We will now proceed to recapitulate the values of the elements necessary and sufficient for the determination of the curve in the general cases.

For the ellipse and hyperbola, the co-ordinates of the centre are

the semi-axes, transverse and conjugate, are given by the values

{ ac2 +bd2 — 2cde—(ab—c2) ƒ }

a+b+m

A=

(ab-ce)

In the ellipse ab- is positive, and m is always to be taken positive in the hyperbola ab--2 is negative, and m must be taken of

:

the same sign as the quantity within the

The inclination (0) of the transverse axis to the axis of r is then given without ambiguity by the equations.

being measured by revolution from the positive part of the axis of x to that of y.

In the parabola, ab-c2=0; the co-ordinates of the focus are

The position of the directrix is given by the angle made by its normal with the positive part of the axis of x ( being measured by revolution towards that of y) and the length p of this normal, including sign as indicating a direct or backward measurement from the origin. These are given without ambiguity by the equations

These elements are sufficient to determine the position and dimensions of the curve as well as the direction towards which its concavity is turned; but the latus-rectum L is also given directly by the value

In particular cases, the ellipse may degenerate into a point, or be wholly imaginary; the hyperbola may degenerate into two intersecting

In the ordinary methods of reduction, this direction is undetermined.

straight lines; both curves have for their limiting form the parabola, which itself may degenerate into two parallel straight lines, or into a single straight line, or be wholly imaginary.

REVIEWS.

By

Chemical Method, Notation, Classification, and Nomenclature. Auguste Laurent, formerly Professor of Chemistry at the Faculty of Sciences of Bordeaux, &c. Translated by William Odling, M.B., F.C.S., Professor of Practical Chemistry and Natural Philosophy at Guy's Hospital. London: Printed for the Cavendish Society by Harrison & Sons. 1855.

Modern Chemistry can boast of few more persevering and successful cultivators than the late Auguste Laurent, who occupied so prominent a position among the most distinguished chemists of France. Not only did he enrich the science with the discovery, we might almost say, of an infinity of new and interesting compounds, but he was led during their investigation to propose theories respecting their formation and constitution, which, although, most fiercely combatted on their promulgation, and for a long period by no means generally received, have during the last few years attracted a large share of attention, and have been, at least in part, almost universally adopted.

Dumas first put forward the idea of substitution, or rather of the law which regulates it, but it was Laurent who first pointed out the real value of the discovery, and immensely extended the theory. While the greatest credit must be allowed to the many eminent chemists whose labors in organic chemistry are daily enriching the science with most interesting discoveries, it cannot be denied that in many cases they are but following in the path opened by the investigations of Laurent.

The career of the celebrated French chemist is peculiarly interesting as connected with the history of chemistry and of chemical polemics, for his publications drew down upon him the ponderous and gigantic learning of Berzelius, and the acute and cutting irony of the belligerent Liebig. Some of the most learned, but at the same time most polemical papers of the celebrated chemist of Giessen, arose from his discussions with Laurent. Many who have watched the progress of chemistry during the last twenty years will well remember the doubt, not to say ridicule, with which many of Laurent's assertions were received, both in France and Germany, but they will also confess that

many of our present theories and assumptions are but echoes of what we once were taught to consider absurd. Chemistry is essentially progressive, and a science of facts; theories and views, founded on a comparatively small number of facts, must necessarily receive alteration when new facts, bearing on these theories, are discovered. We should scarcely be willing to adopt Williamson's explanation of the nature of ether and of its formation, were it not for the discovery of the compound ethers; the discovery of the compound anhydrous acids has led to some remarkable changes in our theories respecting the organic acids generally.

Liebig more than once quizzed Laurent about his spirit of prophecy, but was in himself a remarkable instance of a true prophet, having predicted in 1839 the existence and properties of the compound ammonias, which were discovered in 1849 by Wurtz.

The idea of the dualistic nature of the vegetable alkaloids, maintained by several of the older chemists, seems to be entirely refuted, for we can scarcely believe that the composition of the natural products can be different from that of the artificial ones which they so closely resemble. It is not at all extraordinary that those who commenced the study of chemistry when that science was almost in its infancy, and when all organic relations were compared to inorganic, should have been induced to extend to the one department, the dualistic theory so generally adopted in the other; every man has his own peculiar hobby, swears by his own side of the shield, and is very unwilling to admit the arguments of others. For long years the conflict raged among chemists of the different schools, but at the present day there seems to be a fusion between the opposing factions, while portions of the compound radical theory are conceded to be erroneous, parts of the Laurentian hypotheses, and of those of the newer French school, are willingly adopted.

Laurent's papers are diffused through so large a number of journals, and his views have been so imperfectly represented in most manuals of chemistry, that the publication of this excellent translation of his last work (on which he was engaged, as Biot says, even when in the grasp of death,) will prove an exceedingly acceptable addition to the library of every chemist.

Laurent alludes to most of the attacks which have at different times been made upon his theories and researches by Berzelius, Liebig, Wöhler and others, and with no feeble pen makes a fierce onslaught upon the dualistic hypothesis. However ingenious his propositions with regard to chemical nomenclature, we cannot conceive that they will ever be generally adopted; nitronaphthase and nitronaphthise are

by no means preferable to nitro, binitro, and trinitro-naphthalide, for when we once assume that the numerical prefix shall indicate the number of equivalents of hydrogen, replaced by N O the words nitro, binitro, and trinitro, indicate three numbers much more directly and distinctly than the a, e and i in the final syllable of the Laurentian names. In the present work we meet with an overwhelming mass of new names with which it is sincerely to be hoped chemical nomenclature (already sufficiently confused) will not be deluged. Aplones, Diamerones, Dianhydes, Anames, Anoses, Aziles, Aleses, Alcinyles, Metoyles, Rhizonyles, Diameraies, Synehteres, Dixerides, Udolides, &c., &c., ad infinitum. But these are euphonious compared with Gmelin's designations of which the following may serve as specimens: Alan, Alen, Ofun, Apuk, Patakplatek, Patanafintalkanafin, and last, but not least, for simple Alum, Atolantelminojafinweso!!

