PROCEEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. Vol. XXXVII. FROM MAY, 1901, TO MAY, 1902. BOSTON: PUBLISHED BY THE ACADEMY 1902. John Wilson and Son, Cambkidge, U. S. A. 2d "J (o CONTENTS. Page I. The Possible Significance of Changing Atomic Volume. By Theodore William Richards 1 II. Preliminary Diagnoses of New Species of Laboulbeniacae. — IV. By Roland Thaxter 19 III. The Law of Physico-Chemical Change. By Gilbert jSTewton Lewis 47 IV. The Visible Radiation from Carbon. By Edward L. Nichols . 71 V. On Ruled Loci in n-Fold Space. By Halcott C.Moreno . 119 VI. The Arc Spectnmi of Hydrogen. By O. H. Basquin .... 159 VII. The Standard of Atomic Weights. By Theodore William Richards 175 VIII. Studies on the Reactions of Lima x maximus to Directive Stimidi. By Peter Frandsen 183 IX. The Algae of Jamaica. By Frank Shipley Collins . . . 229 X. Modifications of HempeVs Gas-Apparatus. By Theodore Wil- liam Richards 271 XI. The Parametric Representation of the Neighborhood of a Singular Point of an Analytic Surface. By C. W. M. Black . . . 279 XII. A Preliminary Enumeration of the Sorophoreae. By Edgar W. Olive 331 XIII. I'he Decomposition of Mercurous Chloride by Dissolved Chlorides : A Contribution to the Study of Concentrated Solutions. By Theodore William Richauds and Ebenezer Henry Archibald 345 XIV. A New Investigation Concerning the Atomic Weight of Uranium. By Theodore William Richards and Ben.jamin Shores Merigold .... 363 XV. The Signifcance of Changing Atomic Volume. II. — The Prob- able Source of the Heat of Chemical Combination, and a New Atomic Hypothesis. By Theodore William Richards . 397 IV CONTLNTS. Page XVI. On the Accuracy of the Improved Voltameter. By Theodore William Richards and George W. Heimrod . . . 413 XVII. 1. The Northern Carices of the Section Hypan-henae. 2. The Variation of Some Boreal Carices. By M. L. Fernald 445 XVIII. Apatite from Minot, Maine. By John E. Wolff and Charles Palache ?i''|ji- XIX. A Description of Epidote Crystals from Alaska. By CnA^ ^t.s Palache . ... 529 XX. On the Specif c Heats and the Heat of Vaporization of the Par- affine and Methylene Hydrocarbons. By Charles F. Mabery and Albert H. Goldstein ...... 537 XXI. Certain Sense Organs of the Proboscis of the Polychaetous Anne- lid Rhynchobolus dibranchiatus. By Adele Oppenheimer 551 XXII. The Compositio7i of Petroleum. By Charles F. Mabery . 563 Records of Meetings 599 A Table of Atomic Weights. By Theodore William Richards . . 630 Report of the Council 635 Biographical Notices . 635 Augustus Lowell 635 Truman Henry Saflford 654 Horace Elisha Scudder 657 Joseph Henry Thayer 661 John Fiske 665 James Bradley Thayer .... * 679 Officers and Committees fou 1902-1903 683 List of the Fellows and Foreign Honorary Members . . . 685 Statutes and Standing Votes 693 RuMFORD Premium 703 Index 705 Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 1. —June, 1901. THE POSSIBLE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. By Theodore William Richards. THE POSSIBLE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. By Theodore William Richards. Presented May 8, 1901. Received April 16, 1901. Compressibility is a universal property of matter. It is so essential an attribute of the experimental universe that it is ascribed even to the imponderable and imaginary ether as vrell as to " material." The three states of matter are compressible in very varying degrees, dilute gases being compressible to a great extent, highly compressed gases and liquids to a far less extent, and solids to an extent usually even less than liquids. The first case has been studied in great detail, the last two scarcely at all. Compressibility is simply an evidence of work done upon a system by a given pressure. If the application of considerable pressure in a system causes only a slight change of volume, it is evident that there must be other powerful influences at work. Clearly a clue as to the variation in these influences can be found in the quantitative study of the phenomena. In all reversible cases which may be studied directly, an increase in pressure is accompanied by an increase of resistance to pressure and a diminution of volume. This depends upon the fundamental idea of equilibrium, and is a special case of the general principle sometimes named after Le Chatelier. Working backwards from this idea, one may infer with regard to any given substance at a given temperature, that it is under the influence of great pressure if its volume-change is unusually small under addition of a given pressure. There are two conceivable causes of great compression in a substance. The pressure may be applied from the outside, or it may be due to the mutual internal attraction or affinity of the smallest particles of the substance for one another. That is, the substance may be compressed either by an outside pressure, or by the intensity of its own cohesion. The first may be typified by highly compressed gases, the second by liquids, whose small compressibility may be taken as evidence of great compression. 4 PROCEEDINGS OF THE AMERICAN ACADEMY. In solids one must consider also the directive agency which manifests itself in crystalline form and optical structure. In a few cases the ' ' crystallogenic force" seems to be rather directive than attractive; in other cases it seems to have both properties, for considerable diminution in volume may occur. The presence of the crystal-making force compli- cates the phenomena and is a considerable stumbling-block in the way of the study of the internal tension of solids. In view of these facts, it seemed to me possible that the study of com- pression as manifested by atomic volume under different circumstances, as well as of atomic compressibility, might afford some light as to the affinities at work. The attempt, while only just begun, has not been wholly unsuccessful. Evidently the li(iuid is the most suitable state in which to study the effects of molecular and atomic compressibility. It is most suitable because the irregularities in the behavior of liquids are very great, indi- cating various internal stresses, and because they are nevertheless not at the mercy of the directive crystal-making tendency which superposes its own influence upon that of cohesion. The great difficulty in the subject lies in the fact that the total compressibility of a substance is usually made up of a number of parts ; the molecular compressibility might be due partly to a diminishing of the so-called " free-space" between the mole- cules, as well as to a diminishing of the distance between the atomic centres. In words free from hypothesis, we may say that the compressi- bility may be made up of a chemical and a physical compressibility. When one comes to compute from compressibility the probable affinities, one is still more at a loss, — for each affinity is a mutual affair, concern- ing two specific substances. The immense number of variables thus introduced has discouraged most investigators, and I can find little if any hint of the significance of chemical compressibility in the literature familiar to me.* In a case of this kind, one naturally seeks at first cases as simple as possible. A study of the volume changes which take place on mixing liquids reveals at first no apparent regularity. In some cases an expan- sion occurs, but more usually a contraction ; sometimes heat is evolved, and at other times heat is absorbed. One law may, I think, be detected in the midst of the confusion, namely : Similar liquids exhibit less change of volume on mixing than dissimilar ones do. That is, where the * The considerations of Nordenskjuld are too seriously complicated by nncer- tain assumptions to have much value. (See Ostvvald's Lelirbuch, I. 850 (1891), for these and similar considerations.) RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME, 5 affinity of a substance for itself is not unlike that of the substance for another, no great contraction or expansion occurs on mixing. Thus benzol and tuluol when mixed scarcely change in volume at all, while alcohol and water contract considerably. That is just what would be expected if affinity is the cause of contraction. In order to use such facts it is not necessary to imagine an atomic theory adapted to them. Such a theory is ventured upon at the end of this paper, but the facts are significant without it. One only has to bear in mind that liquid and solid substances resist compression, and hence that when we find them compressed we have reason to believe that pressure has been applied upon them. It is rather a matter of common sense than a hypothetical abstract conception. In order to present in a clear light the complications involved in the study of even a simple series of cases of chemical compression, the facts concerninij the molecular volumes of several metals and their oxides are recorded and discussed below. Molecular Volumes of Oxides. Substance. Weight of metal com- bined with 16 grams oxygen. Density of metal. Density of oxide. Space oc- cupied by given weight of metai. Space oc- cupied by corresponding weight of oxide. Excess of volume of oxide. 2 Ag . . . 215.86 10.-56 7.521 20.55 31.55 -m.oo Hg 200.00 1.3.59 11.130 14.71 19.4 + 4.7 Cu . . . . 63.6 8.95 6.40 7.10 12.4 + 5.3 Ni .... 58.7 8.9 6.39 6.60 11.75 + 5.15 Cd . . . . lV2.Pj 8.67 6.5 12.95 19.7 -f- 6.75 Zn . . . . 65.4 6.9 5.6 9.5 14.5 -f 5.0 Mg 24.30 1.74 34 14.0 12.0 - 2.0 2Na ... 46.1 0.973 2.80 47.4 22.6 -24.8 2 II ... 2.0 0.07 1.00 28.2 18.0 -10.0 Si .... 