ART. LVIII.-On the Composition of Permanent Illuminating Gas obtained from the decomposition of Petroleum Naphtha; by H. H. EDGERTON. With a prefatory note by B. SILLIMAN. THE conversion of the light napthas resulting from the rectification of Pennsylvania petroleum into a permanent gas, suited for economical use as an illuminant, either by itself or when mixed with poor gas, or atmospheric air as a diluent, is a problem of no little importance; especially in view of the enormous volume of these light products, equal to at least one-eighth part of the total production of crude petroleum. A process for converting this volatile material into a permanent gas has been devised, and is coming into notice under the name of "Rand's process," which is in fact founded upon an invention patented some years since by Dr. L. D. Gale. In this process the vapor of naphtha evolved in a distillating apparatus by a steam coil is carried into an iron retort heated to redness where it is in great part converted into permanent gases of very high illuminating power. Small portions of the denser oils which escape destructive distillation are delivered by a syphon into a suitable receptacle; while the gas, after cooling is carried to the holder and is fit for immediate use. It is so rich, however, in illuminants as to be unfit for use in common gas burners, and hence is usually reduced by admixture with atmospheric air, of which it requires about an equal volume to bring it to a standard of 25 candles by the photometer. As this problem possesses considerable scientific interest, aside from its economical importance, I have requested Mr. H. H. Edgerton, Superintendent of the Gas works at Fort Wayne, Indiana, who is a well instructed and skillful gas chemist, to communicate for publication his analytical results upon the constitution of the naphtha gas, which are subjoined. The "Memphis Gas" quoted in these analyses is the gas made at Memphis, Tennessee, by this method, that city being thus lighted. By "Fort Wayne N. Gas" Mr. Edgerton means the naphtha gas made by himself at Fort Wayne. In a letter Mr. Edgerton says he has calculated the gases which are not absorbed by Nordhausen acid as methyl or marsh gas, and the absorbable gases as CH + CH,, although he adds, "I am convinced these gases do not co-exist, but go to form an intermediate gas, of less simple relation of volumes." The economical details of this interesting research are given in a separate form elsewhere. It will be a source of great satisfaction should this method of utilizing light naphtha become an established industry, since in this manner alone can we hope, by consuming the raw material, to avoid those constantly recur ing disasters from the use of "dangerous kerosene," made dangerous by the fraudulent addition of these volatile hydrocarbons, by reason of which many hundreds of lives are annually sacrificed. B. S. Condensation of Hydrocarbons absorbable by concentrated Sulphuric acid. In analysis of Memphis gas. According to previous analysis, due non-absorbable gases. Gas employed, 6.819, of which 55.81 pr. ct. absorb. Vol. 3.806. Second trial.-Gas employed, 7.000, of which AM. JOUR. SCI.-THIRD SERIES, VOL. I, No. 6.--JUNE, 1871. Analyses of Petroleum Naphtha Gas, February and March, 1871. 66 After R. V. R. V. Pyro- R. V. R. V. с R. V. RN CO 2 used. con- For 1 or 100 volumes. CO 2 C 249-28 235-05 483-90 441.70 408.51 Ft. Wayne N. Gas, 180-34 158-56 156-26 608-88 392-41 13:08 14.23 32.54 31-39 230-76 205.76] 28.10 42.20 73.63 57.50 2.33 188.57 151.16 6.819 15-18 24.68 16:15 133.82 112.78 5.461 9.018 16-522 13-186 1.651 3.025 2.414 V. Volume. R. V. Residual Volume. R. V.-RN=Residual vol. employed after deducting N found. tion made on Another trial of residual gas after absorption of illuminating gases, the absorpglass holder; sp. gr. of same by Bunsen's To find condensation of absorbable hydrocarbons. Analysis of residual gas from same after standing over water. * Memphis gas before going into "air mixer," supposed to be pure Naphtha gas. Combustion of same gas (No. 5, second series) before absorbing hydrocarbons to ascertain condensation-two trials. **Analysis of residual gas after passing No. through Liebig bulbs containing bromine, through water and caustic potash solution. Weight taken before and 95.580 106,220 Vol. of gas passed,. 