(Benedict), was born at Amsterdam the 24th November 1632. His father was a Jew of Portugal, by profession a merchant. After being taught Latin by a physician, he applied himself for many years to the study of theology, and afterwards devoted himself entirely to philosophy. He began very early to be dissatisfied with the Jewish religion; and as his temper was open, he did not conceal his doubts from the synagogue. The Jews, it is said, offered to tolerate his infidelity, and even promised him a pension of a thousand dollars per annum, if he would remain in their society, and continue outwardly to practise their ceremonies. But if this offer was really made, he rejected it, perhaps from his aversion to hypocrisy, or rather because he could not endure the restraint which it would have imposed. He also refused the legacy of a very considerable fortune, to the prejudice of the natural heirs; and he learned the art of polishing glasses for spectacles, that he might subsist independently of every one.
He would probably have continued in the synagogue for some time longer, if it had not been for an accident. As he was returning home one evening from the theatre, he was stabbed by a Jew; the wound was slight; but the attempt naturally led Spinoza to conclude that the Jews had formed the design of assassinating him. After leaving the synagogue, he became a Christian, and frequented the churches of the Lutherans and Calvinists. He now devoted himself more than ever to his favourite philosophical speculations; and finding himself frequently interrupted by the visits of his friends, he left Amsterdam, and settled at the Hague, where he often continued for three months together without ever stirring from his lodging. During his residence in that city, his hostess, who was a Lutheran, asked him one day if he could be saved while he continued in her religion? "Yes (replied Spinoza), provided you join to your religion a peaceable and virtuous life." From this answer it has been concluded that he was a Christian in appearance only, while in reality he regarded all religions as indifferent. But this conclusion would be too severe, even if the woman had been a Mahometan. His Tractatus Theologico-politicus, which was published about that time, is a better proof of his sincerity than a thousand such conclusions; for this book contains all those doctrines in embryo which were afterwards unfolded in his Opera Posthuma, and which are generally considered as a system of atheism.
His fame, which had now spread far and wide, obliged him sometimes to interrupt his philosophical reveries. Learned men visited him from all quarters. While the prince of Condé commanded the French army in Utrecht, he intreated Spinoza to visit him; and though he was absent when the philosopher arrived, he returned immediately, and spent a considerable time with him in conversation. The elector Palatine offered to make Spinoza professor of philosophy at Heidelberg; which, however, he declined.
He died of a consumption at the Hague on the 21st February 1677, at the age of 45. His life was a perpetual contradiction to his opinions. He was temperate, liberal, and remarkably disinterested; he was sociable, affable, and friendly. His conversation was agreeable and instructive, and never deviated from the strictest propriety.
The only edition of the works of Spinoza that we have seen is in two volumes small 4to; the former of which was printed at Hamburg in the year 1673; and the latter we know not where, in 1677, a few months after his death. In the Tractatus Theologico-politicus, already mentioned, he treats of prophecy and prophets; and of the call of the Hebrews, whom he affirms to have been distinguished from other nations only by the admirable form of their government, and the fitness of their laws for long preserving their political state. He is likewise of opinion, or at least pretends to be so, that God may, in what we call a supernatural way, have given political institutes to other nations as well as to the Hebrews, who were, he says, at no time a peculiar people to the Supreme Lord of heaven and earth; for, according to him, all history, sacred and profane, testifies that every nation was blessed with the light of prophecy. That light indeed, if his notions of it be just, was of very little value. He labours to prove, that the prophets were distinguished from other men only by their piety and virtue; that their revelations depended wholly on their imaginations and the dispositions of their minds; that they were often grossly ignorant and highly prejudiced; that the speculative opinions of one prophet are seldom in unison with those of another; and that their writings are valuable to us only for the excellent rules which he acknowledges they contain respecting the practice of piety and virtue. He then proceeds to treat of the divine law and of miracles; and endeavours to prove that no miracle, in the proper sense of the word, can have been at any time performed; because everything happens by a necessity of nature, the result of the divine decrees, which are from all eternity necessary themselves. He acknowledges, that in the Scriptures, which he professes to admit as true history, miracles are often mentioned; but he says that they were only singular events which the sacred historians imagined to be miraculous: and he then gives some very extraordinary rules for interpreting the books of the Old and New Testaments where they treat of miracles, or appear to foretell future events. See our articles Miracle and Prophecy.
