condition of the clouds to be negative, and that positively electric clouds are comparatively but of rare occurrence. Volta, on the other hand, considers the general electric condition of clouds to be positive, and accounts for negatively electric clouds as a secondary occurrence, occasioned by the repulsive influence of a more formidable electro-positive cloud. Hence Volta's opinion is, that all clouds, at their formation, are positively electric. Now, although the latter view is exactly the same as our own, it must be confessed that M. Volta has by no means shewn how it happens that vapour becomes positively electrical. That philosopher, according to the views of Dr. Franklin, considers that water, when converted into vapour, assumes a greater capacity for the electric fluid than before; and, therefore, would become negatively electrical the moment that it assumes the shape of vapour, conformable to Franklin's can and chain apparatus. That this is the fact we are quite certain, even though the vessel, with its remaining water, become negatively electric also. To clear up this point, we have only to consider that, as soon as the first stratum of steam or vapour is formed on the surface of the water, it has a greater capacity for the electric fluid than before, and consequently, for a short time, assumes a negative electric condition: but this new electric condition of the vapour allows of its being invaded by a portion of that electric-fluid which was left in the water, and also by a portion of that of the vicinal air; by which means it becomes supplied to a certain extent, and thus becomes less negative than at first, and in a short time afterwards it will have attained the whole quantity that is due to it as a vapour, but not more: therefore, it would be impossible for the vapour to assume a positive electric state by the simple process of evaporation, though it is quite certain that it may assume a negative electric state for a considerable time when its formation is very rapidly carried on. Why, then, did Volta's experiments shew that the cloud of vapour was positively electrical? Volta's experiments did not shew that the vapour was positively electrical. The indications of the electrometer, in those highly interesting experiments, were occasioned by the vapour condensing, and again becoming water, on the metallic appendages of his electroscope. The vapour, being condensed, had its capacity for the electric fluid lessened, and now yielded to the instrument a portion of the electric fluid which it had absorbed whilst in the state of vapour : hence the reason of the electroscope indicating positive electric action. It is easy to see how the dish and water would be left in a negative electric condition, which would also be the case with the vicinal air. It is thus, also, that aqueous vapours from the earth, by assuming a greater capacity for the electric fluid than they previously had whilst in the state of water, absorb, and carry up, an immense quantity of it; and that vapour must either be electronegative or electro-neutral, until condensation again takes place, and can never become electro-positive until the degree of condensation is sufficiently great to lower the electric capacity beyond that required to maintain an electric equilibrium with the surrounding air. The curiosity of philosophers, concerning Volta's experiments, having soon become subsided, we hear very little more of the production of electricity by evaporation till the celebrated experiments of Messrs. Armstrong and Pattison, in the neighbourhood of Newcastle-upon-Tyne, the particulars of which have been made known. to the readers of these Annals of Electricity, &c., vol. v., pp. 452, 453, 456. Vol. vi., pp. 37, 42, 305, 311. The results of the scientific part of these famous experiments are perfectly reconcilable to the theoretical views we have already taken respecting the electrical condition of vapours in M. Volta's original experiments, viz., that vapour or steam, at its first production, is in a negative electrical condition, and that it is only by recondensation that it shews positive electric action. Dr. Charles Schaf haentl made a series of experiments, from which he also concludes that the developement of the positive electricity is occasioned by "the sudden condensation and separation of water from the steam."* But he also supposes that the steam itself, in order to produce electricity, should be produced in a peculiar manner, "by the sudden boiling of the water, and the conversion of a portion of it into a fine spray, &c." Such an inference might also be drawn from Volta's experiments, in which he obtained the greatest electric action by throwing a spoonful of water on burning coals. There can be no doubt of the action being greater under these circumstances; but we are far from considering that this condition is essential to the absolute production of electric action by evaporation. Indeed, our own experiments shew the contrary.