The work is of such a nature as scarcely to allow of any extracts, but we have appended a note in which Laurent explains the difference between his and Dumas' ideas respecting substitution, which were by many considered to be identical.

"The notion of substitutions, if we understand thereby, as we ought to understand, the replacement of chlorine, by bromine, iodine, and fluorine, or the replacement of silver, by copper, iron, or potassium, is as ancient as are the ideas of Richter and Wenzel upon the decomposition of salts. We have known for a long time that the single bodies displace one another mutually from their combinations, most generally by exchanging equivalent for equivalent, but not unfrequently in a different

manner.

We have known that chlorine, by its action upon certain organic substances, as cyanhydric acid, essence of bitter almonds, wax, &c., expels a certain number of atoms of hydrogen, which are replaced by an equal number of atoms of chlorine. We have known that oxygen sometimes comports itself in a similiar manner, and also, that in some bodies the hydrogen set free is not replaced by its equivalent of chlorine.

Two questions present themselves: 1°. Can we know à priori, whether the hydrogen set free, will or will not be replaced by its equivalent of chlorine, and how much of it may be liberated without substitution? 2°. What becomes of the chlorine in the new chloro-compounds; what function does it fulfil; of what nature are the compounds into which it enters, either by an equivalent, or a non-equivalent substitution?

These two questions are, we perceive, altogether independent.of each other. We might discover the law presiding over substitutions, without knowing what takes place within the chloro-compounds, and vice versâ.

Dumas confined himself to the first question, and under the name of the theory of substitutions (he himself remarked that he ought to have said law of substitutions) he announced the two following propositions:

1o. When we treat an organic substance by chlorine, bromine, iodine, or oxygen, these bodies generally set free hydrogen, and for one equivalent of hydrogen liberated, there is retained in the compound one equivalent of chlorine, bromine, iodine, or oxygen.

2o. If a part of the hydrogen of the organic substance exists in the state of water (as in alcohol), it will be set free by the chlorine or oxygen, without substitution. The law is precise, and void of ambiguity: I do not purpose to inquire whether or not it is correct (vide what I have said concerning chlorine and oxygen substi tutions in this and the preceding chapter respectively). All that I have to say is, that I have not adopted this law, and that I have myself formulated certain propositions which are altogether different, and are applicable almost solely, to the hydrocarbons. I then have nothing whatever to claim in the above law of substitutions. It belongs entirely to Dumas.

With regard to the second question, Dumas never concerned himself with it, unless indeed, after I had done so. It is this subject that I have for a long time had in view in my researches (vide my opinion thereon in this chapter); it is in reference to it, that I have advanced the following proposition: when there is EQUIVALENT substitution of chlorine or bromine for hydrogen, the chlorine actually takes the PLACE that was occupied by the hydrogen, and to a certain degree, fulfils the functions thereof, consequently the chloro compound must be analogous with the compound from which it was derived.

Thus there is but little analogy between my opinion, my propositions--and the law of Dumas. Here is the reply of this illustrious chemist to Berzelius, by whom he had been rendered somewhat responsible for my extravagances. 'Berzelius attributes to me, an opinion precisely contrary to that which I have always maintained, namely, that the chlorine in this case* takes THE PLACE of the hydrogen. I have never said anything of the kind, neither can anything of the kind be deduced from the opinions I have put forward with regard to this order of facts. To represent me as saying that hydrogen is replaced by chlorine, which fulfils the same functions, is to attribute to me an opinion against which I protest most strongly, as it is opposed to all that I have written upon these matters. The law of substitutions is an empiric law and nothing more; it expresses a relation between the hydrogen expelled, and the chlorine retained. I am not responsible for the gross exaggeration with which Laurent has invested my theory; his analyses moreover do not merit any confidence.'

Dumas and I made use of the same word substitution, from which circumstance arose much of the confusion that prevails on this subject. This confusion was still further augmented, by our employment of special terminations in ase, ese, and ise, &c., terminations conceived by Dumas as expressive of the relation between the number of hydrogen atoms liberated, and the number of other atoms retained, but employed by me to indicate that the chloro-compound in the case of an equivalent substitution, must still preserve the constitution of the original substance.

Thus Dumus represented the constitution of essence of canella by this formula: C18H1402+H2; that of chloride of cinnamyl by this: C18H1402+C12; and the composition of chlorocinnose (=the hydride-4H2+4C12) by C18HC1802, observing that he called the body chlorocinnose provisonally, inasmuch as he did not know how to represent its molecular constitution, nor with what body to compare it. My opinion was very different. If I had considered essence of canella as forming a unique molecule C18H1602, and had named it cinnamyl, I should have called the

"I had just made the chlorhydate of chloretherise, and an acetate of chloromethylene. I maintained that the first body had the same constitution as Dutch liquid, and that in the second, the atoms were disposed exactly as in the acetate of methylene. It was in reference to this opinion, that Berzelius chose to render Dumas responsible for my errors."