SHELVE: DAEDALUS PROCKEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. VoL. XXXVIII. FROM JUNE, 1902, TO MAY, 1903. BOSTON: PUBLISHED BY THE ACADEMY. 1908. Anibversity WBress ; Joun Witson AnD Son, CAmBripcGg, U.S. A. Peay) VI. WALET- CONTENTS. . An Apparatus for Continuous Vacuum Distillation. By CHARLES F. MABERY . . Preliminary Diagnoses sr New Speses oy Laboulbeniaceae. — V. By Rotanp THAXTER : On Cauloglossum Transversarium Friss (Bosc). By Joun Ri JOHNSTON Sy Noes ag et), te Co eens Flora of the ee, Islands. By B. L. Rosinson. (With the collaboration of specialists. ) Parone Concerning Gas-Analysis by Measurement in Constant Volume under Changing Pressure. By Turopore WitttAmM RIcHARDS . A Method for Determining the Index of Refraction of Solid Hydro- carbons with the Pulfrich Refractometer. Index of Refraction of the Solid Hydrocarbons in Petroleum. By Cuarires F. MABERY AND LEE SHEPHERD — The Significance of Changing Aine Volume. III. — The Rela- tion of Changing Heat Capacity to Change of Free Energy, Heat of Reaction, Change of Volume, and Chemical Gers By THEODORE WILLIAM RICHARDS . The Speed and Nature of the Reaction of Bromine upon Oxalic Acid. By Turoporr WititiaAmM RIcHARDS AND WILFRED NEWSOME STULL . Regular Singular Points of a ae of Serene Linear Dif ferential Equations of the First Order. By Otto DUNKEL . The Influence of Atmospheres of Nitrogen and Hydrogen on the Are Spectra of Tron, Zinc, Magnesium, and Tin, Compared with the Influence of an Atmosphere & Ammonia. By Roya A. PoRTER Mets Ae . Babingtonite from Somerville, Mass. 5 Babingtonite from Athol, Mass. By C. PALACHE AND F. R. FRAPRIE . . On the Thermal es of 0 the Spark pra we Carbon. By Henry CREW AND JOHN C. BAKER The Universally Exact Application of Faraday’s Law. By TnKo- DORE WILLIAM RICHARDS AND WILFRED NEWSOME STULL Page 281 291 319 339 371 381 395 407 lv CONTENTS. XIV. An Apparatus for the Measurement of the Expansion of Gases by Heat under Constant Pressure. By Tutopore WILLIAM Ricuarps AND KennetH LAMARTINE Mark XV. The Transition Temperature of Sodic Sulphate Referred anew to the International Standard. By THreopore WILLIAM RicHaARDS AND RoGerR CLARK WELLS. ..: . . XVI. A Revision of the Atomic Weight of Caesium. By THroporE Witiiam RicHArpbs AND EBENEZER HENRY ARCHIBALD XVII. On the Multiple Points of Twisted Curves. By Joun N. Van DER VRIES XVIII. Mendel’s Law of Heredity. By W. E. Castle XIX. On the Temperature Coefficients of sik made bees Chiiled Gast Iron.” Bye O07 PEIRCE 2 = 5 XX. The Pressure due to Radiation. By E. F. Nicuoxis anp G. F. Hui XXI. The Heredity of Albinism. By W. E. CasttE and GLOVER M. ALLEN. XXII. Diffusion and Supersaturation in Gelatine. By Harry W. MorskE And GEORGE W. PIERCE XXIII. On the Thermal Conductivities of Certain Pieces of Rock from the Calumet and Hecla Mine. By B. O. PEIRCE XXIV. On Families of Curves which are the Lines of Certain Plane Vectors either Solenoidal or Lamellar. By B. O. Prerrcr XXV. The Spectra of Gases and Metals at High Temperatures. By JouN TROWBRIDGE . « Recorps oF MEETINGS A Table of Atomic Weights. By Turopore WILLIAM RICHARDS . REPORT OF THE COUNCIL BroGRAPHICAL NOTICES Alpheus Hyatt . John Daniel Runkle OFFICERS AND COMMITTEES FOR 1903-1904 List oF THE FELLOWS AND Forr1iGN Honorary MEMBERS . STATUTES AND STANDING VOTES Rumrorp PREMIUM INDEX . PAGE 429 441 471 533 549 557 601 731 Proceedings of the American Academy of Arts and Sciences. Vou. XXXVIII. No. 1.— June, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XLII. AN APPARATUS FOR CONTINUOUS VACUUM _ DISTILLATION. By Cuarves F. MABeEry. a fyi RL r a A) CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XLII. AN APPARATUS FOR CONTINUOUS VACUUM DISTILLATION.* By CuHarues F. Masery. Received May 18, 1902. THE occasional contributions to methods for vacuum distillation seem to indicate that a method is still wanting that shall combine convenience and efficiency. It is quite true that the various attachments that have been suggested and that are described in dealers’ catalogues fall short of efficiency in essential details. In the great amount of vacuum distillation carried on in this laboratory during the last fifteen years, probably much exceeding what has been done elsewhere in a single line of work, a durable apparatus has been gradually evolved in which this work can be carried on as expeditiously as distillations under ordinary pressures. One of the most essential features is a regulator to maintain a constant tension, and the stopcock G with lever attachment formerly described + and constantly in use is very satisfactory. The chief features to be provided for in a convenient apparatus are the following: 1. Exclusion of air from hot oil in still during change of receiver. 2. Admission of distillates into still without interruption. 3. Admission of air into receiver~before removal of each fraction. 4, Exhaustion of receiver for new fraction without connection with still. The complete apparatus in the form used at present is shown in the following figure : — * This method is a part of the work that is carried on in this laboratory with aid granted by the Academy from the C. M. Warren fund for chemical research. t These Proceedings, XXXL. p. 10. 4 PROCEEDINGS OF THE AMERICAN ACADEMY. The fractions are drawn into the still through the tube closed by the nipper tap A. The still is exhausted by the tube N connecting the tube O with the vacuum reservoir D. The reservoir C is exhausted by the tube H which connects with the water pump through the tube P. Air is let into the receiver C by means of the cock I, and kept from the still by the cocks E and F. The tube with the stopcocks E and F afford a convenient means for separating fractions without interruption, and without admission of air into the still. The tube M leads to the manometer. By means of a single efficient water pump the entire apparatus may be kept under a tension of 12mm. or less during con- tinuous distillation. By means of common corks, the apparatus is readily set up and easily kept tight by the use of rubber lute. The tubes If and N may be given less rigidity by putting them together in sections with connectors. Any water that may occasion- ally run back from the pump is readily drawn out if the pipe P extends to the bottom of the reservoir D. The apparatus in this form is especially adapted for the separation of fractions with high boiling points. For very high temperatures the still must be packed in asbestos. For more volatile distillates a condenser should be inserted between the still and tube O, best by passing the exit tube of the still through the condenser. Our distillation flasks are made with a high exit tube to give a long neck, which is filled with MABERY.— CONTINUOUS VACUUM DISTILLATION. 5 broken glass resting on a piece of glass rod with a head as previously described. As is evident from the figure, this apparatus may readily be set up from supplies always at hand in the laboratory, except the tube O, which any glass-blower can make. Suggestions as to details have been made by various assistants, espe- cially by Mr. O. J. Sieplein, instructor in chemistry, who prepared the drawing. . Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 2. —June, 1902. CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF HARVARD UNIVERSITY. —L. PRELIMINARY DIAGNOSES OF NEW SPECIES OF LABOULBENIACEAE. — V. By RoLanp THAXTER. CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF » HARVARD UNIVERSITY. —L. PRELIMINARY DIAGNOSES OF NEW SPECIES OF LABOULBENIACEAE. —V. By Roitanp’ THAXTER, Presented May 14, 1902. Received May 15, 1902. Dimeromyces Forficulae nov. sp. Male individual. Receptacle consisting of three superposed cells, the upper distinguished by a well-defined black septum from a short two-‘to three-celled terminal appendage, the subbasal septum of which is also blackened ; the subbasal cell of the receptacle producing a suberect, short-stalked, rather long and narrow antheridium; the neck relatively - broad, blunt, about as long as the stalk and venter. Total length to tip of antheridium 60 »: the antheridium, including stalk, 28-30 x 7-8 p. Female individual more or less tinged with purplish-brown, especially the body of the perithecium. Receptacle consisting of usually five cells obliquely superposed, with the exception of the uppermost, successively smaller from below upward, the series more or less strongly curved out- ward from the male; the subbasal cell bearing a simple differentiated appendage, its basal cell more or less geniculate and separated from the basally inflated, tapering, brown, five- to six-celled distal portion by a blackish constriction ; the cell next above it producing the single peri- thecium ; the next a simple cylindrical slightly tapering appendage with a black subbasal constricted septum ; the terminal cell bearing terminally a short, simple, few-celled primary appendage, distinguished by a con- stricted black basal and a pale subbasal septum, and laterally a similar appendage distinguished by a subbasal blackish constricted septum. Perithecium rather elongate, subclavate or subfusoid, the stalk not. distinguished from the body of the perithecium, and sometimes show- ing irregular septa; the tip often somewhat abruptly distinguished, blunt, slightly asymmetrical. Spores about 85 X 3.0. Perithecia, including 10 PROCEEDINGS OF THE AMERICAN ACADEMY. stalk, 90-110 x 18-22. Longest appendage 80. Receptacle 60-70 p. Total length to tip of perithecium 150-185 p. On all parts of Forficula taeniata Dohrn.; Mus. Comp. Zodl., No. 1355; Guatemala. Monoicomyces Oxypodae nov. sp. Receptacle very small, the two cells subequal, the basal cell involved by the blackening of the foot and hardly distinguishable ; the terminal appendage straight and tapering, its basal cell hyaline, nearly isodia- metric ; the subbasal cell brown, slightly inflated and twice as long; the two cells above inflated, brown, distinguished by constrictions at the dark septa. Receptacle giving rise to a branch on either side; one usually sterile, short, blunt, extending externally above the subbasal cell of the primary appendage, and wholly blackened to its base: the other fertile ; consisting of a single cell which is brown, broadly blackened externally, the blackening involving its narrow base almost completely; its distal half becoming more than twice as broad, and giving rise to a single antheridium terminally and a stalked perithecium subterminally on its inner side; stalk of the antheridium brown, two-celled (?), equal in diameter to the branch cell which bears it, and like it externally black- ened; the basal cells small and forming with the wall and antheridial cells a compact antheridium twice as long as broad, distally rounded and slightly sulcate; one only of the terminal cells growing out to form a rather short colorless appendage. Stalk-cell of the perithecium arising immediately below that of the antheridium on the inner side, its narrow base black and opaque, resembling a “foot,” distally hyaline, broader, about as long as the antheridium; the basal cells hyaline, rather small ; the perithecium faintly purplish, rather long and narrow, relatively large, the tip rather abruptly distinguished and usually slightly bent. Spores 45x 4.5. Perithecia 75-90 X 18-204. Antheridia 25-35 x 107 p, the appendage 40-50. Receptacle 10, its appendage 75. ‘Total length about 150-166 p. On the inferior tip of the abdomen of Oxypoda sp; Intervale, N. H., July 17,1901. A species most nearly related to D. furcillatus and like that species placed only provisionally in the present genus. Monoicomyces nigrescens nov. sp. Receptacle minute, its basal cell hardly distinguishable above the foot, bearing distally a simple appendage the basal cell of which is hyaline, the subbasal somewhat longer than those above and deeply tinged with THAXTER. — NEW LABOULBENIACEAE. 11 blackish brown below. Fertile branches two or more, usually four, each consisting of a single cell which bears an antheridium terminally and a perithecium subterminally: the primary branches normally two, lateral and symmetrical, edged externally with blackish brown, the blackening contrasting and continuous with a similar coloration which extends to the tip of the primary antheridium: the secondary fertile branches arising, when present, between the primary and resembling the latter, except for the absence of the black discoloration; the whole group of branches forming, with their closely crowded antheridia and perithecia, a compact fan-like usually symmetrical tuft. Antheridia relatively long, suffused with smoky brown, more deeply blackish externally, the sec- ondary ones with a more or less conspicuous foot-like blackened base ; the stalk clearly two-celled, shorter than the main body; two of the distal cells growing upward to form the two unequal terminal append- ages, which are smoky brown, darker about their blackened basal septa, the cells immediately below them projecting upward very slightly on either side. Perithecia furnished with variably developed stalk-cells the bases of which are blackened, but which are otherwise hyaline, as is the rest of the rather short, often stout, subconical, bluntly pointed perithecium. Perithecia 60-75 x 22-25 uw; the stalk-cell 12-55 p. An- theridia, including stalk, 35, the appendages 35-50. Total length 100-160 p. At the tip of the abdomen of Calodera sp. and of Tachyusa sp. ; Intervale, N. H., No. 1357. The hosts frequenting fleshy fungi. HERPOMYCHS nov. gen. Sexual organs normally separated on different individuals. Antheridia simple. Male individual consisting of several (four) superposed cells termi- nated by a characteristically modified spinous or small foot-like process or by both; the basal cell attached by a small normal foot: one or more of the distal cells giving rise to short branches which may bear from one to several antheridia terminally, or become more or less copiously branched; the branchlets terminated by antheridia, or in some cases sterile. Antheridia long, flask-shaped. The subbasal cell of the receptacle sometimes producing a fertile branch as in the female indi- vidual from which are produced secondary receptacles which give rise to antheridial branches. Female individual consisting primarily, as in the male, of several super- posed cells similarly modified at the tip, and attached by a small normal 12 PROCEEDINGS OF THE AMERICAN ACADEMY. foot; the basal and subbasal cells constituting a “ primary receptacle ;” the latter giving rise to a variably developed fertile branch (sometimes apparently dividing to several cells each of which may produce a fertile branch) from which is developed a “secondary receptacle,” or, as a result of branching, more than one. Secondary receptacles consisting of a partly double series of cells, variable in number, one or more of which may be fertile, the rest sometimes specially differentiated, or unmodified; those in contact with the host perforating the chitinous integument by means of fine haustoria. Trichogynes short filamentous. Perithecium borne on variably developed stalk-cells, the ascigerous portion including three tiers of wall-cells, more or less clearly distin- guished from the distal portion, the wall-cells of which are more or less differentiated, four or five in each row. Spores minute, of the usual type, normally discharged in pairs the members of which produce male and female individuals. Asci apparently eight-spored. The discovery of this very remarkable genus is due to Mr. Charles Bullard, who first observed it on Hetobia and Periplaneta in Cambridge. Though perhaps distantly related to Moschomyces it is in some respects unique, and with the exception of Dimeromyces is the only genus which contains species inhabiting orthopterous hosts. The peculiar cell rela- tions of the perithecia and secondary receptacles seem unlike those of most genera, but a further description of them seems undesirable in the . present connection. Herpomyces chaetophilus nov. sp. Male individual consisting of four superposed cells, hyaline, the distal cell terminated by a blackish projection similar to the small foot. The three distal cells, sometimes only the terminal one, usually producing slight outgrowths which bear the single, nearly erect, long, slender antheridia directly; or may separate a cell which bears one, or very rarely two such antheridia; the latter nearly as long as the four-celled individual. ‘Total length to tips of antheridia 50-06 p. Female individual. Primary individual similar to the male, but stouter; terminated by a similar blackish projection. The fertile branch arising laterally from the subbasal cell, growing down in the form of a slender filament variable in length, usually of two or three cells, enlarg- ing abruptly to form the single secondary receptacle. Secondary recep- tacle pale dirty brownish yellow, consisting of a vertical series of cells partly double above, simple below ; the cells thick-walled, the long (trans- verse) axes directed obliquely upward and outward, about five to fifteen THAXTER. — NEW LABOULBENIACEAR. 13 in number, their points of contact with the host surrounded by a slightly blackened irregular foot-like haustorial margin, and giving rise to single simple, or very rarely branched, haustoria which penetrate the wall of the spine at right angles to its surface; the cells all sterile with the exception of the proximal one from which arises the solitary, nearly erect perithe- cium. Perithecium relatively large, rather stout; the ascigerous portion large, slightly inflated, longer than the outwardly curved distal portion, which tapers to the bluntly pointed unmodified apex; the tip bent abruptly outward. Spores 30-35 X 3p. Perithecia 125-185 x 35-48 p. Total length of primary individual 35-40. Secondary receptacle 35-75 X 22 p. On spines of legs, antennae and anal appendages of Periplaneta sp.., Zanzibar, Africa; Mus. Comp. Zodl. On Periplaneta sp., Mauritius ; Mus. Comp. Zodl., No. 1357. _ Herpomyces Periplanetae nov. sp. Very variable according to the host and the position of growtn. Male individual consisting of four superposed cells, the two upper, in simpler individuals, producing one or two antheridia which are either sessile or borne on a single stalk-cell: in more highly developed indi- viduals the two distal cells producing short branches which may bear several antheridia directly, or on secondary branchlets, some of which appear to be occasionally sterile; the total number of antheridia. some- times six or more. Greatest length of well-developed forms, to tips of antheridia, 90 », &{ small specimens 60 yz. Female individual, hyaline or nearly so. Primary receptacle sur- mounted by two or more sterile cells, the uppermost often asymmetrical, ending in a terminal spinous process and bearing the minute character- istic black projection laterally: the subbasal cell sometimes several times divided, each resultant cell apparently giving rise to a single branch from which is developed the very variable secondary receptacle. Sec- ondary receptacle in simple individuals growing on spines of host ; consisting of a vertical series of from four to twenty or more obliquely superposed cells, alternating to form a double row, otherwise similar . to that of H. chaetophilus and like it producing a single erect peri- thecium from one of its uppermost cells: 7 individuals growing on the integument of host; consisting of a variable number of cells; certain fertile ones disposed subhorizontally on either side of the primary recep- tacle, the fertile cells, of which there may be from one to six, together with the male individual when present, and the bases of the perithecia, 14 PROCEEDINGS OF THE AMERICAN ACADEMY, protected by a shield or shell-like, usually very unequally bilobed cellular upgrowth, rounded or bluntly pointed above, the symmetrically curved successive cells which compose it enormously elongated transversely, their lumen scarcely wider than the intervening walls and forming a series of concentrically arranged arcs, the concavities directed downward. Perithecia one to six, commonly five in well-developed specimens, slightly divergent from the median line, long, pointed, tapering from the slightly, more or less asymmetrically inflated base; the distal portion not clearly differentiated, tapering more or less, curved, the slender upper portion bent abruptly inward toward the tip; the pointed apex bent inward, subtended externally by a terminal, slightly incurved, rather slender, bluntly pointed unicellular process, the cells of the cell row which it terminates distinctly larger than the other wall-cells ; basal cells some- what prominent. Spores 161.5. Perithecia 145-220 x 30-36 p, the process 14. Secondary receptacle, including protective shield, in well-developed individuals 125 xX 75»; in small specimens 35 X 50 yp; when vertically developed without shield 35-110 x 18 yp. On Periplaneta Americana Sauss. (type form), Cambridge (Mr. Bul- lard): Bermuda; Mus. Comp. Zool. On Periplaneta Australasiae Sauss.,. Bermuda. On Periplaneta spp., Mexico, West Indies, Panama, Brazil, Africa, South Seas, China. All Mus. Comp. Zoél. On Stylopyga orientalis Scudd., Boston, Mus. Comp. Zodl. Herpomyces arietinus nov. sp. Male individual consisting of four superposed cefls, the basal one relatively long, the distal ones bearing two to three antheridia. Length about 29». Antheridia about 20 p. Female individual hyaline. Primary receptacle surmounted by two sterile cells, the upper terminated by an erect distally mucronate append- age; the subbasal cell giving rise to two branches (or to a branch which becomes immediately furcate?) each branchlet producing a secondary receptacle. Secondary receptacles two, symmetrically paired, each con- sisting of a horizontal series of about twelve or more vertically elongated, subfusiform, more or less curved cells, corresponding to and external to the fertile cell which bears the primary perithecium, the external margin free, other fertile cells (of which there appears to be but one in the type) completely hidden behind it. Ascigerous portion of the perithecium relatively long, hardly inflated, tapering slightly above, where it passes into the distal portion ; which is about half as long, tapers very slightly, and is terminated by an incurved, tongue-like, slender, subcylindrical THAXTER, — NEW LABOULBENIACEAE. 15 prolongation of the apex on the inner side, and by a relatively long straight erect slightly tapering subtending terminal unicellular process. Spores about 20 X 2. Perithecia 100 x 22 p, the terminal process 18 p. Secondary receptacles, together, 55 X 18 p. On the antenna of a small brown wingless roach taken under stones and bark near the mouth of the Mammoth Cave, Kentucky ; Mus. Comp. Zool., No. 1370. Herpomyces Zanzibarinus nov. sp. Male individual consisting of four cells, the distal one furnished with a sharp colorless terminal spine and a small blackish subterminal process, both of which become pushed to one side by the development of one, or sometimes two, sessile antheridia; the subterminal cell somewhat larger, sterile, or producing an antheridium laterally. Total length 28 x 6.5 p. Antheridia 25 p. Female individual colorless. Primary receptacle surmounted by two sterile cells, the upper terminated by a sharp spinous process subtended by a blackish process, as in the male: the subbasal cell apparently divided at least once, the two (or more?) cells producing fertile branches from which, normally, two few-celled, paired, compact secondary recep- tacles are produced ; each of which bears a single perithecium, the cells rather irregular, about five or six in number, subhorizontal in position, without characteristic modification. Ascigerous portion of the perithecium relatively stout, inflated on its inner side, almost twice as long as the distal portion, which tapers from it rather abruptly : distal portion curved inward abruptly at the pointed tip, which diverges from an erect blunt unicellular process which subtends it, at an angle of more than 90°. Peri- thecium, including base, to tip of terminal process, 125 x 28-32 p; the process 10 long. The pair of fertile receptacles together about 30-35 xX 45 p broad (horizontally). On the antenna of a large black wingless roach, Zanzibar, Africa ; Mus. Comp. Zodl., No. 1354. =e Herpomyces forficularis nov. sp. Male individual minute, consisting of four superposed cells, the three upper subequal, nearly round, constricted at the septa, the distal one terminated by a short bluntly pointed appendage resembling a minute foot, which is commonly turned to one side by the development later- ally from the same cell of a single slender antheridium. Total length 18 x 5p. The antheridium about 35 p. 16 PROCEEDINGS OF THE AMERICAN ACADEMY. Female individual. Primary receptacle consisting of two superposed cells terminated by a single abruptly smaller sterile cell, which is slightly longer than broad and is terminated by a bluntly pointed append- age similar to that of the male, but larger; the subbasal cell much enlarged, somewhat inflated, the fertile branch apparently at once furcate so that two secondary receptacles are formed symmetrically placed on either side of and just below the primary receptacle. Secondary recep- tacles distinctly yellowish externally, consisting of a nearly horizontal series of about ten sterile cells, very narrow from the great elongation of their transverse axes which are vertical in position, and so arranged as to cover more or less completely the single fertile cell, which is sub- triangular and gives rise to a solitary perithecium. Base of the peri- thecium nearly as broad as the secondary receptacle, forming a short stout neck: perithecium relatively large, the ascigerous portion some- what longer than the distal part, very slightly inflated, nearly isodia- metric, the base of the trichogyne persistent as a rather conspicuous hyaline projection between it and the distal part which is but slightly narrower, hardly tapering, the large lateral cells thick-walled, the rows similar on either side and terminating in large incurved tapering bluntly pointed brownish-yellow unicellular projections, which surmount the perithecium like a pair of mandibles, the inner somewhat shorter and straighter: the short, pointed apex included between their bases and bent slightly inward. Spores about 18 x 2. Perithecia including base 200 X 86; the terminal projections, longer, 8354. Secondary recepta- cles 85 X 20-385. Primary receptacle including sterile terminal cell 20x 7p. Total length to tip of perithecium 220-250 p. On antennae of a wingless roach, Mauritius (?); Mus. Comp. Zodl., No. 1303. Herpomyces Diplopterae nov. sp. Male individual; four-celled, the two middle cells roundish-oblong, the distal longer and subcylindrical, terminated by the usual minute blackish projection; the subterminal and subbasal cells each producing one or two nearly sessile, or short stalked, antheridia, with well-differ- entiated slender necks. Total length to tips of antheridia about 50 p. Female individual. Primary receptacle similar to male, the sub- terminal and subbasal cells subcylindrical, longer than broad; the fertile branch producing two symmetrically placed secondary receptacles, as in Hi. forficularis, the sterile external cells yellowish, somewhat larger and more distinct, about twelve or more in number; the series extending THAXTER. — NEW LABOULBENIACEAE. 17 externally and inferiorly to form a free buttress-like margin, much as in HI. Paranensis, which almost wholly covers the single fertile cell. Peri- thecium yellowish, straight, nearly erect, the base bulging very slightly ; but hardly broader than the ascigerous part, which is relatively large, long, subcylindrical, or slightly inflated; the distal part, relatively short, rather abruptly distinguished; the posterior cell row, which is external in relation to the host, more prominent, with larger thick-walled cells, the fifth from below prolonged to form a long, bluntly tipped, erect, horn-like, subterminal projection, distally curved inward above the short slightly ineurved pointed subconical tip. Total length of perithecium (exclusive of base) to tip of process 150 »; to tip 110 »: ascigerous part 70-75 X 28-30 p, distal part to tip 35-40; the process, free part, 25-30», whole cell 40-44. Secondary receptacles both together 55-65 X 25. Total length to tip of process 175-185 up. On Diploptera dityscoides Serv., Ascension Island, South Adauties Mus. Comp. Zodl., No. 1371. Herpomyces tricuspidatus nov. sp. Male individual variably developed, the terminal cell rounded apiculate, but as a rule soon indistinguishable through proliferation, the simpler forms very similar to well-developed individuals of H. Periplanetae, the more complicated and most frequent type similar to the fertile branches of the male individual in H. Hcetobjae, producing, through continued successive proliferation, a dense compact more or less appressed tuft of antheridia which appear to be associated with undifferentiated sterile branchlets. Antheridium long flask-shaped, hardly distinguished from the usually several celled branchlet which it terminates. Total length to tips of antheridia 75 p. Female individual. Primary receptacle small, surmounted by two rounded cells constricted at the septa, the distal one bearing a small sharp spine subtended by the usual minute blackish projection: the subbasal cell producing apparently a single fertile branch which divides at once, growing in opposite directions to form the somewhat irregular, and variably developed, secondary receptacles, which may creep exten- sively ; the component cells, which are often very numerous, being verti- cally elongated and becoming arranged in two more or less complete rows; the inner mostly fertile, producing perithecia of which there may be twelve or rarely more; the outer becoming several times closely divided vertically, the cell-group which thus gives rise to the perithecial stalk, laterally connected with corresponding adjacent cell-groups through- VOL. XXXVIII.— 2 18 PROCEEDINGS OF THE AMERICAN ACADEMY. out its lower third only, the upper two thirds forming a free, or nearly free, continuation of the perithecial stalk, forming no free protective margin above, while below they develop a continuous, irregularly lobed, spreading haustorial margin in close contact with the host. Perithecia raised on a well-developed stalk, consisting of two unequal and asymmet- rical cells placed side by side; that on the side toward which the tip of the perithecium is bent (anterior) attenuated below and extending higher than the posterior, which becomes narrower upward from its broad base ; the stalk becoming gradually and slightly broader from below upward, and directly continued by the base of the perithecium from which it is not distinguished. Ascigerous portion of the perithecium distinguished from the base by a very slight prominence, and about as long as the stalk and base combined; becoming distally slightly broader, the two lower tiers of wall-cells separated by a slight elevation; the third wall- cell of the anterior row small, and forming a prominent elevation fol- lowed by a depression which subtends a large, erect, tapering, bluntly pointed, distally incurved spinous process formed by an outgrowth of the lowest cell in the anterior row of wall-cells of the distal portion (fourth anterior wall-cell) which extends upward higher than the tip of the perithecium, its upper two thirds forming a free spine; the lower cell of one of the corresponding lateral rows (fourth lateral wall-cells) pro- ducing a similar process, shorter, slightly sharper, curved inward distally toward the apical pore, this process always external in relation to the host and thus developed on the right or left side according as the peri- thecium is formed from the receptacle at the left or at the right of the original insertion toward which the anterior sides of all the perithecia are turned: the rest of the terminal portion above the bases of these outgrowths short, abruptly tapering, its outer margin vertical, slightly prominent and not distinguished from the posterior margin of the asciger- ous portion, which is directly continued by it; its inner margin running abruptly inward and upward from the base of the anterior process to the small blunt tip, which is curved abruptly inward and is subtended by a nearly erect, short, sharp spinous process ; the whole nearly symmetrical with the anterior process which is very slightly longer. Spores about 12, long. Perithecia, ascigerous portion 45-50 X 25 y, terminal part to tip 28 p, anterior process 30-34 p, apical process 8 yp, stalk, including basal cells, 45-58 x 16-18». Total horizontal extent of larger individ- uals including both receptacles 220. Fertile cells below perithecial stalks 30-40 x 18-15. Total height to tip of perithecial process 175-200 p. THAXTER. — NEW LABOULBENIACEAE., 19 On Blabera sp. and Epilampra (?) sp.. Panama; Mus. Comp. Zool, No. 13864. On Epilampra sp., No. 13860, St. Kitts, W. I. (type), No. 1366, Hayti. On a wingless form labelled “China?” All Mus. Comp. ZoOol., and in all cases on the antennae. Herpomyces Paranensis nov. sp. Male individual similar to the simpler forms of /Z. tricuspidatus, but the terminal cell distally modified to form a long slender fiexuous taper- ing unicellular prolongation extending above the tips of the antheridia. Total length to tip of terminal prolongation 250; the prolongation 185. Antheridia about 60-70 p. Female individual. Primary receptacle very small, the distal cells rounded, the uppermost prolonged as in the male. Secondary recepta- cles developed on either side of the primary, the cell series apparently turning inward from either side so that the perithecia are more or less clustered (younger ones appearing behind the two primary ones), and protected by a shield-like structure external to the base of the first fertile cell, developed like a buttress, the outer and upper margins of which are free, consisting of sterile cells which are greatly elongated vertically and very narrow, similar and successively fewer-celled buttresses being formed behind the primary one in connection with each of the remain- ing perithecia, of which there may be from four to six. Perithecia very similar to those of the preceding species, but with the following differ- ences: the greatly elongated fertile cell of the receptacle extends nearly to the base of the perithecium, the posterior stalk-cell extending down- ward beside it nearly to its base, covered by the protective shield except at its distal end, which is connected by a narrow isthmus with an abrupt short broad terminal enlargement; the anterior stalk-cell small, short, subtriangular in outline ; the base of the perithecium abruptly somewhat broader, its cells protruding more or less distinctly ; the ascigerous region thus somewhat clearly distinguished, especially posteriorly, relatively distinctly larger than in the preceding species, somewhat inflated; the conformation of the distal portion similar in general, but the third wall cell of the anterior row is not modified to form a prominence at the base of the anterior spiniferous cell, the upper half of which forms a free spi- nous process slightly incurved distally and equalled or even exceeded by the lateral spinous process: the free tip of the perithecium about twice as long relatively, slightly incurved, the erect incurved spinous process, which subtends it externally, more than twice as long as that of the pre- ceding species and sublateral; the tip between the base of this spine and 20 PROCEEDINGS OF THE AMERICAN ACADEMY. the inner angle of the anterior spine relatively shorter and broader. Spores about 15 X 1.6. Perithecium: ascigerous portion 58 X 30 p; terminal portion to tip, 40; anterior process, free portion, 22-25 pn, whole cell, 50-54; subterminal process, free part, 17; total length, 123 y, including basal cells. Width of two outer buttresses together 85-100; height of shield-like upgrowth 36-40 ,; length from inser- tion to base of perithecium 60-80; total length from insertion to tip of perithecial spine 180-218 p. On antenna of a wingless roach (? Blabera), Para, Brazil; Mus. Comp. Zodl., No. 1862. Herpomyces Hctobiae nov. sp. Male individual consisting of four superposed cells terminated by the characteristic blackish projection, the distal cells producing a dense ap- pressed tuft of coherent antheridial branchlets and antheridia; the sub- basal cell usually giving rise to a fertile branch, simple or furcate, which produces a secondary male receptacle consisting of an irregularly double straggling series of cells, some of which are sterile, while others bear short-stalked, unilateral, dense antheridial tufts similar to the primary one (which may sometimes be lacking ”). Female individual colorless. Primary receptacle as in the male, ter- minated by two short cells, the upper of which bears distally the charac- teristic blackish minute foot-like projection, the subbasal cell producing a simple or furcate fertile branch. The fertile receptacles, like those of the male, often creeping extensively, consisting of an irregularly double series of obliquely seriate cells, sterile or fertile without definite sequence, the whole plant producing sometimes twelve or even more perithecia developed as a rule in irregularly acropetal succession. Perithecia sub- sessile, inflated below, attenuated above, the extremity bent or sometimes slightly recurved, the apex unmodified. Spores 20 X 2.5. Perithecia, including base, 80-90 X 204. ‘Total length of secondary receptacle, longer, 200-225 X 15. Primary individual 22 p. On Ectobia Germanica Scudd., Cambridge, Mr. Bullard. On etobia sp., Zanzibar; Mus. Comp. Zodl., No. 1857: St. Kitts, West Indies ; Mus. Comp. Zool., No. 1861. Although aberrant from the fact that the male develops secondary receptacles, this species corresponds exactly to the generic type in all other respects. THAXTER. — NEW LABOULBENIACEAE, 21 Corethromyces longicaulis nov. sp. Receptacle abnormally developed, very small, the basal and subbasal cells arising almost side by side immediately above the foot; the basal cell long and narrow, strongly curved so as to become concave externally, its wall very thick, the cavity becoming almost obliterated; the distal half nearly horizontal, slightly bulging and becoming wholly deep black brown, except along its upper (in position) margin which is transparent yellowish and closely applied to the lower surface of the basal cell of the appendage, beyond which it hardly projects externally and which thus appears to arise from it; the subbasal cell larger, nearly hyaline exter- nally, convex, bulging below, with a more or less distinct constriction below its slightly enlarged upper portion, which gives rise distally to the broad stalk-cell of the perithecium and sublaterally to that of the append- age. The appendage much reduced, nearly hyaline, consisting of three superposed cells; the basal (stalk-cell) squarish or rounded, the lower half or less of its inner margin connected with the subbasal cell of the receptacle. its subbasal cell smaller, bearing usually a single short anther- idial branchlet; the upper cell still smaller, often hardly distinguishable, bearing one or two short antheridial branchlets and a short sterile termi- nal branch. Antheridia terminal, one to three in a series. Stalk-cell of the perithecium relatively very large, often curved, usually as large as the other parts of the plant combined, brown, slightly constricted at its insertion, nearly cylindrical, slightly and gradually broader toward and below the basal cells, which are relatively small and barely separate the cavity of the perithecium from that of the stalk-cell; body of the peri- thecium concolorous with the stalk-cell, slightly inflated, tapering distally almost symmetrically to the blunt tip, which is somewhat asymmetrical from the slightly greater prominence of one of the lip-cells ; the series of wall-cells strongly spiral, completing as a rule somewhat more than one whole turn. Spores 303 y. Perithecia 65 X 20y, the stalk-cell 90- 110xX12y. Receptacle 254. Appendage 30-40p. ‘Total length to tip of perithecium, average 200 p. < On Stilicus angularis Lec., at the base of the head on the upper side ; Arlington, Mass., June. Sometimes associated on the same host with C. Stilict Thaxt. ACOMPSOMYCEHES Tuaxter. The past season has yielded two additional species of this well-marked genus, the material of which is sufficiently abundant to determine with greater accuracy than was formerly possible its distinctive characters. D2 PROCEEDINGS OF THE AMERICAN ACADEMY. The appendage is very uniform in type, clearly distinguished above its basal cell: the terminal cell bearing distally a single antheridium, which is furnished with a spinous process; the subterminal cell is sterile in all cases; the cell next below producing, normally, from one to three anther- idia laterally and somewhat irregularly; the antheridia being of charac- teristic form with large appressed venters and stout necks curved outward. Although in the single type the cavity of the perithecium appears to be, as was formerly stated, continuous with that of the stalk-cell, as in genera like Dimorphomyces, this is certainly not the case in the new forms de- scribed below, the basal perithecial cells of which are clearly defined. As it is highly improbable that A. Corticariae differs from other species in this respect, it may be assumed that the basal cells in the unique type are obscured by the abrupt curvature of the type specimen in this region. Acompsomyces Atomariae nov. sp. Colorless or very faintly brownish. Receptacle short, the distal cell squarish ; the basal cell twice as large, narrow below, bulging beneath the base of the antheridial appendage from which it thus appears to arise terminally. Basal cell of the antheridial appendage rather long and narrow, not distinguished from the receptacle, to the distal cell of which its lower half is closely applied, while its upper half is in equally close contact with the stalk-cell of the perithecium; the rest of the appendage free, compact, slightly inflated, with evenly curved outline, faintly tinged with brown, consisting of three cells: the lower subtriangular in outline with the largest angle outward, bearing distally three closely appressed antheridia neither of which arises from its outer side; the cell next above somewhat larger, sterile, subtriangular with the largest angle external ; the terminal cell smaller, separated by a horizontal septum from the terminal antheridium, the neck of which is curved inward, the spinous process conspicuous and external. Stalk-cell of the perithecium well developed, rather slender, about as long as the receptacle, the basal cells well distinguished: body of the perithecium narrower below, its inner margin nearly straight with slight constrictions at the septa, the outer bulging distinctly and more or less symmetrically; the tip distinctly but not abruptly distinguished, short, stout, slightly but rather abruptly ex- panded below the flat-conical apex, from the middle of which project abruptly the small short appressed prolongations of the lip-cells, forming a terminal apiculus. All the cells thick-walled. Spores very slender, 44 x 34. Perithecia 36-46 x 25-30, the stalk-cell 25-30 x 104. THAXTER. — NEW LABOULBENIACEAE. a8 Receptacle 25 ». Free appendage to tip of spinous process 36 X 12 p. Total length to tip of perithecium 125-150 p. On elytra of Atomaria ephippiata Zimm., Kittery Point, Maine, and Intervale, N. H. Acompsomyces pauperculus nov. sp. Hyaline or nearly so. Receptacle short, somewhat bent; the distal cell very small, irregular, sharply pointed below, externally separated from the basal cell by an oblique septum; the basal cell three or four times as large, narrow below, expanded above its distal point, forming 2 right angle, the septum on one side applied to the base of the stalk-cell of the appendage. The latter subtriangular, its lower half in contact on the inner side with the two cells of the receptacle, its upper with the stalk-cell of the perithecium; the rest of the appendage free, relatively large, hardly inflated, its lower cell about as large as the two upper combined and bearing commonly one, sometimes three, antheridia as in A. Atomariae ; the two cells above it nearly equal cr the upper often smaller and bearing its antheridium subterminally, so that the spinous process of the latter appears to terminate the appendage, the wall dis- tinguishing this antheridium being commonly invisible from its obliquity. Stalk-cell of the perithecium about as large as that of the appendage and similarly shaped, except that its position is reversed, separated distally from the basal cells of the perithecium by a very oblique septum: the body of the perithecium short, stout, bent asymmetrically, and consider- ably inflated; the inner margin straighter, the short squarish tip rather abruptly distinguished, the apex subtended by four distinct symmetrical prominences, which form a crown surrounding the four appressed pro- longations of the lip-cells, which appear as a blunt, conical protuberance within it: all the cells rather thin-walled. Spores 45 x 4p. Perithecia 70 X 80-35 p, the stalk-cell 12-18 x 9. Receptacle 20-304. Free appendage 32-36. Total length to tip of perithecium 110 uz. On elytra, prothorax, and legs of Atomaria sp., Kittery Point, Maine, June. ACALLOMYCES nov. gen. Receptacle consisting of two superposed cells, the lower sometimes apparently obliterated or indistinguishable from the foot, the upper bearing a single perithecium and an antheridial appendage. Appendage consisting of six superposed cells, the basal cell closely associated with the receptacle and the stalk-cell of the perithecitum; the terminal-cell 94 PROCEEDINGS OF THE AMERICAN ACADEMY, bearing a spine-like process and becoming converted into a simple antheridium, the subterminal-cell cutting off a cell laterally which be- comes an antheridium, the remaining cells sterile. Perithecium stalked, normal in structure. A genus of very simple structure, closely allied to Acompsomyces, from which it differs chiefly from the characters of its antheridial appendage. Acallomyces Homalotae nov. sp. Hyaline, becoming faintly tinged with straw color. Receptacle very small, the lower half becoming tinged with smoky-brown ; the basal cell hardly distinguished from the foot and commonly obliterated by a thick- ening of the walls in this region, so that the receptacle appears to be one-celled. Basal cell of the antheridial appendage separated from the distal cell of the receptacle by a somewhat oblique septum, and nearly similar to that of the stalk-cell of the perithecium, to which it is closely united on its inner side; the subbasal cell very small, and becoming scarcely distinguishable in mature individuals ; the two cells above it similar, rather distinctly differentiated, the pair forming a slight sym- metrical enlargement; the subterminal cell above larger and longer than these two combined, the base of the antheridium extending its whole length ; both this and the terminal antheridium above it relatively large, the necks very long, straight, or but slightly bent, and somewhat diver- gent. Stalk-cell of the perithecium somewhat broader than long, the basal cells small, the perithecium proper relatively large and somewhat inflated above the base, distally tapering gradually to the tip; the lip-cells forming four corresponding projections, the anterior larger and broader, the posterior narrow and bluntly pointed, subtended by a more or less well-defined hump, the two lateral usually shorter, blunt, slightly divergent, sometimes not clearly differentiated, varying in shape and position. Spores 35 X 3.5 yp. Perithecia 75-95 X 25-52, the stalk- cell 10-12 ». Appendage, above basal cell to tip of terminal anther- idium, 36. Icon.! Kuphorb. t.5; Rose (1), 1837; Rob. & Greenm. (1), 148. — Cuatuam Isxi.: Darwin ; covering large volcanic rocks near the shore, Andersson (hb. Gr.); A. Agassiz ; southwest end, lower region, Baur, no. 253 (hb. Gr.) ; northern part, Baur, no. 254 (hb. Gr.) ; Snedgrass & Heller, no. 493 (hb. Gr.). Endemic. Var. GLABRA, Rob. & Greenm. (1), 144, 148.— CuHar.zs Ist.: Cuevas Bay, Baur, no. 386 (hb. Gr.). Endemic. E. pitutirera, L. Amoen. Acad. iii. 115 (1756) ; Hook. f. (3), 182; Anderss. (1), 233, & (2), 100; Boiss. in DC. Prodr. xv. pt. 2, 21. — CHARLES Isu.: cultivated ground, middle region, Andersson; Lee (hb. U. S. Nat. Mus.); Snodgrass & Heller, no. 439 (hb. Gr.). CuatHam Ist.: Snodgrass & Heller, no. 519 (hb. Gr.). James Ist. : Darwin. Distrib. general in warm countries. KE. PUNCTULATA, Anderss. (1), 235, & (2), 102; Boiss. 1. ¢ .17; Rob. & Greenm. (1), 148.— Atsemarte Ist.: in very dry places, Andersson. Duncan Isu.: Baur, no. 262 (hb. Gr.). Hoop Ist.: Baur, no. 263 (hb. Gr.). Endemic. Ey REcuRYA, Look. 4. (3); 182: Anderss: (1), 234, ((2)s ls Boiss. in DC. Prodr. xv. pt. 2, 16.— Cuatuam Isu.: Darwin ; in lower stony region, Andersson (hb. Gr.). Endemic. E. viminrea, Hook. f. (8), 184; Anderss. (1), 235, & (2), 101, t. 12, f. 3; Boiss. in DC. Prodr. xv. pt. 2, 17; Rob. & Greenm. (1), 136, 138, 148. E. viminea, forma albemarlensis (typica), Rob. & Greenm. (1), 1388. — AnBemarLe Isu.: Macrae ; eastern part, Cowley Bay, Baur, no. 252 (hb. Gr.); southern portion, Baur, no. 251 (hb. Gr.); Elizabeth Bay, Snodgrass & Heller, no. 277 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 164°(hb. Gr.). Endemic. Forma BARRINGTONENSIS, Rob. & Greenm. (1), 189. — BARRINGTON Ist.: Baur, no. 244 (hb. Gr.). Brypor Ist.: Baur, no. 248 (hb. Gr.) ; Snodgrass & Heller, no. 761 (hb. Gr.). Endemic. Forma CAROLENsIs, Rob. & Greenm. (1), 1389.— Cares Ist. : Andersson (hb. Gr.). Endemic. Forma CASTELLANA, Rob. & Greenm. (1), 188. — Tower Isu.: Baur, no. 247 (hb. Gr.) ; Snodgrass & Heller, no. 805 (hb. Gr.). Endemic. Forma CHATHAMENSIS. Rob. & Greenm. (1), 138.—CuHatuam Ist. : Andersson ; Baur, no. 245 (hb. Gr.). Endemic. FLORA OF THE GALAPAGOS ISLANDS. 169 Forma JACOBENSIS, Rob. & Greenm. (1), 158.— James Ist. : Orchilla Bay, Baur, no. 249 (hb. Gr.). Endemic. Forma JERVENsIS, Rob. & Greenm. (1), 139. — Jervis Isu.: Baur, no. 200 (hb. Gr.). Endemic. Var. ABINGDONENSIS, Rob. & Greenm. (1), 1389. — ABinepon Ist.: Baur, no. 246 (hb. Gr.). Endemic. For a discussion of these forms see Rob. & Greenm. (1), 138, 139. FE. viminea was collected on the Galapagos Ids. also by Habel. KE. sp. aff. EH. articulata, Anderss.— Binpiokr Isxi.: Snodgrass & Heller, no. 780 (hb. Gr.), sterile. Leaves narrowly ovate-oblong from a cordate base, otherwise much like EH. articulata, which in its typical form grows upon the same island. E. sp. Anderss. (1), 237, & (2), 102. — CuHarnam Ist.: Andersson. E. sp. Hook. f. (8), 185; Anderss. (1), 237, & (2), 102. — Cuartes Ist. : Darwin. Hrpromanr, L. H. Mancinecta, L. Sp. 1191 (1753); Anderss. (1), 237, & (2), 103. — GarapaGcos Ips.: Habel. ALBemMaRLeE Isx.: Elizabeth Bay, Snod- grass & Heller, no. 279 (hb. Gr.); Iguana Cove, Snodgrass & Heller, no. 49 (hb. Gr.). CuHatruHam Iszt.: Andersson. Further distrib. S. United States, Mex., W. Ind., Northwestern S. Am. Manrnor, Adans. . M. vurivissimaa, Pohl. Pl. Bras. Ic. i. 32, t. 24 (1827); Muell. Arg. in DC. Prodr. xv. pt. 2, 1064; Caruel (1), 625. — Cuatuam Ist. : Chierchia. Widely distrib. in tropical countries. PHYLLANTHUS, L. P. CAROLINENSIS, Walt. Fl. Car. 228, as caroliniensis (1788); Ca- ruel (1), 625; Rob. & Greenm. (1), 148. P. obovatus, Muhl. ex Willd. Sp. iv. 574 (1805); Hook. f. (3), 185; Anderss. (1), 237, & (2), 103. — ALBEMARLE Ist.: Andersson; Iguana Cove, Snodgrass & Heller, no. 106 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 194 (hb. Gr.). Carvers Isu.: Darwin; Andersson (hb. Gr.). CHATHAM Isu.: Chierchia ; southwest end, middle region, Baur, no. 268 (hb. Gr.). James Ist.: James Bay, common on lava rocks, Snodgrass & Heller, no. 38) (hb. Gr.). Narsoroucu Ist.: northern part, Snodgrass & 170 PROCEEDINGS OF THE AMERICAN ACADEMY, Heller, no. 296 (hb. Gr.) ; southern part, Snodgrass & Heller, no. 332 (hb. Gr.). Further distrib. northern 5. Am., Mex., W. Ind., southern and central U. S. Ricinus, L. R. communis, L. Sp. 1007 (1753) ; Anderss. (1) 241, & (2), 105. — Cnarturs Ist.: in cultivated ground, Andersson. Widely distrib. in warm countries, CALLITRICHACEAE. CaLuitricHe, L. C. sp. Wolf, (1), 284. — Cuarves Isx.: in brook near hacienda ace. to Wolf. l.c. CELASTRACEAE. Maytenus, Feuill. M. opovata, Took. f. (3), 230; Anderss. (1), 233, & (2), 100; Rob. & Greenm. (1), 145.— ALBEMARLE IsL.: southern part, Baur, no. 49 (hb. Gr.); Elizabeth Bay, on lava fields near beach, Snodgrass & Heller, no. 936 (hb. Gr.); Iguana Cove, Snodgrass & Heller, no. 66 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, nos. 158 (hb. Gr.), 877 (hb. Gr.). Barrineton Ist.: Baur, no. 52 (hb. Gr.). CHaRLes Isu.: Andersson; Baur. Cuatuam Ist.: Darwin; in woods of lower region, Andersson ; southwest end, middle region, Baur, no, 483 (hb. Gr.). Duncan Ist.: Snodgrass & Heller, no. 685 (hb. Gr.). Hoop Isu.: Baur, no. 51 (hb. Gr.). JAmes Ist.: James Bay, scattered along the sandy beach, Snodgrass & Heller, no. 371 (hb. Gr.). Jervis Ist. : Baur. Narsoroueu Ist.: common ace. to field notes of Mr. Heller. Seymour Ist.: south, Snodgrass & Heller, no. 597 (hb. Gr.). Endemic. SAPINDACEAE. CarpiosrerMum, L. C. Cortnvum, L. Sp. ed. 2, 526 (1762); Radlk. Sitzungsb. Kgl. Bayer. Akad. 1878, p. 261; Rob. & Greenm. (1), 145, in part (as to pl. Chatham). C. molle, HBK. Nov. Gen. & Sp. v. 103 (1821); Hook. f. (3), 231; Anderss. (1), 231, & (2), 99; Caruel (1), 623. — ALBE- MARLE Isxt.: Andersson; mountain north of Elizabeth Bay, Snod- FLORA OF THE GALAPAGOS ISLANDS, g(a grass & Heller, no. 281 (hb. Gr.). CHartes Ist.: Andersson. CuatuamM Ist.: Darwin, Andersson (hb. Gr.); Chierchia ; southwest end, lower region, Laur, no. 60 (hb. Gr.) ; southwest end, upper region, Baur, no. 59 (hb. Gr.) ; Snodgrass & Heller, no. 512 (hb. Gr.). Inpr- FATIGABLE Ist. : Andersson. JAmeEs Isi.: Andersson ; common about James Bay, Snodgrass & Heller, no. 359 (hb. Gr.). Wernman Ist. : Snodgrass & Heller, no. 8 (hb. Gr.). Further distrib. trop. 5. Am., Mex., southwestern U. S. C. GALAPAGEIUM, Rob. & Greenm. Proc. Am. Acad. xxxii. 58 (1896). C. Corindum, Rob. & Greenm. (1), 145, in part (as to pl. Albemarle), not L.— ALBEMARLE IsL.: southern part, Baur, no. 61 (hb. Gr.). INDEFATIGABLE IsL.: northern part, Snodgrass & Heller, no. 675 (hb. Gr.). Endemic. Doponaka, L. D. viscosa, Jacq. Enum. Pl. Carib. 19 (1762); L. Mant. ii. 228; Rob. & Greenm. (1), 145. Forma typica.— ALBEMARLE IsL.: eastern part, Cowley Bay, Baur, no. 62 (hb. Gr.); southern part, Baur, no. 63 (hb, Gr.). Further distrib. general in warm countries. Var. SPATHULATA, Benth. Fl. Aust. i. 476 (1865). — ALBEMARLE Isu.: Tagus Cove, Snodgrass & Heller, nos. 876 (hb. Gr.), 904 (hb. Gr.) ; mountain east of Tagus Cove, Snodgrass & Heller, no. 244 (hb. Gr.). Specimen imperfect and doubtful, but clearly representing a very different form of the species from those collected on the same island by Baur. Further distrib. general in warm countries. Sapinpus, L. S. SaponartA, L. Sp. 367.(17538) ; Sarg. Silv. ii. 69,t. 74, 75. “8S. near S, acuminatus, Willd.” Rob. & Greenm. (1), 145. — ALBEMARLE Isi.: southern part, Baur, no. 57 (hb. Gr.). Form with leaflets glabrous beneath. Further distrib. of species trop. Am., Mex., W. Ind., south- eastern U. S. RHAMNACEAE. DiscartA, Hook. D. paucitFLoRA, Hook. f. (3), 229; Anderss. (1), 233, & (2), 100; Rob. & Greenm. (1), 145. D. sp. Rob. & Greenm. (1), 145. — ALBE- MARLE Isi.: Darwin; Baur ; common about Elizabeth Bay, acc. to Mr. Heller; forming dense thickets, Tagus Cove, Snodgrass & Heller, no. 143 (hb. Gr.). Barrineron Isx.: Baur, no, 55 (hb. Gr.) ; abundant, 172 PROCEEDINGS OF THE AMERICAN ACADEMY. Snodgrass & Heller, no. 478 (hb. Gr.). CHARLEs Ist.: from this island Professor Caruel (1), 624, reports a spiny shrub collected by Chierchia and supposed to belong to the Rhamnaceae. It may well have been this species. CuatTHAm IsL.: woods near shore, Andersson ; southwest end, lower region, Baur. Duncan Ist.; not common, ace. to Mr. Heller. Hoop Ist.: Baur, (hb. Gr.), juvenile form with serrate leaves. INDEFATIGABLE IsL.: north coast, acc. to Mr. Heller. James Isv.: James Bay, near beach in sand, ace. to Mr. Heller. Srymour Ist.: north, uncommon, acc. to Mr. Heller; south, abundant, Snodgrass & Heller, no. 608 (hb. Gr.). Further distrib. collected by Dr. Baur at Posorja on the Gulf of Guayaquil, Ecuador, where perhaps introduced from the islands. VITACEAE. Cissus, L. C. stcyorpes, L. Syst. Nat. ed. 10, 897 (1760). Vitis sicyoides, Mig. Ann. Mus. Bot. Lugd. Bat. i. 83 (1863-1864).— ALBEMARLE Ist.: Iguana Cove, Snodgrass & Heller, nos. 26, 45, 89, 101 (all in hb. Gr.). Binpioe Isi.: common near the shore, ace. to field notes of Mr. Heller. Caarues Ist.: Lee (hb. U. S. Nat. Mus.). NarBporoucH Ist.: bordering beaches, acc. to Mr. Heller. Further distrib. Mex., W. Ind., S. Am., southward to Paraguay. Vitis, L. V. vinirera, L. Sp. 202 (1753) ; Caruel (1), 623. — CHar.es Ist.: in sterile state, Chierchia acc. to Caruel. Probably introduced through cultivation. Further distrib. Old World. TILIACEAE. Corcuorus, L. C. prropoius, Link, Enum. Hort. Berol. ii. 72 (1822); Jacq. Ecl. t. 163 as CO. bullatus. —GAaLAPAGos Ips.: Habel? ALBEMARLE IsL.: Snodgrass & Heller, no. 90. GARDNER Ist.: Snodgrass & Heller, no. 645 (hb. Gr.). Further distrib. trop. S. Am., W. Ind., Mex. TriumFerta, L. T. SEMITRILOBA, Jacq. Enum. Pl. Carib. 22 (1762), Stirp. Am. 147, & Hort. Vindob. iii. t. 16. — ALBEMARLE IsL.: Iguana Cove, Snodgrass & Heller, nos. 69, 70, 107, 858, 859 (all in hb. Gr.). Further distrib. general in trop. and subtrop. Am. [S) FLORA OF THE GALAPAGOS ISLANDS. a Lv MALVACEAE. ABUTILON, Gaertn. A. ANDERSSONIANUM, Garcke in Anderss. (1), 230, & (2), 98, t. 15, f. 1.— Apinepon Ist.: Snodgrass & Heller, no. 847 (hb. Gr.). Barrineton Isz.: Snodgrass & Heller, no. 479 (hb. Gr.). BinpLoe Ist.: Snodgrass & Heller, no. 788 (hb. Gr.). Cartes Isu.: dry places, lower region, Andersson. CuatHam Ist.: dry places, lower region, Andersson (hb. Gr.); Snodgrass & Heller, no. 507 (hb. Gr.). Duncan Ist.: Snodgrass & Heller, no. 702 (hb. Gr.). GARDNER Ist.: Snodgrass & Heller, no. 632 (hb. Gr.). INDEFATIGABLE ISL. : northern part, Snodgrass & Heller, no. 662 (hb. Gr.). Tower Ist. : Snodgrass & Heller, no. 794 (hb. Gr.). Endemic. The forms on Duncan and Gardner Ids. are smoother and greener than the others. A. DEPAUPERATUM, Anderss. (1), 230, & (2), 98. A. Andersson- ianum, Rob. & Greenm. (1), 145, not Garcke. Sida depauperata, Hook. f. (3), 232.— ALBEMARLE IsL.: Iguana Cove, Snodgrass & Heller, nos. 76, 82 (both in hb. Gr.). Barrineron Isx.: Baur, no. 16 (hb. Gr.), determined from character. Cuarves Isx.: Darwin. Endemic. Perhaps only a dry soil form of A. Anderssonianum. Awnopa, Cav. A. wastaTa, Cav. Diss. i. 38, t. 11, f. 2 (1790).° A. acerifolia, DC. Prodr, i. 459 (1824) ; Rob. & Greenm. (1), 145, where by error ascribed to Chatham Island. —Cuarves Ist.: Zee (hb. U. S. Nat. Mus.) ; Baur, no, 20 (hb. Gr.); Snodgrass & Heller, no. 449 (hb. Gr.). Further distrib. southern U. S., Mex. to Chili. Bastarpia, HBK. B. viscosa, HBK. Nov. Gen. & Sp. v. 256 (1821); L’Her. Stirp. t. 53 bis; E: G. Baker, Jour. Bot. xxxi. 68. B. quayaquilensis, Turcz. Bull. Soc. Nat. Mose. 1858, p. 201. Sida viscosa, L. Syst. ed. 10, 1145 (1760).— AtBemarteE Ist. : Iguana Cove, Snodgrass & Heller, no. 105 (hb. Gr.). CuatHam Ist.: Snodgrass & Heller, no. 533 (hb. Gr.). Further distrib. western S. Am., Mex., W. Ind. Gossypium, L. G. BARBADENSE, L. Sp. 693 (1753). G. purpurascens, Hook. f. (3), 231; Anderss. (1), 228, & (2), 97; Rose (1), 136; not Poir. 174 PROCEEDINGS OF THE AMERICAN ACADEMY. G. Klotzschianum, Rob. & Greenm. (1), 145, not Anderss. — Gara- PAGos Ips.: Habel. Aptnepon Isxt.: Snodgrass & Heller, no. 828 (hb. Gr.); ALBEMARLE Ist.: Baur; Iguana Cove, Snodgrass & Heller, nos. 46 (hb. Gr.), 854 (hb. Gr.). Barrineton Ist.: Baur, no. 24 (hb. Gr.). Cartes Ist.: Andersson (hb. Gr.) ; Snodgrass & Heller, no. 402 (hb. Gr.). CuHaruam Isx.: Darwin; southwest end lower region, Baur, no, 22 (hb. Gr.) ; northern part, Baur, no. 25 (hb. Gr.). Dunoan Isu.: A. Agassiz. Garpner Isu.: Snodgrass & Heller, no. 635 (hb. Gr.). Hoop Ist.: Baur, no. 21 (hb. Gr.); Snodgrass & Heller, no. 752 (hb. Gr.). James Ist.: Darwin. Srymour Ist.: south, Snodgrass & Heller, no. 599 (hb. Gr.). Further distrib. general in tropics. G. Kiorzscuianum, Anderss. (1), 228, & (2), 97. — GALaPaGos Ips.: Edmonston (hb. Gr.). ALBEMARLE IsL.: Andersson. BINDLOE Ist.: Snodgrass & Heller, no. 772 (hb. Gr.). Cuarves Isx.: Anders- son (I. ¢., but his spec. so labelled in hb. Gr. is clearly G. barbadense). CuatTHam Isx.: Andersson. INDEFATIGABLE IsL.: northern part, Snod- grass & Heller, no. 656 (hb. Gr.). Endemic. Andersson (2), 97, states that this species was collected upon Chatham and James Islands by Darwin, but this appears to have been a clerical error and to refer to the preceding species. Hreiscus, L. [. rrntaceus, L. Sp. 694 (1753). Paritium tiliacewm, Hook. f. (4), 262; Anderss. (1), 229, & (2), 98.— Cuartes Ist.: Hdmonston. Further distrib. general in tropics. Maracura, L. M. capirata, L. Syst. ed. 12, 458 (1767); Hook. f. (8), 231; Anderss. (1), 229, & (2), 98; Giircke in Engl. Bot. Jahrb. xvi. 348. — James Ist.: Darwin acc. to Hook. f.,1.c. Further distrib. trop. S. Am., W. Ind., Mex., sparingly introd. in trop. of Old World. Sipa, L. S. acuta, Burm., var. CARPINIFOLIA, K. Schum. in Mart. Fl. Bras. xii. pt. 8, 8326 (1891) ; E. G. Baker, Jour. Bot. xxx. 238. 8. carpint- folia, L. £. Suppl. 307 (1781); Anderss. (1), 229, & (2), 98, excl. synon. — Cuartes Ist.: dry places of middle region, Andersson. Further distrib. general in trop. and subtrop. regions. FLORA OF THE GALAPAGOS ISLANDS. 175 S. ANGUSTIFOLIA, Lam. Dict. i. 4 (1783). S. tenuicaulis, Hook. f. (3), 232, ace. to EK. G. Baker. S. spinosa & S. tenuicaulis, Anderss. (1), 229, & (2), 98. WS. spinosa, var. angustifolia, Griseb, Fl. Brit. W. Ind. 74 (1859); E. G. Baker, Jour. Bot. xxx. 237. S. rhombi- folia, Rob. & Greenm. (1), 145, in part (as to pl. Charles and pl. Inde- fatigable). — ALBEMARLE Isu.: Lee (hb. U. S. Nat. Mus.); Iguana Cove, Snodgrass & Heller, nos. 84 (hb. Gr.), 104 (hb. Gr.). CHARLES Ist.: Andersson; Baur, no. 17 (hb. Gr.); Snodgrass & Heller, no. 438 (hb. Gr.). Cuatuam Ist.: lower region, Andersson (hb. Gr.). Duncan Isi.: Snodgrass & Heller, no. 701 (hb. Gr.). GARDNER Iszt.: Snodgrass & Heller, no. 629 (hb. Gr.). INDEFATIGABLE ISL. : Andersson ; south of Conway Bay, Baur, no. 18 (hb. Gr.). James IsL: Darwin ; Andersson. Narsorouca Ist.: northern part, Snodgrass & Heller, no. 298 (hb. Gr.). Further distrib. general in warm countries. S. corpiFoiia, L. Sp. 684 (1753); K. Schum. in Mart. FI. Bras. xii. pt. 8, 331, t. 62. — ALBEMARLE IsL.: Iguana Cove, below 310 m. alt., Snodgrass & Heller, no. 860 (hb. Gr.). Sterile. Further distrib. general in trop. and subtrop. regions. S. panicuLaTa, L. Syst. ed. 10, 1145 (1760) ; Rob. & Greenm. (1), 145; E. G. Baker, Jour. Bot. xxx. 294. S. atrosanguinea, Jacq. Ic. Rar. t. 136. S. floribunda, HBK. Nov. Gen. & Sp. v. 258, t. 473 (1821). —Gaxapacos Ips.: Habel ace. to Hemsl. in litt. ALBE- MARLE Isu.: Iguana Cove, Snodgrass & Heller, nos. 71 (hb. Gr.), 86 (hb. Gr.). Cares Isit.: Baur, no. 19 (hb. Gr.) ; Snodgrass & Heller, no. 401 (hb. Gr.). Further distrib. trop. S. Am., W. Ind., Mex. S. RHOMBIFOLIA, L. Sp. 684 (1753) ; Hook. f. (4), 262; Anderss. (1), 229, & (2), 98; Rob. & Greenm. (1), 145, in part (as to pl. Chatham); E. G. Baker, Jour. Bot. xxx. 239, q. v. for synon.— CuAr tes Ist.: Edmonston ; Lee (hb. U. S. Nat. Mus.) 3 Snodgrass & Feller, no. 448 (hb. Gr.). CuaruHam Isi.: stony places, lower region, Andersson; southwest end, middle region, Baur, no. 15 (hb. Gr.) ; Snodgrass & Heller, no. 532 (hb. Gr.). Further distrib. general in warm countries. S. sprnosa, L. Sp. 683 (1753); Gray, Syn. FI. i. pt. 1, 324. — GarapaGcos Ips.: Habel. ALBEMARLE IsL.: common on tufa soil, Tagus Cove, Snodgrass & Heller, no. 206 (hb. Gr.). Further distrib. general in warm countries. In distinguishing this species and S. angus- tifolia, I have followed Dr. Gray’s treatment and distinctions. 176 PROCEEDINGS OF THE AMERICAN ACADEMY, S. VERONICAEFOLIA, Lam., var. HUMILIS, K. Schum. in Mart. FI. Bras. xii. pt. 3, 320 (1891), q. v. for extensive synon.; E. G. Baker, Jour. Bot. xxx. 293. S. humilis, Cav. Diss. v. 277, t. 134, f. 2 (1788). — ALBEMARLE Isx.: Iguana Cove, Snodgrass & Heller, no. 85 (hb. Gr.). Further distrib. general in tropics. STERCULIACEAE. WaALrTHeRIA, L. W. retTicuLATA, Hook. f. (3), 231; Anderss. (1), 231, & (2), 99; Rob. & Greenm. (1), 149. — This endemic species which has now been found upon no less than nine islands of the archipelago shows the same sort of formal variation that has been described in the case of Huphorbia viminea, Hook. f. (see Rob. & Greenm. (1), 188-139). The original characterization was unfortunately drawn from mixed material from Chatham, James, and Albemarle islands. We may, however, take as typical the form with a very close fine tomentum, small thickish leaves, 1.5 to 2.5 em. long, with strongly crisped margins. The leaves are rounded rather than cordate at the base, and their indumentum becomes decidedly yellowish in a dried state. This form, assumed as typical, has been collected on Gatapacos Ips.: Hdmonston (hb. Gr.). ALBE- MARLE Isu.: Macrae; southern part, Baur, no. 32 (hb. Gr.) ; Elizabeth Bay, Snodgrass & Heller, nos. 269 (hb. Gr.), 289 (hb. Gr.) ; Iguana Cove, Snodgrass & Heller, no. 75 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, no. 162 (hb. Gr.). CuHaries Isu.: Andersson; Baur, no. 33 (hb. Gr.). James Iszt.: Douglas; “ Macrae ;”' James Bay, along edge of new lava, Snodgrass & Heller, no. 867 (hb. Gr.). Jervis Ist.: Baur (this may belong to one of the following forms). Endemic. From this may be distinguished : — Forma acamata, tomento imprimis ramulorum crassiore valde flaves- cente; foliis magnis crassiusculis cordatis. — INDEFATIGABLE IsL,. : Baur, no. 27 (hb. Gr.) ; Andersson? Endemic. Forma Anderssonii, indumento ac illud formae typicae tenui densoque sed griseo et nullo modo flavescente; foliis multo majoribus 4—5.5 cm. longis, 3.2—4.2 latis cordatis. — BarrineTon Isi.: Baur, no. 26 (hb. Gr.); Snodgrass & Heller, no. 474 (hb. Gr.). Caarnam Isi.: An- dersson (hb. Gr.); Darwin 2? NarsoroucH Ist.: northern part, Snodgrass & Heller, no. 301 (hb. Gr.). Tower Isi.: Baur, no. 30 (hb. Gr.); Snodgrass & Heller, no. 797 (hb. Gr.). Endemic. 1 Cited by Andersson, but probably a mistake for Scouler. FLORA OF THE GALAPAGOS ISLANDS. V7 Forma intermedia, tomento typico sed minus flavescente: foliis quam illi formae typicae majoribus 3-4 cm. longis sed quam hi formae Anderssonii minoribus et minus cordatis. — ABINGDON IsL.: Snodgrass & Heller, no. 840 (hb. Gr.). Binpior Isi.: Baur, no. 28 (hb. Gr.) ; Snodgrass & Heller, no. 757 (hb. Gr.). Cares Isu.: Lee (hb. U.S. Nat. Mus.); Cuevas Bay, Baur, no. 34 (hb. Gr.); Snodgrass & Heller, no. 426 (hb. Gr.). Garpner Ist. : Snodgrass & Heller, no. 640 (hb. Gr.). Narporoucu Isi.: southern part, 300 to 615 m. alt., Snodgrass & Heller, no. 326 (hb. Gr.). Endemic. TURNERACEAE. Turnera, L. T. uLtmirouia, L. Sp. 271 (1753) ; Hook. f. (4), 262; Anderss. (1), 221, & (2), 93; Urb. Jahrb. Bot. Gard. Berlin, ii. 138 (where spec. is elaborately subdivided).— Cuar.es Ist.: Hdmonston (hb. Gr.). Fur- ther distrib. general in the tropics. PASSIFLORACEAE. Passirtora, L. P. roretTipa, L. Sp. 959 (1753) ; Cav. Diss. 458, t. 289; Anderss. (1), 221, & (2), 93; Rose (2), 137; Rob. & Greenm. (1), 146. — Cuarves Ist.: upper region, Andersson; A. Agassiz. CHaTHam Ist: A. Agassiz ; southwest end, middle region, Baur, no. 159 (hb. Gr.) ; Snodgrass & Heller, no. 496 (hb. Gr.). Further distrib. general in trop. and subtrop. Amer. P. LINEARILOBA, Hook. f. (8), 222. P. linearifolia, Anderss. (1), 221, & (2), 938. ? P. tridactylites, Hook. f. (8), 222; Anderss. (1), 221, & (2), 938. P. suberosa, var. lineariloba, Masters in Mart. FI. Bras. xiii. pt. 1, 579 (1872). P. suberosa, var., Rob. & Greenm. (1), 146. — Gatapacos Ips.: Habel. Cuarues Ist.: Darwin ;? Anders- son. GARDNER Isu.: Snodgrass & Heller, no. 625 (hb. Gr.). Hoop Isu.: Baur, no. 160 (hb. Gr.). James Isu.: Scouler; Douglas. Nar- BorRoUGH IsL.: southern part, trailing on bushes, rare, 615 m. alt., Snodgrass & Heller, no. 321 (hb. Gr.). Endemic. This species seems very different from continental specimens of P. suberosa, L., at hand. P. puseruta, Hook. f. (3), 223; Anderss. (1), 221, & (2), 93.— JAMES Isi.: Darwin. Endemic. Perhaps a form of P. suberosa, L., as considered by several writers. VOL. XXXVIII. — 12 178 PROCEEDINGS OF THE AMERICAN ACADEMY. CARICACEAE. Carica, L. C. Papaya, L. Hort. Cliff. 461, & Sp. 10386 (1753); Anderss. (1), 223, & (2), 94.— CuaArtes Ist. : about habitations, Andersson. Further distrib. general in tropics. LOASACEAE., MENTZELIA, L. M. aspera, L. Sp. 516 (1753); Anderss. (1), 222, & (2), 94; Rob. & Greenm. (1), 146. ?Acrolasia squalida, Hook. f. (3), 222; Anderss. (1), 222, & (2), 98. — Arsemarte Ist.: Andersson; Iguana Cove, Snodgrass & Heller, no. 102 (hb. Gr.); Tagus Cove, common from beach to 310 m. alt., in shady places, Snodgrass & Heller, no. 173 (hb. Gr.). Cuarves Ist.: Darwin; Andersson; Cuevas Bay, Baur, no. 162 (hb. Gr.); Snodgrass & Heller, no. 429 (hb. Gr.). CHaTHam Ist. : Andersson ; southwest end, lower region, Bawr, no. 161 (hb. Gr.) ; Snodgrass & Heller, no. 530 (hb. Gr.). Duncan Isu.: Snodgrass & Feller, no. 689 (hb. Gr.). GARDNER IsL.: Snodgrass & Heller, no. 614 (hb. Gr.). Hoop Ist.: Snodgrass & Heller, no. 719 (hb. Gr.). INDEFATIGABLE Isxt.: Andersson; northern part, Snodgrass & Heller, no. 664 (hb. Gr.). James Ist.: Andersson; James Bay, abundant on lava soil in shade, Snodgrass & Heller, no. 876 (hb. Gr.). Towrr Isu.: Snodgrass & Heller, no. 803 (hb. Gr.). Further distrib. N. Am. ScLEROTHRIX, Presl. S. rascrcuLata, Presl, Symb. Bot. ii. 3, t.53 (1858). Ancyrostemma micranthum, Poepp. & Endl. Nov. Gen. & Sp. iti. 65 (1845). — ALBE- MARLE Isx.: Iguana Cove, Snodgrass & Heller, nos. 123, 128 (both in hb. Gr.). James Ist.: James Bay, common on lava rocks near beach, Snodgrass & Heller, no. 373 (hb. Gr.). Narsoroucy Ist.: southern part, tolerably common, alt. 615 m., Snodgrass & Heller, no. 31da. Further distrib. Mex. to Peru and Brazil. CACTACEAE. [The plants of this family secured by Messrs. Snodgrass & Heller have been kindly identified by Prof. Karl Schumann of the Royal Botanical Museum, Berlin. ] FLORA OF THE GALAPAGOS ISLANDS. 179 Cerevs, Mill. C. GALAPAGENSIS, Weber, Bull. du Mus. d’hist. nat. Paris, 1899, p- 812 (1899).— Cuartes Iszt.: Du Petit-Thouars. Endemic. This can scarcely be regarded as a described species. C. nesioticus, K. Sch. nov. sp. in litt., “humilis 30 cm. longitudinem non attingens ; caulibus caespitosis et e basi communi in omnes partes more spinarum Echini radiantibus costatis ubique spinulis numerosis atrocastaneis tectis ; costis humilibus 8 mm. vix superantibus alte crenatis et in tubercula fere perfecte dissolutis; areolis orbicularibus, 2.6 mm. diametro lano sparso exigue tectis; spinis quam 40 pluribus inaequalibus saepe (praesertim infimis) apice fractis in unam centralem et alias exteriores non distributis, maximis 3 cm. longis omnibus quam setae equinae vix rigidioribus erectis strictis divaricatis non pungentibus; floribus 7 cm. longis; ovario subgloboso subobliquo leviter tuberculato et spinulis ad 5 mm. longis flavo-fuscis radiantibus armato; tubo perigonii angusto item in areolis spinoso, lobis exterioribus lanceolatis 1.2 cm. longis vix 2 mm. latis, interioribus etiam angustioribus et magis linearibus verosi- militer albis; staminibus prope faucem, filamentis perbrevibus non 1 mm. longis, antheris bis vel paulo ultra longioribus; fructu ellipsoideo in summo spinoso-areolato basi acuto 2.0 cm. longo et 1.5 cm. crasso ; seminibus numerosis, 1.2 mm. longis ellipsoideis rufis leviter punctatis.” — ALBEMARLE IsL.: Black Bight, Snodgrass & Heller, no. 923 (hb. Berl. & hb. Gr.); lava fields, Elizabeth Bay, Snodgrass & Heller, no. 939 (hb. Berl. & hb. Gr.); Point Christopher, Snodgrass & Heller, no. 932 (hb. Berl. & hb. Gr.). NarsoroueH Ist.: eastern side, on barren black lava, Snodgrass & Heller, nos. 919 (hb. Berl. & hb. Gr.), 927 (hb. Berl. & hb. Gr.). “Note. — This species is a very peculiar one from its long brown non-pungent spines, which clothe the stem so densely that its surface is invisible. JI have never before seen a species of the genus with such short filaments as in this. The petals are also uncom- monly narrow. Probably the flower is white. I think it can hardly be compared with either of the two species of Cereus thus far known from the Galapagos Islands. From C. Thouarsit, Weber, which is said to be similar to O. multangularis, it is perfectly distinguished by the mode of growth and by the much smaller fruit which does not at all resemble a large prune” [K. Sch. in litt.]. Endemic. C. sclerocarpus, K. Sch. nov. sp. in litt., “ arborescens ; caule prin- cipali 83-6 m. alto 15-22 cm. diametro ramos paucos sibi saepius paral- lelos gerente ; articulis costatis, costis in sectione transversa triangularibus 180 PROCEEDINGS OF THE AMERICAN ACADEMY. obtusis 1 cm. altis ope sulcorum acutorum separatis; areolis orbicularibus 3.5 mm. diametro tomento brevi tectis; spinis 20-25 in radiales et cen- trales non distributis rectis pungentibus maximo 4.5 cm. longo; floribus circa 10-11 cm. longis; ovario tereti squamato; squamis sparsis 1-1.5 min. longis ovatis acutis ; perigonii tubo gracili paucis bracteolis brevibus ornato; lobis exterioribus subspathulatis 8 cm. longis apice eroso- denticulatis, interioribus brevioribus angustioribus acuminatisque ; staminibus prope faucem perigonii affixis 2 cm. longis; stilo florem fere aequante ; stigmatibus 11 fere 2 cm. longis filiformibus; fructu duro strato exteriori perfirmo ovoideo acuto flore marcido coronato 7 cm. longo 3 cm. diametro; seminibus haud numerosis (ovulis plurimis abortivis) disciformibus 1 mm. diametro nigris lucidis leviter foveolatis.’” — ALBEMARLE Isu.: Pt. Christopher, Snodgrass & Heller, nos. 933 (hb. Berl. & hb. Gr.), 934 (hb. Berl. & hb. Gr.) ; Black Bight, Snod- grass & Heller, no. 935 (hb. Berl. & hb. Gr.). “ Note. — There is only one species in the Galapagos Islands which may be compared with this, namely C. galapagensis, Weber. ‘The characterization of the latter is, however, so imperfect that I cannot identify my species with it.” [K. Sch. in litt.]. Endemic. In his field notes Mr. Heller reports a giant Cereus on Bindloe (where rare), Chatham, James, and Narborough Islands which was probably C. sclerocarpus. It grew upon barren lava. C. Tuovarsu, Weber, Bull. du. Mus. d’hist. nat. Paris, 1899, p. 312 (1899). —Cuares Ist.: Du Petit-Thouars. Endemic. Not satis- factorily described. OpunTIA, Raf. O. GALAPAGEIA, Hensl. Mag. Zodl. & Bot. i. 467, t. 14, f. 2 (1837) ; Hook. f. (3), 223; -Anderss. (1), 224, & (2), 95; Hemsl. Gard. Chron. ser. 3, xxiv. (1898), p. 265, f. 75; Lindberg, Monatschr. Kakteenk. iv. 120-122, 134—135, & v. 10; K. Schumann, ibid. ix. 19,20, x. 173, & Gesammtbeschr. Kakteen, 747. Cuar.ies Isu.: Hassler Exp., acc. to ms. note of Engelm. (hb. Mo. Bot. Gard.). JAmes Ist.: Darwin; Hassler Exp., acc. to ms. note of Engelm. (hb. Mo. Bot. Gard.). Jervis Ist.: Hassler Exp., acc. to ms. note of Engelm. (hb, Mo. Bot. Gard.). Endemic. O. Helleri, K. Sch. nov. sp. in litt., “ humilis plus minusve prostrata 30-60 cm. alta dense caespitosa ramosa ; articulis lineari-oblongis apice basique acutis planis 11 cm. longis 4 cm. latis tenuibus apice setis fuscis munitis; areolis orbicularibus 2 mm. diametro non manifeste in tuber- culis editis capillis paucis albis tectis etiam tomento flavido in parte FLORA OF THE GALAPAGOS ISLANDS. 181 superiori instructis; spinis circa 20 inaequalibus 1.5 cm. non superanti- bus non pungentibus plus minusve arcuatis flavo-fuscis; glochidiis paucis (circa 50) in summa parte areolae sitis et non arcte pungentibus apice obtusis; spinis lateralibus glochidiarum non eminentibus ; ovario paulo quam 3 cm. longiore turbmato tuberculato; areolis quam illae articularum non minoribus et a lano modice copioso tectis et a spinis capillaceis modice laxis ad 2 em. longis flavo-fuscis munitis; perigonio 3—3.5 cm. maximo diametro; lobis exterioribus subulatis, 3 mm. longis, sequenti- bus late ovatis acutis mucronatisve verosimiliter flavo-viridibus, intimis subobovatis fere 2 em. longis; staminibus fere in fundo infimo floris crateriformis insertis permultis ; stilo 2 cm. longo crasso ; stigmatibus 6 erectis incurvatis carnosis percrassis.”” — WENMAN IsL.: Snodgrass & Heller, no. 917 (hb. Berl. & hb. Gr.). “Note. — The relatively large flower brings this species near O. myriacantha, Web., from which it differs in the mode of growth, smaller articles, and non-pungent spines.” [K. Sch. in litt.]. Endemic. O. myrraAcANTHA, Weber in Bois, Dictionn. d’horticult. 894 (1898), & Bull. du Mus. d’hist. nat. Paris, 1899, p. 313 (1899). — ALBEMARLE Ist.: Hassler Exp., ace. to ms. note of Engelm. (hb. Mo. Bot. Gard.). Cuarues Isu.: Du Petit-Thouars [ Dr. Néboux] (hb. Mus. dhist. nat. Paris, & hb. Mo. Bot. Gard.). InperatTiGABLe Isu.: Hassler Exp. ace. to ms. note of Engelm. (hb. Mo. Bot. Gard.). Endemic. Opuntias also occur (ace. to field notes of several collectors) upon Abingdon, Barrington, Bindloe, Chatham, Culpepper, Duncan, Hood, Narborough, North and South Seymour, and Tower Islands, but as no specimens of them have been secured it is impossible to refer them with definiteness to any of the foregoing species. Dr. Baur’ says of the genus: “Die grosse Opuntia hat einen verschiedenen Charakter beinahe auf jeder Insel. Die Opuntia von Barrington, Indefatigable und siid-Albemarle z. B. entwickelt einen sehr hohen Stamm; die von Hood und Charles besitzt einen verhiiltnissmiissig niederen und dickeren Stamm; die Opuntia von Jervis wiederum einen sehr niederen; die Verzweigung beginnt schon kurz~iiber dem Boden; die Opuntia von Tower hat gar keinen Stamm, die Verzweigung beginnt sofort am Boden, es ist ein niederer Busch, aber. kein Baum. Die Form von Bindloe zeigt Charaktere, die zwischen den Individuen von Tower und Jervis liegen.” It seems not unlikely that the low plant on Tower lacking the main trunk may be the same as Professor Schumann’s O. f/elleri from the not very distant island of Wenman. 1 Biol. Centralbl. xii. 247 (1892). 182 PROCEEDINGS OF THE AMERICAN ACADEMY. LYTHRACEAE. CupHea, P. Br. C. paruua, St. Hil. Fl. Bras. Merid. iii. 101; Caruel (1), 624; Koehne in Engl. Jahrb. ii. 165 (1882).— Cuatuam Isx.: Chierchia, ace. to Caruel, 1. c. Further distrib. Brazil. RHIZOPHORACEAE. Ruizoryora, L. R. Maneur, L. Sp. 448 (1753); Hook. f. (8), 225; Anderss. (1), 247, & (2), 108. — ALBEMARLE IsL.: in swamps north of Tagus Cove, ace. to ms. notes of Mr. Heller; also fringing lagoons on the south and west shores of Elizabeth Bay, acc. to Mr. Heller. CHatHam Ist.: Darwin. Duncan Isu.: in a swamp on the west coast, acc. to Mr. Heller. INDEFATIGABLE IsL.: about lagoons, acc. to Mr. Heller. NareorouGa Isi.: forming large swamps fringing lagoons, on the east aud southeast sides of the island, Snodgrass & Heller, no 918 (hb. Gr.). Further distrib. general on trop. shores. MYRTACEAE. Psip1um, L. P. GALAPAGEIUM, Hook. f. (3), 224. P. galapagejum, Anderss. (1), 247, & (2), 109. — ALBEMARLE IsL.: Iguana Cove, above 125 m. alt., bushes 2.4 to 3.6 m. high, Snodgrass & Heller, no. 126 (hb. Gr.). JAMES Isu.: Scouler; Darwin. Endemic. COMBRETACEAE. Conocarpus, Gaertn. C. erectus, L. Sp. 176 (1753) ; Jacq. Stirp. Am. 78, t. 52; Anderss. (1), 247, & (2), 108. — ALBemaRLE IsL.: Iguana Cove, Snodgrass & Feller, no. 44 (hb. Gr.). Crataam Isi.: somewhat marshy woodland in the littoral region, Andersson. James Is_.: Andersson (hb. Gr.); abundant along sandy beach, James Bay, Snodgrass & Heller, no, 382 (hb. Gr.). Further distrib. W. Ind., Mex., southern U. S., trop. 8. Am., introd. in Africa. FLORA OF THE GALAPAGOS ISLANDS. 183 LAGUNCULARIA, Gaertn. L. RACEMOSA, Gaertn. Fruct. iii. 209, t. 217, f. 2 (1805); Brandis in Engl. & Prantl, Nat. Pflanzenf. iii. Ab. 7, 127, f 64.— ALBEMARLE Isu.: Elizabeth Bay, lava fields near beach, Snodgrass & Heller, nos. 270 (hb. Gr.), 937 (hb. Gr.) ; Point Christopher, Snodgrass & Heller, no. 931 (hb. Gr.). NarsBoroucGHu Ist.: east side, Snodgrass & Heller, no. 920 (hb. Gr.). Further distrib. shores, Mex., W. Ind., S. Am., trop. Afr. Not before recorded from the Galapagos Ids. MELASTOMACEAE. Miconia, R. & P. M. Robinsoniana, Cogniaux, nov. sp. (sect. Zamonea); M. sp. Rob. & Greenm. (1), 146; “glaberrima; ramis junioribus acute tetragonis non alatis; foliis breviuscule petiolatis, anguste ligulato-oblongis, leviter obtuseque acuminatis, basi breviter attenuatis vel subrotundatis, margine integerrimis, trinerviis vel obscure 5-nerviis, nervulis transversalibus numerosis tenuissimis; floribus sessilibus, secus ramulorum paniculae solitariis; calyce oblongo, limbo leviter dilatato, brevissime 5-lobato, lobis late rotundatis ; staminum filamentis glaberrimis. “ Rami robustiusculi, laeves. Petiolus gracilis, leviter tortuosus, 1—-1.5 em. longus. Folia rigidiuscula, utrinque laevia, siccitate non nitida, 14-16 cm. longa, 3-3.5 cm. lata, nervis subtus satis prominentibus. Paniculae majusculae, multiflorae, trichotome ramosae, ramis gracilibus, erectis vel paulo patulis, leviter compressis, articulatis. Bracteae paten- tissimae, rigidae, triangulari-ovatae, acutae, 1-1.5 mm. longae. Calyx laevis, basi rotundatus, sub apice leviter constrictus, circiter 5 mm. longus. Petala erecta, anguste obovata, obtusa, 6 mm. longa. Stami- num filamenta capillaria, 8-4 mm. longa; antherae valde arcuatae, apice longe attenuatae, 4-5 mm. longae. Stylus crassiusculus, glaber, apice arcuatus caeteris rectus, 5 mm. longus, stigmate paulo incrassato. — Affinis MW. nitidissimae, Cogn. in DC. Monogr. Phan. vii. 748, sed bene distincta.” — CHATHAM IsL.: southwest end, upper region, Baur, no. 163 (hb. Gr. & hb. Cogniaux). Endemic. HALORRHAGIDACEAE. Myriopnytium, L. M. sp. Wolf (1), 284.— Cartes Isx.: in brook near the hacienda, ace. to Wolf, l. c. 184 PROCEEDINGS OF THE AMERICAN ACADEMY, UMBELLIFERAE. Aprium, L. A. LACINIATUM, Urb. in Mart. Fl]. Bras. xi. pt. 1, 343 (1879). Helosciadium laciniatum, DC. Mém. Soc. Phys. Genev. iv. 495 (1828) ; Hook. f. (3), 215; Anderss. (1), 219, & (2), 92.— CHartzs IsL.: Darwin, ace. to Hook. f., 1. ¢c. Further distrib. Peru to Chili. A. LEPTOPHYLLUM, F. Muell. acc. to Benth. Fl. Austr. ili. 8372 (1866). A. Ammi, Urb. in Mart. Fl. Bras. xi. pt. 1, 341, q. v. for extensive synon. LHelosciadium leptophyllum, DC. Mém. Soc. Phys. Genev. iv. 493 (1828); Hook. f. (3), 215; Anderss. (1), 219, & (2), 92. — ALzrg- MARLE Ist.: Iguana Cove, Snodgrass & AHeiler, no. 41 (hb. Gr.). James Ist.: Darwin. Further distrib. N. Am, Mex.,S. Am., Austral., etc. CENTELLA, L. C. astatica, Urb. in Mart. Fl. Bras. xi. pt. 1, 287 (1879). Hydro- cotyle asiatica, L. Sp. 234 (1753). H. repanda, Pers. Syn. i. 302 (1805); Caruel (1), 623.— Cuatuam Ist.: Chierchia, acc. to Caruel. Further distrib. N. Am., S. Am., Asia, etc. Hyprocotytr, L. H. galapagensis, nov. sp., glaberrima, repens, radicibus ad nodos fibrosis petiolis erectis teretibus, foliis orbicularibus peltatis prope centrum insertis 12—13-radiati-nervatis, margine duplo dentata, nervis venulisque translucentibus, pedunculis erectis, umbellis simplicibus sub .16-floribus non proliferis: involucris bracteis ovatis brevibus pedicellis flores quadri- quintuple excedentibus : cealycis limbo obsoleto, petalibus ovatis obtusis patentibus, albis, fructu latiori quam longo basi rotundato vel subcordato. H. umbellata, Rob. & Greenm. (1), 146, not L. — Cuatuam Ist. ; southwest end, upper region, Baur, no. 150 (hb. Gr.). Near H. wmbel- lata, L., which it resembles rather closely in habit, flowers, and fruit, the leaves, however, differ rather conspicuously by their doubly dentate not crenate margin from the Linnaean species. Transitional forms have been sought in vain in material of H. wmbellata from many other parts of the world. PETROSELINUM, Koch. P. sativum, Hoffm. Gen. Umb. 177 (1814); Anderss. (1), 219, & (2), 92. Apium Petroselinum, L. Sp. 264 (1753). Carum Petrose- FLORA OF THE GALAPAGOS ISLANDS. 185 linum, Benth. & Hook. f. Gen. i. 891 (1867).— Cuartes Ist.: culti- vated ground, middle and upper region, Andersson (hb. Gr.). Introd. from the Old World. PLUMBAGINACEAE. PLUMBAGO, L. P. scANDENS, L. Sp. ed. 2, 215 (1762); Hook. f. (3), 194; Anderss. (1), 172, & (2), 65; Caruel (1), 623; Rob. & Greenm. (1), 147.— ALBEMARLE Isx.: Darwin; southern part, Baur, no. 235 (hb. Gr.) ; mountain north of Elizabeth Bay, Snodgrass & Heller, no. 284 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, no. 220 (hb. Gr.). CHarves Ist. : Darwin ; Andersson (hb. Gr.) ; Chierchia ; Lee (hb. U. S. Nat. Mus.) ; Baur, no. 234 (hb. Gr.); Snodgrass & Heiler, no. 411 (hb. Gr.). CuatHam Isut.: Andersson; Snodgrass & Heller, no. 506 (hb. Gr.). Duncan Ist.: Baur, no. 236 (hb. Gr.). InpDEFATIGABLE ISL.: Andersson. Further distrib. general in warm countries. (P. tomentosa, Hook. f., 1. c., is a typographical error for Plantago tomentosa. ) APOCYNACEAE. Vatcesia, R. & P. V. cymBarrouia, Ort. Hort. Matr. Dec. 58 (1798). V. glabra, Link, Enum. Hort. Berol. i. 207 (1821); Hook. f. (8), 205 ; Anderss. (1) 195, & (2), 78. Rauwolfia glabra, Cav. Ie. iii. 50, t. 297 (1795). Psychotria angustata, Rob. & Greenm. (1), 146, not Anderss. — GaLa- pacos Ips.: Edmonston (hb. Gr.). ALBEMARLE IsL.: Point Christopher, Snodgrass & Heller, no. 929 (hb. Gr.); Tagus Cove, Snodgrass & Heller, uo. 926 (hb. Gr.). Cuaruam Isx.: Darwin ; Andersson. Hoop Isu.: Baur, no. 149 (hb. Gr.). Further distrib. S. Am., Mex., W. Ind., Florida. V. puBESCENS, Anderss. (1), 195, & (2), 79. — Cuartss Ist. : Snod- grass & Heller, no. 451 (hb. Gr.). CHaruam Ist.: woods in lower region, Andersson ; Snodgrass &~Heller, no. 518 (hb. Gr.). Endemic. ASCLEPIADACEAE. ASCLEPIAS, L. A. ANGUSTISSIMA, Anderss. (1), 196, & (2), 79. Vincetoxicum ? Rob. & Greenm. (1), 147, in part (as to pl. Albemarle). — ABINGDON 186 PROCEEDINGS OF THE AMERICAN ACADEMY. Ist.: Snodgrass & Heller, no. 845 (hb. Gr.). ALBeMARLE Ist.: in the driest part of the middle region, Andersson ; southern part, Baur, without number (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 146 (hb. Gr.). dndemic. VincEToxicum, Moench. V.? Rob. & Greenm. (1), 147, in part (as to pl. Charles). — Cuartes Ist.: Cuevas Bay, Baur, without number (hb. Gr.). Sterile and doubtful. CONVOLVULACEAE. Catystecia, R. Br. C. SotpanEetta, R. Br. Prodr. 483 (1810); Hook. f. (4), 261; Anderss. (1), 212, & (2), 87. Convolvulus Soldanella, L. Sp. 159 (1753); Engl. Bot. v. t. 314; Gray, Syn. Fl. N. A. ii. pt. 1, 215. — Cuar.es Isxt.: EHdmonston, acc. to Hook. f., 1. c. Further distrib. general, Pacific shores of N. and 8S. Am., also in Eu., N. Zealand, ete. Cuscura, L. C. acuta, Engelm. Trans. Acad. Sci. St. Louis, i. 497 (1859) ; Anderss. (2), 89.—BinpLor Ist.: Snodgrass & Heller, no. 769 (hb. Gr.), identity doubtful. Caries Isi.: Andersson. CHATHAM Ist.: Andersson. NarsorouGu Ist.: southern part, not common, 600 m. alt., Snodgrass & Heller, no. 318 (hb. Gr.). Endemic. C. GymnocarpPa, Engelm. Trans. Acad. Sci. St. Louis, i. 496 (1859) ; Anderss. (2), 89; Rob. & Greenm. (1), 147. C. sandvicensis, var. Mimosae, Hook. f. (3), 205; Anderss. (2), 89 (sandwicensis). C. sandwi- chiana, var. Mimosae, Anderss. (1), 214.— GaLapaGos Ips.: Habel. ALBEMARLE IsL.: eastern portion, Cowley Bay, Baur, no. 205 (hb. Gr.), parasitic on Borreria suberecta, Hook. f., and doubtfully identical with the plant of Darwin. James Isu.: Darwin. Endemic. Evotvouuvs, L. E. GLABER, Spreng. Syst. i. 862 (1825) ; Hallier, Jahrb. Hamb. Wiss. Anst. xvi. 22. ZH. hirsutus, HBK. Nov. Gen. & Sp. iii. 117 (1818), not Lam. /. mucronatus, Sw. acc. to Wikstr. Vet. Acad. Handl. Stockh. 1827, p. 61. #. glabriusculus, Chois. Diss. Conv. 156 (1838) ; Hook. f. (3), 205; Anderss. (1), 211, & (2), 87; Rose (1), 137; Rob. & Greenm. (1), 147. — ALBeMARLE IsL.: Andersson; Iguana Cove, FLORA OF THE GALAPAGOS ISLANDS. 187 Snodgrass & Heller, no. 82 (hb. Gr.). CHarues Isi.: Snodgrass & Heller, no. 432 (hb. Gr.) ; A. Agassiz (hb. Gr.); Baur. Cuatuam Ist. : Andersson (hb. Gr.); southwest end, middle region, Baur, no. 203 (hb. Gr.); Snodgrass & Heller, no. 517 (hb. Gr.). Duncan Ist.: Snodgrass & Heller, no. 687 (hb. Gr.). INDEFaTIGABLE IsL.: Anders- son. JAmES Isxt.: Scouler. Stymour Isu.: north, Snodgrass & Heller, no. 564 (hb. Gr.). Further distrib. S. Am., W. Ind. Said by Hallier, l. c, to have been collected on Chatham and Hood Islands by Steindach- ner; but Dr. Steindachner visited neither of these islands. E. stmpLex, Anderss. (1), 211, & (2), 87; Rob. & Greenm. (1), 147. — Cuar.es Ist.: Baur (hb. Gr.); Snodgrass & Heller, no. 431 (hb. Gr.). CuatHam Isx.: Andersson ; Baur, no. 201 (hb. Gr.). INDEFATIGABLE Ist.: Andersson (hb. Gr.); northern part, Snodgrass & Heller, no. 659 (hb. Gr.). James Isx.: common on bluff near beach, James Bay, Snod- grass & Heller, no. 384 (hb. Gr.). Endemic. Ipomora, L. J. prtopa, Forsk. F]. Aegypt.-Arab. 44 (1775) ; Hook. f. & Jacks. Ind. Kew. i. 1223. J. Pes-caprae, Sweet, Hort. Suburb. Lond. 35 (1S13)/3" oth, (Nov PI. Sp. 109); Anderss..'(1),' 212, & (2),-87- "2. maritima, RK. Br. Prodr. 486 (1810); Hook. f. (3), 204. — Arsr- MARLE Isu.: Black Bight, Snodgrass & Heller, no. 257 (hb. Gr.) ; pebbly beach, Iguana Cove, Snodgrass & Heller, no. 125 (hb. Gr.). CuatHam Isi.: Darwin; Andersson. Widely distrib. in trop. reg. I. Bona-nox, L. Sp. ed. 2, 228 (1762); Sims, Bot. Mag. t. 752. — ALBEMARLE Isz.: Snodgrass & Heller, no. 872 (hb. Gr.). Widely distrib. and extensively cultivated. I. CAMPANULATA, L. Sp. 160 (1753); Wight, Ic. Pl. Ind. iv. t. 1375. — ALBEMARLE Isr. : Iguana Cove, Snodgrass & Heller, no. 43 (hb. Gr.). Further distrib. East India, Malayan Archipelago. This is, I believe, the only instance in which an Old World species occurs on the Galapagos Ids. which has not been reported from any part of the American continent. ; I. GALAPAGENSIS, Anderss. (1), 213, & (2), 88. — ALprmaRLE Ist.: Lee (hb. U. S. Nat. Mus.); Iguana Cove, Snodgrass & Heller, nos. 33 (bb. Gr.), 94 (hb. Gr.). Cartes Isu.: slndersson ; Snodgrass & Heller, no. 464 (hb. Gr.). CHatnam Ist.: Andersson. Duncan Ist,: Snodgrass & Heller, no. 690 (hb. Gr.). Hoop Isu. : Snodgrass & Heller, no. 728 (hb. Gr.). James Is~.: common in any soil, James 188 PROCEEDINGS OF THE AMERICAN ACADEMY. Bay, Snodgrass & Heller, no. 374 (hb. Gr.). Srtymour Isu.: south, Snodgrass & Heller, no. 583. (hb. Gr.). Endemic. I. Hapettana, Oliv. in Hook. Ic. t. 1099 (1871). JZ. sp. Rose (1), 187. — Binvtog Ist.: Snodgrass & Heller, no. 759 (hb. Gr.). Don- can Isut.: A. Agassiz (hb. U. S. Nat. Mus.); Snodgrass & Heller, no. 712 (hb. Gr.). Garpner Isi.: Snodgrass & Heller, no. 616 (hb. Gr.). Hoop Ist.: Habel (hb. Kew); Snodgrass & Heller, no. 751 (hb. Gr.). Tower Isu.: Snodgrass & Heller, no. 799 (hb. Gr.). « Endemic. A peculiar species with entire ovate-lanceolate attenuate glabrous leaves 12 to 18 cm. long, oblong obtuse sepals and a tubular corolla 9 to 15 cm. long. Iam indebted to Dr. H. Hallier of Hamburg for his examination of this species. I. Kinperel, Anderss. (1), 212, & (2), 88; Rob. & Greenm. (1), 147. —Garapacos Ips.: Habel. Asinapvon Isx.: Snodgrass & Hel- ler, no. 839 (hb. Gr.). CHatuam Isz.: Andersson. INDEFATIGABLE Ist.: Andersson ; south of Conway Bay, Baur, no. 195 (hb. Gr.) ; northern part, Snodgrass & Heller, no. 674 (hb. Gr.). Jervis Ist.: Baur, no. 196 (hb. Gr.). Tower Isu.: Snodgrass & Heller, no. 801 (hb. Gr.). Wenman Isx.: Snodgrass & Heller, no. 5 (hb. Gr.). Endemic. J. LINEARIFOLIA, Hook. f. (3), 204; Anderss. (1), 212, & (2), 88. — JAMES Ist.: Darwin, acc. to Hook. f. Endemic. Secured by no other collector. Ascribed in the Index Kewensis to the Cape Verde Ids. I. Nit, Roth, Catalect. i. 36 (1797). JI. acuminata, Morong & Britt. Ann. N. Y. Acad. Sci. vii. 169 (1893) ; Rob. & Greenm. (1), 147; not R. & 8. Pharbitis Nil, Choisy, Mém. Soc. Phys. Genéy. vi. 441 (1883). — Cuarzes Isi.: Snodgrass & Heller, no. 418 (hb. Gr.), CHaTHAM IsuL.: southwestern end, lower region, Baur, no. 200 (hb. Gr.) ; Snodgrass & Heller, no. 511 (hb. Gr.). Further distrib. general in warm regions. An indeterminate Ipomoea from Indefatigable Isl., mentioned and briefly described by Andersson (1), 214, & (2), 88, may well have been this species. I, PENTAPHYLLA, Jacq. Coll. ii. 297 (1788), & Ic. Pl. Rar. ii. 10, t. 8319; Rob. & Greenm. (1), 147. Batatas pentaphylla, Choisy, Mém. Soc. Phys. Genev. vi. 408 (18388); Anderss. (1), 214, & (2), 89. Merremia pentaphylla, Hallier in Engl. Jahrb. xvi. 552 (1893). — ABinGpDoN Isx.: Snodgrass & Heller, no. 846 (hb. Gr.). CHARLES Ist.: Andersson. CuHatuam Isu.: Andersson. Duncan Ist.: Snor- FLORA OF THE GALAPAGOS ISLANDS. 189 grass & Heller, no. 707 (hb. Gr.). Garpner Ist.: Snodgrass & #teller,: no: 623° (hb. Gr.)." Hoop: Isu.: Baur, no. 198 (hb. ‘Gr.); Snodgrass & Heller, no. 729 (hb. Gr.). INDEFATIGABLE IsL.: Ander's- son ; northern part, Snodgrass & Heller, no. 671 (hb. Gr.). JAmeEs Isy.: Andersson. Jervis Ist.: Baur, no. 199 (hb. Gr.). Seymour Ist.: north, Snodgrass & Heller, no. 568 (hb. Gr.). Tower Ist. : Snodgrass & Heller, no. 804 (hb. Gr.). Further distrib. general in trop. I. tusirLorA , Hook. f. (3), 204; Anderss. (1), 213, & (2), 88. — James Ist.: Darwin, ace. to Hook. f.,1.c. Endemic. Secured by no other collector. BORAGINACEAE. Coripenta, L. C. Darwini, Giirke in Engl. & Prantl, Nat. Pflanzenf. iv. Ab. 3a, 90 (1893). C. Darwinii, Rob. & Greenm. (1), 147 (excl. p!. Albe- marle). Galapagoa Darwini, Hook. f. (3), 196; Anderss. (1), 210, & (2), 86, t. 16, f. 1. —Garapacos Ips. : Edmonston (hb. Gr.) ; Habel. ALBEMARLE Ist.: Macrae. Binpioe Isi.: Baur, no. 383 (hb. Gr.) ; Snodgrass & Heller, no. 764 (hb. Gr.). CHatruam Isxi.: Darwin ; Andersson (hb. Gr.). INDEFATIGABLE IsL.: Conway Bay, Bawr, no, 385 (hb. Gr.) ; northern part, Snodgrass & Heller, no. 679 (hb. Gr.). James Isu.: Orchilla Bay, Bawr, no. 384 (hb. Gr.), Endemic. C. rusca, Giirke in Engl. & Prantl, Nat. Pflanzenf. iv. Ab. 3a, 90 (1893); Rob. & Greenm. (1),147. CO. Darwinii, Rob. & Greenm. (1), 147, as to pl. Albemarle. Galapugoa fusca, Hook. f. (3), 197; Anderss. (1), 210, & (2), 87, t. 16, f. 2.— ALBEMARLE IsL.: common on tufa soil about Tagus Cove, from beach to summit of hills, Snodgrass & Heller, no. 180 (hb. Gr.) ; southern portion, Baur, no. 382 (hb. Gr.). Barrineton Isx.: Snodgrass & Heller, no. 468 (hb. Gr.). CHaries Ist.: Darwin. CHATHAM IsL.: southwest end, lower region, Baur, no. 217 (hb. Gr.). Hoop Ist.: Baur, no. 218 (hb. Gr.). INDEFATI- GABLE Isx.: in dry sandy places*on the shore, Andersson (hb. Gr.).- Seymour Ist.: south, Snodgrass & Heller, no. 587 (hb. Gr.). - Endemic. Corpia, L. C. AnpErssonI, Giirke in Engl. & Prantl, Nat. Pflanzenf. iv. Ab. 3a, 83 (1893). Varronia canescens, Anderss. (1), 203, & (2), 83, t. 11, f. 2. V. leucophlyctis, Anderss. (1), 203, & (2), 83, t.11, f. 1, not 190 PROCEEDINGS OF THE AMERICAN ACADEMY. C. leucophlyctis, Hook. f.— CHARLES IsL.: in wooded places, lower region, Andersson (hb. Gr.); Lee (hb. U. S. Nat. Mus. & hb. Gr.). CaatHam Isz.: Andersson (hb. Gr.). Endemic. C. GALAPAGENSIS, Giirke, ].c. C. scaberrima, Rob. & Greenm. (1), 147, not HBK. C. sp., Rob. & Greenm. (1), 147. Varronia scaber- rima, Anderss. (1), 202, & (2), 82, t. 11, f. 3. — ALBEMARLE Ist.: eastern part, Baur, no. 210 (hb. Gr.) ; Cowley Bay, Baur, no. 212 (hb. Gr.); Iguana Cove, Snodgrass & Heller, nos. 75 (hb. Gr.), 136 (hb. Gr.), 857 (hb. Gr.) ; mountain north of Elizabeth Bay, Snod- grass & Heller, no. 291 (bb. Gr.) ; Tagus Cove, from near beach to 1300 m. alt., Snodgrass & Heller, nos. 195 (hb. Gr.), 881 (hb. Gr.), 893 (hb. Gr.). Duncan Isx.: Baur, no. 215 (hb. Gr.). Inprraric- ABLE Isi.: Andersson ; south of Conway Bay, Baur, no. 211 (hb. Gr.). NArsBorouGH Isi.: southern part, growing 1.3 m. high, spread- ing 2 m. or more, altitude 650 m., Snodgrass & Heller, nos. 831 (hb. Gr.), 342 (hb. Gr.). Endemic. C. Hooxerrana, Giirke, 1. c. C. linearis, Hook. f. (8), 199 ; Rob. & Greenm. (1), 147; not DC. Varronia linearis, Anderss. (1), 204, & (2), 84,t. 11, f 4. Lithocardium Hookerianum, O. Kuntze, Rev. Gen. 11. 976 (1891). — ALBEMARLE Isi.: Elizabeth Cove, Snodgrass & Feller, no. 272 (hb. Gr.); Iguana Cove, Snodgrass & Heller, no. 28 (hb. Gr.) ; southern portion, Baur, no. 2138 (hb. Gr.); Tagus Cove, Snodgrass & Heller, nos. 155 (hb. Gr.), 196 (hb. Gr.), above 650 m., no. 897 (hb. Gr.). Cuarves Ist.: Baur, no. 214 (hb. Gr.). James Isx.; Darwin ; Andersson. NarsporouGa Isu.: arborescent, 3 or 4 m. high, common in southern part at 600 m, alt., Snodgrass & Heller, no. 327 (hb. Gr.), Endemic. C. LEUCOPHLYCTIS, Hook. f. (8), 199; Giirke, I. c. 83; Rob. & Greenm. (1), 147. Lithocardium leucophlyctis, O. Kuntze, Rev. Gen. ii. 977 (1891).— Garapacos Ips.; Habel. AtBemarRLE Isz.: Macrae; Darwin. James Isu.: Scouler; ? Orchilla Bay, Baur, no. 209 (hb. Gr.). Endemic. C. ruTeA, Lam. Ill. i. 421 (1791); Hook. f. (3), 198; Rose (1), 137; Rob. & Greenm. (1), 147. C. rotundifolia, Ruiz & Pavon, FI. Per. ii. 24, t. 148, fig. a@ (very bad, especially as to corolla), 1799 ; Hook. f. & Jacks. Ind. Kew. i. 614 (where ascribed to Panama instead of Peru). Varronia rotundifolia, DC. Prodr. ix. 469 (1845). V. flava, Anderss. (1), 201, & (2), 82. — GaLapaGos Ips.: Habel. ABINGDON Ist.: Snodgrass & Heller, no. 821 (hb. Gr.). ALBemarve Ist.: Lee FLORA OF THE GALAPAGOS ISLANDS. - 191 (hb. U. S. Nat. Mus.) ; Macrae ; Iguana Cove, Snodgrass & Heller, no. 74 (hb. Gr.); mountain north of Elizabeth Bay, Snodgrass & Heller, no. 294 (hb. Gr.) ; also on lava fields near beach, Elizabeth Bay, Snod- grass & Heller, no. 940 (hb. Gr.); Tagus Cove, Snodgrass & Heller, nos. 159 (hb. Gr.), 925 (hb. Gr.). Barrineton Isi.: Baur, no. 231 (hb. Gr.) ; Snodgrass & Heller, no, 473 (hb. Gr.). Brnpior Ist. : Baur, no. 232 (hb. Gr.); Snodgrass & Heller, no. 787 (hb. Gr.). Cuarues Isu.: Andersson; A. Agassiz; Baur, no. 228 (hb. Gr.) ; Snodgrass & Heller, no. 419 (hb. Gr.). CHatHam Ist.: Darwin ; Andersson (hb. Gr.); southwest end, lower region, Baur, no. 208 (hb. Gr.) ; Snodgrass & Heller, no. 524 (hb. Gr.). Duncan Ist.: A. Agassiz (hb. Gr.); Baur, no. 230 (hb. Gr.) ; very abundant on hills, Snodgrass & Heller, no. 708 (hb. Gr.). GARpDNER IsL.: Snodgrass & Heller, no. 642 (hb. Gr.). Hoop Isu.: Baur, no. 229 (hb. Gr.). INDEFATIGABLE Isu.: Andersson. James Ist.: Andersson; James Bay, 2 to 3 m. high, not common, Snodgrass & Heller, no. 365 (hb. Gr.). Jervis Ist.: Baur, no. 283 (hb. Gr.). Seymour Ist.: north, Snodgrass & Heller, no. 569 (hb. Gr.); south, Snodgrass & Heller, no. 604 (hb. Gr.). Tower Isu.: Snodgrass & Heller, no. 793 (hb. Gr.). Further distrib. Ecuador, Peru, Bolivia. To our present knowledge this is the most widely distributed plant on the Archipelago, occurring as it does upon no less than fourteen islands. It is, however, remarkably constant in its characters. C. revotura, Hook. f. (3), 199. Varronia revoluta, Anderss. (1), 204, & (2), 84. Lithocardium revolutum, O. Kuntze, Rev. Gen. ii. 977 (1891). — Gatapacos Ips.: Habel. CHarures Isx.: Darwin. Endemic. Var. NIGRICANS, Hook. f. (3),199. Varronia revoluta, var. nigricans, Anderss. (1), 204, & (2), 84. — ArBemarLe Isi.: Macrae. Endemic. C. Scourert, Hook. f. (3), 200; Rob. & Greenm. (1), 147. Var- ronia Scouleri, Anderss. (1), 204, & (2), 83. Lithocardium Scouleri, O. Kuntze, Rev. Gen. ii. 977 (1891). — Cuatuam Ist. : Andersson ; southwest end, middle region, Baur, no. 216 (hb. Gr.). James Ist.: Scouler. Endemic. C. nov. sp.? C. dasycephala, Anderss. (1), 204, & (2), 84, not HBK. Varronia dasycephala, Hook. f. (4), 261, not Desv.— Cuarues Ist. : Edmonston (hb. Gr.). Certainly different from any other species on the Islands, and clearly distinguished from O. dasycephala by the simple widely spreading tawny setae which cover the stem. Unfortunately the material is too poor for description. Endemic. 192 PROCEEDINGS OF THE AMERICAN ACADEMY. Hexrorrorium, L. Hl. Anderssonii. H. asperrimum, Anderss. (2), 86, not R. Br. Sareanthus asperrimus, Anderss. (1), 209.—InNpEFaATIGABLE IsL.: Andersson (hb. Gr.). Endemic. H. curassavicum, L. Sp. 180 (1753); Hook. f. (3), 198; Anderss. (1), 208, & (2), 86; Rose (2), 137, in part; Rob. & Greenm. (1), 147. — GaALapaGos Ips.: Habel. Binpioek Isxt.: Snodgrass & Heller, no. 766 (hb. Gr.). Cuarnam Iszt.: Darwin; Andersson (hb. Gr.) ; A. Agassiz (hb. Gr. & hb. U. S. Nat. Mus.); Baur, no. 219 (hb. Gr.) ; Snodgrass & Heller, no. 514 (bb. Gr.). Hoop Ist.: Snodgrass & Heller, no. 725 (hb. Gr.). INbDEFATIGABLE IsL.: northern part, Snod- grass & Heller, no. 660 (hb. Gr.). Stymour Isx.: south, Snodgrass & Heller, no. 560 (hb. Gr.). Further distrib. wide, especially upon trop. shores, H. inpicum, L. Sp. 180 (1753); Hook. f. (4), 261. Heliophytum indicum, DC. Prodr. ix. 556; Anderss. (1), 208, & (2) 86. — CHARLES Ist.: Hdmonsten ; Lee (hb. Gr. & hb. U. S. Nat. Mus.) ; Snodgrass & Heller, no. 447 (hb. Gr.). Widely distrib. weed of warm countries. H. PARVIFLORUM, L. Mant. 201 (1771); Hook. f. (8), 198; Rob. & Greenm. (1), 147. H. curassavicum, Rose (1), 137, in part. Helio- phytum parviflorum, DC. Prodr. ix. 553 (1845); Anderss. (1), 208, & (2), 86.— GarapaGcos Ips.: Hubel. Asinapon Isut.: Snodgrass & Heller, no. 812 (hb. Gr.), ALBEMARLE Isx.: Iguana Cove, Snod- grass & Heller, no. 80 (hb. Gr.); Tagus Cove, most abundant near the coast, but also found inland to 300 m. alt., Snodgrass & Heller, nos. 160 (hb. Gr.), 200 (hb. Gr.). Barrineron Ist.: Snodgrass & Heller, no. 486 (hb. Gr.). CuHartes Isi.: Darwin; Andersson; Lee (hb. Gr.); Baur; Snodgrass & Heller, no. 463 (hb. Gr.). CHarHam Is. : Andersson (hb. Gr.) ; A. Agussiz (hb. Gr. & hb. U. 8S. Nat. Mus.) ; southwest end, upper region, Baur, no. 220 (hb. Gr.) ; lower region, Baur, no. 221 (hb. Gr.); Snodgrass & Heller, no. 510 (hb. Gr.). GARDNER Isi.: Snodgrass & Heller, no. 639 (hb. Gr.). Hoop Ist. : Baur, no. 222 (hb. Gr.), through typographical error ascribed to Duncan Isl. by Rob. & Greenm. 1. ¢.; Snodgrass & Heller, no. 747 (hb. Gr.). INDEFATIGABLE Isu.: Andersson. James Isi.: Douglas ; James Bay, scattered in lava soil, Snodgrass & Heller, no. 357 (hb. Gr.). NarsorouGH Ist.: southern part, rather common at 650 m. alt., Snodgrass & Heller, no. 848 (hb. Gr.). Tower Isx.: Snodgrass & Helier, no. 792 (hb. Gr.). Widely distrib. in warm countries. FLORA OF THE GALAPAGOS ISLANDS. 193 Tournerortia, L. T. urrsutissima, L. Sp. 140 (1758); Caruel (1), 622. —CHatHam Ist. : Chierchia, ace. to Caruel. Further distrib. trop. Am. I suspect that Chierchia’s specimen will on examination prove to be 7. rufo-sericea, Hook. f. T. LAURIFOLIA, Vent. Choix Pl. 2 (1803). TZ. syringaefolia, Vahl, Symb. iii. 23 (1794) ; Anderss. (1), 206, & (2), 84, not Miq.; ? Caruel (1), 622. — Cuatuam Isxi.: Chierchia, acc. to Caruel, sterile and doubt- ful. James Isu.: Andersson. Further distrib. Mex., trop. S. Am. A doubtful member of the Galapageian flora. T. psirtostacuya, HBK. Nov. Gen. & Sp. iii. 78 (1818); Cham. Linnaea, iv. 470; DC. Prodr. ix. 525; Hook. f. (3), 198 (pstlostachys) ; Anderss. (1), 208, & (2), 85; Rob. & Greenm. (1), 147. ? 7. difformis, Anderss. (1), 206, & (2), 85.— ALBEMARLE IsL.: Iguana Cove, the commonest shrub, everywhere from the beach to 650 m., Snodgrass & Heller, nos. 81 (hb. Gr.), 120 (hb. Gr.). CHaries Isx.: Lee (hb. U.S. Nat. Mus.) ; Snodgrass & Heller, no. 436 (hb. Gr.). CHATHAM Ist. : Andersson (T. difformis, Anderss.). Hoop Isu.: Baur, no. 227 (hb. Gr.). James Ist.: Douglas & Scouler, acc. to Hook. f.; common near sandy beach, Snodgrass & Heller, no. 363 (hb. Gr.). Further distrib. trop. S. Am. ‘This species appears to have recently become abundant in the Galapagos Islands. T. puBESCENS, Hook. f. (3), 198; Anderss. (1), 206, & (2), 84; Rob. & Greenm. (1), 147. 7. opaca, Anderss. (1), 205, & (2), 84; Rob. & Greenm. (1), 147.— AtBemarLe Isu.: Iguana Cove, abun- dant near beach, and to 650 m. alt., Snodgrass & Heller, no. 119 (hb. Gr.) ; bushes 2 to 4 m. high, Snodgrass & Heller, nos. 135 (hb. Gr.), 870 (hb. Gr.) ; mountain east of Tagus Cove, Snodgrass & Heller, no. 255 (hb. Gr.); southern part, Baur, no. 225 (hb. Gr.). Carvers Is..: Lee (hb. Gr.). Cuatuam Isx.: Darwin ; southwest end, middle region, Baur, vo. 206 (hb. Gr.). Duncan Isxu.: Baur, no. 226 (hb. Gr.). INDEFATIGABLE ISL.: in wooded places of the lower region, Andersson (hb. Gr.). Endemic. I am quite unable to separate 7. opaca, Anderss., which appears to be only a glabrate state. T. nuFO-sERICEA, Hook. f. (8), 197; Anderss. (1), 205, & (2), 84; Rob. & Greenm. (1), 147.— Axsinepon Isi.: Snodgrass & Heller, no. 816 (hb. Gr.). ALBEMARLE IsL.: Iguana Cove, up to 630 m. alt., Snodgrass & Helier, nos. 54 (hb. Gr.), 853 (hb. Gr.), 868 (hb. Gr.) ; southern part, Baur, no. 207 (hb. Gr.) ; Tagus Cove, 1300 m. alt. VOL. XXXVIII.— 138 194 PROCEEDINGS OF THE AMERICAN ACADEMY. Snodgrass & Heller, nos. 883 (hb. Gr.), 884 (hb. Gr.). CHaArues Ist. : Andersson (hb. Gr.) ; Lee (hb. Gr. & hb. U. S. Nat. Mus.). James Ist.: Darwin. Endemic. T. strigosa, Anderss. (1), 207, & (2), 85, t. 9,f.3; Rob. & Greenm. (1), 147. — ALBEMARLE Ist.: southern part, Baur, no. 224 (hb. Gr.). Cuarues Ist.: wooded places, lower region, Andersson. CHATHAM Isu.: Andersson. Endemic. This species is reduced to 7. psilostachya by Hook. f. & Jacks. (Ind. Kew. ii. 1091), but it differs from that species considerably in pubescence and inflorescence, if (as seems prob- able) Andersson’s plant is represented by Baur’s no, 224. VERBENACEAE. AvicenniA, L. A. orrictnauis, L. Sp. 110 (1753). A. tomentosa, Jacq. Stirp. Am. 178, t. 112 (1763); Hook: £: (3); 199; Anderss.: (1), 201, & (2), 62; Rob. & Greenm. (1), 147.—Gaxrapacos Ips.: Hdmonston ; Habel. ALBEMARLE IsL.: Elizabeth Bay, about lagoons with Ahizophora, ace. to Mr. Heller. Cuarues Ist.: Cormorant Bay, Baur, no. 171 (hb. Gr.). CuatuamM Ist.: Darwin. INDEFATIGABLE IsL.: forming swamps in lagoons on the north coast, acc. to Mr. Heller. James Ist.: Andersson ; tree 8 to 6 m. high, along margin of a salt pond, James Bay, Snodgrass & Heller, no. 368 (hb. Gr.). Narsorouen Ist.: fringing lagoons on the east coast, acc. to Mr. Heller. Stymour Ist.: south, Snodgrass & Heller, no. 605 (hb. Gr.). Further distrib. general on trop. shores. CLERODENDRON, L. C. moLtLe, HBK. Nov. Gen. & Sp. ii. 244 (1817); Hook. f. (8), 195; Anderss. (1), 201, & (2), 82; Caruel (1), 622; Rose (1), 187; Rob. & Greenm. (1), 147. — Garapacos Ips.: Habel. ALBEMARLE IsL,: southern portion, Baur, no. 168 (hb. Gr.); Iguana Cove, rather com- mon from beach to 300 m. alt., Snodgrass & Heller, nos. 59 (hb. Gr.), 116 (hb. Gr.), 855 (hb. Gr.). CHarues Isu.: Darwin; Andersson ; Lee (hb. U. S. Nat. Mus.); A. Agassiz ; Snodgrass & Heller, no. 443 (hb. Gr.). CHatuam Ist. : Andersson ; Chierchia; A. Agassiz (hb. Gr.); in upper wooded region, Baur, no. 170 (hb. Gr.). James Ist. : Scouler ; Andersson ; common on lava coast, Snodgrass & Heller, no. 569 (hb. Gr.). Further distrib. Ecuador. FLORA OF THE GALAPAGOS ISLANDS. 195 C. sp. Hook. f. (4), 261, Anderss. (1), 201, & (2), 82.— CHaRLEs Ist.: EHdmonston, acc. to Hook. f., 1. ¢. C. sp. Hook. f., 1. c.; Anderss. ll. cc. — Cuartes Isi.: Hdmonston, ace. to Hook. f,, 1. ¢. Douranta, L. D. Piumrert, Jacq. Stirp. Am. 186, t. 176, f. 76 (1763). — ALBE- MARLE IsL. : mountain east of Tagus Cove, alt. 925 m., Snodgrass & Heller, nos. 248 (hb. Gr.), 906 (hb. Gr.). Widely distributed in trop. Am. The form on Albemarle has entire leaves and is closely matched by some specimens from Mexico. Lantana, L. L. pepuNcuLARIS, Anderss. (1), 200, & (2), 81; Rob. & Greenm. (1), 147; Z. sp. Rose (1), 187. Reduced to LZ. odorata, L., by Griseb. Fl]. Brit. W. Ind. 496, and with scarcely a doubt the Z. recta and L. canescens of Hook. f. (8), 195, and Anderss. ll. cc. and consequently ZL. odorata, Anderss. ll. ce. — Gatapacos Ips.: Andersson, no. 215 (hb. Gr.). Axsrinepon Ist.: Snodgrass & Heller, no. 813 (hb. Gr.). ALBEMARLE Isi.: Darwin (L. recta, Hook. f.) ; Andersson ; mountain north of Elizabeth Bay, Snodgrass & Heller, no. 293 (hb. Gr.) ; eastern portion, Cowley Bay, Baur, no. 174 (hb. Gr.) ; Iguana Cove, Snodgrass & Heller, no 64 (hb. Gr.); Tagus Cove, from beach to 300 m. alt., not common, Snodgrass & Heller, no. 201 (hb. Gr.). Barrineron Ist. : Snodgrass & Heller, no. 476 (hb. Gr.). Brxpioer Isi.: Baur, no. 187 (hb. Gr.) ; Snodgrass & Heller, no. 758 (bb. Gr.). CHarues Ist. : Darwin ; Andersson ; Lee (hb. U. S. Nat. Mus.); A. Agassiz (hb. U. S. Nat. Mus.); Baur, no. 173 (hb. Gr.); Snodgrass & Heller, no. 445 (hb. Gr.). Caatuam Isz.: Andersson ; Snodgrass & Heller, no. 515 (hb. Gr.), doubtful form. Duncan Ist.: Baur ; Snodgrass & Heller, no. 700 (hb. Gr.). GARDNER IsL.: Snodgrass & Heller, no. 613 (hb. Gr.). Hoop Ist.: Snodgrass & Heller, no. 736 (hb. Gr.). InperaticaBLe Isu.: Andersson; Snodgrass & Heller, no. 657 (hb. Gr.). James Ist.: Andersson ; the most abundant bush, everywhere in lava soil, 1 to 2 m. high, Snodgrass & Heller, no. 381 (hb. Gr.). Jervis Ist.: Baur, no. 176 (hb. Gr.). NaArsorovenr Isx.: southern part, 600 m. alt., Snodgrass & Heller, no. 351 (hb. Gr.). Tower Iszt.: Snodgrass & Heller, no. 806 (hb. Gr.). Endemic ? While treating the plants, here mentioned, provisionally as a single endemic species, I suspect that they may be ultimately identified with 196 PROCEEDINGS OF THE AMERICAN ACADEMY. one of the continental American species (cf. L. lilacina and L. canes- cens, FBK.), or segregated into several more or less distinct forms. The indefiniteness which now prevails regarding the S. American species of the genus is such as to render the further classification of the Galapageian forms, for the present, impracticable. LieriA, Houst. L. canescens, HBK. Nov. Gen. & Sp. ii. 263 (1817). L. lanceolata, Rose (1), 187, not Michx. JL. nodiflora, Cham. Linnaea, vii. 213 (1832) ; Rob. & Greenm. (1), 147; not Michx.— Cuaruss Isx.: Lee (hb. U.S. Nat. Mus.); Baur. Cuaruam Isi.: A. Agassiz (hb. U.S. Nat. Mus.) ; Baur, no. 178 (hb. Gr.), a green form. Duncan Isu.: Snodgrass & feller, no. 709 (hb. Gr.). Hoop Ist.: around a mud lake, Snodgrass & Heller, no. 755 (hb. Gr.). Further distrib. S. Am. L. ROSMARINIFOLIA, Anderss. (1), 198, & (2), 80; Rob. & Greenm. (1), 147.— Asinepon Isi.: Snodgrass & Heller, no. 827 (hb. Gr.). ALBEMARLE Ist.: in very dry places of the middle region, Andersson ; Elizabeth Bay, Snodgrass & Heller, no. 280 (hb. Gr.); eastern part, Buur, no. 179 (hb. Gr.) ; Tagus Cove, not common, 150 to 460 m. alt., Snodgrass & Heller, nos. 168 (hb. Gr.), 147 (hb. Gr.) ; mountain east of Tagus Cove, Snodgrass & Heller, nos, 233, 251, 888, 890, & 896 (all in hb. Gr.). Nos. 888, 890 & 896 show that the leaves on some branches become strongly toothed. Endemic. Baur’s nos. 181 and 182 (both in hb. Gr.) from eastern Albemarle are probably branches of this species (sterile). L. sALiciroLiA, Anderss. (1), 198, & (2), 80.— Cuartes IsL.: in woods on the side of the mountain summit. Andersson (hb. Gr.). Endemic. STACHYTARPHETA, Vahl. S. picnoToma, Vahl, Enum. i. 207 (1804); Caruel (1), 622. S. ur- ticifolia, Sims, Bot. Mag. t. 1848 (1816). Verbena dichotoma, Ruiz & Pav. FI. Per. i. 23, t. 34, fig. b (1798). ouchea sp. Rob. & Greeum. (1), 147. — Cuartss Isu.: Chierchia, acc. to Caruel, |. c.; Lee (hb. Gr.) ; Baur, without number (hb. Gr.). Further distrib. trop. and subtrop. Am. VERBENA, L. V. carouina, L. Syst. ed. 10, 852 (1760); Mill. Dict. ed. 8, no. 7. V. polystachya, ABK. Nov. Gen. & Sp. ii. 274 (1817); Hook. f. (3), FLORA OF THE GALAPAGOS ISLANDS. 197 195, as var. V. caroliniana, Anderss. (1), 199, & (2), 81. — James Is..: Darwin, ace. to Hook. f. Further distrib. Mex., Andean S. Am. V. grisea, Rob. & Greenm. (1), 142, 147, where by typographical error ascribed to Albemarle Island. — Duncan Isu.: Baur, no, 180 (hb. Gr.). Endemic. V. tiroraLis, HBK. Nov. Gen. & Sp. ii. 276, t. 187 (1817) ; Hook. f. (3), 195; Anderss. (1), 200, & (2), 81; Rob. & Greenm. (1), 147.— Cuares Ist.: Darwin; Baur, no. 172 (hb. Gr.). CuatrHam Is..: Andersson (hb. Gr.). Further distrib. Mex., S. Am. V. OFFICINALIS, L. Sp. 20 (1753); Hook. f. (1), 194; Anderss. (1), 199, & (2), 81.— James Isx.: Darwin. Tropics of both hemispheres. LABIATAE. Hyptis, Jacq. H. capirata, Jacq. Ic. Pl. Rar. i. t. 114; Hook. f. (4), 261; Anderss. (1), 197, & (2), 80. — Cuartes Isi.: Hdmonston. Further distrib. trop. S. Am., Mex., W. Ind. H. suBvertici“tyata, Anderss. (1), 197, & (2), 80. — ALBEMARLE Isu.: in very sterile places, middle region, Andersson (hb. Gr.). INDE- FATIGABLE Isu.: Baur. (Of this plant, called H. spicigera by Rob. & Greenm. (1), 147, unfortunately no specimen was retained at herb. Gray, and it is now impossible to examine the material. I have little doubt, how- ever, that it was H. subverticillata.) James Isxu.: James Bay, common on lava rocks, Snodgrass & Heller, no. 356 (hb. Gr.). NARrRBOROUGH Isu.: northern part, Snodgrass & Heller, no. 299 (hb. Gr.). Endemic. Satvia, L. S. OCCIDENTALIS, Sw. Prodr. 14 (1788), & Fl. Ind. Oce. i. 43; Hook. f. (3), 200; Anderss. (1), 196, & (2), 79; Rob. & Greenm. (1), 147.— ALBEMARLE Ist.: Iguana Cove, Snodgrass & Heller, nos. 61 (hb. Gr.), 96 (hb. Gr.); ,Tagus Cove, Snodgrass & Heller, no. 217 (hb. Gr.). Cuartes Isu.: Darwin; in dry places, upper region, Andersson, (hb. Gr.); Baur, no. 167 (hb. Gr.); Snodgrass & Heller, no. 407 (hb. Gr.). Cuatuam Ist.: southwest end, middle region, Baur, no. 166 (hb. Gr.). James Isu.: Darwin ; common on rocks near beach, Snodgrass & Heller, no. 362 (hb. Gr.). Further distrib. Mex., W. Ind., S. Am. This may perhaps have been the sterile “ Lamiacea” collected by Chierchia and mentioned by Caruel (1), 622. 198 PROCEEDINGS OF THE AMERICAN ACADEMY. S. prostrata, Hook. f. (8), 200; Anderss. (1), 197, & (2), 79. — JAMES Isxt.: Darwin. Endemic. S. TILIAEFOLIA, Vahl, Symb. iii. 7 (1794); Hook. f. (8), 200; An- derss. (1), 196, & (2), 79. — Cuarues Isu.: Darwin, acc. to Hook. f., l.e. Further distrib. Mex., trop. S. Am. Treucrium, L. T. inFLATUM, Sw. Prodr. 88 (1788); Hook. f. (8), 201 ; Anderss. (1), 197, & (2), 79; Rob. & Greenm. (1), 147. — CHarues Isx.; Dar- win; grassy places, upper region, Andersson (hb. Gr.). CHATHAM IstL.: southwest end, middle region, Gaur, no. 164 (hb. Gr.). Further distrib. S. Am. SOLANACEAE. Acnistus, Schott. A. ELLIpTIcus, Hook. f. in Miers, Lond. Jour. Bot. iv. 343 (1845), & (3), 203; Anderss. (1), 218, & (2), 91 (Ancistus). — Cuartes IsL.: Darwin. Endemic. A. insularis, nov. sp., frutex; ramis a cortice griseo-brunnea tectis ; ramulis pallidioribus in specimine siccato rugoso-striatis apice foliatis ; foliis approximatis alternis obovatis integris penninervatis supra atroviridibus parce pubescentibus subtus pallidioribus molliter pubescentibus basi cu- neatis apice rotundatis; pilis indumenti crispis; umbellis sessilibus 2—4- floris; pedicellis elongatis filiformibus nutantibus subglabris apice in calycem incrassatis; calyce campanulato tenui subglabro truncato; corolla tubulosa gradatim ampliata pilis crispis pubescenti; limbo 5-fido; dentibus deltoideis subobtusis; antheris in parte faucium superiori subsessilibus ; stylo recto filiforme glabro ; stigmate capitato. — A. sp. Rob. & Greenm. (1), 147. — Cuaruam Ist.: southwest end, middle region, June, 1891, Baur, no. 193 (hb. Gr.). Endemic. Leaf-blade 6 to 8 mm. long, half as broad; petiole 1.5 to 2 cm. long; pedicels 2 to 2.5 cm. long; corolla 3 cm. long; flowers more inclined to be nodding or even pendulous than indicated on the plate. This species must in many points resemble A. ellipticus, Hook. f. That, however, is described as having leaves attenuate at both ends and glabrous, the calyx-limb 5-crenate, the style somewhat curved and the stigma obscurely bilobed. Parte 2, Fic. 3. FLORA OF THE GALAPAGOS ISLANDS. 199 Capsicum, L. C. annuum, L. Sp. 188 (1758) ; Anderss. (1), 215, & (2), 90; Rob. & Greenm. (1), 147. — Cuartes Ist. : Andersson (hb. Gr.). CHATHAM Ist.: Baur. Widely distrib. in trop. reg. Datura, L. D. Tatura, L. Sp. ed. 2, 256 (1762). — Cuartes Ist.: Snodgrass & Heller, no. 412 (hb. Gr.). Further distrib. U. S., Mex., S. Am. D. sp. — ALBEMARLE Ist.: Iguana Cove, Snodgrass & Heller, no. 124 (hb. Gr.). Differing from the preceding in the having a fine but — rather copious pubescence throughout, and fewer weaker bristles on the fruit. Lycivum, L. L. sp.— Hoop Ist.: Baur, and probably the same from SrEYmMourR Isxi.: south, Snodgrass & Heller, no. 584 (hb. Gr.). » Both sterile and indeterminate. Lycorersicum, Hill. L. escuLentouM, Mill., var. minor, Hook. f. (3), 202 (Lycopersicon) ; Anderss. (1), 216, & (2), 90. L. peruvianum, Anderss. (1), 216, & (2), 91, at least as to his own plant from Chatham, which entirely lacks the large foliaceous bracts of the S. Am. plant. JZ. esculentum, Rob. & Greenm. (1), 147.— Astnepon Isu.: Snodgrass & Heller, no. 843 (hb. Gr.). ALBEMARLE IsL.: Andersson ? southern part, Baur, no. 188 (hb. Gr.); Pt. Christopher, Snodgrass & Heller, no. 928 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 911 (hb. Gr.). Cuatuam Isxi.: Andersson. Hoop Ist.: Baur, no. 189 (hb. Gr.); Snodgrass & Heller, no, 741 (hb. Gr.). James Ist.; Darwin ; Snod- grass & Heller, no. 399 (hb. Gr.). Narsoroven Ist.: Mangrove Point, on rocks above beach, Snodgrass & Heller, no. 305 (hb. Gr.). Further distrib. S. Am., Polynesia. L. peruvianum, Mill. var. parvirLtorum, Hook. f. (8), 202 (Lycopersicon peruanum). — Cuatnam Ist.: Darwin, ace. to Hook. f. Further distrib. Andean S. Am. I have seen no specimens from the Galapagos Ids. with the foliaceous bracts said to be characteristic of this species. A variety of L. peruvianum was collected on the Galapagos Islands by Habel. L. PIMPINELLIFOLIUM, Mill. Dict. ed. 8, no. 4 (Lycopersicon, 1768) ; Dun. in DC. Prodr. xiii. pt. 1, 28; Hook. f. (8), 202 (Lycopersicon) ; 200 PROCEEDINGS OF THE AMERICAN ACADEMY. Anderss. (1), 216 & (2), 91. Solanum pimpinellifolium, L. Amoen. Acad. iv. 268 (1759).— GaLapacos Ips.: Goodridge (hb. Gr.). Cuaries Isu.: Andersson. CuatHam Iszt.: Darwin ; Andersson. JAmEsS Ist.: Andersson. Further distrib. Andean. L. sp. —Cuatuam Isz.: Snodgrass & Heller, no. 526 (hb. Gr.). Very likely a mere variety of L. escudentum, Mill., but although minutely glandular, quite destitute of the spreading-hirsute character shown by the other Galapageian specimens at hand. s Nicotiana, L. N. etutinosa, L. Sp. 181 (1753); Hook. f. (3), 202 ; Anderss. (1), 215, & (2), 89. — Cuartes Isut.: Hdmonston ; Darwin; Andersson. Further distrib. Andean S. Am. N. Taspacum, L. Sp. i. 180 (1753); Caruel (1), 622. — Coarurs Ist.: Chierchia,:acc. to Caruel, 1. c. Further distrib. trop. Am. and widely introduced through cult. N. sp. Hook. f. (4), 261.