-EDIT. Dr. Schafhaentl's experiments and reasoning thereon will shortly be placed before the readers of these Annals. An Account of the Magnetic Observations made at the Observatory of Harvard University, Cambridge, by JOSEPH LOVERING, Hollis Professor of Mathematics and Natural Philosophy, and W. CRANCH BOND, Astronomical Observer to the College. (Memoirs of the American Academy.) (Concluded from page 112.) In 1837, Gauss published his "Allgemeine Theorie des Erdmagnetismus." This was the first attempt to subject the problem of the earth's magnetism to strict mathematical analysis. The solution was embarrassed and complicated, being of the nature of those which had already been performed in determining the figure of the earth and the tides. It required the use of Laplace's celebrated co-efficients, a powerful instrument, but difficult of management. Besides, it laboured under the peculiar disadvantage of not being supplied with sufficient data, derived from observation, for calculating with precision the value of the constants. The whole developement may be found in the original or translated memoirs of Gauss, and a general idea of the analysis can be obtained from the able article on Terrestrial Magnetism, in the London Quarterly Review, to which reference has already been made. What is here called a theory, makes none or the most general assumptions as to the nature and distribution of magnetism in our planet. The investigation, which is mathematical throughout, depends, at last, on ascertaining the values of certain constants from observed data. Here the want was felt of a complete series of such as were nearly accurate and strictly comparable. It cannot be entirely relieved until the accomplishment of the present magnetic enterprise. With insufficient data, but the best that the state of science afforded, many of which were obtained through the assistance of the German and Russian Magnetic Association, Gauss calculates on the principle of least squares, which allows more places on the earth to be represented than there are unknown quantities, the values of his co-efficients. After passing the formulæ through several new forms, the chief object of which was to make them more simple and to facilitate the application, he brings the three components of the function into the following shape : X, Y, and Z, are the three co-ordinates of the magnetic force, exerted upon a given point of the earth, whose longitude is reckoned east from Greenwich. The auxiliary angles A', A", &c., B', B", &c., Ci, C, &c., depend upon the latitude. X = a + a' cos. (+4) + a" cos. (2+) + al cos. (3+) +acos. (4+1). Y = b' cos. (^+B) +b" cos. (2λ+B) + b cos. (3 + B) +bi cos. (4λ+Biv). Z = c + c' cos. (x+C) + c cos. (21+C) + c cos. (3x+C) + civ cos. (4+Criv). Professor Peirce has calculated the value of X, Y, and Z, by these formulæ for the Cambridge Observatory, whose longitude is 71° 7'.5 W., and whose latitude is 42° 22′ N. Here λ = 288° 52′.5. The equations give these values for the co-efficients and auxiliary angles: log. ai = 195.01 al 1.60487- 40.26 log. a+ log. cos. (3X+4iii) = 1.30251=+ 20.07 log. av log. cos. (4λ+A1ˇ) = .64970== 4.46 X, Y, and Z, being thus determined, if we represent the declination by &, the inclination by i, the total intensity by , and the horizontal intensity by w, we have these two formulæ to find and w: After dividing the numbers which represent the horizontal and total intensity by 1000 to reduce them to the arbitrary unit in com mon use, we have the following values of the elements for 1837, calculated according to Gauss' formulæ :— We are now able to add one more to the list of 99 places for which Gauss has compared the computed and observed values of the elements. The difference which appears in all cases between the two is produced by several causes. The observations are not cotemporaneous, and they are visited by accidental errors and the strange anomalies of the magnetic force. The co-efficients, which depend upon the grouping of the observed values, must suffer from the same influences; and hence the computed places, by no fault of the theory, are involved in uncertainty. In some cases the two errors may balance each other; at other times they will conspire to produce a great difference. Thus we explain those considerable discrepancies which occasionally appear between the results of observation and calculation. So far as declination is concerned, Cambridge suffers particularly from these causes; there are only 3 out of the 97 places for which Gauss has made the computation where the difference is so great between the computed and observed element. In these instances, it amounts respectively to 5° 45', 4° 42′, and 5° 15'. In regard to inclination the case is more favourable, as there are 40 places in Gauss' catalogue where the difference is greater than at Cambridge; the maximum difference being 4° 38', or 5 times that of the latter place. Out of the 98 places for which the declination has now been calculated, the difference is plus in 52 instances, and minus in 46; and out of 100, for which the inclination has been computed, the difference is plus 66 times, and minus 34 times. This is satisfactory proof that the error proceeds from the observations, and not from the theory. Before sentence can be fairly pronounced upon the latter, better observations must be possessed for comparison and the determination of the arbitary co-efficients. It is especially to be desired that cotemporaneous observations of great accuracy should be made in every quarter of the globe, that the calculated values of the co-efficients may be general and impartial. Until this is done we cannot expect that the theory, however complete in itself, will give correct expressions of the elements for all parts of the earth. Thus we explain the large difference between the calculated and observed declination for Cambridge and a few other places. We must, however, never lose sight of the fact, that remarkable local disturbances may sometimes derange the observed value of the element, so as to leave still a few cases of unusual discrepance. Part VII. of the "Scientific Memoirs" contains maps of the lines of declination and inclination on the globe for 1838, drawn by Gauss according to his theory. In |