Having thus divested the Scriptures of every thing characteristic of a revelation from heaven, he next calls in question their authenticity. He affirms, in contradiction to the clearest internal evidence, that the Pentateuch and all the other historical books must have been written by one man; and that man, he thinks, could not have flourished at a period earlier than that of Ezra. The grounds of this opinion are unworthy of the talents of Spinoza; for that he had talents is incontrovertible. His principal objection to the authenticity of the Pentateuch is, that Moses is made to speak of himself in the third person, and to talk of the Canaanites being then in the land; and because he finds in his writings, as well as in the books of Joshua, Judges, Ruth, Samuel, &c., places denoted by names which he supposes they had not in the early ages of which these books contain the history, he concludes that these writings must be one compilation from ancient records made at a very late period; more especially as the author often speaks of things of great antiquity remaining to this day. The books of Esther, Ezra, Nehemiah, and Chronicles, must have been compiled, he thinks, under the Maccabees; and he seems to consider as of equal value with them the story of Tobit, and the other two apocryphal treatises intitled the Wisdom of Solomon and Ecclesiasticus.
These scribblers cavil, worthy only of one of those modern freethinkers whose learning, in the opinion of Bishop Warburton, is not sufficient to carry them even to the confines of rational doubt, we have sufficiently obviated in another place (see Scripture, n 8—31.) Spinoza urges them against the other books of the Old Testament. The prophecies of Isaiah, Jeremiah, Ezekiel, Daniel, Hosea, and Jonah, are, as we have them, only fragments, he says, of the writings of those men compiled by the Pharisees under the second temple from ancient and voluminous records.
In the midst of this dogmatical skepticism, if we may use such a phrase, he bears such a testimony to the last chapters of the book of Daniel, as we should not have looked for in the writings either of a Jew or of a Deist. After detailing the various hypotheses which in his time were held respecting the author and the intention of the book of Job; in which, he says, Momus is called Satan, he proceeds in these words: "Transeo ad Danielis librum; hic sine dubio ex cap. 8. ipsius Danielli scripta continet. Unde autem priores septem capitata decripta fuerint, neficio;" thus admitting the famous prophecy of the seventy weeks. The canon of the Old Testament, he says, was finally settled by rabbins of the Pharisaical sect, who wished to exclude from it the books of Proverbs, Ecclesiastes, and Ezekiel, as they had actually excluded others of equal value; but the three books in question were inferred by the influence of two of the rabbis of greater wisdom and integrity than the rest.
That so paradoxical a writer, who had been originally a Jew, and was now almost a Deist, should have treated the New Testament with as little ceremony as the Old, will not surprise the intelligent reader. He begins his remarks, however, with affirming, that no man can peruse the Christian Scriptures, and not acknowledge the apostles to have been prophets; but he thinks that their mode of prophesying was altogether different from that which prevailed under the Mosaic dispensation; and that the gift, whatever it was, forsook them the instant that they left off preaching, as their writings have to him every appearance of human compositions. This distinction between Christian and Jewish prophecy is the more wonderful, that he founds it principally on the dissimilarity of style visible in the writings of the Old and New Testaments; though, in his second chapter, which treats of the works of the Jewish prophets, he says expressly, "Stylus deinde prophetiae pro eloquentia cuiusque prophetae variabit, prophetiae enim Ezekielis et Amosis non sunt, ut illae Esaiae, Nachumi elegantissimi, sed rudiori stylo scriptae." That the Hebrew scholar may be convinced of the truth of this remark, he recommends to him to study diligently the writings of these prophets, and to consider the occasions on which their prophecies were uttered: "Quae si omnia recte perpendatur (says he) facile offendant, Deum nullum habere stylium peculiarem dicendi, sed tantum pro eruditione, et capacitate prophetae euenus esse elegantem, compositiorem, ferventem, rudem, prolixum, et obscurum." Another objection brought by Spinoza against the prophecies of the New Testament arises from the authors of them having been at all times masters of themselves. This, says he, was peculiarly the case of St Paul, who often confirms his doctrine by reasoning, which the Jewish prophets never condescended to do, as it would have submitted their dogmas to the examination of private judgment. Yet, with singular inflexibility, he affirms, that the Jewish prophets could not know that the impressions made on their imaginations proceeded from God, but by a sign given them, which by their own reason or judgment they knew would never be vouchsafed to an impious or a wicked man.