— Cartes Ist.: Edmonston, acc. to Hook*rt., (xe. Puysatts, L. P. aneuiata, L. Sp. 183 (1753); Anderss. (1), 215, & (2), 90; Rose (1), 187. — Cuarues Isi.: Andersson ; A. Agassiz, ace. to Rose, l.c. Cuatuam Ist.: Snodgrass & Heller, no. 522 (hb. Gr.). Further distrib. general in trop. Am. P. rxocarpa, Brot. in Hornem. Hort. Hafn. Suppl. 26 (1819) ; Rydberg, Mem. Torr. Club, iv. 334. P. aequata, Jacq. f., acc. to Nees, Linnaea, vi. 470 (1831). P. pubescens, Rob. & Greenm. (1), 147, as to pl. Charles. — Cuar.es Isi.: Cuevas Bay, Baur, no. 186 (hb. Gr.) ; Snodgrass & Heller, no. 434 (hb. Gr.). Widely distrib. in Am. P. pupescens, L. Sp. 183 (1753); Rob. & Greenm. (1), 147, as to pl. Chatham; Rydberg, Mem. Torr. Club, iv. 322. — ALBEMARLE IsL.: Tagus Cove, abundant in shady places near beach, Snodgrass & Heller, nos. 185 (hb. Gr.), 187 (hb. Gr.). Binpior Ist. : Snodgrass & Heller, no. 768 (hb. Gr.). Cuartes Isz.: Snodgrass & Heller, no. 4383 (hb. Gr.). CratHam Ist.: southwest end, upper region, Baur, no. 185 (hb. Gr.). Hoop Isu: Snodgrass & Heller, no. 740 (hb. Gr.), a robust large-fruited form of doubtful identity. JAmes Isi.: James Bay, in sand near beach, Snodgrass & Heller, no. 388 (hb. Gr.). Nar- FLORA OF THE GALAPAGOS ISLANDS. 201 BOROUGH IsL.: southern part, Snodgrass & Heller, no. 303 (hb. Gr.). Widely distrib. in Am. P. sp. Hook. f. (4), 261. — Cuartes Ist.: Hdmonston. Soranum, L. S. EpmonsTonel, Hook. f. (3), 201; Dun. in DC. Prodr. xiii. pt. 1, 45; Anderss. (1), 216, & (2), 90.— CHartes Ist.: Hdmonston. Endemic. S. nigRuM, L. Sp. 186 (1753); Hook. f. (3), 201; Anderss. (1), 216, & (2), 90; Rob. & Greenm. (1), 147. This is, with little doubt, the S. Berterii of Caruel (1), 622, perhaps also of ‘* Hort. Par, 1835” [1829 ?], a nomen nudum, so far as I have learned. — ALBEMARLE IsL.: southern part, Baur, no. 192 (hb. Gr.). CHarues Isu.: Darwin ; Andersson (hb. Gr.). Cuataam Ist: Chierchia; Snodgrass & Hel- igo. o2) (hb. Gr.). Duncan Isu.3 Baur, no. 191 (hb. ‘Gr.). James Ist.: Scouler; Darwin ; James Bay, scattered on sandy beach, Snodgrass & Heller, no. 887 (hb. Gr.). Further distrib. general. Various forms have been distinguished as to foliage and pubescence. [S. ruBeRosum, L., was included by Andersson in his second work (p. 90) but only on the basis of cultivated specimens. | S. veRBASCIFOLIUM, L. Sp. 184 (1753); Jacq. Hort. Vindob. i. t. 13; Hook. f. (8), 201; Anderss. (1), 215, & (2), 90.— CHarRLes Ist.: Andersson. James Ist.: Darwin. NarsorouaH Ist.: south- ern part, rare, 650 m. altitude, Snodgrass & Heller, nos. 329 (hb. Gr.), 353 (hb. Gr.). Further distrib. wide in trop. reg. Andersson, ll. cc., distinguishes two Galapageian forms on foliar differences. S. sp. Hook. f. (4), 261.—Cuarues Ist.: Hdmonston, acc. to Hook. f. S. sp. Hook. f., 1. c. — Cuartes Isu.: Hdmonston, acc. to Hook. f. ( THINOGETON, Benth. T. Hooxert, Anderss. (1), 217. — INDEFATIGABLE IsL.: Andersson, Endemic. Omitted by Andersson from his second paper. T. Mrersi, Miers, Ann. & Mag. Nat. Hist. ser. 2, iv. 359 (1849) ; Anderss. (1), 217, & (2), 91; Dun. in DC. Prodr, xiii. 689. Dictyo- calyx Miersii, Hook. f. (3), 203; Dun. in DC. Prodr. xiii. 588. Caca- bus Miersti, Wettst. in Engl. & Prantl, Nat. Pflanzenf. iv. Ab. 3b, 16 (1891). Solanacea, Rob. & Greenm. (1), 147. — ALBEMARLE Ist. : Macrae ; Black Bight, Snodgrass & Heller, no. 258 (hb. Gr.) ; Iguana 202 PROCEEDINGS OF THE AMERICAN ACADEMY. Cove, Snodgrass & Heller, no. 42 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 167 (hb. Gr.). Barrineton Isx.: Snodgrass & Heller, no. 475 (hb. Gr.). CHarzes Isxt.: Darwin ; Andersson. CHATHAM Ist.: Andersson; Snodgrass & Heller, no. 523 (hb. Gr.). CuL- PEPPER Ist.: Snodgrass & Heller, no. 2 (hb. Gr.), a tomentose form with more sharply toothed leaves. Hoop Ist.: Baur, no. 194 (hb. Gr.). NarporouGu Ist.: Mangrove Point, Snodgrass & Heller, no. 807 (bb. Gr.); northern part, Snodgrass & Heller, no. 302 (hb. Gr.). Endemic. Mr. Heller remarks that this species as it occurs upon Cul- pepper Island recalls a cucumber vine and bears large brown berries. This seems to be a well marked genus, not to be united with Cacabus. SCROPHULARIACEAE. CaprariA, L. C. srrtora, L., var. PILOsA, Griseb. Fl. Brit. W. Ind. 427 (1861). C. biflora, Anderss. (1), 218, & (2), 91; Rob. & Greenm. (1), 147.— Cuartes Ist.: in very dry places, Andersson (hb. Gr.); Baur, no. 184 (hb. Gr.). Cuatuam Iszt.: Snodgrass & Heller, no. 509 (hb. Gr.). Further distrib. trop. and subtrop. regions of the New World. C. peruviAna, Benth. in DC. Prodr. x. 430 (1846). — CHartLes Ist.: Lee (hb. U. S. Nat. Mus.). Further distrib. coast of Ecuador to the uplands of Peru. Well marked, although by Hook. f. & Jacks. Ind. Kew. referred to ©. biflora. Scopartia, L. S. putcis, L. Sp. 116 (1753); Hook. f. (8), 200; Anderss. (1), 218, & (2), 91; Caruel (1), 622; Rob. & Greenm. (1), 147. — Cuartes Ist.: Darwin; in arid grassy places of the middle and upper region, Andersson ; Baur, no. 183 (hb. Gr.). CHatruam Ist.: Chierchia, ace. to Caruel, ].c. Further distrib. general in trop. and subtrop. Am. ScrROPHULARIACEA, Hook. f. (8), 200. A dwarf indeterminate plant. — James Isu.: Darwin, acc. to Hook. f. (3), 200. BIGNONIACEAE? Tecoma, Juss. ? T. sp. ? Caruel (1), 622. — Cuatuam Ist.: Chierchia, acc. to Caruel, l.c. Sterile and doubtful even as to family. i) co) eo FLORA OF THE GALAPAGOS ISLANDS. ACANTHACEAE. DICLIPTERA, Juss. D. PERUVIANA, Juss. Ann. Mus. Par. ix. 268 (1806); Nees in DC. Prodr. xi. 478; Hook. f. (8), 195; Anderss. (1), 219, & (2), 92. Dianthera mucronata, Ruiz & Pav. FI. Per. i. 11, t. 16, fig. a (1798). Justicia peruviana, Lam. Dict. i. 633 (1783).— James Isu.: Darwin, ace. to Hook. f., 1. c. Further distrib. Andes of Peru. Justicia, L. J. (Leprostacuya) galapagana, Lindau, nov. sp., “herbacea tota glanduloso-pilosa caulibus sexangularibus vel subteretibus, patente pilosis. Folia petiolis 1-2 cm. longis ovata basi rotundata et subito angustata, apice sensim acuminata, acutiuscula, margine integro, cystolithis vix visi- bilibus. Inflorescentiae pauciflorae, axillares, dichotomae, folia aequan- tes, apice spiciformes, floribus in axillis bractearum alternantibus. Pedicelli subnulli. Bracteae bracteolaeque subulatae, 0.2 mm. longae, pubescentes pilis glandulosis intermixtis. Calycis laciniae 4, subulatae, 4 mm. longae, 0.75 mm. latae, pubescentia ut in bracteis. Corolla extus dense pubescens tubo 4 mm. longo, basi 2 mm. diametro et apice usque ad 3 mm. ampliato. Labium superum 4 mm. longum, basi 4 mm. latum, dentibus apice minimis, intus rugula’ instructum, inferum 4 mm. longum, lobis 3 rotundatis, 2mm. diam. metientibus. Filamenta glabra, 3 mm. jonga, antherum loculo supero 1 mm. longo obtuso, infero 1 mm. longo basi in calcar 0.5 mm. longum producto. Pollinis granula pro genere typica, 46-58 w longa et 27-30 » diam. Discus adest. Ovarium 1.5 mm. altum, pubescens. Stylus 6 mm. longus, pilosus. Capsula 12 mm. longa, 4 mm. lata, usque ad medium fere in stipitem contracta, pubescens pilis glanduligeris intermixtis, jaculatoribus hamatis, 0.2 mm. longis. Semina 4, brunneo-tomentosa, lentiformis, 0.38 mm. diametro.” — Apincpon Ist: alt. 520 m., Snodgrass & Heller, no. 820 (hb. Gr.). “Obs. Proxima Justiciae Pringlei~ Robins., a qua differt pubescentia densiore et magis glutinosa, stylo ovarioque pilosis et maxime seminibus, quae sunt in J. Pringlei foveolata et pubescentia, sed in J galapa- gana laevis et brunneo-tomentosa.” 1 “Qugula, i.e., ruga longitudinalis a duobus lobis membranae labii superi for- mata, in qua stylus est inclusus.” 204 PROCEEDINGS OF THE AMERICAN ACADEMY. TETRAMERIUM, Nees. T. nisprpum, Nees in DC. Prodr. xi. 468 (1847); Gray, Syn. Fl. ii. 330; Hemsl. Biol. Cent.-Am. Bot. ii. 525. Probably the Tetrame- rium, n. sp.? Hook. f. (3), 195; Anderss. (1), 195 & (2), 78. — ALBE- MARLE Ist.: Iguana Cove, Snodgrass & Heller, nos. 34 (hb. Gr.) 197 (hb. Gr.) ; mountain north of Elizabeth Bay, Snodgrass & Heller, no. 288 (hb. Gr.) ; Tagus Cove, from the coast to 450 m. alt. ; Snodgrass & Heller, no. 213 (hb. Gr.). James Ist.: Darwin (identity doubtful). Further distrib. Cent. Am., Mex., southwestern U. S. PLANTAGINACEAE. PLANTAGO, L. P. masor, L. Sp. 112 (1753); Caruel (1), 624. — Cuatuam Ist.: Chierchia. Further distrib. cosmop. P. TOMENTOSA, var. (?) PUMILA, Hook. f. (8), 194 (where by typo- graphical error published as Plumbago), & (4), 262; Anderss. (1), 171, & (2), 65.—James Isu.: Darwin, acc. to Hook. f., 1. c. Identity doubtful. RUBIACEAE. BorreriA, Meyer. B. BasaLis, Anderss. (1), 191, & (2), 76, t. 8, f. 4. — CHatuam Ist: in densely grassy regions, Andersson. Endemic. B. Baurn, Rob. & Greenm. (1), 140, 146. Spermacoce Baurit, Rob. & Greenm. (1), 141. — CuatHam IsL.: lower region, southwest end, Baur, no. 144 (hb. Gr.). Endemic. B. pispeRsA, Hook. f. (8), 217; Anderss. (1), 191, & (2), 76, t. 8, f. 1; Rob. & Greenm. (1), 146. — ALBEMARLE IsL.: Iguana Cove, Snodgrass & Heller, no. 137 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 215 (hb. Gr.). CHarues Ist.: Darwin; Baur. Cuatuam Ist.: southwest end, middle region, Baur, no. 743 (hb. Gr.). INDEFATIGABLE IsL.: grassy places of the lower region, Andersson (hb. Gr.). JAmEs Isi.: Darwin. Endemic. B, pivaricaTa, Hook. f. (8), 219; Anderss. (1),.198, & (2), 77; Rob. & Greenm. (1), 146. — Cuartes Ist.: Darwin; Cuevas Bay, Baur, no. 141 (hb. Gr.). Endemic. FLORA OF THE GALAPAGOS ISLANDS, 205 B. ERICAEFOLIA, Hook. f. (8), 218; Anderss. (1), 192, & (2), 77, t. 8, f. 2; Rob. & Greenm. (1), 146.— Asinepon Ist.: Snodgrass & Heller, no. 831 (hb. Gr.). ALBEMARLE IszL.: Cowley Bay, Aaur, no. 139 (hb. Gr.) ; Elizabeth Bay, Snodgrass & Heller, no. 275 (hb. Gr.) ; Iguana Cove, Snodgrass & Heller, no. 38 (hb. Gr.); mountain east of Tagus Cove, alt. 615 m., Snodgrass & Heller, no. 236 (hb. Gr.) ; southern portion, Baur, no. 137 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, no. 157 (hb. Gr.), Caries Iszt.: Cormorant Bay, Baur, no. 138 (hb. Gr.). CnatHam Ist.: Darwin; Andersson. Narporouca Isx.: Mangrove Point, common, scattered in crevices of lava from the beach to 615 m. alt., Snodgrass & Heller, no. 308 (hb. Gr.). Endemic. The forms here included in this species differ from each other somewhat in the size, acuteness and pubescence of the leaves. It is not improb- able that some of them may be B&B. basalis, Anderss., Bb. parvifolia, Hook. f., or B. falcifolia, Hook. f., nearly related species which, to judge from the material at hand, do not appear likely to prove distinct in nature. B. rauciro.iA, Hook. f. (3), 219; Anderss. (1), 193, & (2), 77. B. lancifolia, Anderss. (1), 191, & (2), 76, evidently a typographical error for falcifolia. — ALBEMARLE IsL.: Macrae? ace. to Hook. f., 1. c. Endemic. B. GALAPAGEIA, Rob. & Greenm. (1), 140, 146. Spermacoce gala- pageta, Rob. & Greenm. (1), 141. —- Duncan Isu.: Baur, no. 145 (hb. Gr.). Endemic. B. LINEARIFOLIA, Hook. f. (3), 217; Anderss. (1), 191, & (2), 76. — JAMES Isu.: Darwin. Endemic. B. ovatts, Anderss. (1), 192, & (2), 76, t. 8, f. 3. Leaves 6 to 8 mm. long, rounded at the apex. — CuHARLes Isi.: in dry and grassy places on the upper part of the island, Andersson (hb. Gr.). Endemic. Forma abingdonensis. J. ovalis, Rob. & Greenm. (1), 149, as to pl. Abingdon. Foltis ad 1.5 cm. longis plus minusve acutis, — ABING- pon Ist.: Baur, no. 142 (hb. Gr.). Endemic. B. pacirica, Rob. & Greenm. (1), 140, 146. Spermacoce pacifica, Rob. & Greenm. (1), 141. —INDEFATIGABLE IsL.: south of Conway Bay, Baur, no. 146 (hb. Gr.). Endemic. B. Parviroxia, Hook. f. (8), 218; Anderss. (1), 193, & (2), 77. — GacapaGos Ins.: Habel. ALBEMARLE Isx.: Macrae. Endemic. A pubescent form of B. ericaefolia? 206 PROCEEDINGS OF THE AMERICAN ACADEMY. B. perpusitua, Hook. f. (3), 218; Anderss. (1), 192, & (2), 77. — James Isu.: Darwin. Endemic. B. roTunpirourA, Anderss. (2), 77.— INDEFATIGABLE IsL.: in grassy places, Andersson. Endemic. B. superecta, Hook. f. (3), 217; Anderss. (1), 191, & (2), 76. DB. linearifolia, Rob. & Greenm. (1), 146 (at least in part), not Hook. f. — ALBEMARLE Isxt.: Macrae ; Iguana Cove, Snodgrass & Heller, no. 129 (hb. Gr.) ; southern part, Baur, nos. 135 (hb. Gr.), 140 (hb. Gr.) ; Ta- gus Cove, near beach, Snodgrass & Heller, no. 204 (hb. Gr.), probably the forma 8 of Hook. f., 1.c. Barrineron Isx.: Baur (identity doubt- ful). Endemic. B. sp. Slender simple stems 5 to 7 cm. high from an apparently annual root: leaves oblong-lanceolate, hispidulous on and near the strongly revolute margin. — CuaTuam Isu.: Snodgrass & Heller, no. 536 (hb. Gr.). Perhaps a distinct species, but more probably a starved state of one of the above. Curococca, P. Br. C. racemosa, L. Syst. ed. 10, 917 (1760); Jacq. Stirp. Am. 68; Hook. f. (3), 220; Anderss. (1), 195, & (2), 78. ©. trisperma, Hook. f. (3), 219; Anderss. (1), 194, & (2), 78,t.9,f.2. C.? Hook.f. (3), 220. — Garapacos Ips.: Habel. Axstnepon Ist.: Snodgrass & Heller, no. 823 (hb. Gr.). ALBEMARLE Isx.: Macrae; Andersson; Elizabeth Bay, Snodgrass & Heller, no. 267 (hb. Gr.) ; Iguana Cove, Snodgrass & feller, nos. 60 (hb. Gr.), 874 (hb. Gr.) ; Tagus Cove, 150 to more than 650 m., Snodgrass & Heller, nos. 144 (hb. Gr.), 172 (hb. Gr.), 899 (hb. Gr.) ; mountain east of Tagus Cove, alt. 620 m., Snodgrass & Heller, no. 235 (hb. Gr.), alt. 930 m., Snodgrass & Heller, no. 234 (hb. Gr.). Brinptoe Iszt.: Snodgrass & Heller, no. 789 (hb. Gr.). Cuares Isz.: Andersson (hb. Gr.). Cuaroam Ist.: Darwin; An- dersson. JAmeES Isu.: Scouler. NARBorouGH Isx.: southern part, 300 to 600 m. alt., scattered but common, 3 to 5 m. in height, Snodgrass & Feller, no. 350 (hb. Gr.). Widely distrib. in trop. Am. The size of the leaves varies greatly, and changes somewhat with the age of the plant; the fruit is often 2-carpelled and 3-carpelled on the same individual. Diopra, L. D. Raptxa, Cham. & Schlecht. Linnaea, iti. 342 (1828); Schumann in Mart. Fl. Bras. vi. pt. 6, 25. Dorreria (Spermacoce asperifolia, Mart. FLORA OF THE GALAPAGOS ISLANDS, 207, & Gal. ?), Rob. & Greenm. (1), 146. — Caatuam Ist.: southwest end, upper region, Baur, no. 147 (hb. Gr.). Further distrib. Brazil. Psycnortria, L. P. aneustata, Anderss. (1), 193, & (2), 78, t. 9, f.1. Probably P. sp. ? Hook. f. (5), 220. — Cuarues Ist.: Darwin?; in most fertile forest regions of the island, Andersson. Endemic. P. ruFIPES, Hook. f. (3), 220; Anderss. (1), 193, & (2), 77; Rob. & Greenm. (1), 146.— Asinapon Ist.: Snodgrass & Heller, no. 817 (hb. Gr.), ALBEMARLE Isx.: Iguana Cove, below 300 m. alt., Snod- grass & Heller, nos. 117 (hb. Gr.), 864 (hb. Gr.), 865 (hb. Gr.). Cuarves Isu.: in the most fertile forests, Andersson; Lee (hb. U. S. Nat. Mus.). CHaTHam Isx.: southwest end, middle region, Laur, no. 148 (hb. Gr.). James Isxt.: Darwin. Endemic. Reitspunium, Benth. & Hook. f. R. sp. tubia sp. Hook. f. (8), 216; Anderss. (1), 190, & (2), 75; near fe. Relbun. — Cuarwes Isu.: Darwin. Further distrib, Peru, acc. to’ Hook. f., I. c. SPERMACOCE, L. S. renuior, L. Sp. 102 (1753), excl. syn. Dill.; Hook. f. (8), 219; Anderss. (1), 193, & (2), 77; Rob. & Greenm. (1), 146. — CuatTHam Ist.: southwest end, upper region, Laur, no. 136 (hb. Gr.). JAMEs Ist.: Darwin. Widely distrib. in trop. and subtrop. Am. CUCURBITACEAE. Citrutius, Neck. C. vutearts, Schrad. ex Eckl. & Zeyh. Enum. 279 (1836), & Lin- naea, xii. 412; Cogn. in DC. Monogr. iii. 508. Cucurbita Citrullus, L. Sp. 1010 (1753). Cucumis Citrullus, Ser. in DC. Prodr. iii. 301 (1828) ; Anderss. (1), 224, & (2), 95.—CuarR.es Isxt.: Andersson, no. 166. Widely distrib. in warm countries. CucursitTa, L. C. Pero, L. Sp. 1010 (1753); Cogn. in DC. Monogr. iii. 545. C. Melopepo, L. 1.c.; Anderss. (1), 223, & (2), 94. Cartes Ist.: culti- vated ground, upper region, Andersson. Cosmopolitan. 208 PROCEEDINGS OF THE AMERICAN ACADEMY. ELATERIUM, Jacq. E. corpatoum, Hook. f. (3), 224; Anderss. (1), 224, & (2), 95; Cogn. in DC. Monogr. iii, 859.— James Ist.: Darwin (hb. Kew) ; Andersson. Endemic. Momorpica, L. M. CuaranttA, L. Sp. 1009 (1753); Sims, Bot. Mag. t. 2455; Cogn. l.c. 436; Rob. & Greenm. (1), 146 (Charanta). — ALBEMARLE IsL. : southern part, Baur, no. 158 (hb. Gr.). Widely distrib. in trop. reg. Sicyos, L. S. vitLosus, Hook. f. (3), 223; Anderss. (1), 224, & (2), 95; Cogn. l. c. 874. — Coartes Isut.: Darwin, acc. to Hook. f. Endemic. CAMPANULACEAE. Lope.ia, L. L. xALApPENsIs, HBK. Nov. Gen. et Sp. iii. 315 (1818); Hook. f. (3), 206; Anderss. (1), 190, & (2), 75. — CHarLes IsL. and JAMES Ist.: ace. to Hook. f., probably collected by Darwin as suggested by Andersson. Further distrib. Mex., W. Ind., S. Am. to Peru. GOODENIACEAE. ScaEVOLA, L. S. Lopetra, Murr. Syst. ed. 18, 178 (1774). S. Plumiert, Vahl, Symb. ii. 36 (1791); Hook. f. (8), 205; Anderss. (1), 190, & (2), 75. Lobelia Plumieri, L. Sp. 929 (1753). — Gavapagos Ips.: Hdmonston (hb. Gr.). CuatHam Isx.: Darwin ; Andersson. Widely distrib. in warm countries. COMPOSITAE. ACANTHOSPERMUM, Schrank. A. LECOCARPOIDES, Rob. & Greenm. (1), 141, 146.— Hoop Ist.: Baur, no. 128; Snodgrass & Heller, no. 744 (hb. Gr.). Endemic. A. microcarpum, nov. sp., annuum erectum ramosum 3 dm. altum ; caule terete albide hirsuto ; foliis oppositis obovato-rhomboideis crenulatis vel obsolete dentatis 3-nervatis parce hirsutis subtus haud vel paulo pali- FLORA OF THE GALAPAGOS ISLANDS. 209 dioribus apice obtusis basi longiuscule angustatis sessilibus 3-4.5 cm. longis 1.5—2 cm. latis; capitulis sessilibus ; involucri squamis exterioribus 4—6 oblongis obtusis conspicue ciliatis 4 mm. longis; fructibus triangu- laribus 6 mm, longis compressis pallidis minute granulatis et spinis brevibus conicis haud vel paulo uncinatis armatis; floribus disci circa 7; corollis pallidis, tubo gracile faucibus subnullis limbo ampliato. —CuHar es Is_.: May, 1899, Snodgrass & Heiler no, 446 (hb. Gr.). Endemic. Nearly related to A. hispidum, DC., but differing considerably in the fruit, as will be seen from PLATE 1, FIGURES 3 and 4, where the fruits of both species are contrasted. AGERATUM, L. A. LATIFOLIUM, Hemsl. Biol. Cent.-Am. Bot. ii. 82 (1881), not Cav. (Coelestina latifolia, Benth. in Oerst. Vidensk. Meddel. 1852, p. 71; Anderss. (1), 175, & (2), 67; Caruel (1), 623. A. conyzoides, Hook. f. (3), 207; Anderss. (1), 175, & (2), 67; Rob. & Greenm. (1), 146; not L. — Cuartss Ist.: Darwin ; Andersson ; Baur ; Snodgrass & Heller, no. 423 (hb. Gr.). CHataam Isu.: Chierchia, acc. to Caruel, 1. ¢. Further distrib. Costa Rica. APLOPAPPUS, Cass. A. tanatus, Hook. f. (3), 215; Anderss. (1), 177, & (2), 68 (Haplo- pappus). — GAtapaGcos Ips.: Du Petit-Thouars. Endemic. Baccuaris, L. B. prtutartis, DC. Prodr. v. 407 (1836); Hook. f. (4), 261; Anderss. (1), 178, & (2), 69; Gray, Syn. Fl. i. pt. 2, 222. — Cartes Isx.: Edmonston, acc. to Hook. f., 1. c. Further distrib. coastal region of California and Oregon. I cannot avoid a suspicion that the Galapageian plant (of which I have seen no specimen) will prove to be not the Cali- fornian species but one of several habitally similar plants of trop. S. Am. s B. Pinerata, DC., var. ancustissima, DC. Prodr. v. 420 (1836) ; Rob. & Greenm. (1), 146.— ALBEMARLE Is~L.: eastern part, Cowley Bay, Baur, no. 124 (hb. Gr.) ; mountain east of Tagus Cove, alt. 960 m., Snodgrass & Heller, no. 242 (hb. .Gr). Identification doubtful. Further distrib. coast of Chili. B. Sreerzi, Anderss. (1), 177, & (2), 68.— Cuartzs Isx.: in dry places in the middle of the island, Andersson (hb. Gr.). VOL, Xxxvi1I.—14 210 PROCEEDINGS OF THE AMERICAN ACADEMY. ‘ Bivens, L. B. cumiensis, DC. Prodr. v. 603 (1836).— ALBEMARLE IsL.: Tagus Cove, 1230 m. alt., Snodgrass & Heller, no. 887 (hb. Gr.). Further distrib. Chili. B. ritosa, L. Sp. 832 (1753). B. leucantha, Willd. Sp. iii. 1719 (1804) ; Anderss. (1), 187, & (2), 74; Caruel (1), 623; Rob. & Greenm., (1), 147. — AtpemArtE Ist.: Andersson. CHARLEs IsL.: Andersson. Cuaruam Isi.: Andersson; Chierchia ; southwest end, middle region, Baur (hb. Gr.); Snodgrass & Heller, no. 634 (hb. Gr.). Widely distrib. in trop. reg. B. rerracta, Brandegee, Zoe, i. 310 (1890). — AtBemarRte Ist.: Iguana Cove, Snodgrass & Heller, no. 92 (hb. Gr.); Tagus Cove, not common inland at 150 to 300 m. alt., Snodgrass & Heller, no. 178 (hb. Gr.). Cartes Ist.: Snodgrass & Heller, no 420 (hb. Gr.). Hoop Ist.: Snodgrass & Heller, no. 732 (hb. Gr.). James Ist.: James Bay, most abundant herb, growing everywhere in shade of bushes on lava soil, Snodgrass & Heller, no. 380 (hb. Gr.). NarsoroucH Ist.: southern part, abundant at 600 m. alt., Snodgrass & Heller, nos. 316 (hb. Gr.), 338 (hb. Gr.). Probably a recent introduction from Mexico or Lower California. Palmer’s no. 925 (coll. of 1890) from Manzanillo, Mexico, appears to be identical. Puare 2, rre. 4 (drawn from a Galapageian specimen). BLaInvILLEa, Cass. B. RHoMBOIDEA, Cass. Dict. xxix. 493 (1823); Anderss. (1), 178, & (2), 69; Rob. & Greenm. (1), 146. Verbesina dichotoma, Murr. Comm. Goett. ii. 15, t. 4 (1779). — ALBemaRLeE Isu.: Lee (hb. U. S. Nat. Mus.); Iguana Cove, Snodgrass & Heller, no. 99 (hb. Gr.) ; Tagus Cove, growing everywhere in tufa soil up to 300 m. alt., Snodgrass & Heller, no. 184 (hb. Gr.). Barrineton Ist.: Snodgrass & Heller, no. 482 (hb. Gr.). CHaries Ist.: Baur, no. 118 (hb. Gr.); Snodgrass & Heller, no. 442 (hb. Gr.). Cuaraam Ist.: Andersson (hb. Gr.) ; Snodgrass & Heller, no. 535 (hb. Gr.). Duncan Isu.: Baur, no. 119 (hb. Gr.) ; Snodgrass & Heller, no. 698 (hb. Gr.). Hoop Ist. : Baur, no. 117 (hb. Gr.) ; Snodgrass & Heller, no. 720 (hb. Gr.). INDEFAT- IGABLE Isu.: Andersson ; northern part, Snodgrass & Heller, no. 681 (hb. Gr.). James Ist.: James Bay, common in lava soil, Snodgrass & Heller, no. 389 (hb. Gr.). NarsorouGcH Ist.: southern part, tolerably common at 615 m. alt., Snodgrass & Heller, no. 314a (hb. FLORA OF THE GALAPAGOS ISLANDS. 211 Gr.). Seymour Ist.: north, Snodgrass & Heller, no. 563 (hb. Gr.) ; south, Snodgrass & Heller, no. 600 (hb. Gr.). Widely distrib. weed in trop. reg. Apparently of recent introduction in the Galapagos Ids. B. renurcautis, Benth. & Hook. f. Gen. Pl. ii. 870. Wedelia tenu- teaulis, Hook. f. (3), 215 ; Anderss. (1), 179, & (2), 69; and doubtfully acc. to Hook. f. & Jacks. Ind. Kew. ii. 1226, Wedelia fruteseens, Hook. f. (4), 261; Anderss. (1), 179, & (2), 69; not Jacq. — ALBEMARLE ISsL.: Macrae. Cares Ist.: Hdmonston (identity doubtful). Endemic. BrIcKEx.iA, Ell. B. pirrusa, Gray, Pl. Wright. i. 86 (1852). — ALBEMARLE IsL.: Iguana Cove, Snodgrass & Heller, nos. 51 (hb. Gr.), 72 (hb. Gr.), 93 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 214 (hb. Gr.). Further distrib. Mex. to Braz. Apparently of recent introduction on the Galapagos Islands. CHRYSANTHELLUM, Rich. C. rrectum, Anderss. (1), 188, & (2), 74. C. pusillum, Rose (1), 137, in part (as to pl. Chatham Isl.).— Cuaruam Ist.: A. Agassiz (hb. U. S. Nat. Mus.) ; Snodgrass & Heller, nos. 505 (hb. Gr.), 538 (hb. Gr.). INDEFATIGABLE IsL.: in the most grassy places of lower region. Andersson (hb. Gr.). NarsBorouea Ist.: southern part, Snod- grass & Heller, no. 314 (hb. Gr.). Endemic. . C. pusittum, Hook. f. (3), 214 ; Anderss. (1), 188, & (2), 74, t. 6, f. 2; Rose (1), 157, in part (only as to pl. Charles), — ALBEMARLE IsL.: Darwin. CHares Isu.: in dry somewhat grassy places of lower region, Andersson (hb. Gr.) ; A. Agassiz (hb. Gr.) ; Snodgrass & Heller, no. 413 (hb. Gr.) Cuatuam Isi.: Andersson. Endemic. Eciipeta, L. KE. erEcTA, L. Mant. ii. 286 (1771); Caruel (1), 623. J. alba, Hassk. Pl. Jav. Rar. 528 (1848); Rob. & Greenm. (1), 146. £. pro- cumbens, Michx. Fl. Bor. Am. ii, 129 (1803). —Cuartes Ist.: Snod- grass & Heller, no. 417 (hb. Gr.). Caatuam Ist.: Chierchia, acc. to Caruel, 1. c.; southwest end, middle region, Baur, no. 106 (hb. Gr.) ; Snodgrass & Heller, no. 539 (hb. Gr.). Hoop Ist.: on margin of a mud lake, Snodgrass & Heller, no. 721 (hb. Gr.). A widely distributed weed, probably of recent introduction on the Galapagos. Wey PROCEEDINGS OF THE AMERICAN ACADEMY. Exvira, Cass. E. inelegans. Desmocephalum inelegans, Hook. f. (3), 209; Anderss. (1), 178, & (2), 69. — Cuartes Ist.: Darwin, Endemic. KE. repens. Microcoecia repens, Hook. f. (3), 209; Anderss. (1), 179, & (2), 69. — ALBEMARLE Isx.: Tagus Cove, alt. 1230 m., Snod- grass & Heller, no. 880 (hb. Gr.). James Ist.: Darwin (hb. Gr.). Endemic. The plant from Albemarle Island differs from the original material from James Island in not rooting at the lower nodes. Further- more, the outer bract of the involucre is broadly obovate and subtruncate instead of acuminate as described by Hooker. Mr. W. B. Hemsley has been so kind as to compare the Albemarle plant with some of the original material at Kew and regards them as the same species. A fragment of the Darwin plant, sent many years ago by Mr. Bentham to Dr. Gray, is unfortunately sterile, but agrees closely with the Albemarle plant in all vegetative features except in its evident repent character. Enceria, Adans. E. nisprpa, Anderss. (1), 186, & (2), 73. — Cuartes Isx.: Andersson. Cuatuam Isv.: in dry grassy places of lower region, Andersson (hb. Gr.). Endemic. ErIceron, L. E. Lancrro.tus, Hook. f. (3), 208; Anderss. (1), 176, & (2), 67. — ALBEMARLE Ist.: Darwin; Elizabeth Bay, Snodgrass & Heller, no. 278 (hb. Gr.) ; Point Christopher, Snodgrass & Heller, no. 930 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, no. 909 (hb. Gr.). Nargporouau Ist.: southern part, common, bushes 6 to 9 dm. high, 150 to 600 m. alt., Snodgrass & Heller, no. 328 (hb. Gr.), leaves acute; and no. 344 (hb. Gr.), leaves obtusish to rounded. (Obviously only foliar forms of the same species.) Endemic. E. yintrotius, Willd. Sp. iii. 1955 (1804); Gray, Syn. FI. i. pt. 2, 221. HE. sp. Rob. & Greenm. (1), 146. Oonyza ambigua, DC. FI. Fr. Suppl. 468 (1815). — Cuarues Isxt.: Baur, no. 120 (hb. Gr.). Widely distrib. in trop. and subtrop. reg. E. Tenuirouius, Hook. f. (3), 207; Anderss. (1), 176, & (2), 68 (as to pl. Darwin); Rob. & Greenm. (1), 146.— Axsinepon Ist.: Snodgrass & Heller, no. 841 (hb. Gr.). ALBEMARLE IsL.: mountain north of Elizabeth Bay, Srodgrass & Heller, no. 295 (hb. Gr.); mountain east of Tagus Cove, Snodgrass & Heller, nos. 237 (hb. Gr.), 255 (hb. FLORA OF THE GALAPAGOS ISLANDS, Site Gr.); southern part, Baur, no. 121 (hb. Gr.) ; Tagus Cove, alt. 1250 m., Snodgrass & Heller, no. 889 (hb. Gr.). CHaries Isi.: Darwin. Duncan Ist.: Baur, no. 122 (hb. Gr.). James Isx.: Darwin ; James Bay, scattered along the edge of new lava flow, Snodgrass & Heller, no. 370 (hb. Gr.). Endemic. Leaves varying in length. E. sp. HE. tenuifolius, Steetz (not Hook. f.) in Anderss. (AD ee digo & (2), 68; Rob. & Greenm. (1), 146.— Cuarves Ist.: Andersson (hb. Gr.); Baur, no. 123 (hb. Gr). Endemic. Unfortunately known only from sterile specimens. Evpatorium, L. E. FILICAULE, Sch. Bip. in Gray, Proc. Am. Acad. xxi. 384 (1886). — ALBEMARLE Ist.: Iguana Cove, Snodgrass & Heller, no. 29 (hb. Gr.). Further distrib. Mex. to Venezuela. The Galapageian plant has a slightly denser inflorescence and more copious and sordid indumentum than the Mexican, but good floral differences do not appear. E.? sp. Hook. f. (4), 261.—Cuarves Ist.: Hdmonston, acc. to Hook. f.,].c. Endemic? Andersson (1), 189, & (2), 74, suggests the possibility that this may be Mlaveria Contrayerba, Pers. FLAVERIA, Juss. F. Contrayersa, Pers. Syn. ii. 489 (1807); DC. Prodr. v. 635; Anderss. (1), 189, & (2), 74.— Cuarues Ist.: Andersson. Further distrib. trop. Am. Hemizonia, DC. H. squatipa, Hook. f. (3), 208; Anderss. (1), 190, & (2), 75. — GaLapaGos Ips.: Du Petit-Thouars, ace. to Hook. f., 1. ¢. Endemic. JAEGERIA, HBK. J. GRACILIS, Hook. f. (3), 213; Anderss. (1), 179, & (2), 69.— CHARLES Ist.: Darwin. Endemic. From the description of the in- volucre this can hardly be a Jaegeria. J. PROREPENS, Hook. f. (3), 214; Anderss. (1), 179, & (2), 69; Robinson, Proc. Am. Acad. xxxy. 318.—JaAmes Ist.: Darwin. Endemic. Neither this nor the preceding has been secured by any other collector. Lecocarpus, Decaisne. L. FOLIOSUS, Decaisne, Bot. Voy. Venus, 20 (1864). LZ. pinnati- jidus, Decaisne, |. c. t. 14 of Atlas; Hook. f. (3), 210 (identity of the 214 - PROCEEDINGS OF THE AMERICAN ACADEMY. forms with less cut leaves may be doubted) ; Anderss. (1), 186, & (2), 73; Rob. & Greenm. (1), 146. — GanapaGos Ips.: (presumably CHARLES) Edmonston (hb. Gr.); Habel. Cuarves Isu.: Darwin; Du Petit- Thouars; in dry places, upper region, Andersson (hb. Gr.); Baur. Cuatuam Isu.: Darwin, ace. to Hook. f. Endemic. Lirpocuarta, DC. L. LARrcIFOLIA, Gray, Proc. Am. Acad. y. 131 (1862); Rose (1), 137. Macraea laricifolia, Hook. f. (3), 210; Anderss. (1), 186, & (2), 72; Caruel (1), 623; Rob. & Greenm. (1), 147. Trigonopterum Ponteni, Anderss. (1), 184, & (2), 72, t.6, f. 1. Lippia? Rob. & Greenm. (1), 147. — Garapacos Ips.: Habel. Apinepon Ist.: Snodgrass & Heller, no. 830 (hb. Gr.). ALBEMARLE Ist.: Dar- win; Macrae; Andersson; Cowley Bay, Baur, nos. 181 (hb. Gr.), 182 (hb. Gr.) ; Tagus Cove, Snodgrass & Heller, nos. 146 (hb. Gr.), 913 (hb. Gr.) ; common bush on hills near the cove and to 180 m. alt., also inland to 450 m., Snodgrass & Heller, no. 166 (hb. Gr.). CHARLES Ist. : Darwin; wooded region, middle of the island, Andersson (hb. Gr.); Zee (hb. U. S. Nat. Mus.); A. Agassiz; Baur, no. 126 (hb. Gr.) ; Snodgrass & Heller, no. 408 (hb. Gr.). Cuarnam Isx.: Chierchia ; southwest part, Baur, no. 127 (hb. Gr.), NarsoroucGa Ist. : southern part, bushes 1.3 to 2 m. high at 320 to 650 m. alt., Snodgrass & Heller, no. 335 (hb. Gr.). Endemic. A species of special interest, showing the strongest of several on the whole rather slight traces of affinity between the flora of the Galapagos Islands and that of the Sandwich Islands (on which occur the remaining species of this small genus). PEetris, 0; P. Anderssonii. P. linearis, Rob. & Greenm. (1), 147, not La Llave. Lorentia linearis, Anderss. (1), 174, & (2), 66. — INDEFATIGA- BLE Ist.: alt. 60 m., Andersson ; south of Conway Bay, Baur, no. 125 (hb. Gr.). Endemic. P. Hookeri. JLorentia gracilis, Hook. f. (3), 206; Anderss. (1), 174, & (2), 66. Pectis gracilis, Rob. & Greenm. (1), 147 (excl. pl. Chatham), not Baker. — ALBEMARLE Isu.: Macrae. BARRINGTON Isu.: Baur, no. 115 (hb. Gr.) ; Snodgrass & Heller, no. 465 (hb. Gr.). CHARLES Ist.: Baur. Hoop Ist.: Snodgrass & Heller, no. 726 (hb. Gr.). James Isu.: James Bay, abundant on lava rocks near beach, Snodgrass & Heller, no. 878 (hb. Gr.). Jervis Ist.: Baur, no. 114 (hb. Gr.). Seymour Ist.: south, Snodgrass & Heller, no. 592 (hb. Gr.). Endemic. FLORA OF THE GALAPAGOS ISLANDS. 2V5 P. LiniFOLiA, L. Syst. Nat. ed. 10, 1221 (1760); Fernald, Proc. Am. Acad. xxxiii. 85. P. punctata, Jacq. Enum. Pl. Carib, 28 (1762), & Stirp. Am. 216, t. 128; Gray, Syn. Fl. i. pt. 2,362. Verbesina linifolia, L. Syst. Nat. ed. 10, 1226 (1760). Pectidium punctatum, Less. Linnaea, vi. 707 (1831); DC. Prodr. v. 98; Anderss. (1), 172, & (2), 65. P. subciliaris, Anderss. (1), 174, & (2), 66. — CaatHam Isx.: Andersson. INDEFATIGABLE Isu.: Andersson. Srxymowr Isx.: south, Snodgrass & Heller, no. 591 (hb. Gr.). Further distrib. Mex., W. Ind., northern S. Am. Several forms are distinguished by Andersson. P. supsquarrosa, Sch. Bip. in Seem. Bot. Herald, 809 (1852-1857). Lorentia subsquarrosa, Hook. f. (3), 206.— GaAxrapacos Ips.: Habel. CuatHam Ist.: Darwin. Endemic. P. renurrotra, Sch. Bip. in Seem. Bot. Herald, 309 (1852-1857) ; Rob. & Greenm. (1), 147. P. gracilis, Rob. & Greenm. (1), 147, as to pl. Chatham. Lorentia tenuifolia, DC. Prodr. v. 103 (1836) ; Hook. f. (3), 206; Anderss. (1), 174, & (2), 66. ZL. subsquarrosa, Anderss. (1), 175, & (2), 67, as to pl. Albemarle. — ArBemarte Isu.: Macrae (type); Andersson ; Black Bight, Snodgrass & Heller, no. 256 (hb. Gr.) ; eastern portion, Cowley Bay, Baur, no. 1165 (hb. Gr.); Elizabeth Bay, Snodgrass & Heller, no. 274 (hb. Gr.); southern part, Baur, no. 116 (hb. Gr.); Tagus Cove, Snodgrass & Heller, no. 148 (hb. Gr.). CHARLES Ist.: Andersson (hb. Gr.), labelled in Andersson’s hand but not re- corded in his published papers; Snodgrass & Heller, no. 437 (hb. Gr.). CuatHam Ist.: Andersson (hb. Gr.); northern part, Baur, no. 112 (hb. Gr.), leaves minutely pubescent; Snodgrass & Heller, no. 537 (hb. Gr.). InpEFaTIGABLE IsL.: northern part, Snodgrass & Heller, no. 665 (hb. Gr.), leaves minutely pubescent, involucral bracts acutish. Seymour Ist.: north, Snodgrass & Heller, no. 573 (hb. Gr.). Further distrib. shores of Peru? P. Surchellit, Bak. in Mart. Fl. Bras. vi. pt. 3, 287 (1884), is habitally similar, but differs in pappus. PoROPHYLLUM, Vaill. P. ELLIPTICUM, Cass. Dict. xliii. 56 (1826); Anderss. (1), 189, & (2), 75; Rose (1), 187; Rob. & Greenm. (1), 147. P. ruderale, Cass. l.c. Cacalia Porophyllum, L. Sp. 834 (1753); Cav. Ic. iii. 11, t. 222. — GaLapagos Ips.: Habel, Aptnevon Ist.: Snodgrass & Heller, no. 848 (hb. Gr.). ALBEMARLE Isxt.: Tagus Cove Mountain, Snodgrass & Heller, no. 224 (hb. Gr). Cuarues Ist.: Andersson; Baur; Snod- grass & Heller, no. 430 (ub. Gr.). Cuaruam Isz.: Andersson (hb. Gr.) ; 216 PROCEEDINGS OF THE AMERICAN ACADEMY. A, Agassiz (hb. Gr.); southwest end, lower region, Baur, no. 133 (hb. Gr.); Snodgrass & Heller, no. 508 (hb. Gr.). Duncan Ist.: Snodgrass & Heller, no. 688 (hb. Gr.). Hoop Ist.: Baur, no. 131 (hb. Gr.); Snodgrass & Heller, no. 745 (hb. Gr.). INDEFATIGABLE Isu.: Snodgrass & Heller, no. 654 (hb. Gr.). James Isx.: Orchilla Bay, Baur, no. 134 (hb. Gr.); James Bay, abundant on all kinds of soil, Snodgrass & Heller, no. 358 (hb. Gr.). JERvis Ist.: Baur, no. 133 bis (hb. Gr.). Widely distrib. in trop. Am. Now one of the most abundant and generally distributed plants of the islands, but apparently of recent introduction, as it was not noted by Darwin or any of the earlier collectors. Andersson in 1852 found it upon two islands, Baur in 1891 upon five, and Snodgrass & Heller in 1899 upon seven. ScaLesiA, Arn. S. arrints, Hook. f. (3), 212; Anderss. (1), 182, & (2), 71; Hemsl. in Hook. f. Ic. Pl. xxviii. t. 2718. — CuHartes Ist: Darwin. Endemic. S. aspera, Anderss. (1), 180, & (2), 70, t. 7, f. 3. — InpeFatte- ABLE Isx,: alt. 65 m., Andersson (hb. Gr.). Endemic. S. ATRACTYLOIDES, Arn. in Lindl. Introd. Nat. Ord. ed. 2, 264, 443 (1836); DC. Prodr. vii. 808; Hook. & Arn. in Hook. Jour. Bot. iii. 312; Hook. f. (8), 210; Anderss. (1), 179, & (2), 69. — GaLapacos Ips.: Cuming. long. Heads 1.2 cm. in diameter. With its thin flat soft-pubescent leaves this can scarcely be Mr. Hemsley’s S. retrofleca nor does it agree with any of the other species heretofore characterized. Although near S. dneisa, Hook. f., it has more ovate leaves and acuter involucral bracts than that species. PLatTE 3, FIG. 1. S. mvctsa, Hook. f. (3), 210; Anderss. (1), 179, & (2), 70; Hemsl. in Hook. f. Ic. Pl. xxviii. t. 2716. — CHATHAM Isut.: Darwin. Endemic. 218 PROCEEDINGS OF THE AMERICAN ACADEMY. S. microcephala, nov. sp., gummifera; ramulis teretibus gracilibus brunneis tenuiter griseo-puberulis, apice foliosis et corymbiferis; foliis ovato-lanceolatis vel lanceolato-oblongis integerrimis attenuato-acutissimis basi rotundato vel ad petioli insertionem subacuminatis dense tomenteilis penninervatis subtus pallidioribus 4 to 6 cm. longis 2 cm. latis; petiolis gracilibus exalatis 1.5 cm. longis; capitulis pluribus graciliter pedicellatis corymbos terminales sessiles a foliis superatos formantibus eradiatis 1 cm. longis 7 mm. latis gummiferis ; squamis involucri anguste campanulati lanceolato-linearibus attenuatis laxe imbricatis subaequalibus sordide pubescentibus; flosculis 9 nullis, § 9-12; corollae tubo gracillimo in fauces non ampliato 5 mm. longo minutissime puberulo, limbo 5-dentato recurvato ; achenio compresso sparse pubescenti nigrescente lineari- oblongo 4 mm. longo 0.8 mm. lato summo dentes duas nunc breves nune in aristas parvas productas gerenti; paleis conduplicatis angustis apice argute 3-dentatis puberulis. — ALBEMARLE IsL.: Tagus Cove, 20 Jan- uary, 1899, Snodgrass & Heller, no. 910 (hb. Gr.) ; mountain east of Tagus Cove, alt. 770 m., Snodgrass & Heller, no. 254 (hb. Gr.). NarsorouGH Ist.: abundant in southern part at 600 m. alt., forming bushes 2.6 to 4 m. high, Snodgrass & Heller, no. 3843 (hb. Gr.). This last specimen is sterile and somewhat doubtful. It has leaves 7 cm. long and 3 cm. broad. Endemic. Parte 3, Fries. 2 and 3. S. microcephala is well marked among its congeners by its small and more numerous heads, also by the presence of an abortive pappus. These features, however, in the presence of an otherwise close resem- blance to the genus Scalesta do not appear to form any good ground for generic separation. S. narbonensis, nov. sp., ramis fistulosis foliosis dense breviterque pubescentibus vel subvelutinis teretibus striatis ; foliis alternis late ovatis, praeter basis integerrimae acuminati-attenuatae serratis acute acuminatis molliter adpresse pubescentibus, in pagina inferiore pallidioribus supra basem 5-nervatis, nervis lateralibus ramosis; petiolis distinctis semiteretibus exalatis ; pedunculis in dichotomis supremis solitariis teretibus gracilibus erectis unibracteatis a foliis superatis : capitulis solitariis involucro cam- panulato, squamis circa 13 oblongis acutis dense pubescentibus ; flosculis @ circa 12 squamas involucri paulo excedentibus corollis tubo gracili pubescenti in ligulam breviter oblongam pallidam 5-nervatam dilatatis, achenio pergracili tereto, abortivo: paleis oblongis puberulis valde condu- plicatis apice argute 2—3-dentatis: flosculis @ numerosis, corollo breviter pubescenti a tubo brevi gracile in fauces teretes longiores 5-nervatis FLORA OF THE GALAPAGOS ISLANDS. 219 ampliato: limbo breviter 5-dentato albo-puberulo: achenio puberulo compresso breviter oblongo apice calvo. — NarBoroueH Isv.: northern part, Snodgrass & Heller, no. 297 (hb. Gr.) ; southern part, common at 650 m. alt., Snodgrass & Heller, no. 341 (hb. Gr.). Endemic. Leaf- blade 6 to 11 em. long, half as broad, petioles 1 to 1.5 cm. long: heads 2 cm. in diameter; ray-flowers including the achene 12 mm. long. ‘This species approaches S. affinis, Hook. f., but differs in its alternate more finely toothed leaves, in the branched lateral leaf-nerves which (if the figure in Hook. Icon. t. 2718 be correct) are simple and marginal in S. affinis. SS. affinis would from the figure seem furthermore to have a longer more hirsute type of pubescence. PLATE 3, Fics. 4, 5, 6, and 7. S. ovata, Anderss. (1), 181,.& (2), 70.— Cuarurs Isi.: upper wooded region, Andersson; Lee (hb. U. S. Nat. Mus.). Endemic. S. PEDUNCULATA, Hook. f. (8), 211; Anderss. (1), 181, & (2), 71; Hemsl. in Hook. f. Ic. Pl. xxviii. t. 2717.—James Isui.: Darwin. Endemic. S. reTROFLEXA, Hemsl. in Hook. f. Ic. Pl. xxviii. t. 2715 (1901). — INDEFATIGABLE Ist.: Habel. Endemic. S. Snodgrassii, nov sp. S. Baurii et S. retroflexae affinis, fruticosa, 6-9 dm. alta; ramis teretibus glabrescentibus foliosis in specimine siccato brunneis tenuiter, striatis ramuiis parce pilosis et tenuissime glanduloso- puberulis; foliis planiusculis alternis ovato-oblongis penninervatis supra pilis minutis conicis albis obstitis subtus paulo pallidioribus tenuiter pubescentibus pinnatisectis; lobis obtusissimis ‘et obtuse dentatis sinis angustatis ; petiolis exalatis puberulis; pedunculis ad apicem ramuli sub- tribus gracilibus saepius unibracteatis puberulis et parce pilosis; capitulis eradiatis ; involucri hemisphaerici squamis obovato-oblongis brevissime acuminatis 3—d-nervatis pubescentibus et breviter ciliatis; floribus om- nibus %; corollae tubo gracili hispidulo-puberulo saepius arcuato in fauces dilatato; limbo 5-dentato recurvato; achenio compresso griseo glabro apice subtruncato obsolete 2-dentato ; paleis striatis conduplicatis argute 2—3-dentatis tenuiter parceque puberulis. — Wrenman Isi.: 8 December, 1898, Snodgrass & Heller, no. 10 (hb. Gr.). Endemic. This species is probably nearest S. retroflexa recently described by Mr. Hems- ley from Indefatigable Island. That, however, has the leaves recurved and somewhat crisped, of slightly different dentation and a corolla de- cidedly ampliate in the throat; also villous petioles. S. Baurii differs in its rugulose leaves, S. Hopkinsii in its very different indumentum, and JS. ineisa in leaf contour and the bluntly toothed chaff. Parte 3, FIG. 8. 220 PROCEEDINGS OF THE AMERICAN ACADEMY. S. n. sp. ?— ALBEMARLE Isx.: Iguana Cove, below 300 m. alt., Snod- grass & Heller, no. 856 (hb. Gr.); 300 to 600 m. alt., Snodgrass & Heller, no. 869 (hb. Gr.); Tagus Cove, 1230 m. alt., Snodgrass & Heller, no. 875 (hb. Gr.). Differing from all the other species in its large broadly ovate more or less cordate subentire leaves. Unfortunately all the specimens are sterile so that there is a slight doubt as to the genus. Endemic. Soncuus, L. S. oLteRAcEuS, L. Sp. 794 (1753). — AtBemMaARLE Isx.: Snodgrass & Feller, no. 908 (hb. Gr.); Iguana Cove, Snodgrass & Heller, no. 50 (hb. Gr.). CHartes Isx.: Snodgrass & Heller, no. 404 (hb. Gr.). Cosmop. weed. SPILANTHES, L. S. Acmetia, Murr. Syst. ed. 138, 610 (1774); Hook. f. (4), 261; Anderss. (1), 188, & (2), 74.—- CHartes Ist.: Hdmonston, acc. to Hook. f., 1. c. NaArsporoueH Isu.: southern part, Snodgrass & Heller, no. 315 (hb. Gr.). Sterile and doubtful. Widely distrib. in trop. reg. S. pirrusa, Hook. f. (3), 214; Anderss. (1), 188, & (2), 74. — Cuarures Ist.: Darwin. James Isu.: in a smaller form, Darwin, acc. to Hook. f.,1.c. Endemic. ’ TaGetes, L. T. erecta, L. Sp. 887 (1753); Caruel (1), 623. — Caatnam Ist.: Chierchia, acc. to Caruel, 1. c. Widely distrib. in warm reg. as a result of cult. re oO N FLORA OF THE GALAPAGOS ISLANDS. 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Indefatigable. Galapagos Ids. | Wenman. Abingdon. Albemarle. | Barrington. | Bindloe. Charles. | Chatham. | Culpepper. Gardner | Narborough. Nephrodium villosum Nephrolepis acuta pectinata. . Nothochlaena sulphurea Pellaea geraniaefolia Polypodium angustifolium aureum cues crassifolium incanum . lanceolatum . lepidopteris . loriceum . paleaceum pectinatum . percussum Phyllitidis pleiosorum rude c squamatum . S meme snett Marcin: water storks Pteris aquilina, var. escu- lenta incisa . pedata . propinqua, var Cuming. jana. BESS is Taenitis angustifolia Azolla caroliniana Salvinia sp. : : Lycopodium clavatum . dichotomum sp. SD eee era Potamogeton pectinatus Ruppia maritima. . Najas marina, var. latifolia Anthephora elegans . Aristida divulsa repens . subspicata villosa . Bouteloua pilosa . ‘ Cenchrus distichophy lus . granularis : platyacanthus . See aeha Get Chloris anisopoda elegans radiata Chusquea sp. + -f VOL. XXXVIII.— 15 Eleusine aegyptica indica . 348 Eragrostis bahiensis . ciliaris major . pilosa . ¢ Eriochloa distachya . Leptochloa albemarlensis . filiformis . Lindleyana . mucronata virgata Oplismenus setarius . Panicum colonum fasciculatum fluitans fuscum hirticaulum . var. minus molle ae multiculmum sanguinale serotinum Paspalum canescens . conjugatum . distichum longe-pedunculatum . penicillatum scrobiculatum . Site: pee Sow Pennisetum pauperum . Setaria floriana setosa . SPare esses ved ty: Sporobolus domingensis indicus aay bo bar 00) (0) Stenotaphrum glabrum Stipa rostrata : Cyperus aristatus brachystachys . confertus . esculentus fugax galapagensis grandifolius . laevigatus ligularis Mutisii rotundus . PROCEEDINGS OF THE AMERICAN TABLE II. —continued. Barrington. | Galapagos Ids. Abingdon. Albemarle. Chatham | Culpepper. ACADEMY. Indefatigable. | Narborough. Seymour. + ott +H + Fett +t Hit + | +ttttt+s | Cyperus rubiginosus var. cornutus strigosus . suranimensis . tristachyus . BS eects fe use: sp. Dichronema leucocephala . Eleocharis fistulosa . . mutata Fimbristylis capillaris diphylla . : Hemicarpha subsquarrosa. Kyllinga pumila . . Scleria pratensis Lemna sp. . . 8 Tillandsia insularis Commelina nudiflora Commelinacea? . . . Hypoxis decumbens . Epidendrum spicatum . Peperomia flagelliformis galapagensis : Gallordesye me sn petiolata . ramulosa . Snodgrassii . Nn. sp. SDiger tem Fleurya aestuans. . . Parietaria debilis. . . Pilea Baurii . : muscosa . . peploides . Phoradendron florianum galapageium Henslovii. : uncinatum .. . Polygonum acuminatum galapagense. . . Atriplex sp. . SDs icc Alternanthera radicata . rigida . subscaposa Amaranthus caracasanus . celosioides sclerantoides . forma chathamensis “6 FLORA OF THE GALAPAGOS ISLANDS. oOoG TABLE II.— continued. 2 3 ; AEE alls z S| : HIS ls|m/s/a/F/Slals| is 2\8| | S)Slalslel2isalslslelgleielalisieisia SIZISZEISEISISISIS/SIS/B/EIEIBIEIZ SlalalalslsloldslalolaleiSiS lz lBis lz +/+} |+] [+ + =- oe = a ° + ab + a. + + _ + + — + — —|+ 4. = -}- +. + : + +/+ —| |+ + \+ + |+ —|+ + ‘ + + + - oa oo +|+ — 5 + — + a . + . hoodensis . bo bo (00) TABLE II. — continued. Amaranthus spinosus squarrulosus urceolatus THONG o. 2 6 6 © 6 oC Froelichia juncea . lanigera nudicaulis scoparia Tresine Edmondstonei Pleuropetalum Darwinii Telanthera echinocephala . imino, gE flavicoma . . frutescens glaucescens . Helleri peeks var. obtusior . nudicaulis rugulosa. . . Snodgrassii . strictiuscula vestita Batis maritima Boussingaultia baselloides Phy tolacca decandra Boerhaavia erecta paniculata . . scandens. .. . VASCOSAN sy iG Lees Cryptocarpus pyriformis Pisonia floribunda Nyctaginacea?. | Mollugo flavescens var. floriana gracillima Snodgrassii. . Sesuvium Edmonstonei Portulacastrum .. . Trianthema Portulacastrum . Portulaca oleracea . .. . Portulaca sp. Drymaria cordata Cissampelos Pareira . Brassica campestris . . . SHMEHONSHCUEN 5 6 Ig 6 Raphanus sativus Senebiera pinnatifida Sanguisorbea?. .... . Acacia farnesiana macracantha »|a|o|]8 e iee Olslelelel-/slelala 2\mleleisiS|Si/Fls| sic 22 SES) Shes e| 25 S(2 (aS l/s Gls lS lalsia + S-[4= ar + 4+ + + + |— + +)+)+} |+]+ 3 35 Si == Salat == A= + 45 =F ar qf a + sf == os ae eu ar SP WI +r SF lar Se sei — ae + AF ialliaia a = aF “pF ae = aE -- ae) arl=|| \aelse se 3e sill ata se lar i Stal ate ar [AF + +)— | Indefatigable. | James. | Se PROCEEDINGS OF THE AMERICAN ACADEMY. ie | [++ | + | Jervis. + | Narborough. + +++ | Seymour. | Tower. Wenman. FLORA OF THE GALAPAGOS ISLANDS. 229 TABLE II.— continued. Abingdon. Indefatigable. Albemarle Barrington. Culpepper. Narborough. Seymour. Wenman. | Galapagos Ids. Chatham.. Acacia tortuosa + Eh Ute seks. ope ee Astragalus Edmonstonei Caesalpinia Bonducella pulcherrima Canavalia obtusifolia Cassia hirsuta . occidentalis . picta sericea : Crotalaria glabrescens : pumila : setifera Dalea parvifolia tenuicaulis . . . Desmanthus depressus . Desmodium a clang : incanum . : molle spirale . uncinatum Erythrina velutina Galactea Jussiaeana, var. volu- bilis ; var. glabrescens [++ | + +Fi+ +1 + 4+ ils Gab sc Geoffraea superba Mimosa asperata . Neptunia plena Parkinsonia aculeata Phaseolus adenanthus . mollis . - semierectus . Piscidia Erythrina Prosopis dulcis Rhynchosia minima . reticulata Sone: py! ov oe Oke Stylosanthes scabra . Tephrosia cinerea Vigna owahuensis Oxalis carnosa . Cornelli corniculata . Linum oligophyllum Kallstroemia adscendens Tribulus cistoides . 230 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE II. — continued. Bindloe. Indefatigable. Galapagos Ids. Abingdon, Albemarle. Barrington. Chatham. Culpepper. Gardner. Narborough. Seymour. Tribulus cistoides var. ana- canthus . sericeus BPs ves, ele Zanthoxylum Pterota Castela galapageia ... . forma albemarlensis “« bindloensis « carolensis « duncanensis . « jacobensis “jervensis . Bursera graveolens . malacophylla Polygala Andersonii galapageia : var. insularis . Acalypha Adamsii albermarlensis . Baurii chathamensis cordifolia diffusa . flaccida parvula reniformis . sericea spicata strobilifera velutina . var. minor. BPoee ees Croton Scouleri : var. albescens ; forma microphyllus var. brevifolius . “ grandifolius “ Macraei . Euphorbia amplexicaulis . apiculata . c articulata . diffusa flabellaris galapageia nesiotica . nummularia . FLORA OF THE GALAPAGOS ISLANDS. TABLE II.—continued. Abingdon. Albemarle. Bindloe. Charles, Chatham. | Culpepper. Duncan, Gardner. Hood. | Galapagos Ids. } | Barrington. Indefatigable. James, | Jervis, Narborough, | Seymour. Tower. ° Wenman. Euphorbia nummularia, var. glabra pilulifera . 5 See JOWUNGHVENIE, 5 5 6 6 4 = ae + RACHA 6 Gg of G8 + viminea . . + forma barringtonen- SIs May Benes +)+ SaCanOlensisiasirs + “ castellana Euphorbia viminea, forma chathamensis . ale forma jacobensis . « jervensis . var. abingdonensis 35 HS 6 o oF Go Go & Als aie Spams Me ea Se as + Sistem ce Hoyas Rioa — Hippomane Mancinella Manihot utilissima . .. . = Phyllanthus carolinensis Ricinus communis . .. . — Callitriche sp. . Maytenus obovata : Cardiospermum Corindum galapageium Dodonaea viscosa . . var. spathulata . . Sapindus Saponaria . Discaria pauciflora Cissus sicyoides | Vitis vinifera Corchorus pilobulus . Triumfetta semitriloba . Abutilon Anderssonianum . a depauperatum . Anoda hastata . Bastardia viscosa . rae acs Gossypium barbadense. . . ar Klotzschianum . : FHubiscusitiliaceus\..s-)0 9.) 1 = Malachra capitata ; Sida acuta, var. carpinifolia : angustifolia. . oak cordifolia paniculata rhombifolia. . spinosa veronicaefolia, var. hu- milis . + + + +1 | p++ + f+ +F++4+4+4+4H+ ++ b + | +- -b +o +++ + | ++ 232 PROCEEDINGS OF THE AMERICAN ACADEMY, TABLE II. — contznued. Galapagos Ids. Abingdon. Albemarle. Barrington. Culpepper. Dunean. Gardner. | Indefatigable. Narborough. | Seymour. ' Wenman. + Waltheria reticulata forma acamata «¢ Anderssonii “intermedia . Turnera ulmifolia . | Passiflora foetida . lineariloba puberula . Carica Papaya Mentzelia aspera . ; Sclerothrix fasciculata . Cereus galapagensis . nesioticus sclerocarpus Thouarsii Opuntia galapageia . Helleri j myriacantha + Bb ob Sas Cuphea patula . Rhizophora Mangle . Psidium galapageium Conocarpus erectus . Laguncularia racemosa. Miconia Robinsoniana . Myriophyllum sp. Apium laciniatum leptophyllum Centella asiatica . : Hydrocotyle galapagensis . Petroselinum sativum Plumbago scandens . Vallesia cymbaefolia pubescens .. . Asclepias angustissima . Vincetoxicum sp... Calystegia Soldanella Cuscuta acuta . gymnocarpa Evolvulus glaber . simplex Ipomoea biloba Bona-nox . campanulata galapagensis Habeliana Kinbergi . linearifolia ISI Seo omen pentaphylla . FLORA OF THE GALAPAGOS ISLANDS. 233 TABLE II. —continued. ie 3 ” a\g/2is| . aleieelecle he 2 |: : e/3| 2/2/3|/2/4| 2] 812) /elalellelsle S2/3/Els/S/S/S/S/2/S/S/2/E/S/S/E1E S/... + Lantana peduncularis . . . See eee |e elle re |e ie | SE) th) |i Lippia canescens . AN gins oy ee rosmarinifolia . . . . + I+ salicifolia -- Stachy tarpheta dichotoma ~ Verbena carolina. ... . = HURRY o- G a. oo. fan ec + litoralis ta pa ave +}+ OCHAOMENE, Goo oc ce o aa Hyptis capitata . an oman — subverticillata . os Sb) sel) ee Salvia occidentalis + au) ee st prostrata . fie tiliaefolia . Baie. wie Cats — Teucrium inflatum ... . +)+ Acnistus ellipticus . . . . — Inswlariss i 9. 3 ce *s =F Capsicum annuum .. . . +)/+ Datura Tatula . Aas Fae ta -. Sema eersunts. is een. us ae Lycium sp. ERE ae a. 4. Lycopersicum esculentum, Vibe MINOL. 5 + \4- _ + + ae 34 PROCEEDINGS OF THE AMERICAN Lycopersicum _peruvianum, var. parviflorum pimpinellifolium SPat rey. eee ak Nicotiana glutinosa Tabacum Tonad) ot Aah ae ; Physalis angulata . ixocarpa. . . pubescens . - sp. Solanum Edmonstonei . AION og verbascifolium . SPer ehsct el os SD ramnaiian co aaeches Thinogeton Hookeri IMiersiniiersn ete ae Capraria biflora . . Scoparia duicis . . Scrophulariacea . . Tecoma sp.? . Dicliptera peruviana Justicia galapagana . Tetramerium hispidum . Plantago major . . tomentosa, var.? . Borreria basalis Baurii accra dispersa . . divaricata . ericaefolia . falcifolia . galapageia : linearifolia . . ovalis . forma abingdonensis pacifica . . parvifolia perpusilla . . rotundifolia . suberecta Speer : Chiococca racemosa . Diodia Radula . Psychotria angustata rufipes Relbunium sp. . : Spermacoce tenuior . Citrullus vulgaris TABLE II.— Charles. | Chatham. | Culpepper. | Gardner, | Hood. | Galapagos Ids. | Duncan. | Abingdon. | Barrington. | Albemarle. | Bindloe. pa ata! | a = 2 xs 0 ae lala ~~ mn = < a) || oi ia =| lala Bin | ++ ++ | +++ I+ | + + +14 ACADEMY. | Narborough. | Jervis. | Seymour. | Tower. | Wenman. FLORA OF THE GALAPAGOS ISLANDS. 235 TABLE II.— continued. | Galapagos Ids. | | Abingdon. | Albemarle, | Barrington. | Bindloe. | Chatham. | Culpepper. | Gardner. | Indefatigable. Narborough. | Seymour. | Wenman. | Cucurbita Pepo . } Elaterium cordatum . ! Momordica Charantia Sicyos villosus . Lobelia xalapensis Scaevola Lobelia . Sue Acanthospermum lecocar- poides microcarpum Ageratum latifolium Aplopappus lanatus . Baccharis pilularis : Pingraea, var. angustis- sima caus Steetzii Bidens chilensis pilosa . refracta Blainvillea rhomboidea . tenuicaulis Brickellia diffusa. . . Chrysanthellum erectum pusillum . Eclipta erecta . Elvira inelegans repens. Encelia hispida | Erigeron lancifolius . linifolius . tenuifolius ORM ce Ode ORC Eupatorium filicaule Gebe 5b 6 Oo 6 Flaveria Contrayerba # Hemizonia squalida . | Jaegeria gracilis prorepens Lecocarpus foliosus . Lipochaeta laricifolia } Pectis Anderssonii Hookeri linifolia subsquarrosa tenuifolia - Porophyllum ellipticam Scalesia affinis aspera. . atractyloides Baurii . : var. glabrata . +#1++1+ + + + + + 236 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE. II. — continued. Abingdon. Barrington. | Galapagos Ids. | Albemarle. Bindloe. | Chatham. | Culpepper. | Indefatigable. | Narborough | Seymour, | Wenman. ! Scalesia Darwinii decurrens divisa . gummifera . Helleri Hopkinsii incisa . microcephala narbonersis . ovata . c pedunculata . retroflexa Snodgrassii . H n. sp. ¢ 5 | Sonchus oleraceus Spilanthes Acmella . diffusa ; Tagetes erecta . GENERAL FEATURES OF THE FLORA. The habital traits of the vegetation on the Galapagos Islands have been graphically although rather gloomily pictured by Darwin (2), 140, and by Wolf (1), 277. A. Agassiz (1), 57-62, and Baur, who visited the islands at a more favorable season, describe the flora as somewhat more luxuriant. The lower slopes of all the islands, however, are relatively sterile, arid, and rough, much of the surface being covered with irregular blocks of lava. The air, although not excessively hot, is very dry. Trade winds are said to be moderate in force, but almost constant. The perennial vegetation of these lower parts of the islands is predomi- natingly of a small-leaved xerophytic type, being composed of scattered and often spar8e, stemmy shrubs and undershrubs, or wiry herbs and grasses, over which rise the bulky and grotesque trunks of arborescent species of Cereus and Opuntia. On those islands, which, like Gardner, Hood, Tower, and Bindloe, are entirely low, not attaining an altitude of 300 m., this is the only kind of perennial vegetation, except a few halophytes along the shores. On the higher islands, however, like Albemarle, Charles, Chatham, James, and Indefatigable, the upper parts FLORA OF THE GALAPAGOS ISLANDS. 237 penetrate higher, moister strata of the air, and support a much more luxuriant vegetation of a mesophytic type. Between these chief types of vegetation there are perceptible but ill-defined belts of an intermediate nature. A few lakes and ponds, some muddy and others briny, support a littoral vegetation, chiefly of Cyperaceae, a family represented by sev- enteen species and varieties of Cyperus and one or two each of Dichro- nema, Eleocharis, Fimbristylis, Hemicarpha, Kyllinga, and Scleria. A cold spring on Charles Island contains an Azolla (Andersson), and in a small brook on the same island a Salvinia, a Callitriche, and a Lemna have been found (Wolf) ; but as both springs and streams are rare and small, such true hydrophytes are few and relatively unimportant in the archipelago. Halophytes are more abundant, and occur not only on-the sandy beaches in the brackish marshes along the shore, but to some extent around the saline lakes of the interior portions of the islands. The chief halophytes are C’ssampelos Pareira, Tephrosia cinerea, Rhizophora Mangle, Laguneularia racemosa, Sesuvium Portulacastrum, S. Edmonstonet, Calystegia Soldanella, Ipomoea biloba, I. Habeliana, Batis maritima, Avicennia officinalis, Verbena litoralis, Heliotropium curassavicum, Scaevola Lobelia, Ruppia maritima, Najas marina, var. latifolia, and probably Thinogeton Miersii, T. Hookeri, and two undeter- mined species of Atriplex. The lower arid slopes support not only the stemmy, suffrutescent veg- etation described above, but also are covered from time to time by an ephemeral growth of desert annuals, which spring up shortly after the rainy season begins, mature rapidly, and quickly dry up completely. Examples of this type of plants are found in Porophyllum elliptieum, Evolvulus simplex, and several species of Boerhaavia, Kallstroemia, Tribulus, and Bidens. Trees, if we except the arborescent cacti, occur chiefly upon the upper parts of the islands and never attain great size. In many cases, however, the same species which form a tree-like growth in the upper region extend well into the lower or even to the shore as shrubs, stunted by the extreme drought and sterility of their environment. The trees and shrubs are in great part armed with spines or thornis, e. g. Mimosa, Acacia, Parkinsonia, Discaria, Castela, Zanthorylum, Cereus, and Opuntia, — genera, all of which, it will be noticed, belong to the chori- petalous dicotyledons. On the other hand, species protected by poisonous Juices or stinging hairs appear to be few. The climbing plants of the islands are chiefly of the genera Boussingaultia, Cissampelos, Galactea, Rhynchosia, Cardiospermum, Ipomoea, Elaterium, Momordica, and Sicyos. 238 PROCEEDINGS OF THE AMERICAN ACADEMY, They are neither so numerous nor conspicuous as in the tropical parts of continental America, and it may be noticed that the climbers of the Galapagos Isiauds are herbaceous, the true woody liana, so common in tropical jungles, being almost unknown upon these islands. Epiphytes occur only at the higher altitudes and are neither abundant nor showy. ‘Their ecological class is chiefly represented by one Tilland- sia, one Hpidendrum, and several Peperomiae. Of phanerogamic para- sites there are four species of Phoradendron and two of Cuscuta. The phanerogams of the Galapagos Islands have prevailingly small and inconspicuous flowers, although exceptions are not infrequent. It is also worthy of remark that the flowers are in most cases regular and of a rather simple structure. Zygomorphic flowers are not numerous, and even in such genera as Hpidendrum, Salvia, etc., where zygomorphy is universal, the Galapageian species show this trait only moderately devel- oped. Similarly, flowers with other highly developed mechanisms for securing cross-pollination seem to be very rare in the islands. Fruits with hook apparatus or spines to aid their distribution by mammals are found in Cenchrus, Tribulus, Acanthospermum, Bidens, and Lecocarpus ; but by the decided reduction in the spines of most of the species of Cenchrus, and in a variety of Tribulus cistotdes, as well as in Acantho- spermum microcarpum, it is easy to remark a tendency toward abortion in this apparatus, —a fact readily explained by the paucity of indigenous mammals. Of course the settlement of the islands has brought intro- duced mammals in considerable quantity, but it is too recent to have had a perceptible influence in this matter. AFFINITIES OF THE FLORA. The flora of the Galapagos Islands is almost wholly American in char- acter. It contains, it is true, a very few plants which are not found in America. Thus a slight relationship to the flora of the Hawaiian Islands might be inferred from the genus Lipochaeta, of which one species is Galapageian and the others Hawaiian. There is also a report ofa Vigna common to the Hawaiian Islands, the Galapagos, and Chili, —a matter which I have been unable to verify. Jpomoea campanulata of the East Indies and Malayan Archipelago occurs on the Galapagos Islands, but not to my knowledge upon the continent of America. This is probably a chance introduction. Several species of the Old World, such as Vitis vinifera, mentioned by Caruel (1), 623, Brassica campes- tris, B. Sinapistrum, and Raphanus sativus, are of course relics of cultivation or introduced weeds. leocharis fistulosa, ascribed by Caruel FLORA OF THE GALAPAGOS ISLANDS, 939 (1), 622, to Chatham Island, is with scarcely a doubt an erroneous determination. ; While it is thus clear that the Galapageian flora is only an outlying portion of the American flora with a strong specific differentiation, it is impossible to trace its relationship closely to any one section of the Pacific American vegetation. It can only be said in a general way that nearly all the plants of the archipelago are identical with, or obviously related to, species of the Sierras and Andes or of the Pacific Slope between Lower California on the one hand and northern Chili on the other. The xerophytic elements in the Galapageian flora show a con- siderable resemblance to the desert flora of southern Peru and the drier parts of the Andes. ‘The mesophytes, on the other hand, correspond most nearly to plants of Ecuador, Colombia, Central America, and southern Mexico. Those who have written upon the phytogeography of the Galapagos Islands have frequently mentioned the West Indian affinities of the flora, but here I can find no close resemblance or significant relationship. It is to be noticed that Hooker, who first employed the term “ West Indian” regarding the flora of the Galapagos Islands, either used it to include, or expressly qualified it by the addition of, the flora of Panama and the adjacent lowlands of the continent, —a qualification which has not always been sufficiently regarded by subsequent authors. But, on the other hand, the discoveries of*the last half century have shown.a much greater difference between the flora of the Antilles and of the Panama region than was to be inferred when Hooker wrote ; so although a definite relationship can be traced between the Galapageian flora and that of the lower slopes of Colombia, it does not follow that there is any marked affinity to the flora of the West Indian Islands. Indeed, of the species common to the Galapagos and the Antilles there are none (if we except a sterile and doubtfully identified specimen of the Cuban Cenchrus distichophyllus) which do not also occur upon the adja- cent parts of the continent, and nearly all, like the halophytes of the shores, are species of wide tropical-distribution. Hooker (4), 239, 250, drew attention to what appeared to be an inter- esting double relationship between the plants of the Galapagos Islands and those of other regions, as follows: ‘“ Here, as in other countries, the vegetation is formed of two classes of plants, — the one peculiar to the group, the other identical with what are found elsewhere. In this there are even indications of the presence of two nearly equal Floras, — an in- digenous and introduced, — and these are of a somewhat different stamp ; 240 PROCEEDINGS OF THE AMERICAN ACADEMY, for the introduced species are for the most part the plants of the West Indian Islands and of the lower hot parts of the South American coast, whilst the peculiar Flora is chiefly made up of species not allied to the introduced, but to the vegetation which occurs in the Cordillera or the extra-tropical parts of America.” But, after repeated efforts, I am unable to verify this double relationship, and must infer that subsequent discoveries, both upon the mainland and upon the islands, have done much to weaken the grounds upon which these conclusions once rested. Many cases could now be cited to show that the endemic plants of the Gala- pagos Islands, far from forming a marked or peculiar class, are often the nearest allies of species or varieties which are common to the islands and the continent. Both classes include alike the most widely diverse ele- ments, — xerophytic, mesophytic, and halophytic types, annuals and peren- nials, herbs, shrubs, and trees, climbers and epiphytes, —and both occur in common at all altitudes and in every sort of habitat the islands afford. Accordingly it is not remarkable to find their closest congeners occupying the same diverse habitats upon the mainland from the hot, moist lowlands about Guayaquil and Panama to the cool parts of the Andes, dry regions of Peru or western Mexico, and in a few instances the more fertile up- lands of Colombia, Central America, and Mexico. Moreover, the endemic forms show all grades of differentiation from their continental allies ; some are well marked specific types, others mere varieties, while still others are scarcely distinguishable forms. It appears, therefore, that very diverse floral elements have reached the archipelago, probably at different times and from widely different habitats. Presumably all have been subjected on the islands to influences of a kind to bring about change in their nature; and in two-fifths of the plants now known on the islands more or less pronounced evidences of such change can be observed. ‘These plants, which show modification, form, as we have seen, no sharply marked class, but pass over very imper- ceptibly into nearly related forms which it is impossible to differentiate from plants of the mainland. That some plants have reached the Gala- pagos from the West Indian Islands during the subsidence of the Isthmus of Panama is by no means impossible, but as we should expect, these plants, if such there were, have established themselves in like manner upon the western coast and slopes of the continent, so that it is now quite impossible to trace any direct floral affinity between the West Indies and the Galapagos which the latter do not exhibit even in a higher degree with the western parts of the mainland. Mr. Hemsley has already commented upon the wide divergence be- FLORA OF THE GALAPAGOS ISLANDS. 241 tween the flora of the Galapagos group and that of Cocos Island. The latter is situated about three-sevenths of the way from the coast of Costa Rica to the Galapagos Archipelago. Until very recently the flora of Cocos Island has been scarcely known at all. Largely through the efforts of Professor H. Pittier and Messrs. Snodgrass & Heller, about eighty plants have now been secured on the island, and of these only the following eighteen are common to the flora of the Galapagos group: Plagiochila Anderssonii Paspalum conjugatum Acrostichum aureum Paspalum distichum Asplenium rhizophyllum Caesalpinia Bonducella Nephrolepis acuta Euphorbia pilulifera Polypodium aureum Ricinus communis Polypodium lanceolatum Hibiscus tileaceus Polypodium Phyllitidis Ipomoea biloba Eleusine indica Ipomoea Bona-nox. Panicum sanguinale It will be noticed that with the exception of the hepatic (Plagiochila Anderssonii) all of these species are weeds or plants of wide tropical distribution. CoMPOSITION OF THE FLORA. As with most insular floras, the vegetation of the Galapagos Islands is striking rather by the absence of certain great groups than by the number and diversity of the genera and families represented. For in- stance, in the pteridophytes there is a total lack of arborescent forms on the one hand and of the filmy ferns ( Zrichomanes, Hymenophyllum, etc.) on the other. There are no gymnosperms; and among the monocotyle- dons there are no palms, aroids, rushes, or Liliaceae. Indeed, if we except the grasses and sedges (both well represented), the monocotyledons are shown only by some half-dozen scattered species. Among the di- cotyledons the families best represented are the Amarantaceae, Nyctagi- naceae, Aizoaceae, Leguminosae (about 10 per cent of the phanerogamic vegetation), Huphorbiaceae (about 12 per cent), Malvaceae, Cactaceae, Convolvulaceae, Boraginaceae, Verbenaceae, Labiatae, Solanaceae, Rubiaceae, and Compositae (about 13.5 per cent). Several great dicoty- ledonous families, widely distributed and abundant in the tropics of continental America, such as the Sapindaceae, Myrtaceae, Melastomaceae, Lythraceae, and Onagraceae, are scarcely or not at all represented in the VOL. XXxXVIII.— 16 242 PROCEEDINGS OF THE AMERICAN ACADEMY. flora of the archipelago. Altogether there have been 72 families? of flowering plants and ferns found on the islands. Of these families 39 include endemic forms, and 383 contain only plants common to other regions. Excluding some indeterminate forms, there are 232 genera of pteridophytes and spermatophytes upon the islands. Notwithstanding the uncertainty with which some plants are here reckoned as species, and others as varieties or forms, the following figures regarding the plants of the Galapagos Islands will have an interest : Species. Varieties, Forms. Indeterminate. Total. Ferns 52 2 0 1 55 Fern-allies 2 0 0 2 4 Pteridophytes o4 2 0 3 59 Spermatophytes 445 17 19 50 531 Vascular plants 499 1g) 1S) 53 390 Of endemic ferns there are only 3, that is, but 5 per cent. Of endemic spermatophytes there are 202 species, 15 varieties, and 19 forms, —a total of 236, that is, 44.4 per cent of the whole flowering flora. The total number of vascular plants which are endemic is 239, or 40.5 per cent. Of these endemic plants 130, that is, more than half, are con- fined to a single island. The ratio of (determined) species to genera is as 2.16: 1. The ratio of species, varieties, and forms to genera is as 2.55: 1. It is noteworthy that, although there is such a high percentage of peculiar forms, varieties, and species, there is no corresponding peculiarity among the genera of these islands.? Of the several genera which have from time to time been characterized as exclusively Galapageian, only two, Scalesia and Lecocarpus, are now maintained, while all the others have been reduced to genera of continental America, with the single ex- ception of Macraea, which falls into a genus of the Hawaiian Islands. Even Scalesta is not a strong genus, as it is not easy to show very sharp generic distinctions between it and some allied Helianthoideae in Mexico and Central America. 1 This does not include the Rosaceae and Bignoniaceae, which rest, so far as their Galapageian occurrence is concerned, upon single and doubtful determinations. 2 The statement of Darwin (2), 165, regarding the genera of Compositae, is, as pointed out by Mr. Hemsley, quite erroneous, and must have rested upon some misapprehension of data furnished him. FLORA OF THE GALAPAGOS ISLANDS. 943 FAMILIES CONTAINING VASCULAR PLANTS PECULIAR TO THE ISLANDS. 2. £8 2 i oe AS at) Family. EE ES § 3 3 Family. 3s s 33 g 4 3 a& g2 as & ge af GS &. Filices tO 0 0 3 | Sapindaceae 1 0 0 1 Gramineae 5 ale! 1 QO 14 | Malvaceae. . 3 0 0 3 Cyperaceae 4 il 0 5 | Sterculiaceae . 1 0 3 + Bromeliaceae ] 0 0 1 | Passifloraceae 2 0 0 2 Orchidaceae . 1 0 0 1 | Cactaceae . 7 0 0) U Piperaceae 5 0 0 5 | Myrtaceae . 1 0 0 1 Urticaceae 1 0 0 1 | Melastomaceae 1 0 0 1 Loranthaceae . 4 0 0 4 | Umbelliferae . 1 0 0 il Polygonaceae 1 0 0 1 | Apocynaceae . il 0 0 1 Amarantaceae . . 29 1 2 382 | Asclepiadaceae . 1 0 0 il Nyctaginaceae 1 0 0 1 | Convolvulaceae. . 8 0 0 8 Aizoaceze . 4 1 0 5 | Boraginaceae 5 Ie 1 0 13 Leguminosae . 6 0 0 6 | Verbenaceae . 4 0 0 4 Oxalidaceae 1 0 0 1 | Labiatae 2 0 0 2 Zygophyllaceae . 2 1 0 3 | Solanaceae 5 0 0 5 Simarubaceae 1 0 6 7 | Acanthaceae . a al 0 0 1 Burseraceae . 1 0 0 1 | Rubiaceae . » UG 0 i ale Polygalaceae . 2 il 0 3 | Cucurbitaceae Ayer 0 0 2 Euphorbiaceae . . 26 7 7 389 | Compositae . . 39 1 0 40 Celastraceae . ee 0 0 il ABINGDON ISLAND. Abingdon is, with the exception of the rather remote islets of Wenman and Culpepper, the most northern of the archipelago. It is about 14 km. long, and attains a height of 600 m. It was visited by Dr. Baur for a few hours, September 8th, 1891, and by Messrs. Snodgrass and Heller in June, 1899. Fifty flowering plants and ferns are known to occur on the island, and of these four are peculiar to it, namely: Huphorbia vimined, var. abingdonensis, Lorreria ovalis, forma abingdonensis, Justicia galapagana (with close Mexican congener), and Scalesia Hopkinsit. The peculiar element is thus 8 per cent of the flora. Peperomia galiotdes of , Mexico and tropical South America occurs upon Abingdon, but upon no other of the Galapagos Islands. The remaining plants are common to other islands of the group, and represent in all 22 families, of which the Filices, Gramineae, Rubiaceae, Euphorbiaceae, and Compositae have the greatest number of species. Although Abingdon lies, as we have seen, to the northward of the main archipelago and on the side toward Wenman and Culpepper, it has, so far as we yet know, only one plant in common with the former and none with the latter. Agrostis, 725. AIZOACEAE, 148, 241, 243. Albemarle Island, 244. Alectoria, 86. ALGAE, 89. Allochlamys, 737. Alsophila, 772, 261. Alternanthera, 134, 135, 738, 140, 227. AMARANTACEAE, 134, 241, 243, 244, 251. Amaranthus, 135, 186, 227, 228, 248. AMARYLLIDACEAE, 151. Amblogyna, 136. Amblogyne, 135, 136. Amphiroa, 93. Amphochaeta, 124. Ancistus, 298. Ancyrostemma, 178. Anoda, 173, 231. ; Anthephora, 116, 224. Apium, 184, 232. Aplopappus, 209, 235. APOCYNACEAE, 185, 243. Ardisia, 263. Aristida, 116, 117, 126, 225, Aroids, 241. Arthonia, 83, 84. ASCLEPIADACEAE, 185, 243. Asclepias, 185, 232. Aspidium, 106, 720, 224. Asplenium, 106-108, 224, 241, 261. Astragalus, 148, 229. 264 Atriplex, 184, 227, 237, 252. Aulescus, 90. Avicennia, 194, 233, 237. Azolla, 115, 225, 237. Baccharis, 209, 235. Barrington Island, 245. BaseLuacran, 141. Bastardia, 178, 231. Batatas, 188. BaTipaceag, 141. Batis, 141, 228, 237. Biddulphia, 90. Bidens, 210, 235, 237, 238. BIGNONIACEAE, 202, 242. Bindloe Island, 245. Black Beach, 246. Blainvillea, 210, 211, 235. Blechnum, 108, 224. Boerhaavia, 79, 141, 142, 143, 228, 237. Boletus, 8&3. BoraGinacEak, 189, 241, 243, 248, 249. Borrera, S6. Borreria, 204-206, 234, 243, 247, 249, 255. Bouchea, 196. Boussingaultia, 141, 228, 237. Bouteloua, 117, 223. Brachycladia, 95. Brandesia, 137. Brassica, 146, 228, 238. Brattle Island, 245. Brickellia, 211, 235. BROMELIACEAE, 180, 243. Bryopsis, 89. Bryopteris, 100. Bucholtzia, 138, 139. Buellia, 84, 85. Bursera, 86, 88, 159, 160, 230, 250. BursEerRAckEAB, 159, 243. Byssus, Sd. Cacabus, 207. Cacalia, 215. CacTacEAE, 178, 241, 243. Caenopteris, 107. Caesalpinia, 148, 229, 241. Calamagrostis, 721. CALLITRICHACEAB, 170. Callitriche, 170, 231, 237. Callophyllis, 93. Calymperes, 102. Calyptrocarya, 262. PROCEEDINGS OF THE AMERICAN ACADEMY, Calystegia, 186, 232, 237. CAMPANULACEAE, 208. Campylodiseus, 90. Campyloneurum, 173. Campylopus, 102, 103. Canavalia, 148, 229, 245. Capraria, 202, 234. Capsicum, 199, 233. Cardiospermum, 170, 171, 231, 237, 252. Carica, 178, 232. CARICACEAE, 178. Carpomitra, 90. Carum, 784. CARYOPHYLLACEAE, 145. Cassia, 148, 149, 229. Castela, 158, 159, 230, 237, 245, 247, 249. Catopsis, 263. Caulerpa, 89. CELASTRACEAE, 170, 243. Cenchrus, 118, 225, 238, 239. Cenomyce, 895. Centella, 184, 232. Cereus, 179, 180, 232, 236, 237, 245, 246. Chaetochloa, 125. Chaetomorpha, 90. Charles Island, 246. Chatham Island, 246. Cheilanthes, 108, 209, 224. CHENOPODIACEAE, 134. Chiococea 206, 234. Chiodecton, 85. Chloris, 118, 119, 225, 262. CHLOROPHYCEAB, 89. Chondrus, 94. Chrysanthellum, 211, 235. Chrysodium, 104. Chusquea, 119, 225. Cissampelos, 146, 228, 237. Cissus, 172, 237. Citrullus, 207, 234. Cladonia, 85. Clerodendron, 194, 195, 233. Cocos Island, 241, 261. Coelestina, 209. Coffee tree, 134. Coldenia, 189, 232. CoMBRETACEAB, 182. Commelina, 1380, 227. Commelinacea, 131, 227. CoMMELINACEAE, 130. ComposiTAk, 208, 241, 242, 243, 248, 249, 25 L. FLORA OF THE GALAPAGOS ISLANDS. Conferva, 89. Conocarpus, 182, 232. Conostegia, 263. Constantinea, 98. CONVOLVULACEAE, 186, 241, 243, 248, Qi. Convolvulus, 756. Conyza, 212. Corallina, 94, 95. Corchorus, 172, 231. Cordia, 189-191, 233, 245. Coronopus, 146. - Crotalaria, 149, 229, 261. Croton, 165, 166, 230, 245, 246, 247, 249, 251. CrucIFERAE, 146. Cryptocarpus, 142, 228. Cucumis, 207. Cucurbita, 207, 235. CucurBITACEAE, 207, 243. Culpepper Island, 247. Cuphea, 182, 232. Cuscuta, 186, 232, 238. CYANOPHYCHAB, 89. CYPERACEAE, 126, 237, 2438. Cyperus, 126-129, 226, 227, 237, 251, 262. Cystopteris, 109, 224. Dactyloctenium, 29. Dalea, 150, 229. Daltonia, 103. Darea, 107. Dasya, 94. Datura, 199, 233. Dendrographa, 87. Desmanthus, 150, 229. Desmocephalum, 272. Desmodium, 150, 151, 229. Dianthera, 203. DIATOMEABR, 90. Dichronema, 129, 227, 237. Dicksonia, 267. Dicliptera, 203, 234. Dicranum, 102. Dictyocalyx, 201. Dictyota, 91. Digitaria, 723. Dilsea, 95. Diodia, 206, 234. Disearia, 171, 231, 237, 245. Distichlis, 726. Dodonaea, 171, 2312. 265 Dolichos, 748. Drymaria, 145, 228. Dubreulia, 733. Duncan Island, 247, Duranta, 195, 233. Eclipta, 211, 235. Elaphoglossum, 104, 105. Elaphrium, 159. Elaterium, 208, 235, 237. Eleocharis, 129, 227, 237, 238. Eleusine, 119, 120, 226, 241. Elvira, 212, 235. Encelia, 212, 235. Enteromorpha, 89. Epidendrum, 1381, 227, 238. Epiphytes, 238. Eragrostis, 120, 226. Erigeron, 212, 218, 235. Eriochloa, 121, 226. Erythrina, 151, 229. Eupatorium, 218, 235. Euphorbia, 758, 166-169, 230, 231, 241, 248, 249-251, 255-258. EvPHORBIACEAER, 161, 241, 243, 245, 248, 251. EKutriana, 777. Euxolus, 735. Everina, SS. Evolvulus, 79, 186, 187, 232, 237. Fagara, 158. Favolus, 82, 82. Fiuices, 104, 243. Fimbristylis, 129, 227, 237. Flaveria, 213, 235. Fleurya, 132, 227. Floriana Island, 246. Fomes, 83. Froelichia, 186, 187, 228. Frullania, 100. Fucodium, 90. Fucus, 89, 90, 92, 95, 96, 99. Funel, 82. Galactea, 151, 152, 229, 237. Galapagoa, 189. Galaxaura, 95. Gardner Island, 247. Gelidium, 95, 96, 98. Geoffraea, 152, 229, 248. Geoffroya, 152. 266 PROCEEDINGS OF THE AMERICAN ACADEMY, Gigartina, 96. Gleichenia, 109, 224. Glossophora, 90, 91. Goniophlebium, 722. GOODENIACEAE, 208. Gossypium, 1738, 174, 232. Gracilaria, 96. GRAMINEAE, 116, 243. Grasses, 245, 249. Grossman citanel 246. Guaiacum, 759. Gymnogongrus, 96. Gymnogramma, 109. Gymnogramme, 109, 224, 261. Gymnosperis, 241. Gymnothrix, 124. Halophytes, 237. HALORRHAGIDACEAE, 188. Haplopappus, 209. Hawaiian Islands, 238. Helianthoideae, 242. Heliophytum, 192. Heliotropium, 192, 233, 287. Helopus, 227. Helosciadium, 784. Hemicarpha, 130, 227, 237. Hemionitis, 104. Hemizonia, 213, 235. HEPATICAE, 100. Herpophyllon, 97. Hibiscus, 174, 231, 241, 263. Hippomane, 169, 237. Hood Island, 248. Hydrocotyle, 184, 232. Hymenophyllum, 241. Hypnea, 96, 98, 103. Hypochnus, 8d. Hypolepis, 109, 22 Hypolytrum, 262. Hypoxis, 151, 227. Hyptis, 197, 233. Illicebrum, 738. Indefatigable Island, 248. Ipomoea, 187-189, 232, 233, 237, 288, 241, Bole Tresine, 157, 2 Tridacea, Ak Jaegeria, 213, 235. James Island, 249. Jervis Island, 249. Jungermannia, 100. Jussieua, 263. Justicia, 2038, 234, 243. Kallstroemia, 156, 229, 237. Kallymenia, 98. Kyllinga, 130, 227, 237, 262. Kyllingia, 230 LABIATAE, 197, 241, 243. Laguncularia, 185, 252, 287. Lamiacea, 197. Lantana, 195, 233. Laportea, 732. Laurencia, 98. Lecanora, 83, 85. Lecidea, 84. Lecocarpus, 213,.235, 238, 242. LEGUMINOSAE, 147, 241, 243, 245, 248, Bogle Lejeunea, 267. Lemna, 180, 227, 237. LEMNACEAB, 180. Lepicystis, 122, 113. Lepidium, 746. Leptochoa, 121, 226, 245, 262. Leptogium, 262. Lichen, 85, S6, 88. LICHENES, 83. Liliaceae, 247. LInaAcEAb, 156. Linum, 156, 229 Lipochaeta, 214, 235, 238. Lippia, 196, 274, 233. Lithobrachia, 774. Lithocardium, 790, 191. Lithophyllum, 98. Lithothamnium, 98. Litobrochia, 774. LOASACEAB, 178. Lobelia, 208, 235. Lonchitis, 709. Lopholejeunea, 100. LoRANTHACEAB, 133, 243. Lorentia, 214, 215. Lycium, 199, 253 Lycopersicon, 199. Lycopersicum, 199, 200, 233, 234. LYCOPODIACEAE, 115. Lycopodium, 115, 225, 262. LYTHRACEAE, 182, 247. FLORA OF THE GALAPAGOS ISLANDS. Macraea, 274, 242. Macrolejeunea, 262. Macromitrium, 108. Malachra, 174, 232. MALvackEAE, 173, 241, 2438, 248. Manihot, 169, 237. Marchesinia, 101. Marginaria, 171, 112. Mariscus, 726-128. Mastogloia, 90. Maytenus, 170, 231, 245. Melanocarpum, 757. MELASTOMACEAE, 183, 241, 243. Melobesia, 98. Melosira, 90. MENISPERMACEAE, 146. Mentzelia, 178, 232. Merremia, 788. Miconia, 183, 232. Microcoecia, 22. Mimosa, 152, 229, 237. Mollugo, 145, 144, 228. Momordica, 208, 235, 237. Muscr, 102. Myriophyllum, 185, 232. Myrrackab, 182, 241, 243. NaJADACEAE, 116. Najas, 89, 116, 225, 237. Narborough Island, 250. Navicula, 90. Neckera, 103. Nephrodium, 110, 224, Nephrolepis, 110, 111, 225, 241, 261. Neptunia, 79, 152, 229. Neurocallis, 104. Nicotiana, 200, 234. Nothochlaena, 111, 225. Notothylas, 101. Nyctaginacea, 143, 228. NYCTAGINACEAE, 141, 241, 243, 250. QD5. wow Ochtodes, 99. 3 Oedogonium, 89. Olfersia, 704, 105. Omphalanthus, 101. Onagraceae 241. Oplismenus, 121, 722, 226. Opuntia, 725, 180, 181, 232, 236, 237, 245, 247, 248, 251. ORCHIDACEAE, 181, 243. Orthotrichum, 103, 104. Ossea, 263. OXALIDACEAE, 156, 243. Oxalis, 156, 229. Padina, 91, 92. Palms, 241. Palo Santo, SS, 134, 160. Panicum, 122, 128, 124, 125, 226, 241. Papillaria, 103. Parietaria, 132, 133, 227. Paritium, 174. Parkinsonia, 152, 229, 237. Parmelia, 85, S6. Paspalum, 128, 124, 226, 241, Passiflora, 177, 232. PASSIFLORACEAE, 177, 242. Pectidium, 275. Pectis, 214, 215, 235. Pellaea, 111, 225. Peltolejeunea, 101. Pennisetum, 124, 226. Peperomia, 181, 182, 227, 238, 243, 263. Pertusaria, 83, 85. Petroselinum, 184, 232. Peyssonnelia, 98, 99. Phaca, 148. PHAEOPHYCEAE, 90. Phaseolus, 757, 158, 229. Phoradendron, 138, 184, 227, 238. Phragmicoma, 107. Phyllanthus, 169, 232. Physalis, 200, 201, 234. Physcia, 85. Phytolacea, 141, 228. PHYTOLACCACEAE, 141. Pilea, 138, 227. Pilotrichella, 108. Pilotrichum, 267. PrIPeRaceAg®, 131, 2. Piptadenia, 152. Piscidia, 153, 229. Pisonia, 143, 228. Plagiochasma, 101. Plagiochila, 101, 241, 261. Plagiogramma, 90. PLANTAGINACEAE, 204. Plantago, 185, 204, 234. Platylejeunea, 261. Pleopeltis, 277-113. Pleuridium, 772. Pleuropetalum, 137, 228, 244. Plocamium, 99. 262. , 240. 268 PROCEEDINGS OF THE PLUMBAGINACEAE, 185. Plumbago, 185, 204, 232. Poa, 120. Poinciana, 748. Polygala, 160, 161, 230. PorycGaracean, 160, 243. POLYGONACEAE, 134, 243. . Polygonum, 134, 227. Polypodium, 206, 710, 111-114, 225, 241, 251, 261, 262. Polyporus, 83. Polystichum, 706. Porophyllum, 215, 235, 237. Portulaca, 744, 145, 228. PORTULACACEAE, 145. Potamogeton, 115, 116, 225. POTAMOGETONACEAE, 115. Prosopis, 153, 229. Pseudocyphellaria, 86. Psidium, 182, 232. Psychotria, 185, 207, 234. Pteris; 777, 114; 115; 225. Pycreus, 127. Pyrenula, S4, 86. Radula, 101. Ramalina, 86, 88. Raphanus, 146, 228, 238. Rauwolfia, 785. Relbunium, 207, 234. RHAMNACEAE, 171. Rhizoclonium, 89, 90. Rhizogonum, 267. Rhizophora, 182, 194, 232, 237, 247. RHIZOPHORACEAE, 182. RHODOPHYCEAER, 99. Rhodymenia, 99. Rhynchosia, 79, 154, 229, 237, 261. Riccia, 101. Ricinus, 170, 231, 241." Rinodina, 83, 87. Roccella, 87, 88. Roccellaria, 87, 88. Rolandra, 263. Rosacean, 146, 242. Rubia, 207. RUBIACEAE, 204, 241, 243, 248, 251. Ruppia, 116, 225, 237. Rushes, 247. RuTackakg, 158. Rutilaria, 90. AMERICAN ACADEMY. Salvia, 197, 198, 233, 238. Salvinia, 115, 225, 237. SALVINIACEAE, 115. Sanguisorbea, 146, 228. SAPINDACEAB, 170, 241, 243. Sapindus, 171, 232. Sarcanthus, 792. Sargassum, 92, 93. Sarratia, 736. Scaevola, 208, 235, 237. Scalesia, 216-220, 235, 236, 242-245, 247, 249, 251, 254, 255. Schizophyllum, 83. Schlotheimia, 104. Scirpus, 129, 130. Scleria, 130, 227, 237. Scleropus, 135, 136. Sclerothrix, 178, 232. Scoparia, 202, 234. Scrophulariacea, 202, 234. SCROPHULARIACEAB, 202. Scytonema, 89. Selaginella, 262. Senebiera, 146, 228. Sesuvium, 144, 228, 237. Setaria, 124, 125, 226. Seymour Islands, 250. Sicyos, 208, 235, 237. Sida, 773, 174-176, 231. SIMARUBACEAE, 158, 243. Sinapis, 746. Solanacea, 201. SoLANACEAR, 198, 241, 243. Solanum, 200, 201, 234. Sonchus, 220, 236. Spatoglossum, 93. Spermacoce, 204-206, 207, 234. Sphaeria, 84. Sphaerococcus, 94, 96, 99. Spilanthes, 220, 236. Spondias, 759. Sporobolus, 125, 226. Stachytarpheta, 196, 233. Stenotaphrum, 126, 226. STERCULIACEAE, 176, 243. Sticta, S6, 88. Stipa, 126, 226. Stylosanthes, 79, 154, 229. Surirella, 90. Taenitis, 115, 225. Tagetes, 220, 236. FLORA OF THE GALAPAGOS ISLANDS. 269 Tamonea, 183. Tecoma, 202, 234. Telanthera, 187-140, 228, 247, 251. Teloschistes, 88. Tephrosia, 155, 229, 237. Tetramerium, 204, 234. Teucrium, 198, 233. Theloschistes. See Teloschistes. Thinogeton, 201, 234, 237, 247. TILIACEAE, 172. Tillandsia, 130, 227, 238, 261. Tournefortia, 198, 194, 233. Tower Island, 250. Trianthema, 144, 228. Tribulus, 79, 156, 157, 229, 230, 237, 238, 247, 261. Triceratium, 90. Trichomanes, 241, 262. Trichoneuron, 7727. Trigonopterum, 2/4. Triumfetta, 172, 232. Turnera, 177, 232. TURNERACEABR, 177. Ulva, 90. UMBELLIFERAE, 184, 243. Urtica, 132. URTICACEAE, 182, 243. Usnea, 88. Vallesia, 185, 232. Varronia, 789-191. Verbena, 196, 197, 233, 237, 247. VERBENACEAB, 194, 241, 243. Verbesina, 210, 215. Verrucaria, S6. Vigna, 155, 229, 238. Vincetoxicum, 185, 186, 232. Viscum, 733. VITACEAE, 172. Vitis, 172, 231, 238. Vittaria, 775. Waltheria, 79, 176, 232. Wedelia, 271, 263. Wenman Island, 251. Xanthoxylon, 158. Zanthoxylum, 158, 230, 237. Zonaria, 91, 98, 98, 99. Zygomorphy, 238. ZYGOPHYLLACEAB, 156, 243. EXPLANATION OF PLATES. Puate 1. Fig. 1, Phoradendron uncinatum, Robinson, n, sp. Fig. 2, Bursera malacophylla, Robinson, n. sp. Fig. 3, fruit of ray-flower of Acanthospermum micro- carpum, Robinson, n. sp. Fig. 4, fruit of ray-flower in Acanthospermum hispidum, DC. Figs. 5, 6,7, Telanthera Helleri, Robinson, n. sp. Fig. 8, leaf of Telanthera Helleri, var. obtusior, Robinson, n. var. Fig. 9, Scalesia Helleri, Robinson, n. sp. Fig. 10, the same, a pale of the disk. Puate 2. Fig. 1, Pilea Baurii, Robinson, n.sp. Fig. 2, Telanthera Snodgrassii, Robinson, n.sp. Fig. 3, Acnistus insularis, Robinson, n.sp. Fig. 4, Bidens refracta, Brandegee. Fig. 5, Huphorbia nesiotica, Robinson, n. sp. Prater 38. Fig.1, Scalesia Hopkinsii, Robinson, n.sp. Figs. 2, 3, Scalesia micro- g.4, Pp ’ ’ £ 9%) cephala,. Robinson, n. sp. Figs. 4, 5, 6, 7, Scalesia narbonensis, Robinson, n. sp. Fig. 8, Scalesia Snodgrassii, Robinson, n. sp. ROBINSON.-FLORA GALAPAGOS, PLATE 1. = @) i? fom o ek me. See, — More 1 © Tom ed P Di y Proc. Amer. ACAD. ARTS AND SCIENCES. VOL. XXXVIII. Heliotype Co., Boston. ne NS Se ee ee ee ee eee ee ROBINSON.-FLORA GALAPAGOS. PLATE 2, Proc. AMER. ACAD. ARTS AND SCIENCES. VOL. XXXVIII. Heliotype Co., Boston. ROBINSON.-FLORA GALAPAGOS. Proc. AMER. ACAD. ARTS AND SCIENCES. VOL. XXXVIII. Heliotype Co., Boston, PLATE 3. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 5. — OcToBer, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. CONCERNING GAS-ANALYSIS BY MEASUREMENT IN CONSTANT VOLUME UNDER CHANGING PRESSURE. By THeEoporE WILLIAM RICHARDS. Aaa seth cy ey. ae boot MINT OMe eI eae CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. CONCERNING GAS-ANALYSIS BY MEASUREMENT IN CONSTANT VOLUME UNDER CHANGING PRESSURE. By THEODORE WILLIAM RICHARDS. Received June 2, 1902. In Hempel’s admirable book upon gas-analysis is described a method of exact analysis which has not received the general attention that it de- serves. Instead of measuring the changing volume under constant pres- sure, he suggested measuring changing pressure in constant volume.* Possibly one reason for the neglect under which this excellent method has suffered is the demand made by it for the use of a large quantity of mercury. One object of this paper is therefore to point out that the same principle may be applied conveniently in a simpler manner. In Hempel’s apparatus the gas to be measured is confined in a bulb immersed in a mercury-trough, and the absorption is effected in an Ett- ling-Doyére gas-pipette. It is more convenient to measure the gas in a bulb provided with a capillary outlet at the top, and to conduct the ab- sorption in an ordinary Hempel pipette of small size, or in one of the simpler forms of pipette recently used in this laboratory. f This manipu- lation of course introduces the necessity of using rubber connections, which Hempel desired to eliminate ; butif they are properly connected { and securely wired, their introduction is not usually a serious defect. If not more than 25 per cent of the gas is to be absorbed in any one process, a water column of 2.5 meters, easily obtainable in the labora- tory, is enough to furnish the necessary change of pressure ; hence water may be used as the liquid in the measuring vessel instead of mercury, pro- * Hempel’s Gas-analysis, translated by Dennis, p. 76 (1902), p. 44 (1892) (Mac- millan). + Richards, These Proceedings, 37, 278 (1901). Zeitschr. anorg. Chem. 29, 359 (1902). ¢ Richards, ibid, pages 275 and 362, respectively. VOL. XxXxvi1I.—18 274 PROCEEDINGS OF THE AMERICAN ACADEMY. vided of course that none of the components in the gas to be analyzed is soluble in water. As will be shown, the use of water greatly simplifies the measurement of pressure, for an appreciable error in the height of the column causes no appreciable effect on the result. Hence no cathe- tometer is needed, and the simplest apparatus suffices. Although a marked tube (such as an inverted burette) may be used for the attainment of constant volume, the measuring apparatus consists preferably of a bulb of about 50 ¢.c. capacity with a single mark upon its stem.* This bulb should have a capillary tube above with-an internal diameter not far from 1 mm.,f while below it is provided with a straight tube about 20 cm. long and 7 mm. in diameter, with a sharp line etched just below the bulb. To this tube is attached a levelling bulb by means of arubber tube about 150 cm. long.{ The levelling bulb is conveniently hung from a bent stick, which may be clamped to the iron ring-stand, either above or below the table-top. Of course the bulb should be en- closed in a water-jacket, conveniently made from an inverted broken bottle, in order to insure constancy of temperature. The arrangement is represented in the Figure. In case the full absorption of 25 per cent is expected, it is conven- ient, although not necessary, to begin with an excess of pressure. So much gas is put into the apparatus for analysis that a pressure of about a meter of water (measured by means of a wooden meter-rule) is neces- sary to compress the gas exactly to the mark on the stem. About 10 per cent (9 ¢.c.) more gas than the amount needed to fill the space under atmospheric pressure may be introduced for this purpose. The height of this water-column is reduced to the mercury standard at 0° by multi- plying it by about zr 3 § and the reduced value is added to the barometric * Mr. W. N. Stull has suggested the use of a tube with several connected bulbs with as many marks in order to attain a wider range with less change of pressure. This apparatus will soon be tested in this Laboratory. t+ The rubber tube attached to the capillary should be very thick-walled and have an exceedingly fine bore. It should be wired to the glass in the manner shown in the diagram. + In order to prevent the admission of small air-bubbles into the measuring bulb from the long rubber tube, a trap may be formed by bending the lower glass tube through 100°, or else by making a loop in the rubber tube in the fashion shown in the diagram. This precaution is very rarely necessary, however; it is much better to be certain in the first place that no such air-bubbles are present. § The divisors corresponding to various temperatures of water column are as follows :— 10° Divisor = 13.60 20° Divisor = 13.62 15° p Blsiol 25° = = IBGE: CONCERNING GAS-ANALYSIS. RICHARDS. SS SS ON, 276 PROCEEDINGS OF THE AMERICAN ACADEMY, height. After the absorption of one of the components a lower pressure is needed to effect the same adjustment. The loss of pressure gives the means of computing the percentage composition of the gas. Of course the tension of aqueous vapor should be subtracted from the total readings since the gas is moist; this important correction seems to have been over- looked by Professors Hempel and Dennis in the second English edition, although correctly stated in the first.* The tension of aqueous vapor does not affect the change of pressure unless there is a change of temperature. The following figures, of two trial analyses of air kindly made by Mr. Edward Mallinckrodt, Jr., serve to illustrate the method. The minus sign before the second reading signifies that the counterpoise bulb was be- low the other, almost as far as the level of the floor. II. Difference of water level at first Difference of water level after absorption of oxygen Mercury equivalent to first difference +100 0 cm. —128.0 cm. + 73.3 mm. — 93.8 mm. +100.0 em. —126.5 em. + 73.8 mm, — 92.7 mm. Mercury equivalent to second difference Total loss of pressure . 167.1 mm. 166 0 mm. Barometer (corrected to 0°) Initial pressure of moist gas = 752.2 + 73.8mm. = Tension of aqueous vapor (l° = 27.6) Initial pressure of dry gas = loss of pressure initial dry pressure Percentage of oxygen = At another time, Mr. W. N. Stull kindly made another test of the ap- paratus, finding the following percentages of oxygen in the air of the laboratory :— 100 X 173.5 mm. 831.8 mm. 100 x 170.2 mm. == 20805 818.0 mm. * See page 77 in edition of 1902, and page 69 in edition of 1892 (Macmillan). RICHARDS. — CONCERNING GAS-ANALYSIS. Pa 100 x 168.9 mm. 809.7 mm. = 20.86. The mean of all these analyses indicates 20.85 per cent by volume of oxygen in the air of the laboratory, a value which is probably Very near the truth.* It is interesting to note that the difference between the results 20.94 per cent and 20.80 per cent is caused by a difference of reading in the water column of 15 mm. Hence it is clear that a meter-stick, or a rod provided with labels whose distance apart may be measured at leisure, is quite sufficiently accurate as a means of measurement for ordinary purposes. ; Attention should be called to several possible errors which must be guarded against in this process. (1) Either no air should be permitted to remain permanently in the tube connecting the pipette and the measuring bulb, or else the volume of the residual bubble should be suitably corrected, according to circum- stances. (2) None of the absorbing liquid should be run into the measuring bulb; or if by accident some of the absorbing liquid finds its way into this bulb, it should be washed away with pure water, in order that it may not affect the tension of the aqueous vapor. (8) Care should be taken to allow time for the equalization of the temperature change caused by the compression and expansion of the gas as well as for the running down of adhering water. (4) The temperature must be kept constant, within 0.05° centigrade, a condition which is easily fulfilled by stirring warmer or cooler water into the open receptacle. If an accurate thermometer is not at hand, a sensi- tive air thermometer may be improvised for this purpose, — for change of temperature must especially be guarded against. The ingenious device suggested by Professor Hempel for this correction serves well.f Of course all these precautions apply equally to the usual measurement under constant pressure, but they are not always heeded. Attention may be called also to the fact that neither the constant- volume nor the constant-pressure method necessarily affords the true measure of the volume of the absorbed gas. This would only be true if all gases were perfect gases ; as a matter of fact, no accurate measure- * The method was tried also by a large class of beginners in gas-analysis with successful results. + Hempel (translated by Dennis) (1902), page 84. 278 PROCEEDINGS OF THE AMERICAN ACADEMY. ments of the actual slight contractions or expansions which take place on mixing gases seem to have been made. These are, however, so small, that for ordinary purposes they may be neglected. It may be a matter of interest to call attention one by one to the ‘percentage effect of the various probable sources of error in the deter- mination of oxygen in air, supposing in each case that the particular error under consideration is the only one present. ‘The analysis is sup- posed to be conducted in a room having the atmospheric conditions of 20° temperature and 760 mm. pressure, with the apparatus described above. ‘The error is recorded in percentage of the total volume taken. (1) Omission of the correction for aqueous vapor 0.4 per cent. (2) Error of 1 mm. in reading water column. . 0.01 “ (3) Constant error of 1° in thermometer in water- ACKCU Eye yer me lve aoe (cs A atime tee OO mie (4) Change of 1° in temperature of water-jacket 0.5 ae (5) Constant error of 1 mm. in reading barometer Colmman sn ule 5 PRR SG UAUER eS (6) Change of 1 mm. in Aen Weee PRCESULG ye Olon ws (7) Admission of absorbing liquid into measuring bulb, according to amount oe a ki toperhaps . 1 Ke (8) Maximum error from adhering water, perhaps 0.5 se (9) Possible error from adiabatic contraction, per- TALS ears ives eee chats erent se (10) The retention of a bubble of gas 1 cm. long iInttherlimm= capillary. be ty) lene oe Oe “ That all the significant errors may be sufficiently avoided by reason- ably careful work is clear from the actual results; but the enumeration of their widely varying effects may be useful in showing the novice where to employ his precautions. Most of these errors apply equally to any kind of gas-analytical work, but many of them are persistently disregarded in common practice. If the mixture to be analyzed contains gases easily soluble in water, mercury must of course be employed in the measuring bulb, and a good cathetometer should be used for measuring the changes of pressure. A poor cathetometer is often worse than none. RICHARDS. — CONCERNING GAS-ANALYSIS, 279 SUMMARY. In this paper is described a method of gas-analysis which demands only the simplest apparatus, and yet is capable of yielding results accurate enough for many ordinary purposes. The limitations of this apparatus are compared with those of other gas-analytical methods. In particular the importance of applying the correction for aqueous vapor in all meth- ods which depend upon the measurement of changing pressure in constant volume is emphasized. It is worthy of remark that this simple method forms a highly instruc- tive exercise in gas-analysis for a class of students in this subject. CampBrincGE, Mass., U.S. A. May 31, 1902. ans all taken at t° da * solid ) p = per cent of solvent (100: =sp)== * * golid The mixtures were made of such proportions that each contained ap- proximately 20% of the solid, and two grams was necessary for each determination, one half the full capacity of the cup, which was necessary to maintain a uniform temperature. The index and specific gravity of each solid were taken at two temperatures, 60° and 70°, or 70° and 80°. The following results were obtained with the hydrocarbons from Pennsylvania petroleum : — MABERY AND SHEPHERD. — SOLID HYDROCARBONS. Distillate, 50mm. 260°-262.° CysHys. Per cent of solvent, 77.86. 6 oe gohidym. 2aek4- Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 60° 0.7780 0.7769 49° 9h 3H! ae 0.7711 0.7709 49° 43! Calculated for solid: Ny. Molecular Refraction. 60° 1.4432 110.61 (Us 1.4260 ; 107.68 Distillate, 50mm. 272°-274.° Cy4H 50. Per cent of solvent, 82.53. Cet CP COTS CoN rca Ek ea pate Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 60° 0.7785 0.7771 49° 5! gil Os 0.7734 O19 49° 40! Calculated for solid : De. Molecular Refraction. 60° 1.4482 113.08 70° 1.4251 112.00 Distillate, 50mm. 282°-284°. C,;Hso. Per cent of solvent, 84.05. he Cg ACH TO LS Rg AS Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 70° 0.7724 0.7765 49° 50! 80° 0.7618 0.7632 50° 23! 8! Calculated for solid: Dy. Molecular Refraction. 70° 1.4241 ‘115. 80° 1.4212 . 117. Distillate, 50mm. 292°-294°. Cog Hq. Per cent of solvent, 85.13. eno SOG EOL OLOs « Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 70° 0.7726 0.7780 49° 38! s0°s 0.7618 0.7685 50° 13/ 7! n, 1.4337 1.4304 Theoretical. 107.68 Theoretical. 112.57 Theoretical. 117.2 n 1.4309 1.4373 288 PROCEEDINGS OF THE AMERICAN ACADEMY. Calculated for solid: lity Molecular Refraction. Theoretical. ae Oe 1.4320 22. 80° 1.4505 123.2 TANS Distillate, 5|0mm. 800°-301°. Cy, Hy.. Per cent of solvent, 77.64 fe solid... 920230 Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. n. 70° OMT 0.7757 49° 55! 1.4292 80° 0.7623 0.7655 50° 29! 4! 1.4257 Calculated for solid : Dg. Molecular Refraction. Theoretical. 70° 1.4206 124.2 80° 1.4194 125.45 126.4 Distillate, 50mm. 312°-814°. (C,,H¢s. Per cent of solvent, 86.79. eee Seolidi ay Wigazle. Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture, n. 70° 0.7738 0.7770 49° 40! 6! 1.4297 80° 0.7618 0.7669 50° 14! 6! 1.4272 Calculated for solid: Ny. Molecular Refraction, Theoretical. 70" 1.4184 126.6 80° 1.4170 128.8 131 Having at hand a series of solid hydrocarbons separated from com- mercial paraffine, that correspond in composition to the solid hydrocar- bons from crude Pennsylvania petroleum, determinations of the indices of refraction of these bodies were made for the purpose of comparison. The formulas of the paraffine hydrocarbons are given as they have been determined, although the results have not been published. Distillate, 50mm. 260°-262°. Cy3H4s. Per cent of solvent, 79.84. « & & golid, 20.16. Sp. gr. of mixture. Sp. gr. of solid, Angle for mixtuce, n. 60° 0.7780 0.7706 AG) ot 1.4550 “Ox 0.7668 0.7641 49° 44! 1.4303 é MABERY AND SHEPHERD. — SOLID HYDROCARBONS. Calculated for solid : nN. Molecular Refraction. 60° 1.4256 106.7 70° 1.4374 PEt Distillate, 50mm. 282°-286°. Per cent of solvent, 78.55. C.5H52. «“ & € golid, 21.65. Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 60° 0.7784 O19 4921 O! 70° 0.7721 0.7707 49° 46! Calculated for solid: 60° 1.4206 70° 1.4194 Molecular Refraction. 117.6 1 Distillate, 50mm. 300°-302°. Per cent of solvent, 82.81. Coz A g6. ee ersonde. who. Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. (Us OVT27 0.7770 49° 50! 80° 0.7625 0.7669 50° 13! Calculated for solid: Tig (Us 1.4287 80° 1.4276 Molecular Refraction. 123.4 126.1 Distillate, 50mm. 3812°-314° C,;Hs.. Per cent of solvent, 79.75. 20.25. 79 oe 6s solid, Sp. gr. of mixture. (Oe 0.7737 80° 0.7630 Calculated for solid: Np. 105 1.4285 80° 1.4226 VOL. xxxvi1l1.—19 Sp. gr. of solid. Angle of mixture. AQ STAD! 30° 15/ 0.7806 0.7699 Molecular Refraction. 129.3 129.9 289 Theoretical, 108. Theoretical. 1 ier Theoretical. 126.4 Theoretical. 131 + 290 PROCEEDINGS OF THE AMERICAN ACADEMY, Commercial Paratline gave the following indices: Per cent of solvent, 78.97. ec OliC, ees Uae Sp. gr. of mixture. Sp. gr. of solid. Angle for mixture. 60° 0.7784 0.7788 49° 6! 3g! 70° 0.7727 0.7732 49° 35! 6/! n. 1.4340 1.4311 The results described above show a close agreement in the hydro- carbons separated directly from petroleum, and the corresponding bodies from paratffine, as well as the application of this method for obtaining the molecular refraction of solid bodies. Proceedings of the American Academy of Arts and Sciences. Vou. XXXVIII. No. 7. — Ocroser, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. Ill.— THE RELATION OF CHANGING HEAT CAPACITY TO CHANGE OF FREE ENERGY, HEAT OF REACTION, CHANGE OF VOLUME, AND CHEMICAL AFFINITY. By Turopore WiiiiaAmM RicHaRDs. THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. Ill. THE RELATION OF CHANGING HEAT CAPACITY TO CHANGE OF FREE ENERGY, HEAT OF REACTION, CHANGE OF VOL- UME, AND CHEMICAL AFFINITY. By TuHeopore WILLIAM RICHARDS. Received June 16, 1902. I. Systems Invotvine A Minimum oF CONCENTRATION EFFECT. Jutius Ropert Mayer showed, sixty years ago, that when a gas is compressed, the work of compression reappears almost exactly as heat. One of the circumstances which permitted the discovery of this relation- ship is the fact that the heat capacity of a gas at constant volume is ap- proximately independent of the volume. If the heat capacity of the gas were diminished by the compression while the other influences remained unchanged, it is clear that some of the heat energy already in the system would be displaced by the compression, and hence that the apparent evo- lution of heat would be made up of two added quantities, one due-to the work put into the system from the outside, and the other due to the lessened heat capacity of the system. Thus the total evolution of heat would be greater than the heat corresponding to the work which had been done upon the system, unless the diminution of heat capacity in- volved the storing of energy in potential change. In order to develop the reasoning, step by step, this latter possibility will be waived for the present, and taken up again after the facts have been studied. If @ is used to represent the unknown total heat energy necessary to raise the original system from the absolute zero to the reaction tempera- tures, €V’ that necessary to raise the final system through the same in- terval, W the outside work done upon the system, and U the heat actually evolved, we may represent the possible relationship as follows : — U=W+a-—W Unfortunately 1 and @ are not definitely known, hence the exact solution of the equation is not possible at present. Nevertheless, a qualitative study of the situation in the light of the facts leads to inter- 294 PROCEEDINGS OF THE AMERICAN ACADEMY, esting results, as will be shown. In the case of a perfect gas @ = W, hence the above equation reduces to the form = W, the fact pointed out by Mayer. @ and @ are of course functions of the respective heat capacities. The analogy which has been shown to exist between the work of chemical compression and the work of gaseous compression * seems to afford a means of extending this logic to the liquid and the solid condition, and thus to afford a clue to the vexed question as to the relationship of free energy and total energy. It is well known that the heat capacity of a solid or liquid system usually changes slightly during the course of a reaction, and it has been shown in numerous isolated instances that compression usually tends to diminish the heat capacity of solids and liquids. The diminishing specific heat with increasing specific gravity of the allotropic forms of sulphur, phosphorus, silicon, and carbon may be mentioned as other examples of the same general principle. We should expect, then, if no other complications are involved, to find an excess of heat evolved, over and above the chemical work concerned in the reaction, in all those cases where the heat capacity diminishes during the reaction, and vice versa. But what measures have we of the chemical work involved ? By many the “free energy,” or the energy available for outside work, is taken to represent the chemical energy. For the sake of argument, let us assume temporarily that this is the case, always bearing in mind * After the preceding paper was printed, my attention was kindly called to the fact that in 1881 Miiller-Erzbach pointed out the parallelism of contraction and heat of reaction in some cases (Ber. d. d. ch. Ges., 14, 217, 2048; Wied. Ann., 13, 522.) More recently, Hagemann has called attention to the same relation (a brief paper published privately by Friedlander of Berlin in 1900). These facts were wholly unknown to me at the time of writing. The reason why the discovery has not had more effect upon chemistry is undoubtedly because these investigators did not call attention to the effect of the different compressibility of different sub- stances, and drew no corresponding conclusions from the observations. Unless compressibility is considered, the exceptions to the rule are too frequent to permit satisfactory generalization. For examples of the express or implied denial of the significance of this relation, see Ostwald, Grundriss der allgem. Chem., 187 (1899), also Békétoff, Chem. Centralblatt 1894, II. 229. In neither case was compressibil- ity considered. + Richards, These Proceedings, 37, 399 (1902); Regnault, Ann. Chim., 73, 15 (1840) ; Thomsen, Thermo-chem. Untersuch., 1, 52 (1882); Kahlbaum, Zeitschr. anorg. Chem., 29, 177 (1902). ' ¢ Ostwald, The Chemometer, Zeitschr. phys. Chem., 15, 399 (1894). RICHARDS. — CHANGING HEAT CAPACITY. 295 the fact that it is an assumption, and being ready to abandon the position when it has been proved untenable. The immediate problem under investigation then resolves itself into the following question: Has the change of heat capacity any definite causal relationship to the relative magnitudes of the free-energy change and the heat of the reaction ? Throughout this paper the inductive method rather than the deductive one is to be used in all the reasoning. Hence the first step is the comparison of actual data concerning a number of carefully studied reactions. Unfortunately the change in free energy can be computed from actual data only in the case of easily reversible changes; and these form but a small minority of the cases of chemical reaction. The reversible gal- vanic cell was shown by Helmholtz * to belong to this class, aud may therefore be used as-an example. . Among the many galvanic cells which have been measured, not all are immediately available for the present purpose. In the first place, only a few heat capacities of solutions have been accurately determined; and in the next place, in some of the cells perceptible electromotive energy is to be ascribed to the unequal balancing of osmotic pressures, which has nothing to do with the affinities involved. We must then select cells containing two liquids in which the extent of ionization and the migration velocities are similar, the anion identical, and the electromotive force. and heat of reaction well known. The series of reversible cells which seems to fulfil these conditions most satisfactorily is that composed of pairs of the sulphates of copper, nickel, iron, zinc, and magnesium. ‘The heat capacities of these solutions have been accurately determined by Marig- nac ft and Thomsen ¢ and the electrical potentials have been determined by Wright and Thompson. § In order to illustrate more clearly the table containing the results obtained from these cells, a single case may be given here in detail. The common Daniell cell is chosen for this purpose, using solutions of the strength MSO,.200H,O because the heat capacities of such solutions * Helmholtz, Sitz. ber. Berlin Acad., 2 February and 7 July (1882), Ges. Abh. Teyoh, JUL + Marignac, Ann. Chim. (5), 8, 410 (1876). t Thomsen, Pogg. Ann., 142, 387 (1871). § Wright and Thompson, Phil. Mag. (5), 17, 288 (1884), 19, 1 (1885). This work is revised in connection with others by Wilsmore, Zeitschr. phys. Chem., 35, 291 (1900). 296 PROCEEDINGS OF THE AMERICAN ACADEMY. have in every case been carefully determined. The chemical reaction taking place in the cell may be represented by the following equation : — Zn + CuSO, . 200H,O = ZnSO, . 200H.O + Cu. The change in the heat capacity of this system may be computed easily by subtracting the total heat capacity of the factors from that of the products. The “absolute” standard of heat capacity, the mayer * (or the heat capacity which is raised 1°C by 1 joule of energy), is peculiarly convenient for calculations of this kind; hence it is used below. The following table contains the data in question : — Factors. : PRODUCTS. mayers. mayers. CuSO, 200H,O ZnSO, 200H,0 (0.9516) (8762.7) X (4.181) = 14,970} (0.9523) & (8764.5) X (4.181) = 14,989 Zn = 26} Cu = 24 Total Factors 14,996 Total products 15,018 Difference 1% Thus the heat capacity of the system is increased by 0.11 per cent during the reaction. Since this is the case, we should expect to find that some of the heat energy actually evolved in the reaction would be needed to “ fill” the extra capacity, and hence would not become manifest as rise of tempera- ture. Asa matter of fact, the observed evolution of heat energy in the reaction (210 kilojoules) is less than the electromotive energy (1.10 x 96,580 x 2 = 213 kilojoules) by about 3 kilojoules. Hence the data are consistent with the theory as to sign; and since both figures are small in proportion to the totals, the order of magnitude might also be consistent. A single case does of course suffice to prove a point of such impor- tance, hence ten galvanic cells, comprising every combination of the five metals before mentioned, are given in the following table. Wright and Thompson used amalgamated zinc, but Richards and Lewis ¢ have shown that amalgamation makes no essential difference in the potential of this metal, because of a singular compensation of effects. The table explains itself; the fourth and eighth columns contain the significant results to be compared, namely the change in heat capacity and the so-called “bound energy.” * Richards, These Proceedings, 36, 327 (1900). t Richards and Lewis, Zeitsch. phys. Chem., 28, 1 (1899). RICHARDS. — CHANGING HEAT CAPACITY. 297 Heat Capacities of MS0,+200H,0+M’, Observed Heat of |Chemical Reaction. Electro- motive Energy. Factors in Reaction, Factors. | Products. | Reaction. : | ‘* Bound Energy,” -| or Excess of Heat mayers. mayers, mayers. | kiloj’les. | kiloj’les. Ni+-CuSo, 14,997 | 14,966 | + 31 11 | 131 Fet+Cuso, | 14,996 | 14,955 | + 41 134 Zn+CuSO, | 14,996 | 15,013 | — 17 Mg+CuSo, | 14,995 | 14,889 | +106 Fe+NiSO, 14,967 | 14,957 | + 10 2n+NisO, | 14,966 | 15,016 | — 50 Mg+NiSO, | 14,966 | 14,891 | + 75 Zn+FeSO, 14,955 15,015 — 60 Mg+FeSO, | 14,955 | 14,890 | + 65 Mg+znSO, | 15,014 | 14,890 | +124 The data in this table are reduced as nearly as possible to the same standards. The heat capacities and electromotive forces correspond to solutions containing two hundred molecules of water to every molecule of salt; the electromotive force scarcely changes with dilution. It is not always easy to ascertain from Thomsen’s statements the dilution corre- sponding to the heat of reaction, but in every case the solutions were at least as dilute as this, being sometimes of twice the dilution. Here also such further dilution can cause but a negligible effect on the result. The atomic weights used in Thomsen’s work were unusually crude, even for that day, and all his results have been recalculated to correspond to more accurate values. For example, the values given by him for mag- nesium correspond to the value 24. instead of 24.36; and accordingly since magnesium itself was weighed, all his data for this element must be raised by one and one-half per cent.* The details of these and other similar calculations may be omitted, since their outcome does not seri- ously affect the conclusions attained. * In passing it may be pointed out that a complete recalculation of ail heats of reaction would be demanded if the standard of atomic weights were changed to) ©) = 15:879: 298 PROCEEDINGS OF THE AMERICAN ACADEMY. It will be observed that in every case the loss of heat capacity has the same sign as the excess of heat evolved; and in general, where one is large the other is also large. ‘This relationship is illustrated by the accompanying diagram. In comparing differences between such large numbers one could hardly expect exact parallelism; but the two phe- nomena run so closely together that one is forced to infer the existence of a fundamental connection between them. yi-Cu Fre-Cu \ Zn-Cu Mg-Cu Fe-Ni MUg-Zn DraGram ILLUSTRATING PARALLELISM OF CHANGE OF Heat CapPpaciry AND “ Bounp ENERGY.” Notre. The left-hand zigzag line depicts change of heat capacity in the ten cells given in the previous table, and the right-hand zigzag line depicts the ‘‘ bound energy” or the difference between the heat of reaction and the available free energy of the reaction. In order to avoid confusion, these curves are referred to different ordinate axes, indicated by the two vertical zero lines. A few more similar cells with other anions might have been added to this list from the data of Wright and Thompson, Marignac, and Julius Thomsen. ‘The following exhibit relationships similar to those already given in detail: zinc-copper nitrate; zinc-lead nitrate; zinc-magnesium nitrate; lead-copper nitrate; * legd-magnesium nitrate; copper-magne- sium nitrate; zinc-magnesium chloride. Unfortunately the great bulk * The heat value for this cell, calculated from the results of Jahn (Wied. Ann., 17, 595 (1882]), do not at all agree with the results of Thomsen. For the Ag-Cu- nitrate cell Jahn gives 10.6 Cal. per gram equivalent, while Thomsen gives 17.8 Cal.; and for the Ag-Pb-nitrate cell Jahn gives 21.5 Cal., while Thomsen gives 25.6 Cal. The value for the Pb-Cu-nitrate cell would then be 10.9 Cal. according to Jahn, and 7.8 according to Thomsen. I selected the latter value. RICHARDS. — CHANGING HEAT CAPACITY. 299 of the remaining data cannot be utilized at present because of a lack in each case of one or two of the necessary figures. More complicated cells, in which also the osmotic tendencies are nearly balanced, show the same tendency. For example, in the cell Hg, HgCl, KCl, KNO,, KBr, HgBr, Hg, which has been studied by Bugarszky,* there is a loss of heat capacity of about 26 mayers per gram equivalent during the reaction, while the observed heat energy exceeds the electro- motive energy by 4.3 kilojoules. When the iodides are substituted for the bromides, the loss of heat capacity is 13 mayers, and the electro- motive energy is less than the heat energy by 8.2 kilojoules. On the other hand, when mercurous oxide and potassic hydroxide are combined with the calomel electrode, a cooling reaction yields an electromotive energy algebraically 23.5 kilojoules greater than the heat energy, while the heat capacity gains 44 mayers. These figures are of the same order of magnitude as before, and in the expected direction. They are not included in the table because in them the osmotic energy may amount to an appreciable quantity, which cannot be wholly determined until the solubilities of the nearly insoluble salts are known. Among all the cells which have been studied, including nearly if not quite all of those for which even moderately accurate data exist, only the cells containing aluminum as one of the metals disagree with the generali- zation. The solutions of salts of aluminum have usually a very large heat capacity, but yet the heat evolved is greater than the electromotive energy. Great discrepancies exist in the determination of this last quan- tity, however; for Wright and Thompson give as the potential of the cadmium-aluminum chloride cell only 0.05 volt t, while .Neumann’s $ values indicate 0.87 volt. It is not impossible that even the latter may be too low; for aluminum may be like chromium in its anomalous elec- trochemical behavior. § In the light of the discrepancy it seems permis- sible to reject the cells containing aluminum until more certain knowledge is obtained, From the accepted data two important connected inferences may be drawn with considerable security. ,In the first place, it appears that wn- changing heat capacity is an essential condition in determining the equality of the free electrical and the total heat energy changes, in reactions from * Bugarszky, Zeitschr. anorg. Chem., 14, 145 (1897). + Wright and Thompson, Phil. Mag. [4], 19, 117 (1885). t Neumann, Zeitschr. phys. Chem., 14, 225 (1894). § The use of aluminum as acurrent rectifier is well known (Graetz, Wied. Ann., 62, 189; Pollack, Zeitschr. phys. Chem., 24, 546.). The same question is concerned in this phenomenon, 300 PROCEEDINGS OF THE AMERICAN ACADEMY. which osmotic work is eliminated by the balancing of nearly equal pressures. In the next place, as has been stated, the sign and magnitude of the dif- ference between the free and total energy changes is dependent upon the sign and magnitude of the change of the heat capacity of the system. These inferences are of very great interest, for according to the well- od 7 * Be the temperature-coeflicient of the free energy change is a simple function of the difference between the free and the total energy change. More- over, the effect of the change of heat capacity of the system on the total energy change was pointed out long ago by Kirchhoff in the well-known known equation of Helmholtz, negra — V=ne T we know that U : TRU where A represents a finite change. Hence we may draw the further inference: The change of the available or free energy of a reaction with the temperature must have some fundamen- tal connection with the change of the total energy with the temperature. This fundamental connection becomes manifest on comparing the actual equation —A K= Oh Cl be : AWA values of —— with those of the former quantity being given accord- A aT Or ing to the equation of Kirchhoff by the change in the heat capacities, and the latter being calculated from the difference between the total and free energy changes by the equation of Helmholtz. The following table contains the comparison : — | hive Aire U Wastd Factors of Reaction. —AK= T° T—291°° oT e mayers. mayers. Ni+CuS0O, + 31 — 69 Fe+CuS0, + 41 — 75 Zn+CuSO, —17 Mg—CuS0O, +106 Fe+NiSO, + 10 Zn+NiSO, — 50 Mg+NiSO, + 75 Zn+FeSO, — 60 Mg+FeSO, + 65 Mg+FeS0O, +124 f. 2. 