consideration his advanced age, being near 70, and the weakness of his eye-sight; and apprehensive of his inability to encounter the fatigues and deprivations unavoidable in so extensive a tour; having, to my extreme regret, and the real loss of science, been induced to decline the journey; I had reluctantly abandoned the enterprise, and all hopes of accomplishing my purpose; till hearing that your Excellency had it in contemplation to send travellers this ensuing summer up the Red River, the Arkansaw, and other tributary streams of the Mississippi; and believing that my services might be of advantage to some of these parties, in promoting your Excellency's design; while the best opportunities would be afforded me of procuring subjects for the work which I have so much at heart. Under these impressions I beg leave to offer myself for any of these expeditions, and can be ready at a short notice to attend your Excellency's orders. "Accustomed to the hardships of travelling, without a family, and an enthusiast in the pursuit of natural history, I will devote my whole powers to merit your Excellency's approbation, and ardently wish for an opportunity of testifying the sincerity of my professions, and the deep veneration with which I have the honour to be, "Sir, your obedient servant, "Kingsess, Feb. 6, 1806. "ALEX. WILSON." * Mr. Jefferson had in his port-folio decisive proofs of Mr. Wilson's talents as an ornithologist, the latter having some time before transmitted to his Excellency some splendid drawings of nondescript birds, accompanied with scientific descriptions. Yet with these evidences before him, backed by the recommendation of a discerning and experienced naturalist, so little did Mr. Jefferson regard the pretensions of genius, and the interests of science; so unmindful was he of the duties of his exalted station, or the common civilities which obtain amongst people of breeding and refinement; that so far from accepting the services of our accomplished ornithologist, he did not even deign to reply to his respectful overture; and Wilson, mortified at the cold, contemptuous neglect, locked up his feelings in his breast, not even permitting a sigh to reach the ear of his most intimate friends. This treatment he did not expect from one whom his ardent fancy had invested with every excellence, who had been the object of his encomiums, and the theme of his songs: "Omne ignotum pro magnifico." * Mr. Wilson was particularly anxious to accompany Pike, who commenced his journey from the cantonment on the Missouri, for the sources of the Arkansaw, &c. on the 15th July, 1806. (To be continued.) ARTICLE II. Some Observations on the Relations between the Specific Gravity of Gaseous Bodies and the Weights of their Atoms. By Thomas Thomson, M.D. F.R.S. FROM the numerous papers upon the atomic theory which I have inserted in the successive volumes of the Annals of Philosophy, and from the paper by Berzelius on the theory of volumes, published in the same Journal, I take it for granted that my readers are acquainted with the outlines of both of these theories. Dr. Prout, in a very valuable paper published in the sixth volume of the Annals, has endeavoured to show that the specific gravity of any body may be obtained by multiplying the weight of its atom by half the specific gravity of oxygen gas. This is the same thing as to say that the weight of an atom of every body is always double its specific gravity in the state of gas. As the theory of volumes is exceedingly convenient in chemical experiments, I conceive that it will be interesting to practical chemists to see in one view the very simple relations which exist between the specific gravities of gaseous bodies and the weights of their atoms. ། If we examine all the substances which can be exhibited in a gaseous state, and with the weight of the atoms of which we are acquainted with tolerable accuracy, we shall find that they may be divided into three sets. In the first set the specific gravity of the body, and the weight of its atom, are represented by the same number. In the second set, the weight of an atom is double that of the specific gravity, or of the weight of a volume. And in the third set the weight of an atom is equal to four times the specific gravity, or to four times the weight of a volume of the respective bodies. In order to make this comparison, it is necessary to reduce the specific gravities to the same standard as the weights of the atoms. As we have chosen 1 to represent the weight of an atom of oxygen, we must employ the same number to represent the specific gravity. of that body, and reduce the specific gravity of all the other gaseous bodies in that proportion. The following table exhibits what I consider as the specific gravity of the different gaseous bodies, according to the present state of our knowledge : Weight of 100 135.084 Phosgene gas. Chlorine.. I shall now arrange these different bodies in the three classes to which they respectively belong, reducing the specific gravities in the first column of the preceding table to the numbers which will represent them when we suppose the specific gravity of a volume of oxygen gas to be 1. Set First.