PROCEEDII^GS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. PROCEEDINGS AMERICAN ACADEMY AETS AND SCIENCES. NEW SERIES. Vol. VIII. WHOLE SERIES. Vol. XVI. FROM MAY, 1880, TO JUNE, 1881. SELECTED FROM THE RECORDS. BOSTON: UNIVERSITY PRESS: JOHN WILSON AND SON. 1881. X ^'^' CONTENTS. PAOB I. Dimensions of the Fixed Stars^ with especial reference to Binaries and Variables of the Algol Type. By Edward C. Pick- ering 1 II. Appendix to Paper on the Mechanical Equivalent of Heat, con- taining the Comparison with Dr. JouWs Thermometer. By H. A. Rowland 38 in. No. XXin. — The Magnetic Moment of Fleitman's Nickel. By G. E. Bullard 46 IV. Researches on the Substituted Benzyl Compounds. Ninth Paper. By C. Loring Jackson and J. Fleming White ... 63 V. Contributions to North American Botany. By Asa Gray. . 78 VI. Researches on the Complex Inorganic Acids. By Wolcott GiBBS, M.D 109 VII. A Theory of the Constitution of the Sun founded upon Spec- troscopic Observations original and other. By Charles S. Hastings 140 VIII. XIII. — Acoustic Phenomenon noticed in a Crookes^ Tube. By Professor Chas. R. Cross 155 IX. Contributions from the Chemical Laboratory of Harvard College. By Henry B. Hill 155 Vi CONTENTS. PAGE X. ■ 0)1 the Phosphorograph of a Solar Spectrum, and on the Lines in its Infra-red Region. By John William Draper, M.D 223 XL On the Diiodbromacrylic and Chlorbromacrylic Acids. By C. F. JVIabery and Eachel Lloyd 235 XIL Researches on the Substituted Benzyl Compounds. By C. LoRiNG Jackson 241 XLLL Variable Stars of Short Period. By Edward C. Pick- ering 257 XIV. XIV. — Experiments on the Strength and Stiffness of Small Spruce Beams. By F. E. Kidder 285 XV. Anticipation of the Lissajous Curves. By Joseph Lover- ING 292 XVL Observations on Jupiter. By L. Troctvelot .... 299 XVn. A Papier on the Propagation of Magnetic Waves in Soft Iron. By Harold Whiting 322 XVIII. The Bolometer and Radiant Energy. By Prof. S. P. Langley 342 XIX. On the Use of the Electric Telegraph During Total Solar Eclipses. By D. P. Todd, M.A 359 XX. Large Telescopes. By Edward C. Pickering . . . 364 XXI. Photometric Measurements of the Variable Stars /3 Persei and DM. 81°25, made at the Harvard College Observatory, By Edward C. Pickering, Director, Arthur Searle and O. C. Wendell, Assistants 370 XXII. On the Group "b" in the Solar Spectrum. By William C. WiNLOCK 398 Proceedings 407 Memoirs : — George B. Emerson 427 John Chipman Gray 429 CONTENTS. Vll Memoirs : — paqe Charles Thomas Jackson 430 Stephen Preston Ruggles 433 Louis F. De Pourtales 435 Benjamin Peirce 443 J. Lewis Diman 454 Samuel Sherman Haldeman 456 James Craig Watson 457 Thomas Carlyle 459 William Hallowes Miller 460 Christian August Friedrich Peters 468 List of the Fellows and Foreign Honorary Members . . 471 Index 479 PROCEEDINGS AMERICAN ACADEMY ARTS AND SCIENCES. VOL. XVI. PAPERS BEAD BEFORE THE ACADEMY. Investigations on Light and Heat made and published wholly or in part mth appropriation from the Rumford Fund. I. MARINE BIOLOGICAL LABORATORY. Received J?^:-^^7 . / <5 " / /T ^ Accession No. yi '-:h i> Given by....^.I U'^i^rFhr-^.e-^. r^^ ^ Place, *^*^a book OP pamphlet is to be Pemovad from the Uab- opatopy «iitbout the permission of the Tpustees. lAL OF ks of s de- 'alue. small 1 the icipal ue of ot at ,here- y the values of these constants. Let B, b = the diameters of the Sun and of any given star, as seen from the Earth, expressed in seconds of arc. Let I = the intrinsic brightness of the star, that of the sun being taken as unity ; in other words, let I denote the ratio borne by the quantity of light emitted by the star to that emitted by the Sun from the same superficial area. VOL. XVI. (N. s. vm.) 1 2 PROCEEDINGS OF THE AMERICAN ACADEMY Let S, s = the light of the Sun and of the star expressed in stel- lar magnitudes by means of the scale of Pogson, in which a difference of one magnitude corresponds to the logarithmic ratio, 0.4. This ratio, expressed in numbers, is approximately 2.512. Let p = the parallax of the star in seconds of arc. The observed light of the star will be to that of the Sun as / b^ is to £- ; the difference in their stellar magnitudes, or s — S=2.5 log f^., =2 5log B—o\ogb— 2.5 log I. Hence, log b = \og B + 0.2 S— 0.2 s — 0.5 log /. The radius of the Sun equals 16' 2", and accordingly B= 1924". The value of S is more uncertain. Various determinations of the ratio of the light of the Sun to that of Sirius have been made by different observers. In 1698, Huyghens found the value 756,000,000 by re- ducing the light of the Sun by a minute hole.* Wollaston, in 1829, compared the image of the Sun and of a lamp reflected in a silvered bulb of glass, and deduced the ratio 20,000,000,000.t Steinheil, iu 1836, using the Moon as an intermediate standard of comparison, gave the value 3,840,000,000.t In 1861, Bond determined the rela- tive light of the Sun and Moon by comparing their reflections iu a glass globe with that of a Bengola light. Combining his measures with the comparisons of the Moon and Sirius by Herschel and Seidel, he deduced the value 5,970,500,000.§ In 1863, Clark found that, if the Sun was removed to 1,200,000 times its present distance and Sirius to 20 times its distance, they would appear equally bright, and equal to a sixth-magnitude star. Their ratio, consequently, equals 3,600,000,000.|| Reducing these measures to magnitudes, we obtain the values, Huyghens, 22.20 ; Wollaston, 25.75 ; Steinheil, 23.96 ; Bond, 24.44 ; and Clark, 23.89. The mean of all of these is 24.05, with an average deviation of 0.84. The last three agree well, and give 24.10, with an average deviation of 0.23. Probably 24.0 is not far from the truth, and may be assumed to represent this ratio as closely as it is at present known. If we adopt — 1.5 for the magni- tude of Sirius, from the measures of Herschel and Seidel, we obtain for the stellar magnitude of the Sun — 25.5. * Cosmotheoros, La Ilaye, 1698. t Phil. Trans., cxix. 1^8. J Elemente der Ilelligkeits-Messungen, Munich, p. 24. § Mem. Amer. Acad., viii. n. s., p. 2i)8. II Amer. Jour. Sci., xxxvi. 7G. OP ARTS AND SCIENCES. 3 Substituting in the formula for log h given above, B = 1924" and S= —25.0, we obtain log b = 3.284 — 5.100 — 0.2 s — 0.5 log / = 8.184 — 0.2 s — 0.5 log I. This formula is exact, and would give the true diameter of any star if I was known. An approximate value of I might be determined by the following method. Suppose that an electric current be passed through a plati- num-iridium wire heating it to incandescence, and that the brightness of a short portion of it be compared with an artificial star when the current is varied by a known amount. As the current increases, the color of the light changes, the amount of the blue light increasing more rapidly than that of the red. The ratio of the two may be de- termined by inserting a double-image prism in the collimator of a spec- troscope and viewing the wire through it. The two images may be made to overlap by any desired amount by varying the distance of the double- image prism from the slit of the collimator. The blue rays may thus be comhined with the red, yellow, or green, as desired. The rela- tive brightness of the two images may be varied by a Nicol placed in the eyepiece and turned through a known angle. We may thus combine any portion of the spectrum with any other part in such a proportion as to produce a tint to which the eye is especially sensitive. From the readings of the Nicol when different currents are passed through the wire, we may determine the varying proportion of any two rays, as the ri'd and blue, when the wire is emitting a given amount of light. Observing in the same way the spectra of the Sun and star, and applying to them the law deduced from the observations of the wire, we obtain an approximate value of the comparative light emitted by equal areas of the two bodies. This will not be exact, since the effect of absorption is not allowed for, a difference of temperature being assumed to be the only cause of the observed difference in color. Probably tbe error will not be large, except perhaps in the case of the red stars. Until these measurements are made, we can do no better than to assume that / = 1, or that the emissive power is the same for the Sun and star. As a large portion of the stars have nearly the same color as the Sun, and a similar spectrum, tliis assumption will probably not be far from the truth. The term equivalent diameters may be conveniently applied to the quantities thus computed. They may be defined as the diameters the Sun would have if removed suc- cessively to such distances that it would equal in light stars of the given magnitudes. The expressions, equivalent densities and equiva- lent masses, will be used in the same manner to denote the densi- ties or masses of bodies in their other properties resembling the Sun. 4 PROCEEDINGS OF THE AMERICAN ACADEMY Table I. gives the equivalent diameters of stars of various magni- tudes, assuming ^ = 1. TABLE I. — Equivalent Diameters of Stars of Various Magnitudes. Magn. Diam. Magn. Diam. Magn. Diam. 0 0'.bl528 5 0.00153 10 0.00015 1 .00964 6 .00096 11 .00010 2 .00608 7 .00061 12 .00006 3 .00384 8 .00038 13 .00004 4 .00242 9 .00024 14 .00002 The diameters corresponding to the intermediate magnitudes may be found from Table II., which gives the diameters for every tenth of a magnitude from 0.0 to 4.9. TABLE IL — Equivalent Diameters op Stars for each Tenth of a Magnitude. Magn. Diam. Magn. Diam. Magn. Diam. Magn. 3.0 Diam. Magn. Diam. 0.0 0'!01528 1.0 0.00964 20 0"006O8 0'.()0384 4.0 0'.b0242 0.1 .01459 1.1 .00920 2.1 .00581 3 1 .00366 4.1 .00231 0.2 .01393 1.2 .00879 2.2 .00555 3.2 .00350 4.2 .00221 0.3 .01330 1.3 .00840 2.3 .00530 3.3 .00334 4.3 .00211 0.4 .01271 1.4 .00802 2.4 .00506 3.4 .00319 4.4 .00201 06 .01213 1.5 .00766 25 .00483 3.5 .00305 4.5 .00192 0.6 .01159 1.6 .00731 2.6 .00461 3.6 .00291 46 .00184 0.7 .01107 1.7 .00698 2.7 .00441 3.7 .00278 4.7 .00175 0.8 .01057 1.8 .00667 28 .00421 3.8 .00266 4.8 .00168 0.9 .01009 1.9 .00637 2.9 .00402 3.9 .00254 49 .00160 When the magnitude is increased by five, the diameter will be re- duced ten times, and the decimal point should accordingly be moved one place to the left. Thus, if a star of the 3.5 magnitude has a diameter of 0".003, one of the 8.5 magnitude will have a diameter of 0".0003 and one of the 13.5 magnitude, 0".00003. The diameter of Sirius would be that corresponding to — 1.5 magnitudes, or 0".03, were it not that I is probably greater than 1 owing to the blue color of the star, and the diameter consequently less. Should future measurements render some other value of aS' more probable. Tables I. and II. can still be used, merely changing s by the same amount that S is altered. The smallest star that can be seen in the 15-inch telescope of the Harvard College Observatory has a magnitude of about 15.5, and a corresponding equivalent diameter of 0."000012. OP ARTS AND SCIENCES. 6 When the parallax of a star is known, these principles may be applied to determining its linear diameter. If the San was removed to the distance of the star its diameter would have the same ratio to the parallax that the chord of the Sun's diameter, as seen from the Earth, has to unity. It would therefore equal Ij) sin 16' 2"=: 0.00933 j9. Table III. gives the light in stellar magnitudes which would be emit- ted by the Sun if removed to such a distance that its parallax would have the value given in the first column. TABLE III. — Parallax. Par. Magn. Par. Magn. o"i 6.07 o'.'e 2.18 0.2 4.57 0.7 1.84 0.3 3.68 0.8 1.56 0.4 8.06 0.9 1..30 0.6 2.58 1.0 1.07 If the parallax of « Centauri is assumed to be 0".9, the Sun as seen from it will appear as a star of the 1.3 magnitude. The light of a Centauri is not known with much certainty, as we have to depend upon eye estimates. Assuming the magnitude of the two components to equal 0.0 and 3.0, we find that if ^= 1 for both of them, their diam- eters will be 1.82 and 0.46 times that of the Sun. The parallax of 61 Cygni may in like manner be assumed to be 0".3, and the magnitude of its components 5.0 and 6.0. The Sun would then appear, from this distance, as a star of the 3.7 magnitude, and the diameter of the two components, compared with that of the Sun, if their emissive powers are the same, will be 0.55 and 0.35. I. Binary Stars. In the case of a binary star, another equation of condition may be introduced from Kepler's third law. Let iV denote the mass of the binary in terms of that of the Sun, P the period of revolution in years, a the semi-axis major, or mean distance of the components, and b the equivalent diameter, or the diameter of a star having the same mass as the binary, and the same density and intrinsic brightness as the Sun. Comparing the binary with the system formed by the Sun and Earth seen at the same distance, we see that the two systems have masses in 6 PROCEEDINGS OF THE AMERICAN ACADEMY the ratio of iVto 1, mean distances in the proportion of a to p, and periods of revolution as P to 1. Accordingly, by Kepler's law, N:l={:,:i,o.N= ^. But N= ^^^^^ , since 0.00933;. will equal the diameter of the Sun at the distance of the binary. Hence, equating these two values of N, p is eliminated, and we have J=: 0.00933 a P~"^ The stellar magnitude corresponding to the di- ameter, b, may now be found from Tables I. and II. So far, no hypothesis has been introduced, and the errors in these quantities will depend only on the errors in the photometric measurements and in the micrometric determination of the elements of the orbit. If now we could find the value of / for each of the components, as suggested above, we could determine the true diameter of the two stars, and from their orbits, and the mass of the binary, deduce their average densities. Until these measures are made, we can do no better than assume that both stars have the same density, and that /= 1 for each. On this hypothesis, if h^, h., are the equivalent diame- ters of the two components, and b the equivalent diameter of the binary as computed from the time of revolution and mean distance, the density will equal . •' ^ 6j8 -i- i^3 Since the value of the parallax is eliminated, it follows that these considerations will not aid the determination of the distance of a binary. The time of revolution of a binary would remain unchanged if removed to double the distance, provided that the linear distance of the components and their diameters were increased in the same propor- tion, or that the angular dimensions of the system remained unchanged. In other words, the observed time of revolution of a binary system is wholly independent of its distance from the observer. The relative masses of the two components could be determined micrometrically and independently of the above methods, by measuring the position of each component from the adjacent stars. If tliis was repeated at intervals during an entire revolution of the binary, the components would be found to have described similar ellipses whose dimensions would be inversely proportioned to the masses. From the Proc. Roy. Astron. Soc, x\. 235, it would appear that INIr. Gill will apply this test to the components of a Centanri. If the difference in light is three magnitudes, and the intrinsic brightness and densities the same for the two components, the ratio of the masses would be as 63 to 1. The semi-axis major of the ellipse described by the larger star would therefore be, according to the elements given by Hind, OF ARTS AND SCIENCES. 7 21 80 --■— = 0".34. Owing to the inclination of the plane of the orbit the apparent ellipse would be much less than this. Some other stars would appear better adapted to this test. The smaller difference in light more than compensates for the smaller orbit. From the data given in Table V., the semi-axis major of the ellipse described by several stars has been computed. The name of the star is followed by the time of revolution in years, and the semi-axis of the ellipse de- scribed by the laiger component; y Coronce Australis, 45, 1".2 ; ^ Ur- sce Majoris, 60, 0".8 ; 70 Ophiuchi, 94, 0".4 ; I Bootis, 127, 0".2; Y Virf/inis, 185, 2".0. Some others might give a larger apparent orbit, but a very long time would be required to detect the motion. When the inclination of the orbit is not zero, the apparent ellipse will be less than that comjiuted in this manner in the same proportion that the apparent orbit is less than the real orbit described by the com- panion. Similar observations might be made on any double stars whose components appear to be physically connected. The proper motion, however, complicates the phenomenon, and cannot be distin- guished from the orbital motion as long as the latter appears to be rectilinear. So many large telescopes are now devoted to the measurement of double stars that there is great danger of an unnecessary duplication of work. A valuable contribution might be made to our knowledge of stellar motion by determining the positions of the components of a double star with regard to several adjacent stars. Even if the masses of the components could not thus be determined, we should at least provide the material for an accurate measurement of their proper mo- tions in the future. The same may be said of the determination of the proper motions of other stars, which could be observed in this way with much greater precision than by the usual meridian observations. Useful work could be done by an observer unprovided with means for measurements by simply examining a large number of double stars and stars having a large proper motion, and noting the approximate position and distances of any adjacent stars near enough and bright enough for accurate measurement, A list would thus be formed from which the selection of suitable objects would be easy. The spectroscope, which has opened so rich a field for work in astronomy, may be applied also to the study of the binary stars. If measurements could be obtained of the approach or recession of the two components, several interesting conclusions could be derived from them. A single measurement would not give the relative masses of the components, since the effect of the proper motion cannot be dis- 8 PROCEEDINGS OF THE AMERICAN ACADEMY tinguished from that caused by the inequality of the masses. The proper motion may be eliminated if the observations are repeated in different parts of the orbit of the binary, since its effect would be always the same, while that due to the inequality of the masses would be continually altering, becoming zero and altering its sign twice during each revolution. If the ratio of the masses could be determined micrometrically as described above, the measures with the spectroscope would determine the component of the proper motion in the direction of the line of sight. The principal use of the measures with the spectroscope would be to determine the true dimensions of the orbit, and consequently the distance of the binary. Let Q, denote the position angle of the node of the binary, ^ tlie inclination of the plane of its true to that of its apparent orbit, s the distance, and p the position angle at the time of observation ; let c?s and dp represent the annual changes in these quantities. Let us make a transformation to a system of rectangular co-ordinates in which the axis of X shall coincide with the line of nodes, the axis of Z coincide with the line of sight, and the axis of J' be perpendicular to both of them. Then dz will equal the annual change in the distances of the two components from the observer, or will measure in seconds of arc the same quantity that the spectroscope measures by the difference in velocity of the two components. But dz ■=. dy tan i and y = « sin {p — Q,) ', hence dz = tan i sin (jo — Q>) ds-\- s tan i cos {p — Q,) dp. Substituting the proper numerical values we obtain dz in seconds of arc ; it should be remembered that dp must be expressed in terms of the radius, or 57°. 3 must be taken as the unit. This method may be employed if we have an ephemeris of the star, the inclination of the orbit, and the position angle of the line of nodes. If the elements of the orbit are given without an ephemeris, a different formula must be used. Let p denote the real distance of the components, and u the angle from the node measured in the plane of the orbit. If a system of co-ordinates is employed such that X' lies in the line of nodes, T' perpendicular to it in the plane of the orbit, and Z' in the line of sight, we have y' ■=: p sin t<, and dz' = dy' sin { = sin i sin u d p -\- p sin i cos u d u. If the orbit is circular, u increases uniformly with the time, and p is constant and equals a ; hence dz' ^=. a sin i cos u d u. If in this expression du=z~ , or denotes the fraction of the orbit OF ARTS AND SCIENCES. 9 , . J , 2 IT a sin i mt • i /« traversed in one year, dz' =: - p — cos u. Ihe maximuna value of this expression occurs when m ^ 0° or tt, and is . If the orbit is elliptical, p and u may be deduced from the elements, and dz may be expressed as a function of the eccentricity, node, and time, a sin I multiplied by the factor, which is constant for each orbit. Let V denote the velocity of light, v the velocity of approach of a star, X the wave-length of a given ray of light, and I the corresponding change it undergoes, due to the velocity. Then V-\- v:V=X-\-l: X or V = V-r; v and Fare commonly expressed in kilometers per second, I and X in ten-millionths of a millimeter; F= 300000. The line F is frequently used in these measures, and for it X = 4865, Sub- stituting these values, v = 62 ?. For the D line, X = 5900, and since the interval between the two components equals 6, a velocity of 305 kilometers per second will be required to produce a deviation equal to the interval between these lines. It will be more convenient to measure the velocity of a star in terms of m, the annual motion, tak- ing the distance from the Earth to the Sun as a unit. This may then be reduced to seconds of arc, if tlie distance of the star is known, by multiplying by the parallax p- Light traverses the distance from the Earth to the Sun in about 498 seconds, or would traverse 63300 times this distance in a year. Accordingly, v =. 63300 — ; for the F line V = 13 /, for the interval of the D lines, r = 64 Z. If / is positive or the line moves toward the red end, it denotes that the star is receding from the observer. We have thus two values of the relative motion of the stars in the line of sight ; one, d z, deduced by computation from the micrometer measurements ; the other, v p, or 13 I p, if the F line is observed, found by the spectroscope. Equating these values, since p is the only unknown quantity, jo = \^- '^^® dimensions of the orbit a , .... are now found directly, since - will equal the semi-axis major in terms of the distance of the Sun from the Earth. It not uufrequently happens that we have an estimate of the differ- ence in magnitude of the two components of a double star by one observer using a telescope, and also an estimate of their combined light by another observer viewing them with the unassisted eye. From these data we wish to determine the brightness of either component alone. Sometimes we have the opposite problem, given the magnitude of tlie separate stars to find that of both, as seen by the eye or in a 10 PROCEEDINTxS OP THE AMERICAN ACADEMY telescope not capable of separating them. Let I denote the light of the fainter star in terras of the brighter, and m the magnitude of the fainter minus the magnitude of the brighter. Then, on Pogsou's sys- tem, m = — 2.5 log I. If Mis the magnitude of the brighter star minus that of a star equivalent to the two combined, or having the light (I -\- l), then M^ — 2.5 log (1 -j-Z). From these formuls we can always find the corresponding values of J/ and m. The maximum value of Jf == 0.75 when ?« is zero or the stars are equal. Table IV. enables us to determine M to the nearest tenth of a magnitude for any value of m. As an example, suppose two stars have magnitudes 2.0 and 3.0; then m = 3.0 — 2.0 = 1.0, and M, from the table, lies between 0.35 and 0.45 or equals 0.4. The light of both combined will therefore equal 2.0 — 0.4= 1.6. TABLE IV. — Combination of Two Stars. M. m. m'. 0.05 3.32 1.90 0.15 2 07 1.06 0.25 1.47 0.G4 0.;35 105 0.34 0.45 0.72 0.11 0.55 0 45 — 0.G5 0.22 — 0.75 0.00 — It is sometimes convenient to know what would be the magnitude of a star whose mass was equal to that of the two components of a double star of the same density and brightness. Let m' equal the difference in magnitudes of the two components, and / and n, the light and mass of the fainter in terms of the brighter. Then m' = — 2.5 log I = — 2.5 log n^ = — 1.G7 log n, since the light is proportional to the square, and the mass to the cube, of the diameter. If then 31 equals the magnitude of the brighter component minus that of both combined, we shall have AI = 1.67 log (1 -|- n), from which 31 is determined as before from any given value of ?«'. The third column of Table IV. gives the value of m' corresponding to every odd twentieth of a magnitude of 31. The value of the latter may thus always be determined to the nearest tenth of a mngiiitude. The maximum value of 31 is 0.50, when m' = 0. Adopting the same magnitudes as in the last example, if two stars have the magnitudes of 2.0 and 3.0, m' will equal 1.0. This value from the third column of Table IV. will correspond to a value of JI/ lying between 0.15 and 0.25, or will equal 0.2. The magnitude OF ARTS AND SCIENCES. 11 of a star having the same mass as the binary will therefore have a magnitude 2.0 — 0.2 = 1.8. ]\Iost of the binary stars whose orbits have been computed are com pared in Table V. The successive columns give a current number, the name of the star, the number of the Dorpat Catalogue, the right ascension and declination for 1880, the semi-axis major in seconds, the eccentricity, the period in years, and the inclination of the plane of the orbit in degrees. The next two columns give the magnitudes of the components as estimated by Struve. Three of the stars are not con- tained in the Dorpat Catalogue, and for them the mngnitudes given have been assumed. The next column gives the equivalent diameter 0.00933 a P"', or the magnitude of a star having the mass of the binary and the density and brightness of the Sun. From the magni- tudes of the components we may compute, by the third column of Table IV., the brightness of a star having the same mass as the binary and the same brightness and density as its components. Subtracting from this quantity that given in the preceding column gives the next column. If these quantities were small, we might assume that they were due to errors in the assumed magnitudes of the stars. Their variations are, however, far too large to be explained in this way. As they are almost all negative, we may hifer that the assumed light of the Sun is too small, or that a larger value should have been given on page 2 to S. A great part of the difference must be ascribed to variations in the density or brightness of the stars. We have at present no way of discriminating between these causes. Such a method as has been proposed on page 3 for determining I would serve to distin- guish them. Until then, it will be convenient to reduce this differ- ence fi-om magnitudes to the relative diameters of two stars of equal density and brightness, one having a mass, the other emitting a lio-ht equal to that of the binary. Assuming the diameter of the first of these stars as a unit, the diameter of the other is given in the next column, and may be denoted by G. In almost all cases this quantity is greater than unity, from which we should infer that most of the stars enumer- ated are either much brighter or much less dense than the Sun, unless, as suggested above, the measurements of the light of the Sun are largely in error. Let d denote the density, b the brightness of the components of the binary, and D the equivalent diameter of the binary in terms of the same unit as C. Then D^ : C^ =: 1 : b, and D^ : V = 1 : d ; eliminating D, C = ^, or the brightness is propor- tioual to the square of C and the density inversely as its cube. If 12 PROCEEDINGS OF THE AMERICAN ACADEMY . _ S aj S OOOOO0OOOOOOOO0OOO0OOOOC0 3OOO ooo k5 ■* o m I-. ■* — ' O -C C-1 -ti -* O C: l^ O TO - t- lO O 1^ I- cr M Ol rH t^ (X O — •-^ OTO Ct CCTOt*c oi x to •»< 35 ooci e m oiSc-iroi-i • -cSoj • -i--^ 3icr ■CO - cc I-, cote ■£ c «i-cji-4.r to— 5 r_ o ^ 05 rH • • lb S-i • • c-1 cr. o = TO -# 1- a: o :: 01 o n o -^ 1.- 1 - c — S = 5^.2,5 o p ^ Co & ! C -. f CC . : u i2 = a 1 ;^U/iSn Q 3 C !c 2 4W ?- I- o ^--i. 3 ft.; cl >'2 C t£ t£ t = 3 ! < ^ -_ -J :-■ c <: f-((MM-*lOCDt*000:0-^C1W'**»CCOI^OOCSOt-'C-1TO***iOCOI'.crC5Q-^WC OF ARTS AND SCIENCES. 13 then the star has the same density as the Sun, the square of (7 will give its briglitness. Again, if the star has the same brightness as the Sun, its density will equal one divided by the cube of G. The product of the semi-axis major by the sine of the inclination and divided by the period is given in the last column but one. It serves as a measure of the annual approach or recession of the two components. Neglecting the eccentricity, the maximum motion in sec- onds will equal this quantity multiplied by 2 tt = 6.28. The last column gives the name of the astronomer by whom the orbit was computed, which is adopted in this discussion. An inspection of the last column but one shows that the value of -^ — in several cases amounts to 0''.03 or even more. Neglecting the eccentricity, the maximum motion would therefore equal 2 tt times this quantity, or nearly 0".2. The eccentricity in some cases would diminish the motion, but in other cases it would increase it. An ec- centricity of 0.5 might vary it from 0".l to 0".4, according to the position of the peri-astron. This value of ■ would probably be even larger for some of the recently discovered stars, in which P is still smaller than in the stars given in the table. It is commonly supposed that the parallax of an average first-magnitude star does not much exceed 0".l. That of a sixth-magnitude star would then be about 0".01 unless the fainter stars are really smaller than the brighter, or unless there is a perceptible absorption of light in space. Substituting the values dz^=. 0".2, p = 0".01, in the formula for the inline, » = — -, given on page 9, we deduce Z= — ~— = 1.5. Ac- 13/ ^ 13 /J ccordingly the difference in the positions of the F line would be 1.5 times as great as the deviation observed in the case of Sirius. As the spectra of the two components could be observed in turn (or perhaps simultaneously) without disturbing the spectroscope, many of the causes of uncertainty present in similar measures of single stars would be removed. In any case, if the F line could be seen in both components, we could assign a limit within which we could be certain that it was the same for both, and this would give a value of the parallax which must be less than the true parallax. A determination of the outside limit of distance of a star would appear to have nearly the same im- portance as the inside limit of distance found by micrometric distance. Moreover it does not seem probable that a star will be found whose parallax is very large, or previous observation might have detected it. 14 PROCEEDINGS OF THE AMERICAN ACADEMY The search for a star with a very small parallax seems more hopeful, since it could not have been detected by other measures. The observation would have value if we could determine the direc- tion of the motion, even if we could not measure its amount, since it would show which portion of the orbit was turned towards the observer. This cannot be found from the micrometric measurements, since, although we can obtain from them the amount of the inclina- tion, we cannot determine its sign. It is also possible that some method of greater delicacy may be dis- covered, so that the spectroscope may be replaced by a more sensitive instrument, as it has been by the interferential refractometer in measuring the index of refraction of gnse^. The semi-axes major of 2 3121, 1768, 22G2. and 2055 are not given in the original publications of the orbits. The values inserted in Table V. are those given in the Handbook of Double Stars, by Messrs. Crossley, Gledhill, and Wilson. This work has also proved most useful in various ways in the preparation of this paper. The value of a given by Dr. Auwers for a Canis Majoris is 2.33. This relates to the ellipse described by the bright star. As the companion is assumed to have a mass — times as great as this, the value of a must be multiplied by 3.05, and therefore 2.33 X 3.05 = 7.11 is the value adopted. It is obvious that for this star the intrinsic bright- ness of the two components is by no means the same. If the density is the same, the diameter of the companion would be 0.79 that of the primary. The area of its disk would be 0.62, while its light* is only 0.0001 of that of its primary. The very large relative diameter of y Leonis is remarkable. Its brightness must be about three hundred times that of the Sun, if it-* density is the same. On the other, hand, if no brighter tlian the Sun, its density would be only one seventh of 'that of attnosphorie air at the standard density and pressure, to give it a sufficient bulk to emit its ol)served light. If the other binaries have the same density as the Sun, their brightness must vary from 100 in the case of c^ Ci/f/nt to 0.06 in the case of p Eridani, the brightness of the Sun bi-ing taken as the unit. The semi-axis major and period of 61 Ci/gni are taken from Newcomb and Ilolden's Astronomy. Although this star is com- moidy regarded as a binary, the evidence in favor of this view seems to depend upon the large proper motion of both components, and the fact that both appear to be comparatively near the Sun. It is doubt- ♦ Ann. Ilarv. Coll. Obscrv , xi. 177. OP ARTS AND SCIENCES. 15 fill whether the observations yet made are sufficiently exact to prove a connection between the components. To establish this proposition, and also as an example of a convenient means of distinguishing a binary star from one which is optically double, the following investiga- tion is given of the more important observations of 61 Gygm. We cannot conclude that a star is binary unless the path described by one of its components appears to be concave with respect to the other. If the motion appears to be rectilinear, it is more probably that due to the proper motion of one of them, or rather to the combined effect of the proper motions of both. On the other hand, if the path is con- vex, it is extremely probable that there is a real connection between the two, as there is no instance known of a star describing a curved path due to proper motion alone. The motion, if rectilinear, should also be uniform, while, if curved, the motion should be most rapid when nearest the other star. The law that the area described by the radius vector is proportional to the time, cannot be used to distinguish between those motions, since it will apply to both. Suppose that the measures are transformed to a system of rectan- gular co-ordinates, having one component as the origin, and the axis of X nearly parallel to the path of the other component. Except for the accidental errors, the value of y, if the motion is rectilinear, should be the same for all the observations from the beginning to the end of the series. If the axis of X. is not exactly parallel to the line of motion the values of y should increase slowly from one end of the series to the other. If they are corrected by an amount which will be proportional to the time, this variation should disappear. If the star is binary, however, the value of y will vary, in general having its greatest value during the middle of the period, and being smaller at the beginning and end. The values of a:, if the motion is rectilinear, will vary uniformly with the time, and, if corrected by a constant, plus another constant multiplied by the time, will leave residuals that are very small. If the motion is curved, on the other hand, this condition will not be fulfilled. A reduction of the observations of 61 Cygni is given in Table VI. Of the measurements made during the last half-century only those made by the Struves and by Dembowski have been employed. The position angles are first corrected for precession and reduced to the epoch of 1880 by the formula 0°.00557 sin « sec b (t — 1880) = — 0°.005 {t — 1880). 16 PROCEEDINGS OF THE AMERICAN ACADEMY A simple computation shows that the direction of the motion is nearly that of the position angle 256°. We have accordingly, y=.s cos {p — 166°), and a; = s sin (^ — 166°). In the successive TABLE VI.— Path op 61 Cygni. No. Date. Obs. Cor. p. s. X y A X AJ/ 1 1753.8 Bradley. 34.8 19.63 — 12.93 14.77 — 0.29 — 0.43 2 1778.0 Mayer. 50.4 15.24 — 6.59 13.74 -f 0.97 — 1.46 3 1781.9 Herschel. 53.3 16.33 — 6.30 15.07 4-0.44 — 0.13 4 1793.6 Lalande. 52.3 14.87 — 5.98 13.61 — 1.70 — 1.59 5 1800.0 Piazzi. 69.8 19.27 — 2.08 19.16 4-0.86 4-8.96 6 1805.0 « 78.1 14.50 + 0.53 14.49 4-2.42 -0.71 7 1812.3 Bessel. 78.8 16.74 + 0.82 16.72 4-1.18 4-1.52 8 1813.8 Lindenau. 68.8 16.56 — 2.08 16.43 — 2.04 4- 1.23 9 1814.5 W. Struve. 68.6 15.20 — 1.96 15.08 — 2.06 — 0.12 10 1820.5 " 83.2 15.11 + 1.89 14.99 -^0.53 — 0.21 11 1822.7 " 85.5 14.93 4- 2.46 14.73 -f 0.63 — 0,47 12 1828.7 " 89.1 15.31 H h 3.47 14.91 4-0.38 — 0.29 13 1831.7 " 90.9 15.63 - - 4.02 15.11 4-0.30 — 0.09 14 1832.8 <( 91.8 15.79 - 4.30 15.20 -f-0.35 0.00 15 1835.6 '« 93.6 15.97 - - 4.83 15.22 4- 0.29 4-0.02 -f 0.07 16 1836.6 " 94.2 16.08 - - 5.02 15.27 4-0.37 17 1837.7 " 95.2 15.93 - - 5.24 15.04 4-0.26 — 0.16 18 1843.5 0. Struve. 98.8 16.67 - - 6.46 15.44 -^0.26 -f 0.24 19 1847.5 " 100.7 17.02 4- 7.11 15.46 -f-0.07 -f 0.26 20 1850.3 " 102.3 17.18 + 7.61 15.40 4-0.01 4-0.20 21 1851.8 " 103.5 17.34 + 8.02 15.38 4-0.08 -f-0.18 22 1852.7 " 104.4 17.46 + 8.30 15..36 4-0.17 -h0.16 23 1854.2 " 105.1 17.57 -^ 8.54 15..35 4-0.10 -f 0.15 24 1857.2 " 106.4 18.02 + 9.12 15.55 4-0.05 4-0.35 25 1800.8 " 108.6 18.22 + 9.82 15.35 — 0.01 -f 0.15 26 1868.5 " 112.4 18.81 4-11.16 4- 12.51 15.14 — 0.28 — 0.06 27 1874.7 " 116.1 19.42 14.85 — 0.24 — 0.35 28 1854.7 Dembowski. 105.4 17.29 -- 8.49 15.06 — 0.06 — 0.14 29 1855.8 " 106.0 17.34 — 8.67 15.02 — 0.11 — 0.18 30 1856.6 (I 106.-3 17.45 -- 8.80 15.07 — 0.15 — 0.13 31 1857.6 " 107.2 17.73 — 9.19 15.17 4-0.03 — 0.03 32 1858.5 " 107.7 17.73 -- 9.32 15.08 — 0.02 — 0.12 33 1862.8 " 109.3 18.36 --10.08 15.35 — 0.17 4-0.15 34 1863.4 " 109.5 18.37 — 10.14 15.32 — 0.23 4-0.12 35 1864.7 " 110.-3 18.53 — 10.44 15.31 — 0.21 4-0.11 36 1865.6 " 110.8 18.57 — 10.60 15.25 — 0.24 — 0.05 37 1867.2 " 111.6 18.72 — 10.90 15.22 — 0.27 4-0.02 38 1868.7 " 112.7 18.83 — 11.25 15.10 — 0.24 — 0.10 39 1869.7 It 113.4 18.96 4-11.52 15.06 — 0.18 — 0.14 40 1870.6 ct 11.3.9 19.16 -H11.77 15.12 — 0.12 — 0.08 41 1871.6 " 114.2 19.23 4-11.89 15.10 — 0.21 — 0.10 42 1872.6 " 114.3 19.33 4-11.98 15.11 — 0.33 — 0.09 43 1873.6 " 114.8 19.44 4-12.18 15.15 — 0.34 — 0.05 44 1874.5 " 115.3 19.50 4-12.35 15.05 — 0.35 — 0.15 45 1875.6 t< 115.9 19.58 4-12.56 15.02 — 0.38 — 0.18 columns of Table VI. are given a current number, the date, the name of the observer, the corrected position angle, the distance, and OP ARTS AND SCIENCES. 17 the values of x and y. The value of y is approximately 15". 20 ; that of X, 0".21 {t — 1814). Residuals are accordingly given in the last two columns by subtracting the values of y and x thus obtained from those observed. The residuals in the last two columns are evidently not due to acci- dental errors, but whether they are caused by curvature of the path or systematic errors of the observer is less evident. The first nine sets are so discordant, that little dependence can be placed upon them. The values of Ay show a very slight increase, followed by a diminu- tion in the later values. A a: seems to diminish slowlj', the later values of the Struves and of Dembowski being somewhat less than the earlier. The curvature is so slight, that it has been thought to indicate an hyperbolic orbit. The observations so far made will however be very nearly satisfied by a large circular orbit seen obliquely, so that the part described during the last century has been that near the end of the minor axis of the apparent ellipse. If we take the mean of the residuals, we find the values for A re of 0".25 and for A y of 0''.15. As these include all kinds of systematic errors, the deviations from a straight line can scarcely be regarded as certain. II. Variable Stars of the Algol Type. Variable stars may be divided into several classes, according to the nature of the fluctuations of their light. First, temporary stars, which appear suddenly, and gradually fade away during the next few months. The most famous star of this class is that observed in 1572, by Tycho Brahe. The new stars in Corona Borealis in 18G6 and in Cygnus in 1876, are recent exami)les of this class. Second, a large part of the variable stars pass from their maximum to their minimum and back again, in from six months to two years, the period and the bright- ness at the maximum and minimum being somewhat variable. The change in light is generally very great, amounting to several hundred, or even thousand times. The most striking examples of this class are o Ceti and -^ Cygni. Thirdly, we have the slight changes to which many (or, according to Dr. Gould, most) stars are liable. These changes seem to be irregular in many cases ; at least, their law is not j^et known. Examples of this class are furnished in a Orioiiis and a Cassiopeice. Fourthly, certain stars continually vary, going through a series of changes in the course of a few days, which appears to be repeated ex- actly. Two causes seem here to be superimposed, one producing one VOL. XVI. (n. S. VIII.) 2 18 PROCEEDINGS OF THE AMERICAN ACADEMY maximum and one minimum in each period, the other two maxima and two minima in the same time. As examples, /3 Lyres and S Cephei may be noted, f^ifthly, we have a class of stars which during the greater part of the time remain unchanged in brightness, but at regu- lar intervals lose in the course of a few hours a large part of their Tight, and regain it with equal rapidity. These changes appear to be repeated with the greatest regularity, so that the interval can be com- puted in some cases within a fraction of a second. Algol, or i3 Persei, is the most striking example of this class to which 8 Cancri and 8 LihrcE also belong. Various theories have been advanced to account for these phenomena. Probably different causes act in the case of the different classes. One theory would assume that by a collision, or by the liberation and ignition of a vast amount of hydrogen, the star was suddenly heated to incan- descence, and gradually lost its light by cooling. This explanation would apply only to stars of the first class; it is strengthened in the case of the new star in Cygnus by the observations with the spectro- scope. The spectrum gave at first the lines of incandescent hydrogen which disappeared as the light faded. It has been urged that, to account for the rapid cooling, the star must have been small, perhaps only a few miles in diameter, and consequently not very distant. This view is contradicted by the absence of perceptible parallax. If we con- sider how quickly a meteorite becomes heated, and again gives up its heat, this argument loses its force. The star may be large and dis- tant, the surface only being heated, and soon losing its heat by radia- tion and conduction. This explanation appears more probable than that the light is cut off by clouds of smoke or steam, as has been sug- gested by some astronomers. Stars constituted like our Sun, but in which the variations in size of the spots would be far greater, might undergo considerable changes in light. While it is difficult to account for the great changes in class two in this way, those in class three may be thus explained. A popu- lar theory for the variation of stars of short period is that it is due to the revolution of the star upon its axis, when the different portions are of unequal biightnoss. The variation in light of lapetus, the outer satel- lite of Saturn, is commonly explained in tliis way. A similar effect would be produced if the star was not spherical, and in revolving ex- posed a disk of varying area. A great variation could not thus be produced without the revolving body assuming a condition of unstable equilibrium. For the application of these principles to lapetus, see Annals of Harvard College Observatory, xi. 204. This theory may ex OF ARTS AND SCIENCES. 19 plain the variations of stars of the fourth class. Another theory would account for the changes of liglit by an opaque body or satellite passing between the star and the observer. It will be the object of the fol- lowing discussion to show how fully this explanation will account for the variations of stars of the fifth class. A modification of this theory would replace the single eclipsing body by a cloud of meteorites. Su(;h a theory will account for almost anything by suitably modifying the dis- ti-ibution of the meteors. If we can show that all the effects may be explained by a single body, or what amounts to the same thing, a spherical cloud of meteors so dense as to be opaque, there seems to be no reason for assuming a cloud of another form. All that can be claimed for any theory is that it explains all the facts. If then the computed variations of light agree with the observations within the limits of errors of observation, that is all that can be asked, and the theory should be accepted as the most probable explanation until some new fact is discovered which it will not explain, or some new theory which agrees equally well with observation and appears to be less improbable. The diminution in light might be caused by the inter- position of a body which was self-luminous, instead of dark. We should then have a close double-star, one component of which passed in front of the other. If the orbit was circular, we should have two min-ma during each revolution, and at these times the star would appear of unequal brightness, unless the intrinsic brightness of the two bodies was the same. When the darker body passed in front of the brighter, the light would be less than when the brighter passed in front of the darker. If the orbit was elliptical there might be only one minimum. In the case of Algol more than half the light is cut off at the minimum; consequently one body must be darker than the other. As no second minimum has ever been observed, it is probable that the eclipsing body is not self-luminous. We must now show that neither of the other theories named above will explain the variations of Algol and of other stars of the fifth class. The regularity of the variation disposes of the theory of a volcanic eruption, a collision, or a system of sun-spots. These effects also could scarcely be repeated so frequently without exhausting the source of en- ergy from which they were derived. The theory that the variation is due to the revolution of the star appears more probable, and the regular- ity and shortness of the period add weight to it. On the other hand, it is difficult to account by this theory for the sudden changes in the light. If the light was reduced by a dark portion of the star being turned towards the observer, the minimum should last until, by the 20 PROCEEDINGS OF THE AMERICAN ACADEMY revolution of the star, this part had been turned around so as to dis- appear on the other side. The short minimum observed could only be caused, according to this theory, by supposing a large dark star with a small bright spot near its polar regions, and that the pole was directed at such an angle from the observer that a large part of the spot would disappear for a short time during each revolution. Even then we have still the apparently insurmountable ditficulty that the bright spot would change its a2i[)arent size and the angle at which it emitted its light to tlie observer, and therefore vary iu brightness dur- ing the whole period of revolution. No such variation has been estab- lished in the light of Algol. Before showing how far the theory of an eclipsing body will account for the observed phenomena, we must see what knowledge we have of these variations in light. Only five stars are at present known to belong to the Algol class of variables. These are ^ Persei, S Cancri, X Tauri, 8 Libra, and U Co- ronce. Of these, the first is the only one whose variations are known with sufficient precision to justify a discussion in the present article. The variations of fi Persei, or Algol, have been carefully studied by three observers, Argelander, Schmidt, and Schonfeld. Argelander's observa- tions extend from 1840 to 1866, and are nearly two thousand in number. He compared Algol from time to time with the adjacent stars of nearly equal brightness, and noted the apparent difference in steps or grades {Stufen). Arranging his comparison stars in the order of brightness, and determining the number of grades between each from all his meas- ures, he was then able to denote them all in grades. Thus, suppose at a given time he observed that Algol was sligiitly, if at all, brigliter than star A, or that the difference was one grade ; again, that it was per- ceptibly fainter than B, or differed from it by two grades ; if then he found in his final discussion that A = 12.0 grades and B= 14.9, the first observation would make Algol lo.o grades, and the second 12.9. These comparisons are all given in tl:e Buiin Obsercalions, vii. 31.5, but, unfortunately, they have not been reduced, so that at present no use can be made of tiiem. I undertook their reduction, but was in- formed that this had been done at Bonn. No answer has, however, been received to letters of inquiry on this point. The observations of Dr. Schmidt extend from 1846 to the present time, and the results up to 1875 are published in i\\Q Astronomische Nachrichten, Ixxxvii. 193. His object was only to determine the time of the minima, and accordingly these only are given, without the comparisons. He also generally used a single comparison star, which OF ARTS AND SCIENCES. 21 has the advantage of eliminating an error in estimating its brightness, but does not give a good determituition of tlie light curve. Dr. Schon- feld observed Algol, according to liie method of Argelander, from l8-'>9 to the present time, and has given the results up to 1870, in the Sec/isti>iddreissi(/ster Jahreshericht des Mannheimer VWeins fur Natur- kunde, p. 70. He has not published his comparisons, but has given his resulting light curves, which will be nia5 15.78 -j-1.57 16.06 9.882 0.762 3.0 18.08 17.71 -fO.!>7 18.20 9.935 0.861 3.5 19.59 19.19 -f0.40 19.39 9.904 0.920 4.0 20.24 20 23 -j-n.oi 20.24 9.98(5 0.908 4.5 20.70 20.75 —0.05 20.72 9.998 0.995 4.6 20.8 20.8 0.00 20.80 0.000 1.000 From this table it appears that the law respecting the increase of light is not the same as that of its diminutiou. At a given interval of time from the minimum, the light is greater when decreasing than ■when increasing. The mean value will first be considered, and the cause of this dillurence then discussed. We shall first assume that the star and satellite present circular OF ARTS AND SCIENCES. 23 disks, one uniformly bright, the other dark, and that the form of orbit is circuhir. Three cases may occur, corresponding to a total, an annu- lar, and a partial eclipse of the star. In the first case, all the light would be cut off for a longer or shorter time ; in the second, the mini- nuHu light would be maintained during the transit of the .satellite across the face of the star ; and in the third case the light would diminish until the minimum was attained and then immediately begin to increase. Algol appears to belong to the last of the classes. We must next determine the relative diameters of the satellite and star. A minimum diameter of the satellite may be computed from the mini- mum light. To reduce the light to 0.416, or to cut off O.o84 of the light, the diameter of the satellite must be at least y 0.584 = 0.764 times that of the star. In this case it would just pass completely on to the disk before it began to pass off. No maximum can be deter- mined in this way, so that the diameter is only limited between 0.764 and infinity. A change in diameter will, however, produce a change in the law of variation of the light. We may deduce the diameter from the values agreeing most nearly with observation. We must now determine the amount of light remaining when the star is par- tially eclipsed by a satellite of radius r. The radius of the star is taken as the unit. The area of the segment of a circle of radius unity whose versed sine is z, is equal to versin~-^2; — (1 — z) \2z — z^. A table is given in the eighth edition of the Encyclopcedia Britannica, xiv. 525, Art. Ilensnration, which gives this quantity for values of z varying by hundreds from 0.00 to 1.00. The portion of the disk cut off will always be composed of two segments having the radii 1 and r, and having a common chord which may be computed when we know the distance of the centres. The area of each may be taken from the table, multiplied by the square of the radius of its circle, and the two areas added. This will give the required diminution in light. If now we assume r the radius of the satellite, several of the ele- ments may be computed. The period of revolution of the satellite is given with much pre- cision from the observations of the minima. It appears to undergo slight changes, but may be assumed for the present time to equal 2 days 20 hours 48.9 minutes. Calling w the longitude of the satel- lite in its orbit reckoned from its minimum, the mean change in w per hour will equal 5°.023. Since the beginning and ending of the ob- scuration precede and follow the minimum by 4'' 35™, the corre- sponding values of w will be 337°.0 and 23°.0. At these points the centre of the satellite will be at a distance (1 -j- r) from the centre 24 PROCEEDINGS OF THE AMERICAN ACADEMY of the star, or the disks will touch each other. They correspond to the first and last contacts of an eclipse. The orbit is projected into an ellipse whose major axis, a, equals the true distance of the centres, and whose minor axis, b, equals the distance at the time of greatest obscuration. When ?' = 0.74G, 6=1 — 0.74G = 0.254. For other values of r, b must be determined from a computation of the area eclipsed, by successive approximations, until such a value is found as will reduce the light to 0.416. If x and y are the co-ordinates of the point in the orbit reached by the satellite at the time of first contact, by the properties of the ellipse x = a sin w, and y =^ b cos w. The square of the distance of the centres, or D-, may be written 2)2 = (1 -\- rY = (x^ -\- If) = a~ sin- w -\- b' cos^ lo = a" — (a- — b'^) cos^ iv. Since w = 23^.0, (1 -f r)2 = 0.153 a'- + 0.847 b'\ Substituting the proper values of r and b, a may be deduced. The cosine of the inclination, ^, of the oi'bit will equal -. The three lines of Table IX. give the values of a, b, and i computed by these formu- las for the minimum value of r = 0.764, for r = 1.000, and for r = 2.000. There is no maximum value of r, which may be indefi- nitely large. Let li be any large value of r, and \et a = Ji -\- A, b=. E -\-B, and D^ R -\-d ; substituting these values in the formula, D'^^a- sin^ iv -\- b'- cos'-^ ?p, the terms containing E- cancel each other, and we have 2 R d^ 2 RA sin'^ w -\- 2 RB cos'- w, omitting the terms not containing R, since when R is very large they may be neglected. Dividing both sides hj 2 R gives d = A sin'^ w -\- B cos^ lo. When IV = 23°, d must equal 1, and when w =: 0°, B will equal — 0.132, since the arc of the large circle becomes sensibly a straight line, and the segment whose versed sine is 1.000 — 0.132 has an area of 0.416, or the minimum area of the uneclipsed portion. From these values, we may deduce A = 7.300. The two axes, therefore, become R — 0.132 and R-\-7.S00.' The inclination in this case contin- ually diminishes as R increases, and would equal zero if Ji became infinite. The residuals which will be deduced below at first led to the belief that the phenomenon might be that of an annular eclipse. This case has therefore been included to show the change effected in the variation of the light, although the residuals are not materially reduced. If the eclipse is annular, the value of r must be 0.764. OF ARTS AND SCIENCES. 25 The value of h cannot be determined directly, but must be deduced from the times of internal and external contact. The interval be- tween the internal contacts is assumed to be 24 minutes, or that during which the satellite moves through 2° of longitude. In the equation D- = a^ sin'^ w -\- b^ cos'^ to, we have for w = 1°, J) = (l—r)= 0.236, and as before for w =: 23°, J)=l -\-r = 1.7Gi. From these conditions the values of a and b given in the last column of Table IX. are deduced. TABLE IX. — Elements of Orbits. Elements. r = 0.764 r = 1.000 r = 2.000 r = R Ann. Minor semi-axis, b Major semi-axis, a Inclination, i 0.236 4.480 87°.0 0.666 4.872 82°. 1 1.783 6.427 73°.9 i? — 0.132 E 4- 7.300 Small. 0.223 4.482 87°. 1 "We must next compute the amount of obscuration at the end of each half-hour, for the various values of r. The distance between the centres is first computed by the equation D"^ = a^ — (a^ — b^) cos" w, substituting successively, w = 2°. 5, 5°.0, 7°.5, 10.°0, 12°. 6, 15°.], 17°.6, and 20°.l. The first part of Table X. gives the values of B corresponding to those assigned to rat the head of each column. The triangles formed by the centres of the two bodies and one end of the segment now become known, since their three sides equal 1, r, and D. Calling the angle at the centre of the luminous body a, we have r^=l'^ -\- D^ — 2 D cos a. From this we deduce cos « and versin «, or the height of the segment bounded by the circle having a radius unity. The height of the other segment will equal i? — J^ -\- ^os u, from which the areas of the segment, and consequently of the uneclipsed portion, may be deduced. This area is given in the second portion of the table. For comparison the observed light is repeated, in the last column from the last column of Table VIII. The residuals, or the observed values minus those computed with each value of r, are given in the third part of Table X. The residuals are all zero when the time equals 0.0 or 4.6, and are therefore omitted. The average residuals are given in the last line. 26 PROCEEDINGS OF THE AMERICAN ACADEMY TABLE X. — Distances of Centres. Hours. 0.764 1.00 2.00 R — D 0.764 0.0 0 28G 0.666 1.783 —0.132 0.223 0.5 0,307 0.700 1.806 —0.116 0.2'.i8 1.0 0463 0.794 1.865 —0.072 0.457 1.5 0 629 0917 1.957 — 0.005 0.625 2.0 0.811 1 072 2,081 +0.092 0.807 2.5 0.988 1.233 2.223 +0.211 0 986 3.0 1.191 1.425 2 404 +0 375 1.190 35 1.373 1.60G 2.583 + 0.548 1.372 4.0 1.5-56 1.789 2.773 +0.748 1.5.55 4.6 1.764 2.000 3.000 + 1.000 1.764 Light of Uxeclipsed Portion. Uv^urs. 0.764 1.00 2.00 R 0.764 Obs. 0.0 0.410 0.410 0.416 0.416 0.416 0.416 0.5 0.434 0.436 0.432 0.427 0.430 0.433 10 0 500 0.4'.)1 0.469 0.454 0.497 0.480 1.5 0.579 0562 0.527 0.497 0578 0.566 2.0 0 668 0.648 0.603 0.559 0667 0.685 25 0.751 0.7.J1 0.686 0.633 0.750 0 762 3.0 0.838 0.822 0.785 0.733 0.838 0.861 3.5 0.907 0.898 0.874 0.831 0.907 0.920 4.0 0.968 0.959 0.949 0.927 0.U68 0968 4.0 1.000 1.000 1.000 1.000 1.000 1.000 Residuals. Hour.^. 0.761 1.00 2.00 R 0.71-4 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 — .001 — .020 — .013 + .017 + .011 4- .023 4- .013 .000 — .003 — .011 + .004 + .037 + .0:'.l + .039 + .022 4- .009 + .001 + .011 + .039 + .082 + 076 + .076 + .04(5 + .019 + .006 4- .026 4- .069 + .120 + .129 + .128 + .089 + .041 + .003 — .017 — .012 + .018 + .012 + .023 + .013 .000 ±.012 ±.020 ±.044 ±.077 ±.012 The residuals are all expresi^ed in terms of the full light of the star. They therefore represent a larger error expressed in logarithms, or stellar magnitudes, when the star is faint than when it is bright. If reduced to logarithms their mean values become .008, .012, .027, .049, .008. Dividing these quantities by 0.4 to reduce them to magnitudes, OF ARTS AND SCIENCES. 27 we see that while a lirge value of r would give an average residual of over one tenth of a magnitude, the value of r = 0.7 G4 would make this quantity less than two hundredths of a magnitude. In all of them, however, there is a distinct systematic variation, the computed light being too small when t is large, and sometimes becoming too large when t is small. It appeared that this error might be reduced by assuming that the eclipse was annular, or that the light retained its minimum value for a short time. The corresponding residuals are given in the last column. They reduce the positive residuals wliea the star is faint, but do not sensibly affect the others, although the time between the internal contacts is assumed to be twenty-four minutes. The observations scarcely admit so great an interval, and certainly would not justify its increase. As the average residual is not dimin- ished by the assumption of an annular eclipse, and as the observations do not indicate that the light remains constant during the minimum, we cannot do better tlian to assume the value of r = 0.764, and adopt the values of the second column of the table. Several explanations may be offered of the small systematic error that remains. The most plausible seems to be that derived from the residuals given in the last column of Table VII. They show that, from a comparison of the estimated grades of Schonfeld with the measures of Wolff, that Schonfeld estimated the liglit too faint when the star was funt, and too bright when the star was bright. In other words, that a grade did not have the same values when expressed in logarithms for a faint as for a bright star. Assuming the photometric measures of TVolff to be free from systematic error, we should therefore increase tiie estimates of Schonfeld when the star was faint, and diminish them when it was bright, without affecting the actual maximum and mini- mum values. Such a correction would make the systematic error noted above disappear, or even give it an opposite sign. This view receives a slight confirmation from the measures of Seidel, but the accidental discrepancies far exceed this small systematic error. We may therefore conclude that the computed light agrees with observa- tion as closely as the brightness of the fundamental stars is at present known, and there is no evidence of a real systematic difference between the two. Another explanation of the residuals in Table X. has suggested itself. The presence of lines in stellar spectra leads to the belief that the stars, like our Sun, are surrounded by an absorbing atmosphere. They also, therefore, probably resemble it in presenting a disk brighter in the centre than at the edges, owing to the greater thickness of the 28 PROCEEDINGS OF THE AMERICAN ACADEMY atmosphere and consequent greater absorption at the edges. The effect of such an absorption is best determined by the consideration that if, owing to absorption, the average light of the eclipsed portion is less than tliat of the whole disk, the effect of the atmosphere will be to diminish the proportion of the light cutoff; in the opposite case, it will increase it. Now when a small portion only of the star is eclipsed, evidently the average light of this portion, since it lies near the edge, must be less than that of the whole. The atmosphere, although then diminishing the light of the remaining portion, will not reduce it as much as it does that of the entire disk ; the relative light will therefore be increased. On the other hand, when a large part of the eclipsed portion is from the central and brightest portion the opposite effect will be produced. We should therefore expect, when t is large, that the computed light should be increased. When t is small, it may be diminished. In the case of the Sun the effect is so slight, except close to the borders, that the previous ex2:)lauation seems more probable. We return now to the consideration of differences in the rate of diminution and increase of the light. The observations ought to give this quantity with much accuracy. An error in estimating the light of the standard stars will not sensibly affect it, since the same stars are used in measuring the increase and diminution. The effect of atmospheric absorption is reduced, since some of the comparison stars are always above and others below the variable, and besides, although, when observed before passing the meridian, the star is brighter when increasing than when diminishing, yet the opposite effect is produced wlien the star is west of the meridian. Nevertheless this difference is doubted by many astronomers, and if it exists it is evident that an important cori-ection should be applied to the observed minima of Algol. If the curve found by Schonfeld is correct, an error of ten minutes in the time of the minimum might be caused by comparing with a star like £ Pejsei, having a brightness of about twelve grades, and taking the mean of the times when the two stars appeared equal. Three explanations may be offered for tiiis phenomena. First, that the satellite is not spherical, but egg-shaped, and that the large end is turned forwards ; or that the satellite is of unequal density, and that the heaviest portion is forward. In this case the centre of gravity of the disk would follow that of the satellite, or for a given distance of the centres the interposed area would be greater when the satellite was passing off, than when coming on. So great a deviation from the spherical shape would be needed to produce the observed difference OF ARTS AND SCIENCES. 