3. 4. 6. 6. Uk 8. $ —" S * In this equation n represents the number of equivalents, ey represents 96,580 coulombs, z the potential, U the total heat of action, and 7 the absolute temperature. RICHARDS. — CHANGING HEAT CAPACITY, 301 : U The last inference drawn above is supported by this table. Clearly me is related to The two always bear opposite signs, and in general Vi one is large ree the other is large. The ratio of these two coefficients varies from 1 : 0.13 to 1 : 1.70, neglecting the fifth cell, where the values are too small to be significant. The average is 1 : 0.53 — that is to say, the free energy of a given reaction changes on the average about twice as fast as the total energy with change of temperature, but in the opposite direction. When the total energy increases, the free energy diminishes. OA uel Oy i QT” Expressed algebraically, in which the value of J/ aver- ages about 2. The relation of these two series of data is pointed out yet more clearly by means of the accompanying diagram, in which several of the cells are represented graphically. In this diagram energy is plotted vertically, and temperature in the direction of the axis of abscissae. The lines marked U give the actual quantities of heat evolved in the chemical reactions, the change with the temperature being calculated from Kirchhoff’s equation, while the lines marked A give the actual magnitude of the electromotive energy per gram molecule. (See next page.) On extrapolating the several lines, it is evident that each pair tends to converge at a point not far from absolute zero. There is no reason for surprise at this fact; indeed, such a result is a necessary consequence of the equation of Helmholtz, in which A — U=0 when 7° =0°. The interest centres about the fact that the U always increases when A de- creases with the temperature, and vice versa. It will be noticed that in order to converge at the absolute zero these lines must be not exactly straight, but slightly curved, — at least the lines for the free energy must be. This is only natural; for if U steadily in- creases with the temperature when A is diminishing, 7 — A will grow at a rate which is greater than that due to the change in A alone. —A A are Se : dA Hence gee 7 also will increase as the temperature rises. ap could be constant, or A: 7’ a linear relationship only in the case of the constancy of U. Asa matter of fact Bugarzsky’s results enable one to conclude that the temperature coefficient is on the average about 3 per cent higher at 30° than it isat 10°.* Of course more accurate measure- * This calculation is based upon all except one of the cells for which Bugarzsky gives data. The mercuric sulphide cell is rejected because of known irregularity. Zeitschr. anorg. Chem., 14, 157 (1897). 302 PROCEEDINGS OF THE AMERICAN ACADEMY. | “mall iC ir | T Soe EEE oe 500 kj REE ET i ae Het L H | = [ [ aim Sle | JE Mg-Cu Sw ah 400 kj ES | a TN. +t 7 Me = 300 kj al i ua el i | ile | | y st 200 kj FE ial ibabaleaires = } Zn Cu | sal inane na SS stapes = SURES aor a5 ae, ZL Fe-Cu» Steafmuls rE aI = == asset == a = { T i qelaSe -— mi J Ni-Cu 100 kj dei d | EEEEEEEEEE Ea : bebe eee mo oot OF le [ais ah ioe iP Zn-Fe | Fac i | (Loss ae Le feat pe oe —-—+- 4-F + 3-954 4 \ Ni-Fe) | —=t a a aH | 213°C 200°C, -100°C orc U = heat of reaction. A = electrical energy. Ordinates represent energy, abcissae temperature (Centigrade). RICHARDS. — CHANGING HEAT CAPACITY. 303 ments are necessary to attain a precise knowledge of this relationship of the temperature coefficients ; and moreover it probably differs with dif- ferent cells. The foregoing calculations are merely for the purpose of orientation. Qualitatively all the results correspond with the theory at first proposed. In every case where the heat capacity diminishes, the heat evolved is greater than the free-energy change. But in some cases the difference is very great; and the suspicion arises that perhaps the free-energy change is at least as much smaller than the sum of the attracting energies as the heat of reaction is greater than this sum. Is there any method of determining quantitatively the heat which has been displaced by the change of heat capacity in order to test this question? If the free- energy change could be proved to be equal to the total-energy change after correction for change of heat capacity, it would be fairly safe to assume that this two-fold result really represented the attracting energies. If, on the other hand, the heat evolved is still the larger, even after correc- tion for the change of heat capacity, there would be valid reason to suspect that the free-energy change is less than the sum of the affinities. Thus the question is a very fundamental one; but unfortunately the exact computation of how much of the heat energy which has been needed to raise the system from the absolute zero is still present as heat vibration, and how much has been expended in separating the atoms, and thus stored as potential energy, is impossible.* Nevertheless, the heat still present as vibrational activity obviously cannot exceed the total heat which has been put into the system, and this total may be calculated with considerable exactness when the specific heat of ice at very low temper- atures is known with accuracy. For the present, as usual, an approximate calculation must suffice. Making allowance for every circumstance, it is hardly conceivable that more than 2500 kilojoules of heat energy have thus been introduced into the system Mg + CuSO, + 200H,0, in order to raise it from absolute zero to 20°C. But in this system as given in the table on p. 297 the heat capacity changed 106 mayers during its subsequent reaction, or 0.71 per cent of the whole. ‘This change, entirely apart from any heat which might be evolved from the affinities concerned, might cause an isothermal displacement of 0.71 per cent of the heat energy present, f —= * Boltzmann has calculated that about half of the energy is used for each pur- pose, but the result is doubtful. Sitz. ber. Wien. Akad., 63, II. 1871. {+ This assumption is uncertain, but lack of data forbids greater accuracy (p. 293). The result given is probably a maximum, which is all that is desired. 304 PROCEEDINGS OF THE AMERICAN ACADEMY, or at most 0.0071 x 2500 = 18 kilojoules. The actual evolution of heat in excess of the free energy is, however, 170 kilojoules, a figure far greater than the calculated value. Other cells yield the same result; in no case in which osmotic phenomena cause no disturbance is the greatest possible amount of heat displaced enough to correspond to the deficiency of free energy. ‘Two alternatives are now open,—either the free energy does not fully represent the “attracting energy,” or else the heat evolved is too large to correspond to the “attracting energy,” even after correction for the change of heat capacity. Before going further it is well to define precisely one of the terms employed above. The phrase “attracting energy” is used to represent the sum of the work done by all those tendencies which exert a positive attraction. These tendencies may be three in number, — purely chemi- cal attraction or “‘chemism” (such attraction as binds chlorine to itself in chlorine gas), gravitation (which seems to be important chiefly in the heavy metals), and electrical attraction ; but if any other attractive ten- dencies exist, they too are included. In the preliminary study of the phenomena of changing atomic volume, use was made of the possible analogy between an atom ani an elastic sphere of gas, in which every portion of the interior gas was supposed to exert an attraction upon every portion of another similar sphere. Further use of this analogy makes it possible to explain the relation between free and total energy in a plausible manner. ‘The illustration must, however, be somewhat modified as it becomes more detailed and concrete ; for while the temperature of a sphere of gas is supposed to be traceable to the motion of molecules within it, we must imagine the temperature of an atom to be due to the elastic bodily oscillation of the greater part of its substance. Two such elastic balls colliding in space would compress one another. Unless some adhesive tendency caused them to cling together, they would immediately fly apart again with their original velocities, tending to absorb as much heat in their consequent expansion as they gave out during com- pression. Except for the change of direction, their condition would be the same as if they had never met, and no violation of either the first or the second law of thermodynamics would be involved. Tf, on the other hand, some attracting or adhesive tendency caused them to cling together, permanently and irreversibly, they would con- tinue in internal oscillation, the additional energy * of which would be a * That is to say, the energy over and above their original energy of progres- sion before they affected one another. RICHARDS. — CHANGING HEAT CAPACITY. 305 direct measure of the energy of compression. But this additional oscil- lation would signify an evolution of heat.* Suppose now that instead of colliding irreversibly, the two imaginary balls were arrested by an outside mechanism, being allowed to attain gently the same united equilibrium, thus utilizing the energy which would otherwise have become manifest in oscillations as outside work. It is conceivable that in this way all oscillation might be prevented, in which case no heat would have been evolved, and the equivalent of the energy which would otherwise have caused the oscillations will have been used for some outside purpose by the mechanism. The Daniell cell, or better, the Ni-Fe cell, may serve as the actual type of such a conception. It does not necessarily follow, however, that the mechanism would be capable of using all the attracting energy, or would be able to perform an amount of outside work which would be equivalent to the heat. Indeed, the distortion of both atoms caused by their mutual compression might well be expected to cause an expenditure of energy within the atom; hence less would be available for outside work. Such distortion would naturally tend to restrict the heat vibration, and hence diminish the heat capacity. Hence one might have predicted that when there is a loss of heat capacity in the system, the free energy could not equal the attract- ing energy, and that some of the attracting energy must inevitably appear as heat, not available for outside work. In symbolic language, according to the first law of energy, @ = A’ + 9, where € represents chemical attracting energy, A’ free energy, and 72 energy needed to effect a dim- inution of heat capacity. On the other hand, the vibrational activity of heat energy may be supposed to be continually striving to evercome the restrictions which circumstances impose upon it. Hence when the opportunity of an enlarged heat capacity is offered by the progress of a chemical change, this heat energy may be able to perform outside work in addition to * A perfectly symmetrical elastic ball in collision with another symmetrical elastic ball might be supposed to cause this other to rebound reversibly even if attraction existed between them. As ah illustration of this one may conceive of a perfectly elastic ball bouncing on a perfectly elastic surface under the influence of gravity, —its oscillation would continue forever. If, however, one or both of the atoms under consideration is irregular in shape, it is clear that the shock might be so split up into cross-vibrations as to scatter the energy which would otherwise have been used to cause the rebound. Thus heat would be evolved, and the union would be permanent. It is possible that this need of asymmetry in the atom may be the reason why simple pure substances will not combine, but need the catalytic effect of a third substance such as water. VOL. XXXvIII. — 20 306 PROCEEDINGS OF THE AMERICAN ACADEMY. that capable of being performed by the chemical affinity alone. The result would be a cooling reaction and an excess of free energy. This behavior would not be a contradiction of the second law of thermody- namics, because the law states only that heat cannot of ttself do work at constant temperature. Thus the hypothesis of compressible atoms not only is consistent with the ordinary applications of the two laws of energy, but also affords a conceivable picture of the cause of the newly discovered relation OU aA ONE eae On the basis of the present data it is unprofitable to attempt the calcu- : : : 2) A : lation of the mathematical relation of ap to — or to probe further into Cc the mechanism of the change. When more exact data have been ob- tained, it may well be possible to arrive at more definite conclusions. If the contraction of volume on combination could only be interpreted in the light of accurate determination of the compressibilities involved, it seems reasonable that this contraction might be a more exact measure of the affinity than either the free or the total energy change. The foregoing facts and logic seem to lead to the conclusion that the change of free energy of a process does not really represent the attrac- tive energy at work in the process, unless the heat capacity of the system remains unchanged during the reaction. If the heat capacity diminishes during the reaction, the free energy is less than the affinity, and vice versa. This conclusion is contrary to the common belief. If warranted, it shows that the free energy change is a no more satisfactory guide to the affinity than is the heat evolved in the reaction, even when no concen- tration effect is present. The free energy seems to represent rather the remainder left after a resisting energy has been subtracted from the attracting energy. Only when the heat capacity does not change during the reaction may we suppose that the attracting energy, the change of free energy, and the heat of reaction are equal. A consequence of this equality is that the attracting energy, like the free and total energy changes, cannot change with the temperature when the heat capacity is invariable. It is of course true that the change of free energy is the total resultant effect which determines whether or not the reaction will take place. To put the question in another way, the present reasoning seems to afford RICHARDS. — CHANGING HEAT CAPACITY. 307 some basis for separating the change of free energy into two components, one representing the sum of all the attracting energies, and the other a resisting tendency which is connected with the restriction of the heat capacity. It seems to me that further light upon the question of atomic energy is to be had only by means of some such analysis of those com- posite effects which thermodynamics is content to leave superposed. The results of this section may be summed up once more in the fol- lowing sentences : — When the heat capacity of a system does not change during a reaction, and concentration influences are balanced, the free-energy and total-energy changes of the reaction are equal and unchangeable with the temperature, and each may be supposed to represent the total “ attracting energy,” — a term which covers gravitational and electrical attraction as well as purely chemical attraction. When, on the other hand, in such a system the heat capacity of the system changes, it seems reasonable to suppose that the “ attracting energy” lies between the free-energy and thé total-energy change, one being too small and the other too large. II. SysTeEMs INVOLVING APPRECIABLE CONCENTRATION EFFECT. Allusion has been made more than once to the osmotic or gas-pressure work which results trom differences of concentration. Even in the most favorable cases given above, this modifying influence must have had a slight although negligible effect. The present chapter will show how slight this effect may be supposed to have been, as well as indicate the manner of its action in other cases. It is well known, according to the work of Helmholtz, Nernst, and others, that in dilute solutions the potential due to difference of concen- tration is approximately represented by the equation 7 = hn Obviously the reaction falls off in speed more rapidly than would have been expected according to any simple interpretation of the results. It was therefore necessary to study the effect of varying, in turn, each con- dition which might affect the rate of change, in order to find the cause of the anomaly. RICHARDS AND STULL.— BROMINE AND OXALIC ACID. S25 Il. Tue Errect oF VARYING THE CONCENTRATION or Oxatic AcInD. In the following series of experiments the weight of oxalic acid present varied from 0.0587 gram to 4.112 grams in 63.3 cubic centimeters, while the same amount of bromine (0.1601 gram) was originally present in each case. ‘The time of the reaction in each case was 60 minutes. SERIES II. Weight of Oxalic Acid in 63 3 ¢.c. of Solution. Weight of Br. used in an Hour. Weight of Br, remaining. 0.0587 . 0598 0.1175 O90 0692 0.2957 y 0789 0.5873 0765 .0838 0.8810 07 0865 1.1746 073: .0869 1.4682 1.7619 2.0556 2.3462 2.5700 4.1120 The most evident feature of these results is the fact that the speed of reaction does not increase indefinitely with increasing concentration, but that above a point corresponding to about three per cent of oxalic acid by weight, the speed decreases. For a considerable space, between con- centrations containing 0.7 per cent to 4 per cent of oxalic acid, the speed scarcely changes. Kohlrausch and Holborn * state that the specific conductivity of a 3.5 per cent solution of oxalic acid is 508 (10«‘;s), while a 7 per cent solution has a conductivity of 785. ‘The comparison of these data with * Leitvermogen der Electrolyte, p. 157 (1898). 32 PROCEEDINGS OF THE AMERICAN ACADEMY. the newly presented fact concerning the speed of the bromine-oxalie acid reaction furnishes new evidence that the C,O,” ion is that which is attacked by the bromine. The following reasoning will make this point clear. The two following equations represent the two possible equilibria ex- isting side by side in the oxalic solution : — (COO).” + 2H: S$ (COOH), (1) (COO),H’ + H: S (COOH), (2) If C=concentration of the ion C,O,”, C, = concentration of the ion C,0O,H’, C, that of the hydrogen ion, and C; that of the undissociated acid, the law of “mass-action”’ demands the following equations of equilibrium : — C 0,2 = KO, or i (3) Gi C, — K C; or OF eae (4) 2 The concentration of the singly charged oxalic ion will therefore vary inversely as hydrogen concentration, while the double charged ion, (COO),”, will vary in concentration inversely as the square of the hy- drogen concentration. It is fair to conclude from this argument, there- fore, that the repressing action due to ionized hydrogen would be vastly more effective in eliminating doubly charged ions from the solution than those with a single charge. ‘Therefore we might expect a maximum concentration of C,O,” at a moderate concentration of oxalic acid; and since such a maximum is found in the action of bromine upon the solution, we may suppose this action to take place upon the group C,0,”.* THI. Tue Errect or ForeIGN SUBSTANCES. It became now a matter of interest to test the conclusions yet further by adding various foreign substances capable of affecting the ionization of the oxalic acid. Accordingly hydrochloric acid and sodic acetate were used as means of respectively increasing and decreasing the concentration of the hydrogen ion. Each of the following solutions had a volume of 58.3 c.c. and contained 1.496 grams of oxalic acid and 0.1375 gram of bromine. Each was allowed to react for two hours, at 23°.0 * Mr. F.R. Fraprie has lately shown in this laboratory that while alkaline oxalates readily reduce K, Pt Cl, to K, Pt Cly, oxalic acid solutions free from alkali effect this reduction only slowly if at all. This is evidently another case where the zon of oxalic acid is the active group. RICHARDS AND STULL.— BROMINE AND OXALiC ACID. 9327 SERIES III. Weight of Bromine Foreign Substance added. enatitaolklanes gram. INOS, GS Ob. heb 46.60 aes, eo 0.0942 0.34 gram hydrochloric acid (HC!) 0.0642 3.4 grams hydrochloric acid. . . 0.0029 1.0 gram sodic acetate* . .. . 0.1128 Sodie hydroxide to neutralization . 0.1875 (all) Thus both substances acted in harmony with the hypothesis, the hy- drochloric acid retarding the reaction and the sodic acetate hastening it. It is worthy of note that the retarding effect of the acid increases at a faster rate than its concentration, and taking into account the ionized hydrogen already present, it seems quite possible that the relation may be the quadratic one demanded by theory. Another possible disturb- ing influence will be pointed out in the sequel. These observations were verified by repeating the experiments with more dilute solutions, but they need not be recorded, since they furnish no further light upon the problem. Sulphuric acid was found to give a result corresponding to hydrochloric acid. (Exps. 29 to 33.) It became now a matter of interest to determine if the original time- curve might be corrected for the growing concentration of ionized hydro- gen caused by the substitution of bromine as an anion instead of the group C,0,”. Preliminary calculation led at once to the conclusion that the slight increase in the ionized hydrogen could by no means ac- count for the rapid loss of speed observed in the first series. It seemed therefore possible that hydrobromic acid might possess some specific ef- fect, and preliminary experiments showed that this was indeed the case to a surprising degree. In two hours 0.0008 mole per litre of hydro- bromic acid was found to produce as much depressing effect on the total progress of the reaction as was caused by 0.01 mole of hydrochloric acid. * Tt is not impossible that the acetate ion itself may be slightly attacked by bromine, but considerable action is not likely at the low temperature employed. 328 PROCEEDINGS OF THE AMERICAN ACADEMY. Clearly, then, the growing presence of hydrobromic acid must be the cause of the abnormal loss of speed in the original time-curve. But in what manner can the substance effect this change ? The next step was to study in great detail the actual effect of hydro- bromic acid of varying strengths. IV. Tue Errect or Hyprosromic AcIp. The following series give a basis for more certain conclusions con- cerning the action of hydrobromic acid. Series IV is merely a repeti- tion of Series I with a somewhat more dilute solution of oxalic acid, Series V contained a few centigrams of hydrobromic acid, and Series VI contained about twice as much of this acid. In each the total vol- ume was 59.30 cubic centimeters, containing at the start 1.495 grams of anhydrous oxalic acid and 0.1536 gram of un-ionized bromine. As before, the temperature was 23°.0. SERIES IV. Time of Weight of Weight of Reaction Bromine Bromine in Minutes. remaining. used. 10 1091 0445 20 .0970 .0566 30 ; 06387 45 RICHARDS AND STULL.— BROMINE AND OXALIC ACID. 329 SERIES V. ContarininG 0.0675 Gram or HBr. Time of Weight of Weight of Reaction Bromine Bromine in Minutes. remaining. used, 30 124 0286 60 SERIES VI. ConTAINinG 0.148 Gram or HBr. Time of Weight of Weight of Reaction Bromine Bromine in Minutes. remaining. used. 10 1476 .0060 1410 0126 The results given in these tables are plotted in Figure 2, the bromine present at any time being drawn as ordinate, and the time as abscissa. In these experiments the amount of oxalic acid (about 2.5 per cent) by weight was so chosen that the concentration of the reacting oxalic molecular species remained essentially constant during the reaction. In Eee ae | af {tT a If ratte avo SREBIEUE; HH 447 BHS0 SSaoa0ean HH OB van A +t} a PSHSSHELSR08 SERRE egeevecee a BY GUD eSSenee asa Bae ee Gas HH HH BeB4a8 FECES AEE HEHE sae aeedeee acu sieet cectast/ tacts HEUER au8% SAE +t ttt GSB8 Ga BBoe Figure 2. Time in minutes is plotted vertically; the weight of bromine remaining is plotted from right to left. The right-hand curve represents Series IV, the middle curve Series V, and the left-hand curve Series VI. RICHARDS AND STULL.— BROMINE AND OXALIC ACID. 301 the second series it had been found that the solution might contain any amount from one per cent to five per cent of oxalic acid without any serious variation in the speed. Hence the peculiarities exhibited by these curves must be due e:sen- tially to the presence of varying hydrobromic acid gud bromine. ‘The immensely retarding effect of the hydrobromic acid is at once mani- fest, without further calculation, and evidently the greater the amount of hydrobromic acid, the less rapid is the change of rate as the reaction progresses. Thus the downward convexity in Series IV is strongly marked, while in the case of Series VI the curve is but slightly bent. The question at once presents itself, — Would the reaction reduce to a monomolecular one, depending upon the concentration of the bromine alone, if the effect of the hydrobromic acid were eliminated? ‘The results in hand furnish the data for answering this question. An approximate estimate of the speed of reaction at any point in any one of these curves may be obtained by placing a straight-edge tangent to the carefully drawn curve, and noting the ordinate, or bromine value, which corresponds to a given time. ‘This was done quite independently by each of the authors, ana tle rates thus found agreed essentially with one another. The averages of several series of such readings are re- corded in the following table, together with the amounts of hydrobromic acid and the bromine present in each case. The time interval was always reduced to five minutes. ‘The various points are designated by giving the series and the times from the commencement of the reaction, hence they may all be identified upon the diagram, although of course the actual curves from which the readings were taken were drawn upon a much larger scale. The last column contains a function which would be constant if the speed were directly proportional to the concentration of the bromine and inversely proportional to the concen- tration of the hydrobromic acid. (See page 332.) In view of the complicated relations concerning the dissociation of the hydrobromic acid, it is surprising that even an approximately con- stant function could be found. Nevertheless, it is obvious that the require- ee d0h : ment of the function —— is nearly fulfilled. In a case as complicated as 5 4 this the safest method of solution is to eliminate one variable at atime, not attempting to analyze the reaction at once in a single expression. The conditions of the experiment were so planned that such a method of treatment is possible in this case. PROCEEDINGS OF THE AMERICAN ACADEMY. COLLATED DATA CONCERNING SPEED OF REACTION. Designation, Series and Numb of Minutes. (a) Rate = Bro- a mine used in five Minvtes, Milligrams, (0) HBr present. Milligrams, (c) Bromine present. Milligrams. 4.0 3.0 2.4 It is reasonable to suppose that the effect of the hydrobromic acid will be eliminated if we compare speeds of reaction in solutions containing equal concentrations of hydrobromie acid. It is true that the cause of the retarding action of this substance may affect its available concentration, but clearly a first approximation may be reached in this way. We should expect to find the residual difference in rate to be due to the bromine alone, and hence be able to discover at once to what type the bromine reaction belongs. It is easily seen that Series IV contained 124 milligrams of hydrobromic acid after 240 minutes, while Series V contained the same amount after only 89 minutes. Now the amounts of bromine present in these two cases were respectively 32 and 98 milligrams, while the rates were RICHARDS AND STULL. — BROMINE AND OXALIC ACID. 338 0.58 and 1.7 respectively. These numbers are so nearly pro- portional as to indicate beyond question a monomolecular reaction, di- rectly dependent upon the concentration of the bromine alone. The : ab i : corresponding values of —— are respectively 2.2 and 2.1, which of course P g ; Pp y, express the same relation. For further evidence one may compare the values corresponding to 98 to 134 milligrams of hydrobromic acid, in each of which cases a similar equality of the “ constant” is to be noted. The simplest interpretation of this result is to ascribe to hydrobromic acid a catalytic retarding action. This would be rather a classification than an explanation, however, — for no one pretends to understand the exact mechanism of catalytic changes. In cases like the present one, where some of the side influences are difficult to interpret, every possible means of determining the order of a reaction should be employed. The other chief methods which have been proposed are those due to van’t Hoff,* who suggested calculating according to the equation of each of the orders so as to find which answers; or else studying the reaction with varying dilutions, and com- paring the results; and the “isolation method,” which consists in putting in so great an excess of all except one of the reacting substances that it alone changed perceptibly during the reaction. The present case is too complex for the first two methods ; accordingly the last method was tried, but without notable success. When fifteen or twenty times as much hydrobromic acid is added to the solution as will be formed during the reaction, the speed is.so repressed that in order to bring about any appreciable reaction, we were compelled to work at comparatively high temperatures. Even at 50° C. the action was ex- ceedingly slow, and a great part of loss of bromine at this temperature was found to be due to its reaction with water according to the equation 2,0 + 2Br,=0O,+ 4HBr. It might be argued that we could have obtained the value of the speed of this last reaction, and by subtraction eliminate the error introduced by it into the apparent bromine-oxalic acid reaction. Such a course, however, would be unsafe, inasmuch as we know nothing of the mutual influence of the two reactions. Very probably the speed of reaction resulting from the action of water and * Van’t Hoff, Vorlesungen, I, p. 193 (1898). t See Ostwald, Lehrbuch fir allg. Chem., 2, II. 288. Further information con- cerning these matters may be had from the papers by A. A. Noyes, Zeitschr. phys. Chem., 18, 118 (1895), 19, 599 (1896), also T. S. Price, ibid. 27, 479 (1898), etc. Sat PROCEEDINGS OF THE AMERICAN ACADEMY. oxalic acid on bromine is not equal to the sum of the speed of water on bromine plus the speed of the bromine-oxalic acid reaction. The assump- tion of such an equality would at all events be hazardous. Since bromine has no appreciable action on water in the dark at ordinary temperatures, this objection has no important weight when offered against the main portion of the work outlined in this paper. It becomes now a matter of importance to determine the cause of this remarkable specific action of the hydrcbromic acid. That the relation is a complex one goes without saying. As has already been pointed out, the smallness of the effect caused by hydrochloric acid indicates that the de- pression of the dissociation of the oxalic acid is not the only cause at work. On comparing the effect of different concentrations of -hydro- bromic acid in the presence of like concentrations of the other substances, it is seen that the retarding effect grows faster than the concentration of the hydrobromic acid. Thus when 88 milligrams of bromine were present, 65 milligrams of hydrobromic acid allowed a rate of 5.3, while 134 depressed the rate to 1.3 (IV, 31, and V, 123). till A B Cc D E F FIGURE 3. Air was drawn through the solutions, and the liberated iodine in B and E titrated with thiosulphate. Free iodine, equivalent to 22.80 e.c. 7%, thio- sulphate, was found in bottle B, while the acid solution of bromine, D, had given up to E only the equivalent of 2.50 c.c. of 7% thiosulphate. No iodine was set free in Cor F. This experiment was repeated, letting the air first pass through the bromine solution containing hydrobromic acid and then through the aqueous solution of pure bromine. ‘The bromine containing the acid lost bromine equivalent to 2.10 c.c. of thiosulphate ;"5, while the solution free from acid lost the equivalent of 21.00c.c. The strength of the hydrobromic acid was about five per cent. Tt is evident from this that hydrobromic acid in some way combines with bromine. A solution of potassium bromide was found to act in the same way. Similar results have been attained by Jakovkin* by studying the distribution of bromine between carbon disulphide and solutions of bro- mides. He found that even chlorides in solution possess a slight, although far less marked tendency ‘to diminish the reacting tendency of bromine, while the effect of bromides is very great. This effect must be due, of course, to the formation of tribromides in solution, and there is good reason to believe that these are about as highly ionized as the bromides from which they are formed. Hence the retarding action of hydrobromic acid may be supposed to be due chiefly to the tendency of the bromide ion to add bromine, and thus to remove this bromine from the field of action. | The essential details of the action of bromine on oxalic acid may therefore be supposed to take place in accordance with the following scheme, in which the main reaction under investigation is underlined. * Zeitschr. phys. Chem. 20, 19 (1896). 336 PROCEEDINGS OF THE AMERICAN ACADEMY. C,0,” + Br, > 2Br’ + 2CO, == 5 He 4 3Bri sehr =e ay Ht 4 Be’ S HBr ; | Ar But how is it possible to reconcile this complex reaction with the : 5 ao : : simple mathematical expression — which was found to hold approxi- ce mately for moderate dilutions? If we represent by fa* the concentra- tion of the active bromine, by 6 the total concentration of the hydrobromic acid, and by e the total bromine, the requirement of “mass law” would be at least as complicated as (fa) | —“ e—fa)| i h(e— fa)". This is on the assumption that the law holds exactly, and that the hydro- gen tribromide is ionized to the same extent as the hydrobromic acid. Qualitatively this equation holds true; for an increase in ¢ actually causes an increase in a, as the equation demands. If all the 2 values are assumed to be unity, it is clear that fa@ must grow in greater propor- tion than ec — fa with increasing e and constant 6. Moreover, ¢ must grow faster than e — fa; and it is not at all impossible that for mod- 5 : : “al erate concentrations the relation might be such that ee aie @ observed approximate fact. In view of the many-sided relationships shown by the reaction dia- gram, incomplete as it is, and the inaccuracy of the “law of mass- action”? when applied to electrolytes, it is hardly worth while to attempt to construct any more precise mathematical relationship. That which has been pointed out, taken in connection with facts concerning other reactions and the known existence of polybromides, seems to indicate that it is not necessary to class the action of hydrobromic acid among catalytic phenomena; the reaction indicated on this page seems a more probable explanation. SUMMARY. The following me may be nepeated as the chief outcome of the present investigation : * a signifies the rate of change; the active bromine may be assumed as a function of this rate. RICHARDS AND STULL. — BROMINE AND OXALIC ACID. 5oT 1. Bromine water reacts slowly upon oxalic acid at ordinary room temperatures, and rapidly at higher temperatures. 2. The concentration of the oxalic acid may be varied through wide limits without seriously changing the speed of the reaction. 3. Neutralization or the addition of salts of weaker acids immensely accelerates the reaction. 4, The addition of strong acids retards the reaction. 5. Hydrobromic acid has a retarding effect more than ten times as great as hydrochloric acid. 6. The bromine-vapor pressure of bromine water is likewise greatly diminished by the addition of hydrobromic acid or a bromide. 7. Taking all these facts into consideration, it is shown with the help of the “ Law of Mass Action,” and the hypothesis of electrolytic dis- sociation, that the main reaction under consideration is probably the following: C,0,” + Br. S 2Br’ + 2CO,; but that this reaction is greatly retarded, as the change progresses, by the conversion of some of the otherwise available bromine into the complex ion Br3’ by union with the bromine ion formed in the main reaction. CamBriIpGE, Mass, U.S. A. June 6, 1902. VOL. XXXVIII. — 22 ‘ mya a Th QT) iv. : ae Ma ae Me Min Proceedings of the American Academy of Arts and Sciences, Vout. XXXVIII. No. 9.—Ocroserr, 1902. REGULAR SINGULAR POINTS OF A SYSTEM OF HO- MOGENEOUS LINEAR DIFFERENTIAL EQUATIONS OF THE FIRST ORDER. By Otto DUNKEL. REGULAR SINGULAR POINTS OF A SYSTEM OF HOMO- GENEOUS LINEAR DIFFERENTIAL EQUATIONS OF THE FIRST ORDER.* By Orto DUNKEL. Presented by Maxime Bécher, May 14, 1902. Received July 10, 1902. WE will consider in the present paper a system of n differential equa- tions of the form: dy; = fs, 7 : (1) nn DS = +a,,;)y; (Cie 5 che Lp Lz in which the p,,’s are constants, and the a, ,’s are functions, not neces- sarily analytic, of the real independent variable x, continuous in the interval : On = oh We shall require that |a; ,| be integrable up to the point x = 0. For the development of certain sets of solutions we shall make the additional requirement that even after certain powers of log x have been multiplied into | a, ;| the resulting function shall be integrable up to the point z = 0; this requirement will be stated more explicitly later. The point « = 0 satisfying these conditions may be called a regular singular point of the system of equations (1) in conformity with the use of that term by Professor Bécher in the study of linear differential * This paper was accepted in June, 1902, by the Faculty of Arts and Sciences of Harvard University in fulfilment of the requirement of a thesis for the degree of Doctor of Philosophy. + The requirement that the functions a, , should be continuous in 0 Ayz, Ga Ty 2eateoas p=" in which the A’s are constants whose determinant is not zero, is that the characteristic determinants of the two systems have the same elementary divisors. ‘This theorem enables us to simplify the solution of the system (3); for we can write down a second system of differential equations having the same elementary divisors as (3), as follows: (ee Ih Pe, oo m 8) des Fe ees i eee where Zp * Cf. Muth: Theorie und Anwendung der Elementartheiler, p. 2. DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 345 The characteristic determinant of (8) is: (9) A@)= and it will be easily seen that it has the elementary divisors (r — r,)", (r — ie Shes we y= r,,)’. Then, by the theorem above referred to, there exists a set of n? constants A,,,, whose determinant is not zero, such that: k=m l=e, (10) ye i Daley Ga eye k=1 I=1 The system of differential equations (8) we may speak of as the canonical system ; and now it is easily seen that: The canonical system of equations admits e, solutions, corresponding to the elementary divisor (r — rx), of the following simple form : Zp 0 k+ k Gi\rz.7— 0 Lla Topi dint (08 2) ‘ataie SC Tf r, is a multiple root of the characteristic equation which furnishes s elementary divisors with the exponents e,, Cette Sets—1) then the constants <: A; Key? A; «+1, eet? A; «+s—l, &+s—1 ’ are s linearly independent solutions of the equations (4) when r = ry. § 2. SOLUTION OF THE CANONICAL SYSTEM IN THE GENERAL CASE BY SUCCESSIVE APPROXIMATIONS. We shall now return to the system of equations (1); and here again we shall make use of the linear transformation (10) to reduce the system to the canonical form : (16) —— +e + We dx Rl x h, e- k,l = fe (eae OS Bia) (Ue, Bo bea Gah The coefficients 0;’, are linear functions with constant coefficients of the coefficients a, , in (1). We shall now make use of the method of successive approximations to develop solutions of (16) about the point x= 0. It will be convenient to write the equations (16) in the form: a T i=m j=e; (17) Po > > he: lj The first approximation will be indicated by a third subscript 0, and is obtained as a solution of the system of equations resulting from (17) by making the right side zero: * This reduction is used by Sauvage in the case of a system of equations with analytic coefficients. L.c., pp. 89, 90. 348 PROCEEDINGS OF THE AMERICAN ACADEMY. d 1 r (18) pe cece = Zh tet0 = = Fa.40 =) We have seen how to solve this system. Any one of the 7 solutions that we have obtained may be used as the first approximation. This approximation having been chosen, we insert it in the right side of (17) and obtain the following relations for the first correction : i=m S25 d 1 os j 57 G7 — — 2 —-—Zz = OD - SAIL &, é—1,1 Dak > Ss) Ry l a; AO, dx = ee 1 =). The right side is now a known function of x; and we have, conse- quently, a system of non-homogeneous linear differential equations to solve for z,,,- Having determined this first correction, it is inserted in the right side of (17), and the resulting equations are solved for the second correction. ‘This process is repeated again and again, the relation connecting the gth and the (g + 1)th correction being: i 1 i=m j=e; = (19) Fe OB Gel > 3 yg = ay, 4g+1 = => mee ba Lies dx x r=) Each equation (19) may be written: a 1 i— aj —e DOE Ce Pars ae =e 7B hy b @+1 yh he = kt 79,99 3 Cal Feat whence: (20) i=m j=e; —r canon = fz Ta ae i Dn tiied »|. lj! Cee Cae Now writing out the value of z, ,4,,,, in the same way, and substitut- ing it in the first integral of (20), we have: a x . 1 r, —l—r enna asl f 2s x Gee Paar dx e CEL Cet i=m S i=m j=e; +f: fe Ee >be 1 2,9 AL a Ps Dee: tJ, vas | Cent > g=1 Cee —Jh fel DUNKEL, — LINEAR DIFFERENTIAL EQUATIONS. 349 Now substitute in this result the value of z,, 911; in the result thus obtained the value of z,,-5 .1:, ete. After a certain number of substitu- tions we have: x x +4 { ees Ql) 2rea aol fies. , fe Te ae ae Cn Ce r+) Zz t=—I—L a 1 —r oe fie: fe = eee | TW Gan Ce HI—s a a where L < l. When Z = 0 we have: t=1 mY i=m jee, < r > —r > > (22) 2p, 0, q+l ee hed ee ae & by eee Hl Cre a ees Ki G The lower limits ¢,, will be determined later to satisfy several con- ditions. We may choose at pleasure any one of the m elementary divisors, say (r —r,)**, and then select any one of the corresponding e, solutions of (18) for the first approximation. We shall take then for the first ap- proximation z, 9, the values given in (11) fora particular X; the inte- gers « and ) will remain fixed for the solution we are now developing. For the development of the solutions corresponding to (r — r,)°*, we shall make the following further assumption as to the coefficients tae Let us examine all the exponents of the elementary divisors (r — r;)°, which are such that Rr, = Rr,, where Rr, means “real part of r,,” and pick out one exponent, say ex, that is as great as any one in this special set of exponents ; 15 Gis (23) Cpr Ons Where. fete — "lit, The assumption is that the integrals : b as ex—l k — 1, 25 oe oe M J 80 Hoe Gz ae converge. If in particular 7, is a simple root, and no multiple roct has the same real part as it, then eg — 1=0, and this further restriction drops out. Or it might happen that 7, is a multiple root, but that all the 350 PROCEEDINGS OF THE AMERICAN ACADEMY. exponents of the set (23) are unity, and in this case the restriction drops out also. The lower limits of integration in (22) will be determined as follows : eR > are Cee OUD) PAG eas Se ae PS Ln arg tate Y . rr, = VK eee b> L Ti) en = eer (pei) where ¢ is a constant not zero, which will be determined more closely later (cf. p. 358). It will be proved in § 3, that even in the cases in which the lower limit is zero, the integrals converge. When all these conditions have been satisfied, we build from the first approximation and the successive corrections the infinite series : qa 4 (dea Vara ace est)! (25) Zh, 0 — > tats ies i 2 ), ae peteretee which will be proved in § 4 to converge and to form a solution of the system of equations (16). It will be convenient to consider in place of the functions z,,, certain new functions ¢,,,, which will be defined by the following formulae : when Rr, + Fry, 249 =X" bang or =Rr,=Rr. k+xandl< L, or k=x«and lS %, (26) ee —_ ak (log aE an Ter, — Tete, k = K and L < I< x5 = x"* (log x)’ ox ser: x, lq kK, 1,q For the case of g = 0, i.e., the first approximation, the ¢’s are certain constants (cf. (11)); for all other values of q the formulae (26) define them as continuous functions of x so long as x is not zero; and we shall see later (Proof of Convergence, p. 358 et seq.) that each one approaches zero when x approaches zero. We shall therefore define each ¢,,,, when q > 0, as zero for x = 0; and with this definition they will be continuous functions of xz in the whole interval 0d. These ¢’s can be computed from the following recurrent formulae, which are easily obtained from (21), (22), (24), and (26) : DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. Bok I ha Rare Ho x COC ee es af oda. =i c ay we : i=—m j=e; = —(rz,—r, hij : f ute f , : De > se 41-1 Pi,7,¢ (log x) - dz, x ‘ — ijl t integrations where h, ; is a positive integer whose value it will not be necessary to write out, noting, however, that : (28) hiy = (7 a A. be 4. — are. @)) haa SS tr te (29) ; Oo ee > ne divets j= 2 a x i=m j=e, f ae ir core > > bat d:.3,¢ (log x) dec. 0 0 i 1 t integrations i) bbe, hic 1 Se, (30) $n. = aoe f — daz oft dx fe x aT) gb, Loti AX (l—L) intopratipiis S oy i=m jee; = % “n = +> fear. ‘ dx: [ ree DS = be, 41-2 Pi,7, 9 (log x) ax | i=) j=1 t etione c) kaw, ISD t=l (31) berea= > eo . t=1 & Lim joe, os, = Be Oe 41-0 big (log a)" dex. ily t eee ‘ SP PROCEEDINGS OF THE AMERICAN ACADEMY. DN YB = Pah OM ESS IDE 1 tL a (82) dxee41 = ——. Ea ee UA Mee (log x) t= x x x =n 1 i were ; [ce > > bx: te, $:, 3 g (log x) Mid dx. 0 = # integrations e) ny Wa ee 2 1 a1 Px, 2,041 = ae 2) ee — dx be z,qt1 (log x)" “« dar (l—L) integrations t=I—L 7 =m j=e, - 1 Oo Er fi af DD Bilan die (og ards | aa c le \ t integrations Ill. Rr, < Rr,: ® Here we have the formula (29) again. In § 4 we shall consider the x series : (34) b= DS bane (ate 22 b= 2 be: which are such that if we multiply each by its proper factor «”* (log x)", where h,, is given in (26), we obtain the m series (25). We thus reduce the proof of convergence of (25) to the question of the con- vergence of (34), and this last question will be settled by reference to certain formulae to be established in the next section. § 3. Lemmas Concerninc MuttieLe INTEGRALS. We now prove a number of lemmas, which will be useful in the proof of convergence, and which also verify the statement that we have made that the integrals of the last section, in which the lower limit is zero, converge. Lemma I. Jf b ds a function of x, continuous in the interval 0 1. Lemma III. Jf b is a continuous function of x in the interval 0 aa hk (= 41 = 1 DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 359 J — ob eee 7) < 1 @ b) b] 4 (48) Ipsne] SL i; — 1 AAA 4) For g = 0 they are obviously true. Assuming them true for a special value of g, g = 41, we will consider the cases outlined in (24) in turn. I. From (27) we have: (49) IP, eee = —/ 4 * Pea) Re f sla! ls. fs | da if gh) BMX | log a |x| dz | t=1 ie c ig < t integrations after replacing I4,,,,b Hogi, SS 1 respectively by the greater values M%, |logx|*", B (Cf. (28), (80), (382)). =) a 1 1 + Iz, 1,q411 = 2” py Ee [2 [log x |**~"| der| (LemmaIV.) = C kK < Mm Cf Bllog 2 || de < Mf OB\tog «| do| c c fe [log a: |" de (Lemma II.) = 0 x ir qi Blog «| dx t=! 0 360 PROCEEDINGS OF THE AMERICAN ACADEMY. since the greatest value ofie, —A+#—1 is é—A+t¢ L—-1=&—At Ce—& $A) — l=ex—i. ) ie a (51) Pe nqaal S MOE f Blog 2 ie ol@ IIA M* M(x) |log x 4] =e i B| log x |°« —\ ae | (Lemma VII.) t=! t=1—-L Sa lewis 2 / Blog «| dex =I e 9) approaches zero at the point x = 0. The inequalities (48) furnish the sufficient condition of Weierstrass for the absolute and uniform convergence of the series (34) in the in- terval OS a < ec. Accordingly the series (25) converges absolutely and uniformly in any sub-interval 0 << «5 a4Se. It remains now to show that we have a solution in the system of functions z,,. For this purpose let us select any sub-interval 0 Be ile poe Taking the sum of such series for all values of ¢ and 7 we have: i=m je; i=m j=e;, q=o a3 ny Oo > Se Se S Bras il i=! om =e) i=m j=e; Se aa > — DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 363 where the last transformation is valid since we are dealing with abso- ‘lutely convergent series. Also: 1 ear (98) i TS = > 2p,(—-1,q9 q=0 r =e) r - RB Re (59) PT a > hee? q=0 Adding (57), (58), (59), and changing slightly the summation on the right, we have: 1 i=m je; (60) = Rea + get Bo > b67 25 i=! j=) a anne ry, => zB 0 ri = 2, Doe = Fe cg a a phe oH i=m je, are a 2 | — The series on the right is an absolutely and uniformly convergent series of continuous functions. If we replace the terms by their values given in (18) and (19), we can also write the series in the form: d q=00 qe d (61) da 0 S25 = a 2k, ,g+1 — > dan he? q=9 which is the series of derivatives of the terms of (25). From this it follows that, if we differentiate the series for z,, term by term, we shall obtain an absolutely and uniformly convergent series of continuous functions; and therefore z,, has a continuous derivative at each point of our sub-interval, which is precisely (61), and this, as we have seen, is the same as the right side of (60). We can therefore write (60) in the form a 1—m j=e; 1 == +S fa. + >: > be 2:33 =D) og) and now giving k and / all possible values we have precisely the system of equations (16). We have, then, the following result: In any sub-interval of 0c, not including the point x = 0, the functions Z,,, represented by the series (25) are continuous in x, have continuous 364 PROCEEDINGS OF THE AMERICAN ACADEMY. first derivatives with regard to x, and satisfy the canonical system of equations at every point. The terms of the series for z,,, are given by the formulae (26), in which the functions p,,, are continuous in x through- out the whole of the interval 0b, and reduce to zero when x = 0, except wheng=0. The functions $;,,9 are constants, zero tn all cases but the following : i see ae ® aie Pe n0 (¢— x)! AS(S &. § 5. LINEAR INDEPENDENCE OF THE SOLUTIONS OF THE CANONICAL SYSTEM. We have shown that corresponding to each elementary divisor (r — re)*, there are e, solutions of (16) obtained by giving A the values 1,2,...e; and for the development of these solutions we have re- quired that | 8,”,| | log x |**—" shall be integrable up to 2 = 0, where ex is determined for the root 7, by the condition (25). We have, then, m solutions which may be written as follows: when Rr, + Rr, K,A = ae ge S0OF S| fit Mes eased 0 Seo, Ue kc andl SN Pe) A k,l (G2), — = (lone), 7p wr, ek ee and ie eee Eo =z (log a) ae ny Nel ee . K,A = ° where the functions (Pe are continuous in x and kt « K,A aoe ( (63) Pr, 1 5 ae (or k==x and Tay K,A at 1 an sy Se, (gee db 745 id. 0 10) CN eee): It is worth while to note three facts in regard to the 2’s, which will be useful later on : 1G Ze does not involve log x explicitly whenever A > 7; (64) IL. limit “2? = 0 when Rr, > Rr; z=0 ? III. nut x '* (log x) “e) zie = 0 in all cases except the 1 one, k = x and / = e,; and then the limit is DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 365 We will now show that the x solutions (62) are linearly independent. Suppose they were not and that there were m constants C’,,. not all zero such that: k=m A=e, Tit. rn 5 == Uys aie (65) SS Cad oan e It will be convenient to suppose that our notation is such that: (66) Tee TS. a TT Consider first those equations of (65) for which Rr,= Rr, We have: k=m A=e, (67) limit YS Ce Rar as =0 Rr,= Rr, k=] A=) (Z — 1, 2, ORD €x)« Now let /=1 in (67), and consider the limit of each term for any given value, within the range indicated, for k. For each term in which Rr, > kRr,= Kr, the limit is zero by I. We have left, now, only the terms: ally 2 KA in Bes! (68) Coye a Ti Teoh Gee rae According to I. no logarithms appear explicitly in (68), and we can write : tie eS Ui eaiy K,A co) CES pas Cant Pane Now by (63) the limit of all such terms is zero except in the one case «x == kand A = 1, and for this term we have: Ae as ie. Rare 2, (70) Hn Opens Cicer = He Oe Eee a ee — Ye So in the case of 7 = 1 the limit (67) turns out to be C,, when we evaluate the limit term by term. Now this is impossible unless C,,; = 0; and so we must have, writing now x in place of k: (71) C1 = 0 Rr = Rr. Now consider in the same way the cases of (67) in which / = 2; and choose any one of the values of & indicated. Here again by II. the limit of each term is zero when Rr, > Rr,; and we have left the terms: (72) em. Rr, = Rr, = Rr, Ne DD (9) 366 PROCEEDINGS OF THE AMERICAN ACADEMY. Now by I. no logarithms appear explicitly in the terms (72), for the only case in which they could occur would be for A = 1, but by (71) such terms do not appear. We can then write each term of (72) —ry. _K, A f =. a 73) Cane of ee) aCe ear bps : and by (63) the limit of each is zero except in the one case: (74) limit O, 907 2 = aly Cy, PES — C2 . = We have then, reasoning as before, and including the previous result, (75) C.3=C.s=0 Tei — sree Now the same reasoning can be applied until we have finally (76) Can 0); i NZ 1 and there are left in (65) only those solutions for which Rr, > Ry. Having thus disposed of all the 7’s in (66) such that Rr, = Rr, we consider the next set of 7’s whose real parts are all equal and as small as any other in the new set of 7’s, and show, in exactly the same way, that the corresponding constants, C,,, are zero. Continuing in this way, we finally reach the result that all the constants in (65) are zero, and that the assumption made as to the dependence of the solutions leads to a contradiction. Zhe n solutions are therefore linearly independent. ¥ § 6 ReTURN FROM THE CANONICAL SySTEM TO THE ORIGINAL SYSTEM. We will now return to the original system of equations (1). Each solution of the canonical system (16) determines a solution of the original system (1) on account of the relation (10). We have then the following n solutions of (1) : k=m l=e, i Lez waste ] (77) get > AR ee «= 1,2,...m k=1 I=1 Nes My 2 gts teed) Now these » solutions are linearly independent, for the z solutions are linearly independent, and the determinant of the constants A,;,, is not zero. DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 367 Now consider the following limit: (78) limit x "* (log a) «—) yf x z—0 k=m =e, =limit > > Agua *(log a) 20 a == On the right, if we take the limit of each term in the summation, we shall find that it is zero in every case except the one in which & = « and ie, (ef. (64) IDL). We have, then: 1 79 limit a~"* (log v7) @e™ y®* = Aire. It’ (79) por (log «) ¥; 1,1 ee (e, — A)! So we can write as a set of solutions of (1), corresponding to the ele- mentary divisors (7 — r)"*: K,A NaN el FP eet 1) where the functions ee are continuous in the interval 0 < x ", are continuous in the neighborhood of x = 0 and, Ky A pate EY fear aa (92) ie fy == Te (Me —= L)) os Ke — ee A) Even for the equation of the second order this theorem does not merely give the results of Professor Bécher’s paper aboye quoted, but goes a step farther, since in the case in which the two roots of the characteristic equation are equal, we require merely that: b b i (log «) |p. | dx, iF (log a) | po| dx 0 e converge, while Professor Bécher’s method made it necessary for him to require that b b [ dog x)” | p | dx, f (og x)” | po | da 0 0 roe * conver ge. * Lc. p. 48. The function xq; in this paper is the same as our p2. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 10. — Novemser, 1902. THE INFLUENCE OF ATMOSPHERES OF NITROGEN AND HYDROGEN ON THE ARC SPECTRA OF IRON, ZINC, MAGNESIUM, AND TIN, COMPARED WITH THE INFLUENCE OF AN ATMOSPHERE OF AMMONIA. By Roya A. Porter. INVESTIGATIONS ON LIGHT AND Heat, MADE AND PUBLISHED WHOLLY OR IN PART WITH APPROPRIATIONS FROM THE RuMFORD FunND. Ce SS ee hay iw DAWG 97, Pe . oot by si ‘y vat ur o Mi : : Agate ae : fd ‘ial ¥ ih am iM i A a ay ns) Lh ee TA : a uy * i % wae - PAU a Vy : ou i par ls a - yy - ath hie i = Wha S. pay av ae ‘ron wad, en | : Ld. (ci eon wie THE INFLUENCE OF ATMOSPHERES OF NITROGEN AND HYDROGEN ON THE ARC SPECTRA OF IRON, ZINC, MAGNESIUM, AND TIN, COMPARED WITH THE INFLUENCE OF AN ATMOSPHERE OF AMMONIA. By Royat A. PorTER. Presented by C. R. Cross, May 14, 1902. Received October 8, 1902. Ir has been frequently assumed that chemical reactions in the electric arc have a considerable influence on the character of its radiations.* It seems not unreasonable to expect that the oxidation of the electrodes at high temperature in air would tend to increase the intensity over that obtained when the arc is operated in nitrogen alone. ‘This presumed higher temperature might be sufficient to produce atomic vibrations entirely distinct from the vibrations at a lower temperature. If the atmosphere does have any such influence, the effect might be apparent in the spectrum of the arc. In the case of a hydrogen atmosphere ¢ the most marked effects on the are spectra of iron, zinc, magnesium, and tin have been found to bea general diminution of intensity and a change of relative intensity among the lines. The lines relatively enhanced by hydrogen are spark lines. Liveing and Dewar ¢ have noted the effect of atmospheres of hydrogen and nitrogen on a number of lines in the magnesium arc and spark, and of these and other atmospheres on the cyanogen § bands in the carbon arc, but as far as I am aware no extensive study has been made of the influence of nitrogen and ammonia on the arc spectrum of metals. From * Liveing and Dewar, Proc. Roy. Soc., 30, 161 (1880); 32, 192 (1881); O. H. Basquin, Astroph. Jour., 14, 11-12 (1901); A. S. King, Astroph. Jour., 14, 820- 330 (1901). + H. Crew, Astroph. Jour., 12, 167 (1900); Liveing and Dewar, Proce. Roy. Soc., 32, 192, 402-408. t Proc. Roy. Soc., 32, 189-205 (1881). § Ibid., 30, 152-162. 374 PROCEEDINGS OF THE AMERICAN ACADEMY. a study of the effects of hydrogen and nitrogen on certain spark lines of magnesium, Liveing and Dewar * were led to remark that “it is possible that the atmosphere may, besides the resistance it offers to the discharge, in some degree affect the vibrations of the metallic particles.” This conclusion in regard to the spark seems to have been borne out with reference to the arc by the results obtained with a hydrogen ¢ atmosphere. Nitrogen resembling hydrogen in its inability to combine directly with metals, it seemed reasonable to expect that it would have a very similar effect on the iron, zinc, and tin arcs. As magnesium ¢ combines directly with nitrogen a different effect might be expected in the magnesiun arc. — METHOD AND APPARATUS.§ In order to eliminate the effect of gases other than the one whose effect was being studied, the enclosed rotating metallic arc,|| with “ chemi- cally pure” zinc, magnesium, and tin electrodes, was used. The iron used, however, was “commercial.” The speed of the rotating electrode was approximately eleven hundred revolutions per minute. Excepting in two instances noted later, the arc was operated by a 104 volt alternating circuit. The spectrum was photographed with a Rowland ten-foot concave grating, four exposures being made on each plate, as shown in the diagram. Long exposure, arc in air. Long exposure, arc in gas. Short exposure, arc in gas. Short exposure, arc in air. Near the top of the plate was photographed the spectrum of the are in air; just below this, was photographed the same arc operated in an atmosphere of the gas being studied ; below this, again, was made a short exposure with the arc in the same gas; and at the bottom, a short * Proc. Roy. Soc., 32, 203 (1881). + Astroph. Jour., 12, 167-175 (1900). t Liveing and Dewar, Proc. Roy. Soc., 32, 161. § The funds to meet the expense of this experiment were kindly appropriated by the Committee in charge of the Rumford Fund of the American Academy of Arts and Sciences. || Crew and Tatnall, Phil. Mag., 38, 879-886 (1894). PORTER. — ON CERTAIN ARC SPECTRA. 375 exposure with the arc in air. The exposures were so timed as to make the intensities of the two inner photographs intermediate between the intensities of the two outer ones. By comparison one can readily deter- mine from such a plate whether any change in intensity is due to length of exposure or to change of atmosphere. This plan of making four exposures on each plate has some additional advantages: (1) it affords a test of uniformity of results; (2) the two short exposures allow an easier comparison of lines so strong as to be ordinarily over-exposed ; (3) the second exposure in the gas being made immediately after the first, and without opening the “hood” of the arc, a photograph is obtained of the spectrum of the arc in its final atmosphere; that is, in an atmosphere which includes the gaseous products of the arc, if there be any. The effect of hydrogen was taken from the results published by Professor Crew * and from the original plates obtained by him. These negatives were made under the same conditions as here described, except in a different atmosphere and with a direct current. The change from a direct to an alternating current, however, produces no effect on the spectrum. In the case of the tin are less dust is produced when a direct current is used, and I have therefore employed such a current in photographing the spectrum of tin in ammonia. The hydrogen atmosphere was obtained by the electrolysis of acidu- lated water. The ammonia used was taken from a drum of compressed ammonia gas such as is used in refrigeration. Nitrogen was generated by the reaction of ammonium sulphate and sodium nitrite solutions. Professor J. H. Long kindly suggested an arrangement of the nitrogen generator by which air was excluded from the entire system throughout the work. Traces of oxygen were removed by pyrogallic acid, while the water vapor was taken out by passage through concentrated sulphuric acid and over phosphorus pentoxide. Before commencing an exposure a stream of nitrogen was kept flow- ing through the hood for at least twenty minutes. ‘The same plan was used in filling the hood with ammonia. During an exposure a stream of the gas was kept flowing through the hood, both for the purpose of keeping a fresh supply of the gas about the arc and to drive out the dust which formed. The spectra of the following four metals have been examined photographically in the region lying between A 2300 and ) 5300. * Astroph. Jour., 12, 167-175 (1900). 3876 PROCEEDINGS OF THE AMERICAN ACADEMY. MAGNESIUM. The ordinary are lines of magnesium seem to be almost wholly unaffected by substituting nitrogen for air. The heavy spark line at 4481, which appears also in the spectrum of the rotating arc, is reduced by nitrogen to about one-fifth its intensity in air. Naturally, the mag- nesium oxide fluting at 5007 is practically blotted out in nitrogen and greatly intensified in oxygen. On the other hand, no new lines make their appearance in nitrogen. The intensity and reversal of the characteristic line at \ 2852, which are so strongly affected by hydrogen * and ammonia, are unaffected by nitrogen, while the sharp line at A 4571 is slightly reduced by hydrogen and ammonia, although not changed by nitrogen. The magnesium-hydrogen fluting beginning at 5210, discovered by Liveing and Dewar,f appears in ammonia, as does also the F line of hydrogen. Fairly intense hazy lines at approximately 4580, 4434, 4430, and 4390 also appear in ammonia. These lines are apparently intensi- fied by oxygen also. By nitrogen they are unaffected. A very faint trace of these lines can be seen in air. I have not yet succeeded in identifying them. TIN. Of the four metals studied, tin is the one whose spectrum is most modified by changes of atmosphere. In air, nitrogen, and oxygen, the tin arc works well. But in hydrogen and ammonia the arc is very short and is maintained with difficulty. The inteusity of the tin are in nitrogen is estimated at one-third its intensity in air; while in ammonia its intensity is not more than one- twentieth its intensity in air; and in pure hydrogen it is even less. Not only is the average intensity of the tin spectrum strongly affected, but also the character and relative intensity of its individual lines. In Kayser and Runge’s table of wave-lengths of the tin are more than forty lines are described as reversed. Many of these reversals show very clearly on my plates. When the arc is surrounded with nitrogen, how- ever, some of these lines appear to be doubly reversed, the rest not reversed at all. On the other hand many of the lines that are reversed in air appear to have their reversal widened by ammonia. These reversals are not affected by an atmosphere of oxygen. * Astroph. Jour., 12,171 (1900). Liveing and Dewar, Proc. Roy. Soc., 32, 192. t Proc. Roy. Soc., 27, 494-496 ; 30, 93-99. PORTER. — ON CERTAIN ARC SPECTRA. Ste The two very strong spark lines at 13351 and 3282, appearing also in the spectrum of the rotating arc, have their relative intensity de- creased by nitrogen. But by ammonia they are relatively enhanced at least twenty times. In the are in air, these two lines are barely visible ; but in ammonia they become two of the most prominent lines of the spectrum. These two lines are similarly affected by hydrogen ‘The spark line at X 2368 is also intensified in ammonia but less than the two preceding. The spark lines of wave-lengths 2449, 3471, 38539, 3574, appear plainly in ammonia and hydrogen but not at all in air or nitrogen. They are more enhanced by hydrogen than by ammonia. At A 3360 and 3370 appear two unidentified lines of intensity 6 and 3 (on a scale increasing from 1 to 10), respectively, in ammonia, and not quite so intense in nitrogen, which can scarcely be detected in air and hydrogen. These same lines appear also in the magnesium and zinc arcs in air, nitrogen, and ammonia; but oxygen has the effect of im- mensely weakening both of them in the tin and magnesium arcs. A 3370 appears in the tin spark, but A 3360 does not. ZINC. The average intensity of the lines of the zinc arc spectrum is reduced approximately one-half by nitrogen. The width of reversed lines is not affected. The only zine lines that suffer a disproportionate reduction by an atmosphere of nitrogen are \ 2558 and 42502. These, with A 5182, are the lines which are enhanced by hydrogen. They are strong spark lines. In ammonia their intensity is two or three times as great as it is in air, although the average intensity of the zinc spectrum is diminished perhaps five times by ammonia. Iron. The substitution of nitrogen for air about the iron are produces very little change in the spectrum. The general intensity is not altered. Compared with the number of lines relatively affected by hydrogen, the number of iron lines affected by nitrogen is small, as has been found to be the case with other metals. Many of the lines that are affected by nitrogen are impurity lines. Of fifty iron lines between \ 3660 and A 4060 that are markedly enhanced by hydrogen, six are distinctly reduced by nitrogen. On examination of the region between 43600 and 4600 I found twenty-six lines that are particularly affeeted by nitrogen. A few others 378 PROCEEDINGS OF THE AMERICAN ACADEMY. are slightly changed. Of these twenty-six lines seventeen are from two to ten times as strong in nitrogen as in air. But these seventeen lines were all found to be due to impurities, fifteen belonging to manganese, one to chromium, and one to cobalt. The remaining nine lines are reduced by nitrogen to from one-half to one-tenth their intensity in air. Part. if not all, of these lines are iron spark lines. EFrFect oF ExcitupinGc NITROGEN. The effect of pure nitrogen being so slight, it seemed possible that the presence of so large a percentage of nitrogen in the air about the ordi- nary are might account for the smallness of the change. I therefore attempted to determine the effect of nitrogen by a process of exclusion. This was done by substituting for air an atmosphere of commercial oxy- gen taken from an ordinary stereopticon gas-cylinder. A stream of this oxygen was kept flowing through the hood of the arc. ‘ If the chemical affinity of the electrodes for the atmosphere has any effect on the spectrum, one might certainly expect this effect to be exhib- ited when such easily oxidizable metals as iron, magnesium, and tin are employed in the atmosphere of oxygen. Mr. A. S. King* found that the metallic lines were intensified by increasing the supply of oxygen about the carbon arc. But just the con- trary seems to be true with reference to the metallic arc. A current as large as ten amperes was tried with chemically pure magnesium elec- trodes, but the oxygen had little effect on the working of the arc or the appearance of the so-called ‘‘flame.” To the eyes the “flame,” espe- cially with iron electrodes, appears to be less blue and more yellow. Of eighteen exposures made with the iron, tin, and magnesium arcs in oxygen, all but one show a greater average intensity for the same length of exposure in air than in oxygen. This is not the only respect in which the action of oxygen on the metallic arc resembles that of hydrogen and ammonia. The metallic lines that have been noted as being rela- tively enhanced or reduced by hydrogen are precisely the ones which are so affected by oxygen. The changes produced by oxygen are not so great as those produced by hydrogen, but they are in the same direction. SUMMARY. The results of these experiments may therefore be summarized as follows: * Astroph. Jour., 14, 329 (1901). PORTER. — ON CERTAIN ARC SPECTRA. 379 1. The average intensity of the iron and magnesium arcs is not changed by substituting pure nitrogen for air as an atmosphere. ‘The average intensity of the zinc and tin arcs is reduced two or three times by nitrogen. By hydrogen the average intensities are reduced from five to twenty times as much as by nitrogen. Ammonia apparently does not produce quite so great a reduction as does hydrogen. 2. The relative intensity of many lines depends upon the atmosphere. The lines that are relatively reduced by nitrogen are spark lines. Asa rule these lines are relatively enhanced by hydrogen or ammonia. 3. The influence of ammonia on intensities and reversals is intermedi- ate between that of nitrogen and hydrogen, and in general it seems true that the effect of ammonia is approximately equal to the sum of the effects of its constituents. This, in fact, is the particular point which I had in mind to determine when I began these experiments. 4, The influence of oxygen is similar to that of hydrogen. 5. Nitrogen affects the reversed lines of tin by either destroying the reversal or producing faint double reversals. These results seem sufficient to show that the readiness of an atmos- phere to form chemical union with the electrodes under ordinary condi- tions ts a very small, probably insignificant, factor in determining the intensity of the arc. The intensity appears to be due to electrical causes rather than to chemical reactions. Some experiments have been performed by Professor Basquin* which seem to confirm the theory that the intensification of spark lines in hydrogen is caused by the increased resistance due to the hydrogen atmosphere about the arc. This greater resistance has been attributed to the absence of chemical reaction in the hydrogen are. Such a change of resistance in the products of the are may explain the phe- nomena which occur in hydrogen. But if the resistance of the arc depends on the reactions in it this fact makes it difficult to see how the spark lines can be intensified by an atmosphere of oxygen. This work was done under the direction of Professor Crew, who, in fact, himself began it and to whom I am indebted for continued advice and assistance. NORTHWESTERN UNIVERSITY, EVANSTON, ILLINOIS. 22 April, 1902. * Astroph. Jour., 14, 14-17 (1901). Proceedings of the American Academy of Arts and Sciences, VoL. XXXVIII. No. 11. — DEcEMBER, 1902. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — XII. 1. BABINGTONITE FROM SOMERVILLE, MASS. 2. BABINGTONITE FROM ATHOL, MASS. By C. PALACHE AND F. R. FRAPRIE. Witu Two Piatess. - atin shetin ska virkte ae ber bb Mata eel UA eee Oe ie ay, Nie ; we ' 4 (ae ee ibis SY Wana z. apk me Kil ceong mn eo) ah ake Lay gee A : Tags oy)" Oa heh Ai Lee - as cA - p Pa is CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — XII. 1. BABINGTONITE FROM SOMERVILLE, MASS. 2. BABINGTONITE FROM ATHOL, MASS. By C. PALAcHE AND F. R. FRAPRIE. Presented by J. E. Wolff, October 8, 1902. Received October 8, 1902. BABINGTONITE FROM SOMERVILLE, Mass. Occurrence and Paragenesis. THE occurrence of babingtonite at Somerville has long been recorded, but no adequate description of it seems to have been published. We first find mention of it in a description by Teschemacher * of the minerals of the Charlestown sienite quarry, where it is called “hornblende in the form of oblique rhombic prism with modifications c, k,1; crystals are small and black on white prebnite.” In Alger’s Phillip’s Mineralogy, 1844, p. 79, it is stated on the author-’ ity of Professor Nuttall that babingtonite occurs at Charlestown and that this is the only American locality. No description of the mineral by Nuttall has been found, and Alger probably had the information privately from Nuttall. This statement was copied in Brooke and Miller’s Mineralogy (1852), but appears never to have found its way into the American text-books, the only further mention of it being in Dana’s System (1892), where, although not referred to in the text, the mineral is listed in the Catalogue of Localities, p. 1059, as occurring at Somerville. [ The babingtonite occurs in veins and pockets composed chiefly of prehnite, which traverse a large dyke of diabase.f This dyke is well exposed in an old quarry, recently abandoned, on Granite Street, Somer- * Proc. Boston Soc. N. H., June, 1839,in Am. J. Sci., XXX VIIL., 1840, p. 194. { For a description of this rock, which is called sienite in all of the above refer- ences, see Wadsworth, Proc. Bos. Soc. N. H., XIX. (1879), p. 228, and Jaggar, Am. Geol., XXI. (1898), pp. 203-218. 384 PROCEEDINGS OF THE AMERICAN ACADEMY. ville, formerly known as the Milk Row quarry, Charlestown, and it is from this quarry that the material here described has all been obtained. The mineral is not abundant, and it was only after several years of collecting in the fresh quarry openings that sufficient material for analy- sis and adequate crystallographic study was accumulated. In addition to the material now in the Harvard Mineral Cabinet, several fine speci- mens from the same locality were placed at our disposal by Mr. H. I. Johnson. The minerals commonly associated with the babingtonite are prehnite, quartz, epidote, pyrite, chlorite, feldspar, and calcite. Other minerals reported from the locality are laumontite, stilbite, chabazite, melanolite (known only from here and a doubtful species), and chalcodite. Prehnite is much the most abundant mineral in the veins, always lining the walls and often forming the whole vein-filling. It varies in color from pure white to quite a deep green, which often fades on exposure to light. It has the characteristic drusy reniform surface of prehnite, the crystals rarely individual. Occasionally the crystals com- posing the globular or barrel-shaped groups are sufficiently distinct to show that they are tabular parallel to ¢ (001) with edges formed by m (110) and sometimes also a (100). A single specimen showed a num- ber of lath-shaped crystals attached by one end to massive prehnite, on which only the three pinacoids were present. Prehnite also forms fine- grained granular masses of dull white color. Quartz is sparingly present, generally as small pellucid crystals im- planted on prehnite. In one specimen the quartz is in the form of capillary crystals stretching from wall to wall of small cavities in massive prehnite. Most of the crystals are combinations of the common forms m (1010), r (1011), and z (0111) but a few were observed and measured of more complex character on which the following less common forms were found: d (1012), ~ (0112), G (18.0.13.9), s, (1121), (9272), y (4151). These forms were present as narrow truncations of edges of the common forms. The alternate edges of the unit prism were also truncated by planes of a trigonal prism, apparently etch faces, which gave distinct readings at variable angles not corresponding to any known form of quartz but near (10.1.11.0). Epidote occurs quite commonly in minute yellowish-green needles implanted on prehnite or coating and intimately intergrown with babing- tonite and quartz. The crystals are not measurable. Pyrite is found occasionally in clusters of minute crystals resting on prehnite or babingtonite. The crystals are too minute and too poorly PALACHE AND FRAPRIE. — BABINGTONITE. 385 developed to permit of measurement, but they appear to be dominated by the cube. Chlorite is not common with the babingtonite, but is apt to occur intermixed with the massive form of the prehnite. Feldspar is found with prehnite and babingtonite in a few specimens, in the form of small imperfect pinkish crystals. They are similar in appearance to the pinkish labradorite of the enclosing diabase and were not further determined. This mineral is found only in certain pockets of oval form entirely enclosed in the diabase. The dyke at this point contains many inclusions of various rocks, and it is probable that these pockets represent inclusions in which the original material has been almost wholly replaced by prehnite and calcite. Wadsworth* found pseudomorphs of prehnite after feldspar here, which fact to some extent strengthens this conclusion, based chiefly upon the form of the pockets. Calcite occurs in both veins and pockets as the last substance deposited, filling up all the interstices of the other minerals. It is white and glassy, often in large individuals, but never, so far as observed, in developed crystals. Near the surface of the veins the calcite has generally been removed by solution, but away from the zone of weathering it seems always to be present, and all the finer specimens of prehnite and bab- ingtonite were obtained by dissolving away the infilling of calcite with dilute acid. Of the remaining minerals recorded above from the locality one only, chabazite, has been seen by the authors. It occurs in well-formed twin rhombohedrons, pure white in color, implanted on a specimen of massive prehnite. The specimen was not collected by us and this mineral has not been found at the locality for some years. The babingtonite is usually in distinct crystals implanted upon, and in rare instances wholly embedded in, prehnite. The crystals are often but slightly attached to the prehnite, and are therefore not infrequently completely bounded by crystal planes. They are generally small, rarely exceeding 2 or 3 mm. in greatest dimension ; but a few larger crystals were obtained, the largest measuring 1.5 x 1 X.4cm. The complete detached crystal shown in figure 3 is 1 X.7 X.2 cm. and is perhaps the largest perfect crystal preserved from the locality. Granular aggregates of babingtonite are also found embedded in prehnite, composed sometimes of fine grains and again of individuals so large that cleavage surfaces of several square centimeters’ area may be observed. * Loc. cit., p. 228. VOL. XXXVIII. — 25 386 PROCEEDINGS OF THE AMERICAN ACADEMY. The babingtonite is black in color and of a brilliant vitreous lustre. It is, however, very subject to decay, and when the protecting calcite has been removed and the babingtonite exposed to the weather it becomes dull and gradually alters to limonite, of which complete pseudomorphs are frequently found. ‘The decay is most active along the incipient cleavage cracks, and crystals which appear on the surface fresh and sound are often found on being broken to be permeated throughout by limonite films. This character proved to be so universal in the larger crystals that all attempts to prepare plates from them for the study of the optical properties were unsuccessful. Crystallography. Twenty of the smaller crystals were measured and the following forms determined, those marked with an asterisk being new to the mineral ; c (001), b (010), a (100), h (110), g (210), f (820), k *(110), u *(054), o (011), v *(035), w *(025), s (G11), d (101), x *(805), y *(205), nA (TO1) pC) et i 2) a (2) The faces of the prism zone are generally deeply striated parallel to the prism axis, and the basal plane is often curved or faceted. It was found too that even where all the faces were plane there was often a lack of parallelism in opposite faces, especially those of the prism zone, which made the accurate adjustment on the goniometer difficult ; and for this reason many of the crystals were measured both by the two-circle method and by adjusting one plane in polar position and determining the interfacial angles of the others to it. Both groups of measurements are presented in the tables which follow, and the wide range of values for many of the angles gives a measure of the irregularities to which the crystals are subject. The position here adopted for babingtonite is that of Dauber, and his elements have been used for the calculation of the table of angles.* * The choice of this position rather than. the one taken by Dana and Hintze, which is designed to bring out the similarity in form between babingtonite and the monoclinic pyroxenes, may be justified on several grounds. The dominant habit of the crystals, as may be seen from the figures, is prismatic in the direction of Dauber’s prism zone, so that this is the natural position in which to orient them and very much simplifies the adjustment and measurement. In Dana’s position this zone is made a pyramid zone. Furthermore Dauber’s position gives much simpler symbols for the forms, as may be seen in the accompanying table. The position of Goldschmidt (Winkeltabellen) gives symbols as simple, but, like Dana’s, PALACHE AND FRAPRIE, — BABINGTONITE. 387 Dauber’s elements were based on a very large number of measure- ments on crystals of babingtonite from Arendal. His values for many angles show a considerable range, up to a degree or more, on either side of the mean value. Our measurements of interfacial angles, as shown in Table I, show a like range, and the means agree on the whole so closely with Dauber’s calculated values that it was deemed best not to attempt to establish new elements for the Somerville mineral. Moreover the co-ordinate angles calculated from them for the two-circle readings agree closely with the measured angles, as may be seen in Table II. The forms may be characterized as follows. In the prism zone a (100) and b (010) are always present, generally brilliant and free from striations, but often slightly curved. h (110) is generally present as a very narrow, brilliant face. g (210) and f (320) are generally both present, most often in oscil- latory combination as a broad, gently curved surface striated vertically — a very characteristic feature of crystals from this locality. When f is absent g is less deeply striated, but is rarely perfectly plane. Notwith- standing their striation, both faces give good reflections. k (110). A number of faint reflections were observed in the vicinity of the faces f and g, but the only one which was observed more than once and was assignable to a definite form was the new form k, which was found with both faces on one crystal and a single face on another. The faces were narrow and reflection poor, but the form seems assured. e (001) is always present, generally plane, but sometimes faintly striated parallel to intersection with s and o, or faceted. The domes o (011), s (011), and d (101) are always bright faces giving good images. ‘They are all three present on many crystals, s is never lacking, and d is more frequently absent than o. They vary much is unsatisfactory in not making the dominant and most easily recognized zone the prism zone. Dauber. Dana. Goldschmidt. Dauber. Dana. Goldschmidt. c (001) M(110) (010) _ n (101) (221) (011) b (010) m (110) b (100) u (054) (010) (540) a(100) ¢c(001) a (001) v (035) (410) (350) h (110) —h (221) ~—q (101) w (025) (730) (250) g (210) g(lll) r (102) x (305) (10. 10.3) (053) f (320) f (443) ‘1 (208) y (205) (551) (052) k (110) (221) (101) p (111) (401) (111) 0 (011) a(100) 0 (110) t (112) (621) (121) s(011) b(010) _ s (110) i (112) (261) (121) d(101) (221) ~—8 (011) 388 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. Angle calculated. Measured (Mean). Limits. No. of Readings, ab 67 48 67 54 66 49- 68 40 15 ab’ 112 12 112 04 111 13-112 47 13 ac 87 28 87 O01 86 44— 87 28 6 ac’ 92 32 92 45 92 18- 93 15 5) af 09 36 09 26 09 038— 59 48 £ al’ 120 24 120 33 120 12-120 57 4 ag 47 33 47 15 46 59- 47 22 4 ag’ 132 27 132 42 132 38-132 50 3 ah 43 05 43 37 43 12— 44 30 8 ah’ 136 55 136 20 135 45-136 49 6 fg 12 00 12 58 11 42- 13 51 6 fh 7h 18 76 48 73 49- 77 32 6 gh 89 18 89 04 88 25- 89 34 6 be 92 36 91 48 91 26- 92 20 8 be’ 87 24 87 43 _ 87 17— 88 26 6 bf 52 36 02 37 d1 5d- 53 14 6 bf’ 127 24 127 07 126 46-128 01 5) bg 64 59 64 48 64 26- 64 59 4 bg’ 115 21 115 12 115 04-115 35 6 bh 24 43 2415 23 O1- 25 07 iit bh’ 155 17 155 438 155 16-156 48 11 bo 47 23 46 46 46 25- 47 18 6 bo’ 152 37 132. 42 i bs 44 40 44 48 44 20- 45 17 2 bs’ 135 20 134 53 134 03-1385 58 6 cg 85 27 84 59 84 40- 85 18 5) cg’ 94 33 94 37 94 08- 95 13 5) co 45 13 45 10 44 19- 4613 11 co’ 134 47 154 43 134 33-134 53 2 cs 42 44 43 08 42 33-— 44 00 6 cs’ 137 16 136 51 136 13-137 33 3 9 ced 29 55 29 38 29 16-— 29 58 in size from being dominant terminating planes to narrow truncations of the edges between c and faces of the prism zone. The remaining forms observed are all new and vary much in quality. Of the domes, n (101) is well established, having been observed on six PALACHE AND FRAPRIE. — BABINGTONITE. 389 TABLE II. ELEMENTs. A = 92° 86’|a = 1.685 jag = 1.8257 |a = 86°09’)x9)= 0.0662 |d=0.08038 Po = 0.59098 Calculated. Measured (Mean). Limits. Limits. No. Quality. g p p Pp Oo 7 oll7 oLtZ O} E7 Oo) Oy pi (oy o- c 001 12424 436 119387 4654 11602-1253 412-500 8 very good b 010 0000 9000 0000 9000 a ok 20 ss a 100 67 48 9000 67 55 9000 66 49- 68 47 28 s ss h 110 2442 9000 2416 9000 23 01- 2507 22 oe “ g 210 11524 9000 11512 9000 11504-11535 10 “ fs f 320 12724 9000 12716 9000 126 44-128 05 11 ms s k 110 143 38 9000 .14350 9000 14327-14418 phate) 3 poor u 054 316 49 26 326 4931 324- 328 4842-5020 2 fair o O11 407 4248 406 43 00 347- 420 4234-4345 8 very good v 035 704 28 22 708 2907 et toe it «poor w 025 1059 19138 11038 1925 1045- 1122 1854-1957 3. poor s O11 17615 4529 17551 4529 17523-17617 4503-4544 10 very good d 101 7349 3239 73387 8245 73 02- 7356 38240-8254 8 3 § x 305 7720 2204 76 56 2200 ie Sfatr y 205 8114 1608 8005 1650 =e a tee ae 1 s n101 —11912 2855 —11908 2844 11820-11931 2833-2852 6 ve p fll 2811 6229 2819 5227 28 15- 2827 6217-5248 2 very good ta 8144 32 56 3120 3317 1 poor 1 112 —16204 3401 —16503 3437 1 “ crystals with small but plane faces giving angles agreeing closely with calculated positions.* x (305) and y (205) were each observed but once as narrow faces between d and ¢, giving fair reflections and moderately close to calculated positions. They need confirmation, u (054) was observed on two crystals as a narrow face between o and * In the figure of babingtonite in Dana (System, 1892, p. 382) a plane lettered n is shown corresponding to this form (101), which would be the pyramid (221) in Dana’s position. No mention of this form is made in the text, nor is it found in the figure in Des Cloiseaux (Atlas, Pl. XII. Fig. 66), which is assigned as the source of Dana’s drawing. Hintze (Mineralogie, II. p. 1169, Fig. 422) seems to have repro- duced Dana’s figure without correcting this apparent draughtsman’s error. 390 PROCEEDINGS OF THE AMERICAN ACADEMY. b. It may be regarded as assured, although the values for the two obser- vations differ rather widely. w (025) was found on three crystals as a narrow face between o and c and may be regarded as established. v (035) was observed but once as a faint line face between o and c. Its position is fairly good, but it needs confirmation. Of the pyramids, p (111) was measured on two crystals and observed on several others. It is always a distinct face giving brilliant reflections, and is well established by the close agreement of measured and calculated angles. t (112) and i (112) were each measured but once as narrow trunca- tions of the edges between d and o and s and n respectively. The reflec- tions were poor and the angular positions are not very close to calculated values, but their positions in the zones and the fact that each was observed several times, although with faces too narrow to give measurable reflec- tions, seem to assure both of these forms. The drawings, each presenting a plan and a clinographic projection of a crystal, illustrate the various habits of the Somerville babingtonite and especially the occurrence of the new forms. Figure 3 is a simple combi- nation particularly characteristic of the larger crystals. Figures 4, 5, and 6 are as nearly as possible in the proportions of the crystals on which the various new forms were found. Figure 6, with the omission of the planes u, x, and w, would reproduce very well the appearance of the majority of the smaller crystals. Figure 7 is an ideal combination of all the forms here described, and is represented as terminated below by the perfect basal cleavage, which is very commonly developed. The gnomonic projection, Figure 1, also brings out well the relations of the forms. Chemical Analysis. The material for analysis was obtained from a single large pocket of prehnite in which the babingtonite was embedded in fine granular form. The whole mass was roughly hand-picked, and the babingtonite crushed and passed through a coarse sieve, washed to remove dust, and treated with dilute acid to remove traces of calcite present. It was quite free from limonite. It was then separated with an electro-magnet, which readily attracted the babingtonite, leaving behind the prehnite and almost all of the epidote, of which a very small quantity was present. After a second treatment under the magnet with a slightly less powerful field, the material was placed in methylene iodide at its maximum density, 3.34, PALACHE AND FRAPRIE. — BABINGTONITE. 3891 in which the larger portion of the babingtonite slowly settled, leaving floating all fragments with adhering prehnite. About 3 grammes was thus obtained, which under the microscope showed no appreciable impurity. The analysis, by Fraprie, was made according to the method of Hille- brand for silicate analysis, except that the manganese was precipitated with bromine water. Recalculated to 100% Analysis. omitting H,0. Molecular Ratio. SiO, 02.29 02.66 0.8777 TiO, 0.18 0.18 0.0023 ' peee iu aye gS ANO} 5.27 5.31 0.0521 Fe,0; 7.49 7.55 0.0472 ' Oot ae FeO 11.05 11.14 0.1547 } MnO 1.94 1.96 0.0276 | CaO 20.36 20.52 0.3664 -0.5630 5.67 MgO 0.46 0.46 0.0115 (K, Na).O 0.22 0.22 0.0028 } Loss (H,O) 0.29 Total 99.51 100.00 The analysis shows a babingtonite somewhat lower in manganese and much higher in aluminum than the average, but otherwise of normal character. It may be expressed by the formula, (Ca,Fe,Mn) SiO; : (Fe,Al). (SiOs)s with the two molecules present in the proportion of about 53: 1. 2. BABINGTONITE FROM ATHOL, Mass. Babingtonite was first reported from Athol by Shepard * in 1849, and the locality was cited for the mineral in his Mineralogy, 1857, p. 183. J. D. Dana was the first to examine the crystals critically, and his measurements, made on very small crystals, were not conclusive, as they agreed but. poorly with the angles of babingtonite from Arendal. His figure and measurements are to be found in his Mineralogy, 1854, p- 368, and the question of the identity of this mineral has remained unset- tled. In Dana’s System, 1892, reference is simply made to the descrip- tion cited above, the matter being still left in doubt. — * A.J. Sci., VIII. (1849), p. 275. 392 PROCEEDINGS OF THE AMERICAN ACADEMY. Through the kindness of Professor B. K. Emerson we were given the opportunity of studying a suite of specimens of the Athol babingtonite belonging to the Amherst Mineral Cabinet, and the result of our exami- nation is to establish Shepard’s original determination as correct. Milt . eee. we Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 12, — DECEMBER, 1902. ON THE THERMAL DEVELOPMENT OF THE SPARK SPECTRUM OF CARBON. By Henry Crew anv Joun C. BAKER. INVESTIGATIONS ON LIGHT AND HEAT, MADE AND PUBLISHED WHOLLY OR IN PART WITH APPROPRIATIONS FROM THE RUMFORD FUND. ~ i mM me siRene oe an ay \ Fes ; : twlth, of bey A etm (che be oUt a inte ke ks! ip gad Pat aa eae ae es eae i ON THE THERMAL DEVELOPMENT OF THE SPARK SPECTRUM OF CARBON. By Henry CREW AND JOHN C. BAKER. Presented by Charles R. Cross, October 8, 1902. Received October 8, 1902. DurinG the course of some experiments which Professor Basquin was making on the production of arc and spark spectra from the same elec- trodes, it was observed by one of us, standing at the eyepiece of his spec- troscope, that the lines of the spark spectrum made their appearance gradually, and not suddenly, beginning at the instant at which the direct current feeding the are was cut off and the high-voltage current producing the spark was switched on. It was evident at once that the appearance of these lines in deliberate succession was due, primarily at least, to the gradual cooling of the elec- trodes and of the region between them. But we were uncertain whether, after all, the effect was not merely a physiological one, the lines first observed being the stronger lines, and those observed later being the weaker lines. We accordingly set about making a series of photographs which should show the spark spectrum at each successive instant begin- ning at the time at which the arc current is interrupted. At first our attempt was to employ metallic spark-electrodes for the spectrum and to use the carbon arc to heat the spark gap. And in order to retard the development of the spark as much as possible, the carbon electrodes were en- closed between two saucer- shaped clay scorifiers as shown in Figure 1. The terminals of the spark circuit were intro- duced into this cell at right angles to those of the are. Various other forms of cells, hollowed limes from the stere- opticon, clay pipes, fire brick, Figure 1. 398 PROCEEDINGS OF THE AMERICAN ACADEMY, etc., were tried. But in each case, as soon as the region inside got hot enough to affect the character of the spark and render it quiet, we found (as, indeed, ought to have been anticipated) that the walls of the vessel became conducting. We tried next to get a gradual variation of temperature by moving the spark gap slowly from the centre to the edge of an ordinary carbon arc, knowing that, at the centre of the arc, the spark was quiet and non- luminous, while just outside the are it became noisy and brilliant. But in carrying the spark electrodes from one of these positions to the other, we encountered a peculiar discontinuity, i.e. a position at which the spark instantly changed character. When the spark was passed through the “horsetail ” above the hori- zontal arc at a distance of from 3 to 2 centimeters from the arc, the quiet discharge mentioned above was still obtained and a spectrum of feeble intensity could be observed. When, however, the terminals were removed slightly farther above the arc, a point was reached at which the discharge instantly assumed the ragged character of the ordinary cold spark; and when the spark was then moved back toward the are it did not resume its quiet character, but blew the “horsetail” away, and in most cases put out the arc. It did not seem possible to obtain any inter- mediate stages. The instability was very marked. The spark was liable at any time to break down into the ragged character, and when it had once done so it retained that character until the circuit was broken. APPARATUS AND MetTuHop. Accordingly we had recourse to soft-cored carbons worked in air, using the same electrodes for both are and spark ; in other words, we used the hot region between the poles of an ordinary carbon arc as the heated medium in which to study the slowly developing spark. The next step consisted in isolating the particular phase of the development which we wished to examine. This was accomplished by means of a device (designed with the gener- ous aid of Professor Basquin) which performs automatically the following cycle of operations : — 1. Closes the are circuit and lights the arc, thus heating the carbon electrodes and the region between them to a very high temperature. 2. After an interval of a few seconds, sufficient for the carbons to become thoroughly heated, interrupts the arc circuit. 3. After an interval which is less than one-tenth of a second, closes the spark circuit. CREW AND BAKER, —SPARK SPECTRUM OF CARBON. 399 4, After a variable (but definite and measurable) interval of time, opens a shutter in front of the slit of the spectroscope and exposes the plate during any desired length of time, generally between } second and 1 second. 5. Interrupts the spark circuit. 1. Again closes the arc circuit ; and so on, as before. The are was operated with 15 amperes showing 40 volts between the electrodes; while the spark was produced by a large induction coil of the type devised by Rowland in 1887 and described in Kayser’s Hand- buch der Spectroscopie, p. 183. This induction coil, or step-up trans- former, was operated on a 104-volt alternating circuit, of frequency 120, with a primary current of 20 amperes. In parallel with the spark gap was placed a capacity of }, microfarad. The arrangement of the circuit is shown in Figure 2 where s; and s, are each double pole mercury switches so fixed that one can be closed only after the other is opened. 8, is kept closed by a spring until an electromagnet Carbon’ Electrodes: begins to close s, by rocking a light beam of which its armature is a part. The question of Are Circuit. changing from arc to spark circuit is then merely a question of closing the battery circuit which actuates this elec- | . | } | — 8 Ose Peat Se tromagnet. This battery circuit is closed ‘oO ——_- Citeult. and opened by a continuously rotating Wrenn: switch (shown at the left in Figure 3) which is driven at the uniform rate of 10 R. P. M. by a small electric motor. This rate of rotation is maintained constant by means of a pair of cone pulleys and a heavy flywheel. This same rotating switch, or commutator, by means of the sliding contact marked ‘‘2” in Figures 3 and 5, opens the shutter in front of the slit of the spectroscope at any phase of the spark desired and holds the shutter open for a small but definite period of time varying usually from 4+ second to 1 second. On this same rotating commutator shaft is a stud (D, Figure 3) which, immediately after the arc circuit is closed, pushes a carbon rod into the are gap for an instant and thus ‘‘ lights” the are. By clamping the sector P (Figure 5) to the rotating commutator in successive angular positions about its axis, one is enabled to open the slit 400 PROCEEDINGS OF THE AMERICAN ACADEMY. for the successive phases of the spark which he may wish to photograph ; not only so, but he can repeat any phase as many times as he likes, and thus obtain a strong com- posite in cases where a single exposure would produce no visible effect. In this manner we have photographed the spark spectrum of carbon, with a ten-foot concave grating, in nine different phases,* which may be roughly de- scribed as follows : — 1. Exposure begins 4 second after breaking arc and lasts } second. Here the carbon poles are still white hot and the spark is practically silent when compared with the noise which the cold spark makes. In this stage the luminosity is so exceedingly feeble that, with a slit of the same width as in the rest of the series, six to ten hours (i.e. about 5000 exposures) are required to get a fair negative. Ficure 4. Ficure 5, 2. Exposure begins } second after breaking of arc and lasts for 1 second. The middle of the exposure, therefore, occurs 3 second after the beginning of the spark. Here, again, the image of the spark on the slit of the spectroscope is quite invisible during the entire exposure. * The purpose of this experiment, it will be observed, is therefore fundamen- tally different from that in which Sir Norman Lockyer examined the spark spectra of salts volatilized in flames and which he described in Proc. Roy. Soc., 30, pp. 22-31 (1879). CREW AND BAKER, — SPARK SPECTRUM OF CARBON, 401 3. Exposure begins } second after breaking of arc, and lasts for 1 second; middle of exposure one second after beginning of spark. Here the image of the spark is barely visible just before the slit is covered. The spark is distinctly louder than in the preceding phases. 4. Middle of exposure 1} seconds after beginning of spark. 5. Middle of exposure 1? seconds after beginning of spark. 6. Middle of exposure 22 seconds after starting spark. 7. Middle of exposure 5} seconds after starting spark. Here the electrodes begin to show merely red, instead of white, hot. 8. Middle of exposure 7% seconds after beginning: spark distinctly noisy. 9. The last photograph in the series was taken at twelve seconds after the beginning of the spark, the duration of the exposure being, as in the preceding cases, one second. Even at this late stage a distinct crescendo is still noticeable in the noise of the spark. The enormous increase of brilliancy from the hot spark to the cold may be judged from the fact that in order to make the cyanogen band at 3883 of uniform intensity the exposure time for the first of the series was eight hours and for the last of the series twenty minutes. RESULTS. As in the case of the Swan spectrum and the carbon are, so also in the case of the carbon spark, the flutings are, of course, the dominant fea- tures of the entire spectrum. The first question, therefore, which natu- rally arises, in the development of the spark, is concerning the order and the relative intensity in which these cyanogen bands make their appear- ance. A second question might be asked concerning the stage at which the air lines make their appearance. A third query is when and how do the numerous metallic impurities present themselves? Our photographs permit at least partial answers to these three questions for the region lying between A4500 and 3000. The phenomenon is one which cannot be accurately observed by the eye, and the exposure times are so long as to render photographing in the visible region well-nigh impracticable. I. CarsBon FLutTines AND LINES. The cyanogen bands at A 4216, 3883, and 3590 all make their appearance on the first photograph of the series. Their relative inten- sity is practically the same as in the case of the spark between cold electrodes, which, for the sake of brevity, we shall hereafter call the VOL. XXXVIII. — 26 402 PROCEEDINGS OF THE AMERICAN ACADEMY. ‘cold spark.” In view of this fact we have employed these three bands as standards of intensity; and have called any two spectra of “ equal intensity” when these three bands were of equal intensities on the respective negatives. Each member of the series was, in this way, made of practically the same intensity. As to the carbon lines, very few appear in this region. The line at 4556.3 does not appear in the hot spark, i. e. in the earliest phase of the series described above. The broad hazy line at \ 4267.5, which Eder and Valenta* call the ‘‘ chief carbon line,” disappears completely on introducing inductance into the circuit of the cold spark. And it does not appear at all in the hot spark. These two facts raise the question as to whether this line is due to carbon. The line at A3361 persists ia the hot spark; but it also appears in the aluminium spark and, greatly enhanced, in the copper spark when there is no capacity in the circuit. As to the remaining lines which Eder and Valenta describe in this region AA 3920.8, 8877.0, and 3848.0, they are weak, and we have not been able to identify them to our satisfaction. II. Arr LINEs AnD FLUTINGS. Not one of the ordinary air lines appears on any photograph whose phase is earlier than ? second. On the plate whose phase is 3 second appear only the very heaviest of the air lines, viz., AX4630: 4447: 3995 : 3433: 3330. Indeed the elimination of air lines is so complete in these earlier phases that non-appearance in the hot spark might be used as one criterion for air lines, analogous to the inductance test dis- covered by Schuster and Hemsalech. As to nitrogen flutings which appear in spark spectra, when the electrodes are close together or when inductance is placed in series with the condenser, the case is very different — quite reversed, indeed — from that of ordinary air lines. The nitrogen flutings with heads at AA 3371.1 and 3158.7 respectively come out very strong in the earliest phase; at 3 second they begin to weaken ; after 3 seconds, only a trace of them is left. The nitrogen flutings of wave-length longer than 3371 do not appear in the spark under the conditions in which we are working, namely, a 3-millimeter spark gap in series with a condenser of ;!5 microfarad capacity ; no inductance. We have not found any description of these nitrogen bands as they * Eder and Valenta, Denksch. K. Akad. Wien, 60, 249 (1893). CREW AND BAKER, — SPARK SPECTRUM OF CARBON. 403 appear in the spark spectra of elements in air at barometric pressure. At first we took the band at 4 3371.1 to be a hitherto undescribed carbon band; and it was only through an excellent suggestion from Professor Hale that we discovered our mistake. He advised us to try the spark without capacity. On trying this experiment, we found the band at 3371.1 strongly present in the spectra of aluminium, zinc, and other metals in air; but when the spark was worked in atmospheres of oxygen or coal gas, these flutings all disappeared save the merest trace of the strongest two. The cold carbon spark (unlike that of metals) without capacity shows these bands only with extreme faintness; and the condensed carbon spark does not show them at all; but carbon when white hot shows them strongly, as indicated above. In this connection, the question may be raised whether the band de- scribed by Professor Hutchins * does not belong to this nitrogen group. For we have found in the spark spectrum of aluminium a band, with its edge at 1 3914.41, which shows a weak line alternating with a strong one exactly as in Hutchins’s photograph. But on examining this spark in a current of oxygen, not the slightest trace of the band was found. Since it is found in metals, but not in the carbon spark, and since it disappears when nitrogen disappears, it seems to us more probably due to nitrogen f than to carbon. What is apparently the same band may be seen very distinctly on McClean’s map of the spark spectrum of copper; and again a similar fluting has been found by Deslandres at the negative electrode of a spectrum tube filled with nitrogen. For Deslandres’ drawing see Comptes rendus, 9 Aug., 1886. This is probably also the same band * Hutchins, Astrophysical Journal, 15, 310 (1902). + Mr. F. J. Truby has measured the first 14 lines of this fluting, which form a group lying between the edge and the heavy impurity line at A 3905.74. His values are as follows : 3914.41, head 8909.95, weak 8913.89 > 3909.30, strong 3913.35 3908.52, weak 3912.62, strong 3907.80, strong 3912.17, weak 3906.88, weak 3911.70, strong 3906.16, strong 0911.17, weak 8905.74, impurity 3910.61, strong There are possibly two other weak lines near the head which Mr. Truby’s definition does not permit him to measure. 404 PROCEEDINGS OF THE AMERICAN ACADEMY. which is marked very strong at \ 3914.4 in Hemsalech’s* table of ni- trogen bands. ‘The fact that Hutchins is able to intensify the band he describes by making and breaking the arc circuit would seem to indicate that it appears in the arc spectrum primarily in consequence of high electromotive force. IIT. Metratzuic ImMpPuritiss. The only electrodes which we have employed are the unplated, cored carbons sold by A. T. Thompson, 25 Bromfield St., Boston, for use in projection lanterns. Their size is 7} x } inches and they are marked “imported.” The metallic impurities which present themselves are practically only aluminium, calcium, copper, iron, and potassium. Pos- sibly others might be detected by very long exposure or by study of portions of the spectrum other than that to which we have limited our- selves, namely, \ 4500-A 8200. The strongest lines in this region of the hot spark spectrum are two at A 4047.358 and A 4044.294 belonging to the principal series of potassium. They are faintly represented in the carbon are; but no trace of them can be found in the ordinary, or *‘ cold,” carbon spark. Is it not rather surprising to find on a spark spectrum plate that the strongest lines are due not only to an impurity, but to an impurity which is introduced apparently by the condition of high tem- perature in the medium? For, so far as the energy delivered by the spark itself is concerned, this would seem to be enormously greater in the loud and brilliant cold spark than in the quiet and invisible hot spark. We use the expression “ high temperature ” in this connection only with great hesitation, and then only with reference to the medium after the heating current has been cut off. But this potassium pair persists very distinctly for five seconds after the heating (are) current has been inter- rupted. Accordingly we find it difficult to imagine any electrical effect, other than heat, which would persist for this length of time, especially, as the electrodes were placed always horizontally so that strong convec- tion currents were sweeping out anything in the nature of electrolytic products. It seems not improbable that these effects of the hot spark are brought about through an increased conductivity — and hence a lowered electro- motive force — between the poles of the spark gap. So that, in the series described above, the earlier phases partake of the character of the * Hemsalech, Recherches expérimentales sur les spectres, etc., p. 126 (Paris, 1901). CREW AND BAKER. -— SPARK SPECTRUM OF CARBON. 405 arc, while the later phases represent the spark. (Jf this be true, the nine members of this series constitute nine different steps between the are and the spark spectra. A similar diminution of E. M. F. between the hot poles is indicated by the work of Schenck, * who finds that, with hot poles, the ‘Mg. spark line at \ 4481 shrinks down close to the electrodes, while the arc triplet at 45170 does not.’”? And this view is rendered all the more probable by a fact noted by Basquin,f viz. that an auxiliary cold spark gap, in series with the hot spark gap, suffices to render the spark lines immediately visible. The general effect of the hot spark upon metallic impurities may perhaps be most clearly described in the following three statements : 1. Some zew impurities are introduced, e. g. Potassium A 4047.34, 4044.29, 3447.49, 3446.49. ‘This is analogous to the introduction of the nitrogen fluting at \ 3371 above mentioned. 2. Among lines due to a single element some may be diminished while others are enhanced in intensity. ‘Thus the calcium pair at AA 3968.6 and 3933.8, and also the calcium pair at AA3179.4 and 3159.0, are immensely diminished, while the calcium line at A 4226.9 is so greatly enhanced by the hot spark that, after the potassium pair, it becomes the strongest in the entire region studied. It is perhaps worth noting that all of the lines belonging to any one of Kayser and Runge’s series are similarly affected. It would be interesting to know just how this behavior of potassium and calcium is explained in terms of the dissocia- tion hypothesis. 3. The lines of some elements are affected either not at all, or very slightly, by the hot spark. ‘This class is illustrated by the omnipresent copper pair at AX38274 and 3247; also by the aluminium pair between Fraunhofer’s H and K; and by the great majority of the iron lines. In general, it may be noted that there is nothing in the nature of a sudden change anywhere in the series. Indeed the growth of the air lines and the diminution of certain impurity lines is so gradual and defi- nite that one might use their relative intensities to determine the phase at which any particular photograph was taken. The triplet formed by the potassium pair at \A 4047 and 4044, together with the strong iron line between them, serve to illustrate this principle and also to point out an exception to the rule that the iron lines are generally unaffected by the hot spark. For curiously enough this tron line increases in intensity as the spark-gap (the medium) cools down, while, as noted above, the * Schenk, Astroph. Jour., 14, 131 (1901). + Basquin, Ibid., 14, 15 (1901). 40 lor) PROCEEDINGS OF THE AMERICAN ACADEMY. Ke Hew Wk Phase ;°; second: merest trace of Fe line. a Phase $ second: Fe line distinct. Phase 1 second: Fe line half as strong as side line. == Phase 1} seconds: Fe line still the weakest one in the triplet. Phase 1} seconds: Fe line equal to weaker K line. Phase 23 seconds: Fe line equal to stronger K line. Phase 5} seconds: Fe line strongest one in triplet, *hase 77 seconds: A lines very weak, but distinct. *hase 12 seconds: merest trace of K lines. Cold spark: & lines invisible. AREER Ficure 6. potassium pair diminishes with the temperature. In this comparison the three cyanogen bands are taken as the standard of intensity, and have essentially the same density on each plate. The triplet thus assumes the successive appearances shown in the accompanying figure. If we had measured the temperature of the region between the carbon poles at each of these nine phases, we could have identified with certainty each of these temperatures from the appearance (relative intensity) of the triplet. It is not to be forgotten that the temperature here referred to is not the much-talked-of and little-understood “temperature of the spark ;”’ nor is it any temperature peculiar to certain “streaks” as perhaps is the case in the Geissler tube discharge. The temperature here referred to is that of the medium at the instant in which the shutter of the spectrograph is opened. The appearance of this triplet is then a criterion for a temperature which may be measured directly with a thermo-electric couple of sufficiently fine wire ; it is a function of the phase, and not of the duration, of the exposure. NorTUWESTERN UNIVERSITY, Evanston, ILLinots, July 19, 1902. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 18. — DEcEMBER, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE’ UNIVERSALLY EXACT APPLICATION OF FARADAY’S LAW. By THEopoRE WILLIAM RicHARDS AND WILFRED NEWSOME STULL. ig Me : ei th, vl she Wi i a | Ne rte iit LS. thm ite ay ' Ny vs et Vids tH? wag af 1a Aye iW 4 ie fi A} ne CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE UNIVERSALLY EXACT APPLICATION OF FARADAY’S LAW.* By THEopoRE WILLIAM RICHARDS AND WILFRED NEWSOME STULL. Presented by T. W. Richards, November 12, 1902. Received October 9, 1902. RECENTLY it has been shown f in this Laboratory that Faraday’s Law holds with great precision at ordinary temperatures in aqueous solutions, for the two metals silver and copper. The long series of experiments, with probable errors of less than one in twenty thousand, yielded a ratio of the electrochemical equivalents equalling the ratio of the chemical atomic weights, within this small range of error. While this was indeed but the comparison of a single pair of elements, it seems, nevertheless, safe to conclude that when side-reactions are wholly eliminated all other cases of comparison in aqueous solution would yield similar results. ‘The experiments in question do not in the least serve to show that the law is independent of the nature of the solvent or the temperature, however. In attempting to probe into the meaning of this fundamental law, definite knowledge concern- ing these conditions is necessary; hence, new experiments at high temperature and with different solvents seemed highly desirable. It will be remembered that approximate experiments at high tempera- tures and with other solvents have already been made by several experi- menters ;¢ and there could have been no doubt as to the approximate * A preliminary announcement of this work was made at the meeting of the Am. Asso. Adv. Sci. at Pittsburg in July, 1902, and an abstract was published in “Science ” (N. 8.) 