transfer it to the first term, we put x-113 in the place of x, and thus get u= .001+.026 sin (x 0+297°21')+.211 sin (2 x 0+82°53′) which does not differ greatly from the equations obtained by Cauchy's method and the method of least squares, as given in the Coast Survey Report. Similar results would be obtained by dividing the given series into eight or twelve groups, and computing the values of the first five constants from formulas (d) or (e). These results would probably be a little more accurate than the preceding, being in accordance with the principle of least squares, as already stated. In cases where the data for interpolation are the mean values M1, M2, M3, &c., of the ordinate, taken within intervals formed by equal divisions of the circular period N, our formulas (a), (b), (c), &c., will still be applicable. For instance, with three intervals, we shall have S=1M,N, S.=} M,N, S2 = M2N Formula (a) then gives the values of the three constants, and since S=Mn, formula (78) becomes 1 M=A+ sin (no)[B, sin (x0)+C, cos (x0)] which expresses the mean value M of the ordinate within any interval n. To illustrate this, let us take the corrected mean temperatures at New Haven (Transactions of the Connecticut Academy, Vol. I, p. 233) for intervals of four months: January to April... May to August... September to December... = M, 34°. 35 Fahr. M, 46°, 15 To obtain from these an equation for the series of daily means, we have N=3651, and consequently This equation expresses the mean temperature of any interval of n days. The angle o is If we also take n=1, the equation of daily means is found to be M=49.11+22.91 sin (x 0+68°58') The origin of co-ordinates is at the middle of the year. REPORT ON THE TRANSACTIONS OF THE SOCIETY OF PHYSICS AND NATURAL HISTORY, OF GENEVA, FROM JUNE, 1870, TO JUNE, 1871. BY M. HENRI DE SAUSSURE, PRESIDENT. [Translated for the Smithsonian Institution.] The year which has just passed has been marked by events which have left but little time for the peaceful occupations of science. The war burst upon us almost at the moment that our scientific year commenced, and we can hardly yet say that it has terminated. If Switzerland has not been oppressed by belligerent armies, she has, nevertheless, been obliged to play an active part in the duties which her neutrality imposes upon her, and there are few present who during this sad period have not been in one way or another diverted from their regular occupations. Several members of the society have not hesitated to make the sacrifice of their precious time to works of charity which the evils of war have rendered every day more indispensable; in fact no one has been able to escape the preoccupations occasioned by the important events which have transpired in a neighboring theater of our frontier. On this account the convocation of the scientific congress, announced for the second half of the year 1870, has been countermanded. The Helvetic Society of Natural Sciences, convoked at Frauenfeld for the month of August, has not been able to assemble, and a geological congress, organized at Geneva under the superintendence of MM. Favre, father and son, and of M. F. J. Pictet de la Rive, has been obliged to be postponed to some other time. We can therefore scarcely be surprised that our society should itself be somewhat affected by the exterior agitations, and that the meetings should have been less frequented than in ordinary times. If, however, the catastrophes to which I have alluded, have somewhat diminished the activity of our members, they have procured us, by a kind of compensation, the inappreciable advantage of having seated among us a number of foreign savants, who, exiled from their homes through the vicissitudes of war, have found in the shelter of our neutrality a refuge both peaceful and hospitable. In attending our meetings, and in favoring us with their communications, they have cast upon our reunions a luster of which our records will preserve the remembrance. These savants were M. M. Regnault, of the Institute, and M. P. Cap, of the Academy of Medicine at Paris; M. le Professor Fée, of Strasburg; and M. Guénée, of Chateaudun. The assiduity with which these gentlemen have associated themselves with us in our labors, the desire which they have manifested to continue with us in relations in which the interest of the society has been so largely increased, has induced us to confer upon them the title of honorary members; and your president before resigning his place to his successor had the pleasure of expressing to them the faithful interpretation of our sentiments. To the names of the savants whom I have just mentioned, I must add those of several gentlemen who have sojourned with us only a short time, particularly M. Bigot and M. Duperrey, who have only appeared at our meetings at brief intervals. Lastly, we have welcomed in our city our emeritus member, M. Dumas, perpetual secretary of the Academy of Sciences, whom we delight to claim as one of ourselves; for none of you can forget that it was at Geneva that M. Dumas published his first works, and that he stands to-day among the