29 that this theory does not seem very probable. We shouhl also, in this case, assume that the time of revolution was exactly equal to that of rotation of the satellite. A second explanation would assume that one portion of the disk of Algol was darker tiian the rest, so that when the satellite entered the disk it would cut off the dark portion, or affect the light less than when passing off and obscuring the brighter parts. In this case we must assume that Algol does not rotate, or it would show a variation independent of the eclipse by its satellite. Its axis of rotation might be parallel to the path of the satellite and the varia- tions in light on its surface be distributed in zones, but such a theory seems improbable. The third explanation is that the orbit of the sat- ellite is elliptical, and that the difference is due to the varying velocity of the satellite. An analytical solution of this problem may be found by reducing the observed light to distances of centres, either by interpolation from the values computed above, or by successive approximations. The case then becomes that of a binary stai", in which we have given the period and a number of distances, but no position angles. It is of course impossible to deduce the position angles of the peri-astron or other point of the orbit, but its other dimensions may be determined. The solution of this problem will be undertaken at another time should the accumulation of observations of Algol and other similar stars render it desirable. For the present, it will be sufficient to obtain an approximate solution. The nature of the variation is not so simple as would appear at first sight ; since the observed time of increase equals that of diminution, we must assume that the apparent motion, when compared with that in a circular orbit, is less at the beginning and end, and greater in the middle of its path. The satellite must therefore either pass its peri-astron during the eclipse, or it must be approaching this point, so that the increased obliijuity of its path to the line of sight will produce the apparent diminution in its motion. An ellipse was constructed, having an eccentricity of 0.5 and divided into thirty-two parts, corresponding to the position of the satellite at the end of each thirty-second of its time of revolution. The eccen- tric anomaly was derived from the mean anomaly by the tables of Dr. Doberck, Astronomische Nachrichten, cxii. 275. As the time of eclipse is very nearly one eighth of that of revolu- tion, four of these divisions correspond to the {)assage of the satellite over the star. Laying this ellipse on a sheet of rectangular paper and turning it around its focus, the effect of a change in the position of the peri-astron could be determined. The problem is greatly sim- 30 PROCEEDINGS OF THE AMERICAN ACADEMY plified by the fact that the apparent path of the satellite during the eclipse is nearly rectilinear. It was found that, if tlie longitude of the line of nodes was made equal to 17°, the periods of ingress and egress would be nearly equal. The peri-astron then happens to coincide with the point of egress. The variation in light due to tliis orbit is compared with observation in Table XI. The successive columns give the time, the observed light in grades, the logarithm of this light, and its value compared with the full light of the s^tar. The next col- umn gives the light already found in the second column of the second part of Table X., and which may be called A. The next column gives the variation in light for the elliptical orbit assumed above, which will be denoted as B. The second part of the table gives the residuals found by subtracting these values of the light from those observed. The last columns give the residuals found by subtracting the logarithms of these quantities. Although the residuals even of A are not very large, they are systematic, being positive when the light diminishes, flnd negative when it increases. The residuals B are much smaller than those of A during ingress, but they are larger during egress. In other words, while the systematic error of ingress has been nearly eliminated, a nearly equal error has been introduced during egress. Accordingly the average residual is not diminished. We have so far adopted the times of first and last contact given by Schon- feld. An inspection of the table from which he derived his curve shows that the weight he assigns to his observations when more than three hours from the minimum is small, and that consequently the times of contact must be somewhat uncertain. The exact time of minimum must also be uncertain, although to a less d'-gree than that of the two points just mentioned. An approximate solution by least; squares was therefore made, with the times of contact and of minimum as unknown quantities. One half weight was given to the equations of condition formed from the observed terms of contact. From this a correction to the observed minimum was found of 5 minutes, or the true minimum appears to occur nearly one tenth of an hour later than that given by the curve. The time of first contact should also be diminished by about 2 minutes, and the time of last contact increased by about 13 minutes. The columns (7 give the values of the light and of the residuals corresponding to this orbit. The third j)lace of deci- ma's is not always exact, as tliis would have involved a great increase in the labor of computation and the accuracy attained appears to be all tliat is at present justified by the observations. The residuals thus obtained are quite satisfactory as regards their OF ARTS AND SCIENCES. 31 magnitudes and the number of clianges of sign, but the orbit is open to a criticism of a wholly dift'erent kind. Its serai-axis major is only 3.00, and as the eccentricity is 0.500, the distance of the centres at peri-astroii is 1.775. Now as the radius of tlie star is 1.000 and of the satellite .764, it is evident that, although they would not actually TABLE XL — Comparison of Orbits. Hours. 4.6 Grades. LogL L A S C D 20.8 1.000 1.000 1.000 0.999 1.000 1.000 4.0 20.24 0.986 0.968 0.968 0.982 0.986 0 987 8.5 19.59 0.970 0.933 0.907 0.945 0.949 0.937 8.0 lS.(i8 0.947 0.885 0.838 0.883 0.890 0.866 2.5 \1M 0.914 0.820 0.751 0.809 0.815 0 788 2.0 15.28 0.862 0.728 0.668 0714 0.725 0 697 Lo 12.05 0.781 0.604 0.579 0.013 0.626 0 601 1.0 8.48 0.692 0.492 0.500 0.517 0.534 0518 0.5 6.26 0.686 0 432 0.434 0.440 0.450 0.416 0.0 5 56 0.619 0.416 0.416 0.416 0.416 0.416 0.5 C20 0.635 0.432 0.434 0.440 0.429 0.426 1.0 7.60 0.670 0.468 0.500 0.515 0494 0.486 1.5 9.81 0.725 0.531 0.579 0.603 0.576 0.570 2.0 1317 0.809 0.614 0 668 0.695 0.665 0 660 2,5 15.78 0 874 0.748 0 751 0.785 0.754 0.753 :iO 17 71 0.923 0.838 0.838 0.858 0.830 0.839 3.5 19 19 0.960 0.912 0.907 0.926 0.899 0.909 4.0 20.23 0.9S6 0.968 0.968 0.975 0.953 0.970 4.0 20.8 1.000 1.000 1.000 1.000 0.995 1.000 Hours. A B C D A B C D 4.6 .000 —.001 .000 .000 .000 .000 .000 .000 4.0 .000 —.014 —.018 —.019 .000 —.006 — .008 —.008 3.5 + 026 —.012 -.016 — .004 +.012 —.005 —.007 — .002 3.0 +.047 +.002 —.005 +.019 + .024 +.001 —.002 +.009 2.5 +.069 + 011 +.005 -4- ,032 +.038 +.006 + .003 + .018 20 +.060 +.014 +.003 +.031 +.037 +.008 +.002 +.019 1.5 +.025 —.009 —.022 +.003 —.018 —.007 —.016 + 002 10 —.008 —.025 —.042 —.026 —.007 —.022 —.036 —.022 0.5 — 002 —.008 —.018 —.014 —.002 —.008 — 017 —.013 0.0 .000 .000 .000 .001) .000 .000 .000 .000 0.5 —.002 —.008 +.003 + .006 —.003 — ,009 +.003 +.006 1.0 —.032 —.047 —.026 —.018 —.029 —.042 — 024 —.017 1.5 —.048 —.072 —.045 — .0:;9 —.038 —.055 —.035 — .o;;i 2.0 —.024 —.051 —.021 —.016 — 016 —.033 — 014 —.011 2.5 —.003 —.037 —.006 —.005 —.002 —.021 —.003 —.003 3.0 .000 —.020 +.008 —.001 .000 —.011 + 004 —.001 3.5 +.005 —.014 +.0)3 +.003 +.002 —.007 +.006 +.001 40 .000 —.007 + .015 —.002 .000 — .003 +.007 —.001 4.6 .000 .000 —.005 .000 .090 .000 —.002 .000 ±.018 ±.019 ±.014 ±.012 ±.012 ±013 ±,010 ±.009 32 PROCEEDINGS OP THE AMERICAN ACADEMY touch, yet they would come so near that the least disturbance would at once produce a catastrophe. This, therefore, gives the limiting value to the eccentricity. A computation with a smaller eccentricity gave less satisfactory residuals. The question now arises, will it not be possible to satisfy the observations by returning to the circular ele- ments, since we have permitted a change iu the times of contact and of minimum. Columns D give the residuals for a circular orbit with a diminution of 0.1 hour in the time of minimum, and assuming that the periods of ingress and egress are each equal to 4.45 hours instead of 4.6 hours. In other words the ingress occurs about fourteen min- utes later, and the egress two minutes earlier, than was assumed by Schonfeld. The errors which remain, even in the last orbit, are not wholly acci- dental ; but their values are so small, and the changes of sign so fre- quent, that it is not safe to base important conclusions upon them. Their average value is only .012, or expressed in logarithms .009, and in magnitudes .02. Accordingly, we may compute the variation in the liglit of Algol, which shall not differ from observation on an average more than a fiftieth of a magnitude. If then this is not the true cause of the variation of the liglit, it at least satisfies it well within the errors of observation. The orbit D may therefore be adopted as repre.senting the law of variation as well as it is at present known. The stellar magnitude of Algol is about 2.0, so that by Table 11., if its brightness equals that of the Sun, its diameter will equal 0".006. The diameter of the orbit of the satellite will be about 0".028. The motion of the bright star, if its density is the same as that of its sat- ellite, will equal 0".009, since its mass in this case will be to that of its satellite as 1.000 is to 0.446. It would therefore be useless to attempt to observe the motion micrometrically. For the same reason, there seems to be no means by which we can determine the position angle of the satellite, or the direction of tlie axes of the ellipse into which the orbit is projected. Even if future observations should ren- der a larger value of the radius probable, the motion would be scarcely perceptible micrometrically. If r = 2.000, the diameter of the orbit becomes 0".08 and the motion of Algol about 0".07. It would be difficult to measure so small a quantit}^ although, as it is traversed in less than a day and a half, many sources of systematic error would be eliminated. Below are given, in successive columns, the corresponding values of several elements of the orbits A^ B, C, and D. The diameter of Algol is assumed to be 0".006. The times are given in minutes from the OF ARTS AND SCIENCES. 83 minimum adopted by Schonfeld. A negative sign denotes that the time precedes the minimum ; a positive, that it follows it. Elements. A. B. c. D. 0.00 0".0138 87°. 1 — 261 + 6 + 273 Eccentricity . . . Semi-axis major . . Inclination .... L()ny;itu(le of nodes Time of first contact " minimum " last contact . 0.00 0".0134 87°.0 — 276 0 + 276 0.50 0".0109 84°.3 17° — 279 — 1 + 273 0.50 0."0106 84°.2 17° — 278 + 5 + 289 The elliptical orbits B and 0 are much smaller than the others. Since the eclipse takes place near the peri-astron, the angular motion is so great that the radius vector must be reduced to maintain the same duration of eclipse. To give a more tangible idea of the dimensions of this system a projection is given of the orbit denoted by D in its own plane in Fig. 1, TT sen TjT Fig. 1. Fig. 2. and as seen from the Earth in Fig. 2. In both projections A denotes the primary, B the satellite at first contact, C when half across the disk, D at the last contact, and E and F at its elongations. The scale is one hundredth of a second to a centimeter. Accordingly, if Fig. 2 is removed to a distance of 206 kilometers, or about 120 miles, it would appear of the same size as Algol when seen from the Earth. The application of the spectroscope to this binary star oflers a most interesting field for work. Assuming the same data as before, we find the circumference of the orbit equals 2 tt X 0".0138 = 0".087 ; or VOL. XVI. (n. S. VIII.) 3 34 PROCEEDINGS OP THE AMERICAN ACADEMY multiplying by 0.446 and dividing by 1.446 will give a motion of Algol of 0".027 in each revolution. This corresponds to 3".43 an- nually. If the parallax of Algol is O'M, this would correspond to a velocity of about 160 kilometers (100 miles) per second. Substituting the values in the equation on page 9, t; = 13 /, we have 1= 2.6, or the F line would be deviated through an interval equal to nearly half the space between the D lines. Moreover, as this quantity would be alternately positive and negative every thirty-five hours, the system- atic errors which are so troublesome in such measures could be eliminated, and the quantity to be observed would be doubled. If the parallax of the star is more than 0".l the motion would be less, but on the other hand the parallax would then become a suitable object for micrometric measurement. If the parallax is much less than O'M the motion would be so large that its variations might be determined with some accuracy, and the form of the orbit computed from the varying velocity along the line of sight. These measures would also determine the dimensions of the orbit, and if we assume the value of the briglitness, I, they would give the distance and par- allax of the star. The spectrum of Algol has already been examined without the detection in it of any peculiarity. The time selected for observation would be more likely to be near its minimum, to detect any changes in the spectrum accompanying its variation in light. But this is the very time when the motion along the line of sight is zero, which may be the reason why this phenomenon has as yet escaped detection. Two objections have been offered to the theory that tlie variation in light was due to the interposition of a non-luminous satellite. First, the large size of the satellite ; and, secondly, the rapidity of its motion. It has been said that, according to the prevalent theories regarding the formation of the stars, so large a body could not well have lost all its heat while the lumhious star is still so bright. This argument would have some force, if we were sure of the true origin of the stars, and also if we knew that both bodies are of the same age. They may, however, have had a wholly independent origin, and have come together through their proper motion, under the influence of a resisting medium or other disturbing force. The objection to the rapidity of motion cannot be defended in tliat form. By tlie law of gravitation we can compute what should be the velocity with a given density, and the only proper criticism would be that to produce the observed velocity an improbable density would be required. To determine this density we may use the formula of OP ARTS AND SCIENCES. 35 page 6 for the equivalent diameter of the system, using as a unit the radius of the star. We thus find, b = 0.00933 aP-i = 0.00933 X 4.60 (0.00785)-* = 1.087. Accordingly, a body having the density of the Sun, and a diameter but little more than half that of Algol, would give the observed time of revolution to the satellite. If, there- fore, the velocity is remarkable, it is remarkable that it is not greater. If the satellite of Algol has a diameter of 0.7 G4, and its density equals that of the primary, its relative mass will be 0.446. The two bodies combined would form a sphere having a radius of 1.130 and a diameter of 2.260. This is 2.08 times that of the equivalent diameter, and shows that the average density can be only 0.11 of that of the Sun, or about one seventh of that of water. It may be noted that the density affords a means of distinguishing between a satellite and a spherical cloud of meteors. If the individual meteors were very minute, they might completely cut off the light, and yet bear a very small ratio in volume to the space between them. Accordingly, if the density of the eclipsing body could be shown to be very small, we might infer that it was composed of meteorites. In this case the motion of Algol would be insensible, as seen in the spectroscope. The observed times of minima of Algol seem to show that its period has undergone a diminution during the last century. Such a change is easily explained on the theory of a secondary satellite. The disturb- ance caused by a third body, or by a resisting medium, might very sensibly vary the period from year to year. The law of this change is not yet known, but its nature is shown in Table XII. The minima are distinguished by successive numbei's, JS, that occurring on Jan. 1, 1800, being designated as 0. Those preceding 9000 have been ar- ranged in groups of 500 each. Since 1870 the observations of each year are grouped together. The successive columns of the table give a current number, the mean of the numbers of the minima, the corre- sponding year and tenth and the number of minima included in the group. In the last nine groups, which relate to a single year, the minimum corresponding to opposition is used, instead of the mean of those observed. The first eleven sets were observed by various astronomers ; sets 12 to 18 were made by Argelander ; sets 19 to 21 by Schonfeld ; and sets 22 to 30, by Schonfeld and Schmidt. Sets 18 and 19 relate to the same period of 500 revolutions from 7500 to 8000. The fifth column is found by subtracting from the observed time that given by the formula of Schonfeld on page 94 of his memoir, — 36 PROCEEDINGS OF THE AMERICAN ACADEMY Ep. E= 1867, Jan. 0 11 1.2 M. Z. Paris + 2*20 48.9 {E — 8534). For the earlier observations the reduction given by Argelander {Bonn Observations, p. 347) are used, after reducing them to the above formula by subtracting 35o'"- — 0.0749 J^. The sixth column gives the ordi- nates of a smooth curve without points of inflection drawn through the points whose abscissas and ordinates are respectively given in the third and fifth columns. The last column gives the difference between the fifth and sixth columns. TABLE XII. — Minima of Algol. No. Mean Epoch. Date. No. Min. Obs. Curve. O.-C. 1 — 2101 1783.5 27 — 510 — 507 — 3 2 — 1860 178.5.4 17 — 488 — 489 + 1 3 — 1308 1789.8 17 — 450 — 446 — 4 4 — 706 1794.5 6 — 400 — 401 + 1 5 — 250 1798.0 10 — 368 — 367 — 1 6 + 214 1801.7 2 — 308 — 332 + 24 7 + 734 1805.7 2 — 280 — 293 --13 8 + 1831 1814.4 2 — 211 — 210 — 1 9 + 2282 1817.9 6 — 180 — 177 — 3 10 + 2574 1820.2 5 — 155 — 155 0 11 4- 3212 1825.2 3 — 114 — 108 — 6 12 + 4081 1832.0 2 — 44 — 46 + 2 13 + 5259 18413 16 + 25 + 24 + 1 14 + 5741 1845.1 4 + 37 + 25 + 12 15 + 6154 1848.4 6 + 24 + 24 0 16 -f 6838 1853.7 16 + 21 + 20 + 1 17 + 7308 1857.4 17 + 10 + 15 — 6 18 + 7688 1860.4 4 — 1 + 11 — 12 19 + 7799 1861.3 6 — 6 + 9 — 14 20 + 8374 1865.9 12 + 2 + 2 0 21 4- 8791 1869.0 15 — 1 — 6 + 4 22 4- 9026 1870.9 13 + 1 — 8 + 9 23 + 9153 1871.9 12 — 4 — 10 + 6 24 + 9281 1872.9 19 — 7 — 12 + 5 25 + 9408 1873.9 IG — 1 — 14 + 13 26 + 9535 1874.9 4 — 8 — 17 + 9 27 -}- 9662 187.5.9 9 — 7 - 20 + 13 28 -(- 9789 1876.9 13 — 22 — 23 + I 29 + 99 IG 1877.9 9 — 46 — 26 — 20 30 + 10043 1878.9 4 — 29 — 29 0 The numbers in the last column nearly equal the accidental errors of observation. There is a slight grouping of negative signs about 1860, and of positive signs soon after 1870. This could not be avoided .without giving to the curve a point of inflection. The average value of these residuals is about six minutes, which shows the accordance to be expected from any assumed formula. OP ARTS AND SCIENCES. 37 Adopting the curve described above as representing the true varia- tion, its ordinates for every ten years have been read off, and are given in the third column of Table XIII. The direction of its tangent has also been determined, and the seconds of the resulting period is en- tered in the fourth column. To this is to be added 2*^ 20''- 48'"- The second column gives approximately the corresponding value of E. TABLE XIII. — Variation of Period. Tear. E. Curve. Period. 1780 — 2545 m. — 541 58.6 1790 — 1273 — 444 58.6 1800 0 — 348 58.5 1810 + 1273 — 252 58.5 1820 4- 2545 — 157 58.4 1830 + 3818 — 64 58.3 1840 4- 5090 + 16 66.6 1850 4- 6363 + 24 53.7 1860 4- 7635 + 11 53.3 1870 4- 8908 + 7 53.0 1880 +10180 + 31 52.7 An inspection of the curve of variation of the times of minimum shows that a curious change took place between 1830 and 1850. Be- fore then, the period given by Wurm of 2^ 20^- 48™ 58.5' repre- sents the observations well; after 1850, the formula of Schonfeld appears to be more nearly correct. There seems, during this interval, to have been a change of four or five seconds in the period, and that besides this there has been a small but gradually increasing diminution in the period throughout the century. Harvard College Observatokt, Cambridge, U. S. 38 PROCEEDINGS OP THE AMERICAN ACADEMY Investigations on Light and Heat, made and published wholly or in part with appropriation from the RuMFORD Fund. II. APPENDIX TO PAPER ON THE MECHANICAL EQUIV- ALENT OF HEAT, CONTAINING THE COMPARISON WITH DR. JOULE'S THERMOMETER. By H. A. Rowland. Presented, March, 1880. In the body of this paper I have given an estimate of the departure of Dr. Joule's thermometer from the air thermometer, based on the comparison of thermometers of similar glass. But as it seemed im- portant that the classical determinations of this physicist should be reduced to some exact standard, I took to England with me last summer one of my standards, — Baudin, No. 6166, — and sent it to Dr. Joule with a statement of the circumstances. He very kindly consented to make the comparison, and I now have the results before me. These confirm the estimate that I had previously made, and cause our values for the equivalent to agree with great accuracy. The following is the table of the comparison. Readings. Temperatures. Baudin, No. 6166. Joule. By perfect Air Thermometer according to No. 6166. By Joule's Thermometer. Difference. 21.88 41.930 48.782 53.705 58.916 64.914 73.374 80.176 85.268 90.564 94.243 99.168 22.62 59.410 72.200 81.340 90.877 101.777 117.291 129.990 139.255 148.834 155.460 164.400 o 0 1.590 2.126 2.511 2.918 3.382 4.039 4.667 4.961 5.370 6.654 6.036 o 0 1.578 2.127 2.519 2.928 3.396 4.061 4.606 5.003 5.414 5.698 6.082 o 0 —.012 +.001 .008 .010 .014 .022 .039 .042 .044 .044 .046 OF ARTS AND SCIENCES. 39 Readings. Temperatures. l?y perfect Baudin, No. 6166. Joule. Air Tliermoineter aocordint; to No. 6166. By .Joule's Thermometer. Difference. o o o 10L080 173.140 6.413 6.457 .044 ll)S.y(i3 182.040 6.789 6.839 .050 n;;.70(; 190 885 7.165 7.218 .053 114.000 191.382 7.188 7.239 .051 *121.507 *219.497 *7.772 *8.445 135.858 231.115 8.890 8.944 .054 140467 239.939 9.249 9.309 .060 143.405 245.006 9.479 9.540 .061 146.445 250.566 9.717 9.778 .061 152. 360 261.481 10.180 10.246 .066 158.770 273.2.39 10.681 10.761 .070 164.635 283.957 11.138 11.211 .073 170.485 294.739 11.695 11.670 .075 175.436 303.682 11.979 12.067 .078 182.795 316.968 12.660 12.627 .077 188.705 327.746 13.008 13.089 .081 193.954 337.220 13.412 13.495 .083 199.558 347.294 13.844 13.928 .084 206.054 259.060 14.343 14.432 .089 211.528 368.953 14.764 14.857 .093 216.440 377.826 15.142 15.237 .095 221.858 387.562 15.660 16.655 .095 229.601 401.419 16.158 16.249 .091 235.598 412.367 16.623 16.719 .096 241.028 422.258 17.045 17.143 .098 247.436 433.800 17.541 17.638 .097 253.704 445.267 18.028 18.1.30 .102 259.786 456.286 18.600 18.603 .103 266.086 467.817 19.991 19.097 .106 273.143 480.643 19.639 19.648 .109 280.176 493.442 20.086 20.197 .111 287.634 506.906 20.666 20.774 .108 294.927 620.052 21.232 21.338 .106 304.148 536.832 21.947 22.058 .111 310.397 548.152 22.432 22.-544 .112 316.596 569.336 22.916 23.023 .107 321.271 568.061 23.282 23..397 .115 327.148 578.528 23.742 23.846 .104 333.661 590.061 24.251 24.367 .116 339.664 601.596 24.719 24.836 .117 346.557 614.004 25.254 25.369 .115 352.878 625.510 25.746 25.862 .116 369.986 638626 26.299 26.421 .122 365.080 647.833 26.697 26.820 .123 371.811 660.071 27.225 27.345 .120 382.770 680.149 28.087 28.206 .119 We can discuss the comparison of these thermometers in two ways ; either by direct comparison at the points we desire, or by the repre- sentation of the differences by a formula. * Evidently a mistake in the readings. 40 PROCEEDINGS OF THE AMERICAN ACADEMY Joule's result in 1850 was referred to water at about 14° C, and in 1878 to water at 16°. 5 C. Taking intervals in the above table of from 6° to 12°, so that the mean shall be nearly 14° and 16°.0, I find the following for the ratios : — 1.0044 1.0042 1.0042 1.0042 1.0049 1.0040 1.0047 1.0030 1.0047 1.0035 1.0052 1.0035 Mean, 1.0047 1.0037 So that we have the following for Joule's old and new values : — Correction for thermometer " " latitude " " sp. ht. of copper Old. 423.9 2.0 .5 .7 New. 423.9 1.6 .5 My value ■ 427.1 427.7 426.0 427.1 Difference .6 1.1 or 1 in 700 and 1 in 390 respectively. But the correction found in this way is subject to local irregulari- ties, and it is perhaps better in many respects to get the equation giving the temperature of Joule's thermometer on the air thermom- eter. Let T be the temperature by Joule's thermometer, and t that by the air thermometer. Then I have found < = 0.002 + 1.00125 r— .00013 {lOO— T'j [l — .003(100+ r) } The fiictor 1.00125 enters in the formula, probably because the thermometer which Joule used to get the value of the divisions of his thermometer was not of the same kind of glass as his standard. The relative error at any point due to using the mercurial rather than the air thermometer will then be E= 1 — j'' = —.00125 + .00000039 { 23300 — 666 < + 3 ^^ j From this I have constructed the following table. OP ARTS AND SCIENCES. 41 Temperature. £. Approximate ALlJition to Equivalent as measured on .Joule's Thenuoiueter. Metric System. English System. 0 6 10 15 20 25 30 .0078 .OUtJG .0054 .0042 .00.31 .0021 .0011 3.3 2.8 2.3 1.8 1.3 .9 .5 6.0 5.1 4.2 32 2.4 1.6 .8 Corrected in this way we have, — Joule's value Reduction to air thermometer " latitude of Baltimore Correction for sp. ht. of copper My value Difference Old. New. 423.9 423.9 1.9 1.7 .5 .5 .7 427.0 427.7 42G.1 427.1 .7 1.0 or 1 in 600 and 1 in 426 respectively. But it is evident that all the other temperatures used in the experi- ment must also be corrected, and I have done this in the following manner. The principal other correction required is in the capacity of the calorimeter, and this amounts to considerable in the experiments on mercury and cast-iron, where no water is used. Dr. Joule informs me that the thermometer with which he compared mine was made in 1844, but does not give any mark by which to designate it, although it is evidently the thermometer called "A" by him. I shall com- mence with the experiments of 1847. The calorimeter was composed of the following substances, whose capacities I recompute according to what in my paper I have considered the most probable specific heats. Weight. Capacity accord- ing to Joule. Most probable Specific Heat. Most probable Capacity. "Water 77617 grains 77617 1.000 77617 Brass 24800 " 2319 .0900 2232 Copper 11237 " 1056 .0922 1036 Tin (?) Total capacity 363 • • • 363 81355 81248 42 PROCEEDINGS OF THE AMERICAN ACADEMY F. Equivaleu t found 781.5 at about 59' Correction for thermometer 3.3 a " capacity 1.3 a " latitude .9 Corrected value 787.0 or 442.8 at 15° C. on the air thermometer. The other experiment, on sperm oil, made at this time, is probably hardly worth reducing. The experiments of 1850 are of the highest importance, and should be accurately reduced. In the experiments with water the capacity of the calorimeter is corrected as follows: — Weight. Capacity used by Joule. Most probable Specific Ueat. Most probable Capacity. Water 93229.7 93229.7 1.000 93229.7 Copper 25541. 2430.2 .092 2349.8 Brass 18901. 1800.0 .091 1720.0 Brass stopper .... 10.3 . . . 10.3 Total capacity 97470.2 97309.8 Therefore correction is .0016. Hence the result with water requires the following corrections : - Joule's value 772.7 at 14° C. Correction for thermometer 3.2 " " latitude .9 " " capacity 1.2 778.0 or 426.8 on the air thermometer in the latitude of Baltimore at the temperature of 14° C, nearly. In the next experiment, with mercury, Joule determined the capa- city of the apparatus by experiment. The mean of the experiments was that the apparatus lost 20°.33155 F. in heating 143430 grains of water 3°. 13305 F. To reduce these to the air thermometer we must divide respectively by 1.0042 and 1.0056. Therefore the capacity must be divided by 1.0014. Therefore the corrected values are: — 772.8 at 9° C. 775.4 at 11° C. Correction for thermometer 4.4 4.0 " " capacity 1.1 1.1 " " latitude .9 .9 779.2 781.4 OP ARTS AND SCIENCES. 43 The reduction to the air thermometer was made for the tempera- tures of 9*^0. and 11° C. respectively, but they both refer to the temperature of the water used when the capacity was determined ; this was about 9° C. Hence these experiments gave 427.5 and 428.7 on the air thermometer, with the water at about 9° C. The next experiments, with cast-iron, can be corrected in the same manner, and thus become 776.0 773.9 Correction for thermometer 4.2 4.3 " " capacity « " latitude 1.1 .9 1.1 .9 782.2 780.2 and these are as before for water at 9°. The determination by the heating of a wire, whose resistance was measured in ohms, can be thus reduced. The value found by Joule was 429.9 in the latitude of Baltimore at 18°. 6 C. Using the capacity of the copper .0922, as I have done in my paper, this quantity will be increased to 430.3. But I have given reasons in my paper on the " Absolute Unit of Electrical Resistance " to show that there should be a correction to the B. A. Committee's experi- ments, which would make the ohm .993 earth quadrant -4- second, instead of 1.000 as it was meant to be, which nearly agrees with the quantity which I found, namely, .991. Taking my value .9911, Joule's result will reduce as follows : — 429.9 at 18°.6 C. Correction for thermometer -f" 1-^ " " capacity -)- .4 « " ohm —3.8 Corrected value 428.0 at 18°.6 C. The last determinations in the " Philosophical Transactions " of 1878 can be reduced as follows. The capacity of the calorimeter was determined by experiment, instead of calculated from the specific heet of copper given by Reg- nault, as in the older experiments. The value used, 4842.4 grains, corresponded to a specific heat of brass of about .090, which is almost exactly what I have considered right. The reduction to the air thermometer will decrease it somewhat, and the correction for the increase of the specific heat of brass and the decrease of the specific heat of water will also change it somewhat. In all, the amount will be about 1 in 200. Hence the reduction becomes as follows : — 44 PROCEEDINGS OF THE AMERICAN ACADEMY 772.7 774.6 773.1 767.0 774.0 3.2 3.7 3.1 3.3 2.8 .2 .2 .2 .2 .2 .9 .9 .9 .9 .9 — .9 — .9 — .9 — .9 — .9 776.1 778.0 776.4 770.5 777.0 at 14°.7 at 12°.- at 12° .5 at 14° .5 at 17°.3 Joule's values Correction for thermometer " " capacity " . " latitude " to vacuum Corrected values To reduce the values in English measure to meters and the Centi- grade scale, I have simply taken the reducing factor 1.8 X .304794, although the barometer on the two systems is not exactly the same : for this is taken into account in the comparison of the thermometers. However, a barometer at 30 in. and 60° F. is equivalent to 759.86 mm. at 0° C. which hardly makes a difference of 0°.01 C. in the tempera ture of the hundred-degree point. Joule's Value re- duced to Air Ther- ■§-s" Tein. TouIp'r mometer and Lati- Rowland's No. Date. Method. of water. Value. tude of Baltimore. Value. J. — R. English Metric meajiure sy.stem. 0 1 1847 Friction of water 0 15 781.5 787.0 442 8 427.4 -t-15.4 2 1850 " water 14 772.7 778.0 426.8 427.7 — .9 10 3 « " mercury 9 772.8 779.2 427.5 428.8 — 1.3 2 4 tl " mercury 9 775.4 781.4 428.7 428.8 — .1 2 5 " " iron 9 776.0 782.2 429.1 428.8 + -3 1 6 << " iron 9 773.9 780.2 428.0 428.8 — .8 1 7 1867 Electric lieating 18.r. 428.0 426.7 + 1.3 3 8 1878 Friction of water 14.7 772.7 776. i 425.8 427.6 — 1.8 2 9 " " " 12.7 774.6 778.5 427.1 428 0 — .9 3 10 " It ii 155 773.1 776.4 426.0 427.3 — 1.3 5 11 " ti « 14.5 767.0 770.5 422.7 427.5 — 48 1 12 " it tt 17.3 774.0 777.0 426.3 426.9 — .6 1 In combining these so as to get at the true difference of Joule's and my result, we must give these different determinations weights according to their respective accuracy, especially as some of the results, as No. 11, have very little weight. Joule rejected quite a number of his results, but I have thought it best to include them, giving them small weights, however. In this way we obtain a value for Joule's experiment of 426.75 at 14°. 6, my value at this point being 427.52. The difference amounts to 1 in 550 only. Giving the observations equal weights, this would have been 1 in 480 nearly. The quantity 426.75 is what I find at 18° C. So that my result at this particular temperature differs from that of Joule only the amount that water changes in speciQc heat in 3°.4 C. OF ARTS AND SCIENCES. 46 Joule's value is less than my value to the amount given, but the value from the properties of air, 430.7 at l-i° C. is greater, although the method can have little weight. It might be well to diminish my values by 1 part in 1000 so as to make them represent the mean of Joule's and my own experiments. It is seen that the experiment by the method of electrie heating agrees very exactly with the other experiments, because I have reduced it to my value of the ohm. Hence I regard it as a very excellent confirma- tion of my value of that unit. Baltimore, Feb. 16, 1880. 46 PROCEEDINGS OP THE AMERICAN ACADEMY III. CONTllIBUTIONS FROM THE PHYSICAL LABORATORY OF HAR- VARD COLLEGE, UNDER THE DIRECTION OF PROFESSOR JOHN TROWBRIDGE. No. XXIIL — THE MAGNETIC MOMENT OF FLEIT- MAN'S NICKEL. By J. E. BULLARD. Presented June 9, 1880. In March, 1879, H. Th. Fleitman published, in the Berichte der Deutschen Chemischen Gesellschaft, No. 5, 1879, p. 454, a paper on nickel, in which he stated that the porosity of nickel was caused by an absorption of carbonic acid in melting, and that the addition of a small portion of magnesium in the metal bath would prevent this absorption. The addition of even one eighth per cent, of magnesium entirely changed the structure of the nickel ; it became very ductile and malleable, took a high polish, and resisted the action of the air. As this discovery is of very great importance in the arts, I have endeavored to ascertain whether the magnetic properties of the nickel are changed by the addition of the magnesium which causes such changes in the mechanical properties of the metal. The apparatus used was an ordinary telescope and scale, and a magnetometer. A short cylindrical bar of Fleitman's nickel, fully magnetized, was placed before the magnetometer. The method used was the observation of deflections, using the formula M= i r^ J'tan <^. Mis the magnetic moment of the bar; T' is the horizontal intensity of terrestrial magnetism ; r is the distance of the centre of the magnet from the mirror of the magnetometer, in millimeters ; and (p is the de- flection of the mirror caused by the magnet. In the present case, — The length of the bar of nickel was 67 mm. and its diameter 6 mm. r = 277.5 mm., 7' (for Cambridge) = 1.65, and log tan (f> = 9.6882. Hence J/ is found to be 8,600,000. OF ARTS AND SCIENCES. 47 A bar of stub steel, of the same dimensions, was found to have a magnetic moment of 8, 750, 000. This variety of steel is used for the common grade of tools, and is comparatively soft. The magnetic moment of a bar of ordinary cast nickel was then obtained. Both bars were highly tempered to render the conditions of comparison as nearly equal as possible. With the same formula the magnetic moment of a bar of cast nickel was found to be only 30,330; that is, about one two-hundred- and-t\Ventieth as much as the moment of Fleitman's nickel. These numbers are, of course, not perfectly exact, for the changes of magnetism in bars from time to time preclude perfect exactness ; still the relation of the magnetic moments may be considered very accurate. This result is certainly surprising; that the addition of ^ per cent of magnesium to a bar of nickel should increase the masfnetism 220 times shows that change of structure in a metal increases its magnetic capacity. No. XXIV.— THERMAL CONDUCTIVITY OF GLASS AND SAND. By C. B. Penrose. Presented June 9, 1880. In determining the conductivity of glass I used the same method that Forbes employed in determining the conductivity of iron. A bar of glass is maintained, at one end, at a constant temperature. When the bar has reached a permanent state of heat, that is, when the amount of heat received by any portion exactly equals the amount given out by that portion, the temperature of a number of points on the bar are determined. The bar is taken so long that the heat at the heated end will not be sufficient to raise the temperature of the other end above that of the air. The temperatures determined are laid off as ordinates, the abscissas. being the corresponding lengths of the bar. The equation of the curve thus formed can be determined. Then an exactly similar bar to the preceding is heated to a known tempera- ture, and as it cools the temperatures are taken every minute, and thus the loss of temperature per minute is determined. 48 PROCEEDINGS OP THE AMERICAN ACADEMY These diminutions of temperature, each corresponding to a known temperature of the bar, are laid off as ordinates of a second curve, each ordinate corresponding to an ordinate of the first curve, which expresses. the temperature of tlie bar at any point. Thus every ordi- nate of the second curve will give the loss of temperature per minute, from that portion of the bar which is at the temperature given by the corresponding ordinate of the first curve. And the area of a definite portion of the second curve multiplied by the specific heat of the glass gives the amount of heat lost from a corresponding definite portion of the bar, in unit of time. If we have a vertical section of any substance, of thickness x, one face at the constant temperature t^ and the other at the temperature t, and k = the conductivity of the substance, the quantity of heat that passes through an area A in unit time = Q, where X A '0 — ^ X If the section is an infinitely thin lamina of thickness d x, and if d t = the difference of temperature of the two sides, — A d± d X K=. ~ -r- ■=, at the limit, ^ Tr~ • ' A Dxt Dj can be found for any point of the bar, by finding the tangent at the corresponding point of the first curve. Hence if ^ = area of cross-section of bar, S ■= the specific heat of the glass, and " area " = the area of the second curve beyond the point in question, the conduc- tivity at that point is -ff^ = -7- -y— - . The area of the second curve beyond the point in question, multi- plied by S, evidently equals the whole amount of heat that passes, in unit time, through the section of the bar at that point; for the end of the bar is at the same temperature as the air. I used a bar of flint glass, about 30 cm. long and 1.1 cm. in diameter. One end was inserted in the side of a metallic vessel, and heated to 100° by boiling water. The other end was supported on a piece of wood. Two screens of card-board were placed in front of the can and lamp to prevent the bar being heated by radiation. Seven points were marked on the bar : the first, 3 centimeters from the can, and the others, 1, 2, 3, 5, 7, and 9 centimeters from the first point. The temj^eratures were measured by a thermopile made by a junction of copper and iron wires, fastened like two links of a chain, so that they OF ARTS AND SCIENCES. 49 could be placed astraddle the bar, and thus make a very close con- uection. After the water had boiled one hour the bar reached a permanent state. I then took the following observations of the temperatures of tlie different points, as shown by the deflections of the galvanometer. The temperatures are expressed in centimeters of the galvanometer scale, and consequently give the excess of the temperatures above that of the air. 1st pt. 2dpt. 3dpt. 4th pt. 5th pt. 6th pt. 7th pt. 72 4.9 2.9 2.3 1.4 1.0 0.4 7.2 4.9 29 22 1.4 1.0 0.4 8 2 4.9 3.2 2.3 1.7 1.1 0.4 7.9 4.7 2.9 2.0 1.4 0.9 0.4 6.9 4.2 2.7 1.9 1.4 1.2 0.4 7.7 5.0 3.0 1.9 1.4 0.9 0.4 7.1 4.4 2.8 2.2 1.3 0.9 0.7 Average ) ^ ^^ value, J 4.71 2.91 2.11 1.43 1.0 0.44 These average values are laid off as ordinates of a certain curve whose abscissas are the corresponding lengths of the bar. We can find an equation to satisfy these seven known points of the form : — In drawing the curve I found that the sixth point would not come in the symmetrical curve, and so I threw it out ; thus we shall have a curve of the fifth degree, the constants of whose equation can be determined from the following equations : — y^Ax^-^-Bx^-^Gx^ + Dx'^Ex^F Eq. (1) F=1A. 4.7 — ^_|_ 5_|_ c -{- D -\- E -\- F. 2.9 = 32 ^4- 16.5+8 (7+4 D -\- 2 E -^ F. 2.1 = 243 ^ + 81 ^ + 27 O + 9 i) + 3 ^ + i^. 1.4 = 3125 ^ + 625 ^+ 125 G-\-2bD-\-bE-\-F. 0.4 = 6561 X 9 ^ + 6561 ^+729 C+81 D -\- ^ E -{- F. Solving these equations, we find the coefficients A B C D E F, and substituting in Eq. (1), we get the equation of the first curve : — y = —.000238 x^ + .00598 x* — .0799 x" + .701 x"" — 3.326 x + 7.4. The next step is to determine the second curve, or the rate of cool- VOL. XVI. (N. S. VIII. j 4 60 PROCEEDINGS OF THE AMERICAN ACADEMY ing. I took a piece of the bar used in the preceding experiment, aud heated it in boiling water for twenty minutes. The rod was then tal^en out, wiped dry, placed horizontally across two wooden props, and the thermo-electric junction of copper and iron was placed upon the centre in a deep groove to insure a close connection. As the bar cooled the deflections on the galvanometer scale were read every minute. I performed the experiment four times, but the results were so nearly alike that I take only the last. The following numbers give the ex- cesses of temperature above that of the air every minute: — 8.2 3.1 1.2 0.6 1.2 0.5 0.2 0.1 7.0 2.6 1.0 0.5 1.1 0.3 0.1 0.1 5.9 2.3 1.9 0.4 1.0 0.3 0.1 0.1 4.9 2.0 0.8 0.3 0.8 0.3 0.1 0.1 4.1 1.7 0.7 0.2 0.5 0.2 0.1 3.6 1.5 0.4 0.3 From these numbers we see that if any portion of the bar is at the temperature 8.2 it loses 1.2 units of temperature in one minute, etc. If these losses are laid off as ordinates right below the corresponding temperature, (as given by the ordinates of the first curve,) we shall have the second curve, whose area, for any definite portion, represents the loss of temperature per minute from a<;orresponding portion of the bar. If this second curve is drawn on co-ordinate paper, its area can be found by actual measurement, and we need not obtain its equa- tion. The errors of such a method of measurement will be no greater than those which are liable to enter as experimental errors. Making the measurement in the manner indicated above, and using the equation, ir= —— ' I found for point 2, 1.97 ^ = -2 2Tr4 = -^8. For point 3, For point 4, From these results it appears that the conductivity decreases as the temperature increases. It has al.so been shown, by Forbes, that the conductivity of iron decreases as the temperature increases. OF ARTS AND SCIENCES. 51 The units in which the preceding conductivities are expressed are the centimeter, the minute, a centimeter deflection on the galvano- meter scale, and the unit of heat is the amount of heat required to raise the temperature of 1 cm.^ of the glass one unit of deflection. To compare these conductivities with those determined hy Forbes for iron, we must reduce them to functions of the units : the foot, the cen- tigrade degree, and the minute. /iS and D^t are ratios, and are independent of units. A contains cm.'^ and " area " contains cm.* 1 cm.2 = .155 sq. in. =: .00107 sq. ft. 1 cm.3 = .061 cu. in. = .000035 cu. ft. In determining the relation between one degree centigrade and one unit deflection, I made four measurements, using heated sand, the thermometer and thermopile being buried side by side. 5.5 cm. corresponds to a rise in temp, of 12.0 8.5 « " " 16.3 5.0 « « « 10.8 6.7 « « « 14.2 From these results, evidently, o 1 cm. corresponds to a rise in temp, of 2.18 1 « « « 1.91 1 "^ « « 2.16 1 «' « " 2.11 4)8.36 Average 2.09 Hence, to reduce K to the required system of units, we divide by 2.09 and .00107 and multiply by .000035, or we multiply by .015. The conductivities determined before become in the new system of units, K= .00270. K= .00315. K= .00420. These results can be summed up as follows. The numbers in the first row give, in centigrade degrees, the excess of the temperature of the bar above that of the air, and the second row the corresponding conductivities. The air was about 21° C. 62 PROCEEDINGS OF THE AMERICAN ACADEMY Temperature of bar . . 19°.8 6°. 08 4°.4 Conductivity .... .00270 .00315 .00420 The conductivity of iron, as determined by Forbes, varied from .01337 at 0° C. to .00801 at 275° C. And the conductivity of sand- stone, determined by burying thermometers from three to twenty-four feet below the surface, was found to be .000G89. The conductivity which I found for glass, therefore, lies between that of iron and that of sandstone. It also, like the conductivity of iron, increases as the temperature decreases. It has not been deter- mined how the conductivity of sandstone varies with the temperature. Conductivity of Sand. To determine the conductivity of sand I used the following method. The sand is put in a thin metallic vessel ; inside of this is put an exactly similar smaller metal vessel, which rests on the bottom of the outer one. Thus the sand forms a layer, protected on each side by the thin metal. These two vessels are entirely immersed in a larger vessel containing a known volume of water. The interior of tlie inner ves- sel is kept at a constant temperature (by means of steam). With a thermometer we can find the temperature of the outside water every minute, and thus construct a curve ; the abscissas being the times and the ordinates the corresponding temperatures. In the next place, fill the outside vessel with the same volume of water used in the preced- ing experiment, heat it to a known temperature, and find the rate at which it cools. For this purpose we construct a second curve, having the times for abscissas and the temj^eratures for ordinates. Take any ordinate t, of the first curve, and let d t^ ^ the gain of temperature in time d T, then, if V= the volume of the water, d t^.V = the amount of heat gained in time d T. Take the same ordinate <, of the second curve, and let d t.^ =■ the loss of temperature in time d T, then dt^. V = the loss of heat from the water, when the temperature is t, in time d T. Hence the whole amount of heat that passes through the layer of sand in time d T=: Q = d t^ . V-{- d t,^ . V. The formula for the quantity of heat that passes, in time T, through a section of thickness x, and area A, is Q = K . A . — — 7\ In X the present case T= d T, and we have found the value for Q, dt,.V-\-dt,.V—K.A. '-5^ d T; OF ARTS AND SCIENCES. 63 ''[^+^] = ^'-^'^' At the limit we find the quantity of heat that passes through when the temperature of the water is t From the first and second curve Dj-t^ and D^t^ are easily obtained, and as all the other quantities are known, A" can be determined. In my experiment I used for the outer vessel a tin can 7.1 cm. in height. Tliis was covered with the exception of a hole in the top, around which was a collar. In this hole was placed a large test-tube of glass which just fitted the hole. The space between the test-tube and the walls of the can was filled with sand. This was placed in a larger tin can almost full of water, and suspended about 4 cm. from the bottom by a string. Steam was passed from a retort into the test- tube, and several times during the experiments I placed a thermometer in the test-tube, and it always showed that the temperature was 100° C At the start the water was 23.3°. I took down the temperatures every minute for almost an hour, but as I do not use these in con- structing the curve, I give only the temperature determined every five minutes, after the first hour : — Temperature. Excess above 23°.3. Temperature. Excess above 23^.3. 29!4 o 6.1 34!0 lOJ 30.1 6.8 34.3 11.0 30.7 7.4 34.6 11.3 31.3 8.0 34.9 11.6 31.8 8.5 35.1 11.8 32.3 9.0 35.3 12.0 32.8 9.5 35.5 122 33.3 10.0 35.7 12.4 33.6 10.3 35.9 12.6 The temperature of the air was 23.3°. The curve given by these points is not very regular ; it changes several times from concave to convex. I therefore determined to take a small arc, find its equation, and investigate the conductivity as given by this arc. I considered only the points 7.4, 8.0, 8.5, 9.0, 9.5, 10.0. If five small divisions of the co-ordinate paper are taken as one unit, an equation of the fifth degree, satisfying these six points, is found from : — 64 PROCEEDINGS OF THE AMERICAN ACADEMY 1.7 = 32A-{-16B-\-8G-^4:I) + 2B-\-^- 1.8 = 243 ^ + 81 B-\-27 0+9 B -\- 3 B -^ F. 1.9 = 1024^4-256^+ 64 (7+ 16 B -\- 4c F -\- F. 2.0 = 3125 A 4- Q'25 B -^ 125 C-\-2oB-\-5F-\-F. From these equations A B C B E F are found, and the required equation is : — y = —0.0005 a:* + 0.006 x^ — 0.0245 x" + 0.139 x + 1.48. Next, the same volume of water used in the preceding experiment was heated to 36°. The can was then placed on the same wooden props used before, and by means of the same thermometer the temperatures were read off every five minutes. The temperature of the air and of the water at starting was 23°. The following were the temperatures every five minutes : — Temperature. Excess above Air. Temperature. Excess above Air. 36!o i3!o 0 32.1 o 9.1 35.3 12.3 31.5 8.5 34.5 11.5 30.9 7.9 33.7 10.7 30.3 7.3 32.8 9.8 I consider here only the temperatures included by the first equation ; that is, from 9.8 to 7.3. The equation of this second curve is found by the same process as in the first curve to be y = 0.12 a: -|- 1-46 ; therefore, the curve is a right line. The thickness of the layer of sand was 2.7 cm. = x. To determine A, I took the mean radius of the layer = 1.35 cm. .-. A = 2 7i . 1.35, 7.1 = 00.21 cm.^ h = height of the can = 7.1 cm. F= volume of water. The water weighed 906 grammes; therefore, its volume was 906 cm.'' V J X is constant, and = 40.62. .■ . K = A0.Q2 (Brt, + BrQ j^. Brt^ = IB^y'] and B^t.., always = .12. [i),y], = o = 0.139 ; . . . i)^/, + Brf, = . 259, and /„ — < = 1 00 — 30.7 = 69.3 ; .•.A'=.1518. OF ARTS AND SCIENCES. 66 ami /„ — < = 100 — 31.3 = G8.7 ; .-. A'=.133G. [^xy]x^2 = 0-097 ; .-. Drt,-\r Drt, = .217, and pho-tuugstate. and to add this to the solution of the acid so as to insure the separation of any remaining traces of chlorhydric acid. After complete subsidence the supernatant liquid is to be liltered oflf clear and then evaporated in vacuo over sulphuric acid. The sirupy OF ARTS AND BCIEXCES. 116 faintly violet liquid gives splendid large transparent crystals of phospho- tungstic acid, which are sometimes colorless and sometimes sulphur- yellow. The crystals effloresce with great rapidity, and therefore do not admit of measurement. They appear to be regular octahedra. The solution of the acid is colorless, and has a strongly acid reaction and bitter taste. Of these crystals, — 1.2791 gr. lost on ignition 0.1809 gr. water = 14.14% 1.3005 gr. lost on ignition with fused borax 0.1842 gr. water = 14.16% 1.4151 gr. gave 1.2130 gr. WO, + P^O^ = 85.72% 1.5416 gr. gave 1.3201 gr. WO, -f PjO^ = 85.64% 1.7365 gr. gave 0.0616 gr. Pp-Mg^ = 2.269^ Pp, l"Tie analyses lead to the formula 24 WO3 . P2O5 . 6 H/J + 47 aq, or VT^^'P/^n^^^O)^ + 47 aq, which requires : — Calc'd. Mean. 24 WO3 5568 83.55 83.57 83.53 83.61 P'^S 142 2.13 2.11 2.11 53HjO 954 14.32 14.15 14.14 14.16 6664 100.00 99.83 As the phosphoric oxide in the analysis was determined after a single precipitation, a correction of 0.15 is applied to the direct result of the analysis. The crystals had slightly effloresced in drying, which explains the deficiency in the water. A quantity of the 18-atom potassium salt 18 WO, . P^O^ . 6 K^O -\- 26 aq was dissolved and precipitated by mercurous nitrate. The mer- curous ?alt was then decomposed by dilute chlorhydric acid, and the solution of phospho-tungstic acid obtained evaporated in a flask at about 50^ C. by means of a water air-pump, and then allowed to stand in a partial vacuum over sulphuric acid. After some days splendid col- orless crystals formed, which appeared to be octahedra, but which on standing became columnar in structure, opaque, and yellow. The analyses of these crystals corresponded very closely to the formula 24 WO3 . P^Oj . 6 HjO + 34 aq, or ^.uPiOn(^^)u + ^^ aq, as the following analyses show: — 1.4482 gr. lost on ignition 0.1636 gr. water =z 11.30^ and gave 0.0492 gr. P.O.Mg, = 2.17% P^O, 1.5109 gr. lost on ignition 0.1708 gr. water = 11.31% and gave 0.0521 gr. P^O-Mg^ = 2.20% PjOj 116 PROCEEDINGS OF THE AMERICAN ACADEMY Oalc'd. 24W03 5568 86.59 86.50 86.53 PP5 142 2.20 2.20 2.17 40H2O 720 11.21 11.30 11.31 6430 100.00 The yellow columnar mass, after re-solution and standing over sul- phuric acid in pleno gave perfectly colorless regular octahedra, which corresponded to the formula, 24W03 • P205 . 6 H2O + 55 aq, or W,,PAi(HO),3 + 5 Oalc'd. 24W03 5568 81.78 81.75 81.76 PP5 142 2.08 2.14 2.15 61 H^O 1098 16.14 16.11 16.09 6808 100.00 In the cases of the two last-mentioned hydrates of the acid, the phosphoric oxide was determined by two successive precipitations as ammonio-magnesic phosphate. The analyses leave no doubt as to the constitution of the acid. Scheibler obtained two different phospho- tungstic acids, to which he gave respectively the provisional formulas Hj5PWi,0,3 + 18 H,p, and HuPWioOgg + 8 H,0. I should double these and write 22 WO3 . T.,0, . 6 H.,0 + 45 aq, or W,,P,0,,(H0),2 + 45 aq. 20 WO3 . P,0, . 6 lifi + 21 aq, or wl-p]o^,(nO),l + 21 aq. I have not obtained the acid of the 20-atom series, though I shall show further on that there is at least one well-defined salt in which the ratio of tungstic to phosphoric oxide is as 20 to 1. Scheibler does not give the method which he employed for the separation of the two oxides, and I consider it at least probable that his acid 22 WO3 . P2O5 . 6 up -f 45 aq is identical with the first of the three hydrates which I have described above. The solution of phospho-tungstic acid forms a colorless heavy oily liquid, with a high refracting power. It has an acid as well as bitter taste, and readily expels carbonic dioxide from carbonates. On stand- ing for some days, the solution undergoes partial decomposition with deposition of a white crystalline powder. This powder is also almost alwaj's deposited, iu greater or less quantity, in the preparation of the OF ARTS AND SCIENCES. 117 acid, but I could not obtain it in a state of purity sufficient for analysis. It may be worth wliile to note as a possible source of differ- ence, that Scheibler obtained his acids by the decomposition of the cor- responding barium salts by dilute sulpliuric acid. The method of preparation which I employed is, I think, preferable. 24 : 2 Acid Sodic Phospho-tungstate. — AVhen chlorhydric or nitric acid is added in large excess to a solution of normal sodic tungstate, and of hydrodisodic phosphate containing 24 molecules of the former to 2 of the latter, a salt is obtained which is usually colorless when chlorhydric acid is employed, and pale sulphur yellow when nitric acid is used. This salt crystallizes more easily than the other salts of sodium. According to Dr. Gooch, the small granular crystals appear to be either monoclinic or triclinic. They are readily soluble in water, but invariably undergo a slight decomposition in the act of solution, a small quantity of a white crystalline powder being formed which is in- soluble, or but slightly soluble. The yellow and the colorless crystals have the same crystalline form and the same reactions. Their consti- tution is also the same, as the following analyses show : — I. 1.4900 gr. lost on ignition 0.1107 gr. water 1.1100 gr. gave 1.0016 gr. WOg + PgO- 1.8072 gr. " 0.0679 gr. l\O^Mg^ II. 0.9913 gr. lost on ignition 0.1809 gr. water 0.8945 gr. « « 0.0658 gr. " 1.0745 gr. gave 0.9698 gr. WO3 + P^O., 1.1508 gr. " 0.0420 gr. PgO.Mg^ III. 1.4933 gr. lost on ignition 0.1115 gr, water 1.3273 gr. gave 1.19G9 gr. WO3 + PgO^ 1.5424 gr. " 1.3920 gr. " 1.2990 gr. " 0.0470 gr. PgO^Mg^ 1.1503 gr. « 0.0428 gr. " IV. 1.8027 gr. lost on ignition 0.1349 gr. water 1.1559 gr. " " 0.0860 gr. " 1.1269 gr. gave 1.0151 gr. WO3 + P2O6 0.9624 gr. « 0.0367 gr. PA^^ga 0.6787 gr. « 0.0263 gr. 7.43% 90.23% 2.40% P2O, 7.34% 7.32% 90.26% 2.33% P2O5 7.47% 90.18% 90.25% 2.31% 2.38% 7.48% 7.44% 90.08% 2.44% 2.48% 118 PROCEEDINGS OF THE AMERICAN ACADEMY Analyses I. and II. were made with two different preparations of the colorless crystals ; III. and IV. were made with the sulphur-yellow salt. The determinations of (WO3 + P2O5) in !•> Hv and III. were made by the evaporation process without the use of mercuric oxide, but in IV. the oxide was employed. As a check upon the quantity of sodic oxide two direct determinations were made in III. the oxide being weighed as nitrate. In this manner, 1.3273 gr. gave 0.0875 gr. NOgNa = 2.40% 1.2593 gr. " 0.0924 gr. » = 2.68% Na^O The mean of these two is 2.54%. As the phosphoric oxide in the analyses above cited was determined from a single precipitation as animonio-magnesian phosphate, I have, as usual in such cases, applied a correction of 0.15% to the mean. These analyses lead to the formula 24 WO3 . P2O5 . 2 Na,0 . 4 H^O -f 23 aq. or. W,,Pp,,(NaO),(HO)3 + 23 aq. 24 WO3 5568 Calc'd. 88.10 Mean. 88.04 87.98 88.08 88.02 88.02 88.09 PA 142 2.25 2.24 2.25 2.18 2.16 2.13 2.29 2.33 2 Na^O 124 1.97 7.68 2.27 7.49 7.43 7.50 27 H^O 486 7.32 7.34 7.47 7.48 7.44 6320 100.00 The mean of the five determinations of (WO3 -|- PjO^) is 90.20. The formula requires 90.35. There can, I think, be no reasonable doubt as to the constitution of the acid sodium salt, though it is difficult to obtain it in a state of absolute purity. The salt is very conveniently prepared, however, and makes an excellent reagent for alkaloids. For this special purpose it is best to mix the normal tungstate and hydrodisodic phosphate in the proportion of 24 atoms of the former to 8 or 4 of the latter, boil the mixed solutions for a short time, filter, and add chlorhydric acid in excess, but in small successive portions. A precipitate is usually formed on each addition of acid which disappears on stirring the liquid. On standing, a mass of crystals of the acid salt separates. This should be drained, washed with a little cold water, then dissolved in cold water for a reagent, the clear liquid only being used. The 24 : 2 acid phospho-tungstate of sodium appears to be always formed when an excess of chlorhydric or nitric acid is added to a so- OP ARTS AND SCIENCES. 119 lution containing sodic tungstate and phosphate, in which the propor- tion of the latter to that of the former is as 1 to 12, or as 1 to any number less than 12. In other words, it appears to be the limiting term of all the series. When the salt is fused with sodic carbonate, carbonic dioxide is given off, but not in the proportion which might be expected. In one experiment, 2.2298 gr. lost 0.5408 gr. COj and Ufi = 16.94% 1.2621 gr. lost on simple ignition 0.0922 gr. HgO = 7.31% The ratio of the WO3 in the salt to the COg expelled is here as 38 : 22, or very nearly as 24 : 13. If the ratio were as 24 : 13, the reaction would be represented by the equation 24 WO3 . P^Og . 2 Na^O + 13 COgNa, = 12 (2 WO3 . NaP) -f PP, . 3 Na,6. A small proportion of neutral tungstate, WO^Nag, is probably formed by the further action of the acid tungstate on the alkaline car- bonate. The 24 : 2 acid sodium salt gives no precipitate with the sulphates of zinc, manganese, and copper; a white crystalline precipitate with argentic nitrate, and after a short time with baric chloride and ammo- nic nitrate ; no precipitates with calcic and strontic chlorides, but after a short time scanty crystalline salts. The 24 : 2 acid salt is the only sodium compound of the 24-atom series which I have been able to prepare. When a solution of this salt is carefully neutralized with sodic carbonate, the 6-atom or fully saturated salt, 24 WO3 . PgO^ . 6 NagO, possibly exists in the solu- tion, but a definite salt could not be obtained by evaporation. When neutral sodic tungstate and hydrodisodic phosphate are mixed in the proportion of 24 : 2, and acetic acid is added to the solution after boiling for some time, no precipitate is formed, but alcohol throws down a colorless oil which soon solidifies to a white gummy mass. I did not obtain a crystalline well-defined salt from this by re-solution and evaporation, but others may perhaps be more successful. When a sufficient quantity of sodic carbonate is added to a solution of the acid sodic phospho-tungstate, a mixture of sodic tungstate and Bodic phosphate appears to be formed. 24 WOg . Pp, . 2 Na^O -f 25 CO^Na^ = 24 (WO3 . Na^O) + P2O5 . 3 Na^O. The phospho-tungstate is formed again on adding an excess of acid. 120 PROCEEDINGS OF THE AMERICAN ACADEMY 24 : 3 Acid Potassium Salt. — When a solution of the 24 : 2 acid sodic salt is added to one of a salt of potassium, a heavy ^vhite crystal- line very slightly soluble precipitate is formed, either immediately or after a short time. The salt forms very small granular crystals. It requires a large quantity of water for solution, a white much more insoluble salt being formed in small quantity by the action of water, so that the liquid is, and for a long time remains, milky. It is best, therefore, simply to wash the precipitate with cold water until this begins to give a turbid filtrate, and then to dry the salt by pressure with woollen paper. The salt is also formed when chlorhydric or nitric acid is added to a solution of potassic phosphate and tung^tate in the proportion of 2 molecules of the former to 24 molecules of the latter, — the two solutions being previously boiled together for some time in a platinum vessel. The reaction in this latter case may be expressed by the equation 24 WO.K, + 2 PO.KH^ + 44 HCl = 24 WO3 . P.O^ . 3 K,0 + 44 KCl + 24 aq, and in the. case of precipitation by the acid sodium salt, by the equation 24 WOg . P,03 . 2 Na.,0 . 4 H,0 + 6 KNO3 = 24 WO3 . P.O^ . 3 K,0 . 3 H,0 + 4 XaNO. + 2 XO.H -[- 3H2O. ' In this salt, — 1.1478 gr. gave 1.0588 gr. WO3 + P^g =92.25^ 1.1764 gr. •' 0.0468 gr. PA^ga = 2.049^ P^ 1.7383 gr. lost on ignition 0.0576 gr. water = 3.31 r^ 1.7638 gr. " " 0.0578 gr. " = 3.28% The analyses lead to the formula 24 WO3 . P.,0, . 3 K,0 . 3 H2O + 8 aq. Calc'd. Mean. 24W03 5568 89.93 89.86 89.86 P,0, 142 2.29 2.39 2.39 corrected. 3 K.,0 283 4.57 4.45 . . . 11 h',0 198 3.19 3.30 3.28 3.31 6191 100.00 100.00 n another preparation of the same salt, — 0.7340 gr. gave 0.6660 gr. ^0^ -f- P,,0, = 90.74^^ 1.1400 gr. " 1.0317 gr. " = 90.50% 0.8028 gr. " 0.0310 gr. P20-^g2 = 2.47% P^Og 1.5568 gr. lost on ignition 0.0805 gr. water = 5.17% 0.8822 gr. " " 0.0455 gr. " =5.16% OF ARTS AND SCIENCES. 121 The analyses correspond to the formula 24 WO3 . PA • 3 K,0 . 3 H^O + 14 aq. Calc'd. Mam. 24 WO3 5568 88.38 88.30 88.42 88.18 V,0. 142 2.26 2.32 2.32 3 K2O 283 4.49 4.21 17 H,0 _306 4.87 5.17 5.16 5.17 6299 100.00 100.00 24 : 3 Acid Ammonium Salt. — When a solution of a salt of am- monium is mixed with one of sodic tuiigstate and phosphate, no precipi- tate is formed, even after standing ; hut if a large excess of clilorhydric or nitric acid is poured in, a white or very pale yellowish heavy crys- talline salt is thrown down in large quantity. This salt is an acid phospho-tungstate of ammonia, the constitution of which varies with the proiDortions of the salts employed in its prei>aration and with the conditions of the experiment. The different salts, however, resemble each other very closely, and may be described in the same terms. They are either perfectly white or have in mass a faint tinge of yellow and an extremely fine-grained crystalline structure. They are very slightly soluble even in hot water, and give milky emulsions which settle very slowly. Like many other phospho-tungstates and tungstates, they are difficult to wash, as they pass through the closest filter-paper with extraordinary facility. This difficulty may, however, be overcome by adding ammonic nitrate to the wash-water. The acid phospho-tungstates of ammonium are soluble in ammonia-water, but the crystals obtained from such solutions are either ammonic tungstates or salts of series different from that to which the salt dissolved belonged. They are readily decomposed by a red heat, leaving a mixture of tungstic and phosphoric oxides. When boiled with mercurous nitrate, they yield mercurous salts and ammonic nitrate. In one preparation in which sodic tungstate and phosphate were mixed in the proportion of 20 atoms of the former to 2 of the latter, ammonic nitrate was added, and afterward nitric acid. The precipitate was washed with solution of ammonic nitrate, and after- ward with alcohol and water, and dried by pressure with woollen paper. Of this salt, — 122 PROCEEDINGS OF THE AMERICAN ACADEMY 1.3460 gr. lost on ignition 0.1405 gr. H2O + NH3 = 10.44% 1.6407 gr. lost on ignition 0.1707 gr. Ufi + ^^3 = 10.40% 1.2038 gr. gave 0.0430 gr. P20^Mg2 =: 2.27% PgOg (twice precip.) 