that in B and C. The height of the meniscus in both tubes is easily adjusted sensibly equal, by a little manipulation. I always raise the mercury above the point at which readings are to be taken, and then lower it, so as to read on a falling meniscus. This is highly important. Some trouble was occasionally experienced at first, from electro-static induction between the mercury in B, and the glass above it. This was shown by distortion of the meniscus when it was brought very near the glass. The difficulty was partially, but not wholly remedied, by putting mercury in the outside open end of the gauge head, and connecting it by a flexible conductor with the mercury in the cistern F. A complete remedy was effected, by moistening the inside of the gauge head with a dilute solution of phosphorus pentoxide. This became completely dried by the anhydrous phosphorus pentoxide in N, but was of course not dehydrated; and hence always remains conducting, and dissipates static charge. Large pressures, up to a thousand millionths or more, are readily measured with this apparatus, by finding with the cathetometer the distance between the mercury in B, and the end of the head above it from this is quickly calculated the necessary multiplier for the number of millimeters difference in height between the columns in B and C, also measured by the cathetometer, in order to express the result in millionths. For very small pressures, the micrometer wires are set at such a distance apart, as to give a convenient constant (usually 2); and the column in B is adjusted this distance away from the glass; careful allowance being made for the thickness of the wires. Then the micrometer is used for repeated measurements of the difference in height of the mercury in B and C. The disturbing effect of bias is entirely eliminated by giving the micrometer screw a partial turn after each reading. In a sample set of thirty readings, the calculated probable error of the thirty readings taken together was less than a thousandth part of a millionth of atmospheric pressure. The probable error of the three mean results, considered as single readings, is only eleven hundredths of a unit in the third decimal place of millionths. The net result may be expressed as follows, in terms of atmospheric pressure: considered as thirty measurements, 0.000 000 434 60 ± 0.000 000 000 92; considered as three measurements, 0.000 000 434 60±0.000 000 000 11. Here we have the measurement of a total quantity of less than half a millionth of atmospheric pressure, with a probable error of only about a fifth of one per cent of the quantity measured. In another example, we have the measurement of about two millionths of atmospheric pressure, with a probable error of only one part in three thousand, of the quantity measured. From the foregoing, we may safely conclude that, with the apparatus described, small gaseous pressures may be easily measured, with a probable error of less than a thousandth part of a millionth of atmospheric pressure. [This paper is printed in the Philosophical Magazine.] ON THE COEFFICIENT OF EXPANSION OF CERTAIN GASES. By Prof. EDWARD W. MORLEY and Prof. DAYTON C. MILLER, Cleveland, Ohio. THE COëfficients of expansion of hydrogen, nitrogen and carbon dioxide have been determined by the International Bureau of Weights and Measures with great precision, the experiments having been undertaken in connection with investigations on the air-thermometer. The coefficients of a few other gases have been determined with much less precision, while those of many gases have not been determined at all. The method used in the experiments here described is a differential one in which the expansion of the unknown gas is compared with that of hydrogen. Two glass globes of five liters capacity are to be either packed in ice or subjected to a steam bath. These globes can be connected by glass joints to the air pumps and the gas generators, or can be sealed by fusion at pleasure. They are also connected by symmetrical capillary glass tubes, to a differential mercury manometer, having mercury columns twenty-five millimeters in diameter. By means of a suitable cathetometer and illuminating device, the difference in the heights of the mercury columns can be read with certainty, to less than the hundredth of a millimeter. Both globes were exhausted and filled with hydrogen to seventy-six centimeters pressure, and subjected to the ice and steam baths alternately, to enable us to study the behavior of the globes themselves. Then the hydrogen was removed from one globe and another gas was introduced at very nearly the same pressure. By again surrounding the globes with ice and steam alternately, the expansion of this unknown gas as compared with that of the hydrogen, which was in this same globe under similar condition, was