The examination of one, or even two or three compounds of any element may give a very different result from that which would be obtained from a larger number of determinations. For instance, Kopp's earlier experiments upon a small number of liquids gave him the number 4:7 as the atomic volume of carbon (C=6), but, upon examining a larger number of compounds he obtained the number 5.5. Doubling these to agree with the modern atomic weight of carbon, and we have a difference of 1.6. Therefore my results in the cases of the elements above named are useful as confirmatory of Kopp's. My determinations for boron, bismuth, vanadium, selenium, and zinc, however, are entirely new. The atomic volume of mercury at its boiling point I have calculated directly from the metal itself, by the data furnished by Regnault. According to According to this chemist, the specific gravity of mercury at 0° is 13:5959, its boiling point is 350°, and one volume of the metal at 0° becomes at 350°, 1.065743 volumes. From these data I find the specific gravity of mercury at its boiling point to be 12-7572, and dividing the atomic weight by this number I get 15.68 as the atomic volume. It will be seen here that I assume that mercury when free has the same atomic volume as when combined. This appears true for bromine, ammonia, cyanogen, and hyponitric acid, according to Kopp's determinations, and therefore it seems allowable to regard mercury as following the same rule. Possibly this metal may have more than one atomic volume, like oxygen, nitrogen, or sulphur; in that case 15.68 is probably either one of them or their mean. If all elements possessing but one atomic volume in their liquid compounds follow after bromine, then we can calculate approximately their specific gravities at their boiling points. That of hydrogen would be 0.1818, and that of carbon 1.0909. This, however, is a mere matter of curiosity at present. Having now the atomic volumes of twenty elements in their liquid compounds at their boiling points, we may proceed to compare the numbers, and see if there are any definite relations between them. Of the relations found between the atomic volumes of compounds by Schröder and Kopp I shall have nothing to say, since more important relations between the elements seem to exist Hydrogen, having in liquids the atomic volume 5:5, is most readily substituted, atom for atom, by chlorine, bromine, iodine, and hyponitric acid. These have respectively, according to Kopp, the atomic volumes 22:8, 27.8 37.5, and 33. The last of these is an exact multiple by a whole number of that of hydrogen, and the second varies but 0:3, the first by 08, and the third by 1.0 from multiples of the same. Now since Kopp does not claim rigid accuracy for his numbers, perhaps we may be justified in altering these to multiples of 5-5. Then for chlorine, bromine, and iodine we shall have the atomic volumes 22, 27-5, and 38-5. The last of these, it will be seen, is the same number which I deduced from the vapor volumes of nine compounds of iodine. The lower number was deduced from only three compounds,—the iodids of methyl, ethyl, and amyl, whose atomic volumes were determined by actual experiment. The atomic volume of iodid of methyl, according to Kopp, is from 65.4 to 683, that of iodid of ethyl from 85-9 to 86-4, and that of the amyl compound from 152.5 to 158 8. If now we calculate the atomic volumes of these three compounds, we shall find that if we regard iodine as having the atomic volume 37-5, we shall get a better agreement with the numbers found for the second of these compounds than if we ascribe to this element the value 38:5; but in the first and third cases, although the lower value for iodine agrees best with the lower of the two numbers between which the atomic volume of each compound varies, the value 38.5 agrees more nearly with them than between those numbers. In other words, we shall get a closer agreement with the results of experiment, if we ascribe to iodine the atomic volume 38.5, than if we give it the lower number obtained by Kopp. The atomic volumes of seventeen organic liquids containing chlorine, have been determined by Kopp. When two values are given for one liquid I take the mean between them, and then I find upon calculating their atomic volumes, that the number 22 for chlorine agrees best with the determinations in seven cases, while Kopp's number affords a closer agreement with the numbers found for the remaining ten, For bromine, out of five compounds whose atomic volumes have been actually determined, Kopp's number coincides best with the results found for four, while the altered number is nearer to the value obtained for the remaining one. Yet the alteration of Kopp's numbers is least in the case of bromine. Let us now examine some other groups of elements in a similar manner. Since hyponitric acid, replacing as it does, hydrogen atom for atom, possesses an atomic volume an exact multiple of that of hydrogen, let us take this compound as our starting point for the nitrogen group. According to Kopp, nitrogen has three atomic volumes ; in ammonia 2:3, in hyponitric acid 8:6, and in cyanogen, 17.0. If now we alter the first to 2.15, and the third to 17.2, leaving the second (our starting point) as it is, then the second becomes exactly four times the first, and the third just twice the second. In other words, the higher atomic volumes of this element become multiples by whole numbers of the lower. This coincidence seems too remarkable to be accidental. For boron, phosphorus, vanadium, and arsenic, the number 25.8 was found as the atomic volume. This is exactly three times 8:6, our starting point for this group. The number obtained for 'antimony, 33-3, it will be seen lacks 1:1 of a multiple of 8:6. But of the six compounds of antimony from which I calculated, two contain chlorine, and two bromine. In my calculation I employed Kopp's values for those elements. "If, however, the altered numbers are the true atomic volumes of chlorine and bromine, then we must re-calculate the atomic volume of antimony. Doing this, using the altered values for chlorine and bromine, we obtain as the atomic volume of antimony, the number 34.2. If we take the atomic volumes actually found for the chlorid and bromid of antimony, and from them determine the value of antimony, using the new numbers for chlorine and bromine, we obtain a mean of 34:5. 