1.3960 gr. gave 0.0504 gr. F^^Mg^ = 2.31% " " 1.4890 gr. gave 0.0720 gr. NH^Cl. = 2.35% (NHJ^O These analyses lead to the formula 24 WOj . , P,0, . 3 (NH,) 2O . 3 H^O + 26 aq. Calc'd. Mean. 24 WO3 5568 87.17 87.29 87.27 87.31 P,0, 142 2.22 2.29 2.27 2.31 3 (NH,)20 156 2.44 2.35 2.35 29 HgO 522 8.17 8.07 8.05 8.09 6388 100.00 100.00 It will be observed that in this case the 24-atom salt was obtained under conditions which a priori should have yielded a 20-atom salt. I have already stated that salts of urea are precipitated from their solu- tions by acid sodic phospho-tungstate 24 WO3 . PgO^ . 2 'Nix.fi . 4 HgO. The precipitation is, however, not complete, and the process does not appear to be available as a method of analysis. When phosphate of aniline and 10 : 4 sodic tungstate are dissolved together, and the solution is boiled for a short time, chlorhydric acid gives an abundant yellowish-white precipitate. On re-solution the precipitate yields pale sulphur-yellow crystals, which are readily solu- ble in alcohol. Phosphate of para-toluidin behaves in a similar man- ner ; the phospho- tungstate formed is readily soluble, and crystallizes in long yellow silky needles. I did not succeed in making the insolubility of the acid ammonia phospho-tungstate available in analysis, either for the determination of ammonia or for that of phosphoric acid. For the last-named esti- mation the phospho-molybdates appear to be far better adapted. 24 : 3 Acid Barium Salt. — When 10 : 4 sodic tungstate is dissolved and a small quantity of phosphoric acid is added, the hot solution gives with baric chloride a heavy white flocky precipitate, which readily dis- solves in hot dilute chlorhydric acid. The solution, after filtration from a small quantity of flocky matter, is pale yellow, and after some time deposits splendid nearly colorless crystals, which appear to be octahe- dra. These are readily soluble in hot water without decomposition, and may be repeatedly recry stall ized without difficulty. Of these crystals, — OF ARTS AND SCIENCES. 123 0.7672 gr. gave 0.6278 gr. WO, + P^Og = 8 1 .83 % 1.5557 gr. lost on ignition 0.1872 gr. water = 12.03^ 1.3732 gr. lost on ignition 0.1641 gr. water = 11.95^ 1.6196 gr. gave 0.1547 gr. SO^Ba = 6.27% BaO and 0.0581 gr. Pp^Mga = 2.29% P^Og 1.2094 gr. gave 0.1158 gr. SO^Ba = 6.28% BaO The analyses agree fairly well with the formula 24 WO3 . P2O5 . 3 BaO . 3 H^O + 43 aq, or, W,,PAi(Ba0^3(H0), + 43 aq. The same salt is formed when two atoms of 12 : 5 sodic tungstate are boiled for a time with two atoms of sodic phosphate and chlorhydric acid is added in excess. Baric chloride then gives after a time crys- tals exactly similar to those described above. In a salt prepared in this manner, — 1.0020 gr. gave 0.8173 gr. WO3 + P^O^ = 81.56% 1.4718 gr. gave 0.1648 gr. SO.Ba = 6.97% BaO and 0.0518 gr. PgO^Mg^ = 2.25% PPg 1.4841 gr. lost on ignition 0.1717 gr. water = 11.57% Calc'd. Mean. 24WO3 5568 79.57 79.57 79.69 79.46 PgOg 142 2.03 2.12 2.14 2.10 3 BaO 459 6.56 6.62 '"e^iT" 6.28 6.97 46 H^O 828 11.84 11.78 12.03 11.95 11.57 6977 100.00 100.09 The phosphoric oxide determinations are corrected in both analyses. The percentage of baric oxide as determined by difference, which is the more accurate method, is 6.53. The salt effloresces with extraordi- nary rapidity, so that it is very difficult to dry it for analysis by pres- sure between folds of woollen paper. Twenty-two Atom Series. — The phospho-tungstates containing 22 atoms of tungstic oxide to 1 of phosphoric oxide are represented by apparently well-defined salts of potassium, sodium, and ammonium. I have not succeeded in preparing the corresponding acid. As already stated, Scheibler has given provisionally the formula Hi6PW,,0,3 + 18H,0, or 22 WO3 . PA • 6 H,0 + 45 aq, 124 PROCEEDINGS OF THE AMERICAN ACADEMY to an acid which he obtained by the decomposition of a salt of barium, and it may be that this is really the acid of the 22-atom series. Further investigations must decide the point. The salts of the 22- atom series closely resemble those of the 24-atom series already de- scribed, and are only to be distinguished from them by analysis. 22 : 2 Putassiam Salt. — The 18-atom potassium salt, 18 WO3 . P^Oo • ^ l^P + 30 aq, gives with chlorhydric or nitric acid a heavy white fine-granular precip- itate of an acid salt which belongs to the 22-atom series, and which has the formula 22 WO3 . P2O5 . 2 lv,0 . 4 11,0 4- 2 aq, as the following analyses show : — 1.5679 gr. lost on ignition 0.0318 gr. water = 2.03^ 1.0728 gr. lost on ignition 0.0222 gr. water = 2.07^ 1.5061 gr. gave 1.4250 gr. WO. + P^O. = 94.61 % 1.1873 gr. gave 1.1253 gr. WO3 -f Vfi^ = 94.78% 2.1607 gr. gave 0.0927 gr. Pp.Mg, = 2.74^^ P^O^ 2.2367 gr. gave 0.0950 gr. Pp^Mgj = 2.72% " Calc'd. Mean. 22WOj 5104 92.08 92.11 92.20 92.03 P.O^ 142 2.56 2.58 2.59 2.57 corr. 2 K^o' 189 3.41 3.26 6 HgO 108 1.95 2.05 2.03 2.07 5543 100.00 The salt is very slightly soluble in water. The solution becomes milky, and remains so for a long time. Its formation from the normal 18-atom salt may perhaps be expressed by the equation, 10 (18 WO., . P.O. . 6 K.O) -i- 84 HCl + 36 H^O = 9 (22 WOg . P.,0, . 2 K2O . 4' HP) -f 2 (P.,06 . 3 K.,0) 4- 84 KCl + 42 11,0. ' 22 : 3 Ammonium Salt. — An acid ammonium salt of this series was obtained from a mixture of sodic tungstate and phosphate, to which ammonic nitrate and excess of chlorhydric acid had been added exactly as in tlie preparation of the 24-atom salt already described. The salt was in very small colorless granular crystals, slightly soluble in cold water, but dissolving to some extent in hot water, giving a milky liquid, settling very slowly. Its other properties are not distinguish- able from those of the 24-atom salt. Of this salt, OP ARTS AND SCIENCES. 125 Qt. Gr. Per ct. Per ct. 0.8G07 0.0805 water and ammonia = 9.26 = 90.73 WO3 + i'A 1.5911 lost on 0.1470 = 9.24 = 90.76 (( 0.908G ignition 0.0837 = 9.21 = 90.79 (( ( 1.0934 . 0.1009. = 9.21 = 90.79 (( h. 0934 gave 0.0439 P,0,Mg2 =2.63 P^O, 1.7970 " 0.0993 NII.'ci =2.68(NHJ20 These analyses correspond very closely to the formula, 22 WO3 . PA .3 (NHJ.O.S up -I- 18 aq, which requires: — Calc'd. Mean. 22 WOg 5104 88.30 88.29 88.25 88.28 88.31 88.31 PA 142 2.46 2.48 2.48 corr . . . 3(NH,)20156 2.69 2.68 2.68 • . . 2IH2O 378 6.55 6.60 6.58 6.56 6.53 6.53 5780 100.00 100.05 22 : 2 Sodium Salt. — It has already been mentioned that, in die preparation of the acid sodium salt of the 24-atom series, a white very slightly soluble crystalline powder is formed in greater or less quantity. This salt cannot be recrystallized for analysis, and must therefore be washed with cold water to remove traces of the soluble acid salt. Hot water dissolves it in small proportion only, the solution remaining milky for a long time. In one preparation of this salt, — ■ ( 0.8405 gr. gave 0.7962 gr. WOg + V.,0^ = 94.73% ( 0.8405 gr. " 0.0330 gr. PArMg/ = 2.51% |-/^^Xd1PA 1.4990 gr. lost on ignition 0.0403 gr. water = 2.69% These analyses lead to the formula 22 WO3 . P^O, . 2 Na,0 . 4 H^O + 5 aq. Calc'd. >2 WOg 5104 92.26 92.22 P2O5 142 2.56 2.51 2 Nap 124 2.25 2.58 9 HP 162 2.93 2.69 5532 100.00 22: 4 Barium Salt. — This salt was obtained by mixing neutral sodic tungstate and hydro-disodic phosphate in the proportion of 24 : 2, neutralizing with acetic acid, and adding a solution of baric chloride. Small sharp prismatic crystals formed after a short time, soluble in hot 126 PROCEEDINGS OF THE AMERICAN ACADEMY water apparently without any decomposition, and separating again from the solution in colorless needles. Of this salt, — 0;6900 gr. gave 0.5494 gr. WO3 -f- Pp. = 79.62% 0.6900 gr. « 0.0826 gr. PAiUg = 2.34% P^O^ 0.6734 gr. " 0.5372 gr. WOg-f P^O^ =79.71% 1.5296 gr. " 0.2163 gr. SO.Ba = 9.24% BaO 0.9682 gr. lost on ignition 0.1076 gr. water = 11.12% 0.7064 gr. " " 0.0787 gr. " = 11.14% These analyses lead to the formula or. 22 WO3 . P2O5 . 4 BaO . 2 H^ + 39 aq, W22P20o,(Ba02),(HO), + 39 aq. Calc'd. Mean. 22 WO3 5104 77.37 77.33 77.37 PPo 142 2.15 2.34 2.34 4 BaO 612 9.28 9.24 9.24 41 H2O 738 11.19 11.13 11.12 77.28 11.14 6596 100.00 100.04 The phosphoric oxide was precipitated twice. Twenty Atom Series — The salts of this series closely resemble those which have been described. I did not succeed in preparing the acid, though I made repeated attempts to do so by mixing sodic tungstate and phosphate together in the proportion of 20 molecules of the former to 2 of the latter, neutralizing with nitric acid, precipitating by mercurous nitrate, and decomposing the mercurous salt by dilute chlor- hydric acid. The acid formed always underwent partial decomposition upon concentration, a white crystalline powder being separated while the 24-atom acid was formed. The only well-defined salt of the series which I liave obtained is the normal barium compound. From this it will doubtless be possible to obtain others by double decomposition. Normal Id-atom Barium Salt. — As the bai-ic phospho-tungstates crystallize in general much more readily than the corresponding sodic salts, I employed them to determine what compounds are formed when sodic tungstate and phosphate are mixed in various proportions. To solutions of the two salts in the ratios of 24 molecules of the for- mer to 2 of the latter, of 18 to 2, and of 12 to 2, chlorhydric acid was added until the reaction became just distinctly acid. Baric chloride was then added in excess, and the solutions were quickly filtered from the insoluble white precipitate formed. Beautiful colorless crystals OF ARTS AND SCIENCES. 127 formed, which were readily soluble in hot water, and could be recrystal- lized without dilRculty. These salts proved to have in all cases the same composition, and are represented by the formula 20 WO5 . P.O^ . 6 BaO + 48 aq, as the following analyses show : — I. 1.1103 gr. lost on ignition with fused borax 0.1458 gr. = 13. 14^ water. 1.1831 gr. " " " " 0.1560gr. = 13.18% " 1.0691 gr. gave 0.7775 gr. WO3 and V^O^ = 72.72% 0.9390 gr. " 0.6850 gr. " =72.84% 11. 1.0676 gr. lost on ignition 0.1400 gr. = 13.11% water. 0.6550 gr. gave 0.4763 gr. WO3 and P^O^ = 72.72% III. 1.1110 gr. lost on ignition 0.1461 gr. = 13.15%water. 0.6409 gr. gave 0.4667 gr. WO, and F^O, = 72.81 % and 0.0704 gr. P2O11U2 = 2.18% PgO^ 0.6222 gr. gave 0.0710 gr. P^Oi^Uj = 2.26% " Analyses I. were made with the salt from the 24 to 2 ; II. from that obtained from the 12 to 2 ; and III. from the salt of the 18 to 2 mix- ture. The phosphoric oxide was precipitated twice. 70.50 70.62 70.50 70.59 2.18 2.26 13.14 13.18 13.11 13.15 The salt dissolves readily in hot water, giving a somewhat milky solution. Chlorhydric acid gives no precipitate at first, but after a time a white crystalline powder is formed, which is the acid salt of the 24-atom series already described. The fact that the same salt is formed independently of the propor- tions of sodic tungstate and phosphate is an important one, and illus- trates the peculiarities of the series of phospho-tungstates which I have already pointed out. Eighteen Atom Series. — When normal sodic tungstate and hydro- disodic phosphate are dissolved together in the proportion of 20 molecules of the former to 2 of the latter, and acetic acid is added to Calc'd. Mean. 20 WO3 4640 70.67 70.55 pp. 142 2.17 2.22 6 BaO 918 13.99 14.09 48 H^O 864 13.17 13.14 6564 100.00 100.00 128 PROCEEDINGS OF THE AMERICAN ACADEMY the boiling solution until a distinctly acid reaction is obtained, alcohol in excess precipitates a white indistinctly crystalline salt. This dis- solves ..very readily in water, but gives on evaporation a gummy mass, and distinct crystals cannot be obtained. The solution of this salt gives no precipitate at first with salts of potassium, but after a short time beautiful colorless crystals are formed in abundance. The salt dissolves in a rather large excess of water, leaving a small quan- tity of a white insoluble compound. It crystallizes best from a solu- tion which is not very concentrated, and which is allowed to evaporate spontaneously in the air. The crystals obtained in this way are color- less and well-defined prisms. On re-solution it almost always leaves a small quantity of the slightly soluble salt; but when the whole is dissolved together, the more soluble compound crystallizes without perceptible admixture of the other. From very concentrated solu- tions I obtained a white graiuilar salt, which, on re-solution in a rather large quantity of water, gave the colorless crystals again. Of the colorless transparent crystals, — 1.1470 gr. gave 0.9372 gr. WO3 + P.O^ = 81.71% 1.5149 gr. " 1.2:387 gr. " =81.77% 1.3494 gr. lost 0.1089 gr. water r= 8.07% 1.5806 gr. " 0.1277 gr. " = 8.08% 1.1391 gr. gave 0.0498 gr. Mg^V^Oj = 2.80% Pp^ 1.1856 gr. « 0.0506 gr. " 1.5149 gr. « 0.4738 gr. AgCl These analyses correspond to the formula 18 WO3 . P2O. . 6 K,0 + 23 aq. = 2.93% = 10.26% potassium. ich requires : — CalcM. Mean. I8WO3 4176 78.81 79.12 78.95 79.01 PA 142 2.68 2.62 2.65 2.58 6K,0 566.4 10.69 10.24 31 H2O 414 7.82 8.08 8.07 8.08 5298.4 100.00 Of the white granular hydrate, — 1.3868 gr. gave 1.0985 gr. WO3 -f P^O^ = 79.21% = 79.30% = 2.57% PA = 2.56% « 0.9528 gr. " 0.7556 gr. " 1.0396 gr. " 0.0409 gr. PgO^Mgg 1.0614 gr. « 0.0425 gr. " 1.0102 gr. lost on ignition 0.1009 gr. water 1.7974 gr. « « 0.1800 gr. " = 9.99% = 10.01% OF ARTS AND SCIENCES. 129 The corresponding formula is 18 WO3 . P2O5 . 6 K^O -f- 30 aq, which requires — Calc'd. Mean. 18 WO3 4176 76.98 76.84 76.89 76.80 P.O, 142 2.62 2.42 2.41 2.42 6 K,0 566.4 10.44 10.74 . . . . . . 30 H^O 540 9.96 10.00 9.99 10.01 5424.4 100.00 The prismatic and granular salts, therefore, only differ in water of crystallization. It must be remarked, however, that the corrected percentages of the phosphoric oxide in the analyses of the granular salt are too low, which is unusual. 18 : 1 Acid Potassium Salt. — When the normal salt is dissolved in water and chlorhydric acid is added in excess, a white crystalline precipitate is formed, which is but very sparingly soluble in water. Of this salt, — 1.2955 gr. gave 1.1828 gr. WO3 + PA =91.30% 1.3200 gr. " 1.1994 gr. " =90.86% 1.1390 gr. « 0.0592 gr. PA^ga = 3.32% PA 1.5900 gr. " 0.0817 gr. " = 3.29% " 1.5225 gr. lost on ignition 0.1087 gr. water == 7.14% 1.1966 gr. " " 0.0856 gr. " = 7.16% These analyses corrrespond to the formula 18 WO3 . PoOs , . KP . 5 H, P+1 4 aq. Calc'd. Mean. 18 WO3 4176 87.84 87.93 88.15 87.71 P2O5 142 2.99 3.15 3.17 3.14 corrected. K2O 94.4 1.98 1.77 . . . . . . 19 HjO 342 7.19 7.15 7.16 7.14 4754.4 100.00 100.00 Ammonium Salt. — The ammonium salt of the 18 atom series may be prepared in the manner given above for the normal potassic com- pound. When ammonic acetate and alcohol are mixed with a concen- trated solution of the sodium salt, no precipitate is formed at first, but after some hours a mass of white crystals is thrown down. After washing with alcohol and re-solution, crystals may sometimes be ob- tained, but the salt usually forms a nearly colorless gummy mass. In this case white opaque crystals separate from a thick and sirupy VOL. XVI. (n. S. VIII.) 9 130 PROCEEDINGS OF THE AMERICAN ACADEMY mother liquor. The crystals are soft and gummy to the touch. I did not succeed in obtaining the salt in a state of purity suitable for analysis. Sixteen Atom Series. — The only representatives of this series which I have obtained are salts of calcium, potassium, and ammonium. They are all well defined and more or less distinctly crystalline. 16:1 Acid Calcium Salt. — When calcic tungstate, WO^Ca, is boiled with a pure dilute solution of phosphoric acid, the salt is dissolved very slowly ; but on addition of a few drops of chlorhydric acid, the tungstate passes quickly into solution. The liquid deposits on evap- oration colorless flat tabular crystals readily soluble in water. Of these crystals, — r 0.7356 gr. gave 0.6992 gr. WO3 -f Vf>^ = 95.05'^ 1 0.7356 gr. « 0.0390 gr. P^O.Mg^ = 3.39% P2O5 1.0347 gr. lost on ignition 0.0366 gr. water = 3.54% The phosphoric acid was twice precipitated. The analyses lead to the formula 16W03 . P.O. . .CaO . SH^O + 3 aq, ich requires : — Calc'd. 16 WO3 3712 91.56 91.66 P2O, 142 3.50 3.39 CaO 56 1.38 1.41 (diff.) 8H2O 144 3.56 3.54 4054 100.00 16:4 Acid Potassium Salt. — In the attempt to prepare the sodium salt to which Scheibler gave provisionally the formula Na^HiiWgP^Ogi -f 13 aq, I obtained a thick sirupy liquid, which on dilution with water gave with potassic bromide, after standing a few hours, beautiful colorless needles. The salt is readily soluble in hot water. After recrystalli- zation, — 0.5991 gr. gave 0.5000 gr. WO3 + P.O^ = 83.46% 2.1547 gr. " 0.1005 gr. PA-^^Sa " = 2.98% Vf>^ 1.0492 gr. lost on ignition 0.0841 gr. water = 8.01% The analyses give the formula 16 WO3 . P2O, . 4 K,0 . 2 H,0 -f- 19 aq, W,,P,0„(K0),(H0),4-19aq, OF ARTS AND SCIENCES. 131 which requires : — Calc'd. I6WO3 3712 80.53 80.48 P.O^ 142 3.08 2.'J8 4 K,0 377.6 8.19 8.53 (diff.) 21 Ilf> 378 8.20 8.01 4609.6 100.00 16:6 Ammonium Salt. — This beautiful salt was prepared by adding a solution of amnionic chloride to the sirupy liquid obtained by boiling 12:5 sodic tungstate with half its weight of a strong solution of pure phos{)horic acid. After standing twelve hours an abundant precipitate of the ammonium salt was formed. This precipi- tate, after being well drained and twice recrystallized, gave very fine flat prismatic crystals. It is the best-defined ammonium salt which I have obtained. The salt is readily soluble in hot water, and crystal- lizes as the solution cools. Of this salt, — 1.4108 gr. lost on ignition 0.1G27 gr. YL.fi + NH3 = 11.58% C 0.7705 gr. " " 0.0886 gr. " = 11.49% (0.7705 gr. gave 0.1243 gr. P^OnUo = 3.21% P.^ 0.9629 gr. " 0.1430 gr. NH^Cl = 7.17% (NHil.^O The analyses correspond with the formula 16 WO3 . Vf>, . 6 (NII,)20 + 10 aq, which requires : — Calc'd. Mean. 16 WO3 3712 85.41 85.28 85.30 85.26 PA 142 3.27 3.21 3.21 6 (Nlljp 312 7.18 7.17 7.17 10 H^O 180 4.14 4.34 4.32 4.36 4346 100.00 100.00 Fourteen to Two Series. — The only compound of this series which I have obtained is a sodium salt with the empirical formula 14 WO3 . 2 P2O5 . 5 Nap + 42 aq. I regard this as a double salt, or perhaps as a compound of an 8-atom and a 6-atom salt. 14 : 5 Sodium Salt. — In the communication already referred to,* Scheibler described briefly a sodium salt to which he gave provision- ally the formula Na,H„P,Wp,i + 13 H,0. * Beriohte der Deutschen Chemischen Gesellschaf t, V. 801. 132 PROCEEDINGS OF THE AMERICA.N ACADEMY This salt was obtained by boiling 12:5 sodic tungstate with half its weight of phosphoric acid. After a short time the salt separates in beautiful crystals. As Scheibler's salt evidently belongs to a 6-atom series, and has therefore a special theoretical interest, I endeavored in various ways to prepare it, but in all cases without success. By boil- ing 12:5 sodic tungstate with half its weight of phosphoric acid I ob- tained a thick sirupy liquid, which after long standing gave crystals. In another experiment about 75 gr. of the sodium salt were boiled with 13 gr. of sirupy pure phosphoric acid. After dilution and standing for some days, splendid colorless prismatic crystals separated, identical in appearance with those of the last experiment. These were redis- solved and recrystallized several times. Of this salt, — 0.5551 gr. gave 0.4272 gr. WO3 + T^O, = 76.95% 0.5787 gr. " 0.4459 gr. " =z 77.06% 1.5430 gr. " 1.1884 gr. " =77.02% 1.0058 gr. « 0.0980 gr. VjO.Mg^ = ^-00% P^Og 1.0285 gr. " 0.1014 gr. " = 6.34% " 1.0023 gr. " 0.3214 gr. P^OjiUj = 6.38% " 1.0152 gr. lost on ignition 0.1656 gr. water = 16.31% 1.0240 gr. " " 0.1677 gr. " =16.37% 0.9922 gr. " " 0.1612 gr. " =16.24% These analyses correspond fairly well to the formula 14 WO3 . 2 P2O5 . 5 Na^O + 42 aq, which requires : — Calc'd. Mean. 4 WO3 3248 70.64 70.65 70.59 70.70 70.66 2P,0, 284 6.18 6.36 6.35 6.34 6.38 5 Na,0 310 6.74 6.65 . . . . . . . . . :2 H,0 756 16.44 16.34 16.31 16.37 16.34 4598 100.00 The phosphoric oxide, which was twice precipitated, is too high, but it may be that in such salts a third precipitation is necessary to effect a perfect separation. I should write the formula of the salt, provisionally, either, 6 WO3 . P2O5 . 3 Na,0 . 3 H^O + 8 WO3 . P^O^ . 2 Na^O . 4 H,0 -f 35 aq, or, 6 WO3 . P2O5 . 2 Na,0 . 4 H^O -f 8 WO3 . F^O, . 3 Na,0 . 3 H^O + 3 5 aq. There appears to be no reason for distributing the sodic oxide in one way rather than in the other. On the other hand, it is perhaps equally OP ARTS AND SCIENCES. 133 probable that the salt is a compound of two acid salts of a 7-atoin series, and that its formula is 7 WO3 . P2O5 . 3 Na^O . 3 H^O + 7 WO3 . F,0, . 2 Na^O . 4 H^O + 35 aq. Amoug the corresponding phospho-molybdates there is at least one series in which the number of atoms of the teroxide is odd. Po- tassium and ammonium salts in this series have respectively the formulas 5 M0O3 . P2O5 . 3 K2O . 3 H2O + 4 aq, 5 M0O3 . P^Og . 3 (NHJ^O . 3 H2O + 4 aq, if, provisionally, we consider the acid as 12-basic. With respect to the formula given above, and which is that of an acid double salt, I may remark that I shall describe farther on a salt of the 5-atom molybdenum series with the formula 5 M0O3 . PA . 3 (NHJP . 3 HP + 5 M0O3 . ¥^0, . 2 (NHJP . 4 H^O, and that Rammelsberg has already described the corresponding potas- sium compound. From the general analogy between tungsten and molybdenum, the existence of phospho-tungstates with an uneven number of atoms of tungstic oxide may be fairly inferred from that of phospho-molybdates of the type of the 5-atom compounds above mentioned. I must leave the question undecided, for the present at least, as I have not succeeded in obtaining corresponding salts of potassium, ammonium, strontium, or calcium. The salt crystallizes in long, flat prismatic forms, and appears to be perfectly homogeneous, so that I believe it should be regarded as a definite compound, and not as a mixture. It is very soluble in water, and crystallizes only from sirupy solutions. It has a strongly marked sweet taste, which is at the same time astringent and very slightly bitter. The solution of the sodium salt gives with potassic bromide a beautiful crystalline precipitate, already described, and having the formula 16 WOg . P0O5 . 4 Kp . 2 H2O -f- 19 aq, and with ammonic chloride, the ammonium salt 16 WO3 . P2O5 . 6 (NH,)^© + 10 aq, also noticed above. I endeavored to obtain the normal 6-atom sodium salt 6 WOg . PjOg . 6 Na20 by boiling six atoms of neutral sodic tungstate with 134 PROCEEDINGS OP THE AMERICAN ACADEMY the calculated quantity of pure phosphoric acid, but the experiment was unsuccessful. AVhea a solution of hydro-disodic phosphate is heated, and freshly prepared tungstic oxide is added, in small portions at a time, the oxide is readily dissolved with formation of a colorless or faintly bluish liquid. The solution gave crystalline precipitates with baric chloride and argentic nitrate, but the salts formed proved on analysis to be only mix- tures. An ammonium salt was prepared by adding ammonic nitrate and nitric acid to the solution of the sodium salt. The ratio of tung- stic to phosphoric oxide in the white crystalline salt formed was as 20:1 very closely ; but this does not lead to any inference as to the formula of the sodium salt in solution. Tribasic sodic phosphate also dissolves tungstic oxide readily, and the same is true as regards am- monic phosphate ; but I could not obtain definite salts from either solution. Potassic phosphate dissolves tungstic oxide very slowly, and only by long boiling. No definite compound was formed in this case. When hydro-disodic phosphate and tungstic oxide are fused together the latter dissolves and forms a colorless fused mass. This is soluble in water, but, as in the other cases, gives no single well defined salt. I have made no experiment to determine whether phospho-tung- states of the lower orders dissolve freshly precipitated tungstic oxide so as to form the higher terms in the series. The extraordinary amount of time and labor which I have already spent upon the subject must be my excuse for leaving this and many other interesting points to other investigators. There is no part of the subject which will no* amply repay a new and careful study. ARSENIO-TUNGSTATES. When solutions of alkaline tungstates and arsenates are mixed it frequently happens that white crystalline precipitates are formed, the supernatant liquid becoming strongly alkaline. These precipitates are arsenio-tungstates, and, as might be expected, correspond in a general way to the class of phospho-tungstates already described. They appear to be as a rule less well defined than these last, and, so far as I have been able to discover, exhibit no character of special interest. In analyzing the few salts of this series which I have studied, I have em- ployed tlie same methods which I have used for the analysis of the phospho-tungstates. Only the conditions are necessarily in some re- spects different. Arsenic and tungstic oxides were precipitated together OF ARTS AND SCIENCES. 135 uy mercurous nitrate, mercuric oxide being employed to secure per- fect neutrality. The mercurous salt was then separated upon an asbestos filter, and, after drying, ignited — finally with the blast-lamp — until a constant weight was obtained. In this manner very nearly the wliole of the arsenic oxide was volatilized. There is no danger of a reduction to metallic arsenic if the crucible containing the asbestos and precipitate is placed within another, covered, and then cautiously heated. The arsenic oxide is best determined as ammonio-magnesian arsenate, using a large excess of magnesia-mixture in the first precipitation. Two precipitations are necessary to secure a perfect separation ; the salt is to be collected on an asbestos filter, and dried in the usual man- ner. In determining water, or water and ammonia, in these salts, it is best to ignite with a weighed quantity of fused sodic tungstate, as sug- gested to me by Dr. Gooch ; only it must be observed that the fused tungstate is rather deliquescent. With all these precautions fairly good results may be obtained. I endeavored to separate arsenic from tungstic oxide by boiling the salt with dilute phosphoric acid, reducing the arsenic to arsenous acid by sulphurous acid, and then precipi- tating by sulphydric acid as AsgSg. This method appears to give a complete separation, but is very tedious and circumstantial. Acid 3-atom Potassic Arsenio-tungstate. — When 12:5 acid potassic tungstate is dissolved, and a solution of potassic arsenate, AsO^KH.^, is added, a white very fine-grained precipitate is formed. When an excess of the arsenate is employed, and the mixed solutions are evap- orated upon a water-bath, a perfectly white insoluble salt is separated, which is the acid arsenio-tungstate 6 WO3 . As,0, . 3 K^O . 3 H2O. The formation of this salt may be represented by the equation 12 WO3 . 5 K2O + AsA . Kp . 2 H^O + 4 H^O = 2 {6 WO3 . AS2O5 . 3 K2O . 3 H2O} . For analysis the salt was washed upon a filter with hot water, then dried upon paper, and. afterward — as the mass remained pasty — upon a water-bath, where it finally dried to a hard white mass. Of this salt, — 0.8276 gr. gave 0.5902 gr. WO3 = 71.81% 0.7197 gr. " 0.5130 gr. " = 71.28% 1.9815 gr. " 0.3841 gr. AsAMg^CMHJa + H.O^ 11.73% As^Og 1.3507 gr. lost on ignition 0.0357 gr. water = 2.64% 136 PROCEEDINGS OF THE AMERICAN ACADEMY The formula requires 6 WO3 1392 Calc'd. 71.05 71.31 71.28 • As,0, 230 11.75 11.73 3K2O 3H2O 283 54 14.45 2.75 14.33 (diff.) 2.64 1959 100.00 The salt dissolves readily in alkaline hydrates. Its chief interest lies in the fact that it serves to establish the existence of a 6-atom series of arsenio-tungstates. Acid 6 : 4 Ammonium Salt. — When amnionic arsenate AsO^NH^ and neutral sodic tungstate are dissolved together, no precipitate is formed at first, but after a short time a dense white crystalline salt is thrown down, which after twelve hours becomes abundant. Boiling water dissolves this salt readily, but it does not crystallize well from the solution, forming only a thick white mass. If this mass be dissolved in water, nitric acid added in excess gives a white crystalline precipitate, but slightly soluble in the acid liquid and in water. Of this salt, after washing with cold water, — 0.8255 gr. gave 0.6013 gr. WO3 = 72.84% 1.9486 gr. " 0.3980 gr. As,0,Mg2(NIIj2 + Hp = 12.36% As,0. 1.2494gr. " 0.2635 gr.NH.Cl =10.25% The analyses agree — though not very closely — with the formula 6 WO3 . AS2O5 . 4 (NHJ2O . 2 H^O + 3 aq, which requires : — Calc'd. 6W03 1392 72.50 72.84 As,0, 230 11.98 12.36 4 (NHJ.O 208 10.83 10.25 5 HP 90 4.69 4.55 (diff.) 1920 100.00 The differences are, I think, not greater than may be expected in cases in which the salt analyzed cannot be purified by recrystalliza- tion. Normal 16 : 6 Silver Salt. — I obtained this salt by the following process : 100 gr. neutral sodic tungstate and 25 gr. arsenic acid were dissolved together and the solution boiled for some time, then filtered and evaporated upon a water-bath. After a day much sodic arsenate separated in crystals. The filtrate from these crystals deposited a OF ARTS AND SCIENCES. 137 wliite indistinctly crystalline mass. This was redissolvcd and potassic bromide added in excess, when an abundant white crystalline fine-grained precipitate was thrown down, which was drained on the filter-pump, and then washed with cold water. This was dissolved in much boil- ing water, and argentic nitrate added, when a white crystalline salt was thrown down mixed with brownish-red crystals of argentic arsenate. The mass was treated with very dilute nitric acid, which readily dis- solved the arsenate, the undissolved j)ortion appearing under a lens as made up of opaque white acicular crystals. These were well drained, washed with cold water, and dried on paper by pressure, when the mass showed a faint yellowish tint. The salt is but slightly soluble in cold water. Of this salt, — 0.7488 gr. gave 0.5024 gr. WO3 = G7.09% 0.7531 gr. " 0.5067 gr. " = G7.29% 2.0321 gr. « 0.6147 gr. AgCl = 24.45% Ag^O 1.0215 gr. « 0.3096 gr. " = 24.48% " 0.9209 gr. lost on ignition 0.0340 gr. water = 3.69% The analyses correspond tolerably well to the formula 16 A\^03 . As.p^ . 6 Ag,0 + 1 1 aq, which requires : — Calc'd. 16 WO3 3712 67.10 67.09 67.29 As,0, 230 4.16 4.65 (diff.) 6Ag,0 1392 25.16 24,45 24.48 11 H^O 198 3.58 3.69 5532 100.00 I do not place implicit confidence in the formula given, as the two determinations of argentic oxide are too low. It is very possible that the salt was slightly decomposed by the dilute nitric acid employed to remove the arsenate. But in any case it is proved that arsenio-tung- states exist in which the ratio of WO3 to As^O^ is higher than 6:1, and a method of obtaining such compounds is pointed out. General Conclusions. — The general results of my investigation of the phospho-tungstates may be stated briefly as follows : — 1. The phospho-tungstates form a series of which the lowest term probably contains six atoms of tungstic to one of phosphoric oxide, and the highest, twenty-four atoms of tungstic to one of phosphoric oxide. 2. At least the greater number of phospho-tungstates contain an even number of atoms of tungstic oxide. The homologizing term for these cases is therefore 2 WO,. 138 PROCEEDINGS OF THE AMERICAN ACADEMY 3. The highest number of atoms of base observed in any case is six (old style), which implies that each acid contains twelve atoms of hydroxyl. 4. In all cases observed the number of atoms of hydroxyl replaced by a monatomic metal is even. 5. One instance occurs in which two acid phospho-tungstates of different orders appear to unite to form a definite compound ; but this case admits of a different explanation. 6. In all phospho-tungstates studied the number of atoms of base or of hydroxyl is more than sufficient to saturate the phosphoric oxide present, if we admit that the acid is 12-basic. At least a part of the hydroxyl or base must therefore be v.nited to tungstic oxide. For greater facility of comparison I have brought together the formulas of all the compounds described in this paper, writing them both with the old and the new notation. 24 WO3 . P0O5 . 6 H.O + 47 aq W24P20-,(HO)ii, + 47 aq 24 WO3 . P^Og . 6 HoO 4- 34 aq WoiPaO^iiHO),^ + 34 aq 24 WO3 . P2O5 • 6 H2O -f 55 aq Wo4P.,0.i(HO)io + 55 aq 24 WO3 . P0O5 . 2 NaoO . 4 H.fi +23 aq Wo4P20.i(NaO)4(HO)8 + 23 aq 24 WO3 . P2O5 . 3 K^O . 3 HoO + 8 aq W24P207i(KO)6(HO)6 + 8 aq 24 WO3 . P2O5 . 8 KoO . 3 HoO + 14 aq W24P207i(KO)o(HO)6 + 14 aq 24 WO3 . P0O5 . 3 (NH4)oO. 3 H2O + 20 aq Wo4P207i(NH40)6(HO)6 + 26 aq 24 WO3 . P2O5 . 3 BaO . 3 H2O + 43 aq Wo4Po0^i(Ba02)3(HO)6 + 43 aq 22 WO3 . P2OS . 2 KoO . 4 H2O + 2 aq W22P2065(KO)4(HO)8 + 2 aq 22 WO3 . P2O5 . 3 (NH4)20 . 3 H2O + 18 aq W22Po065(NH40)6(HO)6 + 18 aq 22 WO3 . P2O6 . 2 NaiO . 4 H2O + 5 aq W2.2P2065(NaO)4(HO)8 + 5 aq 22 WOg . P2O5 . 4 BaO . 2 ILO + 39 aq W2.2P2065(Ba02)4(HO)4 + 39 aq 20 WO3 . P2O5 . 6 BaO + 48 aq W2oP2059(Ba02)6 + 48 aq 18 WO3 . PjOg . 6 K2O + 23 aq Wi8P2053(KO)i2 + 23 aq 18 WOg . P2O5 . 6 K2O + 80 aq Wi8P2053(KO)i2 + 30 aq 18 WOg . PoOg . K2O . 5 H2O + 14 aq Wi8Po053iKO)2(HO)io + 14 aq 16 WO3 . PoOg . CaO . 5 H2O + 3 aq Wi6P2047(Ca02)(HO)io + 3 aq 16 WO3 . P2O5 . 4 K2O . 2 HoO + 19 aq WigP2047(KO)8( 110)4 + 19 aq 16 WOg . P2O5 . 6 (NH4)20 + 10 aq Wi6P2047(NH40)i2 + 10 aq 14 WO3 . 2 P^Og . 5 NaoO + 42 aq 6 WO3 . AsoOg . 8 K,0 . 3 H2O W6AsoOo-(KO)c(HO)6 6 W08.As205.4(NIl4)20.2H20 + 8ao W6As20o7(NH40)8(nO)4 + 3 aq 16 WOg . AS2O6 . 6 AgaO + 11 aq Wi6As2047(AgO)i2 + 11 aq OF ARTS AND SCIENCES. 139 In writing these formulas I have assumed that all the acids are 12-basic, smce it has been shown that there are salts of the sixteen-, eighteen-, and twenty-atom series which correspond with this view. I shall resume the discussion of the subject in connection with the phospho-moljbdates, and at the same time examine in detail the ques- tion of the existence of a distinct class of pyro-salts of the tungstic and moljbdic series. i^To be continued.) 'i4Q PfiOCEEDINGS OP THE AMEIUCAN ACADEMY iNVEsnSAHCiNS on Light and Heat, made and published wholly or in part with appropriation from the Rumford Fund. VII. A THEORY OF THE CONSTITUTION OF THE SUN, FOUNDED UPON SPECTEOSCOPIC OBSERVATIONS, ORIGINAL AND OTHER. By Chakles S. Hastings. Presented Oct. 13, 1880. Fraunhoper discovered the lines in the solar spectrum, known by his name, in 1814. Many efforts to determine their origin followed. One of the most ingenious and carefully considered was that of Pro- fessor Forbes in 1836.* He concluded that, if their origin is in the solar atmosphere, the light from the limb must exhibit stronger lines than that from the centre. His method was to examine the spectrum before and during an annular eclipse ; as he found no recognizable change, his deduction was, " that the sun's atmosphere has nothing to do with the production of this singular phenomenon." The point was again touched upon by Sir David Brewster and Dr. Gladstone in a joint study of the spectral lines, published in 1860.t Here '^ each of the authors came independently to the conclusion, that there is no perceptible difference in this respect between the light from the edge and that from the centre of the solar disk." In 1867 Angstrom t repeated the experiment with negative results. Lockyer's § efforts also, in 1869, were attended with no better results. In 1873, four years later, I devised and made an apparatus by which a perfect juxtaposition of the spectra of the centre and limb was secured. This apparatus and certain of the results gained by its use were described in a note " On a Comparison of the Spectra of the Limb and the Centre of the Sun," published in the American Journal of Science, (1873,) Vol. V. pp. 369-371. I was then a student at * Note relative to the supposed Origin of the Deficient Rays in the Solar Spectrum. Pliil. Trans., 1836, pp. 453-456. + On the Lines of the Solar Spectrum. Phil. Trans., 1860, pp. 149-161. t Phil. Mag., 1867, p. 76. § Proc. R. S., xvii. 350. OF ARTS AND SCIENCES. 141 Yale College, and soon after left New Haven, when the research was necessarily interrupted. I hoped, however, that the novelty and interest of the observations might lead others, possessed of the neces- sary apparatus, to develop the results of this method of investigation. But as nothing has been published on this subject since that time, I was glad to have an opportunity to continue the investigation in tlie summers of 1879 and 1880. The results of my labor are embodied in this paper. The method adopted in the recent observations is exactly the same as that described in the article cited ; instead, however, of the equa- torial of the Sheffield Scientific School, I used a Clark equatorial of 9.4 in. aperture and 120 in. focal length, which was kindly placed at my disposal by the gentlemen in Hartford to whom it belongs.* The New Haven spectroscope, too, of twelve effective prisms, was replaced by one of which the dispersing member was a Rutherford grating on speculum metal, either of 8,648 or 17,296 lines to the inch, at will. These gratings were of the largest size, having a ruled surface of about If in. square. The immediate results I give in the order of the refrangibility of the lines observed, as no observed variations in them can be attributed to anything other than the temporary modifications of transparency in o our atmosphere. The numbers are the places on Angstrom's maps, as nearly as could be ascertained without a micrometer. Line (C) 6561.8 is cleaner and wider at limb, i. e. the haze on either side of the line as ordinarily seen is much reduced. 6431 is slightly stronger at centre than at limb. 6371 is visible at centre, but not at limb. (Z)i) 5894.8 slightly less hazy at limb. (Z)^) 5889.0 decidedly cleaner at limb. A fine line very close to its more refrangible side is either wanting or much fainter in spectrum of limb. 5577.5 is much stronger at limb. o 5440 rb (not on Angstrom's chart) is a little stronger at limb. The Mg. lines 5183.0, 5172.0, 5166.5 {b^ b.^ b^) are cleaner at limb. The line b^, belonging to a different element, does not show such a peculiarity. 5045 (a faint line not in Angstrom) is stronger at limb, * My acknowledgments for this courtesy are gratefully accorded to Mr. Edgecomb, its former owner, and to Mr. Howard and Mr. Chapin, its present owners. 142 PROCEEDINGS OF THE AMERICAN ACADEMY 4919 ±, a faint line slightly stronger at limb. (F) 4860.6 is much cleaner, more free from haze at limb. 4702.3 seems cleaner at limb. 4340.0 cleaner at limb. 4226.4 shows less haze at limb. o 4101.2 is a very hazy line, so represented by Angstrom, but at limb i is practically free from haze, — a striking difference. 4045 is slightly less hazy at limb. Other differences have been recorded, but only these have been ob- served more than once each. Any theory of the sun, worthy of attention, must not only explain the above-described phenomena, but also others better known, and as yet not accounted for satisfactorily. Of these the most noteworthy is the spectroscopic appearance of a spot and its penumbra. As is well known, such a spectrum exhibits a very strong general absorption, with a very sliglitly modified elective absorption. A few faint lines appear in the spot spectrum which are not otherwise seen ; and a few faint lines of the ordinary spectrum are strengthened. A careful ex- amination has persuaded me that the spectrum of a spot differs from that of the unbroken photosphere, just as the spectrum of the limb dif- fers from that of the centre of the disk, save that the variations are more pronounced. Indeed, I could have considerably extended the list of lines strengthened at liml< by an examination of the spot spec- trum, where the variations appeal to the eye more clearly. The accepted theory of the spots attributes the phenomenon to the absorption of the solar light by cooler, denser gases of the sarae nature as those producing the Fraunhofer lines. Familiar experiments teach, however, that, as the density of a gas increases, the change in the char- acter of its radiation is shown in its spectrum by the broadening of its distinctive spectral lines, which at the same time grow more ill defined. Therefore it follows that, according to the law connecting radiation and absorption, dark lines produced by such a gas must also, under similar conditions, show increased breadth and diminished sharp- ness. That no such changes are to be recognized, is a fatal objection to the theory. Another class of unexplained phenomena is the duplicity of certain lines of the solar spectrum, lines which are single in the spectra of ter- restrial sources. Of these Professor Young has discovered £^, b^, and b^, with others. My own observations can be arranged very simply in classes, and will then better lend themselves to theoretical discussion. OP ARTS AND SCIENCES. 143 T. The most important fact of all is that the differences in the two spectra of centre and limb are extremely minute, escaping all but the most perfect instruments, and all methods which do not place them in close juxtaposition. II. Certain lines, the thickest and darkest in the spectrum, notably those of hydrogen, magnesium, and sodium, which appear with haze on either side, in the spectrum of the centre of the solar disk, are deprived of this accompaniment in that of the limb. III. Certain very fine lines (four observed) are stronger at limb. IV. Other very fine lines (two or three observed) are stronger at centre. The ordinarily accepted theory of the origin of the Fraunhofer lines fiiWs to explain the phenomena as observed. That is, if we suppose the photosphere, whether solid, liquid, gaseous, or cloud-like, to yield a con- tinuous spectrum which is modified only by the selective absorption of a surrounding atmosphere, then the absorption must be greater at the limb than at the centre of the solar disk ; and this must be true inde- pendently of the thickness of that atmosphere, as well as of the form, rough or otherwise, of the surface of the photosphere. This evident consequence, pointed out in the first place by Forbes, nearly half a century ago, cannot be avoided. There is but one way of maintain- ing the theory and escaping Forbes's conclusion already quoted, and that the course pursued by Kirchhoff in the original statement of his theory of the solar constitution,* namely, by assuming that the depth of the reversing atmosphere is not small compared to the radius of the sun. But innumerable observations during the score of years which have lapsed since that time prove that such a reversing atmosphere must be very thin. The famous observation of Professor Young dur- ing the total eclipse of 1870, when he saw appreciably all the Fraun- hofer lines reversed, has naturally been received as the strongest confirmation of Kirchhoff's views as to the locus of the origin of the dark lines. But this very observation restricts the effective atmos- phere (save for hydrogen and one or two other substances) to a depth of not more than 2". Thus, singularly enough, the very observa- tion which led to the firmest belief among spectroscopists in the cor- rectness of Kirchhoff's view exposed, at the same time, its most vulnerable point. Another theory of the solar constitution, that of Faye, assigns a diflerent seat to the stratum producing the Fraunhofer lines, namely, * Untersuchungen iiber das Sonnenspectrum, (Berlin, 1862,) pp. 14, 15. 144 PROCEEDINGS OF THE AMERICAN ACADEMY the photosphere itself. Regarding the principal radiation of the sun as coming from solid or liquid particles floating in a gaseous medium, the cloud-like stratum thus formed is necessarily somewhat transpar- ent. According to his views, these particles are the sources of the continuous spectrum, and the medium in which they float is the locus of the selective absorption.* Thus he attempts to reconcile the gen- eral theory of Kirchhoff with the observations and deductions of Forbes, which, as we have seen, were a constant stumbling-block in the way of accepting Kirchhoff's explanation. Lockyer seems to have accepted this theoiy, and to have defended it in the earlier portion of his work ; t but in 1872, after Young's im- portant observation of 1870 and its confirmation in 1871, he changed his views, and regarded the layer just outside the photosphere as the true seat of the selective absorption producing the Fraunhofer lines.J I supposed in 1873 that my observations then published could be explained on Faye's hypothesis. There is, however, a fatal objection to the explanation as given by this theory. If the luminous particles are precipitated from the vapors of the photosphere, they cannot be at a higher temperature than the circumambient gases ; on the contrary, on account of their greater radiating power, they must be slightly cooler. But the fundamental theory of absorption demands a lower temperature for the vapor pro- ducing dark lines than that of the principal source of light behind it; consequently this view of Faye cannot be accepted without great modifications. Before advancing any theory of my own, it may be well to empha- size two principles taught by the theory of absorption, to which all hypotheses must be conformable. That Faye's fails in this is suflScient cause for its rejection. 1. To produce dark lines in a spectrum by absorption, the source of absorbed light must be at a higher temperature than that of the absorb- ing medium. 2. There is an inferior limit of brightness, below which the source of absorbed light cannot go without the spectral lines becoming bright. Of these, the first is familiar, and requires here neither proof nor * Comptes Rendus, Ix., 1865. t See " A Lecture delivered at the Royal Institution," May 28, 18G9, quoted in Lockyer's Solar Physics, pp. 220, 221; also "The Rede Lecture," May 24, 1871, quoted in Solar Physics, pp. 317, 318. X See revised report of two lectures delivered at Newcastle-upon-Tyne in October, 1872, Solar Physics, p. 400. OF ARTS AND SCIENCES. 145 comineut ; the second, thougli not less evident, is less familiar because less important. As we shall make use of it, however, it may be well to enforce it by reference to common experience. Were it not true, it would be impossible to see bright lines in the spectrum of any flame to which daylight had access, for in this case the conditions demanded by the first principle are fully met, the sun being the origin of the daylight. That we do not see absorption lines is due then alone to the lack of necessary brilliancy in the daylight. Thus much premised, we can frame a theory which explains all the observed phenomena exhibited by the spectroscope, and is also ren- dered highly probable by the revelations of the telescope. As is well known, the solar surface, when examined with a powerful telescope of large aperture, presents a granulated appearance, the granules in general subtending an angle of a fraction of a second only. Probably this appearance is better known to the majority of astrono- mers by means of Professor Langley's admirable drawings,* rather than by personal observation. These granules I regard as marking the locus of currents directed generally from the centre of the sun. About these currents are necessarily currents in an opposite direction, which serve to maintain a general equilibrium in the distribution of mass. Let us consider the action of such an ascending current. Starting from a low level at a temperature which we may regard as above the vaporizing point of all elements contained in it, as it rises to higher levels, it cools, partly by radiation, more by expansion, until finally the temperature falls to the boiling point of one or more of the substances present. Here such substances are precipitated in the form of a cloud of fine particles, which are carried on suspended in the cur- rent. The change of state marked by the precipitation is accompanied by a sudden increase in radiating power ; hence these particles rapidly lose a portion of their heat, and become relatively dark, to remain so until they are returned to lower levels by the currents in a reverse direction. In this theory, it will be observed, there is nothing which does vio- lence to our accepted notions of the solar constitution. Indeed, it differs chiefly from that of Faye in localizing the phenomena of pre- cipitation, instead of regarding it as proper to all portions of the pho- tosphere ; and, what is quite as important, in supposing the precipitation confined to one or two elements only. I shall attempt to define these elements farther on. * Am. Jour. Sci., Vol. VH., 1874, and Vol. IX., 1875, Plates. VOL. XVI. (N. S. VIII.) 10 146 PROCEEDINGS OF THE AMERICAN ACADEMY In our theory, then, the granules are those portions of upward cur- rents where precipitation is most active, while the darker portions, between these bodies, are where the cooler products of this change with accompanying vapors are sinking to lower levels. Having stated the theory, we will now apply it to the four classes of phenomena defined above. From the nature of the condensation the granules or cloudy masses must be very transparent, because the condensation is confined to elements which have very high boiling-points, and because such ele- ments can be but a portion, perhaps but a small portion, of the whole matter contained in the upward currents. It is not a priori improb- able that we receive light from many hundreds of miles below the general outer surface of the photosphere. Since these cloud-like sources of intenser radiations are surrounded on all sides by descend- ing currents of colder vapors, all the white light which comes to us must have passed through media cajDable of modifying it by selective absorption. Again, since at the centre of the solar disk we can see as far into the photosphere as at the limb, and practically no farther, the phenomena of absorption ought to be, on the whole, the same in both regions. Thus the fundamental and most important class of phenomena above classified finds a simple and logical explanation. With regard to the phenomena of Class II. we have but to define the problem in order to find the solution at hand. All the lines of Class II. belong to vapors which lie high in the solar atmosphere, as is evident from their frequent reversal in the chromosphere. On the centre of the disk these lines are hazy or " winged," but not so at the limb. To the spectroscopist this aspect is characteristic of greater pressure, that is, of more frequent molecular impact. The observation then proves that the dark lines of hydrogen, magnesium, sodium, etc., as seen at the centre of the solar disk, are produced by the elements in question at a higher pressure than the corresponding lines at the limb. Accepting our theory, this must be so ; for, supposing the trans- parency of the photosphere is such that we can see into it a distance of 2,000 miles, then at the centre of the disk we have light modified by selective absorption all the way from the extreme outer chromo- sphere down to 2,000 miles below the upper level of the photosphere ; while 10" from the limb the light, though coming from the same depth of vapor measured along the line of vision, has its lowest origin more than 1,700 miles farther from the sun's centre than in the previous case. Of course the numbers here used have no definite significance, OF ARTS AND SCIENCES. 147 but, modify them as we will, within the bounds of probability, the reasoning remains the same. Suppose now a certain vapor which is confined to the upper stratum of the photosphere, or, rather, one of which the lower limit is thus re- stricted ; then, according to the reasoning of Forbes, the force of which has been shown, its absorption lines ought to be strongest at the limb. This is the condition which produces the phenomena of Class III. Before discussing the final class, we must recall a fact familiar to the most casual observer of the sun, namely, that lying upon the photo- sphere is a stratum producing a very strong general absorption, so strong indeed that the disk is probably less than a fourth as brilliant near the edge as at the centre. This layer is very thin, as proved by the great difference in brilliancy between the upper and lower por- tions of faculfe. Since the difference of absorption at the two levels is very great, the conclusion follows, because the facula itself is so low that it rarely, if ever, appears as a projection on the limb of the sun. For conven- ience let us call this layer A. Imagine then, a stratum of vapors, B, above the layer just de- scribed, which are not represented at all in the photosphere, and which are of nearly the same temperature as this layer A.* Then (for the sake of simplicity regarding this layer as having no elective absorption) suppose all beneath the two spherical shells in considera- tion to be removed. In the spectroscope, light from such a source as the two layers A and B would yield a continuous spectrum ; for the inner shell (A), radiating only white light, would be robbed of nothing not supplied in equal quantity by radiation from the outer shell (B), since they are of the same temperature. If such layers as these really do exist about the sun, we can now readily state the appear- ances which would be presented by a sun so constituted, if the three- fold system should be studied spectroscopically. In the centre of the projected disk, the lines proper to the exterior shell (B) would be * This supposition is not opposed to probability, for though we must regard the temperature as generally decreasing in passing from the photosphere outward, it does not follow that this decrease is continuous. A similar general law may be stated for our own atmosphere, but in a clear night the air in the immediate vicinity of the ground is colder than that just above. The explanation of this phenomenon is familiar in the theory of dew and hoar-frost. Analogous causes for irregularity in the distribution of temperature in the solar atmosphere must be even more efficacious, since the layer A is probably a more vigorous radiator than the earth, and the gases above it are certainly far more diathermous than our atmosphere. 148 PROCEEDINGS OF THE AMERICAN ACADEMY reversed, i. e. dark. As we approached the edge, however, oiving to the opacity of the inner shell, the conditions would approximate to what they would be if the layers A and B existed alone, the central body being removed, and the lines would fade ; if faint, they would vanish. This is our explanation of the phenomena of Class IV. Every theory involves certain conditions. We finally judge of the Soundness or unsoundness of any theory largely from the consideration of these implied conditions, and of the extent to which they are ful- filled by it. For instance, our explanation of the fact that certain very fine lines are stronger at the centre (IV.) demands that the sub- stances giving such lines should be found in the chromosphere, indeed mainly restricted to the chromosphere. Fortunately I can say that one of them (6371), which I first discovered and measured carefully, is identical with the fourteenth line of Young's second Catalogue of Chromosphere Lines. The other one, the wave-length of which I took from Angstrom's chart without correction, may correspond with Young's ninth (6429.9) hne of the same Catalogue, which differs in place by only one sixth the distance between the D lines. This I shall test at the earliest opportunity. If the theory I have jjroposed is correct, it affords the first definite evidence of the existence of chemical compounds in the sun, for in accordance with it the lines of Class III. and Class IV. belong to sub- stances which are not found in the lower photosphere. We know however that all gases must increase in density in passing from theii outer limit towards the centre of the sun ; and we have seen a proof of this in the case of hydrogen and certain other vapors in the discus- sion of our observations, which showed that the characteristic lines indicated greater density when they originated at greater depths. The only escape from the contradiction is in the assumption that the lines of the last two cases (III., IV.) are due to compound vapors hav- ing a dissociation temperature below that of the lower photosphere. Of course, the substances of Class IV. have a lower dissociation tem- perature than those of Class III. A naturally suggested and legitimate subject of speculation is as to the nature of the substance which, by precipitation, forms the cloud- masses of the photosphere. We may predicate three properties with greater or less positiveness, viz. : — 1st. The substance has a boiling-point above that of iron, for iron vapor at a lower temperature exists in the immediate neighborhood. 2d. The molecular weight is probably not great ; for, though pre- cipitated below the upper natural limit of its vapor, there are few ele- OP ARTS AND SCIENCES. 149 ments found in abundance above it, and those in general of low vapor density. 3d. The element is not a rare one. Of these guides the last is perhaps of the least value. The substances which apparently meet all these conditions are car- bon and silicon : nor is it easy to name any other which will. Accept- ing for a moment as an hypothesis that the light coming from the sun is radiated by solid or liquid particles of carbon just at the point of vaporization, let us see if the facts of observation fulfil the implied conditions. As a first consequence, we see that the temperature and light of the photosphere are defined as those of solid carbon at the point of volatili- zation. In the electric arc there is a very small area of the positive carbon pole at this high temperature. Though this area is in a very disadvantageous position for observation, and can consequently have but a disproportionately small share in producing the total effect, the splendor of the electric light might almost tempt us to believe the guess a valid one. Another consequence implied, however, — namely, that the spectral lines proper to simple carbon are absent in the solar spectrum, — is doubtless better adapted as a crucial test of the hypoth- esis than a study of the electric light. There has been evidence recently offered that carbon lines are present in the solar spectrum. Granting this, we perceive that the photosphere contains solid or liquid particles hotter than carbon vapor, and consequently not carbon, I am then inclined to suspect that the photospheric material may be silicon, which, though denser in the gaseous state than carbon, is not improbably more abundant. There is also good reason to suppose that carbon is precipitated at a higher level ; and the analogous but less common element boron may add a minor effect. In the explanations which I shall give of the remaining phenomena, it may serve to fix the ideas, to think of the granules which charac- terize the sun's photosphere as clouds of a substance like precipitated silicon. At any rate, we are sure that the substance in question, so far as we know it, has properties similar to those of the carbon group, I have given plausible explanations of all the phenomena included specially in my own observations. It remains to discuss the others, briefly mentioned above. The substance precipitated cools very rapidly, as it is an excellent radiator separated from space only by extremely diathermous media. It forms then a smoke-like envelope, which ought to exert just such a general absorption as that observed at the limb of the sun. It is thin 150 PROCEEDINGS OF THE AMERICAN ACADEMY because of the relatively great density of the substance in the liquid or solid state ; thus the apparent brilliancy of the faculae is readily understood. If there is any disturbing cause which would tend to direct currents of gas, over a considerable area of the solar surface, toward a point, this smoke, instead of quietly settling down to lower levels between the granules, would concentrate about this point, there exercising a marked general absorption which would betray itself as a spot. At this place the suspended particles would sink to lower levels with constantly increasing temperature, until finally, heated to intense in- candescence, they would revolatilize. Thus the floor or substratum of every spot must be a portion, dejiressed it is true, of the photosphere. All the spectroscopic phenomena of spots, which have proved so per- plexing, are thus naturally and easily explained. In the immediate neighborhood of a spot, the centripetal currents bend down the ordinary convection or granule-producnig currents, so that they are approximately level. Before, the latter cooled suddenly by rarefaction in their upward course ; now, they cool mainly by the much slower process of radiation ; thus, while before the locus of pre- cipitation was restricted, it is now greatly extended. This is the cause of the great elongation of the granules in the penumbra, — a real elongation, I imagine, and not merely an apparent one. Finally, concerning the close duplicity of certain lines, we may rea- son thus: — If we could surround the sun by a stratum of gas hotter than the photosphere and much rarer than that producing the corre- sponding Fraunhofer lines, we should, as is shown by a course of rea- soning which I have given in another place,* see each dark line divided by a sharp bright line in its centre, that is, doubled. But as a consequence of the theory this supposed condition must be practically met in the case of certain vapors in the sun. The gases just over the granules, in the vertical currents, are at a very high temperature, essentially that of the condensing material itself, consequently much hotter and I'arer than the relatively low-lying vapors which, as we have seen, produce the F'rauuhofer lines. There are, however, certain evident limitations to these conditions ; in other words, we cannot expect to see all the dark lines doubled by any increase of dispersive power. For instance, a line must have a marked tendency to broaden with increased pressure, otherwise the duplication cannot be pronounced. Again, the layer of rare vapor must * On Lockyer'e Hypothesis. Am. Jour. Clicni., i. 16. OF ARTS AND SCIENCES. 151 be thin, or its temperature cannot be relatively high throughout, as demanded by the theory. This evident condition doubtless gives the reason why the hydrogen lines, though the broadest in the solar spec- trum, are not sensibly double. The theory of the constitution of the sun above proposed may be briefly recapitulated thus : — Convection currents, directed generally from the centre of the sun, start from a lower level, where the temperature is probably above the vaporizing temperature of every substance. As these currents move upward they are cooled, mainly by expansion, until a certain element (probably of the carbon group) is precipitated. This precipitation, restricted from the nature of the action, forms the well-known granules. There is nothing which has come under my observation which would indicate a columnar form in these granules under ordinary circum- stances. The precipitated material rapidly cools, on account of its great ra- diating power, and forms a fog or smoke, which settles slowly through the spaces between the granules till revolatilized below. It is this smoke which produces the general absorption at the limbj and the " rice-grain " structure of the photosphere. When any disturbance tends to increase a downward convection current, there is a rush of vapors at the outer surface of the photo- sphere toward this point. These horizontal currents, or winds, carry with them the cooled products of precipitation, which, accumulating above, dissolves slowly below in sinking. This body of smoke forms the solar spot. The upward convection currents in the region of the spots are bent horizontally by the centripetal winds. Yielding their heat now by the relatively slow process of radiation, the loci of precipitation are much elongated, thus giving the region immediately surrounding a spot the characteristic radial structure of the penumbra. This conception of the nature of the penumbra implies a ready in- terpretation of a remarkable phenomenon, amply attested by the most skilful observers, and, as far as my knowledge goes, wholly unex- plained ; namely, the brightening of the inner edge of the penumbra in every well-developed spot.