a single flame and mirror offered great facilities for making these observations in a reliable manner. The following mode was employed: the light from the mirror was allowed to fall on the unobstructed screen, and the mirror was drawn up till the spot had disappeared, when the observation was registered; the next compensation was made by pushing the mirror away, and so on alternately, the compensations by pull and push being registered on separate fillets of paper by two pens. In the first experiment fourteen compensations were made by the advancing, and an equal number by the retreating mirror, and the mean of these twenty eight quantities was taken as the true distance of the mirror from the screen; then on comparing the mean of either set of compensations with this true distance, it was easy to ascertain how great a difference from the truth had been tolerated by the eye under the given circumstances. In the first experiment this quantity was found to be, in a second similar trial 1 of the total amount of light. The "screen" in these experiments was quite new, and an inferior result was obtained by using a "screen, "screen," which had for six weeks been exposed quite unprotected to the action of the air; here the usual darkening of the edges had begun and progressed so far as to be faintly visible during compensation. In the experiments just detailed the highest average sensitiveness of the eye is only, while as before shown in practical use the average difference from the mean is less than of the whole. This higher degree of accuracy results naturally from the mode in which the compensations are made, (alternately by approach and recession,) and the fact that the compensations are thus interwoven, in such a manner as to eliminate errors introduced by the slightly varying sensibility of the eye. Experiments on the amount of light transmitted by plates of glass at a perpendicular incidence. A knowledge of the amount of light transmitted and reflected by colorless transparent substances has a certain degree of interest from a technical point of view, enabling opticians to calculate the loss necessarily experienced in various instruments from this source, as well as the intensity where the light is reflected from a single or from two parallel surfaces of glass or other material. Of far more importance, however, is the interest attaching to this subject from a theoretical point of view, and especially in connection with the Undulatory Theory of Light. Formulas for the intensity of the reflected and transmitted beams at all angles have been deduced by eminent supporters of this theory, which in some cases have occasioned considerable discussion. The following very simple formula for the intensity of common light reflected at a perpendicular incidence was first given by Thomas Young; I = (n-1)3 ; the intensity of the incident beam being equal to unity, and n being the index of refraction of the reflecting substance. The same formula was afterwards reached by Poisson in a rigid and learned analysis of the subject, and it was again deduced by Fresnel.* As is well known Fresnel's formulas were subsequently modified by the celebrated Cauchy, but in Cauchy's formula for reflection as soon as the incidence of the light differs considerably from the polarizing angle, the small quantities which depend on e, the coefficient of ellipticity, become so much reduced that they can be omitted from the numerator and denominator, and Cauchy's formula becomes identical with Fresnel's.† It hence appears that the formula above quoted is as well theoretically established, as any which has been deduced under the guidance of the Undulatory Theory, and one would naturally suppose that it had been often tested carefully by experiment. This does not seem to have been the case, and I do not know that it has ever been rigidly tried by a delicate photometric method. On this account I have made a series of observations on plates of colorless glass which are detailed below. Mode of experimenting. When a beam of light falls on a plate of glass or other transparent colorless substance, a certain portion will be reflected, another portion transmitted, a third absorbed. If the plate of glass be colorless and thin, the portion absorbed will be smaller than the necessary errors of observation, so that it can safely be neglected. For example, Bunsen found that in using a plate of crown glass 47 millimeters thick, that it absorbed only of one per cent of the chemical rays that fell on it at a perpendicular incidence. The thickest plate of glass employed by me was 1.67 millimeters from surface to surface, i. e. about one-third of that used by Bunsen, and as we know that the chemical rays are extinguished by glass in a far larger proportion than those which are luminous, it follows that in the plates mentioned below we can safely neglect the internal extinction. This point being settled, the mode of proceeding becomes quite simple; it is only necessary to measure the amount of light transmitted, and the difference between the incident and transmitted light gives the amount of that reflected, and after making a correction for internal reflection, we shall have the means of comparing the results of theory and experiment. *Pogg. Annalen. Bd. xxii, p. 98. Pogg. Annalen, Bd. ci, p. 241. Jamin in Pogg. Erg., Bd. iii, p. 256. Mode of determining the indices of refraction. In my experiments on transparent substances, always where it was possible prisms of the substance were ground and the index of refraction of the sodium line determined as usual with a graduated circle, collimating and observing telescope. In the particular experiments detailed at the termination of this article, the plates of glass used were so thin that it was not practicable to grind from them prisms, and for all such cases I contrived, tested and used two somewhat new modes of procedure, as neither the method of the Duke de Chaulnes (alteration of the focus of a microscope,) nor that of Bernard (displacement of an image viewed obliquely through a plate,) were here found to give reliable results. 