determined by comparisons with the hydrogen in the "comparing globe," which is not disturbed during the whole series of experi ments. Using this method three series of measurements were made of the expansions of oxygen, nitrogen, carbon dioxide and air. Other gases are to be experimented upon in the future. The results so far obtained are, the coefficient of hydrogen being assumed as 0.0036625, that of carbondioxide is 0.003712, of oxygen 0.003673, of nitrogen 0.003672, of air 0.003672. NOTE ON THE CONSTRUCTION OF A SENSITIVE RADIOMETER. By Prof. ERNEST FOX NICHOLS, Colgate University, Hamilton, N. Y. In this paper the construction of a new form of compensating torsion radiometer, used recently in a number of researches in the remote infrared spectrum, was described in detail. The instrument is capable of a higher degree of sensitiveness than either the spectro-bolometer or linear thermopile. A steadiness of action and freedom from extraneous disturbances, when working at high sensitiveness. are secured by means of the compensating action of two precisely equal vanes symmetrically mounted on either side of the axis of a quartz fiber suspension. The system, in consequence, is acted upon differentially by all accidental disturbances, while rays to be measured are concentrated upon one of the vanes. The degree of sensitiveness actually attained in one instance was so great that the influence of rays from a single candle, at a distance of one-third of a mile, could be detected and roughly measured. THE PHOTOGRAPHY OF MANOMETRIC FLAMES. By Prof. EDWARD L. NICHOLS and Prof. ERNEST MERRITT, Cornell University, Ithaca, N. Y. THE manometric flame used in this investigation was similar to that employed by Merritt in 1893'. Acetylene gas was, however, substituted for the enriched coal gas used in the former experiments. This gave a flame of great actinic brightness. Instead of a glass plate shot past a slit in the camera, celluloid films were used. These were mounted upon a drum 110 cm. in circumference. The drum, which was driven by means of an electric motor, was given a nearly uniform speed of about 1 m. per second. The photographs obtained were used in the study of the following points: First, for the comparison of the motion of the flame produced by initial consonants, followed by various vowels, with the movements produced by the same consonant when occurring in the middle of a word or at the end. Secondly, to determine in how far small differences of speech show themselves in the flame photographs. Thirdly, to bring out the gradual change in quality of vowel sounds as the organs of speech are modified in articulation. It was found that the records produced by consonants were very insignificant as compared with those produced by vowel sounds, and that in many cases it was difficult to distinguish between the cessation of motion of the flame during the enunciation of a consonant in the middle of a word and the pause occurring between successive words in a spoken sentence. The records obtained were, however, sufficiently definite to indicate that this method might be of great use in the graphical study of phonetics. Not only are differences of dialect easily distinguishable in the records, but likewise differences in the individual voices of those speaking the same dialect. 1 Physical Review, Vol. 1, p. 166. ON THE ELECTROSTATIC CAPACITY OF A TWO-WIRE CABLE. By Prof. G. W. PATTERSON, JR., University of Michigan, Ann Arbor, Mich. (Read in Joint-Session with Section A.) "THE electrostatic capacity of a cable made of two equal wires is microfarads per kilometer, when K is the specific inductive capacity of the dielectric, R the radius of each conductor, and d the least distance between them and common logarithms are to be used." [This paper will be printed in the Physical Review.] THE TREATMENT OF DIFFERENTIAL EQUATIONS BY APPROXIMATE METHODS. By Prof. W. F. DURAND, Ithaca, N. Y. (Read in Joint-Session with Section A.) [FOR ABSTRACT, SEE PROCEEDINGS SECTION A.] A NEW METHOD OF SOLVING CERTAIN DIFFERENTIAL EQUATIONS THAT OCCUR IN MATHEMATICAL PHYSICS. By Prof. ALEXANDER MACFARLANE, Lehigh University, So. Bethlehem, Pa. (Read in Joint-Session with Section A.) [FOR ABSTRACT, SEE PROCEEDINGS SECTION A.] ON THE RATE AT WHICH HOT GLASS ABSORBS SUPERHEATED WATER By IF water under pressure is heated in glass tubes, the volume of water contained decreases as the square, whereas, the chemically active area decreases as the first power of the diameter. In proportion as the tube is more capillary, the action of the water on the glass produces accentuated volume effects. Thus it was shown that the confined volumes of glass and included water undergo contraction at 180°, forming an eventually solid silicate, while compressibility increases to fully three times its value at |