be three equations of the error of the clock, the transit axis being assumed perfectly horizontal. Then if c is sought, the coefficient of one part of the effect of the errors of observation on its value is But n―n' is always a proper fraction in our latitude for instruments having only a southern exposure, and is in fact as far as the latitude whose tangent is 3. The same is true of n'—n", m-m', and m'-m". But n' - n" m' - m" is also a fraction, since the numerator is a less fraction than the denominator. = For m' - m" sin (p-d′). sec d'— sin (9 — d''). sec d′′ Differentiating cos 9. tan 8" we have cos . sec2 d′′. d8', Hence we have cos .sec2 8". ds"> sin d". sec2 8".dd" when 90°-. From this we have cos .(tan d tan 8")>(sec d' The same is true when one of the declinations is negative, since observations will not be made near the horizon. Then m' — m'>n' — n' when the greatest declination is less than the complement of the latitude of the place of observation. Hence n'-n" m' — m" · (m — m'), it follows that the reciprocal of (n−n')· which is the coefficient of one part of the effect of the errors of observation, is integral when the transit has only a south exposure. If the instrument commands the whole meridian, we may show that the coefficient of one part of the effect of the errors of observation, cannot be largely fractional without making the coefficient of the other part integral. The denominators of the two coefficients are If the first expression is largely integral, m-m' must be so also, inasmuch as the compound factor can never exceed 2.6. Differentiating and establishing the condition of a maximum, we find sec d′′ —c' = (tan d". cos o — c''). sin d' sin d' Substituting in ; the greatest possible the original expression, it reduces to value of which in our lat. is 1:33. Taking this twice we have 2.6. Making, then m-m' very large in expression (2), let us ascertain its greatest value. It is evident that this expression is the greatest, other things being equal, when est, i. e. when d" is the greatest and is m" - m' is the great n". ・n' the least. n" - n' "88° 30' declin. of Polaris and 8'=0, we find m" - m' Taking =-1.29. Now the maximum value of expression (2) is when sin d"= n" — n' m" - m' . cos 9, 97 in the lat. of New Haven, i. e. when 8"=76° 56', and may be found by calculation to be 76. Hence it appears that if one of the two coefficients is a small fraction, the other must be integral. The remaining point is evidently established, if we show that there is no likelihood that either set of errors is greater than the corresponding single error of the other expression. Each set of errors in the expression which gives the effect of the errors of observation in the common method, is the algebraic sum of a number of errors. Let us conceive two of these errors to be taken at hazard. Then there is no probability that their algebraic sum is greater than the greatest of them, inasmuch as there is no probability that both have the same sign. Now let another error be taken in the same manner. Then there is no probability that the sum of the three is greater than the sum of the two first, for the same reason as before: and, as there is no likelihood that the sum of the two is greater than the greatest of them, there is none that the sum of the three is greater than the greatest of the two errors taken at hazard. In the same manner we might go on adding single errors and reasoning reversely, and thus prove that there is no probability that the algebraic sum of any given number of errors is greater than the greatest of any two of them, taken at random. But now there is no probability that this greatest of the two is greater than the error corresponding to the set in the first factor of the second expression, and therefore none that the algebraic sum of all the errors constituting the set, is greater than this error. SCIENTIFIC INTELLIGENCE. I. CHEMISTRY AND PHYSICS. 1. On Ozone; by M. BERZELIUS, (Berzelius's Jahresbericht, xxvi; Chem. Gazette, 109, p. 71.)—After detailing the results of Marignac's experiments in thirteen propositions, M. Berzelius goes on to say, "From these experiments Marignac has drawn the conclusion that ozone is most probably a peculiar modification of oxygen; but considering the circumstance that it is not produced by absolutely dry gases, he has left it undecided whether it may not perhaps contain some hydrogen. "The last uncertainty, however, has been removed by an experiment of De la Rive. Chlorate of potash is fused to remove all moisture, and then a slow current of dry oxygen disengaged from it; this is passed through a glass tube of about one line internal diameter, into which two pieces of platinum wire have been fused, so that they are a small distance from and opposite to each other. Now when a current of electricity is conveyed to the earth through the wires of the conductor of an electrical machine in action, a succession of sparks results between the wires, and the oxygen is thereby converted into ozone, which is recognized by its powerful odor and its reactions, especially towards iodide of potassium and starch, which is most readily observed. As soon as the electric current ceases, unaltered oxygen again issues from the tube. "We have thus arrived at the highly important result, that ozone is no peculiar element, and likewise that it is not an unknown combination of known elements, but that it is oxygen in a different allotropic condition, from the ordinary oxygen gas, as this is contained in the atmosphere or obtained in chemical experiments. Our knowledge of the dissimilar allotropic states of the elementary substances has thus obtained an unexpected and highly remarkable addition. In accordance with the other elements, we may represent it by the symbols Oa and 03. Oa is distinguished from 038 by its odor, and by the tendency it has to form combinations in circumstances under which the latter is perfectly inactive, similar to what likewise occurs with other elements. Whether these modifications are preserved in the combination or only one of these states, and which belongs to the oxygen in combination, are questions which still remain to be answered. We have seen that the electrical spark converts a certain quantity of O3 (probably corresponding to the capacity of the spark) into Oa, and this satisfactorily explains the electric odor. We have, moreover, learned that those bodies which become oxydized at low temperatures, for instance phosphorus, are likewise capable of producing a change, but that in this case the presence of another gas besides oxygen is absolutely requisite, as hydrogen, nitrogen, or carbonic acid; but whether these gases take an active part, or remain passive and merely dilute the oxygen, is not yet known. I may call to mind the effects of phosphorus upon oxygen by mere rarefaction under the air-pump, which have not yet been SECOND SERIES, Vol. IV, No. 11.