16, 284 (1902). + Richards, Collins, and Heimrod, These Proceedings, 35, 123 (1899); Rich- ards and Heimrod, ibid., 37, 415 (1902); also Zeitschr. phys. Chem., 32, 3821 (1900), 41, 302 (1902). t Faraday ; see Ostwald, Electrochemie, 520; Kahlenberg, J. Phys. Chem., 4, 849 (1900) ; Merrill, Phys. Rev., 10, 169°(1900) ; Helfenstein, Z. anorg. Chem., 23, 255 (1900). 410 PROCEEDINGS OF THE AMERICAN ACADEMY. fulfilment of the law under widely varying conditions. But none of these series of experiments yielded results trustworthy within one part in a thousand, and most of them showed deviations of at least one per cent; hence the possibility of slight deviations remained open. In the experiments which are described below, a single metal, silver, was deposited in two successive, widely different cells by the same current. The conditions were so chosen as to make possible the elimi- nation or determination of all conceivable side-reactions. One of the cells consisted simply in the porous cup voltameter, or coulometer, which has been shown to give consistent and accurate results.* The other was a precisely similar arrangement of apparatus filled with a solution of argentic nitrate in fused potassic and sodic nitrates, maintained at about 250°. This mixture of nitrates has a double advantage over pure argentic nitrate as an electrolyte. In the first place, the comparatively small concentration of silver diminishes the danger of accidental reduction, and in the next place, the foreign solvent enables one to determine the amount of mother liquor included in the crystals. The solution- tensions of the alkali metals are so high as to prohibit the electrolytic deposition of a weighable trace of either in the presence of an excess of dissolved silver. It is true that this plan of experiment introduced two variables at once into the problem, a proceeding logically incomplete. If a difference were found between the two deposits of silver, further experiments would be needed in order to determine if this difference were due to the change of solvent or to the change of temperature. Such further experiments would have been made if they had seemed necessary; but the chances against accidental coincidence seemed so great as to elimi- nate any serious danger from the interpretation given below. ‘This is fortunate, for it is not easy to find a single solvent capable of yielding satisfactory results over so large a range of temperature. Although all three nitrates were prepared in a state of great purity by known methods, it was found very difficult to obtain fused solutions free from a slight precipitate of reduced silver. Hence, in order to avoid danger of error from this source, the fused mixture was filtered by its own gravity through an asbestos mat in a Gooch crucible, the whole apparatus being heated to 250° in a clean air-bath. Thus may be obtained a limpid and colorless fused mixture, which was used imme- * Richards and Heimrod, loc. cit. RICHARDS AND STULL. — FARADAY’S LAW. 411 diately for the electrolysis, being maintained at the high temperature with the help of a suitably arranged alcohol lamp. Great care was exercised to prevent the possibility of electrical leakage, the connections being made by carefully insulated air lines. When a first crude experiment had shown the feasibility of the arrangement, three more careful preliminary experiments were made. After the completion of each allotted time, the current of 0.2 ampere was broken, the two porous cups removed, and the two electrolytes decanted. Each cathode-crucible was thoroughly rinsed and allowed to stand for fifteen to eighteen hours in water. Two more washings with water, two with alcohol, and a thorough drying at 160° C. completed - the treatment. In those cases when a trace of metallic silver was found in the decanted liquid, this trace was carefully collected on a Gooch crucible, thoroughly washed, and weighed. It was noted that the upper- most crystals deposited at the higher temperature were somewhat larger than the others, and also that no “anode dust’’ formed at 250°. The first of these facts may be ascribed to local action, due to slight thermal inconstancy * while the second is probably due to the rapid adjustment of equilibrium at the high temperature. Thus the chemical explanation given by Richards and Heimrod f of the appearance of the “ anode dust ” in aqueous solutions is supported; for if the anode dust were due solely to the mechanical detaching of bits of silver, there is no obvious reason why this process should not occur at high temperatures as well as at low temperatures. Since all crystals formed from solutions contain included mother liquor, concealed in inaccessible cells, { the silver which had been de- posited from the molten solution was now examined for included sodic and potassic nitrates by dissolving it in pure nitric acid, precipitating the silver by hydric sulphide, evaporating the filtrate, dissolving and filtering the residue, drying once more, and finally weighing. Hydric sulphide was used in order that platinum vessels might be employed throughout. The mother liquor included in the crystals deposited from aqueous solution was assumed to be_0.016 per cent, the average of many determinations. § * Gladstone and Tribe (Phil. Mag.), (5) 11, 508. + These Proceedings, 37, 428 (1902). ¢ The effect of such inclusion is particularly obvious in the work of Merrill already quoted. § Richards and Heimrod, These Proceedings, 37, 441. 412 PROCEEDINGS OF THE AMERICAN ACADEMY. PRELIMINARY COMPARISON. Silver deposited at 250°, Silver deposited at 20°. Difference. Observed. Impurity. | Corrected. Observed. Corrected. Ing. per cent. grams. m.g. grams. grams. grams. 0.5761 0.4 0.5757 0.5758 0.5757 ! 0.00 0.5942 0.2 0.5940 0.5789 0.5758 b 0.03 1.1729 if, 1.1718 1.1720 1.1718 Y 0.00 IAVETHEG ieia. Je (eat LA eat ta EERO According to these preliminary results the varying conditions seemed to affect the weight of silver by only one part in ten thousand, the higher temperature yielding this slight excess of weight. It became now a matter of interest to determine if this slight differ- ence might be yet further reduced by the employment of yet greater care. Accordingly three much more accurate experiments were made, in a large dark-room which was for the time devoted wholly to this work. No injurious gases were allowed in the vicinity, and dust was as much as possible excluded. The current of 0.2 ampere was open for nearly two hours in each experiment. The impurity included in the crystals was more carefully determined in every case, the deposit from the aqueous solution being ignited at a dull red heat, while the alkali nitrate residues were converted wholly into sulphate, and freed from a last trace of stlver by means of hydrochloric acid. The final dried residues of mixed sulphates weighed respectively 0.30, 0.54, and 0.32 milligrams. Since the nitrates of sodium and potassium were present in molec- ular proportions, and since the hot mother liquor contained ten per cent of argentic nitrate, these values correspond to corrections of 0.39, 0.69, and 0.42 milligrams respectively — corrections which are applied below. The mother liquor included in the silver formed in the cool cell must also have contained dissolved argentic nitrate to the extent of about 0.02 milligrams in each case, an unimportant amount which is neverthe- less subtracted below for the sake of completeness. All weighings were made by substitution on a very precise balance with weights carefully corrected; and in general all the precautions needed in work upon atomic weights were observed. The final figures thus obtained are as follows : — RICHARDS AND STULL. — FARADAY’S LAW. 413 FINAL COMPARISON. Silver deposited at 250°. Silver deposited at 20°, Difference. Observed. Corrected. Corrected. F per cent. grams. grams. grams. 1.14958 1.14919 1.14916 0.003 1.12264 1.12195 1.12185 0.009 1.10242 1.10200 1.10198 0.002 Average The largest difference is thus one tenth of a milligram, an amount not much greater than the possible experimental error, while the average difference has sunk to one in twenty thousand. It may be noted that of the six experiments, preliminary and final, four show no significant dif- ference at all. The decreasing average difference with increasing care suggests that the slightly larger weights of silver obtained from the fused salt might be due to reduction of silver by organic dust, which it is dif- ficult wholly to exclude. But even without this explanation, the results are close enough for present purposes, because an accuracy greater than one part in twenty thousand is rarely attained in other physicochemical measurement at the present time. SUMMARY. In this paper it is shown that a galvanic current deposits essentially ‘the same amount of silver from a solution of argentic nitrate in other nitrates at 250° as it does from an aqueous solution at 20°, within 0.005 per cent. Taken in connection with the previous work of Richards, Collins, and Heimrod, this result shows that Faraday’s law is not a mere approximation, but is rather to be ranked among the most precise and general of the laws of nature. (we oy A ’ ee Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 14. — DecemsBeEr, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. AN APPARATUS FOR THE MEASUREMENT OF THE EXPANSION OF GASES BY HEAT UNDER CONSTANT PRESSURE. By THEODORE WILLIAM RICHARDS AND KENNETH LAMARTINE Mark. INVESTIGATIONS ON LIGHT AND HEAT, MADE AND PUBLISHED WHOLLY OR IN PART WITH APPROPRIATIONS FROM THE RUMFORD FuND. - NY by pel | eer ‘ + ae ee Pe nat Pay hg Dy ei Va | hs Tee ; CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. AN APPARATUS FOR THE MEASUREMENT OF THE EXPANSION OF GASES BY HEAT UNDER CONSTANT PRESSURE. By THEODORE WILLIAM RICHARDS AND KENNETH LAMARTINE MARK. Presented November 12, 1902. Received October 22, 1902. Most of the work which has been done upon the relation to the law of Gay-Lussac or Dalton* has involved the measurement of changing tension in constant volume. The results are neither numerous nor com- prehensive enough to justify their use in connection with the scanty data concerning Boyle’s law, for the construction of the isobars or isopiestic lines representing the temperature-vclume relation. Since in some respects this temperature-volume curve is less difficult to interpret than the temperature-pressure curve, and since our knowl- edge of the fundamental tendencies underlying the slight but weighty irregularities of aeriform material cannot be complete without it, the present investigation was undertaken with the object of directly measur- ing the expansion of gases under constant pressure. It is needless to point out that the results when complete may throw important light on the new theory of compressible atoms; indeed this hope really caused the beginning of the research. In planning an investigation of this kind it is highly important to study the degree of definition required by the various experimental observations. The coefficient of expansion of hydrogen is not far from 0.00366 at 0°; and if the next decimal place of this value is to be determined accurately, the temperature, when the range is between 0° and 100° C., must be known to within 0.03° C., the pressure under which the gas is measured to within 0.02 mm. of mercury, and the volume to within one part in four thousand. * Or Charles. See Klassiker der exakt. Wiss., 44, 14 (1894). VOL. XXXVIII. — 27 418 PROCEEDINGS OF THE AMERICAN ACADEMY. Volumes, together with the correction for the expansion of the glass, can easily be measured with the required accuracy. The temperatures, also, of melting ice and of steam, are certainly known to within 0.03° C.; but in the pieces of apparatus previously used, not all of the gas which was being measured has been at the temperature of the bath, except in some constant volume experiments. In the apparatus of Regnault,* the bulb which contained the gas to be measured was connected by a capil- lary tube to a graduated cylinder, where the expansion was read by the rise and fall of the mercury which closed the lower end of this cylinder. Some doubts may be entertained as to the accuracy of the correction to be applied for the temperature of the gas in the capillary tube, and also as to the perfect equality of temperature throughout the water bath which surrounded the graduated cylinder. With the exception of Magnus f (who used an apparatus, modelled after Gay-Lussac’s, which proved very unsatisfactory because of leakage), other investigators, as Mendeléeff, t Andrews, § Kuenen and Randall, || and Callendar, ** have employed methods similar to that of Regnault. Callendar, instead of correcting for the amount of gas outside the bath, introduced a system of automatic compensating tubes. The attainment of the required accuracy in the reading of pressures is a far more difficult matter than the problem offered by constancy of temperature. Regnault states his belief that the height of the barometer can be read only to one-tenth of a millimeter. Chappuis, ft however, has devised an apparatus, open to the atmosphere, for measurement of increased tension in constant volume, by which he makes record of pres- sures to the thousandth of a millimeter. Of course, this extra care would have been needless if the barometer had been at fault. Cal- lendar $f has overcome the difficulty by using a constant artificial at- mosphere, attained by keeping a large gas reservoir packed in ice, and by using sulphuric acid instead of mercury in the manometer. The very recent work of Travers §§ also attained great uniformity of condition. Unfortunately none of these investigators have made any extended * Mémoires de l’Académie des Sciences, 21, 112-120 (1847). t+ Poggendorf Annalen, 55, 1-27 (1842) ; 57, 177-199 (1842). t Abstract in B., 8, 1681 (1875) ; B., 9, 1811 (1876); B., 10, 81 (1877). § Philosophical Transactions, 166, 421-449 (1876). || Proceedings of the Royal Society, 59, 60-65 (1895). ** Proceedings of the Royal Society, 50, 247-251 (1891). t+ Travaux et Mémoires du Bureau Internat. des Poids et Mesures, 16 (1888). tt Proceedings of the Royal Society, 50, 247-251 (1891). §§ Abstract in Proc. Roy. Soc., 70, 484 (1902) ; also Chem. News, 86, 61. RICHARDS AND MARK.— EXPANSION OF GASES. 419 determinations of the expansion of a gas under constant pressure, and Regnault’s observations furnish still the only considerable data concern- ing this condition. Tue APPARATUS. The apparatus about to be described has several advantages over others. In the first place all the gas is within the constant bath. Again, a smaller range of temperature is used, thus involving less uncertainty on account of the changing of coefficient of expansion with the temperature. The two fixed points used were the melting point of ice, 0°, and the transition temperature of sodic sulphate, 52.383°.* Lastly, the pressure exerted by the gas can be certainly read to within the hundredth of a millimeter of mercury and always under the same conditions, which are entirely independent of atmospheric pressure. The last object is attained by comparing the pressure in a special reser- voir (which is not open to the atmosphere and which is protected from changes in temperature) with the pressure of the gas under investigation, and then reading the pressure within this reservoir with the required degree of accuracy by means of the admirable barometer devised by Lord Rayleigh.t In this way the pressure can always be read under the same conditions and entirely independently of the accidental state of the atmosphere. It must, of course, be proved that the means of comparing the pressure of the investigated gas and the pressure within the reservoir introduces no new source of error. The arrangement which has been devised is as follows: The gas to be experimented upon is contained in the bulb A (Figure 1), which is firmly held in place in the bath B. In adjusting the apparatus at the lower of the two temperatures (0°) the mercury is raised by means of the levelling bulb V, which is carried by a finely threaded screw, until elec- trical contact with the platinum point @ is established. The establish- ment of this contact between the platinum point and the mercury is shown by the movement of a galvanometer needle. Preliminary experi- ments proved that by this method a smaller change in the level of the mercury could be detected than could be noted by observation through the telescope ; that is, a change less than the hundredth of a millimeter. * Am. J. Sci., 6,201; Zeit. phys. Chem., 26, 690 (1898). A more accurate study of this point has been made recently, and very trustworthy data, giving its true value in terms of the international standard, have been obtained. This investiga- tion, by T. W. Richards and R. C. Wells, will be published in this Volume. t Lord Rayleigh, Proc. Roy. Soc., 53, 185-188 (1898). 420 PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 1. RICHARDS AND MARK. — EXPANSION OF GASES. 421 The electromotive force and strength of the indicating current should be very small, in order to avoid the occurrence of sparks. This point a fixes both the volume and the level of the mercury. After the position of contact with a has been fixed, the pressure in the opposite arm C’ is adjusted by changes in the amount of mercury in the insulated reservoir 7, so that contact is just made with the second point a’ also. The reservoir # is the outside reservoir referred to above, and consists of a glass bottle of one and one-half litres capacity, packed in cotton and resting inside a wooden box. The time between the final adjustment of pressure within this reservoir and the reading of this pressure is so short (from one to two minutes), that with this amount of packing, perceptible change in pressure due to change in temperature does not take place. The pressure of the gas in A is the same as the pres- sure in C’ and in the connecting reservoir #, plus or minus the difference in height between the points a and a!. Before proceeding, the adjust- ment at these two points is made again several times, in order that each may be certainly established. The pressure in C and in # is now measured with great accuracy by means of the Lord Rayleigh pressure gauge, shown in the left part of the figure. Here contact is made with the lower point / of the iron rod F. The observation is made through a magnifying glass perma- nently fixed in position. The space # is exhausted by a Sprengel pump and the vacuum obtained is measured by a McLeod gauge G. The pressure in the tube C' and reservoir & is thus measured by the height of the mercury meniscus m above the point 7. . This is easily determined by measuring through a telescope the distance between point m and the meniscus m, since the distance from the point / to the point n of the iron rod F'can be directly measured. This reading completes the per- formauce at the lower temperature. The ice in the bath B is then replaced by about ten kilograms of sodic sulphate at its transition temperature, and a similar setting is made, using the points } and 0’ instead of a anda’. Since the tubes are essentially alike at a, a’, 6, and 0’, and since the volumes are so arranged that there is very little change in pressure upon change in temperature of the bath, the conditions of measurement of pressure are always the same, and the measurements may be made very accurately. This uniformity of conditions eliminates constant errors, such as those due to capillarity and a possible refraction of the glass. 422 PROCEEDINGS OF THE AMERICAN ACADEMY. MEASUREMENTS. The first measurement to be undertaken was the determination of the required volumes. The bulb A and side tube C, before being placed in the bath, but while held in an upright position, were filled with mercury. The end of the side tube was then closed firmly with a pinch-cock at d, and the mercury filling the space between the stop-cock at the top of the bulb and the point a, and that between the point a and the point 6 were in turn run out and separately weighed. Allowance was made for the weight of mercury held by the stop-cock. The temperature was noted, and the volume calculated from the tables of the specific gravity of mercury given by Landolt and Bornstein. In correcting for the expan- sion of the glass, the value 0.000025 for the coefficient of expansion of glass was assumed as accurate enough for preliminary experiments. In conclusive work this value should of course be determined. Weight of Weight of ‘Centigrade, meteury in mereuryin “putbacoeGs © bulbat 25°C. grams. grams, c.c, cc. 20.0° 3709.7 441.90 273.72 32.631 20.0° 8710.5 442.02 273.77 32.640 20.0° 3709.5 441.93 273.70 32.633 Average . . . 273.73 + 0.01 32.635 + 0.002 The “ probable errors,” obtained by the well known method of least squares, show that the average values are sufficiently accurate. The large bulb must have been 0.222 c.c. larger at 32.4” than at 0°. Thus, since the volume of the large bulb at 0° is 273.73 c.c., that of the total, as far as the point 6, at 32°.4, is 806.59 c.c. In an ideally perfect apparatus of this type the distances between the platinum points a and 6 on the one side and the points a! and 0’ on the other should be exactly the same. Since, however, it is not possible to seal these platinum points into the glass tubes with the requisite accuracy of position, it is necessary actually to measure the distances between the two sets of points and apply the corrections thus obtained to the succes- sive observed readings of the pressures in the reservoir A. In measuring the difference between the distances a to b and a' to 0’, the bulb, before being mounted in its final position, was inclined very slightly, at such an angle that the points band 0! were at exactly the same level, as shown by their simultaneous electrical contact on slowly raising the mercury in the tubes. The difference in level between the RICHARDS AND MARK. — EXPANSION OF GASES. 423 points a and a’ was then observed by means of the micrometer-telescope of an excellent Geneva cathetometer. ‘The divisions of the micrometer had previously been standardized by reference to various parts of an accurate Geneva brass meter-stick placed at the same distance from the telescope as was the bulb. For the sake of greater simplicity in cal- culations, this distance (79 cm.) between the scale and the object lens of the telescope was always adopted whenever the telescope was used. Five determinations on different parts of the scale gave an average value of one division of the micrometer screw dial as equal to 0.01248 mm. In order to verify the measurement of the platinum points, the upper pair were afterwards levelled, and the heights of the lower pair were observed through the telescope. The following nine determinations showed the distance between the points in the side tube to be greater than that between those in the bulb by 0.90 mm, 0.89 mm., 0.86 mm., 0.88 mm., 0.89 mm., 0.88mm., 0.87 mm., 0.86 mm., 0.87 mm.; average 0.88 mm. The bulb was then placed into its position in the bath, joined at d by a rubber connector to the rest of the apparatus, and firmly clamped to a massive horizontal iron rod. This part of the apparatus is not shown in the diagram. It is absolutely essential that this clamping be as rigid as possible, since a change in the position of the bulb between one set of readings and another would be fatal to the accuracy of the experiment. The ends of the horizontal rod were clamped to two firm iron supports a meter apart. In order to cause a change in the observed relative heights of the platinum points great enough to affect the result of the experiment, one end of the rod would have to be raised five tenths of a millimeter above the other end. In our apparatus, the unequal coeffi- cients of expansion of the supports caused as a matter of fact a slight displacement of this kind, which will be obviated in further work. An empirical evaluation of this effect showed it to amount to 0.025 mm. (at the points) per degree ; but this correction was often eliminated, since the observations were made as much as possible at constant temperature, when the bulb was unalterable in position. The bath consisted of a large inverted glass bottle, from which the bottom had been cut off. It was surrounded by cotton, then by a coil of lead pipe through which warm water was passed when the bath was filled with sodic sulphate, and then again by cotton. The whole was enclosed in a wooden box, which served as a support and which was securely screwed to the immovable desk upon which all the apparatus stood. 424 PROCEEDINGS OF THE AMERICAN ACADEMY. In order to dry the bulb, it was exhausted five times by means of a Sprengel mercury-pump, while the bath was filled with water at 70° C. ’ The air which entered was dried by passing through sulphuric acid and over phosphoric oxide. The hot water of the bath was next replaced by a mixture of hydrous and anhydrous sodic sulphate, which was kept at its transition temperature by the passage of warm water through the lead-pipe coil surrounding the bath. ‘The temperature of the sodic sul- phate bath was verified by very accurate thermometers.* It was found necessary to fill the bulb at the higher temperature, because that mixture of rubber and paraffine, used as a lubricant for the stop-cock, which was of the proper viscosity at 32° C., became so stiff at 0° C. that the stop-cock could not be turned at that temperature without leakage. The exhausted bulb was now filled with hydrogen, which had been made electrolytically from hydrochloric acid with a zinc amalgam anode.f The hydrogen was purified by passing through strong sodic hydroxide and over phosphoric oxide. After filling the bulb, the hydrogen was allowed to stream through it for half an hour, passing out at the stop-cock e. The enclosing within the bulb an amount of hydrogen suitable for the experiment is a somewhat delicate operation. In the first place the connection between the bulb and the side tube C was closed by mercury. By regulating the amount of mercury in the reser- voir #, a pressure was obtained in the tube C which caused the mercury in the Lord Rayleigh barometer to stand within a millimeter of the upper iron point x when the lower point 7 was just in contact. The pressure in the bulb itself was next made approximately equal to that in C, as shown by simultaneous contacts at the points 6 and 6’. This was accomplished by adding hydrogen to or removing it from the bulb by means of another small bulb with mercury inlet attached to the hydrogen supply system. The stop-cock at the top of the bulb was then closed. A more accurate adjustment of the pressure in the reservoir A was now made, so that the contacts of the mercury with the platinum points b and 0! were perfectly simultaneous ; the contact at the lower point / of * The Baudin thermometers No. 9389 and No. 9390, used for the determination of the transition temperature of sodic sulphate by Richards and Churchill (Amer- ican Journal of Science, 6, 201 (1898), also Zeitschr. phys. Chem., 26, 690, were employed for this purpose. Their relation to the international scale has since been verified by Richards and R. C. Wells with the greatest care. + Cooke and Richards, These Proceedings, 23, 168 (1887). RICHARDS AND MARK.— EXPANSION OF GASES. 425 the iron rod of the gauge was made with great care; and finally the dis- tance between the meniscus m and the point was read through the telescope. It was found possible to be certain of this very important reading within 0.01 mm. when the illumination was properly arranged. The pressure in the upper part H of the gauge was immediately taken by means of the McLeod gauge G — the reading of which multiplies the real pressure by fifty — and also the temperature of the Lord Rayleigh barometer was observed by means of two thermometers placed one at its top and one at its base. It is necessary that this temperature be known to within the tenth of one degree, in order to correct for the unequal expansion of the mercury column and the iron rod. To prevent sudden changes of temperature the barometer was incased in a wooden air- jacket, the lower iron point being observed through a glass window. When the room containing the apparatus varied rapidly in temperature, the jacket was not always adequate for its purpose, hence the observatiens were usually made when the room was at constant temperature. After the first setting, which involved the admission of the suitable amount of hydrogen into the bulb, subsequent determinations consisted merely in adjusting the pressure in the side tube so as to make simultaneous con- tacts at the platinum points, and in making the readings on the Lord Rayleigh barometer. This process took about five minutes and was repeated at intervals during the day. When the temperature of the room remained nearly constant, these readings were very uniform, show- ing that the setting of the instrument could be accomplished with sufficient accuracy. For example, three successive readings in a typical case were 1.30 mm., 1.51 mm., and 1.50 mm. The readings at the lower temperature were made in every particular in the same manner as those just described. The purity of the ice in the bath was tested by the temperature of melting, recorded by the same thermometers as were used in the sodic sulphate, and also by the anal- ysis of the water coming from the melted ice. A complete observation, then, consisted of one series of readings at high temperature, and a similar one at low temperature. It will be noticed that the essential part of the experiment consisted in the observation of slight changes in pressure, measured in such a way that any error tends to eliminate itself. These changes were so small that Boyle’s law may safely be used in referring them to changing volume. In calculating the coefficient of expansion, let a equal the expansion per degree centigrade of unit volume at 0°C. Let V equal the volume at 0°C; v the increase in volume ; ¢ the difference in temperature between 426 PROCEEDINGS OF THE AMERICAN ACADEMY. the two baths; P the original pressure; p the small increase of pressure in the gauge on the reading at higher temperature; and KX the constant value to be subtracted from p due to the greater distance apart of the platinum points in the side tube over the distance apart of those in the bulb. (P+p—K)(V+v)—PV Then a = P Vi It will be seen that it is not necessary to know the numerical value of P very accurately, while p must be known as precisely as possible. The values V, v, and K are constant, and have already been given as V = 273.73 cc. v = 32.86 cc., A=0.88 mm. The value ¢° would also be a constant, but for the fact that the sodic sulphate in the bath was not always perfectly pure. A correction for the exposed stem of the thermometer was made in taking this temperature, and the tempera- ture was then reduced to the international hydrogen scale. The results of the experiments on hydrogen appear in the following table. The first few determinations are omitted, since the manipulatiou of the apparatus had not at that time become perfected. HYDROGEN. Dp. mm 744.5 0.16 ; 3 0.003659 742.7 —0.40 2. 0.003656 742.7 —0.19 2. 0.005657 742.7 —0.15 32. 0.003659 742.7 —0.17 : 0.005659 742.7 —0.20 Ke 0.003658 742.7 —0.17 : 0.003660 742.7 —0.29 32.3% 0.003660 743.9 —0.29 2.0% 0.003660 2. 3. 4. 5. 6. ie 8. oy AWVCTAGE’ oscar ia aes 0.003659 RICHARDS AND MARK, — EXPANSION OF GASES. 427 Since the temperature of the sodic sulphate is referred to the inter- national hydrogen scale, — that is, to the increase in tension of hydrogen at constant volume,—this series of results is merely a comparison between the thermal coefficient of hydrogen at constant volume and that at constant pressure. A mixture of ninety-eight per cent of nitrogen and two per cent of hydrogen had the following coefficient of expansion : IMPURE NITROGEN. 0.005660 0.005660 0.005660 0.005661 0.005660 Carbon dioxide made by the action of hydrochloric acid on marble, and purified by passing through acid sodic carbonate solution, sulphuric acid and over phosphoric oxide, gave the following results: CARBON DIOXIDE. 0.003741 0.008729 0.003724 0.003750 0.003726 Average of last4 . . . 0.005727 428 PROCEEDINGS OF THE AMERICAN ACADEMY. The comparison of these last two tables with that concerning hydrogen is instructive and valuable even if a small undetected constant error is concealed in them all, — for such an error must be the same in each, and thus eliminate itself during comparison. Evidently the coefficient of expansion of nitrogen under constant pressure must be very nearly the same as that of hydrogen, while that of carbon dioxide is far greater. The newly found value 0.003727 for carbon dioxide is larger than the value found by Regnault (0.00371) ; but it must be remembered that the latter is merely an average value over a wide range of temperature, while the former involves only the change from 0° to 32.38°, where carbon dioxide is rather a vapor than a gas. ‘The highest value found in the first experiment is probably to be attributed to the adsorption of the gas, which seems to have varied consistently thereafter. This sub- ject will be treated in greater detail in subsequent communications. We are much indebted to the Rumford Fund of the American Acad- emy for valuable pecuniary assistance in this investigation. SuMMARY. The desirability of new determinations of the coefficient of expansion by heat under constant pressure for various gases is pointed out. An ap- paratus is described which possesses the advantages of having all the gas at known temperature, of affording the means of measuring pressure to within one-hundredth of a millimeter of mercury, of using a small temperature-interval, and of eliminating many possible constant errors by making the observations of pressure always under similar conditions. A table of results of experiments on the expansion of hydrogen under constant pressure, as compared to its previously determined tension in constant volume, shows the possibility of attaining an accuracy equal to that desired, namely, one part in thirty-six hundred. ‘Two other sets of measurements are appended which show that nitrogen expands at essentially the same rate as hydrogen, while carbon dioxide exhibits a very great deviation. It is proposed to make a large number ot experiments on different gases at different pressures with the aid of this apparatus. It may also be worthy of note that for the first time sodic sulphate has been used on a large scale for maintaining a constant temperature. Proceedings of the American Academy of Arts and Sciences. Vout. XXXVIII. No. 15. — DEcEMBER, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE TRANSITION TEMPERATURE OF SODIC SUL- PHATE REFERRED ANEW TO THE INTERNATIONAL STANDARD. By THEODORE WILLIAM RICHARDS AND RoGER CLARK WELLS. INVESTIGATIONS ON LIGHT AND HEAT, MADE AND PUBLISHED WHOLLY OR IN PART WITH APPROPRIATIONS FROM THE RUMFORD FUND. , x ake ue ~ oo 1 box CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE TRANSITION TEMPERATURE OF SODIC SULPHATE REFERRED ANEW TO THE INTERNATIONAL STANDARD. By TuHropore WILLIAM RICHARDS AND ROGER CLARK WELLS. Presented November 12. Received October 22, 1902. In a previous paper * it was shown that the transition temperature of sodic sulphate serves as a very well defined fixed point in thermometry, The precautions to be observed in its determination were there stated and a preliminary value was given, referring the transition temperature to the international standard. This value was found by means of two accurately standardized Tonnelot thermometers, Nos. 11142 and 11145, kindly loaned by the Jefferson Physical Laboratory ; but in order to obtain more certain knowledge of a point so important, obviously more instruments should be used. Furthermore, there was involved an uncertain correction for the column of mercury in the stem, which, owing to the long divisions of the scale, necessarily projected a consider- able distance into the air. From final determinations such uncertainty must be eliminated. This present paper describes a number of determinations wholly independent, although in excellent confirmation of the older results. These new determinations, in the first place, obviate the uncertain cor- rection for the projecting column. Secondly, by means of three new Baudin thermometers acquired by this Laboratory and recently standard- ized by the International Bureau of Weights and Measures, at Sevres, the transition temperature is very accurately referred to the international standard. * Am. J. Sci., [4], 6, 201 ; Zeit. phys. Chem., 26, 690 (1898). 432 PROCEEDINGS OF THE AMERICAN ACADEMY. The general plan of the apparatus used in this work was similar to that described in the previous papers, but there were some modifi- cations in detail. The essential parts of the arrangement are shown in the accompanying figure. The sodic sulphate was placed in a large test tube in a Beckman freezing-point apparatus. It was found absolutely necessary to surround this test tube by an air-jacket in order to prevent a too sudden inflow of heat, which results in the rapid transition of the hydrated salt and conse- quent superheating. ‘The outside bath was easily maintained about half a degree above the transition temperature by means of a small platinum resistance coil in the water. The galvanic current used to supply this energy was regulated by an external rheostat. With this arrangement the transition temperature was easily maintained many hours at a time. As is well known, the true reading of a mercury thermometer is obtained only when the whole stem is the same temperature as the bulb. It was evidently inconvenient to surround the whole stem with sodic sulphate, so the following device was employed. A long tube, of clear glass and even bore, of a diameter about three times as great as the thermometer, was used as a jacket to enclose the thermometer. Through the jacket was kept running a stream of pure water, maintained at a definite temperature by a large thermostat. ‘The water, which entered through a long thin tube parallel with the thermometer, rose through the jacket and flowed out at a side neck at the top. The thermometer bulb emerged from the jacket below through a rubber connection, which was carefully wired with fine platinum wire. In use the jacket almost touched the surface of the sodic sulphate. The diagram facilitates the understanding of the arrangement. Since the cubic dilation of mercury is 0.000182 and that of hard glass is about 0.000022, the apparent dilation of mercury in glass is about 0.00016. A projecting column thirty-six degrees in length, subjected to a change in temperature of 0°.2 C., will therefore record a change of 0°.001 C.in its reading. Since, if possible, we did not wish the error to exceed this amount, the thermostat was not allowed to vary in constancy more than 0°.2 C., and the thermometer used to record its temperature was itself standardized with sodic sulphate. It should be remarked that in most cases an auxiliary thermometer would be a sufficient guide to the correction for the projecting column since this great degree of accuracy is not often sought. ‘The jacket was used in this particular case in order to make certain of the temperature of the stem throughout its RICHARDS AND WELLS. — TRANSITION TEMPERATURE. 433 A, Air-jacket. B, Bath, 338°.0. C, Thermostat, 32°.5. D, Water-jacket for ther- mometer stem. N, Tube to supply this jacket with water. SSS NU ONDA NON OO RATED = ix O, Outflow from jacket. P, Inverting mixture. S, Stirring apparatus. T, Thermometer. VOL. XXXVIII. — 28 434 PROCEEDINGS OF THE AMERICAN ACADEMY. whole length.* To prevent the introduction of an error, on the other hand, from refraction in the glass of the jacket as well as of the ther- mometer, readings were made from various sides, and the average taken ; this error of refraction was of barely perceptible magnitude, and was surely corrected by the diversity of our readings. Great care was taken to place the thermometer in a vertical position. In all, five thermometers were used. The oldest Baudin thermometer No. 9389 and the Tonnelot No. 11143 have been described in the former paper. The latter was standardized in June, 1894. The new Baudin thermometers were especially constructed for this transition- temperature work, each one including the temperature 32°.38. They are numbered 15200, 15275, and 15276, and were standardized in June, 1900. Their bulbs are no larger in diameter than the stem. No. 15200 has no enlargement of the capillary throughout its entire length, and the scale runs from —5° to 104°. Each degree is about six millimeters in length. No. 15275 has an enlargement between +2° and 380°, being intended to give readings from —11° to +2° and from 30° to 112°. Its degrees are about as long as those of No. 15200. After its use in the present research, it will serve as a means of verifying thermometers to be used for determining the freezing and boiling points of solutions. No. 15276, lastly, has one enlargement between 38° and 65°, another between 67° and 98°; it-is intended to give very accurate readings between —2 and 38°, its degrees being each eight millimeters long. On account of the diversity in the forms of these thermometers, each had to be calibrated by the Bureau in a different fashion, and especial confidence may therefore be placed in the average of their readings. In the first place it seemed desirable to determine if sodic sulphate made in various ways would yield the same value for the transition point. The first sample was made from commercially “pure” Glauber’s salt. A filtered solution was allowed to crystallize ; this recrystallization was found to raise the transition temperature only a few hundredths of a degree. After five recrystallizations, readings of its transition tempera- ture were taken on the old sensitive but only approximately standardized Baudin thermometer, No. 9389, which alone was used in the preliminary comparisons of the various preparations. * After the experiments were finished, it was found that in spite of the rapid circulation of water through the jacket, its temperature was about 0°.4 lower than that in the thermostat. Hence a correction of 0°.002 must be added to the final result. RICHARDS AND WELLS. — TRANSITION TEMPERATURE, 435 The second sample of sodic sulphate was made by neutralizing with sulphuric acid a quantity of sodic bicarbonate, which had been well washed with cold water. The product thus obtained was recrystallized many times, and readings taken as recorded below. Sample III was later made from the filtrates of the various recrystal- lizations, and sample IV was made from a mixture of I and II when they became too small in amount to recrystallize separately. It was convenient in this preliminary work to take successive read- ings of the transition temperature of several samples of salt, and then to take the reading of the thermometer in melting ice. In all cases except the first two, the lower fixed point was determined immediately after the upper one. Since commercial ice was found to contain impurity enough to change its melting point by several thousandths of a degree, pure ice was made for the zero observations. The purest water, twice redistilled, was frozen in platinum. After using some ice thus prepared it was found that 100 grams of the resulting water gave, on evaporation, a residue of only 0.0006 gram, the effect of which on the freezing point would be negligible in this work even if it had all consisted of sodic chloride. The results of these measurements, recorded in terms of the hydrogen scale, were as follows: Sample, Temperature of Transition. (1) iE dth recrystallization 32.376° (2) if 6th “ 32.372° (3) II, 6th “ 32.376° (4) ae 7th « 32.384° (5) 106 8th « 32.380° (6) i, 8th cs 32.380° (7) II, Ist “ 32.376° (8) 10 2d «“ 32.383° (9) II, 3d «“ 32.376° (10) Tey, Ist « 32.389° (11) IV; 2d ee 32.376° MVeTAGE:. 2) 3. eR al, oe odes OLOO In the previous communication already quoted, this same thermometer is reported to have given as the transition of sodic sulphate the value [3] 32.482 in mercurial degrees, or 82°.378 on the hydrogen basis. ‘Thus it 436 PROCEEDINGS OF THE AMERICAN ACADEMY. is clear that the newly made sodic sulphate is identical with that pre- pared in 1898; and since the most serious deviation to be observed above is seen in the two determinations of the purest sample (No. IV) it is evident that the slight irregularities are to be ascribed rather to the difficulties of thermometry than to any fault of the preparations. The preliminary values with this one thermometer having thus proved that the salt made by different methods gives identical results within the limit of error of the experiment, readings were taken with the more accurate thermometers. In the final work, all the precautions mentioned by Guillaume to be observed in using thermometers were adhered to as closely as possible.* Inasmuch as it was not convenient to make large quantities of pure ice where it was desired to make only one reading at a time, we preferred to make our ice readings in a tube similar to that used for the sodic sulphate; but the tube was always well filled with the pure ice and the requisite volume of purest cold water and then surrounded with a large jar of ordinary ice. ‘The thermometer, in a vertical position, was read with an accurate Geneva cathetometer. The purest sodic sulphate, as obtained by the methods given above, was used. It was found that a slight efflorescence was amply sufficient to supply the anhydrous phase of the sodic sulphate. The average specific gravity of the inverting mixture was found to be about 1.5. Besides the barometric pressure, the depth of immersion of the ther- mometer in the solution was always noted in order to correct for external pressure. The complete record of an observation is given below in order to show the manner of applying the corrections : | — No. 15, March 7, 1901. Baudin, 15200. Corrected Barometer 766.3 mm. 766.3 mm. 59 mm. pressure of salt 6.6 6c ee of water 4.3 773.9 mm. 770.6 mm. * Guillaume, Traité pratique de la Thermométrie de Précision (1889). + See “Notice sur les Thermométres & mercure,” Paris, Gauthier-Villars et Fils, 1896. This paper accompanies the thermometers. RICHARDS AND WELLS. — TRANSITION TEMPERATURE. 437 Reading in salt 32.486° inice .054° Correction, calibration —.002 .000 se exterior pressure —.002 —.001 i interior Ke +.039 +.009 Corrected reading in ice —.062 062° 32.459° Correction, fundamental interval -+.023 32.482° Correction, hydrogen scale —.104 32.318° Eleven such observations were made, with the help of four very ac- curately standardized thermometers of the finest possible workmanship. Since the salt was essentially the same in each case, these are grouped below according to the instruments. The question no longer concerns the accuracy of the temperature, but it concerns rather the accuracy of the several thermometers. If they can be shown to be in substantial agreement, the certainty of the reference to the international standard will be correspondingly assured. FINAL DETERMINATIONS. (HyproGEeNn STANDARD.) Baudin 15200 (12) 32.379° (13) 32.380° (14) 32.377° 15 32.378° a) 2 Average, 32.3879° Baudin 15275 (16) 32.385° 17 32.386° eee Average, 32.385° Baudin 15276 (18) 32.378° 19 32.376° ae : Average, 32.377° Tonnelot 111438 (20) 32.380° (21) 32.381° 22 52.386° e) Average, 32.382° Total Average. 2. iit by aie Pepa earebtg ecbomeren beg Correction (footnote, p. 434) i435 te Pete ee OO Birra le resrll tasmi cathe cod eesti vo tat ot cede Listes ober 45 PROCEEDINGS OF THE AMERICAN ACADEMY, It will be seen that the maximum variation of any minor average from the total average is only 0°.004. The Tonnelot thermometer, standard- ized by the Bureau Internationale des Poids et Mesures in 1894, gives essentially the same result as the average of the three new thermom- eters —a result which indicates in the clearest manner the excellent quality of the work of the Bureau. The final result, 82°.383, is only 0°.004 higher than the value found by one of us in 1898 —a difference about equal to the average deviation of the older experiments from their mean. If each experiment of the recent series is taken as of equal weight, the “ probable error ” — of the total average is 0°.0007; while if each minor average is considered as an observation, the “ probable error’ becomes 0°.001. These very small figures indicate that further multiplication of observations is needless. The transition temperature of sodic sulphate has been determined in terms of the international standard to within the limit of accuracy of the standard itself. Before closing this report, it is perhaps worth while to emphasize in comparison the possible uncertainties of the three fixed points in the thermometric scale, — 0°, 32.383°, and 100°. The freezing point of water (an equilibrium of two phases) is depend- ent upon three essential conditions: first, the pressure ; secondly, the purity of the water; thirdly, the homogeneity of the crystal form of the ice. It is well known both theoretically and practically, that pressure lowers the melting point of ice, because this substance is more volumi- nous than water. The temperature chosen for the international standard of thermometry is not the true triple point of the substance, but a point 0°.007 lower, — the freezing point under atmospheric pressure. Ordi- nary variations in this pressure cause an effect on the temperature smaller than the necessary errors of observation; hence the effect of changing atmospheric pressure may be disregarded, as well as the effect of the pressure of a few centimeters of liquid above the thermometer bulb. The second possible cause of deviation, impurity in the water, causing a lower freezing point because of its osmotic pressure, is easily avoided. Water is more easily purified than almost any other substance, and even commercial ice often approximates the required purity within a few thousandths of a degree. Attention should be called, however, to the danger of dissolving volatile impurities from the atmosphere. This danger is much less when the interstices between the pieces of ice are wholly filled with pure water; and it is obviously well to add water which has been boiled in a platinum or silver flask and rapidly cooled, RICHARDS AND WELLS. — TRANSITION TEMPERATURE. 439 rather than to wait for the ice to supply the needed liquid by melting. Marek * has shown that pure ice after being rinsed and drained may indicate a freezing point as much as 0°.016 too low; and six carefully conducted experiments of our own indicated almost as great an error from this source (0°.008). It is almost needless to state that in the final experiments above the ice was properly mixed with the purest water. The third cause of irregularity in the melting point of ice is not so frequently considered. Nichols ¢ has shown that the specific gravity of ice may vary from 0.9161 to 0.9180, according to circumstances ; and it is hardly conceivable that such varieties could give identical melting points. Tt may be that after a skeleton of freely forming crystals has been built, the interstices between the crystals are filled with a less compact struc- ture.{ Tyndall’s well known experiment on the “ flowers of ice” seems to support this conclusion. Marek has shown that even the strains produced in cracking the ice may cause serious errors, unless much water is present. In our own experiments, as already stated, the ice was made by freezing the purest boiled water in a platinum dish, and was wholly clear and devoid of apparent crystalline structure. ‘The pressure under which the ice was formed was essentially the atmospheric pressure, the layer of liquid being shallow, and the ice was easily broken. The transition temperature of sodic sulphate, a quadruple point, com- pares favorably with this long established fixed point, in every respect. The volume changes so little during the transition that even the pressure of an atmosphere produces no perceptible effect on the temperature,$ the purity of the substance is quite as easily obtained as that of water, and the certainty of definite crystalline form and consequent homogeneity is probably greater, because the habit of growth causes many independent freely growing crystals, rather than a commingled heterogeneous mass. The somewhat lower “latent heat of melting” is not a serious drawback if reasonable precautions are taken to prevent the inflow of heat from outside. The third constant point, 100°, involves pressure and the purity of substance, like the others; but since no solid enters into the question, the doubt as to homogeneity is eliminated. To neutralize this advantage, two disadvantages appear; first the danger of superheating the vapor ; * Guillaume, Traité, p. 118. + Nichols, Phys. Rev., 8, 21 (1899) ; Z. phys. Chem., 36, 240. t See also Pernet, Guillaume’s Traité, p. 118. § Dr. G. N. Lewis has found in this Laboratory that the volume change is not over 0.5 per cent. 440 PROCEEDINGS OF THE AMERICAN ACADEMY. and secondly the necessity of knowing the pressure with the greater pre- cision, since the tenth of a millimeter changes the boiling point by 0°.004. Hence, without a barometer of the best construction, and many precautions, one can hardly hope to attain a result accurate to within O.0L°. The causes of error in the three fixed points just mentioned are in- herent in the nature of the equilibria, and to these must be added those dependent upon the method of thermometry. The behavior of the liquid mercury, usually used to indicate temperature, leaves little to be desired ; but as is well known, the glass receptacle is far less satisfactory. Its sluggish expansion and contraction may easily introduce errors of a degree or more at high temperatures, and the effect of this cause of error becomes the more important as the temperature-interval increases. Even at 100° serious mistakes may thus result. Hence it is important to choose as a standard some temperature as near as possible to the tem- perature read. In this respect 52°.383 is far superior to either of the usually accepted standards, because most temperature measurements lie in the neighborhood of 20°. The careful study of the transition temperatures of other salts has been continued, and while it has led to results which may be of subsidiary importance, no salt has been found which seems to be as generally useful as sodic sulphate. Hence we unhesitatingly recommend this substance as providing one of the most convenient means known for attaining a pre- cisely, definite temperature. It has even been used in this Laboratory with success on a large scale in a bath containing over ten kilograms ; the description of this undertaking will be found in the preceding paper. The writers are much indebted to the Rumford Fund of the American Academy for pecuniary assistance in this investigation. SuMMARY. The present paper contains the record of experiments which verify in a satisfactory manner the earlier estimate of the transition temperature of sodie sulphate. Its exact place on the international hydrogen scale is found to be 32°.383 + 0.001, by means of four thermometers standard- ized by the Bureau International des Poids et Mesures. It is recom- mended as being at least as trustworthy as the other two fixed points used for defining temperature, and is possibly the most generally useful of the three. CamBripes, Mass., 1900-1902. Proceedings of the American Academy of Arts and Sciences. Vou. XXXVIII. No. 16. — JANuARY, 1903. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF CAESIUM. By TuHEopore WILLIAM RicHarps AND EBENEZER HENRY ARCHIBALD. Ton, ee Hi) CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF CAESIUM By THEODORE WILLIAM RICHARDS AND EBENEZER HENRY ARCHIBALD. Presented December 8, 1902. Received November 8, 1902. CONTENTS. Page J. Introduction. . . Mets cls eal Mth SRL ASY Koa K Oy aa ey ay eee II. Review of Earlier Detaeinindions SU aA RM Mibiaah ts ge Nanas AMR Gk pee Ee ies The, Analysis of Cacsie Chionde. 65 2h 66 ea eis fa Li SAG (a); Preparationiof Materiala) 25.06. 60 o bd a fod <4’ lai Ler! oh pe foe AAG (b)p Method af Analysign (2 24205 gals. ele shot df ome yen noes ee SO (e)}sHesnltsiot Amulysis? 2) <3) 3) span ee el ane) oo rss Cn tea an COD bVe-LhevAnalynis of Potassie: Chloride a ft fa) os. ee on ee a) 486 V. The Quantitative Decomposition of Nitrates ........ . 488 Wie ‘The Analysers of Potassig Nitrates yo. ais. S28 ee a ee Sy a2 Mills) The Analysis of Caesie Nitrate: Gey og) feel he «dare OS VIII. The Analysis of Caesic Bromide. . . . : & Welguate aeetoe IX. The Atomic Weights of Caesium, eataeencn) and Nireeen ns eee S57 SXCs SUMMA Ysa et Peres ep aye Ns rcs, ahh chs ah st ha ug one aOO I. INTRODUCTION. SEVERAL considerations led to the renewed investigation of the atomic weight of caesium. Forming as it does the highest known member of an important and well-marked series, this metal might furnish data for the discovery of the long-sought mathematical relationship between the atomic weights; moreover, its study might also lead to the discovery of a yet higher member filling the supposedly vacant place in the classified system. In case both of these somewhat illusory hopes remained unful- filled, there would yet be obtained data concerning an important constant of nature whose value possessed previously an undesirably large possible error. Moreover, the highly electropositive nature of caesium and its univalence combined to promise the probability of definite results from 444 PROCEEDINGS OF THE AMERICAN ACADEMY. several compounds, which might throw light upon the possible variability of atomic weights. All these inducements caused us to accept with alacrity the exceedingly kind offer from Professor Horace L. Wells of a large quantity of very pure caesium material, with a view to determin- ing its atomic weight with precision. fe Il. Review or EARLIER DETERMINATIONS. Since the discovery of caesium by Bunsen and Kirchhoff in 1860 only four investigations concerning its atomic weight have been made; two by Bunsen * himself, one by Johnson and Allen, f and one by Godeffroy. ¢ In 1861 Bunsen published the results of his first determination. The material used in this investigation was recovered from 150 tons of water taken from the mineral spring at Durkheim. The amount of caesium obtained from this large quantity of water was only about twelve grams, and the difficulty in purifying so small a portion probably accounts for the inaccuracy of the results. Bunsen purified his material by recrystal- lizing the chlorplatinate, which is not nearly as soluble as the corre- sponding rubidium salt. The first value found by Bunsen for the atomic weight of caesium was 142.35, but this number was soon afterwards rejected even by himself, since his salt undoubtedly contained traces of rubidium. A year later, Johnson and Allen, of the Sheffield Scientific School, New Haven, having discovered a much richer source of caesium, began their work on the atomic weight of this element. From the mineral lepidolite found in Hebron, Maine, which contained about three per cent of caesic oxide, they prepared a mixture of lithic, sodic, potassic, rubidic, and caesic chlorides. On treating this mixture with chlorplatinic acid the rubidium and caesium were thrown down as the corresponding chlor- platinates. To separate the rubidium from the caesium, the chlorides were converted through the carbonates into the bitartrates. The acid tartrate of rubidium being only one-eighth as soluble as the correspond- ing caesic salt, successive fractional recrystallization left the mother liquor nearly free from rubidium. A portion of the salt thus obtained was treated with chlorplatinic acid in quantity sufficient for complete precipitation, and the caesic chlorplatinate thrown down was washed, and reduced in a stream of hydrogen. * Bunsen, Zeit. anal. Chem., 1, 137 (1862) ; Pogg. Annal. 119, 1 (1862). t Johnson and Allen, Am. Jour. Sci. and Arts (2), 35, 94. ¢ Godeffroy, Annal. der Chem., 181, 176 (1876). RICHARDS AND ARCHIBALD, — ATOMIC WEIGHT OF CAESIUM. 445 For the purpose of finding the atomic weight of caesium, they made four determinations of the amount of chlorine in the chloride prepared as above. Silver nitrate was used to precipitate the chlorine, and the pre- cipitated argentic chloride was collected on filter paper. Their highest result was 133.15 and their lowest 132.89, the average being 133.04, if oxygen is taken as 16.000 and the correction to vacuum is applied. A few months after the appearance of Johnson and Allen’s paper, Bunsen published the results of his second investigation. His method of purification was now not unlike that used by the other investigators, the most important difference consisting in the fact that several recrys- tallizations of chlorplatinate were made, and each successive product was analyzed. The method of analysis also resembled that of Johnson and Allen. The three final results were 132.949, 133.04, and 132.98, averaging 132.99. In 1865 Redtenbacher * pointed out that there is a greater difference in solubility between the alums of caesium and rubidium than between the chlorplatinates ; that therefore these metals might be separated more completely through the former salts than through the latter. Godeffroy made use of this fact in preparing his pure caesium chloride. When he had obtained caesium alum entirely free from rubidium, the alum was dissolved in hot water and the aluminum precipitated with ammonia. After filtering, the solution was evaporated to dryness in a platinum dish, and heated to drive off ammonic sulphate. The residue was then dissolved in water, and baric chloride was added to precipitate the re- maining sulphuric acid. After filtering off the baric sulphate the solu- tion was treated repeatedly with ammonia and ammonic carbonate in order to eliminate the last traces of aluminium and barium. The caesium chloride obtained by this treatment was fused in a platinum dish to drive off any trace of ammonium salts that might have been present. On dissolving this fused mass in water, the solution was found to be alkaline, but the crystals deposited by evaporation were not hygro- scopic. Godeffroy weighed the chlorine in this salt as argentic chloride, as usual, obtainivng four results, which ranged from 132.50 to 1382.71; averaging 132.57. | This low result is probably due to the admixture of sodium salts coming from the utensils employed in the complicated manipulation of the material. The salt used by the earlier experimenters was undoubt- edly much purer; their errors probably lay in the analysis, and had the * Redtenbacher, Wiener. Acad. Anzeiger f., 1865, 39. 446 PROCEEDINGS OF THE AMERICAN ACADEMY. opposite tendency. Lither the loss of chlorine from the caesic chloride during its ignition, or the solution of argentic chloride by the water used in washing would tend to increase the apparent atomic weight. Hence one might have expected the atomic weight of caesium to lie between 133.0 and 132.6; probably nearer the former than the latter value. The value usually selected by Clarke and others, 152.9, has been in accord with this conclusion, and the present investigation shows it to have been surprisingly accurate. Ill. Tue ANAtysis or CarEsic CHLORIDE. (a) The Preparation of Materials. Caesic chloride is a colorless salt, crystallizing in anhydrous cubes which are very soluble in water. The aqueous vapor tension of the saturated solution is somewhat greater than that of the average air of American steam-heated laboratories, hence the crystals are deliquescent only on damp days. The German ascription of deliquescence to the salt is due evidently to the moister conditions prevalent in that country. The addition of alcohol to its solution precipitates much of the dissolved salt; and since it has no great tendency to form an acid chloride in solu- tion, hydrochloric acid also precipitates it. Caesic chloride fuses into a limpid, colorless liquid at about 600°, losing a trace of its chlorine thereby if moisture is present and hydrochloric acid absent. On the other hand, the salt shows no trace of alkalinity after fusion in perfectly dry air, especially if it has been recrystallized from a hydrochloric acid solution. In the latter case, acid must always be present in the micro- scopic inclusions wherever water is, and the trace of hydrolysis on fusion is effectually prevented. Its properties thus fit it admirably for accurate work. Wells * has shown that caesium may be separated from rubidium and other alkali metals by making use of the difference in solubilities of their trihalide salts. Of these the dichloriodide (CsCl,I) offers peculiar advan- tages ; for this salt not only is from eight to ten times less soluble than the corresponding rubidium salt, but also will crystallize below 70° ina rhombohedral form, while the other metals give the corresponding salts in the orthorhombic form only. By keeping the temperature below this point, crystals of the caesium salt may be obtained which are not likely to carry down rubidium, because of this helpful heteromorphy. * Wells, Am. J. Sci. (3), 43, 17 (1901); Chem. News, 84, 2184, Oct 4 (1901). RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 447 The recrystallization may be carried out very easily without much decomposition by cooling from moderately dilute hydrochloric acid (sp. gr. 1.06). The crystals should then be dried at room tempera- ture; but after they have become almost dry they can be heated to Tos or 80° without much decomposition. In order to test the efficiency of this method, we experimented upon a mixture of 150 grams of lithium, sodium, potassium, rubidium, and caesium chlorides. From this mix- ture were obtained, after six recrystallizations as dichloriodide, about eight grams of caesic chloride, spectroscopically free from all the other metals, while only traces of caesium remained in the last few residual mother liquors. The greater part of the caesium used in this research had been prepared by Professor Wells in this way.* ‘To test its purity as regards rubidium, the mother liquor from one recrystallization had been evaporated down to an extremely small bulk by systematic recrys- tallization, and was finally tested in the spectroscope. Not the slightest trace of rubidium could be detected. In all four successive recrystalliza- tions as dichloriodide were made from about a kilogram of the salt, the crystals being well washed each time, and nothing was used over from any mother liquor. The product, weighing about 280 grams, was re- ceived from Professor Wells in this state, and our results show that it had reached a remarkable degree of purity. To obtain the normal chloride from this pure caesium dichlorio- dide, the latter was placed in a porcelain crucible, and heated at from 90° to 100° in an electric oven,—a temperature far below the melting point of this salt (about 240° C.). The iodine and extra chlo- rine are slowly driven off, leaving the chloride beautifully white and very porous. To eliminate any possible trace of iodine which might remain, one might dissolve the salt in a very small amount of warm water, and pre- cipitate with pure alcohol. A better method, however, seemed to be to precipitate it by saturating the solution with hydrochloric acid. The caesic chloride was therefore transferred to a platinum dish, and dis- solved in the least possible amount of warm water; hydrochloric acid gas from pure boiling concentrated aqueous hydrochloric acid was passed into the solution by means of a platinum tube; the mixture was allowed to cool, and the mother liquor was poured off into another platinum basin, the precipitate being washed with a little pure concentrated hydrochloric acid. This salt was again dissolved in water, precipi- * The source of this material was pollucite, found at Mt. Mica, Paris, Maine. 448 PROCEEDINGS OF THE AMERICAN ACADEMY. tated, washed as before, and partly dried by suction, in a platinum Gooch crucible. After further drying for some time the salt was ready for use. The portion thus prepared was used as Sample I. As will be seen, the atomic weight of caesium found from this sample was 132.886. A second sample was prepared from the mother liquor of the first by evaporating further in platinum vessels and precipitating, as before, with hydrochloric acid gas. The product thus obtained was again dissolved and again precipitated, and after being washed and dried gave Sample I, which yielded the atomic weight 132.883. It was essentially similar to Sample I, and is classed with it below. The temperature of the caesic chloride solution containing an excess of hydrochloric acid in contact with platinum, must not be allowed to rise above 60° or 70°, otherwise the platinum will be attacked, and some caesium chlorplatinate precipitated, — a mishap which causes much trouble. ‘This difficulty was probably due to the presence of a residual trace of undecomposed dichloriodide. The careful analyst well knows that platinum, which he is forced to use, forms by no means the inert recep- tacle which he desires. This fact was apparent more than once during the present research, and it is not impossible that both Samples I and II contained traces of platinum from this source, accounting for the slightly high atomic weight. Subsequently this error was yet more vigilantly guarded against, and the later specimens were as free as pos- sible from platinum. A third sample of caesic chloride was prepared from a somewhat impure caesium alum. In the first place the sulphuric acid was elimi- nated by means of baric chloride; the dichloriodide was obtained from the filtrate by adding to it an excess of aqua regia, and subsequently adding somewhat more than the calculated amount of iodine. The trihaloid salt separated out, upon cooling, in beautiful rhombohedral crystals. The iodine used in this preparation had been carefully re- sublimed. The dichloriodide was recrystallized eight times, no trace of rubidium being found by the spectroscope after the third recrystalliza- tion, although the original alum had contained much of this impurity. The normal caesic chloride was prepared from this product by heating in the electric oven at 95° for a much longer time than before, until long after all traces of iodine had disappeared ; and great care was taken not to allow the solution of caesic chloride to become at all hot when precipitating this salt with hydrochloric acid gas in the platinum vessel. The atomic weight obtained from this third sample was 132.873. A RICHARDS AND ARCHIBALD, — ATOMIC WEIGHT OF CAESIUM. 449 trace of thallium was found spectroscopically in the extreme mother liquors. * In the search, which proved fruitless, for an unknown heavier metal like caesium, a fourth sample of material was prepared. Since the in- solubility of the dichloriodides seems to increase with the atomic weight of the basic element, the unknown element would probably be found in the extreme fraction of crystals. Hence, the most likely way of con- centrating a trace of such an element would be to subject a large quan- tity of the caesium dichloriodide to systematic recrystallization, until a very small amount of substance remained. Such a process was carried out, starting with 150 grams of the di- chloriodide belonging to the sample used in the first analysis. This was systematically fractioned by crystallization twenty-five times, when only about one gram of the substance remained. The normal chloride was pre- pared from this, and its spectrum was carefully examined. No difference could be distinguished between the spectrum given by this portion and that given by any of the other preceding samples, or the extreme mother liquor. The last four extreme crops of crystals, averaging twenty-three crystallizations, were now combined, and enough caesium chloride was obtained from these for several analyses. The value of the atomic weight obtained from this fourth sample was 132.878, or about the mean of the preceding values. This result agrees with the verdict given by the spectroscope, showing that recrystallization has in no way affected the purity of the caesium chloride. It must be concluded from this that the most efficient means known to us at present are not capable of isolating any unknown element from this material; and further, that the occurrence of such an element in the original mineral is unlikely. Wells has independently come to the same conclusion. Having gained considerable experience in the technique of all parts of the determination, it now seemed advisable to make a series of determinations in which the highest possible degree of accuracy would be attained at every step. To this end a fifth portion of caesium chloride was prepared from the already pure chloriodide of Wells. The method of preparation was iden- tical with that employed before, except that in every step greater care was taken, and in driving off the iodine and extra chlorine the salt was * This experience agrees with that of Wells, kindly communicated to us ina private communication. It is not impossible that thallium really represents the recurrence of the alkaline characteristics in the periodic system, modified by con- flict of overlapping tendencies belonging to other groups. VOL, XXXVIII. — 29 450 PROCEEDINGS OF THE AMERICAN ACADEMY. heated for two or three days in the electric oven after all apparent traces of iodine had disappeared. This treatment left a salt which gave a perfectly colorless solution when dissolved in a small amount of water. Even the mother liquor that remained after precipitating the chloride with hydrochloric acid gas showed no trace of the yellow color due to platinum or iodine. The salt was precipitated twice successively with hydrochloric acid, each time being washed with a concentrated aqueous solution of the same acid. The analysis of this last sample, as will be seen, was conducted with all known precautions, but yielded, nevertheless, a result 132.877, essentially identical with the last. Silver. Since the ratio of silver to caesic chloride was to be deter- mined, as well as the ratio of argentic chloride to caesic chloride, the purity of the silver to be used must be unquestioned. The method of obtaining the pure metal was so nearly similar to that previously used in this Laboratory that further detailing is scarcely necessary. During the electrolytic part of the purification it is well to wrap the anode in a washed filter, as the “anode dust” is then prevented from mingling with and possibly contaminating the pure silver. The sparkling crystals were thoroughly washed, and fused on sugar charcoal, before the blow-pipe, and cooled in a reducing flame. The melted globule was clear, and free from any film; after cooling it showed no traces of having contained absorbed oxygen. ‘The button was now scrubbed with pure water and clean sand, and cut into small pieces with a clean steel chisel. These pieces were then digested for a short time with dilute nitric acid and washed with ammonia water, in order to remove any traces of iron. To shield them from injurious gases they were kept under distilled water in a small flask. This silver was used in all the analyses, excepting in Nos. 11, 12, 18, 28, 24, and 25. For these analyses the silver was fused in a vacuum on a boat of lime.* The hydrochloric and nitric acids used were carefully redistilled, the first and last portions of the distillate being rejected. The nitric acid, of course, showed no trace of opalescence with excess of silver nitrate after suitable dilution. t The phosphoric oxide was resublimed in an oxidizing environment. ‘The water used was redistilled, first with alka- line permanganate, and subsequently with a trace of acid potassic sul- * For further information concerning the preparation and purity of silver, see Proc. Am. Acad., 29, 64 (1898); 32, 62 (1896); 33, 121 (1897), etc.; Z. anorg. Chem., 6, 98 (1898) ; 13, 90 (1896) ; 16, 371 (1897). + Proc. Am. Acad., 29, 74 (1893). RICHARDS AND ARCHIBALD.— ATOMIC WEIGHT OF CAESIUM. 451 phate, using in the second case a pure block-tin condenser, fitted to the neck of a Jena flask. It was kept in Jena flasks, and used as soon after distilling as possible. Portions were always tested with the nephel- ometer * for the presence of chlorine. (b) Method of Analysis. Having now obtained pure material, it was essential to free the chlor- ide from all traces of moisture without loss of a trace of chlorine. It was soon found that this condition is assured when the substance is fused in a current of nitrogen and bottled in an atmosphere of dry air. For this purpose the apparatus which has been employed in this Labo- ratory to such advantage in determining other atomic weights is suitable and convenient, — namely, the “ bottling apparatus,’ devised first for preparing and weighing pure magnesic chloride. f This device enables the substance to be ignited in a boat contained in a tube of the hardest glass or porcelain in the purest of dry nitrogen; and the final transfer- ence of the boat to the weighing bottle filled with dry air takes place without an instant’s exposure to the outside atmosphere. The platinum boat, which had been freed from superficial iron in other investigations, was boiled in several different portions of nitric acid, and finally hydro- chloric acid. Afterwards it was scrubbed with clean round sand, washed, ignited, and cooled in its own weighing bottle. Another weighing bottle, containing an appropriate amount of metal, of the same weight and volume as the first, was used as tare. The platinum boat was now Ficure 1.— Borritine Apparatus, HorizontTaL SECTION. A = weighing bottle. B= stopper of bottle. C C=hard glass tube. D = Platinum boat containing fused caesic chloride. weighed in its bottle, the weighing being done by substitution, and all precautions used in recent work done in this Laboratory were strictly followed. t This weight of tube and boat scarcely changed throughout * Richards, Proc. Am. Acad., 30, 385 (1894) ; Z. anorg. Chem., 8, 269 (1894). + Richards and Parker, These Proceedings, 32, 55 (1896); Z. anorg. Chem.., 13, 81 (1896). { Richards, Proc. Am. Acad., 26, 240 (1891) ; 28, 1 (1898); 29, 55; 30, 369; Z. anorg. Chem., 1, 150 (1892) ; 6, 441 (1898), ete. 452 PROCEEDINGS OF THE AMERICAN ACADEMY. the whole series of investigations, and during a single experiment no appreciable variation in weight could be detected. The boat was now filled with caesic chloride, and placed within the drying apparatus in the position indicated in the diagram, which illus- trates the “bottling apparatus,” but not the elaborate purifiers of air and nitrogen. The weighing bottle belonging to the platinum boat is placed in the extreme left of the tube A, while its stopper rests in the crevice B, and pure nitrogen thoroughly dried by means of phosphoric oxide was allowed to traverse the apparatus. After about three-quarters of an hour the platinum boat was gradually warmed by means of a large “fish-tail” spreader on the Bunsen burner, so that the whole of the boat may be equally heated. The caesic chloride soon fused, and was kept in a state of tranquil fusion until it was reasonably certain that every trace of residual water must have been expelled. The tempera- ture was now gradually lowered, and the boat was finally allowed to cool to the temperature of the room. A current of air dried by phos- phoric oxide was then turned on by opening the appropriate stop-cock, and was allowed to flow for about an hour before the bottling, so as to sweep out all the nitrogen. While the dry air was still flowing, a glass rod was inserted at the right, and the boat was pushed back into its weighing bottle. The stopper was now rolled out of its hiding-place, and was pushed by means of the glass rod firmly into the neck of the weighing bottle. After the tube A had been removed, the weighing bottle was partly removed by means of a hooked wire, and transferred by the aid of a pair of tongs to the desiccator. After suitable delay, the tube, boat, and substance were weighed in the same manner as before. Since argentic chloride is essentially insoluble in solutions containing either silver or chloride, the chlorine in this pure, dry caesic chloride was precipitated by means of an excess of argentic nitrate. Since, more- over, it was desired to determine the weight of silver needed to effect the precipitation, this argentic nitrate was prepared from a carefully weighed portion of pure silver, and the excess in the filtrate also was weighed as chloride. It is not necessary to describe again the many precautions necessary to carry out, in a strictly quantitative fashion, the solution, mixing, and filtration of these materials, because previous communications from this Laboratory have discussed them in adequate detail. Due care was taken concerning the use of nonactinic light, the collection of the fragments of asbestos often lost from the Gooch cruci- bles, the traces of water retained by argentic chloride even at 150°, RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 453 and all the other small causes of error. ‘The most serious cause of difficulty is the dilemma introduced by two conflicting tendencies of argentic chloride, — namely, its solubility and its tendency to absorb argentic nitrate. When it is washed with very dilute argentic nitrate it does not dissolve, but it retains some of the dissolved nitrate; on the other hand, when repeatedly shaken with pure water it retains no im- purity, but dissolves to an appreciable extent. In analyses 1 to 10 and 14 to 22, below, the chief precipitate was thoroughly washed by shaking with a solution containing a very small known amount of ionized silver, and the residual liquid moistening the Gooch filter was displaced by a few cubic centimetres of pure water. This reduces each error to a minimum, and almost balances their slight residual effect; but the fused argentic chloride thus obtained is not perfectly white and pearly. There- fore, in the final determinations (11 to 13, and 23 to 25) a safer but more troublesome procedure was adopted. After the precipitate had been well shaken in its glass-stoppered Erlenmeyer flask with several portions of wash water, containing a known amount of silver nitrate, and rinsed with about 50 c.c. of pure water, it was again shaken vio- lently with five separate portions of water (in all about 500 c.c.) which contained no silver nitrate. This treatment was found to remove all traces of adsorbed silver nitrate. These wash waters were kept by themselves, and the amount of dissolved silver chloride which they contained was estimated by means of the nephelometer, this correction being added to the observed weight of silver chloride. Argentic chloride thus washed fuses into a beautiful translucent pearly white mass. The balance used in this research was the one which has been used in the investigations of many other atomic weights.* It is short armed, and sensitive to about one-fiftieth of a milligram, with the largest load used in this work. The weights were of brass, gold plated. They were very carefully standardized, according to the method suggested by one of us,f and were used in no other work. All weighings were reduced to the vacuum standard. For this pur- pose the specific gravity of caesic chloride was determined. 1.0436 and 0.8877 grams of the salt were found to displace, respectively, 0.2513 and 0.1965 gram of benzol at 20°. The specific gravity of the benzol referred to water at 4° was 0.880, hence the two values for caesic chlo- * Richards, Proc. Am. Acad., 26, 242 (1891). + Richards, Jour. Am. Chem. Soc., 22, 144; Z. Phys. Chem., 33, 605 (1900). 454 PROCEEDINGS OF THE AMERICAN ACADEMY. Tur CoMPARISON OF CAESIC AND ARGENTIC CHLORIDE. Ag = 107.930; Cl = 35.455. No. of Sample Weight of CsCl Weight of AgCl | Ratio AgCl: CsCl | Atomic Weight Analysis. of CsCl. in Vacuum. in Vacuum. = 100.000 : z. of Caesium. 3.85054 3.26240 117.415 132.901 3.95120 3.86532 117.409 132.892 2.272387 1.98555 117.402 182.882 3.02935 2.58003 117.415 132.901 3.19774 2.72382 117.3899 152.878 Average (a) . . . 117.408 182.891 2.35068 2.00258 117.386 182.858 2.06246 1.75678 8 182.878 2.56372 2.18858 117.409 182.892 Average (b) . . . 117.398 152.876 2.01881 1.71972 117.3892 182.868 1.77391 1.51093 117.405 132.886 Average (c) . . . 3 | 182.877 3.08160 2.62484 117.401 132.881 3.13117 2.66720 ~| 117.895 132.872 5.06656 4.31570 117.298 132.876 Average (d) . . . 117.898 | 132.876 ride were 3.970 and 3.975. The average, 3.972, agrees sufficiently well with the value 3.992, found by Setterberg.* ‘Therefore, for every gram of caesic chloride, as weighed in air, 0.00016 gram has been added to correct the observed weight. * Oefvers. Stockh. Acad. Forh., 39, No, 6, 28 (1882). RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 455 Tue CoMPARISON OF CAESIC CHLORIDE AND SILVER. Ag = 107.980; Cl = 35.455. . \ Weight of Ratio > é No. of 8 1 Weight of CsCl < “i s 1 At Weight Analyeie: of CsCL. fi Vaediutch Lance = aa n. oe Cassini, 14 I 3.838054 2.45600 155.967 132.880 15 I 3.95120 2.53351 155.958 132.871 16 i 2.27237 1.45686 155.977 152.891 17 II 3.02935 1.94244 155.956 132.868 18 II 3.19774 2.05023 155.970 182.883 Average (e) 155.966 182.878 19 Ill 2.35068 1.50720 155.963 182.876 20 Il 2.06245 1.32251 155,950 132.862 Average (f) 155.957 132.869 21 IV 2.01881 1.29434 155.972 132.886 _ 22 IV 1.77391 1.18743 155.958 132.871 Average (g) 155.965 182.878 | 23 Vv 3.08160 1.97590 155.959 132.872 24 Vi 3.18117 2.00760 155.966 132.879 25 V 5.06656 3.24850 155.966 132.879 Average (h) 155.964 32.877 (c) Results of Analysis of Caesie Chloride. The eight average values when collated give the following mean value : 456 PROCEEDINGS OF THE AMERICAN ACADEMY. From (a) )Analysis - 1 too 208 2 py 32.891 « (b) MB tO Bids ick. 2 es ABO B U6 ‘ (c) &“ Oo Oy, sete seao em OesOnel “ @d) “ Lil stoic 4. uh ay Loki Wa esonie “ (e) “ LASEOL1 Sree ey ees 6 (f) 6 LOFto ZO se la2ss69 a); “ DA oe Gays, piles eds ty (Gh) “ QStOrwO LPL een Me ora Mean value! vote) ae ear Bo 878 The ‘ probable error ” of this result, obtained according to the method of least squares, is only about + 0.001, if each average is counted as a single determination. Of course, however, this ‘probable error” gives no clew as to the presence or absence of a possible constant error. The accuracy of the work and the purity of the silver may be better tested by comparing the weight of silver taken with that of the argentic chloride obtained ; thus 22.93252 grams of silver gave 30.46482 grams of chloride, or 75.275 to 100.00; while Stas found the ratio 75.276 to 100.00. This agreement is as close as could be desired; it shows that no weighable trace of iodine remained in the preparations. The means (d) and (h) represent by far the most careful work, and the six experiments included in them give the average 132.877 (+ 0.0007). This seems to be the most trustworthy value of the atomic weight of caesium as obtained by the analysis of the chloride. IV. Tse ANAtysis OF Potassic CHLORIDE. As a further test of the purity of the materials and the accuracy of the method it seemed worth while to make a few similar determinations of the atomic weight of potassium. Since this value is already well known from the accurate work of Stas, the present work upon this element was far less searching than the preceding investigation. For this purpose pure potassic chloride was prepared as follows. ‘* Chemically pure” potassic chloride was dissolved in pure water, and to this was added a carefully prepared solution of chloroplatinic acid solution. The potassium chlorplatinate was well washed and reduced by ignition. ‘The potassic chloride was dissolved with hot water in a platinum vessel and the solution was allowed to stand for some time in order that any chlorplatinate which had not been reduced might separate out. The solution was then evaporated, and the potassic chloride repeatedly precipitated with hydrochloric acid gas. No better method RICHARDS AND ARCHIBALD, — ATOMIC WEIGHT OF CAESIUM. 457 could be found for eliminating the last traces of chlorplatinate ; for since this latter salt yields a dissimilar anion, it is even more soluble in strong hydrochloric acid than in water, while potassic chloride is almost insoluble in concentrated hydrochloric acid. The successive precipitation was repeated long after the last apparent traces of platinum had disap- peared, and the last snow white crystals were washed with a little water and thoroughly dried over potash in a desiccator. Tue ComMPaARISON OF PoTassic AND ARGENTIC CHLORIDES. Ag = 107.930; Cl = 35.455. Weight of Weight of Atomic Ratio KCl in AgCl in AgCl: KCl Weight of Vacuum. Vacuum. = 100.000: a. Potassium. No. of Analysis, = 2.50019 4.80600 52.022 2.50891 4.81525 52.021 INGEN 6 6 626 a 6 oo GAY Tur ComMPARISON OF Porassic CHLORIDE AND SILVER. Weight of Weight of Ratio Atomic KCl in Ag in Ag: KCl Weight of Vacuum. Vacuum. = 100.000 : x. Potassium. No. of Analysis, 2.50019 : : 39.140 2.50391 6 39.141 Average: «2° 1 a. eee) ne ee SOUS 39.141 Mean value of SeriesITandII .. . 89.139 = The method of analysis was precisely similar to that used in the earlier analyses of caesic chloride, and the same sample of silver was used. The only difference worthy of note is in the fact that while dry- ing the potassic chloride for analysis, fusion did not take place at the highest temperature attainable in the hard glass tube; but the salt was finely powdered, and the heating was maintained for a considerable length of time at about 700°, so as to afford as muca opportunity as pos- 458 PROCEEDINGS OF THE AMERICAN ACADEMY. sible for the escape of the last traces of water and hydrochloric acid. Moreover since the mother liquor contained almost as much chlorine as the potassic chloride, weight for weight, the inclusion of a trace would not greatly affect the result. The results for the potassic chloride are given in the foregoing table. The mean value 39.139 agrees very closely with the value obtained by Stas, whose later experiments with the chloride gave values ranging from 39.142 to 39.15. Thus the evidence of this work affirms the trustworthiness of the experiments with caesic chloride. V. Tue Quantitative Decomposition oF NITRATES. If a process could be devised which involved the use of a different set of apparatus, and another series of salts, any constant error which might possibly have crept into the previous method would probably not appear, and the new results would furnish a severe test of the correctness of the values found from the chlorine determinations. Hence a search was instituted for an entirely new method, involving different manipulation. It is well known that when silicic oxide is heated with the nitrate of such a metal as caesium, the salt breaks up according to the following reaction : — 2CsNO; + SiO, = Cs,0 (SiO,) + N.O; the nitrogen pentoxide decomposing and passing off, leaving the caesic silicate. Therefore, from the loss in weight of a mixture containing a known weight of caesic nitrate and an excess of silica one might compute the atomic weight of caesium. This method, commonly used to determine nitric acid, has never before served for this exact purpose. A series of preliminary experiments were of course necessary to deter- mine the limit of accuracy attainable. The silicic dioxide was prepared from a very pure specimen of natural _ sand. ‘This material was washed several times with boiling water and then digested with hot concentrated sulphuric acid for several days. Subsequently it was again washed with water and covered with boiling aqua regia. It was allowed to stand on the steam bath in this solution for at least a week. Upon washing and drying the product, it was found to be beautifully white, and when heated to a high temperature in the blast lamp, it came almost at once to a constant weight. After powder- ing very finely in an agate mortar and heating again it was ready for use. Subsequently very pure artificial silica made from alkaline silicate RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 459 was tried, but its use was abandoned because of the very great difficulty found in expelling every trace of water from it. All the experiments described below were made with the pure powdered quartz sand. A rough experiment was first made in order that one might see where errors were likely to appear and what special precautions would have to be taken. A large platinum crucible containing a short platinum spatula was half filled with the silicic dioxide, ignited for a short time, cooled in a desic- cator and weighed, using another platinum crucible containing an equal amount of sand as a tare. Some pure powdered potassic nitrate was then added to the silicic dioxide, and the two were thoroughly mixed with the platinum spatula. The whole was again weighed in order to find the weight of nitrate added. Subsequently a large amount of the dioxide was spread over the top until the crucible was three-quarters full, and the whole was weighed again. ‘This layer on top serves to catch any of the nitrate which might otherwise be carried away with the escaping vapors of the oxides of nitrogen. In order to find whether or not any moisture had been taken up during the mixing, the crucible was heated in the electric oven for two hours at about 150° C., cooled ina desiccator and weighed. The loss actually found after this additional drying never amounted to more than 0.00004 of a gram. ‘The last weight was of course taken as the true one. The mixture was now very carefully heated in the flame of the Bunsen burner, keeping the temperature at a comparatively low point for several hours and gradually increasing the heat until the temperature of the blast lamp was reached. The melting point of potassic nitrate is about 339° C., while the caesic nitrate melts near 414° C.*; the full heat of a Bunsen burner should bring the silicate to a constant weight in either case. It was soon noticed that the nitrate had a tendency to creep over the sides of the crucible, when a little above the fusing point. That part of the nitrate next the platinum, not being entirely surrounded by the sand, evidently had not the same opportunity of combining with the silica as the remainder of the salt; the exposure of this nitrate obviously might cause a loss by sublimation at a high temperature. This danger was eliminated by using a small platinum crucible inside * This temperature was found in a capillary hard-glass tube by means of a nitrogen-filled mercury thermometer, using a bath of potassic nitrate. The ther- mometer was suitably standardized and corrected for the cool column. 460 PROCEEDINGS OF THE AMERICAN ACADEMY. the larger one, in which to mix the nitrate and sand; this small cru- cible was completely surrounded and covered with a layer of silicic dioxide. If with this arrangement the heating is conducted slowly and cautiously, no evidence appeared of loss by sublimation. No trace of deposition was found upon the under surface of the clean cool platinum lid of the crucible. Potassic and caesic silicate both seem to be essentially permanent and non-volatile at 1000°, as far as the present experiments were concerned, and constant weight was easily reached. The next problem to be solved was the finding of the best source of heat. In the first place, in order to avoid the danger of contamination from the impurities in illuminating gas, an electric furnace giving the desired temperature was used. We soon found, however, that the platinum heat-producing resistance was volatilized to a serious extent. The fire-clay of the oven was soon partially coated by a black film of sublimed platinum, and an empty crucible heated in the oven for an hour gained 0.0002 gram. Qualitative analysis showed beyond doubt the nature of this sublimate, when deposited upon pure porcelain. This tendency of platinum under certain circumstances to volatilize has been studied by Hall;* it brought an unwelcome complica- tion into the present work. Evi- dently platinum cannot safely be used as a resistance for obtaining high temperatures in accurate work ; we had almost introduced a large error into the investigation while trying to eliminate a small one. Of course the temperature of the wire in the electric drying oven previously mentioned is too low to cause any danger from this source. Recourse was now had to a contrivance which had been used Figure 2. * Hall, J. Am. Chem. Soc., 22, 8, 494 (1900). RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 461 in this Laboratory in other work. Its general character will be seen from the diagram taken from the original paper. * A large especially made crucible of Berlin porcelain fits tightly into a jacket or furnace of fire clay; the platinum crucible to be ignited is placed inside this, being protected from the porcelain by a spiral of platinum wire between the two crucibles. As a further protection from the impurities of the gas flame, the platinum crucible is fitted with a small porcelain cover, while a larger cover is placed above it. A circular opening is cut in two ignited asbestos sheets, lying on top of the furnace, into which the larger outside crucible fits tightly ; these sheets serve as a further means of deflecting the impurities from the flame, since the only escape for the products of combustion is through the draught holes in the side. ‘The asbestos sheets are not shown in the diagram. By means of this furnace the crucible can be heated at a uniform temperature tor any length of time. Experiments were made to ascertain if in this furnace any platinum volatilized from the crucible at high temperatures. When half full of silicic dioxide, no appreciable loss or gain was observed, either in the Bunsen flame or in the full flame of the blast lamp. When empty, how- ever, although the crucible lost nothing in the Bunsen flame, it lost 0.00012 grams when heated for an hour in the blast. Evidently traces of platinum were volatilized from the cnside of the vessel into the open air space. The outside annular space was probably kept saturated with platinum vapor from the platinum wire. Since the crucible was always more than half full of silica when placed in the furnace during the work described below, it was assumed that no platinum was lost by volatilization. When the precautions indicated in this chapter are carefully followed no further complications arise, and the method easily yields constant results which seem to be unimpeachable. The chief objections to the method lie in the fact that the nitrate must be wholly free from water (an end easily attained by gentle fusion in the present case ¢), and the further fact that any error which may occur is intensified in the calculation, as is always the case when the two sub- stances weighed both contain either the element whose atomic weight is sought or the standard of reference. * Richards, Proc. Amer. Acad., 33, 399 (1898); Am. Chem. J., 20,701 (1896). +t Stas (Aronstein), Untersuchungen, 235 (1867). 462 PROCEEDINGS OF THE AMERICAN ACADEMY. VI. Tue ANALYSIS OF PorTassic NITRATE. The details of experimentation having been mastered, three careful analyses of potassic nitrate were made. The salt lends itself easily to purification by recrystallization, on account of the great temperature coefficient of its solubility ; it was recrystallized eight times in Jena glass vessels and four more times in platinum. ‘The product thus obtained was carefully dried and fused in a platinum dish at the lowest temperature possible, in order to avoid the formation of ever a trace of nitrite. The pure white solid was finely powdered and again dried. Although, as Hempel has shown,* a hard mineral causes con- siderable abrasion in an agate mortar, a soft substance like potassic nitrate may be powdered safely in one. In every case at least five times as much of the silica by weight was used as of the nitrate. In order to reduce the observed weights to the vacuum standard, the specific gravity of the potassic nitrate was taken as 2.09.f It was assumed that the contraction which takes place when potassic oxide com- bines with silica is negligible as far as the reduction to vacuum is con- cerned, and hence that the specific gravity of potassic oxide may be taken as 2.65, according to Karsten. } Following are the results of the three consecutive determinations of the atomic weight of potassium, using the nitrate prepared in the manner described above. REsutts oF ANALysiIs OF Potassic NITRATE. O = 16.000; N = 14.040. No. of Weight of Weight of Ratio Atomic aaiveis N,O; in KNO, in N.O; : K,0 Weight of DENYS: Vacuum. Vacuum. = 100.00: a. Potassium. grams, grams. 0.96692 1.81034 : 39.158 1.68005 3.14564 : 389.142 1.86512 2.55598 : 39.142 INGER Gio A. od id : 39.141 * Hempel, Chem. Centralbl., 2, 719 (1901). + Landolt and Bornstein, Tabellen (1894), 184. This is the most probable average of many determinations. t Karsten, Schweigger’s Ann., 65, 419 (1882). RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 463 The average of these results (39.141) agrees well with that obtained from the chloride (39.139), and the constancy of the results indicates that the method is adequate for its purpose. VII. THe Anatysis or Carsic NITRATE. The decomposition of caesic nitrate may be effected in precisely the same fashion as that of potassic nitrate. The only points to be considered especially are the preparation of the pure salt and the data necessary for reduction to the vacuum standard. Very pure caesic nitrate prepared from the four times recrystallized dichloriodide, and subsequently twice recrystallized, had already been prepared for us by Professor Wells. Like potassic nitrate, it is very easy to recrystallize.* After gentle fusion this preparation was finely powdered, and served for the first two analyses. In order to test its purity, a portion was twice recrystallized in platinum vessels, very carefully fused in platinum, powdered as before, and subjected to analysis. Because the results were identical with those obtained from the first sample, further purification seemed unnecessary. No measurements of the specific gravity of caesic nitrate could be found, therefore this constant was determined, since its value is needed in order to find the weight of air displaced. 1.7638 grams of fused caesic nitrate displaced upon one occasion 0.4210 gram and at another time 0.4208 gram of rectified benzol at 28° C. The specific gravity of the benzol was 0.880, 20°/4° ; therefore the specific gravity of the caesic nitrate must be 3.687. In determining the air displaced by caesic oxide when combined with silica, the only fact available is the density of the hydrate. If we assume that the same contraction takes place when caesic oxide combines with water as when it combines with silica, the specific gravity of caesic oxide under these conditions is easily computed to be 4.9 if caesic hydroxide has a specific gravity 4.0,f as follows. Twice the molar volume of caesic hydroxide is 57 c.c. greater than that of water, and if the molar weight of caesic oxide is divided by this difference, the result given above is obtained. This assumption would have given in the case of potassium about the same result as that used under that head; and while it is of course inexact, it will answer sufficiently well the present purpose. In * Wells, Am. J. Sci., 3, 46, 186. + Békétoff, Bull. Acad. St. Petersb., 2, 171 (1890) ; Ch. Centralbl., 2, 451 (1891). 464 PROCEEDINGS OF THE AMERICAN ACADEMY. applying the corresponding correction, it was subtracted from that com- puted for the nitrate, and the difference added to the final weighing, in order to determine the true loss of weight which corresponds to the nitric pentoxide. * RESULTS OF THE ANALYSIS OF CaEsic NITRATE. O = 16.000; N = 14.040. No. of Weight of Weight of Ratio Atomic Analysis. NO; in CsNOz in O; : Cs,0 Weight of N > “ Vacuum, Vacuum. = 100.000 5 9. Caesium. 1.04278 8.76112 260.699 182.882 0.92416 3.33384 260.689 132.876 1.83590 4.81867 260.706 152.886 1.39960 5.04807 260.679 182.871 INVA) 5° 5 Gf oo oa AGUAS 132.879 In this case, as in all the other cases treated in this paper, the analyses were consecutive, and the table contains all that were made excepting such as were intentionally of a preliminary nature and not worthy of detailed mention. The results will be discussed in connection with the other data at the close of the paper. VIIL Tue ANAtysis or CAgEsic BROMIDE. While the preceding results seemed to be conclusive as to the atomic weight of caesium, it was thought desirable to study the bromide also, because this salt is capable of especially exact analysis. The bromide is easily prepared. In the first place, by adding to the nitrate an excess of hydrobromic acid and bromine, the tribromide is obtained on cooling in the form of deep orange crystals. Pure materials, prepared by the well known methods of Stas, were used in this process. After having been freed from chlorine and iodine the bromine was redistilled five times; and the hydrobromic acid made from it was * Let a = weight of nitrate in air, and m = its correction to the vacuum standard ; } = the weight of the oxide in air, and n = its correction to the vacuum standard ; c = weight of silica. Then the weight of nitric peroxide in vacuum = true loss of weight ="(a +c) + m—[(b+c) +n] = (a — bd) + (m —n). RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 460 thoroughly washed in the gaseous state as well as twice distilled in aqueous solution, rejecting the first and last portions. Hence there is no possibility that the product could have contained either chlorine or iodine. The trace of mother liquor included in the crystals of tribromide was eliminated by means of several successive recrystallizations and washings with hydrobromic acid. After drying the crystals as thoroughly as possible in a centrifugal machine, they were placed in a porcelain dish and kept at a temperature of 80° C. in an electric drying oven until all obvious signs of the extra bromine had disappeared. ‘The pure white bromide was then heated for eight hours at 150°, and subsequently dis- solved in a little water and precipitated by means of pure concentrated hydrobromic acid. The crystals were provisiovally dried over potash and were then ready to fuse. Like the chloride, they were not deliques- cent in the ordinary air of the laboratory. The apparatus for fusing, bottling, and weighing the bromide was similar to that used in the case of the chloride, except that an addition was provided for the sake of introducing a slight amount of perfectly dry hydrogen bromide into the nitrogen during the fusion. * This ‘was done because the loss of a trace of bromine was feared, although indeed none was ever noticed. After partial cooling the acid was wholly replaced by pure dry nitrogen and finally by air, which had passed through a freshly filled train of purifiers and freshly sublimed phosphoric oxide. The fused product, like the chloride, affected neither methyl orange nor phenol phthalein in the preliminary tests made to prove the normality of the salt. Caesic bromide fuses at a point somewhat above 600° Cx although below the softening point of hard glass, but the exact point was not determined. The analysis of the salt was less troublesome than the analysis of the chloride, because of the very meagre solubility of argentic bromide, which served as the means of precipitating the bromine. ‘The silver used was from the same sample as that used in the case of the chloride, its weight was determined as before, and the very faint trace of bromide in the last pure wash-waters was estimated with the nephelometer as in the case of analyses 11, 12, and 13. The specific gravity of caesic bromide was found by Setterberg f to be 4.37 ; in verification of this value the following determinations of this constant were made. At different times 0.9964 and 0.8456 gram of * Richards and Baxter, Proc. Am. Acad., 33, 124 (1897). + Oefvers. Stockh. Acad. Forh., 39, No. 6, 23 (1882). We are indebted to Mr. F. R. Fraprie for this reference, which has been generally overlooked. VOL. XXxvilI.— 30 466 PROCEEDINGS OF THE AMERICAN ACADEMY. the salt displaced 0.2004 and 0.1699 gram of benzol respectively, therefore the two results (since the benzol had the specific gravity 0.880 referred to water at 4°) were 4.382 and 4.378 respectively, the mean value being 4.380. The temperature was 20°. This value was used in correcting the weight of caesic bromide to the vacuum standard. COMPARISON OF CaESIC AND ARGENTIC BROMIDES. Ag = 107.93; Br = 79.955. No. of Weight of CsBr Analysis. i in Vacuum. grams, 37 3.49820 38 6.20409 39 7.17800 Weight of AgBr in Vacuum. grams. 3.08815 5.47673 6.38213 Atomic Weight of Cs. 182.878 182.883 132.880 Mean = 182.880 CoMPpARISON OF CAEsIC BROMIDE AND SILVER. Ag = 107.98; Br = 79.955. No. of Analysis. Weight of CsBr in Vacuum. grams, 40 3.49820 6.20409 7.17800 Weight of Ag in Vacuum, grams. 1.77402 3.14606 3.63740 Atomic Weight of Caesium. 132.873 182.885 182.884 Mean = 182.881 The agreement of these analyses with one another and with the pre- vious results seems to indicate their trustworthiness. may be laid upon this consistency by pointing out that the 8.55748 grams of silver produced 14.8970 grams of argentic bromide, which must then have contained 57.444 per cent of silver. Stas found 57.445 per cent, or essentially the same value. Further emphasis RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 467 IX. Tae Atomic Weicuts Or Carstum, PorasstumM, AND NITROGEN. In the preceding description are recorded analytical results involving the atomic weights of caesium, potassium, nitrogen, chlorine, bromine, silver, and oxygen. Of these, by common consent, the value for oxygen is fixed; the others may be calculated in many ways from the data in connecticn with the data obtained by other experimenters. No attempt was made to explore any such complete experimental field as that suggested by Clarke* in his recent paper on the calculation of atomic weights. This omission was due not so much to lack of time as to the feeling that some of the results would have been fruitless. Ex- perimental skill in attaining uniformity of conditions can almost always reduce the so called “ probable error” of manipulation to a vanishingly small quantity; but constant errors of a chemical nature are much harder to avoid and much more serious when perpetrated. Hence the * probable error” is little or no clue to the trustworthiness of the results, and can rarely be used as a reliable measure of the relative preponder- ance to be ascribed to the respective members of a series of conflicting figures.t Instead of attempting to observe the weight of every element which combines with a given weight of every other without discrimina- tion, it seems much wiser to select those operations in which the constant errors, by long and thorough study. have been discovered and rendered susceptible of elimination. A single series of experiments, and thor- oughly investigated and properly executed, is of more value than ten series containing unknown and incorrigible errors. The preceding figures involve seven different ratios for determining the atomic weight of caesium, assuming in each case one or more of the other atomic weights to be known. Five of these are obvious in the results given; the other two refer the salts of caesium to those of potas- sium. ‘These latter ratios are of interest because they eliminate, at least in part, any possible constant errors in the processes immediately em- ployed, by virtue of the parallelism between the experiments with the two metals. The atomic weight of caesium should therefore be influenced only by chose constant errors which already affect the assumed atomic -weight of potassium. 100.000 parts of silver were found to be equivalent to 155.964 and 69.115 parts of caesic and potassic chlorides respectively, hence these two weights must be equivalent to one another, or 100.000 * Am. Chem. J., 27, 321 (1902). + Richards, A Table of Atomic Weights, Am. Chem. J., 20, 543 (1898). 468 PROCEEDINGS OF THE AMERICAN ACADEMY. of potassic to 225.659 of caesic chloride. Again, 100.000 parts of argentic chloride were found to result from the precipitation of 117.398 and 52.022 parts of the same chlorides, a result which gives the almost equal ratio 100.000 : 225.670. The average of these two, 225.665, is given below. In the same way, 100.000 parts of nitric anhydride were found to be equivalent to 87.232 and 260.693 parts of potassic and caesic oxides respectively. A similar calculation might be performed with the bromide, using Stas’s data obtained from potassic bromide; but this result would not have the same significance because the experimental work would not then have been done all by the same hands under the same conditions. Below is given a table containing the results for the constant in question computed from the several ratios. After each standard sub- stance is given its assumed molecular weight, and after each value of the atomic weight of caesium is given the “mean error” or average deviation from the mean. This is chosen rather than the “ probable error’ because the latter is in most cases too small to possess important significance. In the cases of the last two ratios the average of the mean errors of the potassium and caesium series is recorded. From AgCl (143.385) : CsCl, Cs = 132.876 + 0.003 “Ag, 07-93), = CsCl, Cs = 152877, £0,003 “« AgBr (187.885) : CsBr, Cs = 132.880 + 0.002 & Ag (107.93), >. (CsBr (Cs. 13288) 105004 “ NO; (108.08) : Cs,O, Cs = 132.879 + 0.005 KCI (f4.599) * 2 (Cs@l Cs 132879 200027, « ~K,O (94.280) : Cs,0 Cs = 132.879 + 0.003 Average | ole i. uice ce ee Vaz Oman It is of interest to note that not one of these seven independent figures deviates from the average of all by an amount greater than its mean experimental error. The inference to be drawn from this is that constant errors have been essentially eliminated from the various chemical processes involved. For the atomic weight of potassium we have three direct ratios, which give the following results : — * This value of potassic chloride is known directly with reference to oxygen from the analysis of potassie chlorate, which (according to Clarke) contains 39.154 per cent of oxygen. Tt If O = 15.879, Cs = 181.874. RICHARDS AND ARCHIBALD. — ATOMIC WEIGHT OF CAESIUM. 469 AgCl (143.385) : KCl gives K = 39.137 + 0.001 Ag (107.93) : KCl gives K = 39.141 + 0.001 N,O; (108.08) : K,O gives K = 39.141 + 0.002 Averages) 2494.) 8g! s 3 S940 This result confirms the results of Stas, but disagrees with Clarke’s value (39.11) by nearly one tenth of a per cent. The reason for the difference is to be traced chiefly to the influence of some relatively inexact analyses of potassic iodide by Marignac, which have seriously reduced Clarke’s average value ; moreover Clarke’s estimate of chlorine is some- what lower than ours. ‘The value given above, 39.14, seems to us to represent more nearly the true atomic weight of potassium. On the other hand, assuming from the experiments with the halides, that the atomic weights of caesium and potassium are respectively 132.879 and 39.139, it becomes possible to calculate the atomic weight of nitrogen from the analysis of the nitrate. Since the atomic weight sought is not included in both of the substances weighed, an error is not magnified by the calculation. Cs,O (281.758) : N.O;, N = 14.040 K,O (94.278) : N.O;, N = 14.037 Average, = U4) IN =) 14,039 This value affords another confirmation of the remarkable work of Stas. ; Many other combinations of the preceding data with those of other experimenters might have been made, but the preceding are enough to show the most important features of the new investigation. It is a pleasure to acknowledge our indebtedness to the Cyrus M. Warren Fund for Research in Harvard University for some of our apparatus, and to Dr. Wolcott Gibbs for invaluable platinum utensils, as well as to Professor Wells for his great generosity in providing the caesium material. A X. SuMMARY. 1. As an outcome of forty-two analyses involving seven different ratios and three compounds of caesium (the chloride, bromide, and nitrate), the atomic weight of caesium is found to be 132.879, if oxygen is 16.000. 2. Incidentally it is found that the atomic weights of potassium and nitrogen most consistent with the new data are nearly 39.14 and 14.04. 3. In confirmation of Wells, caesium dichloriodide is found to afford t 470 PROCEEDINGS OF THE AMERICAN ACADEMY. a convenient and exceptionally thorough means of purifying caesium material. 4. No evidence was found indicating the presence of any similar ele- ment of higher atomic weight, except a trace of thallium. 5. The specific gravities of caesic chloride, bromide, and nitrate were found to be respectively 3.972, 4.380, and 3.687; and the melting point of the nitrate was found to be 414° C. 6. The precautions necessary to effect the precisely quantitative de- composition of alkaline nitrates are described. CAMBRIDGE, MAss. October, 1900, to November, 1902. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIL. No. 17. —Janvary, 1903. ON THE MULTIPLE POINTS OF TWISTED CURVES. By Joun N. Van DER VRIES. ae eae ee ie te ” " 7 : ine 1, 1. rss % - 4 a Sn -_ 7 ei hee 7 ims or My as Peas eee ne (re we: a) CANE Oat ee ghar ae ‘€ i, ere Wahit A ba) 2k pa ef i od aft * a , ay \ - cor) Ghee kM oe , ' - ize J : 5 me ® F Pa | P , * 7 cs * > al te ti : es sD ! ; . 5 ? ‘i 5 e i) t >) : r* ; bs - - a : . 7 _ at m4 ( i e a é ; : - ih - & f v : aN r ie I ° ny ; a Rijs, (Nag ert 4 iy ’ -] t ‘? nena sf te * ial ye "7 : Ms on aan ors i : * ’ wey wes) Ay adi , r a? a, ha _ i ae edi Bor Wik ‘ ; oo oa ee, i a id . a 4 i k | t 4 ; 4 anne well , v I . s Ay ‘; . ‘ le i li , Ps ; ; ON THE MULTIPLE POINTS OF TWISTED CURVES. By Joun N. VAN DER VRIES. Presented by W. E Story, May 14, 1902. Received October 8, 1902. J. Introduction .. ROP ee el ATi II. Consideration of @urvee that here Muleple ‘Paints che Tangents at which do or do not liein one Plane .. . 