14.2 2.00 2.30 7.1 13.14 + 6.0 In compounds of carl on, accort ling to posi tion. . . ... 4.' I to 12.0 In liquid oxyiien at — 119° and i JO atni. (s] \ gr. = 0.6 5). . . 0 = 24.5 c.c. In liquid oxygen at — 181° and I atm. . . • • • • . . . 0: = 14.1 c.c. 6 PROCEEDINGS OP THE AMERICAN ACADEMY. "While in the first part of this paper no atomic hypothesis is assumed, the words atomic volume, atomic weight, and atomic heat will be used in a purely matei-ial sense, as the actual constants pertaining to quantities chemically consistent. The results recorded in this table are typical of the variety of degrees of contraction which take jjlace when substances combine with oxygen. It is evident that in some cases the product occupies considerably more space than the metal from which it was formed, and that in others (typified by magnesium and sodium above) the oxide occupies consid- erably less space than the metal. This last remarkable circumstance at once emphasizes the absurdity of estimating the atomic volume of an element in a compound by discovering the volume-change which takes place when that element is replaced by another. Oxygen cannot be said to occupy a minus quantity of space, — the only possible outcome of the false assumption in this particular case. The false method gives fairly consistent results among carbon compounds only because of the great similarity of their composition. This consideration leads to the first law underlying the change of volume in chemical or physical change, namely. The atomic volume is not a constant, but is dependent upon the environment. This law was first suggested by Horstmann,* but he looked upon it rather as the absence of a law than as the presence of one. If the affinity of oxygen for the metal were the only variable entering into the figures given above, it is obvious that the total contraction, the difference between the volumes of factors and product, would be at once a comparative measure of the attractive forces which produce the compression. This reasoning of course rests upon the plausible ground that a state of being which resists pressure, such as liquid oxygen or solid metal, may be compressed only by the application of pressure. In this case pressure may be supposed to be applied by the mutual affinity. But unfortunately the case is not so simple. It is clear that in each case recorded above at least three affinities are concerned : first, the affinity of the metal for itself; second, the affinity of oxygen for itself ; and third, affinity of the metal for oxygen. The second of these is constant throughout the series, hence for the present comparison it may be considered as a known quantity. Therefore each change of volume may concern at least two unknown quantities. Hence if it were possible to measure either of the two * Horstmann, Ostwald's Lehrbuch, I. 389 (1891). RICHARDS. — SIGNIFICANCE OP CHANGING ATOMIC VOLUME. 7 vai'iable affinities, au approximate idea could be obtained concerning the other from these data concei'ning atomic and molecular volume. A slight uncertainty is caused also by the possible varying intensity of the '• crystal-making tendency " which determines the structure of solids. The small differences caused by this uncertainty may be seen from the following typical calculation. If solid rather than liquid mercury had been chosen above, the atomic volume of the mercury would have become = 14.2 instead of 14.7, and the excess of 14.1 volume of the oxide would have been 5.2 instead of 4.7. These differences are unimportant compared with the larger values under consideration ; the precise state of the solids or liquids makes less difference than one would have supposed. Is there any direct method of determining either the mutual affinity of the two elements or the affinity of the metal for itself? Countless attempts to measure the former have so continually resulted in failure that many chemists are inclined to deny the existence of chemical affinity. The electrometric method suggested by Ostwald * clearly measures one of the ways in which chemical affinity may accom- plish work, but it is limited in application and only represents a small fraction of the possibilities. The thermal relations are complicated by well-known thermodynamic irregularities, and would be fully significant only at the imaginary absolute zero. The direct determination of the affinity of a substance for itself is an easier matter, for many of the properties of a single substance, such as volume, compressibility, tenacity, must be associated with this affinity. Let us seek to study these relationships more closely. If one could only be sure that all substances, when relieved of their self-affinity, would occupy the same volume, the atomic volume itself would be the simplest and most direct means of comparing this property in different substances. The smaller the actual atomic volume, the greater must be the self-affinity. Such an assumption would at first sight seem to be justified, for those elements which have the largest atomic volumes have the least inclination to remain in the elementary states. Deserting the elementary state means introducing other affini- ties, however ; hence the assumption would be unsafe. It has been already pointed out that compressibility, if measured over a wide range of pressures, might afford a clue to the extent of compres- * Ostwald, Tlie Chemometer, Z. phys. Chem. 15, 399 (1894). 8 PROCEEDINGS OF THE AMEKICAN ACADEMY. sion already existing in any given substance. But the comparison of different substances involves the dangerous assumption that all substances would be alike compressible if freed from self-affinity, — an assumption which seems more probable than the last, but which nevertheless must be rejected. A much safer measure of the stress under which a single substance rests is the work which heat is able to do upon it. The changing of a simple substance from t° to t° + dt° Centigrade must involve the addition to it of an amount of internal work which is represented by the rise of temperature multiplied by the heat capacity of the substance, or C dt. In a simple elementary substance, when this work does not involve the alteration of crystalline form or any other apparent change except increase in size, it seems reasonable to consider no other variables, at least as a working hypothesis. If this is the case, we may write G dt — P dv, in which P is the internal stress against which the heat-energy is doing work, G the molecular lieat capacity, t temperature, and v volume. The stress against which this work is being done is due only to the internal stress and to atmospheric pressure (which latter may be neglected by comparison with the very large value G dt of the former), hence the stress — P =— — This can apply precisely only to infinitesimal changes, because in all probability P will vary with the volume. While it cannot be claimed that the expression just given certainly expresses a single pressure pitted against temperature-work, the expression certainly represents a resultant tendency which opposes expansion by heat, and therefore, by infereuoe, opposes all other forms of expansion.* It is the inward tendency, the opposite to the driving tendency t or fugacity.t While then this stress, represented by the quotient of energy divided by change of volume, can hardly represent anything very definite, it must nevertheless be supposed in a general way to increase when the self-affinity increases. Hence, while giving no certain knowledge, its study may give an indication of affinity. A typical comparison may be made of the two elements zinc and mercury. They are simple, similar, and yet widely different as to their power of holding oxygen. In each case the atomic contraction on union with oxygen is about the same. If we take as the atomic volume of * All the slight data which we possess upon compressibility seem to run parallel with the coefficients of expansion. 1- Richards, These Proceedings, 35, 471. J Lewis. RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 9 oxygen the atomic critical volume, the contractions are as follows : 14.7 + 24.5 — 19.4 = 19.8, in the case of mercury, and 9.5 + 24.5 — 14.5 = 19.5, in the case of zinc. If the metals were originally subject to the same internal stress, we should infer from the similarity of con- tractions that the affinities concerned in the two cases were about equal. This inference is, however, overthrown by other facts. Both elements have about the same atomic heat capacity, hence no internal rearrange- ment takes place in one which is not approximated in the other. On the other hand, the increase in atomic volume for a rise of 1° of tem- perature exhibited by one is much greater than that exhibited by the other. If a gram atom of one element increases more rapidly in size than the gram atom of another, it is only reasonable to suppose that the heat energy is finding less opposition in the former case. The co- efficient of cubic expansion of mercury is 0.000179 at 0°C. and the heat required to raise a gram through 1° is 0.139 joule. With zinc the corresponding numbers are 0.000087 and 0.392. * The respective atomic volumes are 14.7 and 9.5. Substituting these values in the equation we obtain. „ (200X0.139) T^.