34:4 is just four times 8:6! This seems to lend additional strength to the idea that the chlorine group of elements have atomic volumes which are multiples by whole numbers of that of hydrogen. If, however, we re-calculate the atomic volume of antimony on the basis of new values for chlorine and bromine (iodine also, whenever necessary), we must do the same for boron and the elements classed with it. Doing this, we obtain the number 26:4, a variation of only 0:6 from the multiple of 8 6 previously found. In making these corrections it must be borne in mind that whenever the atomic volume of an element is deduced from the vapor volume of a compound, if that vapor volume is compared with that of a compound containing either chlorine, bromine, or iodine, then the atomic volume of the latter must itself be corrected, before deducing from it that of the element in question. Passing now to th> oxygen group, we have two atomic volumes given by Kopp for oxygen, 7:8 and 12.2. Between these two I have yet found no relation. But mercury, as calculated from the metal, has the atomic volume 15.68. 15:6 is just twice 7.8. Zinc, having according to my calculation the atomic volume 23:6, exceeds by only 0.2 a multiple of 7-8 by 3. For sulphur, Kopp gave the numbers 22:6 and 286. Between these two I have found no relation, but the lower one varies only 0:8 from three times 7.8. For selenium I obtained the number 23.2, only 0.2 less than the same multiple of 7.8. Hence it seems very probable that the true lower atomic volume for sulphur and selenium is 23.4. I have found no relation, however, between the higher atomic volumes of oxygen and sulphur. One more group remains, that of tetratomic elements. Of these, carbon, as determined by Kopp, has the atomic volume 11. For silicon I obtained the number 33:1, almost exactly three times 11. Altering this, as in the case of antimony, to agree with the altered atomic volumes for chlorine, bromine, and iodine, we get 33.7, still near enough to 33 to be regarded as following the usual rule. In the case of tin we meet the first and only obstacle to this rule in the list of elements whose atomic volumes have been determined. For this metal I obtained by means of the vapor volumes of ten of its compounds, the atomic volume 41 8. Corrected for chlorine, bromine, and iodine, it stands 41-5, the nearest multiple of 11 to this being 44. Therefore either tin is an exception to the generality of cases, or else my determination of its atomic volume is incorrect. For the chlorid of tin, the atomic volume found was 131.4. If we regard chlorine as possessing the atomic volume 22, then tin in this compound has the value 43.4. Also from the vapor volume of stanntrimethylethyl I obtained the number 44:0 as the atomic volume of tin. Therefore it is not unlikely that a more accurate investigation will decide the atomic volume of this metal in its liquid compounds to be 44, but for the present it must remain in doubt. This comparison of the atomic volumes of these elements in their liquid compounds at their boiling points, makes it therefore extremely probable that the atomic volume of every element in the liquid condition is a multiple by a whole number of that of the element typifying its group. That is, the atomic volumes of monatomic elements are multiples of 5-5, those of diatomic elements, of 7.8, those of triads, of 8:6, and lastly those of tetrads, multiples of 11, and consequently also of 5.5. Tin may Tin may be an exception, but the only one in twenty elements. Whether this rule be absolutely true or not, however, it will be seen to be very near the truth, since in only one case, that of iodine, have I altered the number found by so high a quantity as 1:0, and that in many cases, a change of only from 0·1 to 0:3 was necessary. Furthermore, the numbers 5.5, 7.8, and 8:6 are not numbers for which we would expect to get exact multiples, unless some definite law accounted for it. Coincidences in two or three cases might be ascribed to accident, but in nineteen cases, all probability is against such an idea. I should not venture to alter any of Kopp's numbers, had he claimed rigid accuracy for them, and the variations between his own earlier and later results for carbon, seem to render such alterations as I have made, more justifiable. His later numbers for oxygen, hydrogen, and carbon, having been deduced by comparing the atomic volumes of forty-five compounds containing them, it will be seen I have not changed at all. His numbers for chlorine, bromine, iodine, and sulphur, however, which I have altered the most, were obtained from a comparatively small number of compounds containing them. If my alterations be accepted, and also my new determinations, then the list of the atomic volumes of elements in their liquid compounds at their boiling points will stand as follows. Hydrogen 5:5, chlorine 22-0, bromine 275, iodine 38:5, oxygen 7.8 and 12-2, sulphur 23:4 and 28:6, selenium 23:4, mercury 15:6, zinc 23:4, nitrogen 2:15, 8:6, and 17:2, boron, phosphorus, vanadium, and arsenic 25:8, antimony, and possibly also bismuth 34:4, carbon 11.0, silicon, and titanium 33.0, tin, doubtful, either 41-5 or 44:0, probably the latter. Note. - For the benefit of any who may wish to consult the authorities upon the subject of atomic volumes, I will state that, apart from Kopp's original articles, previously referred to, the best summaries I have been able to find are in the following works. "Watts' Dictionary,” vol. 1, article" Atomic Volume." Kekulé's “Lehrbuch der Organischen Chemie,” vol. 1, and Buff, Kopp, and Zamminer's “Lehrbuch der Physikalischen und Theoretischen Chemie." ART. XIV.-On the Occultator; by Prof. LEWIS R. GIBBES, Prof. Astronomy, &c., in College of Charleston, Charleston, S. C. In the years 1848–1854, I was much engaged in observing occultations of fixed stars by the moon, and as a means of obtaining the approximate times of disappearance and reappearance with less labor than by calculation, I devised and constructed, in 1849 or 1850, an instrument for that purpose, to which I gave no special name. This instrument is still in my possession, but not in use, as certain parts, presently to be mentioned, have deteriorated with the lapse of time. The Rev. Thomas Hill, of Cambridge, Mass., has published in the Nov, number of this Journal, a description and figure of an instrument for the same purpose, invented by him in 1842, and called by him the occultator. As the two instruments have the same end in view, there is a general agreement in plan, but the details differ. Mine is founded on the well known method of orthographic projection usually adopted in projecting eclipses and occultations, and I have published no description of it, nor do I propose doing so at the present time; but I wish to mention now, the devices I adopted to overcome certain difficulties which present themselves in both instruments, |