475 III. Consideration of a Curve as the Partial Intersection of a Guna on a Monord) = 2). Oe) Fae ae cee soup eea aod IV. On the Composition of Multiple ‘Points ‘ : 512 V. Classification of Quintic, Sextic, and Septimic urres that oe Mul- tiplesROiMtgey pam ey str cuties en ceeteM ch), oll Sw ikskewte bah, fy) MOLE I. INTRODUCTION. TWISTED curves have been studied in detail by Cayley, * Salmon, ¢ Halphen, ¢ and Nother, § and to some extent by Genty, || Picquet, Rohn, Weyr, Kohn,{| Hoppe, Stickel, and others. In the consideration of these curves attention has been paid not only to the surfaces on which they lie and the surfaces which contain them as their complete or partial intersections, but also to the singularities of the curves themselves. Among these singularities we wish to emphasize in particular the mul- tiple points and the apparent double points. It has in general been over- looked that multiple points may be of different kinds according to the way in which the tangents at these points lie. It has been stated that * Considérations générales sur les courbes en espace. Comptes Rendus, LIV. pp. 55, 896, 672. On Halphen’s characteristic n in the theory of curves in space. Jour. fiir Math. CXI. (1893), pp. 347-352. + Geometry of Three Dimensions (1882), pp. 278-382. t Mémoire sur les courbes gauches algébriques. C. R., LXX. p. 380. § Zur Grundlegung der Theorie der algebraischen Raumcurven. Kronecker Journal, XCIII. pp. 271-318. | Etude sur les courbes gauches unicursales. Bull. de la Soc. Math., t. 9. {] Ueber algebraische Raumcurven. Wien. Ber. LX XXII. pp. 755-770, 474 PROCEEDINGS OF THE AMERICAN ACADEMY. double points and points of higher multiplicity than two have no effect on the number of apparent double points. Halphen* gives as the lower limit of the number of apparent double points of a curve of order ; eeniay WON : m the greatest integer contained in a ; the curve then being the : - ; m m+1 intersection of a quadric cone and a surface of order — or » accord- -- 2 2 ing as m is even or odd. According to this, the lower limit of the num- ber of apparent double points of a quintic is four; and Salmonf gives four quintics having four or more apparent double points. Genty,t in his consideration of the maximum number of actual double points of a twisted curve, makes use of the lower limit of the number of apparent double points as given by Halphen anda applies it to all curves. Picquet, in a note to Genty’s paper, states that Halphen’s lower limit holds “pour une courbe gauche quelconque.” Dr. Williams, § however, gives a quintic curve that has a triple point and only three apparent double points; thus one less than the number given by Halphen’s formula. This diminution is due to the fact that the curve has a triple point at which the tangents do not lie in one plane. It is the object of this paper to consider curves that have multiple points of different kinds and to investigate the effect of these different kinds of points on the other singularities of the curves; to consider the curves first as the intersection, partial or complete, of any two surfaces whatever that may contain them, and then as the intersection, partial or complete, of a cone and a monoid; to consider the number of actual and apparent double points to which a multiple point may be equivalent; and finally to consider in detail all quintic, sextic, and septimic curves that have multiple points. In the consideration of the curve as the inter- section of a cone and a monoid, we are led to the consideration of the different kinds of lines possible on a monoid and the effect on the curve of intersection when these lines are common to the cone and the monoid. In the consideration of the composition of multiple points we shall only consider points of multiplicity not greater than seven. * Loe. cit. p. 381. + Loe. cit. p. 318. + Loe. citsp) lol: § Geometry on Ruled Quartic Surfaces. Proceedings of the American Acad- emy of Arts and Sciences, Vol. XXXVI. No. 3, July, 1900, p. 60. VAN DER VRIES, — MULTIPLE POINTS OF TWISTED CURVES. 475 II. CoNSIDERATION OF CURVES THAT HAVE MULTIPLE POINTS, THE TANGENTS AT WHICH DO OR DO NOT LIE IN ONE PLANE. 1. Every algebraic curve is the complete or partial intersection of two algebraic surfaces. Two surfaces of orders u and v, say S, and S,, re- spectively, intersect in a curve of order .v, which may, however, break up into components of lower orders. This curve or these curves may have points that are not ordinary points, but points of higher multiplicity. The number of these points on any component is generally finite; if infinite, the component is a multiple curve. Points that are ordinary points on both surfaces are in general ordinary points on the curve of intersection. The tangent line to the curve at any ordinary point of it is the intersection of the tangent planes to the two surfaces at that point. There may be points of multiplicity p on the curve for which the tangents all lie in one plane. Such a point does not in any way imply a singularity on any surface that contains the curve. It simply means that the two surfaces lie so close together in the neighborhood of the point that they intersect in p directions from the point, i. e. that there are p lines that meet the curve there in p+1 points each. Such a multiple point, say the point A, that has its tangent lines lying in one plane may, however, be a multiple point on one of the two surfaces that contain the curve, but it must be an ordinary point on the other surface. Namely, if a curve having a multiple point A lie on a surface S, that has the point A as an ordinary point, the tangents to the curve at A are tangent lines to S, at that point, i. e. they lie in the tangent plane to S, at A. If A be also an ordinary point on the surface S, the tangents lie in the tangent plane common to S, and S,, but if it is a multiple point on S, the tangents are the intersection of the tangent cone to S, by the tangent plane to S, at that point. The curve obtained in the latter case can, however, always be obtained as the intersection of two surfaces, each of which has, the point A as an ordinary point, e. g. by the intersection of the surface S, with the surface S,+S,—,8S,, if v = mw, or with the surface S, S,—,.+ Sv, if w x 3 a | | at | a A) . . . . ~D 3 w . . ° . . . am S S >) i) on - wn nw n- n~ - e . . . . . e . =e A a 5 . rey . P MS = e 5 an) 5 2 . LL hae Re x e o S e | 7 (pe!) &-1) @ - 1]; GD also, h+W 4+ H" =} [pv (ue—1)v—-1)—- SAU E-1)(H'—-1)]. CID It is evident from these formulae that multiple points of the curve that are ordinary points on either surface have no effect on the number of apparent double points. Thus, if a curve is the complete intersection of two surfaces, we can at once find its number of apparent double points by means of (I). A sextic with a quadruple point that is the complete intersection of a quadric cone and a cubic surface that has the vertex of the cone as a double point has four apparent double points. From formula (II) it is evident that, when the number of apparent double points of one com- ponent is known, the number of the other component can be obtained at once. Thus, if the quadric and cubic surfaces mentioned above have a line in common, the residual intersection will be a quintic curve having a triple point. We then have Movi Ae 2) pion) oh! = 0; then, substituting these in (II), we obtain h = 3. The quintic with a triple point thus has three apparent double points. 5. We have next to find the number of points in which two surfaces S,, and S, can touch when they have a point in common that is a /-tuple point on S, and a k/-tuple point on S, in the case where the complete intersection does not break up. This intersection is then of order pv and has on it a point of multiplicity £4’. A cone of order wv drawn from an arbitrary point to a curve of order »v cannot have more than eee aoe double edges. The edge to the kk!-tuple point kk! (kk! — 1) 2 ing number the number due to apparent double points, we have the counts as double edges. If we subtract from the remain- maximum number that can be due to contacts. We have then (uv—1)(uv—2) kE(ER—1) pv(u—1) (v—1) , kk'(k—1)(k!—1) 2 2 2 2 pv(ptv—4) kk (k+ hk — 2) ming me ee a 484 PROCEEDINGS OF THE AMERICAN ACADEMY. Every point of multiplicity £4! of this kind reduces the possible number kk! (k + k! — 2) aimee A kk’-tuple point on a curve that is the complete intersection of two surfaces that contain the point as points of multiplicities k and k’, respect- kk! (k + k! — 2) kk! (k — 1) (k' — 1) 2 2 of actual double points of the curve by Therefore: — ively, is equivalent to actual and apparent double points. The quadruple point on the sextic curve mentioned on page 483 is equivalent to four actual and two apparent double points. This will be discussed more in detail later. 6. It is also possible to find an upper limit to the number of actual intersections of the two components of orders m and m! into which the curve may break up; where m + m! = pv. Two curves of orders m and m! have mm’ intersections, actual and apparent. A point that is a p-tuple point on one curve and a p’-tuple point on the other curve counts as pp! intersections of the two curves. We have then mm =t+ H" + pol, (IV) where ¢ is the number of actual intersections of the two curves. Sub- stituting the value of from (III) into (IV), we get {GG eee Coaealed EP EL t=mm!—pp The maximum or minimum number of actual intersections of the two curves thus corresponds to the maximum or minimum number of apparent double points of the two components. A twisted curve of order m with a p-tuple point can be projected into a plane curve of order m with a p-tuple point. This plane curve of order m cannot have more than } (m—1) (m—2) —}p(p—1) double points. The component of order m cannot therefore have more than } (m— 1) (m— 2) —4p (p—1) actual and apparent double points. If it have 6 actual double points, we must have h =} (m—1) (m2) — 3p (p—1) 8 Similarly, for the component of order m! with a p/-tuple point and 0! actual double points, we have MZ 4 (ml — 1) (m! —2) — $l —1) ~ 9 VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 485 Substituting these limits for A and A’ in (IIT) we obtain BAC ae la es 2) es i 5 +5+ 0 —2., Hmm! —pp’ —4) ki (k+hkh'—2 fe ee Sa a ee If the intersection of a quartic cone and a quadric surface, not passing through the vertex of the cone, break up into two quartic curves, and neither quartic has a double point, we have ¢ = 10, i.e. the two quartics cannot intersect each other in more than ten points. Similarly, the quintic curve with a triple point mentioned above cannot meet the line that is the residual intersection of the quadric and the cubic surfaces in more than one point in addition to the vertex. 7. An irreducible curve C;, of order m lying on a surface S, of order v can be cut out of this surface by some surface S, of order pp. If the curve C,, is not the complete intersection of the two surfaces, it may be necessary in the classification of the curves to consider the residuals and classify according to them also. In such a case it is possible, when the one surface S, is given, to determine the second surface in such a way that the residual may take a particular form. It is always possible to find a value of pw that will suffice to make S, cut Ci, out of S,. A sur- face of order p is determined by } (u + 1) (u + 2) (u + 3) — 1 points. These points must be taken in such a way that the surface S,, contains the curve. This can be done by making S, contain mp + 1 points of Cn. ‘There are in general enough points at our disposal to do this if » satisfies the inequality : — mye +let (+1) M+ 2) @t+3)—1. If, however, this inequality gives a value of « that is greater than v, care must be taken that S, does not contain S, as a factor. Thus, if the points left at our disposal after we have made S, contain C,, are greater in number than the number necessary to determine a surface of order p. — v, these can be taken in such a way that S, does not break up into S, and a surface S,_, of order » — v. We must then determine p from the inequality : — Ee =v $1) Gv + 2) Gy + 3) pk+1Zh(ut1) (wt 2)(wt3)—sh (E+) (E+2)5 (V) or, if this gives a value of w such that v = qu, by the inequality : — aie anal my a an AE (u—v+1)(@w—vt+ 2) (u—v+ 3) +4 (k—k) (k—W +1) (k—# +2), that is by /n—m(E- 1)-5 ii 444437 een ev E+E WED UDI -2 Boe Eu-(+2-2). (VI) It is thus possible to find a surface S, that will cut the curve from the given surface S,, where » is the smallest integer that satisfies (V) or (VI); using (V) if it gives a value ~ < vy, otherwise using (VI): It may be possible to cut the curve out of S, by a surface of lower order VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 487 than the smallest integer that satisfies (V) or (VI), but we need never take a surface of higher order. If, however, the surface S, is not considered as given, we can deter- mine its order as the smallest integer that satisfies the inequality : — my —> pk +123 (v+1) V+2) (v+8)— E> M41) H42)-1. (VII) The order of S, being obtained from (VII), the order of S, can be ob- tained from (VI) above. From the above three inequalities we can always find the orders of two surfaces that will contain a given curve as their complete or partial intersection. iy CONSIDERATION OF A CURVE AS THE INTERSECTION OF A CONE AND A MOonoIb. A. 1. If a twisted curve is not the complete intersection of two surfaces, difficulties may arise in the determination of the characteristics of the residual and therefore of the curve itself. If the residual is a proper curve of an order less than four it is definitely determined, but if of an order as great as four there will be difficulty in determining to what. species it belongs. A convenient method of representing a curve in general is as the intersection of a cone and a monoid, a monoid being a surface that has a point of multiplicity one less than the order of the sur- face. This method is due to Cayley.* The advantage of this method lies in the fact that the residual consists entirely of straight lines through a point. The cone K drawn from an arbitrary point in space to a curve C,, of order m will in general be of order m, that is, every edge f of the cone will meet the curve in one, and only one, point. A multiple edge counts for the number of simple edges to which it is equivalent; the number of points of C,, on a k-tuple edge of A, thus being &. There are, however, curves that are met by lines from certain points in two, three, or more points, e.g. any curve that is wound around a cone a number of times, or a curve, say the curve Op, of order pq, that is the complete intersection * Comptes Rendus, t. LIV. (1862) pp. 55, 396, 672. + Hereafter, when we speak of an edge, we shall mean a simple edge unless it is otherwise designated. 488 PROCEEDINGS OF THE AMERICAN ACADEMY. of two cones of orders p and q not having the same vertex. Every edge of the first cone meets the curve g times and every edge of the second cone meets it p times. As Trofessor Story has proved, all simple generators of a cone of any order whatsoever meet any curve lying on it in the same number of points. Thus if a generator of a cone A, of order a meets a curve lying on it in £ points, every generator will meet it in 8 points, and the curve, if it does not pass through the vertex, will be of order af. The cone A, in this case is the cone K, taken B times. It is, however, only for special positions of the vertex that this breaking up of the cone A, can occur. In the case of the curve Cy, of order pq mentioned above, if we take the point (0, 0, 0, 1) as the ver- tex of the one cone and the point (0, 0, 1, 0) as the vertex of the other cone, and eliminate y between the equations of the two cones, we shall get a homogeneous expression of degree pq in x, z, and s._ This is in general the equation of a cone of order pq having the point (0, 1, 0, 0) as its vertex, and the curve C'pg as its base. This vertex is an arbitrary point, and so a line from a point off the curve meets the curve in general in only one point. For the eliminant above will not in general break up into two, three, or more equal factors, as would be necessary in order to have every edge of the cone from the point (0, 1, 0, 0) to the curve meet the curve in two, three, or more points. There may be certain points that, taken as vertices of this cone, will cause it to break up, but ‘for an arbitrary point it will not generally do so. Thus in the case of the quartic of the first kind, if we consider it as the intersection of two quadric cones, there are at most two other quadric cones on which the curve may lie, i.e. there are at most two other points off the curve from which an infinite number of lines can be drawn to meet the curve in two points. Excluding these quadric cones, any other cone whose base is the quartic in question will be a cone of the fourth order, every edge of which meets the curve once. ‘Thus we can always take the vertex of the cone K in such a way that the cone will be of the same order as the curve, an edge meeting the curve in only one point. There is, however, from an arbitrary point in space a finite number of lines that meet the curve. C;, in two distinct points. These correspond to the apparent double points of the curve and are double edges on the cone Ky. As a curve has only a finite number of apparent double points, it will not in general have an apparent multiple point of multi- plicity greater than two. A simple edge of the cone is thus due to an ordinary point on the curve, a double edge to an actual or apparent double point on the curve, and a multiple edge of multiplicity greater VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES, 489 than two to an actual multiple point of the same multiplicity. As before, it is not necessary to consider the case where the line from the vertex to a multiple point crosses the curve again. Nor shall we consider the case where the vertex lies on a tangent to the curve, these tangents gener- ating a definite developable surface on which the arbitrary vertex may also be assumed not to lie. The fact that we can always find a point such that an edge of the cone having this point as vertex and the curve as base generally meets the curve in only one point euables us to obtain any curve C,, as the partial intersection of a cone A, and a monoid JM, of order » having the same vertex as K,,. For, every line through the vertex of M/,, and therefore every edge of K,,, meets M, in one point distinct from the vertex ; viz., the point where C,, crosses the edge of K,,. An ordinary edge of A, is not necessarily a line on JZ, ; a certain number of them, however, gener- ally lie on the monoid. A double edge of the cone due to an apparent double point of the curve always lies oo the monoid. For it meets Cy, and therefore the monoid J, on which Cy, lies, in two points distinct from the vertex. It thus meets M4, iv »« + 1 points and therefore lies on it. A line to an actual double point or to a multiple point that has its tangents lying in one plane meets the curve in general only once at that point, which is not enough to make it lie on M,. The line from the vertex toa multiple point that does not have its tangents all lying in one plane is a line on M,. This will be shown more fully later. The general equation of J, is of the form: — Wie WS. 0): where u,—, and u, are homogeneous functions of x, y, and z of degrees # — land yp respectively. These functions thus represent cones, known as the inferior and superior cones, respectively, of the monoid. The number of independent constants in the above equation is u(u + 2). In order to make J/, contain Cy, we must make it contain mp + 1 points of the curve. We can do this if mp+1eu(u + 2), “alee m — 2 Sere Z ES BSE C2 ERE Ph ie. if a7 t+ hvmt — Amt 8Z uy, ie. If m—leup; that is, we can always obtain the curve as the intersection ofa cone of order m and a monoid of order m— 1. We may be able to obtain the 490 PROCEEDINGS OF THE AMERICAN ACADEMY. curve as the intersection of the cone with a monoid of lower order, but we need never take a monoid of order higher than m — 1. Thus far we have not taken into account the multiple points of the curve. It will be shown later that even when this is done the monoid need not be of an order higher than m — 1. ‘The lines of intersection of the inferior and: superior cones, (« — 1) in number, are commonly known as the lines of the monoid. The cones u,—) and Ky, have m(u— 1) edges in com- mon, all of which meet C,, and therefore JZ, in a point distinct from O, where O is the point (0, 0, 0,1). They therefore lie on JZ,, and with the curve C,, form the complete intersection of A, and M,. Since p= m— 1, more lines are common to A, and JM, than there are lines on M,. Some lines of MW, must therefore count two or more times as lines common to A, and M,, that is, they must be double lines or hnes of higher multiplicity on A,, corresponding to apparent multiple points on C;,. As the vertex of A, has been taken in such a way that the curve Cy, has no apparent multiple points of multiplicity greater than two, we see that at least (m — uw) (u — 1) lines of M, must be double edges on Ay. There will be just this number if all lines of JZ, lie ou Kn, an additional double edge on A, being necessary for every line of M,, that does not lie on Ay. The curve Cp of order m that is the par- tial intersection of A, and JM, thus has in general at least (m — p)( — 1) apparent double points. Assuming « = m — 1, we see that a curve of order m having no multiple points never has less than m — 2 apparent double poiuts. We wish now to investigate the effect of a multiple point of Cy on this number of apparent double points. If the point is a mul- tiple point on J, the line joining it to the vertex will bea line on M,, for it meets J, in enough points distinct from the vertex to make it lie on M,. We are thus led to the consideration of lines and, in particular, of multiple lines on J/,, and: to the investigation of the effect of these on the curve of intersection when they are common lines of A, and JZ, . 2. Ordinary or multiple lines on any surface may be of different kinds. A line is torsal or scrolar on a sheet of the surface containing it according as the tangent plane to that sheet of the surface is or is not the same at every point of the line.* If the line xy is a k-tuple line ona surface, the equation of the tangent planes along that line will be given by the terms of the Ath degree in x and y in the equation of the surface. According as the equations of these planes, separately or collectively, do or do not contain z and s will these planes be dependent or independent * See Cayley, Collected Papers, VII 384. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 491 of the position of the point of tangency on the line. A multiple line may thus be torsal on all sheets, torsal on some and scrolar on the re- maining, or scrolar on all sheets of the surface that contain it. A line that is scrolar on any or all sheets containing it may, moreover, be scrolar of different kinds. By scrolarity of the first kind we mean that the tangent plane revolves through an angle of 180° as we pass along the line. A generator, say the line xy, of the quadric x (linear function of z and s) + y (linear function of z and s) isa line of this kind. A k-tuple line on a surface may be scrolar of the first kind on each of a number of sheets separately, or it may be scrolar of this kind on a num- ber of sheets taken together. In the latter case the sheets are inseparably connected, the tangent planes to them together revolving through 180°. If a line is scrolar of the Ath kind, the tangent plane revolves through & x 180°. There are then & points along this line that have the same tangent plane, that is, every tangent plane is a &-tuple tangent plane. A number of sheets in this case may also be inseparably connected, as in the case of lines scrolar of the first kind. As the lines of MZ, are the lines common to the inferior and superior cones of M/,, it is evident that for a line to be a line on UM, it must be a line on both cones, and for it to be a k-tuple line on M/, it must be a live of multiplicity £ on one cone and of multiplicity not less than & on the other cone. A number of cases must therefore be considered according to the relative multiplicities of the line on the two cones of /,. I. We shall first consider the case where the line ry is a k-tuple line on the superior cone and a (& + 1)-tuple line on the inferior cone. The equation of J/, can then be put into the form: — (vepa 22! 4 vppe 2P—? +...) so + (we zPtl + wey 2? +...) = 0, where p = p — k—13; v, and w, being homogeneous functions of de- gree a in x,y, and z. The tangent planes along the line zy are given by w,; = 0; the line is therefore torsal on all & sheets passing through it. There are no points on the line of higher multiplicity than & distinct from the vertex. We assume w; + 0, otherwise the line ry is a (k + 1)- tuple line on both cones, and therefore also on M,; this is a case to be considered later. The line xy therefore counts as k(k +1) of the p(w — 1) lines on &@,. This case includes the case where Oy = Opry ee Op OF i.e., where the line is a (k + g)-tuple line on the inferior cone, while only a k-tuple line on the superior cone. We assume 229 Zu—k— 1. 492 PROCEEDINGS OF THE AMERICAN ACADEMY, The line is still a k-tuple line on JZ,, torsa) on every sheet through it, but counts as &(& + g) lines of ,. The polynomials vy, and w, may have any number « (where x = &) of their linear factors equal, i.e. « sheets of J/, may touch « sheets of both u,-, and u, along ry. The line in this case counts as k (k + g) + « lines of M@,. There is no diffi- culty in seeing the effect of any combination of tangent planes on the number of lines on J/,. The quantity w, may break up io a great variety of ways, e.g. x7 y8..... ; xy being torsal on all & sheets of M,,, the number of lines adjacent to x y alone being affected by the way in which vz4g and wz break up. II. The next case is where the line zy is a k-tuple line on botb cones. The equation of the monoid can then be put into the form: — (v, 2P + opti 2PI +... ) st (wy Pt! + wey 2P 4 ..0.. ), = 0250) We assume wz + 0; otherwise the line wil] not be a &-tuple line on botb cones, but will belong to a later case. We also assume vz 0) w, * (and .. vy = 0); otherwise we shall have (v7, 2? + te Fo La Jae eas ys + (a vx zpt+l + ODay SEs site ‘) = (i): Substituting s — az for s, this reduces to . (vy 2P + veg 2P-14..... ys + [wre — @vn41) 2P +... = 0: which is a later case. The line vy is a k-tuple line on the monoid whose equation is (1), and has no point on it of multiplicity greater than &. The tangent planes along this line are given by the terms vj s + wy z. As we have assumed 2; 0) wr, sand z cannot factor out, and the line xy must be scrolar of the first kind on one or more sheets of M,. If vz and w; have no common factor, that is if the line xy is torsal on no sheet of M,, it is scrolar on all & sheets. These & sheets, however, are insepar- ably connected, that is the tangent planes to all of them together revolve through 180°, If vj; and w; have a factors in common (where a < k — 1), the line is torsal on a sheets of WM, and scrolar of the first kind on the remaining & —a sheets together. The inferior and superior cones then touch the monoid along this line on a sheets. The line zy counts in general for k® lines on M,, but for k? + a lines if v; and wz have a * The sign © should be read: contains as a factor; the sign © should be read: does not contain as a factor. VAN DER. VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 493 factors in common. It may count for more lines in the same way as the line xy in the preceding case. III. The third case is where the line ry is a k-tuple line on the inferior cone and a (& + 1)-tuple line on the superior cone, ‘The equa- tion of the monoid will then be of the form (v7, ZP + UE41 CON Aa cas ) $+ (Wr44 2P + W492 BN es -) Gye (2) We assume v;, + 0, otherwise the line will belong to the preceding case. We also assume wy41 ) v,; (and .*. w.41 + 0), otherwise we shall have (vg 2P + vey, P14...) 8 + (paz? + wepo2P 1 +..... y= 0; where a is a linear function of x andy. Substituting s — a for s, this reduces to our next case. The line xy is a k-tuple line on the monoid whose equation is (2) above, and has a point (0, 0, 1, 0) of multiplicity k+1lonit. The tangent planes along xy are given by v;; the line is thus torsal on all the sheets that pass through it. The tangent cone at the (& + 1)-tuple point is given by the terms v% s + wy41. The line xy is also a k-tuple line on this tangent cone. This cone can never break up into £+1 planes, as this would require wz11 © vg. Nor can it break up into factors of which more than one are proper cones, as it could not then contain the line zy as a k-tuple line. If it breaks up at all, it must break up into factors of which all but one are planes, and this remaining factor a proper cone of a certain order, say o, having the line xy as a (o — 1)-tuple line. The plane or planes into which the tangent cone at the (& + 1)-tuple point may break up belong to the & tangent planes through the £-tuple line. The line xy counts in general for k (k + 1) lines of J,, but may count for more as in the preceding two cases. IV. The next case is where the line is a £-tuple line on the inferior cone, and a (k + 2)-tuple line on the superior cone. The equation of the monoid can then be put into the form (vx 2P + VEL Zea? ees ) s+ (weye P+ weg 2P2 + .....)=0. We assume vx = 0, otherwise the line will belong to the preceding case. The tangent planes along the line xy are given by the term v;,; the line is thus torsal on all sheets that contain it. The point (0, 0, 1, 0) is a (& + 1)-tuple point on M,, the tangent cone at it being given by vx s. The tangent cone thus breaks up into the & tangent planes along the k-tuple line, and the plane s. The line xy counts here for k (& + 2) 494 PROCEEDINGS OF THE AMERICAN ACADEMY. lines of M/,. The case where wyy2 = ..... = wetg-1 = 0, that is where the line is a (4 + g)-tuple line on the superior cone while only a k-tuple line on the inferior cone belongs to this case. We assume 382g =au—k. The line now counts for & (k + q) lines of M,, other- wise it is not different from the general line belonging to this case. We thus have in reality four kinds of lines, as shown by the four cases above. We shall designate these lines as of kinds I, I, III, and IV, respectively. Lines of kinds IJ, III, and IV are torsal on all sheets of M,, that contain them, whereas lines of kind II are scrolar on at least one sheet of the monoid. Lines of kind III differ from lines of kind IV only in regard to the breaking up of the tangent cone at the (k + 1)-tuple point. 3. Consider now the character of the curve of intersection of Aj, and M, in the neighborhood of lines of the above kinds when they are common lines of A, and M,. The point where the line is crossed by a branch of the curve can be determined by considering the intersection of M, by the tangent plane to a sheet of A, along that line. We can, however, determine more than this. If a plane, say x = 0, is taken to be the tangent plane to a sheet of the cone along the line xy, we can develop x in terms of y.* We neglect all terms in the development after the first, as we are concerned only with points in the immediate neighborhood of the line xy. Substituting the value of z from this development in the equation of the monoid that has the line zy as a line of one of the above four kinds, we obtain not only the point of crossing of the line by the curve but also the direction of the tangent to this curve at that point. The equation of the cone A, having the line ry as a k-tuple line can be put into the form ty, 2m—k 4 thi gm hal ne oe le ae ae ty = OS where ¢, is a homogeneous function of x and y of degree a. This equa- tion can be transformed into an equation in x and y alone (putting z=1). If the plane x is a tangent plane to an ordinary sheet of Kn through the line x y, the development will be of the form x=—ay’+ by’ + ete. If the plane z is a tangent plane along a keratoidal cuspidal edge of K,,, we shall have * This can be done by the Newton-Cramer method, explained in Salmon’s Higher Plane Curves (1878), p. 44. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 495 x=—cy? — dy’ + ete. If the line zy is a tacnodal edge, having the plane x as tangent plane, we shall obtain two developments, viz. : — x= ey + etc., and x = fy? + ete. If the line is a ramphoidal cuspidal edge, the development will be of the form r=gy + hy? + ete. In all these cases, a, 5, c, d, e, f, g, h depend on the coefficients of the equation of Ay. It is evident that, using only the first term in each development, these cases reduce to two, viz. : — 1°. x=—ay’ where the sheet of A;, simply touches the tangent plane along the line. 2°. x == — cy, where the sheet in question touches the line, and then turns back leaving the tangent plane on the opposite side from that on which it approached it. We shall consider the different kinds of lines separately, treating one case of a line of kind I in detail, and giving the results in all other cases. If the line xy is an ordinary line of kind I on ™,, the equation of JZ, in non-homogeneous codrdinates will be of the form (a,x? + Birytyiy?t ete.) s+ (agx+ Boy +yox?+ d,xy+ ey? + etc.) = 0. Substituting « = — ay? in this equation, we get an equation in y and s, which is the equation of a curve that in the neighborhood of xy is the same as the curve of intersection of A, and M/,. Of this equation y is a factor, the line xy thus counting once as a line common to A» and J/,. From the resultant equation, taking account only of the lowest terms, we obtain ies ayy +a,ay—eay— Be ny Putting y= 0 in this expression, we obtain s = 0; the line xy thus meets the curve above at the vertex, i.e. the curve of intersection of Ki, and M, passes through the vertex. (Similarly if 2 = — cyi, there is a point of the curve at the vertex.) If, however, 8, = 0, i.e. if the cone and the monoid touch along xy, we get a point of the curve distinct from the vertex. For y factors out once more from the above, that is the line xy counts twice as a line common to Ay, and M,, and we have 496 PROCEEDINGS OF THE AMERICAN ACADEMY. , — ay + (2 a — &) y (ols) (Oh = This reduces to s = <2 for y=0. The curve of intersection thus y1 a2 a — €y At courdinates so that ag @ = €,, we obtain (x = y = s = 0) as the point of crossing and y,; s — 6. ay = 0, x = 0 as the equations of the tangent line to the curve at that point. Thus it is evident that in the case of lines of kind I, whatever be the multiplicity of xy on MV/,, if no sheet of Ky, touches a sheet of J, along this line, the curve of intersection will always pass through the vertex. As we are considering a point off the curve as vertex such cases need not be considered. In the case where two sheets of A, unite to form a cuspidal sheet that touches a sheet on M, along xy, the curve of intersection will either pass through the vertex or it will have 2 yas tangent line at a point of it. As we have also assumed the vertex not to lie on a tangent to the curve, these cases may both be avoided. There will be a point of the curve on xy distinct from the vertex and not having xy as tangent at it, only in the case where a sheet of K,, touches a sheet of J/, along the line xy and the sheet of Ay, is one for which development 1° on page 35 holds. It does not matter whether the sheet of JZ, is single, cuspidal, or tacnodal. There will be as many branches of the curve crossing xy as there are such sheets of A, touching sheets of J/,. As the vertex has been taken in such a way that the curve has no apparent multiple point of multiplicity greater than two, the case where there are more than two distinct points of the curve on xy may be avoided. For special relations between the coefficients, x of the points on xy may coincide and form a «-tuple point on the curve. This will, however, in general necessitate the monoid to be of an order higher than m— 1. For the equation of J/,_; that has a line as a «-tuple line of kind I contains in general m? — x? — 2x — 2 arbitrary constants. In order to make this monoid contain a curve Cy that has a point of the «-tuple line as a «-tuple point we must make it contain m (m — 1) — x* + 1 additional points of Cm. We can therefore always make M, cut Cp out of Km, if crosses xy at the point (« =f — As) Transforming our m(m—1)—x*? +12 m?— %* — 2x — 2, 1./0.\1f 2k+3am. Thus if x = 3, it is only possible when 9 = m; if «x = 4, when 11 = m; etc. As will be shown later, the curve Cy, that has a multiple point can VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES, 497 always be obtained as the partial intersection of A,, with a monoid of order m — 1 that has a line of kind II] or lV. We shall therefore not use a line of kind I to obtain a curve with a multiple point. If MZ, contains a line of kind II, every sheet of A;, that passes through this line intersects J/, in a branch of a curve that crosses xy at the point where the tangent plane to the sheet of A;, coincides with the tangent plane to the scrolar sheet of M/,. If xy is a x-tuple line on Aj, there will be « branches of the curve crossing the line due to the scrolar sheet of M/,. No torsal sheet of J/, can cause an additional branch of the curve ; for this would necessitate the line to be of a multiplicity greater than x on Ay», which in turn would cause more than « branches of the curve to be due to the scrolar sheet alone; and so on ad infinitum. We therefore need a line on W/, that has torsal sheets passing through it in addition to the scrolar sheet. If two sheets of A, unite to form a cus- pidal sheet along xy, there is either a branch of the curve touching ry at the point where the tangent plane to the cuspidal sheet coincides with the tangent plane to J/,, or a branch of the curve passing through the vertex. Both of these cases may be avoided. A number of conditions must be imposed on the coefficients of JJ to make the « points of cross- ing of the line by the curve coincide. We shall therefore not use a line of kind II to obtain a multiple point on the curve. We need not there- fore in general consider the case where the line «y is more than a double line on Ay. Lines of kind II are only necessary on J/, to produce the apparent double points of the curve, and only ordinary lines of this kind are then needed. The line to an apparent double point counts thus in general for two lines common to K,, and M,, while only for one line on M,. If we consider M/, as of order m — 1, it is evident that A, must have at least m — 3 double edges in addition to the double edge caused by this apparent double point. The curve must therefore have at least m — 3 apparent double points in addition, i.e. at least m — 2 in all, as on page 490. If M, has aline xy of kind III on it, there will be a branch of the curve through the multiple point for every sheet of A, that passes through xy. If xy is a x-tuple line on A, and a k-tuple line of kind III on M,, there will be « branches of the curve through the (& + 1)- tuple point of MJ,. The point will thus be a x-tuple point on the curve having its « tangents lying in general on a cone of order & + 1 that has the line zy asa k-tuple edge. For the tangents to the curve at this multiple point are the lines of intersection of the tangent cone at this multiple point by the « tangent planes to Kin along xy, each plane intersecting VOL. XXXVIII. — 32 : 498 PROCEEDINGS OF THE, AMERICAN ACADEMY. the tangent cone in the line xy k times and in one other line, which is a tangent to the curve. If the tangent cone breaks up into g planes and a cone of order k —g + 1 (where 2 => —g + 1) that has the line ry asa (k — g)-tuple edge, the x tangents to the curve will lie on this cone of order k—g-+ 1. In this case it is only necessary to have the line xy as a (k — g)-tuple line of kind III on M/,. We need not consider the case where one or more sheets of A,, touch MZ, and therefore the tangent cone at the multiple point along the line xy, for this line is then tangent to the curve. Nor can any sheet whose tangent plane is one of the com- ponents of the tangent cone at the multiple point cause a branch of the curve by having contact with a sheet of the cone. If MM, contains a line xy of kind IV, every sheet of £,, that passes through this line cuts out of J/, a branch of the curve that passes through the multiple point on J/,. The tangent lines to the curve in this case all lie in one plane, viz. the plane that is tangent to JZ, at the multiple point but does not contain the line xy. Thus, if the line x y is a «-tuple edge on A,,,, the curve of intersection will have a x-tuple point, the tan- gents at which all lie in one plane. As the only sheet of JZ, that affects the curve is the sheet that does not pass through the multiple line, it is not necessary to have the line from the multiple point to the common vertex of A, and M, asa line on M,. The single sheet of J, simply cuts the «x branches of the curve out of the « sheets of the cone, its tan- gent planes intersecting the « tangent planes to A, in the x tangent lines to the curve at that point. 4. We can therefore always obtain a curve of order m having a x-tuple point, the tangents at which lie on a cone of order & +1 that has the point as vertex and has an arbitrary line through this point as a /-tuple line, as the partial intersection of a particular cone and a particular monoid. ‘The cone is of order m, has its vertex on the £-tuple edge of the cone of order &+ 1, and has this edge as a k-tuple edge. The monoid is of order p, and has the multiple point of the curve as a (k + 1)- tuple point and the line from this point to the common vertex of the two surfaces as a k-tuple line. The line from the common vertex to the multiple point counts thus as /« lines common to Ay, and M,, and as k(k +1) lines of 1/,. The cone and the monoid have m (wu + 1) — kk additional lines in common, whereas there are only u(u— 1) —& (k + 1) additional lines on M,. The cone K,, must therefore have at least miu — 1) — he =pG@ — ad) k(t 2) i.e. (nm Wile be ES 1 Sia VAN DER VRIES; — MULTIPLE POINTS OF TWISTED CURVES. 499 double edges, i.e. the curve CO, must have at least a apparent double points. It is thus evident that the multiple point reduces the necessary number of apparent double points by k(x —k&—1). This also holds true when the tangents lie in one plane. For we then have k + 1 =1, i.e.k =0. The line from the multiple point to the common vertex is neither a line on the monoid nor a line in the tangent plane. We then have k(x —k —1) =0; that is, such a multiple point does not affect the necessary number of apparent double points. It is thus evident that multiple points whose tangents do not lie in one plane affect the number of apparent double points, whereas multiple points whose tangents lie in one plane do not affect this number, as well in the case of curves that are the partial intersection of a cone and a monoid as in the case of curves that are the complete intersection of two surfaces. This is also shown if we employ the method used in determining the number of apparent double points of the complete intersection of two sur- faces of orders u and v.* This number was found to be one half of the num- ber of intersections of the curve with a surface s of order (u — 1) (v— 1). The complete intersection in the case under consideration consists of the curve C, of order m, a number of lines that are «-tuple lines on Aj, and k-tuple lines on J/,, a number / of lines that are double lines on Am and ordinary lines on M,, and finally a number [viz. m (wu — 1) — Dd ke- 2h] fof lines that are ordinary lines on both surfaces. There are certain points of apparent intersection of C,, with the lines common to Ay, and MM, that are included among the points of inter- section of C, and S. Among these are (m—k)k« points for every line to a «-tuple point, 2 (m— 2) points for every line to an apparent double point of the curve when viewed from the vertex of A, and m—1 points for every line that is an ordinary line on both surfaces. The x-tuple point of Cy, moreover, is a point of multiplicity £(« — 1) on S and therefore counts as k«(« — 1) of the m(m — 1) (u — 1) points of intersection of C,, and S. Calling 4’ the number of apparent double points of O;, when viewed from an arbitrary point in space, we have m(m—1) (u—1) — Sx [(m— x) ch + (kK —1) chk] —2(m—2DHh — (m—1)[m(u—1) —->« kk — 2h] =2h'; i. e. hi=,h, * See page 481. + In the = we take account of all lines to points that are x-tuple points on Om and (£ + 1)-tuple points on My. 500 PROCEEDINGS OF THE AMERICAN ACADEMY. Thus, as a multiple point at which the tangents do not lie in one plane is a point on S, a number of apparent double points disappear when it is formed on the curve. A multiple point, however, at which the tangents all lie in one plane, can be obtained, as we have seen, by means of a monoid that has it as an ordinary point. It is therefore a 0-tuple point on S and has no apparent double points in its composition. This will be shown more in detail later. Every x-tuple point, however, whether its tangents do or do not lie in one plane, has the same effect on the posstble number of apparent double points; each reduces it by $«(«k — 1). Thus a curve of order m having a number of «-tuple points can never have more than 4 (m — 1) (m — 2) —$ > «(k—1) apparent double points; where the summation includes all points for which 22x 2m — 2. 5. There is an upper limit to the necessary order of the cone on which the tangents to a curve at a multiple point lie. The equation of a cone of order £ +1 that has a certain line as a k-tuple edge has 2k + 2 arbitrary constants, that is, such a cone can in general be made to pass through 2k + 2 arbitrary lines through the multiple point. We can therefore always pass a cone of order k + 1, having an arbitrary line through the x-tuple point of the curve as a k-tuple edge, through the « tangent lines at the «-tuple point of the curve, if x = 2k + 2, ie. if K-22 _ opm k, or : =k+1. We need, therefore, never take k greater than KS 2 e . = if x is even, nor greater than 5 may, however, in some cases lie on cones of lower orders than those given by the expressions above. We can in fact classify multiple points according to the orders of cones of the lowest order that can be passed through the tangents at them, this order taking any value from 1 to eas if x isodd. The tangents K k+l 5 : : : = or — —, according as x is even or odd. We must also bear in mind 2 2 that the order of the cone places a limit on the number of the tangent lines that can lie in one plane. If A tangents at a «-tuple point of a twisted curve of order m lie in one plane, the curve is met by that plane in at least 2A +«—A or «+A points. We must therefore have KtAZSM, 1.e. k zm—xX, orAem—k. A curve of order six can therefore not have a quadruple point, three of the tangents at which lie. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 901 in one plane. Ifa cone of order g can be passed through the « tangents at a «-tuple point, the cone is met by the curve in at least (g + 1)« points. We must therefore have — = = g (g+t1)xkimg; 1 SEES aD if we do not wish the curve to lie entirely on the cone. Thus, if _m : ; f wl ee a otherwise the curve is a plane curve. A twisted curve of order m can therefore never have a point of multiplicity greater than m—1 m. ‘ : : : — if m is even, or greater than if m is odd, if the tangents all 2 as _ 2m hae : lie in one plane. Ifg=2,« 2 mari that is, if a twisted curve of order 2m - m having a point of multiplicity greater than has the tangents at this point lying on a quadric cone the curve will lie entirely on that cone. Similarly for cones of higher orders. 6. We shall now determine the order u of the monoid of lowest order that will in general cut C;,, out of Aj, in the manner described above ; that is, that value of w that will always suffice to obtain C,. The equation of a monoid of order uw that contains a 4-tuple line of kind III has just (u + 1)?— (& + 1)?— 1 arbitrary constants. We can make this monoid contain the curve CO, that has a x-tuple point at the (4 + 1)-tuple point of M@, if we make it contain mp — x (K+ 1) + 1 additional points of Cn. This is always possible if mp weet a (a1) Gale —2 i.e. if 5 +4? 4m +4 + 8k hx — 4x + D2 = fe Summing for all x-tuple points on Cn, we have m — 2 BaF eg y/mt—tmt8—4 DEF) («—e-H Zu; | where in the summation each x-tuple point has its own value of k. We need never take the order of J/, greater than the smallest integer value of w that will satisfy this inequality. The curve ©, may nevertheless in certain cases be cut out of A;, by a monoid of lower order. If the x-tuple points are all of the most general kind, that is, if the correspond- 502 PROCEEDINGS OF THE AMERICAN ACADEMY. aes = ing values of & are determined by aa or * z , according as « is odd or even, we must have in general 1°. If the «’s are all even, leit (m— 27 Set 4 Sy; (11) 2°. If the «’s are all odd, m— 2 SSeS SS Sor ee ie (III) \ It is to be noticed that > (k + 1) (x —k&—1) in (1) above is always greatest when the x-tuple points are all of the most general kind. The sufficient value of m is therefore always least in this case, that is when is given by (II) or (III) above. The quantity (k + 1) (k —&—1) in (1) is never less than zero; the quantity under the radical sign is thus never greater than m?—4m-+ 8; therefore «= m—1 will always satisfy the conditions. We need therefore never take w greater than m—1. 7. The inequalities above give values of w greater than which we need never take the order of the monoid. We can, moreover, find values of w smaller than which we can never take the order. As M, has u (u — 1) lines on it, we must always have ht DkR+1 +06 Zu(u—1); (IV) where / corresponds to the ordinary lines of J, that are double lines on yO ye (k + 1) to the k-tuple lines of M,, that are x-tuple lines on Kn, and o to the ordinary lines of M/, that are ordinary lines on Kn. As Ky, intersects J, in m (u — 1) lines, we must have 2h—Ske+o=m (u—1). (V) By eliminating / from (IV) and (V), we obtain >t Qk—K—2) +0 ZF (2u—m) (u— 1), i.e. Se p/n 29 +8 SAK «2480 Sus (VI) VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES, 503 that is, uw must always be taken as great as the quantity on the left side of this inequality. The smallest value of this quantity occurs when o = 0, and otherwise depends on the values of & (2k — x + 2), that is on the orders of the cones on which the tangents at the multiple points lie. = 2 The greatest value of £ (24 — x — 2) will then be — (: = =) (* = *\ I). If« is even, & can take any value from zero up to inclusive. if x — 2 is an evenly even number, or ome eae a) Ca): if ek — 2 is an oddly even number. We must therefore always have Bt? +4 /@—7— > MSy if every x = 27”, m+ 2 a a = é or + 8 4/(m— 2)?— Se (k—4) Z my ifevery «= 40. (Here m is an odd number, whereas x! is any integer.) We can thus never take uw less than the quantities on the left-hand sides of these inequalities, if the «’s are all even numbers. It is also evident from (VI) that, if the points are all such that the tangents at them lie in K planes or on cones of order 3? We must have m+ 2 4 a ile V(m — 2) 4% (24 —« + 2) will thus occur when all the points are such that k—3 4 an evenly even number. If x’s are all odd numbers, we must thus have 1 5 > , according as « is one more than an oddly even or Ko k= or Meth y/@—7-DSe-Y) «63 Em It is evident from (VI) above: that 2 EEE TAC SEL, = ea : MS th y(n +4 SD Ew by k—1 5 for each x; or Sy ae if & = 0) for each’x, The lower limit for u when « is odd thus varies between me tb m2 > KD) 2) m + 2 SSRESESnnTG ara and ee according to the way in which the tangents to the curve at the different multiple points lie. It is thus evident that « can in no case be taken less than ma a/R > 6D Using the formulae found above we can tabulate as follows : — | ou (or) for) x1 -1 = aS “S| (oe) co oe co ioe) AU CUTVENlOnt OW OLdeCE ie) ig) oe) 278 having a point (or te of multi- plicity . aiafiks Pals can be cut out of a cone of order m having Cy, as base wy a monoid OmOrder «= ss ~ 2 6 + M=]3/3) 414/415) 5) 5 4/5|5!15/6 that has the multiple point (or points) of C, as point (or points) of multiplicity . nk — 1 =/2)2/2/38)/2/2)2]2,2)3)2)38) 212 B. 1. Every curve C,, of order m can also be obtained as the partial intersection of a cone of order m — 1 and a monoid of order uw, where wis to be determined. The cone Ay,_1 is a cone that has an ordinary point of C,, as its vertex and Cy as its base. There being an infinite number of ordinary points on Cyn, the special positions of the vertex from which every line drawn to C,, meets Cy, in two or more points can be avoided. The vertex can therefore be taken in such a way that the cone of order m — 1 does not break up into cones of orders that are sub- multiples of m—1. Every edge of Aj 1 thus has on it one point of C,, in addition to that at the vertex; C, can therefore be cut out of Km—1 by a monoid M,. We shall consider the case of a curve that has points of multiplicity x, at which the tangents lie on cones of order & + 1 that have the lines from the multiple points to the vertex of A,,_1 as k-tuple edges ; the case of curves with no multiple points being but a special case of this. It can be shown, as in the previous case, that the lines from the common vertex of A,,_; and JM, to these «-tuple points are «-tuple lines on Am_1 and k-tuple lines of kind III on 1/,. The 506 PROCEEDINGS OF THE AMERICAN ACADEMY. equation of a monoid of order » that has a k-tuple line of kind III con- tains in general (u + 1)?— (k+1)?—1 arbitrary consonants. In order to make this monoid J, contain a curve C,, that has the vertex of M,, as an ordinary point and a (& + 1)-tuple point of JZ, as a «-tuple point, we must make it contain mu — (u—1)—x«(k+1) +1 addi- tional points of C,. This is possible if mu—(we—I—KE+1) +12 @+1?—E€+1°—-14 i.e. if ma 4 bvn— Om + TFET aaa or, summing for all «-tuple points of CO, that are (£ + 1)-tuple points on M/,,, we must have m—3 m—6m+17—4>(k+1)(k—k—-1) Zp. (I) The smallest value of uw that satisfies (1) will in general suffice as the order of a monoid that can be made to cut C,, out of Kyi. As (k + 1) (k —&—1) is never less than 0, it is evident that « = m — 2 will always suffice. As in the previous section, & can take any value sles ; 3 from 0 to ~ SN Ta inclusive. We can show in the same way as there that « can never be less than the smallest integer that satisfies m—1 AI th y/m—6m4+14+8 Sk Qk—K+2) + 80 Sh (11) Using (I) and (II), we can tabulate as follows : — A curve of order having a point (or points) of multiplicity Pips can be obtained as the intersection of a cone oforder. . ...m—l and a monoid of order . . # = that has the «-tuple point (or points) of the curve as points of ue ae ityays hel = VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 507 Thus a quintic curve with a triple point can be obtained as the partial intersection of a quartic cone that has a triple edge and a quadric monoid that has the triple point of the curve as a double point; that is, as the partial intersection on a quartic and a quadric cone not having the same vertex but having a line in common that is a triple edge on the quartic and an ordinary edge on the quadric cone. This edge and the quintic curve constitute the complete intersection of the two surfaces. 2. The complete intersection of A,—1 and JM, is of order (m — 1) u. The cone A, meets the inferior cone of J, in (m — 1) (u — 1) lines, of which all but one (namely the tangent to O, at the vertex O of Kn—1) meets C,, in points different from O and not consecutive to it. These lines therefore lie on M4/,, and together with C,, constitute the complete intersection of AKm—1 and J/,. As there are only u(u — 1) lines on J/,, it is evident that Aj, has in general at least CaS ee 2) that is, mu — uw? — m, double edges. OC, has therefore in general at least mu — uw” — m apparent double points when viewed from a point of the curve, that is, at least mu —y? — 2 when viewed from an arbitrary point in space.* If, however, the curve has x-tuple points that are (k + 1)-tuple points on J/,, the lines from these points to the vertex count as > k « lines common to A,,_; and /, and as De (& + 1) lines on M,. The cone A,,—; must therefore have at least (m—1)p—m— Ske-pu—-lyt+ DEN double edges, that is, O;, must have at least mu — u? — 2 —Sh(« —k—1) apparent double points. Each multiple point thus reduces the necessary number of apparent double points by £(« — k — 1), as in the previous section. If we take « = m — 2, it is evident that we must always have 2m—6— Sk(e-k-1 Zh ~ OF 1. A curve C,, having a point A as a x-tuple point lies in general on a cone K of order m — «x that has the point A as its vertex and the curve Cy as its base. This excludes those curves that are met by every line through the multiple point in two or more additional points if at all, * See Salmon’s Geometry of Three Dimensions (1882), No. 3380, Ex. 2. 508 PROCEEDINGS OF THE AMERICAN ACADEMY. e.g. curves of order m that are wound a times around a cone of order iit — VK and pass « times through the vertex of this cone. Such curves cannot be obtained as the partial or complete intersection of a coneand a monoid that have this multiple point as their common vertex. They can be obtained as the intersection, partial or complete, of a cone of order WM aK and a surface of order w that has the vertex of the cone as a a (uw — a)-tuple point; every line through the (u — a)-tuple point, and therefore every edge of the cone, meets this surface in a additional points, which are the a points of the curve on this edge. We can avoid doing this by considering these curves as lying on cones of order m or m — 1, as we did in the previous two sections. We shall treat in this section only those curves that are met by an edge of K,_, in one point distinct from the vertex. Such curves can be cut out of Ky, by some monoid of order p. , I. Suppose m — x = p. Thenin order to make M, contain Cp with- out breaking up into A;,_, and a monoid of order u — m + x, we must have Oh ps an =) oN Fee (ie ne re ga the vertex counting as x(u— 1) points of intersection of C, and M/,. We must therefore have in general (m — «x —1)? + (« + 1) m—kK H+ DY] —[@imtn«t1e—-S@-W 4+] —41 (m—x—1)?+ («+ Il) — > K-41) - < m— kK 1.€. M3 (I) where the summation extends over all multiple points of C, (except the one at the vertex of AKym_,) that are (£’ + 1)-tuple points on M@,. The smallest value of u that satisfies (I) is the order of the monoid that will in this case cut Cp out of Ay—,x + VAN DER VRIES, — MULTIPLE POINTS OF TWISTED CURVES. 509 II. Suppose m — « > wu. We must then have mux (« — 1) +1 Z (m+ 1)? 1, i.e. “$b Vm BP FATE FD Ey, if we wish to make MM, contain C,,. If, however, the curve C,, has in addition to this x-tuple point certain «’-tuple points that are (&’ + 1)-tuple points on J/,, we must have ke 2 ste 5) +- by/(m —xk—2)? + 4(k+1)— 2G 1)(x’ —k'—1) Su, (11) where the summation extends over all the multiple points except the one at the vertex. We know that m = u(m—k), ie. =u. Thus m—x Zu, m—k whenever (m—x)? = m. We therefore use (I) whenever (m — x)? = m, that is, when m — 1/m = x, and (II) whenever (m — x)? >™m, that is, when « << m—%/m. We can then tabulate as follows : — A curve of order . having a point of multiplicity and a point of multiplicity can be obtained as the inter- section of a cone of order m having the «-tuple point as vertex and a monoid of order having the «-tuple point as vertex and the «’-tuple point as a point of multiplicity #’+1= ~ D. 1, We shall now consider in particular the case where the multiple point that is taken as the vertex of the cone is an (m — 2)-tuple point. Every such twisted curve Cy, of order m that has an actual (m — 2)- tuple point is unicursal. For a plane passing through any line that 510 PROCEEDINGS OF THE AMERICAN ACADEMY. joins this (m — 2)-tuple point to any point of C, never contains more than one other point of Om; nevertheless during its revolution around the line, it contains successively all the other points of the curve. If we take an ordinary point of O, as vertex and construct a cone with Cy, as base, this cone will be of the (m — 1)st order. This cone contains the line joining the (m — 2)-tuple point to the vertex as an (m — 2)-tuple edge, and can therefore have no double edges. ‘The curve can therefore have no apparent double points when viewed from an ordinary point of the curve. We therefore have h = m — 2;* thus a twisted curve of order m that has an (m — 2)-tuple point has m — 2 apparent double points. 2. Let On be a twisted curve of order m having an (m — 2)-tuple point at A (where 4 = m). This curve will lie on a cone of order two, say K., whose vertex is A; for any plane through the point A can con- tain only two other points of Cm, the lines joining these points to A being generators of a quadric cone. Not more than two tangents to On at A can lie in one plane, for the plane would then meet the curve in more than m points, which is only possible if the plane contains the curve. Every unicursal curve of order m with an actual (m — 2)-tuple point thus lies on a quadric cone. We can show that Cp can be cut out of this cone K, by a monoid. Clearly Cy, is the complete or partial intersection of AK, with some surface of order p, say S,, having a k-tuple point at A. Now m — 2 2 2k, since 2k is the multiplicity of A on the complete intersection of S, and A,. It is evident that & is the order of the cone that contains the m — 2 tangents to Cy, at A that lie on Ay, provided m —2= $k (k 4+ 8) —4 (k — 2) (+1) — 1, where 2 <4, i.e. provided m — 2 = 2k, where 2 = &. We can thus always take k = m—2 m—1 Dav ta ee kauple point at A is determined by } (u +1) (u + 2) (4+ 3) — Gh (k + 1) (k + 2) —1 points. In order not to have S, break up into A, and a component of order « — 2 having a (& — 2)-tuple point at A, we must take } (u— 1) w (wu + 1) — 3 (k — 2) (A — 1) & of these points off K,. There are u (u + 2) — &® points remaining that can be taken arbitrarily, but in such a way that S, shall contain Cm. Sy meets Cr in k (m — 2) points at A, and will therefore contain C,, entirely if it contains mm — (m — 2) k + 1 additional points of C,. S, can therefore be determined so as to contain Cy, if , according as m is even or odd. The surface S, with a * Salmon’s Geometry of Three Dimensions (1882), No 330, Example 2. VAN DER VRIES,— MULTIPLE POINTS OF TWISTED CURVES. 6511 mu—(m—2)k+1 Zp (ut 2) —F. If there are still points left at our disposal, we may use them in different ways, and may cause the residual curve to break up in different ways. The complete intersection of A, and S, is of order 2; and as Cy, is of order m the residual is of order 24 — m. As the complete intersection has a point of multiplicity 2 at A, the residual has a point of multi- plicity 2k —m-+ 2 there. Every edge of A, meets S, in & + 1 points of which £ are at A. If we can take u — k additional points on some of these edges, these edges will contain « + 1 points in all and will lie com- pletely on S,. Therefore if there are enough points left at our disposal to enable us to take « —& additional points on each of 2u—m—1 edges of K,, the residual will consist of these 24 — m — 1 edges of K, and (since the entire residual is of order 2“ — m) another straight line, which can only be another edge of A,. The residual can then be made to consist entirely of straight lines if ye neta oy eran, We Sora i ie. if (u—k—1) (w—k—2) 1; which can only occur if k = w — 1, or k = w — 2. We may then always take k = —1, that is take S« to be a monoid. Thus p=k+1= m m+1 oe, | A unicursal curve of order m that has a point of multiplicity m — 2 can always be considered as the partial intersection of a quadric cone and a monoid of order w, where w = 3 or Thus the quintic curve with a triple point can be obtained, as we have seen before, as the partial intersection of a quadric cone and a cubic monoid that have the same vertex. The cubic monoid is determined by 15 points, but 4 of these must be taken off the quadric in order not to have the monoid contain the quadric as a component. We thus have 11 points at our disposal. In order*to make the cubic monoid contain a quintic curve that has a triple point at the vertex of the monoid, we must make it contain 8° 5 —2:+38-+ 1 or 10 additional points of the curve. Wecan do this and still have one point left at our disposal. This point can be taken on any generator of the cone, causing this generator to be the residual intersection of the cone and the monoid. Similarly, a sextic curve with a quadruple point can be obtained as the according as m is even or odd. Therefore: — 1 : : according as m is even or odd. ad PROCEEDINGS OF THE AMERICAN ACADEMY. complete intersection of a quadric cone and a cubic monoid. The cubic monoid is determined by 15 points, of which 4 must be taken off the quadric to insure the monoid not containing it as a factor. In order to make this monoid contain the sextic that has a quadruple point at the vertex of the monoid, we must make it contain 6:3 —4:2+41 or 1l additional points. ‘This is the exact number at our disposal. IY On THE ComposiITION OF MULTIPLE PorntTs. 1. If a curve of order m has an (m — 2)-tuple point, it can have no other multiple point. The curve is unicursal. We assume d = m. The tangents to the curve at this multiple point cannot lie in a plane, but they lie on a quadric cone. As we saw on page 510, this curve has m — 2 apparent double points. It can have no more apparent singular- ities. A curve with an (m — 3)-tuple point can have at most one other actual multiple point, viz. a double point. If it had more it would nec- essarily be a plane curve. Thus a twisted quintic cannot have three actual double points. A curve of order m having an (m — 3)-tuple point and a double point lies in general on a cone of order m — 2 having the double point as vertex and the curve as base. This curve cannot (m — 8) (m—4) 2 vertex to the (m — 3)-tuple point counts for just this number of double edges. The cone can therefore have no more double edges; that is, when viewed from the double point of the curve, the number of apparent double points of this curve is zero. According to Salmon,* the number of apparent double points of the curve is 2m — 6 more when viewed from an arbitrary point in space than when viewed from a double point of the curve. A curve of order m with an (m — 3)-tuple point and an actual double point has therefore just 2m — 6 apparent double points. Tt can have no other actual multiple point or apparent singularity. It is thus evident that when one of the branches through the double point moves into the (m — 3)-tuple point, the curve loses m — 4 apparent double points, that is an (m — 2)-tuple point may be formed from an (m — 3)-tuple point, a double point and m — 4 apparent double points. A triple point on a quintic curve is thus equivalent to two actual double have more than double edges. The edge joining the * Salmon’s Geometry of Three Dimensions (1882), No. 330, Example 2. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 9513 points and one apparent double point. This triple point does not have its tangents lying in one plane. Consider now a curve of order m with an (m — 4)-tuple point and a triple point. The curve can have no other actual multiple point. We assume 6 = m. In this case we take the vertex of the cone at the triple point, and must therefore know the reduction in the number of apparent double points of a curve when it is viewed from a triple point of the curve. We shall, however, consider the general case and consider the reduction when the curve is viewed from a k-tuple point on it. Plucker’s formulae * give x = 8v (v— 2) — 67 — 8, (1) 3u = 8v (v—1) —67— 91, (2) i= 3p (u— 2) —65—8x, (3) k=} [u(u—1) — 28-7}. (4) In the case we are considering, Cm he ve 2h” KK Bs Substituting these values in (1) and (2), and combining, we have t= B—3 (m—k)+4+ 3 (r— 2h). Substituting the same values in (3), we have “1 Ss P(e — 1) ; i= 3 (m—k) (m—k—2)—6(38,+ > 5 — 8B; 2 where > extends to all multiple edges due to all multiple points other 2 than the vertex, and where 6, is the number of double edges due to apparent double points. Eliminating 7 between these last two equations, we have ~ 2( 3,4 SPP”) — (mam 4 8k 1 5p, (5) - Now take the vertex of the cone at an arbitrary point in space. If 6 is the number of double edges on this cone, we have * Salmon’s Geometry of Three Dimensions (1882), No. 325, footnote. VOL. XXXVIII. — 33 514 PROCEEDINGS OF THE AMERICAN ACADEMY, eye Sa 2s = 2 Substituting in formulae (4), we have Bes [mom 1) -2(44 SEDs >t )-+] 6) 2 Comparing (5) and (6), we have 6 =h-mk+k(k+1); that is, the number of apparent double points is less by mk — k (k + 1) when viewed from a k-tuple point on the curve than when viewed from an arbitrary point in space. Cousider now a curve of order m that has an (m — k — 1)-tuple point and a k-tuple point. Then the curve can have no more actual double or multiple points. It will in general lie on a cone of order m — & that has the k-tuple point as vertex and the curve as base. This cone cannot (m — k —1) (m—k — 2) 2 (m — k — 1)-tuple edge to the (m — k —1)-tuple point counts for just this number. ‘The cone can therefore have no double edges, that is the curve can have no apparent double points when viewed from the /-tuple point. It has therefore just mk — k (k+ 1) apparent double points when viewed from an arbitrary point in space. It can have no more apparent singularities. have more than double edges. The Let P,, denote an n-tuple point on the curve. A curve of order m can thus have a Pm—,z—1, a Px, aud [mk — k (kK + 1)] apparent double points, or a Py—x, a Pei, and [m (k— 1) —k (kK —1)] apparent double points. We can therefore write symbolically Pm—n+ Pri = Pm—rat+ Pr + (m— 2k) apparent double points. (1) [ We obtained mk — k (k + 1) apparent double points by assuming the vertex to be taken at P,. If we interchange and take the vertex at Pm—k—1, we get the same result, viz. : Pi, Pm—x—1, and m (m — k — 1) — (wm —k — 1) (m—k) apparent double points, i. e. Pry Pm—x—1, and mk — k (k + 1) apparent double points. ] VAN DER VRIES, — MULTIPLE POINTS OF TWISTED CURVES. 9515 If we use a and 6, where a + 6 = m —1, in (1), we obtain Py + Py + (m — 25) apparent double points = Payi + Pos. If m is odd, we have pests, {es 1 coe ay apparent double points = ma + Pye t [PO | apparent double points, i. e. 2 P,,-1 + 1 apparent double point = P,1, + Pr_s. a25i Rae air Thus, ifm = 2a+ 1 2 Pa +1 apparent double point = Pasi + Po-1. If m is even, we have ain 7) _ain a) 4 5 apparent double points 2 2 i ee ee * = rar eae ae =) apparent double points, i. e. Pn + Pasa + 2 apparent double points = se + Poy. Ty Thus if m = 2 a, Pa + Pa: + 2 apparent double points = Pa41 + Pa. Therefore, in general, Ifm=2a+4+1, 2 Pa + k? apparent douhie points = Parr + Pax; also, Patr+ Pa—nr+ 9 (g + 2k) apparent double points = Payrsg + Pang: If m = 2'a, Pa + Pai + k (k + 1) apparent double points = Pa+, + Pa—x-13 516 PROCEEDINGS OF THE AMERICAN ACADEMY. also, Par + Pa—r-1 + 9 (g + 2% + 1) apparent double points = a+k+g ees a—k—g—1+ A sextic curve can thus have a quadruple point and four apparent double points, or a triple point, a double point, and six apparent double points. A quadruple point on a sextic curve is thus equivalent to a triple point, a double point, and two apparent double points. Similarly a septimic curve can have a quintuple point and five appar- ent double points, or a quadruple point, a double point, and eight apparent double points, or two triple points and nine apparent double points. A quintuple point on a septimic is thus equivalent to a quadruple point, a double point, and three apparent double points, or to two triple points and four apparent double points. Likewise a quadruple point and a double point on a septimic curve are equivalent to two triple points and one apparent double point. 2. We shall now examine different kinds of multiple points and deter- mine the number of actual and apparent double points to which they are equivalent. We shall consider in detail all kinds of multiple points from the triple point to the septuple point inclusive, and shall then draw some conclusions for multiple points in general. I. Triple Points. A triple point on a curve can, as we have seen, be of two kinds according as the tangents to the curve at this point do or do not lie in one plane. We shall consider the way in which a triple point can be formed. A curve C,, with a double point can be obtained as the partial intersection of a cone K and a monoid J, where the double point of C,, is a double point on A and an ordinary point of MZ. The line from this point to the common vertex of K and J/is a double edge on £ but does not lie on MZ. Let another sheet of A that passes near this line intersect M in a new branch of O,. This new sheet of A intersects the two sheets through the double line in two lines that are also double edges on K. These double edges must be due to actual or apparent double points of C,,. If A is deformed in such a way that these two edges coincide with the first double edge and form a triple edge, Ci, will have a triple point. The tangents at this triple point will all lie in one plane, as they are cut out of the three tangent planes to K along the triple line by the one tangent plane to Wat this point. The last two double edges of K must have been due to actual double points of Cp, these double points being the points of intersection of the ordinary sheet of MW by the VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 9517 double edges of K. This triple point is thus equivalent to three actual double points. If, however, when we deform K we also deform J/ in such a way that it has a double point at the double point of C,, it is evident that the three tangents in the limit will not lie in one plane. For they are the intersections of the tangent cone at the double point of M by the three tangent planes to A along the triple line. The tangent line to the third or new branch intersects the plane of the tangents to the other two branches in the limit at an angle; the new branch must therefore be considered as meeting the first two branches together once at that point. The two double edges of A caused by the third sheet cannot in this case both be considered as due to actual double points of Cm, as the three tangents would then in the limit lie in one plane. Nor can both double edges be considered as due to apparent double points, for the new branch actually meets the other two branches together in the limit. One must therefore be considered as due to an actual and one to an apparent double point. This kind of triple point is thus equivalent to two actual and one apparent double point. This agrees with what we obtained on page 512. II. Quadruple Points. (1). If the four tangents all lie in one plane, as in 1,* the quadruple point is equivalent to 6 actual double points. This is shown in the same way as the case of the triple point of the first kind. (2). If three tangents lie in one plane, as in 2,* the quadruple point is equivalent to 4 actual and 2 apparent double points. For if a curve having such a quadruple point is obtained as the partial intersection of a cone K and a monoid &, the point must be at least a triple point and the line from it to the vertex at least a double line of kind III on /; other- wise three tangents cannot lie in one plane. Let a curve C,, with a triple point at which the tangents lie in one plane be obtained as the partial intersection of a cone AK and a monoid JM that has the point as a triple point. This means that the three lines in which (in addition to the line from the multiple point to the vertex 6 times) the three tangent planes to K intersect the tangent cone at the triple point of lie in one plane. Let a new branch of C;, passing near the triple point be caused by another sheet of A intersecting JZ ‘This sheet meets the three sheets through the triple edge of A in three lines, which are thus double lines on K. These lines must be due to actual or apparent double points * These numbers and succeeding ones refer to figures on the accompanying plate. 518 PROCEEDINGS OF THE AMERICAN ACADEMY. of ©,. As in the case of the triple point it is evident that one and no more must in the limit be considered as due to an actual double point. This quadruple point is thus equivalent to the triple point, one actual double point, and two apparent double points, that is, to four actual and two apparent double points. (3). If no three tangents lie in one plane, as in 3, the quadruple point is equivalent to 3 actual and 3 apparent double points. For, a curve having a triple point at which the tangents lie on a quadric cone but not in a plane can be obtained as the partial intersection of a cone K and a monoid J that has the point as a double point and a line from it to the vertex as an ordinary line of kind III. A new branch of the curve can be added, as in the previous cases, to form a quadruple point. The tan- gent to this branch will be cut out of the tangent cone at the double point of M by the tangent plane to the new sheet of AK. As this tangent does not in general lie in the plane of any two other tangents, the new branch must be considered as meeting the three branches together once at the triple point. This quadruple point is therefore equivalent to the triple point and one actual and two apparent double points, that is, to three actual and three apparent double points. This agrees with what we obtained on pages 501 and 516. We can go on in this way obtaining the different kinds of points of any multiplicity by adding a new branch to points of one less multiplicity. Ill. Quintuple Points. (1). If all the tangents lie in one plane, as in 4, the quintuple point is equivalent to 10 actual double points. This is obtained by adding a new branch to a II (1) * in such a way that its tangent lies in the plane of the four tangent lines at the quadruple point. (2). If four tangents lie in one plane, as in 5, the quintuple point is equivalent to 7 actual and 3 apparent double points. This can be obtained from a II (1). (3). If three tangents lie in one plane, and the other two lie in a plane with one of these, as in 6, the quintuple point is equivalent to 6 actual and 4 apparent double points. This can be obtained from a II (2) by adding a new branch in such a way that its tangent in the limit lies in a plane with the tangents to two other branches. It is therefore equiva- lent to a II (2), two actual double points and two apparent double points. In Figure 6, let us consider the line 123 as the cross section of a plane that contains the lines whose bases are 1, 2, and 3, and the line 145 as a IS a a * We mean by II (1) a quadruple point of kind (1), ete. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 519 the cross section of a plane that contains the lines whose bases are 1, 4, and 5; where the five lines have not yet united to form a quintuple point. The lines then have six actual intersections, Viz. V2) 15,28; 14, 15, and 45, and four apparent intersections, viz. 24, 25, 34, and 369. Considering these lines as the tangents to a curve we see that this quin- tuple point can in the limit be considered as composed of six actual and four apparent double points. (4). If three tangents lie in one plane and the other two do not lie in a plane with one of these, as in 7, the quintuple point is equivalent to 5 actual and 5 apparent double points. This quintuple point can be obtained from a II (2) by adding a new branch with its tangent in the limit not in the plane of two other tangents, or from a II (3), by adding a new branch with its tangent in the limit in the plane of two other tangents. (5). If no three tangents lie in one plane, as in 8% the quintuple point is equivalent to 4 actual and 6 apparent double points. This is the kind of quintuple point mentioned on page 516. It can be obtained from a II (3) by adding a new branch in such a way that its tangent does not in the limit lie in the plane of two other tangents at the quadruple point. It does not matter whether this new branch is added in such a way that the five tangents in the limit lie on a quadric cone that contains an arbitrary line as an edge or on a cubic cone that contains this line as a double edge. The multiplicity of the point on the monoid only affects the composition of the multiple point on the curve by placing an upper limit on the number of tangent lines that can. lie in one plane. The only relations between the tangent lines that directly affect the number of actual and apparent double points to which the multiple point is equivalent are the number of lines that lie in one plane and the number that lie in two or more planes containing two or more other tangent lines. IV. Sextuple Points. (1). If six tangents lie in one plane, as in 9, the sextuple point is equivalent to 15 actual double points. This can be obtained from a III (1). . (2). If the tangents lie by threes in four planes, as in 10, the sex- tuple point is equivalent to 12 actual and 3 apparent double points. For let 1, 2, 3, 4, 5, and 6 represent not only the bases of the tangent lines, as in 10, but also the tangent lines themselves, where the branches have not yet united to form the sextuple point. We suppose 1, 2, and 3 to lie in one plane, and 1, 4, and 5 in another plane, but no three of 520 PROCEEDINGS OF THE. AMERICAN ACADEMY. these lines to meet in one pomt. The line 6 is added in such a way that it lies in the plane not only of 2 and d but also of 3 and 4. The lines before we have reached the limit then lie as in the tetrahedron in Figure 11. The actual intersections are 12, 13, 14, 15, 23, 25, 26, 34, 36, 45, 46, and 56, and the apparent intersections are 16, 24, and 35; thus twelve actual and three apparent double points in the composition of the sextuple point. (3). If five tangents lie in one plane, as in 12, the sextuple point is equivalent to 11 actual and 4 apparent double points. This can be obtained from a III (1). (4). If four tangents lie in one plane, and the other two lie in a plane with one of the four, as in 13, the point is equivalent to 9 actual and 6 apparent double points. This can be obtained from a III (2). (5). If the tangents lie by threes in three planes, as in 14, the point is equivalent to 9 actual and 6 apparent double points. This can be obtained in the same way as case (2) above. ‘The lines before we reach the limit lie as in Figure 15. The actual intersections are 12, 13, 14, 15, 28, 25, 26, 45, and 56, and the apparent intersections are 16, 24, 34, 35, 36, and 46. (6). If four tangents lie in one plane and the other two do not lie in one plane with one of these, as in 16, the sextuple point is equivalent to 8 actual and 7 apparent double points. This can be obtained from a III (2). (7). If three tangents lie in one plane and two lie in a plane with one of these, and the six in no plane with two others, as in 17, the sex- tuple point is equivalent to 7 actual and 8 apparent double points. This can be obtained from a III (3). (8). If three tangents lie in one plane and the other three in a plane that does not contain one of the first three, as in 18, the point is equiva- lent to 7 actual and 8 apparent double points. This can be obtained from a III (4). (9). If three tangents lie in one plane and none of the remaining lie in a plane with two others, as in 19, the point is equivalent to 6 actual and 9 apparent double points. This can be obtained from a III (4). (10). If no three lie in one plane, as in 20, the point is equivalent to 5 actual and 10 apparent double points. This can be obtained from a III (5). V. Septuple Points. (1). If the tangents all lie in one plane, as in 21, the point is equiva- lent to 21 actual double points. This can be obtained froma IV (1). VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. .521 (2). If the tangents lie by threes in six planes, as in 22, the point is equivalent to 18 actual and 3 apparent double points. This will be ex- plained with the following case. (3). If the tangents lie by threes in five planes, as in 23, the point is equivalent to 16 actwal and 5 apparent double points. The branches of a sextuple point of kind (2) before they unite to form the sextuple point have their tangents lying as edges of a tetrahedron, as in ]1. Adding 7 in the plane of 3 and 5 causes the intersection not only of 7 with 3 and 5, and of 3 with 5, but also of 1 with 6. The lines 1, 2, 3, 4, 5, and 6 now meet in one point. This septuple point is thus equivalent to a IV (2), four actual and two apparent double points, that is, to 16 actual and 5 apparent double points. If moreover 7 is added in such a way that it also lies in the plane of 1 and 6, it meets 1 and 6 and two more actual double points must be added. A septuple point of kind (2) is thus equivalent to 18 actual and 3 apparent double points. (4). If six tangents lie in one plane, as in 24, the point is equivalent to 16 actual and 5 apparent double points. This can be obtained from a FV (1). (5). If four tangents lie in one plane, and the others as in 25, the point is equivalent to 15 actual and 6 apparent double points. This can be obtained from a IV (2). (6). If the tangents lie as in 26, the point is equivalent to 15 actual and 6 apparent double points. The tangent lines before the branches of the curve unite to form the septuple point lie as in 27, which have twelve points of intersection. (7). If five tangents le in one plane, and ée other two lie in a plane with one of these, as in 28, the point is equivalent to 13 actual and 8 apparent double points. This can be obtained from a IV (3). (8). Ifsix of the tangents he by threes in four planes, and the seventh is not in a plane with two others, as in 29, the point is equivalent to 13 actual and 8 apparent double points. This can be obtained from a IV (2), (9). If five tangents lie in one plane, and the other two do not lie in a plane with one of these, as in 30, the point is equivalent to 12 actual and 9 apparent double points. This can be obtained from a IV (3). (10). If four tangents lie in one plane and the other three lie in a plane with one of these, as in 31, the point is equivalent to 12 actual and 9 apparent double points. This can be obtained from a IV (4). (11). If four tangents lie in one plane, and the other three as in 32, the point is equivalent to 12 actual and 9 apparent double points. This can be obtained from a IV (5). H22, PROCEEDINGS OF THE AMERICAN ACADEMY. (12). If the tangents lie by threes in four planes, as in 33, the point is equivalent to 12 actual and 9 apparent double points. This can be obtained from a IV (5) by adding 7 so as to lie in a plane with 6 and 4; thus causing 6 and 4 to meet. (13). If four tangents lie in one plane, and two lie in a plane with one of these, and the seventh lies in no plane with two others, as in 34, the point is equivalent to 10 actual and 11 apparent double points. This can be obtained from a IV (7). (14). If four tangents lie in one plane, and the other three lie in a plane not containing one of the first four, as in 35, the point is equiva- lent to 10 actual and 11 apparent double points. This can be obtained from a IV (8). (15). If the tangents lie as in 36, the point is equivalent to 10 actual and 11 apparent double points. This can be obtained from a IV (5). (16). If four tangents lie in one plane, and none of the other three lie in a plane with any two, as in 37, the point is equivalent to 9 actual and 12 apparent double points. This can be obtained from a IV (9). (17). If the tangents lie by threes in three planes, as in 38, the point is equivalent to 9 actual and 12 apparent double points. This can be obtained from a IV (7). (18). If the tangents lie as in 39, the point is equivalent to 8 actual and 13 apparent double points. This can also be obtained from a LV). (19). If three tangents lie in one plane, and three in another plane, and the seventh in no plane with two others, as in 40, the point is equivalent to 8 actual and 13 apparent double points. This can be obtained from a IV (8). (20). If three tangents lie in one plane, and none of the remaining four lie in a plane with any two, as in Figure 41, the point is equivalent to 7 actual and 14 apparent double points. This can be obtained from a TV} (21). If no three tangents lie in one plane, as in 42, the point is equivalent to 6 actual and 15 apparent double points. This can also be obtained from a IV (10). VI. Multiple Points in General. Considering multiple points in general, it is evident that a 4-tuple point is equivalent to at least k — 1 actual double points. For, every branch of the curve has in the limit at least one actual intersection with the totality of kK — 1 other branches. It is also evident that if the tangents at the multiple point lie in a number of planes of which no two have a VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES, 523 tangent line in common the totality of the branches whose tangents lie in one plane must be considered as having at least one connection or inter- section with the totality of branches whose tangents lie in the other planes. The whole system of tangent lines or of branches themselves may thus in the limit be considered as forming a connected system. ‘The k(k—1). Saag the number of apparent double points contained in the composition of the k-tuple point. A (kK + 1)-tuple point can be obtained by causing a new branch of the curve to pass through a k-tuple point of the curve. If this new branch is added in such a way that its tangent lies in a plane with the tangents to A of the branches through the k-tuple point, it must be considered as meeting the & branches together A times at the k-tuple point ; and we have : — Pry = Py + d actual d. pts. + (& — A) apparent d. pts. difference between the number of actual double points and If the new branch is added in such a way that its tangent in the limit lies in o planes that contain two other tangents to the curve at the k- tuple point, we must in general add three actual double points to the value of the multiple point for each of these o planes, viz. two for the in- tersection of this new branch with the two whose tangents lie in the same plane with its tangent and one for the intersection of these two branches. This is shown if we considera V (2) as obtained from a IV (5). The new branch is added in such a way that its tangent lies in the limit in three planes each of which contains two other tangents to the curve; nine actual double points thus being added to the value of a IV (5) to obtain the value of a V (2). If, however, in the k-tuple point y connections were necessary involving branches whose tangents lie in these o planes, we must add only 30 — y actual double points. Thus, if we consider a V (6) as obtained from a IV (8), we add only eight actual double points, for the three branches through the sextuple point whose tangents lie in one plane are considered as having one connection in the limit with the branches whose tangents lie in the other plane. If the new branch is added in such a way that its tangent lies in the limit in p planes that contain respectively Ay, As, As... .-A, other tangent lines, where 3 = X,, we must in general add 6 = Ay + Ap +AgZ+..... +A, actual double points. If, however, in the limit there were a connections necessary between these different sets of branches of the k-tuple point, we must add only 6 — a actual double points. Thus, if we consider a 524 PROCEEDINGS OF THE AMERICAN ACADEMY. V (10) as obtained from a IV (8), we add only five actual double points, for the branches of the sextuple point whose tangents lie in one plane are considered as having one connection in the limit with the branches whose tangents lie in the other plane. V. CLASSIFICATION OF QuINTIC, SEXTIC, AND SEPTIMIC CURVES THAT HAVE MuLTIPLE Pornts. A. Quintic Curves. A quintic curve, according to the enumeration of Salmon,* can have a) 2and 47; a’) land5; a’) Oand6; b) 1 and 4; b’) 0 and 5; c) 0 and 4. Tn addition to these there is the quintic that has a triple point at which the tangents do not lie in one plane.} This quintic can have no actual double point in addition to the triple point. It can be obtained as the partial intersection of the quadric cone ab — d? and the cubic monoid abd-+ b’c + (6? + d?) e that have the point a 6d as the common vertex. The residual intersection is the line dd. The point abd being a quad- ruple point on the complete intersection and an ordinary point on the line 6d is a triple point on the quintic curve. As the tangent lines at the triple point are the three lines that in addition to the line dd form the complete intersection of the quadric cones a 6 — d? and 0? + ad”, it is evident that they do not lie in one plane.§ As the quadric cone a 6 — d? can have no double edge, the quintic curve can have no apparent double point when viewed from the triple point. It has, therefore, mk—k(k+ 1) =5-3—83-4 or 8 apparent double points when viewed from an arbitrary point. The triple point on the quintic is equivalent, as we have seen, to two actual and one apparent double points. The quintic can therefore be obtained directly from a) above, as there are * Salmon’s Geometry of Three Dimensions (1892), p. 318. + The two numbers in each case correspond to the number of actual double points and apparent double points, respectively. t{ Salmon’s Geometry of Three Dimensions (1882), p. 820. § No two of the three lines can coincide, as the plane through this line and the third line would meet the curve in six points. VAN DER. VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 525 just three apparent double points when two actual and one apparent double points are taken to form the triple point. ‘The curve can be obtained from a’) or a’’) only by having one or two apparent double points change to actual double points in the limit; this produces no new kind of curve. The curve cannot be obtained from b), b’), or c) as there will not be enough apparent double points remaining. There is thus only one species of quintic curve having a triple point, and it has three apparent double points. B. Sextic Curves. A sextic curve, according to the classification of Salmon,* can have Pet wal eos taseea ics. 9) al)> Ved) yal) OndO); bygon0 sb) aad Bi els 8s), bl!) 0.9" ejrar Gar cl) i wae!) 80583 ay ASG 0575 e) 0, 6. In addition to these are the sextics that have multiple points. 1. A sextic curve may have a quadruple point. The tangents at this point cannot lie in one plane, as this plane would meet the curve in eight points. A quadruple point at which three tangents lie in one plane is equivalent, as we have seen, to four actual and two apparent double points. A sextic with such a quadruple point thus seems to be derivable from a curve of class a) above. ‘The plane of the three tangents would, however, meet the curve in seven points, which is not possible in the case of a twisted sextic. It is thus evident that although a curve may have actual and apparent double points sufficient to form a certain multiple point nevertheless there are cases where the points cannot unite to form this multiple point. This is analogous to the case of plane curves.— The only quadruple point possible on a sextic curve is one at which no three tangents lie in one plane. This curve has been con- sidered on page 511, as the complete intersection of a quadric cone and a cubic monoid. It has four apparent double points. The quadruple point on this curve is equivalent to three actual and three apparent double points. The curve can thus be obtained directly from a’) above. It cannot be formed from a) as it cannot have a double point in addition to — * Salmon, Cambridge & Dublin Mathematical Journal, Vol. V. t Salmon’s Higher Plane Curves (1873), p. 27. 526 PROCEEDINGS OF THE AMERICAN ACADEMY. the quadruple point. It can be obtained from one of the remaining a)’s only by having some of the apparent double points change to actual double points in the limit. This can give no new species of sextic curve. It is not possible to obtain the curve from any b), c), d), or e), as there will not be enough apparent double points remaining. There is thus only one species of sextic curve with a quadruple point and it has four apparent double points. 2. A sextic curve may have a triple point at which the tangents do not lie in one plane. This sextic lies on a cone of order three that has the triple point as vertex and the curve as base. This cone can have at most one double edge. The curve can therefore have at most one actual double point or one apparent double point when viewed from the triple point. As the number of apparent double points of a sextic when viewed from an arbitrary point in space is six more than when viewed from a triple point of the curve it is evident that a sextic having such a triple point may have either 0 and 6, 1 and 6, or 0 and 7. These sextics can be cut out of the cubic cone by a cubic monoid. A cubic monoid is determined by fifteen arbitrary points other than the vertex. In order to make this monoid contain the curve we must make it contain nineteen points of it. As the vertex, however, counts for six points common to the curve and the monoid, it is only necessary to make the monoid con- tain thirteen other points of the curve. There are thus two points left at our disposal. ‘The cubic cone meets the inferior cone of the monoid in six lines, of which three are the tangent lines to the curve at the triple point and three are lines common to the cone and the monoid. These three lines and the sextic make up the complete intersection of the two cubic surfaces. As the tangent lines at the triple point lie on the quadric inferior cone of the monoid they do not lie in one plane. As there are six lines on the monoid and only three lines common to cone and monoid it is evident that it is not necessary for the cone to have a double edge due to an apparent double point. If the cone and the monoid have three distinct lines in common the curve has no apparent double points when viewed from the triple point. It may or may not have an actual double point in addition according as the cone does or does not have a double edge. If the cone and the monoid have only two lines in common, the curve must either have an apparent double point when viewed from the triple point, or one of the lines common to the cone and the monoid must be a line to an actual double point of the curve. All three kinds above can therefore be obtained as the partial intersection of a cubic cone by a cubic monoid. These three kinds can VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 527 be obtained directly from b’), a’), and a/’) above. The other cases eitlier give us these in the limit, or give a curve with more actual double points or fewer apparent double points than the sextic curve can or must have. The sextic with a double point in addition to the triple point can be obtained as the partial intersection of a quartic cone, having the double point as vertex and the curve as base, and a cubic monoid having the triple point of the curve as a double point and the line from it to the vertex as an ordinary line of kind III. The quartic cone meets the inferior cone of the monoid in eight lines, of which two are tangent lines at the double point and six are lines common to cone and monoid. The line to the triple point counts as three of the six lines of the monoid. The cone need therefore have no double edges, and in fact cannot have, as it already has a triple edge. Three lines in addition to the line to the triple point must therefore be common to cone and monoid. The three branches of the curve at the triple point are cut out of the monoid at the double point by the three sheets of the cone that pass through the triple line. The tangent lines at the triple point are the three lines in which, in addition to the line from the triple point to the vertex three times, the tangent planes to the three sheets of the cone intersect the tangent cone at the double point of the monoid. As the curve can have no apparent double points when viewed from the double point, it has 2m — 6 or 6 apparent double points, when viewed from an arbitrary point in space. 3. A sextic curve can have a triple point at which the tangents lie in one plane. Such a sextic can be obtained as the intersection of a cubic cone and a quadric (monoid) that passes through the vertex of the cone but has no line in common with it. The vertex, being a triple point on the cone and an ordinary point on the monoid, is a triple point on the curve. The tangents at this point lie in one plane, for they are the inter- sections of the cubic cone by the tangent plane to the quadric at this point. The cone can have no double edge due to an apparent double point of the curve, for this would cause the sextic to break up into a quartic curve and the line doubled. It may, however, have a double edge due to an actual double point of the curve. The curve, whether it has an actual double point or not, has therefore no apparent double points when viewed from the triple point. We thus obtain two species of sextics with such a triple point, viz., 1) 0 and 6, and 2) 1 and 6. A sextic, curve with such a triple point can also be obtained as the partial intersection of a quintic cone and a cubic monoid. The quintic cone has an ordinary point of the curve as vertex and the line from this point to the triple point of the curve as a triple edge. The monoid is 528 PROCEEDINGS OF THE AMERICAN ACADEMY. determined by 15 points. In order to make it contain the curve we must make it contain 19 points of it. As the vertex counts for two of these points, it is only necessary to make the monoid contain 17 addi- tional points of the curve. If we take the triple point of the curve as one of the 15 points at our disposal, it is evident that there are just enough points to make the monoid contain the curve. The quintic cone meets the inferior cone of the monoid in 10 lines, of which one is the tangent to the curve at the vertex and the other nine are lines common to the two surfaces. As there are only six lines on the monoid, it is evident that at least three lines common to cone and monoid are double lines on the cone due to apparent double points of the curve. The cone can, however, not have more than three double edges in addition to the triple edge ; every line of the monoid must therefore lie on the cone. This sextic has therefore three apparent double points when viewed from an ordinary point of the curve, or seven apparent double points when viewed from an arbitrary point. We can obtain the three species directly from b), 2), and a’), respect- ively. As the triple point is equivalent to three actual double points, it is evident that no other species can be obtained. The sextic that has a double point in addition to this triple point can also be obtained as the intersection of a quartic cone and a cubic monoid that have the double point of the curve as their common vertex. (Oh Septimic Curves. A septimic curve, according to Genty,* always has at least 9 apparent double points. The possible cases are then : — 4)96)9)5 valr5, 105. a!) 45019: al 31 Deta™)- 2513): ay), 145 a Ode -b) 5,9; b/) 4,10; b!) 3,11; b/”) 2,12; bY) 1,13; bY) 0,14: Cee 5 Gel) ek, 10s Melis Ili te!) V2 erm) OSs d) 3,9; a’) 2,105 a’) 1,11; a’) 0,12; a); eos sre Os te!) Ons f) 1,9; f") 0,10; g) 0,9. We shall describe in detail the septimic curves that have multiple points. 1. A septimic curve can have a quintuple point provided no three of the tangents lie in one plane. Such a quintuple point is equivalent to + * Bull. de la Soc. Math., t. 9, 10 (1881), p. 153. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES. 529 four actual and six apparent double points. This septimic can be obtained as the partial intersection of a quadric cone and a quartic monoid, the residual intersection being a straight line. This curve has, as we have seen, five apparent double points. It is thus obtainable from a/’) above and is the only species of twisted septimic with a quin- tuple point. 2. A septimic curve can have a quadruple point at which three of the tangents lie in one plane. Such a quadruple point is equivalent to four actual and two apparent double points. This curve will lie on a cubic cone that has the quadruple point of the curve as vertex and the curve as base. If we wish to cut this curve out of the cubic cone by means of a monoid, we must take a monoid that has the multiple point of the curve as a point of multiplicity not less than three ; otherwise the three tangents cannot lie in one plane. The monoid must therefore be of an order as great as four. A quartic monoid is determined by 24 points. Four of these points must be taken off the cubic cone to insure the monoid not breaking up into this cone and a plane. In order to make this quartic monoid contain the septiric curve that has the vertex of the monoid as a quadruple point, we must make it contain 4*7—3°4—1 additional points of the curve. There are thus still three points left at our disposal. The cubic cone meets the inferior cone of the monoid in nine lines, of which four are tangent lines to the curve at the quadruple point and five are lines common to the two surfaces. It is evident, as in previous cases, that either four or five of the lines of the monoid are edges of the cubic cone, this cone having at most one double edge. Septimic curves with quadruple points of the above kind are thus of three kinds, viz., 1) 0,8; 2) 1,8; and 3) 0,9. These can be obtained directly from b’), a’), and a’’) above; there are no other possible cases. 3. A septimic curve with a quadruple point at which no three tangents lie in one plane can be obtained as the partial intersection of a cubic cone and a cubic monoid. The cubic cone has the quadruple point of the curve as vertex and the curve as base. The cubic monoid is determined by 15 arbitrary points. In order to make it contain a septimic curve that has the vertex of the monoid asa quadruple point, we must make it contain 8° 7— 2°4+ 1 or 14 additional points of the curve. There is thus one point left at our disposal. The cubic cone meets the inferior cone of the monoid in six lines, of which four are tangents to the curve at the quadruple point and two are lines common to the cone and the monoid. ‘These two lines and the septimic make up the complete inter- section of the two surfaces. As in the previous case, it is evident that VOL, XXXVIII.— 34 530 PROCEEDINGS OF THE AMERICAN ACADEMY. this septimic can have: 1) 0,8; 2) 1,9; and 3) 0,9. The quadruple point in this case is equivalent to three actual and three apparent double points. The above three species can thus be obtained directly from curves of kinds b!’), a/’), and a!!’), respectively ; no other species are possible. 4, A septimic curve with two triple points, the tangents at each of which lie in one plane, can be obtained as the partial intersection of a quartic cone having a triple edge and a quadric (monoid) that has a line in common with the cone. The vertex is a point of multiplicity four on the complete intersection and therefore, since the line passes through the point, a point of multiplicity three on the septimic curve. As the point is an ordinary point on the quadric, the three tangents to the curve at the triple point lie in one plane. The other triple point is the point distinct from the vertex where the sheet of the quadric crosses the triple line. The quartic cone having a triple edge can have no double edge in addition, due either to an actual or an apparent double point. ‘The curve has therefore just 7:3 — 8-4 or 9 apparent double points. This species can be obtained directly from a); it is the only possible species. 5. A septimic curve with two triple points, one of each kind, can be obtained as the partial intersection of a sextic cone and a quartic monoid. The sextic cone has an ordinary point of the curve as vertex and the curve as base; and the quartic monoid has the triple point at which the tangents do not lie in one plane as a double point, and the line from it to the vertex as an ordinary line of kind HI. This quartic monoid is determined by twenty arbitrary points in addition to its vertex and the double point. In order to make this monoid contain the septimic that has the vertex as an ordinary point and the double point as a triple point, we must make it contain 4:7 — 3 —2:°3 + 1, or 20 additional points on the curve. This is just the number at our disposal. The sex- tic cone meets the inferior cone of the monoid in 18 lines, of which one is the tangent line to the curve and 17 are lines common to the cone and the monoid. The monoid has 12 lines on it. The line of kind III counts as two lines of the monoid and as three lines common to cone and monoid. There are thus 10 other lines on the monoid that must be made to count for 14 lines common to cone and monoid. The sextic cone therefore has 4 double edges; these are due to apparent double points, as the curve can have no actual double points in addition to the two triple points. As the quartic cone cannot have more than 4 double edges in addition to the 2 triple edges, it is evident that all lines of the monoid must lie on the cone. The three branches of the curve at one triple point are cut VAN DER VRIES, — MULTIPLE POINTS OF TWISTED CURVES. 531 out of the monoid at the double point by the three sheets of the cone, and thus do not have their tangents lying in one plane. The three branches of the curve at the other triple point are cut out of the cone by an ordinary sheet of the monoid at the point where the sheet crosses the second triple line; the tangents at this point thus lie in one plane. This curve has 4 apparent double points when viewed from an ordinary point of the curve, or 9 apparent double points when viewed from an arbitrary point. It can be obtained directly from a’) above. 6. A septimic curve that has two triple points of the second kind can be obtained as the partial intersection of a quartic cone and a cubic monoid. The quartic cone must have one of the triple points as vertex and the curve as base. The cubic monoid must have the second triple point as a double point and the line from it to the vertex as an ordinary line of kind III. This monoid is determined by 11 points in addition to the vertex and the other double point. In order to make this monoid contain a septimic curve that has each of the double points of the monoid as a triple point, we must make it contain 3: 7—2°3—2-°3+41 or 10 additional points of the curve. There is thus one point left at our dis- posal. The quartic cone meets the inferior cone of the monoid in 8 lines, of which 3 are tangent lines to the curve at the triple point at the vertex and 5 are lines common to the cone and the monoid. The quartic cone can have no double edge in addition to the triple edge to the second triple point. The curve has therefore no apparent double points when viewed from one of the triple points; it therefore has just 9 when viewed from an arbitrary point in space. This curve can be obtained from a septimic of kind a’’), the two triple points counting as 4 actual and 2 apparent double points. It is to be noticed that when we wish to ob- tain a curve having a multiple point from a curve that has only double points, we cannot always use the curve that has the minimum number of apparent double points. 7. A quartic cone and a quadric (monoid) that have a line in common intersect in addition in a septimic curve that has a triple point at the vertex of the quartic cone. The tangents to the curve at the triple point lie in the tangent plane to the quadric at this point. The quartic cone may have three double edges, but none due to an apparent double point, for such an edge would count twice as a line common to cone and monoid. The curve therefore has 7 - 3 — 3 - 4 or 9 apparent double points. This is also evident from our formula : — Oe ee he a Spy PROCEEDINGS OF THE AMERICAN ACADEMY. Here p= 4 y= 2k = sen, h'=0, H'! = 8; therefore h = 9. This septimic may have as many as three actual double points in addition to the triple point. A septimic curve with a triple point at which the tangents lie in one plane can be obtained also as the partial intersection of a quartic cone and a quartic monoid. We can then obtain the following species : — (1). Those having 9 apparent double points ; these may have as many as three actual double points in addition. (2). Those having 10 apparent double points; these may have as many as two actual double points in addition. (3). Those having 11 apparent double points; these may have one actual double point in addition. (4). Those having 12 apparent double points. These cases can be obtained directly from d), c), b), a), ¢’), b’), a’), b’’), a!’), al’), respectively. 8. A septimic curve having a triple point at which the tangents do not lie in one plane can be obtained as the partial intersection of a quartic cone and a quartic monoid. We shall then obtain species similar to the four above. These different septimics can be derived directly from a’); e!), b!), -a'), ce"); bl’); al); bl), ‘all’),“a), respectively. VAN DER VRIES. — MULTIPLE POINTS OF TWISTED CURVES, Beare /\, Proc, AMER. ACAD. ARTS AND SCIENCES, VOL. XXXVIII. Proceedings of the American Academy of Arts and Sciences, VoL. XXXVIII. No. 18. — January, 1908. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 186. MENDEL’S LAW OF HEREDITY. By Wa. bh. CASTER: ee. { aay H bf an x - is 7 b ini Mea AED art) = ata CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR.—No. 1386. MENDEL’S LAW OF HEREDITY. By W. E. Caste. Presented January 14, 1908. Received December 20, 1902. Wauat will doubtless rank as one of the great discoveries in biology, and in the study of heredity perhaps the greatest, was made by Gregor Mendel, an Austrian monk, in the garden of his cloister, some forty years ago. The discovery was announced in the proceedings of a fairly well- known scientific society, but seems to have attracted little attention and to have been soon forgotten. The Darwinian theory then occupied the centre of the scientific stage and Mendel’s brilliant discovery was all but unnoticed for a third of a century. Meanwhile the discussion aroused by Weismann’s germ-plasm theory, in particular the idea of the non-inheri- tance of acquired characters, had put the scientific public into a more receptive frame of mind. Mendel’s law was rediscovered independently by three different botanists engaged in the study of plant-hybrids, — de Vries, Correns, and Tschermak, — in the year 1900. It remained, how- ever, for Bateson, two years later, to point out the full importance and the wide applicability of the law. This he has done in two recent pub- lications with an enthusiasm which can hardly fail to prove contagious. There is little danger, I think, of Mendel’s discovery being again forgotten. 1. The law of dominance. When mating occurs between two animals or plants differing in some character, the offspring frequently all exhibit the character of one parent only, in which case that character is said to be “dominant.” Thus, when white mice are crossed with gray mice, all the offspring are gray, that color character being dominant.. The char- acter which is not seen in the immediate offspring is called “ recessive,” for though unseen it is still present in the young, as we shall see. White, in the instance given, is the recessive character. The principle of heredity just stated may be called the law of dominance. The first in- stance of it discovered by Mendel, related to the cotyledon-color in peas 536 PROCEEDINGS OF THE AMERICAN ACADEMY, obtained by crossing different garden varieties. Yellow color of coty- ledons was found to be dominant over green ; likewise. round smooth form of seed was found to be dominant over angular wrinkled form; and violet color of blossoms, over white color. Other illustrations might be mentioned both among animals and among plants, but these will suffice. 2. Peculiar hybrid forms. The law of dominance is not of universal applicability ; Mendel does not so declare, though some of his critics have thus interpreted him. In many cases the cross-bred offspring possess a character intermediate between those of the parents. This Mendel found to be true when varieties of peas differing in height were crossed. Again, the cross-breds may possess what appears to be an intensifica- tion of the character of one parent, as when in crossing dwarf with tall peas the hybrid plant is ¢aller than either parent, or as when, in crossing a brown-seeded with a white-seeded variety of bean, the offspring bear beans of a darker brown than that of the brown-seeded parent. Thirdly, the cross-bred may have a character entirely different from ‘that of either parent. Thus a cross between spotted, black-and-white mice, and albino mice, produces commonly mice entirely gray in color, like the house-mouse. Again, in crossing beans, a variety having yellow- ish-brown seeds crossed with a white-seeded variety yields sometimes black mottled seed, a character possessed by neither parent. These three conditions may be grouped together by saying — the hybrid often possesses a character of its own, instead of the pure character of one parent, as is true in cases of complete dominance. ‘lhe hybrid character may approximate that of one parent or the other, or it may be different from both. There is no way of predicting what the hybrid character in a given cross will be. It can be determined only by experiment, but it is always the same for the same cross, provided the parents are pure. Often the hybrid form resembles a supposed ancestral condition, in which case it is commonly designated a reversion. Illustrations are the gray hybrid mice, which are indistinguishable in appearance from the house-mouse, and slate-colored pigeons resulting from crossing white with buff pigeons. 3. Purity of the germ-cells. The great discovery of Mendel is this: The hybrid, whatever its own character, produces ripe germ-cells which bear only the pure character of one parent or the other. Thus, when one parent has the character A, and the other the character B, the hybrid will have the character AB, or in cases of simple dominance, A(B)* or * The parenthesis is used to indicate a recessive character not visible in the individual. CASTLE. —- MENDEL’S LAW OF HEREDITY. dat B(A). But whatever the character of the hybrid may be, its germ-cells, when mature, will bear ecther the character A or the character B, but not both ; and As and Bs will be produced in equal numbers. ‘This perfectly simple principle is known as the law of ‘* segregation,’ or the law of the “purity of the germ-cells.” It bids fair to prove as fundamental to a right understanding of the facts of heredity as is the law of definite proportions in chemistry. From it follow many important consequences. A first consequence of the law of purity of the germ-cells is polymor- phism of the second and later hybrid generations. The individuals of the first hybrid generation are all of one type, provided the parent races are pure. Each has a character resulting from the combination of an A with a B, let us say AB. [In cases of dominance it would more properly be expressed by A (B) or B(A).] But in the next generation three sorts of combination are possible, since each parent will furnish As and Bs in equal numbers. The possible combinations are AA, AB, TABLE I. Characters, —> A. AB. Plants bearing Flowers in Color, | Magenta Red. DOM OTAA Sy sek ase the! 19 “ec 73 9 Se) at, Seen See 12 Debt aig ie he Uke . 