^nn A ""' "^ (14.7 X 0.000179) "^ 1^^'^^^ megadynes per square cm. ^^" ^ (9.5 X 0.000087) ^ ^l^'^O^ megadynes per square cm. Both these pressures are very large, for a megadyne exerts on a square centimeter a pressure of almost an atmosphere. As has been said, they signify a resultant tendency which resists expansion. It is interesting to note that these stresses agree in their indications with the comparison of boiling points and latent heats of evaporation. The boiling point of mercury is 357° C. and that of zinc about 930° C. The latent heat of evaporation of zinc is not known, but there is no reason for believing that in its case Trouton's rule is broken. Hence the criteria all indicate that zinc is harder to dissociate from itself than mercury is. A comparison of the energy-quotients of several metals, measured in this way, may be of interest. * All figures not otherwise designated were taken from the tables of Landolt and BiJrnstein, 1894. 10 PROCEEDINGS OP THE AMERICAN ACADEMY. Metal (in order of boiling point). Boiling point 760 m.m. Heat capacity (mayers per gram) C Cubic coefficient of expansion. Energy quotient p_ Cdt atom, expan. megadynes ~ mol. weight. Mercury . . Cadmium . Sodium . . Zinc .... Copper . . . Magnesium Lead .... 357° C=: 630° A 770° C = 1043° A 860° C = 1133° A 930° C = 1203° A unknown 1100°i = 1400°A 1400O-1- = 1700° A 0.139 0.23 1.21 0.392 0.375 1.02 0.120 0.00018 0.000093 0.00022 0.000087 0.000050 0.000081 0.000088 106,000 214,000 53,700 310,000 672,000 ' 224,000 162,000 Silicon . . Diamond . unknown unknown 0.7 0.5 0.00002.30 0.0000036 755,000 4,900,000 In these figures one may find traces of many properties associated with firmness of structure or intensity of self-affinity. For example, the order of sequence of the energy-quotients agrees essentially with that of tenacity and of hardness. There is some relationship also to boiling points and melting-points, although here there are more ex- ceptions. " Chemical affinity " is so much affected by electrical relations and by atomic volume that one would expect to find regularity only on comparing similar elements. Such comparison (zinc with cadmium, or carbon with silicon) seems to show that the energy-quotient tends to increase with diminishing atomic weight. Having thus plausible inference, from independent sources, as to the relative values of the compressing agencies existing in metals at the ordinary temperature, it is worth while to study the correction which must be applied to the volume-change exhibited in chemical combina- tion with another element. In zinc the self-affinity is so great (boiling point = 1200° A), and the metal is hence already so compressed, that a given further pressure causes less change in its volume than it would cause in the case of mercury. That is, the mercury contracts more than zinc when it is oxidized. Hence the difference between the volume of the oxide and the volume of the metal gives too low a value for the volume of the combined oxygen in the case of mercury. RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 11 Thus the contraction of the oxygen is really less in the case of mercuric oxide, although it appears to be the same. Without going further, one can explain by means of these considera- tions the behavior of zincic and mercuric oxides when subjected to high temperatures. The sixteen grams of oxygen in mercuric oxide occupies a larger space than an equal weight in the case of zinc, hence one infers that it is less compressed by its affinity, hence the affinity must be less. This smaller affinity siiould be more easily overcome by rising temperature, a prediction which agrees with facts, TJius there appears to he in this case a connection between the compression of substances and their tendency to combine one with another. The case under consideration is typical. In the case of sodium and magnesium, the affinity of the metal for oxygen is so enormous as to overcome easily the large affinity of the metal for itself, and besides this to compress both metal and oxygen together into a space smaller than that previously occupied by the metal. This fact corresponds with the great difficulty of decomposing sodic and magnesic oxides. Metallic magnesium probably has as energy-quotient a stress more than four times as great as sodium (see table on p. 10) ; hence the total contraction on combination with oxygen is less than in the case of sodium. Compari- son with the cases of mercury and zinc will show that this small con- traction does not necessarily conflict with the fact that magnesium decomposes sodic oxide at high temperatures. Again, the contraction involved in the formation of argentic oxide is very slight. In this case the large volume of oxygen is not concealed by the contraction of the metallic element, as it was in the case of mercury, for silver is not par- ticularly compressible. Hence one can infer that the affinity of silver for oxygen is smaller than that of magnesium for oxygen, — an inference which agrees with fact. Moreover, since the relation is nearly additive, that is, neither silver nor oxygen change much in volume on com- bination, their combination is easily shifted, that is to say, silver oxide is easily decomposed by heat. Of course many tables comparing the molecular volumes of solids and liquids might be drawn up, since a very great number of specific gravi- ties have been determined. A table containing chlorides of the metals already considered may be of interest. Here the variations in contraction are less than they were before. Chlorine evidently possesses more equally distributed affinities than oxygen does, and apparently somewhat weaker ones. The two most interesting features of this table, which may be seen without the elimi- 12 PROCEEDINGS OP THE AMERICAN ACADEMY. MOLECDLAR VOLUMES OF ClILOKIDES. Substance. Weight of metal com- bined with 35.5 grams of chlorine. Density of metal. Density of chloride. Volume of given weight of metal. Volume of corresponding weight of chloride. Excess of volume of chloride above metal. Ag. . 108. 10.56 5.53 10.27 45.90 +15.63 iHg. 100. 14.00 , 5.42 7.30 25.5 +18.2 Hg. . 200. 14.00 7.10 14.00 83.2 +19.2 iCu . 31.8 8.95 3.05 7.10 25.4 +18.3 iCo . . 28.5 9.00 2.94 3.16 21.8 18.64 iCd . 5G.2 8.67 3.7 6.47 24.8 18.33 1 Zn . 32.7 6.9 2.753 4.75 25.0 +20.25 Mg. . 12.2 1.74 2.177 7.0 21.95 +15.00 • Na . . 23.05 0.973 2.15 23.7 27.2 + 4.2 K. . . 39.14 0.875 1.995 45.7 37.3 - 8.4 Rb . . 85.44 1.52 2.21 56.1 55.0 - 1.0 H . . . 1.01 0.07 1.27 14.1 (7) 28.9 fl4.7 Combined witli ca rbon . . 22.8 Liquid chlorine at -80° (boilii ig point, 7 60 mm.) (sj ). gr.r=1.66) 21.5 Liquid clilorine at +80° (sp. g ',r. = 1.20) • • • 29.6 nation of the self-affinities of the several metals, are the small excess in the case of silver, and the larger excess in the case of mercurous chloride. This is quite in accord with the facts ; for argentic chloride is more stable than the oxide, and mercurous chloride easily splits into mercuric chloride and mercury.* The case of the hydroxides is especially interesting. The density of the hydroxide of zinc has not been accurately deter- mined ; indeed the data concerning cobalt, cadmium, and magnesium are not very trustworthy on account of the amorphous condition of most hy- droxides. It is interesting to note that in this table, where the substances are arranged in the order of the contraction which ensues when hydroxyl combines with the metal, should also be arranged in the electro-chemical * Richards, These Proceedings, 33, 9 (1807). RICHARDS, — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 13 MOLECDLAR VOLUMKS OF HYDROXIDES. Substance. Weight of metal com- bined with 17 grams hydroxyl. Density of metal. Density of hydroxide. Volume of given weight of metal. Volume of hydroxide corresponding. Excess of volume of hydroxide above metal. Ag i Hg . . . 1 Ca . . . The hydroxide is exceedingly unstable. It is doubtful if the hydroxide exists. The hydroxide cannot be dried without decomposition. i Co . . . 1 ca . . . i Mg . . . i Sr ... Na . . . . K 28.5 56.2 12.2 43.83 23.05 39.14 9. 2.54 0.973 0.875 3.597 4.79 2.36 3.62 2.13 2.044 3.16 6.47 7.0 17.3 23.7 45.7 12.67 15.25 12.90 17.0 18.80 27.5 + 9.51 + 8.78 + 5.90 - 0.3 - 4.9 -18.2 Hydroxyl in organic compounds +12.0 Hydroxyl in hydrogen dioxide (sp. gr. = 1.50) . . 11.4 order. That is to say, the solution tension of a metal appears to be associated with the excess of affinity of the metal for hydroxyl over its affinity for itself, and intensity of potential seems to be associated with intensity of atomic compression. The inference to be drawn from this comparison is of coarse that the formation of the metallic ion in water is connected with the affinity of the metal for water, — an affinity which manifests itself even when both of the " bonds" of oxygen are filled.* Similar attraction for nitrogen or sulphur would explain cases in which the solvent does not contain oxygen. If this is true, contraction should take place when salts are dissolved in water. This inference is amply verified by facts. In some cases the solution occupies even less space than the water alone, involving a total contraction greater than the volume of the salt itself. The best known of these cases are those of lithic, sodic, and baric hydroxides, and * Briihl has suggested that oxygen is the cause of dissociation, but he ascribes it rather to quadrivalence than to a general affinity. 