* * Relating to this phenomenon we see important observations by Professor Langley, Am. Jour. Sci., Vol. IX. (1875,) p. 194; also Le Soleil, par Le P. A. Secclii, Paris, 1875, Chap. IV. p. 81, and particularly Fig. 46, p. 90, with explanatory text. 152 PROCEEDINGS OF THE AMERICAN ACADEMY This interpretation is perhaps most readily imparted by a compari- son of the hot convection currents in the two cases. "When the con- vection current is rising vertically, the medium is cooled by expansion until the precipitation temperature is reached, when all the condensible material appears suddenly, save as it is somewhat retarded by the heat liberated in the act. Immediately afterward the particles become rela- tively dark by radiation. In the horizontal currents a very different con- dition of things obtains. Here the medium does not cool dynamically by expansion, but only by radiation ; hence, since the radiation of the solid particles is enormously greater than that of the supporting gas, practically by that of the particles themselves. Thus after the first particle appears, it must remain at its brightest incandescence until all the material of which it is composed is precipitated. From this we see that such a horizontal current must increase gradually in brilliancy to its maximum, and then suddenly diminish, — an exact accordance with the facts as observed. John Hopkins University, Baltimore, September, 1880. OP ARTS AND SCIENCES. lf>^ VIII. CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY. XIIL — ACOUSTIC PHENOMENON NOTICED IN A CROOKES' TUBE. By Professor Chas. R. Cross. Presented Nov. 10, 1880. A SHORT time since, while experimenting with a Crookes' tube, I noticed a phenomenon which was quite striking, and so evident that it hardly seems possible that it has not been observed before, though I have never seen any notice of the fact. In working with the tube, in which a piece of sheet platinum is rendered incandescent by the concentration upon it of electrified parti- cles repelled from a concave mirror, I noticed that when the mirror was made the negative electrode, so that this concentration took place, a clear and quite musical note issued from the tube. I thought at first that the pitch of this note would coincide with that produced by the circuit-breaker of the coil, which made about 120 breaks per second, but this did not prove to be the case, for very great changes in the rate of the circuit-breaker did not affect the note given by the tube. The effect seemed to be produced by the vibration of the sheet platinum under the influence of the molecular impact, which vibra- tions were communicated to the glass walls of the tube by the en- amelled rod to which the platinum was attached. This gave rise to a sound somewhat resembling that caused by the pattering of rain against a window-pane, but higher in pitch and more musical. The sound changed its character very greatly when the direction of the current was reversed, only a feeble murmur being heard. I obtained a similar musical note, though far less loud, with the " mean free- |)ath " tube, best when the middle plate was positive. With a tube containing phosphorescent sulphide of calcium the note was very dull i:.4 rUOCKFAMN-O^ OF TUK AMKIUO.VX ACMHIMY iu it., uu^^itv, *ud knv iu pitch, but still quito jvrwpiible. With this tulv -i ohHxi> in tho dir^vtiou of the ourrv^ut did uot att'ect the note prvxliKwl. \ did uot obtain this musicil note from aiiy tube that I possess if. >vhioh the ourmu enters and leaves by a straight wir^, except in the o^se of one Geissler s tul>e exhaustevl so as to give stratido*tious, iu which it \^-as very feebly heard. OF ARTS AND SCIENCES. 155 IX. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. By Henry B. Hill. Presented Juno 9, 1880. FUKFUROL, ONE OF THE PllODUCTS OF THE DrT DISTILLA- TION OF Wood 158 Ptroxanthin 161 MucoBuoMic Acid 168 MucocHLORic Acid 204 Substituted Acrylic Acids from Brompropiolic Acid 211 Theoretical Considerations 218 In December, 1876, by the kind invitation of Dr. E. R. Squibb, I had the opportunity to examine the working of a new process for the manufacture of acetic acid by the dry distillation of wood at a low and carefully regulated temperature, as it was carried on under his direc- tion at Brooklyn, N. Y. I then noticed that, in the rectification of the crude wood spirit, a yellowish oil passed over with the vapor of water after the more volatile portions had been distilled off. Its high specific gravity and its peculiar odor made me anxious to examine it more closely. A short study of it was sufficient to show that it contained large quan- tities of furfiirol which could be isolated in a jjure state with little trouble, and I therefore undertook at once the study of the constitution of furfurol and pyromucic acid. Before my investigations were far advanced, Baeyer * published the first of his papers upon the constitu- tion of furfurol, in consequence of which my own work was naturally discontinued. At the same time, however, I wrote to Professor Baej^er asking if I could not make use of the large supply of material which I had at hand without interfering with the plan of his research. In reply I received the extremely considerate intimation that a study of mucobromic acid and its derivatives would in no way interfere with his work. * Berichte der deutsch. chem. Gesellsch., x. 355. 156 PROCEEDINGS OF THE AMERICAN ACADEMY This investigation was begun in 1877 ; and, although it is not yet completed, so many facts have accumulated that I have thought it best to lay before the Academy the results already obtained. Different portions of this research I have carried on with Mr. 0. R. Jackson and Mr. C. F. Mabery, assistants in this laboratory, and with Mr. W. Z. Bennett. In my description of our results, I shall make plain the share which each of these gentlemen has had in the work. My most sincere thanks are due to Dr. Squibb for the generous supply of material, without which it would have been impossible for me to have undertaken this investigation. FURFUROL ONE OF THE PRODUCTS OF THE DrT DISTILLATION OF Wood. Although the products formed in the dry distillation of wood have repeatedly been made the subject of investigation, I can find in the literature of the subject but little reference to the presence of furfurol among them. That furfurol is thus formed is asserted by Gmelin * on the authority of Volkel, but a close examination of Volkel's origi- nal papers f fails to show any sufficient foundation for the assertion. Although Volkel had already shown that furfurol was formed in the dry distillation of sugar, and had established its presence by analysis,! in his subsequent work upon the dry distillation of wood he seems to have based his conclusions solely upon qualitative tests by no means conclu- sive. Although he makes a number of general statements concerning the presence of furfurol among the products he obtained, I can find nothing more definite than is contained in the following passage.§ After describing the extraction of a yellowish brown oil from the pyroligneous acid by means of ether he proceeds : " In Kalilauge lost sich das Oel unter Entwicklung eines betaubenden Geruchs auf, der von einer geringen Menge einer organischen Basis herriihrt, well er auf Zusatz von Saure wieder verschwindet. Die dunkel gefarbte alkalische Losung triibt sich in kurzer Zeit durch Ausscheiden eines gelbbraunen Korpers, der Pyroxanthin enthalt. Aus der abfiltrirten noch stark gefarbten alkalischen Fliissigkeit wird durch verdiinnte Schwefelsaure ein anderer brauner Korper abgeschieden, und zugleich * Gmelin's Handbuch, vii. 599 ; Suppl., ii. 972. t Poggendorff's Annalen, Ixxxii. 496 ; Ixxxiii. 272 and 557 ; Ann. Chem. a. Pharm., Ixxxvi. Q6. J Ann. Chem. u. Pharm., Ixxxv. 59. § Ibid., Ixxxvi. 83. f 4 OF ART&i AND SCIENCES. 157 der Geruch des Kreosots wahrgenommen. Aus diesen Reactionea ergiebt sich dass das Oel . . . ein sehr gemengtes . . . ist. Ei entlialt eia eigenthiimliches Oel (Pyroxanthogen), das durch die Ein- wirkung von Alkalien in Pyroxanthin ubergeht ; Kreosot ; fernei mehrere fliichtige Oele, die durch Alkalien in braune Korper umge- andert werden die in Kali theils loslich theils unloslich sind. Diese letzteren Oele sind unstreitig identisch mit den fluchtigeren Oelen die bei der Destination des Zuckers erhalten werden, Furfurol, u. s. w." I have quoted the passage with but little abbreviation, that the char- acter of the qualitative tests upon which Volkel based his conclusion may be aj^preciated. Quite recently since the publication of a preliminary note by me upon this subject, V. Meyer * has found in the commercial glacial acetic acid of the continent, a small quantity of furfurol which mani- fested itself by the intense red color developed when the acid was mixed with aniline. Although these two observations are all I can find recorded of the presence of furfurol among the products of the dry distillation of wood, its formation from wood by other means has been more frequently noticed. Although Doberciner t could obtain no furfurol from sawdust by distillation with sulphuric acid, Fownes t none from linen, and Cahours § and Gudkow IT were equally unsuccessful with pure cellu- lose, Emmet ** obtained it by the same method from woody fibre, Stenhouse tt ^oni sawdust, afterward from mahogany M and madder.§§ Gr. Williams Hlf also found that it was formed when wood was heated under pressure with water, although none could be obtained at ordi- nary pressures. Similar results were obtained by H. Miiller.*** A brief description of the method of distillation which has furnished the material for this investigation may prove of interest: since the product obtained in this way contains considerable quantities of fur- furol, while the percentage formed by the ordinary methods must be * Berichte der deutsch. chem. Gesellsch., xi. 1870. t Journ. pract. Chem., xlvi, 168. J Pharmaceutical Journal and Transactions, viii. 113. § Ann. Chim. Phys., [3] xxiv. 277. 1 Zeitschr. fiir Chem., 1870, 360. ** Amn. Jour., xxxii. 140. tt Ann. Chem. u. Pharm., xxxv. 301. tt Ibid., Ixxiv. 278. §§ Ibid., Ixxx. 325. Tl Chem. News, xxvi. 231 and 293. *** Ibid., xxvi. 247. 158 PROCEEDINGS OF THE AMERICAN ACADEMY very small to have escaped notice so generally. The wood, chiefly oak, is cut into small pieces and filled into rectangular retorts of boiler iron, each one capable of holding a charge of from five to six thou- sand kilogrammes. The retorts when charged are placed in separate cells of an oven heated by hot-air flues. The temperature of this oven is carefully regulated by means of long mercurial thermometers built into each cell, and the thermometer readings vary from 150° at the beginning of a distillation to 200° at the end. The average time required is six days, and during this time the wood loses about thirty- two per cent of its weight. The volatile products pass through an outlet pipe at the top of each retort, and are condensed in a set of ordinary coolers. The wood left in the retorts after distillation is darker in color and somewhat more brittle than the fresh wood : its composition agrees essentially with that given by Payen * for dried oak wood. The specimens of wood for analysis were taken while still warm from the I'etorts, and kept hermetically sealed until analyzed. I. 0.4480 grm. substance gave 0.8950 grm. CO,, 0.2545 grm. B^O and 0.0040 grm. ash. II. 0.3880 grm. substance gave 0.7810 grm. COj and 0.2220 grm. II2O. 1.2725 grm. of the same wood gave 0.0070 grm. ash. III. 0.3270 grm. substance gave 0.6390 grm. CO2, 0.1740 grm. HjO and 0.0015 grm. ash. c. I. 50.01 Found. II. 54.89 m. 53.30 Payen. 54.44 H. 5.88 6.29 5.78 6.24 Ash. 0.89 0.55 0.46 The volatile products of the distillation are subjected to the ordinary processes of rectification. In fractioning the wood spirit, after the more volatile portions have passed over, the distillate throws down a heavy yellow oil upon dilution with water, and somewhat later the slightly acid aqueous distillate contains an abundance of the same heavy oil in suspension. The quantity of oil which thus separates in the course of distillation amounts to between three and four tenths of one per cent of the crude wood spirit taken, although I am unable to form even an approximate estimate of what proportion this may be of the total amount present. The oil, as I received it, was feebly acid to test paper, and had a « N. Ann. Sci. Nat., xi. 24. OF ARTS AND SCIENCES. 159 peculiar aromatic odor. It was bright yellow in color, and slightly heavier than water. It was washed with water dried over calcic chlo- ride and submitted to fractional distillation. The liquid began to boil a little above 100° ; but the thermometer rose rapidly, and had reached 160° before any considerable quantity had passed over ; between 160 -170° it remained stationary for a long time, and then rose again rapidly to over 200°. After several distillations, about sixty per cent of the oil taken distilled between 160° and 165°, the greater part of which boiled steadily at 162^*. The boiling point and general charac- ter of the oil at once suggested the presence of furfurol, and this was readily proved by its conversion into furfuramide, furfurine, and pyro- mucic acid. The behavior of the oil to alkalies, however, showed that it was still by no means homogeneous. When shaken with a dilute solution of potassic or sodic hydrate, a brilliant yellow color was de- veloped ; and in a few moments the clear liquid became turbid with the separation of a flocculent yellow precipitate, which proved to be chiefly pyroxanthin. In following out the method of purification which was thus suggested, I found it most convenient to separate from the crude oil, only so much of the higher boiling constituents as could be removed by rejecting that which passed over above ITS'^ in two successive distillations. The distillate collected below 175° was then gradually mixed with one-fourth its volume of a concentrated solu- tion of sodic hydrate, taking care to keep the mixture cool, and shaking the two well together. After standing a short time, the oil was separated from the alkaline solution, washed with a little water, and distilled with steam. The furfurol thus obtained was suflaciently pure for all ordinary purposes, and from such a product was made all the pyromucic acid which has been used in the course of the following investigations. For its conversion into pyromucic acid, it was mixed with an equal volume of a concentrated alcoholic solution of sodic hydrate, and care- fully stirred until the violent reaction was over. The sodium salt was then thoroughly washed with ether, dissolved in hot water, and decora- posed by concentrated hydrochloric acid. For the purification of the crude acid, it was dissolved in a cold dilute solution of sodic carbonate, taking care that the solution should remain slightly acid. The filtered solution of the sodium salt was boiled with bone-black filtered, con- centrated by evaporation, and finally acidified with hydrochloric acid. The acid which separated on cooling was then recrystallized from boiling water, and was found on analysis to be sufficiently pure for further use. 160 PROCEEDINGS OP THE AMERICAN ACADEMY 0.8140 grm. substance gave 1.5910 grm. CO2 and 0.2910 grm. H2O. Calculated for CjH^Oj. Sonnd. c 53.57 53.31 H 3.57 3.97 The acid prepared in this way melted at 128-129° ; and, since the melting point of pyromucic acid is usually given somewhat higher, it seemed advisable to subject this product to further purification. Mr. J. J. Thomsen, therefore, prepared the ethyl-ether of the acid by satu- rating its solution in absolute alcohol with hydrochloric acid, precipitat- ing with water, and washing first with a dilute solution of sodic carbonate and then with water. He then found that the carefully dried ether distilled from the first drop to the last unchanged at 195° (Mercury column completely in vapor) under a pressure of 766 mm. On cooling, it crystallized in large transparent prisms, which melted at 34°. According to Malaguti,* ethyl pyromucate melts at 34°, but boils at 208 - 210°, under a pressure of 756 mm. For the determination of boiling point, we employed about 30 grm. of the ether, and an analysis showed its purity. 0.5615 grm. of substance gave 1.2330 grm. COo and 0.2940 grm. Calculated for C5H3O3C2H5. Found. C 60.00 59.8 H 5.71 5.81 A portion of this ether was saponified with sodic hydrate, the acid liberated from the sodic salt, recrystallized from hot water several times, and finally melted. The solidified acid melted at 130°, 5 (uucom.), while an acid made directly from mucic acid melted at 130°. The corrected melting points of the two were 133° and 132.°5; whereas Schwanertf gives the corrected melting points 134°. 3 and 132. °6 respectively for substance made from furfurol and from mucic acid. The chief constituent of the oil under investigation was thus shown to be furfurol. From the higher boiling portions, I have as yet been able to isolate no well-marked substances. On distillation, the ther- mometer rose slowly to over 300°, and even after long fractioning there appeared to be no tendency towards constant boiling points. By far the greater portion was insoluble in alkalies, and I could obtain no characteristic derivatives by the action of various reagents. # Ann. Chim. Phys., [2] Ixiv. 279. t Ann. Chem. u. Pharm., cxvi. 267. OF ARTS AND SCIENCES. 161 From the sodic hydrate used for washing tlie crude furfurol could be separated in small quantity an oil volatile with steam, and possessing a strong odor like smoked fish. It had the general characters of a phenol, but I have not as yet further identified it. Since a large quantity of material has been accumulated in prejjaring the furfurol necessary for the following researches, I hope before long to make further study of the less volatile constituents which are present in smaller quantity. Ptroxanthin. I have already mentioned the yellow flocculent precipitate, formed by the action of alkalies upon the crude furfurol, which upon exam- ination proved to consist chiefly of pyroxanthin. This substance was discovered in 1835 by Dr. Scanlan, * of Dublin, in the residue from the preparation of methyl alcohol from crude wood spirit by means of lime. In 1836, it was further studied by Apjohn and Greg- ory, t who deduced from their analyses the formula CjiIIigO^, although they did not succeed iu confirming this formula by the preparation and analysis of any of its derivatives. This formula was subsequently changed to Cj^HgOo by Gmelin, J although this change was apparently not based upon any further experimental work. Although I have not as yet had any very considerable quantity of material at my com- mand, I have studied some of its reactions and prepared two well- marked bromine derivatives whose percentage composition necessitates the adoption of the formula CjjHjgOg. In the method I have described for the purification of the crude furfurol, after that portion which is volatile with steam has been dis- tilled off, there remains a red viscous oil in the retort, which, on cooling, partially solidifies. If this semi-solid mass is then treated with small quantities of cold alcohol, the red oil, which results, in part at least, from the action of the sodic hydrate upon the furfurol, dis- solves, while the greater part of the pyroxanthin is left behind in minute crystals. Occasionally, this viscous residue crystallizes only after the addition of the alcohol and vigorous stirring. The pyro- xanthin seems to be more neatly separated, if the furfurol is slightly acidified with acetic acid after separating the alkaline solution before distilling with steam. After the crystals have been well washed with * Phil. Mag., [3] xli. 395. t Koyal Irish Acad. Proc, 1836, xxxiii. Ann. Chem. u. Pharm., xxi. 143. t Gmelin's Handbuch, vii. 157. VOL. XVI. (N. 8. VIII.) 11 162 PEOCEEDINGS OP THE AMERICAN ACADEMY cold alcohol, they are recrystallized from boiling alcohol until the substance has a bright, clear, orange-yellow color. Boiling the alco- holic solution with bone-black facilitates the removal of the red impurities. Pyroxanthin is completely insoluble in water, and very sparingly soluble in ether or carbonic disulphide ; in hot alcohol, benzol, or glacial acetic acid it dissolves abundantly, and crystallizes in well- developed forms on cooling. From alcohol it crystallizes in small, brilliant, orange-yellow needles with a blue reflex ; from benzol in tolerably large reddish-yellow monoclinic prisms ; and from glacial acetic acids in flat radiated needles, which are formed by the develop- ment of the prism in the direction of the orthodiagonal. The crystal- lographic examination which I made of the substance gave the following results. ClLYSTALilNE FOJiil OF PtEOXANTHIN. ooi Z Monoclinic System. Forms observed {001} ^TOl} |100| plO}. a: ^:c=: 2.748 : 1 : 1.413 ac = 87° 56' Angles between Normals. Found. 110 :T10 40° 1' TOl : 001 26° 46' TOl :T00 61" 10' TlO : TOO 69° 54' TlO : TOl 80° 25' Calcalat*d. Fundamental angles. 69° 59' 80° 30' OF ARTS AND SCIENCES. 163 For analysis the substance was crystallized from aloohul and dried at 100°. I. 0.2673 grm. substance gave 0.7341 grm. CO., and 0.1279 grm. 11,0. II. 0.2432 grm. substance gave 0.6690 grm. CO.^ and 0.1141 grm. H,0. Calculated for CieH,jOs. Found. Apjohn and Gregory. C 75.00 74.91 75.01 74.27 H 5.00 5.31 5.25 5.61 Since the substance was very refractory and needed a high tempera- ture in a stream of oxygen for complete combustion, my results show a sufficiently close agreement with those of Apjohn and Gregory. This substance melts at 162° and volatilizes with partial decompo- sition at a higher temperature, although it may be sublimed without difficulty by careful heating in a current of air. In concentrated sul- phuric acid it dissolves with an intense purple, and in hydrochloric or hydrobromic acid with a crimson color. From these solutions water precipitates the substance apparently unchanged. In alkaline solutions it is completely insoluble, and by melting caustic potash it is merely carbonized. Bromine attacks it vigorously, and, under certain condi- tions, forms well-crystallized products. Dibrompyroxanthintetrabromide^ C^HjoBrgOgBr^. When pyroxan- thin is suspended in ten times its weight of carbonic disulphide, and three and a half parts of bromide diluted with an equal weight of car- bonic disulphide are added, the pyroxanthin instantly dissolves and forms a clear deep-red solution. After standing for a short time, clouds of hydrobromic acid are given off, and soon after the separation of a beautifully crystalline substance begins. After twenty-four hours the carbonic disulphide is poured off, and the crystals which have separated are thoroughly washed with ether. For analysis I recrystallized the substance from boiling chloroform and dried it in vacuo. I. 0.5598 grm. substance gave 0.5136 grm. COg and 0.0842 grm. H,0. II. 0.6814 grm. substance gave 0.5758 grm. COj and 0.0845 grm. R,0. III. 0.3094 grm. substance gave 0.4884 grm. AgBr.* IV. 0.3128 grm. substance gave 0.4936 grm. AgBr. * All the determinations of halogens in this and the subsequent investiga- tions were made according to the method of Carius. In most cases the asbestos 164 PROCEEDINGS OF THE AMERICAN ACADEMY Salcula c ted for CisHjijBraOs. I. 25.07 25.02 Found. II. 24.87 H 1.39 1.67 1.49 Br 66.85 rn. 67.16 IV. 67.13 These percentages agree closely with those required by the for- mula Cj-Hj^BrgOg, and the behavior of tlie substance is such that it must be considered dibrompyroxanthintetrabromide. It crystallizes in small, brilliant, colorless prisms which belong to the triclinic system. On heating, it is decomposed below 100° with carbonization and the evolution of hydrobromic acid. It is very sparingly soluble in ether or carbonic disulphide ; in boiling benzol or chloroform it dissolves quite freely, and the greater part again separates on cooling. In cold alcohol or glacial acetic acid, it is sparingly soluble ; but, on warming, it dissolves with decomposition and then forms a yellow solution. In the cold, it is unaltered by concentrated sulphuric acid ; on heating, it is carbonized. A crystallographic study of the substance gave the following re- sults : — ■ CRYSTALLINE FORM OF DIBROMPYROXANTHINTETRABROMIDE. Triclinic System. Forms observed, |001} \0U\ {OlT| \UQ\ {{\0\ \J0\\. a:b: c= 0.733 : 1 : 2.370. ic = 74° 43'; ac = 83° 40'; ai = 96' 46'. filter of Dr. Gooch was used. The great saving of time and labor as well as the increased accuracy attainable by vliis method renders it invaluable in de- terminations of this sort. OF ARTS AND SCIENCES. 165 Angles between Hormals. OTl OTl OTl TTO TTO TOl TIO 001 001 001 001 Found. TTO TOl Oil TOl TIO TIO OIT TIO : Oil 001 : TTO TIO OTl Oil TOl . 47° 15' 1 G9° 50' 135° 27' 34° 18' 76° 57' 48° 49' 61° 14' 58° 6' 73° 59' 93° 8' 54° 6' 81° 21' 63° 37' Calculated. ^ Fundamental anjiles. 48° 58' 61° 12* 57° 41' 74° 18' 93° 41' 53° 49' 81° 38' 63° 57' Bromine when moderately diluted with carbonic disulphide has no further action upon this substance. It is attacked, liowever, when exposed to the vapors of bromine, and deliquesces rapidly, forming a dark-red syrup, which over lime in vacuo gradually solidifies. From this product I have as yet been unable to isolate any substance with characters sufficiently well marked to encourage further study. Dihrompyroxanthin, CjgHjgBrjOg. The subtraction of bromine, on the other hand, gave a beautifully crystalline product with sharply marked characteristics. This substance I first made by the action of phenol. If the dibrompyroxanthintetrabromide is gently warmed with a little phenol, to which sufficient water has been added to keep it liquid, it dissolves, forming a highly colored solution, which is red by transmitted and green by reflected light. If alcohol is then added, it causes the separation of an abundance of fine, felted brilliant-yellow needles, which may be recrystallized from alcohol. This same substance may also be made by boiling the tetrabromide with absolute alcohol, and adding zinc dust or finely powdered metallic antimony. The latter method is perhaps most advantageous, since little or no product is obtained if the phenol solution is too strongly heated, or, if the zinc dust contains a large percentage of oxide. For analysis, the substance was dried at 100° after several recrystal- lizations from alcohol. The material used in analyses L and II. was made with phenol, while that used in analysis III. was made with antimony. 166 PROCEEDINGS OF THE AMERICAN ACADEMY I. 0.3816 grm. substance gave 0.6333 grm. CO, and 0.0918 gnu, HA II. 0.3137 grm. substance gave 0.2978 grm. AgBr. III. 0.2577 grm. substance gave 0.2419 grm. AgBr. Calculated for CijHioBrjOj. Found. I. II. m. C 44.22 45.25 H 2.51 2.67 Br 40.20 40.40 39.94 The analyses showed that the substance was dibrompyroxanthin, and that it was formed from the bromine derivative already described by the subtraction of bromine. In hot alcohol it dissolves readily, although in cold it is sparingly soluble. It is quite soluble in ether or carbonic disulphide, and very readily in benzol, chloroform, or glacial acetic acid. From a solution in warm chloroform, it crystallizes in large, compact, twinned forms of the monoclinic system, which are dichroic. In con- centrated sulphuric acid, it dissolves with an intense, pure blue color. This blue solution, on dilution with water, throws down a yellow pre- cipitate, which is apparently the unchanged substance. If quickly heated upon platinum foil, it melts to a perfectly clear yellow liquid ; but it is impossible to determine its melting point, since it decomposes and carbonizes when its temperature is more gradually raised. A solution in carbonic disulphide, when mixed with bromine, gradually deposits well-formed crystals of the tetrabromide. This simple sub- stitution product I have not succeeded in making directly from pyroxanthin. In every case where a smaller quantity of bromine was employed, the addition product was still formed, and a part of the pyroxanthin remained unaltered. I have also studied the action of aqueous bromine, but have not been successful in obtaining any definite products. If pyroxanthin is suspended in water, and bromine gradually added, or the vapors of bromine carried in by a current of air, a white amorphous substanceis slowly formed, which is almost insoluble in water, but extremely solu- ble in other ordinary solvents. By evaporation of such solutions, the substance again separates in an amorphous condition. In alkalies it dissolves, forming a deep-brown solution, from wliich nothing can be precipitated by the addition of acids. Since there appeared to be little hope of effecting its purification by ordinary methods, I proceeded to analyze carefully prepared material. OF ARTS AND SCIENCES. 167 I found, however, tliat the substance turned brown on standing over sulphuric acid, and tJie analysis of two diflerent preparations showed conclusively that no constant results could be obtained in this way. I. 0.3726 grm. substance gave 0.3142 grm. COg and 0.0594 grm. 11,0. IT. 0.2016 grm. of the same preparation gave 0.2773 grm. AgBr. III. 0.5255 grm. substance gave 0.4142 grm. COj and 0.0734 grm. H,0. IV. 0.3853 grm. of the same preparation gave 0.5731 grm. AgBr. I. n. ni. IV. C 23.00 21.50 H 1.77 1.55 Br 58.53 63.30 These results showed merely that oxidation had taken place together with the substitution .of hydrogen by bromine. On boiling with bromine-water, total decomposition seemed to en- sue, and no definite products could be isolated except oxalic acid and a small quantity of a volatile oil which had the odor of bromoform, and gave the characteristic odor of phenyl isocyanide when heated with anilin and alcoholic potash. Although I have already carried on the investigation of pyroxan- thin in several other directions, I have not as yet been able to study the reactions involved as much in detail as I could wish, and I must therefore reserve for a subsequent paper all description of these ex- periments. Concerning the origin and mode of formation of the pyroxanthin, I can at present add nothing. Its high melting point, and its general behavior when compared with the properties of the oil from which it is made, lead directly to the conclusion that it results either from polymerization or condensation. Its formula, Cj^Hj^Og, naturally sug- gests a trimolecular polymeric form ; the composition of its bromine derivatives, on the other hand, favors rather the view that its mole- cule is the product of condensation. Schweizer,* in 1848, prepared from pyroligneous acid an oil to which he gave the name pyroxanthogen, as the substance from which the pyroxanthin was formed. He attempted no explanation of the mode of formation, and made no analysis of his product. Although * Jour, pract. Chem., xliv. 129. 168 PROCEEDINGS OF THE AMERICAN ACADEMY his description is not very precise, it is sufficient to show that it was a mixture tolerably complex in its nature. All my own attempts to isolate from the crude furfurol the sub- stance essential to the formation of the jiyroxanthin have been unsuc- cessful, its separation from the furfurol is a matter of some difficulty, not only on account of the small quantities present, but also since it appears to be closely allied to furfurol. In its boiling point or in its behavior towards reagents, I have as yet found no differences suffi- ciently well marked to form the basis for a method of separation. For the present, at least, a more careful study of the pyroxanthin itself would seem to be the most speedy way to discover the mode of its formation. MucoBROMic Acid. Mucobromic acid was first made by Schmelz and Beilstein, * in 1865, by the action of bromine and water upon pyromucic acid. They found its salts so unstable that they made little attempt to isolate them, but confined themselves chiefly to the study of the decomposition which ensued when it was boiled with alkalies, and of the reaction effected by argentic oxide. They found that the acid was rapidly decomposed when boiled with baric hydrate, that bromacetylen was set free, and that baric carbonate was precipitated. In solution, they found, beside baric bromide, a sparingly soluble barium salt, to which they gave the name, baric muconate, and the formula, BaC^Og . HoO. This formula was, how- ever, based upon a single barium and two water determinations. They also prepared the free muconic acid, but made no further study of it than to establish the fact that it was a crystalline solid readily soluble in water, and that its lead salt was insoluble. They expressed the reaction which they supposed had taken place by the equation : — 2 C^H.Bvfi, + IJ.,0 = C.H.Og + CoHBr -f 2 CO^ + 3 HBr. They also found that mucobromic acid was attacked when boiled with argentic oxide and water, that argentic bromide was formed, and at the same time a silver salt quite insoluble in water. This silver salt, according to their calculations of the analytical results which they obtained, had the formula C-HoBrgAgjO^, and they regarded this as an intermediate product standing between mucobromic and muconic acids. The acid was found to be a crystalline solid, which appeared to give * Ann. Chem. u. Pharu., Suppl., iii. 276. OP ARTS AND SCIENCES. 169 broraacetylen and muconic acid when heated with baric hydrate. The reaction with argentic oxide they wrote: — 2 C,H,Br,03 + 2 Ag.fi = C,H,Br3Ag30, + AgBr + 11,0 + CO,. In the course of the investigations upon mucic acid and its deriva- tives, which were begun in Limpricht's* laboratory in 1868, muco- bromic acid received more or less attention. Although it was found to be the only product when pyromucic acid was treated with wafer and an excess of bromine at ordinary pressures, Limpricht and Del- briick showed that it was completely decomposed when heated in a sealed tube to 120° with bromine and water, provided that three mole- cules of bromine, at least, were used to one of mucobromic acid. As products of the decomposition, they found, beside carbonic dioxide and hydrobromic acid, tribromethylenbromide, CgHBr^, perbromatbylen- bromide, C^Brg, tetrabrombutyric (?) acid, C^H^Br^O,, and dibrom- fumaric (?) acid, C Ji^^r fi^. The marks of interrogation appear in Limpricht's original paper. Limpricht and Lessing also found in one experiment that, by the reduction of mucobromic acid, a liquid was formed which boiled at about 120° and contained 84.8 per cent of carbon, 8.8 of hydrogen, and the remaining 6.4 per cent was oxygen. They were, however, unable to repeat the experiment with a like result. In attempting the preparation of mucobromic acid, Mr. 0. R. Jack- son and I found that we were unable to obtain a satisfactory yield by following the method given by Schmelz and Beilstein or by Lim- pricht. Schmelz and Beilstein say that the quantity of water taken is not a matter of indiiference, but neither they nor Limpricht make any specific statements as to the amount which they found to be most advantageous. They agree, however, that the bromine should be added slowly as long as it is taken up in the cold, that the solution should then be heated and bromine added as long as the color con- tinues to disappear. According to this method, we were unable to get more than 25 per cent of the theoretical yield; and at the same time we were obliged to use quite a large excess over the amount of bromine calculated from the equation : — C,H,03 + 4 Br, -f 2 H,0 = C,B,Brfi, + CO, + 6 HBr. * Berichte d. deutsch. chem. Gesellsch., ii. 211; iii. 90, 671; iv. 805; Zeitschr. fur Chem., 1869, 599; Ann. Chem. u. Pharm., clxv. 253. 170 PROCEEDINGS OF THE AMERICAN ACADEMY We soon found that our yield was greatly increased and the excess of bromine proportionately decreased if the bromine was added rapidly. Later, when it was found that a low temperature was essen- tial to the formation of mucochloric acid, the pyromucic acid and water were cooled with ice until the bromine had all been added, but the yield was not perceptibly affected. We have obtained the best results by the following method : Pyro- mucic acid is suspended in ten times its weight of water contained in a flask fitted with reverse cooler and drop-funnel. The calculated amount of bromine is then rapidly added, cooling only so far as may be necessary to avoid loss of bromine. After the bromine is all added, the flask is heated, and the liquid kept boiling for ten or fifteen min- utes. The solution may then be allowed to crystallize direct, although we have usually evaporated it until the hydrobromic acid began to volatilize in abundance before allowing it to cool. In either case the crystals should be well washed with cold water and recrystallized from boiling water. In this way we have found it easy to obtain 70 per cent and over of the theoretical yield.* The acid recovered from the mother liquors is usually very dark colored, and it cannot be purified by recrystallization from water either with or without the addition of bone-black. We have found, however, that such an acid may be obtained perfectly white by one or two recrystallizations from dilute sulphuric acid (1 : 4). As to the properties of mucobromic acid, we can only confirm the statements of Schmelz and Beilstein. It crystallizes ordinarily from water in irregular leafy aggregates, from acid solutions or from cer- tain other solvents in distinct rhombic plates. From a solution in concentrated hydrobromic acid, we have frequently obtained it in large compact crystals, with edges 10 to 12 mm. in length, but so striated as to render measurement impossible. It is sparingly soluble in cold water, very readily in hot water, in alcohol or in ether. In benzol or carbonic disulphide, it is very sparingly soluble in the cold, but dissolves quite readily on heating. Chloroform takes uji a little when hot, most of which it deposits on cooling. In warm concen- trated sul[)huric acid, it dissolves freely, and, if not too strongly heated, crystallizes out on cooling or on dilution. It melts at 120-121°, and at a higher temperature it distils in part unchanged. * Under conditions favorable to complete crystallization from tlie concen- trated hydrobromic acid which forms Mie mother liquors, we have obtained 78 per cent. tIculaU c (d for CiHjBrjOs. 18.60 I. 18.75 n. 18.55 Found. in. H 0.77 1.02 0.85 Br 62.02 62.( OF ARTS AND SCIENCES. 171 The following analyses may serve to show the purity of the material used in the course of the following investigations: — I. 0.7840 grm. substance gave 0.5390 grm. CO., and 0.0720 grm. 11,0. II. 0.9326 grm. substance gave 0.6340 grm. COj and 0.0712 grm. H,0. m. 0.2347 grm, substance gave 0.3421 grm. AgBr. IV. 0.2331 grm. substance gave 0.3410 grm. AgBr. IV. 62.25 Salts of Mucobromic Acid. Schmelz and Beilstein found that mucobromic acid decomposed baric carbonate, and that the barium salt thus formed was readily soluble in water, although it was decomposed during the spontaneous evaporation of the solution. As it seemed a matter of some interest to determine whether mucobromic acid was capable of forming salts, Mr. 0. R. Jackson and I pursued the investigation one step further. Baric Mucohromate, Ba(C^HBr20g)2. We found that an aqueous solution of mucobromic acid dissolved baric carbonate readily, that the solution on standing soon turned brown, deposited a brownish flocculent precipitate, and contained then a baric bromide in abun- dance. On heating, the same change took place more rapidly, and when the solution was boiled a substance was volatilized with the steam which had a sharjj, acrolein-like odor, and reduced silver oxide on heating. Although this change was rapid near 100°, we found that it was sufficiently slow at 50-60° to allow the preparation of a solu- tion saturated at this temperature which on cooling with vigorous stirring deposited crystals of the barium salt. The mucobromic acid was suspended in very little water, the whole warmed to 50-60°, baric carbonate added in excess, and the solution filtered and cooled as rapidly as possible. Even with these precautions we found it difficult to saturate the acid completely without bringing about decided decomposition. The salt, therefore, usually contained more or less free acid, from which it could be completely freed by washing with ether. The salt when dried in vacuo over sulphuric acid hardly lost weight at 100°, but when heated a few degrees higher it turned 172 PROCEEDINGS OP THE AMERICAN ACADEMY brown and gave out the sharp, penetrating odor mentioned above. Analyses I. and II. were made with a preparation crystallized from water without subsequent washing, III., IV., and V. with substance washed with ether. I. 0.9479 grm. gave 0.5018 grm. COo and 0.0547 grra. 11,0. II. 0.3434 grm. gave, on ignition with HgSO^, 0.1165 grm. BaSO^. III. 0.4186 grm. gave, on ignition, 0.1482 grm. BaSO^. IV. 0.5747 grm. gave, on ignition, 0.2030 grm. BaSO^. V. 0.7638 grm. gave, on ignition, 0.2695 grm. BaSO^. Calculated for Ba(C4HBr203)2. Found. I. n. m. IV. V. C 14.74 14.44 H 0.30 0.63 Ba 21.04 19.95 20.82 20.77 20.74 This salt is readily soluble even in the cold water, and soluble also in alcohol. On boiling its aqueous solution, the decomposition described above ensues, with the evolution of carbonic dioxide. This reaction has not yet been farther studied. Argentic Mucobromate, AgC^HBrjOg. The silver salt may be. made by adding a concentrated solution of argentic nitrate to a solution of the barium salt. Since it is quite soluble even in cold water, it is better to use, instead of the barium, the calcium salt, in order to facilitate washing. It is precipitated in fine, felted needles, which blacken quite rapidly on exposure to diffused light, and are decom- posed at once on moistening with alcohol or warming with water ; argentic bromide is formed, together with some metallic silver. This substance was dried in vacuo for analysis : — I. 0.8601 grm. gave 0.1862 grm. AgBr. II. 0.5640 grm. gave 0.2903 grm. AgBr. Calculated for AgCiUBroOa. Found. I. ir. Ag 29.59 29.70 29.56 Ethyl Mucobromate. The ethyl ether of mucobromic acid may readil}' be made by saturating its solution in absolute alcohol with hydrochloric acid, or more conveniently by warming this solution with concentrated sulphuric acid. If considerable sulphuric acid be used, the ether often crystallizes out on standing in large, well-formed crys- tals, otherwise it is precipitated by the addition of water and washed OP ARTS AND SCIENCES. 173 with a dilute solution of sodic carbonate. Tlie crude product con- tains impurities which can be removed only by repeated recrystal- lization from alcohol. This recrystallization is more conveniently accomplished if the moderately saturated solution is cooled to 0°. The ether crystallizes in large, transparent forms of the monoclinic system, which melt at 50-51° and boil at 255-2G0° with partial decomposition. When slightly warmed it has a pungent, aromatic odor. The analysis of substance dried in vacuo over sulphuric acid gave : I. 0.8583 grm. substance gave 0.7933 grm. COg and 0.1686 grm. H,0. II. 0.7000 grm. substance gave 0.6432 grm. CO^ and 0.1377 grm. Calculated for CtHBrjOj . (!jHg. Found. I. II C 25.17 25.24 25.05 H 2.10 2.18 2.18 Mr. Mabery has studied the crystalline form of this substance, and obtained the following results : — CRTSTALLINE FORM OF ETHYL MUCOBROMATR. ooi 2 Monoclinic System. Forms observed,— {111} {111} {100} {001} {HO}. a:b:c= 1.053 : 1 : 1.221 ; ac = 78° 27' 17-i TROCEEDINGS OF THE AMERICAN ACADEMY Angles between Normals. Found. Calculated. ni : TU 82° 11' ■ no : TIO 92° 7' > Fundamental anglej Til : TIO 32° 56' Til : 001 64° 53' 64° 46' Til :-lll 72° 11' 71° 50' 001 :-lll 52° 44' 52° 53' ITO :-lll 29° 8' 29° 17' 110 : TIO 87° 50' 87° 53' no : 001 81° SO' 82° 1' TlO : 001 98° 4' 97° 59' TIO : TOO* 45° 37' 46° 4' Action of Phosphoric Pentabromide and Acetylchloride. Mr, O. R. Jackson studied with me tlie behavior of mucobromic acid towards phosphoric pentabromide and acetylchloride. Mucubromi/lbromide . When mucobromic acid is mixed with about four times its weight of phosphoric pentabromide, and the mix- ture heated for a short time at 110-115°, a quiet reaction sets in, the mass becomes liquid, and water then precipitates a heavy red oil, which after thorough washing with water gradually solidifies at ordi- nary temperatures, or immediately if cooled to 0°. This substance is very soluble in alcohol, ether, benzol, chloroform, or carbonic disul- phide, but crystallizes well from a solution in a little hot alcohol when this is cooled to 0°. After repeated crystallization from alcohol, it forms small, slender prisms, which melt at 55-56°, and have the percentage composition corresponding to mucobromylbromide. I. 0.6643 grm. substance gave 0.3755 grm. COg and 0.0374 grm. ILO. II. 0.2598 grm. substance gave 0,4573 grm. AgBr. lU. 0.2252 grm. substance gave 0.3964 grm. AgBr. m. Calculate c »d for C^HBrgOj. 14.96 I. 15.41 Found. H 0.31 0.63 Br 74.77 74.8i 74.89 ♦ The form { 100 } was observed upon two or three individuals only, and the reflections were imperfect. OF ARTS AND SCIENCES. 1''" The behavior of this substance towards alkalies is especially charac- teristic. The reaction may best be observed when banc hydrate « cautiously added to a dilute alcoholic solution. An .ntense .n.hgo- bL color is at once developed, which, however soon passes through green to reddish yellow, with the simultaneous format.on of a brown- fed, fiocculent precipitate. The same brown prectp.tate .s formed wh n the muoohromylbromide is boiled in an excess of bar.c hydrate but the two products which are most char.acteris«c of the decompos- tion of muoobromic acid under the same conditions,* hromacetylen and malonic aci.l, are formed in such small quantities that they maj-as^y be overlooked. This peculiar behavior led us to suppose at fl St we had not the simple bromanhydride of mucohromic ..cd u, our hands, b t that an hyd'ro.yl group outside the carbo.yl bad been repla^d. A more careful study showed, however, that such was not he ^se^ Although this mucobromylbromide is apparently bttle affected even ^y hot-water, on boiling it is gradual, ^'^^^^l^:^. then contains mucobroinic aci.l (in. pt. 1/u i^' ) hoi decomposes it with more difficulty ; still, after several I'ou s bod- in. with reverse cooler, on evaporating the excess of alcohol and c„:ii„.r strongly, crystals separated which had the charactenst.c form Jthe e.hyh:.ucobroma.e,and which tnelted at 51" after recrystalhza- tion from alcohol. -i • i *„;i ;,^ « ^f.rMo,nic Actankyiride. When mucobrom.c acd ts heated ma sealed tube for several hours with an excess of -^^^'^^^ ^ or when it is heate.1 under ordinary pressure wth acct.c ■"■'' J 'l'"^*' ^ Istaucc is foru..d, which is very soluble in alcohol, ether or chbr- form. a„d which may be purified by prec.p.tafon by w er n U alcoholic sohnion. It falls as a colorless 0,1, whah gradually sohd.hes in slc.i.ler, dendritic needles, which melt at 53-54 . 0.9015 grm. gave 0.8050 grm. CO, and 0.1290 grm. H,0. Calculated for C«UBr,0, . C,U,0. iT^^ C 24.00 ^^-^y H 1.33 1-^^ That the acetyl group enters the carboxyl in this c.ase is show„ by Ae behavior of ethylmucobromate to acety ch bnde. After sev eral hours' heating, with an excess of acetylchlor.de, at UO-loO , r e er was fou'ud to be unaltered. T'- substance wh.ch wa. obtained crystallized in the form of the c.hyl-e.her, -^Itecl at 0 a„d upon analysis proved to eon.ain tl«^;equire^^^ * Cf. p. 188 el seq. 176 PROCEEDINGS OF THE AMERICAN ACADEMY 0.2720 grm. gave 0.3600 grm. AgBr. Calculated for C^HBrjOj . CjHg. Found. Br 55.94 56.32 Action of Br 0 mi e. Limpricht and Delbriick studied in delr i1 the action of bromine and water upon mucobromic acid, but they made no experiments witli dry bromine. It therefore seemed advisable to investigate the action of dry bromine ; since the reactions in this case would naturally be less complicated tlian with aqueous bromine, and on that account might prove to be of more service in determining the constitution of muco- bromic acid. Li my first experiments I employed equal molecules of bromine and mucobromic acid, but soon found that one molecule of bromine sufficed for tlie complete decomposition of nearly two molecules of mucobromic acid, although tlie products of the reaction were esseutiiilly the same whether the bromine was used in excess or not. At 100°, vejry little action was noticeable; at 120-130°, the action was marked, but so slow tliat the temperature was raised to 140°. Here the I'eaction ran rapidly, and after two hours the bromine had disappeared. On cooling, the tubes were filled with long, prismatic crystals, which were permeated with a nearly colorless oil. On open- ing the tubes, hydrobromic acid gas escaped in abund:mce, and with it could be detected a comparatively small amount of cai'bouic dioxide. The partially solidified product of the reaction was treated with small quantities of cold water. The greater part of the prismatic crystals were in tliis way carried into solution ; while the oil, in which a small quantity of crystals were yet to be seen, was left undissolved. This aqueous solution, upon evaporation, left a white, crystalline acid, very soluble in water, which for purification was converted into tlie barium salt. Before neutralizing the aqueous solution with baric carbonate, I found it best to evaporate to dryness, and take up a second time with a little cold water, in order to remove the small quantity of uude- composed mucobromic acid which often was present. The barium salt was precipitated several times from aqueous solution by alcohol, and finally crystallized from water by evaporation. Thus purified, it formed brilliant, transparent, rhombic plates, which lost water in desiccator slowly, but which I was unable to dehydrate perfectly by heat, either at ordinary pressures or in vacuo, without causing partial decomposition. The analysis of the air-dried salt gave percentages OP ARTS AND SCIENCES. 177 required by a barium salt of dibrommaleic acid containing two mole- cules of water of crvstallization. I. 0.8687 grm. of substance lost, at 120°, 0.0G24 grm. II^O. Of this dried salt, 0.414^ i^rm. gave, by ignition, 0.2341 grm. BaSO,. II. 0.5780 grm. of air-dried salt gave, by ignition, 0.3010 BaSO^. Calculated for BaCiBrjO^ . 2 HjO. Found. I. n. Ba 30.78 30.86 30.63 H„0 8.09 7.07 This salt is hardly more soluble in boiling water than in cold ; in dilute alcohol, it is almost insoluble. The solubility in water was de- termined according to the method of V. Meyer. I. 7.1377 grm. of a solution saturated at 19° gave, on evaporation with H^SO, and ignition, 0.2296 grm. BaSO^. II. 6.9649 grm. of a solution saturated at 19° gave 0.2249 grm. BaSO,. An aqueous solution saturated at 19°, therefore, contains of the anhydrous salt the percentages : — I. II. 5.65 5.67 The silver salt could best be made by the precipitation of a solution of the free acid by argentic nitrate. From dilute solution, it separated in long, flat needles ; from concentrated solutions, it was precipitated in small prisms. It proved to be almost insoluble even in hot water. The dry salt exploded violently on heating, or by percussion. 0.6311 grm. of the salt, dissolved in dilute nitric acid, gave 0.4859 grm. AgBr. Calculated for AgoC4Br204. Found. Ag 44.27 44.22 The lead salt fell as a crystalline precipitate upon the addition of plumbic acetate even to a dilute solution of the free acid. The acid was liberated from the pure barium salt by the addition of normal sulphuric acid, in quantity insufficient for complete precipita- tion; the aqueous solution was allowed to evaporate spontaneously ; and the acid >vas then separated from the excess of barium salt by means of ether free from alcohol. Prepared in this way, the acid formed a VOL. XVI. (n. S. VIII.) 12 178 PROCEEDINGS OF THE AMERICAN ACADEMY mass of indistinct, aggregated needles, extremely soluble in water, ether, or alcohol ; and almost insoluble in boiling chloroform, benzol, ligroin, or carbonic disulphide. From a mixture of ether and chloro- form, it could be crystallized in the form of fine, felted needles. After standing in desiccator, the acid gave on analysis too high a percentage of bromine (I.). It was therefore washed with chloro- form, the excess of chloroform evaporated in a paraffine desiccator according to Liebermann's suggestion ; but the percentage of bromine remained essentially unaltered (II.). I therefore dissolved the acid in hot water, allowed the solution to evaporate spontaneously, and dried by exposure to the air alone, but failed to alter its composition (III.). Subsequently I dissolved the pure anhydride described below in hot water, and found that the acid obtained by spontaneous evapo- ration of this solution when air-dried also contained more bromine than the formula of the acid required (IV.). I. 0.2050 grm. substance gave 0.2860 grm. AgBr. II. 0.2305 grm. substance gave 0.3200 grm. AgBr. III. 0.2150 grm. substance gave 0.3000 grm. AgBr. IV. 0.2500 grm. substance gave 0.3475 grm. AgBr. culate d for CjUjBrjG^. Found. I. n. II r. IV. Br 58.38 59.37 59.08 59.38 59.15 From these experiments it would appear that the acid, even at ordinary temperatures, is partially converted into its anhydride. This change goes on rapidly at temperatures near 100°, so that it is impos- sible to obtain constant melting points. The preparations analyzed melted at 120-125° when warmed with ordinary rapidity. The acid was but slightly volatile with steam, but could be distilled with greatest readiness with the vapor of concentrated hydrobromic acid. From this acid the anhydride could be obtained without difficulty in a pure state, by heating to 120° in a current of dry carbonic dioxide. The sublimation began at 100°, or possibly lower, but became rapid at 115-120°. The anhydride condensed in lustrous, flattened needles, which melted at 114-115°. In cold water it dis- solved but slowly ; in alcohol, ether, benzol, ligroin, chloroform, or carbonic disulphide, it was readily soluble. I. 0.3672 grm. gave 0.2510 grm. CO, and 0.0010 grm. H^O. II. 0.2630 grm. gave 0.3870 grra. Agiir. OF ARTS AND SCIENCES. 179 doulati ed for CjBrjOj. J Found. c 18.75 18.65 II — 0.02 Br 62.50 n. 62.61 The aqueous solution obtained by treating the original product from the action of bromine with cold water, therefore, contained mainly an acid of the composition of dibrommaleic acid. In the mother liquors from the baric dibrommaleate there appeared to be a trace of a more soluble barium salt beside baric bromide ; but its quantity was too small to admit of separation and analysis. The oily residue left undissolved by water gradually solidified upon standing. Cold chloroform dissolved the greater portion of It, leav- ing a small quantity of short, prismatic crystals. Upon evaporation of the chloroform, an oil was left, which gradually solidified in masses of radiated prisms, contaminated with a small quantity of au oily impurity whose nature could not further be determined. After sev- eral crystallizations from alcohol, this substance melted at 55-56°, and v/hen treated with baric hydrate gave the characteristic reactions of mucobromylbromide. It was still further identified by analysis. 0.2280 grm. substance gave 4000 grm. AgBr. Calculated for CiUBrjOj. Found. Br 74.77 74.68 The prismatic crystals, which were sparingly soluble in cold water and chloroform, were recrystallized from hot water, and showed then the characteristic properties of ordinary dibromsuccinic acid. On heat- ing, they remained unaltered till the temperature had risen to over 200° ; at a somewhat higher point, they had completely volatilized. The sublimate condensed in the colder portions of the tube in oil drops, which gradually solidified. The melting point of the solid thus obtained, after pressing with filter paper, was found to be 126°. According to Fittig and Petri, f the sublimate formed under the same conditions from dibromsuccinic acid has the melting point of mono- brommaleic acid (128°). The quantity of dibromsuccinic acid formed in this reaction was quite small. 0.2855 grm. substance gave 0.3880 grm. AgBr. Calculated for C4ll4Br204. Found. 57.97 57.83 t Ann. Chem. u. Pharm., cxcv. 68. 180 PROCEEDINGS OP THE AMERICAN ACADEMY When the original product of the reaction was treated at once with dry chloroform, the greater part was instantly carried into solu- tion ; and the dibromsuccinic acid, together with a small quantity of mucobromic acid, were left undissolved. The filtered chloroform solu- tion, when shaken with a few drops of water, gradually solidified with separating crystals of dibrommaleic acid ; so that the original product must have contained the dibrommaleic acid as anhydride. The two main products of the reaction were, therefore, dibrom- maleic anhydride and mucobromylbromide. The relative weights of these two products were such as to suggest at once the equation : — 2 C.H^Br.Og + Br^ = C.H^Br^O, -f C.HBrgO^ + HBr, when the dibrommaleic acid would readily pass into its anhydride. The weights obtained in successive preparations were, however, found to vary so much that I am inclined to consider the anhydride as the direct product of the reaction, and the mucobromylbromide a second- ary product formed by the action of the hydrobromic acid set free. In either case, the formation of dibromsuccinic acid can hardly be ex- plained without assuming a reducing action of the hydrobromic acid, like that which is normal to hydriodic acid. Although reductions of this sort by the action of hydrobromic acid have seldom been noticed, the conversion of tartaric acid into monobromsuccinic acid by this means, noticed by Kekule* in 18G4, would seem to be perfectly analo- gous. Dibrommaleic Acid of Kekule. In 1864 Kekule f found among the products of the action of bromine and water upon succinic acid an acid, C^H2Br204, to which he gave the name dibrommaleic acid. It formed white, clustered needles, which were extremely soluble in water, alcohol, or ether, and melted at 112° ; at higher temperatures the acid distilled apparently un- changed, and it volatilized readily with steam. For the further characterization of the acid, Kekule made the silver and lead salts. The silver salt could be precipitated from an aqueous solution of the acid, by the addition of argentic nitrate ; and, according to the concen- tration of the solution, it appeared as a granular, crystalline precipi- tate, or in slender, glistening needles. The dry salt exploded vio- lently by heat or percussion. The lead salt was thrown down by the * Ann. Chem. u. Pliarm., cxxx. 30. t Ann. Chem. u. Pnarm., cxxx. 1. OF ARTS AND SCIENCES. 181 addition of plumbic acetate to an aqueous solution of the acid, and when air-dried it was found to contain a molecule of water. Since its discovery by Kekule, the acid prepared in this way has been mentioned but twice, as far as I know ; and these notices con- tain no additional facts which could serve to assist in its identification. Bourgoin * gives its melting point as 110°, and asserts that it distils imaltered. Fittig and Petri,t in their attempts to prepare the tri- bromsuccinic acid, which had been described by Bourgoin, obtained dibromsuccinic acid and a substance crystallizing in hemispherical aggregations, which, from their melting point (112°) and volatility with steam, they recognized as dibrommaleic acid. In 1873 Limpricht and Delbriick J described an acid of the same composition, which they made by the action of bromine and water upon mucobromic acid. They found it difficult of purification ; and, in their study of it, they were to all appearance hampered by lack of material. The acid melted at 108-120°, and by sublimation it was converted into its anhydride, C^BrgOg, which melted at 95-120°. The barium salt they obtained in colorless, tabular crystals, to which they assigned the formula, BaC4Br20^.2H20. The silver salt they found to be insoluble ; but it did not explode either by heat or percussion. They assumed, apparently without hesitation, that this acid was isomeric with that of Kekule, and therefore named it dibromfumaric acid. The acid made by the action of bromine upon mucobromic acid, which I have just described, agreed in most respects closely with the acid described by Kekule ; and yet the higher melting point and the ready formation of the anhydride rendered a further comparison neces- sary in order to settle the question of identity. In the preparation of dibrommaleic acid, I followed in general the method of Kekule ; but, since this was to be the main product of the reaction, I was obliged to use a greater proportion of bromine and water, in order to get any considerable yield. I obtained good results by using to one part of succinic acid two of water and four of bromine, and heating twenty hours at 140°. The mother liquors from which the greater part of the dibromsuccinic acid had been separated were distilled, the distillate neutralized with baric carbonate, and the baric dibrommaleate precipitated from the filtered * Bull. Soc. Chim. [2], xxi. 404; xxii. 443. t Ann. Chem. u. Pliarra., oxcv. 76. } Ann. Chem. u. Pbarm., clxv. 294. 182 PROCEEDINGS OP THE AMERICAN ACADEMY solution. After several precipitations from aqueous solutiou by alco- hol, it was crystallized from water by evaporation, and dried by exposure to the air. The salt could not be distinguislied in outward appearance from that made from mucobromic acid. I. 2.4931 grm. of air-dried salt lost in weight, at 125-130°, 0.2136 grm. 0.7670 grm. of this dried salt gave, on ignition with H^SO,, 0.4398 grm. BaSO^. 11. 0.5899 grm. air-dried salt gave 0.3102 grm. BaSO^. ilated for CiBrj04Ba.2H,0. Found. I. II. Ba 30.78 30.79 30.91 HgO 8.09 8.15 The solubility of this salt was determined according to the method of v. Meyer. 8.9481 grm. of a solution saturated at 20° gave 0.2912 grm. BaSO,. The aqueous solution saturated at 20°, therefore, contains 5.71 per cent of the anhydrous salt. From this barium salt, the free acid was made in the manner above described. In its behavior towards solvents, it resembled perfectly the acid made from mucobromic acid, and it melted between 120° and 123°. This acid I did not analyze; but the analyses published by Kekule show too high a percentage of bromine, and in this respect do not differ essentially from those 1 have given above. Calculated for C^H^BrjO^. Found by Kekule. I. II. Br. 58.38 58.98 59.08 By heating this acid in a stream of carbonic dioxide, the anhydride could readily be made in appearance and behavior perfectly identical with the compound already described, and melting at 114°-115°. I. 0.4160 grm. substance gave 0.2860 gr. CO.. and 0.0032 grm. 11,0. II. 0.2840 grm. substance gave 0.4165 grm. AgBr. Calculated for C^BrjOj. Found. I. U. C 18.75 18.75 H — 0.10 Br 62.50 62.34 OF ARTS AND SCIENCES. 183 The identity of the dibrommaleic acids made by the action of dry bromine upon mucobromic acid and aqueous bromine upon succinic is thus sufliciently established. They each give an anhydride melt- ing at 114—115°; their barium salts have the same composition, BaC^Br.,0^.2II.,0 ; and the solubility of these two salts in water is the same, the saturated aqueous solution containing in one case 5.66 per cent of the anhydrous salt at 19°, in the other 5.71 per cent at 20°. Although I have several times tried the action of bromine and water upon mucobromic acid, according to the method of Limpricht and Delbriick, I have not as yet submitted the product obtained in this way to any very extended investigation. In all qualitative reac- tions it is identical with the acid I have described ; and, considering the mode of its formation, one can hardly doubt its identity. More- over, with regard to the slight differences which would seem to have induced Limpricht and Delbriick to consider their acid isomeric with Kekule's, I have been unable to confirm their observations. The melting point (95-120°) given by them for the anhydride does not give confidence in the purity of their material. The higher percent- age of barium (31.9) * which they found in their barium salt would be in no way at variance with my results, even if its purity were granted, since the material they analyzed had been dried in vacuo (over sulphuric acid ?), and my own experiments have shown that it slowly effloresces under these conditions. Although the foregoing facts seemed to warrant the conclusion that the dibrommaleic acid of Kekule belonged to the maleic series, inasmuch as the anhydride was the direct product of the reaction of bromine upon mucobromic acid, still I thought it advisable to prove this directly, more especially since all analogy pointed to the forma- tion of a derivative of fumaric acid under the conditions essential to its preparation from succinic acid. I therefore dissolved in water the pure anhydride prepared from succinic acid, neutralized the solution with baric carbonate, precipitated the barium salt by alcohol, and recrystallized it from water. This salt proved to be identical with that which was obtained directly from the acid. 0.7525 grm. of the air-dried salt lost on heating to about 120° 0.0581 grm. ; 0.6933 grm. of this dried salt gave 0.3922 grm. BaSO^. * Limpricht and Delbriick erroneously calculated tlic percentage of barium in the salt BaC4Br204.2H20 as 31.9 per cent, instead of 30.78, and therefore gave the same formula. 