-Sept., 1847. 34 satisfactorily explained. Is Oa likewise formed under these circumstances? There still remains to examine the comprehensive field of extremely interesting comparisons between the different properties of these two allotropic modifications, a subject of inquiry of the greatest importance for science. We have already become acquainted with the mysterious statement of Leuch, according to whom Oa (galvanized air) can be used with considerable advantage for bleaching purposes, and indeed surpasses all other bleaching materials.* 2. On the relations of Glycocoll and Alcargene; by T. S. HUNT, (communicated for this Journal.)-The similarity which exists between the compounds of nitrogen and arsenic is such, that they are regarded as belonging to the same natural group and capable of replacing each other in combination. Kakodyle and its derivatives are as yet the only organic bodies known which contain arsenic; of these, M. Gerhardt has shown that alcarsine is to be regarded as an alkaloid in which arsenic takes the place of nitrogen, but the parallel substance containing nitrogen is as yet unknown; and hitherto we have been unable to complete the analogy between these elements, by the discovery of two corresponding compounds, the one containing nitrogen and the other arsenic. The substance known as glycocoll, or gelatine-sugar, is shown by the recent researches of Horsford and Laurent,† to have the composition before suggested by Gerhardt and declared by Dessaignes from the results of the decomposition of hippuric acid. Its equivalent is represented by the formula C4H,NO. The alcargene or kakodylic acid of M. Bunsen is produced by the slow oxydation of kakodyle or alcarsine; one equivalent of alcarsine and eight of oxygen, yield two of alcargene and two of water.‡ CH12As2O2+80=2C1H, AsO4+2HO. The equivalent of this substance then is represented by C,H,ASO4, which differs from the formula of glycocoll only in the substitution of As for N. 4 5 5 A notice of some of the characters of the two substances will serve to show their close affinity. Both glycocoll and alcargene are capable of exchanging one equivalent of their hydrogen for a metal; and in addition to this character in which they resemble acids, act the part of organic bases by combining directly with acids to form definite crystallizable compounds. Some of these corresponding combinations are here represented. Glycocoll, CH,NO, 66 Alcargene, CH, ASO1 Argentic C(HAg)NO, Argentic C1(H1Ag)AsO Hydrochloric " CH NO,HC Hydrochloric CH, ASO1,HCI 4 5 4 5 4 To these characters we may add that both glycocoll and alcargene are readily soluble in water, sparingly soluble in alcohol, crystallize with *For a notice of the history and nature of ozone, see this Journal, vol. ii, ii Series, 103. † This Journal, ii Series, vol. iii, pp. 267-258 and 369. See the corrected formula for this substance in M. Gerhardt's Précis de Chimie Organique, vol. ii, p. 445. facility, and are not volatile without decomposition. They also resemble each other in having no deleterious action upon the animal system, a property that is very remarkable in a body which like alcargene contains more than 72 per cent. of arsenic. From these facts the conclusion seems unavoidable, that alcargene is the arsenical species of a genus of which glycocoll may be regarded as the type. Glycocoll is isomeric with the hyponitrous ether of Liebig. This substance which is regarded by M. Gerhardt as the nitric species of acetene CH, is, like many other bodies of a similar constitution, decomposed by the action of sulphuretted hydrogen. When a current of this gas is passed into an alcoholic solution of the ether, previously mixed with a little solution of ammonia, it is rapidly absorbed, while the liquid assumes a dark orange-red color, and deposits a large amount of sulphur. In this process a volatile substance of a powerful alliaceous odor and pungent taste is formed, but the small quantity which I obtained in a single experiment, did not allow me to determine its nature. It may perhaps be a body corresponding to alcarsine, of the formula CH12N2O2, or a sulphuretted species of it. Four equivalents of the ether, and eight of the sulphuretted hydrogen, would yield one equivalent of this compound with the separation of six equivalents of water and eight of sulphur; the tendency of the bodies of the acetic series to unite and double their equivalent, is well known. This however is merely a probable conjecture, and I shall take the earliest opportunity to determine its truth or falsity. The substance C,H12N2O2 should yield glycocoll by oxydizing agents. 12 21 It will be very important to examine the action of reducing agents and sulphuretted hydrogen upon glycocoll, as alcargene, by these means, affords alcarsine, and a species in which its oxygen is replaced by sulphur. I have commenced some researches upon these, the results of which I will send you as soon as they are completed. Montreal, May 25th, 1847. 3. Varrentrapp and Will's Method for the Determination of Nitrogen: An Improved Apparatus; by Prof. E. N. HORSFORD, (commu. nicated for this Journal.)-The excellence of the method of MM. Varrentrapp and Will, in the combustion of bodies whose per-centage of nitrogen is low, has secured its almost universal adoption. Two objections have been made to it, and both of them by the gentlemen to whom we are indebted for the labor of removing the practical difficulties which necessarily surround this and every new process. The first is in the determination of nitrogen in bodies, where nitric acid is present. The per-centage is uniformly too low. No plan has yet been suggested by which to surmount this difficulty. The other is, generally, with bodies in which the proportion of nitrogen is large. It arises from the impossibility of perfectly controlling the current of evolved ammonia and other gaseous products. When from any cause the combustion proceeds for a moment slower than it should, or the first bulb of the apparatus becomes suddenly cooled, the hydrochloric acid retreats into this bulb, occasioning with the suddenly and greatly increased surface, as the acid issues from the neck, an instantaneous absorption of the ammonia-a partial vacuum and a consequent rush of the acid in jets into and across the bulb. Not unfrequently |