14 PROCEEDINGS OF THE AMERICAN ACADEMY. cobalt, uickel, zinc, and magnesium sulphates,* but undoubtedly others exist. In a large majority of cases when an electrolyte is dissolved in water, the sura of the volumes of salt and of the solvent taken together considerably exceeds the volume of the solution. This contraction is usually ascribed wholly to the dissolved substance in dilute solutions,! but it seems to me that the behavior of the salts named above proves the falsity of this method of calculation. The water as well as the salt must contract when a salt is dissolved. So many complications are concerned in the act of the solution of an electrolyte that it is difficult to unravel the tangled clues ; but the wide deviations exhibited by different sub- stances seem to indicate that there are present overlapping contractions and expansions, the resultant of which is a smaller quantity than some of the individual influences. Such contractions and expansions are just what one would expect to find in a readjustment of affinities. In considering the simpler case of solid non-electrolytes, one usually finds here also a contraction upon solution, although less marked than in the extreme cases named above. For this reason, one is inclined to ascribe the act of solution of all kinds primarily to the affinity of the solvent for the dissolved substance. The solution tension of a metal or salt becomes simply a balance or ratio of attractions, — the separating tendency of heat upon the dissolving phase is much assisted by the attraction from outside. This is of course no new idea. The possible method of treating mathematically these balanced influences is suggested in a recent paper on the "driving tendency " of reaction. $ That electi'olytic separation also should be assisted by the outside attraction for the solvent is almost a foregone conclusion. This may be inferred from the contraction shown by most electrolytes on dissolving. Hence may arise the various contact-potentials exhibited by the same substance in different solvents ; for different solvents must possess differ- ent affinities. Hence also one would expect to find a much greater potential needed for the dissociation of gases than for that of dissolved substances. The mechanism of electrolytic dissociation in gases is now usually * Thomsen, Thermochemische Untersuchungen, I. 45 (1882). MacGregor, Trans. Eoy. Soc. Canada, 1890, p. 19; 1891, p. 15; Trans. Nova Scotia Inst. Nat. Sc, 7, 368 (1890). t Van't Hoff, Vorlesung. phys. theoret. Cliem., III. p. 41 (1900). Drude and Nernst (Z. pliys. Cliera., 15, 79 (1896)) ascribe this contraction to "Electro- striction." t Ricliards, Jour. Phys. Chem., 4, 385 (1900). See specially p. 391. RICHARDS. — SICxNIFICANCE OP CHANGING ATOMIC VOLUME. 15 explained by the aid of the ingenious hypothesis of "electrons," as amplified by J. J. Thomson and his students in the brilliant experimental researches published in the recent volumes of the Philosophical Magazine. This daring hypothesis must not be accepted without reservation, how- ever. Some physical objections to it have been suggested by Ernest Merritt in his interesting address to the American Association for the Advancement of Science ; * and other objections arise when one tries with its aid to unravel the tangle of influences involved in purely chemical action. The rejected alternative of imagining the atom as indivisible, but as capable of receiving widely varying electric charges under widely different conditions, has some advantages which the opposite hypothesis does not possess. The subject is much too large for discus- sion here, however. One phase of it, which bears directly upon the sub- ject of the present paper, may receive brief notice. The results of Thomson, Towusend, Zeleny f and others seem to indi- cate that the bearer of the negative electricity not only carries the high charge referred to above, but that it is very small, while the bearer of the positive electricity is very large. May it not be the atom itself which thus expands and contracts ? This agrees with the verdict of the results of atomic compression given above. Change of atomic volume seems to be associated with electric stress. This assignment of electric expansibility to the atomic sphere of influence might explain other phenomena con- cerning the behavior of electrified gases, for example, the increase of pressure which is observed when a gas is highly charged. $ Again, the great conductivity of a gas with adequate potential and quantity of electrical discharge § seems to indicate that then the situation must resemble that in a metal, where the spheres of stress fill the whole volume occupied by the substance. The temperature must be so high under these circumstances that the gas is probably in a condition of thermal dissociation. Hence one is inclined to refer the great conduc- tivity to the electrical susceptibility of evenly compressed or undistorted atoms. The fact that pure metals conduct electricity better than alloys or compounds seems to support this conclusion. The permeability of solids to cathode rays might be explained by supposing that the smallest particles of both solid and gas are much contracted by the negative charge. * Proe. Am. As. Adv. Soc, 1900, p. 49. t Phil. Mag. [5] 46, 120, (1898). See also Am. Chem. Journ., 25, 340 (1901), for a resume of this work. X De la Rue and Miiller, Phil. Trans., 1880, 86. § Trowbridge and Richards, Phil. Mag. [5] 43, 349 (1897). 16 PROCEEDINGS OF THE AMERICAN ACADEMY. It is with some diffidence that this paper attempts to reconcile the facts with any hypothesis, for hypotheses sometimes lead to dangerous delu- sions. If, however, one never forgets the essential difference between fact and hypothetical inference, a theory may afford useful suggestions for further research. The facts under discussion in the present paper seem to me to be adequately connected by none of the current concep- tions concerning atoms, hence it has seemed not wholly pointless to postulate a theory which might serve better. The essential elements of this theory must be evident from the trend of the hypothetical discussion above ; they are not wholly new. Since changes of atomic volume seem to be so closely associated with the most intimate properties of substance, it seems necessary to assign more importance to the atomic " sphere of influence " or the " free space " around the atomic centres than is cus- tomary. Indeed, the properties of material seem to be as much concerned with the " atomic shell " as with the " atomic centre." The two hypothet- ical conceptions are so closely related as to be inseparable. Such a point of view leads to the conception of an atom as a compres- sible field of force possessing two attractive attributes, chemical affinity and gravitation, both of which may be concerned in chemical action. Mass may be supposed to be causally connected with gravitation. The fact that in many cases affinity diminishes with increasing atomic weight,* taken together with the Laws of Faraday and of Dulong and Petit, suo-o-ests that the two attractive forces in the atom may bear some sort of reciprocal or additive relationship to one another, — that the product or sum of the two may afford a constant basis for the vibrations of heat and electricity. This relation is often hidden by electrical attrac- tion, which plays so important a role in chemical action that it is some- times hard to distinguish the intensity of chemical affinity proper. In such an atom one can imagine that either thermal or electrical vibration misht cause distention. The phenomena of electricity suggest that electricity plays around the atomic surface, while heat seems to be concerned with a more fundamental or central agitation. Light-vibra- tion, which seems also to be intimately concerned with atomic structure, would be assumed to be a surface effect like electrical vibration. Such an atom would be compressible under the influence of its own affinities as well as under the influence of external pressure. Permanent * Van't rioff, Vorl. th. phys. Chem., III. 87 (1900). Compare also the relation of the energy-quotients of similar metals referred to on p. 10 of the present paper. RICHARDS. — SIGNIFICANCE OP CHANGING ATOMIC VOLUME. 17 atomic distortion would accompauy chemical union, and the heat of the reaction would be the outcome of the resulting decrease of internal energy. Atomic volume and atomic compressibility might limit the possibility of distortion ; hence would arise a possible explanation for quantivalence, stereochemistry, and crystal form. Many other proper- ties of material, too numerous to mention, seem to be explicable in a similar way. It would be unreasonable to expect the hypothesis thus briefly de- scribed to correspond to all known facts. No hypothesis has ever been proposed which is wholly satisfactory ; our knowledge is incommensurate with the possibilities involved. If, however, a given theory is found to explain some relationships better than other hypotheses, it may be of service in suggesting new expei'imental research. Such a service is of course the best one which a hypothesis can perform. The idea discussed above has been already applied in plausible fashion to a wide range of chemical and physical phenomena. If future experi- mentation to be carried on here seems to warrant it, these applications may form the subject of another communication. The object of the present paper may be summed up in a few words, as follows : It is pointed out that changing atomic volume may be used as an approximate measure of the pressure which causes it, and therefore of the affinity which causes the pressure. Some of the difficulties in the way of exact interpretation are pointed out, and hints are given as to possible modes of overcoming the difficulties. The chief outcome of the paper is the following postulate : The atomic volume is not constant, hut a function of pressure and temperature, and probably of electric stress. In this connection it is pointed out that chemical affinity is possibly a reciprocal function of mass. To explain these and many other facts, a modification of the atomic hypothesis is tentatively proposed which contends that we have no right to disregard the compressible environments around the centres of gravity and affinity. Cambridge, Mass. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 2. — June, 1901. CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF HARVARD UNIVERSITY. — XLVII. PRELIMINARY DIAGNOSES OF NEW SPECIES OF LABO ULBENIA CEAE. — IV. By Roland Thaxter. MARINE BIOLOGICAL LABORATORY. Received ).b^<<^.../^.^.^., Accession No. /o.^/J, Given by _^.^.':nr:^^l^ ^. Total length to tip of perithecium 250-460 fj. On Isomnhis Conradti Fauvel. Derema, Usambara, East Africa. Berlin Museum, Nos. 847-848. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 3.— June, 1901. THE LAW OF PHYSICO-CHEMICAL CHANGE. By Gilbert Newton Lewis. THE LAW OF PHYSICO-CHEMICAL CHANGE. By Gilbekt Newton Lewis. Received April 6, 1901. Presented by T. W. Richards, April 10, 1901. Introduction. The many-sided application of thermodynamics to physical chemistry in recent years has led to a maze of mathematical expressions which is bewildering to the beginner and confusing even to the initiated. The great majority of these physico-chemical formulae are based not only upon the two laws of thermodynamics but also upon some empirical law or approximation, and are as a rule not rigorously true, but are useful in so far as the system considered does not deviate too widely from certain ideal conditions. The difficulty of treating mathematically equations which are not strictly exact is probably the chief reason for the con- tinued separate existence of the large number of formulae which, though not identical, are tantalizingly similar in form. It seemed probable that if the present formulae could in any way be replaced by rigorously exact ones, without sacrificing concreteness or immediate applicability, then these exact equations might be so systematized that one might serve where a number of isolated equations are now in use, with a great gain in simplification. With this object in view the present investigation has been carried on, and with the unexpected success of finding a single law which is simple, exact, general enough to comprise in itself many laws and yet concrete enough to be immediately applicable to specific cases. The following development will be based upon four laws of nature and upon no other hypothesis or assumption of any kind. These laws are the following : — 1. The first law of thermodynamics. 2. The second law of thermodynamics. 3. Every gas, when rarefied indefinitely, approaches a limiting condi- tion in which Pv = BT, (1) if P represents pressure ; v, molecular volume ; K, the gas constant ; T, the absolute temperature. . VOL. XXXVII. — 4 60 PROCEEDINGS OP THE AMEEICAN ACADEMY. 4. Every solution diluted indefinitely approaches a limiting condition in which Tlv = RT, (2) if n represents osmotic pressure. The present paper will discuss the laws which govern systems com- posed of a single, chemically simple, substance, and will be followed by a second paper in which the laws governing mixtures will be studied. I. Clausius' Formula Simplified. Clausius showed that if Q represents the heat change in a reversible change, the second law of thermodynamics may be expressed by the equation Q _dQ 'T~'dT' (^) which is valid for every cyclic process ; moreover, that since in a cycle there is no change in internal energy, d Q represents the work of the cycle, and that when the process is one in which the system undergoes a finite change of volume at constant pressure, and no other work is done, where P represents the pressure and Vx and Vo, the original and final volumes. In the specific case in which the system is composed of a liquid and its vapor we obtain the equation Q _ (vi — ^2) dp T~ dT ' in which p represents vapor pressure ; Q, the total heat of vaporization of one gram-molecule ; and Vj and Vo, the molecular volumes of vapor and liquid respectively. Transposing the equation gives an expression for the change of vapor pressure with change of temperature, dp _ Q dT- (v,- V,) T ' (^) This equation of Clausius is both general and exact, but in practice it is replaced by a simpler equation, which is derived from it if two assumptions are made : First, that v^ is negligible compared with Vi, and therefore approximately, ri — ^2 = Vx- LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 51 Second, that the vapor obeys the gas law, RT Vi = P These two equations substituted in (4) give the familiar equation, d\np_ Q dT E T' (5) While neither of the two assumptions made above is in any case strictly true, they differ in that the second represents a true limit as the vapor approaches the perfect gas in its behavior, but the first is always mathematically absurd, for the volume of a liquid cannot be made to approach zero even as a limit. For an exact equation, therefore, we must return to equation (4), notwithstanding its rather complicated form. There is in fact a lack of simplicity in this equation which does not appear in certain analogous expressions that will be developed in this paper. That this lack of simplicity is, however, not inherent in every exact equation for the influence of temperature on vapor pressure, but is due rather to the complex conditions for which equation (4) is proved, will be evident from the following considerations. It is well known that at constant temperature the vapor pressure of any substance is changed by a change in the total pressure on its surface, according to the equation first obtained by Poynting,* ^ = ^ (6) dP Vi . in which p represents vapor pressure ; P, total pressure ; t^ and Vi, mo- lecular volumes of liquid and vapor respectively. When, therefore, the I temperature of a liquid is raised, the resulting increase in vapor pressure -/ brings an increase in the total pressure on the surface, and this in itself is • a cause of further change in vapor pressure. The observed change in vapor pressure is the sum of the change due merely to temperature change and the change due to the change in total pressure upon the surface. Let us therefore determine the change in vapor pressure with change of temperature when the total pressure on the surface is kept constant by artificial means. Figure 1 represents such an arrangement. The space E D contains liquid kept at constant pressure by a piston, F. B D contains an inert insoluble gas. B C is a membrane impermeable to this gas, but permeable to the vapor of the liquid used. A B contains * PhU. Mag., (5) XU. 32 (1881). 52 PROCEEDINGS OF THE AMERICAN ACADEMY, this vapor alone. A change of temperature will change the vapor pres- sure in A B without changing the total pressure on the liquid, which is always equal to the outside pressure on F. We may simplify this arrangement by making the layer of inert gas so thin that it may be regarded together with the membrane B C merely as a single membrane, which is impermeable to the liquid but permeable to the vapor. In A C D B E B FiGUKE 1. Figure 2. Figure 2 it is represented by the dotted line B. The spaces B C and A B are filled with liquid and vapor respectively, and the pistons A and C can be moved up and down so as to distribute the substance between the liquid and gaseous phases as desired. The whole is removed from the influence of gravity. Let us start with one gram-molecule of the sub- stance, all in the liquid state, and pass through the following reversible cycle, during which the pressure, P, upon the piston, C, remains constant, while the pressure upon A is always kept equal to the vapor pressure. At first the piston A is at B ; the space B C has the volume v^. (1) The temperature is raised from T' to T + d T, the pressure on A being raised at the same time from p, the original vapor pressure, to p -\- dp, ?,o that none of the liquid evaporates. The piston C moves down on account of the expansion, dv^, of the liquid. (2) All the liquid is evaporated at temperature T -\- d T, C moving to B, and A moving up to furnish the volume, Vi. (3) The temperature is again brought to T; the pressure on A to jo. A moves down on account of the contraction dv^. (4) All the vapor is condensed and the original condition is restored. The amounts of work done by the system in the several steps are : — Fi = Pdv^, F2 = - P (^2 + dv^) + (jo + dp) (fi + rfvi), TF3 = — pdvi, Wi = Pv^ — pvi. LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 53 The total amouut of work gained, the sum of these terms, is equal to the total amount of heat transformed into work, that is, W, ^ W, + W, + W, = d Q = ^d T, from equation (3). Adding the terms we obtain, Q or writing so as to express the constancy of P, Q (9p\ _J T (7) This important result may be derived directly from equations (4) and (6) and for solids as well as liquids. Since the vapor pressure is a func- tion of the temperature, T, and the pressure on the surface, P, we may write ^9 T J p \9 P y T Now, in general, when only a pure substance and its vapor are present, the change in pressure on the surface of the substance is merely the change in vapor pressure, that is, dP=dp. Moreover, ( ^^ ) = — , from equation (6), therefore, dp. • / ,\ Substituting for -^ from equation (4), dT oritfe^ =A, 9TL, v^T which is equation (7). "We have in this equation a marked simplifica- tion of the Clausius formula with no loss of exactness. We could now, by making the single assumption that the vapor obeys the gas law, throw equation (7) into the form analogous to (5), namely. \9T )p~ RT-' 54 PROCEEDINGS OF THE AMERICAN ACADEMY. Instead of using this equation we may introduce here a quantity with the aid of which it is possible to substitute for approximate equations of the type of (7) other entirely exact equations of the same form. This quantity is one whose utihty I have shown in a recent paper.