184 PROCEEDINGS OP THE AMERICAN ACADEMY Calculated for BaC4Br204 . 2H2O. Found. Ba 30.78 30.69 H2O 8.09 7.72 The solubility was also determined by the method of V. Meyer. 7.6833 grm. of the solution saturated at 19°.5 gave, on evaporation with H2SO4 and ignition, 0.2446 grm. BaSO^. An aqueous solution saturated at 19°. 5 contained therefore 5.58 per cent of the anhydrous salt. This proves that dibrommaleic acid may be carried unchanged through its anhydride, and that it consequently belongs to the maleic series, unless, indeed, its behavior is radically changed by the com- plete replacement of its hydrogen by bromine. That such is not the case lias recently been shown by Bandrowski,* who has discovered an acid of the same composition, which is undoubtedly dibromfumai'ic acid. This acid melts at 219-220°, and by distillation is converted into dibrommaleic acid. Mucohromic Acid with Oxidizing Agents. The close connection between mucobromic acid and dibrommaleic, as shown by its behavior when heated with bromine, naturally sug- gested the direct conversion of the one into the other by oxidation. An aqueous solution of chromic acid does not act upon mucobromic acid at ordinary temperatures, even after standing for weeks. On warming, carbonic acid is freely given oflf, and at the same time a sharp, acrolein-like odor is noticed. If one atom of oxygen is employed for every molecule of mucobromic acid, a portion of the mucobromic acid seems to be completely destroyed, while nearly one half of it remains unaltered, and may be extracted with ether after the reaction is completed. When two atoms of oxygen are taken, but little muco- bromic acid escapes oxidation ; but I have been unable to isolate well-marked products of the reaction, in any considerable quantities. When the solution is distilled, the substance possessing the sharp, pungent odor passes over with the steam. It is quite soluble in water, although not in all proportions, and its aqueous solution reduces silver energetically from the oxide even in the cold. Although this is the most striking product of the oxidation, it is formed in such small quantities that I have as yet been unable to study it further. After * Berichte der dcutsch. chem. Gesellscli., xii. 2213. OP ARTS AND SCIENCES. 185 this volatile product has been distilled off, but a trace of organic acid can be extracted from the retort residue by ether. This acid is chiefly mucobromic; but with it I have found dibrommaleic acid in quantity barely sufficient for the recognition of its barium salt under the microscope when precipitated from aqueous solution by alcohol. The oxidation with nitric acid gives somewhat better results. When mucobromic acid is boiled with ten times its weight of nitric acid of sp. gr. 1.20, ca'rbonic dioxide is slowly given off, the escaping gas ren- ders a solution of argentic nitrate turbid, and yet, if the heat is con- tinued for several hours, a considerable portion of the mucobromic acid is found to be converted into dibrommaleic acid. In one experi- ment I obtained, after several hours' boiling, from 5 grm. of muco- bromic acid 2.3 grm. of baric dibrommaleate and 1.5 grm. of unal- tered mucobromic acid. This corresponds to nearly forty per cent of the theoretical yield of dibrommaleic acid from the mucobromic acid which entered into the reaction. Stronger nitric acid oxidizes more rapidly, but the yield of dibrommaleic acid is smaller ; if much more dilute acid is used, the mucobromic acid is hardly altered. Precisely the same effect is produced by long boiling with bromine water, carbonic dioxide being evolved as before, and the yield of dibrommaleic acid remaining essentially the same. The identity of the acid made by bromine water was established by the analysis of the barium salt. This salt was precipitated several times from aqueous solution by alcohol, recrystallized from water, and contained then the required percentage of barium. 0.5493 grm. of the air-dried salt gave 0.2887 grm. BaSO^. Calculated for BaC4Br204.2H20. , Found. Ba 30.78 30.90 Limpricht found that mucobromic acid was the only product when pyromucic acid suspended in water was treated with an excess of bromine at ordinary pressures. Since mucobromic acid is itself con- verted into dibrommaleic acid by boiling it with bromine water, it fol- lows that the latter acid must of necessity be formed in the preparation of mucobromic acid. For its detection, the mother liquors, from which the mucobromic acid had been separated as completely as pos- sible, were distilled. The distillate, consisting chiefly of concentrated hydrobromic acid (b. pt. 126°) was partially neutralized with potassic carbonate, and thoroughly shaken out with ether. The residue left on evaporation of the ether was taken up with water, and the acid solution saturated with baric carbonate. Alcohol precipitated from 186 PROCEEDINGS OF THE AMERICAN ACADEMY the filtered solution baric dibrommaleate in characteristic form. For analysis, the salt was recrystallized from water, and dried by exposure to the air. . 0.4709 grm. of this salt gave 0.2516 grm. BaSO^. Calculated for BaC4Brj04.2H,0. Found. Ba 30.78 31.41 Since the percentage of barium was found to be too high, for further identification the acid was set free, and converted into the anhydride by sublimation. This crystallized in the characteristic flattened needles, which melted at 114°. The quantity of dibrommaleic acid formed in the ordinary preparation of mucobromic acid is very incon- siderable, and amounted in one case to about one per cent of the pyromucic acid emjjloyed. The quantity must, however, of necessity be very variable. The oxidation of mucobromic acid by means of argentic oxide was investigated by Schmelz and Beilstein. They gave to the chief prod- uct of the reaction the formula, AgjC^HgBrgO. ; but it is evident from an inspection of their analyses that they had in their hands the silver salt of dibrommaleic acid in a nearly pure condition. Calculated for AggC^HjBrjOj. for AgjCiBrjOi- C 11.51 9.84 I. 10.07 Found by Schmelz and Beilstein. II. III. IV. V. VI. 10.64 11.30 H 0.27 — 0.64 0.37 0.32 Br 32.87 32.78 32.47 Ag 44.38 44.27 44.25 44.26 With this close agreement between the observed and calculated per- centages, I did not consider it worth while to analyze, myself, this silver salt. Still it was evidently necessary to prepare from it the barium salt in order to compare this with the product I had already studied. Since argentic bromide is readily formed when tlie silver salt of mucobromic acid is heated with water, I added at once an excess of argentic oxide to a warm solution of mucobromic acid, and heated it quickly to the boiling point. The oxidation seemed to be more neatly accomplished in this way than by the gradual addition of the argentic oxide, although even then there was formed a considerable quantity of argentic broniide. After the action had ceased, the whole was acidified with hydrochloric acid, and the filtered solution shaken out witli ether. The acid left upon evaporation of the ether was then taken up with water, neutralized with baric carbonate, and the barium salt purified as OF ARTS AND SCIENCES. 187 before. An analysis of the air-dried salt, and a determination of its solubility, proved that the acid was identical with that made by the action of bromine upon succinic or mucobromic acid. 0.5225 grm. of the air-dried salt gave 0.2741 grm. BaSO^. Calculated for BaC«Br,04.2II,0. Found. Ba 30.78 30.84 9.2092 grm. of an aqueous solution saturated at 18°. 5 according to the method of V. Meyer, gave on evaporation with H^SO^ and ignition 0.2944 grm. BaSO,. According to this determination, an aqueous solution saturated at 18°. 5 contains 5.61 per cent of the anhydrous salt. This oxidation of mucobromic acid by means of argentic oxide into dibrommaleic acid, C,H2BrA + 0 = C,H,BrA, would seem to show conclusively that it is the half aldehyde of the dibasic dibrommaleic acid. Decomposition by Heat. If mucobromic acid is quickly heated, the greater part of it distila unchanged ; but, if the temperature is so regulated that it can distil but slowly, a great part of it suffers decomposition. The reaction which it undergoes I have, as yet, studied only so far as to prove that dibrommaleic acid is one of the chief products. If the acid is mixed with sand and slowly distilled, streams of hydrobromic acid and car- bonic dioxide are given off, and a colorless oil passes over, which, on standing, partially solidifies. On the addition of water, the solid por- tion dissolves, leaving an oil which is volatile with steam, and is not wholly insoluble in water. Its aqueous solution reduces argentic oxide, and possesses an intolerably sharp, pungent odor. In the inves- tigation of this oil, I have not yet obtained definite results. The aqueous solution contained dibrommaleic acid, which was identified by an analysis of its barium salt. The solution of the barium salt obtained, at first was highly colored, and from it pure material could be made only by repeated precipitation from aqueous solution with the smallest possible quantity of alcohol. In this way, a per- fectly colorless salt was made, and it was then recrystallized from water. 0.6652 grm. of the air-dried salt gave 0.3498 grm. BaSO^. 188 PROCEEDINGS OF THE AMERICAN ACADEMY Calculated for BaCiBrjOi . 2HsO. Found. Ba 30.78 30.91 The amount of dibrommaleic acid tlius formed is about 1 5 per cent of the mucobromic acid taken, and 30 per cent of the total weight of the distillate. Action of Baric Hydrate. The action of baric hydrate upon mucobromic acid was first studied by Schmelz and Beilstein, The results they obtained were extremely interesting, but needed extension in several directions. More espe- cially inviting was the muconic acid which they considered formed in the reaction, and to which they gave the formula HjC^Og. In begin- ning this investigation, Mr. O. R. Jackson and I thought it best at the outset to test experimentally the truth of the equation, 2CJl2^r,Os + HgO = C.HgOg + C^IIBr + 200^ + 3HBr which Schmelz and Beilstein had given as an expression of the reac- tion, and at the same time to determine the conditions most favorable to the formation of baric muconate. The qualitative results we found to be precisely in accordance with their statements, and it was only necessary to study the reaction quantitatively. A weighed quan- tity of mucobromic acid was introduced into a flask fitted with reverse cooler, and dissolved in a little warm water. The upper end of the cooler was then connected with a series of wash-bottles which were filled with an ammoniacal solution of cu-prous oxide, made by reduc- ing an ammoniacal solution of pure cupric sulphate with metallic copper. The air in the apparatus was then displaced by pure hydro- gen, a measured quantity of a standard solution of baric hydrate introduced into the flask, and heat applied. When the action appeared to be finished, we determined the weight of the baric carbonate which had been formed in the reaction, the weight of tlie baric carbonate which could be precipitated from the filtered solution by carbonic dioxide, and the weiglit of the baric muconate left on evaporation after washing out the baric bromide with cold water. In order to deter- mine the amount of bromacetylen, we filtered off the voliuninous pre- cipitate of acetylen copper which had separated in the wash-bottles, acidified the filtrate, and precipitated the bromine with argentic nitrate. The results which we obtained are given in the following table ; in each case 2 grm. of mucobromic acid were taken. OP ARTS AND SCTENCES. 189 No Ba0.jHj taken. BnCOj by COj. Br. BaOOi fonncd. "Dnric muoonute." I. 1.094 0.372 0.57 V. VI. 2.971 2.971 trace trace 0.293 0.333 1.07 1.05 0.40 0.55 II. III. IV. 5.988 5.942 6.942 3.52 3.25 3.40 0.135 0.146 0.128 0.54 0.50 0.53 0.85 0.87 0.97 VII. VIII. 8.044 8.044 5.75 5.90 0.135 0.112 0.47 0.35 0.95 0.90 In order to compare these results more conveniently, we calculated from them the corresponding molecular ratios. The following table contains the number of molecules of baric hy- drate which we used in the various experiments for the decomposition of one molecule of mucobromic acid, the number of molecules of baric hydrate which actually entered into the reaction, and the fractions o.f a molecule of bromacetylen, carbonic dioxide, and baric muconate which were formed in each case. In accordance with the results which we afterwards obtained, the muconate is here calculated as baric malonate. No. Baric hydrate. Bromajoetylen. Carbonic dioxide. " Baric muconate." taken. used. I. V. VI. II. III. IV. VII. vin. 1.50 2.24 2.24 4.. 51 4.48 4.48 6.07 6.07 1.50 2.24 2.24 2.21 2.35 2.25 2.30 2.17 0.60 0.47 0.54 0.22 0.24 0.21 0.22 0.18 0.37 0.70 0.69 0.35 0.33 0.35 0.31 0.23 0.20 0.28 0.43 0.44 0.49 0.48 0.45 These results were sufficient to show that, in the decomposition by baric hydrate, we had to deal with at least two independent reactions ; that one of these reactions led to the formation of carbonic dioxide and bromacetylen, while the second had for its chief product the sparingly soluble barium salt, — the baric muconate of Schmelz and Beilstein. Moreover, it was evident that, in order to obtain the best yield of the latter salt, a large excess of baric hydrate should be em- ployed. 190 PROCEEDINGS OF THE AMERICAN ACADEMY In the preparation of the sparingly soluble barium salt, we used five or six molecules of baric hydrate to one of mucobromic acid. When the reaction appeared at an end, we precipitated the excess of baric hydrate with carbonic dioxide, and evaporated the filtered solu- tion to a small volume. When this solution was slowly evaporated upon the water bath, we found, in accordance with the statements of Schmelz and Beilstein, that the salt separated in thin crusts which had no visible crystalline structure. If, however, the solution was boiled down rapidly over the lamp, at a certain point the salt suddenly separated in fine, silky needles, which were still further increased as the solution cooled. These crystals were well washed with cold water, redissolved in boiling water, and precipitated with plumbic acetate. In this way a granular lead salt was thrown down, which, when examined under the microscope, was seen to consist of well- formed rhombic plates. For analysis, the salt was dried at 110°. I. 0.5939 grm. substance gave 0.2434 grm. COj and 0.0470 grm. of H,0. II. 0.3459 grm. gave, by ignition with H^SO^, 0.3402 grm. PbSO^. Calculated for PbCiOj. Calculated for PbCsHjO^. Found. I. n. C 15.84 11.65 11.18 H 0.65 0.88 Pb 68.32 66.99 67.22 It will be seen that the percentages found correspond closely with those required by plumbic malonate, and differ widely from those re- quired by the formula of Schmelz and Beilstein. The barium salt also agrees well with the description of baric malonate given by Heintzel * and Finkelstein.f The analyses we have made of the salt have given us too high a percentage of barium, although materially lower than that found by Schmelz and Beilstein. I. 0.5212 grm. of the salt, dried at 120°, gave 0.5214 grm. BaSO,. II. 0.3455 grm. of the salt, dried at 100°, gave 0.3159 grm. BaSO,. III. 0.2139 grm. of the salt, dried at 100°, gave 0.1956 grm. BaSO<. Calculated for BaC3Hj04.H,0. Found. I. 11. III. Schmelz and Beilstein Ba 53.33 54.70 53.75 53.73 56.32 * Ann. Chem. u. Pliarm., cxxix. 133. t Ann. Clicm. u. riarm., cxxxiii. 343. OF ARTS AND SCIENCES. 191 The result of Schmelz and Beilstein is here calculated for the hydrous salt. They fouud that the salt, when dried at 100°, lost 4.15 per cent of water at 200°, and contained then 58.6 per cent of barium. From the lead salt we made the free acid by means of hydric sul- phide, and found it very soluble in water or alcohol, less freely in ether. From aqueous solution it crystallized in irregular rhombic plates, occasionally in more compact prismatic forms. After several recrys- tallizations from water, and thorough drying over sulphuric acid, these crystals melted at 131.5-132°. This agrees with the melting point of malonic acid, as given by Heintzel, although it is somewhat lower than that more recently given by Pinner.* A combustion left no doubt of the identity and the purity of the acid. 0.3849 grm. substance gave 0.4871 grm. CO2 and 0.1395 grm. IlgO. Calculated for C.<,Il404. Found. C 34.61 34.51 H 3.85 4.03 The quantity of baric malonate which we obtained from muco- bromic acid agreed with the results of our experiments upon a smaller scale, and amounted to nearly 50 per cent of the theoretical yield. The mother liquors contained, beside baric bromide, baric formiate, whose presence could readily be established by qualitative tests. Although the gaseous product formed by this decomposition with baric hydrate agreed closely in its qualitative reactions with brom- acetylen, it seemed to us advisable to prove its identity a little more rigorously. We therefore passed the gas, diluted with hydrogen, into bromine and water. The crystalline solid which resulted we washed with dilute sodic hydrate, then with water, and finally recrystallized it from alcohol. Thus purified, it formed long, brilliant prisms, which melted at 54°. The melting point of pentabromethan is given by Lennox t as 48°; by Reboul, $ 48-50° ; by Limpricht and Delbriick, § 50-52° ; and by Boui-goin, || 56-57°. The j^rismatic angle could readily be determined, and the measurement of several individuals * Berichte der deutsch. cliem. Gesellsch., viii. 965. t Lond. R. Soc. Proc, xi. 257; Ann. Chem. u. Pliarm., cxxii. 122. t C. R., liv. 1229; Ann. Chem. u. Pharm., cxxiv. 267; Bull. Soc. Chim., 1862, 75. § Ann. Cliem. u. Pharm., clxv. 297. II Ann. Chim. Phys. [6], iv. 423; Bull. Soc. Chim. [2], xxiii. 175, 257. 192 FSOCEEDINGS OF THE aXEP.ICaN ACADEMY gave as its mean value lO-t" 17. Reboul gives the same angle in crvsials of pentabromethan as 104r 20'. and Bourgoin as 104" 16 . The idendtr of the substance was still further established by analysis* 0.11-51 grm. substance gave 0.2547 grm. AgBr. Caknjased Sir CMBr^. Fonni. Br 9il2 94.17 After we had proved that malonic acid was one of the final products of the decomposition of mucobromic acid when boiled with an excess of baric hydrate, we attempted, by various modifications of the mode of decomposition, to isolate intermediate products, which might give us infi^rmation concerning the nature of the reaction. After many unsuccessful experiments, we foimd that such products resulted from the action of alkalies at ordinary temperatures, and they were most conveniently studied when baric hydrate was employed. Baric Dibromacn/late. Ba(CjH Br^O^\. If mucobromic acid is gradu- ally addei to a solution of baric hydrate containing a large excess of baric hydrate in suspension, it dissolves readily, and the crystals of baric hydrate at the same time gradually disappear. After a while a beautifully crystalline barium salt begins to separate, the amount of which increases rapidly as the acid is added. In order to prepare this salt, we found it best to add the mucobromic acid until one mole- cule had been used for every one and a half molecules of baric hydrate. At first we used two parts of crystallized baric hydrate and four of water to one part of mucobromic acid, but subsequently we re- duced the amount of water one half. After the necessary amount of mucobromic acid had been added in small portions, care being taken to prevent any elevation of temperature, the whole was allowed to stand for a short time, and the crystals which had separated were then filtered off on the pump. These were washed with a little cold warer. exposed to carbonic dioxide imtil neutral in their reaction, and then recrystallized from water or diluted alcohoL From alcohoL the salt crystallized in pearly rhombic plates : from water, in irregular leafy forms, or, on slow evaporation, in massive aggregates of rhombic plates. When dried by exposure to the air, they lost nothing over sulphuric acid or when heated to 80^. At 100^ they slowly lost in weight. The air-dried salt gave on analysis the percentages required by the barium salt o£ a dibromacrylic acid. OF ARTS AND SCIENCES. 193 I. 1.0621 grm. of the salt gave 0.4745 grm. CO., and 0.0780 grm. H.,0. II. 1.0363 grm. of the salt gave 0.4609 grra. CO2 and 0.0743 grm. H,0. III. 0.6187 grm. gave, on ignition with H^SO^, 0.2415 grm. BaSO^ IV. 0.6180 grm. gave 0.2434 grm. BaSO^.' V. 0.5785 grra. gave 0.2269 grm. BaSO^. VI. 0.3522 grm. gave 0.1381 grm. BaSO^. Calculated for Ba(C,HBrjOj)2. Found. I. n. m. rv. V. YL C 12.10 12.19 12.14 H 0.34 0.82 0.80 Ba 23.03 22.95 23.15 23.05 23.05 Argentic Dihromacrylate, AgCgHBr,©.,. From the barium salt, or, better, from a solution of the free acid, the silver salt was made by the addition of argentic nitrate. It is precipitated in the form of fine, felted needles, even from a dilute solution of the acid; it may be re- crystallized from hot water without any essential decomposition, and forms then long, flattened needles. The salt was dried over sulphuric acid for analysis. I. 0.9755 grm. substance gave 0.3890 grm. of CO., and 0.0432 grm. of H,0. n. 0.3200 grm. substance gave, by the method of Carius, 0.3545 grm. AgBr. III. 0.7148 grm. substance, precipitated with. HBr, gave 0.4005 grm. AgBr. IV. 0.3668 grm. gave, with HBr, 0.2056 grm. AgBr. IV. 32.20 Plumbic Dihromacrylate^ Pb(C3HBr.^O.,)2. The lead salt is precipi- tated in pearly rhombic scales by the addition of plumbic acetate to a solution of the free acid. It is readily soluble in hot water, sparingly in cold. "When dried over sulphuric acid in vacuo, it gave : — VOL. XVI. (n. s. viii.) 18 lat€d for AgCsHBrsOj. C 10.69 I. 10.87 Found. n. in. H 0.30 0.49 Br 47.47 47.14 Ag 32.05 32.1S c 10.82 H 0.30 Pb 31.13 194 PROCEEDINGS OF THE AMERICAN ACADEMY I. 0.3232 grm. substance gave 0.1289 grm. COg and 0.0230 grm. H,0. II. 0.4060 grm. gave 0.1858 grm. PbSO^. III. 0.4908 grm. gave 0.2230 grm. PbSO,. Calculated for PbCCjHBrjOj),. . Found. I. n. in. 10.86 0.79 31.27 31.05 Calcic Dlbromacrylate, Ca(C3HBr20^)2.3H20. On neutralizing a so- lution of the acid with calcic carbonate, and concentrating the solution on the water bath, the calcium salt was obtained in clusters of radiat- ing needles, tolerably soluble even in cold water. The salt gradually effloresced over sulphuric acid, and lost its crystal water completely at 80-85°. 0.7342 grm. of the air-dried salt lost, at 80-85°, 0.0695 grm. of HjO. Calculated for Ca-iC^WRv^O^)^ . SHjO. Found. H^O 9.78 9.47 0.4951 grm. of the salt, dried at 80-85°, gave, on ignition with HjSO^, 0.1354 grm. CaSO^. Calculated for Ca(C3nBr202). Found. Ca 8.03 8.04 Potassic Dibromacrylate, KCgHBr^Og. The acid neutralized with potassic carbonate and evaporated gave, on cooling, crystals of the potassium salt. From neutral solutions it crystallizes in transparent, six-sided, clustered plates. If but a small amount of free acid is present, it crystallizes in fine, felted needles. Both forms are anhy- drous, and do not lose in weight at 80°. 0.5506 grm. gave, on ignition with HgSO^, 0.1792 grm. K2S0^. Calculated for KCaHBrjOj. Found. K 14.58 14.61 An acid salt much less soluble in water may be made by adding acid to a solution of the potassium salt. It crystallizes in long needles, which are aniiydrous. The salt is not particuLarly stable, and the excess of acid may be washed out with ether. The salt was dried by exposure to the air, after several recrystallizations from hot water. I OP ARTS AND SCIENCES. 195 I. 0.61 IG grm. substance gave, on ignition with HgSO^, 0.1151 grm. 11. 0.o3*Jo grm. of substance gave 0.0959 grm. K._,SO^. Calculated for KCallUrjO, . CsUaBrjO,. Found I. n. K 7.85 8.45 7.98 Dihromacrylic Acid. From the pure barium salt we "set free the acid by the addition of liydrochloric acid, and extracted it from the solution witli ether. The ether left, upon evaporation, a wliite, crys- talline acid, which was very soluble in alcohol, ether, or chloroform, and but sparingly soluble in benzol, carbonic disulphide, or ligroin. Under water, it melted at about 20°, dissolved in every proportion on heating, and was but slowly volatilized with steam. The acid, when melted under water, could be made to crystallize either by cooling with ice or by the addition of a mineral acid. After recrystallization from benzol, it melted at 83-84°, and this melting point we were unable to raise by further recrystallization from this or other solvents. Although our analyses left no doubt of the formula of the substance, they showed that it was still impure. I. 1.3074 grm. substance gave 0.7692 grm. CO. and 0,1121 grm. 11,0. II. 0.9833 grm. substance gave 0.5797 grm. COg and 0.0877 grm. H,0. III. 0.2042 grm. gave 0.3366 grm. AgBr. IV. 0.2447 grm. gave 0.4044 grm. AgBr. V. 0.2083 grm. gave 0.3453 grm. AgBr. VI. 0.2005 grm. gave 0.3309 grm. AgBr. VII. 0.2132 grm. gave 0.3517 grm. AgBr. V. VI. TO. 70.53 70.23 70.20 Our results had sufficiently established the fiict that a dibromacrylic acid was formed from mucobromic acid by the action of baric hydrate in the cold, but a more extended investigation of it was evidently needed to determine the nature of the impurity which was so difficult of removal. Since Wallach and Reincke* had shortly before an- * Beridite der deutsch. cliem. Gesellscli. x. 2128. Calculated for CJl^rfi^. I. C 15.65 16.04 IT. 16.08 in. Found. IV. H 0.87 0.95 0.99 Br 69.56 70.15 70.33 196 PROCEEDINGS OP THE AMERICAN ACADEMY nounced tliat they were engaged in making from bromalid a dibrom- acrylic acid, which we thought probable, although upon very insuffi- cient grounds, would prove to be identical with ours, we felt compelled for the moment to suspend our investigations. The other portions of the re^earch afterward claimed so much attention that no study of the acid has yet been made sufficiently extended to establish the condi- tions essential to its preparation in a pure state. It has been found, however, that an acid melting at 84-85° contains but a slight excess of bromine (I.), and that the pure acid (II.) melts at 85-86°. I. 0.2204 grm. substance gave 0.3621 grm. AgBr. XL 0.2650 grm. substance gave 0.4336 grm. AgBr. Calculated for CaHjBrjOj. Found.- I. n. Br 69.56 69.90 69.65 For purposes of comparison, certain determinations of the solubility of the acid and its barium salt may find a place here, although they were not made with absolutely pure material, and are therefore sub- ject to revision. In determining the solubility of the acid, the satu- rated solution, made according to the method of V. Meyer, was neutralized with baric carbonate, and the dissolved barium determined by precipitation with sulphuric acid. I. 14.7798 grm. of a solution, saturated at 20°, gave 0.4488 grm. BaSO,. II. 8.6788 grm. of a solution, saturated at 20°, gave 0.2630 grm. BaSO,. According to these determinations, an aqueous solution of the acid, saturated at 20°, contains the percentages : — I. n. 5.98 5.98 8.4992 grm. of a solution of the barium salt, saturated at 20°, gave, on evaporation with HgSO^ and ignition, 0.1912 grm. BaSO^. The aqueous solution of baric dibromacrylate, saturated at 20°, therefore contains 5.74 per cent of the dry salt. In studying the behavior of this dibromacrylic acid towards reagents, we have been able to use only the product melting at 83-84°, which may easily be obtained in any quantity desired. When boiled with an excess of baric hydrate, the acid is completely decomposed, baric carbonate is precipitated, bromacetylen set free, and at the same time baric malonate is formed in abundance. For complete identification, OF ARTS AND SCIENCES. 197 the baric malonate was converted into the lead salt, and the latter analyzed. 0.5179 gnu. of the salt, dried at 110°, gave, on ignition with HgSO^, 0.5062 grm. PbSO,. Calculated for PbCsHjO^. Found. 66.99 66.79 The amount of baric malonate formed in this decomposition with an excess of baric hydrate was found to be forty-nine per cent of the theoretical yield as the mean of two determinations. The behavior of the acid towards hydrobromic acid was studied by Mr. C. F. Mabery. It is not altered by ordinary concentrated hydro- bromic acid (b. pt. 126°), nor is it affected in the cold by an acid saturated at 0° ; but it forms an addition-product when heated with it for several hours at 100°. The reaction is by no means neat, and a large portion of the substance is charred. The tribrompropionic acid which is thus formed differs essentially in its melting-point (116- 117°) and other physical properties from the acid melting at 93° men- tioned by Linnemann and Penl,* and recently more fully described by Michael and Norton ; f and also from the acid melting at 53°, which was obtained by Fittig and Petri,t by the action of hydro- bromic acid upon their dibromacrylic acid. It is sparingly soluble in cold water, readily in hot, and may be crystallized without difficulty from hot water. It is readily soluble in alcohol or ether, somewhat less soluble in chloroform. From water it crystallizes in pearly scales, which melt at 116-117°. Argentic nitrate precipitates from an aqueous solution of the acid, the silver salt in clustered rhombic plates. 0.1892 grm. of the acid gave 0.3453 grm. AgBr. Calculated for CgHjErgOa. Found. Br 77.16 77.64 If one molecule of bromine is added to dibromacrylic acid dissolved in chloroform, the color of the bromine gradually disappears, and after the lapse of some time tetrabrompropionic acid separates in large, well-formed crystals, which melt at 125°. This acid is at present under investigation in this laboratory. * Berichte der deutsch. chem, Gesellsch., viii. 1098. t Amer. Chem. Journ., ii. 18. J Ann. Chem. u. Pharm., cxcv. 73. 198 PROCEEDINGS OF THE AMERICAN ACADEMY One well-marked product of the decomposition of mucobromic acid by cold baric hydrate had been shown to be baric dibromacrylate ; it only remained to study the more soluble products of the reaction. In continuing the investigation with Mr. O. R. Jackson, the filtrate from the crystals of baric dibromacrylate was treated with carbonic dioxide to remove the excess of baric hydrate, filtered from the baric carbon- ate, and the filtrate evaporated at a gentle heat (40-50°). In the course of this evaporation, a certain amount of baric dibromacrylate crystallized out, which was removed from time to time. When the liquid had been reduced to about one third its original volume, it was precipitated by the addition of two volumes of alcohol. The bulky crystalline precipitate thus thrown down proved upon qualitative ex- amination to consist chiefly of baric formiate. When purified by repeated precipitation from aqueous solution by alcohol and recrystal- lization from water, it showed the characteristic form of baric formiate. 0.3964 grm. substance gave, on ignition with H^SO^, 0.4054 grm. BaSO,. Calculated for Ba (CHOjjj. Found. Ba 60.36 60.13 The lead salt made from the barium salt crystallized in the charac- teristic form of plumbic formiate, and gave on analysis the required percentage of lead. 0.4149 grm, of the salt gave, on ignition with HgSO^, 0.4221 grm. PbSO,. Calculated for Pb (CHOj),. Found. Pb 69.69 69.50 In the alcoholic filtrate from the baric formiate, we were able to find, beside baric bromide, only a crystallizable barium salt, well marked by its qualitative reactions, but so unstable that we were not able to effect its purification. The behavior of this salt, and the analyses which we made of it in an impure state, led us to the conclusion that it was the barium salt of bronipropiolic acid, formed by subtraction of hydro- bromic acid from the dibromacrylic ; and this view was subsequently proved to be correct by a study of the addition products which the corresponding acid formed with the halogens and the haloid acids. Since all our attempts to isolate a pure salt from a solution con- taining baric bromide had proved unsuccessful, we attempted to take advantage of a remarkably stable molecular compound which the corresponding acid forms with dibromacrylic acid. This compound OP ARTS AND SCIENCES. 199 may readily be made by acidifying the baric hydrate sohition of muco- bromic acid, without removing the separated baric dibromacrylate, and extracting the solution with ether. Tlie same compound, although in smaller quantity, may also be obtained, after that portion of the barium salt which separates spontaneously is removed. From dibrom- acrylic acid it may be made by the action of baric hydrate in the cold. For its preparation we usually have employed a solution of potassic, instead of baric, hydrate. The proportions which we have found most advantageous are 70 grm. of potassic hydrate and 400 c.c. of water to 100 grm. of mucobromic acid. Care must be taken in adding the muco- bromic acid, and also in the subsequent acidification with hydrochloric acid, that no sensible elevation of temperature takes place. When the solution is partially acidified, the acid potassium salt of dibroraacrylic acid usually separates in abundance, but dissolves ujDon further addi- tion of acid. The solution is then thoroughly extracted with ether; and this leaves on distillation a liquid residue, which, on cooling, gradually solidifies in large, well-formed, monocliiiic (?) prisms. These are readily soluble in water, alcohol, ether, or chloroform, and may be purified by crystallization from hot benzol, or more conveniently by melting with a little water. Thus purified, the substance melts at 104—105° ; and this melting point is not altered by repeated recrystal- lizations from various solvents. I. 0.9023 grm. substance gave 0.6440 grm. CO^ and 0.0850 grm. H,0. II. 0.4403 grm. substance gave 0.3157 grm. COj and 0.0433 grm. III. 0.2263 grm. substance gave 0.3386 grm. AgBr. IV. 0.2241 grm. substance gave 0.3321 grm. AgBr. V. 0.2092 grm. substance gave 0.3139 grm. AgBr. IV V. 63.66 63.03 63.84 Although the percentages we have found show a considerable varia- tion from those calculated for equal molecules of dibroraacrylic and brompropiolic acids, they agree better with this than with any other formula equally simple ; and, moreover, the qualitative behavior of the substance is such as to render this formula tolerably certain. Its Calculated for CijHaBrsOt. Found. I. ir. III. c 19.00 19.43 19.54 H Br 0.79 63.33 1.05 1.09 63.66 200 PROCEEDINGS OF THE AMERICAN ACADEMY aqueous solution gives, on the addition of plumbic acetate, an imme- diate crystalline precipitate of plumbic dibromacrylate. 0.3560 grm. gave, on ignition with H^SO^, 0.1628 grm. PbSO^. Calculated for PbCCsHBxjOj)!. Found. Pb 31.13 31.25 So also if it is neutralized with baric carbonate, the solution gives, on spontaneous evaporation, crystals of baric dibromacrylate, while in solution remains a much more soluble salt, with all the characters of baric brompropiolate. That this substance contains the brompropiolic acid is shown by the evolution of carbonic dioxide and bromacetylen when its aqueous evolution is boiled. Starting with this molecular compound melting at 104— 105°, we made various attempts to isolate the brompropiolic acid and its salts in a pure state. The barium salts of dibromacrylic and brompropiolic acids showed such marked differences in their solubility in water or in alcohol that we hoped through them to effect a complete separation of the two acids. We found, however, that it was difficult to obtain in this way a colorless salt of brompropiolic acid which appeared even tolerably pure. "We therefore attempted to separate the two acids by converting them into their ethyl-ethers and submitting these to frac- tional distillation. We dissolved the molecular compound (m. pt. 104°) in absolute alcohol, added concentrated sulphuric acid, and warmed. The ethers soon separated in part, and were precipitated with water, washed with dilute sodic carbonate, and dried over fused calcic chloride. These mixed ethers had an extremely sharp, pungent odor, and their vapor attacked the eyes violently. On attempting to separate the two by distillation, we found that a large portion of the liquid was carbonized in each distillation, and that but one volatile product could be isolated. This was a mobile liquid, of an agreeable aromatic odor, which boiled between 209 and 215°, without any very noticeable decomposition. The portion of this which boiled between 212-214° was analyzed, and found to be essentially the ethyl-ether of dibromacrylic acid, although still impure. Since our chief object was to isolate the ether of the brompropiolic acid, and this had evi- dently been for the most part destroyed, the substance was not farther examined. 0.5235 grm. of substance gave, on combustion, 0.4675 grm. COg and 0.1250 grm. U.fi. OP ARTS AND SCIENCES. 201 Calculated for CgHBr^Oj . C^IIj. Found. c 23.23 24.36 H 2.33 2. Go Finally, we attempted to separate the two acids by fractional satura- tion. Although the products thus obtained gave us analytical results that were far from satisfactory, we found that the separation could be effected with tolerable precision, the brompropiolic acid being the stronger acid, and that this was the most convenient way of preparing material sufficiently pure for further work, in any considerable quan- tity. Pure substance melting at 104-105° was dissolved in water, and a little less than the calculated amount of baric carbonate was added. The clear solution was then freed as completely as possible from dibromacrylic acid by repeated extraction with ether, and the baric brompropiolate obtained by spontaneous evaporation. Our analytical results show that the material analyzed was not pure, and yet they leave no doubt as to its nature. I. 0.6974 grm. of substance, dried over HgSO^, gave 0.3968 grra. CO2 and 0.0347 grm. H,0. II. 0.3060 grm. of substance, dried over H^SO^, gave 0.1657 grm. BaSO,. III. 0.1829 grm. of substance, dried over HgSO^, gave 0.0973 grm. BaSO,. IV. 0.4325 grm. of substance, dried over H^SO^, gave 0.2305 grm. BaSO^. Calculated for Ba(CsBr02)2. Found. I. II. ni. IV. C 16.63 15.52 H — 0.55 Ba 31.63 31.84 31.27 31.32 "We have been unable to make any satisfactory determinations of the water of crystallization, since the salt cannot be heated, and even on standing over sulphuric acid in the cold it is slowly decomposed. The salt when crystallized from water probably contains four mole- cules of water. I. 2.1104 grm. of the air-dried salt lost over sulphuric acid 0.2803 grm. II. 0.9828 grm. of air-dried substance lost over HgSO^ 0.1316 grm. Calculated for Ba(C3Br02)2.4H20 Found, I. II. HjO 1426 13.28 13.39 202 PROCEEDINGS OF THE AMERICAN ACADEMY In one instance the salt precipitated from alcoholic solution by the addition of ether was found to contain but a single molecule of water. 1.0639 grm. of air-dried salt lost over H2S0^ in vacuo 0.0458 grm. Calculated for BaCCaBrOjlj.HjO. Found. H2O 3.99 ' 4.30 The salt usually crystallized, on the slow evaporation of its aqueous solution, in small, oblique prisms ; but it sometimes separated, on long standing, in more compact, clustered, rhombic plates. When dry, it is decomposed quite rapidly at 50°, and deflagrates at about 125°. In aqueous solution it is recomposed on boiling, with the precipitation of baric carbonate and the evolution of carbonic dioxide and bromacety- len. From solutions containing an excess of the acid, a somewhat more stable salt separates in fine, felted needles, less soluble in water than the neutral salt. This would seem to be an acid salt, corre- sponding to the acid potassium salt of dibromacrylic acid ; but we could obtain no satisfactory analytical results. When argentic nitrate is added to a solution of the barium salt, or of the free acid, a white, amorphous silver salt is precipitated, and at the same time if the solution is concentrated the evolution of carbonic dioxide is noticed. The precipitate turns yellow on washing, and is evidently still further decomposed on drying. When gently warmed with water, it is slowly decomposed ; but, when suddenly heated nearly to 100°, it explodes violently, with the separation of large quantities of carbon. In a dry state it explodes when heated to about 75°. In dilute nitric acid it dissolves at first; but the solution soon grows turbid, smells strongly of bromacetylen, and argentic bromide is precipi- tated. One could hardly expect trustworthy results from the analysis of so unstable a substance. One silver determination, however, showed that it must be considered a derivative of bromacetylen, rather than of brompropiolic acid. 0.2313 grm. of substance, dried over HjSO^ in vacuo, gave 0.1975 grm. AgBr. Calculated for AgCsBrOj ; for AgCjBr. Found. Ag 42.19 50.94 49.05 Although the barium salt had given unsatisfactory results on analy- sis, we made from it the acid, and hoped then to be able to effect its purification. We therefore precipitated the barium from a cold, aqueous solution, with a slight excess of sulphuric acid, and extracted the acid from the filtered solution with ether. We obtained in this OP ARTS AND SCIENCES. 203 way long, slender prisms, extremely soluble in water, alcohol, or ether, readily in chloroform or benzol, more sparingly in carbonic disulphide, and but slightly soluble in ligroin. The crystals obtained from aqueous solution by spontaneous evaporation appeared to contain water of crystallization. When pressed with paper they melted at 60-65° ; but over sulphuric acid they soon became opaque, and the melting point had risen to 80° or over. AVe attempted the purification of the acid by repeated recrystalliza- tion from ligroin to which a little ether had been added. The long, silky needles thus obtained melted at 86°, but gave on analysis no satisfactory results (I. and II.). Although the acid was blackened and apparently completely decomposed at a temperature but little over 100°, we found that it could be sublimed readily between watch- glasses at steam heat. The melting point was, however, lowered rather than raised, by successive sublimations, and analyses (III. and IV ^ of the sublimed product gave too high a percentage of bromine. I. 0.3010 grm, substance gave 0.4025 grm. AgBr. II. 0.1198 grm. substance gave 0.1582 grm. AgBr. III. 0.2010 grm. substance gave 0.2580 grm. AgBr. IV. 0.1820 grm. substance gave 0.2339 grm. AgBr. Calculated for CgHBrOj. Br 53.69 The acid is decomposed, with the formation of carbonic dioxide and bromacetylen, on boiling its aqueous solution. When heated with an excess of baric hydrate, baric carbonate is precipitated, bromacetylen is evolved, and at the same time baric malonate is formed in abun- dance. It unites with dibromacrylic acid immediately to form the characteristic addition-product. An ethereal solution containing a mixture of the two acids, approximately in molecular pi'oportions, gave on evaporation a substance which, without purification, melted at 103°. With the halogens and haloid acids, it forms addition-products with the greatest readiness. The substituted acrylic acids which are thus formed, according to the equations, — CgHBrO^ + HX = C5H2BrX02 C3HBr03 + X,=:C3HBrXA, are easily purified, and their formation can leave no doubt of the nature of the brompropiolic acid. Several of these acids will be described later in this paper. Found. I. II. ni. IV. 56.90 56.21 54.63 54.69 204 PROCEEDINGS OP THE AMERICAN ACA.DEMY The decomposition of mucobromic acid by baric hydrate, under the conditions described, may be expressed by the following equations. The first action would seem to be the assimilation of a molecule of water and the formation of dibromacrylic and formic acids. C.H^BrA + H,0 = C3H,Brp, + CH,0, This action is immediately followed, even in the cold, by the subtrac- tion of hydrobromic acid, — CsH^BrPj — HBr = CgHBrO^ The brompropiolic acid is then either decomposed by heat, — CgHBrOg = C^HBr + CO^, or is converted into malonic acid, — CgHBrO^ + 2H2O = CgH.O, + HBr Since a large percentage of dibromacrylic acid was converted into brompropiolic acid in this reaction, and it had previously been proved that a portion of the mucobromic acid entirely escaped decomposition when the proportion of baric hydrate was materially lessened, I re- cently attempted to increase the yield by reversing the mode of pro- cedure. I therefore added baric hydrate, gradually, to mucobromic acid suspended in a little water ; taking care, after the acid was neu- tralized, to make the solution but slightly alkaline, and to wait until it was again neutral before further addition. I found, however, that an entirely different reaction had taken place under these conditions, and that among the products of this reaction little or no dibromacrylic acid could be found. This decomposition is at present under investigation in this laboratory, and all discussion of the results we have already obtained must therefore be reserved for a subsequent paper. Mdcochloric Acid. Mucochloric acid was discovered in 18 Go by Schmelz and Beil- stein,* and since that time, as far as I know, it has never been further studied. The discoverers found its preparation so very laborious, and the yield which they obtained so small, that they made no extended investigation of it, but contented themselves with giving a short de- scription of the acid, together with the analyses necessary to establish its composition. Although their account was certainly not encourag- * Ann. Chcni. u. Pharni., Suppl., iii. 280. OP ARTS AND SCIENCES. 205 ing, it seemed to me worth while to attempt its preparation, more especially in order to study the dichloracrylic acid derived from it, and to compare this with the acid of the same composition which "Wallach * had already made from chloralid. This investigation Mr. W. Z. Bennett undertook with me. The method followed by Schmelz and Beilstein in making mnco- chloric acid was as follows : Pyromucic acid suspended in water was treated with chlorine at first in the cold and afterwards at boiling heat. When all action appeared to be over, the solution was some- what concentrated on the water bath, and finally brought to crystal- lization by evaporation over sulphuric acid in vacuo. This method gave in our hands precisely the same discouraging quantitative results that Schmelz and Beilstein had obtained ; and it was only after a long series of unsuccessful experiments that we succeeded in finding a simple modification of the method which enabled us to prepare mate- rial sufficient for investigation. We suspended the pyromucic acid in ten times its weight of water, cooled the whole well with ice, and passed in a rapid stream of chlorine until the liquid was thoroughly saturated. The temperature was carefully kept within a few degrees of the freezing point during this treatment with chlorine, and not unfrequently considerable quantities of the crystalline hydrate of chlo- rine separated. When the solution was saturated it was heated to boiling, after a few moments again cooled to 0°, and saturated once more with chlorine. When this operation had been repeated several times, crystals of mucochloric acid began to appear as the solution cooled. At first we filtered these crystals off", and subjected the fil- trate to further treatment; but we found by experience that little or no product was gained after the sixth ohlorination, and we, there- fore, usually proceeded to this point before we removed the acid formed. We then collected the crystals which separated as the solution cooled, and evaporated the mother liquors on the water bath to the point of crystallization. The crystals were drained, pressed, and recrystallized from hot water. We further found it convenient to add to the pyromucic acid a small percentage of iodine. Although this was by no means essential, we found that our results were then more constant and the average yield greater. As the result of several preparations which we made in the course of the investiga- tion, we obtained 129 grm. of mucochloric acid from 202 grm. of pyromucic acid. This corresponds to a little more than forty per * Berichte der deutsch. chem. Gesellsch., viii. 1580. 206 PROCEEDINGS OF THE AMERICAN ACADEMY cent of the theoretical amount, as our average product, although in single instances our yield has reached 50 per cent. The product made in this way crystallized from water in well-formed rhombic plates, which in their properties agreed in every particular with the description of Schmelz and Beilstein. The acid melted at 125°, and was very soluble in alcohol or ether, sparingly soluble in cold water, readily in hot. Boiling benzol or chloroform dissolved it with readi- ness, while in carbonic disulphide or ligroin it was almost insoluble. The purity of our material was shown by the following analyses : — L 0.7408 grm. substance gave 0.7617 grm. COj and 0.0831 grm. H,0. II. 0.5512 grm. substance gave 0.5687 grm. COj and 0.0621 grm. H,0. TIL 0.2090 grm. substance gave 0.3564 grm. AgCl. ni. 42.16 Although mucochloric acid appears to form derivatives in some respects more stable and readily studied than the corresponding deriv- atives of mucobromic acid, we bave thus far taken up more in detail only the dichloracrylic acid which may easily be made from it by the action of alkalies. DicJiloracrylic Acid. In 1877, "Wallach* obtained a dichloracrylic acid as a product of the reduction of chloralid. This acid was afterward more carefully studied by Wallach and Hunaus,t and quite recently Wallach | has published a paper still further describing the acid and its salts, and correcting the work of Iluntius in several important particulars. At the time this investigation was begun, this acid was tlie only disubsti- tuted acrylic acid known, and since its constitution was fairly established by the mode of its preparation, it seemed desirable to prepare the dichloracrylic acid from mucochloric, in order to compare the two acids. Calculated for C4II2CI2O3. Found. I. II. C 28.40 28.06 28.13 H 1.18 1.25 1.25 CI 42.01 * Berichte der deutsch. chem. Gcsellsch., viii. 1580. t Ik'richte der deutsch. ehem. Gesellsch., x. 507. Ann. Chem. u. Pharm. cxciii. 19. I Ann. Chem. u. Pharm. cciii. 83. OF ARTS AND SCIENCES. 207 The decomposition of mucochloric acid into dichloracrylic and formic acids, under the influence of alkalies, is much more neatly accomplished than the corresponding reaction with mucobromic acid. Under ordi- nary conditions, but little hydrochloric acid is split off, and the yield of dichloracrylic acid is nearly 90 per cent of that required by the equation, — C,H,C1,03 + 11,0 = C3H,C1,0, + CH^O,. We never have noticed in the preparation of dichloracrylic acid either chlorpropiolic acid or any compound corresponding to that which brompropiolic acid forms with dibromacrylic. We usually have dissolved mucochloric acid in quite an excess of potassic hydrate, allowed the solution to stand for a short time, acidified with hydro- chloric acid, and extracted with ether. The dichloracrylic acid left on evaporation of the ether may be purified by melting it several times with a little water. When dried over .sulphuric acid it gave the fol- lowing results on analysis : — I. 0.5280 grm. substance gave 0.4894 grm. CO, and 0.0720 grm. HoO. II. 0.3670 grm. substance gave 0.3399 grm. CO, and 0.0477 grm. H,0. III. 0.1037 grm. substance gave 0.2123 grm. AgCl. IV. 0.2674 grm. substance gave 0.5420 grm. AgCl. Calculated for CgHjCljOj. Found. ni. IV. C 25.54 H 1.42 CI 50.36 50.62 50.10 This dichloracrylic acid forms small rhombic prisms which vol- atilize rapidly on exposure to the air. It is readily soluble in water, alcohol, ether, or chloroform, and it also dissolves freely in boiling benzol, carbonic disulphide, or ligroin. It melts at 85-86°, and, when solidified by quick cooling, melts again at the same temperature. The yS dichloracrylic acid of Wallach, on the other hand, melts at 76-77° and its melting point falls to 63-64° when melted and suddenly cooled. Argentic Dichloracrylate, AgCgHCl202. The silver salt was precip- itated in the form of fine felted needles on the addition of argentic nitrate even to a dilute solution of the acid. The salt was quite stable and could be recrystallized from hot water without any marked decomposition. I. II. 25.28 25.25 1.51 1.45 Calculated for AgCgHCUO, Found. I. n. m. c 14.52 14.03 14.12 H 0.40 0.60 0.58 CI 28.63 28.65 A" 43.54 208 PROCEEDINGS OP THE AMERICAN ACADEMY I. 0.5460 grm. substance gave 0.2808 grm. CO., and 0.0299 grm. II. 0.4819 grm. substance gave 0.2494 grm. COj and 0.0253 grm. H.O. III. 0.2511 grm. substance gave, by Cairus' method, 0.2910 grm. AgCI. IV. 0.2078 grm. substance gave, by Cairus' method, 0.2401 grm. AgCl. V. 0.2089 grm. substance, precipitated by HCl, gave 0.1209 grm. AgCl. VI. 0.6768 grm. substance, precipitated by HCI, gave 0.3909 grm. A-Cl. IT. V. VI. 28.56 43.55 43.49 Baric Dichloracrylate, Ba(C,HC]202)o • H^O. The barium salt was prepared by neutralizing the aqueous solution of the acid with baric carbonate and concentrating the solution upon the water bath. On cooling, the salt separated in rhombic plates which were permanent in the air, and did not lose in weight over sulphuric acid in vacuo. I. 0.2185 grm. of the salt lost, when heated to 80°, 0.0088 grm HjO and gave, on ignition with H^SO^, 0.1174 grm. BaSO^. II. 0.1941 grm. of the salt gave, on ignition with H2S0^, 0.1041 grm. BaSO^. III. 0.2402 grm. of the salt gave, on ignition with HgSO^, 0.1281 grm. BaSO^. IV. 0.9167 of the salt lost, when heated to 80°, 0.0395 grm. HjO. rv. 4.31 For the further characterization of this salt we determined its solu- bility in cold water by the method of V. Meyer. I. 5.6625 grm. of an aqueous solution, saturated at 18°, gave, on evaporation and ignition with H.,SO^, 0.1956 grm, BaSO^. II. 2.416 grm. of a solution, saturated at 18°. 5, gave 0.0801 grm. BaSO^. Calculated for Ba(C3HCljOj)j.HjO. I. Ba 31.49 31.59 Found. n. in. 31.53 31.36 HP 4.14 4.03 OF ARTS AND SCIENCES. 209 These determinations give as the percentages of the anhydrous salt contained in the hot solutions saturated at 18° and 18°.5 respectively I. II. 6.28 6.19 Calcic Dichloracrylate, Ca(C3HCl202)2-3H20. The calcium salt, which was extremely soluble in water, was made by neutralizing a solution of the acid with calcic carbonate. On cooling the concen- trated solution, the salt separated in long, flat radiating needles, which were permanent in the air, but slowly effloresced over sulphuric acid. I. 0.4077 grm. of the air-dried salt lost, on heating to 95-100°, 0.0580 grm. HgO, and gave, on ignition with H^SO^, 0.1488 grm. CaSO^. 11. 0.61&3 grm. of the air-dried salt lost, on heating, 0.0875 grm* H,0. III. 0.3217 grm. of the dried salt (II.), corresponding to 0.3749 grm. of the air-dried salt, gave, on ignition with HgSO^, 0.1348 grm. CaSO^. Calculate Ca id for Ga(C3HCl202)2-3HjO. 10.69 I. 10.73 Pound. n. in. 10.58 H,0 14.43 14.23 14.20 Potassic Dichloracrylate, KCgllCljOg. The potassium salt crystal- lizes from a solution of mucochloric acid in an excess of potassic hydrate (1 : 4) when this is strongly cooled. Although it is quite soluble even in cold water, it may readily be purified by recrystalliza- tion from hot water. From concentrated solutions it crystallizes on cooling in long, slender needles, which are anhydrous. I. 0.3054 grm. of the salt gave, on ignition and evaporation with HCl, 0.1283 grm. KCl. II. 0.2159 grm. of the salt gave 0.0908 grm. KCl. Caioulated for KC3HCI2O2. Found. I. n. : 21.84 22.03 22.06 The foregoing results seemed to us to show with sufficient precision that our acid was essentially different from the /? dichloracrylic acid of Wallach, since the two acids differed markedly in their physical properties, and their salts were also quite dissimilar. Following the 210 PEOCEEDINGS OP THE AMERICAN ACADEMY analyses of Hun a us, "Wallacli * had assigned to the barium salt of the y8 dichloracrylic acid the formula Ba(C8HCl202)2 • SHgO, and to the calcium salt the probable formula Ca(CoHCl202) . l^HjO ; while the corresponding salts of our acid we had found to have the formulge ■Ba(C3HCl202)2 . HgO and Ca(C3HC102)2 • SH^O. Although the po- tassium salt of neither acid contained water of crystallization, one crys- tallized in plates, the other in needles. Quite recently Wallach f has published the results of several deter- minations made since the publication of a preliminary notice t of our dichloraci'ylic acid. These determinations show that the formulas which had previously been assigned to the barium and calcium salts of his acid were incorrect, and that they probably each contained two molecules of water. To these determinations, however, Wallach would attach but little weight for the identification of the acid, although he considers the isomerism of the two dichloracrylic acids to be fully established. " Ich mochte aber nach den gemachten Erfahrungen diesen Bestim- mungen vorliiufig keinen besonderen Werth fiir die Charakterisirung der Dichloracrylsaure aus Chloralid beilegen. Man wird besser thun, sich dafiir an die scharf bestimmbaren Eigenschaften der gemessenen freien Saure und allenfalls an die tafelformige Ausbildung des was- serfreien Kalisalzes, sowie an die angegebenen krystallographischen Daten des Baryumsalzes, austatt an die bisher ausgefiihrten Wasser- bestimmungen zu halten ; fiir letztere miissen noch weitere Versuche vorbehalten bleiben. Jedenfalls muss aber der Zweck der obigen Angaben jetzt schon als erreicht bezeichnet werden : namlich die vollige VerscMedenheit der Dichloracrylsaure aus Chloralid der nur die Foi-mel CCU^CH-COgH zukommen kann, von der, welche Ben- nett und Hill aus 3fucochlor saure erhielten dejiniiiv zu bestdtigen." § Unfortunately we have as yet been unable to obtain either our acid or its barium salt in a form which would admit of crystallographic study. Still, the differences already established leave no reasonable doubt that the two acids are isomeric, and the acid from mucochloric acid may therefore be distinguished for convenience as the a dichlor- acrylic acid. The behavior of this acid towards reagents has thus far been little * Ann. Cliem. u. Pharm., cxciii. 23. t Ibid., cciii. 83. } Berichte der deutsch. chem. Gesellsch., xii. 665. § Loc. cit., p. 80. OF ARTS AND SCIENCES. 211 examined. On boiling with an excess of baric hydrate, it is decom- posed in essentially the same way as the dibromacrylic acid, baric malonate being formed in abundance. This decomposition with alka- lies we have not followed further, since it was evident that cblorpro- piolic acid should be the intermediate product formed; and we wished not to interfere with the researches which Wallach had already under- taken with Bischof,* concerning the decomposition of /? dichloracrylic acid by alkalies. Although the acid does not add bromine when heated with it to 100° in chloroform solution, it readily forms an addition product when heated for some time with undiluted bromine at 100°. Tlie dichlordi- brompropionic acid which is thus formed is at present under investi- gation in this laboratory. Substituted Acrylic Acids from Brompropiolic Acid. Mr. C. F. Mabery has studied with me some of the substituted acrylic acids which may readily be made by the addition of halogens or haloid acids to brompropiolic acid. Dibromacrylic Acid of Fittig and Petri. Brompropiolic acid dissolves easily in concentrated hydrobromic acid (b. pt. 126°), and on standing for a short time the solution deposits abundant crystals of a dibromacrylic acid, which is identical with that described by Fittig and Petri as resulting from the decomposition of tribromsuccinic acid. This acid may also be prepared to advantage from the solution of baric brompropiolate and baric bromide which is obtained in the pre^jaration of baric dibromacrylate by the action of baric hydrate upon mucobromic acid. It is only necessary to pre- cipitate the barium with dilute sulphuric acid, and to concentrate the solution upon the water bath. The acid which separates as the solu- tion cools is easily purified by recrystallization. From a hot concentrated solution, the acid falls at first as an oil ; but, after the solution has cooled somewhat, it separates in pearly scales, which melt at 85-86°. In analysis they gave the required percentage of bromine. 0.2614 grm. of substance gave 0.4283 grm. AgBr. Calculated for C3H2Br202. Found. Br 69.57 69.72 * Berichte der deutsch. chein. Gesellsch., xi. 751 ; xii. 57. 212 PROCEEDINGS OP THE AMERICAN ACADEMY The solubility of the acid in water at ordinary temperatures we determined by neutralizing with baric carbonate the solution made according to V. Meyer's method, a-nd evaporating the filtered solution with sulphuric acid. I. 12.5364 grm. of a solution, saturated at 20°, gave 0.2070 grm. BaSO,. 11. 11.6241 grm. of a solution, saturated at 20^^, gave 0.1712 grm. BaSO,. III. 8.4358 grm. of a solution, saturated at 20°, gave 0.1248 grm. BaSO,. IV. 10.6740 grm. of a solution, saturated at 20°, gave 0.1581 grm. BaSO^. As the result of these determinations, we find that an aqueous solu- tion of the acid saturated at 20° contains the following percentages : — I. n. ni. rv. 3.16 2.91 2.92 2.93 Fittig and Petri found that the dibromacrylic acid made from tri- bromsuccinic gave at 20° a solution which contained 3.355 per cent of the acid. Baric Dibromacrylate, Ba(CgHBr202)2-2H20. An aqueous solution of the acid was neutralized with baric carbonate, and the filtered solu- tion evaporated on the water bath. On cooling, the barium salt crys- tallized in rectangular plates, whose angles were, however, often more or less modified. The air-dried salt lost, on heating to 100°, two molecules of water. I. 0.4018 grm. of air-dried salt lost at 100° 0.0226 grm. H.O. 11. 0.4644 grm. of air-dried salt lost at 100° 0.0261 grm. H^O. in. 0.5086 grm. of air-dried salt lost at 100° 0.0299 grm. H2O. Calculated for Ba (C3HBr202)2.2H20. Found. I. II. in. H.O 5.71 5.62 5.62 5.88 The anhydrous salt then gave : — I. 0.3425 grm. of substance, dried at 100°, gave on ignition 0.1353 grm. BaSO^. II. 0.4383 grm. of the salt, dried at 100°, gave 0.1723 grm. BaSO^. III. 0.2934 grm. of the salt, dried at 100°, gave 0.1153 grm. BaSO^. Oaloulated for Ba(C3HBr,0i),. Ba 23.03 I Found. L II. m. 23.23 23.11 23.10 OF ARTS AND SCIENCES. 213 Fittig and Petri fouud in two determinations of water, in the bariuna salt of their acid, a somewhat higher percentage' (6.73 and 7.27), and therefore assign it the formula Ba(C3HBr202)2-25H2^ — (calculated 7.03 per cent). The solubility of the salt we determined by V. Meyer's method. I. 3.9749 grm. of a solution, satui-ated at 23°, gave, on evaporation with H^SO^ and ignition, 0.1748 grm. BaSO^. n. 3.9148 grm. of a solution, saturated, at 20°, gave 0.1719 grm. BaSO,. According to these determinations, the aqueous solution saturated at 20° contained the following percentages of the anhydrous salt : — I. II. 11.23 11.21 Calcic Dihromacrylate, Ca(C3HBr202)2.3|^H20. The calcium salt we prepared by neutralizing a solution of the acid with calcic carbo- nate. On cooling the concentrated solution, the salt separated in long radiating needles. I. 0.5625 grm. of the air-dried salt lost, when heated to 100°, 0.0668 grm. H2O, and gave, when ignited with H2S0^, 0.1356 grm. CaSO^. 11. 0.3460 grm. of the salt lost at 100° 0.0394 grm. B.f> and gave 0.0850 grm. CaSO^. Calculated for Oa(C3HBr202)2.3iHjO. Ca 7.13 HgO 11.23 Fittig and Petri found in two determinations of water, in the cal- cium salt of their acid, the percentages 11.56 and 11.47, from which they calculate the formula with ^\ molecules of water given above. The physical properties of the acid, and the analyses of the barium and calcium salts, leave no doubt of the identity of this dibromacrylic acid with that described by Fittig and Petri, although our results differ slightly in some respects from theirs. The acid from tribromsuc- cinic acid we have made only in sufficient quantity to assure ourselves that no qualitative differences are to be detected in the properties of the two acids, or in the habit of several of their salts. I. 11. 7.09 7.22 11.88 11.39 214 PROCEEDINGS OF THE AMERICAN ACADEMY lodhromacrylic Acid. Brompropiolic acid dissolves readily in concentrated hydriodic acid, (b. pt. 127°) and so rapid is the action that in a few moments the solu- tion is filled with crystals of the addition-product. The crude acid is pressed between folds of filter paper, and recrystallized from hot water. The acid separates from a hot concentrated solution as an oil, but at a lower temperature it crystallizes in pearly scales, which melt at 1 10°. The acid is readily soluble in alcohol, ether, or chloroform, but sparingly in benzol, carbonic disulphide, or ligroiu. I. 0.3800 grm. substance gave 0.1828 grm. Cog and 0.0307 grm. H,0. II. 0.2945 grm. substance gave 0.4480 grm. AgBr -\- Agl. Calculated for C3HjBrI02. Found. I. n. C 12.99 13.12 H 0.70 0.90 f1 74.73 74.47 The solubility of the acid in cold water we determined by neutral- izing the saturated aqueous solution, made according to the method of V. Meyer with baric carbonate, and evaporating with sulphuric acid. I. 11.1382 grm. of a solution, saturated at 20°, gave 0.0785 grm. BaSO,. 11. 10.8923 grm. of a solution, saturated at 20°, gave 0.0783 grm. BaSO^. According to these determinations, the aqueous solution of the acid saturated at 20° contained the following percentages : — I. 11. 