14 54 Per cent of whole and BB. The first sort will consist of pure As and will breed true to that character ever afterward, unless crossed with individuals having a different character. Similarly the third sort will be pure Bs and will breed true to that character. But the second sort, AB, will consist of - hybrid individuals, like those of which the first hybrid generation con- sisted. If, as supposed, germ-cells, A and B, are produced in equal numbers by hybrids of both sexes, and unite at random, combinations AA, AB, and BB should occur in the frequencies, 1: 2:1. For in unions between two sets of gametes, each A + B, there is one chance each for the combinations AA and BB, but two chances for the com- bination AB. 538 PROCEEDINGS OF THE AMERICAN ACADEMY, If the three forms AA (or simply A), AB, and B are all different in appearance, it will be a very simple matter to count those of each class and determine whether they occur in the theoretical proportions, 1 : 2:1. One such case has been observed by Bateson (:02, p. 183) among Chinese primroses (Primula sinensis). An unfixable hybrid variety known as “ Giant Lavender,” bearing flowers of a lavender color, was produced by crossing a magenta red with a white flowering variety tinged faintly with pink. By seed the hybrid constantly produces plants bear- ing magenta-red and white flowers respectively, as well as other plants bearing lavender flowers. The numerical proportions observed in two successive seasons are shown in Table I. The observed numbers, it will be seen, are quite close to the theo- retical, Tis: 2°) 1. In cases wherein the hybrid is indistinguishable from one of the parent forms (i.e. in cases of complete dominance of one parental TABLE IL. HEREDITY OF COTYLEDON-COLOR AMONG CROSS-BRED PEAS. Offspring. Parents crossed. Gen. III. character), only two categories of offspring will be recognizable and these will be numerically as 3:1. But further breeding will allow the separation of the larger group into two subordinate classes, — first, individuals bearing only the dominant character; secondly, hybrids ; that is, into groups A and A(B), which will be numerically as 1 : 2. Observed results are in this case very close to theory. Mendel, by crossing yellow with green peas, obtained, as we have seen, only yellow (hybrid) seed. Plants raised from this seed bore in the same pods both yellow seed and green seed in the ratio, 3: 1. (See Table II.) The green seed produced in later generations green seed CASTLE. — MENDEL’S LAW OF HEREDITY, 539 only. It bore only the recessive character. Of the yellow seeds, one in three produced only yellow offspring, i.e. contained only the dominant character ; but two out of three proved to be hybrid, producing both green and yellow seed, as did the hybrids of the preceding generation. These are precisely the theoretical proportions, A + 2 A(B) + B. The experiment has been repeated and confirmed by several different observers. In mice, my friend and pupil, Mr. G. M. Allen, finds the second hybrid generation, obtained by crossing gray with white mice, to con- sist of gray mice and white mice approximately in the ratio, 3:1. (See Table III.) The white are pure recessives, producing only white offspring, when bred inter se. What portion of the grays are pure dominants has not yet been determined, but we may confidently expect that it will prove to be not far from 1 in 3. TABLE III. HEREDITY OF COAT-COLOR AMONG CROSS-BRED MICE ORTAINED BY MATING Wuite Mice (W) with Gray Mice (G). Offspring. Parents crossed Gen. III. A further test of the correctness of Mendel’s hypothesis of the purity of the germ-cells and of their production in equal numbers, is afforded by back-crossing of a hybrid with one of the parental forms. For example, take a case of simple dominance, as of cotyledon-color in peas or coat-color in mice. We have here characters D (dominant) and R (recessive). The first generation hybrids will all be D(R). Any one of them back-crossed with the recessive parent will produce fifty per cent of pure recessive offspring and fifty per cent of hybrids. For the hybrid produces germ-cells . . . . D+R The recessive parent produces germ-cells . . R-+ R The possible combinations are . . . . . 2D(R) + 2R This case has been tested for peas and for mice and found to be substantially as stated. 540 PROCEEDINGS OF THE AMERICAN ACADEMY. We have thus far considered only cases of cross-breeding between parents differing in a single character. We have seen that in such cases, no new forms, except the unstable hybrid form, are produced. But when the parent forms crossed differ in two or more characters, there will be produced in the second and later hybrid generations individuals possessing new combinations of the characters found in the parents ; indeed all possible combinations of those characters will be formed, and in the proportions demanded by chance. ‘Thus when parents are crossed which differ in ¢wo characters, A and B, let us designate the dominant phase of these characters by A, B, the recessive phase by a, b. The immediate offspring resulting from the cross will all be alike, AB(ab),* but the second and later generations of hybrids will contain the stable (i.e. pure) classes, AB, Ab, aB, ab, in addition to other (unstable, or still hybrid) forms, namely AB(ab), A(a)b, and aB(b). In every six- teen second-generation offspring there will be, on the average, one of each of the stable combinations. Two of these combinations will be identical with the parent forms, the other two will be new. But the difficulty of establishing a stable (i. e. pure) race is greater in this case than in that of one variable character. Only the individual which possesses both recessive characters can at once be set aside as pure. For to each of the stable individuals possessing one dominant and one recessive character, there will be two other individuals, exactly like it in appearance, but hybrid in one of the two characters. The one pure individual can be distinguished from the two impure individuals only by breeding tests. Again, nine out of every sixteen of the second-generation hybrids will possess the two dominant characters, and so will be in appearance exactly like their parents, the first-generation hybrids. But only one of the nine will be pure with reference to those characters. Of the remain- ing eight, four will be hybrid in one character, and four will be hybrid in both characters exactly like the entire first generation of offspring. The greater the number of separately variable characters involved in a cross, the greater will be the number of new combinations obtain- able; the greater, too, will be the number of individuals which it will be necessary to raise in order to secure all the possible combinations ; and the greater, again, will be the difficulty of isolating the pure (i.e. * This is Mendel’s use of lower-case letters to designate recessive characters, with which I have combined the use of a parenthesis when a character by nature recessive is not visible in the individual. CASTLE. — MENDEL’S LAW OF HEREDITY. 541 stable) forms from such as are similar to them in appearance but still hybrid in one or more characters. Mendel has generalized these state- ments substantially as follows: In cases of complete dominance, when the number of differences between the parents is x, the number of different classes into which the second generation of offspring fall will be 3”, of which 2” will be pure (stable); the remainder will be hybrid, though indistinguishable from pure individuals. The smallest number of individuals which in the second hybrid generation will allow of one pure individual to each visibly different class, will be 4". See Table 1V. TABLE IV. Sere A eae Smallest Number yey pene Total Classes, of Offspring Seay) Pure and allowing one taing one Pure A ane = Individual. Bybee Tara te Number of Dif- ferences between Parents. Qn Tested by Mendel correct. Calculated. for peas and tound i ) The law of Mendel reduces to an exact science the art of breeding in the case most carefully studied by him, that of entire dominance. It gives to the breeder a new conception of “ purity.” No animal or plant is “ pure” simply because it is descended from a long line of ancestors possessing a desired combination of characters ; but any animal or plant is pure if it produces gametes of only one sort, even though its grand- parents may among themselves have possessed opposite characters. The existence of purity can be established with certainty only by suitable breeding tests (especially by crossing with recessives), but it may be safely assumed for any animal or plant descended from parents which were like each other and had been shown by breeding tests to be pure. Special cases under the law of Mendel. It remains to speak of some special cases under the law of Mendel, which apparently are exceptions to one or another of the principles already stated, and which probably result from exceptional conditions known to us only in part. These special cases have come to light in part through Mendel’s own work, in part through that of others. nag PROCEEDINGS OF THE AMERICAN ACADEMY. 1. Mosaic inheritance. It occasionally happens that in crosses which bring together a pair of characters commonly related as dominant and recessive, the two characters appear in the offspring in patches side by side, as in piebald animals and parti-colored flowers and fruits. The normal dominance apparently gives place in such cases to a balanced relationship between the alternative characters. What conditions give rise to such relationships is unknown, but when they are once secured they often prove to possess great stability, breeding true inter se. This, for example, is the case in spotted mice, which usually produce a large majority of spotted offspring. ‘The balanced relationship of characters possessed by the parents is transmitted to the germ-cells, which are, not as in ordinary hybrid individuals D or R, but } DR. This has been shown to be the case in spotted mice by G. M. Allen and myself, in a paper published elsewhere. ‘The balanced condition of D and R, which exists in the gamete, is upset when that gamete unites with a pure R (and probably also when it unites with a pure D); for spotted mice bred to white mice regularly gave only uniformly gray or black individuals, after the formula } DR + R= D(R).* But an exceptional spotted male, own brother to those which gave the described result, apparently produced gametes D and R as well as others } DR, for by white females he had pure white offspring as well as those which were gray or black in color. This result can be expressed by the formula : — Sperm. Ovum. Offspring. } DR + R= D(R)* ) ordinary gray or D+ R= D(R) black hybrids. R+ R=R, white (pure). 2. Stable hybrid forms. This isa case, in some respects similar to the last, which was familiar to Mendel (:70) himself. It sometimes happens, as we have seen, that the hybrid has a form of its own different from that of either parent. To such cases the law of dominance evidently does not apply. In a few cases — Hieracium hybrids (Mendel), Salix hybrids (Wichura) — it has been found that the hybrid form does not break up in the second generation and produce individuals like the grandparents, but breeds true to its own hybrid character. This can be explained only * Observations made since the foregoing was written indicate that the offspring in this case are, sometimes at least, }D(R)*(R). For when an individual of this sort forms gametes, they apparently are, not pure D and R, but 4 DR and R respec- tively. This hypothesis accounts for the reappearance of spotted mice after their disappearance for a generation in consequence of crossing. CASTLE. — MENDEL’S LAW OF HEREDITY. 5438 on one of two assymptions. Either the germ-cells bear the two charac- ters in the balanced relationship, } AB, as do spotted mice ordinarily, or, of the two gametes which unite in fertilization, one invariably bears the character A, the other the character B. 3. Coupled characters. This is the phenomenon of correlation of characters in heredity. It is sometimes found that, in cross-breeding, two characters cannot be separated. When one is inherited, the other is inherited also. Thus, in crossing different sorts of Datura (the James- town weed) it has been found that purple color of stem invariably goes with blue color of flowers, whereas green stems are constantly associated with white flowers. Again in mice, rabbits, and most other mammals, white hair and pink eyes occur together and may not be separated in heredity. Very rarely, however, as I have observed, an otherwise per- fectly white guinea-pig has dark eyes; further the ordinary albino guinea- pig with pink eyes has usually smutty (brown-pigmented) ears, nose, and feet. These exceptional conditions probably represent stable couplings of a part only of the dominant character (pigmented coat) with the reces- sive character (white coat), and are similar in kind to the } DR character of the spotted mice. For guinea-pigs do occur entirely devoid of the D character, i. e. without dark nose, ears, and feet, and with pink eyes. These doubtless represent the pure recessive condition. Further, coupling may occur between a number of characters greater than two, so that they form, to all intents and purposes, in heredity, one indissoluble compound character. Thus, Correns (:00) observed that in crosses between two species of stocks (Mathiola incana DC. and M. glabra DC.) the second generation hybrids showed reversion to one or the other of the parental forms in all three of the principal differential characters studied, viz., hairy or glabrous stems, violet or yellow-white flowers, and blue or yellow seed. A blue seed always produced a hoary plant bearing violet flowers; a yellow seed always produced a glabrous plant bearing yellow or white flowers. 4. Disintegration of characters. ‘This is the converse of the foregoing process. Not only may characters apparently simple be coupled together in heredity to form composite units of a higher order, but characters which ordinarily behave as units may as a result of crossing undergo dis- integration into elements separately transmissible. Thus the gray coat- color of the house-mouse is always transmitted as a dominant unit in primary crosses with its white variety; but in the second cross-bred generation a certain number of black mice appear, some or all of which are probably hybrids. For similar black mice obtained by crossing black- 544 PROCEEDINGS OF THE AMERICAN ACADEMY. white with white mice have been shown, by breeding tests, to be hybrids, since on crossing with white mice they produce white mice, black mice, and, in one or two cases, gray mice also. Accordingly black mice clearly belong with grays in the category of dominant individuals [ D or D (R) ], but they have visibly only the black constituent of the gray coat, the re- maining constituent, a rufous tint, having been separated from the black in consequence of cross-breeding. ‘There is reason to believe that the rufous constituent may become recessive (i. e. latent) either in the black individuals or in the reverted whites, or in both. It is seen separated from both the black and the white characters, in the chocolate-brown and reddish-yellow individuals obtained in cross-breeding. A fancier of rabbits tells me that there occurs a similar disintegration of the composite coat-color of the * Belgian hare,” when that animal is crossed with ordinary white rabbits, the result being the production of black, yellow, and mottled individuals, in addition to ordinary gray- browns. The various distinct colors or color patches of the guinea-pig have doubtless originated in a similar way, — by resolution of the composite coat-color of the wild Cavia, upon crossing with an albino sport. This subject is now undergoing investigation. Correns (:00) mentions a case in plants, which probably belongs in this same category. In crossing the blue-flowered (dominant) Mathiola incana with the yellowish-white flowered (recessive) M. glabra, the second generation recessives produced in some cases pure white flowers, in others yellow flowers. In this case the recessive character, rather than the dominant, underwent disintegration. 5. Departures from the theoretical ratios of dominants to recessives. Considerable departures are to be expected when the number of offspring taken into consideration is small, but with increase in the number of offspring examined, the departures should grow less. This is usually found to be true. Mendel’s numbers are shown by Weldon (:02) to be well within the limits of probable error. But certain cases have been observed in which departures of a particular sort persist even with con- siderable numbers of offspring. Thus Allen and I have found the recessive character, white, in mice to be inherited in about three per cent more than the calculated number of cases, while the equally recessive dancing character is inherited in about thirty-three per cent less than the calculated number of cases. These fairly uniform departures indicate, to my mind, a vitality, on the part of the recessive gamete, in one case somewhat superior, in the other much inferior to that of the dominant CASTLE, — MENDEL’S LAW OF HEREDITY. 545 gamete. Inferior vitality of gametes of either sort would result in greater mortality and so in a diminished number of individuals derived from such gametes. Of course other explanations are possible, as, that the two sorts of gametes are not produced in equal numbers. More extended investiga- tions of such cases can alone make their meaning clear. 6. Reversal of Dominance. Exceptional cases are on record in which crossing of a dominant with a recessive has resulted in the production of pure dominants, or recessives, instead of hybrids. Such cases are, I believe, correctly referred by Bateson to the category of “ false hybridi- zation ” as described by Millardet, a phenomenon akin to parthenogenesis, in which sexual union has served merely to stimulate one gamete to development without bringing about its union with the other gamete. It is possible, however, that there are cases in which one of a pair of characters is sometimes dominant, sometimes recessive. ‘Tschermak (:01) believes that he has found a few such cases among cross-bred beans. Sex and certain other dimorphic conditions found in the higher animals and plants may prove to be cases of this sort. Acceptance of Mendel’s principles of heredity as correct must lead one to regard discontinuous (or sport) variation as of the highest im- portance in bringing about polymorphism of species and ultimately of the formation of new species. A sport having once arisen affecting some one character of a species, may by crossing with the parent form be the cause of no end of disinte- gration on the part of any or ali of the characters of the species, and the disintegrated characters may, indeed must, form a great variety of new combinations of characters, some of which will prove stable and self- perpetuating. Even if a particular combination of characters is uniformly eliminated by natural selection under one set of conditions, it may reappear again and again, and finally meet with conditions which insure its success. We now have an explanation of the long-recognized principle that new types of organisms are extremely variable, whereas old types vary little. A new type which has arisen as a sport will cross with the parent form. The offspring will then inherit some characters dominant, others latent, and polymorphism of the race results. Only selection continued through long periods of time will serve to eliminate completely the latent recessives, and so to cause the disappearance of certain aberrant variations. Bateson makes the pregnant suggestion that even cases of continuous VOL. XXXVIII. — 39 546 PROCEEDINGS OF THE AMERICAN ACADEMY. variation may possibly prove conformable with Mendelian principles. Take, for example, the height of peas. It has been found in certain crosses of a tall with a dwarf variety of pea, that the hybrid has an intermediate height. Now, if the hybrid produces pure germ-cells, dwarf and tall respectively, in equal numbers, the next generation will consist of three classes of individuals, dwarf, intermediate, and tall, in the pro- portions, 1: 2:1. But if each of the original characters should undergo disintegration, we might get a dozen classes, instead of three, resulting in a practically continuous frequency-of-error curve. SUMMARY. 1. The basic principle in Mendel’s discoveries is that of the purity of the germ-cells ; in accordance with this a cross-bred animal or plant pro- duces germ-cells bearing only one of each pair of characters in which its parents differ. From it follow the occurrence in the second and later hybrid generations of a definite number of forms in definite numerical proportions. 2. Mendel’s principle of dominance is realized in the heredity of a considerable number of characters among both animals and plants. In accordance with this principle, hybrid offspring have visibly the character of only one parent or the other, though they transmit those of both parents. 3. In other cases the hybrid has a distinctive character of its own. This may approximate more or less closely the character of one parent or the other, or it may be entirely different from both. Frequently the distinctive hybrid character resembles a lost ancestral character. In some cases of this sort, as in coat-color of mammals, the hybrid character probably results from a recombination of the characters seen in one or both parents, with certain other characters latent (that is, recessive) in one parent or the other. 4, There have been observed the following exceptions to the principle of dominance, or to the principle of purity of the germ-cells, or to both : — (a) Mosaic inheritance, in which a pair of characters ordinarily related as dominant and recessive occur in a balanced relationship, side by side in the hybrid individual and, frequently, but not always, in its germ-cells also. This balanced condition, once obtained, is usually stable under close breeding, but is readily disturbed by cross-breeding, giving place then to the normal dominance. (6) Stable (self-perpetuating) hybrid forms result from certain crosses. These constitute an exception to both the law of dominance and to that CASTLE. — MENDEL’S LAW OF HEREDITY. 547 of purity of the germ-cells. For the hybrid is like neither parent, but the characters of both parents exist in a stable union in the mature germ- cells produced by the hybrid. (c) Coupling (i. e., complete correlation) may exist between two or more characters, so that they form a compound unit not separable in heredity, at least in certain crosses. (d) Disintegration of characters apparently simple may take place in consequence of cross-breeding. (e) Departures from the expected ratios of dominants to recessives may be explained in some cases as due to inferior vigor, and so greater mortality, on the part of dominants or recessives respectively. (f) Cases of apparent reversal of dominance may arise from “ false hybridization ” (induced parthenogenesis). Possibly in other cases the determination of dominance rests with circumstances as yet unknown. 5. Mendel’s principles strengthen the view that species arise by dis- continuous variation. ‘They explain why new types are especially vari- able, how one variation causes others, and why certain variations are so peristent in their occurrence. BIBLIOGRAPHY. Bateson, W. :02. Mendel’s Principles of Heredity, a Defence. With a Translation of Mendel’s Original Papers on Hybridisation. 12mo, 212: pp. Cambridge. [England. Contains bibliography and portrait of Mendel. ] ; Bateson, W., and Saunders, E. R. :02. Experimental Studies in the Physiology of Heredity. Reports to the Evolution Committee of the Royal Society. Report I. 160 pp. London. Correns, C. :00. G. Mendel’s Regeln iiber das Verhalten der Nachkommenschaft der Rassenbastarde. Ber. deutsch. bot. Gesellsch., Jahrg. 18, pp. 158-168. Mendel, G. :66. Versuche iiber Pflanzenhybriden. Verh. Naturf.-Vereins in Briinn, Bd. 4, Abh,, pp. 3-47. [Translation in Bateson, :02 ] Mendel, G. :70. Ueber einige aus kiinstlicher Befruchtung entnomennen Hiera- cium-Bastarde. Verh. Naturf.-Vereins in Briinn, Bd. 8, Abh., pp. 26-31. [Translation in Bateson, :02. ] = 548 PROCEEDINGS OF THE AMERICAN ACADEMY. Tschermak, E. :00. Ueber kiinstliche Kreuzung bei Pisum sativum. Zeitsch. f. land- wirths. Versuchswesen in Oester., Jahrg. 3, pp. 465-555. Tschermak, E. :01. Weitere Beitriige uber Verschiedenwerthigkeit der Merkmale bei Kreuzung von Erbsen und Bohnen. (Vorliufige Mittheilung. ) Ber. deutsch. bot. Gesellsch., Jahrg. 19, pp. 35-51. Vries, H. de. :00. Sur la loi de disjonction des hybrides. Compt. Rend., Paris, Tom. 130, pp. 845-847. ' Vries, H. de. :00°. Das Spaltungsgesetz der Bastarden. Ber. deutsch. bot. Gesellsch., Jahrg. 18, pp. 83-90. Weldon, W. F. R. :02. Mendel’s Laws of Alternative Inheritance in Peas. Biometrika, Vol. 1, pp. 228-254, pl. 1, 2. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 19. — Fesruary, 1903. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. ON THE TEMPERATURE COEFFICIENTS OF MAGNETS MADE OF CHILLED CAST IRON. By B. O. PEIRCE. INVESTIGATIONS ON LIGHT AND HEAT, MADE AND PUBLISHED WHOLLY OR IN PART WITH APPROPRIATIONS FROM THE RUMFORD FUND. ; ON THE TEMPERATURE COEFFICIENTS OF MAGNETS MADE OF CHILLED CAST IRON. By B. O. PEIRCE. Presented January 14, 1903. Received January 14, 19038. BesipEs a number of d’Arsonval galvanometers, furnished with hardened forged steel magnets, from the shops of well known makers in America and in Europe, there are in the Physical Laboratories of Harvard University about thirty similar instruments in which the per- manent fields are due to chilled and seasoned cast iron magnets. These latter have proved very satisfactory, and, after a trial of three years, we are about to add to their number. Although chilled cast iron magnets were used years ago in some forms of telephones, straight magnets are most conveniently made of steel ; indeed if they are to be employed in measuring the intensity of the earth’s field, the best tool steel, ground slowly into shape under water after the hardening, is not too homogeneous for the purpose. Steel for permanent magnets, however, needs special skill in the handling, if the results are to be satisfactory, and not every successful tool maker knows how to forge and to harden, well and quickly, even a horseshoe magnet, unless it be of very simple form. Two straight, hollow bar magnets were made and ground most carefully for use in the Jefferson Physical Laboratory, by a firm which manufactures machine tools of the highest grade. These were supposed to be as nearly alike as possible, but they proved to be magnetically very different, for the permanent moment of one was twice that of the other. > Of late I have been using magnets made of soft iron castings, subse- quently chilled, to furnish the artificial field in an oil damped ampere- meter, and in a similar voltmeter firmly set up in the laboratory, and, since it was desirable that the indications of these instruments should be trustworthy within one part in a thousand of their larger deflections, it became necessary to test the permanency of the magnets, and to a4 PROCEEDINGS OF THE AMERICAN ACADEMY. determine their temperature coefficients. This paper gives the results of measurements made on a number of magnets of this kind. Most of the magnets experimented upon were made of castings chilled by Mr. G. W. Thompson, the mechanician of the Jefferson Physical Laboratory, who has had a great deal of experience with the process. They were first heated to a bright red in a gas furnace under a power blast, and then plunged into a cold acid bath kept in violent agitation. The castings thus hardened were relaxed by long exposure to boiling water or steam, then magnetized to saturation, and finally seasoned, after prolonged boiling, by being alternately heated in steam and cooled in tap water. The whole seasoning process reduced the magnetic moment of each specimen by perhaps twenty per cent of the value it had just after the magnetization. If, after a magnet has been seasoned, its temperature be suddenly raised from 0° C. to 100° C. and then as suddenly lowered again, it may not wholly recover its original strength until after the lapse of an hour or two: if, however, the range be only 40° or 50° C., I have been unable to detect any lag in the attainment of the whole of the original moment after the heating. Although there is no advantage in using cast iron for straight magnets, I had a number made for comparison with fine steel magnets of the same dimensions. The cast iron magnets looked rough in comparison with the others, but the moments of a large number of them seemed to differ less among themselves than the moments of the same number of the steel magnets. ‘The strongest steel magnet that I tested had a moment about four per cent greater than that of the strongest cast iron magnet, but the average moment of the cast iron magnets was practically the same as (in fact two per cent greater than) the average of the seasoned steel magnets. In determining the temperature coefficients, the straight magnet to be experimented upon was fixed firmly in a non-magnetic holder inside a non-magnetic tube so as to be in Gauss’s A Position east of a mirror magnetometer. By the help of a system of pipes and cocks, tap water, steam, or a stream from a bath water heater at almost any desired tem- perature, between 15° C. and 100° C. could be sent through the tube containing the magnet. On the west of the magnetometer, so placed in Gauss’s A Position as to bring the needle back exactly into the meridian, was a short, seasoned, compensating magnet, fixed wholly within a wooden holder and completely shielded from sudden temperature changes. If ay is the needle deflection which the compensating magnet would cause if the magnet to be tested were removed, JA, the moment of the last PEIRCE, — TEMPERATURE COEFFICIENTS OF MAGNETS. 553 named magnet at the temperature ¢) at which the adjustments have been made, and M, the moment of this magnet when, its temperature having become raised to ¢, the needle is deflected through the angle a, M,—M tana Moe tao Since the temperature coefficients of seasoned bar magnets of a given length and of given material are in general larger the greater the cross section of the bar, it is necessary in comparing materials to take magnets of nearly the same dimensions. Besides a number of chilled cast iron magnets 18 centimeters long and about 0.95 centimeters in diameter, I had many carefully made steel magnets of the same area of cross section and of almost the same length. In the case of all these, the rate of loss of moment per degree of rise of temperature was greater at higher tem- peratures than at low ; we may, however, for the purpose of comparison, use the mean loss, per degree, of the magnetic moment, when the magnet is heated from about 10° C. to 100° C., expressed in terms of the moment at the lower temperature. ‘These mean losses were found to be 0.00042 in the case of the seasoned chilled iron magnets. ‘0.00046 in the case of the seasoned magnets made of “ Crescent Steel Drill Rod.” 0.00046 in the case of the seasoned magnets made of Jessop’s Round Black Tool Steel. 0.00070 in the case of the seasoned magnets made of Jessop’s Square Tool Steel. I had bar magnets made of many other materials, for instance of Jessop’s and Mushet’s self-hardening steels, but none of exactly the di- mensions of the cast iron magnets. No kindof steel that I tested had, however, when proper allowance was made for dimensions, quite so small a temperature coefficient as the chilled iron. The mean temperature coefficient of chilled cast iron magnets 18 centi- meters long and 1.25 centimeters in diameter, as obtained from a number of specimens, was 0.00056, which is very low. The forms of some of the magnets which we have used (either singly or with others of the same kind), in various instruments, are shown in the subjoined figure. The shapes marked 1, 2, 3, 6, are employed, with the long way of the opening between the poles vertical, in d’Arsonval gal- vanometers ; two or three castings of the shape marked 4, and a number of thin plates of the shape marked 8, are used together in other instru- 554 PROCEEDINGS OF THE AMERICAN ACADEMY. ments of the same kind. Magnets of the shapes marked 5 and 7 produce the artificial fields in laboratory amperemeters and voltmeters. For our present purpose we may define the temperature coefficients of one of these magnets as the rate of change of the whole magnetic induc- tion across a given surface between the poles, when the temperature of the magnet is raised by one degree. This can be measured with sufficient accuracy, by pulling out, from a definite position between the Jaws, a coil of suitable shape made of manganine wire and connected with a ballistic galvanometer. In order to be able to make the determinations con- veniently I had a brass box made of the shape indicated in the figure. The box itself was first cast in one piece, and then a slot for the coil was PEIRCE. — TEMPERATURE COEFFICIENTS OF MAGNETS. 555 cut on a milling machine, and a rectangular cavity, open to the outside air but closed to the inside of the box, was constructed by soldering two thin pieces of brass into the end and top of the slot. Into this cavity a set of forms carrying thin coils of the shapes needed, fitted exactly. The box itself, and the cover, were mounted on the face plate of a lathe and turned off smooth, so that when a piece of rubber packing was inserted between the two, and the whole was screwed together, the case thus made was water-tight. The box was mounted on a wooden frame which had sliders for the forms which carried the coils. The magnet to be tested was fastened firmly in place by a holder not shown in the figure, and the box was connected with a set of pipes so that cold water, warm water, or steam could be sent through it at pleasure. The temperature coefficient of a bent cast iron magnet, as defined above, generally increases with the temperature, but for purposes of com- parison, we may use the mean value A of this coefficient between 10° C. and 100° C. Three magnets of the form marked 1, chilled by Mr. Thompson and weighing as much as 1250 grams each (nearly three pounds), gave for K the values 0.00086, 0.00037, and 0.000384 respectively ; another magnet of the same pattern treated by a maker of hardened cast iron machinery, yielded the value 0.00082. Whatever the secret process employed in this last case, the resulting magnet was by no means so useful as those made from castings chilled in the manner described above. Unchilled castings make very undesirable magnets, for the temperature coefficients are usually five or six times as large as in the case of chilled magnets, and it seems impossible to get their magnetic moments really permanent. Curiously enough the chilling process makes a casting less brittle than before, and causes the grain of a fracture to be finer and more uniform. The values of A seem to indicate that the whole interior of the casting is affected by the chilling, whereas it is extremely difficult to harden a thick piece of steel uniformly. It did not appear that a magnet made up of a lot of thin plates chilled separately had a smaller temperature coefficient than a solid magnet of the same dimensions. Castings of the shapes marked 3, 4, and 6 weighed about. 260 grams, 160 grams, and 500 grams, respectively, and yielded for A the values 0.00040, 0.00040, 0.00031. The actual temperature coefficients at low temperatures are always less than these mean values, and in the case of the last mentioned form the coefficient is not greater than 0.00013 between 10° C. and 40° C. I have myself never found a value quite so small as 556 PROCEEDINGS OF THE AMERICAN ACADEMY, this for a massive steel magnet, though several observers have obtained extremely low coefficients for very slender steel wires, and even negative coefficients for comparatively weak magnets made of some alloys. Using such chilled magnets as I have described, and employing com- posite galvanometer coils of manganine and copper, with permanent manganine shunts, it is not difficult to make a cheap fixed amperemeter, the indications of which shall be almost wholly independent of the room temperature. In the case of a d’Arsonval galvanometer of the usual form, slight temperature changes in the torsional rigidity of the suspen- sion wire have to be taken into account. JEFFERSON PHYSICAL LABORATORY, December, 1902. Proceedings of the American Academy of Arts and Sciences. Vout. XXXVIII. No. 20. — Aprin, 1908. CONTRIBUTIONS FROM THE WILDER PHYSICAL LABORATORY OF DARTMOUTH COLLEGE. THE PRESSURE DUE TO RADIATION. By E. F. Nicuors anp G. F. Hutt. INVESTIGATIONS ON Light AND HEAT MADE OR PUBLISHED, WHOLLY OR IN PART, WITH APPROPRIATIONS FROM THE Romrorp Funp. THE PRESSURE DUE TO RADIATION. By E. F. Nicuots anp G. F. HULt. Presented December 10, 1902. Received February 5, 1903. ConreENTS. PAGE Historical Literature. . . Oey oie es Ba oes > ua: Gee se ae OOS Outline of Preliminary Worle SPE e Ds Weecinsoh) Sona kan tals Ca eo OE ae OO ita Wve Gilbane le cehd BR Ro My eal ls SAeeibuceerwoer 4 6 ST leqtermzressune sVicasirementser tes foe ence ca aoe: he ant menOOS MRORMOrsione al anGery st eetes ete Ala Bases, | ehmvase ag ia (a3. Ux Statin eeOOS Acranscment of Apparatas) 7) (4/0 ay apis <4 (04 cle ayce Fei ey i 1 OO MIT GN? Oliahecehiton. ope le a wha & Up hee Wes wb Rebus alice SiuibcumEUmnce temeuce sre VLi((r- Torsion Coefficient of Balance . . . CGRP AG sry ish oeece ctuce hk Remo. Reduction of Observations to Standard anne sori Lhe Agent ae RE bec ta; Static Method of Pressure Measurements ............ . + 578 Methods for the Elimination of Gas Action . ..... .:.... . S574 Ballistic Method of Pressure Measurements . . No Bun hee RN Pressure of Beam of Standard Intensity for Different Wave: ne Bede Math eK Apparatus and Method of Energy Measurements . ..... .. . . O84 Calibration of Silver Disc . . a ate Ea DSD Energy of Beam of Standard Merete a irrerent Rave! “CLOUDS Wwe OSS Reflection Coefficients of Surfaces . . . .... | apis St: eg PARES OL Corrections and Final Computations . . . BUMS died cl aie de SIP Estimate of Uneliminated Gas Action in Final ivaines Dp aay Be Bie, ERY Accuracy of the Various Measurements entering into the Final Values. ee OUS As early as 1619 Kepler * announced his belief that the solar repul- sion of the finely divided matter of comets’ tails was due to the outward pressure of light. On the corpuscular theory of light Newton con- sidered Kepler’s idea as plausible enough, but he was of the opinion that the phenomenon was analogous to the rising of smoke in our own atmosphere. In the first half of the eighteenth century DeMairan and DuF ay ¢ contrived elaborate experiments to test this pressure of light * DeMairan, Traité physique et historique de l’Aurore Boréale (Seconde Edi- tion), pp. 357-358. Paris, 1754. + Isaaci Newtoni Opera quae Existant Omnia. Samuel Horsley, LL.D., R.S.S. Tom. III, pag. 156, Londinium, 1782. ¢t DeMarian, l.c., p. 371. This treatise contains also the accounts of still earlier experiments by Hartsoeker, p. 868, and Homberg, p. 869. The later experiments are of more historic than intrinsic interest. 560 PROCEEDINGS OF THE AMERICAN ACADEMY. theory in the laboratory, but, because of the disturbing action of the gases surrounding the illuminated bodies employed in the measurements, they obtained wholly confusing and contradictory results. Later in the same century the Rev. A. Bennet* performed further experiments, but could find no repulsive force not traceable to convection currents in the gas surrounding the body upon which the light was projected, due in his opinion to the heating effect of the rays. Finding no pressure due to radiation, he made the following unique suggestion in support of the wave theory of light: “ Perhaps sensible heat and light may not be caused by the influx or rectilinear projection of fine particles, but by the vibrations made in the universally diffused caloric or matter of heat or fluid of light. I think modern discoveries, especially those of elec- tricity, favor the latter hypothesis.” In the meantime Euler, f accept- ing Kepler’s theory attributing the phenomenon of comets’ tails to light pressure, had hastened to the support of the wave theory by showing theoretically that a longitudinal wave motion might produce a pressure in the direction of its propagation upon a body which checked its progress. In 1825 Fresnel } made a series of experiments, but arrived at no more definite conclusion than that the repulsive and attractive forces observed were not of magnetic nor electric origin. Crookes § believed in 1873 that he had found the true radiation pres- sure in his newly invented radiometer and cautiously suggested that his experiments might have some bearing on the prevailing theory of the nature of light. Crookes’ later experiments and Zollner’s || measure- ments of radiometric repulsions showed that the radiometric forces were in some cases 100,000 times greater than the light pressure forces with which they had been temporarily confused. Zollner’s experiments are among the most ingenious ever tried in this field of work, and he missed the discovery of the true radiation pressure by only the narrowest margin. An excellent bibliography of the whole radiometric literature is given by Graetz,{] and an account of some of the older experiments not mentioned above is given by Crookes.** * A. Bennet, Phil. Trans., p. 81 (1792). + L. Euler, Histoire de l’Academie Royale de Berlin (2), p. 121 (1746). t A. Fresnel, Ann. Chem. et Phys., X XIX. 57, 107 (1825). § W. Crookes, Phil. Trans., p. 501 (1873). || F. Zollner, Pogg. Ann., CLX. 156, 296, 459 (1877). 7 L. Graetz, Winckelmann’s Handbuch der Physik, 2b, p. 262. Breslau, ** W. Crookes, l.c., p. 501. x NICHOLS AND HULL. — PRESSURE DUE TO RADIATION. 561 In 1873 Maxwell, * on the basis of the electromagnetic theory, showed, that if light were an electromagnetic phenomenon, pressure should result from the absorption or reflection of a beam of light. After a discussion of the equations involved, he says: “ Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves and numerically equal to the energy in unit volume.’ Maxwell com- puted the pressure exerted by the sun on the illuminated surface of the earth and added: “It is probable that a much greater energy of radiation might be obtained by means of the concentrated rays from an electric lamp. Such rays falling on a thin metallic disc, delicately suspended in a vacuum, might perhaps produce an observable mechanical effect.” Apparently independent of Maxwell, Bartoli ¢ announced in 1876 that the Second Law of Thermodynamics required the existence of a pressure due to radiation numerically equal in amount to that derived by Maxwell. Bartoli’s reasoning holds for all forms of energy streams in space and is of more general application than Maxwell’s equations. Bartoli contrived elaborate experiments to verify this theory, but was balked in the search, as all before him had been, by the complicated character of the gas action which he found no way of eliminating from his experiments. After Bartoli’s work the subject was dealt with theoretically by Boltz- mann,t Galitzine,$ Guillaume, || Heaviside,’ and more recently by Gold- hammer.** Fitzgerald, ff Lebedew,t} and Hull $$ have discussed the bearing of radiation pressure upon the Newtonian law of gravitation with special reference to the repulsion of comets’ tails by the sun. Arrhenius |||| has recently discussed the cosmical consequences of radiation pressure not only concerning comets’ tails, but, by combining radiation pressure with the known properties of negative ions, has endeavored also to account * J.C. Maxwell, A Treatise on Electricity and Magnetism (1st Edition), II. 391. Oxford, 1873. 7; A. Bartoli, Sopra i movementi prodotti della luce e dal calorie, Florence, Le Monnier (1876), also Nuovo Cimento, XV. 193 (1884). t L. Boltzmann, Wied. Ann., XXII. 31, 291 (1884). § B. Galitzine, Wied. Ann., XLVII. 479 (1892). || Ch. Ed. Guillaume, Arch. de Gen. (8), XXXI. 121 (1894). J O. Heaviside, Electromagnetic Theory, I. 334. London, 1893. ** D, A. Goldhammer, Ann. Phys., IV. 834 (1901). tt G. F. Fitzgerald, Proc. Roy. Soc. Dub. (1884). it P.Lebedew, Wied. Ann., XLV. 292 (1892). Astrophys. Jour., XIV. 155 (1902). §§ G. F. Hull, Trans. Astron. Soc. Toronto, p. 123 (1901). || S. Arrhenius, Konigl, Vetanskaps. Akademiens Fordhandlingar, p. 545 (1900). VOL, XXXVIII. — 36 562 PROCEEDINGS OF THE AMERICAN ACADEMY. for the aurora borealis. Swartzschild* computed from radiation pressure on small spherical conductors the size of bodies of unit density for which the ratio of radiation pressure to gravitational attraction would be a maximum. Before the Congres International de Physique in 1900, Professor Lebe- dew} of the University of Moscow described an arrangement of apparatus which he was using at that time for the measurement of light pressure. He summarizes the results already obtained as follows: “ Les résultats des mesures que j’ai faites jusqu’ici peuvent se résumer ainsi: L’expéri- ence montre qu’un faisceau lumineux incident exerce sur les surfaces planes absorbantes et réfléchissantes des pressions qui, aux erreurs prés d’observation, sont égales aux valeurs calculées par Maxwell et Bartoli.” No estimate of the “errors of observation” was given in the paper nor other numerical data. Unfortunately the proceedings of the Paris Congress did not reach the writers nor any intimation of the methods or results of Professor Lebedew’s work until after the publication of their own preliminary experiments. _ The writers} presented the results they had obtained by measure- ments of radiation pressure at eight different gas pressures, in a prelim- inary communication to the American Physical Society, meeting with Section B of the American Association at Denver, August 29, 1901. A condensed abstract of this paper follows. In the experiments of earlier investigators every approach to the experimental solution of the problem of radiation pressure had been balked by the disturbing action of gases which it is impossible to remove entirely from the space surrounding the body upon which the radiation falls. The forces of attraction or repulsion, due to the action of gas molecules, are functions, first, of the temperature difference between the body and its surroundings, caused by the absorption by the body of a portion of the rays which fall upon it; and second, of the pressure of the gas surrounding the illuminated body. In the particular form of apparatus used in the present study the latter function appears very com- plicated, and certain peculiarities of the gas action remain inexplicable upon the basis of any simple group of assumptions which the writers have so far been able to make. * K. Swartschild, Kgl. Bayer. Akademie d’ Wissenschaften, XX XI. 293 (1901). {+ P. Lebedew, Rapports présentés au Congres International de Physique (2), p. 183. Paris, 1900. ¢ E. F. Nichols and G. F. Hull, Science, XIV. 588 (Oct. 18, 1901), and Phys. Rey., XIII. 298 (Nov., 1901). NICHOLS AND HULL.— PRESSURE DUE TO RADIATION. 563 Since we can neither do away entirely with the gas nor calculate its effect under varying conditions, the only hopeful approach which remains is to devise apparatus and methods of observation which will reduce the errors due to gas action to a minimum. The following considerations led to a method by which the elimination of the gas action was practi- cally accomplished in the present experiments. 1. The surfaces which receive the radiation, the pressure of which is to be measured, should be as perfect reflectors as possible. This will reduce the gas action by making the rise of temperature due to absorp- tion small, while the radiation pressure will be increased ; the theory re- quiring that a beam, totally reflected, exert twice the pressure of an equal beam, completely absorbed. 2. By studying the action of a beam of constant intensity upon the same surface surrounded by air at different pressures, certain pressures may be found where the gas action is less than at others. 3. The apparatus — some sort of torsion balance — should carry two surfaces symmetrically placed with reference to the rotation axis, and the surfaces on the two arms should be as nearly equal as possible in every respect. The surfaces or vanes should be so constructed that if the forces due to gas action (whether suction or pressure on the warmer surface) and radiation pressure have the same sign in one case, a reversal of the suspension should reverse the gas action and bring the two forces into opposition. In this way a mean of the forces on the two faces of the suspension should be, in part at least, free from gas action. 4. Radiation pressure, from its nature, must reach its maximum value instantly, while observation has shown that gas action begins at zero and increases with length of exposure, rising rapidly at first, then more slowly to its maximum effect, which, in many of the cases observed, was not reached until the exposure had lasted from two and a half to three minutes. For large gas pressures, an even longer exposure was ne- cessary to reach stationary conditions. The gas action may be thus still further reduced by a ballistic or semi-ballistic method of measure- ment. The results of ballistic observations of radiation pressure at different gas pressures are given below in Table I, in which p indicates the pres- sure of the surrounding gas in millimeters of mercury, and d the static equivalent of the ballistic throws of the torsion balance. The results were obtained with substantially the same apparatus and method de- scribed on page 568 et seq. : — 564 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. Taking the product of the average deflection in centimeters by the con- stant of the torsion balance, the radiation pressure was : — 2.25 x 4.65 x 10° = 1.05 x 10-4 dynes. THE BoLomeEter. To compare the theoretical value of radiation pressure with the above value, it was necessary to measure the energy of the radiation causing the pressure. ‘This was attempted with the aid of a bolometer constructed as follows : — On a sheet of platinum 0.001 mm. thick, rolled in silver (by the firm Sy & Wagner, Berlin), a circle P (Fig. 1), 11.25 mm. in diameter, was drawn. ‘The sheet was cut from the edges inward to the circumference of the circle, in such a way as to leave five principal strips A, B, C, D, £, connected to the circle in the manner shown. Other narrower strips, as €, m,n, 0, etc., were left to give the disc additional support. The disc, by means of the connecting arms, was mounted with asphalt varnish centrally over a hole, 14 mm. in diameter, bored through a slab JS of thin slate. Portions of the silver not to be removed by the acid were care- fully covered by asphalt varnish. Thus on the strips A and ¥#, the silver was protected to the very edge of the circle, while on all the other arms, the silver was left exposed back to the edge of the boring in the slate. The whole system was then plunged into warm nitric acid, and the silver eaten away from all unvarnished surfaces, leaving only the thin platinum sheet which was blackened by electric deposition of platinum by Kurlbaum’s* method. At A, B, C, D, E, holes were bored extending * Kurlbaum, Wied. Ann., LX VII. 848 (1899). NICHOLS AND HULL.— PRESSURE DUE TO RADIATION. 565 through the slate. Copper washers were soldered to the silver strips and binding posts were attached. The torsion balance was removed from under the bell-jar, the bolom- eter was put in the place of one of the vanes and was covered by the bell-jar. Connections to the bolometer were made as schematically shown in Fig.1. The disc P was the exact size of the light image thrown on the vanes in the pressure measure- ments. The intention was to heat the disc by “allowing the image to fall on it, and then, with the light turned off, to heat it to the same temperature by sending a current through it from A to B. If r be the resistance from A to Bin ohms, when exposed to the lamp, and 2 be the current in amperes which gives the same temperature in Pas that given by the absorbed radiation, then 277 x 107 will be the activity of the beam in erg-seconds. The temperature of the disc, whether exposed to the radiation or heated by the current, was shown by the resistance, C to D-H, which was made one arm of a Wheatstone Bridge. The relation of the heating current to the Riewae i bridge was adjusted as follows: With the key K open, so that no current flowed through the bridge, the heating current from six storage cells , was turned on, and the sliding contact at F’ so set that the bridge galvanometer zero was not changed by reversing the heating current. The point F, equipotential to c, was found very near the middle of the wire ad, which showed the current distribution of P to be symmetrical with respect to a diameter at right angles to A B. The key K was then closed making the bridge current, and the bridge was bal- anced. The bolometer was next exposed to the radiation, and simultaneous observations of the intensity of the beam were made on galvanometer G (Fig. 1), and the Jamp galvanometer G,. The deflection of galvanom- eter G, was reduced to standard lamp (a deflection of 100 divisions), as was done in the pressure observations. After shutting off the light the heating current was turned on. It was regulated by means of the variable resistance Ff, (Fig. 1), so that nearly the same throw was ob- tained from the galvanometer G', as when the bolometer was exposed to the lamp. All deflections of the galvanometerG, were taken with the 566 PROCEEDINGS OF THE AMERICAN ACADEMY. bridge current both direct and reversed to eliminate any local disturb- ances in the bridge and also with the heating current both direct and reversed. A Siemens & Halske direct-reading precision milliampere- meter was used to measure this current. From repeated observations the current which gave the same heating effect as the light beam was ¢ = 0.865 amp. The resistance between the binding posts A and B was measured with the lamp on and gave r = 0.278 ohm. The intensity of the beam in erg-seconds was thus: r 7? x 10’, or 0.278 x 0.75 x 107. Using 0.92 as the reflection coefficient of silver, the pressure computed from the energy measurements was p = 1.34 x 10-4 dynes. The observed pressure was only 78 per cent of this value. No correction for the diffuse reflection of the blackened bolometer face nor for the differ- ence in reflecting power between the two faces of the silver coating, discovered later, was made. ‘The two corrections, however, nearly bal- ance, so no considerable change in the result would have been effected by using them. It was later discovered that, in dissolving the silver from the platinum when the bolometer was made, the acid had eaten away the silver from the strips A and JB for a distance of nearly a millimeter under the asphalt. The resistance 0.278 ohm given for the disc was thus too high. It was impossible to redetermine the resistance by the direct method because of an accident to the bolometer by which the disc was nearly severed from the strip £. The disc was therefore carefully torn away from its supports, mounted on a glass plate and cut on a dividing engine into strips, 1 and 2 mms. wide, parallel to A 5. The resistance along these strips was measured by the fall of potential method. The resist- ance was found to vary slightly in different parts of the disc due to lack of uniformity in the thickness of the metal. After many measurements, an average value was reached and the resistance of the disc computed theoretically as follows : — The resistance of a conducting sheet of infinite extent, when the current enters and leaves the sheet by electrodes* of relatively great conductivity, is where o is the resistance of any square of the oO 42’ sheet, and C is the electrostatic capacity of the two electrodes. If the electrodes are cylinders, the lines of flow are circles orthogonal to them. When the sheet, in place of being infinite, is bounded by one of these circular lines of flow, the resistance is In particular, if the elec- o CW * J.J. Thomson, Electricity and Magnetism, 2d Edition, p.314. Cambridge, 1897. NICHOLS AND HULL.— PRESSURE DUE TO RADIATION. 567 trodes of radii 7 are on a diameter of this circular sheet of radius 7, then the resistance can be shown to be o Dye eS de 4/4 ee 7 loge 277 Assuming for the moment that the leading-in strips of the bolometer (Fig. 1) were of great conductivity compared to that of the thin platinum sheet and that they terminated in circular arcs orthogonal to this circular sheet, the resistance would be 0.922 xX a, giving to r the value of 2.79 mms. and to & the value 11.25 mms. But the leading-in strips ter- minated on the boundary of the large circle. The resistance was there- fore altered by two facts, — the lines of flow were changed and the distance between the electrodes was increased. ‘The latter is the impor- tant item. It is necessary therefore to find approximately the resistance of these gibbous portions of the large disc previously considered as electrodes. ‘This may be done by estimating the area of these parts and by considering the average equipotential line as midway between the chord and arc of the cylindrical electrode. It results that the amount to be added on account of this calculation is 0.471 X o. Hence the resist- ance between the electrodes is now (0.922 + 0.471) o = 1.393 x a. The value of o as found by the fall of potential method was 0.148 at 19° C. When corrected for the temperature of the disc exposed to the lamp, o becomes 0.160. Hence the resistance of the disc when hot was 1.393 x 0.160 = 0.221 ohm.* Substituting this computed value of the resistance in place of the one used, the energy of the standard beam becomes 0.221 x 0.75 x 10" ergs-seconds and ve, 1.92 5 OL22T Se O75 5< 10 Ry 3 x 10% This result is in accidental agreement with the observed pressure. If necessary corrections, determined by later experiment, had been applied, the difference between the observed pressure and the pressure computed from the energy measurements would have been about three per cent. Moreover the probable error of the final result was roughly double this amount. In the November number of the Annalen der Physik for 1901 Pro- fessor Lebedew ¢ published the results of a more varied series of =: 1.05 x 10-* dynes. * The resistance of a trial disc was measured experimentally with the result that the experimental value differed from the theoretical by about one per cent. t P. Lebedew, Ann. Phys., VI. 433 (1901). 568 PROCEEDINGS OF THE AMERICAN ACADEMY, measurements of radiation pressure than the early measurements of the present writers. The principal difference between the methods employed by him and by the writers for determining the pressure was that he used very thin metallic vanes surrounded by gas at extremely low pressures, thus following Maxwell’s suggestion literally, while the writers used silvered glass vanes and worked at large gas pressures for which the gas action had been carefully and exhaustively studied and found to be negligibly small for short exposures. From our knowledge of the variation of gas action in different vacua, we feel sure that our method would not have been successful in high vacua because of the relatively large gas action. Professor Lebedew’s own results, with blackened vanes of lower heat conductivity, show that his success in eliminating gas disturbance was due to the high heat conductivity of thin vanes rather than to the high vacua employed. Professor Lebedew’s * estimate of the accuracy of his work is such as to admit of possible errors of twenty per cent in his final results. An analysis of Professor Lebedew’s paper and comparison with our prelimi- nary experiments seems to show that his accidental errors were larger than ours, but through the undiscovered false resistance in the bolometer our final results were somewhat further from the theory than his. Either of the above researches would have been sufficient to establish the exvst- ence of a pressure due to radiation, but neither research offered, in our judgment, a satisfactory quantitative confirmation of the Maxwell-Bartoli theory. Later PrRessuRE MEASUREMENTS. Description of Apparatus. — The Torsion Balance. The form of suspension of the torsion balance, used to measure radia- tion pressure in the present study, is seen in Fig. 2. The rotation axis ab was a fine rod of drawn glass. A drawn glass cross-arm c, bent down at either end into a small hook, was attached to the axis. The surfaces Cand D, which received the light beam, were circular microscope cover- glasses, 12.8 mm. in diameter and 0.17 mm. thick, weighing approxi- mately 51 mgs. each. To distinguish the two vanes from each other, in case individual differences should appear in the measurements, and also to mark the two faces of each vane for subsequent recognition, a letter C’ was marked on one, and D on the other by diamond scratches. Through each glass, a hole 0.5 mm. or less in diameter, was drilled near the edge, * P. Lebedew, Ann. Phys., VI. 457 (1901). NICHOLS AND HULL. — PRESSURE DUE TO RADIATION, 569 by means of which the glasses could be hung on the hooks on the cross- armc. On opposite sides of the rotation axis at d two other drawn- glass cross-arms were attached. The cover glassses slipped easily between these, and were thus held securely in one plane. Further down on @é, a small silvered plane mirror m, was made fast at right (2) 6 cms. FIGuReE 2. angles to the plane of Cand D. "This mirror was polished bright on the silver side, so that the scale at S; (Fig. 3) could be read in either face. A small brass weight m; (Fig. 2), of 452 mgs. mass and of known dimen- sions, was attached at the lower end of ab. The cover-glasses which served as vanes were silvered and brilliantly polished on the silvered sides, and so hung on the small hooks that both silver faces or both glass faces were presented to the light. A quartz fiber f,, 3 cms. long, was 570 PROCEEDINGS OF THE AMERICAN ACADEMY. made fast to the upper end of a6, and to the lower end of a fine glass rod d, which carried a horizontal magnet m,. The rod d, was in turn suspended by a short fiber to a steel pin e, which could be raised or lowered in the bearing 4. The whole was carried by a bent glass tube ¢, firmly fastened to a solid brass foot F, resting on a plane _ground-glass plate P?, cemented to a brass platform mounted on three levelling screws not shown. A bell-jar 5, 25 cms. high and 11 cms. in diameter, covered the balance. The flange of the bell-jar was ground to fit the plate P. A ground-in hollow glass stopper fitted the neck of the bell-jar, which could thus be put in connection with a system of glass tubes leading to a Geissler mercury pump, a MacLeod pressure gauge, and a vertical glass tube dipping into a mercury cup and serving as a rough manometer for measuring the larger gas pressures employed during the observations. The low pressures were measured on the MacLeod gauge in the usual way. A semicircular magnet MV, fitted to the vertical curvature of the bell-jar, was used to direct the suspended magnet m, and thus to control the zero position of the torsion balance. By turning M/ through 180°, the opposite faces of the vanes Cand D could be presented to the light. THe ARRANGEMENT OF APPARATUS. A horizontal section of the apparatus through the axis of the light beam is shown in Fig. 3. The white-hot end of the horizontal carbon S,, of an A. T. Thompson 90° arc-lamp, fed by alternating current, served as a source. The are played against the end of the horizontal carbon from the vertical carbon which was screened from the lenses L, and LZ, by an asbestos diaphragm d,. A lens, not shown, projected an enlarged image of the arc and carbons on an adjacent wall, so that the position of the carbons and the condition of the arc could be seen at all times by both observers. The cone of rays passing through the small diaphragm d, fell upon the glass condensing lenses Z,, L,. At d; a diaphragm, 11.25 mm. in diam- eter, was interposed, which permitted only the central portion of the cone of rays to pass. Just beyond ds, the beam passed to a shutter at S). This shutter was worked by a magnetic escapement, operated by the seconds contact of a standard clock. The observer at 7, might choose the second for opening or closing the shutter, but the shutter’s motion always took place at the time of the seconds contact in the clock. Any exposure was thus of some whole number of seconds’ duration. The opening in the shutter was such as to let through, at the time of expo- sure, all of the direct beam which passed through d;, but to shut out NICHOLS AND HULL. -— PRESSURE DUE TO RADIATION. i stray light. Just beyond the shutter and attached to the diaphragm d; was a 45° glass plate which reflected a part of the beam to the lens Z,, by means of which an image of d; was projected upon one arm of a bolometer at A. The glass lens ZL, focused a sharp image of the aper- ture d; in the plane of the vanes of the torsion bal- ance B, under the bell-jar. The bell-jar was provided with three plate glass win- dows W,, W., Wz. The first two gave a circular opening 42 mm. in diam- eter, and through the third, deflections of the balance were read by a telescope and scale. The lens Ls was arranged to move hor- izontally between the stops S; and S, These were so adjusted that when the lens was against S; the sharp image of the aperture ds fell centrally upon one vane ; and when against S, the image fell centrally upon the other. This ad- justment, which was a very important one, was made by the aid of a telescope T,, mounted on the car- riage of a dividing engine. This was used to observe and measure the position ‘@ Guang SUt2 OF 571 572 PROCEEDINGS OF THE AMERICAN ACADEMY. of the rotation axis, as well as the positions of the images of d;, when the lens 1, was against the stops. For the latter measurements, the vanes could be moved out of the way by turning the suspension through 90° by the control magnet M (Fig. 2). To make sure that the balance as used was entirely free from any magnetic moment or disturbance, the small magnet m, was clamped in one position to maintain a constant zero, and the period of the balance was accurately measured with the axis of the large magnet JM in the ver- tical plane of the vanes and again when the axis was at right angles to the plane of the vanes. Several series of this sort failed to show a difference of 0.1 second in the period of the balance for the two positions of the magnet. Lo galv. G, Yy Yy Yj yyy yay tHe. Yy GY Y Yy Uy yyy Yo Lo galv. G; FIGureE 4. The bolometer at & (Fig. 3) was of sheet platinum 0.001 mm. thick, rolled in silver. The strip was cut out in the form shown in Fig. 4, and mounted on a thin sheet of slate S.. Two windows had been cut in the slate behind the strips at ABCD where the silver had been removed leaving the thin platinum. The platinum surfaces were blackened by Kurlbaum’s process. ‘The image from Z, (Fig. 3), fell at D. The sil- ver ends between A and C were connected with # and F respectively. On the heavy wire Fa sliding contact ¢ served to balance the bridge, all four arms of which are shown in the figure. MeruHops oF OBSERVATION. The observations leading to the results given later were of three differ- ent kinds: (1) The calibration of the torsion balance; (2) the measure- NICHOLS AND HULL. — PRESSURE DUE TO RADIATION, 578 ment of the pressure of radiation in terms of the constant of the balance; and (3) the measurement of the energy of the same beam in erg-seconds by the rate of temperature rise of a blackened silver disc, of known mass and specific heat. 1. The determination of the constant of the torsion balance was made by removing the vanes C' and D and accurately measuring the period of vibration. Its moment of inertia was easily computed from the masses and distribution of the various parts about the axis of rotation. The moment of torsion for 1 mm. deflection on a scale 105 cm. distant was 0.363 x 10~'dyne X cm. This value divided by one-half the distance between the centres of the light spots on the two vanes gave the force in dynes per scale division deflection. As the light spots were circles 11.25 mm. in diameter the area of the image was very nearly 1 (cm.)?, hence the above procedure gave roughly the pressure in dynes per square centimeter. 2. In the measurements of radiation pressure, it was easier to refer the intensity of the beam at each exposure to some arbitrary standard which could be kept constant than to try to hold the lamp as steady as would otherwise have been necessary. For this purpose, the bolometer at R (Fig. 3) was introduced, and simultaneous observations were made of the relative intensity of the reflected beam by the deflection of the galvanometer G,, and the pressure due to the transmitted beam by the deflection of the torsion balance. The actual deflection of the balance was then reduced to a deflection corresponding to a galvanometer deflec- tion of 100 scale divisions. The galvanometer sensitiveness was carefully tested at the beginning and end of each evening’s work. All observa- tions of pressure were thus reduced to the pressure due to a beam of fixed intensity. At each series of radiation pressure measurements, two sets of observa- tions were made. In one of these sets, static conditions were observed, and in the other, the deflections of the balance due to short exposures were measured. In the static observations, each vane of the balance was exposed in turn to the beam from the lamp, the exposures lasting until the turning points of the swings showed that stationary conditions had been reached. The moment of pressure of radiation and gas action combined would thus be equal to the product of the static deflection and the constant of the balance. The torsion system was then turned through 180° by rotating the outside magnet, and similar observations were made on the reverse side of the vanes. All turning points of the swinging balance in these observations were recorded. From the data 574 PROCEEDINGS OF THE AMERICAN ACADEMY. thus obtained the resultant of the combined radiation and gas forces could be determined for the time of every turning point. Every value was divided by the deflection at standard sensitiveness of the galvanometer G, read at the same time and was thus reduced to a standard lamp. Results thus obtained, together with the ballistic measurements, showed the direction and extent of the gas action as well as its variation with length of exposure. The reasons for reversing the suspension follow: The beam from the lamp, before reaching the balance, passed through three thick glass lenses and two glass plates. All wave-lengths destructively absorbed by the glass were thus sifted out of the beam by the time it reached the balance vanes. The silver coatings on the vanes absorbed therefore more than the glass. ‘The radiation pressure was always away from the source irrespective of the way the vanes were turned, while the gas action would be exerted mainly on the silvered sides of the vanes. At the close of the pressure and energy measurements, when the re- flecting power of the silver faces of the vanes was compared with that of the glass-silver faces, the reflection from the silver faces was found very much higher than that for the glass faces backed by silver. This result was the more surprising because the absorption of the unsilvered vanes was found by measurement to be negligibly small.* This unexpected difference in reflecting power of the two faces of the mirrors prevented the elimination of the gas action, by the method described, from being as complete as had been hoped for. But by choosing a gas pressure where the gas action after long exposure is small, the whole gas effect during the time of a ballistic exposure may be so reduced as to be of little con- sequence in any case. By exposing each of the vanes in turn and by reversing the suspension and averaging results, nearly all errors due to lack of symmetry in the balance or in the position of the light images with reference to the rota- tion axis, or errors due to lack of uniformity in the distribution of intensity in different parts of the image, could be eliminated. The changing character of the gas action, both with time of exposure and gas pressure surrounding the balance vanes, is well illustrated in eight series of static observations in which the glass faces of both vanes were exposed. The results obtained on the two vanes were averaged * Lord Rayleigh records a similar difference between the reflection from air- silver and glass-silver surfaces. Scientific Papers, Cambridge, IL 538-539 (1900). + Observations were also made on the silver faces, but the gas action when the glass faces were exposed was nearly double that for the silver faces, so the least favorable case is shown. NICHOLS AND HULL. — PRESSURE DUE TO RADIATION, 575 Ti a ead a a Peace Pee Rane ce niente mirmn arr h oe CEPA EEE ae eee t Et eS a eee JSSBESNeIOREPs cane eRB Senn SCaOaT Ae Bearer eR aaenOReeneee fecal PN eee SEE EL ele al alalaa Pmmleliea ot oh Re ee aii | BREDIe Ree EEE Cen eae ee te alae let te eee el Ss L Pe eon alae SE CA/PERRS eH Y Eee oe 8 A & “ap aa Seees4eess=4555-- Pol e-d ees ences bo cee poem dee eeeee “ys 20, = an ee ome eae eee eneeconele aaiice SS) ALIS 2 Sr SS S SSh= = - a 0m eR S es eg eee ee ee aetna ieee ee See eo eee oer Ss " [RS pe es + ———} ——} 5 AEH ee Acinic < @ LAA EEE oer eee WGGete same ABB | el NNEC Liono} te Saabs 1 POMEL CELL CCE Lic. ls aio RI OBEN rs St ee ede ed a Pa an amp oat) Pag ee ee ee a PEEEA EL eS RSEEEHEE PEPPERS CELE I\ Nema Be BEEP ae oe eee ef emsv a e a fs a hi lo EERE Ree RE err mPiceite cca ame ese ah eA RE Cs es CoH 0 Cm a dS SI ELE eaee ee ale iz Be ap ee er os moe | Figure 5. and plotted as curves in Fig. 5, where static deflections due to combined radiation pressure and gas action are shown as ordinates and duration of exposure, in seconds, as absciss.* A horizontal line through the diagram * Ordinates of the curves are proportional to moments. 576 PROCEEDINGS OF THE AMERICAN ACADEMY. gives the mean value of the moment of radiation pressure computed from the data in Table II. Decrease of the deflection with time indi- cates gas repulsion on the warmed silver faces and increase in deflection, gas suction. It will be seen from the curves that beginning at a gas pressure of 66 mm. of mercury, the gas action was repulsion changing to suction in passing from 19.8 to 11.2 mm. In the last two cases the total gas action is small. For lower pressures the suction increases to 0.05 mm. At a gas pressure of 0.02 mm. the gas action is again a strong repulsion. The curves indicate the existence of two gas pressures, at which the gas action in our arrangement of apparatus should be zero, one between 19.8 and 11.2 mm. and the other between 0.05 and 0.02 mm.* The former region was chosen for the ballistic measurements and nearly all of the observations were made at a gas pressure of approximately 16mm. Even for the two pressures where the decrease in the static deflection was most rapid, i. e. at gas pressures of 66 and 0.02 mm., the first throw was always in the direction of radiation pressure. The gas action is strongly influenced by very slight changes in the inclination of the plane of the vanes to the vertical and also by any object intro- duced under the bell-jar anywhere near the vanes. For instance, a very considerable effect was observed when a small vessel of phosphoric anhydride was placed under the jar behind the vanes, though the nearest wall of the vessel was separated from the vanes by a distance of at least 3 cms. During the observations, the polished silver coatings on the vanes deteriorated rapidly ; new coatings rarely lasted for more than two even- ings’ work. As the balance had to be removed and the mirrors taken from the hooks, silvered, polished, and replaced a great number of times during the entire series of measurements, although great care was taken in setting the plane of the vanes vertical, it is not likely that precisely the same conditions for gas action were ever repeated. The principal value of the static results was in indicating favorable gas pressures for work, rather than affording quantitative estimates of the gas action in short exposures. The dotted parts of the curves are not based on results of observation and might perhaps have been omitted without loss. * Crookes in his work with the radiometer discovered certain gas pressures for which the combined gas and radiation forces neutralized, but as he did not discriminate between forces due to radiation and gas forces his results were apparently capricious and his reasoning somewhat confused. See Phil. Trans., p- 519 (1876). NICHOLS AND HULL. — PRESSURE DUE TO RADIATION. 577 It was plain, therefore, that further elimination of the gas action must be sought in exposures so short that the gas action would not have time to reach more than a small fraction of its stationary value. This led to the method of ballistic observations. Tue BA.L.ListTic OBSERVATIONS. In passing from the static to the ballistic observations it must always be possible to compute the static equivalent of the ballistic swings. Furthermore the exposures should be made as short as possible without reducing the size of the swing below a value which can be accurately measured. If the exposure lasts for one-half the period of the balance, the deflec- tion, if the gas action be small and the damping zero, is equal to 2 8, where @ is the angle at which the torsion of the fibre will balance the moment produced by the radiation pressure. If the duration of the exposure be one-quarter of the period of the balance, the angle of deflec- tion is 04/2. The deflection is thus reduced by 30 per cent, but the effect of the gas action is reduced in greater proportion. It was decided therefore to expose for six seconds, one-quarter of the balance period. Neglecting the gas action, the equation * of motion of the balance is given by 36 o6 where x = the moment of inertia of the torsion balance, e = the damping constant, G = the moment of torsion of the fibre for 6 = 1 radian, and = the moment of the radiation force. The solution of this equation is L — Box: iron-constantan thermo- junctions, made by sold- ering 0.1 mm. wires of the two metals, were drawn through the holes into the centre of the disc. To insulate the wires from the disc, fine drawn glass tubes B were slipped over them bie arene te and thrust into the holes, leaving less than 2 mm. bare wire on either side of the junctions. The wires were sealed into the tubes, and the tubes into the disc by solid shellac. The tubes projected 15 mm. or more from the disc and were bent upward in planes parallel to the faces of Water Jacket Ficure 6. NICHOLS AND HULL. — PRESSURE DUE TO RADIATION. 585 the disc. The general arrangement will be seen in Fig. 6. The disc was suspended by the four wires some distance below a small flat wooden box. On the box was fastened a calorimeter can swathed in cotton and filled with kerosene in which the constant thermo-junctions were immersed. Copper wires soldered to the two ends of the thermo-electric series were brought out of the calorimeter, and the circuit was closed through 1000 ohms in series with the 500 ohms resistance of galvanometer G,. The thermo-junctions in the disc were in series, and as each junction was mid- way between the central plane of the disc and either face, it was assumed that when the disc was slowly warmed by heating one face the electro- motive forces obtained corresponded to the mean temperature of the disc. One face of the disc was blackened by spraying it with powdered lampblack in alcohol containing a trace of shellac. This method was suggested by Prof. G. E. Hale and gives very fine and uniform dead black coatings not inferior to good smoke deposits. For the energy measurements the bell-jar and the torsion balance were removed from the platform P (Fig. 2) and a double walled copper vessel, AB (Fig. 6), which served as a water jacket surrounding a small air chamber C, was mounted in the same place. A tube 2 cm. in diameter was soldered into the front face of the jacket to admit the light beam into the chamber C. This opening was covered by a piece of plate glass similar to the plates forming the larger windows in the bell-jar. The needle system in Gj, a four-coil du Bois Rubens galvanometer, was suspended in a strong magnetic field so that its period was about four seconds. The system was heavily damped by a mica air-fan of large surface. The disc junctions and galvanometer responded quickly to the radiation, as was shown by the reversal of motion of the magnet system 1.2 seconds after the light was cut off from the disc when the latter was a few degrees above the temperature of the room. The disc was calibrated for temperature in-terms of the deflection for a definite sensitiveness of the galvanometer G,. For this purpose the disc was immersed in a kerosene bath and the galvanometer deflection measured for two different temperatures of the disc. One of these was about 18° C. above the comparatively steady temperature of the room, or calorimeter containing the standard temperature junctions (see Fig. 6), and the other about the same number of degrees below the room temper- ature. These two temperatures were measured by a Fuess Standard Thermometer divided into tenths of a degree and calibrated at the Reichsanstalt. Two calibrations of the silver disc were made some days apart. One of these series appears in full in Table V. The first three 586 PROCEEDINGS OF THE AMERICAN ACADEMY, TABLE V. CALIBRATION OF SILVER Disc. Cold Bath. G, Readings. dbase ag Means of 1 alternate Direct. s P - | Deflee’ns. 20° 20 ~hN WOW SL 20°.22 Spo Wp Wp WS 20°.26 INES SS ONO RS Wr wm 8s bo 36.3 : 20°.30 Lee) Sok SSS) &s SS) S to tS ee a Correction to T; = 0°.00. Warm Bath. 41°.45 | 20°.40 419.85 | 20°.42 3. 216.1 | 20.98 41°.25 | 20°.44 : 214.1 | 20.81 41°.08 | 20°.50 ; 211.7 |. 20.58 40°.90 | 20°.55 : 209.4 | 20.35 40°.80 | 20°.60 : 207.6 | 20.20 40°.67 | 20°.61 : 205.8 | 20.07 | 40°.55 | 20°.63 8 | 2042 | 19.92 429.4 40°.43 | 20°.65 209.8 | 20°.41 Correction to T, = 0°.10. Corrected, 20.51 NICHOLS AND HULL. — PRESSURE DUE TO RADIATION. 587 columns of the table give the zero, direct and reversed reading of the gal- vanometer G,. The fourth column gives the temperature of the bath in which the disc was immersed, and the fifth, that of the constant tempera- ture calorimeter. The sixth column gives the deflections of G;. The seventh column the means of the alternate deflections. The eighth, the mean of the two columns preceding it. The last column gives the difference in temperature between the two calorimeters in degrees C. For the total temperature range in the table, 39.11°, the deflection of G, was 393.8 scale divisions for a sensitiveness of G,= 996. A range of one degree would thus give a deflection of 10.03 divisions for a sensitive- ness of G,= 1000. The mean of two separate calibrations was 9.96 scale divisions for one degree temperature difference. Before beginning a series of intensity measurements the disc was suspended in an air-chamber containing phosphoric anhydride and sur- rounded by a jacket of ice and salt. The disc was thus lowered to a temperature of about zero degrees and was then quickly transferred to the chamber C (Fig. 6), and the beam was directed upon it. When its temperature had risen to within five or six degrees of that of the chamber C, galvanometer readings were made at intervals of five seconds until the disc was heated to a temperature several degrees above its surroundings. The temperature of the chamber C was determined by removing the disc and cooling it to a point near the room temperature, then replacing it and observing its rate of temperature change for several minutes. The notebook record of one series of observations showing the heat- ing of the disc by the light beam is given in full in Table VI. It will be seen from the table that the temperature of the disc passed that of the chamber thirty seconds after the beginning of the series. The readings of G, at equal time intervals on either side of the zero are on horizontal lines. The last column of the table contains the rate at which the galvanometer deflection was changing when the disc and its surround- ings were at the same temperature. Energy series were made ‘through air,” “through red glass,” and “through water cell,” as in the pressure measurements. During the experiment the black coatings were frequently cleaned off from the disc and new ones deposited. The final result therefore does not correspond to an individual, but to an average coating. To correct for any inequality between the two disc thermo-junctions or any lack of symmetry in their positions, referred to the central plane of the disc, which might prevent the mean temperature of the two junctions from representing the mean temperature of the mass, series of 588 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE VI. Avucust 16. ENERGY MEASUREMENTS. THROUGH AIR. SERIES 4. Zero of Galvanometer G, (closed circuit) determined by method of cooling = 216.8 = reading at room temperature. AG,. 78.7 60 secs. 65.3 50 62.3 39.0 26.1 13.1 Average The lamp reading (G,) was 924. The sensitiveness of G, was 667, and of G, was 996 G At 108 x 0.954 all OSE sue Siat SS Ee x 10° dynes 3 x 10% "0.954 = (7.05 + 0.03) x 10~ dynes ; 1.848 y 0.986 3 x 10% " 0.954 BRU erica ne ure uC = 1.078 x gS 0n * 0.954 she 10 dynes = (6.86 + 0.03) x 10-° dynes; (6) through red glass = E, X 1.848 0.995 (c) through water = resis Je * 3x 10 x 0.954 1.848 0.995 = 1,008 x —=————. x —~— x 10° dynes 3 x 10° “ 0.954 = (6.48 + 0.04) x 107° dynes. * As the average pitch of the cone of the incident beam was about one part in forty, no correction need be applied for inclination. Furthermore, the inside of the bell-jar was blackened and the zero of the balance was so chosen that energy reflected from the window admitting the beam could produce no pressure effects. NICHOLS AND HULL. —PRESSURE DUE TO RADIATION. 597 A comparison of observed and computed pressures follows : — Observed values Computed values Obs.-comp. in 10-5 dynes. in 10~5 dynes. in percentages. Through air, p= C.0lc- 0:02 * 7.05 + 0.038 — 0.6 Through red glass, p = 6.94 + 0.02 6.86 + 0.03 + 1.1 Through water, p= 6.02 + 0.03 6.48 + 0.04 — 0.6 An estimate of the approximate magnitude of the gas action, not elimi- nated by the ballistic method of observation, may be reached from the following considerations. When radiation falls upon a vane of the torsion balance, part of it is absorbed by the silver surface. From the amounts directly and diffusely reflected, as given in Table X, the amount transmitted by the average surface (experimentally determined but not given in Table X), the effect of the glass rod and the reflection coefficient of the glass surface, it was found that, when the silver side of the vane was toward the radiation source, the absorption coefficient for radiation through air was 6 per cent, and when the glass surface was forward, it was 18 per cent. The total force acting on the vane is made up of two parts, that due to radiation pressure and that due to gas action. Let F, be the force due to the first cause, assuming that all the radiation is absorbed, and F, the effect due to the second, on the same condition. Then the total effect, when the silver side of the vane is forward and the radiation is “through air,” is 1.92 F,+ 0.06 F,. When the glass side is forward the total effect is 1.776 F,— 0.18 F,. Making these expressions equal to the reduced deflections (Table III, columns 11 and 12) on the silver and glass surfaces respectively, we have two equations by means of which the values of F, and #, may be obtained. Hence the effect due to gas action on each face of the vane is approximately determinate, as is * The pressure and energy measurements for the three different wave groups through air, red glass, and water cell, constitute three independent experiments. In the values for pressure, 7.01, 6.94, and 6.52, equality is not to be looked for. The difference arises from the different reflecting power of the 45° glass plate (Fig. 5) for the different beams and from the fact that the indications of the lamp galvanometer G, connected with the bolometer R, were probably not strictly pro- portional to energy for throws differing as widely as 33, 60, and 100, which, roughly, were the relative intensities of the beams through water cell, red glass, and air. The function of the lamp bolometer and galvanometer was purely to keep a check on the small variations of the lamp which rarely fluctuated more than 10 per cent on either side of the mean value. 598 PROCEEDINGS OF THE AMERICAN ACADEMY. also the part (0.06 /,) not eliminated when we average the two columns to obtain column 13. Applying this method to all the results of Table III (with the exception of those results taken with poor mirrors as shown by our notes), the gas action present in the ballistic deflections “ through air” is 0.8 per cent. Applying the corresponding data and equations to Table IV, the gas action present in the red glass values is 1.1 per cent and in the water cell values, 0.3 per cent. The sign of /, comes out negative, which means that the gas action was suction. This reasoning assumes that the glass faces of the vanes during the six seconds exposure are not warmed by absorption nor by the conduction of heat through the thin glass from the silver coating. The effect of any such absorption or conduction would be to diminish the computed gas action. As estimated from the static observations, the gas action in the ballistic measurements is comparable in magnitude with the computed values obtained above, and of the same sign. Both results show that the uneliminated gas action by the most liberal estimate cannot have ex- ceeded 1 per cent of the radiation pressure. Because of its smallness and indefiniteness no correction for gas action has been made to the final pressure values. If corrections were applied its effect would be to slightly reduce the observed pressures. Aside from the measurements of pressure and energy for which the probable errors are given, the percentage accuracies in the other measurements entering into the computations, and their effects upon the final result follow :— 1. Quantities which affect individual series : (a) Pressure values, — Period of balance T, accurate to 0.2% ; effect on result 0.0% Lever arm of balance J, 2 0.1% ; a x 0.0% Constant of galv’meter Gy, a 0.5% ; a te 0.0% Estimate of possible error due to changing ratio of period of G, to length of exposure of bolometer 0.4% ; cc “ 0.1% (6) Energy values, — Constant of galv’meter G, « 0.1% ; ue « 0.0% 3 73 G., ““ 0.5% ; 66 “ 0.0% NICHOLS AND HULL. — PRESSURE DUE TO RADIATION. 599 2. Quantities which affect final averages : (a) Pressure values, — Torsion of fibre, accurate to 0.2% ; effect on result 0.2% Reducing factor, 1.357 é OS = 6 és 0.1% Reducing factor, 1.550 for G, 66 0.2% ; ‘< ms 0.2% Reflection of surfaces of vanes “c 0.4% ; i! a 0.2% (6) Energy values, — Mass of silver disc es 0.1% ; ae = 0.1% Thermal calibration of disc We 0.5% ; es - 0.5% Diffuse reflection black coating “6 5.0% ; “ “ 0.1% From the agreement within the probable error of the air, red glass, and water values with the theory, it appears that the radiation pressure depends only upon the intensity of the radiation and is independent of the wave length. The Maxwell-Bartoli theory is thus quantitatively confirmed within the probable errors of observation. To Professor J. L. Mann, and Messrs. J. A. Brown, Philip Fox, L. E. Woodman, H. R. Willard, H. E. K. Ruppel, and A. V. Ruggles, the writers are indebted for friendly assistance given at some of the stages in the protracted course of these experiments. Wiper Lasoratory, DartmoutH COLLEGE, Hanover, N. H. Proceedings of the American Academy of Arts and Sciences. Vout. XXXVI. No. 21. — Apri, 1903. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 142. THE HEREDITY OF ALBINISM. By W. E. CAsTtLe AND GLOVER M. ALLEN. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR.—No. 142. THE HEREDITY OF ALBINISM. By W. E. CastLe AND GuLoverR M. ALLEN. Received March 11, 1903. ConTENTS. PAGE I. Introduction .. . 5 Ae OMA MORIN Gee ces If. Complete Albinism a Pavesi Omer Jeti New Cuan ares ele! (@)) Abi MING 5 bc Sh en ieotay a) wate ornate GU () In Other Miataenals) in Eehes Ane in ‘Plants skate lp 606 III. Partial Albinism a Mosaic of Dominant and Recessive Chatactees) and asWmithneeeredityany ys cv cy cules stone siemens Venlseat ee nea OO NY, Binge? havo! Jehylorel MOREE VG ood 6 ot 6. ob Yao 6 2 Seto tg 6 Colil V. Pureand Impure Recessives. . . Bo oe (als VI. Cross-breeding, Reversion, and the Doctrine of Gameuc Bante Boo, (alley AVAL SUTIN AT Val Estey look ei yell cf cgeem epirell hhh ct fe vib st et scot el Oimigh elle sf rena! cea IG VICI SO GNSS oe 6 ol fo Bde © Bose 6 0 6 o GAT I. INTRODUCTION. TuHIs paper contains a preliminary statement of certain results of breeding experiments with mice, guinea-pigs, and rabbits, which have been conducted in the Zodlogical Laboratory of Harvard University during the last two and a half years. The experiments with mice are the work principally of the junior author; those with guinea-pigs and rabbits, of the senior author. Albinism, or absence of the normal pigmentation of an organism, is a not infrequent phenomenon in both animals and plants, yet its occurrence in nature is sporadic and has usually been interpreted as an indication of organic weakness. But this interpretation is probably erroneous, for albino races of domesticated animals are apparently not inferior in vigor to other races. Such is demonstrably the case with albino mice. The idea that albinos lack constitutional vigor may have its origin in the observation that, in crosses between albinos and normal individuals, 604 PROCEEDINGS OF THE AMERICAN ACADEMY, no albino offspring are produced. But the disappearance of albinism in this case is not final. The albino character has not ceased to exist, but has merely become latent in the offspring. It will reappear unimpaired in the next generation if the cross-bred individuals be mated znter se. II. CompLetTe ALBINISM A RECESSIVE CHARACTER. The disappearance of the albino character for a generation, and its subsequent reappearance under close breeding, show that it is inherited in conformity with Mendel’s law of heredity,* and that it is, in the terminology of that law, a recessive character. (a) In Mice. In mice this has been conclusively demonstrated by Cuénot (: 02), who, on crossing wild gray house-mice with albinos, obtained always gray mice indistinguishable in appearance from the pigmented parent. Yet these gray hybrids, when bred inter se, produced both gray and white offspring approximately in the Mendelian ratio, 3:1. The exact numbers recorded are 198 gray: 72 white, or 26.6 per cent albinos. According to Mendelian principles the grays of this second filial gener- ation should consist in part of pure grays, which would not transmit the albino character, and in part of hybrid grays like their parents, — the first filial generation, — which would transmit alike the pigmented and the albino characters. This Cuénot demonstrated to be actually so, for certain pairs formed by random selection of the grays gave only gray offspring (189 individuals); the remaining pairs produced albino as well as gray offspring, and in the expected ratio, 3 grays: 1 albino. * A brief statement of Mendel’s law has been made by one of us elsewhere (Castle, :03*). Fora fuller exposition, see Bateson (:02), Bateson and Saunders (:02), de Vries (:02), or Correns (:O1). + In an earlier paper (Castle, :03*) the first published recognition of the reces- sive nature of albinism in mice is erroneously credited to Bateson (:02). The papers of Cuénot (:02, :02*), which at that time were unknown to us, apparently antedate Bateson’s. Crampe (’85) seems to have been the first to recognize clearly that the first cross between pigmented and unpigmented (albino) varieties gives rise, in the case of rats, to pigmented individuals, not to albinos. Crampe crossed gray, black, gray-white, and black rats (Mus norvegicus) with albinos, and found that in each cross the albino character disappeared. He noticed also that the albino character might reappear in subsequent generations, but he did not discover the conditions necessary for this reappearance beyond establishing that albino offspring were produced under close breeding by those pigmented! rats only in whose immediate ancestry there had been a cross with the albino form. CASTLE AND ALLEN. — THE HEREDITY OF ALBINISM. 605 The precise numbers recorded are 162 grays: 57 albinos, or 26 per cent albinos. Cuénot’s observations are fully substantiated by experiments performed by the junior author of this paper, a full account of which will be pub- lished elsewhere. Wild gray mice were crossed with albino mice, and the offspring, sixty-four in number, were all gray like the wild parent, though a single litter of three young, which died without attaining their full growth, were of a somewhat lighter gray than the wild parent. Certain of the cross-breds were paired together, and produced 66 off- spring, 42 of which were gray, 24 white. This is a considerable devia- tion from the expected ratio, 3:1, but it should be remembered that the total number is relatively small. ‘The result is of the nature expected, in that both gray and albino offspring are produced, and of the former a larger number than of the latter. To determine whether the grays are, as expected, of two sorts, one hybrid, the other pure, six pigmented individuals have been crossed with the parental white stock. ‘Three of the six have thus far produced only pigmented offspring, indicating that they are pure; the other three have produced both gray offspring and white offspring, showing that they are hybrids. The two sorts of offspring produced in the case last mentioned should, according to Mendelian expectation, be equally numerous. The numbers thus far recorded are 35 pigmented individuals: 23 albinos, a result agreeing with expectation in that both gray and white offspring are produced, though these are not in the exact proportions demanded by Mendel’s laws. ' If we combine the results of this cross with those obtained by inter- breeding hybrids of the first filial generation, we get for the whole a close agreement between expectation and observation. The expectation is 78.5 gray: 45.5 white; the observed result is 77 gray: 47 white. White mice obtained by one or the other of these crosses have repeatedly been bred together, but without the occurrence of a single exception to the expected Mendelian result, the offspring being invariably albinos. A further test of the Mendelian hypothesis as applied to albinism in mice was made by Cuénot. By back-crossing hybrid grays with the an- cestral white stock he obtained gray as well as white individuals, which in the phraseology of breeders should be 3, 3, %, etc., white “ blood,” yet all the grays, irrespective of ancestry, gave precisely similar results in crosses with whites, viz. equal numbers of gray and white offspring. It is evident, then, that when a pure gray race of mice is crossed with a pure white race, the gray character invariably dominates in the off- 606 PROCEEDINGS OF THE AMERICAN ACADEMY. spring, and in subsequent generations both gray individuals and white individuals occur approximately in the proportions demanded by Mendel’s principles of dominance and segregation. No better illustration of Men- del’s law has yet been produced than is afforded by the cross between gray and white mice. (6) In Other Mammals, in Fishes, and in Plants. Tn the case of guinea-pigs, we have many times mated together albinos born of mottled parents, or obtained by mating a mottled with a white animal, but never with any but the expected Mendelian result, all the young being albinos. In the case of rabbits, the same law appears to hold. Professor R. T. Jackson kindly placed at our disposal last summer three white rabbits, a male and two females, all born in the same litter, of spotted parentage. The two females have borne by their brother, in three litters, seventeen young, all albinos. In man, Farrabee (:03) and Castle (: 03) have recently shown albi- nism to be in all probability recessive. As to fishes, Dr. Hugh M. Smith, of the United States Fish Commis- sion, informs us that in one of the State fish-hatcheries of this country there is bred as a curiosity a race of albino trout which “ breed true,” indicating that the albino character is recessive. In plants, more than two-thirds of the Mendelian cases mentieeed by de Vries (: 02, p. 146) are cases of “ depigmentation ” of flowers or fruit, the depigmented condition being invariably recessive in crosses with the normal condition. It appears, then, that in organisms in general, albinism behaves as a recessive character in heredity.* III. Partiat Atpsrnism A Mosaic or DOMINANT AND RECESSIVE CHARACTERS, AND A UNIT IN Herepity. Darbishire (:02 ) finds that in crosses between a peculiar race of par- tial albino mice and true albinos, the albinism does not entirely disappear in the offspring, and he thinks that this weighs heavily against the entire * The only exception known to the writers is the dominance of white plumage, in certain crosses of poultry, as recorded by Bateson and Saunders (: 02). Yet the dominant character in this case is one of partial albinism only, and its dominance is not invariable. We suspect that the dominance of white plumage results from its coupling in the gametes with some other character strongly dominant by nature. CASTLE AND ALLEN. — THE HEREDITY OF ALBINISM. 607 Mendelian hypothesis. In reality Darbishire’s observations, when rightly interpreted, afford strong evidence in favor of that hypothesis. It may be weil, therefore, to examine them with some care. But before doing so one or two earlier observations should be noticed. Haacke (’95) crossed spotted blue-[black-]and-white Japanese dancing mice with albino mice, and obtained offspring uniformly gray in color, like the wild house-mouse, or uniformly black. Occasionally, however, one of the gray or black offspring bore a fleck of white on forehead or belly. Von Guaita (’98, :00) repeated the experiment, crossing spotted black- and-white Japanese dancing mice with an inbred stock of albinos. He obtained twenty-eight young, all uniformly gray like the house-mouse. These gray mice bred znter se yielded in subsequent generations gray, gray-white, black, black-white, and white offspring. Darbishire’s experiment consisted in crossing albino mice with a peculiar race of Japanese dancing mice which had pink eyes and were uniformly white except for patches of pale fawn-color on the cheeks, shoulders, and rump. The dancing mice had been tested and found to breed true inter se. From the cross between these partial albinos and true albinos forty-eight young were obtained, of which all except two were marked more or less extensively with gray; those two were fawn- color all over except on the belly, where — we infer from Darbishire’s likening them to certain of his gray mice — they were either of a lighter fawn-color or else white. Of the forty-six young which were marked with gray, fifteen were gray all over except on the belly and tail, where they are said to have been “nearly white.” What is meant by this expression we do not know, unless it be a light shade of gray. If this is the author’s meaning, then the fifteen mice were really gray all over. The wild house-mouse itself is often lighter colored on the belly and tail, and these fifteen individuals must be regarded as substantially complete reversions to the gray pigmented type of the wild house-mouse, a type radically different from that of either parent. This result agrees with that obtained by Haacke (95), von Guaita (’98, :00), and ourselves, upon crossing spotted with albino mice. In thirteen of the forty-six gray-marked mice obtained by Darbishire, the gray covered much more of the body than did the fawn in the Japanese parent; while in eighteen others the gray corresponded roughly in distribution with that of fawn in the Japanese parent. In no case is the gray described as being less extensive than the fawn in the Japanese parent, and no mention is made of any hybrid 608 PROCEEDINGS OF THE AMERICAN ACADEMY. having pink eyes, though both parents had unpigmented eyes.* Not only were the offspring not intermediate in pigmentation between the two parents, as we should expect on any hypothesis other than the Mendelian one, but not a single mouse in the forty-eight contained as little pigment as was found in the pigmented parent. In every case the pigmentation was greatly increased over what it had been in the pigmented parent, either in intensity or in extent, and usually in both respects. ot a single albino was produced, though the mother had been in every case an albino. Yet Darbishire maintains that the case is not one of Men- delian dominance ! It is hard to imagine a plainer case of Mendelian dominance than this, — a spotted mouse is bred to a white mouse; the offspring are all spotted, none white. The spotted character is plainly dominant, the white, recessive! What would Darbishire require to satisfy him that the case is a Mendelian one? Offspring all like nether parent, but like a third form, a supposed ancestral form. But is this simple dominance? No, it is dominance associated with something else, reversion, i.e., the coming again into activity of a character long latent, in this case the formation of black pigment. Because the reversion is not in every case complete, Darbishire maintains there is no dominance, a conclusion utterly fallacious. What is the true explanation of cases of heredity like that observed by Darbishire? The explanation has been given elsewhere by one of us (Castle, :03"), but it may be well to repeat it here. Albinism is in mice and other mammals a character recessive in relation to the pigmented condition. But the spotted mouse is not a simple dominant (pigmented) individual as contrasted with simple recessive (albino) individuals. The spotted mouse is a peculiar kind of individual, in which are found both the dominant and the recessive characters, yet not in their usual relationship (one latent, the other alone visible), but both visible side by side, in distinct areas of the animal’s body. Such an individual is called a mosaic. In the soma of a mosaic individual the law of dominance is suspended, but cross-breeding serves usually to bring it again into opera- tion in the next generation, for the crossing of a mosaic with a normal, or with a recessive individual, results usually in the production of nor- mally pigmented individuals only. ‘Thus when spotted rats or mice are crossed either with gray individuals (dominants) or with albinos (reces- * This significant omission was observed by Bateson also, who mentions it in a letter received since the above paragraph was written. CASTLE AND ALLEN,—THE HEREDITY OF ALBINISM. 609 sives), the offspring are commonly all gray or black in color, none spotted. Here we find that dominant and recessive characters have abandoned the balanced relationship which they had in the spotted parent, and returned to the ordinary relationship of a dominant to a recessive character. Just as in mosaic individuals the law of dominance is suspended, so, too, in the formation of their gametes the law of segregation is commonly suspended also. The gametes, as well as the soma, of a mosaic indi- vidual are commonly mosaic, containing side by side the dominant and the recessive characters. For it is evident from the experiments of Haacke, von Guaita, and Darbishire that the spotted mice employed by them in crosses with albino mice did not form any gametes containing only the recessive (albino) character, otherwise albino offspring would have been produced, but not one was produced. Hence segregation of the pigment-forming character from the albino character cannot have occurred at the formation of gametes in these several cases, but the gametes themselves must have possessed a mosaic (or else a dominant) character. A similar explanation must be made of certain results obtained by one of us in crossing black-white (not dancing) mice with albino mice. Two spotted males of a black-white stock which bred true inter se, were crossed with albinos. The offspring were like those obtained by Haacke in crossing Japanese dancing mice with albinos, namely, mice uniformly gray or black in color, though sometimes with a fleck of white on-the belly, or with one or more white bands on the tail. Of the forty-three young produced by this cross, twenty-eight were gray, and fifteen black. The fact that no albino offspring were produced shows that the spotted males formed no recessive gametes, but only those which were either mosaic, or else purely dominant, in character. But if dominant gametes had been formed by segregation from a dominant-recessive mosaic, we should expect that by a residual process recessive gametes would be formed also. The latter not having been formed, it is safe to suppose that the former were not formed either, but that all the gametes formed by these spotted males were mosave. That the albino character entered as a latent constituent into the gray or black hybrids formed by the cross just described, is shown conclusively by the character of their offspring. When bred inter se they produced albino as well as pigmented offspring, and approximately in the ratio, 1:3; or, when bred to albinos, in the ratio, 1:1. Accordingly, in the original cross described, we have a case of simple VOL, XXXVIII.— 89 610 PROCEEDINGS OF THE AMERICAN ACADEMY. dominance of the pigment-forming over the albino character. This dominance is attended, in about two cases out of three, by reversion to the particular form of pigmentation found in the wild house-mouse. The reversion is due to the coming into activity of a capacity (previously latent) to form yellow pigment, which with black pigment forms gray. This latent capacity must have been present in one or the other or possibly in both of the parents crossed. Darbishire’s results differ from ours only in degree, not in kind. He, too, gets invariably dominance of the pigment-forming over the albino character, and this is associated in all except two out of forty-eight cases with reversion to the ancestral kind of pigmentation, gray. The only differences between his results and our own are as follows: — 1. In our experiments yellow was the latent constituent of gray which was brought into activity by a cross with albinos; in the experiments of Darbishire black was the latent constituent brought into activity. 2. In our experiments white disappeared for the most part from the bodies of the hybrids ; but in Darbishire’s experiments the disappearance of white was much less complete. ‘There was a strong tendency for the mosaic gamete to dominate as a unit without serious disturbance of the balanced relationship of pigmented and unpigmented areas in the mosaic structure. This tendency is observable in thirty-one out of forty-eight cases. ‘The remaining seventeen cases are strictly comparable with our own. In fifteen of them the black character, latent in one or possibly in both parents, has become active and, combining with yellow (fawn), visible in one parent, has formed gray; in the other two offspring, black, if present, has remained latent, leaving the individuals fawn-colored. This result is comparable with the production of black hybrids in our own experiments. In Darbishire’s experiments, as in our own, the effect of a cross with albinos is to release the dominant character from the strict localization which it had in the mosaic parent. In Darbishire’s mosaic mice the localization of pigment was much more rigid than in our own. His mice bore pigment only on the shoulders and rump, and had pink eyes; ours were pigmented over at least half of the body and had black eyes. It is not surprising, then, that the pigmentation should be less extensive in Darbishire’s hybrid mice than in our own. Yet it is evident that in all his hybrids there occurred release, more or less complete, of the pig- ment-forming character from its localization in the original mosaic. In every case, apparently, the hybrid had pigmented eyes, though neither parent possessed this character. CASTLE AND ALLEN.— THE HEREDITY OF ALBINISM. 611 IV. Pure anp Hysrip Mosaics. In our experiments in crossing spotted with albino mice, a third black- white male was employed. He was a half-brother* to the two spotted males previously mentioned, born of the same mother but by a different sire. The white areas on his body were less extensive than those on his two brothers. He was bred to the same stock of white females as they, but with different results. By him the albinos bore albino as well as pigmented offspring; of the former twenty-one, of the latter twelve, ten being gray and two black. The albino offspring were found in this case, as in all others tested, to breed true inter se. It is evident that the third black-white male differed in nature from his two half-brothers, for he formed recessive gametes, whereas they did not. Examination of other breeding records of spotted mice kept by us during the past two years shows that it is possible in these also to dis- tinguish two different sorts of mosaic individuals. These are: — 1. Pure mosaics, spotted and forming only mosaic gametes, DR. They bred true inter se, but when crossed with albinos produce only individuals of the following class. 2. Hybrid mosaics, usually more extensively pigmented than pure mosaics, often pigmented all over. (Compare the results of Haacke, von Guaita, and Darbishire.) They form, in approximately equal numbers, mosaic and recessive gametes, D/? and # respectively. Accordingly, when bred inter se, they produce offspring of three different sorts, D R, DR: (Rk) [or D(R) + (&)],F and R£, that is, pure mosaics, hybrid mosaics, and recessives. Theoretically these three classes of offspring should be numerically as 1: 2:1. There is reason to believe that these proportions are approximated in our experiments, but this matter has not yet been fully tested. When bred to albinos, hybrid mosaics produce (in equal numbers?) hybrid mosaic and albino offspring. It is possible to recognize in the experiments of von Guaita also these two different classes of mosaics. Von Guaita’s original stock of dancing mice consisted of pure mosaics, for they bred true iter se and when bred * In an earlier paper (Castle, :03, p. 542) it is stated erroneously that this mouse was an own brother to the other two. + The period is used to indicate the distinctness, in the zygote, of the gametes which united to form that zygote, as well as to show that, when in the hybrid individual segregation of characters takes place at gamete formation, splitting will occur at the point marked by the period, producing gametes DR and R. 612 PROCEEDINGS OF THE AMERICAN ACADEMY. to albinos produced only pigmented offspring. These offspring, though not themselves spotted, were clearly hybrid mosaics, for when bred inter se they produced spotted as well as albino offspring, of the former nine, of the latter fourteen, in a total of forty-four young; the expectation on our hypothesis is eleven of each! The idea that there are, as just explained, two different sorts of mosaic individuals, originated with the junior author of this paper. It constitutes a discovery of no small importance, one which lends strong support to the Mendelian hypothesis of essential gametic purity. It shows that alternative parental characters, when united in fertilization, do not mix, but that each retains its own identity and subsequently separates from the other when gametes are formed. This takes place even when one of the parental characters ts itself a mosaie! Herein we have a confirmation of the conclusion based upon morphological observations, that the pa- ternal and maternal contributions to the zygote retain each a distinct individuality. Further, the idea of Bateson receives confirmation, that the gray color of mice obtained by crossing black-white with white mice is itself a “ heterozygote ” character. Darbishire’s premature conclusion, that in his spotted hybrids “ albinism is not recessive,” will undoubtedly be abandoned by him when he has reared from them a second generation of hybrids. From our own ex- periments and those of von Guaita we confidently predict that he will obtain. approximately one in four of albino mice, and of the pigmented mice obtained, part will be pure mosaics (as defined by us), but a larger part will be hybrid mosates like their parents.* * This prediction has been fulfilled sooner than we had expected. In a paper just received Darbishire (:03) states that his hybrid mice bred inter se have produced 66 young. Of these 13 are albinos, and 17 are (in our terminology) pink-eyed mosaics, while the remaining 86 have dark eyes. The last named class consists clearly of hybrid mosaics like their parents. The Mendelian expectation is that half the offspring, or 33, will be of this sort; the observed number is 386. The other two classes (albinos and pure mosaics) should theoretically number 16.5 each, or together 83; they number 18 and 17 respectively, or together 30. The correctness of this interpretation of Darbishire’s results can easily be tested by further breeding of his animals. The pink-eyed individuals, if really pure mo- saics, as we suppose, will, when bred to albino individuals, produce only dark-eyed offspring; whereas their dark-eyed brothers and sisters when similarly mated will produce both dark-eyed individuals (like themselves) and albinos, in approximately equal numbers. Further, the pink-eyed individuals will probably breed true inter se, whereas dark-eyed individuals will continue to produce in subsequent genera- tions, as in the case already observed by Darbishire, offspring of three sorts, CASTLE AND ALLEN.