1. A minute angular fragment of the glass to be experimented on was placed in a cell, on a glass slide, like those used for mounting microscopic objects, and surrounded with a mixture of "body-sperm-oil" and oil of cassia, the proportions being varied till the refraction of the glass for the sodium line had been exactly compensated by the oil. Olive oil became turbid when mixed with the oil of cassia and hence could not be used. The mode of comparing the refractive power of the mixture of the oils and glass was as follows: at the distance of half an inch below the level of a microscope stage was a fine slit, cut in tinfoil which had been pasted on glass; the microscope was focussed on this, a sodium flame being used to illuminate it; the cell with the oil and fragment of glass was then placed on the stage of the microscope, and moved so that the light from the slit passed through the angular fragment, when it would happen. that the line of light would be refracted to the right or left hand according as oil or glass predominated in refractive power, which made it instantly evident whether sperm oil or oil of cassia was needed. A number of experiments were made to test this method, which was found to answer well, the index of refraction as determined by prism corresponding with that obtained by the use of the fragment: so in the case of a sample of crown glass a triangular prism gave the index of refraction as 1526,* while by the new method it was found to be 1529. This method, however, is capable of still more accurate results, as in the above mentioned experiments, the compensation was pushed only far enough to answer my immediate purpose; that is to say, the fragment may be considered to consist of one large triangular prism with a moderate angle, and a number of smaller prisms, some of which are sure to have very large angles; these latter become effective when the glass is under oil, total reflection no longer taking place, and they act powerfully on the light coming from the slit, still furnishing faint images having a considerable deviation even after the main portion of the glass fragment has ceased to perceptibly deflect it. In no case did I push the compensation far enough to gather in all these outstanding beams. 2. Another method, which in the case of crown glass was found to answer quite well enough for my purpose and to be very convenient, consisted in fusing to a spherical globule a fragment of the glass, placing it in the mixed oils and effecting compensation by observing when the globule ceased to act as a lens, for which purpose a small telescope or the microscope can be employed. Thus, for example, a certain kind of crown glass when ground into a prism gave as index of refraction for the sodium line 1526, while when tested according to this second method, the results of two experiments were 1.5232 and 1·5235. : I give now the results of careful sets of experiments on the amount of light transmitted by two different samples of crown glass in each case the results of four independent trials are given, each trial being worked out with the aid of seven double compensations. In the first case the thickness of the glass was 15 millimeters, the index of refraction 15236, and allowing for the effects of internal reflection, it should, according to theory, have transmitted 91.736 per cent of the light falling on it. periment gave: Ex 92.227 91.371 91.019 91.143 91.440 The difference 296 being hardly larger than the necessary error connected with the method of making the determination. In the second case the index of refraction was 15225, the thickness 1.677 millimeters, and by theory it should have transmitted 91.763 per cent of the light falling on it. Below are the actual results obtained: 90.886 90-948 90.892 91-895 91.155 1 200 The difference here of 500 per cent, or of the whole amount, is almost equally satisfactory, and these experiments show, I think, that the reflecting power of glass with the above index of refraction, conforms in the closest manner to the predictions of theory. Elaborate experiments were also made with flint glass, quartz and calc-spar, but I suppress the results, as it after wards turned out that they were contaminated with minute errors of the character described in this article under the head "mode of adjusting, &c." 3rd; the adjustment alluded to having indeed been always made, but not with a sufficient degree of care to exclude the last trace of error. New York, March 29th, 1870. ART. II.-The Ethers of Arsenic Acid and of Arsenious Acid; by J. M. CRAFTS.* MR. FRIEDEL and I observed, while studying the ethers of silicic acid, that the silicate of ethyl is readily decomposed by heating it with anhydrous boracic acid in a sealed tube; that pure borate of ethyl is formed, and that silicic acid, or an ether containing a very large proportion of silicic acid, is deposited in the tube. It occurred to me that a similar reaction might offer a convenient method of preparing the ethers of feeble acids. The ethers of the acids of arsenic and antimony and of tungstic acid have not yet been obtained, and experiments were made with a view to their preparation, but I have only succeeded in the case of arsenious acid in obtaining a new ether by the action of the acid upon silicic ether. Another method, however, afforded the means of preparing the ethers of arsenic acid, and several different methods of preparing the ethers of arsenious acid have been discovered. The present paper is devoted to the description of the methylic, ethylic and amylic ethers of both acids of arsenic.. ARSENIATE OF ETHYL. The first attempts were made to prepare this body by the action of arsenic acid on the silicate of ethyl. The arsenic acid was dried by heating it in a current of dry air, and it was then sealed in a glass tube with the silicate of ethyl, and heated in an air-bath. After heating 10 hours at 210° centigrade there appeared to be no reaction; on heating 3 hours longer at 230°, a considerable quantity of the arsenic acid dissolved and at a little higher temperature the tube exploded, probably in consequence of the oxydation of the ether by the arsenic acid. In another experiment 20 grams of silicate of ethyl were heated with 8 grams of arsenic acid for 6 hours at 220°-230°. A gelatinous silicate of ethyl was deposited, and on opening the tube about litre of a gas having the properties of ethylene was evolved. A considerable quantity of common ether was formed, and the remainder of the liquid contents of the tube was par *The chemical symbols used have the values which belong to them in the new system. |