After these very free remarks on the Scriptures of the Old and New Testaments, he naturally enough expresses a suspicion, that by those who consider the Bible as the epistle of God sent from heaven to men, he will be thought to have sinned against the Holy Ghost by vilifying his dictates. This leads him to inquire in what sense the Scriptures are the word of God; and he gravely determines them to be so only as they actually contribute to make men more virtuous and holy. It is not enough that they are calculated to improve virtue and holiness: for should the words of the languages in which they are written acquire in process of time a figuration different from what they had originally; should mankind lose all knowledge of these languages; or even should they agree to neglect the books, whether from ignorance or from wilfulness—those books would cease to be the word of God, and become nothing better than waste paper and ink; just as the two tables, which Moses broke on observing the idolatry of his countrymen, were not the covenant between Jehovah and the Israelites, but merely two pieces of stone! The Scriptures, however, are the word of God, because they teach the true religion of which God is the author; and they have taught it in such a manner, he says, that it can never be lost or corrupted whatever become of the books of the Old and New Testaments, or of the languages in which they are written. The whole of religion, as the Scriptures themselves testify, consists in the love of God above all things, and of our neighbours as ourselves: whence it follows, that we must believe that God exists, and watcheth over all things by his providence; that he is omnipotent, and has decreed the pious to be ultimately happy, and the impious miserable; and that our final salvation depends solely on His grace or favour. These truths, with their necessary consequences, are the word of God; they are clearly taught in the Scriptures, and can never be corrupted; but every thing else in these volumes is vain, he says, and of no greater importance to us than facts related in any other ancient and authentic history.
Such are the opinions which were entertained of revelation by a man whom a critic, writing in a Christian country, and professing to be a zealous Christian himself, has lately pronounced to have been a chosen vessel. For what purpose he was chosen it is not easy to conceive. His religion, as it appears in the Tractatus, is the worst kind of Deism; and his politics are such as our monthly critics are not wont to teach, and such as we trust shall never be seriously taught by any British subject. By the law of nature, he says, every man before the formation of civil government has an unquestionable right to whatever appears eligible either to his reason or to his appetites; and may get possession of it by treaty, by violence, by fraud, or by any other means attended with less trouble to himself (five vi, five dolo, five precibus, five quocunque dumnum modo facilius poterit); and may treat as an enemy every person who shall attempt to obstruct his purpose. But when men agree to devolve this right upon others, and to constitute a political state, which both reason and appetite must persuade them to do, then are they in duty bound to obey every mandate of the government; however absurd it may be (omnia mandata tamefi absurdissima), as long as that government can enforce its edicts, and no longer; for, according to him, right and power are so inseparably united, that when a government loses its power, it has no longer the smallest claim to obedience. This doctrine, he says, is most obviously just when taught of democratical governments; but it is in fact equally true of monarchies and aristocracies: "Nam quisquis humain habet potentatem, five unus fit, five pauci, five deinde omnes, certum est ei futurum jus quod velit imperandi, competere: et praetera quisquis potentatem se defendendi, five sponte, five vi coacta, in aliud transfult, cum quo jure naturali plane cessisse, et consequenter eidem ad omnia absolute decreveri, quod omnia praetare tenetur, quamdiu rex, five nobilis, five populus humain, quam accepérunt, potentatem, quae juris transferendi fundamentum fuit, conservant; nec his plura addere opus est." We heartily agree with him, that to this precious conclusion it is needless to add a single word.
