of saturation which are improbable, if not contrary to expe rience. It may be observed, that the quantity of water found in this double salt was greater than that contained in the two salts separately; and, as it is to be presumed that the strong base, rather than the weak one, would combine with a more than usual quantity of water, this bicarbonate of potash must have contained three times as much water as in its isolated state; and the water in each of the two salts must have contained three times as much oxygen as the base. The composition of this double salt may therefore be expressed by the formula KC Aq® + 2 Mg C2 Aq*: from which we conclude its exact composition to have been, I have been minute in describing the examination of a salt which may appear uninteresting and obscure; but I thought it right to be so, because a careful and exact examination of what allows itself to be determined with ease, enables us to judge of what ought to happen in cases where a similar examination is not equally possible. The analysis of this double salt is highly important in two points of view. In the first place, it shews that two salts formed by the same acid, at different degrees of saturation, with different bases, may unite and constitute a double salt. And this fact confirms those formulas, which have been deduced from the analyses of several substances in the mineral kingdom; of the emerald, for example, the apophyllite, the mesotype, the tremolite, and others; the composition of which being found with sufficient accuracy, connects silica with earths which serve it as salsifiable bases, and exhibits siliciates in different degrees of saturation. Secondly, our analysis proves that the quantity of water which exists in a double salt, is not always the same as that which exists in its component salts, taken * These symbols have already been explained.-Transl. separately; an important circumstance in analysing those bodies, the composition of which is multifarious and complicated. (To be continued.) ART. XII.-Comparison between the length of the Seconds Pendulum, as determined by Mr Whitehurst and Captain Kater. By EDWARD TROUGHTON, Esq. F. R. S. IN examining Mr Whitehurst's experiments on the length of the Seconds Pendulum, Mr Troughton observed, that the result admitted of various corrections, which were not applied by the gentleman who calculated the length of the pendulum from these experiments*. He therefore proceeded to compute the amount of those corrections, and obtained the following results. The length of the Seconds Pendulum, as calculated by Dr Rotheram, and examined and approved of by Dr Hutton, was 39.11960 inches, when vibrating in a total are of 6° 40′, and in air at the temperature of 60°. Whitehurst's length of the pendulum,............... Correction for the weight of the wire rod,............ Sum of positive corrections,....... Sum of negative corrections,.... Inches. 39.11960 + 0.01654 0.00080 0.00052 + 0.00030 Difference to be added to the length of the pendu lum,...... + 0.01956 Whitehurst's length of the pendulum,............. 39.11960 Whitehurst's length of the pendulum corrected, .................. 39.13916 ........ The object of Mr Whitehurst was not to obtain the length of the simple pendulum; but, from two pendulums of different lengths, to obtain a measure, in such a way, that every other person who used the same means could obtain the same measure. He had no occasion, therefore, to apply any corrections to his results. Now, the length of the pendulum, as obtained by Captain Kater, is 39.1386, at the temperature of 62'; but Mr Troughton has proposed a slight correction upon this length, for the following reasons. Captain Kater's pendulum was composed of three different kinds of brass, as stated in the following table. From these numbers Captain Kater deduces 8.469 as the specific gravity of the pendulum, and uses this number in his calculations; but, it is obvious, that the true mean of the above specific gravities, taking into account both the quantity and quality of the brass, is only 8.2601. Beside this circumstance, Captain Kater has omitted to carry the deal ends of his apparatus to the account of buoyancy. When these two sources of error were calculated by Mr Troughton, he found their amount to be 0.00017, which, added to 39.13860, gives 39.13877 for the true résult of Captain Kater's experiments. Hence, we have, Whitehurst's length of the pendulum corrected,....... 39.13916 Captain Kater's length of the pendulum corrected,.... 39.13877 Difference,........ 0.00039 If Captain Kater's table of specific gravities is wrong printed, as Mr Troughton suspects, from the circumstance that no workman was likely to use brass so porous as to have its specific gravity so low as 7.816, then the most material part of the correction of 0.00017 is without foundation. A result nearly the same as that of Captain Kater and Mr Whitehurst, has been recently obtained at Greenwich by our celebrated astronomer-royal Mr Pond. His experiments were made with the apparatus which had been used in France, and which was left at the Royal Observatory by M. Arago in the summer of 1817.