1.68 1.71 For the further characterization of the acid, we prepared the barium, calcium, and silver salts. Baric lodbromacrylate, Ba(CgHBrI02)2-3H2C)- The barium salt we made by saturating the aqueous solution of the acid with baric carbonate and concentrating on the water bath. From concentrated solutions it crystallizes in fine needles ; from more dilute, in rectangu- lar plates. The air-dried salt contains three molecules of water, which it loses in vacuo over sulphuric acid. OP ARTS AND SCIENCES. 215 I. 0.4G60 ffrm. of air-dried salt lost in vacuo over H„SO, 0.0360 grm. HjjO, and lost then nothing at 80°. II. 0.2832 grm. of air-dried salt lost in vacuo over H^SO^ 0.0208 grm. HjO, and afterwards, when heated to 80°, 0.0011 grm. Calculated for Ba(CsHBrI0j),.3Hj0. Found. I. II. HgO 7.27 7.73 7.35 0.4427 grm. of the dried salt gave, on ignition with H^SO^, 0.1498 grm. BaSO^. Calculated for Ba(CsHBrlOj),. Found. Ba 19.88 19.90 The solubility of the salt in cold water we also determined. I. 2.0G36 grm. of a solution saturated at 20° gave, on evaporation with H.SO^, 0.0967 grm. BaSO^. II. 3.0991 grm. of a solution saturated at 20° gave 0.1457 grm, BaSO,. From these determinations it follows that the aqueous solution, saturated at 20°, contains the following percentages of the anhydrous salt : — I. II. 13.86 13.90 Calcic lodhromacrylate, Ca(C3HBrI02)2-3jH^O. The calcium salt resembles the barium salt closely in appearance, but is more soluble in water. The air-dried salt loses its crystal water completely in vacuo over sulphuric acid, or when heated to 80°. I. 0.7622 grm. of the air-dried salt lost 0.0771 grm. H.O at 80°. II. 0.7172 grm. of the air-dried salt lost 0.0698 grm. H^O at 80°. Calculated for Ca(C3HBrIOij)2.3JH20. Found. I. II. HgO 9.89 10.12 9.73 0.6518 grm. of the salt dried in vacuo gave, on ignition with HjSO^ 0.1465 grm. CaSO^. Calculated for Ca(C3HBrI0j)2. Found. Ca 6.76 6.61 Argentic lodbromacrylate, AgCgHBrlOa- The silver salt was pre- cipitated from an aqueous solution of the acid by the addition of ar- gentic nitrate. It formed short, clustered needles, which could be recry stall ized from water, with but little decomposition. 216 PROCEEDINGS OP THE AMERICAN ACADEMY I. 0.4509 grm. of substance gave 0.1597 grm. AgCl and 0.0063 grm. metallic silver. II. 0.7458 grm. substance gave, on precipitation with HBr, 0.3635 ■grm. AgBr. Calculated for AgCgHBrlOs. Found. I. n. Ag 28.13 28.05 27.99 With hydrochloric acid, the addition takes place much more slowly ; still, after long standing, the chlorbromacrylic acid is formed. Of the products formed by the addition of halogens to brompropiolic acid, we have thus far examined in detail only the tribromacrylic, although we have also made the diiodbromacrylic by the addition of iodine. Tribromacrylic Acid. Tribromacrylic acid may easily be made by adding slowly a slight excess of bromine to an aqueous solution of brompropiolic acid. The color of the bromine gradually disappears, and the product of the reaction separates partially in the form of an oil. This oil gradually solidifies, and more of the same product can be extracted with ether from the aqueous solution. The resulting solid must be well pressed out, and may then be recrystallized from chloroform, or, better, from benzol. Thus prepared, it forms colorless, oblique j^risms, which are very soluble in ether or alcohol, less soluble in cold chloroform or benzol, readily in hot, and soluble in carbonic disulphide or ligroin. It is but sparingly soluble even in boiling water. Melting point, 118°. I. 0.3449 grm. of the acid gave 0.1428 grm. CO., and 0.0183 grm. H,0. II. 0.1782 grm. substance gave 0.3229 grm. AgBr. III. 0.1433 grm, substance gave 0.2625 grm. AgBr. Calculated for CgHBraOs. Found. I. II. m. C 11.65 11.29 H 0.32 0.59 Br 77.67 77.13 77.94 The acid when boiled with an excess of baric hydrate is hardly affected, although it is slowly decomposed by a boiling alcoholic solu- tion of potassic hydrate. We have as yet isolated no products of this decomposition. The solubility of the acid in water at ordinary temperatures we have also determined by the method of V. Meyer. OF ARTS AND SCIENCES. 217 I. 11.4429 grm. of a solution, saturated at 20°, gave, after neutrali zation with BaCOj and evaporation with H^SO^, 0.0597 grm. BaSO,. n. 12.7846 grm. of a solution, saturated at 20°, gave 0.0643 grm. BaSO,. According to these determinations, the aqueous solution of the acid saturated at 20° contains the following percentages : — I. II. 1.38 1.33 Baric Tribromacrylate, BaC8Brg02.3H20. The barium salt we made by neutralizing the acid with a solution of baric hydrate. On cooling the concentrated solution, it crystallizes in long needles, which effloresce over sulphuric acid. I. 0.7888 grm. of the air-dried salt lost over HjSO^ 0.0532 grm. H,0. II. 0.7585 grm. of the air-dried salt lost in vacuo over HgSO^ 0.0506 grm. H^O. III. 0.4900 grm. of the air-dried salt lost at 80° 0.0324 grm. HgO. IV. 0.7024 grm. of the anhydrous salt gave, on ignition with H^SO^, 0.2185 grm. BaSO,. V. 0.4486 grm. of the anhydrous salt gave 0.1398 grm. BaSO^. Calculated for BaCCsBrjOjlj.SH^O. Found. I. n. m. H^O 6.68 6.75 6.67 6.61 Calculated for Ba(C3Br302)2> Found. IV. V. Ba 18.20 18.29 18.32 The solubility of this salt in cold water was determined by the method of V. Meyer. I. 3.2130 grm. of a solution saturated at 20° left, on evaporation with H2SO4 and ignition, 0.2349 grm. BaSO^. II. 2.9600 grm. of a solution saturated at 20° gave 0.2170 grm. BaSO,. The aqueous solution saturated at 20° therefore contained the fol- lowing percentages of the anhydrous salt : — I. II. 23.62 23.69 Calcic Trihromacrylate Ca(C3Br302)2-H20. The calcium salt was made by warming the acid with water and calcic carbonate. It crys- 218 PROCEEDINGS OF THE AMERICAN ACADEMY tallized in needles which were permanent in the air, but lost in weight over sulphuric acid. I. 0.4924 grm. of the air-dried salt lost at 80° 0.0099 grm. H,0. II. 0.8678 grm. of the air-dried salt lost at 80° 0.0248 grm. U^O. III. 0.4794 grm. of the anhydrous salt gave, on ignition with HjSO^, 0.1001 grm. CaSO,. IV. 0.8266 grm. of the anhydrous salt gave, on ignition with HjSO^, 0.1707 grm. CaSO^. Calculated for Ca(CaBr80j)j. H,0. I. Found. n. HP 2.67 2.01 2.86 Calculated for CaCCgBrgOj),. m. Found. rv. Ca 6.10 6.14 6.07 Argentic Trihromacrylate, AgCgBi-gOg. The silver salt is precipi- tated when argentic nitrate is added to an aqueous solution of the acid, but is more readily prepared from a solution of the acid in diluted alcohol. The salt is tolerably stable, and crystallizes in small, six-sided plates. 0.5267 grm. of the salt gave 0.1848 grm. AgCl. Calculated for AgCjBraOj. Found. Ag 25.96 26.40 Mr. Mabery has undertaken the study of the clilorbromacrylic and diiodbromacrylic acid, and will present the results of these investiga- tions in a separate paper. Theoretical Considerations. Schmelz and Beilstein,''' from a comparison of the formula of mel- litic acid, C^H^O^ (as it was then written), with that of mucobromic acid, C^HgEPj^Og, were led to suspect a close connection between the two ; but their investigations undertaken with the hope of proving this point yielded negative results. In 1869, Limpricht t suggested that a series of compounds, among which were furfurol and its derivatives, contained a ring of four car- bon atoms, and that they were therefore derived from an hypothetical hydrocarbon, — * Ann. Chcni. u. Pliarn., Suppl. iii. 280. t Berichte der deutsch. chem. Gesellsch., ii. 212. OP ARTS AND SCIENCES. 219 H — C = C — H I I II — C = C — H just as the various compounds of the aromatic series were derived from benzol. As the formula which naturally suggested itself for mucobromic acid he gives, — HOC = COHO 1 I BrC = CBr although I am at a loss to know precisely how this formula is to be interpreted. This hypothesis received temporary support from the discovery of the so-called tetraphenol by Limpricht and Rohde ; * but further experiments made in Limpricht's laboratory failed to sustain it, and in the subsequent detailed account of these investigations t no allusion is made to it. In this paper Limpricht described the forma- tion of fumaric acid by the action of bromine and water upon pyro- mucic acid, as well as the substance C^H^Og, which he called fumaric acid aldehyde, and regarded as the product from which mucobromic acid was derived by substitution. In 1877 Baeyerf showed that this latter substance was in fact the half-aldehyde of fumaric acid, in that it could be converted into fumaric acid by the action of argentic oxide. At the same time he pointed out the difficulty of supposing that mucobromic acid, which empirically was a substitution-product from this aldehyde, could be formed from it by the direct action of bromine. In 1878, Wallach and Bischo£P§ published a paper upon the action of alkalies upon the /3 dichloracrylic acid, which Wallach 1[ had previously made by the reduction of chloralid. In a subsequent paper || upon the same subject, they assumed that the structure of the dibromacrylic acid from mucobromic, which 0. R. Jackson and I ** had shortly be- fore described in a preliminary notice, was established quite surely by its ready conversion into malonic acid, and Wallach was therefore led to append a note containing a suggestion which he had previously * Berichte der deutsch. chem. Gesellsch., iii. 90. t Ann. Cliem. u. Pliarm., clxv. 278. } Rerichte der deutsch. chem. Gesellsch., x. 1362. § Ibid., xi. 751. T Ihid., viii. 1580. II Il)id., xii. 57. ** Ibid., xi. 1671. 220 PROCEEDINGS OF THE AMERICAN ACADEMY made, that the constitution of mucobromic acid was probably repre sented by the formula, — CBr^ = CH — CO — COOH In 1879, Toennies,* in investigating the action of bromine upon dibrompyroraucic acid f in Baeyer's laboratory, found that a sub- stance, C4H2Br202, was formed according to the equation, — C,R,Bv,0, + Br^ + H^O = C.H^Br^O^ + CO^ + 2HBr, and that this could readily be converted into mucobromic by oxidation. This mode of formation led Toennies to the conclusion that muco- bromic acid was the half-aldehyde of dibromfumaric acid. Further investigation in this direction Toennies relinquished in order to avoid interference with my work. At the time of the publication of this paper by Toennies, my own experiments had shown that this view was in part correct. The conversion of mucobromic acid by the action of argentic oxide or other oxidizing agents into the dibrommaleic acid of Kekule showed with sufficient precision that it was the half-aldehyde of this acid. On the other hand, it was evident that the dibrommaleic acid itself did not belong to the fumaric series, as could fairly be inferred from its mode of preparation ; but that it was in reality a substituted maleic acid, since it could be carried unchanged through its anhydride. A more direct proof of this fact was furnished by the discovery by Bandrowski J of an isomeric acid of higher melting point, which could be converted into this by distillation. Although it cannot be said that the constitution of fumaric and maleic acids is definitely established, the brilliant researches recently published from Fittig's laboratory leave but little doubt that the formula of maleic acid is, — CK, — COOH I = c — coon If this view of its structure be adopted, the structure of mucobromic acid must be represented by one of the formulte, — * Berichte der deutsch. chem. Gesellsch., xii. 1202. t Ibid., xi. 1Q88. } Ibid., xii. 1232. I OF ARTS AND SCIENCES. 221 CBr„ — CHO CBr. — COOH ! I = C — COOH = C — Clio The ease with which it is decomposed, even in the cold, by alkalies and the aldehyde group thus converted into formic acid, would pos- sibly incline one to adopt the first of these formulae. Unfortunately, no independent evidence concerning the position of the bromine atoms can as yet be drawn from the constitution of the dibromacrylic acid, which is formed at the same time, since none of its reactions give a clew to its structure. It may only be asserted, with tolerable certainty, that its formula is not, — CBr„ II CH COOH since the corresponding chlorinated acid made from mucochloric acid appears to be essentially different from the dichloracrylic acid of Wallach, and the formation of the latter from chloralid shows its formula to be, — CCL II CH I COOH If the structure of mucobromic acid is represented by one of the formulae given above, it follows that the dibromacrylic acid obtained from it has one of the forms, — CBr„H = CH I I = C CBr„ 1 I COOH COOH The formation of a tribrompropionic acid, melting at 116-117° by the addition of hydrobromic acid, would in itself be a sufficient reason for rejecting the second formula, if the structure of the tribrompro- pionic acid, melting at 92°, could be shown to be, — 222 PROCEEDINGS OF THE AMERICAN ACADEMY CHgBr CBr^ COOH Although this is the constitution assigned to it by Michael and Nor- ton,* it is evident that this formula is based upon a pure assumption concerning the structure of the a monobromacrylic acid from which it is made. No more decisive arguments against the second formula can be drawn from the reactions or the derivatives of the dibromacrylic acid, although the formation of malonic acid follows more simply from the first formula, and the forms, — c = II '■'Br and C = II CBr 1 COOH which the second formula renders necessary for bromacetylen and brompropiolic acids, seem hardly in its favor. It would therefore seem probable that the structure of mucobromic acid is, — CBr^ — CHO = C — COOH The close connection between the disubstituted acrylic acids derived from mucobromic and mucochloric acids and maleic acid makes their further study extremely desirable, more especially in order to obtain additional evidence bearing upon the position of the halogen atoms. Investigations in this direction are now in progress in this laboratory. * Amer. Chem. Journ., ii. 18. OF ARTS AND SCIENCES. 223 I>;vESTiOATioxs ON LiGHT AND IIeat, made and published wholly or in part with appropriation from the Rumford Fond. X. ON THE PHOSPHOROGRAPH OF A SOLAR SPECTRUM, AND ON THE LINES IN ITS INFRA-RED REGION. By John William Draper, M.D. Professor of Chemistry in the University of New York. I PROPOSE in this communication to consider: 1. The peculiarities of a 25hosphorograph of the solar spectrum as compared with a photo- Ejraph of the same object ; 2. The antagonization of effect of rays of higher by those of lower refrangibility. There is a striking resemblance between a photograph of that spec- trum taken on iodide of silver and a phosphorograph taken on lumi- nous paint, and other phosphorescent preparations. There are also differences. I. Description op the Photographic Spectrum. In 1842, I obtained some very fine impressions of the first kind (on iodide of silver), and described them in the " Philosophical Maga- zine" (November, 1842), and again in February, 1847. One of these was made the subject of an elaborate examination by Sir J. Herschel. His description and explanatory views of it may be found in that journal, February, 1843. From these it appears that such a photograph, taken in presence of a weak extraneous light, may be considered as presenting three regions. 1. A middle one extending from the boundary of the blue and green to a little beyond the violet ; in this region the argentic iodide is blackened. 2. Below this, and extending from the boundary of the blue and green to the inferior theoretical limit of the prismatic spec- trum^ is a region strongly marked in which the action of the daylight has been altogether arrested or removed, the daylight and the sunlight having apparently counterbalanced and checked each other. 3. A similar protected region occurs beyond the violet. This, however, is very much shorter than the preceding. The sketch annexed to Herschel's paper represents these facts as well as they can be by an uncolored drawing. 224 PROCEEDINGS OF THE AMERICAN ACADEMY II. Desceiption of the Phosphorographic Spectrum. In a phosphorograpli on luminous paint, the same general effects appear.- If the impression of the spectrum be taken in the absence of extraneous light, there is a shining region corresponding to the black- ened region of the photograph. But if, jDreviously or simultaneously, extraneous light be permitted to be present, new effects appear. The shining region of the phosphorograph has annexed to it, in the direc- tion of the less refrangible spaces and extending toward the theoreti cal limit of the spectrum, a region of blackness in striking contrast to the surrounding luminous surface. This blackness is, however, broken at a distance below the red by a luminous rectangle of consid- erable width. This occupies the space, and indeed arises from the coalescence of the bauds a, (3, y, discovered by me in 1842. It may be separated into its constituent bands, which are very discernible when registered on gelatine as presently described. And since this is not so easily done with the upper lines of the spectrum, we may infer that these are very much broader than the Fraunhofer lines, a result strengthened by the fact that these dark intervals can be more easily recognized by the thermopile than those lines. The blackness is then resumed. It extends to a short distance, and there the phos- phorographic impression comes to an end. This shining rectangle has long been known to students of phos- phorescence, but its interesting origin has not until now been ex- plained. But more, just beyond the region of the violet, the same kind of action occurs, — a dark space, which, however, is of very much less extent than that beyond the red. The photograph and the phosphorograph thus present many points of similarity. But though there are these striking points of resem- blance, there are also striking differences. In a spectrum four or five centimetres long, though the photograph may be crossed by hundreds of Fraunhofer lines, not one is to be seen in the phosphorograph, except those just referred to. The spectrum must be dispersed much more before they can be discerned, III. Of the Propagation op Phosphorescence from Particle to Particle. The explanation of this disappearance of the Fraunhofer lines is obvious. A phosphorescing particle may emit light enough to cause others in its neighborhood to shine, and each of these in its turn may OF ARTS AND SCIFNCES. 225 excite others, atul so the himinosity may spread. In a former rcemoir I examined tliis in the case of chlorophane, and concluded tliat in that substance such a communication does not take place. But now, using more sensitive preparations, as follows, I have established in a satis- factory manner that it does. The test plate referred to in the next paragraph was thus made. A piece of glass was smoked on one side in a flame, until it became quite opaque. When cool a few letters or words were written on it. Some j^hotographic varnish was poured on it and drained. This, drying quickly, gave a black surface which could be handled without injury. A phosphorographic tablet was made to shine by exposure to the sky. It was then carried into a dark room, and the test plate laid upon it. On the test plate another non-shining phosphorographic tablet was laid, and kept in that position a few minutes ; then, on lifting this from the test plate, the letters were plainly visible, especially if it were laid on a piece of hot metal. So the light radiating from the first tablet through the letters of the test could produce phospho- rescence in the second tablet, through glass more than a millimetre thick. This lateral illumination is therefore sufficient to destroy the im- pression that is left by the fixed lines, unless indeed their breadth be sufficiently exaggerated, and as short an interval as possible permitted between the moment of insolation and that of observation. It has been remarked that a photograph taken from a phosphoro- graph is never sharp. It looks as if it were taken out of focus, and this even though it may be a copy by contact. The light has spread from particle to particle. Under such circumstances, sharpness is impossible, because the phosphorograph itself is not sharp. For this reason, also, the bright rectangle in a phosphorograph of the solar spectrum, arising from the coalescence of the infra-red lines a, ^, y, is never sharp on its edges. It seems as if it were fading away on either side. It is also broader than would correspond to the actual position and width of those lines, and, particularly, it is some- what rounded at its corners. If we could obtain a thermograph of the solar spectrum, it would correspond very closely to the phosphorograph. The particles heated would radiate their heat to adjacent ones. Nothing like sharpness of definition could be obtained, except m very brief exposures Delore the effect had had time to spread. 226 PROCEEDINGS OP THE AMERICAN ACADEMY IV. Examination of Phosphorescent Tablets by Gelatine Photography. The examination of a phosphorescent surface can be made now in a much more satisfactory manner than formerly. The Hght we have to deal with, being variable, declines from the moment of excitation to the moment of observation. And, though the phosphori now prepared are much more sensitive and persistent than those formerly made, they must still be looked upon as ephemeral. To examine them properly, the eye must have been a long time in darkness to acquire full sensitiveness. It was recommended by Dufay to place a bandage over one eye that its sensitiveness might not be disturbed, whilst the other being left naked could be used in making the necessary preparations. But this on trial will be found, though occasionally useful, on the whole an uncomfortable and unsatisfactory method. The exceedingly sensitive gelatine plates now obtainable remove these difficulties. The light emitted by blue phosphori, such as luminous paint, consists largely of rays between H and G, and these are rays which act at a maximum on the gelatine preparation. So if a gelatine plate be laid on a shining blue phosphorus it is powerfully affected, and any mark or image that may have been impressed on the phosphorus will on development in any of the usual ways be found on the gelatine. The gelatine has no need to wait after the manner of the eye. It sees the phosphorus instantly. It is impressed from the very first moment, and whilst the eye is accommodating itself and so losing the best of the effect, the gelatine is gathering every ray and losing nothing. Moreover, the effect upon it is cumulative. The eye is affected by the intensity of the emitted light, the gelatine by its quantity. Each moment adds to the effect of the preceding. The gela- tine absorbs all the light that the phosphorus emits from the moment of excitation, or by suitable arrangement any fractional part thereof. It has another most important advantage. The phosphorus is yielding an ephemeral result, and is momentarily hastening to extinction, so tliat for a comparison of such a result with otliers of a like kind the memory must be trusted to. But the gelatine seizes it at any pre- determined instant and keeps it forever. These permanent represen- tations can at any future time be deliberately compared with one another. To these still another advantage may be added. Very frequently an impression is much more perceptible on a gelatine copy than it is OF ARTS AND SCIENCES. 227 on the phosphorus from vvhicli that copy was taken. This arises from the fact that the eye is made less sensitive by the light emitted from surrounding phosphorescent parts, and cannot perceive a sombre point or line among them. That is a physiological effect. But a gelatine copy in no respect dazzles or enfeebles the eye. For this reason, for instance, we may not be able in a phosphorograph to resolve visually the infra-red briglit rectangle into its constituent lines, but we recog- nize them instantly in the gelatine. I have made use of sensitive gelatine plates ever since their quality of being affected by phosphorescent light was announced by Messrs. Warnecke and Darwin. The more sensitive of these plates receives a full effect by an exposure of less than one minute. But all kinds of phosphori will not thus affect a photographic tablet : there must be a sympathy between the jjhosphorescent and the photo- graphic surfaces. Thus a phosphorus emitting a yellow light will not affect a photographic preparation which requires blue or indigo rays. This principle I detected many years ago. In my memoir on phos- phorescence (Phil. Mag., February, 1851), it will be seen that the green light emitted by chlorophane could not change the most sensi- tive photographic preparation at that time known — the daguerreotype plate — and hence I was obliged, in measuring the light it emits, to resort to Bouguer's optical method. The result would have turned out differently had the light to be measured been more refrangible, blue or indigo or violet. A photographic surface agrees with the retina in this, that it has limits of sensitiveness. The eye is insensible to rays of much lower refrangibility than A, and much higher than H. Gelatine cannot perceive rays lower than F, but it is affected by others far higher than H. There is therefore a range for each, having its limits and also its j)lace or point of maximum sensitiveness. But some substances, such as the iodide and bromoiodide of silver, under special methods of treatment are affected either positively or negatively throughout the entire range of the spectrum. In experiments for obtaining quantitative results, it should be borne in mind that there is generally a loss of effect. Between the moment of insolation and that of perception, either by the eye or by gelatine, emitted light escapes. The moment of maximum emission is the moment of completed insolation, and from this the light rapidly de- clines. It is necessary, therefore, to make that interval between the two moments as short as possible. 228 PROCEEDINGS OF THE AMERICAN ACADEMY V. Of the Extinction of Phosphorescence by Red Light. I turn now to an examination of those parts of the phosphorographic spectrum from which the light has been removed. They are from the line F to the end of the infra-red space, and again for a short distance above the violet. The effect resembles the protecting action in the same region of a photograph. Now, if similar effects are to be attributed to similar causes, we should expect to find in the photograph and phosphorograph the manifestation of a common action. Several different explanations of the facts have been offered. Her- schel suggested that the photograph might be interpreted on the opti- cal principle of the colors of thin films. Very recently Captain Abney has attributed the appearance of the lower space to oxidation. But this can scarcely be the case in all instances. Mr. Claudet showed, in a very interesting paper on the action of red light, that a daguerreo- type plate can be used again and again by the aid of a red glass, and that the sensitive film undergoes no chemical change. (Phil. Mag., February, 1848). It was known to the earliest experimenters on the subject that if the temperatui'e of a phosphorescent surface be raised, the liberation of its light is hastened, and it more quickly relapses into the dark condition. In the memoir to which I have previously referred (Phil. Mag., February, 1851), I examined minutely into this effect of heat, and determined the conditions which regulate it. And since, on the old view of the constitution of the solar spectrum, the heat was supposed to increase toward the red ray, and when flint-glass or rock salt-prisms are employed to give its maximum far beyond that ray, it was sup- posed that this heat expelled the light, and consequently in all those parts of the phosphorus on which it fell the surface became dark through the expulsion or exhaustion of the light. I speak of this as " the old view," because, as I have elsewhere shown, the curves supposed to represent heat, light, and actinism so called, have in reality nothing to do with those principles. They are merely dispersion curves having relation to the optical action of the prism and to the character of the surface on which the ray falls. (Pliil. Mag., August, 1872, December, 1872.) But this heat explanation of the phosphorescent facts cannot be applied to the photographic. Nothing in the way of hastened or secondary radiation seems to take place in that case. In phosphorescence the facts observed in the production of this OF ARTS AND SCIENCES. 229 blackness are these. If a shining phosphorescent surface be caused suddenly to receive a solar spectrum, it will instantly become brighter in the region of the less refrangible rays, as will plainly appear on the spectrum being for a moment extinguished by shutting off the light that comes into the dark room to form it. If the light be re-admitted again and again, the like increase of brilliancy may again and again be observed, but in a declining way. Presently, however, the region that has thus emitted its light begins to turn darker than the surround- ing luminous parts. If now we no longer admit any spectrum light, but watch the phosphorescent surface as its luminosity slowly declines, the region that has thus shot forth its radiation becomes darker and darker, and at a certain time quite black. The surrounding parts in the course of some hours slowly overtake it, emitting the same cpiantity of light that had previously been expelled from it, and eventually all becomes dark. Now, apparently, all this is in accordance with the hypothesis of the expulsion of the light by heat. There are, however, certain other facts which throw doubt on the correctness of that explanation. On that hypothesis, the darkening ought to begin at the place of maximum heat, that is, when flint glass apparatus is used, below the red ray, and from this it should become less and less intense in the more refrangible direction. But, in many experiments carefully made, I have found that the maximum of blackness has its place of origin above the line D, and indeed where the orange and green rays touch each other. Not infrequently, in certain experiments the exact condi- tions of which I do not know and cannot always reproduce, the dark- ening begins at the upper confines of the green, and slowly passes down to beyond the red extremity ; that is to say, its propagation is in the opposite direction to that which it ought to show on the heat hypothesis. Still more, as has been stated, there is a dark space above the violet. Now it is commonly held that in this region there is little or no heat. If so, what is it that has expelled or destroyed the light ? The experiments above referred to I made with the recently intro- duced luminous paint. It presented the facts under their simplest form. But I have also tried many other samples, for which I am indebted to the courtesy of Professor Barker of Philadelphia, Among them I may mention as being very well known the specimens made by Dubosc, enclosed in flat glass tubes, contained in a nialiogany case, and designed for illustrating the different colored phosphorescent lights emitted. They are to be found in most physical cabinets. 230 PEOCEEDINGS OF THE AMERICAN ACADEMY These, however, do not show the facts in so clear a manner. On re- ceiving the impress of a solar spectrum they present patches of light and shade irregularly distributed. Though in a general way they confirm the statements made above, they do not do it sharply or satisfactorily. Dubosc's specimens to which I have had access are enumerated as follows: 1. Calcium violet; 2. Calcium blue; 3. Calcium green; 4. Strontium green ; 5. Strontium yellow ; 6. Calcium orange. Restrict- ing my observation to the space beyond the red, — which, as has been said, presents a bright rectangle in the darkness, about as far below the red as the red is below the yellow, — I found that this rectangle is not given by 1 and 2. In 3 it is doubtful. In 4 it is quite visible, and in 5 and 6 strikingly so. Is the blackening then due to heat ? That it occurs beyond the violet, that is, beyond the lines H, seems to render such an opinion doubtful, for it is commonly thought that the eflfect of heat is not rec- ognizable there. And in the phosphorogenic spectroscope I have used, the optical train, prism, lenses, &c., is of glass, which must of course exercise a special selective heat-absorptiou ; but the traces of this in the phosphorograph I could never detect. In the diffraction spectrum, I had attempted nearly forty years ago to ascertain the distribution of heat (Phil. Mag., March, 1857), but could not succeed with the experiment in a completely satisfactory manner, so small is the effect. I exposed a tablet of luminous paint to such a diffraction spectrum formed by a reflecting grating, having 17,296 lines to the inch, and was not a little surprised to see that from the blue to the red end of the spectrum there is an energetic extinction of the light, and darkness is produced. I repeated this with other gratings, and under varied circumstances, and always found the same effect. Now, considering the exceedingly small amount of heat available in this case, and considering the intensity of the effect, is there not herein an indication that we must attribute this result to some other than a calorific cause ? I endeavored to obtain better information on this point by using the rays of the moon, which, as is well known, are very deficient in heat- ing power. Many years ago I had obtained some phosphorographs of tliat object. With the more sensitive preparations now accessible, and with a telescope 11 inches in aperture and 150 inches focus, there was no difliiculty in procuring specimens about 1.4 inch in diameter. These represented the lunar surface satisfactorily. At half-moon an I OP ARTS AND SCIENCES. :^81 exposure of three or four seconds was sufficient to give a fair i)roof. But, on insolating a phosphorescent tablet, and causing the converging moon rays to pass through the red glass which I commonly use as an- extinguisher, no effect was produced by the red moonlight on the shining surface. I repeated this experiment using a lens 5 inches in diameter and 7 inches focus so arranged that the moon's image could be kept station- ary on the phosphorescent tablet. That image was about ^ inch in diameter. Then, insolating the tablet, the moon rays, after passing through a red glass, were caused to fall upon it. The exposure con- tinued ten minutes, but no effect was produced on the shining surface. The lunar image was so brilliant that when the red glass was removed, and a non-shining phosphorescent surface was exposed to it, a bright image could be produced in a single second. But in order to remove the effect of the more refrangible rays by the less, the latter must not only have the proper wave length but also the proper amplitude of vibration. This principle applies both to photographic and phosphorographic experiments. In my memoir on the negative or protecting rays of the sun (Phil. Mag., February, 1847) it is said, " Before a perfect neutralization of action between two rays ensues, those rays must be adjusted in intensity to each other." It requires a powerful yellow ray to antagonize a feeble daylight. It is owing to the difference in amplitude of vibration that the heat of radiation seems so much more effective than the heat of conduction. A temperature answering to that of the boiling point of mercury must be applied to a phosphorescent tablet for quite a considerable time before all the light is extinguished. But the red end of the spectrum and that even of the diffraction spectrum, in which the heat can with difficulty be detected by the most sensitive thermometer, accomplishes it very quickly. VI. Op the Intba-bbd Lines or Bands in the Sun's Spectrum. At a distance about as far below the red as the red is below the yellow in the solar spectrum, I found in 1842, in photographs taken on iodide of silver (Daguerre's preparation), three great lines or bands, with doubtful indications of a fourth still further off. I designated them as a, (3, y, and published an engraving of them in the Philosophi- cal Magazine for May, 1843. In 1846, MM. Foucault and Fizeau having repeated the experi- 232 PROCEEDINGS OP THE AMERICAN ACADEMY ment, tlms originally made by me, presented a communication to the French Academy of Sciences. They had observed the antagonizing action above referred to, and had seen the infra-spectral lines a, ^, y. They had taken the precaution to deposit with the Academy a sealed envelope, containing an account of their discovery, not knowing that it had been made and published long previously in America. Sir J. Herschel had made some investigations on the distributioc of heat in the spectrum, using paper blackened on one side and moistened with alcohol on the other. He obtained a series of spots or patches, commencing above the yellow and extending beyond the red. Some writers on this subject have considered that these observations imply a discovery of the lines a, /3, y. They forget, however, that Hers >liel did not use a slit, but the image of the Sun, — an image which was more than a quarter of an inch in diameter. Under such circumstances, it was impossible that these or any other of the fixed lines could be seen. I have many times repeated this experiment, but could not obtain the same result, and therefore attributed my want of success to unskil- fulness. More recently Lord Eayleigh (Phil. Mag., November, 1877), having experimented in the same direction, seems to be disposed to atti'ibute these images to a misleading action of the prism employed. Whatever tlieir cause may be, it is clear that they have nothing to do with the fixed lines a, /3, y, now under consideration. In these experiments, and also in others made about the same time on the distribution of heat in the spectrum, I attempted to form a dif- fraction spectrum without the use of any dioptric media, endeavoring to get rid of all the disturbances which arise through the absorptive action of glass by using as the grating a polished surface of steel on which lines had been ruled with a diamond, and employing a concave mirror instead of an achromatic lens ; and, though my resTilts were im- perfect and incomi^lete, I saw enough to convince me that it is abso- lutely necessary to employ a spectrum that has been formed by reflection alone. (Phil. Mag., March, 1857, p. 155.) In 1871, M. Lamanski succeeded in detecting these lines or bands by the aid of a thermoniultiplier. He was not adequately informed on what had already been done in the matter in America, for he says that " with the exception of Foucault and Fizeau, in their well-known experiments on the interference of heat, no one as yet has made refer- ence to these lines." Nearly thirty years before the date of his memoir I had pul)Ushed an engraving of tliem. (Phil. Mag., May, 1843.) After I had discovered these three lines, I intended to use the grat- OF ARTS AND SCIENCES. 233 ing for the exploration of tliat region, since it extends It, far more than the prism can do; but, on making the attempt, was discouraged by the ditficulty of getting rid of tlie more refrangible lines belonging to the second spectrum. I had hoped to eliminate these by passing the ray on its approach to the slit through a solution of the bichromate of potash. But the bichromate in long exposures permits a suiiiciency of the more refrangible rays to pass, to produce a maj-ked photographic effect ; and hence I feared that any experiments supposed to prove the existence of lines in the infra-red would be open to the criticism that they, in reality, belonged to the more refrangible regions of the spec- trum of the second order, and that a satisflictory examination of the case would exclude the use of the grating and compel that of the prism. With the prism I could not obtain clear evidence of the exist- ence of more than three lines, or perhaps groups, and doubtful indi- cations of a fourth. If in these examinations we go as far as wave length 10,750, the limit of Captain Abney's map, we nearly reach the line H" of the third spectrum. This would include all the innumera- ble lines of spectrum 2, and even many of those of spectrum 3. In such a vast multitude of lines, how would it be possible to identify those that properly belonged to the first, and exclude those of the second and third spectra ? Besides, do we not encounter the objec- tion that this is altogether beyond the theoretical limit of the priamatic spectrum ? This brings us to Captain Abney's recent researches, which, by the aid of the grating, carry the investigation referred to the prismatic spectrum -is far below the red as the red is below the yellow. They are not to be regarded as an extension of exploration in the infra-red region, — for they really do not carry us beyond my own observations in 1842, — but as securing the resolution of these lines or bands into their constituent elements. I had never regarded them as really single lines. The breadth or massiveness of their photographs, too, plainly suggests that they are composed of many associated ones. The princi- ple of decreasing refrangibility with increasing wave length incapaci- tates the prism from separating them, but the grating which spreads them out according to their wave length reveals at once their compo- site character. In Captain Abney's map, after leaving the red line A, we find three groups: (1) ranging from about 8150 to 8350; (2) from 8930 to 9300 ; (3) from 9350 to 9800. These, admitting that the lines of the subsequent grating spectra have been excluded, are then the resolution of a, /3, y. 2-S4 PIIOCEEDINGS OF THE AMERICAN ACADEMY I suppose that care has been taken to make sure of that, either by absorbent media or by a subsidiary prism. If the grating had been ruled in such a manner as to extinguish the second sjjectrum, incon- veniences would arise from the characteristics thereby impressed on the first. In the phosphorographic spectrum on luminous paint, this vast mul- titude of lines is blended into a mass which probably can never be completely resolved into its elements, on account of the propagation of phosphorescence from particle to particle. I have resolved it into two or three constituent groups, and frequently have seen indications of its capability of its resolution into lines, in the serrated aspect of its lateral edges. I believe that luminous paint enables us to approach very nearly, if not completely, to the theoretical limit of the prismatic sj^ectrum. The history of these interesting infra-red lines is briefly this. They were discovered by me in 1842, and an engraving and description of them given in the " Philosophical Magazine." They were next seen by Foucault and Fizeau in 1846, and a description of them presented to the French Academy of Sciences. They were again detected by Lamanski with the thermopile in 1871. Their resolution into a great number of finer lines was accomplished by Abney, who gave a Bukerian lecture describing them before the Royal Society in 1880. Finally, they have been redetected by me in the shining rectangle, just above the theoretical limit of the prismatic spectrum, given by many phosphorescent substances. University of New York Dec. 1, 1880. OF ARTS AND SCIENCES. 236 XI. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OP HARVARD COLLEGE* ON THE DIIODBROMACRYLIC AND CHLORBROM- ACRYLIC ACIDS. By C. F. Mabery and Rachel Lloyd, Presented by H. B. Bihh. The readiness with which brompropiolic acid unites with the halo gens and the haloid acids to form members of the acrylic acid series has been described by Prof. H. B. Hill,t and certain of these addition products have been studied in detail by him and one of us. J The products which result by the action of iodine and of hydro- chloric acid on brompropiolic acid will be described in this paper. Diiodbromacrtlic Acid, CnlgBrO^H. Diiodbromacrylic acid is formed when brompropiolic acid is allowed to stand for some time with a solution of iodine in ether. As this method of preparation was found to be somewhat tedious from the length of time required to complete the reaction, we tried the effect of raising the temperature. Brompropiolic acid, with a slight excess over the calculated weight of iodine and five parts by weight of ether, was heated for two hours under a return condenser on the water bath. The residue left after the evaporation of the ether was extracted with successive portions of warm water, and the solution concentrated by evaporation/ Diiodbromacrylic acid was deposited from this solution, on cooling, in glistening plates, which were purified by recrystalliza- tion from hot water. * This research was conducted in connection with the Summer Course of Instruction in Chemistry. C. F. M. t Berichte der deutsch. chem. Gesellscli., 1879, p 660. t These Proceedings, p. 211. 236 PROCEEDINGS OF THE AMERICAN ACADEMY The yield of pure product by this method has been about sixty per cent of the amount theoretically required. The mother liquors of the first crystallizations gave by evaporation an oily product, which solidi- fied on standing, but which could be purified only with considerable difficulty. This substance crystallizes in flat, white, six-sided plates, very sparingly soluble in cold water, readily in hot, and very soluble in ether, alcohol, carbonic disulphide, and ligroin. It melts at 160°, and sublimes slowly at higher temperatures, apparently unchanged. A yellow coating is formed on the surface when it is exposed to the action of light, yet the decomposition by nitric acid in the estimation of the halogens is not complete below 300°. The following results were obtained by analysis : — 0.5188 grm. substance gave 0.1682 grm. COj and 0.0180 grm. HgO. 0.2004 grm. substance gave by Carius' method 0.3276 grm. Agl -(- AgBr. Calculated for CaTjBrOjH. Found. C 8.93 8.84 H .25 .39 I^ + Br 82.87 82.96 The solubility in cold water was determined by the method of V. Meyer. The filtered solution was neutralized with baric carbonate, evaporated to dryness, and the barium estimated by ignition with sulphuric acid. I. 11.7286 grm. solution gave 0.0707 grm. BaSO^. II. 13.3239 grm. solution gave 0.0793 grm. BaSO^. The solution, saturated at 20°, contains, therefore, the percent- ages : — I. n. 2.08 2.05 Hence diiodbromacrylic acid requires for solution 48.37 parts water at 20°. Salts of Diiodbromacrylic Acid. Baric Diiodbromacrylate, Ba(C8T2Br02)2-4H20. A solution of the acid was heated with an excess of baric carbonate, filtered, and con- centrated by evaporation. The salt crystallized, on cooling, in flat prisms arranged in stellate groups. It is very soluble in hot, less soluble in cold, water. OP ARTS AND SCIENCES. 237 I. 0.8805 grm. air-dried salt gave 0.0638 grm. II.,0 at 80°. 11. 0.8981 gi-m. air-dried salt gave 0.0629 grm. II^O at 80". III. 0.80i9 grm. anhydrous salt gave 0.2002 grm. BaSO^. Calculated for Ba(CjI,BrO,)a.4n,0. Found. I. n. HjO 7.11 7.24 7.00 Calculated for Ba(Csl26r0j)s. Found. Ba 14.55 14.62 To determine the solubility in cold water, a hot solution was kept at 20° for four hours, with occasional stirring. The filtered solution was evaporated to dryness, and the barium estimated by ignition with sulphuric acid. I. 3.2417 grm. solution gave 0.1218 grm. BaSO^. II. 7.0500 grm. solution gave 0.2665 grm. BaSO^. This solution contains, therefore, the following percentages : — I. n. 15.17 15.26 Taking the mean of these results, this salt requires for solution 6.571 parts water at 20°. Calcic Diiodhromacri/Iate, Ca(CgT2Br02)2. This salt was prepared by neutralizing a solution of the acid with calcic carbonate, and evapo- rating the filtered solution. The salt crystallizes in branching needles, which are very soluble in water. 0.5995 grm. of the air-dried salt lost 0.0031 grm. at 80°. This was probably due to the presence of a trace of hygroscopic moisture. 0.5964 grm. of the salt, dried at 80°, gave 0.0945 grm. CaSO^. Calculated for Ca(C3TjBr02)j. Found. Ca 4.74 4.66 Argentic Diiodhromacrylate, AgCgljBrOg. Argentic nitrate, added to a solution of the acid, caused a voluminous precipitate of the silver salt, which was washed and dried over sulphuric acid for analysis. It forms oblique prisms, very slightly soluble in cold water, but readily soluble in dilute niti'ic acid. 0.9585 grm. salt gave 0.2677 grm. AgCl. 238 PROCEEDINGS OP THE AMERICAN ACADEMY Calculated for AgCgljBrOj. Found. Ag 21.17 21.02 Poiassic Diiodbromacrylate, KC3l2Br02.2H20. A solution of tde acid was neutralized with potassic carbonate, and evaporated on the water bath. On cooling, the salt separated in the form of oblique prisms, which are quite soluble in water. 1.8818 grm. of the air-dried salt gave 0.1381 grm. HjO at 80°. 1.7460 grm. anhydrous salt gave 0.3347 grm. KgSO^. Calculated for KC3l2BrOs.2HjO. Found. HgO 7.55 7.33 Calculated for KCsIjBrO,. Found. K 8.87 8.50 Chlorbromacrtlic Acid, CgClBrCgHg. Chlorbromacrylic acid may be made by the action of ordinary fuiu ing hydrochloric acid on brompropiolic acid. This reaction, however, takes place slowly in the cold ; and, although the application of heat causes a more rapid formation of the chlorbromacrylic acid, it pro- duces a secondary decomposition which renders the purification of the product somewhat difficult. We therefore tried the action of hydro- chloric acid saturated at 0°. The acid solution soon became filled with crystals of the addition product ; and after standing twenty-four hours the reaction was complete. The excess of hydrochloric acid was removed by decantation, and by pressure between folds of filter paper, and the chlorbromacrylic acid was purified by crystallization from hot water. It separates as an oily liquid from a hot aqueous solution ; but when nearly cold it crystallizes, forming elongated, flat prisms or needles. This acid melts at 70°, and sublimes quite freely at a somewhat higher temperature. It is much more soluble in hot than in cold water, and readily soluble in ether, alcohol, benzol, and carbonic disul- phide. Its composition was determined by the following analyses : — 0.4462 grm. substance gave 0.3126 grm. COj and 0.0337 grm. HoO. 0.1792 grm. substance gave, by the method of Carius, 0.3186 grm. AgCl -f- AgBr. Calculated for CsClBrOjHj. Found. C 19.40 19.11 H 1.08 .84 Cl-fBr 62.26 61.94 OF ARTS AND SCIENCES. 239 The solubility of this acid in cold water was determined by the same method as the diiodbromacrylic acid. I. 11.6861 grm. solution gave 0.4178 grm. BaSO^. II. 14.4534 grm. solution gave 0.5264 grm. BaSO^. The solution, saturated at 20°, contains the percentages : — I. n. 5.69 5.80 The mean of these results gives 17.41 parts as the quantity of water required for solution at 20°. Salts of Chlorbromacrtlic Acid. The salts of this acid were made by the same methods as the corre- sponding salts of diiodbromacrylic acid. Baric Chlorbromacrylate, Ba(C3ClBr02H)2.2H20. This salt crys- tallizes in flattened prisms, which belong apparently to the monoclinic system. Its composition was established by the following analyses : — I. 0.3730 grm. air-dried salt gave 0.0263 grm. HP at 80°. II. 0.6283 grm. air-dried salt gave 0.0437 g rm, . H„0 at 80°. III. 0.3467 grm. anhydrous salt gave 0.1606 grm. BaSO^. IV. 0.4468 grm. anhydrous salt gave 0.2053 ; grm. BaSO^. Calculated for Ba(C3ClBr02H)2.2H20. Found. TT I. HgO 6.64 7.05 11. 6.96 Calculated for Ba(C8ClBr02H),. Found. ni IV. Ba 27.07 27.23 27.02 The solubility in cold water was determined by the method of V. Meyer. I. 2.8936 grm. solution gave 0.1914 grm. BaSO,. 11. 5.1385 grm. solution gave 0.3378 grm. BaSO^. From these results the following percentages were calculated : — I. 11. 14.06 14.28 This salt, therefore, requires for solution 6.985 parts of water at 20°. Calcic Chlorhromacrylate, Ca(C3ClHrO,II),.4H,,0. This salt forms branching needles, which are very soluble in hot, less soluble in cold, water. 240 PROCEEDINGS OF THE AMERICAN ACADEMY I. 0.4981 grm. air-dried salt gave 0.0762 grm. H,0 at 80°. II. 0.6211 grra. air-dried salt gave 0.0956 grm. Hfi at 80°. III. 0.4219 grm. anhydrous salt gave 0.1424 grm. CaSO^. IV. 0.5096 grm. anhydrous salt gave 0.1713 grm. CaSO^. Calculated for Ca(C3ClBr02H)2.4H20. H^O 14.97 Calculated for Ca{C3ClBr02H), Ca 9.78 I. 15.30 in. 9.93 Found. Found. n. 15.39 IV. 9.87 Argentic Chlorbromacrylate, Ag(C3ClBr02H)2. This salt was pre- cipitated by the addition of argentic nitrate and ammonic hydrate to a solution of the acid. It forms microscopic needles, which are almost insoluble in cold water. I. 0.2760 grm. salt gave 0.1337 grm. AgCl. 11. 0.3445 grm. salt gave 0.1668 grm. AgCl. Calculated for Ag(CsClBrOsH). Found. I. II. g 36.93 36.47 36.88 Potassic Chlorhromacrylate, KCgClBrOjH. This salt forms clusters of irregular, pointed, anhydrous prisms, which are less soluble in cold than in hot water. 0.5346 grra. salt, dried at 80°, gave 0.2132 grm. K^SO^. K Calculated for KCaClBrO^H. 17.49 Found. 17.91 The addition of bromine to chlorbromacrylic acid takes place very readily at the ordinary temperature, with the formation of chlortribrom- propionic acid. A solution of the acid in chloroform was allowed to stand several days, with somewhat more than the calculated weight of bromine. Chlortribrompropionic acid separated from this solution in large prismatic crystals, which after crystallization from carbonic disulphide melted at about 98°. This acid will be submitted to a more extended study. OP ARTS AND SCIENCES. 241 XII. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HAR- VARD COLLEGE. RESEARCHES ON THE SUBSTITUTED BENZYL COM- POUNDS. By C. Loring Jackson. TENTH PAPER. THE RELATIVE CHEMICAL ACTIVITY OF CERTAIN SUBSTI- TUTED BENZYLBROMIDES. Presented November 12, 1879 In the following paper I have the honor of laying before the Acad emy an account of sonae experiments undertaken to compare the ease with which bromine can be removed from the side-chains of the sub- stituted benzylbromides described in the first paper of this series ; in other words, an attempt to establish some relation between the structure of a molecule and its chemical activity. The differences in structure, which I have taken up, are of two sorts, — those depending on difference in the position of the same element, as in the three monobrombenzylbromides ; and those depending on the presence of different but related elements in the same position, as in parachlor-, parabrom-, and paraiodbenzylbromide. After a careful consideration of the reagents by which the side- chain bromine could be removed from these substances in a simple metathetical reaction, I decided that sodic acetate promised the best results, and, after many experiments, adopted a method, which con- sisted in treating equivalent amounts of the substituted benzylbromides, for the same length of time and under the same conditions, with an alcoholic solution of sodic acetate, and determining by volumetric analysis the amount of sodic bromide formed from each according to the following general reaction, — VOL. XVI. (N. S. VIII.) 16 242 PROCEEDINGS OF THE AMERICAN ACADEMY CgH.XCH^Br + NaC^H^O. = QH^XCH^C^HjOa + NaBr in which X stands for the halogen atom attached to the benzol ring. But even this reaction, although less full of sources of error than most of those available, is not so well adapted to work of this sort as I could wish ; since the action takes place so rapidly that small differences in the time of two experiments produce comparatively large differ- ences in their results. I have tried, therefore, to make the time occupied in starting and stopping the action as short as possible, and have reduced the duration of the addition of the sodic acetate solution, by which the reaction is started, to five seconds ; but I have not been so successful in stopping the reaction promptly, as this was done by pre- cipitating the organic matter with water, of which so large a quantity was needed that the average duration of the addition was fifteen sec- onds. This method of stopping the reaction by means of water is not above criticism ; for, although I consider of little or no weight the possible objection that the reaction may continue forming more sodic bromide after the addition of water, yet the presence of even a small amount of the substituted benzylbromide will cause a serious error in the determination of the sodic bromide,* and it is very hard to re- move this completely by filtration ; that it is possible, however, if sufficient care is used, appears from the following experiment : — A mixture of parabrombenzylbromide and parabrombenzylacetate was dissolved in a little alcohol, and, after precipitating with water and filtering, 4 c.c. of a standard solution of argentic nitrate added, upon titrating the liquid 5.3 c.c. of the standard solution of potassic sulphocyanate were found to be necessary, the theoretical quantity being 5.27 c.c. In selecting a solvent, it was necessary to find one which would dis- solve all the substances entering into the reaction ; since Berthelot and Pean de St. Gilles f have shown that, when two liquids which do not mix are used, the amount of action depends to a large extent on the * Tliis point is illustrated by the following experiments : A little parabrom- benzylbromide was dissolved in alcoliol, and precipitated with water ; 2.30 c.c. of a standard solution of argentic nitrate were added, and the mixture allowed to stand fifteen minutes ; on titrating for silver, it was found tliat 0.41 c.c, cor- responding to 0.0069 grm. of AgNOg, liad been lost, while another similar sample which stood for one hour and twenty minutes lost 1.69 c.c, corresponding to 0.026 grm. of AgNOg. t Ann. Chim. Phys., 3d ser., Ixvi. p. 46; Ixviii. p. 238. OP ARTS AND SCIENCES. 243 size of the surface of contact ; and therefore no constant results can be expected. I have confirmed these observations, while studying the action of water on the substituted benzylbromides, as will be de- scribed later in this paper. Under these circumstances, alcohol seemed to be the only solvent admissible ; but its use introduced a new source of error, since it acts on the benzylbromides, forming the correspond- ing ethyl ethers and liydrobromic acid, as is shown by the following experiment. Some parabrombeiizylbromide was boiled with absolute alcohol for fifteen minutes. After removing the organic matter by precipitation with water and filtration, a precipitate was formed on the addition of argentic nitrate. This defect was removed as completely as possible by taking pains that the benzylbromides should be in contact with the alcohol for the same length of time in each series of experiments. Then the results depended, in each case, on two reactions, viz. : — CfiH.XCH.Br + NaaHgO., = CgH^XCH^C^H^O^ + NaBr C6H,XCH,Br + aH.OH = CgH^XCH^OC^Hs + HBr but, as the time of each was the same in all the experiments of a series, the occurrence of the second did not materially affect the result, especially as the amount of substance entering into this second reac- tion was very small. The adjustment of the amount of alcohol to be used was no easy matter, because sodic acetate and bromide are very sparingly soluble in absolute alcohol, and any considerable dilution interferes with the solubility of the benzylbromides; nor could the difficulty be removed by increasing to any great extent the amount of alcohol, as this would have increased the length of time necessary to stop the reaction. More important than any of the sources of error yet mentioned is that proceeding from the differences in volatility of the benzylbromides with alcohol vapor, since this must alter the amount of substance capable of entering into the reaction in each case by the quantity of bromide volatilized with the alcohol in the upper part of the flask ; and it is principally to this cause, which I could find no way of remov- ing, that I am inclined to ascribe the considerable variations in my results. This discussion of the defects in the process shows that no absolute agreement in the numbers obtained can be expected ; but they agree nearly enough to establish certain interesting relations between the rates of decomposition of some of these compounds. 244 PROCEEDINGS OF THE AMERICAN ACADEMY Comparison of the Three Monobrombenzylhromides. One gramme of each substance was weighed in a wide-mouthed flask, the cork of which was fitted with a return-condenser and a short wide tube closed with a cork for the addition of the reagents, 10 c.c of absolute alcohol were added, and the mixture heated for seven minutes in a boiling water-bath. After which, 25 c.c. of a saturated solution of sodic acetate in 99 per cent alcohol, at 60° to 70°, were introduced, and the flask heated for a definite time, varied in each series of exjjeriinents; care being taken that the water-bath boiled violently during the whole time, and that the three flasks to be com- pared were immersed to the same depth, and arranged symmetrically in the bath. The action was stopped by the addition of a large quan- tity of water, the flask being removed from the bath at the same time ; and, after filtering out the organic matter, the quantity of sodic bromide formed by the reaction was determined by Volhard's * excel- lent method of titration with sulphocyanate. The brombenzylbromides used were made in the way described in the first paper f of this series, and purified with the utmost care. The sodic acetate was prepared by drying the crystallized salt in an air-bath. It yielded on analysis the following result : — 0.7720 grm. of NaCgHgO^ gave 0.6655 grm. of Na^SO^. Calculated. Found. Sodium 28.05 27.93 The absolute alcohol did not turn anhydrous cupric sulphate blue, and neither it nor the acidified solution of the sodic acetate gave a precipitate with argentic nitrate. The 25 c.c. of the alcoholic solution of sodic acetate contained a little more than enough of the salt to decompose the one gramme of brombenzylbromide used, since, — 10 c.c. of this solution yielded on evaporation 0.136 grm. of sodic acetate, and therefore, — 25 c.c. contained 0.340 grm. Needed for 1 grm. brombenzylbromide . . 0.328 grm. Excess 0.012 erm. * Ann. Chem. u. Pharm., cxc. p. 1. t Tliese Proceedings, vol. xii. (n. a. iv.) p. 211. OP ARTS AND SCIENCES. 245 The 35 cc. of alcohol preseut were much more than sufficient to dis- solve all the sodic bromide formed, as a rough determination showed that, — 35 CO. of absolute alcohol dissolve 0.627 grm. NaBr. 1 grm. brombenzylbromide yields 0.412 grm. NaBr. All the substances, therefore, were in solution throughout the experi- ment. The accuracy of the method was tested by the following experi- ments, in each of which two portions of parabrombenzylbromide were compared : — L Time, five minutes. A. 1 gramme parabrombenzylbromide lost 0.1164 grm. Br. B. " " " 0.1102 grm. Br. Difference 0.0062 grm. Br. Percentage of total side-chain bromine remoyed. B in per cent of A. A. 36.39 100.0 B. 34.47 94.7 1.92 5.3 II. Time, seven minutes. A. 1 grm. parabrombenzylbromide lost 0.1484 grm. Br. B. " " " 0.1446 grm. Br. Difference 0.0038 grm. Br. Percentage of total side-chain bromine removed. B in per cent of A. A. 46.36 100. B. 45.21 97.5 1.15 2.5 From these results it appears that the method can be trusted within 0.0062 grm. of bromine, or 5.3 per cent when the largest number is taken as 100.* The results of the experiments, comparing the rate of decomposi- tion of the three monobrombenzylbromides, are given in the following table ; the first column of which gives the time from the addition of * The results of these experiments cannot be compared with those given in Table I., because tlie quantity of alcohol used was not the same. 246 PROCEEDINGS OF THE AMERICAN ACADEMY the acetate till the reaction was stopped by dilution with water, while in the other columns, under the name of each substance the amount of bromine removed is given, — first in grammes, and second in per- centages of the total amount of side-chain bromine. Table I. Time in minutes. Parabrombenzylbromide. Metabrombenzylbromide. Orthobrombenzylbromide. Bromine in grammes. Per cent of total. Bromine in grammes. Per cent of total. Bromine in grammes. Per cent of total. 5 10 20 30 0.0855 0.1261 0.1752 0.1880 26.73 39.41 54.75 58.76 0.0621 0.0968 0.1329 0.1517 19.41 30.25 41.54 47.43 0.0533 0.0700 0.1015 0.1412 16.65 21.88 31.72 44.13 On representing the percentages of the total side-chain bromine removed by curves, in which horizontal distance represents time, ver- tical per cents, it is found that those given by the para and meta com- pounds are comparatively regular, but that the ortho curve is decidedly irregular. The same fact is brought out by the following table, in which the amount of bromine removed from the ortho and meta com- pounds in each experiment is given in percentages of the amount derived from the para compound in the same experiment. Table 11. Time in minutes. Para. Meta. Ortho 5 100 73. 62. 10 100 77. 55. 20 100 76. 58. 30 100 81. 75. The differences between the relative amounts of bromine removed from the meta compound in the first three experiments, tabulated above, fall within the limit of error of the process, which amounts to over five per cent when the numbers are given in this form ; and, although the amount of bromine removed during thirty minutes is somewhat larger, the difference between this and the highest of the other numbers is only four per cent. It is probable, therefore, that the relative rate of decomposition for the para and meta compounds remains constant in the interval of time between five and thirty min- utes; and that the slight increase in the numbers with the time in the experiments at 5, 20, and 30 minutes, is entirely accidental, alihouyh OF ARTS AND SCIENCES. 