Taking our leave therefore of his Tractatus Theologico-politicus, we shall now give our readers a short account of his Opera Postuma. These consist of: 1. Ethica, more geometrico demonstrata; 2. Politica; 3. De Emendatione Intellectus; 4. Epistola, ad eas Responiones; 5. Compendium Grammatices Linguae Hebraeæ.
The Ethica are divided into five parts, which treat in order, de Deo; de natura et origine mentis; de origine et natura affectuum; de servitute humana, seu de affectuum viribus; de potentia intellectus, seu de libertate humana. As the author professes to tread in the footsteps of the geometers, and to deduce all his conclusions by rigid demonstration from a few self evident truths, he introduces his work, after the manner of Euclid, with a collection of definitions and axioms. These are couched in terms generally ambiguous; and therefore the reader will do well to consider attentively in what sense, if in any, they can be admitted; for it will not be found easy to grant his premises, and at the same time refuse his conclusions. His definition of substance, for instance, is so expressed as to admit of two senses; in one of which it is just, whilst in the other it is the parent of the most impious absurdity. We shall give it in his own words: "Per substantiam intelligo id, quod in se est, et per se concipitur: hoc est id, cuius conceptus non indiget conceptu alterius rei, a quo formari debet." If by this be meant, that a substance is that which we can conceive by itself without attending to any thing else, or thinking of its formation, the definition, we believe, will be admitted by every reflecting mind as sufficiently distinguishing the thing defined from an attribute, which, he says, is that which we perceive of a substance, and which we certainly cannot conceive as existing by itself. Thus the writer of this article can shut his eyes and contemplate in idea the small 4to volume now before fore him; without attending to any thing else, or thinking of its paradoxical author, or even of the Great Being who created the matter both of him and of it; but he cannot for an infant contemplate the yellow colour of its vellum boards without thinking of triple extension, or, in other words, of body. The book therefore is a substance, because conceivable by itself; the colour is an attribute or quality, because it cannot be conceived by itself, but necessarily leads to the conception of something else. But if Spinoza's meaning be, that nothing is a substance but what is conceived as existing from eternity, independent of every thing as a cause, his definition cannot be admitted: for every man conceives that which in himself thinks, and wills, and is conscious, as a substance; at the same time that he has the best evidence possible that he existed not as a conscious, thinking, and active being, from eternity.
His fourth axiom is thus expressed: "Effectus cognitione causae dependet, et eandem involvit;" and his fifth, "Quae nihil commune cum se invicem habent, etiam per se invicem intelligi non possunt, five conceptus unius alterius conceptum non involvit." The former of these propositions, so far from being self-evident, is not even true; and the latter is capable of two senses very different from each other. That every effect proceeds from a cause, is indeed an axiom; but surely we may know the effect accurately, though we be ignorant of the particular cause from which it proceeds (see Philosophy, n° 36; and Physics, n° 91, &c.); nor does the knowledge of the one by any means involve the knowledge of the other. If different things have nothing in common, it is indeed true that the knowledge of one of them will not give us an adequate conception of the other; but it will in many cases compel us to believe, that the other exists or has existed. A parcel of gunpowder lying at rest has nothing in common with the velocity of a cannon-ball; yet when we know that a ball has been driven with velocity from a cannon, we infer with certainty that there has been a parcel of powder at rest in the chamber of that cannon.