— THE HEREDITY OF ALBINISM. 613 V. PurE AND IMPURE RECESSIVES. Although Darbishire’s interpretation of his results is clearly unsound, he has made an observation of great importance, both theoretical and practical. In his crosses with dancing mice, he employed two different stocks of white mice, and with results somewhat different in the two cases. The two stocks were (1) “pure-bred” albinos purchased from breeders, and presumably descended from white parents, and (2) “ cross- bred” albinos known to be descended from spotted [i. e. hybrid mosaic] parents. The latter, when crossed (four different pairs) with the fawn- white dancing mice, produced only spotted gray-white offspring, nineteen in number. ‘The former, when crossed in the same manner (five differ- ent pairs), also produced gray-white mice, twelve in number, but pro- duced in addition fifteen gray mice (with lighter bellies and tail) and two namely, albinos, dark-eyed individuals, and pink-eyed individuals, approximately in the proportions, 1:2: 1. The numbers of first- and second-generation hybrids which have been reared by Darbishire are now considerable. They show conclusively that both albinism and the dancing character are recessive in relation to the normal conditions. The original cross between pink-eyed dancing mice and albinos has yielded 203 off- spring, all dark-eyed and with bodies more or less extensively pigmented ; none dance. Certain of these hybrids bred to albinos have produced 205 young, of which 111 are albinos; the Mendelian expectation in this case is 102.5 albinos. The remaining (pigmented) offspring of this cross are all dark-eyed like their hybrid parent, and none dance; this is precisely the Mendelian expectation. First-generation hybrids bred inter se have yielded both albinos and dancing individuals. The Mendelian expectation is one in four of either sort. The ob- served number of albinos is, as already stated, 13 in a total of 66; the number of dancers in the entire 66 is not stated, but we are told that, in 87 mice of this gen- eration, 8 were dancers; the Mendelian expectation is 9. Darbishire grants that these facts are “in possible accordance with some form of Mendelian hypothesis,” but holds that “the behavior of eye-color is in every respect discordant with Mendel’s results.” The latter conclusion he reaches only by first assuming that “the possession of pink eyes must on Mendel’s view depend on a separate embryonic element from that which determines coat-color.” This is a wholly unnecessary assumption. The pigmented areas of the eye are mor- phologically and (as far as heredity is concerned) also physiologically parts of the general integument. A pink eye is simply an eye devoid of pigment; it represents an unpigmented area of the integument, and is no more a distinct element in hered- ity than is an unpigmented (white) spot on the side or tail of the animal. In an earlier paper (Castle, : 03, p. 543) one of us has likened a white animal with dark eyes to a white animal with dark extremities, both are essentially mosaics of the dominant and recessive characters. On this view the observed inheritance of eye- color is in every respect accordant with Mendel’s results. 614 PROCEEDINGS OF THE AMERICAN ACADEMY. fawn-colored mice (likewise lighter below). The two fawn-colored mice were borne by a single “ pure-bred” mother. Gray mice were borne by all five “ pure-bred” mothers. This result indicates that not all albinos breed alike when crossed with the same pigmented stock, a conclusion which our own experiments fully substantiate. Darbishire’s white mice clearly show individual differences in the way in which they breed. These differences are even more strik- ing among the “pure-bred” than among the “cross-bred” mothers, doubtless because the former were obtained from different breeders, whereas the latter all came from one source. Darbishire is entirely right in concluding that the ancestry of white mice does “ make a difference” in their breeding capacity, but he is cer- tainly wrong when he surmises that “the more in-bred an albino is the less power it has of transmitting its whiteness,” unless he is willing to limit this statement to the first hybrid generation, which, however, he has not done. ‘The truth probably is that in crosses between albino and spotted races, veversion to the ancestral form of pigmentation is more complete the purer the white stock is. But the ability of the white parent to transmit its whiteness to generations other than the first is certainly not diminished by inbreeding. For, while von Guaita employed a stock of white mice which had been inbred for many generations, and which showed in consequence a considerably diminished fertility, the white stock used by us gave no indications of extensive inbreeding ; and yet in the experiments of von Guaita, as in our own, complete albinism is in- herited in slightly more than the proportions demanded by Mendelian principles. The experiments of Cuénot also show a slight excess of albinos over expectation. Inbreeding, then, does not affect the inheritance of complete albinism in crosses ; whether it affects the character of the pigmentation of the hybrid individuals formed is an entirely different question, one which can be tested only by the use of albino individuals resulting from a cross be- tween unrelated pure albino stocks. Such a cross should serve to coun- teract, at least in part, the effect of any previous inbreeding either in one or in both albino stocks. Our present opinion is that purity of the albino stock, rather than inbredness, is of consequence in determining the extent of reversion to the primitive gray pigmentation in the primary cross with mosaic individuals; but further experiments are needed to settle this point. In the foregoing pages we have used such expressions as ¢mpure albino and impure recessive, expressions which seem incompatible with the hy- CASTLE AND ALLEN. — THE HEREDITY OF ALBINISM, 615 pothesis of gametic purity, and which therefore require justification. Con- strued in the strictest sense, the doctrine of gametic purity is untenable. We cannot accept that interpretation of it which requires that the gametes formed by an individual be the precise equivalents in all respects of the respective gametes which united to form that individual. Mendel him- self would not have assented to such an interpretation, for in the latter part of his original paper (’66) he clearly states the important principle that a composite character may undergo resolution into its elements in consequence of crossing. This allows a part of a complex character to pass into one gamete, while the remaining parts pass into another; in other words, it makes possible the formation of mosaic gametes, into whose composition the dominant and recessive characters may both enter in varying degree. All gametes which contain any portion of a dominant or of a recessive character associated with its opposite, are in reality mosaic ; yet, if a gamete essentially recessive contains only traces of the dominant character, it may be convenient to recognize this fact in its designation, which we do by calling it an ¢mpure recessive. In guinea-pigs the impurity of recessives tainted with the dominant character is commonly visible. Ordinary white guinea-pigs with pink eyes, though they invariably produce albinos when bred inter se, have a greater or less amount of sooty black pigment in the skin and hair of their ears, nose, and feet, showing the presence of a trace of the domi- nant character. Rarely is it possible to obtain an animal free from this visible taint, and even when obtained, we are informed by breeders, such individuals are likely to produce offspring with a certain amount of pig- ment on tlieir ears or feet. The so-called Himalayan rabbit is another illustration of a mosaic with a predominantly recessive (albino) character, in which the dominant (pigment-forming) character is localized precisely as in the impure al- bino guinea-pig, namely, at the extremities. Himalayan rabbits have brownish-black noses, ears, feet, and tails, being elsewhere snowy white and having pink eyes. They breed true inter se, yet, according to Darwin (76, p. 114), may occasionally produce a silver-gray animal, in which the pigment is not restricted to the extremities. This condi- tion must result from liberation of the dominant character from the strict localization which it has in ordinary individuals and which it must have also in the gametes that produce them. In mice, on the other hand, impurity in recessive individuals is not visible, though doubtless sometimes present. So long as the breeder wishes only to obtain white mice, it makes no difference what the ances- 616 PROCEEDINGS OF THE AMERICAN ACADEMY. try of his breeding animals is. All albinos alike will produce only white offspring when bred to albinos. But if the breeder desires to cross his albinos with colored mice, the pedigree of the former is of consequence. Different albinos will, in crosses with the same pigmented stock, yield different results. This is shown both by Darbishire’s experiments and by our own. In October, 1900, we began a breeding experiment in which a family of black-white mice was crossed with two different stocks of albino mice. All three stocks bred true among themselves; but, in crosses with the black-whites, one albino stock produced only gray or black offspring, whereas the other produced no gray offspring, but only black or fawn-colored ones, often extensively spotted with white. Mani- festly the gametes formed by the two albino stocks, though all pre- dominantly recessive, were not all alike. It is probable that some of them at least were impure, containing traces of a latent pigment-forming character. Such a latent character is apparently not liberated, in the case of mice, by a cross with a different stock of albinos; but this result can be secured, probably, by a cross with dominants. We infer this not only from the observed result in crosses between black-white and albino mice, but also from what has been observed to take place in guinea-pigs. On crossing a “dark-pointed” albino guinea-pig with a stock of red guinea-pigs which for a number of generations had bred true ¢nter se, there were obtained offspring which in every instance were predominantly black in color, yet with a certain proportion of red hairs mixed with the black, which gave them a “brindle” or finely mottled black-and-red appearance. This result must be attributed to a liberation of the black-pigment-forming character either from its visible, strict localization in the albino parent, or from a possible latent and invisible occurrence in the red parent. We incline at present toward the former explanation, but the matter has not yet been fully tested. The com- plete disappearance of the albino character in this cross is noteworthy as being parallel to its behavior in the cross between black-white and white mice. Darbishire’s pink-eyed, fawn-white dancing mice were mosaics pre- dominantly recessive, and might with some propriety be designated impure recessives, but they differed from impure guinea-pig recessives in that, when crossed with ordinary recessives, they did not produce pink- eyed animals like themselves, but rather animals which were in a majority of cases extensively pigmented. It seems more appropriate, therefore, to designate them mosaics. “ Dutch-marked” varieties of guinea-pigs, rabbits, and mice, and the CASTLE AND ALLEN. — THE HEREDITY OF ALBINISM. 617 somewhat similarly marked Holstein and Hereford cattle, though they do not breed so true ¢nter se as dark-pointed albino guinea-pigs or Himalayan rabbits or, perhaps, as pink-eyed dancing mice, nevertheless indicate a fairly precise localization of the pigment-forming and albino characters within mosaic germs. If we adopt the Roux-Weismannian idea of the nature of the chromo- somes, it is probable that particular chromosomes, or part chromosomes, in the mosaic germ, contain the dominant character, while the remaining chromosomes, or part chromosomes, contain the recessive character. VI. Cross-BREEDING, REVERSION, AND THE DOCTRINE OF GameETic Pority. Union with a recessive gamete usually, though not always, serves to break up this localization, allowing the dominant character to extend its influence throughout the entire body. ‘This is the case, for example, in the cross between spotted and white mice in the experiments of Haacke, von Guaita, and in part of Darbishire, as well as in our own. It is possible to suppose in such cases either (1) that the resolving effect of the cross is restricted to the soma of the cross-bred, or (2) that it extends also to the germ-cells of the cross-bred. If the former hypothesis is cor- rect, the cross-bred should form gametes D # and # in equal numbers ; if the latter, then only gametes D and Ff should be formed, and these in equal numbers. A simple test is afforded by the breeding inter se of hybrid mice produced by crossing pure mosaics with recessives. On the first hypothesis suggested, the offspring of the hybrids should consist, in at least one case out of four, of spotted mice formed by the union of two pure D & gametes; on the second hypothesis no spotted mice should be produced, but only classes D, D(f), and #, as in breeding together hybrids between wild gray mice and white mice. Von Guaita’s experi- ments show the formation at the second filial generation of nine spotted mice, twenty-one uniformly gray or black mice, and fourteen white mice. The expectation on hypothesis (1) is 11 spotted: 22 gray or black: 11 white mice, which approximates elosely the observed result; whereas on hypothesis (2) there should be no spotted mice, but only such as are pigmented all over or else are albinos. The result is conclusive in favor of hypothesis (1) — that a mosaic gamete, on uniting in fertilization with a recessive gamete, does not lose its own identity nor undergo resolution into its constituent parts.* * Compare the results of Darbishire, as stated on p. 612, footnote. 618 PROCEEDINGS OF THE AMERICAN ACADEMY. Yet we must not fail to observe that a cross of the sort just described is not without its effects on the nature of the gametes; these do not retain their original character. For whereas the mosaic gametes of the original spotted parents produced, on union in pairs, invariably black- white offspring, the mosaic gametes formed by their hybrid offspring, when similarly combined, formed in von Guaita’s experiments eight gray- white offspring, but only one black-white. Accordingly, though it seems certain that mosaic gametes may in crosses retain their mosaic character, the cross is nevertheless able to bring into activity characters latent in the parents, and to add these to the previous visible total of the mosaic, giving it thus a new character. In the original black-white stock, the mosaic consisted of the active characters, black and white, while the char- acter yellow was latent, either in the mosaic gametes or in the recessive gametes with which they united when the cross was made. The cross brought at once into activity the latent character, yellow ; and this com- bined with black to form the composite dominant character, gray, while white, though present in both gametes uniting, usually became for the time being altogether latent. But the gametes formed by the gray hybrid were not, as we should expect on the principle of strict gametic purity, black-white and white, but gray-white and white respectively. The character yellow, latent previous to the cross, having once become active remained so. By this experiment we are put in possession of a principle of great importance, both theoretical and practical. It modifies essentially the Mendelian doctrine of gametic purity as commonly understood, yet without denying the soundness of that doctrine at core. It allows the breeder (as breeders habitually do) to reap substantial benefit from crosses, for in addition to permitting him to secure new combinations of the elementary characters visible in the parents crossed, it places at his disposal char- acters latent in the parents, and particularly facilitates the re-acquisition of lost characters. The gray of hybrid mice obtained as in von Guaita’s experiments is a composite character resulting from the combination of visible black with latent yellow. In Darbishire’s experiments it results from the com- bination of visible yellow with latent black. In either case gray is obtained by synthesis (Bateson) of black and yellow. This view is sup- ported by the observation of the reverse of this process, in crossing wild gray with white mice. In the second and later hybrid generations black pigmented as well as gray pigmented mice are obtained. These must result from a resolution of gray into its constituent elements, black and yellow, of which the latter then becomes latent. CASTLE AND ALLEN. — THE HEREDITY OF ALBINISM. 619 It is not necessary to suppose, as Mendel apparently did, that the segregated elements of a composite character pass invariably into different gametes. There is reason to’ believe that yellow is frequently, if not always, latent in black mice, and black in yellow mice, though such an occurrence has not yet been conclusively demonstrated. We would not, however, deny the possible correctness of Mendel’s explanation in other cases. This should be indicated in breeding experi- ments by the simultaneous appearance in different individuals of the segregated elements of the composite character, and in particular numer- ical proportions. Each new sort should be incapable of producing the other, under either close or cross breeding. ‘This is a subject well merit- ing more careful investigation. VII. Summary. 1. Complete albinism, without a recorded exception, behaves as a recessive character in heredity. 2. Partial albinism is a mosaic condition in which the dominant pig- ment-forming character and the recessive albino character are visible in different parts of the same individual. 3. Pure mosaic individuals form only gametes which partake of their own mosaic nature. They and their gametes may be designated D R. 4, Hybrid mosaics result from the union of a mosaic gamete, D R, with a recessive gamete, 4, as in a cross between a pure mosaic and a recessive individual. Such crosses are made when a race of spotted mice which breeds true is crossed with albinos. 5. Hybrid mosaic mice are usually more extensively pigmented than pure mosaics, frequently they are pigmented all over. When they are spotted with white, we may consider this the result of dominance of the mosaic gamete as a unit and may designate them accordingly, D FR: (L). When they are pigmented all over, it is clear that the dominant element only of the mosaic gamete is visible in them. They should then be designated D(?):(R). 6. The gametes formed by a hybrid mosaic are of two sorts, like those which united to produce it, namely, DR and R. Accordingly when hybrid mosaic individuals breed together, they produce offspring of three different sorts, — pure mosaics, hybrid mosaics, and recessives. We should expect these three classes to be numerically as 1: 2:1, and this is probably the case. When a hybrid mosaic is bred to a recessive, two sorts of offspring are produced, —- hybrid mosaics and recessives. These classes should be of approximately equal size. 620 PROCEEDINGS OF THE AMERICAN ACADEMY. 7. Albinism apparently complete may in reality conceal traces of the pigment-forming character either in an active or in a latent condition. Albinos thus constituted are in reality mosaics of the contrasted char- acters, but with the pigment-forming character (ordinarily dominant) occurring in a condition of partial or complete latency. When bred to other albinos they uniformly produce albinos, hence they may for con- venience be distinguished as impure recessives. In guinea-pigs and rabbits the impurity of recessive individuals is, in certain cases at least, visible ; in mice it apparently is not. 8. Cross-breeding is able to bring into activity latent characters or latent elements of a complex character. This is probably the true ex- planation of many cases of reversion. Conversely it is able to cause one or another element of a complex character to become latent and to remain so under close breeding. This principle probably explains how races of black or yellow mice may be obtained by crossing wild gray mice with albinos. 9. The Mendelian doctrine of gametic purity is fully substantiated by experiments in breeding mice, guinea-pigs, and rabbits, but with the important qualification stated under 8, a qualification which really enhances the practical utility of that doctrine in its every-day application by breeders, BIBLIOGRAPHY. Bateson, W. :02. Mendel’s Principles of Heredity, a Defence. With a Translation of Mendel’s Original Papers on Hybridisation. xiv + 212 pp. Cambridge. [ England. Contains bibliography and portrait of Mendel. | Bateson, W., and Saunders, E. R. :02. Experimental Studies on the Physiology of Heredity. Reports to the Evolution Committee of the Royal Society. Report I. 160 pp. London. Castle, W.E. \ :03. Note on Mr. Farabee’s Observations [on Negro Albinism]. Science, N. S., Vol. 17, No. 419, pp. 75-76. Castle, W. E. :037, Mendel’s Law of Heredity. Proceed. Amer. Acad. Arts and Sci., Vol. 38, No. 18, pp. 535-548. CASTLE AND ALLEN.— THE HEREDITY OF ALBINISM. 621 Castle, W. E. :03>. 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The Variation of Animals and Plants under Domestication. Sec- ond Edition, revised. N. Y., D. Appleton and Co., 2 Vol., xiv + 473 and x + 495 pp. Farabee, W. C. :03. Notes on Negro Albinism. Science, n. s., Vol. 17, No. 419, p. 75. Guaita, G. von. ’98. Versuche mit Kreuzungen von verschiedenen Rassen des Hausmaus. Ber. naturf. Gesellsch. zu Freiburg, Bd. 10, pp. 317-332. Guaita, G. von. :00. Zweite Mittheilung iiber Versuche mit Kreuzungen von verschied- enen Rassen des Hausmaus. Ber. naturf. Gesellsch. zu Freiburg, Bd. 11, pp. 181-138, 3 Taf. 622 PROCEEDINGS OF THE AMERICAN ACADEMY. oa Haacke, W. ’95. Ueber Wesen, Ursachen und Vererbung von Albinismus und Scheck- ung und iiber deren Bedeutung fiir vererbungstheoretische und entwicklungsmechanische Fragen. Biol. Centralbl., Bd. 15, pp. 44-78. Mendel, G. ’°66. Versuche uber Pflanzenhybriden. Verh. naturf. Vereins in Briinn, Bd. 4, Abh., pp. 3-47. [Translation in Bateson, :02. ] Vries, H. de. :02. Die Mutationstheorie. Bd. 2. Die Bastardirung, Lief. 1, 240 pp., 2 Taf., 45 fig. Leipzig, Veit und Co. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 22. — May, 1903. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. DIFFUSION AND SUPERSATURATION IN GELATINE. By Harry W. Morse AND GEORGE W. PIERCE. ee Ae ol & rcs Tale fon sa) Pasir ae or a Tid vA eee > aa AD LW ae , iH 1 iT aa as i Y Ment Y é wh DIFFUSION AND SUPERSATURATION IN GELATINE. By Harry W. Morse anp GrErorGE W. PIERCE. Presented by J. Trowbridge, February 11, 1903. Received March 16, 1903. iE INTRODUCTION. Tue German photographer, R. Ed. Liesegang, in the course of a research on chemical reactions in gelatine,* discovered a phenomenon which Ostwald cites as evidence that there exists a definite limit beyond which, at a given temperature and pressure, the supersaturation of a solution cannot be carried. We have undertaken an experimental study of this subject by a method based on Liesegang’s discovery. Liesegang’s experiment was as follows: A glass plate was covered with gelatine impregnated with potassium chromate. ‘The plate was laid hori- zontal, and upon it a drop of silver nitrate was placed. The silver nitrate diffused slowly out into the gelatine, reacted with the potassium chromate, and formed a pre- cipitate of silver chromate. The silver chromate, instead of growing continuously in the gelatine,.as diffusion of the reacting substances went on, formed in distinct rings about the drop, as shown in Figure 1. The formation of the precipitate in distinct rings is clearly a phenome- non of supersaturation. We have undertaken certain Figure 1. measurements of these rings in the hope of being able to obtain from them some understanding of the conditions that exist in supersaturated solu- * Chemisclie Reactionen in Gallerten. VOL, XXxvil1. — 40 Diisseldorf, 1898. 626 PROCEEDINGS OF THE AMERICAN ACADEMY. tions. In particular we have set for ourselves the problem to calculate from these rings the rate of diffusion of the reacting substances, and to estimate the limit of supersaturation attained when the solid phase is not present, — the so-called “ Metastable Limit” of Ostwald. Before proceeding to the experiments we shall give certain definitions and explanatory paragraphs from Ostwald’s Lehrbuch.* “ Between a solid substance and its supersaturated solution an equilib- rium is formed, which depends on the nature of the substances, the tem- perature, and the pressure. If we leave out of account the influence of the pressure, for every temperature there is a definite equilibrium. This is evidenced by a definite concentration up to which the solid substance dissolves. .. . “ When the solid phase is not present, the concentration of the dissolved substance is arbitrary. The limit of concentration on one side is zero; on the other side the limit is a concentration difficult to determine, which, however, is greater than that of the equilibrium with the solid phase. “ Solutions whose concentrations exceed the concentration of saturation with a possible solid phase are called supersaturated with reference to this solid phase... . “The simplest way of obtaining a supersaturated solution is to produce by change of temperature from the solid substance and the solvent a solu- tion that is more concentrated than a saturated solution at the temperature of the experiment. In most cases the temperature required to produce supersaturation is higher than the temperature of the experiment, but it can also be lower in cases where the solubility decreases with increase of temperature. “A better way to obtain supersaturated solutions, since it is thereby easier to exclude germs of the solid phase, is to employ reactions that produce in the solvent concentrations of the substance in question in appropriate amount. : “Among supersaturated solutions there are some which under definite conditions can be kept indefinitely, if germs are excluded, without forma- tion of the solid phase. Such solutions are called Metastable. “On the other hand, there are some solutions in which, even when germs are excluded, the solid phase appears after a short time. Solu- tions of this type are called Labile. “Metastable solutions always show smaller concentration than the labile solutions of the same substances. By increase of concentration, * Lehrbuch, II. 2, 780-784. MORSE AND PIERCE, — SUPERSATURATION IN GELATINE. 627 therefore, a metastable solution goes over into a labile condition. The concentration at which the transition occurs is called the metastable limit. “The metastable limit is, in the first place, dependent on the nature of the substances, on the temperature, and on the pressure. In addition it is influenced by various other circumstances not yet explained. At the present time (1899) it is hardly possible to speak more definitely concerning the value of the metastable limit and the methods of deter- mining it.” It is in connection with this discussion in the Lehrbuch that Ostwald cites the sharpness and regularity of Liesegang’s rings as evidence that the metastable limit is something definite. But so far as we are aware, no attempt has hitherto been made to study Liese- gang’s rings quantitatively, and to obtain from them the actual numerical value of the metastable limit. In fact, so far as we are aware, there has not been published a determination of the metastable limit in any case. We quote further Ostwald’s explanation* of the formation of Liesegang’s ring-system: — “ By the diffusion of the silver salt into gelatine containing chromate a solution is formed which is supersaturated with respect to silver chromate; precipitation does not take place until the metastable limit has been exceeded. This naturally happens simultaneously in a circle concentric with the drop. Silver chromate, in relation to which the neighborhood of the ring is supersaturated, deposits on the precipitate already formed and strengthens it; this continues until the soluble chromate has been removed from the neighborhood and de- posited on the precipitate. The silver salt, diffusing on far- ther, supersaturates a new circular region, and the process repeats itself. Since the silver nitrate becomes more dilute by diffusion, the critical concentration, at which precipitation begins, is reached later and later, and the rings form farther and farther Figure 2. apart.” K Liesegang has also shown that if the potassium chromate in gelatine is put into a capillary twbe instead of being spread upon a plate, analogous phenomena occur when one end of the tube is dipped into a solution of silver nitrate. The precipitate in the tube is formed in layers, or dises, perpendicular to the axis of the tube. (Figure 2.) * Lehrbuch, II. 2, 778. 628 PROCEEDINGS OF THE AMERICAN ACADEMY. This phenomenon of the formation of a precipitate in rings on a plate or in discs in a tube is not confined to the case of a reaction between silver nitrate and potassium chromate. Liesegang found such a forma- tion of a precipitate in the case of mercurous chromate, lead chromate, and Prussian blue, in the familiar reactions which give these precipitates. We have found that with a proper choice of concentrations rings are: also formed in the following cases : — TABLE I. Diffusing Subs. Subs. in Gel. Nature of Rings. Pb(NO3). Na,SO, Fine. White. Close together. AgNO; K.C,04 is ‘ sc AgNO 3 Na,COs Thick. Far apart. ' AgNO, Na,HPO, Fine. White. AgNOsz NH,CNS AgNO, KBr Co(NOs), NaOH Gelatinous. Thick. BaCl, K,C.04 Distinctly crystalline. HgNO,z KBr Fine. White. FeCl, Na,CO, P Gas bubbles. It is our intention to give a more extended description of the various reactions in this table at some future time. At present, however, in order to discuss the quantitative aspect of the problem, we shall confine our attention to a single case, — the formation of supersaturation rings of silver chromate. The experiment was as follows: A capillary tube of diameter .5 to 1 mm. was filled with a 7; or a zl, normal solution of potassium chro- mate in gelatine. After the gelatine had set, a piece of the tube about 5 em. long, obtained by breaking the tube under water so as to expose a fresh moist surface of the gelatine, was plunged vertically into a water solution of 2N, N or } AgNO, contained in a flat-walled glass vessel. By means of a cathetometer carrying a microscope of low power we watched the formation of the precipitate. After a certain period of time, depending on the concentration of the solution, the precipitate near the MORSE AND PIERCE, — SUPERSATURATION IN GELATINE. 629 advancing front of the diffusing substance began to appear in layers, or discs, widely separated in comparison with their thickness. ‘These discs appeared suddenly as a sharp, thin film, so that the t¢me of their appear- ance could be determined with accuracy. The distance of each disc from the bottom of the tube was read off on the cathetometer. Measurements so obtained are recorded in the appended tables, IV to XXIV. The experiment was conducted in a constant-temperature room, which, except for the short time necessary for the taking of readings, was kept dark, or dimly lighted, to exclude the possible action of light in hardening the gelatine. The reaction is in accordance with the formula: 2AgNO; + K,CrO, 5 Ag,CrO, + 2KNO, The advanee of the reaction in the one sense or the other is conditioned upon the concentration of the active substances. For equilibrium the concentrations must satisfy the quantitative relation : Ag? x CrO, = K. Ag.CrO, (a) where Ag and CrO, are the concentrations of the silver ion and the chromate ion respectively, Ag,CrO, the concentration of the undissociated silver chromate in solution, and X the equilibrium constant. When the solid phase is present the undissociated silver chromate in solution must be in equilibrium with the solid phase, and must, therefore, be present in constant amount. In saturated solution, therefore, Ag? x CrO, = &, (1) where & is the solubility product. ‘ Now in supersaturated solution the mass law (Eq. a) is probably still true, and the question arises; is there a relation similar to (1), with, however, a different constant product that defines the limit of super- saturation ? Is there a formula of the form. Ag? x CrO, = H (2) for the condition that the concentrations must satisfy when the precipitate just begins to form in the absence of the solid phase ? 630 PROCEEDINGS OF: THE AMERICAN ACADEMY, II. THEORETICAL CONSIDERATIONS. We can calculate the value of H in equation (2) provided we can calculate the values of the concentrations of the two ions at the point and at the time at which a ring begins to appear. We propose to attempt to obtain the values of these concentrations by the mathematical theory of diffusion. To avoid possible confusion from the use of general terms we shall take the specific case in which silver chromate is the precipitated substance; the same analysis will, of course, apply to any other case. Suppose a capillary tube (Figure 3), containing in gelatine a dilute solution of potassium chromate, to be plunged at the time ¢ = 0 into a vessel containing a strong solution of silver nitrate; let the distance x be measured from the end of the tube, with its positive direction along the axis of the tube; let wu be + the concentration of the Ag ion at the point x at the time ¢, wv the cor- responding value for the CrQ, ion. At the instant the tube is plunged in, that is, at the time ¢ = 0, wu is equal to UY for all negative values of x, and 0 for all positive values of z. Let 0 and V, be the corre- sponding initial values of v. As a first approximation we may assume that the dissociation of the Figure 3. K,CrO, is complete, since this substance is present in very dilute solution for values of x and ¢ such as we shall need to consider; the con- centration of the silver salt in the tube will also be small, and we shall at present consider it to be completely dissociated. Later we can see how to correct the error introduced by this assumption. Thus if we measure con- + centration in gram-molecules, the concentration of the Ag ion is the same as that of the AgNOs, and the concentration of the CrO, ion is that of the K,CrO,. We are to calculate the two concentrations from the diffu- sion of AgNO; and K,CrQ,. The diffusion constant is defined as the number of units of mass that MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 631 will go through a unit cross-section in a unit of time under head of unit gradient of concentration. Let a? (essentially positive) be the diffusion constant of silver nitrate; then the quantity of silver nitrate that will cross a section s of the tube at a distance x from the origin in a time ét is the diffusion constant x gradient xX time X area of cross-section. Therefore Q=— ae 8S (3) The quantity crossing a section at distance x + dz is Ca 2 OU 2 Oru Cee == aS Oh or (4) The accumulation of silver nitrate in the region between x and x + dz is the difference of these quantities, ou aaa: 8 - oe 8 This accumulation may also be expressed as change of concentration a multiplied by the volume, = du. dz. S; 2 og S88. be. S = bu. be. 83 whence, dividing by ot. da. S Ju du © PS SSS i) ape er ( ) This is Fick’s Law.* Analogous considerations give us an exactly similar equation for the concentration of the CrO, ion at the point x and time ¢; namely, poe 2 (6) Ox? ot where 6? is the diffusion constant for potassium chromate. In deriving these equations we have made the assumption that the formation of earlier precipitates does not materially affect the head under which the ions accumulate for the formation of new precipitates. If we make this assumption we can solve the problem completely. Equations (5) and (6) are exactly alike, but their solutions will be different because they have to satisfy different initial conditions in the two cases. The lower end of the tube was kept constantly, by occasional * Pogg. Ann., XCIV. 59 (1855). 632 PROCEEDINGS OF THE AMERICAN ACADEMY. stirring, at the concentration U, so that equation (5) must be solved subject to the condition «= U) when x = 0 for all values of ¢, and wu = O for all positive values of x at the time¢=0. Equation (6) has for initial values » = Vo for all positive values and v = 0 for all negative values of « whent=0. The theory of differential equations of this type teaches us that if we can obtain any one solution for each of these equa- . tions that satisfies its boundary conditions it is the only solution. The following are unique solutions of (5) and (6) subject to these conditions : = eda (7) Sepals Hh “e** dB, t (8) in which # is merely a variable of integration. These may be seen to be solutions of (5) and (6) respectively if we differentiate them according to the rules for the differentiation of a defi- nite integral and substitute the results in (5) and (6). Equation (7) is also seen to satisfy the initial conditions, for if ¢ = 0 and = is positive, the lower limit of integration becomes + «©, which is the same as the upper limit ; the integral is therefore 0 and w= 0. If x= 0 the lower limit is 0 and the value of the integral is ve Se (Of Similar reasoning shows equation (8) to satisfy initial conditions for v. The metastable product H, as we have defined it on page 8 (Eq. 2), should be given by the following equation : 27 co 2 eee i stain d By ae ap | 2 { e * dB (9) TS x —x 5 2 w/t 2aVz It is our problem to ascertain whether #/ is a constant for several initial concentrations of Uj and Vo. If we knew the diffusion constants a? and 6? we could expand the in- tegrals in (7) and (8), integrate term by term for a given value of x and ¢, and thus obtain wv and v and from them H. This would necessitate a previous independent determination of the diffusion constants, and would * Fourier, Th. an. de Chaleur, § 366 (1822). + Fourier, loc. cit.; Stefan, Wiener Sitzungsber., 79, II. 176 (1879). MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 6338 beside be very laborious, as the series do not begin to converge until after the sixth or seventh term. The difficulty of the series expansion might, however, be obviated by the employment of tables that have been com- puted for the definite integral. We have employed a method in which a previous independent deter- mination of the diffusion constants was not necessary. Before passing to the solution we shall call attention to an important and easy deduction from equation (9). In order for H to be a constant the lower limits of integration x nd —— Vanfe. 20g; should be constant for all rings in a given tube with given initial values t That is, for example, if we plunge a tube containing potassium chromate in gelatine into a solution of silver nitrate and observe with a catheto- meter the distance from the bottom of the tube at which each thin disc of precipitate appears, and note, at the same time, the number of seconds that have elapsed since plunging in the tube, the distance divided by the square root of the time is a constant for all the discs in this tube, and for all tubes with the same initial concentrations of the reacting substances. The sample set of results given in Table II and all the tables, IV to XXIV (pp. 643-648), show with what consistency this conclusion is verified. : x of U, and Vj, and since a and 6 are constants Ti should be a constant. III. DETERMINATION OF THE DIFFUSION CONSTANT AND THE METASTABLE LimIT. This constancy of —~ for any one set of observations under given t conditions does not show, when taken alone, that there is a constant metastable solubility product H, but does show that, for a given concen- tration of one of the ions, there is a definite concentration of the other ion that will cause precipitation. In order to examine into the constancy of H, the product of ionic con- centrations as defined by equation (9), we shall need to employ the data furnished by different initial concentrations of the reacting gubsianeey as collected in Table III, p. 635. Every two sets of initial concentrations, together with the correspond- ing values of ah , will give the data for calculating the diffusion constant t 634 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE II. Temp. 15.7. Srtver Nitrate, N. Porasstom Curomate, 7%. Mean error a and the value of H, as defined by equation (9). For example, if we substitute for , Vo, and — Fi , the respective values of these quantities ie in sections (a) and (b) of Table IIL, we obtain the two following equations : — ay oe ie “as |. fi ferep. (10) i Sue Hos ss: a Pan]. f fore (11) 2a MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 6385 TABLE III. RECAPITULATION FROM TABLES IV-XXIV. Silver Nitrate 2N diffusing into (a) Potassium Chromate, J, Table. Temp. IV. 16.0 We 16.3 VI. 16.3 VIL. 16.1 Mean Silver Nitrate N diffusing into (b) Potassium Chromate, X. (d) Potassium Chromate, ,.. Silver Nitrate X diffusing into (c) Potassium Chromate, N. (e) Potassium Chromate, ,.. Table. Temp. yi Table. Temp. XVIIL 16.6 | .01384— Xx. 17.7 XIX. 16.8 01377 XXI. 16.9 XXIL 16.0 Mean . : . 01880 XXII. 15.5 OV 15.5 Mean 636 PROCEEDINGS OF THE AMERICAN ACADEMY These two equations must be solved as simultaneous. We have been able to do this by the aid of a set of definite integrals given in the appen- dix of Kramp’s Analyse des Refractions Astronomiques et Terrestres, published at Strassburg in 1799. Kramp’s table contains values of the integral ik e Pdp for 301 values of a from 0 to 3.00. This table shows, in the first place, that various values of fre, 26V2 obtained on the assumption that J? is of the order of magnitude of the diffusion constant of an electrolyte, and that ae is of the order of magni- tude given by our experimental data, differ from each other and from x by less than 2 per cent. This means merely that the change of concentration, v, of the substance originally in the gelatine can be neglected. Dividing equation (11) by equation (10), and extracting the square root, we have fo a} u e dB 0158 22 we 2. (12) Ji e dp -0167 2a To solve this equation for a it is only necessary to find two values in Kramp’s table for which the lower limits of integration are in the ratio 0.0167 to 0.0158, and for which the value of the integral corresponding to the second is double the value of the integral corresponding to the first. To give an idea of the procedure in such a calculation we shall give on the next page a few values from Kramp’s table in the neighborhood of the solution, of which the starred value is seen to be the one satisfying equation (12). The ratio of 0.0167 to 0.0153 is 1.091. a and a; are the lower limits of integration, A and A, the correspond- ing values of the integral. The correct solution is singled out by the relation + =a) MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 637 010909 005677 010067 005077 .009668 004837 009284 004632 008555 004164 from which the value of a that most nearly satisfies equation (12) is seen to be 1.80. 0153 . Ovals — 1.80 a = 4.25: >< 10—. The corresponding value A of the integral is .009668. Therefore from equation (11) = 8 Nie = (.009668)? = 1.6 x 10-8 (“Tar -) Oo 7 liter The diffusion constant is not a, but a*, which, reduced to the usual units with the day as unit of time by multiplying a* by 8.64 x 104, becomes 2 a? = 1.56 = ). day In this calculation of H the reacting substances have been assumed to be completely dissociated. The result of the calculation shows that the concentration of the silver ion was about 5}, Normal and that of the chromate ion 7; Normal when precipitation occurred. ‘The dissociation of 5%, silver nitrate differs so little from that of ;35, which enters into the calculation of subsequent cases, that the assumption of its complete dissociation introduces no appretiable inaccuracy. On the other hand, the dissociation of +5 potassium chromate is about 1.05 times the dis- sociation of + , and this factor representing the ratio of dissociation must be introduced into calculations involving different concentrations of potas- sium chromate in the gelatine. Observing this precaution we obtain the following values for a? and from other sets of data of Table ITI. 638 PROCEEDINGS OF THE AMERICAN ACADEMY. For THE DIFFUSION CONSTANT OF SILVER NITRATE AND THE METASTABLE SoLuBILITY PropuctT oF SILVER CHROMATE IN GELATINE AT 16° C. From Table ITI. Diffusion Constant. Metastable Product. Data. cm? (= Mol. \3 day Liter ) (a) and (b) 1.56 1G: X10 (b) and (c) 1.56 16 Xe 10s (a) and (c) 1.56 1.4 x 10-6 (d) and (e) 1.53 1.3 X 10° (b) and (d) 1.50 Veh S< ee (c) and (e) 1.53 1.3 x 10-6 Mean 1.64 14 xX 105 IV. Resvtts. Discussion of Results. — The values obtained for the diffusion constant and for the metastable solubility product are constant within the limit of error of the method, as will be seen by a reference to the recapitulation of Table III. While the value of — for any particular tube is constant t within one or two tenths of one per cent, the same good agreement is not obtained when several series of observations are made upon different tubes under as nearly as possible the same conditions. ‘The mean devia- tion of different tubes from the average is as great as one per cent. We think this deviation can be accounted for by lack of uniformity in the bore of some of the tubes, so that the diffusion takes place in a conical cavity instead of in a truly cylindrical cavity, as the theory requires. That an error of one per cent in the determination of — will account for vt the variations in the values of a? and H may be seen by a glance at the result of a recalculation of these quantities from the data (d) and (e) of Table III, on the assumption that the correct value of ae in (e) is .0130 t 2 instead of .0131; a? comes out to be 1.63 day’ and H becomes 1.9 x 107°. Or, assuming to be .0132 instead of .0131, a? becomes 1.42 and H t becomes 0.7 x 1076 MORSE AND PIERCE, — SUPERSATURATION IN GELATINE. 639 In view of this sensitive dependence of the diffusion constant and the x spe metastable product on the value of —, we consider the results to be t satisfactorily consistent. We have not been able to find elsewhere any determination of the value of the diffusion constant of silver nitrate in gelatine. F. Voigt- laender * has found that the diffusion constants of salts in agar from his own measurements are in some cases smaller, in others equal to or larger than the corresponding constants for water solutions, the solutions employed having varying concentrations. He says that the question whether the diffusion in agar and water is identical can only be answered by further observations on pure water and other gelatinous solvents, such as water glass. Voigtlaender’s measurements point to the con- clusion, however, that the diffusion in agar and that in water are not very different, which makes our result for silver nitrate, 1.54, seem rather high, as the values obtained by Kawalkif would be for silver nitrate at 16° C. 1.13 to 1.20. Calculation of the diffusion constant for silver nitrate by Nernst’s formula LU a? = 0.0477 x 107 — utuv [1 + 0.0034 (# —18)] gives the value 1.29. It should be noted that the value we have obtained is for diffusion through gelatine containing a rather heavy solid precipitate of silver chromate, and should not, therefore, be expected to agree with diffusion in water or pure gelatine. The important fact for this discussion is that a? is a constant and that there is hence no inconsistency in the conclusion that the metastable solubility product of silver chromate in gelatine is a definite constant quantity satisfying the relation ae Ses We Ne? x< CrO, As to the value of H, there are no other determinations of this quan- tity with which we might compare our results. As far as we know there have not been published any numerical data as to the value of the metastable product in any case. The ordinary solubility product of silver chromate in saturated water solution in the presence of the solid phase is 5.1 x 10718 asdetermined by Kohlrausch.t The concentrations * Zeit. Phys. Chem., III. 317 (1889). + W.A., LIT. 300 (1894). t Leitver. d. Elektrolyten, p. 202. 640 PROCEEDINGS OF THE AMERICAN ACADEMY. 3 i eos of Ag,CrO, in the two cases are in the ratio VAX 10 This A. 5d, LO means that the supersaturated gelatine at the concentration of precipita- tion held in solution 145 times the amount of silver chromate ioe to saturate it in the presence of the solid phase. Lobry de Bruyn * and Liesegang + have shown that in the case of a large number of substances, which, like the silver haloids, form amor- phous precipitates, gelatine inhibits precipitation. This phenomenon is especially easy to observe and demonstrate in the case of colored sub- stances like silver chromate and lead iodide. It is well known that electrolytes, whether or not they act chemically on the colloid, may cause the precipitation of a colloid from solution, and it might be supposed that the case we are discussing can be explained as such an action of the diffusing silver nitrate in throwing down colloidal silver chromate. We are of the opinion that this is not the case, because, first, precipita- tion is here sudden and not slow, as is the case when colloids are pre- cipitated by electrolytes, and, second, in the several cases of different concentrations of the reacting substances, the precipitate is formed, not for a constant concentration of the diffusing electrolyte, but for a con- stant value of the product & za Ag? x CrQ,. Purification of the Gelatine. The best commercial gelatine contains usually about two per cent of ash, consisting of phosphates and car- bonates, both of which form insoluble compounds with silver. Although the silver salts of these radicals are more soluble than silver chromate, it was thought necessary to remove them and other salts as thoroughly as possible from the gelatine to avoid their possible influence on the precipitation of the silver chromate. This removal was effected by electrolyzing the gelatine between membranes of parchment paper at five hundred volts continually for a week, during which time the mem- branes and electrodes were frequently washed by a stream of distilled water. Specimens of gelatine so prepared gave but a trace of ash on ignition. Liesegang in his original research on reactions in gelatine solutions in capillary tubes found two classes of rings: the heavy widely separated red deposits of silver chromate, and beyond these and between them * Rec. trav. chim. Pays-bas, XIX. 236. t Phot. Wochenblatt, p. 229 (1894). MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 641 another series, consisting of fine, microscopic white lines. According to Liese- gang’s description, when the time came for the for- mation of a new red line one of the fine white lines suddenly became yellow and grew broader, until it encompassed four of the white lines and developed into the dark red of sil- ver chromate. Liesegang observed, however, that these white lines are not necessary for the forma- tion of the red ones and are not present when Ficure 4. Precipitation in commercial gelatine, showing chromate diffuses into fine white lines between the heavy dark deposits of gelatine impregnated with Ag, CrO,4. Thisis a section of a tube like Figure silver. We are of the opin- 2, magnified 10 diameters. ion that these secondary white lines are due to the presence of impurities in the gelatine, since they appear with the same distinctness when silver nitrate diffuses into com- mercial gelatine to which nothing has been added. They did not appear in our purest electrolyzed gelatine. The addition of soluble chlorides, bro- mides, or iodides in very small quantities causes the white rings to appear. Figure 4 and Figure 5 show them between the Figure 5. Section of a plate like Figure 1, magnified 20 times, showing two sets of rings in commercial gel- larger lines of silver atine. The three heavy dark bands are Ag,CrO,. h VOL, xxxvi.— 41 642 PROCEEDINGS OF THE AMERICAN ACADEMY. chromate. It is our intention to investigate further the possible influence of impurities on the formation of these precipitates. It is of interest to know that gelatine is not necessary for the pro- duction of rings, for when a very fine capillary tube filled with a water solution of potassium chromate is carefully plunged into a silver nitrate solution precisely similar phenomena may be observed. In this case, however, the layer of precipitate exists for only a short time after its formation. It breaks up under the influence of gravity and convection and mingles with the mass of silver chromate below. Three or four layers may exist at the same time, those of later formation being sharp, aud the older ones gradually disintegrating into a mass of precipitate. V. CONCLUSION. We have shown by quantitative measurement that there exists in the case of the formation of silver chromate in gelatine solution a definite constant product ae —— Ag? x CrO, = Jal which determines the limit of supersaturation with respect to silver chromate in the absence of the solid phase. Incidentally we have obtained a value for the diffusion constant of silver nitrate diffusing through gelatine containing solid silver chromate. JEFFERSON PuysicaLt LABORATORY, Harvarkp UNiversiry, CAMBRIDGE, Mass., U. S. A., March 1, 1903. MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 6438 TABLE IV. TABLE V. Temp. 16.0. Sitver Nitrates, 2N. Temp. 16.3. Sitver Nitrate, 2N. Porassrum CHROMATE, 7%. Potassium CHROMATE, 7s. x Vt .01667 01660 .01660 .01662 01661 01663 .01663 .01663 .01662 .01658 .01663 01663 .01666 .01667 TABLE VI. Temp. 16.3. Sitver Nitrate, 2N. TABLE VII. PorassiuM CHROMATE, 7. Temp. 16.1. Srinver Nitrate, 2N. Potasstum CHROMATE, 7%. 644 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE VIII. TABLE IX. Temp. 15.5. Sirver Nitrate, N. Temp. 16.7. Sitver Nitrate, N. Porassium CHROMATE, 75. Potassium CHROMATE, 75. TABLE X. Temp. 16.7. Sirver Nirrate, N. TABLE XL N PoTassIUM CHROMATE, 75. Temp. 17.8. Sitver Nitrate, N. Potassium CHROMATE, 755: MORSE AND PIERCE. — SUPERSATURATION IN GELATINE, 645 TABLE XII. TABLE XIII. Temp. 16.3. Sitver Nitrate, N. Temp. 16.7. Sitrver Nitrate, N. Potassium CHROMATE, 755: PorassiuM CHROMATE, 735: TABLE XV. Temp. 15.5. Sitver Nitrates, N. N Porass1uM CHROMATE, ;35- TABLE XIV. Temp. 16.5. SitvEer Nitrate, N. PorassiuM CHROMATE, 755: 646 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE XVI. TABLE XVII. Temp. 16.6. Srirver Nitrate, N. Temp. 16.6. Sritver Nitrate, N. Potasstum CHROMATE, 735. Porassium Curomate, ;%,. 1080 1246 1425 1630 1865 2130 2460 2790 3170 10050 TABLE XVIII. Temp. 16.6. Sitver Nitrate, 3. Potassium Curomate, +X. TABLE XIX. Temp. 16.8. Sitver Nitrate, 3. Porass1uM CHROMATE, 7%. MORSE AND PIERCE. — SUPERSATURATION IN GELATINE. 647 TABLE XxX. TABLE XXI. Temp. 17.7. SitvER Nirrate, 3. Temp. 16.9. Sitver Nirrare, 3. Porassium CHROMATE, 735: Potassium CHROMATE, 735: x Vt 01274 .01296 .01294 01298 .01297 01295 .01295 .01293 .01288 .01292 PE ea TABLE XXIII. Temp. 16.0. Sitver Nitrate, §. Teme 156: SItveR Nirrate, 3. o N Porass1uM CHROMATE, 735: Potasstum CHRomATE, ;%5. 01829 01384 01331 013385 648 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE XXIV. Temp. 15.5. Sirver Nitrate, 3. N Potassium CHROMATE, 735. zx rm .01290 01299 01290 01297 01503 01301 013805 01506 .01299 Proceedings of the American Academy of Arts and Sciences. Vor. XXXVIII. No. 23.— May, 1903. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. ON THE THERMAL CONDUCTIVITIES OF CERTAIN PIECES OF ROCK FROM THE CALUMET AND HECLA MINE. By B. O. PEIRCE. INVESTIGATIONS ON LIGHT AND HEAT MADE OR PUBLISHED, WHOLLY OR IN PART, WITH APPROPRIATIONS FROM THE RumForD Fonp. (ta OES ty Oa Cb eS SELIM: COA ARS Coren oes Reeth Sa | ‘ ) CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. ON THE THERMAL CONDUCTIVITIES OF CERTAIN PIECES OF ROCK FROM THE CALUMET AND HECLA MINE. By B. O. PrErrce. Presented April 8, 19038. Received April 9, 1903. SEVERAL years ago Dr. R. W. Willson and I presented to the Acad- emy an account of some measurements of the conductivity for heat of several kinds of marble, and we discussed at that time * the theory of our method and described the apparatus we employed in our work. This present paper gives the results of determinations, by the same method, of the thermal conductivities of six representative slabs of rock from the Calumet and Hecla mine, very kindly lent to me by Professor Alex- ander Agassiz. ‘These conductivities are interesting in view of the fact that the rate of increase of mean annual temperature with the depth seems to be very unusually small near the shaft where Dr. Agassiz’s measurements were made. Each of the slabs is a rectangular parallelopiped about four inches thick and two feet square: their average weight is a little over two hundred pounds. ‘There are two specimens of trap, two of amygdaloid, and two of conglomerate. ach of the pieces of trap seems very homo- geneous, and each piece of amygdaloid sufficiently so to make the result of each measurement an excellent determination of the mean conductivity of the slab in question: in the case of conglomerate, some variations in conductivity are, of course, to be expected in different parts of any large piece ; I hope, however, that the figures given below represent with some accuracy the average conductivities of the slabs examined. The deter- minations involved steady work for several months. The size of the blocks to be experimented on made some slight modi- * These Proceedings, August, 1898. Vol. XXXIV. 1. 652 PROCEEDINGS OF THE AMERICAN ACADEMY. FiGure 1. fications necessary in the apparatus used for the work on marble, but the proced- ure was much the same. The square, plane-faced slab of the material to be tested, enclosed between two other thin slabs of similar mate- rial, formed a rectangular parallelopiped or prism, which was clamped and left for many hours, between the steam chest A and the ice-box Z of the apparatus, represented without any of its elaborate system of jack- ets, by Figure 1. The final temperatures at the centres of the faces of the slab to be tested were determined by the aid of thermal elements, and the flux of heat through a definite central portion of the colder base of the prism was measured. The hot chamber A, which weighed about two hundred kilograms, rested in a thick jacket on a heavy table or stand made to hold it: it was connected directly with one (B) of two stout-walled copper boilers, B and B’, each of which held about forty litres of water. a SS Ss Senne Se srahaeet RRO SNe BR “elas! Renee BP BOK & OF CERTAIN ROCKS. LI 2 OMELET Eee LIS 7 -- Es Ficure 4. 655 In the box, P, thus made, was placed a thin-walled copper ice-holder, Q, open at top and bottom, of the same outside diameter below as the inside of the brass pot, but some- 656 PROCEEDINGS OF THE AMERICAN ACADEMY. what smaller above. so as to leave an air-space between it and the walls of the pot. In order that the holder might be easily rotated, a pin soldered to a thin diametral web / which ran across the bottom of the holder was inserted in H, and a vertical brass rod soldered to a similar web, ZH, at the top of the holder passed through a hole in the cover of the pot which it fitted closely. An ebonite thimble fitting tightly on the rod and turn- ing with it, permitted the slow entrance of ice-cold air into the pot with- out allowing any water to leakin. The rod could be clamped at pleasure to a brass yoke which is turned slowly by the electric motor. In order to prevent the introduction of heat into the pot by conduction down the rod, the exposed portion was buried in cracked ice. When the holder was filled with ice and turned by the motor, the web at the bottom compelled the ice to rub over the floor of the casting, since the holder itself had no bottom; and as a result of this, the lower surface of the ice quickly acquired and kept a mirror-like surface. The drip from the pot came out of the edge of the casting Z through a straight hole about 26 cm. long and 0.6 cm. in diameter drilled horizontally in the plate and ending just inside the pot. The whole apparatus was very slightly tipped to insure the steady outflow of the drip. A large cylinder A, 385 cm. high, made of rolled brass 4 mm. thick and open at the top and bottom, was mounted on brass ball-bearings placed on the outside of the hard rubber jacket of the pot, P, by means of six vanes, one of which, X, is shown in Figure 2. K weighed about twenty kilograms when empty, and rested upon 144 brass balls each 12 mm. in diameter. When set in motion by a slight push A continued to rotate for about a minute before coming to rest; it was so truly hung that the outside could be used as a pulley and the whole rotated by means of the belt shown in Figure 1. The vanes reached to within about 2 mm. of the floor of the casting, and when the whole was filled with cracked ice and then rotated, the ice at the bottom which rubbed on Z soon got and held a very smooth surface. A hole in the bottom of Z carried away the drip and prevented any accumulation of water on the floor of the ice-box. To prevent irregu- larities arising from honeycombing of the ice in the box, a suitably loaded brass tripod was used to pack the ice by light blows delivered at inter- vals of about twenty-one seconds by aid of the lever LZ. A train of wheels was necessary to reduce the speed of A to one revolution in twenty sec- onds, though only two wheels are shown in the drawing. The tripod slid in guides which revolved with A, and a swivel at the top prevented the cord from twisting. PEIRCE. — THERMAL CONDUCTIVITIES OF CERTAIN ROCKS, 657 The rotation of A and of the inside ice-holder, Q, which is connected with K at the top by means of a yoke, were matters of much importance. The continual rubbing of the ice over the flat surface of the casting seems to be necessary if the upper face of the prism is to be kept at a uniform constant temperature for hours. ‘The heat produced in rotating Q slowly was so little as to be quite negligible. The ice in K was piled up so as to cover P completely, and I was unable to detect any difference between the temperatures within and without P by fine, properly protected ther- mal junctions introduced for the purpose. If while A revolved, Q was kept still, the amount of ice melted in Q became irregular, though the whole amount of drip in two or three hours was not very different from the amount of steady drip in an equal time when Q was rotating. Only selected lumps of ice were put into Q. The ice to be used was first broken up into pieces weighing something like fifteen grams each, by means of an ice-cracking machine, and these pieces were then put into ice-water so that their sharp edges might become slightly rounded. They were then drained and dropped into Q. In this way a slight amount of water attached to the ice was introduced, but with the method employed, the error due to this cause appeared to be of slight importance. In some experiments the ice to be used was carefully dried in cold blotting-paper, but this precaution did not seem to be necessary if the use of small bits of ice with sharp edges was avoided. @Q’s capacity was about two thou- sand cubic centimeters. After @ had been freshly filled in the course of any experiment while A was rotating, no record was kept for some time, perhaps fifteen minutes, of the amount of drip. Before the expi- ration of this interval the extra water introduced into Q with the ice had drained off, and the indications had become steady. The drip tube always contained a few drops of water, but this amount remained sensibly constant during the progress of an experiment. The drip was collected in a graduated vessel and the approximate amount was noted from time to time to see whether the flow was steady. The whole was then more accurately determined by weighing, at longer intervals. The regularity of drip seemed to be a far more sensitive test of the approxi- mate attainment of the final state of the body experimented on and its surroundings than was a sensibly constant temperature gradient on the axis. In most experiments with the apparatus a sufficiently steady state was attained in about seven hours from the beginning of the heating. Z and A together weighed when filled with ice about three hundred kilo- grams, and many hundreds of pounds of cracked ice were needed for a single day’s experiment. The area a of the bottom of the small ice-pot VOL. XXXVIII. — 42 658 PROCEEDINGS OF THE AMERICAN ACADEMY. was assumed to be 126.70 sq. cm. : this includes a slight correction for the thickness of the brass walls. The latent heat 4 of melting ice was as- sumed to be 79.25. If, then, r= rate of melting of ice in the pot, in grams per second, ¢= temperature of difference between the faces of the slab, d = thickness of the slab, k = mean thermal conductivity of the slab, Pe a AC Ta DrBag 4" k TABLE I. Material, in kilograms. slab in centimeters. Temperature of the warm face of the siab. Temperature of the cool face of the slab. Rate of melting of ice in the pot in grams per second. Thermal conduc- tivity of the specimen. | Weight of the slab Thickness _of the a Te) oO Amy gdaloid Amy gdaloid Conglomerate Conglomerate Table I gives some of the data of my final determinations. It would have been easy to give the value of & with greater apparent accuracy, but, in view of the lack of homogeneity in some of the slabs, this would have been misleading. The trustworthiness of results obtained with the apparatus described above is discussed in these Proceedings for August, 1898. Table II shows the results of other determinations of the thermal conductivities of different specimens of rock. Many of these, as will be seen, were made by Messrs. Herschel, Lebour, and Dunn for the British Association for the Advancement of Science. The names of the dif- PEIRCE. — THERMAL CONDUCTIVITIES OF CERTAIN ROCKS. TABLE IL. Substances. Fire brick Fine red brick Chalk Tough dry clay Devonshire clay slate . Whinstone trap rock Caen stone . Cornish red serpentine English marbles and limestones Granite Sandstone and hard dry grit English plate glass . American plate glass Carrara white marble . American and Italian colored marbles “ Sugar-white marble ” “ Fine-grained gray marble” Calton Hill trap (damp) Craigleith Quarry sandstone (damp) Greenwich Park gravel (damp) Sandy loam Serpentine . Observers. B. A. Committee Peirce and Willson “ “cc Despretz “ec Kelvin “ Everett Neumann “ 659 Conductivities. 0.0017 0.0015 0.0020 to 0.0053 0.0022 0.0027 0.0028 to 0.0048 0.0043 0.0044 0.0047 to 0.0056 0.0055 0.0055 0.0028 0.0026 to 0.0028 0.0051 0.0062 to 0.0076 . 0.0077 0.0097 0.0042 0.0107 0.0125 0.01386 0.0059 ferent substances are of course rather indefinite. My own experience shows that even thick sheets of fine plate glass bought at different times of the same maker may have conductivities which differ from each other by as much as eight per cent; while the conductivities of slabs of dry 660 PROCEEDINGS OF THE AMERICAN ACADEMY. white marble from different quarries may differ as much as thirty per cent. In the table I have, in two or three cases, taken the average of nearly agreeing results. It is evident that the conductivities of the specimens of dry rock which I have examined are relatively rather low. Tue JEFFERSON PHysicaAL LABORATORY, April, 1903. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIII. No. 24. — May, 1908. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. ON FAMILIES OF CURVES WHICH ARE THE LINES OF CERTAIN PLANE VECTORS EITHER SOLENOIDAL OR LAMELLAR. By B. O. PErrRce. epee Lay Ase? y, ON FAMILIES OF CURVES WHICH ARE THE LINES OF CERTAIN PLANE VECTORS EITHER SOLENOIDAL OR LAMELLAR. By B. O. PEIRcE. Presented April 8, 1903, Received April 29, 1903. Ir a vector function has no component parallel to the axis of z and if the tensors of its components taken parallel to the axes of x and y can be expressed by the scalar point functions X = ¢, (#, y), Y = de (a, y), which are independent of z, every line of the vector is a curve parallel to the xy plane, defined by the equations = = = = = and it is sometimes convenient to call the vector itself “plane” and to say that it is ‘coplanar with” z= 0. The projection on the xy plane of any line of such a vector is itself a line of the vector, and a survey of the whole field can be obtained by studying the lines which lie in this plane. The “divergence” of a vector coplanar with the xy plane is the oY quantity = 2 ay. and the “curl” of the vector is a vector, directed CNG SOS Ox (Oy in any region, the vector is said to be “solenoidal” in that region; a vector the curl of which vanishes is said to be “ lamellar.” Given any family of curves in the xy plane represented by the equa- tion uw = f; (x, y) = ¢, it is possible to find an infinite number of plane vectors which have the w curves as lines, by assuming in each case X at pleasure, and then making parallel to the z axis, of intensity If the divergence is zero The vector (X,, Yo) and the vector (R+ Xj, Rk: Y)), where # is any function of xy, evidently have the same lines, and, if (Xj, Y,) has for lines the w curves, no other vector has the same lines unless it is of the 664 PROCEEDINGS OF THE AMERICAN ACADEMY. form (2: X), R: Y,). Of all the vectors which have the w curves for lines some are lamellar, for, if v is any functior orthogonal to u, defined by the equation ou dv .du dv Ba te oa ral OE (1) sede et) Sun oy wake so that the curves of the families « = c,, v = c, cut one another at right ; dv dv Palak angles, the vector which has the components (= Dy has for its lines v oy the wu curves, and it is lamellar, since ov Oy Oz: oy oy ox If (Xj, Yj) which has the w curves for lines is lamellar, so is the vector [X,:F(v), Y,: F(v)], where F represents any ordinary function; and no lamellar vector has the same lines unless it is of the form just given. If (X,, Y,) is a solenoidal vector which has the w curves for its lines, the vector [X, + (wu), Y,- #(u)] has the same lines and is also sole- noidal ; no solenoidal vector has these lines unless it can be written in this form. It will soon appear that of all the vectors the lines of which are the « curves, some are always solenoidal, but no vector which has these curves for lines can be both solenoidal and lamellar, unless u happens to satisfy Lamé’s condition for isothermal parameters,* that is, V2 (u he unless is expressible as a function of wu alone, where O7u =u ou? ou\? V?(w) = = -- Oy eS a) = e If a set of orthogonal curvilinear codrdinates in the xy plane be defined by the functions Uu ig (x, Y), v = fr (x, y)s UO (a y, Van@y) and if represent the magnitudes, at the point (a, y), of the components, taken in the directions in which w and v increase most rapidly, of a vector, Q, coplanar with z= 0; it is not difficult to prove, by direct transforma- * Lamé, Lecons sur les coordonnées curvilignes, p. 81; Lecons sur les fone- tions inverses, p. 5; Somoff-Ziwet, Theoretische Mechanik, I. 115 and 128. PEIRCE. — LINES OF CERTAIN PLANE VECTORS. 665 tion or otherwise, that the divergence of Q is given by the well known expression Div. Q= (z) V? (u) + ,?- mi) + V 3 and that ; Tensor curl Q = hy, he | 5 (ge -)- aAtaik (2) If the lines of Q coincide with the wu curves, the vector has no com- ponent perpendicular to these curves and U is everywhere equal to zero, so that Div. Q= —- V3 (v) + A? - # >(z) (3) Tensor curl V=Ah, -h,: £ (=) (4) where h, is the gradient of v. In applying these expressions it is convenient to remember that h,, sents Vu) dlog( 5") v4(v) _ dtox( 7) lo Ou” h,? dv It is easy to see from (3) and (4) that the statements which follow are true: (a) If Vis to be solenoidal,* we must have ro) V Vv? < ay 0S ZJ=- = . (5) The second member of this equation is expressible as a function of wu and v; if it be integrated with respect to v while w is considered constant, and if the arbitrary function y (w) be added to the result, we shall get y (wu, v) + x (uw) the partial derivative of which with resnect to v is V2 (v) Sega? then hha: eA) ewer. (6) * See equation (18). 666 PROCEEDINGS OF THE AMERICAN ACADEMY. (6). If V is to be lamellar, we may write V= h, a (v), (7) where 7 is any ordinary function. Its divergence is 7 (v)* V*(v) + h,?° 7! (v). If V is to be solenoidal as well as lamellar, we may obtain Lamé’s condition immediately by substituting the value of V from (7) in (5). (c) If, like the vector which defines the field of electromagnetic force within an infinitely long cylinder of revolution which carries lengthwise a uniformly distributed, steady current of electricity, V is solenoidal and a function of wu only, we must have oe aL or 2° ¥2(v) = Oe) @) (d) If, like the attraction within a homogeneous, infinitely long, cylinder of revolution, V is lamellar and a function of v only, the gradient of v cannot involve w, so that h, =f (v), where f is arbitrary, s = 10) (9) (e) If V is lamellar and a function of u only, = must be independent of wu and : oh, Ou . — isa function of w only. (10) v In this case h, is either a function of u only or is expressible as the prod- uct of a function of uv and a function of »v. (f) If V is to be solenoidal* and a function of v only, the expression dv Vv) dv (11) * See equation (27). PEIRCE. — LINES OF CERTAIN PLANE VECTORS. 667 must be either constant or expressible in terms of v. If V is not lamellar, h, must in this case involve wu. (g) If Vis lamellar and if © is a scalar potential function of V, Q must be expressible in terms of v and the divergence of V is equal to dae es LO: Or tena (12) (h) If the tensor of V has the same value for all values of x and y, V is lamellar if, and only if, /, is constant or expressible in terms of v; it is solenoidal if, and only if, 22 (v) = (8) (¢) Whatever wu is, the vector which has the components SO age 70 h, dx Sethe gous and the vector which has the components (vr) a0 dv) | dv XxX, = h, a 7) hy oy ) have the w curves for lines. The tensor of the first is a function of u only, that of the second a function of v only. (7) Ifa solenoidal vector has the u lines for curves, its curl must be of the form (uw) * V?(w) + d!(u) * h,?, where ¢ is arbitrary. If, for instance, the w curves are concentric circumferences, the curl of the vector must be expressible as a function of the distance from the centre. (k) If the tensor of a vector V which has the w curves for lines is a v2 F function of w only, its divergence is of the form Teh 2 = x): If the w curves are concentric circumferences, V must be solenoidal. (J) If the tensor of V is expressible in terms of v, the tensor of its h, Oh eurlis — V=- =. h, Ou a point, the curl is zero and the divergence a function of the distance from the point. The velocity in the case of a steady squirt * motion of a gas illustrates this. If the « curves are straight lines emanating from * Minchin, Uniplanar Kinematics, 178, Examples 21 and 22. 668 PROCEEDINGS OF THE AMERICAN ACADEMY, THE GRADIENTS OF Functions oF Two INDEPENDENT VARIABLES. Before we consider briefly some of the equations of condition which have just been stated, it will be well to make a few simple statements concerning the gradients * of functions of x and y. The gradient of a function may or may not be expressible in terms of the function itself. The gradients of the expressions (x? + y”), (x? — y’) illustrate these two cases. If the gradient of a function v is equal to f(v), it is possible to form a function of v, a the gradient of which is constant. dv OM If the gradient of a function v is equal to the constant a, it is possible b to form two functions of v, namely = and 2 i J (v) dv, the gradients of which are equal, respectively, to the arbitrarily chosen constant 6 and to the arbitrary function f(v), If the gradient of a function v is either constant or expressible in terms of v, the gradient of any differentiable function of v is expressible as a function of ». If h, is neither constant nor expressible in terms of v, no function of v exists the gradient of which is expressible in terms of v. Since the gradients of two conjugate functions are numerically equal, it is clear that if 4, is expressible in terms of v, not all other functions the gradients of which are functions of v, are themselves expressible in terms of v. If, for x and y in the expression dv\? ov\? a naakse —_ w= (32) +)» the quantities X= G (a, y), » = H (a, y) be substituted, we shall obtain the new expression du? ou \? OX Op , OX Op\ (dv dv pee Au Ty (se ace apf, Ge CAYCE CA Cp ous’ tse (x) ole (x) a 2( oe ae Oy” x) sean and if we writeX = («+ yt), p= («x—y?), * Lamé, Legons sur les coordonnées curvilignes, p. 6; Maxwell, Treatise on Electricity and Magnetism, § 17. PEIRCE, — LINES OF CERTAIN PLANE VECTORS. 669 | ae Se . (14) from this last equation it is evident that if the gradient of v vanishes, v is either a function of x + yz? or a function of « — y?. It is often convenient in dealing with differential equations which involve the gradients of functions, to use the independent variables of equation (14) and we may note that w and v, two functions of » and p, are conjugate if, and only if, Ju 72 Ou . ov On ae oe =—12 an . (15) If uw and v are orthogonal functions, du ov Ou dv a-nzat>-~ =0. 16 OW deh Oa ON as) If the gradients of u and v, two real functions of x and y, are every- where equal while the directions of their gradient vectors are different, O(u—v) Mu+v) J(u — v) (wu + v) v) Be Los te pour cn Thay ee Ce and the functions (w—v) and (w+ v) are orthogonal. The converse of this statement is true. If two orthogonal functions have equal gra- dients these functions are conjugate. If the gradient vectors of two functions have the same direction at every point of the xy plane, one of these functions is expressible in terms of the other. Thé quantities « = cos (bx —y), v = sin (by + =) illustrate the fact that the gradient of each of two orthogonal functions may be expressible in terms of the function itself. The quantities w= 2?+ 47, v= tan i illustrate the fact that the gradients of both of two orthogonal functions may be expressible in terms of one of the functions. If the gradient of v, one of two orthogonal functions (w, v) is expressi- ble in terms of x, or is constant, no other but a linear function of v has a gradient expressible in terms of w. If the gradient of each of two orthogonal functions (w, v) is expressi- ble as a product of a function of w and a function of v, so that 670 PROCEEDINGS OF THE AMERICAN ACADEMY, h,=fu).F), h=¢ (@u), ¥ (v); du dv Fu)’ J ¥) tively, the gradient of each of which is expressible in terms of the other. A solution of Laplace’s Equation and any function of its conjugate are orthogonal functions the ratio of the gradients of which is a function of the second function. it is possible to find two functions, » of w and v respec- VeEcToR POTENTIAL FUNCTIONS OF PLANE SOLENOIDAL VECTORS. If u, v define a system of orthogonal curvilinear codrdinates in the xy . plane, and if Q,, Q,, Q. are the components of a vector Q, taken in the directions in which wu, v,; z increase most rapidly, the components of -the curl of Q in these directions are h oe _ 2 (2) | 1 2 (#) -3 | Op hae hoy “| Oz\h, du _|’ SRO tS 10, ti 5G) ~ ae) | We may denote these quantities by K,, A,, K., respectively. If Q is to be a vector potential function of a given solenoidal plane vector (0, V, 0), which has the wv curves for lines, we may assume that the components of @ involve uv and v only, and since in this case, A, = 0, K, = V, write Q, = F(u), where V=—A,,. ee the form [Q,, Q,, /(u)], where Q,, Q,, are any functions of u and v : neo i) Caf eo \ue : subject only to the condition aCe) aa (+), is a vector potential Any vector of function of a solenoidal vector which has the w curves as lines, and there is no vector of this latter kind which does not have as a vector potential a vector of the form just given. In most cases it is simplest to make Q,= Q, =0. If, now, we ask what condition must be satisfied by the function w in order that the curves of the family « = ce may be the lines of a vector the tensor of which involves « only, we learn that, since V is of the form —h,,* F'(u), it is necessary and sufficient that h,, be a function of u only. That is Oh, 3 = 9 (18) PEIRCE. — LINES OF CERTAIN PLANE VECTORS, 671 Since the divergence of any vector V which has the w curves for lines is : may be written in the form h, .h,. - () as well as in the form (3), the condition stated in equation (18) is at once obtained. If we denote the quantities aie Oy’ Apa? Oa. oy’ Oy?’ ee Oy” aa Da. Oy’ 5y2? by p, 7, 7, 8, t, p!, g', 7’, s!, t!, respectively, we have, since « and v are orthogonal, ms pp'+ 97 =0; (19) whence by differentiation we get pa or + g's igs — 0 (20) pistpsii+qt+qt=0. (21) h We have, moreover, = = i = COs (72) — - : * = a ; 9 ! a) ! and, similarly, ond SPEER omy ee aie (22) Ou he’ dv he so that Oh, Oh, On | Ohy Oy 1 (dh, Ou , hy du du dx du dy’ du h\ dx du” dy ” dy pr + 2pqs+ qt Rae er (23) ang ln hy Oe | Shy By _ 1 (Shy Ov | hy do dv Ox Ov dy “dv hi \ ox Ox" dy” dy Elegie) 3G =P) gh, h Since, however, 4,7 = p? + q?, hk? =p?+q"; gG.khfap?.h lake MOL MG aa BGI) 2 and Ov he he ie Equation (18) is equivalent, therefore, to the equation part @—p*)s—pqt=o. (25) 672 PROCEEDINGS OF THE AMERICAN ACADEMY. If for r and ¢ in (25) we substitute their values as obtained from (20) and (21), we shall get the equation g?r —2p'q's' + p?t!'=0. (26) and this is (8) in expanded form. If equation (18) or its equivalent (26) is satisfied, it is evident that by choosing /’(w) at pleasure we may find an infinite number of solenoidal vectors which have the w curves as lines and have tensors which involve u only. A comparison of equations (9) and (18) shows that the condition that the uw curves be possible lines of a set of solenoidal vectors the tensors of which involve w only, is the condition that the v curves be possible lines of a set of lamellar vectors the tensors of which involve wu only. If Q is a vector potential function of a solenoidal vector which has the u curves for lines, and a tensor expressible in terms of v, — h,, F!(w) is a function of v, and /, must be expressible as the product of a function of u and a function of v, that is, ha = J(u) + $(0). (27) If for uw in this differential equation we substitute w, defined by the equation w= a we get the simpler equation Ny h, = $(v) or a 0. (28) It is to be noticed that w has the same lines as uw, and that (27) and (28) define the same curves; the equations (11) and (28) are evidently equivalent. If w is such that a solenoidal vector, V, can be found which has the w curves for lines and a tensor expressible in terms of v, its x and y V ov V ov Ay” Ox? hy” Oy by X, Y, every other solenoidal vector which has the same lines has components of the form X-y(u), Y-:yW(u), and the vector is not a function of v alone unless the factor y (wz) degenerates into a constant, and the vector is a simple multiple of V. A comparison of (10) and (27) shows that if the w curves are possible lines of a solenoidal vector the tensor of which is expressible in terms of components are ( i If we denote these components PEIRCE. — LINES OF CERTAIN PLANE VECTORS. 673 v, the » curves are the possible lines of a lamellar vector the tensor of which is a function of v only. oh oh If —-=0 and =— dv Ou noidal vectors the curls of which are expressible in terms of u only; and the v curves are the lines of a set of solenoidal vectors the curls of which are expressible in terms of v only. = 0, the wu curves are the lines of a set of sole- PossIBLeE Systems or ISOTHERMAL STRAIGHT LINES AND IsOTHERMAL CIRCLES IN A PLANE. (1) Let ax + By =1, where a and f# are any functions of a single parameter w, represent a family of straight lines in the xy plane, then we may write pegs ae ed 2 7 ae a + B de wat ply’ dy adetply’ ~ (le + ply’ Wi@) 2i(aial 1B BOY ala = By (29 Re rma ain RE ) V7(u) . ‘ . If then z2 38 to be a function of uw only, the last term in the second member of this last equation must be expressible in terms of w only, and we have a —'0, or 6’ = 0) or, in general, a! : a! = 6! : 8, so that a =cf+d, where ¢ and d are constants of integration. The equation of the family of lines must be of the form (cB + d)x+ By=1, and 7 chosen at pleasure. If d = 0, the lines are parallel. (2) Let 2? + y? — 2ax —2 By = y, where a, B, y are functions of a single parameter w, represent a family of circumferences in the xy plane, then we may write the lines all pass through the fixed point € — 5): which may be Cees ONe =) Sy SH aes ie eae dx 2a +2Blyt+y!’ Oy 2ada+2hyt+y"’ hws 4(a?+ B? + y) Garr 2 Bly ae Vu) Zac! + 2B! + y! 1 lalla 2p y pl! 30 HT ate eRe ane Bay Dal + 2ply + x" | VOL. XXXvIII. —43 674 PROCEEDINGS OF THE AMERICAN ACADEMY. V?(u) lng of (30) must be expressible in terms of u only. If a’ = f/=0, we have a family of concentric circumferences. In general we may write alla! = 6" 6 yy or fb = man, y= 2kha +L sotman ie equation of the circles must be of the form lt is a function of wu only, the last term in the second member x?+y—2axr—2y(ma+n)—2ka—l=0, (31) where a is the only parameter. If we represent the first member of this equation by S,, the equation S,, — S,, = 0 represents the straight line through the points of intersection of the circles which correspond to the two values a,, a, of the parameter. In this case the line is x + my + k= 0, whatever the values of a; and ag, therefore, as is well known, the system of isothermal circles * must pass through two fixed, real or imaginary, points. FuNCTIONS THE GRADIENTS OF WHICH ARE EXPRESSIBLE IN TERMS OF THE FUNCTIONS THEMSELVES. Several of the conditions stated in the previous pages [see (d), (2), and equation (18)]| require that the gradient of a function be expressible in terms of the function itself, so that the normal derivative of the function has the same numerical value at all points of any one of its curves of level. We may state this requirement in a somewhat simpler form, however, if we remember that since the gradient of any function, , of wu is equal to ¢! (w) « h,,, the lines of all functions which satisfy the equation h, = f(w), whatever f may be, are included in the lines of functions which satisfy the equation h, = 4, where & is any constant (for instance 1). Every such family of lines forms a set of parallel curves. We have to solve, then, the equation a) 2 (2) +()- on one of the standard forms for partial differential equations of the first order. Its complete integral is u=ax+yV/FP—a' +e, and its general integral, * Darboux, Legons sur la théorie générale des surfaces. PEIRCE. — LINES OF CERTAIN PLANE VECTORS. 675 us-art+yVk—a+y(a), (33) subject to the condition 28) 0=2 — — + ' (a). eee) The equation h, = £& is also equivalent to the equation, du du a Sale 54 Teach Co The complete integral of (35) is u=ar+ e + ¢, a and its general integral * may be found by eliminating @ between the equations, u=aht+" + (a), 0=r’—F+ Ha). (35) If « is to be harmonic while /,, is expressible in terms of uw, wu is of the form #(A) + W(u), where A=x+ yi, w=x—yi. Since Ae Ou du No ee an: Ou? we must have ; 4¢' (A) WH) =4f (EQ) +¥ @))] (36) - and if we differentiate both sides of this equation with respect to A and uw we shall get gO) VW) =e -f'[6Q) +¥ WI HOA) WX) = WW) “f [6Q) + ¥Q@)] whence ene 7 ee) (37) vOP Ly @) Since the first member of (37) involves A only, and the second member pw only, we may equate each member to a constant, — 4”, and consider separately the cases where £ is or is not zero. * Forsyth, Differential Equations, p. 307. 676 PROCEEDINGS OF THE AMERICAN ACADEMY. (1) If k=0, p! (A) = 9, W" (u) = 9, f(A) = cA +m, W(u)=dptn and w=cr+du+Q. Ifc and +d are either real and equal, or conjugate complex quantities, the w curves are a set of real parallel straight lines. Q eso. Py. Ge ie Pr w Pete #0) =53'log (PAtm) +a, Ye) =p log Hn tn) +s, and if the constants of integration are so chosen as to make w real or purely imaginary, the « curves are a set of parallel, that is, concentric, circumferences. Every family of isothermal lines which are the curves of a function u which satisfies (18) is either a set of parallel straight lines or a set of concentric circumferences. No other families of parallel curves are isothermal. h THE Equation h, : a = W702). ou We have seen that equations (18) and (26) are equivalent; this equa- tion, therefore, defines the families of straight lines which form the orthogonal trajectories of the families of parallel curves defined by the equation h, = f (v), and we may write ; gr—2pgst+ p?t=O0. (38) Monge’s method yields the first integral wu = F (2), (39) and of this equation par ane =o (St!) (40) is the complete integral and aty ), “= 41 cee a where y (a) — x = (a + y) wy (a), the general integral. Every family of straight lines in the zy plane, that is every set of lines defined by the equation ax + py = 1, where a and p are arbitrary PEIRCE. — LINES OF CERTAIN PLANE VECTORS. 677 functions of a single parameter, are contained as, of course, they should be, in this general integral. It is evident that every family of isothermal lines which are the curves of a function « which satisfies (38) is a set of straight lines which pass through a point. TRANSFORMATION OF THE Equation h, =f (v). Given a function which satisfies (10) or (27), there always exists a function which has the same lines, and a gradient expressible in terms of the orthogonal function alone. The lines of all functions which satisfy these equations are therefore those of functions which satisfy an equation of the form oh ——— Y du © or pr+2pqs+q7t=0. (43) If we take advantage of the Principle of Duality and make p = z’, q=y',px+qy —2z= 7%, we shall get the transformed equation al + tf —Qaly! +s! + yl? +r =O, (44) and if then we put, m = — 2 log (2? + y”), n = tan (2), the result is Ou ou which is equivalent to Fourier’s familiar equation for the linear flow of heat. h If u is to be harmonic, while oh, = 0, we may write Ou u=o(r+yi)+v(«a—y), and substitute this value in equation (43). The resulting equation is [o! (@ + yt] we" (@ —y) + [y @ — yt)? oO" (@ + y) =0, (46) way) "(et y) We-w> Wet (47) or 678 PROCEEDINGS OF THE AMERICAN ACADEMY. This last equation is possible only if each member is constant, (— k”), 1 1 whence = 7° log (A'w + m) + a, $= — 73° log (A+ n) + 6, and the w curves are a family of straight lines meeting in some point. No other families of isothermal lines are possible curves of scalar functions, the gradients of which are expressible in terms of the corresponding orthogonal functions. THE JEFFERSON LABORATORY, CAMBRIDGE, Mass., April, 1908. Proceedings of the American Academy of Arts and Sciences. VoL. XXXVIIL. No. 25.— May, 1903. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD COLLEGE. THE SPECTRA OF GASES AND METALS AT HIGH TEMPERATURES. By JoHn TROWBRIDGE INVESTIGATIONS ON LIGHT AND HEAT MADE OR PUBLISHED, WHOLLY OR IN PART, WITH APPROPRIATIONS FROM THE RuMFORD Funp. ue . ‘ Ji ; ‘ — THE SPECTRA OF GASES AND METALS AT HIGH TEMPERATURES. By Joun TROWBRIDGE. Presented April 8, 19038. Received May 2, 1903. In previous papers I have described certain phenomena which arise in the employment of photography in spectrum analysis — especially the phenomenon of the appearance of dark lines instead of bright lines in the spectra of electrical discharges in Geissler tubes. The application of photography to spectrum analysis has the great advantage of giving an impersonal record of certain phenomena by sub- stituting a chemical method of investigation for eye observations. We thus obviate the personal equation of the observer; but unfortu- nately we bring in vagaries of the photographic plate. The photographic plate can be called an instrument with an infinite number of adjustments. The molecular movements of the silver mole- cules under different degrees of electric stimulation can give us a great number of combinations. In short, the photographic plate does not afford a simple method of observing the effects of different waves of light on the molecules of matter. Its complicated nature is well shown by the records it gives of the intensity of light which provokes its action. It has long been recognized that the blackness of a negative is no crite- rion of relative intensity of light ; in other words, that the negative cannot be employed as a photometer except in the crudest way. A method of illustrating this fact is given in this paper. The photographic method of observation in spectrum analysis, how- ever, is naturally of great use in preserving records of a great multi- plicity of phenomena; but we have to be on our guard in interpreting these phenomena; for, unlike the galvanometer or the bolometer, our recording instrument is complex. Furthermore, when we use an electric spark to agitate the molecules of a gas or the molecules of a metal we use one complicated means to study a still more complicated phenomenon. When one asks what is the spectrum of water vapor, one must define the conditions of the electrical stimulus; for one can, by increasing the ~ 682 PROCEEDINGS OF THE AMERICAN ACADEMY. range of this electrical stimulus, run through a gamut of dissocia- tions and recombinations. One never deals with a strictly pure vapor or gas. The spectra of metals in atmospheric air are the visible evidence of extremely complicated chemical reactions due to the reaction of the metallic vapor and the gases of the atmosphere. The spectra of gases also in narrow containing vessels of glass or of quartz, are modified by the walls of these vessels when the temperature of the gases is very high; moreover, the ordinary method of obtaining photographic spectra either of metals in air or rarefied gases by long continued discharges produced by the Ruhmkorf coil of transformers masks certain funda- mental reactions. It is therefore desirable to study the effect of known quantities of energy successively applied to produce spectra either of metals or gases. This can best be accomplished by charging a condenser to a known amount by a known electromotive force, and by discharging the con- denser between terminals of metals either in air or in gases. If the spectra produced in this manner by discharges varying from one to any desired number are photographed on the same plate and treated alike in the same developer, the ground may be prepared for some generaliza- tion of the extremely complicated reactions I have mentioned ; I believe that this method is a fundamental one to use if order is to be brought out of the chaos of spark spectra. I have applied this method in the following manner: A storage bat- tery of from ten thousand to twenty thousand cells is employed to charge a condenser —.1 to .3 microfarad. By a simple mechanical appliance the condenser is detached from the poles of the battery, and is discharged between suitable terminals. Although it is impossible to avoid a slight spark at the moment of making contact-with the receiving system, an approximately equal quantity of electricity is communicated to this system at each discharge. The method also permits of a definite control. In order to photograph on the same plate the spectra produced by successive discharges the photographic plate must be slid vertically from one position to another, at the focus of a Rowland grating. The most convenient arrangement for the study of gaseous spectra is to employ a grating of short focus, and to enclose it in a light, tight box. For com- pactness, and to dispense with a dark room, I have employed the method of mounting the grating in such a manner that the normal to the ruled surface passes through the slit. The camera swings on the arc of a circle described by an arm of half the radius of the grating. This arm TROWBRIDGE. — SPECTRA AT HIGH TEMPERATURES. 683 is pivoted at a point half way between the ruled surface and the slit. In Figure 1, G is the grating, M the point midway between the grating and the slit, C the camera swinging on the arc described from M. Figure 2 gives a side view and elevation of the camera. P is the photographic plate, O an opening closed by a slide operated by a lever arm which engages with A. The plate holder closed by another slide S, can move up or down in parallel ways. In Figure 1 is shown a lever arm LM with fulcrum at F. This lever lifts another lever AM, which in turn lifts or closes the shutter A, Figure 2. The lever LM is outside the dark box, SUE and the operation of exposing the plate and closing the camera can be performed without opening the box. The method which Rowland used in mounting the grating is undoubtedly preferable to the above, when an accuracy greater than one-tenth of an Angstrom unit is aimed at. The advantage, however, of the method I have employed is in its com- pactness and in the possibility of working in a light room; moreover, in gas spectra an accuracy even to one Angstrom unit is often respectable. The capillaries which I used in this investigation may be termed scientific electric furnaces for studying by photography the spectra of gases at high temperatures, and the spectra of the vapor of metals at such temperatures in rarefied media. These capillaries were from four to five inches long, with internal bore of from one millimeter to’ one and a half millimeters. The metallic terminals were approximately of 684 PROCEEDINGS OF THE AMERICAN ACADEMY. the same diameter as the capillary, and were inserted in the capillaries until the distance between the ends of the terminals in the capillaries varied from one centimeter to two millimeters. The capillaries were made of lead glass; of German glass which did not contain an appreciable amount of lead; and of quartz. When an electric discharge occurs near a luted joint or surface a species of what may perhaps be termed electric distilling takes place. If silicate of soda is the luting agent, the vessel containing the rarefied gas becomes coated with a white film which shows the soda reaction; if a preparation of gums or shellac is used an organic film is obtained. Fra, 7 2 ‘ P By the use of long capillaries in which the discharging metallic points are several inches from the points of luting this distilling action can be entirely avoided. Itis therefore not necessary to use platinum for closing the ends of the capillaries in order to exhaust the latter. Quartz capil- laries can be used without fear of introducing impurities from the luting agents, if long terminals are employed with the luting points at a dis- tance from the discharge points. In the use of capillaries with metallic terminals almost in contact with the walls of the containing vessels there must necessarily be spectra, one would suppose, arising from the substances of these walls and a combina- tion of these substances with the rarefied gases. It is also possible that TROWBRIDGE. — SPECTRA AT HIGH TEMPERATURES. 685 even if the walls do not show a characteristic spectrum they may influ- ence by a species of katalytic action the reaction between the rarefied gases and the vapors of the metallic terminals. It is interesting to observe the appearance of successive orders of spectra photographed by the camera I have described with progressively increasing strengths of electrical discharges as well as repeated discharges of the same strength. When, for instance, the capillaries are filled with rarefied water vapor one generally obtains with comparatively weak electrical discharges hydrocarbon spectra which possibly arise from traces of carbonic acid in the capillaries or from traces of grease in the stopcocks of the pump. ‘These banded spectra decrease in strength as the strength of the electrical discharges increases, and finally disappear with powerful discharges. The hydrocarbon combinations are evidently broken up and new reactions and combinations enter. We therefore may not be able to recognize in these new reactions the presence of a simple component. In the study of the spectra of heavenly bodies which may be con- sidered from the point of view of furnaces, this fact I think should be borne closely in mind. Substances may be present which do not appear in the spectra observed at great distances; 'for the relative brightness of metallic lines and gaseous lines is much modified by the combinations which enter in an environment of high temperature. Figure 3 (the photographs are reproductions of the negatives, and are not positives) is a reproduction of the spark spectrum of calcium in the neighborhood of the H.H. lines of the solar spectrum taken by the method of successive discharges of known amounts of electrical energy. The discharges ran from one to five. It is interesting to notice on the negatives that the photometric intensity of the lines estimated by the blackness is not directly proportional to the amount of energy. Thus the spectrum produced by four discharges is not twice as intense as that produced by two discharges. It is noticeable, also, that the calcium lines, wave lengths 3737 and 3706, are stronger on the negative than those which coincide with the H.H. lines, and always appear with these lines. Figure 4 is a negative of discharges running from one to four in a Geissler tube of glass which did not contain an appreciable amount of lead in its composition. The capillary was two millimeters, internal diameter, and four inches in length. The pressure of hydrogen was one millimeter. It is noticeable that the lines which coincide with the H.H. lines are not accompanied by the lines, wave lengths 38737 and 3706; 686 PROCEEDINGS OF THE AMERICAN ACADEMY. although the intensity of the lines coinciding with the H.H. lines, if they were calcium lines, would require the presence of these lines. A series of experiments was undertaken with metallic terminals one centimeter apart, in lead glass. The diameter of the capillary varied from one to two millimeters. A spectrtm similar to that of Figure 4 was obtained with the addition of certain lead lines, several of which were reversed on the side toward the ultra violet. The portion of these lines not reversed broadened toward the red end of the spectrum; and this broadening increased with the intensity of the discharge (Figure 7). No calcium lines appeared. When cadmium terminals were used many of the cadmium lines were reversed, and here also the bright portion of these lines was much broadened. In the case of cadmium no other lines was observed (Figure 6). The gaseous ions contributed little or nothing to the photographic effect. When iron terminals were employed no iron lines were obtained even when the terminals were only three millimeters apart; nevertheless the lines and bands usually attributed to silicon came out with great in- tensity. When, however, aluminum terminals were substituted for iron terminals, aluminum lines, together with the supposititious silicon lines, were obtained. It was noticeable that the two lines coinciding with H.H. lines of the solar spectrum did not appear, while the two charac- teristic aluminum lines between the H.H lines came out reversed. The lines corresponding with the H.H. lines always appeared when a dis- charge of like intensity produced the spectrum of aluminum in air. The iron of which the terminals were made was ordinary soft iron, with a melting point not far from 1100°, while the melting point of aluminum is between 700° and 800°. If the silicon is volatilized it is difficult to see why the iron gave no spectrum, while the aluminum yielded one, for there is not a very great difference between their melt- ing points. Another series of experiments then were made with metallic terminals in quartz capillaries varying in internal diameter from two to three millimeters, the terminals being one centimeter apart. The same spectra were observed as are represented im Figure 3, with an absence of the lines corresponding with the solar H.H. lines. This absence was no- ticeable, also, when metallic terminals were one centimeter apart in lead glass. Iron terminals gave no iron lines in the quartz tubes, while alu- minum lines appeared when aluminum terminals were used instead of iron terminals. When the metallic terminals were placed three millimeters apart in TROWBRIDGE. — SPECTRA AT HIGH TEMPERATURES. 687 the quartz tubes the light from the tubes was very feeble, traces of metallic spectra appeared, and the walls of the quartz capillaries were speedily covered with thin films of the metals; even at the first dis- charge, before there was a sensible obscuration due to the formation of the films, there was no evidence of gaseous spectra. The main discharge appeared to be carried over by the metallic vapor and no dissociation of the gas was evident. Measured by definite amounts of electrical energy, the rating of the intensity of spectral lines differs totally from existing eye estimates. The lines which coincide with the H.H. lines in the spectra of the metals with high melting points generally came out first on the photographic plate when the method of successive discharges was employed. Rarefied nitrogen gave far less light than hydrogen, water vapor, or oxygen. When oxygen was employed, characteristic groups of doublets were obtained like the A and B groups in the solar spectrum. The heads of these groups apparently coincided with the middle of broad lines shown in Figure 4. The middle of these broad bands or broad lines coincides also with narrow lines usually attributed to silicon. Are certain lines attributed to silicon really oxygen lines? Salet, and also Rowland, assign the photometric intensity of 4 to the lines 4131.5 and 4126.5, 3 to the lines 3905 to 3855.7, and 10 to the line 2881. When the lines given on plate 4 and those on plate 7 are photographed on the same plate by the same number of discharges and are compared in regard to intensity, the rating is completely reversed, the lines at 4131.5 and 4126.5 and 3905 to 3855.7 being 10, and the line 2881 being three or four. The broadening of what have been considered metallic lines in rarefied cases I consider a most interesting phenomenon. Only the strong lines of the spark spectrum of the metal in air seem to be reversed under the effect of powerful discharges in rarefied gases. This broadening appears to be the evidence of reactions between the vapor of the metal and the surrounding gases. In this connection it is well to bear in mind the fact that metals continue to give off gases for a long time when submitted to powerful electrical discharges in vacuum tubes. This has been shown by Dr. Rollins of Boston in his researches on X-rays. These nascent gases are in condition to exhibit complicated reactions with the strongly heated metallic terminals. My experiments lead me to strongly doubt conclusions drawn from the apparent absence of this or that element in the spectra of stars ; for there is a strong possibility that reactions enter which may mask the presence of this gas or that metal. 688 PROCEEDINGS OF THE AMERICAN ACADEMY. The conclusions of my work thus far are as follows: 1. The metallic lines due to terminals in rarefied hydrogen, and rarefied air, when these terminals are one centimeter apart in glass or quartz capillaries, exhibit a reversed action. When this takes place it is generally coincident with the position of the line when the spectrum is taken in air, while the spectrum of the line on the least refrangible side is much broadened. This seems to indicate a gaseous product; an oxidization or hydration due to the dissociation of the air and water vapor present. 2. Highly heated rarefied hydrogen and rarefied air passing over con- taining walls of glass or amorphous silica give broad bands which ap- parently coincide with narrow silicon lines of far lesser intensity. These also I attribute to the dissociation of air and water vapor. The bril- liancy of the light produced in this reaction is far greater when there is an excess of hydrogen in the tubes than when rarefied air fills them. It is a question whether lines produced by metals like silicon in their difficulty of volatilization in air are really due to the metals. I am in- clined to attribute some of them to the environment; that is, to a reac- tion between the metal and the gases present. 3. Spark spectra of metals appear to represent complicated reactions of gases with the metallic vapor. : 4. Metallic vapor carries the main portion of an electric discharge when these terminals are within three millimeters of each other in rarefied hydrogen or rarefied air. ‘The gaseous ions, if the dissociation occurs, give little light. 5. The broadening of the light accompanying the reversed lines, if unsuspected, might lead one to conclude that a shift of the bright portion had occurred. 6. Since the iron lines do not appear under what seems favorable conditions while aluminum lines appear; while in other cases gaseous lines mask metallic spectra, it seems desirable to be cautious in regard to speculations in regard to types of stars. 7. Whatever may be the cause of the reversals of lines observed in narrow capillaries of glass or of quartz, it seems to me that it is a fact which should be reckoned with in photographic study of stars, especially in the case of sudden changes of light. JerrersoN PuysicaL LaBorarory, Harvarp UNIVERSITY. VOL. XXXvi1I. — 44 te quo "G AUNOIY ‘9 GUNS mae ‘p THOo Ly oe =) in 3 ; J } ‘J v Proceedings of the American Academy of Arts and Sciences. VoL. XX XVIII. No. 26.— Jury, 1903. RECORDS OF MEETINGS, 1902-1903. A TABLE OF ATOMIC WEIGHTS. By Tueopore WILLIAM RICHARDS. REPORT OF THE COUNCIL: BIOGRAPHICAL NOTICES. = AupHeus Hyatt. By ALPHEeus S. PACKARD. JoHN DANIEL RUNKLE. By Harry W. TYLER. OFFICERS AND COMMITTEES FOR 1908-1904. LIST OF THE FELLOWS AND FOREIGN HONORARY MEMBERS. STATUTES AND STANDING VOTES. RUMFORD PREMIUM. INDEX. (TirLe Pace and TaBLe OF CONTENTS.) RECORDS OF MEETINGS. Nine hundred and thirty-third Meeting. OcTOBER 8, 1902. — STATED MEETING. The PRESIDENT in the chair. The Corresponding Secretary announced that letters had been received from Arthur James Balfour and W. E, H. Lecky, acknowledging their election as Foreign Honorary Members; from the Chief of the Department of Liberal Arts, World’s Fair, St. Louis, inviting the Academy to make an exhibit of the work of its members ; and from the International Botanical Congress, regarding the organization of the session at Vienna in 1905. Letters from the Trustees of Princeton University, inviting the Academy to be represented by a delegate at the inauguration of Woodrow Wilson. as President of the University, and from the Trustees and Faculties of North- western University, requesting the Academy to appoint one or more delegates to the installation of Edmund Janes James as President of the University, were referred to the Executive Committee. Letters were also received announcing the death of H. von Wild and Gaetano Negri; the institution of a section of ter- restrial magnetism and seismology at the Royal Meteorological Institute of the Netherlands; the reorganization of the National Museum at Buenos Ayres; inviting the President and Secretary to the Jubilee Meeting of the North of England Institute of Mining and Mechanical Engineers. The Chair announced the following deaths : — 692 PROCEEDINGS OF THE AMERICAN ACADEMY. John Daniel Runkle, Class I., Section 1; Horatio Hollis Hunnewell, Class I1., Section 2; Horace Gray, Class III., Sec- tion 1; Charles Greely Loring, Class III., Section 4, Resident Fellows. John Wesley Powell, Class II., Section 1, Associate Fellow. Hervé Auguste Etienne Albans Faye, Class I., Section 1; Heinrich von Wild, Class II., Section 1; Rudolf Virchow, Class II., Section 4, Foreign Honorary Members. On the motion of the Corresponding Secretary, it was Voted, To meet, on adjournment, on the 12th of November. The following gentlemen were elected members of the Academy : — Harry Walter Tyler, of Boston, to be a Resident Fellow in Class I., Section 1 (Mathematics and Astronomy). Alfred Edgar Burton, of Boston, to be a Resident Fellow in Class I., Section 4 (Technology and Engineering). Hugo Miinsterberg, of Cambridge, to be a Resident Fellow in Class III., Section 1 (Philosophy and Jurisprudence). Frederic Jesup Stimson, of Boston, to be a Resident Fellow in Class III., Section 1. Arthur Twining Hadley, of New Haven, to be an Associate Fellow in Class III., Section 3 (Political Economy and History). Luigi Cremona, of Rome, to be a Foreign Honorary Member in Class I., Section 1 (Mathematics and Astronomy), in place of the late Charles Hermite. Joseph John Thomson, of Cambridge, to be a Foreign Hon- orary Member in Class I., Section 2 (Physics), in place of the late Marie Alfred Cornu. Emil von Behring, of Marburg, to be a Foreign Honorary Member in Class II., Section 4 (Medicine and Surgery). John Morley, of London, to be a Foreign Honorary Member in Class III., Section 3 (Political Economy and History). The President gave an account of his explorations of the coral reefs of the Maldives. H. Helm Clayton read a paper entitled ‘“‘On the Observed Movements of the Dust from the Volcanic Eruptions in the West Indies.” RECORDS OF MEETINGS. 693 Edward Atkinson, in presenting the first two copies of a complete report issued by the Experiment Station in Insurance Engineering on Diffusion of Light and Corrosion of Steel, said : ‘¢In our practice as underwriters we are called upon to deal with heat and light from a very different point of view as compared to that of pure science. In order to be prepared for questions in the future on so-called fire-proof construction, corrosion, and other matters, I have called upon my clients in the Factory Mutual Companies to assess themselves at the rate of one cent per hundred dollars of their insurance and to place in my hands a sum of money to be expended in what I have named the Insurance Engineering Experiment Station. In response I have received between fifteen thousand dollars ($15,000) and sixteen thousand dollars ($16,000), in spending which I have a free hand: but I have placed myself under an Advisory Committee consisting of the Directors of the Insurance Company of which I am President; chiefly under the advice of the Executive Committee, Messrs. Arthur T. Lyman, Howard Stock- ton, and Theophilus Parsons. “ We are about to have a sufficient area of land placed at our disposal on a long lease, and the representatives of various types of fire-proof construction are each to put up a building which shall be tested by fire and water and lapse of time, but which will also serve more than ample for our laboratories and experiments. * All this is prelimiuary to laying out a course of instruction in Insur- ance Engineering and a year hence transferring the control of the Station to the Institute of Technology. ‘In the interval if any members of the Academy want an opportunity to apply high temperature at or above the melting-point of cast-iron for a considerable period of time, we expect to have buildings of ten or twelve foot cube constructed for that purpose, and shall place them at their disposal. ‘“‘T will send to any member any reasonable number of copies of the report on the Diffusion of Light and the Corrosion of Steel on applica- tion by card addressed to my office, as we have issued a very large edition in order to interest men of Science, architects, and engineers in the general subject.” The following papers were presented by title: — Contributions from the Harvard Mineralogical Museum.—XITI. (1) “Babingtonite from Somerville, Mass.” (2) “ Babing- 694 PROCEEDINGS OF THE AMERICAN ACADEMY. tonite from Athol, Mass.” By C. Palache and F. A. Fraprie. Presented by J. E. Wolff. “On the Thermal Development of the Spark Spectrum of Carbon.” By Henry Crew and John C. Baker. Presented by Charles R. Cross. Nine hundred and thirty-fourth Meeting. NOVEMBER 12, 1902. — ADJOURNED STATED MEETING. Vick-PRESIDENT TROWBRIDGE in the chair. The Corresponding Secretary announced that letters had been received from Hugo Minsterberg, F. J. Stimson, H. W. Tyler, accepting Resident Fellowship; Arthur T. Hadley, ac- knowledging election as Associate Fellow; KH. v. Behring, John Morley, acknowledging election as Foreign Honorary Members; C. A. Young, accepting his appointment as represen- tative of the Academy at the inauguration of the President of Princeton University; T. C. Chamberlin, accepting his ap- pointment as delegate of the Academy at the installation of the President of Northwestern University ; the Royal Academy of Sciences of Turin, announcing the death of its President, Alfonso Cossa; the Central Meteorological Institute of Sweden, announcing the death of its former Director, Robert Ruben- son; and the Nobel Committee for Chemistry and the Nobel Committee for Physics of the Royal Academy of Sciences of Sweden, inviting competition for the Nobel prizes for 1903. The following papers were presented : — “ The Fall of the Campanile of San Marco.” By Arlo Bates. “Recent Studies of the Lunar Surface.” By William H. Pickering. The Committee of Publication reported the acceptance of the following articles since the Annual Meeting : — Contributions from the Chemical Laboratory of Case School of Applied Science. — XLII. “ An Apparatus for Continuous Vacuum Distillation.” By Charles F. Mabery. Jontributions from the Gray Herbarium of Harvard Uni- RECORDS OF MEETINGS. 695 versity. New Series. -- No. XXIV. (Papers from the Hop- kins-Stanford Expedition to the Galapagos Islands.) By B. L. Robinson. I.—“ Flora of the Galapagos Islands.” Contributions from the Chemical Laboratory of Harvard Col- lege. ‘Concerning Gas-Analysis by Measurement in Constant Volume under Changing Pressure.” By Theodore William Richards. Contributions from the Chemical Laboratory of Case School of Applied Science. — XLIV. “A Method for Determining the Index of Refraction of Solid Hydrocarbons with the Pul- frich Refractometer. Index of Refraction of the Solid Hydro- carbons in Petroleum.” By Charles F. Mabery and Lee Shepherd. Contributions from the Chemical Laboratory of Harvard College. “The Significance of Changing Atomic Volume. III. The Relation of Changing Heat Capacity to Change of Free Energy, Heat of Reaction, Change of Volume, and Chemi- cal Affinity.” By Theodore William Richards. Contributions from the Chemical Laboratory of Harvard College. ‘* The Speed and Nature of the Reaction of Bromine upon Oxalic Acid.” By Theodore William Richards ‘and Wilfred Newsome Stull. . Contributions from the Chemical Laboratory of Harvard College. ‘“ The Range and Invariability of Faraday’s Law.” By Theodore William Richards and Wilfred Newsome Stull. Contributions from the Chemical Laboratory of Harvard College. “An Apparatus for the Measurement of the Expan- sion of Gases by Heat under Constant Pressure.” By Theo- dore William Richards and Kenneth Lamartine Mark. Contributions from the Chemical Laboratory of Harvard College. ‘“ The Transition Temperature of Sodic Sulphate re- ferred anew to the International Standard.” By Theodore William Richards and Roger Clark Wells. 