elders of our society of physics. It is very seldom, gentlemen, that a year passes without our being called upon to mourn the departure of one of our colleagues. To-day we have to lament the death of a highly esteemed savant, who was admitted into our ranks only a few short months ago. Dr. Augustus Waller was born, in 1816, at Elverton, near Ferusham, in the county of Kent, England. He pursued the study of medicine in France, and received in 1840 a diploma of doctor of medicine from the faculty of Paris. He then returned to England and established himself at Kensington, where he practiced medicine for several years. But the ordinary occupation of the physician was not sufficient to satisfy his investigating spirit, and he always found time to devote himself to scientific researches in the domain of anatomy and physiology. His principal investigations were directed to the nervous system, which did not fail to lead to important discoveries, and some well-known experiments which he made in London upon the degeneracy which the nerves and the nervous center undergo, obtained for him the title of member of the Royal Society, and the grand prize of physiology from the Academy of Sciences at Paris. Not finding in London all the facilities necessary to his researches, he resolved to change his residence, and did not hesitate to sacrifice to his studies a practice which had become extensive. He removed with his family to Bonn, where he had full leisure to continue his physiological and microscopical investigations upon the nervous system. The researches which he made in physiology, either alone or in collaboration with Professor Budge, entitled him to more honorable distinction on the part of the Academy of Sciences at Paris. He obtained for the second time the great prize of physiology on account of his discoveries relative to the functions of the great sympathetic nerve, and to the influence of the spinal marrow upon the pupil. From Bonn, Waller repaired to Paris, and after having labored for several years in the laboratory of Flourens, he was called to Birmingham to occupy a chair of physiology and a position as physician to the hospital of that city. He even then felt the first symptoms of the diseases which subsequently carried him off, and was obliged to give up some of his labors on account of his failing health. He next removed to Switzerland, and after having lived in the Canton Vaud for several years, he came in 1868 to reside in Geneva. Although Waller had been obliged to abandon his regular labors, his mind, unusually active and ingenious, could not remain idle, and he never entirely ceased to occupy himself with interesting questions in physiology and medicine. At Geneva, his health having improved, he devoted himself anew to medical practice, to which he was always much attached, and his large experience in that line rendered him especially eminent. In 1869 he was received as a member of our society. The same year he had the honor of being invited to deliver the Croonian lecture to the Royal Society of London, and for that purpose repaired to England. His health, which appeared to be confirmed, was not established. He had suffered several severe attacks of quinsy, a malady which suddenly terminated his existence on the 18th of September, 1870, at the age of fifty-five years. It would take too much time to analyze all the labors of our lamented associate; we shall limit ourselves to a short summary of those which have excited the most interest in the scientific world, particularly his work upon the degeneracy of the nerves. The nerves which are distributed through different parts of the body are, we know, composed of different fibers, intermixed with each other-those which call into action motive-power, and those which convey impressions of sensibility. At their origin, that is to say at their point of emergence, from the spinal marrow, the motor nervous fibers are separated from the sensitive nervous fibers; the former constituting the anterior roots and the latter the posterior. After having demonstrated by experiment that when a complex nerve is cut, the outer segment, suddenly arrested, withers and degenerates, while the central segment, remaining in communication with the nervous center, continues unchanged, Waller studied the degeneration of the nerves taken at their origin. Beginning at the nervous roots, he proved that "the nervous center, which maintains intact the nervous fibers of the anterior roots, is seated in the spinal marrow itself, while the nervous center, which continues intact the nervous fibers of the posterior roots, is situated in the intervertebral ganglion, united to their posterior roots. It was by means of sections of these roots taken at different distances, that Waller made these important discoveries, the application of which immediately occurred to him. The changes which take place in the structure of a nerve after the cutting are so evident that the experimenter can avail himself of it as a means of tracing the distribution of their fibers in the different tissues. It is in this way that he succeeded in perceiving the |