It is upon such ambiguous definitions and axioms as these that Spinoza has raised his pretended demonstrations, that one substance cannot produce another; that every substance must necessarily be infinite; that no substance exists or can be conceived besides God; and that extended substance or body is one of the infinite attributes of God. We shall not waste our own time or the reader's with a formal confutation of these impious absurdities. We trust they are sufficiently confuted in other articles of this work (see Metaphysics, Part III. Providence, and Theology, Part I.); and whoever wishes for a more particular examination of the author's principles, may find it in Dr Clarke's Demonstration of the Being and Attributes of God. The truth, however, is, that no man will need the assistance of that eminent metaphysician to discover the fallacy of the reasoning by which they are attempted to be proved, if he affix any one precise meaning to the definitions and axioms, and adhere to that meaning steadily through the whole process of the pretended demonstrations.
By way of apology for this jargon, it has been lately laid, that "Spinoza takes the word substance in its most simple and perfect sense; which is necessary, as he writes mathematically, and proposes a simple idea as the foundation of his theory. What is the proper signification of a substance? Is it not that which stands alone, which has the cause of its existence within itself?" Gal.
Herder's Dialogues concerning
With this simple meaning of the word could be universally admitted in philosophy. Strictly speaking, no worldly thing is a substance; since all mutually depend on each other, and finally on God, who, in this exalted sense, is the only substance. The word modification found harsh and improper, and therefore it cannot be expected to gain a place in philosophy; but if the school of Leibnitz may term matter the appearance of substances, why may not Spinoza be allowed a bolder term? Worldly substances are kept in union by divine power, as it was by divine power that they had existence. They represent also, if you please, modified appearances of divine power; each according to the station, the time, and the organs, in and with which it appears. The phrase used by Spinoza is concise, and it gives an unity and simplicity to his whole system, however strange it may found in our ears."
From this account of Spinozism, one who had never looked into the works of the author would be led to suppose that his system is the same with that of Berkeley; which, denying the existence of material substance, attributes all our perceptions of what we call the qualities of body to the immediate agency of the Deity on our minds (see Metaphysics, Part II. Chap. 3.) But Spinoza's doctrine is very different. According to him, bodies are either attributes or affections of God; and as he says there is but one extended substance, he affirms that substance to be indivisible, and employs a long scholium† to prove that those are mistaken who suppose it finite and not essential to the Deity. That we do properly misrepresent his sentiments, the learned reader will be convinced by the two following definitions, with which he introduces that part of his ethics which treats of the nature and origin of mind. 1. "Per corpus intelligo modum, qui Dei essentiam, quatenus, ut res extensa consideratur, certo et determinato modo exprimit." 2. "Ad essentiam aliquos rei id pertinere dico, quo dato res necessestari ponitur, et quo sublatu res necessario tollitur; vel id, sine quo res, et vice versa quod sine re nec effici nec concepi potest." In conformity with these definitions, he attempts to prove that God Prop. ii. is an extended as well as a thinking substance; that as a thinking substance it is the cause of the idea of a part of a circle, and as an extended substance of the circle itself; and that the minds of men are not substances, but certain modifications of the divine attributes; or, as he sometimes expresses it, "Quod humanæ mentis actuale constituit, est idea rei singularis actu existentis." Hence, he says, it follows that the human mind is a part of the intellect of the infinite God; so that when we speak of the human mind perceiving this or that, we can only mean that God, not as he is infinite, but as he appears in the human mind or constitutes its essence, has this or that idea; and when we speak of God's having this or that idea, we must conceive of Him not only as constituting the human mind, but as, together with it, having the idea of something else (A). In another place he tells us, that the human mind is nothing but the idea which
(A) Hinc sequitur mentem humanam partem esse infiniti intellectus Dei; ac proinde cum dicimus, mentem humanam We have therefore calculated a table in the form in which it must be most useful and acceptable to those who are engaged in the spirit trade, showing at once the specific gravity which results from any proportion of admixture in hundredth parts of the whole. This answers immediately the chief questions in the terms in which they are usually conceived and proposed. The two first or leading columns show the proportion in gallons, pints, or other cubic measures of the mixture, the whole quantity being always 100. The second column shows the corresponding specific gravity; so that we can either find the proportion of the ingredients by the observed specific gravity, or find the gravity resulting from any proportion of the ingredients.