-In our next Number, we expect to be able to present our readers with an abstract of his results. ART. XIII.-On the Length of the Seconds Pendulum, observed at Unst, the most northern of the Shetland Isles. By M. BIOT, F. R. S. Lond. and Edin. Member of the Royal Institute of France, &c. &c. &c. Communicated by the Author. IN the notice which I published last year of the operations undertaken in England and France for the determination of the Figure of the Earth, I announced that the length of the pendulum at the Shetland Isles, agreed with the oblateness deduced from the lunar theory, and from a comparison of degrees observed in very distant latitudes. This agreement was deduced from a single series of the decimal pendulum, which I had accidentally chosen out of those I had made, and which I had calculated before my departure from Unst. I am now able to give more certainty to this result. I had taken at Unst three systems of measures of the pendulum. In the first I employed a platina ball, different from that which we used in Spain and in France, and the metal of which was given me for this purpose by MM. Cuocq and Couturier of Paris. The length of the pendulum, which was sexagesimal, was measured with a rule of iron, the length of which M. Arago and I had measured in Paris, by comparing it with the metre of the archives. In the second system of observations I employed the same rule, but a platina ball which was used in the experiments of Borda, and which we had also used in France and Spain; and in the third system, I employed the same ball,. but I rendered the pendulum decimal, and measured its length with the same rule which we had used at Bourdeaux, Clermont, Figeac, and Dunkirk, in order that the results might be immediately comparable with those which we had obtained on the arc of France and Spain. The second system of observations, has been completely calculated, partly by myself, and partly by M. Blanc, a young man as much distinguished by the precision as by the extent of his knowledge. The following are the results: Latitude of the place of observation, Length of the seconds pendulum, reduced to a vacuum, and to the level of the sea, 60° 45′ 35′′ north. Metre. 0.994948151. * This result, when reduced to English inches, by using the length of the metre, as determined by Captain Kater, namely, 39,37079, gives 39,1719 inches as the length of the pendulum at Unst.-ED. The time was determined by 49 series of altitudes of the sun, taken with a repeating circle of Fortin, both in the morning and evening, and calculated so as to avoid the influence of the constant errors to which this instrument might be liable. They were observed with an excellent chronometer of Breguet's, which, however, served only as a reckoner; for its indications were transported by comparisons, either before or after each series, and often at both these epochs, to an excellent clock of the same artist, which served for the measures of the pendulum, and which had gone with the greatest uniformity for nearly two months. These results were also confirmed by observing the passages of stars with a fixed telescope. The latitude is certain only within some seconds, because it was calculated only from three or four series of observations of the sun and stars, made to the south of the zenith. This was more than sufficient for the pendulum; but the exact calculation of the latitude ought to be made from the whole serieses of observations on the sun and stars, which amount to 55. A correction of this result must still be made on account of the radius of curvature of the knife's edge employed for suspending the pendulum. This correction will no doubt be extremely small; for, upon observing the edge in a microscope, with an excellent micrometer traced upon glass by M. Le Baillif, I found its width to be less thanth of a millimetre, which gives less thanth of a millimetre for the radius of the edge supposed to be spherical. The correction, however, depending upon this cause will be given directly both by the observations which I have made at Unst with pendulums of different lengths, but with the same knife edge, and by those which I made at Edinburgh with pendulums of equal lengths, but with different knife edges. It is easy to see that the preceding length of the pendulum, combined with that of Formentera, Paris, or Dunkirk, and with these last ones taken together, gives a degree of oblateness in perfect accordance with that which has been deduced from the Lunar Theory, or from the comparison of degrees measured at very great distances. But, in order to deduce this element in a definitive manner, we must wait till all the other observations have been calculated. It is very probable that these results will |