* It may be well to repeat and amplify the definition there given. II. FUGACITY. If any phase containing a given molecular species is brought in contact with any other phase not containing that species, a certain quantity will pass from the first phase to the second. Every molecular species may be considered, therefore, to have a tendency to escape from the phase in which it is. In order to express this tendency quantitatively for any particular state, an infinite number of quantities could be used, such, for example, as the thermodynamic potential of the species, its vapor pres- sure, its solubility in water, etc. The quantity which we shall choose is one which seems at first sight more abstruse than any of these, but is in fact simpler, more general, and easier to manipulate. It will be called the fugacity,t represented by the symbol ij/ and defined by the following conditions : — 1. The fugacity of a molecular sjiecies is the same in two phases when these phases are in equilibrium as regards the distribution of that species. 2. The fugacity of a gas approaches the gas pressure as a limiting value if the gas is indefinitely rarefied. In other words, the escaping tendency of a perfect gas is equal to its gas pressure. That these two conditions are sufficient to define a property of every substance which is not a mathematical, fictitious quantity, but a real physical qu.antity, capable of experimental determination in every case, must now be shown. It is obvious from the above conditions that in any case where our present methods of measurement are unable to show a deviation of the vapor of a substance from the gas law then the vapor pressure is the nearest approximation to the fugacity. In all cases the vapor pressure is an approximation to the fugacity, the approximation being nearer the nearer the vapor is to a perfect gas. When the * Proc. Amer. Acad., XXXVI. 145 (1900) ; Zeit. Phys. Chem., XXXV. 343 (1900). t In the earlier paper this quantity was called the escaping tendency and repre- sented by the same symbol. For the sake of brevity I have chosen to substitute the word " fugacity " for " escaping tendency " without the slightest change in the meaning of the function. LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 55 behavior of the vapor deviates perceptibly from that of the perfect gas the exact value of the fugacity may be found as follows : — From the four laws stated io the introduction it is easy to derive the following, which is a rigorous statement of Henry's law, namely : Tlie coefficient of distribution between a gas and its solution at constant tem- perature approaches a constant with increasing dilution. This constant will be designated by p. At infinite dilution, P _ where p is the gas pressure and 11 the osmotic pressure in solution. Now p, at infinite dilution, is equal to the fugacity of the substance in the gaseous phase, and also in the solution, since the two phases are in equilibrium. Therefore, ^i; = pU. (8) That is, the fugacity of the solute in an ideal solution is equal to its osmotic pressure multiplied by p. If now it is desired to find the fugacity of any molecular species X in any given phase, that phase may be brought in contact with a chosen solvent and the osmotic pressure III of the saturated solution determined. Then by diluting this solution in contact with vapor of X the limit pi of the distribution ratio may be found and so the product pi IIi. So for another solvent we may find the product p2 112 ; for a third, p^ lis, etc. These will all be equal except in as far as the saturated solutions deviate from the ideal solution. Prac- tically, the product will be the same for all solvents in which X is only slightly soluble and will be the fugacity of X. Theoretically, the exact value of the fugacity is the limit approached by the product, p 11, as sol- vents are successively chosen in which X is less and less soluble. We see, therefore, that fugacity is a real physical quantity capable in all cases of experimental determination. A complete appreciation of the meaning of this quantity is essential for the understanding of the follow- ing pages. In order, however, not to distract attention further from our main object, a further discussion of fugacity will be postponed to the last section of this paper, in which another independent method for the determination of i/^ will be offered, using only such quantities as have already been determined in many cases. The great utility of this new quantity will be shown to lie in the fact that the approximate equations containing the vapor pressure and developed rigorously except for the assumption that the vapor pressure obeys the gas law, may be replaced by exact equations of the same form 56 PROCEEDINGS OF THE AMERICAN ACADEMY. or of equal simplicity containing the fugacit}' instead of the vapor pressure. Let us proceed to the determination of the laws according to which fugacity changes with changes in the variables upon which the condition of a substance depends, considering in the present paper only those systems which are composed of a single chemically simple substance. III. Influence of Temperature and Pressure on the Fugacity. Let us consider two phases of a substance at the same temperature and pressure, but not necessarily in equilibrium with each other. A solvent may be chosen in which both phases are soluble without molecu- lar change, and to so slight an extent that the saturated solutions may be regarded as infinitely dilute. In such a case the solubility of each phase is governed by the following equation, which may be obtained directly from equations (2) and (3), '51nn\ Q "^1 RT' in which 11 is the osmotic pressure of the saturated solution and Q the reversible heat of solution (that is, inclusive of the osmotic work). We may write for the two phases, ^1 - ^2 (9) / TT ^ V 9 T RT' Q^ — Q„ may be conveniently replaced in the following way. Let one gram-molecule of the first phase be dissolved in the solvent, this solution then diluted or concentrated to the osmotic pressure lis, and then the gram-molecule removed as the second phase. If these three steps be done reversibly the heat absorbed in each will be respectively lJ-2 The total heat change is a function only of the conditions of the two phases, not of the path by which one passes into the other, and may be designated by ^1,2, thus, LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 57 Q,^, = Q, + ETln^- Q,, or Q, - Q, = Q,,, -ETln ^^. We may therefore write equation (9) as 9 In n. 9T QU2 1 ^' >p BT' T Since we are dealing with infinitely dilute solutions in the same solvent, t/^i = p III and \p. = p Ha, therefore "^ r= — , and the above equation becomes 4'2 ^2 Pln^ . 9 T Ql,2 ET' in^ 7' (10) This is the desired equation connecting temperature and escaping tendency. Its form can be simplified by a slight rearrangement. Considering the quantity Tin -^ we notice that 9T\n'tl 9\J' ^^^T-^ + ln'^,ov 9\J-^ . 9Tln'tl In?^ ^2 9T ~ ' 9T ' ^"./.s'" dT Combining this equation with (10) gives £ ^ {J/o ^2 9 T T 9T\J-^ IA2 , 9T Ql.2 ET (11) Leaving in this form for the present the equation connecting tempera- ture and fugacity at constant pressure, let us determine the influence of pressure on the fugacity at constant temperature. I have already dis- cussed this question in a previous paper,* but instead of using the general equation there derived it has seemed preferable to base all the reasoning of this paper directly upon the four laws stated in the introduction. Let us consider any simple substance and a solvent, so arranged f that the pressure upon the substance in question may be altered without * Loc. cit. t Several such arrangements are described in the paper just mentioned. 58 PROCEEDINGS OF THE AMERICAN ACADEMY. changing the pressure on the solvent and without preventing the sub- stance from passing freely into or out of the solvent. The osmotic • pressure of the saturated solution depends upon the pressure on the substance. If the latter is represented by P and the former by 11, then for P + d P the osmotic pressure will be 11 + , W^ ^(P-\- dP) (v- dv) - (n-\- dU) (v' — dv'), W, = Pdv. Writing the sum equal to zero, vdP—v'dU = 0, or expressing in the equation the constancy of T, (l^),-^- <'^> This is an exact general equation connecting the osmotic pressure of a saturated solution and the pressure upon the pure solute. It is entirely analogous to equation (6). Since we may choose a solvent in which the solute is as slightly soluble as desired we will choose one in which the solution may be regarded as infinitely dilute. Then, PT n = v' from equation (2). Combining this equation with (12) we obtain From equation (8), if/ = pU. Therefore In i/^ = In IT + In p, and \9P'j,~\ 9P ); LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 59 since p is constant at constant temperature. Hence equation (13) becomes Subtracting two such equations we obtain an equation for two phases, *^ ain!