247 this point can be settled only by a new series of observations with a more accurate method. If this is assumed to be true, the mean of the numbers given in the meta column will represent the rate at which the metabrombenzylbromide is attacked, in comparison with that for the para compound taken as 100. This mean is 77; that is, about three quarters as much bromine is removed from the meta as from the para compound in the same length of time. The numbers given in the ortho column show much more serious deviations, the maximum difference amounting to twenty per cent ; but, as I observed that these numbers increased essentially with the time during which the specimen had stood exposed to the air of a desiccator, the experiments having been tried in the following order, — 10 minutes, 55 % ; 5 minutes, 64 % ; 20 minutes, 58 % ; 30 minutes, 75 %, — I was led to the conclusion that the substance was undergo- ing decomposition, which afterwards was proved to be tlie case by the following analyses : I. made before, II. and III. after, the series of experiments. I. 0.2375 grm. of orthobrombenzylbromide gave, by the method of Carius, 0.3565 grm. AgBr. II. 0.2950 grm. of substance gave 0.3705 grm. AgBr. III. 0.4100 grm. of substance gave 0.5210 grm. AgBr. Calculated for CjHgBrj. Bromine 64.00 The complete study of this decomposition must be postponed till a future paper. I can only say here, that no appreciable amount of free hydrobromic acid could be detected in the substance analyzed above, and that I have often found crystals of orthobrombenzoic acid in specimens of orthobrombenzylbromide which had stood exposed to dry air for several months. Whatever may be the nature of the change, it is evident that the ortho numbers are of no value ; and no attempt was made to correct them by new experiments, because such an unstable substance as the orthobrombenzylbromide is entirely unlit for work of this sort. I will add a number of other comparisons, which were made by less accurate processes during the elaboration of the method. They are given as in Table II., the amount of bromine removed from the para * As tliese experiments were made before the orthobrombenzylbromide was obtained in the solid state, 1 had no criterion of its purity except the analysis. Found. I. II. III. 63.87 53.46 54.07* 248 PROCEEDINGS OF THE AMERICAN ACADEMY compound being taken as 100 in each experiment, aud the amounts from the meta and ortho compounds given in percentages of this. Either two or four grammes of substance were taken in each experi- ment. Table III. Time in Minutes. Para. Meta. Ortho. 22 100 78 54 22 100 73 52 23 100 78 54 21 100 — 48 Mean, 100 76 52 These numbers, entitled to very little consideration as independent experiments, confirm the preceding results from the meta compound, even more closely than could be expected when the large limit of error is remembered ; and further would seem to indicate that the rate for the ortho compound is about one half that for the para, if it is assumed, as before, that the relative rate does not vary with the length of time during which the reaction has run ; a result confirmed by the experiment made first in the preceding series, and therefore entitled to the most weight, which gave 55 %. Berthelot and Pean de St. Gilles,* in their classic researches on etherification, found that after a certain time the water set free in the reaction prevented further formation of the ether ; in other words, that there was a limit to etherification. Although it did not seem probable that there would be such a limit to this reaction, some experi- ments were tried to test the question, with the following results : — I. Time somewhat more than two hours : — 1 grm. of parabrombenzylbromide lost 0.3203 grm. of bromine. 1 grm. of metabrombenzylbromide lost 0.2701 grm. of bromine. 0.8200 grm. of parachlorbenzylbromide lost 0.3082 grm. of bromine. To this may be added the following, in which the method was somewhat different ; in II. common alcohol being used, and in III. the reaction taking place in a sealed tube, with dilute alcohol as the solvent. II. Two portions of parabrombenzylbromide, 1 grm. each, lost in twenty-five minutes 0.3113 grm. and 0.3074 grm. of bromine. III. In thirty minutes 0.3046 grm. and 0.3093 grm. of bromine. * Ann. Chim. Phys., 3d ser., Ixviii. p. 225. OF AUTS AiND SCIENCES. 249 The results of these three experiments, calculated into percentages of the side-chain bromine, are given lor the sake of comparison in the following table : — Table IV. I. II. in. Para. 100.1 Para. 97.3 Para. 95.3 Meta. 84.4 " 96.1 " 96.7 Chlor. 96.4 Owing to the different conditions under which they were made these series of experiments are not comparable with each other, or with the series given in Tables I. and II., even I. not having been made under exactly the same conditions ; they show, however, that there is no limit to the reaction in the case of the parabrombenzylbro- mide and probably none in the case of any of these substances. Action of Water on the Monohrombenzylbromides. Another entirely different method was also tried, which consisted in heating the substituted benzylbromides with water in sealed tubes, and determining the amount of hydrobromic acid formed by the reaction, — • CgH.BrCH^Br + Hp = CgH^BrCH^OH + HBr For this purpose one gramme of each substance was weighed in a tube about 14 cm. long and 2 cm. wide; 5 c.c. of water were added, and, after sealing, the tubes were put into a hot chloride of calcium bath, provided with an air-tight tin cover carrying a return-cooler, which thus was kept at a constant temperature throughout the process. After a definite time the tubes were removed, cooled as rapidly as possible with cold water, and the contents washed into a beaker, and titrated with a standard solution of baric hydrate. The following ex- periments were made with two portions of parabrombenzylbromide to test the process. Time in Hours. Temperature. Percentage of side-chain bromine remoTed. Portion a. Portion b. I. 2 132°-134° 16.05 13.3 n. 2| 110°-134° 17.8 16.3 I. n. a 100 100 h 83 92 250 PROCEEDINGS OP THE AMERICAN ACADEMY The marked want of agreement between these numbers is undoubt- edly due to the fact that the mixture was not homogeneous, and there- fore the differences in size of the surface of contact between the water and benzylbromide in the different tubes had a marked effect on the result [Compare p. 242]. In spite of the inaccuracy of the method two experiments were :'arried through with the following results : — Table V. Temperature 135°. Time in hours. Parabrombenzylbromide. Metabrombenzylbromide. Orttiobrombenzy Ibromide . Bromine in grammes. Per cent of total. Bromine in grammes. Per cent of total. Bromine in grammes. Per cent of total. 6 6 0.1421 0.1268 43.85 39.15 0.0969 29.9 0.0763 0.0918 23.55 28.35 These results calculated into the form of Table II. become : — Para. Meta. Ortho 100 54 100 76 72 The very high number for the ortho compound in the second exper iment is probably due to a previous decomposition of the substance similar to that observed in the principal series of experiments [See page 247] . The other results, as far as they go, confirm those obtained by the acetate method. In the following table all the numbers thus far obtained are com- pared : — Table VL Acetate Method. Time. Para. Meta. Ortho 5' 100 72 64 10' 100 77 55 20' 100 76 58 30' 100 81 75 21' 100 — 48 22' 100 78 54 22' 100 73 52 23' 100 78 54 OF ARTS AND SCIENCES. 251 Water Method. 6 hours 100 54 6 hours 100 76 72 Mean 100 76 59 A series of comparative experiments with parachlorbenzylbromide, parabrombenzylbi'omide aud paraiodbenzylbromide was also made by the sodic acetate method, which indicated that they lose bromine at the same rate, when they are used in molecular projiortions. I will give here, however, only the results from the last series of experi- ments, as in the others I did not succeed in overcoming some of the sources of error mentioned in the introduction wholly to my satisfac- tion. These results are given as in Table II. Time in Minutes. Parachlorbenzylbromide. Parabrombcnzylbromide. Paraiodbenzylbromide. 25 100 97 99 Summary. The results of this investigation are, — 1. The side-chain bromine is removed from the three raonobrombenzylbromides approximately at the following rates : — Ortho. 55 (?) 2(?) when the quantity removed is less than 60 per cent of the whole. 2. From parachlor-, parabrom-, and paraiodbenzylbromide at essen- tially the same rate, if quantities proportional to their molecular weights are used. All these results need confirmation by more accurate experiments, but, as Menschutkin in one of the papers* of his beautiful series on the rate of etherification (the first f of which was published a year after the appearance of a preliminary notice J of my work) has an- nounced his intention of studying the eff"ect of aromatic isomerism, and with his better chosen reaction and more delicate method will be able to do the work much more easily and accurately than I could, I have decided not to pursue the subject farther. So far as I have been able to find, the only paper on this subject, as yet published, is one by Post and Mehrtens, § who describe a single * Ann. Chem. Pharm., 197, p. 225. \ Ber. rl. ch. G. 1876, p. 931. t Ber. d. ch. G. 1877, p. 1728. § Ber. d. ch. G. 1875, p. 1549. Para. Meta. 100 76 4 3 252 PROCEEDINGS OP THE AMERICAN ACADEMY attempt to make out the relative acidity of the three nitrophenols by treating weighed amounts of baric carbonate with solutions of the corresponding quantity of the three isomeres, and after one week determining the amount of baric carbonate dissolved. In this way they got results which calculated in percentages of the amount from the para compound become : — Paxa. m.pt. 115°. Meta. m.pt. 96°. Ortho. m.pt. 45°. 100 57 93 and, therefore, agree with mine neither in order nor ratio. ELEVENTH PAPER. As the preceding paper has brought the first part of these researches to a conclusion, I have thought it best to give in the present paper certain corrections and additions which will leave this division of the subject in a more satisfactory state. Parabrombenzyl Compounds. In preparing the alcohol of this series during the work described in the preceding paper, I was surprised to find that its melting-point was much higher than that given by Mr. Lowery in the second paper* of the series, and as in addition to this some portions of that work were left in a decidedly fragmentary state, I have thought it best to submit the parabrombenzyl compounds to a complete revision, which I have done vyith the following results : — Parahromhenzylalcohol, CgH^BrCH20H. This was prepared from the acetate, and purified by crystallization from ligroin, which is by far the best solvent for all the derivatives of the substituted benzyl- bromides described in these papers. 0.2298 grm. of substance gave 0.3765 grm. of COj and 0.0789 grm. of Hp. Calculated for CjHoBrOH. Pound. Carbon 44.92 44.69 Hydrogen 3.74 3.82 ♦ These Proceedings, xii. (n. s. iv.) p. 221. OP ARTS AND SCIENCES. 253 The melting-point of the pure alcohol was 77°.* In other respects its properties are given correctly by Mr. Lowery. Parabromhenzylcyanide melts at 47° (46° Lowery). The alpha- toluylic acid as before at 114°. Parahrombenzyhulphocyanate, CgH^BrCIIjSCN, melts at 25° as given by Mr. Lowery. As this melting-point is much lower than would be expected from that of the benzylsulphocyanate (36°-38° Henry, 41° Barbaglia), I thought it advisable to confirm its formula by the following new analyses : — 0.2318 grm. of substance gave 0.2447 grm. of BaSO^. 0.3804 grm. of substance gave 0.3125 grm. of AgBr. Calculated for CiHsBrSCN, Found. Sulphur 14.03 14.50 Bromine 35.09 34.95 Parabromhenzylamines. Parabrombenzylbromide acts on alcoholic ammonia in the cold, giving a mixture of the three amines, or their brouiides, from which the pure compounds can be easily obtained by washing out the bromide of the primary amine with water, treating the residue with sodic hydrate, and separating the secondary from the tertiary by crystallization from alcohol. The jyrimary amine, set free from its bromide with sodic hydrate, is an oil, which can be distilled with steam, and is soluble in ether ; it is rapidly converted into the carbonate by exposure to the air. The carbonate, obtained by treating the free base with carbonic dioxide, consists of little white prisms arranged in radiating groups, which melt at ]3l°-133°, are soluble in water and alcohol, insoluble or nearly so in ether, benzol, and carbonic disulphide. The chloride, made from the carbonate with hydrochloric acid, forms flattened needles melting with apparent decomposition at 260°, soluble in water and hot alcohol, but slightly soluble in cold alcohol, and essentially insoluble in ether, benzol, and carbonic disulphide. The chlorplatinate (CgH^BrCHjNHg), PtClg made from the chloride, and purified by washing with water, gave the following result on analysis : — * The high melting-point of the parabrombenzylalcohol made me think that the paraiodbenzylalcohol might melt at a temperature higher than that given by Mr. Mabery in the third paper of this series. He has, however, at my re- quest recrystallized some of it from ligroin, and found that the melting-point remained the same (72°) even after three crystallizations. 254 PROCEEDINGS OF THE AMERICAN ACADEMY 0.3020 grm. of the salt gave 0.0755 grm. of Pt. Calculated for (CjHsBrNHjjj.PtClg. Found. Platinum 25.16 25.00 It crystallizes in orange-brown plates, apparently of the monoclinic system, grouped in forms like frost, and is but slightly soluble in cold water, more so in hot, and in alcohol. The secondary amine (CgH4BrCH2)2NH is left on evaporating its alcoholic solution as an oil, which solidifies on stirring, and can be obtained crystallized. It melts at 50°, and is very freely soluble in alcohol and ether. The chloride is obtained in glistening rhombic scales, often pen- nately twinned, by adding strong hydrochloric acid to an alcoholic solution of the base ; it melts at 283°, and is nearly insoluble in cold, somewhat more soluble in hot water, or alcohol, insoluble in ether. The chhrplatinate [(CeH^BrCH.OaNryoPtCl, formed by adding chlorplatinic acid to an alcoholic solution of the free base, after being washed with alcohol, and dried at 100°, gave the following result on analysis : — 0.4716 grm. of salt gave 0.0802 grm. of Pt. Calculated for [(CTHeBrjjNHjloPtClg Found. Platinum 17.58 17.01 It is a yellow powder, nearly insoluble in alcohol and water. The tertiary amine (CgH^BrCH2)8N was purified by recrystalliza- tion from ether, or from ligroin ; in either case a matted mass of needles looking like cotton was obtained, but the melting-jjoint differed according to the solvent used, the crystals from ligroin showing the constant melting-point 92°, those from common ether the constant melting-point 76°-78°. Two recrystallizations from ligroin were enough to raise the melting-point of the crystals from ether to 92°, while the same number from ether lowered it again to 76°-78°. The following analyses, however, prove that the substance dried in vacuo has the composition of the tertiary amine, whichever solvent was used in its purification. I. 0.3800 grm. of the crystals from ligroin, m.pt. 92°, gave 0.6680 grm. CO2 and 0.1200 grm. 11,0. II. 0.2515 grm. of the crystals from ether gave 0.4430 grm. COj and 0.0890 grm. H^O. 0.2020 grm. of the crystals from ether gave 0.2175 grm. AgBr. 0.1888 grm. gave 0.2022 grm. AgBr. t)F ARTS AND SCIENCES. 255 Ciiloulatcl for Found. (CjIIiillrigN. I. (LiRroin.) II. (Ether.) Carbon 48.09 47.93 48.03 Hyclrogen 3.44 3.51 3.93 Bromine 45.81 45.82 45.56 Properties. Fine white needles matted together into a woolly mass, or forming circular radiated gi'oups, insoluble in water, very slightly soluble in alcohol hot or cold, not freely in warm ether, but easily in hot ligroin, from which it crystallizes on cooling. In the preparation from alcoholic ammonia and parabrombenzylbromide it sometimes appears in needles 12 cm. long. No definite chloride could be obtained even by precipitating the platinum as sulphide from the chlorplatinate, and washing with alcohol, as this gave only a viscous varnish. Triparabromhcnzykanine Chlorplatinate [(Cj;H^BrCIT^)oNH]„PtClg made by adding chlorplatinic acid to an ethereal solution of the free base, and purified by washing with water, alcohol, ether, and ligroin, gave the following result on analysis: — 0.3254 grm. of the salt gave 0.0432 grm. of Pt. Calculated for [(CTHeBrJsNHljPtClg. Found. Platinum 13.51 • 13.28 Corn-yellow indistinct crystals, insoluble or nearly so in all the common solvents. Monoparaiodhenzylamine, G^HJGH^NH.^. Mr. C. r. Mabery has, at my request, prepared this substance, which he had not obtained in quantity sufficient for analysis, when he pub- lished his paper on the paraiodbenzyl compounds, by heating paraiod- benzylbromide with a large excess of alcoholic ammonia* in a sealed tube to 120°. It is easily separated from the secondary and tertiary amines by washing with water, and, upon adding sodic hydrate to the solution of its bromide thus obtained, and extracting with ether, the carbonate is left as the ether evaporates in the form of a white solid melting at 113°. The chloride made from the carbonate with hydrochloric acid forms slender white needles melting at 240°, readily soluble in water and alcohol, si)aringly in ether. The chlorplatinate (CgH^ICH2NH3)2PtClg made by adding chlor- 256 PROCEEDINGS OF THE AMERICAN ACADEMY platinic acid to the chloride, and purified by washing with alcohol, gave the following result on analysis : — 0.3560 grm. of the salt gave 0.0795 grm. Pt. Calculated for (C7HeINH3)jPtCl,. Found. Platinum 22.47 22.34 Metabrombenzyl Compounds. In the study of these substances which I undertook with Mr. J. Fleming White, so many difficulties were encountered that the work was far from done at the end of the last college year. As, however, Mr. White has left Cambridge, and I see no immediate prospect of returning to this subject, I have decided to publish our results on the alcohol, and the melting-point of the alphatoluylic acid, reserving an account of the amines until our, at present contradictory, results have been submitted to a thorough revision. Metabromhenzylalcohol, CgH^BrCHjOH, was made directly from metabrombenzylbromide by heating it with water in a sealed tube to 130° for 24 hours, or from the acetate, obtained by heating the bro- mide with an alcoholic solution of sodic acetate, by decomposing it with aqueous ammonia in a sealed tube at 150°, or with an aqueous solution of sodic hydrate in a flask with a return-cooler. The oil thus obtained was purified by distillation with steam, dried in vacuo and analyzed. 0.2890 grm. of substance gave according to Carius 0.2913 grm. AgBr. 0.4660 grm. gave 0.4690 grm, AgBr. Calculated for CjHgBrOH. Found. Bromine 42.79 42.88 42.84 The substance is a colorless oil heavier than water, which did not solidify in a freezing mixture even when vigorously stirred with a sharp rod. ' The cyanide, as obtained by the action of an alcoholic solution of potassic cyanide on metabrombenzylbromide, is a dark-colored oil, and is converted by heating with strong hydrochloric acid in a sealed tube to 115° into the metahromalphatoluylic acid, melting-point 97°, which resembles the isomeric acids already described very closely. The complete study of this acid must be postponed for the present. or ARTS AND SCIENCES. 257 INVE8T10ATION8 ON I/IOHT AND IIeAT, PUnUHHED WITH AN APPROPBUTION FROM TUB RUMFORD Fund. xin. VARIABLE STARS OF SHORT PERIOD. By Edward C. Pickering. Presented February 9, 1881. In a recent communication to this Academy * the following classifica- tion of the variable stars was proposed : — I. Temporary stars. Examples, Tycho Brahe's star of 1572, new star in Corona, 18G6. II. Stars undergoing great variations in light in periods of several months or years. Examples, o Ceti and ^ Gygni. III. Stars undergoing slight changes according to laws as yet un- known. Examples, a Orionis and a Cassiopeice. IV. Stars whose light is Continually varying, but the changes are repeated with great regularity in a period not exceeding a few days. Examples, ft LyrcE and 8 Cephei. V. Stars which every few days undergo for a few hours a remark- able diminution in light, this phenomenon recurring with great regu- larity. Examples, (i Persei and S Cancri. A discussion was given, in the article referred to, of the stars of the last class. It was shown that in the case of jB Persei at least, the observed variations could be very satisfactorily explained by the theory that the reduction in light was caused by a dark eclipsing satellite. The dimensions of this satellite and of its orbit were then computed. The variations of the stars of the fourth class will be considered in the present paper. Both of these papers must be regarded as prelimi- nary, rather than final, discussions. Observations are now in progress at the Harvard College Observatory which greatly increase the preci- sion of our knowledge of many of the constants involved. When these are completed, a revision of the whole investigation is much to be desired. To avoid all prejudice, the present papers are made to * Proc. Amer. Acad., xvi. 1. VOL. XVI. (n. 8. VIII.) 17 25b PROCEEDINGS OF THE AMERICAN ACaDEMY depend entirely ou the work of previous observers. Approximate methods are depended upon throughout, where a rigorous computation would have been employed, if the results were to be regarded as final. In Table I. is given a list of all the known variable stars whose periods are less than three mouths. The successive columns give a current number, the number in Schonfeld's Secoud Catalogue,* the name of the star, and the class to which it belongs, when this is known with cert-aiuty. Then follow the right ascension and declination for 1880, the period in days, and the inaguitudes at maximum and minimum. The data for the southern stars which are not given by Schoufeld are taken from the Uranometria Argentina. The last columns give the name of the discoverer and the year in which the variability was detected. TABLE I. — Variable Stars of Short Periods. a C3 Name. CI. R.A. 1880. Dec. 1880. ■6 0 Max. Min. Discoverer. Year. ^; & & h. m. 0 / 1 — Cephei V 0 51.7 +81 14 2.49 7 10 Ceraski 1880 2 17 )3 Persei V 3 0.4 +40 30 2.87 2.2 37 Montanari 1669 3 19 \ Tauri V 3 54.0 +12 9 8.95 3.4 4.2 Baxendell 1848 4 82 T Monocerotis IV 6 18.7 + 79 27.00 6.2 7.6 Gould 1871 5 34 S Moiiocerotis , , 6 34.4 +10 0 3.40 4.9 5.4 Winnccke 1867 6 36 ( Geniinormn IV 6 57.0 +20 45 10.16 3.7 4.5 Schmidt 1844 7 , , U Moiiocerotis 7 25.1 — 9 32 46.00 6.0 . 7.2 Gould 1878 8 47 S Caiicri V 8 37.1 +19 28 9.48 8.2 9.8 Hind 1848 9 N Vtloruni 9 27.6 —56 30 4.25 3.4 4.4 Gould 1871 10 / Carinas 9 42.0 —6157 31.25 3.7 5.2 Gould 1871 11 R Miiscae 12 34.8 —68 45 0.89 6.6 7.4 Gould 1871 12 66 yV Virginis 13 19.8 — 2 45 1727 8.7-9.2 9.8-10.4 Schonfeld 1866 13 74 5 Libraj V 14 54.6 — 82 2.32 4.9 6.1 Sclimidt 1859 14 T Triang. Aust. 14 58.6 —68 15 1.00 7.0 7.4 Gould 1871 15 li Triang. Aust. 15 9.1 —66 3 340 6.6 7.5 Gould 1871 16 75 U Coronas V 15 13.8 +32 5 3.45 7.6 8.8 Winnccke 1869 17 96 11 Herciilis 17 12.9 +33 14 88.50 4.6 5.4 Schmidt 1869 18 98 X Siigittarii 17 40.0 —27 47 7.01 4 6 Schmidt 186C) 19 99 W Sagittarii , , 17 57.4 —29 35 7.59 6 6.5 Schmidt 1866 20 — Sagittarii 18 9.8 —84 9 2.42 6.2 7.4 Gould 1871 21 16:"] U Satiiltarii 18 24.8 —19 13 6.75 7.0 8.3 Sclimidt 1866 22 105 R Scuti 18 41.1 — 5 50 71.10 4.7-5.7 6.0-8.5 Pigott 1795 23 K Pavonis 18 44.6 —67 23 9.10 4.0 6.6 Gould 1872 24 roe $ Lyras iv 18 4.J.6 +33 18 12.91 3.4 4.5 Goodricke 1784 25 107 R Lyras 18 51.7 +43 47 46.00 4.3 4.G Baxendell 1856 ■lij 108 S Coron. Aust. , , 18 53.1 — 'u 7 6.20 9.8 11.5? Schmidt 1866 27 109 A' Coron. Aust. 18 58.8 -87 7 54,00 10.5-11.5 <12.5 Schmidt 1866 28 116 S Vulpeculaj 19 43 5 +2() 59 67.50 8.4-8.9 9.0-9.5 Hogerson 1887 21) 118 T] Aquilas IV 19 46.4 + 0 4:i 7.18 3.5 4.7 Pigott 1784 80 122 7i' Sagittas 20 8.6 + 15 22 70.42 8.5-8.7 9.8-10.4 Baxendell 1859 31 137 S Cc'phei iv 22 24.7 + 57 48 5.37 3.7 4.9 (ioodricke 1784 * Zweiter Catalog von veriinderlicheii Sternen. Mannheim, lb75. OF ARTS AND SCIENCES. * 259 From this table it appears that only six stars of the fifth class are as yet known. Although the published observations of some of the others are insuiricioiit to determine the nature of their variations, it is probable that most of them belong to the fourth class. The first star on the list, which is DM. 81°.25, has been designated as T Cephei,* but the use of this name has created much confusion. In 18G3,t Arge- lander announced the variability of the star DM. 55°. 2943, and this star is called T Cephei in Chambers' Astronomy, p. 586. In 1871), Ceraski t announced that DM. 67°. 1291 was variable. When cor- rectuig its position § he called it T Cephei. This correction is quoted in the " Astronomical Register," xviii. 322, under the heading " W. Ceraski's new Variable," apparently confounding it with Ceraski's last discovery, DM. 81°.25. The most natural explanation of the variation of a star of short period is that it is due to its rotation around lis axis. In the Annals of the Harvard College Observatory, xi. 264, the variation in light of lapetus, the outer satellite of Saturn, is discussed on this hypothesis. It is there shown that if tlie axis of revolution is perpendicular to the line of sight, the variation of light, L, may be approximately represented by the formula, L =^ a -\- h ?kw v -\- c eos V -|- c? sin 2 w -]- e cos 2 v ; « here denotes the mean light, v the angle of rotation, h and c are constants depending on the comparative brilliancy of the two hemispheres, each of which is supposed to be of uniform intensity, but one brighter than the other ; d and e depend on a supposed deviation of the body from the form of a solid of revolu- tion. This equation may also be written in the form Z = a -f- m sin (y -|- «) -|- « sin (2 v -(- /3), in which a depends upon the angular position of the plane separating the two hemispheres from the line of sight at the epoch from which the variation in light is reckoned ; ^ in like manner depends upon the positions in which the body subtends its largest and smallest discs. Our problem then is to see how far this equation will represent the variation in light of all the stars of the fourth class. Both of these proposed causes of variation may be criticised as improbable ; but what could be more improbable than the phenomenon itself, were it not verified by observation ? With our present knowl- * Science Observer, iii. .SO, 38, 48. English Meclianic and World of Science, xxxii. 2'j7. Astron. Nach. xcix. 87. t Astron. Nach., Ixi 281. X Astron. Nach., xciv. 175. § Astron. Nach , xcviii. 239. 260 PROCEEDINGS OF THE AMERICAN ACADEMY edge of the constitution of the stars it would seem extremely unlikely that certain of them would lose half their light at regular intervals of from one to twelve days. If it can be shown that the hypothesis sat- isfies the observed facts, it seems unreasonable to deny it until some more probable explanation can be offered. The difference in bright- ness of the two sides of a star may be due to spots like those of our sun, to large dark patches, or to a difference in temperature. In the latter case, observations of the distribution in light in the spectrum at the maxima and minima might show a greater variation in the blue than in the red portions. If the body had the form of an oblate ellipsoid rotating around one of its longer axes, its condition of equi- librium would be unstable. If, however, it was a prolate ellipsoid it would be in stable equilibrium, and if sufficiently rigid might revolve in this way indefinitely. If, like our sun, it was in a fluid condition, we might anticipate a return to the form of a solid of revolution. Jacobi h;is however shown * that a fluid ellipsoid having three unequal axes may be in equilibrium when revolving around its shortest axis. An analogous case is found in Plateau's experiment, where a globule of oil suspended in alcohol and water is made to revolve. "With a suffi- cient velocity the globule, if slightly eccentric, elongates before throw- ing off a satellite. We may also assume the existence of two nuclei, or that the two components of a binary star are so close together that both ai"e enveloped in the incandescent gas or photosphere. Another equation of condition would thus be furnished which might serve to determine the absolute diameter of the star in miles. Thus the observations discussed below give the relative dimensions of two of the axes, and the condition that the body shall be in equilibrium will determine the relative length of the axis of revolution. If the star was an ellipsoid of revolution we could compute the flattening at the poles from the diameter and the time of revolution ; we could also compute the diameter if the other two constants were given. Although the problem is more complex, evidently the same principle may be applied to an ellipsoid with three unequal axes. Four of these stars, t, Geminoriim, fS Lyrce^ TjAquiliS, and 8 Cephei, have been observed with great care, so that their variations are known with much precision. Each will therefore be discussed in turn, accord- ing to the following method. As the variation is periodic, it will be convenient to denote the time by an angle, v, such that 360° shall corre- spond to one period or revolution of the star. We now wish the light * Poggeiidorff's Aniialcn, xxxiii 220; see also Jourii Frank. Inst. ex. 217. OF ARTS AND SCIENCES. 261 corresponding to v = 0°, 15°, 30°, 45°, etc. The period is divided into twenty-lour equal parts, and the number of grades corresponding to each is taken from the light curves. Argelander and Schoufeld give the number of grades for each hour, and the number of grades was found from their tables by interpolation. Oudemans represents his results graphically, and the grades were taken from his curves by inspection. These curves were used rather than the original observa- tions, in order to reduce the accidental errors. The results are free from prejudice, since they were drawn by the observers themselves with- out regard to any theoi-y. They are, however, open to the objection that small systematic errors may be present which are not easily detected. We must next pass from grades to the actual intensities of light. For this purpose we cannot rely on an assumed value of a grade, since we have no certainty that this will be the same for lights of different intensity. Accordingly, the comparison stars used by each observer are compared with the measures of Wolff.* Points were constructed whose abscissas equal the assumed light of each comparison star in grades, and their ordinates, the logarithms of the light as measured by Wolff. A smooth curve was then drawn through these points, and served to convert the grades into logarithms. The readings are only made to hundredths, since one unit in this place corresponds to one- fortieth of a magnitude, and all the curves are uncertain by much more than this amount. The largest logarithm is then subtracted from all the others, and the number corresponding to the difference gives the intensity of the light. This is multiplied by one hundred, so that the results are given in percentages. In the equation, L^a -\- m sin (v -\- a) -\- n sin {2 v -\- /3). a is found from the mean of all the observed values of L. The other con- stants might be found from a solution by least squares, forming twenty- four equations of condition with the twenty-four deduced values of L. Sufficient accuracy is, however, obtained by approximate graphical methods. By adding together the values of L, corresponding to values of V differing 180°, we eliminate the term m sin (y -j- «). Their dif- ferences, in like manner, eliminate n sin (2 v -\- /3). Each then may thus be found independently of the others. ^ Geminorum. In 1848, Argelander gave a light curve of this star.f * Photometrische Beobaclitungen an Fixsternen, Leipzig, 1877. t Astron. Nacli., xxviii. 33. 262 PROCEEDINGS OF THE AMERICAN ACADEMY Table II. gives the data for converting the grades into light ratios by means of the comparison stars. The successive columns give the name of the star, its light in logarithms as measured by Wolff, its liglit in grades assumed by Argelander, the corresponding ordinate of the curve, and the second column minus the fourth, or the assumed ei'rors. TABLE II. — Comparison Stars for ( Gemixorum. Name. Wolff. Grades. Curve. w— c ^ Geminorum .... 8.81 9.9 8.81 .00 5 Geininoruin .... 8.78 8.8 8.74 — .01 A. Geniinorum .... 8.68 8.0 8.70 —.02 I Geniinorum .... b.GG 6.0 8.64 +.02 V Geniinorum .... 8.58 33 8.58 .00 If Geniinorum .... 8.55 2.0 8.55 .00 The curve here agrees very well with the measurements, but its inclination is much greater for the brighter than for the fainter stars. In other words, a grade represents a much larger difference in magni- tude when the star is bright tlian when faint. The change is, however, slight between the limits within which the curve is used. Table III. gives a comparison of the light curve with theory. The successive columns give the angle v, the corresponding time from the minimum, and the observed light in grades, in logarithms, and in percentages. The next column gives the light computed by the formula, L = 89.6 -{- 10.0 sin v ; this is followed by the residuals found by subtracting the computed from the observed brightness. As they show a perceptible systematic error, two more columns are given corresponding to the formula L = 89.6 -}- 10.2 sin {v — 11°. 3). This gives an entirely satisfactory agreement with observation, the average deviation amounting to less than one per cent. It cannot be reduced directly to magnitudes, since, when the light equals 100, one per cent equals .011 magnitudes, when 80, .014 magnitudes, and M-hen 50, .022 magnitudes. The average deviation is accordingly only about one hun- dredth of a magnitude. Since two smooth curves are compared, the small irregular variations in the residuals are principally due to the neglected thousandths in the logarithm of the light. They are, how- ever, probably far less than the real errors of the curves. The mean of the residuals is given in the last line of the table. OF ARTS AND SCIENCES. 263 TABLE III. — Variation in Light of ( Geminori'm. V. Time. Gr. Log. Obs. Comp. o-C Com p. 0—C o 0 d. 0 h. 0.0 3.4 8.58 79 80 —•1 79 0 15 0 10.2 3.6 8.58 79 80 —1 80 —1 30 0 20.3 4.1 8.59 81 81 0 82 —1 45 1 6.5 4.7 8.61 85 82 +3 84 + 1 60 1 16.6 6.2 8.62 87 85 -f2 +2 86 +1 75 2 2.8 5.7 8.63 89 87 89 0 90 2 12.9 0.1 8.64 91 90 -j-1 92 —1 105 2 23.0 6.5 8.65 93 92 4-1 94 —1 120 3 9.2 6.9 8.66 96 95 +1 96 0 135 3 19.4 7.2 8.67 98 97 +1 98 0 150 4 5.5 7.3 8.67 98 98 0 100 —2 165 4 15.7 7.4 8.68 100 99 +1 100 0 180 5 1.8 7.4 8.68 100 100 0 100 0 195 6 12.0 7.3 8.67 98 99 —1 99 —1 210 5 22.2 7.1 8.67 98 98 0 98 0 225 6 83 6.8 8.66 96 97 —1 96 0 240 6 18.5 6.4 8.65 93 95 2 93 0 255 7 4.6 6.0 8.64 91 92 —1 90 +1 270 7 14.8 5.5 8.63 89 90 —1 88 +1 285 8 0.9 5.0 8.61 85 87 —2 85 0 300 8 11.1 4.5 8.60 83 85 —2 83 0 315 8 21.3 4.0 8.59 81 82 —1 81 0 330 9 7.4 3.7 8.59 81 81 0 80 +1 345 9 17.5 3.5 8.58 79 80 —1 79 0 Mean . . ±1.1 ±0.5 There seems to be no evidence of the term n sin (2 v -\- /S) ; in other words, the star appears to be a surface of revolution, one side being about four-fifths of the brightness of the other. It is also possible that the star may be elongated with axes in the ratio of four to five, but of equal brightness on all sides, and that its time of revolution is 20.32 days, or double the period commonly given. In this case there may b6 a slight ditference in brightness at the alternate maxima or minima which has hitherto escaped detection, because not antici- pated. From the second formula we may infer that the true maxi- mum and minimum precede that adopted by Argelander, by the angular amount of 11.3°, or 7.6 hours. As this would only affect the light curve by about a fiftieth of a magnitude, it might readily escape detec- tion. It will be noticed that in this case the interval from maximum to minimum is equal to that from minimum to maximum, instead of, as is generally the case, exceeding it. A more direct determination of the correction to the minimum may be found from the light curve, by comparing the times at which the light is equal. In Table IV. are given the light in grades, the corresponding tinicis 264 PROCEEDINGS OP THE AMERICAN ACADEMY taken from the light curves, and the time of the minimum, assuming that it lies midway between them. This last column is found by add- ing to the second column 10** 3.7*, or the period of the star ; add- ing to this the third column, and dividing the result by two ; finally subtracting the quotient from the period, 10** 3.7^. The mean of this value, or 7.4, agrees closely with that given above. TABLE IV. — Minimum of ^ Geminorum. Gr. Increasing. Decreasing. Mean. 4.0 5.0 6.0 7.0 d. h. 0 18,5 1 12.0 2 9.5 3 13.5 d. h. 8 22.0 8 0.5 7 4.5 6 2.0 h. —5.6 —7.(3 —6.9 —9.6 ^ Lyrce. Light curves of this star were given by Argelander in 1842, Asti'on. Nach., xix. 397, and in 1844, De stella ^ Lyras variabili disquisitio. In 1859 he gave a more complete discussion of the problem.* He divided his previous observations into three periods, and derived a curve from each ; concluding that they differed from each other only by their accidental errors, he gave a curve representing the entire series. Oudemans f gives a light curve from his observations, reduced to the same system as that given in Argelander's second publication. This differs so little from the last system of Argelander that the same curve, for reduction to logarithms, has been used for both. In no case, within the limits used, would the difference of the logarithms exceed one or two hundredths. In 1870, Schonfeld gave another curve, Astron. Nach., Ixxv. 1. His grades represent a smaller variation in the light than Argelander's, and, like the latter, a grade is larger for the brighter stars than for the fainter, as in the case of t, Geminorum. The relation of the grades to the logarithms of the light is shown in Table V. The colunms have the same meaning as in Table II., except that three additional columns are given for the comparisons of Schonfeld. • De Stella /3 LyrsB variabili commentatio altera. t Zweijiiehrige Beobachtungen dcr nieisten jetzt bekannten veraenderlichen Sterne. Verhand. Akad. Amsterdam, 1856. OF ARTS AND SCIENCES. 265 TABLE V. — Comparison Staus rou fi Ltr^. Name. Wolff. Argehiude r. Schonfcld. Q Hides. Curve. TV"— C Grades. Curve. W—C y Lvnp . . 8.89 12.7 8.87 +.02 15.0 8.88 +01 fj. Ik'rciilis 8.79 , , 13.0 8.80 —.01 1 Uerciilis . 8.70 10.3 8.75 —.05 103 8.71 —.01 0 IltTculis 8 •;;) 7.6 8.G9 .00 7.8 8.05 +.01 € Lvr;u . . 18.77] 4.9 8.00 [+•17] 4.2 8.58 [+•191 a-yr^^^ ■ . 8.^"it; 3.4 8.56 .00 2.9 8.56 .00 K Lyne . . 8.0tl 2.(3 8.56 +.01 1.6 8.55 +.01 Tlie estimate of e Lyrce has not been included in drawing these curves. As the observations were made with tlie naked eye, in sonae cases aided by an opera-glass, e and 5 LyrcB were treated as a single star. Wolff gives the logarithms of their light as 8.50 and 8.45. Their combined light would therefore equal 8.77, or nearly half a inajrnitude brighter than would be inferred from the estimate in grades, using the curves derived from the other stars. This may also be expressed by the statement that, together, they appear only a quarter of a magnitude brighter than either would alone, while a star of their combined brightness should appear about three quarters of a magnitude brighter than the separate components. It is possible that their proximity affected their measures by Wolff, but this seems less probable since they would be readily separated by the telescope of a ZoUner photometer. Evidently, c Lyrce should not be used hereafter as a comparison star for this variable. Table VI., like Table III., serves to compare the observations with theory. The first column gives the angle ; the second, the correspond- ing time. Three sets of three columns each give the light in grades, in logarithms, and in percentages, for Argelander, Oudemans, and Schonfeld. Although the observations are not of equal value, it would be difficult to decide what weight should be given to each, and espe- cially, to decide how large are the systematic errors to which each is sub- ject. This last quantity should determine the weight, since the accidental errors are in a great measure eliminated by the smoothness of the light curves. Their mean, which is given in the next column, will accord- ingly be employed. The excess of the curve of each observer over the mean is given in the next three columns. An examination of the mean curve shows that it has two equal maxima symmetrically situated on each side of the point where v = 180°. The curve must there- fore have the form L ^ a -{- m sin (v — 90°) -j- n sin (2 v — 90°). 2G6 PROCEEDINGS OF THE AMERICAN ACADEMY The mean value of Z or a is 81.1. When v z= 0°, Z = a — m — n; when V ^ 180°, L = or-|-?« — «; v = 90° or 270°, gives L = a -\- tn — n. Were there no accidental errors, either two of these three equations would determine ?« and «. After various trials the equation Z = 81.1 + 4.1 sin (v — 90°) + 20.0 sin (2 v — 90°) was found to give the most satisfactory results. The brightness computed by this formula, and the residuals found by subtracting them from the mean of the observed values, are given in the last two columns. TABLE VI. — Variation in Light of fi Lyr^. V. Time. Argelander. Oudemaiis. Schbnfeld. g 1 1 1 o. 1 Gr. Log. Obs. Gr. Log. Obs. Gr. Log. Obs. ■^ O ^ o 1 C 6 d. k. 0 0.0 3.4 8.56 49 4.0 8 57 49 36 8.57 51 50 -1 —1 +1 57 _; 15 0 12.9 5.0 8.60 56 50 8.60 52 4.4 8.58 58 65 +1 -3 +3 60 -5 1 SO 1 18 9.2 8.71 ■JO 8.0 8.67 62 9.2 8.71 71 68 +4 -6 +3 68 1 0 45 114 7 11.1 8.78 85 10.6 8.76 76 113 8.79 85 82 +3 —6 +3 78 +4 60 2 3.6 11.8 8.82 93 118 8.82 87 12 2 8.S4 96 ft2 +1 -6 +4 89 +3 V5 216.6 12.2 8.84 98 12 5 8.86 96 126 8.87 102 99 -1 -3 +8 97 +2 !» 3 5.5 12.3 8.85 100 12.6 8.87 98 12.7 8.87 102 100 0 —2 +2 101 -1 105 3 18.4 12.1 8.84 98 12.4 885 93 12.5 8.86 100 97 +1 -4 -3 100 -8 120 4 7.3 11.8 8 82 93 117 8.81 85 119 8.82 91 90 +3 -5 +1 93 -3 l.)5 4 20.2 11.2 8.79 87 10 7 8.76 76 10.9 8.77 81 81 +6 -5 0 84 -3 150 5 9.1 103 8.75 79 10 0 8.73 71 9.9 8.73 74 75 +4 — d -1 75 0 lf55 5 22.0' 8 8 8.69 69 9.2 8 71 68 91 8.70 69 69 0 -1 1) 68 +1 180 6 10.9 8.6 8.69 69 9.1 8.70 66 8.9 8 70 69 68 +1 2 +1 65 +3 195 6 23 8 9.4 8.71 72 9.5 8.72 G9 9.3 8 71 71 71 +1 2 0 68 +3 •210 712.7 10.8 8.77 83 10.7 8.76 76 10.2 8 74 76 78 +5 5 _2 75 +3 225 8 16 116 8.81 91 11.8 8.82 87 112 8.79 85 SB +3 -i -3 84 +4 240 8 14.5 12.1 8.83 96 12.4 8.85 93 12.0 8.88 93 94 +2 —1 — 1 93 +1 255 9 35 12.3 8.85 100 12 8 8.88 100 12.4 8 85 98 99 +1 +1 -1 100 -1 270 9 16.4 12.4 8.85 100 12.9 8.88 lOit 12.4 8.85 m 99 +1 +1 -1 101 _2 2S5 10 5.3 12.2 8.84 98 12.8 8.88 100 12.3 8.85 98 99 -1 +1 -1 97 +2 :',00 10 18 2 11.7 8.81 91 12.4 8.85 9.S 11.9 8.82 91 92 —1 +1 — 1 89 +3 315 11 7.1 10 9 8.77 83 114 8-80 83 10.8 8.77 81 82 +1 +1 -1 78 +4 8:!0 11200 8.4 8.08 68 9.0 8.70 6; 8.0 8.67 65 66 +2 0 .1 68 -2 315 12 8.9 4.0 8.58 64 4.7 8.59 51 4.2 8.58 53 53 +1 2 0 60 — ' Mean ±1.9 ±2.5 ±15 ±2.8 These residuals are much larger than in the case of ^ Geminorum ; hut this is to be expected, since the variations in light are greater. Evidently, if the changes were small, any two smooth curves would agree closely-. Their average value amounts to about .04 of a magni- tiide, and their greatest value does not exceed the greatest diflference of each of the observed curves from the others. The greatest errors of observation are those of the light of the comparison stars. The residuals near the princiijal mininuim may be greatly reduced if the fainter compari.son stars are assumed too faint, with a corresponding change in the value of the fainter grades. The rejection of e LyrcB in Table v., while its effect on Table VI. cannot be eliminated, may account for this apparent error. An increase in the logarithm of the OF ARTS AND SCIENCKS. 2G7 liglii by about .'-H for grades 11 to 12 would reduce the residuals cor- responding to r = 45°, 60°, 210°, 225°, 300°, and 315°. The residu- als for v=:120° aud 135° would, however, be increased. The-e changes are not to be recommended unless indicated by future photo- metric measures of the comparison stars. ■q Aijuike. AigeUiiider gave a light curve of this star in 1842, Astron. ^^ueh., xix. 31)9, based upon 174 observations taken by him- self and by Ileis. In 1857, he gave a second curve dependent on 411 of his own ob>ervations, Astron. Nach., xlv. 97. In Table VII. the liglit of the comparison stars are given in grades and in logarithms, according to Wolif. The cohimns have the same meaning as iu Table V. As V Aquilce was not observed by M. "Wolff, it is unavoidably excluded from the comparison. TABLE VII. — CoMPARisox Stars for -i] Aquil^. Name. Wolff. Grades. Curve. W—C Grades. Curve. W—C 5 AquiliB . . 8.85 13..3 8 85 .00 12.9 8 86 -f.Ol 3 Atjiiilae . . 8.74 8.0 8.72 -f.02 8.1 8.71 —.03 6 Aquihe . . 8 63 6.0 8.66 -.03 6.1 8.64 +.01 I Aqiiilaj . . 8 57 3.0 8.57 .00 3.0 8.55 -f.02 ju Aquil;T3 . . 8.43 —1.4 8.43 .00 —0.6 8.44 —.01 V Aquilie . . —•2.4 •• —1.8 The first seven columns of Table VIII. have the same meaning as in Table III. and give the values of v, of the time, of the light in grades, in logarithms, and in percentages, a computed value, and the residuals from this, or the fifth column minus the sixth. The compu- tation is effected by the formula L = 73.6 -)- 20.0 sin {v — 60°) -|- 6.0 sin (2 y — 120°). The last four columns give the light iu grades, logarithms, and percentages, and the residuals according to the second curve of Argelander. The same theoretical formula is used in this case, adding 1 so that the positive and negative residuals shall be nearly equal. The light in this case, Z' = Z -[- 1 = 74.6 -|- 20.0 sin {v — 60°) + 6.0 sin (2w — 120°). 8 Gephei. Argelander has given a light curve of this star in the Astron. Nach., xix. 395. Curves are also given by Oudemans in the paper cited above, and by Schbnfeld in Astron. Nach., Ixxv. 14. The relation of grades to logarithms is given in Table IX., for Arge- lander and Schonfeld. Oudemans has already reduced his scale to that of Argelander. Unfortunately, Wolflf only measured those of the five 2G8 PROCEEDINGS OF THE AMERICAN ACADEMY TABLE VIII. — Variation in Light of tj Aqdil^. V. Time. Gr. Log. Obs. Comp. O — C Gr. Log. Obs. O — C 0 0 d. 0 A. 0.0 1.2 8.51 50 51 —1 2.1 8.52 54 +2 15 0 7.2 1.7 8.53 52 54 —2 2.4 8.53 55 0 30 0 14.4 3.2 8.57 58 58 0 3.5 8.56 59 0 45 0 21.5 4.8 8.63 66 65 +1 4.8 8.60 65 —1 60 1 4.7 6.8 8.67 72 74 —2 6.2 8.65 72 —3 75 1 11.9 8.1 8.72 81 82 —1 7.8 8.70 81 —2 90 1 19.1 9.6 8.76 89 89 0 9.5 8.75 91 +1 10-5 2 2.3 10.9 8.79 96 94 +2 10 6 8.78 98 +3 120 2 9.4 11.4 8.81 100 96 +^ 10.9 8.79 100 +-i 135 2 16.6 10.9 8.79 96 96 0 10.5 8.78 98 +1 150 2 28.8 10.1 8.77 91 94 —3 9.8 8.76 93 —2 165 3 7.0 9.2 8.75 87 90 —3 9.0 8.74 89 —2 180 3 14.2 8.5 8.74 85 86 —1 8.2 8.71 83 —4 195 3 21.3 8.0 8.72 81 82 —1 8.0 8.70 81 —2 210 4 4.5 7.6 8.71 79 78 + 1 7.8 8.70 81 +2 225 4 11.7 7.2 8.70 78 76 +2 7.2 8.68 78 -fl 240 4 18.9 6.8 8.69 76 74 +2 6.6 8.66 74 — 1 255 5 2.0 G.4 8.67 72 71 +1 6.0 8.64 71 —1 270 5 9.2 5.8 8.65 69 69 0 5.4 8.62 68 —2 285 5 1G.4 4.7 8.62 65 66 —1 4.9 8.61 66 —1 300 5 23.8 3.7 8.59 60 62 —2 4.2 8.58 62 —1 315 6 6.7 2.9 8.56 56 57 —1 3.6 8.57 60 +2 330 6 13.9 2.1 8.54 54 54 0 3.0 8.55 58 -f:^ 345 6 21.1 1.5 8.52 51 51 0 2.4 8.53 55 +3 Mean . . ±1.3 ±18 comparison stars of 8 Cephei, and the logarithms of two of these he found differed by only one hundredth of a unit. Accordingly, we can do no better than to draw a straight line nearly through the points designated by these stars, or assume that the value of a grade is constant. The columns of Table IX. have the same meaning as the corresponding columns of the previous similar tables. TABLE IX. — CoMPARisoNT Stars for 5 Cepiiei. Name. Wolff. Grades. Curve. W— c Grades. Curve. W— c ^Ce{)liei . . 8.84 11.4 8.84 .00 12.4 8.80 —.02 I Cephei . . 8.83 10.8 8.82 +.01 10.9 8.82 +.01 7 Lacertae 7.1 . . . 6.6 1 Cej)liei . . 3.0 € Cephei . . 8.53 2.0 8.53 .66 1.9 8.53 66 Table X. compares the various light cui-ves with theory. The columns have the same meaning as those of Table V. The theoretical values are computed by the formula, L = 72.1 -|- 20.0 sin {r — 45*^) + 7.0 sin (2v — 120°) OF ARTS AND SCIENCES. 269 TABLE X. — Variation in Light of 8 Ckpiiei. .ArgolmuliT. Ouiit'iiians. SchiiiifeW. V. Time. g ^ 1 ^ c. 1 Or. Log. Obs. Gr. Log. Obs. Qr. Log. Obs. s 1 1 1 a 1 b«4 J3 "^ o to '^ S 0 rf. h. 0 0.0 2.8 8.56 55 3.4 8.58 55 3.0 8.56 58 56 -1 -1 tl 52 +4 15 0 5.4 8.0 8.56 55 82 8,57 54 3.1 8.57 59 56 -1 -2 55 +1 30 0 10.7 8.5 8.57 56 3.3 8 57 64 3.5 8 58 60 57 ~ 1 —3 +3 61 - 4 45 0 IC.l 4.7 8.62 68 5.3 8.64 63 4.6 8.61 65 64 -1 —1 +1 69 — 5 60 0 21 5 6 5 8.68 72 75 8.71 74 6 6 8.68 76 74 —2 0 +2 77 —3 75 1 2 8 8 4 8,74 88 10 3 8.81 93 87 8.75 89 88 -5 +5 + 1 86 4 2 00 1 8.2 9 9 8 79 i'3 11.1 8. S3 98 10.0 8,79 98 96 -3 -f-2 4 2 92 + 4 105 1 18 (! 10.7 8.82 lOO 11.2 8,84 100 10.4 8.80 100 100 0 0 0 96 +4 120 1 l!i.0 10.1 8.80 96 10.9 8 83 98 10.0 8.79 98 97 -1 +1 +1 98 -1 135 2 03 9.0 8.76 87 10.4 8.81 93 9.3 8.76 91 90 -3 +3 +1 96 -6 150 2 6.7 8.5 8.75 85 9.6 8.78 87 8.6 874 87 86 -1 + 1 +1 91 -5 H36 2 11.1 8.4 8.74 83 8.6 8.75 81 8.0 8 72 83 82 +1 —1 +1 86 -4 180 2 16 4 8.3 8.74 83 7.7 8.72 76 7.8 8.72 83 81 +2 —5 +2 80 +1 195 2 21.8 7.S 8.72 79 6.8 8.69 71 7.6 8 71 81 77 +2 —6 +4 75 +2 210 3 3.2 7.1 8.70 76 6.2 8.67 68 68 8.69 78 74 +2 -0 +4 71 +3 225 3 85 6.3 8.67 71 5.6 8 65 65 6.2 8.67 74 70 +1 -6 +'1 69 +1 240 3 13 !i 5.6 8.65 68 5.0 8.63 62 5.6 8.65 71 67 +1 -5 +4 67 0 255 3 19 3 5.2 8.64 66 44 8.61 59 5.1 8.63 68 64 +2 -5 +4 66 —2 270 4 0.6 4.7 8 62 68 4.0 8.60 58 4.7 8.62 66 62 +1 -4 +4 64 -2 285 4 6.0 4.3 8.61 62 37 8.59 56 4.3 8.60 6.3 60 +2 —4 +3 62 -2 300 4 11.4 3.!l 8.59 59 3.6 8 58 55 3.9 8 59 62 59 0 -4 +3 59 0 81.3 4 16.7 84 8.58 58 3.6 8.58 55 36 8.58 60 58 0 -3 +2 56 +2 330 4 22.1 3.2 8.57 56 3.6 8.58 55 3.3 8.67 59 67 —1 -2 +2 53 +4 345 5 3.5 2.9 8.56 55 3.5 8.58 65 3.1 8 57 59 57 -1 -1 +3 51 +6 M ean ±1.4 +2.9 +2.8 ±2 8 These residuals are not large, considering the differences between the different observed values. There is, however, a curious alternation of the positive and negative signs. As a similar alternation appears in some of the other residuals, it is important to compare them to see if they can be shown to follow any law. There appear to be three maxima and three minima, or the variation repeats itself at intervals of about 120°. "We should then exaggerate this effect by adding each set of the three residuals differing by 120° ; that is, the residuals cor- responding to 0°, 120°, and 240°, to 15°, 135°, and 255°, etc. This is done in Table XI., in which the first value of v, in each set, is given in the first column, and the suras of the three residuals for the four stars are given in the second, third, seventh, and eleventh columns. The residuals of I Geminorum are so small that we should expect no evidence of systematic error. In the other three cases marked variations are shown. In each case there are only two changes of sign, while there should be on the average four if the vari- ations were accidental. The residuals oi jB Lyrce are well represented by subtracting from the computed value 3 cos 3 v. The residuals which then remain are given in columns four, five, and six. Their average value is l.G instead of 2.8, or they have been reduced nearly one half. The residuals of rj AquilcB, in like manner, leave 1.1 instead 270 PROCEEDINGS OF THE AMERICAN ACADEMY of 1.8, by subtracting the term 3 sin (3 v — 45°). become 1.4 instead of 2.8, if we subtract 4 sin 3 v. Those of 8 Cephei TABLE XI. — Terms involving 3 v. V. a 1 /3 Lyrse 7) Aquilae. S Cephei. 1 Sum. Residuals. Sum. Residuals. Sum. Residuals. o 0 15 30 45 60 75 90 105 0 0 2 + 1 + 1 —1 0 —1 —9 — !) +7 +9 +y 0 —6 —4 0 4-4 -3 -1 4-1 0 0—2 -f2 —1 0 0 0 0 0 4-1 4-2 —1 4-3 —2 —1 4-6 —5 +5 0 —4 —4 — » ■> +0 + ' 0 4-1 —3 0 -1-1 —I -1-2 0 0 —1 —2 -i-f 2 2 -'-2 —1 0 -i-l 0 4-2 0 + 3 — 7 —11 —11 — 2 + 6 +11 +11 4-4 —1 0 +4 —3 +1 0 —1 4-2 —2 —1 4-1 —3 +1 0 —1 —1 —1 0 —1 0 + 1 —2 4-3 Moan . . ±1.6 ±1.1 ±14 jSTo natural explanation can be offered for such terms, and the reduction might be thought accidental did it not occur in so many- different curves. A careful distinction must be made between these terms and those which might be assumed empiricalh^ since their form is clearly pointed out by the residuals. If we tried to represent the residuals by a function of 4 v, we should soon see that the effect was wholly different, nor would any values of the arbitrary, constants in this case materially reduce the residuals. Neglecting these last terms, as their reality may be questioned, we may write the equations of the four stars under each other thus : — C Geminorum, L = 89.6 + 10.2 sin (v — 11.3°) ^Lyr£E, Z=8l.l-i- 4.1sin(v — 90°)-l-20.0sin(2v— 90°) r] Aquilaj, L = 74.6 -[- 20.0 sin (v — 60°) -j- 6.0 sin (2 v — 120°) 8 Cephei, L = 72.1 -j- 20.0 sin {v — 4;)") -j- 7.0 sin (2 y — 120°) To compare them, it will be convenient to make the mean bright- ness equal to unity in all cases, or to divide by n the equation L = a -j- m sin (v -\- «) -\- n sin (2 v -\- (S). Instead of making « = 0, when the light is a minimum, it will also be better to take as the start- ing-point the position in which the shorter axis of the star is turned towards the observer. If v' = v -[- y, we may write L' -=.1 -\- m' sin iv' -j- «') -|- n' cos 2 v'. The various values of these constants are given in Table XII., which contains in successive columns the name of the star, the value of y, of «', of ??i', and of n'. Independently of the form of the star, its light would vary, owing to the unequal bright- OF ARTS AND SCIENCES. 271 ness of tlie two sides from 1 -j- ?«' to 1 — m'. The brightness of tlie \ ^' darker side would therefore equal - — ; ; times that of the blighter. ^ 1 4" m' * In like manner, if the surface was uniformly bright, the variation in area of the disk, or the length of the shorter axis in terms of the 1 n' longer, would be _, , . These quantities are given in the sixth and seventh columns. The last two columns give the average residuals in percentages before and after applying the terms which are functions of 3 V. TABLE XII. — CoAiPARisoN of Light Curves. 1 — m' 1 — »(' Av. Av. Name. y a' \+m' 1 + n' Resid. .Resid. ^ Geininuruni - ]1°3 o +.114 0.80 0.5 3 I.vrffi . . . - 90.0 0 +.051 +.247 0.!)0 0.60 28 1.6 7] AquiliB . . — 105.0 +45 —.268 --.080 0.58 0.85 1.8 1.1 5 Cephei . . — 1U5.0 +G0 +.277 +.097 0 57 0.82 2.8 1.4 From the column 1 - we see that in every case the darker side 1 + m' is more than half as bright as the other, and that the difference in the case of y8 Lyrce amounts only to ten per cent. In other words, if this effect is due to spots, we must conclude that they cover only one-tenth of the hemisphere in the case of /3 Lyrce, and about two-fifths in the cases of rj Aquilce and S Cephei. The next column also shows that P LyrcB is much elongated, the ratio of its axes being as five to three, while the two stars following have this ratio about as six to five. The dark portion of /? Lyrce is at one of the ends, since a' = 0° for this star ; it appears also to be symmetrically situated as regards the longer axis. The dark portions, both of t] Aq%i}Ice and of 8 Cepher, are placed somewhat preceding an end, that is, they are turned towards the observer before the end has been directed to him. For this reason the time from minimum to maximum is greater than that from maxi- mum to minimum. This is probably a general law of stars of this ' class, as it has been noticed in several other instances. One source of systematic error has been disregarded in the above comparison of observation with theory. In the value of L' the term m' sin (y' -\- a') may be regarded as the measure of the effect of the difference in brightness of the two sides, and n' cos 2 v' as due to the form of the body. Their combined effect, however, would not strictly equal their sum, but would be found by adding each to unity and 272 PROCEEDINGS OP THE AMERICAN ACADEMY taking the products of these sums. The actual light would equal (1 -|- m' sin (v' -{- a')) (I -\- 11' cos 2 t'') = 1 + m' sin {y' -}- a) -|- «' cos 2 y' -}- m'n' sin {y' -\- a) cos 2 v'. The value of L' given above is then subject to the systematic error of m'n' sin (v' -\- a) cos 2 v'. The maximum value of this would equal ?n'n', and it would generally be much less. The maximum value for ft Lyrce would be about 1 per cent ; for rj Aquilce, 2 ; and for 8 Cephei, 2.6 per cent. If the star underwent much greater change of light, it might be necessary to take this term into account ; but in the present case it does not seem to sensibly affect the average value of the residuals. Various attempts have been made to determine the light curve of ./3 Lyice photometrically. The observations of Zollner and Wolff are reduced according to the same method in the photometric work of the latter, p. 110. The accuracy of the resuUs does not make this a promising method of determining the light curve, unless the number of observations is greatly increased. The maxima and minima were also determined at the Harvard College Observatory.* Calling the light at either maximum 100, that at the two minima would be 55.8 and 64.7, which agrees very closely with that given by computation, if we neglect the term 3 sin 3 v. One great advantage of the study of the stars by physical instru- ments, such as the spectroscope and photometer, is that some clew is given to certain laws, for our knowledge of which we must otherwise depend on theoretical considerations alone. While the conclusions to be drawn from micrometric measurements are in general much more precise, and the effect of the errors can be more certainly computed, they fail entirely to aid us in studying such laws as those here con- sidered. For example, the present investigation serves to study the following important problem in cosmogony, to which micrometric measures contribute nothing, and which can otherwise only be ex- amined from the standpoint of theory. If we admit a common origin to the stars of the Milky AVay, a general coincidence in their axes of rotation seems not improbable, especially as such an approximate coin- cidence occurs in the members of the solar system. If the coincidence was exact, the direction must be that of the poles of the Sun, or, approximately, that of the pole of the ecliptic. On the other liand, since the stars of the Milky Way are supposed to be arranged in the general form of a flattened disk, we should more naturally expect that the axes of rotation would be symmetrically situated with regard • Annals, xi. 135. OF ARTS AND SCIENCES. 273 to it, or would coincide with its shortest dimension. According to this theory, then, the axes of rotation would be directed towards the poles of the Milky Way. If now we suppose that a great number of varia- ble stars, of the form described above and rotating around parallel axes, were distributed over the iieavens, it is evident that those seen in the direction of their axes would not appear to vary, since as they turned they would always present the same portion of their surfaces to the observer. Those at right angles to this direction would show ihe greatest variation, and, other things being equal, would appear to be more numerous since they would be more likely to be detected. If then the axes are coincident, we should expect that most of these variable stars would lie along the arc of a great circle whose pole would coincide with their axes of rotation. An inspection of a plot of the stars of Class IV. showed that they agreed closely with a great circle whose pole is in R. A. 13* and Dec. -|- 20°. To compare these stars in this and in other respects, they are arranged in the order of their periods in Table XIII. They are divided into three sections ; first, those known to be of the fifth class ; secondly, those of the fourth class, including all of a shorter period than /3 Lyrce ; thirdly, the re- maining variables of longer period, whose position in Class IV. may be open to question. The first column gives the name of the star, and the second its period in days. The distance from the great circle whose pole is in R.A. 13* and Dec. -|-20° is given in the third column. It was found by measurement on a globe, instead of by calculation, and is not therefore exact to the nearest degree. In measuring the stars of the fifth class at the Harvard College Observatory, much difficulty was experienced from the absence of adjacent comparison stars. Stars of the fourth class, on the other hand, have, in almost all cases, stars near them. An unprejudiced comparison is made in the next two columns, by giving the magnitude and distance, in minutes, of the nearest- star of the Durchmusterung. The lines for the southern stars are therefore left blank. If the stars of the fourth class lie near the Milky Way, we should expect an in- creased number of companions due to this cause. Accordingly, a count has been mf.vie of the Durchmusterung stars in a square degree, in which each star is contained. This area is defined as the portion of the Durchmusterung zone in which the star is situated, having an average length of one degree, one half preceding, the other half follow- ing, the variable. The results are given in the sixth column. If these stars were connected with the variables, we might expect that they would lie, approximately, in a plane at right angles to the axes of rota- 274 PROCEEDINGS OF THE AMERICAN ACADEMY TABLE XIII. — Comparison of Variable Stars. Class V. Name. Period. Dist. Slag. Dist. No. Stars. Ang. Birm. 8 Librae . . . 2.32 c +51 / 0 — Cepliei . . . 2.49 + 11 9.5 5i 26 ^ Persei . . . 2.87 —24 8.8 7.5 15 55 (7 Coronse . . . 3.45 +58 9.4 11.5 7 A Tauri . . . 3 95 —41 9.5 17.5 5 S Cancri . . . 9.48 +25 9.1 11.6 16 Mean ±35° lO'.G 126 •• CI ass I V. - - Short Pei-iods. R Muscfe . . . 0.89 0 T Triang. Austr. 1.00 + ?' — Sagittarii . . 2.42 — 1 S Monocerotis . 3.40 — 4 9.4 1.6 29 —31 R Triang. Austr. 3.40 -- 1 N Velorum . . 4.25 -- 1 S Cephei . . . 5 37 — 5 75 1.5 3i —33 S Cornn. Austr. . G.20 — 9 (J SaEfittarii . . 6.75 -- 2 415 A' Sagittarii . . 7.01 — 8 77 Aquilffi . . . 7.18 — 9 9.2 3.2 17 +26 IF Sagittarii . . 7.59 + 3 K Pa von is . . . 9.10 —16 ^ Geniinorura . 10.10 + 5 8.5 1.8 33 + 1 /8 Lyras . . . 12.91 + 14 8.5 1.5 34 —20 Mean io" 1'.7 28.8 ±21° Ch issIV.- - Long 1 -'eriods. IF Virginis . . 17.27 +66 284 T Monocerotis . 27.00 — 8 9.5 G.i 23 6 / Carina; . . . 31.25 — 1 ?( Herculis . . 38.50 +34 9.4 5.0 15 +79 405 [J Monocerotis . 4().00 + 2 R Lyra3. . . . 46.00 + 16 7.i 9.7 17 -78 474 /i' (^oron Austr. . 64.00 — 9 S Vulpeculoe . . 67.50 0 9.5 5.2 20 +53 517 R Sagitta; . . . 7042 — 9 9.3 6.0 2(5 +76 540 R Scuti .... 71.10 + - 6'.2 462 Mean +13° 20.2 ±57° tion, since the planes of revolution of the planets do not differ greatly from the solar equator. Moreover, if the elongation of the variable was caused by one or more disturbing bodies, we should expect that they would lie in this plane. Of cour.-^e, the present distance of these OF ARTS AND SCIENCES. 