-Bodies having the weight of their atoms equal to the specific gravity of their volumes : Set Second-Bodies having the weight of their atoms twice the specific gravity of their volumes: Set Third.-Bodies having the weight of their atoms four times the specific gravity of their volumes :— From these tables it is obvious that there exists a very simple relation between the specific gravity of gaseous bodies and the weight of their atoms. The weight of the atom is either equal to the specific gravity of the gas, or twice that weight, or four times that weight. It seems to follow from this that the ultimate atoms of bodies differ in their weight, and that the ratio of their weights may be determined by the specific gravity. The specific gravity of olefiant gas is twice as great as might have been expected. Hence it is obvious that the volume of carbon and the volume of hydrogen, of which it is composed, must be reduced to half a volume. This is not the case with any of the other binary compounds. This is the reason why the weight of its atom appears equal to the specific gravity of the gas. The atom of all the simple substances (oxygen excepted), namely, chlorine, sulphur, azote, carbon, and hydrogen, is double the specific gravity. This is the law which Dr. Prout pointed out as belonging to all bodies. It will probably be found to apply to all simple bodies except oxygen. The weight of an atom of carbon and of sulphur was obtained by subtracting the specific gravity of oxygen from that of carbonic acid, and the specific gravity of hydrogen from that of sulphureted hydrogen; because it is known that oxygen may be changed into carbonic acid, and hydrogen into sulphureted hydrogen, without undergoing any alteration in their bulk. The composition of the compound bodies belonging to the second class is as follows: Sulphurous acid, composed of 1 vol. sulphur + 1 vol. oxygen. Carbonic acid 1 carbon + 1 oxygen. .. These fractional numbers disappear when we consider these compounds as composed of atoms, in consequence of the weight of the atom being double that of the volume. Of The first four compounds of the third set consist of gaseous compounds which unite without undergoing any condensation. VOL. VII. No V. course their specific gravity is the mean of that of the constituents. Hydriodic acid, muriatic acid, and hydro-cyanic acid, are composed each of one volume of hydrogen united to one volume of iodine, chlorine, and cyanogen, respectively; so that the specific gravity of each is a mean of the two substances of which it is composed. Nitrous gas is composed of two atoms of oxygen and one of azote. Hence its specific gravity is a mean of that of twice the specific gravity of oxygen + the specific gravity of azote. Ammonia is composed of three volumes of hydrogen and one volume of azote condensed into two volumes; so that its specific gravity = =0.53125. of 625 + 0·875. 3 x 2 I have omitted euchlorine in the preceding enumeration, because it presents an anomaly. Its specific gravity is 2.44, or (supposing the specific gravity of oxygen to be 1) 2-196. Now the weight of its atom is obtained by multiplying this specific gravity by 21; for 2·196 × 2·5 = 5.480; and the weight of an atom of it, supposing it composed of one atom chlorine (4.498) and one atom oxygen (1), is 5'498. If this fractional factor continue, after the nature of chlorine has been determined with more rigour than could be expected from the original experiments of Davy, it will show that the ratio between the specific gravity of gaseous bodies and the weight of their atoms, is not always quite so simple as it seems to be from the preceding tables; but the determination of this point must be left to future experimenters. ARTICLE III. Demonstration of the Binomial Theorem for Fractional and Negative Exponents. By Dr. ***. THE binomial theorem requires, according to the nature of the exponent, different demonstrations. In the case of the exponent being an entire number, we have an expansion consisting of a finite number of terms; whereas in the other cases, of its being either a negative quantity, or a fraction, the expansion consists of an infinite number of terms. The first case may be satisfactorily proved by the theory of combinations, as James Bernouilli has done; or by showing the general truth of the law by successive multiplications. But for the other cases these methods entirely fail; and the demonstrations that are usually given of the law of expansion in these cases are far from being complete. Some have derived the general demonstration from the theory of fluxions. Without examining whether the theory of fluxions can be proved without the assistance of this theorem, we shall remark that so elementary and important a problem ought, if possible, to be proved before the theory of |