74-770 These analyses agree in the main, that one volume of absorbable gas forms on explosion 2 vol. of carbonic acid, and the illuminating power, compared with olefiant gas, is one-third greater, or as 1 to 13, according to Mr. Lewis Thompson's rule. The sp. gr. of hydrocarbons, found by an indirect method, was 1-271. The candle-power of the Fort Wayne gas would be, therefore, according to the chemical standard 7441 candles, or 5 to 6 times that of ordinary coal gas. The actual candle-power by photometric test is much higher. The analyses were all made (with one exception) with Prof. Frankland's apparatus. Owing to a disproportion of parts, the "laboratory tube" being exceedingly small, holding only onethird contents of measurer, but a very small quantity of gas could be analyzed,-about c. c. when nitrogen was present. To give an idea of the experimental error on so small a quantity, four analyses of air, by electrolytic H are added. ART. LIX.-A Historical Note on the Method of Least Squares; by CLEVELAND ABBE, A.M. It is well known that the "Method of Least Squares," although first published in printed form by LeGendre in 1806, in his "Nouvelles Methodes," was first invented by Gauss as early as 1795, and had for years been taught by him in his lectures to his students at Göttingen. It was, however, some years before the Gaussian method came into general use, and especially were English scholars very slow to acquaint themselves with its merits. I have, therefore, been much interested in finding that, in 1808, Professor Robert Adrain, at that time in New Brunswick, N. J., published the method of least squares in the "Analyst," having been independently led to this invention by the study of a prize problem offered some months previously in that periodical. As the editor of, and chief contributor to, the Mathematical Correspondent, the Analyst, and the Mathematical Diary, and as Professor in Columbia College and in Pennsylvania University, as well as by his correspondence, Dr. Adrain is well known to have contributed powerfully to the progress of Mathematical studies in this his adopted country-(he was born and educated in Dublin)—and his apparently independent demonstration of the method of least squares seems quite in accordance with the originality shown in many other of the elegant solutions offered by him to the different problems on which he busied himself. A number of interesting and probably valuable mathematical manuscripts still remain in the possession of his family at New Brunswick, New Jersey, which it is to be hoped may some day see the light. At present I would offer toward the history of mathematics in America the following extracts from the Analyst and other publications. The problem "to correct the distances and bearings of a survey, so as to deduce the most probable area of the enclosed field," had been proposed by Professor Patterson in a previous number of the Analyst, and after being a second time renewed as a prize question, was at length in number IV, solved by a course of special reasoning, by Dr. Bowditch, to whom Dr. Adrain awarded the prize. Dr. Bowditch's results coincided with what would have been deduced had the Gaussian method been applied to this case. Immediately following Dr. Bowditch's special solution, the editor adds his own solution of the more general problem as follows: (The Analyst, pp. 93–95 inclusive). "Research concerning the probabilities of the errors which happen in making observations." "The question which I propose to resolve is this: supposing AB to be the true value of any quantity of which the measure by observation or experiment is Ab, the error being Bb; what is the expression of the probability that the error Bb happens in measuring AB? Let AB, BC, &c., be several successive distances of which the values by measure are Ab, bc, &c., the whole error being Cc; now supposing the measures Ab, bc, to be given and also the whole error Cc, we assume as a self-evident principle, that the most probable distances AB, BC are proportional to the measures Ab, bc; and therefore the errors belonging to AB, BC are proportional to their lengths, or to their measured values Ab, bc. If therefore we represent the values of AB, BC or of their measures Ab, bc by a, b, the whole error Cc by C, and the errors of the measures Ab, bc by x, y, we must for the greatest х y probability, have the equation -= Let X and Y be simia b' lar functions of a, x, and of b, y, expressing the probabilities that the errors x, y happen in the distances a, b; and, by the |