696 PROCEEDINGS OF THE AMERICAN ACADEMY. Nine hundred and thirty-fifth Meeting. DECEMBER 10, 1902. The PRESIDENT in the chair. The Corresponding Secretary read letters from L. Cremona and J. J. Thomson, acknowledging their election as Foreign Honorary Members; and from the Entomological Society of Belgium, announcing the death of its President, Pierre-Jules Tosquinet. The President announced the following deaths : — Henry Mitchell, Resident Fellow in Class I., Section 1. Ogden Nicholas Rood, Associate Fellow in Class I., Section 2. Alfred Richard Cecil Selwyn, Associate Fellow in Class II., Section 1. The following papers were presented : — “ Results obtained from the Use of Quartz Geissler Tubes in Spectrum Analysis.” By John Trowbridge. “A Theory of Tone-Relations — Colors, Intensities, Neutral- ity, Values.’ By Denman W. Ross. The following paper was presented by title : — “The Pressure due to Radiation.” By E. F. Nichols and G. F. Hull. Presented by C. R. Cross. Nine hundred and thirty-sixth Meeting. JANUARY 14, 19038.— STATED MEBTING. ~ VICE-PRESIDENT TROWBRIDGE in the chair. On the motion of the Recording Secretary, it was Yoted, To meet on adjournment on the second Wednesday in February. On the recommendation of the Rumford Committee, it was Voted, To appropriate from the income of the Rumford Fund one hundred dollars ($100) for the preparation of a catalogue of the books on light and heat in the library of the Academy. Voted, To transfer the appropriation of seven hundred and fifty dollars ($750), granted to Theodore W. Richards at the annual meeting of 1902, toward the prosecution of researches RECORDS OF MEBRTINGS. 697 on the thermodynamical properties of chemical substances in- volved in chemical reactions. Voted, To appropriate three hundred dollars ($300), from the income of the Rumford Fund to George E. Hale, of the Yerkes Observatory, for the purchase of a Rowland concave grating to be used in the photographic study of the spectra of the brightest stars. On the motion of E. L. Mark, with the written approval of the Committee of Finance, it was Voted, To appropriate from the income of the General Fund two hundred and fifty dollars ($250) for publishing. The following papers were read : — “ Account of some Lunar phenomena.” By N.S. Shaler. ‘*Some Recent Studies on Immunity.” By W. T. Council- man. The following papers were presented by. title : — ‘“¢ Mendel’s Law of Heredity.” By W. E. Castle. “Synopsis of the Genus Lonicera.” By Alfred Rehder. Presented by E. L. Mark. “On the Temperature Coefficient of Chilled and Seasoned Cast Iron Magnets.” By B. O. Peirce. Nine hundred and thirty-seventh Meeting. FEBRUARY 11, 1903.— ADJOURNED STATED MEETING. VICE-PRESIDENT WALCOTT in the chair. The Chair announced the following deaths : — Morrill Wyman, of Class I., Section 4; James Elliot Cabot, of Class III., Section 4, Resident Fellows. Sir George Gabriel Stokes, Baronet, of Class I., Section 2, Foreign Honorary Member. : Harold C. Ernst read a paper entitled, “ A New Method of Stating Ehrlich’s Theory of Immunity.” The following paper was presented by title : — “ Diffusion, Supersaturation, and the Metastable Limit.” By Harry W. Morse and George W. Pierce. Presented by John Trowbridge. 698 PROCEEDINGS OF THE AMERICAN ACADEMY. Nine hundred and thirty-eighth Meeting. Marcu 11, 1908. — Statrep MEETING. The RECORDING SECRETARY in the chair. The Chair announced the death of Gaston Bruno Paulin Paris, Foreign Honorary Member in Class III., Section 4. The Chair appointed the following councillors to serve as Nominating Committee : — Charles R. Sanger, of Class I., Theobald Smith, of Class II., A. Lawrence Lowell, of Class III. The following persons were elected members of the Academy : George Ashley Campbell, of Boston, to be a Resident Fellow in Class I., Section 2 (Physics). Albert Sauveur, of Cambridge, to be a Resident Fellow in Class I., Section 4 (Technology and Engineering). Samuel Franklin Emmons, of Washington, to be an Associate Fellow in Class IT., Section 1 (Geology, Mineralogy, and Physics of the Globe), in place of the late Clarence King. Alfred Thayer Mahan, of New York, to be an Associate Fel- low in Class III., Section 3 (Political Economy and History). Karl Alfred Ritter von Zittel, of Munich, to be a Foreign Honorary Member in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe), in place of the late Friherre Adolf Evik Nordenskidld. The following papers were read : — “The Pompeian Fresco called ‘ The Judgment of Solomon.’ ” By Morris H. Morgan. “Origin of the Great Mountain Ranges.” By William M. Davis. Nine hundred and thirty-ninth Meeting. APRIL 8, 1908. The Academy met in the Geological Lecture Room of the Harvard University Museum, Cambridge. The PRESIDENT in the chair. In the absence of the Recording Secretary, W. M. Davis was appointed Secretary pro tempore. RECORDS OF MEETINGS. 699 The Chair announced the death of Henry Barker Hill, Resi- dent Fellow in Class I., Section 3. The following papers were presented by title : — “On Families of Curves which are the Lines of Certain Plane Vectors either Solenoidal or Lamellar. By B. O. Peirce. “On the Thermal Conductivities of Certain Pieces of Rock from the Calumet and Hecla Mine.” By B. O. Peirce. Contributions from the Gray Herbarium. New Series, No. XXV. “A Revision of the Genus Flaveria.” By J. R. John- ston. Presented by B. L. Robinson. “ Spectra of Gases and Metals at High Temperatures.” By John Trowbridge. The grounds for the award of the Rumford Premium to George E. Hale, of the Yerkes Observatory, were stated by Charles R. Cross, chairman of the Rumford Committee. The medals were presented by the President, and Professor Hale responded, illustrating his recent researches in solar and stellar ‘physics with projections on the screen. The following exhibits in the adjoining halls of the Museum were then inspected : — “ Demonstration of some Phenomena of Optical sigs By J. E. Wolff. “ Photomicrographic Ilustrations of North American Woods.” By E. OC. Jeffrey. “ The Soltwedel Plates of Sugar Cane.” By G. L. Goodale. “Plant Dissections, Illustrating the Study of Herbarium Specimens.” By B. L. Robinson. “Some Recent Discoveries in the New England Flora.” By M. L. Fernald. «© A Method of Keeping Ornithological Notes.” By William Brewster. . “ Types of Indian Basketry.” By F. W. Putnam and W. C. Willoughby. “Phonograph Records of Indian Songs and Note Books of Indian Languages.” By R. B. Dixon. “Model of the Cahokia Mound Group.” By F. W. Putnam and D. I. Bushnell, Jr. 700 PROCEEDINGS OF THE AMERICAN ACADEMY. ‘“‘Tlustrations of the Effects of the Earth’s Rotation.” By W. M. Davis. “Selected Views from the Gardner Collection of Geological and Geographical Photographs.” By P. 8S. Smith. “ Specimens of Fossil Brachiopods showing Details of Struc- ture.” By R. T. Jackson. “ A Two-Circle Goniometer, and a Collection of Cleaved Mineral Forms.” By C. Palache. “ Rocks and Coals from the Rhode Island Coal Field, and other Specimens.” By J. B. Woodworth. “Recent Meteorological Charts and Atlases.” By R. DeC. Ward. ‘‘ Cuspate Capes of our Atlantic Coast.” By M. A. Read. “ Recent Folios of the Geologie Atlas of the United States.” By L. Laforge. “ Thin Sections and Microphotographs of North American Woods.” By E. C. Jeffrey. “Contributions from the Cryptogamic Laboratories.” By R. Thaxter. Nine hundred and fortieth Meeting. ANNUAL MEETING. — May 18, 1908. VicE-PRESIDENT WALCOTT in the chair. The following letters were read : — From Albert Sauveur, accepting Fellowship; S. F. Emmons, A. T. Mahan, acknowledging election as Associate Fellows : Ed. Mazelle, announcing his appointment as Director of the Astronomical-Meteorological Observatory of Trieste. The Chair announced the following deaths : — William Sumner Appleton, Resident Fellow in Class III., Section 2; Josiah Willard Gibbs, Associate Fellow in Class I., Section 2. The annual report of the Council was read by the Recording Secretary. In the unavoidable absence of the Treasurer, and at his re- quest, the Recording Secretary read the annual report of the Treasurer, of which the following is an abstract : — RECORDS OF MEETINGS. GENERAL FunpD. Receipts. Balance, April 30, 1902 Investments Assessments Admission fees Sales of publications Hxpenditures. General expenses Publishing Library Catalosue . . . 4°. Balance, April 30, 1903 Rumrorp Funp. Receipts. Balance, April 30, 1902 Investments Sale of publications Expenditures. UCRCARCNES Ne cy 30 op ura!. 28) .8 sai, Medals . Publishing Library Miscellaneous Balance, April 30, 1903 701 ' $272.42 $5,824.68 985.00 50.00 . 81.84 6,941.52 $7,213.94 Digs aye SdigeAD $2,962.86 1,200.83 104.70 4,268.39 29.13 $7,213.94 és pth, Os CD OBS $2,651.31 407 | 2,650.38 $3,037.34 $2,015.00 331.50 323.11 154.07 . 45.87 . $2,839.55 197.79 $3,037.34 702 PROCEEDINGS OF THE AMERICAN ACADEMY, WARREN Funp. Receipts. iBalanee? April. 30,1902) osetia es eens fe Oona 2 Investments . . . Siege Ode Lesegh icee eee OMIIG Appropriation refunded. Sa A Oh te eels yhoo O06 ceeaae dG leses $1,921.57 Expenditures. Investigations . . ge en Later Ae PN CAVE hth it eaetemen aeRO Balance, April 30, 1903 i, pepioeh we ee ge aiet dee it i ace Menten ceeecen eri $1,921.57 BuiLtpine Funp. Receipts. Balance, April\30, 1902"... os ee a wk) nee Itivestmentis hs... Loe ey is Sel cee Tet he eae a ee 665.37 $1,354.92 Expenditures. Income invested and transferred to capital account . . . $1,250.00 Balance; April30; 1903 is. 2 At) gli gieoss Gere as Eee 104.92 $1,354.92 The following reports were also presented : — REPORT OF THE LIBRARIAN. The card-catalogue has been continued by the Assistant Librarian, who has type-written 2615 cards, making the total number of cards 6300. All the books on light and heat, constituting with periodicals not yet catalogued, the Rumford Library, have been catalogued, besides the books on chemistry, engineering, the useful arts and general natural history, and some 200 books on miscellaneous subjects. The usual ap- propriation of $100 from the income of the General Fund is requested for continuing this work, and $50 is requested from the income of the Rumford Fund for the same purpose. The accessions during the year have been as follows : — RECORDS OF MEETINGS. 703 Vols. Parts of vols. Pams. Maps. Total. By gift andexchange . . . 507 2150 249 24 2935 By purchase — General Fund 35 512 547 By purchase — Rumford Fund = 22 251 Z 272 Rotal Ley eos hae Ws git t2/ D64 2918 251 24 3757 21 volumes and 2 pamphlets on light and heat, recommended by the Rumford Committee, were bought at an expense of $68.96. The expenses charged to the Library are as follows: — Miscellaneous, which includes expenses in no way related to the Library, $602.27; Binding, $324.02, General, and $40.23, Rumford Funds ; Subscriptions, $274.54, General, and $113.94, Rumford Funds; making a total of $1200.83 for the General and $154.07 for the Rumford Funds. An appropriation of $1400 from the income of the General Fund is re- quested in addition to the customary appropriation of $150 from the income of the Rumford Fund for the purchase of books and periodicals. A. LAwRENCE Rortcu, Librarian. REPORT OF THE RuMFORD COMMITTEE. At the last Annual Meeting of the Academy, May 4, 1902, the sum of $1000 was placed at the immediate disposition of the Committee for use in furtherance of research. During the year which has elapsed since that date, the following grants have been made from this appropriation. Dec. 10, 1902. One hundred and fifty dollars to Dr. Ralph S. Minor of Little Falls, N. Y., in aid of his research on the dispersion and ab- sorption of substances for ultra-violet radiation. Jan. 14, 1903. One hundred dollars to Dr. Sidney D. Townley of Berkeley, California, for the construction of a stellar photometer of the type devised by Professor Pickering. Jan. 14, 1903. Two hundred dollars to Professor E. B. Frost for the construction of a special lens for use in connection with the stellar spectograph of the Yerkes Observatory to aid in the study of the radial velocities of faint stars. Jan. 14, 1903. Two hundred and fifty dollars to Professors E. F. Nichols and G. F. Hull of Dartmouth College, in aid of their investi- gation on the relative motion of the earth and the ether by the method of Fizeau’s polarization experiment. It was subsequently voted (April 8, 1903), to allow the grantees to change the application of this grant to 704 PROCEEDINGS OF THE AMERICAN ACADEMY. an investigation of the effect of the motion of the earth on the intensity of radiation. Feb. 11, 1903. One hundred and fifty dollars to Professor E. C. Pickering for the construction of two stellar photometers to be placed at the disposal of the Committee. It was furthermore voted that one of these be placed at the disposal of the Rev. Edmund Goetz, Director of the Southern Station of the Georgetown College Observatory. The following votes have also been passed by the Committee : — Dec. 10, 1902. That the Academy be recommended to appropriate one hundred dollars from the income of the Rumford Fund for the preparation of a catalogue of the books on light and heat in the library of the Academy, this being the second appropriation for the purpose. Jan. 14, 1903. To recommend to the Academy the transfer of the appropriation of seven hundred and fifty dollars voted to Professor Theodore W. Richards at the Annual Meeting of 1902, toward the prosecution of an extended series of researches on the thermo-dynamics of substances involved in chemical reactions. Jan. 14, 1908. To recommend to the Academy the appropriation of three hundred dollars from the income of the Rumford Fund to Pro- fessor George E. Hale of the Yerkes Observatory for the purchase of a Rowland concave grating to be used in the photographic study of the spectra of the brighter stars. These recommendations were acted upon favorably by the Academy. April 8, 1903. To request the Academy to appropriate from the income of the Rumford Fund the sum of seventy-five dollars to Mr. F. L. Bishop of the Bradley Polytechnic Institute in aid of his investi- gation on the thermal conductivity of lead; and also to appropriate the sum of two hundred dollars to Professor Frederick A. Saunders of the Syracuse University in aid of an investigation on the characteristics of the spectra produced under varying conditions, as specified in his application. Feb. 11, 1903. To ask the Academy to appropriate from the income of the Rumford Fund the sum needed to purchase and bind certain books upon light and heat. April 8, 1903. To ask the Academy to appropriate from the income of the Rumford Fund the sum of one hundred and fifty dollars for the purchase and binding of periodicals. April 8, 1903. To request the Academy to appropriate the sum of one thousand dollars from the income of the Rumford Fund for the jmmediate needs of the Committee in furtherance of research. RECORDS OF MEETINGS. 705 May 13, 1903. To request the Academy to appropriate from the income of the Rumford Fund the sum of fifty dollars for cataloguing books and periodicals in the library of the Academy relating to light and _ heat. Reports upon the progress of investigations aided by grants from the Rumford Fund have been received from Messrs. A. L. Clark, E. B. Frost, G. E. Hale, F. A. Laws, R. S. Minor, E. F. Nichols, A. A. Noyes, E. C. Pickering, T. W. Richards, S. D. Townley, R. W. Wood. The Committee has considered the claims of a number of persons for the Rumford Premium but has decided to make no recommendation for an award this year. Cuas. R. Cross, Chairman, Report or THE C. M. WARREN COMMITTEE. The C. M. Warren Committee has the honor to report that Professor Mabery and Professor A. A. Noyes have reported satisfactory progress in the work assisted by grants from the Warren Fund. They regret to be obliged to announce that Professor Charles L. Jackson, owing to pressure of work, felt obliged to resign the Chairman- ship of the Committee. Professor Leonard P. Kinnicutt was elected Chairman to fill the vacancy caused by Professor Jackson’s resignation. The Committee recommends the following appropriations from the income of the C. M. Warren Fund: — To Professor C. F. Mabery, Case School of Applied Science, Cleve- land, O., to complete his researches on petroleum, for which work he has already received various grants from the C. M. Warren Fund, three hundred dollars. To Professor H. O. Hofman, Massachusetts Institute of Technology, Boston, Mass., to complete his research on the decomposition of zinc sulphate, for which work one hundred and sixty dollars was granted last year, three hundred and fifty dollars. To Dr. Samuel P. Mulliken, Massachusetts Institute of Technology, Boston, Mass., to assist him in continuing his investigation on a sys- tematic procedure for the identification of compounds of carbon contain- ing hydrogen, nitrogen, and oxygen; Professor C. L. Jackson dissenting, five hundred dollars. Leonarp P. Kinnicutt, Chairman. VOL. XXXvIiII. — 45 706 PROCEEDINGS OF THE AMERICAN ACADEMY. REPORT OF THE COMMITTEE OF PUBLICATION. The Committee of Publication begs leave to report that there have been published during the academic year 1902-8, one Memoir, Vol. V., No. 12; two numbers of Volume XX XVII. of the Proceedings, and the first twenty-three numbers of Volume XXXVIILI., aggregating 812 pages and 7 plates. Kight numbers of Volume XXXVIII. (Nos. 7, 10, 12, 14, 15, 19, 20, and 23), in all 138 pages, were printed at the cost of the Rumford Fund ($487.52). The total expenditure for printing — including $12.00 for binding — paid from the General Fund was $2962.86. The unexpended balance May 14, 1902, was $443.00. The appro- priation made at the annual meeting on that date was $2400.00. An — additional appropriation of $250.00 was made Jan. 14, 1908, and the return from sales was $81.84. The total amount from the General Fund available for publication was therefore $3174.84, The unex- pended balance is $211.98. The Committee recommends for the year 1903-4 an appropriation of $2600.00. For the Committee, KE. L. Mark, Chairman. May 18, 1903. On the recommendation of the Committee of Finance, it was Voted, To make the following appropriations from the in- come of the General Fund for the expenditures of the Academy during the ensuing year: — For general expenses: +.°.0 12 Se ie Ge ee ee Hor publishing? sa fy eh R= ee) a eerie ee eee) For the library Books and bindmg 7). §) 3 13° 2 ae ee Miscellaneous... «Sj a iity eos ey ee ee Catalogue. yoo, en oye & ome, pee asics Mey eam ea $6900 On the recommendation of the Rumford Committee, it was Voted, To make the following appropriations from the income of the Rumford Fund : — For the immediate needs of the Rumford Committee in furtherance of research, $1000. For the purchase and binding of periodicals, $150. RECORDS OF MEETINGS. T07 For the purchase and binding of certain specified books on light and heat, $100. For cataloguing books and periodicals in the library relating to light and heat, $50. To F. L. Bishop, in aid of his investigation on the thermal conductivity of lead, $75. To F. A. Saunders, in aid of his investigation on the charac- teristics of spectra produced under varying conditions, $200. On the recommendation of the C. M. Warren Committee, it was Voted, To make the following appropriations from the income of the C. M. Warren Fund : — To C. F. Mabery, to complete his researches on petroleum, $300. To H. O. Hofman, to complete his research on the decom- position of zine sulphate, $350. ToS. P. Mulliken, to assist him in continuing his investigation on a systematic procedure for the identification of compounds of carbon containing hydrogen, nitrogen, and oxygen, $500. On the motion of the Recording Secretary, it was Voted, That the annual assessment for the ensuing year be five dollars ($5). The annual election resulted in the choice of the following officers and committees : — Wituram W. Goopvwin, President. JOHN TROWBRIDGE, Vice-President for Class J. Henry P. Watcort, Vice-President for Class IT. JOHN C. GRAY, Vice-President for Class IT. WiturAM M. Davis, Corresponding Secretary. WitutAmM Watson, Recording Secretary. SAMUEL Cabot, Treasurer. A. Lawrence Rotca, Librarian. Councillors for Three Years. Lewis J. JOHNSON, of Class I. Epwarp H. BrAprorD, of Class IT. Morris H. MorGay, of Class III. 708 PROCEEDINGS OF THE AMERICAN ACADEMY. Member of Committee of Finance. Eviot C. CLARKE. Rumford Committee. Erasmus D. Leavitt, Amos E. DOLBEAR, EpWARD C. PICKERING, ArtTHUR G. WEBSTER, CHARLES R. Cross, THEODORE W. RICHARDS, Evinu THOMSON. CO. M. Warren Committee. CuHarLes L. JACKSON, ArtHour M. Comey, SAMUEL CABOT, Rosert H. Ricuarps, LronarD P. KINNICUTT, Henry P. Tacsort. ARTHUR MICHAEL. The Chair appointed the following standing committees : — Committee of Publication. Seru C. CHANDLER, of Class I., Epwarp L. Mark, of Class II., Crawrorp H. Toy, of Class III. Committee on the Library. WILLIAM F. Oscoop, of Class ]., SamueL HensHaw, of Class IL., Henry W. Haynes, of Class IIT. Auditing Committee. Henry G. DENNY, WILLIAM L. RICHARDSON. The following gentlemen were elected members of the Acad- emy :— Oharles Palache, of Cambridge, to be a Resident Fellow in Class IL., Section 1 (Geology, Mineralogy, and Physics of the Globe). William Francis Ganong, of Northampton, to be a Resident Fellow in Class II., Section 2 (Botany). Charles R. Lanman gave an account of ‘* The Completion of Whitney’s Critical Commentary on the Atharva-Veda and the Continuity of Scientific Progress.” RECORDS OF MEETINGS. 709 The following papers were presented by title : — Contributions from the Gray Herbarium of Harvard Univer- sity. New Series. No. XXVI. ‘New and otherwise Note- worthy Angiosperms from New Mexico and Central America.” By J. M. Greenman. Presented by B. L. Robinson. “ Binary Families in a Triply Connected Region, with Espe- cial Reference to Hypergeometric Families.” By D. R. Curtiss. Presented by M. Bocher. “An Explanation of the False Spectra Sue Diffraction Gratings. By Theodore Lyman. *‘ Viscosity of Gases.” By J. L. Hogg. Presented by John Trowbridge. “The Spectra of Gases and Metals at High Temperatures.” By John Trowbridge. “ The Changeable Hydrolytic Equilibrium of Dissolved Chro- mic Sulphate.” By Theodore William Richards and Frederi¢ Bonnet, Jr. “The Anomalous Dispersion, Absorption, and Surface Color of Nitroso-dimethyl-aniline.” By R. W. Wood. Presented by C. R. Cross. On the motion of the Recording Secretary, the following resolution was unanimously adopted : — : Resolved, That the Fellows of the American Academy desire to place upon record their grateful appreciation of the services of their retiring President, Alexander Agassiz, during the nine years in which he has presided over their deliberations. ( 10 Aluminium Antimony . Argon . Arsenic . } Barium. Beryllium . } Bismuth Boron Bromine ' Cadmium . » Cesium Calcium } Carbon . f Cerium . Chlorine Chromium Cobalt . Columbium ; Copper . PROCEEDINGS OF THE AMERICAN ACADEMY. A TABLE OF ATOMIC WEIGHTS OF SEVENTY-SEVEN ELEMENTS. Compiled in April, 1902, from the most Recent Data. By THEODORE WILLIAM RICHARDS. Atomic Weight. Atomic ] Weight. | “ Didymium ” 4 Erbium. j Fluorine 1 Gadolinium | Gallium Germanium } Glucinum . i Gold. ¥ Helium . Hydrogen . { Indium . } Iodine . Iridium. 1 Iron . Krypton Lanthanum Lead Lithium Magnesium Manganese Mercury Molybdenum. Neodymium . Neon . Nickel . Niobium Nitrogen Osmium ake Oxygen (standard) Palladium . Phosphorus Platinum . Potassium . : Praseodymium . Rhodium . Rubidium . Ruthenium Samarium 2 Scandium . Selenium . Silicon . Silver Sodium. Strontium . Sulphur Tantalum . Tellurium . Terbium 2 . Thallium . Thorium 2. Thulium? . Tin Titanium . Tungsten . Uranium Vanadium . Xenon . Ytterbium . Yttrium Zinc . Zirconium . RICHARDS. — A TABLE OF ATOMIC WEIGHTS. a | NOTE. Tue accompanying table of atomic weights is but little changed since last year. Cesium is made 182.88 instead of 132.9; calcium, 40.13 instead of 40.1; iron, 55.88 instead of 55.9; hydrogen, 1.0076 instead of 1.0075; and nickel, 58.71 instead of 56.70. The value for cwsium is due to some work, as yet unpublished, of Richards and Archibald, and that for calcium is increased in accuracy because the recent investigation of Hinrichsen* supports the less recent Harvard value.t The other very small changes are due simply to slight differences in the interpretation of data already well known. ‘The decimal might have been omitted from palladium, because this element may still be a whole unit in doubt; but it has been retained as a compromise. The differences between the present table, that of the German Committee,{ and that of F. W. Clarke,§ are diminishing year by year. Nevertheless to as many as twenty-eight elements out of the seventy-seven are given values in these three tables differing among themselves by over one tenth of a per cent; namely, the atomic weights of antimony, bismuth, cerium, columbium, fluorine, gadolinium, germanium, helium, hydrogen, lanthanum, magnesium, mercury, neon, osmium, palladium, platinum, potassium, samarium, scandium, selenium, tantalum, tellurium, thorium, thulium, tin, titanium, uranium, and zirconium. To this list of uncertain elements should be added erbium, gallium, glucinum, indium, terbium, tungsten, ytterbium, upon which the three tables agree only because of lack of data upon which to base a disagreement. Thus nearly half of the elements are still in doubt by at least one part in a thousand. This circumstance is not so much a reproof to the many earnest workers upon the subject, as an evidence of the great difficulty of some of the problems involved. Three of the elements given in the list above should not properly be included among the uncertain values, namely, hydrogen, magnesium, and potassium. ‘The first finds its way into the list because of the disregard of significant figures by the German Committee, and the second chiefly because Clarke has included in his calculation work upon magnesic oxide undoubtedly erroneous on account of the presence of included gases. || The case of potassium is somewhat peculiar; for in spite of the great wealth of data concerning this element, Clarke assigns to it the value 39.11, while the German Committee chooses 59.15. The low value is chiefly due to very unsatisfactory data concerning potassic iodide. To me it seems that the most recent work of Stas is far more satisfactory than his earlier work or than the work of any one else, hence the value 39.14 has been assigned to potassium in the present table since its first publication. Careful analyses by E. H. Archi- bald and myself confirm this conclusion. ~ * Hinrichsen, Zeitschr. phys. Chem., 39, 311 (1901). + Richards, Journ. Am. Chem. Soc., 22, 72 (1900), also 24, 374 (1902). t Landolt, Ostwald, and Seubert, Extra insertion in Berichte d. d. ch. Ges. 1902. Heft 1. § F. W. Clarke, Journ. Am. Chem. Soc., 24, 201 (1902). || Richards and Rogers, These Proceedings, 28, 209 (1893). AMERICAN ACADEMY OF ARTS AND SCIENCES. ReEpoRT OF THE CoUNCIL. — PRESENTED May 13, 1903. BIOGRAPHICAL NOTICES. PEPE U Se ibiewATIO nen nee 9 ee ence see AUPE ITSs Se) IOACKAIRID: Moras; IDVNISiusis Jejonsna 5 5 6 ooo 6 ooh a p lebimeae W/o abana < ey Et at ee Saleh ip eee SN ha Maen ng PRY MA ee These Vitel a ie x ee Wa = i ; ; b * ny oe oe a ' REPORT OF THE COUNCIL. The Academy has lost seventeen members by death since the annual meeting of May 14, 1902: eight Resident Fellows, — William Sumner Appleton, James Elliot Cabot, Horace Gray, Henry Barker Hill, Charles Greely Loring, Henry Mitchell, John Daniel Runkle, Morrill Wyman ; four Associate Fellows, — Josiah Willard Gibbs, John Wesley Powell, Ogden Nicholas Rood, Alfred Richard Cecil Selwyn; five Foreign Honorary Members, — Hervé Auguste Etienne Albans - Faye, Gaston Bruno Paulin Paris, Sir George Gabriel Stokes, Bart., Rudolph Virchow, Heinrich von Wild. ALPHEUS HYATT. Our beloved and highly honored associate, who, in the ripeness of his intellectual powers, has been so suddenly snatched from us, was cast in no ordinary mould. Whether we regard him as a man, a patriot, a fellow student, a scientific investigator, an organizer of societies, of museums, or of methods of science-teaching, his many-sided life was a rare one. We come together to pay tribute to the memory of ALpHeus Hyarr asa promoter of scientific enterprises, as one of the founders of a new school in the philosophy of biology, as a master in paleontological methods, en- dowed as he was with rare powers of mental absorption and concentration, and an unusual capacity for sound generalization. The nineteenth century, as regards natural science in the United States of America, was a period of pioneer effort, and has been characterized by the careers of several great men. Their lives, unlike those of Euro- pean savants, whose museums, laboratories, and methods of research had often been founded by a previous generation, had to be devoted, so to speak, to opening and laying out roads, to founding and building institutions, and making the way straight for the generations to come. Such men were Henry, Dana, Agassiz, Wyman, Rogers, Hall, Baird, and others, all full of love for original research, but who unselfishly gave up much of their time, so dearly valued for private studies, to develop- Tb ALPHEUS HYATT. ing and expanding the educational and scientific resources of a young people. Those who were pupils of that large-hearted, enthusiastic son of genius, Louis Agassiz, well know the sacrifices he made in the country of his adoption, in devoting the later years of his life to the foundation of the Museum of Comparative Zodlogy, to popularizing science, to illustrating the dignity of scientific studies, and enforcing the value of research in our colleges and young universities. The lines thus drawn were followed by Hyatt; and it is safe to say that the impress he has made on zoological and geological science is deep and lasting. Born in Washington, D. C., April 5, 1838, of Maryland parentage, Alpheus Hyatt was sent to the Maryland Military Academy, but after- wards entered Yale College, completing the freshman year, class of 1860. He then travelled a year in Europe, and as he once told us, strong family and clerical influence were brought to bear upon him while in Rome to induce him to enter the Church, his family being of the Roman Catholic faith. He entered the Lawrence Scientific School in 1858 ; our acquaintance began in 1861. The pupils of Agassiz were then domiciled in Zodlogical Hall, a small two-story wooden building which stood on the site of the Peabody Museum of American Archaeology. We were soon interested and attracted by young Hyatt. Although he originally elected to make engineering his profession, he, with for that period a rather large num- ber of other young men, was attracted by the fame and charming per- sonality of Agassiz, as well as by the zodlogical treasures of the already rich and carefully selected museum. MHyatt’s patience and his dogged perseverance, his powers of concentration, his philosophical tendencies, attracted our attention, while his open, frank, sunny disposition, his com- panionable, jovial, unselfish, pure spirit and scholarly aims, at once secured our love and respect. He was then and through life an all- round man, though very early in his studies specializing on the fossil Cephalopods. ) Tyndall’s “ Heat as a Mode of Motion” had just appeared, and debates on the higher physics, in which he took a leading part, alternated with communications on the position of the Tunicata, of the Polyzoa, Brach- iopods, and other types at the meetings of our Zoological Club. Hyatt was artistic in his tastes, drawing well on the blackboard, and handling the pencil with ease and facility. He read good literature, was a reguiar attendant on the lectures of Professor Lowell, aud constantly present ALPHEUS HYATT. TUT at the courses of that model of scientific lecturers, Professor Jeffries Wyman. He was graduated with high honors under Professor Agassiz in 1862. The Civil War was then raging, and the young patriot, having already received the elements of military training, enlisted, though naturally not without opposition from his family in Maryland, and was active in raising a company in Cambridge. He received a commission in 1862 as a lieu- tenant, but soon rose to the rank of captain in the Forty-seventh Mas- -sachusetts Regiment, serving as aide-de-camp nine months, for the most part in New Orleans. After being mustered out of the army he lived in Boston some time during 1865-66, and it was then, and afterwards in Salem, that we came to know him still more intimately than at Cambridge, as we were at times room-mates. Over our friendship, our mutual love and respect, a cloud never passed. The purity and unaffected goodness, nobility of character, sturdy honesty and reliability as a friend, were as conspicuous then as in his last years. His filial devotion was marked, and in later life the kindness and chivalric courtesy, acts of kind-heartedness and thoughtfulness which in some instances it gave him some trouble to_per- form, to an elderly lady as well as to other friends in need, will be treasured up in our memory. Of his delightful domestic life, the warm- heartedness of his welcome to his hospitable home, his friends will ever retain the most agreeable recollections. In the foundation and organization of scientific and educational enter-- prises, societies, journals, and museums, Hyatt always lent a willing hand. Gifted with a fair amount of executive ability, with clear, persuasive powers of expression, a ready debater, often a powerful speaker, and excellent in planning, besides having a somewhat wide knowledge of men, he was most useful in promoting such undertakings. In 1867 he, with three other pupils of Agassiz, became one of the curators of the Essex Institute, and in 1869 he took an active and most useful part in the foundation of the Peabody Academy of Science at Salem, Mass., where he served as one of the curators. As Custodian of the Boston Society of Natural History from 1870 to the end of his life, he planned an arrangement of the museum in accord- ance, so far as was possible, with the phylogeny of the animal kingdom, beginning with the Protozoa. He was one of the two founders of the Teachers’ School of Science, becoming its manager, and in this way accomplished a vast amount of good in training the teachers of Boston and its vicinity in the elements of natural history. While living in Salem 718 ALPHEUS HYATT. he was one of the founders and editors of the “ American Naturalist,” contributing frequently to its pages. The principal founder of the American Society of Naturalists, we well remember the zeal and interest he took in organizing this at present influential body, the preliminary meeting being held by a few at Spring- field, Mass., in April, 1883. If we mistake not, he gave the name to the society. He was its first president, and a few years ago was elected an honorary member in recognition of his services. He also founded and organized a seaside laboratory at Annisquam, Mass., under the auspices of the Woman’s Education Association of Boston. He took personal charge of it, as his summer home was there. His in- terest in this school, and in marine zodlogy, led him to take part in the foundation of the Biological Laboratory at Wood’s Holl. As an indica- tion of the value of his services as an expert in zodlogy and his ability as an organizer, he was elected the first president of its board of trustees. He was elected a fellow of this Academy in 1869. Throughout his life, after graduation at Harvard University, he was an honorary Assistant Curator in the Museum of Comparative Zodlogy, in charge of the collection of fossil Cephalopods. In 1888 he was offered the position of United States Commissioner of Fish and Fisheries, but pre- ferred to live the almost ideal life, with its rich opportunities for research, which he rounded out at his home in Cambridge. Professor Hyatt was not only a specialist, but a generalizer, a philoso- pher. His special, detailed, observational work was continually leading him to broad, sound generalizations, and not only in the field of embry- ology, taxonomy, and phylogeny, but of general organic evolution. He was a slow worker, very patient, cautious, constantly reviewing his work and conclusions. He was not always luminous in exposition; he some- times, especially early in his life, failed from want of training and practice in writing, to state clearly and pointedly the views that crowded his mind. But this defect was largely outgrown. For this reason his first essay on ‘* Parallelism,” etc., was not understood by Mr. Darwin, as well as others who had not had experience in similar studies, but this defect of style was overcome in his later memoirs. As the result of his manner of investigation, Hyatt became an acknowl- edged master in the methods of paleontology, in a mode of treatment of fossil forms then comparatively new to paleontology, due to his long and thorough training in zodlogy, comparative anatomy, and embryology. Before his time paleontologists, with the exception, of course, of Cuvier, Owen, Huxley, and Agassiz, had had but little training in anatomy and ALPHEUS HYATT. 719 taxonomy. Hyatt’s patient and beautiful studies on the fresh water Poly- zoa, carried on in the sixties; his later studies on the sponges, on the mol- luses, other than Cephalopods ; his experience as a teacher of zodlogy and paleontology in the Massachusetts Institute of Technology from 1870 to 1881, and of zodlogy in Boston University from 1877 to the time of his death, in addition to his museum work, kept him informed of biological methods and results ; while his field work in the paleozoic rocks of southern Labrador, of Newfoundland, and his work about Salem, but more especially his work in 1889 and succeeding years as paleontologist in charge for the U. S. Geological Survey of the lower Mesozoic (Trias and Jura), carried on in Texas and in California, besides his earlier studies at Steinheim, Germany, afforded him the means of observing and accumulating many facts, and of forming broad conclusions from many points of view. His prolonged and life-long studies on the Cephalopods were thorough and exhaustive, and from them were wrung the basal principles of evolu- tion, — work which for thoroughness and far-reaching results has seldom been surpassed, and which not only is of the highest value and interest to students of molluscs, but has already exerted and will continue to exert a wide influence on the progress of general zoOlogy. The permanent fame of our deceased associate will, we venture to claim, be based on his contributions to the embryology, laws of growth of the shells, and the phylogeny of the Cephalopod molluscs ; and on his pro- found studies on the modifications of the tertiary shells at Seems near Stuttgart, Germany. He will also be remembered for his conclusions on the position of the sponges. As far as we are aware he was the first one after McAllister, in a paper published in 1876, entitled “ Sponges considered as a distinct Sub-kingdom of Animals” * to refer these organisms to a separate, inde- pendent branch or phylum of the animal kingdom. The outcome of these studies resulted in his valuable contributions to the philosophy of biology. He was one of the founders and upholders of Neolamarckism, and evenif the value of that phase of the evolution theory be called in question, he will be remembered as having been the discoverer of a series of facts of astonishing number and variety, all converging to one grand result, that of affording a true, solid basis for the theory of organic evolution. * Proceedings Boston Society of Natural History, XIX. Nov. 1, 1876. Hyatt claimed in this paper that during the previous year he regarded the sponges as distinct from the rest of the animal kingdom. l.c., p. 14. In this paper also, he re- jected the position assigned them by Haeckel in the Coelenterata. 720 ALPHEUS HYATT. For a number of years Dr. Hyatt was engaged in a study of the origin and lines of evolution of the land shells peculiar to the Hawaiian Islands, on which the Rev. John T. Gulick had already (1887-1890) made such interesting and suggestive studies. Hyatt had presented several communi- cations to scientific societies, showing the progress made in his work. His beautiful model of the islands, and arrangement of the actual shells fas- tened to the surface of the model, with cords of different colors showing the lines of migration and corresponding segregations and consequent dif- ferentiation of the specific forms, gave promise of the most valuable and fruitful results. He was planning to make a journey to the Hawaiian Islands in March of the present year, when death overtook him. But the results of his long continued labors will, it is hoped, not be lost to science, as arrangements were made previous to his death for their com- pletion by a capable hand. The first paper of a general nature which young Hyatt published * contained the germ of his chief life-work. It gave some of the results of six years’ study on fossil Cephalopods, and was on the parallelism existing between the different stages of life in the individual and those of the tetrabranchiate Cephalopods as a group. It was published in 1866, the same year in which appeared Haeckel’s “ Generelle Morphologie,” which, he (Haeckel) says, constituted the first attempt to apply the general doc- trine of development to the whole range of organic morphology (anatomy and biogenesis). Although both of the Haeckelian principles of palingene- sis and cenogenesis, with all their evolutional implications, were stated with considerable fullness by Fritz Miller in his “ Fiir Darwin,” pub- lished in 1864, Hyatt attempted to show that the life of the individual displays, to use his own words, “during its rise and decline, phenomena correlative with the rise and decline of the collective life of the group to which it immediately belongs.” In this memoir he carried out and greatly amplified D’Orbigny’s views, to which he gives the fullest credit, as to the changes of the larger number of Ammonites from larval, or to use his own term, nepionic, to adult, and from adult to senile stages. The theme, so often discussed by Agassiz before his students, that the development of the individual is an epitome of that of the order or class to which it belongs, with the later vital addition by F. Miller and by Haeckel of the evolution by actual descent, the principle now being * “On the Parallelism between the Different Stages of Life in the Individual and those in the Entire Group of the Molluscous Order Tetrabranchiata.” Memoirs Boston Soc. Nat. Hist., I. 1856. ALPHEUS HYATT. 121 called Haetkel’s “ biogenetic law,” runs through and is the motif of Hyatt’s life-long work. Some of us in our maturer years return to or continue to work along the lines taken up in youth. Hyatt for a period of forty years, in a series of profound studies on the Cephalopods, in publications rich in exact ob- servations and with ample illustrations, many of the drawings beautifully executed by his own hand, independently expanded and illustrated this fundamental phase of evolution, which so impressed him in his student days. His remarkable memoir on the “ Genesis of the Arietidae,” published in 1889 in the Smithsonian “ Contributions to Knowledge,” and jointly with the Museum of Comparative Zodlogy, is a storehouse of facts on which his generalizations are based. When he presented his views to the National Academy of Science at a Washington meeting, Professor Henry expressed his approbation of the value and profoundity of this research. In this work he insists on his law of Morphogenesis, i. e., he attempts to demonstrate that “a natural classification may be made by means of a system of analysis in which the individual is the unit of comparison, because its life in all its phases, morphological and physi- ological, healthy or pathological, embryo, larva, adolescent, adult, and old (ontogeny), correlates with the morphological and physiological his- tory of the group to which it belongs (phylogeny).” In the beginning of his studies, contemporaneously with Cope, he insisted on the fact and results of a process of acceleration and re- tardation and the growth of the individual as well as the evolution of the family, order, or class of which it was a member. “ All modifications and variations,” he says, “in progressive series tend to appear first in the adolescent or adult stages of growth, and then to be inherited in successive descendants at earlier and earlier stages ac- cording to the law of acceleration, until they either become embryonic, or are crowded out of the organization, and replaced in the development by characteristics of later origin.” Another of the nineteen conclusions prefacing this essay is No. 14: — “ The law of acceleration in development seems, therefore, to express an invariable mode of action of heredity, in the earlier reproduction of hereditary characteristics of all kinds and under all conditions. In pro- gressive series it acts upon healthy characteristics, and appears to be an adaptation to favorable surroundings, and in retrogressive series upon pathological characteristics, and is probably an adaptation to unfavorable surroundings, usually leading to the extinction of the series or types.’ VOL. XXXViur. — 46 fda. ALPHEUS HYATT, This law of acceleration was, after the publication of Cope’s and also of Hyatt’s first paper (1870), arrived at independently by Wiirtenberger,* and adopted by the distinguished German paleontologist Neumayr, though he, apparently in ignorance of Hyatt’s much earlier results, gives the credit for its discovery to Wiirtenberger, as does Weismann. These changes Professor Hyatt insisted were primarily due to changes in the environment acting mechanically on the organism at different ages, the Lamarckian factors of use and disuse as well as environmental changes being constantly operative. To explain the facts of retardation or abbreviated metamorphosis Dr. Hyatt formulates the law or process concerned in these phenomena, and which explain the mechanism of gradation, whether progressive or retro- gressive, as follows: “ Changes in environment, which introduce new fame characteristics in the nealogic or adult stages, necessarily add these to the hereditary stages of the younger periods of growth, and thus shorten the develop- ment of the latter by direct development.” He goes on to illustrate this process by citing the changes of insects, of Taenia, and the loss of pro- gressive characters correlated with a highly accelerated mode of develop- ment in man, due to a change from a horizontal to an upright position, and which, he says, were first pointed out nearly a century ago by Lamarck. We will now, as briefly as the subject admits, trace the evolution of Professor Hyatt’s views on evolution. It has been objected to both Cope and Hyatt’s theory that their law or process of acceleration and retardation are merely statements of facts. But both of these observers very soon after working out, each independ- ently of the other, and in very different groups, these facts and processes, arrived at the conclusion that the changes they formulated were primarily due to the Lamarckian factors of change of environment, and to use aud disuse. They, with others of their contemporaries, rehabilitated and extended the Lamarckian factors and became the founders of the Neolamarckian school of evolutionists. Hyatt’s first public avowal of evolutional views was in a paper read in 1870,t though for several years he had practically adopted the theory * Ausland, 1873. + On Reversions among the Ammonites. ‘Proc. Boston Soc. Nat. Hist., XiV. June, 1871. ALPHEUS HYATT. (533 of descent. His 1866 paper on “ Parallelism,” ete., was in this same vein of thought, but in this paper, “conceived along evolutional lines, he did not explicitly state what were the actual dynamic agencies at work to produce the transformation from one form to another. His studies on the geological succession of the Ammonites, and the obvious genetic relations of the series he examined afterwards, naturally led him to adopt such views. He claimed in this paper that the reversionary species he examined “all descended from one.” In 1873 he showed that in the Ammonoids there are everywhere instances of the slow accumulation of differences, according with the Darwinian method, and of their quick and sudden production, ‘according to the law of acceleration as explained by Cope and the writer, and subsequently by Mivart.” * His Lamarckian leanings, however, so far as his published works show, crop out in his “ Abstract of a Memdir on the Biological Relations of the Jurassic Ammonites.” | The stages of growth he describes are here directly attributed to the favorable nature of the physical surroundings, primarily producing characteristic changes which become perpetuated and increased by inheritance within the groups. The production of retro- gressive, senile forms he attributes to “the action of unfavorable sur- roundings.” He carefully guards against “ attributing the origin of these differences to the law of natural selection,” limiting the action of this law “ strictly to the modification of the structural differences which tend. to appear first in the varieties and then by inheritance in larger and larger groups and at earlier and earlier stages in the life of the individual.” Hyatt’s beautiful research on the problems suggested by the fossil pond- snails of Steinheim near Stuttgart, Germany, is an important contribution both to paleontology and to evolutional data. Hilgendorf had previously (in 1866) described the conditions, and his results were regarded in Germany as amounting to a demonstration of the truth of the evolution theory. Hyatt, during a year’s residence in 1872 near Stuttgart, spent five weeks examining the pits and made careful collections. The discussion is a most valuable contribution to the theory of descent. Sir Richard Owen wrote him in 881: “I cannot say more than that I deem it a model of the way and aim in and by which such researches should be conducted in the present phase of Biology.” Hyatt’s patient and long sustained studies led him to the following conclusions: * Proceedings Boston Soc. Nat. Hist., XVI. p. 167. Dee. 3, 1878. t Ibid, XVII. pp. 286-241. Dec. 16, 1874. 724 ALPHEUS HYATT, 1. The extraordinary modifications and series of shells found at Stein- heim are in one way exceptional, and owe their existence to exceptional conditions. 2. These conditions appear to be the isolation of the modified descend- ants of Planorbis laevis, due to the absence of competing types and the character of the environment. Besides other conclusions, he points out that in these and other series of animals which he had studied, “in a given number of generations inherited characteristics of every kind tend to appear in the descendants at earlier stages than that at which they first occurred in the ancestral forms.” These studies led him to explain the frequent occurrence of parallel forms, or, as they are now called, cases of convergence, also to examine into the causes of senescence, of geological extinction, etc. He main- tained that there was no such thing as indefinite variation, and took strong ground, based on extended series of paleontological data, as to the reality of use-inheritance. In this as well as his other memoirs he insists on the inadequacy of natural selection in causing variation and the formation of new groups. , In a later work, entitled ‘“ Phylogeny of an Acquired Characteristic,” * Hyatt is at his best. The results of a life-long study of the genetic series of Cephalopods, of their rise, culmination, decay or senile features, and their final extinction, are portrayed in a masterly way. His conclu- sions are based on the careful detailed survey of a multitude of facts, and the story he unravels from the series upon series of fossil forms which passed in review before eyes so well trained, and a mind so skilled in induction and deduction, forms a chapter in the history of organic evolu- tion which will remain a classic. It was only after long years of research, and the most patient, thought- ful reflection on the series of facts he independently worked out, by his study of the embryology of the protoconch and conch of the Orthocera- tites, and their successors the Nautiloids and Ammonoids, that he thus describes the gross results in a few sentences which show the mode of origin of new orders through the Lamarckian factors of effort and use. In this essay Hyatt struck the keynote to the cause of the origin of new types, or class and ordinal forms, i. e. by the changes in habits, and efforts of the organism to adapt itself to such new conditions of existence. * Phylogeny of an Acquired Characteristic. Proc. Amer. Phil. Soc., XXXII. p. 3871 (1894). ALPHEUS HYATT. iZo These are the Lamarckian or dynamic agencies of use and disuse, brought into action by environmental changes. “ The efforts,” he says, “ of the Orthoceratite to adapt itself fully to the requirements of a mixed habitat of swimming and crawling gave rise to the Nautiloidea; the efforts of the same type to become completely a littoral crawler evolved the Ammonoidea. ‘The successive forms of the Belemnoidea arose in the same way. But here the ground-swimming habitat and complete fitness for that was the object. ‘The Sepioidea, on the other hand, represent the highest aims as well as the highest attainments of the Cephalopods in their evolution into surface-swimming and rapacious forms. We cannot seriously imagine these changes to have resulted from intelligent effort; but we can, with Lamarck and Cope, picture them as due to efforts on the part of the animal to take up new quarters in its environment and thus acquire habits and structures suitable to the changed physical requirements of its surroundings, and this position is better supported by facts than any other hypothesis.” Here are some examples of the complete and thoroughgoing way in ‘which Hyatt thought out, during his painfully slow but sure investiga- tion of facts, broad generalizations which we feel confident will stand the test of time and farther research. After speaking of “the effort to change of habitat and consequently change of habits,’ due to change of environment, and of changes in structure resulting from the efforts on the part of the organism to meet the changes in the physical surroundings, he adds: ‘That this process should end in the production of structures suited to the environment is inevitable. With these factors at work, both without and within the organism, the evolution of their structures obeys a physical law which acts amid a thousand disturbing forces, perhaps, but nevertheless must act with predominating force in one mean path or direction, the resultant determined by the environment and the inherited structures of the organism.” Another beautiful research was his attempt to account by gravity for the spiral shell of molluses. He points out the fact of an obvious correla- tion between the coiling of the shell and the habit of crawling. He shows that those gastropod shells which degenerate and tend to lose the spiral mode of growth and become irregularly straightened out in their older stages of growth, are forms which become attached or which lead sedentary lives, i. e. Vermetus attached late in life, and Magilus which lives buried in coral. He points out the tendency in the descendants of straight shells (Orthoceratites, etc.) to become, as the result of assuming 726 ALPHEUS HYATT. reptant habits, first arcuate and then coiled; these being acquired characters which have been “introduced late in the ontogeny and gradually forced back to younger and younger stages in successive generations, or species, or genera.” He also accounts for the peculiar horizontal growth of the oyster, pecten, etc., by their fixed mode of life. These observations, modes of investigations, and laws or principles so carefully thought out, are the work of a master in biology. They already have been most fruitful in their results, and have been found to apply in other groups of organized beings. Hyatt was thus the founder of a new school in paleontology, and the brilliant results of the work of a younger generation of paleontologists, viz., Beecher, Jackson, Suchert, Smith, and others, all of whom acknowledge him as their master, afford the best of proof of our claim. Certainly the same principles we think will apply to Crustacea, and also to insects, as Hyatt has claimed, and they were applied to vertebrates by Cope and his successors in vertebrate paleontology. For all this work Hyatt’s name will forever be associated with the names of Agassiz, Barrande, Neumayr, Waagen, Mojsisovics, and others who have worked along these lines. Hyatt’s systematic work on the Cephalopods was very extensive. It will be remembered that there are estimated to be about twenty-five hundred species of Nautiloids and five thousand species of Ammonoids. The results of his labors may be seen in the portion he contributed to the translation by Dr. Eastman of the condensed American edition of Zittel’s Paleontology. In systematic work on the Ammonites Hyatt followed hard after Suess, who in 1865 inaugurated the subdivision of the group into genera. As stated by Zittel:* ‘‘A similar reform was advocated by Alpheus Hyatt in his memoir on the Liassic Ammonites (1869). The previous nomenclature of families was discarded by Hyatt, and numerous new genera were erected, whose limits were much more narrowly defined than had been customary. As one might have expected, the new tendency met at first with strong opposition, but it was supported and followed by Laube, Zittel, Mojsisovics, Waagen, and Neumayr.” Dr. Hyatt was not a voluminous writer, but his works are solid, original, independent contributions to science, and will stand, if we mistake not, the test of time. He was elected a member of the National Academy of Science in 1875, and since 1897 has been a corresponding member of the Geological * Zittel’s History of Geology and Palaeontology. Translated by M. M. Ogilvie-Gordon. 1891. p. 402. JOHN DANIEL RUNKLE. T2i. Society of London. In 1898 he received from Brown University the degree of Doctor of Laws. At the time of his death (Feb. 15, 1902) he was the Vice-president of Class II. of this Academy. Endowed by nature with talents of a high order, he cultivated and, to use his own favorite phrase, accelerated their development and increase through his life. His strength of character is evinced by the forceful influence he exerted both in scientific and educational channels. “ Talent,” says Baron Osten Sacken, the venerable diplomatist and naturalist, “is a gift of nature, and does not, for that reason, constitute in itself a merit; the merit lies in the character which makes talent fruit- ful.” And that profound genius and master in biology — Von Baer — has said: “In the domain of Science, talent alone, coupled with diligence and the power of self-control, is of any value.” * We close this notice of our departed friend, who endeared himself to his associates so closely by his amiable and manly qualities, feeling sure that posterity will confirm the estimate here given of his worth as a man, and of the secure place he will hold as a master in science. A. S. Packarp. JOHN DANIEL RUNKLE. JoHn DanieL RUNKLE was born at Root, N. Y., October 11, 1822, and died at Southwest Harbor, Me., July 8, 1902, near the close of his eightieth year. The early years of life on the farm offered little opportunity for study, and he was already twenty-five when he entered the newly established Lawrence Scientific School of Harvard University. His name stands alone in the catalogue of 1848—49 as “student in mathematics.” John W. Draper and James E. Oliver were fellow students; Josiah P. Cooke and William T. Harris, resident graduates. He was a member of the first graduating class, of 1851, with Joseph Le Conte and David A. Wells, receiving the degree of Bachelor of Science, and at the same time, for high scholarship, the honorary degree of Master of Arts. The work of computation for the Nautical Almanac was carried on at this time in Cambridge by a staff including, among other men of subse- quent eminence, Simon Newcomb, Asaph Hall, (Cae W. Hilly iee * Quoted from ‘ An Introduction to the Record of my Life-work in Ento- mology.” By C. R. Von Osten Sacken. 1901. 128 JOHN DANIEL RUNKLE. Safford, and J. M. Van Vleck. Mr. Runkle’s connection with the Almanac began in 1849, and continued in some form as late as 1884. In 1852 he contributed to the “ Astronomical Journal” papers on the “Elements of Thetis ” and on the ‘‘ Elements of Psyche.” In 1855 his “ New tables for determining the values of the coefficients, in the perturbative function of planetary motion, which depend upon the ratio of the mean distances,” were published as one of the Smithsonian Contributions to Knowledge. In 1858 Mr. Runkle founded the “ Mathematical Monthly.” Encour- agement was received and formal indorsement given by the American Association for the Advancement of Science and by several educational bodies. The list of contributors included many distinguished names, among others Arthur Cayley, William Chauvenet, George W. Hill, Simon Newcomb, Benjamin Pierce, John Herschel. The time for the publication of a long-lived mathematical journal was not, however, ripe, and only three volumes appeared. From 1860 until his death Professor Runkle’s time and strength were almost continuously and exclusively devoted to the establishment and up- building of the Massachusetts Institute of Technology. He was first Secretary of the Institute, and at the opening of the school became pro- fessor of mathematics. In October, 1868, he became Acting President in consequence of President Rogers’ serious illness, and in 1870 he was mide President, holding the office for the following eight years. The situation was a most exacting one, making altogether exceptional demands. The school, only five years old, was in no condition to lose the guidance of its founder. It had not yet gathered the momentum necessary for steady, straightforward progress. Opinions did and will differ as to President Runkle’s judgment on the difficult questions that, as time passed, pressed overwhelmingly upon him for solution. No man could have been more devotedly loyal to the school or to its founder, his predecessor and ultimately his successor. None could have shown more steadfast courage, not only against heavy odds, but too often with but feeble support. The more notable events of the Runkle presidency were: the fruitless negotiations with Harvard University for a union; the establishment of the laboratories of mining engineering and metallurgy; the introduction of shop instruction and the foundation of the School of Mechanic Arts ; the development of professional summer schools in the field; the begin- nings of an engineering laboratory; the increased efficiency of military iustruction and the summer encampment at Philadelphia in 1876; the JOHN DANIEL RUNKLE. 729 erection of a gymnasium, including a lunch-room; the admission of women as students. In 1878 Dr. Runkle resigned the presidency of the Institute and spent the following two years in Europe. It had been President Runkle’s merit to be the first to appreciate the American need of mechanic arts instruction based on principles already successfully applied in Russia. He was primarily interested in it as an invaluable addition to existing engineering courses, but he also saw clearly its great potential significance for general secondary education, and so far as possible, under pressure of other needs, demonstrated this by the inauguration of the School of Mechanic Arts, in which boys of high-school age were offered a two years’ course, including mathematics, English, French, history, mechanical and freehand drawing, and shop- work. His visit to Europe enabled him to make a study of Continental schools of similar purpose ; and the results of this study are embodied in a paper presented to the Society of Arts in April, 1881, on ‘ Technical and Industrial Education Abroad,” in an extended contribution to the Report of the Massachusetts Board of Education for 1880-81, and in a “ Report on Industrial Education ” in 1884. Others have taken a more directly prominent share in the introduction and extension of mechanic arts or manual training in primary and secondary schools, but the actual experiment initiated by him in Boston had in its time wide influence and imitation. As a teacher of mathematics, Professor Runkle found his highest use- fulness and most congenial vocation, —a vocation to be happily continued for not less than twenty-one years. His teaching was characterized by stimulating, luminous, unconventional exposition, by quick incisive ques- tioning, by warm personal interest in his students, and by a constant substratum of uplifting earnestness and dignity. None of his students could fail to acquire admiring affection; very few could withstand the incentive to work. Professor Runkle was a man of much intellectual quickness and strength, of ardent, but in later years serene, temperament, of warm and generous affections, of cordial, unaffected courtesy, in all the relations of life a sincere and loyal gentleman. Throughout his early and middle life he was a pioneer, first in the struggle for his own education and that of his brothers, next in the establishment and continuance of a much- needed, but, as it turned out, premature mathematical journal, then and for many years in the development of the Massachusetts Institute of Technology, and the introduction of education in the mechanic arts. In 730 JOHN DANIEL RUNKLE. all these undertakings his insight and courage were invaluable. He made President Rogers’ plans for the Institute his own. He held steadfastly to its fundamental ideals, and, taking account of his scanty resources, made remarkable progress toward their fulfilment. The main changes he initiated have been abundantly justified by time, and he lived to see their fulfilment. He was elected a Fellow of the Academy on the 26th of May, 1857, and served one year (1877-78) as Councillor. New members elected are: Resident Fellows, 6; Associate Fellows, 3; Foreign Honorary Members, 5. The roll of the Academy now includes 197 Resident Fellows, 98 Associate Fellows, and 72 Foreign Honorary Members.* * By the resignation of a Resident Fellow, the death of an Associate Fellow and a Foreign Honorary Member, and the election of new members at the annual meeting of May 13, 1903, the roll stands at date of publication, 198 Resident Fellows, 98 Associate Fellows, 72 Foreign Honorary Members. American Academy of Arts and Sciences. OFFICERS AND COMMITTEES FOR 1903-04. PRESIDENT. WILLIAM W. GoopDwInN. VICE-PRESIDENT. Class I. Class II. Class III. JOHN TROWBRIDGE, Henry P. WALCOTT, Joun C. GRay. CORRESPONDING SECRETARY. WILLIAM M. Davis. RECORDING SECRETARY WILLIAM WATSON. " TREASURER. FRANCIS BLAKE. LIBRARIAN. A. LAWRENCE ROTCH. COUNCILLORS. Class I, Class II. Class III. GEORGE F. SWAIN, ROBERT DE C. WARD, DENMAN W. Ross, Terms expire 1904. ARTHUR G. WEBSTER, EDWARD L. MARK, ARLO BATES, Terms expire 1905. LEwIs J. JOHNSON, EDWARD H. BRADFORD, Morris H. MorGan, Terms expire 1906. COMMITTEE OF FINANCE. WILLIAM W. GoopwIn, FRANCIS BLAKE, Erion ©, Crarike RUMFORD COMMITTEE. CHARLES R. Cross, Chairman, ErRAsMus D. LEAVITT, EDWARD C. PICKERING, Amos E. DOLBEAR, ARTHUR G. WEBSTER, THEODORE W. RICHARDS, ELIHU THOMSON. Cc. M. WARREN COMMITTEE. LEONARD P. KINNICUTT, Chairman, CHARLES L. JACKSON, SAMUEL CABOT, ARTHUR M. Comey, RoBERT H. RICHARDS, HENRY P. TALBOT, ARTHUR MICHAEL. COMMITTEE OF PUBLICATION. EDWARD L. Mark, of Class II., Chairman, SETH C. CHANDLER, of Class I., CRAWFORD H. Toy, of Class III. COMMITTEE ON THE LIBRARY. A. LAWRENCE ROTCH, Chairman, Harry M. Goopwin, of Class I., SAMUEL HENSHAW, of Class IL, Henry W. Haynes, of Class III. AUDITING COMMITTEE. HENRY G. DENNY, WILLIAM L. RICHARDSON. LL See FELLOWS AND FOREIGN HONORARY MEMBERS. (Corrected to June 30, 1903.) RESPDEN LT FELLOW S.—=198. (Number limited to two hundred.) Crass I.— Mathematical and Ph ysical Sciences. — 81. Srcrion II. — 24. Section I. —18. Francis Blake, Weston. Mathematics and Astronomy. SE EweEaIe | matieah Solon I. Bailey, Cambridge. Charles R. Cross, Brookline. Maxime Bocher, Cambridge. | Amos E. Dolbear, Somerville. William E. Byerly, | Cambridge. | A- W. Duff, Worcester. Seth C. Chandler, Cambridge. | H. M. Goodwin, Roxbury. Gustavus Hay, Boston. Edwin H. Hall, Cambridge. Percival Lowell, Boston. Hammond V. Hayes, Cambridge. James Mills Peirce, Cambridge. | William L. Hooper, Somerville. Edward C. Pickering, Cambridge. | William W. Jacques, Newton. William H. Pickering, Cambridge. | Frank A. Laws, Boston. Henry S. Pritchett, Boston. Henry Lefavour, Boston. John Ritchie, Jr., Roxbury. Theodore Lyman, Brookline. Edwin F. Sawyer, Brighton. Benjamin O. Peirce, Cambridge. Arthur Searle, Cambridge. | A. Lawrence Rotch, Boston. William E. Story, Worcester. Wallace C. Sabine, Boston. Henry Taber, Worcester. | John S. Stone, Boston. ‘Harry W. Tyler, Boston. Elihu Thomson, Swampscott. O. C. Wendell, Cambridge, | John Trowbridge, Cambridge. P. S. Yendell, Dorchester.. | A. G. Webster, Worcester. Robert W. Willson, Cambridge. SHCTION LU. —— 2 Physics. A. Graham Bell, Washington, D.C. Chemistry. Clarence J. Blake, — Boston. Samuel Cabot, Boston. 734 RESIDENT Arthur M. Comey, Cambridge. James M. Crafts, Boston. Charles W. Eliot, Cambridge. Charles L. Jackson, Cambridge. Walter L. Jennings, Worcester. Leonard P. Kinnicutt, Worcester. Charles F. Mabery, Cleveland, O. Arthur Michael, Boston. George D. Moore, Worcester. Charles E. Munroe, Wash’gton, D.C. John U. Nef, Chicago, Ill. Arthur A. Noyes, Boston. Robert H. Richards, Jamaica Plain. Theodore W. Richards, Cambridge. Charles R. Sanger, Cambridge. Stephen P. Sharples, Cambridge. Francis H. Storer, Boston. Henry P. Talbot, Newton. Charles H. Wing, Ledger, N.C. Edward 8. Wood, Boston. FELLOWS. Ira N. Hollis, E. D. Leavitt, H. L. Smyth, L. J. Johnson, Gaetano Lanza, Charles S. Storrow, George F. Swain, William Watson, Section IV. —18. Technology and Engineering. Alfred E. Burton, Eliot C. Clarke, Heinrich O. Hofman, Jamaica Plain. 3oston. Boston. Cambridge. Cambridge. Boston. Cambridge. William R. Livermore, New York. Hiram F. Mills, Cecil H. Peabody, | Alfred P. Rockwell, Andrew H. Russell, Albert Sauveur, Peter Schwamb, Lowell. Brookline. Manchester. Manila. Cambridge. Arlington. Cambridge. Boston. Boston. Boston. Crass IL.— Natural and Physiological Sciences. — 68. Srcrion I. — 1d. Geology, Mineralogy, and Physics of the Globe. H. H. Clayton, Milton. Algernon Coolidge, — Boston. William O. Crosby, Jamaica Plain. William M. Davis, Cambridge. Benj. K. Emerson, Amherst. O. W. Huntington, Robert T. Jackson, Newport, R. I. Cambridge. T. A. Jaggar, Jr., Cambridge. William H. Niles, Cambridge. Charles Palache, Cambridge. John E. Pillsbury, Boston. Nathaniel S. Shaler, Cambridge. Robert DeC. Ward, Cambridge. John E. Wolff, J. B. Woodworth, Cambridge. Cambridge. F. S. Collins, John G. Jack, Alexander Agassiz, | Robert Amory, Geo. E. Davenport, William G. Farlow, Charles E. Faxon, Merritt L. Fernaid, William F. Ganong, George L. Goodale, B. L. Robinson, Charles S. Sargent, Arthur B. Seymour, Roland Thaxter, Srction II. —12. Malden. Medford. Cambridge. Jamaica Plain. Cambridge. Northampton. Cambridge. Jamaica Plain. Cambridge. Brookline. Cambridge. Cambridge. Section III. — 25. Zovlogy and Physiology. Cambridge. Boston. RESIDENT FELLOWS. Ja mes M. Barnard, Milton. Henry P. Bowditch, William Brewster, Cambridge. Louis Cabot, Brookline. William E. Castle, Cambridge. Samuel F. Clarke, W. T. Councilman, Charles B. Davenport, Harold C. Ernst, Boston. Chicago, Ill. Edward G. Gardiner, Boston. Samuel Henshaw, Cambridge. Theodore Hough, Boston. John S. Kingsley, Somerville. Edward L. Mark, Cambridge. Charles S. Minot, Milton. Edward S. Morse, Salem. George H. Parker, Cambridge. William T. Porter, Boston. James J. Putnam, Boston. Samuel H. Scudder, Cambridge. William T. Sedgwick, Boston. Jamaica Plain. Williamstown. Jamaica Plain. 735 James C. White, Boston. William M. Woodworth, Cambridge. SECTION IV.— 16: Medicine and Surgery. Samuel L. Abbot, Boston. Edward H. Bradford, Boston. Arthur T. Cabot, Boston. David W. Cheever, — Boston. Frank W. Draper, Boston. Thomas Dwight, Nahant. Reginald H. Fitz, Boston. Charles F. Folsom, Boston. Frederick I. Knight, Boston. Samuel J. Mixter, Boston. W. L. Richardson, Boston. Theobald Smith, Jamaica Plain, O. F. Wadsworth, Boston. Henry P. Walcott, | Cambridge. John C. Warren, 3oston. Francis H. Williams, Boston. Cuass III.— Moral and Political Sciences. — 49. SECTION I: —10. Philosophy and Jurisprudence. James B. Ames, Cambridge. John C. Gray, Boston. G. Stanley Hall, Worcester. Geo. F. Hoar, Worcester. Francis C. Lowell, Boston. Hugo Minsterberg, Cambridge. Josiah Royce, Cambridge. Jeremiah Smith, Cambridge. Frederic J. Stimson, Edward H. Strobel, © Cambridge. Section II. — 20. Philology and Archeology. Charles P. Bowditch, Lucien Carr, Jamaica Plain. Cambridge. Dedham. z Franklin Carter, Williamstown. Joseph T. Clarke, Boston. Henry G. Denny, Roxbury. William Everett, Quincy. J. W. Fewkes, Washington, D.C. William W. Goodwin, Cambridge. Henry W. Haynes, — Boston. Charles R. Lanman, Cambridge. David G. Lyon, Cambridge. Morris H. Morgan, Cambridge. Bennett H. Nash, Boston. Frederick W. Putnam, Cambridge. Edward Robinson, Boston. F. B. Stephenson, Boston. Crawford H. Toy, Cambridge. John W. White, John H. Wright, Edward J. Young, Cambridge. Cambridge. Waltham. RESIDENT FELLOWS. Secrion III. —10. Political Economy and History. Charles F. Adams, Edward Atkinson, Andrew McF. Davis, Ephraim Emerton, A. C. Goodell, Henry C. Lodge, A. Lawrence Lowell, James F. Rhodes, Charles C. Smith, F. W. Taussig, Lincoln. Brookline. Cambridge. Cambridge. Salem. Nahant. Boston. Boston. Boston. Cambridge. Section IV.—9. Literature and the Fine Arts. Francis Bartlett, John Bartlett, Arlo Bates, George S. Boutwell, T. W. Higginson, George L. Kittredge, Charles Eliot Norton, Denman W. Ross, Barrett Wendell, Boston. Cambridge. Boston. Groton. Cambridge. Cambridge. Cambridge. Cambridge. Boston. ASSOCIATE FELLOWS. ASSOCIATE 737 FELLOWS. — 98. (Number limited to one hundred. Elected as vacancies occur.) Crass I.— Mathematical and Physical Sciences. — 36. Section I.—14. A. A. Michelson, KE. L. Nichols, Chicago. Mathematics and Astronomy. Ithaca, N. Y. Edward E. Barnard, Williams Bay, Section III.—8. S. W. Burnham, George Davidson, Fabian Franklin, Asaph Hall, George W. Hill, E. 8S. Holden, Emory McClintock, E. H. Moore, Simon Newcomb, Charles L. Poor, George M. Searle, J. N. Stockwell, Chas. A. Young, Chicago. [Wis. San Francisco. Baltimore. Goshen, Conn. W. Nyack, N.Y. New York. Morristown, N.J. Chicago. Washington. New York. Washington. Cleveland, O. Princeton, N. J. SEcTION II. —6. Physics. Carl Barus, Providence, R.I. Chemistry. So. Bethlehem, Pa. Newport, R.I. New Haven. New Haven. Charlottesville, Va. Cleveland, O. New Orleans. Baltimore. T. M. Drown, Wolcott Gibbs, Frank A. Gooch, S. W. Johnson, J. W. Mallet, E. W. Morley, J. M. Ordway, Tra Remsen, Section IV.—8. Technology and Engineering. Henry L. Abbot, Cyrus B. Comstock, W. P. Craighill, John Fritz, F. R. Hutton, Cambridge. New York.[ Va. Charlestown, W. Bethlehem, Pa. New York. New York. Edge Moor, Del. New York. G. E. Hale, S. P. Langley, T. C. Mendenhall, George 8. Morison, William Sellers, Robt. S. Woodward, Williams Bay, Wis. Washington. Crass II.— Natural and Physiological Sciences. — 31. Section I. — 10. Geology, Mineralogy, and Physics of the Globe. Cleveland Abbe, George J. Brush, T. C. Chamberlin, Washington. New Haven. Chicago. Edward S. Dana, Walter G. Davis, Samuel F. Emmons, G. K. Gilbert, S. L. Penfield, R. Pumpelly, Charles D. Walcott, New Haven. Cordova, Arg. Washington. Washington. New Haven. Newport, R.I. Washington. 738 ASSOCIATE FELLOWS. Secrion II. —6. S. Weir Mitchell, Philadelphia. B H. F. Osborn, New York. otany. : A. S. Packard, Providence, R.I. L. H. Bailey, Ithaca, N.Y. | A. E. Verrill, New Haven. D. H. Campbell, Palo Alto, Cal. | CO. Whitman, Chicago. J. M. Coulter, Chicago. 3. B. Wilson, New York. C. G. Pringle, Charlotte, Vt. John D. Smith, Baltimore. Section IV. —6. Ws TESST es Sp Lames Medicine and Surgery. John S. Billings, New York. Section III. —9. W.S. Halsted, Baltimore. Bociegyand Piya W. W. Keen, Philadelphia. Joel A. Allen, New York. William Osler, * Baltimore. W. K. Brooks, Lake Roland, Md. ‘Wm. H. Welch, Baltimore. F. P. Mall, Baltimore. H. C. Wood, Philadelphia. Crass ILl.— Moral and Political Sciences. — 31. Section I. —7. Section III.—8. Political Economy and History. Henry Adams, Washington. James C. Carter, New York. GP: Fisher, New Haven. Joseph H. CBRE, New York. Arthur T. Hadley, New Haven. Melville W. Fuller, Washington. H. E. von Holst, Chicago William W. Howe, New Orleans. | Frenry ©, pode pies leigh a Charles S. Peirce, Milford, Pa. Alfred T Mah Sa) Nem Vouk G. W. Pepper, Philadelphia. H. Morse Stephens, Ithaca. T. R. Pynchon, Hartford, Conn. | ws @, Sumner Nowikiaven SEecTIon IV. —9. Philosophy and Jurisprudence. Section II. —7. Literature and the Fine Arts. i James B. Angell, Ann Arbor, Mich. Philology and Archeology. L. P. di Cesnola, New York. Timothy Dwight, |New Haven. H. H. Furness, Wallingford, Pa. B. L. Gildersleeve, Baltimore. R. S. Greenough, Florence. D. C. Gilman, Baltimore: Herbert Putnam, Washington. T. R. Lounsbury, New Haven. Augustus St. Gaudens, Windsor, Vt. Rufus B. Richardson, Athens. John S. Sargent, London. Thomas D. Seymour, New Haven. E. C. Stedman, — Bronxville, N. Y. A. D. White, Ithaca, N.Y. W. R. Ware, New York. FOREIGN HONORARY MEMBERS. 739 FOREIGN HONORARY MEMBERS.—72. (Number limited to seventy-five. Elected as vacancies occur.) Crass I.— Mathematical and Physical Sciences. — 23. Section I. — 7. Section III.—6. Mathematics and Astronomy. Chemistry. Arthur Auwers, Berlin. Adolf Ritter von Baeyer, Munich. Luigi Cremona, Rome. Marcellin Berthelot, Paris. George H. Darwin, Cambridge. J. H. van’t Hoff, Berka Sir William Huggins, London. D. Mendeleeff, St. Petersburg. H. Poincaré, Paris. Sir H. E. Roscoe; London. Otto Struve, Karlsruhe. Julius Thomsen, Copenhagen. H. C. Vogel, Potsdam. Section II. —5. Section IV. —5. Physics. Technology and Engineering. Ludwig Boltzmann, Leipsic. Sir Benjamin Baker, London. Oliver Heaviside, Newton Abbot. | Lord Kelvin, Largs. F. Kohlrausch, Berlin. Maurice Lévy, Paris. — Lord Rayleigh, Witham. H. Miiller-Breslau, Berlin. Joseph J. Thomson, Cambridge. W.Cawthorne Unwin, London. Crass Il.— Natural and Physiological Sciences. — 26. Section I. —7. Section II. —6. Geology, Mineralogy, and Physics of the Globe. . Botany. Sir Archibald Geikie, London. EK. Bornet, Paris. Julius Hann, Vienna. A. Engler, Berlin. Albert Heim, Zurich. Sir Joseph D. Hooker, Sunningdale. Sir John Murray, Edinburgh. W. Pfefter, Leipsic. Freih. vy. Richthofen, Berlin. H. Graf zu Solms- Henry C. Sorby, Sheffield. Laubach, Strassburg. K, A. Ritter von Zittel, Munich. Eduard Strasburger, Bonn. 740 FOREIGN HONORARY MEMBERS. Srection III. —6. Section IV. —7. ae oe Medicine and Surgery. OO Ye ane ee Emil von Behring, Marburg. Sir Michael Foster, Cambridge. | Sir T. L. Brunton, London. Ludimar Hermann, Konigsberg. | A. Celli, Rome. A. von Kolliker, Wiirzburg. | Sir V. A. H. Horsley, London. H. Kronecker, Bern. R. Koch, Berlin. E. Ray Lankester, London. Lord Lister, London. Elias Metschnikoff, Paris. F. v. Recklinghausen, Strassburg. Cruass III.— Moral and Political Sciences. — 238. Section I. —5. Section III. —5. Philosophy and Jurisprudence. Political Economy and History. A. J. Balfour, Prestonkirk. | James Bryce, London. Heinrich Brunner, Berlin. Theodor Mommsen, Berlin. A. V. Dicey, Oxford. Sir G. O. Trevelyan, F. W. Maitland, Cambridge. Bart., London. Sir Frederick Pollock, W. E. H. Lecky, London. Bart., London. John Morley, London. Srction II. —7. Section IV. — 6. Philology and Archeology. Literature and the Fine Arts. Ingram Bywater, Oxford. F. Delitzsch, Berlin. E. de Amicis, Florence. W. Dorpfeld, Athens. Georg Brandes, Copenhagen. Sir John Evans, Hemel Hempstead. | F. Brunetiere, Paris. H. Jackson, Cambridge. Jean Léon Géréme, Paris. J. W. A. Kirchhoff, Berlin. Rudyard Kipling, Burwash. G. C. C. Maspero, Paris. Sir Leslie Stephen, London. STATUTES AND STANDING VOTES. ee AST Gy Tins: Adopted May 30, 1854: amended September 8, 1857, November 12, 1862, May 24, 1864, November 9, 1870, May 27, 1873, January 26, 1876, June 16, 1586, October 8, 1890, January 11 and May 10, 1893, May 9 and October 10, 1894, March 13, April 10 and May 8, 1895, May 8, 1901, and January 8, 1902. CHAPTER. I. Or FELLOWS AND FOREIGN HONORARY MEMBERS. 1. The Academy consists of Resident Fellows, Associate Fellows and Foreign Honorary Members. They are arranged in three Classes, according to the Arts and Sciences in which they are severally proficient, viz.: Class I. The Mathematical and Physical Sciences ;— Class II. The Natural and Physiological Sciences ; — Class III. The Moral and Political Sciences. Each Class is divided into four Sections, viz.: Class I., Section 1. Mathematics and Astronomy ;— Section 2. Physics ; — Section 3. Chemistry ;— Section 4. Technology and Engineering. Class II., Section 1. Geology, Mineralogy, and Physics of the Globe ; — Section 2. Botany ;— Section 3. Zodlogy and Physiology ;— Section 4. Medicine and Surgery. Class III., Section 1. Philosophy and Juris- prudence : — Section 2. Philology and Archeology ; — Section 3. Political Economy and History ;— Section 4. Literature and the Fine Arts. : 2. The number of Resident Fellows shall not exceed two hundred. Only residents in the Commonwealth of Massachusetts shall be eligible to election as Resident Fellows, but resident fellowship may be retained after removal from the Commonwealth. Each Resident Fellow shall pay an admission fee of ten dollars and such annual assessment, not ex- ceeding ten dollars, as shall be voted by the Academy at each annual 742 STATUTES OF THE AMERICAN ACADEMY meeting. Resident Fellows only may vote at the meetings of the Academy. 3. The number of Associate Fellows shall not exceed one hundred, of whom there shall not be more than forty in either of the three classes of the Academy. Associate Fellows shall be chosen from persons resid- ing outside of the Commonwealth of Massachusetts. They shall not be liable to the payment of any fees or annual dues, but on removing within the Commonwealth they may be transferred by the Council to resident fellowship as vacancies there occur. 4, The number of Foreign Honorary Members shall not exceed seventy-five ; and they shall be chosen from among persons most eminent in foreign countries for their discoveries and attainments in either of the three departments of knowledge above enumerated. ‘There shall not be more than thirty Foreign Members in either of these departments. CHAPTER II. Or OFFICERS. 1. There shall be a President, three Vice-Presidents, one for each Class, a Corresponding Secretary, a Recording Secretary, a Treasurer, and a Librarian, which officers shall be annually elected, by ballot, at the Annual Meeting, on the second Wednesday in May. 2. At the Annual Meeting of 1901, nine Councillors shall be elected by ballot, one from each Class of the Academy to serve for one year, one from each Class for two years, and one from each Class for three years; and at annual meetings thereafter three Councillors shall be elected in the same manner, one from each Class, to serve for three years; but the same Fellow shall not be eligible for two successive terms. The nine Councillors, with the President, the three Vice-Presidents, the two Secretaries, the Treasurer, and the Librarian, shall constitute the Council. Five members shall constitute a quorum. It shall be the duty of this Council to exercise a discreet supervision over all nomina- tions and elections. With the consent of the Fellow interested, they shall have power to make transfers between the several Sections of the same Class, reporting their action to the Academy. 3. If any office shall become vacant during the year, the vacancy shall be filled by a new election, and at the next stated meeting, or at a meeting called for this purpose. OF ARTS AND SCIENCES, 743 CHAPTER: ITE Or NoMINATIONS OF OFFICERS. 1. At the stated meeting in March, the President shall appoint from the next retiring Councillors a Nominating Committee of three Fellows, one for each class. 2. It shall be the duty of this Nominating Committee to prepare a list of candidates for the offices of President, Vice-Presidents, Corre- sponding Secretary, Recording Secretary, Treasurer, Librarian, Coun- cillors, and the Standing Committees which are chosen by ballot; and to cause this list to be sent by mail to all the Resident Fellows of the Academy not later than four weeks before the Annual Meeting. 3. Independent nominations for any office, signed by at least five Resident Fellows and received by the Recording Secretary not less than ten days before the Annual Meeting, shall be inserted in the call for the Annual Meeting, which shall then be issued not later than one week before that meeting. 4. The Recording Secretary shall prepare for use, in voting at the Annual Meeting, a ballot containing the names of all persons nominated for office under the conditions given above. 5. When an office is to be filled at any other time than at the Annual Meeting, the President shall appoint a Nominating Committee in accord- ance with the provisions of Section 1, which shall announce its nomina- tion in the manner prescribed in Section 2 at least two weeks before the time of election. Independent nominations, signed by at least five Resident Fellows and received by the Recording Secretary not later than one week before the meeting for election, shall be inserted in the call for that meeting. CHAP THER LV. OF THE PRESIDENT. 1. It shall be the duty of the ~President, and, in his absence, of the senior Vice-President present, or next officer in order as above enumer- ated, to preside at the meetings of the Academy; to summon extraor- dinary meetings, upon any urgent occasion ; and to execute or see to the execution of the Statutes of the Academy. Length of continuous membership in the Academy shall determine the seniority of the Vice- Presidents. 744. STATUTES OF THE AMERICAN ACADEMY 2. The President, or, in his absence, the next officer as above enumer- ated, is empowered to draw upon the Treasurer for such sums of money as the Academy shall direct. Bills presented on account of the Library, or the Publications of the Academy, must be previously approved by the respective committees on these departments. 3. The President, or, in his absence, the next officer as above enumer- ated, shall nominate members to serve on the different committees of the Academy which are not chosen by ballot. 4, Any deed or writing to which the common seal is to be affixed shall be signed and sealed by the President, when thereto authorized by the Academy. CHAPTER. V. Or STANDING COMMITTEES. 1. At the Annual Meeting there shall be chosen the following Stand- ing Committees, to serve for the year ensuing, viz. : — 2. The Committee of Finance, to consist of the President, Treasurer, and one Fellow chosen by ballot, who shall have full control and man- agement of the funds and trusts of the Academy, with the power of investing or changing the investment of the same at their discretion. The general appropriations for the expenditures of the Academy shall be moved by this Committee at the Annual Meeting, and all special appro- priations from the general and publication funds shall be referred to or proposed by this Committee. 3. The Rumford Committee, of seven Fellows, to be chosen by ballot, who shall consider and report on all applications and claims for the Rumford Premium, also on all appropriations from the income of the Rumford Fund, and generally see to the due and proper execution of this trust. 4. The C. M. Warren Committee, of seven Fellows, to be chosen by ballot, who shall consider and report on all applications for appropria- tions from the income of the C. M. Warren Fund, and generally see to the due and proper execution of this trust. 5. The Committee of Publication, of three Fellows, one from each Class, to whom all communications submitted to the Academy for publi- cation shall be referred, and to whom the printing of the Memoirs and the Proceedings shall be intrusted. 6. The Committee on the Library, of the Librarian ex officio and three other Fellows, one from each class, who shall examine the Library, and make an annual report on its condition and management. OF ARTS AND SCIENCES. 745 7. An Auditing Committee of two Fellows, for auditing the accounts of the Treasurer. CHAPTER, VI. OF THE SECRETARIES. 1. The Corresponding Secretary shall conduct the correspondence of ‘the Academy, recording or making an entry of all letters written in its name, and preserving on file all letters which are received ; and at each meeting he shall present the letters which have been addressed to the Academy since the last meeting. Under the direction of the Council for Nomination, he shall keep a list of the Resident Fellows, Associate Fellows, and Foreign Honorary Members, arranged in their Classes and in Sections in respect to the special sciences in which they are severally proficient ; and he shall act as secretary to the Council. 2. The Recording Secretary shall have charge of the Charter and Statute-book, journals, and all literary papers belonging to the Academy. He shall record the proceedings of the Academy at its meetings; and after each meeting is duly opened, he shall read the record of the pre- ceding meeting. He shall notify the meetings of the Academy, apprise officers and committees of their election or appointment, and inform the Treasurer of appropriations of money voted by the Academy. He shall post up in the: Hall a list of the persons nominated for election into the Academy ; and when any individual is chosen, he shall insert in the record the names of the Fellows by whom he was nominated. 3. The two Secretaries, with the Chairman of the Committee of Publication, shall have authority to publish such of the records of the meetings of the Academy as may seem to them calculated to promote its interests. CHAPTER, VEE OF THE TREASURER. 1. The Treasurer shall give such security for the trust reposed in him as the Academy shall require. ; 2. He shall receive officially all moneys due or payable, and all bequests or donations made to the Academy, and shall pay such sums as the Academy may direct. He shall keep an account of all receipts and expenditures ; shall submit his accounts to the Auditing Committee ; and shall report the same at the expiration of his term of office. 746 STATUTES OF THE AMERICAN ACADEMY 3. The Treasurer shall keep separate accounts of the income and appropriation of the Rumford Fund and of other special funds, and report the same annually. 4. All moneys which there shall not be present occasion to expend shall be invested by the Treasurer, under the direction of the Finance Committee. CHAPAER Witt Or THE LIBRARIAN AND LIBRARY. 1. It shall be the duty of the Librarian to take charge of the books, to keep a correct catalogue of them, to provide for the delivery of books from the Library, and to appoint such agents for these purposes as he may think necessary. He shall make an annual report on the condition of the Library. 2. The Librarian, in conjunction with the Committee on the Library, shall have authority to expend such sums as may be appropriated, either from the General, Rumford or other special Funds of the Academy, for the purchase of books, and for defraying other necessary expenses con- nected with the Library. 3. To all books in the Library procured from the income of the Rumford Fund, or other special funds, the Librarian shall cause a stamp or label to be affixed, expressing the fact that they were so procured. 4, Every person who takes a book from the Library shall give a receipt for the same to the Librarian or his assistant. 5. Every book shall be returned in good order, regard being had to the necessary wear of the book with good usage. If any book shall be lost or injured, the person to whom it stands charged shall replace it by a new volume or set, if it belongs to a set, or pay the current price of the volume or set to the Librarian; and thereupon the remain- der of the set, if the volume belonged to a set, shall be delivered to the person so paying for the same. 6. All books shall be returned to the Library for examination at least one week before the Annual Meeting. 7. The Librarian shall have custody of the Publications of the Academy and shall distribute copies among the Associate Fellows and Foreign Honorary Members, at their request. With the advice and con- sent of the President, he may effect exchanges with other associations. — OF ARTS AND SCIENCES. T47 CHAPTER IX. Or MEETINGS. 1. There shall be annually four stated meetings of the Academy ; namely, on the second Wednesday in May (the Annual Meeting), on the second Wednesday in October, on the second Wednesday in January, and on the second Wednesday in March. At these meetings only, or at meetings adjourned from these and regularly notified, shall appropria- tions of money be made, or alterations of the statutes or standing votes of the Academy be effected. 2. Fifteen Fellows shall constitute a quorum for the transaction of - business at a stated meeting. Seven Fellows shall be sufficient to con- stitute a meeting for scientific communications and discussions. 3. The Recording Secretary shall notify the meetings of the Academy to each Fellow residing in Boston and the vicinity; and he may cause the meetings to be advertised, whenever he deems such further notice to be needful. CHAPTER). X. Or THE ELECTION OF FELLOWS AND HonorRARY MEMBERS. 1. Elections shall be made by ballot, and only at stated meetings. 2. Candidates for election as Resident Fellows must be proposed by two Resident Fellows of the section to which the proposal is made, in a recommendation signed by them, and this recommendation shall be transmitted to the Corresponding Secretary, and by him referred to the Council for nomination. No person recommended shall be reported by the Council as a candidate for election, unless he shall have received a written approval, signed at a meeting of the Council by at least five of its members. All nominations thus approved shall be read to the Academy at a stated meeting, and shall then stand on the nomination list during the interval between two stated meetings, and until the balloting. No person shall be elected a Resident Fellow, unless he shall have been resident in this Commonwealth one year next preceding his election. If any person elected a Resident Fellow shall neglect for one year to pay his admission fee, his election shall be void; and if any Resident Fellow shall neglect to pay his annual assessments 748 STATUTES OF THE AMERICAN ACADEMY for two years, provided that his attention shall have been called to this article, he shall be deemed to have abandoned his Fellowship ; but it shall be in the power of the Treasurer, with the consent of the Council, to dispense (sub silentio) with the payment both of the admission fee and of the assessments, whenever in any special instance he shall think it advisable so to do. 3. The nomination of Associate Fellows may take place in the manner prescribed in reference to Resident Fellows. The Council may in like manner originate nominations of Associate Fellows, which must be read at a stated meeting previous to the election, and be exposed on the nom- ination list during the interval. 4. Foreign Honorary Members shall be chosen only after a nomina- tion made at a meeting of the Councii, signed at the time by at least seven of its members, and read at a stated meeting previous to that on which the balloting takes place. 5. Three fourths of the ballots cast must be affirmative, and the number of affirmative ballots must amount to eleven to effect an elec- tion of Fellows or Foreign Honorary Members. 6. A majority of any section of the Academy is empowered to pre- sent lists of persons deemed best qualified to fill vacancies occurring in the number of Foreign Honorary Members or Associate Fellows allotted to it ; and such lists, after being read at a stated meeting, shall be re- ferred to the Council for Nomination. 7. If, in the opinion of a majority of the entire Council, any Fellow — Resident or Associate — shall have rendered himself unworthy of a place in the Academy, the Council shall recommend to the Academy the termination of his Fellowship ; and provided that a majority of two thirds of the Fellows at a stated meeting, consisting of not less than fifty Fellows, shall adopt this recommendation, his name shall be stricken off the roll of Fellows. CHAPTER XI. Or AMENDMENTS OF THE STATUTES. 1. All proposed alterations of the Statutes or additions to them, shail be referred to a committee, and, on their report at a subsequent meeting, shall require for enactment a majority of two thirds of the members present, and at least eighteen affirmative votes. 2. Standing votes may be passed, amended, or rescinded, at any OF ARTS AND SCIENCES, 749 stated meeting, by a majority of two thirds of the members present. They may be suspended by a unanimous vote. CHAPTER XII. Or LITERARY PERFORMANCES. 1. The Academy will not express its judgment on literary or scientific memoirs or performances submitted to it, or included in its publications. 750 STATUTES OF THE AMERICAN ACADEMY STANDING VOTES. 1. Communications of which notice had been given to the Secretary shall take precedence of those not so notified. 2. Resident Fellows who have paid all fees and dues charge- able to them are entitled to receive one copy of each volume or article printed by the Academy, on application to the Librarian personally or by written order, within two years from the date of publication. And the current issues of the Proceedings shall be supplied, when ready for publication, free of charge, to all the Fellows and members of the Academy who desire to receive them. 3. The Committee of Publication shall fix from time to time the price at which the publications of the Academy may be sold. But members may be supplied at half this price with volumes which they are not entitled to receive free, and which are needed to complete their sets. 4. Two hundred extra copies of each paper accepted for publi- eation in the Memoirs or Proceedings of the Academy shall be placed at the disposal of the author, free of charge. 5. Resident Fellows may borrow and have out from the Library six volumes at any one time, and may retain the same for three months, and no longer. 6. Upon special application, and for adequate reasons assigned, the Librarian may permit a larger number of volumes, not exceed- ing twelve, to be drawn from the Library for a limited period. 7. Works published in numbers, when unbound, shall not be taken from the Hall of the Academy, except by special leave of the Librarian. 8. Books, publications, or apparatus shall be procured from the income of the Rumford Fund only on the certificate of the Rum- ford Committee that they, in their opinion, will best facilitate and encourage the making of discoveries and improvements which may merit the Rumford Premium. 9. A meeting for receiving and discussing scientific commu- nications may be held on the second Wednesday of each month not appointed for stated meetings, excepting July, August, and September. OF ARTS AND SCIENCES. tor RUMFORD PREMIUM. In conformity with the terms of the gift of Benjamin, Count Rumford, granting a certain fund to the American Academy of Arts and Sciences, and with a decree of the Supreme Judicial Court for carrying into effect the general charitable intent and purpose of Count Rumford, as expressed in his letter of gift, the Academy is empowered to make from the income of said fund, as it now exists, at any Annual Meeting, an award of a gold and a silver medal, being together of the intrinsic value of three hundred dollars, as a premium to the author of any important discovery or useful improvement in light or in heat, which shall have been made and published by printing, or in any way made known to the public, in any part of the continent of America, or any of the American islands; preference being always given to such discoveries as shall, in the opinion of the Academy, tend most to promote the good of mankind; and to add to such medals, as a further premium for such discovery and improve- ment, if the Academy see fit so to do, a sum of money not exceeding three hundred dollars. INDEX. Nore. For index to genera and species of “ Flora of the Galapagos Islands,” see pp. 263-269. Acallomyces, 23. Homalotae, 24. Acompsomyces, 21. Atomariae, 22. pauperculus, 23. Agassiz, A., Explorations of the Coral Reefs of the Maldives, 692; Reso- lution of Thanks to, 709. Albinism, Heredity of, 601-622. Algae, 89-99. Allen, G.M. See Castle, W. E., and Allen, G. M. Angiosperms, 709. Appleton, W. S., Death of, 700. Archibald, E. H. See Richards, T. W., and Archibald, E. H. Assessment, Annual, Amount of, 707. Atharva-Veda, Whitney’s Critical Commentary on, 708. Athol, Mass., Babingtonite from, 391- 393, 693. Atkinson, E., Insurance Engineering Experiment Station, 693. Atomic Volume, The Significance of | Changing, 291-317, 395, Atomic Weight of Caesium, 441-470. Atomic Weight of Nitrogen, 467. Atomic Weight of Potassium, 467. Atomic Weights, Table of, 710. Babingtonite, 381-393, 693. Baker, J. C. See Crew, H., and Baker, J. C. Balfour, A. J., accepts membership, 691. Bates, A., The Fall of the Campanile of San Marco, 694. Behring, E. von, elected Foreign Honorary Member, 692; accepts Membership, 694. VOL. XXXVIII. — 48 Binary Families, 709. Bishop, F. L., Grant from the Income of the Rumford Fund to, 704, 707. Blake, F., Report of Treasurer, 700- 702. Bonnet, F., Jr. See Richards, T. W., and Bonnet, JB die. Bromine, Reaction of, upon Oxalic Acid, 319-337, 695. Buenos Ayres, National Museum at, Reorganization of, 691. Building Fund, 702. Burton, A. E., elected Resident Fel- low, 692. Cabot, J. E., Death of, 697. Caesic Bromide, 464. Caesic Chloride, 446. Caesic Nitrate, 463. Caesium, Atomic Weight of, 441-470. Campanile of San Marco, Fall of the, 694. Campbell, G. A., elected Resident Fellow, 698. Carbon, Spark Spectrum of, 395-406, 694. Case School of Applied Science. Sce Chemical Laboratory. Castle, W. E., Mendel’s Law of He- redity, 533-548, 697. Castle, W. E., and Allen, G. M. The Heredity of Albinism, 601-622. Cauloglossum aegyptiacum, 69. elatum, 69. transversarium, 59-76. Ceraiomyces Selinae, 26. Chamberlin, T. C., accepts Appoint- ment as Delegate to Northwest- ern University, 694. 754 Chemical Laboratory of Case School of Applied Science, Contribu- tions from, 1, 281. Chemical Laboratory of Harvard College, Contributions from, 271, 291, 319, 407, 415, 429, 441. Chromic Sulphate, Changeable Hy- drolytic Equilibrium of Dis- solved, 709. Cionium Carolinense, 67. Clavogaster novo-zelandicum, 69. Clayton H. H., On the Observed Movements of the Dust from the Volcanic Eruptions in the West Indies, 692. Committees, Standing, appointed, 708 ; elected, 708 ; List of, 731. Coreomyces, 56. Corisae, 56. Corethromyces longicaulis, 21. Cossa, A., Death of, 694. Council, Report of, 700, 715-730. Councilman, W. T., Some Recent Studies on Immunity, 697. Cremona, L., elected Foreign Honor- ary Member, 692; accepts mem- bership, 696. Crew, H., and Baker, J. C., On the Thermal Development of the Spark Spectrum of Carbon, 395- 406, 694. Cross, C. R., Report of the Rumford Committee, 705-705. Cryptogamic Laboratory of Harvard University, Contributions from, dn 00s Curtiss, B. R., Binary Families in a Triply Connected Region, with Especial Reference to Hypergeo- metric Families, 709. Curves, Twisted, Multiple Points of, 471-532. Dartmouth College. See Wilder Phy- sical Laboratory. Davis, W. M., Origin of the Great Mountain Ranges, 698; Record- ing Secretary pro tem., 698. Day, M. A., Bibliography of the Botany of the Galapagos Islands, 80-82. Diffusion and Supersaturation in Gelatine, 623-648, 697. Dimeromyces Forficulae, 9. INDEX. Distillation, 1-5, 694. Dunkel, O. Regular Singular Points of a System of Homogeneous Linear Differential Equations of the First Order, 389-370. Continuous Vacuum, Ecteinomyces, 26. Trichopterophilus, 26. Ehrlich’s Theory of Immunity, 697. Emmons, 8S. F., elected Associate Fellow, 698; accepts Fellowship, 700. Equations, Linear Differential, 339— 370. Ernst, H. C., A New Method of Stating Ehrlich’s Theory of In- munity, 697. Evans, A. W., Hepaticae [of the Gala- pagos Islands], 100-101. Faraday’s Law, Universally Exact Application of, 407-413, 695. Farlow, W. G., Algae [of the Galapa- gos Islands], 89-99; Fungi [of the Galapagos Islands], 82-83 ; Lichenes [of the Galapagos Is- lands], 83-89; Musci [of the Galapagos Islands], 102-104. Faye, H. A. E. A., Death of, 692. Fellows, Associate, deceased — Gibbs, J. W., 700. Powell, J. W., 692. Rood, O. N., 696. Selwyn, A. R. C., 696. Fellows, Associate, elected — Emmons, S. F., 698. Hadley, A. T., 692. Mahan, A. T., 698. Fellows, Associate, List of, 737. Fellows, Resident, deceased, — Appleton, W. S., 700. Cabot, J. E., 697. Gray, H., 692. Hill, H. B., 699. Hunnewell, H. H., 692. Loring, C. G., 692. Mitchell, H., 695. Runkle, J. D., 692. Wyman, M., 697. Fellows, Resident, elected, — Burton, A. E., 692. Campbell, G. A., 698. Ganong, W. F., 708. Miinsterberg, H., 692. INDEX. Fellows, Resident, elected, — Palache, C., 708. Sauveur, A., 698. Stimson, F. J., 692. Tyler, Hi. W*, 692. Fellows, Resident, List of, 733. Flaveria, 699. Foreign Honorary Members de- ceased, — Faye, H. A. E. A., 692. Paris, G. B. P., 698. Stokes, Sir G. G., Bart., 697. Virchow, R., 692. Wild, H. von, 691, 692. Foreign Honorary Members elected— Behring, E. von, 692. Cremona, L., 692. Morley, J., 692. Thomson, J. J., 692. Zittel, K. A. Ritter von, 698. Foreign Honorary Members, List of, 739. Fraprie, F. R. See Palache, C., and Fraprie, F. R. Frost, E. B., Grant from Income of the Rumford Fund to, 703. Fungi, 82-83. Galapagos Islands, Bibliography of the Botany of, 80-82; Flora of the, 75-270, 694. (For index of species, see pp. 263-269. Ganong, W. F., elected Resident Fellow, 708. Gas-Analysis by Measurement in Constant Volume under Chang- ing Pressure, 271-279, 695. Gases, Apparatus for the Measure- ment of the Expansion of, 415- 428, 695; Spectra of, at High Temperatures, 679-688, 699, 709 ; Viscosity of, 709. Geissler Tubes, Use of, in Spectrum Analysis, 696. General Fund, 701; Appropriations. from the Income of, 697, 706. > Gibbs, J. W., Death of, 700. Goetz, E., Stellar Photometer placed at the Disposal of, 704. Grants from Income of C. M. Warren Fund, 705, 707; from Income of Rumford Fund, 696, 703-707. Gray, H., Death of, 692. Gray Herbarium of Harvard Uni- versity, Contributions from, 79. 155 Greenman, J. R., New and otherwise Noteworthy Angiosperms from New Mexico and Central Amer- ica, 709. Hadley, A. T., elected Associate Fellow, 692 ; accepts Fellowship, 694. Hale, G. E., Grant from Income of Rumford Fund to, 697, 704 ; Presentation of Rumford Medal to, 699. Harvard Mineralogical Museum, Contributions from, 381. Harvard University. See Chemical Laboratory, Cryptogamic Lab- oratory, Gray Herbarium, Jeffer- son Physical Laboratory, and Zoological Laboratory. Heat Capacity, Changing, 291-317, 695. Hepaticae, 100-101. Heredity of Albinism, 601-622. Heredity, Mendel’s Law of, 533- 548, 697. Herpomyces, 11. arietinus, 14. chaetophilus, 12. Diplopterae, 16. Ectobiae, 20. forficularis, 15. Paranensis, 19. Periplanetae, 13. tricuspidatus, 17. Zanzibarinus, 15. Hill, H. B., Death of, 699. Hofman, H. O., Grant from the In- ° come of the C. M. Warren Fund to, 705, 707. Hogg, J. L., Viscosity of Gases, 709. Hopkins-Stanford Expedition to the Galapagos Islands, Papers from the, 75. Hull, G. F. See Nichols, E. F., and Hull, G. F. Hunnewell, H. H., Death of, 692. Hyatt, A., Notice of, 715: Hydrocarbons, Index of Refraction of Solid, 281-290, 695. Immunity, Ehrlich’s Theory of, 697 ; Recent Studies in, 697. Insurance Engineering, Experiment Station in, Report of, 693. 756 International Botanical 691. Tron, Are Spectra of, 377. Congress, Jefferson Physical Laboratory, Harv- ard College, Contributions from, 549, 623, 649, 661, 679. Johnston, J. R., A Revision of the Genus Flaveria, 699 ; On Caulo- glossum trausversarium Fries (Bosc), 59-76. ‘* Judgment of Solomon,” 698. Kinnicutt, L. P., Report of the C. M. Warren Committee, 705. Laboulbenia acanthophora, 27. Bledii, 27. Borneensis, 28. cauliculata 29. Columbiana, 30. concinna, 31. corniculata, 31. Craspidophori, 32. curvata, 33. dentifera, 34. Disenochi, 34. Dryptae, 35. dubia, 35. Euchilae, 36. Eudaliae, 36. exigua, 37. flaccida, 37. Formicarum, 39. fusiformis, 39. Hawaiiensis, 40. Helluodis, 41. Helluomorphae, 42. humilis, 42. incerta, 43. insignis, 43. Japonica, 44. Latonae, 45. media, 45. Megalonychi, 46. notata, 47. obliquata, 48. Oedichiri, 48. pallida, 49. perplexa, 49. Planetis, 50. Platyprosopi, 51. producta, 52. proliferans, 52. proliferans var. atrata, 53. INDEX. Laboulbenia proliferans var. cincta, 53. proliferans var. divaricata, 53. proliferans var. Liberiana, 52. sphyriopsis, 53. Stomonaxi, 54. Tachyis, 38. Texana, 55. Texana var. incurvata, 55. Texana var. pendula, 55. Texana var. Rostellata, 55. Texana var. Tibialis, 55. Laboulbeniaceae, Preliminary Diag- noses of New Species of, 7-57. Lanman, C. R., The Completion of Whitney’s Critical Commentary on the Atharva-Veda and the Continuity of Scientific Prog- ress, 708. Leckey, W. E. H., accepts member- ship, 691. Librarian, Report of, 702-708. Library, Appropriations for, 696, 704, 706-707. Lichenes, 838-89. Light, Diffusion of, and Corrosion of Steel, 693. Lonicera, 697. Loring, C. G., Death of, 692. Lunar Phenomena, Account of, 697. Lunar Surface, Recent Studies of the, 694. Lycoperdon transversarium, 65. Lyman, T., An Explanation of the False Spectra from Diffraction Gratings, 709. Mabery, C. F., An Apparatus for Continuous Vacuum Distillation, 1—5, 694; Grant from the In- come of the C. M. Warren Fund to, 705, 707. Mabery, C. F., and Shepherd, L., A Method for Determining the Index of Refraction of Solid Hydrocarbons with the Pulfrich Refractometer. Index of Re- fraction of the Solid Hydrocar- bons in Petroleum, 281-290, 695. Magnesium, Arc Spectra of, 376. Magnets made of Chilled Cast Iron, Temperature Coefficients of, 549-556, 697. Mahan, A. T., elected Associate Fel- low,698; accepts Fellowship, 700. INDEX. Maldives, Explorations of the Coral Reefs of the, 692. Mark, E. L., Report of the Commit- tee of Publication, 706. Mark, K. L. See Richards, T. W., and Mark, K. I.. Mazelle, E., appointed Director of Trieste Observatory, 700. Mendel’s Law of Heredity, 533-548. Metals at High Temperatures, Spec- tra of, 679-658, 699, 709. Minor, R. S8., Grant from Income of Rumford Fund to, 703. Mitchell, H., Death of, 696. Monoicomyces nigrescens, 10. Monoicomyces Oxypodae, 10. Morgan, M. H., The Pompeian Fresco called ‘‘ The Judgment of Solomon,” 698. Morley, J., elected Foreign Honorary Member, 692; accepts Member- ship, 694. Morse, H. W., and Pierce, G. W.., Diffusion and Supersaturation in Gelatine, 623-648, 697. Mountain Ranges, Origin of, 698. Minsterberg, H., elected Resident Fellow, 692; accepts Fellowship, 694. Mulliken, S. P., Grant from the In- come of the C. M. Warren Fund to, 705, 707. Multiple Points of Twisted Curves, 471-532. Musci, 102-104. Museum of Comparative Zoology at Harvard College. See Zoologi- cal Laboratory. Negri, G., Death of, 691. Nichols, E. F., and Hull, G. F., Grant from Income of Rumford Fund to, 703 ; The Pressure due to Radiation, 557-599, 696. Nitrates, 458. Nitrogen, Atomic Weight of, 467. Nitroso-dimethy]-aniline, 709. Nobel Committee, Nobel Prizes, 694. Nominating Committee, 698. North of England Institute of Mining and Mechanical Engineers, Ju- bilee Meeting of, 691. Northwestern University, Installa- tion of E. J. James as President of, 691. x T57 Officers elected, 707; List of, 751. Oxalic Acid, Reaction of Bromine upon, 319-337, 695. Packard, A. S., Biographical Notice of Alpheus Hyatt, 715. Palache, C., elected Resident Fel- low, 708. Palache, C., and Fraprie, F. R., Bab- ingtonite from Somerville, Mass. Babingtonite from Athol, Mass., 381-3938, 693. Paris G. B. P., Death of, 698. Peirce, B. O., On Families of Curves which are the Lines of Certain Plane Vectors either Solenoidal or Lamellar, 661-678, 699; On the Temperature Coefficients of Magnets made of Chilled Cast Iron, 549-556, 697; On the Thermal Conductivities of Cer- tain Pieces of Rock from the Calumet and Hecla Mine, 649- 660, 699. Petroleum, Index of Refraction of the Solid Hydrocarbons in, 281- 290, 695. Pickering, E. C., Grant from Income of the Rumford Fund, 704. Pickering, W. H., Recent Studies of the Lunar Surface, 694. Pierce, G. W. See Morse, H. W., and Pierce, G. W. Porter, R. A., The Influence of Atmospheres of Nitrogen and Hydrogen on the Are Spectra of Iron, Zinc, Magnesium, and Tin, compared with the Influence of an Atmosphere of Ammonia, 371-379. Potassie Chloride, 456. Potassic Nitrate, 462. Potassium, Atomic 467. Powell, J. W., Death of, 692. Pressure due to Radiation, 557-599, 696. Princeton University, Inauguration of Woodrow Wilson as President of, 691. Publication, Appropriations for, 697, 706. Publication, Committee of, Report of, 706. Pulfrich Refractometer, 283. Weight of, 158 Radiation, Pressure due to, 557-599, 696 Rehder, A., Synopsis of the Genus Lonicera, 697. Rhachomyces anomalus, 25. thopalogaster, 70. transversarium, 70. Richards, T. W., Concerning Gas- Analysis by Measurement in Constant Volume under Chang- ing Pressure, 271-279, 695; Grant from Income of Rumford Fund to, 696, 704; Significance of Changing Atomic Volume: The Relation of Changing Heat Capacity to Change of Free En- ergy, Heat of Reaction, Change of Volume, and Chemical Affin- ity, 291-317, 695; Table of Atomic Weights, 710. tichards, T. W., and Archibald, E. H., A _ Revision of the Atomic Weight of Caesium, 441-470. Richards, T. W., and Bonnet, F., Jr., The Changeable Hydrolytic Equilibrium of Dissolved Chro- mic Sulphate, 709. Richards, T. W., and Mark, K. L., Apparatus for the Measurement of the Expansion of Gases by Heat under Constant Pressure, 415-428, 695. Richards, T. W., and Stull, W. N., The Speed and Nature of the Reaction of Bromine upon Ox- alice Acid, 319-337, 695; The Universally Exact Application of Faraday’s Law, 407-413, 695. Richards, T. W., and Wells, R. C., The Transition Temperature of Sodic Sulphate referred anew to the International Standard, 429-440, 695. tobinson, B. L., Flora of the Gala- pagos Islands, 75-270, 694. Rocks, Thermal Conductivities of, 649-660, 699. Rood, O. N., Death of, 696. Ross, D. W., A Theory of Tone- telations — Colors, Intensities, Neutrality, Values, 696. totech, A. L., Report of Librarian, 702-703. INDEX. Royal Meteorological Institute of the Netherlands, Institution of a Section of Terrestrial Magnet- ism and Seismology at the, 691. Rubenson, R., Death of, 694. Rumford Committee, Report of, 703- 705. Rumford Fund, 701; Appropriations from Income of, 696, 703-707 ; Papers published by Aid of, 371, 395, 415, 429, 549, 557, 649, 679. Rumford Medal, Presentation of, 699. Rumford Premium, 751. Runkle, J. D., Death of, Notice of, 727. 692 ; Saunders, F. A., Grant from the Income of the Rumford Fund to, 704, 707. Sauveur, A., elected Resident Fellow, 698; accepts Fellowship, 700. Selwyn, A. R.C., Death of, 696. Shaler, N. S., Account of Some Lunar Phenomena, 697. Shepherd, L. See Mabery, C. L., and Shepherd, L. Sodic Sulphate, Transition Temper- ature of, 429-440, 695. Somerville, Mass., Babingtonite from, 383-391, 693. Spectra, Arc, of Iron, Zinc, Mag- nesium, and Tin, Influence of Atmospheres of Nitrogen and Hydrogen on the, 871-379. Spectra, False, from Diffraction Gratings, 709. Spectra of Gases and Metals at High Temperatures, 679-688, 699, 709. Spectrum Analysis, Use of Quartz Geissler Tubes in, 696. Spectrum, Spark, of Carbon, Ther- mal Development of the, 395- 406, 694. Standing Votes, 750. Statutes, 741. Stichomyces Stilicolus, 24. Stimson, F. J., elected Resident Fellow, 692; accepts Fellowship, 694. Stokes, Sir G. G., Bart., Death of, 697. Stull, W. N. See Richards, T. W., and Stull, W. N. INDEX. Supersaturation in Gelatine, 623- 648, 697. Temperature Coefficients of Magnets made of Chilled Cast Iron, 549- 556. Temperature, Transition, of Sodic Sulphate, 429-440, 695. Thaxter, R., Preliminary Diagno- ses of New Species of Laboul- beniaceae, V., 7-57. Thermal Conductivities of Certain Pieces of Rock from the Calu- met and Hecla Mine, 649-660, 699. Thomson, J. J., elected Foreign Honorary Member, 692 ; accepts membership, 696. Tin, Are Spectra of, 376. Tone-Relations, Theory of, 696. Townley, S. D., Grant from Income of the Rumford Fund to, 703. Tosquinet, P, J., Death of, 696. Treasurer, Report of, 700-702. Trowbridge, J., Results obtained from the Use of Quartz Geissler Tubes in Spectrum Analysis, 696; The Spectra of Gases and Metals at High Temperatures, 679-688, 699, 709. Tyler, H. W., Biographical notice of John Daniel Runkle, 727; elected Resident Fellow, 692; accepts Fellowship, 694. Van der Vries, J. N., On the Multi- ple Points of Twisted Curves, 471-582. 759 Vectors, Lines of Certain Plane, 661- 678, 699. Virchow, R., Death of, 692. Volcanic Eruptions in the West Indies, Dust from, 692. Warren (C. M.) Committee, Report of, 705. Warren (C. M.) Fund, 702; Appro- priations from the Income of, 705, 707; Paper published by y.Ole Moy exe) Wells, R. C. See Richards, T. W., and Wells, R. C. Wild, H. von, Death of, 691, 692. Wilder Physical Laboratory of Dart- mouth College, Contributions from the, 557. Wood, R. W., The Anomalous Dispersion, Absorption, aud Sur- face Color of Nitroso-dimethyl- aniline, 709. World’s Fair, St. Louis, Academy invited to exhibit at, 691. Wyman, M., Death of, 697. Young, C. A., accepts Appointment as Delegate to Princeton Univer- sity, 694. Zinc, Are Spectra of, 377. Zittel, K. A. Ritter von, elected Foreign Honorary Member, 698. 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