A third column shows how much the hundred measures of the two ingredients fall short of making an hundred measures of the compound. A simple proportion, which can be done without the pen, will determine what part of this deficiency must be made up by spirit. The use of this table must now be so familiar to the reader's mind, that we need not give further instructions about it.
This is followed by another similar table, giving an immediate answer to the most usual question, "How many measures of alcohol are there really contained in 100 measures?" This is also accompanied by a column of condensation. It would have been somewhat more elegant, had the specific gravities in this table made the equable series and leading column. But we did not advert to this till we had computed the table, and the labour was too great to be repeated for slight reasons. The tables are only for the temperature 60°. To this the spirituous liquors can always be brought in these climates; and in cases where we cannot, a moment's inspection of Sir Charles Blagden's table will point out very nearly (or exactly, by a short computation) the necessary corrections.
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. W. | | | | 100 | 0 | 0.8250 | | 99 | 1 | 0.8278 | | 98 | 2 | 0.8306 | | 97 | 3 | 0.8333 | | 96 | 4 | 0.8360 | | 95 | 5 | 0.8387 | | 94 | 6 | 0.8413 | | 93 | 7 | 0.8439 | | 92 | 8 | 0.8465 | | 91 | 9 | 0.8491 | | 90 | 10 | 0.8516 | | 89 | 11 | 0.8542 | | 88 | 12 | 0.8567 | | 87 | 13 | 0.8592 | | 86 | 14 | 0.8617 | | 85 | 15 | 0.8641 | | 84 | 16 | 0.8666 | | 83 | 17 | 0.8690 | | 82 | 18 | 0.8713 | | 81 | 19 | 0.8737 | | 80 | 20 | 0.8760 | | 79 | 21 | 0.8784 | | 78 | 22 | 0.8807 | | 77 | 23 | 0.8830 | | 76 | 24 | 0.8853 | | 75 | 25 | 0.8876 | | 74 | 26 | 0.8899 | | 73 | 27 | 0.8922 | | 72 | 28 | 0.8944 | | 71 | 29 | 0.8966 | | 70 | 30 | 0.8988 | | 69 | 31 | 0.9010 | | 68 | 32 | 0.9031 | | 67 | 33 | 0.9053 | | 66 | 34 | 0.9073 |
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. W. | | | | 66 | 34 | 0.9073 | | 65 | 35 | 0.9095 | | 64 | 36 | 0.9116 | | 63 | 37 | 0.9137 | | 62 | 38 | 0.9157 | | 61 | 39 | 0.9177 | | 60 | 40 | 0.9198 | | 59 | 41 | 0.9218 | | 58 | 42 | 0.9238 | | 57 | 43 | 0.9257 | | 56 | 44 | 0.9277 | | 55 | 45 | 0.9296 | | 54 | 46 | 0.9316 | | 53 | 47 | 0.9335 | | 52 | 48 | 0.9353 | | 51 | 49 | 0.9371 | | 50 | 50 | 0.9388 | | 49 | 51 | 0.9406 | | 48 | 52 | 0.9423 | | 47 | 53 | 0.9440 | | 46 | 54 | 0.9456 | | 45 | 55 | 0.9473 | | 44 | 56 | 0.9489 | | 43 | 57 | 0.9505 | | 42 | 58 | 0.9520 | | 41 | 59 | 0.9535 | | 40 | 60 | 0.9549 | | 39 | 61 | 0.9563 | | 38 | 62 | 0.9577 | | 37 | 63 | 0.9590 | | 36 | 64 | 0.9603 | | 35 | 65 | 0.9616 | | 34 | 66 | 0.9628 | | 33 | 67 | 0.9640 |
| Compound | Specific Gravity | Cond. per cent. | |----------|------------------|-----------------| | S. W. | | | | 33 | 67 | 0.9640 | | 32 | 68 | 0.9651 | | 31 | 69 | 0.9662 | | 30 | 70 | 0.9673 | | 29 | 71 | 0.9683 | | 28 | 72 | 0.9693 | | 27 | 73 | 0.9704 | | 26 | 74 | 0.9713 | | 25 | 75 | 0.9724 | | 24 | 76 | 0.9734 | | 23 | 77 | 0.9744 | | 22 | 78 | 0.9754 | | 21 | 79 | 0.9763 | | 20 | 80 | 0.9773 | | 19 | 81 | 0.9783 | | 18 | 82 | 0.9793 | | 17 | 83 | 0.9802 | | 16 | 84 | 0.9812 | | 15 | 85 | 0.9822 | | 14 | 86 | 0.9832 | | 13 | 87 | 0.9842 | | 12 | 88 | 0.9853 | | 11 | 89 | 0.9863 | | 10 | 90 | 0.9874 | | 9 | 91 | 0.9886 | | 8 | 92 | 0.9897 | | 7 | 93 | 0.9909 | | 6 | 94 | 0.9921 | | 5 | 95 | 0.9933 | | 4 | 96 | 0.9946 | | 3 | 97 | 0.9959 | | 2 | 98 | 0.9972 | | 1 | 99 | 0.9985 | | 0 | 100 | 1.0000 | In the first table, of which the sole intention is to point out the proportion of ingredients, the specific gravities are computed only to four places, which will always give the answer true to \( \frac{1}{300} \)th part. In the last, which is more immediately interesting to the merchant in his transactions with the excise office, the computation is carried one place further.
