it is explained by pondusculum, as well as in that of Ernest, where it is given as the diminutive of baros. It signified therefore the heavy part of the hydrometer only.

It is equally erroneous when one says, with Muschenbroek and others, that those who among the Romans made it their employment to examine the quality of water with the hydrometer, were called baryllistÆ or barynilÆ. These words do not occur in the works of the ancient Latin authors, nor in any of the completest dictionaries. We read only the following passage in some editions of the Commentary of Servius upon Virgil: “Scrutatores et repertores aquarum (aquilices dicuntur) barinulas dixerunt416.” If these words were really written by Servius, who lived in the fifth century, he either confounded the water-searchers, aquilices, those who sought for springs, with those who examined the nature of water when found, as the hydrometer was of no service to the former in their business; or both employments must at that time have been followed by the same people, and these must have acquired their name from a part only of one instrument they used, which is not at all probable.

I think we may with certainty believe that the hydrometer was not known to Seneca, Pliny, or Galen, who died about the end of the second century. Were not this the case, it would certainly have been mentioned by the first, where he speaks so minutely of the specific gravity of hard and fluid bodies417; by the second, where he says that the weight of water was ascertained by a common balance418; and by the last, where he gives directions how to discover its lightness. Galen adds, that in his time a method had been invented of determining the quality of salt-lye by placing an egg in it, and observing whether it floated419. Have we not reason to think that on this occasion the hydrometer must have occurred to him had it been then used?

But however well-known it may have been in the fifth century, it seems that it was afterwards entirely forgotten, and that towards the end of the sixteenth it was again for the first time revived or invented anew. To George Agricola it was scarcely known; for where he speaks of the weight of different kinds of water, and particularly of that of salt springs420, he does not mention it. Constantin, however, who lived at the same time, must have been acquainted with it, else he could not have explained the before-mentioned passages of Synesius and Priscian.

I am inclined to think that the first account of the hydrometer being again brought into use must be found in the oldest German books on salt-works. It is at any rate certain that from these the modern philosophers became first acquainted with it. One of the earliest who has described it is the Jesuit Cabeus, who wrote about the year 1644421; but he confesses that he acquired his information from a German treatise by Tholden, whom Kircher422 calls a German artist. He was however not properly an artist. He was a native of Hesse; a good chemist for his time; and resided about the year 1600 or 1614 as overseer of the salt-works at Frankenhausen in Thuringia. His treatise, which Cabeus had in his possession, was entitled Tholden’s Haligraphia, printed at Leipsic in 1603. Another edition, printed at the same place in 1613, is mentioned by Draudius; but at present I have not been able to find it; and can say only from Cabeus and Leupold, that Tholden’s hydrometer had a weight suspended to it; and that he speaks of the instrument not as a new but a well-known invention, and on that account has described it only imperfectly.

Kircher, whose works were generally read, seems to have principally contributed towards making it publicly known; and Schott423, Sturm424 and others, in their account of it, refer to his writings. The artists at Nuremberg, who worked in glass, and who constructed a great many hydrometers which were everywhere sold, assisted in this likewise. One, above all, made by Michael Sigismund Hack, was highly valued about the beginning of the last century, as we are told by J. Henry Muller, professor at Altorf. Of this artist, often mentioned by Sturm and other philosophers, an account has been given by Doppelmayer. He died in 1724.

Many improvements, or perhaps only alterations, have been made in this instrument in later times by a variety of artists. The task of collecting these completely in chronological order with explanations, I shall leave to others; and only mention a few of them. One of the first who endeavoured to adapt the hydrometer for determining the specific gravity and purity of metals was Monconys. Almost about the same period Cornelius Mayer and Boyle seem to have conceived the idea of facilitating the weighing of solid bodies by a weighing-scale added to the instrument. The former affirms that this improvement was invented by him as early as the year 1668425; whereas Boyle did not make his known till 1675426. Besides these the following also are worthy of notice: Feuille427, Fahrenheit, Clark428, and Leutmann429, whose improvements have been described by Wolf430, Leupold431, Gesner, Weigel and others.

[The principal hydrometer now in use is that of Sykes, this is adopted in estimating excise duties on liquids. That of BaumÉ is principally employed abroad. Those of Beck or Cartier are but rarely used. These instruments differ merely in their graduation. Sykes’s plan of increasing the extent of the indications without enlarging the instrument is ingenious. It is effected by means of a number of weights which may be appended as collars to the stem of the instrument.

A useful method of ascertaining specific gravities for commercial purposes, consists in using a series of glass beads, previously adjusted and numbered. When thrown into any liquid, the heavier ones sink and the lighter float on the surface; but the one which has the same density as the liquid will remain indifferent, or perhaps slightly below the surface. The specific gravity is then found by the number with which it is marked.]