275 companions is far too great to sensibly affect tlie variables, but other nearer objects may lie in the same plane. The approximate position ani^le of the companion was computed from its Durchmusterung jilace. The position angle of the pole of the variable stars was meas- ured by a protractor, laid upon the globe over the position of the variable star, and stretching a thread to the pole. Each of these determinations is liable to an error of some degrees, but the results which are given in column seven are sufficiently exact for our present purposes. Some of these stars are red, and when they are contained in the Catalogue of Birmingham * their numbers are given in the last column. The numbers of the third column show that the stars of the fifth class are not concentrated in the assumed plane. If uniformly dis- tributed all over the heavens, their average distance should be about 30°, since one half of each hemisphere is contained in a zone of this width. In the short-period stars of the fourth class, however, the agreement is most remarkable. None have yet been found more distant than 16° from the circle, and with two exceptions none are more distant than 10^. There is only one chance in four that a given star should lie within 15° of a given great circle, and about one in six that it should lie within 9° of it. Evidently the chances would be many millions to one against the observed arrangement being acci- dental. As an argument in favor of the parallelisms of the axes, this distribution of the stars fails by proving too much. We should ex- pect, if the axes were jjarallel, to find nearly as many stars between, 10° and 20°, as between 0° and 10°, since the variation would be a function of the cosines of these angles. If the axes were not exactly coincident, we should find the stars still more widely distributed. Of course it is possible that the distribution of these stars may be partly due to the parallelism of their axes of rotation. But we have shown that the latter cause is insufficient. Since then we must assume an arrangement of the stars approximately in a plane, we cannot be sure that their apparent distribution is not wholly due to it, and the evidence in favor of parallelism of their axes is much weakened. It is a little singular that this plane appears to pass through the Sun. We should expect that while the more distant stars mi^ht lie upon a great circle, the nearer, and therefore presumably the brighter, stars, would lie on the opposite side of it from the Sun. As, however, the positive and negative signs are nearly equally distributed, we must * Trans. Roy. Inst. Acad., x.xvi. 24y. 276 PROCEEDINGS OF THE AMERICAN ACADEMY infer that the distance of the Sun from the plane of these stars is small compared with its distance from them. If the stars lay exactly in one plane we might infer their distances from the Sun from these residuals. As the residuals of the brighter stars show no systematic arrangement, it seems probable that the variables of the fourth class lie nearly, but not exactly, in a plane. This plane approaches that of the Milky Way, but does not coincide with it. The pole of the latter is nearly in R. A 12* 40"' and Dec. -f- 28°. Evidently the residuals in column three would be greatly increased if we moved the pole from its assumed position of R. A. 13* and Dec. -\- 20°, by more than 10° to the pole of the Milky Way. The position of the Milky Way, as given in the '' Atlas Coelestis Novus " of Ileis, agrees, however, more closely with the plane of the variable stars. It is not certain whether the stars of longer period given in the third section of Table XII. should be included with those of the fourth class of variables. With two exceptions, IF Virglnis and u Herculis, they lie near the plane of the others. The total number of stars in the Durchmusterung north of the equator is 315,048. Since the area of the hemisphere is 20,626 square degrees, this corresponds to 15.3 stars per degree, or an area of 236 square minutes to each star. A circle having a radius of 8'.7 would have an area equal to this. If, then, a circle having this radius is de- scribed around any star as a centre, it will be an even chance that another star will be contained within it, provided that the presence of the second star is no way affected by that of the first. For circles of other radii the chances will vary as the squares of the radii, or as the areas. We know from the existence of clusters and multiple stars that one star is not without influence on the presence of another, and that this effect may extend to some distance, as is shown in the Pleiades and in Praesepe. This principle may still be used in comparing diff'er- ent classes of stars, although the distance 8'.7 should be diminished. It is, therefore, surprising that the average distance of the companions of stars of the fifth class is as great as 10'.6, especially as two of them, S Cancri and X Tauri^ lie near the large clusters Praesepe and the Hyades, where the average intervals between the stars is much less. A circle of radius 10'. 6 has only two-thirds the area of that of 8'.7, hence these companions are only two-thirds as thickly placed as the stars in other parts of the heavens. This effect extends to the square degree, as is shown in the sixth column. It appears to be probable that there is no physical coimection of these stars with the variables, and that their sparseness is due to their distance from the Milky Way. OP ARTS AND SCIENCES. 277 Passing now to the second part of the table, we find a wholly different condition of things. Every star has a companion near it at an average distance of only 1'.7, or these stars are twenty-six times as thickly placed as in the rest of the heavens, since 8.7'^ : 1.7*^ = 26 : 1. This effect is partly due to the surrounding square degree, which contains nearly double the average number of stars. Only a small part of this effect may, however, be thus explained. We may, therefore, infer that there is a physical connection between these variables and their companions, or that they are at nearly the same distance from the Sun, and not optically double. The singular character of tiiese stars renders them interesting objects for the measurement of parallax. This is especially the case with those of very short period, since from the rapidity of the changes we might infer that they were really small, and therefore near. Now an observer .would be very likely to select the companions as points to measure from, since their distances are much greater than that separating the components of most stars which are binary, or are supposed to be physically con- nected. A measurable parallax might thus escape detection. The stars of longer period occupy an intermediate jjosition as re- gards the distances of the components, and the number of stars in the square degree. If the direction of the components depended wholly on chance, we should find that they would differ, on the average, from that given by any theory, by about 45°. It therefore seems scarcely probable that, in each of the five cases, a chance distribution would give the angle less than 45°, for the stars of short period. The uncertainties in the measurements would in general increase the discrepancies, so that it is to be expected that a more accurate determination would diminish the mean value, although it would doubtless alter the separate results by many degrees. The position of the components of the stars of the fifth class has not been determined, as it seems very improbable that they have any physical connection. The stars of long period, with one exception, give results which do not agree at all with theory. Some more precise test of the class to which these variables should be assigned, is therefore much needed. They are distinguished from many of the stars of the second class only by the length of their period, no other known variables having a period less than that of R Vul- jjeculce, or 137 days. Stars of Class 11. have banded spectra, and are of a red color. This suggested a test dependent upon observations already made. The last column shows what stars have been regarded as red^ and may, therefore, in some cases belong to Class II. The only 278 PROCEEDINGS OP THE AMERICAN ACADEMY Star of Class V. given in Birmingham's Catalogue is P Persei, and many observers may be surprised that this should have been called a red star. It is remarkable that but one star of short 25eriod, U Saglttarii, is called red. On the other hand, six of the variables of long period are given in the catalogue, including all of those wiiich have shown marked discrepancies. Excluding these disposes of the large deviations, 66° and 34°, in column three; and we find no star more distant than 16° from the assumed plane in which the variables lie. Again, the large discrepancies of the last column but one are removed, and T Monoce- rotis probably placed with the variables of the fourth class. This view is confirmed by the light curve given by Schonfeld, page 32 of the catalogue cited above, which shows that in the form of its variations this star closely resembles y] Aquilce and h Cephei. Another reason for excluding W Virginis and the last four stars of the list is, that their light is variable at their maxima, and in four of the five cases at their minima. This frequently happens with stars of Class II., but would not be readily explained in stars of Class IV. The Uranometria Argentina adds U Monocerotis to the list of red stars. All stars whose period lies between 32 and 72 days have, therefore, been called red, except R Coronce Australis. This star is so faint that its color might well have been overlooked. A further discussion would have been made of T Monocerotis, but no means exist for converting into light ratios the scale of magnitudes of its light curve. As the brightness of the comparison stars are not given, we have no means of knowing whether a tenth of a magnitude corresponds to the same light ratio when this star is faint, as when it is briglit. A preliminary trial showed that the maximum appeared to occur more suddenly, and the minimum more slowly, tlian theory would indicate. The large range of variation of this star renders it well suited for study, and the same may be said of some others of the list, as a slight increase in the difference between the maximum and minimum greatly increases the severity of the test the liglit curve offers to theory. The system which appears to govern the position of the companions to these stars suggests an investigation which might lead to important results. The planes of the orbits of the binary stars are defined by their inclination and the position angle of the node. Since we cannot determine micrometrically the direction in which the orbit is inclined, we can only say that the pole of this orbit lies in one of two places. Should any law be discovered, we might then decide for any particular siar what sign should be given to the inclination, and also whether the OF ARTS AND SCIENCES. 279 motion was direct or retrograde. It mijiht also lielp to determine the amount of the inclination when the latter is not lar-xe enouirh to be determined precisely by niicrouictric measurements. Such a law would render an important aid to the study of the orbits of the dark companions of stars of the fifth class. Tlicy would afford a check on the observed inclination, and would define the position angle of the major axis of the orbit, which is now wholly indeterminate. An inspection of the orbits of the binaries fails to show any law, but it is possible that this might be brought out by a more careful exami- nation, as has been done with the pro[)er motion of the stars. The conclusion regarding the motion of the Sun in space is liable to lar<>-e error, in case systematic errors exist iu the catalogues on which the positions of the stars depend. Such an error in Bradley mi^ht greatly change the conclusion generally accepted. The orbits of the binaries, on the other hand, are wholly independent of each other, and there is little danger of a systematic error aflPecting all. The elegant method of Argelander for determining the light curve of the variable stars leaves little to be desired as a means of determin- ing their periods and the times of their minima. Its sirai)licity, and tlie need of no instrument but a telescope powerful enougli to show the variable, are strong arguments in its favor when comparing it with the best [)hotometric methods. If, however, we wish to determine the true light curve, the following sources of error become perceptible. As the comparison stars are selected from the immediate neighborhood of the variable, they are few iu number ; aud if any one of them proves to be itself variable, the errors introduced are large. It is ditiicult to obtain independent estimates, since there is but little range of clioice in the star to be selected at any given time. Much skill is required on the part of the observer to make a grade the same when the variable is bright as when faint, to make it the same on different nights, and to make the interval of two. grades double that of one. In reducing the light to logarithms, it appears to be impossible to render the errors of the measures of the comparison stars as small as those of the light curves. The comparisons given above show that the errors of the measure- ments of the comparison stars probably exceed those from all other sources combined. Three methods may be used for determining the brightness of the stars without a photometer. First, the observer may keep a certain scale in mind, and by it estimate the light of the stars in tenths of a magnitude. He should first estimate several known stars, and compare his result with their true brightness, so as to apply mentally to his 280 PROCEEDINGS OP THE AMERICAN ACADEMY scale proper corrections for the effect of haze, moonlight, etc. He may also observe a large number of known stars, and afterwards reduce his scale for the evening from a discussion of their light. In the second method, which is tliat of Argelander, the observer selects a comparison star of very nearly the same light as the star to be measured, and estimates the difference in grades, a grade being a small interval nearly equivalent to a tenth of a magnitude. A discussion of all the observations serves to determine the intervals in grades between the comparison stars. The value of one grade is then determined from photometric measures of the comparison stars. According to tlie third method, the observer selects two comparison stars, one a little brigliter, the other a little fainter, than the star to be observed, and estimates its difference in magnitudes from the brighter component, with the differ- ence between the two compai'ison stars. The first of these methods is the most rapid, and is well adapted to zone observations, or to any work with a meridian instrument. More skill is, however, required on the part of the observer than by either of the other methods. Besides being able to judge of small intervals of brightness, as in the other methods, he must be able to prevent any changes from taking place in his scale, at least during a single evening. The second method requires less skill, since the observer must merely keep the values of iiis grades con- stant ; but in tlie third method even this is not needed. It is, there- fore, probably the most exact, when tlie results are to be reduced by photometric measures of the comparison stai's. The three methods are directly comparable with those which may be used in estimating linear measures. We may estimate the length of a bar directly in inches, or its excess in inches over a similar bar of known length ; or, thirdly, we may compare it with two bars, one a little longer, the other a little shorter, and estimate its relative length compared with them. It can hardly be doubted that the last of these methods would give the most accurate results. When applied to the stars, the third method has also an advantage in reducing the accidental errors of the photometric measures, since the comparison is made with two stars instead of one. The light curve of a variable may then be determined as follows : — Select as compai-ison stars all those of neai-ly the brightness of the variable, and not too far distant, excepting any which may be thought to be variable, to differ from the variable in color, or which are near other stars. Photometric measures should be obtained, during the period over which the observations of the variable extend, of all of those stars which are used. Each star should be measured in turn under precisely the same conditions, by a Zollner i)hotometer or other OF ARTS AND SCIENCKS. 281 instrument, and this should be repeated on several eveuin;^s. The rela- tive liglit will thus be obtained with great accuracy, as the same errors will be likely to affect them all. If this cannot be done, the Uranome- tria Argentina, with the measures now in progress at the Harvard Col- lege Observatory, will give the brightness of all the naked-eye stars, with an error probably less than a tenth of a magnitude. The light of the variable would be found by selecting two compari- son stars, one a little brighter, the other a little fainter than it, and comparing the interval between the variable and the brighter, with that between the two comparison stars, which may be assumed equal to 10. Thus, a 4: b will denote that the interval between the bright com])arison star a and the variable is estimated at only four-tenths of that between the two comparison stars. Of course the time of each comparison must be recorded. This measure should be repeated with different pairs of comparison stars. Thus, if a and b are brighter and c and d fainter than the variable, we may compare the latter with aCj ad, be, and bd. In like manner, with six. comparison stars we may obtain nine independent measures. The reduction is very simple, since it is useless to carry the estimates beyond tenths of a magnitude. The above paper has suggested several researches of importance, and which are accordingly placed together below : — 1. Determination of the light curves of any of the variables of short period, except f] Persei, t, Geminorum, /3 Lyrce, -q Aquilcs, and 8 Cephei, for which satisfactory curves have already been obtain.ed. The method of Argelander, or that proposed above, may be used with advantage. It must be remembered that the observations will have little value, unless they are reduced and the light curve found. A vast number of excellent observations of these stars already exist, including the larger part of those of Argelander, which will have no value until they are reduced. 2. Determination of the light curve of the stars of the fourth class photometrically. This may be done w^ith great accuracy by an instru- ment similar to that described in the Annals of the Harvard College Observatory, xi. 4, Figs. 1 and 2. The proximity of the companions render these objects especially suitable for photometric measurement. 3. Photometric measures of the comjjarison stars used in (1), of those used by previous observers, and the reduction of the observations by these measures to light intensities. 4. Search for variables of the fourth class, selecting from the Durch- musterung those fulfilling the conditions named above. They may be readily identified by their companions, and observed very rapidly by a 282 PROCEEDINGS OF THE AMERICAN ACADEMY transit instrument, or small equatorial. The first of the three methods of estimating their light is to be recommended for this work. It is sufficiently precise, and the scale used each evening would be readily found fi'om the Durchmusterung magnitudes of the great mass of the stars which would, probably, be invariable in light. Any interesting variable would be detected by observations on a few nights. 5. Measures of the position angles, distances, and magnitudes of the companions. The approximate places given from the Durchmusterung in Table XIII. could tlius be corrected, and the blanks for southern stars filled. The magnitudes could best be measured by the photome- ter recommended in (2). Otherwise especial care should be taken that the light of the fainter star was not affected by the proximity of the brighter. 6. Observations of the color and spectrum of these stars, to decide which ones, if any, should be included in tlie second class. 7. Distribution of the light in the spectra of these stars, and also of those of the second class at their maxima and minima. 8. Computation by Jacobi's method of the true diameter of a liquid ellipsoid in equilibrium, having given the period of rotation and the ellipticity of the equator. 9.. Computation of the Galactic latitude and longitude (or distance and direction from the pole of the Milky Way) of variables of Classes II. and IV., of the planetary and other gaseous nebulae, and of stars whose spectrum is of the fourth type. 10. Computation of the position of the poles of the orbits of the binary stars. The object of the present paper is not to advocate a certain theory which may seem improbable, and, possibly to some, inadequate. It is rather intended to bring together the most important facts bearing on the study of an interesting class of objects, and to exhibit them in a form in which they may be subjected to any desired test. The hy- pothesis advanced has a value as affording a simple geometrical con- ception of the nature of the variations under consideration, even if it proves not to be the true explanation of the cause. The ingenious hypothesis of Zollner, and other explanations of these phenomena, have not been overlooked. It seemed best, however, to leave to another to decide the comparative merits of views in which the precision of the effects must be considered as well as the probability of the causes. One theory, that the variation is due to the absorption of a rotatmg mass of gas, deserves a moment's consideration. This explanation does not appear probable for stars of the fourth class, since no evidence OP ARTS AND SCIENCES. 283 of absorption is in general shown in their spectra bcvonil the appear- ance of lines snch as are seen in our Sun. For the stars of tlie second class, however, this view seems more reasonable, since many of them exhibit specti'a which are strongly banded. Moreover, tlie great varia- tion in light is thus explained. An excellent test of this hypothesis is atlbrded by the variation in light of the different portions of the spectra. For light of any given wave-length the logarithm of the transmitted lay will always vary proportionally to the thickness and density of the absorbing medium, the amount of absorbent effect for any given thick- ness varying with the wave-length. Accordingly, a study of the varia- tion of each ray should show the came law. They would give very different coeilicients of absorptions, those of the dark bands being large, and those of the bright zones being small. The great variation in light will render this test a severe one with even a moderate degree of accuracy in the observations. For the lack of any data, this method of study is for the present unavoidably postponed. The principal conclusions of the above paper may be summarized as follows : — Thirty-one variable stars are known whose period is less than 72 days. Of those six belong to the fifth class, or that of /3 Persei, in which the variation is probably due to the interposition of an opaque eclipsing satellite. Of the remainder, seven may be excluded, since they are red, and may belong to the second class, or that of o Ceti. Nineteen remain, whose periods vary from less than a day to 54 days, and which may be placed in the fourth class. All lie within 16° of a great circle whose pole is in R. A. 13^, Dec. -|- 20°. The distances of eleven are from 0° to 5°, of five at distances 8° and 9°, one at 14°, and one at 16°. The average distance is 5°.o, while if the stars were distributed at random it should be 30°. If the stars of tlie Durchmusterung were uniformly distributed, their average distance apart would be about 8'.7. The five stars of the fifth class have Durchmusterung companions at au average distance of lO'.G. In the fourth class, excluding the red stars, six are in the Durch- musterung, and have companions at an average distance of 2'.5, four being less than 2'.0 distance, one at 3'.2, and one at 6M. In all six cases the direction of the companions is within less than 34° of the plane near which the variables lie, or at an average distance of 18°, while, if distributed by chance, this angle should be 45°. Hence a method of discovering variable stars of this class is offered by look- ing in a certain part of the sky for those having near companions in a given direction. 284 PROCEEDINGS OF THE AMERICAN ACADEMY The light curves of four stars have been determined with sufficient precision to permit a comparison with theory. All of these may be represented by the formula Z'= 1 -f- m' sin (v' + a) -f- n' cos 2v', in which L' is the light when the star has turned through the angle v'. The difference between observation and theory amounts on the aver- age to only about 0.03 of a magnitude. In other words, the light of these stars at any time may be computed with this degree of pi'ecision. Harvard College Observatoev, Cambridge, U. S. OP ARTS AND SCIENCES. 285 XIV. CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY. XIV. EXPERIMENTS ON . THE STRENGTH AND STIFFNESS OF SMALL SPRUCE BEAMS. By F. E. Kidder. Presented by Prof. Charles R. Cross, Feb. 9, 1881. The object of the following experiments was to determine the Moduli of Elasticity and Rupture in small beams of white spruce (Abies alba) ; and such other information as might be derived from the data obtained. The machine used for the purpose consists of two solid wooden frames, carefully levelled and placed forty inches apart. Upon the top of each frame is placed a movable plate of iron, which is care- fully adjusted so that the two plates shall be directly opposite each other, and exactly forty inches apart between the faces. These plates form the supports for the beams. The loads were applied by means of a scale pan suspended from a three-quarter inch bolt, which rested upon the centre of the beam. By means of an iron strap suspended from a horizontal beam placed above the test piece, and resting on two screws, the bolt from which the load was suspended could be raised from or lowered upon the test piece as easily and gradually as could be desired. The deflections of the beams were measured by means of a microm- eter screw, reading to one ten-thousandth of an inch. As the bolt from which the load was suspended rested on the centre of the beam, it was necessary to measure the deflections at a distance of one inch from the centre ; but the deflections used in calculating the values of the Modulus of Elasticity were corrected so as to give the deflection at the centre, supposing the curve assumed by the beam to be the arc of a circle ; from which, in fact, it deviates but little under such small 286 PROCEEDINGS OF THE AMERICAN ACADEMY loads. In reading the micrometer, the principle of electrical contact was taken advantage of. The greatest errors liable to occur in using the machine are as follows : — In measuring the deflections, one ten-thousandth of an inch. In the breaking load, possibly one pound; but in the small loads there could be no appreciable error. In measuring the dimensions of the test pieces, two thousandths of an inch. The experiments were conducted with the utmost care, and every possible precaution was taken to prevent errors. In arranging for the experiments, and while making them, the writer was greatly assisted by Mr. Holman, of the Institute, to whom he extends his acknowledgments. The pieces of wood experimented on were sawn from a spruce plank that had been cut in eastern Maine in the spring of 1880, and the following summer shipped to Boston, where it had lain in the open air until it was cut up in October. The pieces were carefully planed to an approximate size of one and a half inches square and four feet long. They were nearly all straight-grained and had but few defects, and in testing the beams they were placed so that the defects should have the least possible effect upon the strength of the beams. The exact dimensions of the test pieces ai'e given in Table I. TABLE I. No. of Test Piece. Clear lb pan. Breadth. B Depth D. E. E,. R. Centre break- ing weight for beam i"xi"xi'. )n.s. ins. ins. lbs. lbs. lbs. lbs. 1 4U 1475 1.450 1,781,000 1,657,000 11,380 6o2 2 ^, 1.445 1.520 1,550,000 1,528.000 10,330 674 3 ^, 1.409 1.448 1,7C.5.000 1,732,000 10,710 595 4 1.420 1.498 1,7;JO,000 1,030,000 10,830 601 6 1.450 1.485 1.088,000 1,578,000 11,980 605 6 1.480 1.440 1,795,000 1,086,000 11,040 613 7 J, 1.404 1.4li0 1,()82,000 1,501,000 10,570 687 8 )y 1420 1.180 1.047,000 1,556,000 11,280 620 0 1.4G0 1.4(10 1,704,000 l,0o8,0M0 11,180 021 10 „ 1.441 1.4W) 1,010,000 i,5.:o,ooo 12,440 691 In making the experiments, each beam was first subjected to a load of thirty pounds, and the deflection noted. The weight was then h*ft on the beam for a period of time varying from one to four, and in one case forty-four hours, and the deflection again noted. The load was OF ARTS AND SCIENCES. 287 then roinovt'd from tlie beam and the set noted, after which the beam was allowed a certain time to recover from the set. After the piece had returned, or at least nearly returned, to its orig- inal position, it was subjected to a load of forty pounds in the same manner. Table ir. gives the deflection of each piece under the loads of thirty and forty pounds, both immediately after the weight was applied ami after it had rested upon the beam the length of time designated. TABLE II. No. of Test I'ieco. WeiitUt ir. Time applied. Deflection A E. Weight ir. Time applied. Deflection A E. lbs. h. m. ins. Ihs. lbs. h. m. in.s. lbs. 1 30 0 00 00(310 1,744,000 40 0 00 0.0826 1,719,000 " " 2 25 .0G30 1,089,000 " 3 30 .0873 1,627,000 2 30 0 00 .0010 1,636,000 40 0 00 .0801 1,576,000 " " 1 45 .01)30 1,481,000 " 3 00 .0842 1,499,000 3 30 0 00 .0006 1,774,000 40 0 00 .0815 1,757,000 '• " 1 00 .0610 1,759,000 " 1 00 .0840 1,705,000 4 30 0 00 .0582 1,725,000 40 0 00 .0765 1,748,000 •' " 2 25 .0610 1,627,000 " 3 20 .0813 1,645,000 i 5 30 0 00 .0580 1,740,000 40 0 00 .0774 1,637,000 " 2 30 .0618 1,030,000 " 44 15 .0874 1,527,000 6 30 0 00 .0605 1,792,000 40 0 00 .0803 1,799,000 ■' " 3 00 .0639 1,697,000 " 5 12 .0862 1,676,()II0 7 30 0 00 .0624 1,683,000 40 0 00 .0833 I,(i82,(i00 " '< 3 00 .0663 1,584,000 " 16 00 .0911 1,538,000 8 30 0 00 .0632 1,645,000 40 0 00 .0839 1,050,000 " " 4 15 .0666 1,561,000 " 16 30 .0894 1,552,000 9 30 0 1 0 00 30 00 .0619 .0043 .0661 1,701,000 1,038,000 1,614,000 40 0 00 .0823 1,707,000 1*0 30 40 0 00 .0881 1,618,000 ' ' " 2 00 .0691 1,544,000 1 15 .0915 1,556,000 The values of the Modulus of Elasticity calculated from these de- flections are also given. The Moduli of IClasticity obtained from the deflection of the beams immediately after the weight was applied have been denoted by £J, and those obtained from the deflection of the pieces after the weight had been applied one or more hours, by JE^. Table I. gives the values of E and ^j for each piece, obtained by taking the average of the values given in Table 11. IF/3 . The values of B were computed by the formula B = 4 a/j/>3' ^" which fF denotes the weight in pounds producing the deflection ; I the clear span in inches ; A the deflection of the beam at the centre ; B the breadth of the beam, and D the depth, both in inches. After all of the beams had been treated in this way, piece No. 3 was again put in the machine and subjected to a load of 100 lbs., 288 PEOCEEDINGS OP THE AMERICAN ACADEMY which was allowed to remain upon the beam for about two hours, the deflection being measured directly after the weight was applied and just before it was removed. The beam was then allowed a certain time to recover its set. In two cases, the beams, after having been subjected to a load of 100 lbs., finally returned to their original posi- tion, and it appeared probable that all would have done so had sufficient time been allowed for the purpose. After the piece had nearly recovered from the effects of the load of 100 lbs., a load of 150 lbs. was put on the beam, and gradually increased until the breaking point was reached. The remaining pieces were tested with a load of 100 lbs. in the same way, and then subjected to a load of 400 lbs. for one or two minutes, for the purpose of getting the deflection under that load, and immediately after subjected to the full load of 500 lbs., which was gradually increased until the piece broke. As the load approached the breaking weight, it was increased by the addition of only one or two pounds at a time, so that the breaking weight could be obtained with sufficient accuracy. In fact, the breaking weight is so much modified by the time occupied in breaking the beam, that it is difficult to ascer- tain exactly what it really is. For any load, over three-fourths of what is called the breaking weight would probably break the beam if applied long enough. Table I. gives the values of the Modulus of Rupture of each piece, 3 Wl computed by the formula H z=i- 'jri~,, in which JR denotes the Mod- ulus of Rupture ; W the breaking weight of the beam, and the other letters have the same significance as in the formula for E. The load which would break a beam of the same wood, one inch square and one foot between supports, if applied at the centre, is also given in the same table. This load is one eighteenth of the Modulus of Rupture. When the weight of 400 lbs. was applied to piece No. 7, it imme- diately cracked at a knarl in one of the lower edges, about three- fourths of an inch from the centre of the beam. As it was thought that the beam would soon break entirely, the load of 400 lbs. was allowed to remain on the beam ; but at the end of one hundred hours tlie deflection had only increased 0.2224 inches, and as it was evident that it would, at that rate, take a long time for the beam to break, the load was then gradually increased until the piece broke at 550 lbs., giving a Modulus of Rupture considerably above the average. It was noticed in this beam that the deflections under the loads above 500 OF ARTS AND SCIENCES. 289 lbs. were considerably greater than in the other beanis under the same loads. Piece No. 5 gave a very high breaking weight, and broke very sud- denly, more like the harder kinds of wood. Ti)e fracture was very perfect, the upper half of the fibres being very evidently compressed and the lower half suddenly pulled apart, with almost no splintering. This piece had a small knot on the upper side, five inches from the centre of the beam, but it appeared to have no effect upon the strength of the beam. Piece No. 4 broke in a rather peculiar manner. While under a load of 575 lbs., the lower fibres for about a depth of one-tenth of an inch snapped apart, and the beam gradually settled down until the next layer of fibres had apparently the same deflection as did the lower ones at the time of breaking, when they also snapped, making a layer of about the same thickness. In this way the whole lower half of the beam seemed to divide itself into layers of about one-tenth of an inch thick, and to break separately under about the same deflec- tion, so that the beam was a long time in breaking. Observing that under every load that had been applied the deflection kept increasing with the length of time the weight remained on the beam, piece No. 7 was subjected to a load of 275 lbs. for ninety -eiglit hours, during which time the deflection increased 0.079 inches. The weight was then taken off and the beam allowed to recover for twenty- four hours, when it had a set of .0446 inches. The same weight was again applied, and it was found that the deflection, obtained by taking the difference between the readings of the micrometer just before and after the weight was applied, was less than it was the first time the weight was applied, and the rate of increase of the deflection was about the same as before. The beam was thus subjected to a weight of 275 lbs. for three hundred hours in all, after which it was broken in the same manner as the others. It was expected that the effect of such a severe strain for so long a time would diminish its strength ; but, on the contrary, it appeared to increase it, as the beam gave a higher Modulus of Rupture than any of the others, although it did not appear to be of as good quality as many of them. The ultimate deflection of this beam greatly exceeded that in any of the others. Table III. shows the deflection of each beam under loads of 30, 40, 100, 400, 500, and 550 lbs., immediately after the load was ap- plied, and at a distance of one inch from the centre. The small figures under each deflection show what it would be if Hooke's Law held true, taking the deflection under 30 lbs. as the starting-point. 290 PROCEEDINGS* OF THE AMERICAN ACADEMY TABLE in. Deflection in nches under No of Test Piece. Ultimate Deflection. Breaking weight. lbs. 30 lbs. 40 lbs. 100 lbs. 400 lbs. 500 lbs. 550 lbs. 1 0.0010 0.0826 0.2071 0.8303 1.0906 1.2791 1.5646 588 .0610 .0813 .20.30 .8120 10150 1.1165 2 .0616 .0801 .2043 .8177 1.0077 1.2811 1.3941 575 .0016 .0820 .2050 .8200 1.0250 1.1275 3 .0606 .0815 .2023 .8976 1.2764 1.4800* 1.4800* 550 .0606 .0808 .2020 .8080 1.0100 1.1110 4 .0.J82 .0765 .1929 .7929 1.1146 1.3197 1.4058 575 .0582 .0776 .1940 .7760 0.9700 1.0670 5 .0580 .0774 .2004 .7876 1.0170 1.1827 1.5788 637 .0580 .0773 .1933 .7732 0.9665 1.0631 6 .0605 .0803 .2138 1.2520 1.4662 • • ■ • 565 .0605 .0806 .2016 10080 1.1088 7 .0624 .0833 .2083 .sVoi 1.3595 550 .0624 .0832 .2080 .8320 1.0400 8 .00:]2 .0839 .2102 .8315 1.1111 1.'3331 1.5709 585 .0632 .0842 .2106 .8424 1.0530 1.1583 9 .0019 .0823 .2083 1.0800 1.2830 1.4254 580 .0619 .0826 .2063 1.0315 1.1346 10 .0661 .0884 .2220 .9276 1.1772 1.3775 1.8100* 637 .0661 .0881 .2203 .8812 1.1015 1.2116 From these experiments I think we may draw the following con- clusions : — That the Modulus of Elasticity depends not only upon the elas- ticitj^ of the material, but also upon the length of time the load is applied. That when subjected to loads not exceeding one-sixth of the break- ing weight, spruce beams do not take a permanent set. That even under very small loads, if applied for any length of time, there will be a temporary set. That knots and knarls in beams loaded at the centre, when not within one-eighth of the span of the centre of the beam, do not mate- rially affect the elasticity under small loads. That the deflection is very nearly pro])ortional to the load, far beyond the customary limits of strain, and that the Modulus is conse- quently very nearly constant for all moderate deflections. That a high Modulus of Elasticity does not always accompany high transverse strength; for, as shown by Table I., piece No. 10, which had the greatest transverse strength, gave next to the lowest value of E. That in spruce beams the upper fibres commence to rupture by compression under about four-fifths of the breaking weight, and the * Approximately. OF ARTS AND SCIENCES. 291 neutral axis is very near the centre of the beam, as shown by the fracture. That beams which are subjected to severe strains for a long time bend more before breaking than those whicli are broke u in a compar atively short time. That the Modulus of Elasticity of small spruce beams, of a quality such as is used in the best buildinga, may be taken at from 1,600,000 to 1,700,000 lbs., and the Modulus of Rupture at about 11,000 lbs. The only other experiments on American spruce with which the writer is familiar are those made by Mr. R. G. Hatfield, on small beams, 1.6 feet between supports, and some experiments by Mr. Thomas Laslett, of England, on pieces of Canada spruce 2 inches square and 72 inches between supports. Mr. Hatfield gives as the average value of the transverse strength of a unit beam, 612 lbs.,* which would give 11,016 lbs, for the Mod- ulus of Rupture. From data given by Laslett f we obtain as the value of i?, 9,045 lbs. The value generally giveij for the Modulus of Elasticity of spruce is 1,600,000 lbs. * Hatfield's Transverse Strains, Table XLII. t Timber and Timber Trees, Native and Foreign, by Thomas Laslett, In- spector to the Admiralty, London, 1875. 292 PROCEEDINGS OP THE AMERICAN ACADEMY XV. ANTICIPATION OF THE LISSAJOUS CURVES. By Joseph Lovering, Hollis Professor in Harvard College. Presented January 12, 1881. In 1857, Lissajous communicated to the French Academy of Sciences his " Memoire sur I'Etude Optique des Mouvements Vibratoires." * By attaching a mirror to each of two tuning-forks, and reflecting a pencil of light successively from the two mirrors, the resultant motion of the forks was exhibited on a greatly amplified scale. When the vibrations of the tuning-forks were in parallel planes, and the musical interval between them was not exactly in tune, the consequent beats were manifested to the eye, even ^fter they had become insensible to the ear. When the two motions were in rectangular planes, the extremity of the pencil of light described some one of a group of curves, rising to higher orders as the ratio which expressed the musical interval be- came less simple. Each of these groups could be easily resolved into eight distinct varieties, each variety depending on a definite difference of phase in the two movements. Inasmuch, however, as there are innumerable differences of phase between any two well-marked limits, there must be an endless series of curves in each group, through which each variety flows gradually into the next. Lissajous studied the subject analytically as well as experimentally, and then applied it to his optical method of tuning notes, especially those of tuning forks, to any required interval. If the vibrations of the forks were true to the precise ratio of this interval, the resultant orbit of the twice- reflected ray would be invariable : and it would be one or another variety in the corresponding group of curves, as the original difference of phase was smaller or larger. If the movements of the two forks did not conform to the exact ratio, the original difference of phase would change with each successive vibration, and the wliole group of * Annales ile Chim. et iJo I'lij's., vol. li. 18J7. OP ARTS AND SCIENCES. 293 curves would be presented in succession. From the rapidity of this succession, the rate at which the phase changed would he known, and hence the degree of imperfection in the assumed interval. The admiration of physicists was elicited by Lissajous's method of magnifying tlie mere trembling of a rigid tuning-fork into a visible magnitude ; and especially by his optical method of tuning, which, in the hands of even a deaf person, would give better results than were possible to the nicest musical ear. Of these groups of beautiful curves, a few, as the circle, ellipse, parabola, and lemniscate, were not unfamiliar to mathematical and physical science. But most of them were supposed to be novel, and have been introduced into later works on Mechanics and Acoustics under the name of the " Lissajous curves." Many uuHlifications have been introduced into the original experi- ments of Lissajous, either by himself or others. Reeds, driven by a bellows, have been substituted for tuning-forks. A steel rod, with an approjiriate cross-section and mounted with a mirror, admits of the two elementary vibrations in rectangular planes. Two vibrating disks, with rectangular slits, which allow the light to pass only at their in- tersection, answer the same purpose. Sometimes one vibration is given to a small aperture through which the light passes, and the other to a lens which forms its image on a screen or in the eye. Wheatstone produced, in a single reflector, the two rectangular movements by mechanical means. Konig, and more recently Ritchie, have used mechanism with two mirrors. The tonophant of Ladd consists of a compound rod, flattened in two rectangular planes. Barrett succeeded with a round and bent steel wire. It appears that in 1844, Professor Blackburn * of Glasgow experi- mented with a pendulum, in which the bob was suspended by a Y- shaped cord ; the length of the pendulum being virtually the total length, or only that of the lower branch, in the two principal planes of vibration. In 1871, Mr. Hubert Airyf noticed the curious curves described by the end of a twig of acacia and of hazel. In pursuing the subject, he finally adopted Blackburn's compound jjendulum, and reproduced many of the Lissajous curves ; but he makes no allusion either to Lissajous or to Blackburn. Airy calls the orbits he obtained autographic curves, as they were neatly drawn by a pencil or pen, attached to the pendulum. Before and since that time, various ma- chines were contrived for obtaining a permanent record of these * Tait's Dynamics of a Particle, 3d ed. p. 221. t Nature, vol. iv. pp. 310 and 370. 294 PROCEEDINGS OF THE AMERICAN ACADEMY complex and diversified motions, whether produced bj the vibration of elastic bodies or by machinery. Lissajous and Desains, with an apparatus constructed by Froment, scratched the curves upon smoked glass, the style being moved by one vibrating body and the glass by the other. Professor Pickering* moved a pen and paper in rectangular directions by machinery, and described the curves on a much larger scale. Donkin f contrived a machine for the graphical representation of a number of parallel vibrations ; but the most complete apparatus of the kind is Tisley's harmonograph, $ which can be suited to parallel, perpendicular, or oblique vibrations ; and in a great variety of ratios. The motions of the pen and paper are produced by two independent pendulums, delicately mounted and heavily loaded, so as to maintain their vibration for a long time. The ratios can be altered by a change of weight, combined with a change in the length of one of the pendulums. The latter adjustment can be neatly applied, for making or disturbing the exact ratio of the required interval, without stopping the motion of the pendulum. As far back as 1800, Dr. Young § experimented upon the variegated path described by a single point of a silvered vibrating cord, illumi- nated by strong sunlight. In 1827, || Wheatstone invented the kalei- dophone : which was simply a vibrating wire, with a bead at the free end, and short enough to give persistent vision for the orbit. But neither Young nor Wheatstone have given a mathematical analysis of the motions; the exquisite figures they obtained were due, mostly, to the superposition of the higher harmonics, and few of them are identical with the Lissajous curves. In 1832, Edward Sang U of Edin- burgh developed mathematically the resultant of two rectangular vibrations, having different periods and phases, and illustrated his subject b}' experiments with round and flat wires, which produced the peculiar Lissajous curves. Drach, who himself, in 184G,** published his theoretical studies on the combination of two circular motions, with their resulting epicyclical curves, states that Perigal devised ma- chinery which traced curves identical with those of Airy, and, there- fore, with those of Lissajous. This machine was exhibited, in 1846, * Journal of Franklin Institute, January, 1869. t Proo. Koy. Soc. London, vol. xxii. (1874), p. 197. } Engineering, vol. xvii. (1874) p. 101. § Trans. Roy. Soc, London (1800). II Collected Papers. 1 Edinb. Phil. Jour., vol. xii. (1832) p. 817. ** Phil. Mag., London, vols, xxxiv. pp. 418, 440 and xxxv. (1849-50). OF ARTS AND SCIENCES. - 295 at a scieulific soiree in the house of Lord Northtimpton. Three voUimes of Perigal's kinematic curves are preserved in the archives of the Royal Society of London, of the Royal Astronomical Society, and of the Royal Society. But all these anticipations of the Lissajous curves, theoretical and experimental, are antedated by two publications whicli appeared at Boston in 1815.* Li this year Professor Dean, of Burlington, Ver- mont, published a curious memoir on the " Motions of the Earth as seen from the Moon." It is well known that the time of the moon's rotation on its axis is equal to the time of its revolution in its orbit. The result of this equality (whether regarded as a mere coincidence or the effect of gravitation) is seen in the fact that the same side of the moon is always turned towards the earth. This statement would be literally true if the moon's motions of rotation and revolution were in parallel planes, and the momentary velocities as well as the average velocities were always equal. But the plane of the moon's equator is inclined to the plane of the moon's orbit at an angle of 6° 39' ; so that an observer on the earth, at one time, overlooks the north pole of the moon to the extent of 6° 39', and about a fortnight later the south pole. Moreover, the velocity of rotation is uniform, but the velocity of revolution is unequal in different parts of the elliptical orbit. Therefore, although the whole periods are the same for botli motions, the moon at perigee revolves faster than it rotates, and at apogee it rotates faster than it I'evolves. Hence, in the course of one revolu- tion, an observer on the earth overlooks the eastern or the western edge of the moon to the extent of 6° 18' each way. or the greatest equation of the centre of the moon's orbit. These effects are familiar to astronomers under the name of the moon's libratious, which en- able them to see every month four sevenths of the moon's surface, though the remaining three sevenths are forever hidden from view. Professor Dean investigates the influence of these peculiarities in the moon's motion on the position of the earth as seen by a lunar observer. If the two motions of the moon were equal and parallel, without any qualification, the earth would always occupy the same place in the lunar firmament. If the observer were happily situated at the centre of the moon's visible disk, the earth would always be in his zenith. But the inclination of the planes of the moon's equator and orbit will make the earth appear to oscillate over a north and * Memoirs of Amer. Acad, of Arts and Sciences, 1st series, vol. iii. p. 241 (1816). 2^ PROCEEDINGS OF THE AMERICAN ACADEMY soath. liiw?. IS'' IS' in length. The w^uit of uniformitT in the Telocitr of the moon's revolutioo will prodoee an e»steriT and wcsterlj oscilla- lioa in the ' '- " .? the extent of 12~ 36. Nature here offers an as: f. on a grtind scale, of two reotau^ilar Tibmtio&s of nearly equal amplitude. It is the case of a unison, bat a V. ■: exaotlr in tune. For the monthly period which governs be: s is not measured in exactly the same way for bo:ii. The period oi the first oscillation is the time in which the moon revolves fn>m a node to the same node again. The period of the second oscillation is the time occupied by the moon in going from perigee to perigee again. If the node and the perigee were fixed points, the two periods would be equal. But the node and perigee, in the mean while, are both moving : the former about 1|^^ to the west, and the latter about o' to the east- Hen>."e the periods of the two oscilla::oas will be in the ratio of about o-5-Si^ to 060. or of 79 1 to SOi^. In the course of ei«rhty oiscillations, the north and south one would gain one whole Osscillation upon the other: and once, in about every six years, the earth, as seen from vhe moon, would appear to describe upon the sky all the varieties in lissajous's first group of orbirs. To iUostrate the - ' " ~ " -Tsed the compound per " ~ . ;:p-:>sed to have been science twenty-nine ye,. - '"^irds by 6Ia«^bum. The total length of the coed was forty inches and that of the single br.. " e inches- ^^ " -ae realized the ca? .it fault to the _ .e had the saas- facuoo of seeii^ the suspended bob m-^ve over, in the period of eighty vibratioos, the complete series of paths pertaining to all the changes of phase of an imperfect unison. In the same year, an elaborate memoir was published by Dr. Na- tbaniel Bowditch.* ~ On the Modon of a Pendulum suspends - - — :: •— ? Points," which be^^r^s with this paragraph- — - The remarks 7 of morions in a . suspended &om two points, in the car: ~u.s experiment in F- -T^^- : 1 -: "-■ - - - — -' r apparent motion or the earth, as viewed from the :o examine the theory of s. and I hare : the fondamectal eqoa- -. .._ -'- ^--^ - ^ _^... which is the case usually considered : - • ^ of the most important results of this P- 1 _.,_ .. . i the path -i by the end of : . ■ case, iran- * Mc— ;irs Amer. Acad , lit serie*, vol. iii p. 4ii OF AHTS AND SCIENCES. 297 scendental, but became algebraical when the pericxls of the component motions were in some simple ratio, either exactly or approximately. He developed in detail: 1. The unison; 2. The octave; 3. The twelfth; 4. The double octave: and. all of them whether perfect or out of tune. His investigation had no reference to acoustics ; and he describes these cases V>y their ratios, and not by the musical intervals which these ratios may represent. He adds that similar results would be oh)tained if the longer period, divided by the shorter, were expressed by any whole number, either exactly or approximately. Such ratios as 2 : 3 or 3 : 4, etc., did not come within the scope of his paper. Dr. Bowditch obtains the equations for the few cases which he specially examines, and finds that for the unison the path is expressed by an equa- tion of the first or the second order ; for the octave, by an equation of the second or fourth order ; for the ratio 1 : 3, by an equation of the third or the sixth order ; and for the double octave, by an equation of the fourth or eighth order : in each case the equation being of a lower order when the difference of phase in the two movements is zero or 180°. Dr. Bowditch adds : " 1 made a few experiments in order to com- pare the preceding theory with observation." In his first experiment, the two points of suspension were 4.75 inches apart, the single branch of the thread was 46.5 inches, and the vertical height of the double branch only .65 of an inch. Therefore the two movements were more nearly in unison than in Professor Dean's experiment. A ball of lead about half an inch in diameter hung at the bottom. By calcula- tion one movement would gain a whole vibration upon the other in 286 vibrations of the more rapid movement: by experiment the num- ber came out 282. In another experiment, the two points of suspen- sion fvere 69 inches asunder: the single branch of the pendulum was 21.9 inches, and the vertical height of the double branch 64.4 inches. A ball of lead If inches in diameter was attached. In this case the two movements differed in period by the interval of an octave, im- perfect to the extent of one vibration in sixty-seven of the slower move- ment ; and experiment confirmed this conclusion, the whole cycle of orbits being completed in that time. In regard to the two other ratios, Dr. Bowditch says : " A few rough experiments were, however, made in these cases, and the results appeared to be suflaciently conformable to the theory." This kind of experiment is not suited to such ratios as 1 : 3 and 1 : 4. For in these cases the single branch of the cord is only one ninth and one sixteenth of the total length, and the amplitude of its vibration comparatively small. 298 PROCEEDINGS OF THE AMERICAN ACADEMY I have now traced the mathematical analysis and the experimental illustration of the Lissajous curves from France to Great Britain, and thence, across the ocean, to their home in Salem, Massachusetts. The so-called Lissajous curves are the Bowditch curves, except so far as the earth itself had been experimenting upon one set of them for thousands of years. They will continue, probably, to be called the Lissajous curves. But their history should be known, and will be known ; though it is not necessary for the reputation of the self- taught mathematician. Dr. Nathaniel Bowditch. The author of the " Practical Navigator," and the translator of Laplace's " Mecanique Celeste," with its rich commentary, has secured a place in the world of commerce and in the world of science to which nothing need be or can be added. Explanation of the Plate. Figure 1. Professor Dean's diagram, illustrating his pendulum. Figures 2, 3, 4, and 5. Dr. Bowditch's diagrams to show the orbits in an imperfect unison. Figure 6. Dr. Bowditch's diagram to illustrate the progressive changes in the orbit. Figures 7, 8, 9, 10 and 11. Dr. Bowditch's diagram to show the orbits in an imperfect octave. Figures 12 and 13. Dr. Bowditch's diagram for special differences of jihase in the ratio, 1 : 3. Figures 14 and 15. The same when the ratio was 1 : 4. Figure 16. General diagram of Dr. Bowditch's pendulum. All these figures are exact copies of those published in the Plates of the Academy, vol. iii. 1st series, 1815. OP AIMS AND SCIENCES. 299 XVI. OBSERVATIONS ON JUPITER. By L. Trouvelot. Presented March 9, 1881. In the year 187G, a seines of observations on the planets Mercury, Venus, Mars, Jupiter, and Saturn was undertaken with the intention of following each one of these bodies for as many years as necessary to study them on every point of their orbit, in order to arrive at a better knowledge of their 2Jhysical constitution and meteorology. The plan then formed was to make at least one observation and a drawing of each planet on every favorable day, whenever the object would be so situated that it could be advantageously observed. So far, this plan has been carried out, and over 1,500 observations, accompanied by 1,000 drawings, have been made. It is my purpose in this paper to make as brief a statement as possi- ble of those portions of my observations pertaining to the rotation of Jupiter, and the great red spot which made its appearance upon its surface in the year 1878; reserving the rest for publication whenever means shall be found for printing the plates in a suitable manner. The facts here recorded were selected from the 591 observations and 567 drawings of the series made during the last five years. The year 1876, the first of my regular and systematic observations of Jupiter, was one of extraordinary disturbance, and nothing ap- proaching it has since been witnessed. The changes were so rapid that, save in one case, no spots or markings could be recognized the day, nay, sometimes even the hour, after they had been observed. Since that time, the surface of the planet has been remarkably quiet, only an occasional change taking place. During the last four years some of the markings have been very persistent, and remained in sight for years, with but very little apparent change. Mark A. In one case only, as has been said above, was a spot recognized in 1876. This object, first seen on May 19, was recognized ou May 21, 300 PEOCEEDINGS OF THE AMERICAN ACADEMY after having accomplished five rotations, the mean of which equals gh ^jm Qs^ 'pjjQ position of this spot was in the northern part of the equatorial belt, extending as far as its border on that side. For convenience we will call this marking A : the other markings to be described will be similarly designated by a letter of the alphabet. Mark B. In contrast with the usual behavior of the spots seen on the surface of Jupiter in years of calm, and also to show how much these spots are to be relied upon to determine the period of rotation of the planet, I will give a brief account of an observation made in 1S76, from which an idea can be formed of the rapidity with which changes sometimes take place on Jupiter, and of the swiftness which some- times animates these spots. On May 25, Jupiter was observed and a drawing made at 8^ 37". At this time, and at least five minutes later, nothing unusual or re- markable was to be seen on the planet. At 9*^ 4", however, an angular marking resting on the outside border of the equatorial belt, on its south side, was visible near the east limb. This mark advanced rapidly towards the centre of the disk, which it had passed at 9^ 32°, when a third drawing was made. At 9*^ 50™ the angular marking had reached the western limb, having then crossed the disk of Jupiter from east to west in less than an hour's time. The angular mark of which the motion has just been described was formed by an oblique dark band, resting on its preceding side on the xapper band, forming the southern margin of the equatorial belt. As the angular mark advanced on the disk, the space behind it enlarged considerably, the upper band limiting it southwards, keeping the same obliquity with the equatorial belt as far as it could be seen on the east limb. At 9^^ 32° the oblique band on the east limb had a latitude of 50° south. After the angular mark had crossed the western limb, it continued its tremendous onward motion, as could be seen by the con- stantly increasing latitude of the upper band on the west limb, and at lO*" 20° this upper band was parallel with the southern border of the equatorial belt. The space then comprised between this upper band and the southern margin of the equatorial belt was equal to 35°, and was about twice as broad as the latter belt before the disturbance occurred. This space appeared tinted with a delicate pink color, intermingled with white cumulus-like spots resembling exactly those usually seen on the equatorial belt. When the upper band reached OF ARTS AND SCIENCES. 301 parallelism with the equatorial belt, at 10^ 20"", the pink color forraed a wide belt extending from 10° of north latitude to 45° of south latitude, being therefore 55° in breadth. Not only that zone of Jupiter was in commotion, but the whole of the southern hemisphere participated in it up to the pole, as proved by the total change of the markings, and the swelling of all the bands to higher southern latitudes on their following side. One of the bands, which on the western limb was at 30° south, was swollen to the south pole on its following extremity. It is to be noted that, iu this great disturbance, the bands, although enormously swollen on the following side, still maintained the same distance from each other ; each one keeping pace with the other, and following it in all its sinu- osities, the effect being apparently the same as if a wedge had been driven from east to west between the upper border of the equatorial belt and the oblique band described. On many occasions in 1876, this continuous parallelism between the different bands in the midst of dis- turbances was observed, as if the force causing the disturbance had been moving from east to west, between the vapory envelope of Jupiter, and pushing it aside in its passage, as a ship parts the waves of the ocean. On the following day no traces of this great storm appeared ; but everything seemed quiet, the equatorial belt having resumed the same appearance it had on the 25th, before the commotion oc- curred. If we determine the period of rotation of Jupiter from the observa- tions of this angular marking, which will be called B, it is found to be very nearly two hours, a period which is very far from agreeing with that found by the observations on the mark A above described, and the adopted period until lately, viz. 9'' 55" 4P. The last two periods may be called the periods of calm, while the first may be called the period of distui'bance. Mark C. In 1876 the observations on Jupiter were discontinued after Oct. 19, and resumed after conjunction, on April 11, 1877. On that day a very characteristic mark, resembling a step seen in profile, was observed on the southern border of the equatorial belt, which at one point was deflected at a right angle, the western portion of the belt, or preceding side, being narrower than the eastern or following side. This step-like marking, which will be called C, was a new fonn, which had not once been seen in 1876, It remained visible through- 302 PKOCEEDINGS OF THE AMERICAN ACADEMY out the year 1877 as late as Dec. 2, when the observations were abandoned, owing to the proximity of Jupiter to the Sun. In 1878, only a few scattered observations were made from the 10th of February to the end of August, the work being resumed regularly in September only. On the 10th, a step-like marking, resembling that observed the year before, was seen on the southern border of the equatorial belt, apparently at the same place which that mark occupied. It was prob- ably the same object, as seems to result from the calculation of its period of rotation, and from its position in regard to the mark D, which will be next described. In the following table are given the dates and times of the passages of the mark C on the central meridian. Similar tables will be given for the other markings described in this paper. The passages of the markings or spots on the central meridian have not been obtained by micrometrical measurements, but are simple eye estimations. This, of course, renders them liable to errors, which cannot, however, exceed two minutes in most cases, I think. The passages tabulated have not all been obtained by direct tele- scopic observations in the way described just now, about one third only having thus been observed. The others were obtained after- wards from the drawings themselves, the marking being reduced to the meridian from its position on the drawing, either east or west of the centre. These passages, of course, are liable to still larger errors than the former, the chances for error becoming greater as the distance from the centre increases. For this reason, the position of the markings at the time of observation, that is to say, their distance in time east or west of the central meridian, is given after eacli passage thus obtained ; the symbol -\- indicating that it had passed the merid- ian, and was west of it by the time given when tlie observation was made ; and the symbol — indicating that it was east of it, and had not yet reached the meridian, which it would cross only after the time given had elapsed. The passages on the central meridian which were obtained by direct telescopic observation in the manner above de- scribed are distinguished from the others by the words " On meridian " placed in the third column. The time given throughout this paper is the local time, or Cam- bridge mean time. The above remarks apply to all observations and markings tabulated, as well as the arrangement here adopted. On July 25 some changes were observed in the mark C, also on Sept. 16 and 21, when the changes were most striking; possibly a jump may be found on these dates. OP ARTS AND SCIENCES. 303 h. m. h. m. h. m. h. m. 877, April 11 16 50 On meridian. 1877, Sept 12 6 6 + 1 0 " May 3 14 10 + 1 8 " 13 8 37 — 1 40 " 22 14 45 + 0 30 " 16 6 40 + 0 10 " July 3 9 22 + 0 15 " 21 6 40 + 0 30 " 22 10 3 + 0 43 " 30 7 35 — 1 10 " 25 15 45 + 0 50 Oct. 10 G 2 — 0 12 " Aug. 0 16 17 + 0 5 " 15 5 0 — 0 30 8 17 87 + 0 7 K 17 6 50 On meridian " 10 19 46 — 1 0