The consideration of the first of these two tables will furnish some useful information to the reader who is interested in the philosophy of chemical mixture, and who endeavours to investigate the nature of those forces which connect the particles of tangible matter. These vary with the distance of the particle; and therefore the law of their action, like that of universal gravitation, is to be discovered by measuring their sensible effects at their various distances. Their change of distance is seen in the change of density or specific gravity.
Did the individual densities of the water and spirit remain unchanged by mixture, the specific gravity would change by equal differences in the series of mixtures on which this table is constructed; for the bulk being always the same, the change of specific gravity must be the difference between the weight of the gallon of water which is added and that of the gallon of spirit which is taken out. The whole difference of the specific gravities of spirits and water being 1,750 parts in 10,000, the augmentation by each successive change of a measure of spirit for a measure of water would be the 100th part of this, or 17.5. But, by taking the successive differences of density as they occur in the table, we see that they are vastly greater in the first additions of water, being then about 29; after which they gradually diminish to the medium quantity 17\(\frac{1}{2}\), when water and spirits are mixed in nearly equal bulks. The differences of specific gravity still diminish, and are reduced to 9\(\frac{1}{2}\), when about 75 parts of water are mixed with 25 of spirit. The differences now increase again; and the last, when 99 parts of water are mixed with 1 part of spirit, the difference from the specific gravity of pure water is above 14.
The mechanical effect, therefore, of the addition of a measure of water to a great quantity of spirit is greater than the similar effect of the addition of a measure of spirits to a great quantity of water. What we call mechanical effect is the local motion, the change of distance of the particles, that the corpuscular forces may again be in equilibrium. Observe, too, that this change is greater than in the proportion of the distance of the particles. particles; for the density of water is to that of spirits nearly as 6 to 5, and the changes of specific gravity are nearly as 6 to 3.
We also see that the changing cause, which produces the absolute condensation of each ingredient, ceases to operate when 75 parts of water have been mixed with 25 of alcohol: for the variation of specific gravity, from diminishing comes now to increase; and therefore, in this particular state of composition, is equable. Things are now in the same state as if we were mixing two fluids which did not act on each other, but were mutually disseminated, and whose specific gravities are nearly as 9 to 10; for the variation of specific gravity may be considered as the 10th part of the whole difference, in the same manner as 17½ would have been had water and alcohol sustained no contraction.
The imagination is greatly assisted in the contemplation of geometrical quantity by exhibiting it in its own form. Specific gravity, being an expression of density (a notion purely geometrical), admits of this illustration.
Therefore let AB (fig. 4.) represent the bulk of any mixture of water and alcohol. The specific gravity of water may be represented by a line of such a length, that AB shall be the difference between the gravities of alcohol and water. Suppose it extended upwards, towards a, till B a is to A a as 10,000 to 8250. It will suit our purpose better to represent it by a parallelogram a B f e, of any breadth B F. In this case the difference of the specific gravities of alcohol and water will be expressed by the parallelogram ABFE. If there were no change produced in the density of one or both ingredients, the specific gravity of the compound would increase as this parallelogram does, and AGHE would be the augmentation corresponding to the mixture of the quantity AG of alcohol with the quantity GB of water, and so of other mixtures. But, to express the augmentation of density as it really obtains, we must do it by some curvilinear area DABCHD, which varies at the rate determined by Sir Charles Blagden's experiments. This area must be precisely equal to the rectangle ABFE. It must therefore fall without it in some places, and be deficient in others. Let DMHKC be the curve which corresponds with these experiments. It is evident to the mathematical reader, that the ordinates LM, GH, IK, &c. of this curve are in the ultimate ratio of the differences of the observed specific gravities. If A a, a b, &c. are each = 5, the little spaces A a = D, a b = D, &c. will be precisely equal to the differences of the specific gravities 0.8250; 0.8387; 0.8516; &c. corresponding to the different mixtures of water and alcohol. The curve cuts the side of the parallelogram in K, where the ordinate GK expresses the mean variation of density 0.00175. IK is the smallest variation. The condensation may be expressed by drawing a curve dm G k f parallel to DMGKF, making D d = AE. The condensation is now represented by the spaces compendiously between this last curve and the abscissa AGB, reckoning those negative which lie on the other side of it. This shows us, not only that the condensation is greatest in the mixture AG × GB, but also that in mixing such a compound with another AIXIB, there is a rarefaction. Another curve ANPOB may be drawn, of which the ordinates LN, GP, IO, &c. are proportional to the areas A L m d, A G m D, A I / G m D (= A G m d - G I k), &c. This curve shows the whole condensation.
This manner of representing the specific gravities of mixtures will suggest many curious inferences to such as will consider them in the manner of Bozovich, with a view to ascertain the nature of the forces of cohesion and chemical affinities: And this manner of viewing the subject becomes every day more promising, in consequence of our improvements in chemical knowledge; for we now see, that mechanism, or motive forces, are the causes of chemical action. We see in almost every case, that chemical affinities are comparable with mechanical pressures; because the conversion of a liquid into a vapour or gas is prevented by atmospheric pressure, and produced by the great chemical agent heat. The action of heat, therefore, or of the cause of heat, is a mechanical action, and the forces are common mechanical forces, with which we are familiarly acquainted.
"It may be also remarked in the column of contractions, that in the beginning the contractions augment nearly in the proportion of the quantity of spirits (but more slowly); whereas, in the end, the contractions are nearly in the duplicate proportion of the quantity of water. This circumstance deserves the consideration of the philosopher. We have represented it to the eye by the curve a g b d."
We should here take some notice of the attempt made to elude some part of the duties, by adding some ingredient to the spirits. But our information on this subject is not very exact; and besides it would be doing no service to the trader to put fraud more in his power. There are some facts which make a very great augmentation of density, but they render the liquor unpalatable. Sugar is frequently used with this view; 16 grains of refined sugar dissolved in 1000 grains of proof spirits gave it no suspicious taste, and increased its specific gravity from 0.920 to 0.925, which is a very great change, equivalent to the addition of 9 grains of water to a mixture of 100 grains of alcohol and 80 of water.