^ 9P Vl — ^2 RT (15) IV. The General Law of Fugacity. Equations (11) and (15) show a similarity which may be made more striking by a few simple transformations. In equation (11) ^12, the heat absorbed in any reversible transformation of the substance from the first to the second state is equal to the difference in entropy between the second state and the first, multiplied by the absolute tem- perature ; that is, —^ =^ — (aSi — S^, where S^ and So, represent the entropy of the first and second states respectively. Substituting in equation (11) and transposing the constant R, we obtain, 9RTln ^2 9 T -^ p = - (5i - S,). (16) In equation (15) R T is constant, and may be transposed, bringing the equation into the form, 9RT\ntl^ ^2 9P J T Vi — V2. (17) The symmetry of equations (16) and (17) with regard to the quan- tities T and —S on the one hand, and P and v on the other hand, is perfect. This similarity is peculiarly interesting in the light of the brilliant theory of Helm, according to which two quantities are funda- mentally connected with each kind of energy, the one its intensity, the 60 PROCEEDINGS OF THE AMERICAN ACADEMY. other its capacity.* Thus, for example, pressure, surface tension, elec- trical, potential, and temperature are considered to be the intensities concerned in energy changes in which the corresponding capacities are respectively volume, surface, quantity of electricity, and entropy. We may denote in general the intensity of any energy by /and its capacity by H. If vre substitute / and H for T'aud S in equation (16) and for Pand V in (17), the equations become identical except for the minus sign in (16). We are thus led to suspect the existence of a general equation of the form If a simple function can be found which satisfies these two require- ments it may, I think, be accepted, at least provisionally, as the true capacity of heat energy. The entropy of every body is a very complex function of its other variables, and even the entropy of a perfect gas is represented by the complicated equation,* * See Clausius, Warmetheorie, I. p. 214, third edition. h = 62 PROCEEDINGS OF THE AMERICAN ACADEMY. The value of h for a perfect gas may be found from the second of the above conditions, equation (21). For a perfect gas, according to the definition of fugacity, ij/ = P, and therefore We see, therefore, that the value of h which satisfies the condition of equation (21) is expressed by a far simpler function than entropy is. Let us see whether this value for the perfect gas is consistent with the other condition that, dh= ±dS. For a perfect gas the following equations for isothermal change are familiar : dQ Pdv vdP RdP p,, ^ db = ~ = -^ — ~ = p— = — RdlnP, and from equation (22), d h =^ R d In Pj hence, for constant temperature, dh = -dS, (23) and the condition is satisfied. The value R\n P satisfies both the above conditions for h in the case of a single state, the perfect gas. Moreover, every substance is capable of being brought into the state of a perfect gas isothermally by evaporation and indefinite expansion. Consequently it is easy to show that for any state of a substance either of the two conditions will define a value of h which is consistent with the other condition. Thus by the first condition, expressed now by equation (23), the difference in value of h between two states of a substance is equal to the difference in entropy and opposite in sign, that is, h. — ho ^ 02 — *Ji' If we choose as the second state the vapor of the substance at such a low pressure, P.,, that the vapor may be regarded as a perfect gas, A2 == ^In Po, from equation (22), and the last two equations give, h, = S,-S, + R In P„ (24) in which -S, represents the entropy of the vapor at pressure Po. This equation furnishes a complete definition of the value of h for any state. Let us see whether this value satisfies the other condition of equation (21). LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 63 Equation (16), uamely, holds true for the two states which we have just considered, one of which is the vapor in the state of a perfect gas at the low pressure P^. By the aid of equation (24) we may therefore write •As h^- R\n P^. According to (22) 5 r • and the last two equations give by addition which is equation (21). I think, therefore, that we are justified in considering h the true capacity dimension of heat, and in considering equation (21) the special form of equation (19) applied to heat energy. The replacement of entropy in general energy equations by the quantity h will have a further advantage on account of the much greater simplicity of the latter, the approximate value of which may be in all cases very easily determined by assuming that the vapor of the substance in question may be regarded as a perfect gas, in which case equation (24) evidently becomes h = ^ + R\np, (25) where Q is the total heat absorbed in the evaporation of one gram- molecule and p is the vapor pressure.* We have now obtained equations of the form of (19) for two of the * This approximate equation is a special form of a general and rigorously exact equation, h=^ + R\n^, (25a) in which 4' is the escaping tendency of the substance and Q' is the heat absorbed when one gram-molecule is allowed to evaporate irreversibly against an infini- tesimal vapor pressure. Since this equation will not be used in this paper its demonstration may be postponed. 64 PROCEEDINGS OF THE AMERICAN ACADEMY. most important kinds of energy. The fugacity is also known to be a function of a third energy-intensity, namely, surface tension. Let us consider a drop of liquid containing n gram-molecules with a surface a- aud a surface tension t. The change in surface of the drop with a chansre iu its content expressed in gram-molecules, that is, - — , has been called the molecular surface, and we may designate it by s. If the quantity cf n is taken from the drop and added to a large mass of the liquid the process is capable of yielding work. The amount has, I think, always hitherto been written equal to tda-^ the change in surface energy. This is not strictly true. The molecular volume in the drop is not exactly equal to but always slightly less than the molecular volume in the large mass. There is therefore always a small amount of work done against the atmosphere, and the total work capable of being done by the transference oi dn gram- molecules is equal to t d cr -\- P (d v\ — di>)^ where dv^ represents the increase in the volume of the large mass, dv the decrease in the volume of the drop. If the transfer be made reversi- bly in any way the total amount of work obtained must be equal to the above. The transfer may be actually carried out reversibly as follows : Let a solvent be chosen in which the liquid in question is so slightly soluble that the solution may be regarded as an ideal one. The drop and the large mass of liquid will be in equilibrium * with the solution at two different osmotic pressures, 11 and IIo, respectively. We may now take the following steps reversibly: (1) dn gram-molecules of the drop dissolve into its saturated solution, (2) the same amount is diluted to the osmotic pressure n„, and (3) passes out of solution into the large mass. The three steps yield the following amounts of work, in which dvj and d v' represent the volumes occupied by the amount d n in solution at the osmotic pressures H^ and 11, respectively. Wi = li dv' - Pdv, Wo = dnRr\n—, Ws^Pdv,-U,dvJ. The sum of these terms, written equal to the amount of work given above, gives * In order not to affect the surface tension of the drop, it may be separated from the solvent by its own vapor and thus pass into solution through the vapor phase. LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 65 P{dv,-dv) + Udv'-U.dv' +dnRT\n^ = tda- + P(dv„ — dv). Now from equation (2), Jl^dvJ = Ild v', and, as on page 55, Therefore ETln^ = t^ = ts. (26) ) 819; .Innrnal de Physique (2) VI. 26 (1887) ; also Mesure cles Temperatures Elevees (Paris, 1900), Chapter VI. t Barus, Bulletin of the U. S. Geological Survey No. -54; also Americ;in Jour- nal of Science, XLVIIT. .336. t Holborn and "Wien, Wiedemann's Annalen, XLVIL 107 (1892); LVI 560 (1895). VOL. XXXTII. — 6 82 PROCEEDINGS OF THE AMERICAN ACADEMY. high temperatures, it is necessary to make a thorough calibration of the individual thermo-elements involved, or at least of the set of elements manuftictured from any given sample of metal. How important it is to perform such a calibration for one's self may be seen from the fact that Holman, Lawrence, and Barr* obtained an electromotive force of .0303 volts from a platinum, platinum-rhodium (10%) element at the tempera- ture of melting platinum, whereas a similar element constructed of wire fi-om Heraeus gave in the hands of the present writer .0182 volts at the same temperature. Numerous more or less complicated methods of calibration involving the use of various forms of the gas thermometer have been proposed, the carrying out of which involves the use of special apparatus which is difficult of construction and laborious in operation. Fortunately it was possible in the present investigation to substitute for these a new and easy method in which the acetylene flame itself was the source of heat. This method t possesses the advantage of extreme simplicity, and it affords indications the accuracy of which leaves little to be desired. Figure 4. The acetylene flame emi)loyed was of the usual flat form produced by the union of two impinging jets. There are three distinct stages observable in the form of such a flame, depending upon the pressure at which the gas is supplied to the burner. In the first, we have two separate cylindrical jets of small size (Figure 4 o), which, with increasing gas pressure meet without uniting, each being deflected, by impinging upon the other, into a vertical plane (Figure 4 5). At still higher pressures the actual union of the two jets takes place, giving the flame the structure shown in (Fig- * Holman, Lawrence, and Barr, J. Am Acad, of Arts and Sciences (1895), p. 218. t This method of calihration has been separately described in a contribution to the Lorentz Jubilee Volume. The Hague, 1900. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 83 ure 4r), iu which the two cyliudrical jets of gas in the process of combus- tion unite to form a single flat vein or envelope which constitutes the luminous portion of the flame. When this third stage is reached, there is great stability of form and position. Such a flame responds with a sharp lateral motion to air waves such as are produced by the slamming of a door, but is comparatively unaffected by slight drafts. Even in a room not essentially free from air currents the lateral motions of the flame, which may be accurately observed by throwing an enlarged image of it, viewed edgewise, upon a screen, rarely amount to more than .1 mm., and in an especially protected j^lace, these lateral move- ments become entirely imperceptible. The temperature gradient in the layer of air bordering upon the luminous envelope of such a flame is very steep, but it is capable of definite deter- mination by exploration with suitable thermo- elements, and so long as the flame remains undisturbed by lateral drafts its stability is surprising. The burner used is of a well-known form (Figure 5), and is made from a single block of steatite. It is mounted upon a horizontal bar of steel (Figure 6), along which it may be Fiqcrb 5. moved by means of a micrometer screw. The bar is set up in an inner room without windows, being opposite a circular opening in the wall through which the flame may be observed from without. In this opening is placed the lens of a micro-camera. '^^■^^-^j^^ mmr^~\ y Figure G. upon the ground-glass screen of wliich instrument, at a distance of about two meters, an enlarged image of the flame is focussed. The platinum and platinum-rhodium wires to be tested are drawn down to a small 8-1: PKOCEEDINGS OF THE AMERICAN ACADEMY. size (diameter about 0.01 cm.), and a thermo-element is formed by cut- ting pieces of the platinum wire, and of the wire of the alloy to be used, about 70 cm. in length, and binding these to the opposite faces of a rectangular block of wood about 1 cm. in thickness. Beyond this block the wires project about 3 cm. They are bent toward each other until the free ends are in contact, forming a V, and these ends are then fused in the oxyhydrogen flame, forming a junction, which is subsequently trimmed down to the form shown in Figure 7. The apex of the V is cut away until the arch of fused metal ioiuin^ the two wires is considerably less in Figure 7. *" ° . / thickness than the diameter of the wires them- selves, the face of the junction forming a smooth plane surface. The formation of such a junction becomes, with practice, a simple matter, and can be performed, as it is necessaiy to do after each obser- vation, in a few moments. The junction is rigidly mounted upon the steel bar wiih the plane passing through the wires of the V vertical and the plane surface of the metal which forms the face of the junction parallel to the flat face of the acetylene flame. To the free ends of the wires are soldered the copper terminals of the galvanometer circuit, and the junctions are placed in a bath of melting ice. The support carrying the thermo-element is mounted in such a position as to bring the face of the hot junction as nearly as possible into the centre of the field of view of the camera, wi)ere it is clearly visible under the illumination of the acetylene flame, wiiich should, at the beginning of the operation, be about 1 cm. from the junction. The micrometer screw, by means of which the flame is moved along the bar, is operated by means of a long handle with a universal joint ; so that the flame can be shifted by an observer sitting opposite the ground-glass screen. For the measure- ment of the electromotive forces produced by tlie heating of the junction a potentiometer of tlie usual form is used. The metals the melting temperatures of which are to form points upon the calibration curve, are worked into thin foil, and from this foil strips about .03 cm. in width are cut. Such a strip is looped into the angle of the V and drawn snugly into place, the free ends beino; cut away until they project only about 1 mm. beyond the face of the junction. To hold this minute loop of metal in its place, it is only necessary to press the foil carefully together around the junction. The thermo-junction carrying the loop having been mounted, in the manner described, in tlie focus of the camera, NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 85 will be clearly seen upon the ground-glass screen, the ends of the loop of metal projecting towards the flame. The determination of the electromotive force corresponding to the melting-point is made as follows. The observer seats himself in a position where he can watch closely the image of the flame and of the thermo-element and moves the former gradually toward the junction, balancing the potentiometer approximately from time to time as the electromotive force rises with the increasing temperature. At a definite distance from the luminous envelope of the flame, which distance depends upon the character of the metal under investigation, the projecting ends of the loop will be seen to melt. So quiet is the flame, and so well fixed the temperature gradient from its surface out- ward when a proper burner is used, and when the flame is placed in a locality reasonably free from air currents, that the fusion of the succes- sive portions of the metal loop may be brought about fi'om the end in- ward with the greatest nicety; and the electromotive force may be determined at each stage until the fusion has progressed to the plane coinciding with the face of the junction. Even then, in many cases, those portions of the loop of metal which lie within the angle of the junction will remain unfused, although their distance from the melted portion of the loop is only a fraction of a millimeter. The delicacy of this operation under favorable conditions is very great, and the agreement of the successive readings of the melting-points of a given sample of metal is excellent. It is desii'able to make a series of readings, leading up to the true melting-point, for the reason that when the fusion of the metal loop has progressed to that portion which lies in contact with the platinum, an alloy is almost immediately formed between the fused metal and the junction itself, which affects the thermo-electric indications of the couple. For this reason it is not possible to get con- sistent readings by repeating observations with a given junction. The proper procedure is to cut the wires back 2 or 3 mm. from the apex of the V after each set of readings, and to make a new junction of the proper form from the free ends thus produced. This requires but little time after the operator has gained a reasonable degree of familiarity with the method. "When the metal, the melting-point of which is desired, is platinum itself, the platinum wire of the junction begins to fuse at the same time as the loop, the platinum rhodium or platinum-iridium side remaining unmelted. The precise point at which this fusion of the platinum occurs is, however, quite as definite as in the case of metals of lower melting 86 PROCEEDINGS OF THE AMERICAN ACADEMY. temperature. This method has the advantage of avoiding the use of the air thermometer and of furnaces in which fusion of the metals takes place. The amount of metal which it is necessary to melt is almost infinitesimal. The loops used iu each observation weigh only a fraction of a milligram, and the operation may be repeated time after time at the will of the observer with the greatest ease. Ou the other hand it should be noted that the method is applicable only to such metals as will fuse before oxidation in the hot layers of the acetylene flame. It is not prac- ticable with magnesium, aluminium, zinc, or iron, since these oxidize under the conditions of the experiment instead of fusing. For such of the metals of the platinum group as have melting-points below that of the junction itself, and for gold, silver, and copper, the method is a convenient one, and its accuracy is, I believe, fully equal to that of any other method which has thus far been employed. To guard against the deleterious influence upon the thermo-j unction of the vapors of the flame, it is impor- tant to bring the latter up gradually by the slow action of the micrometer screw in the manner which I have already described. The atmosphere with which the junction is surrounded under these conditions contains an Uoo* X- li^O* y\' ■■ of about 25 cm. The region under observation was limited by means of a vertical diaphragm d, 5 mm. in width, wliicli was — i Tod, mounted in a tube in front of a window of the metal vacuum box. The comparison source was the spec- trum of the brightest part of an acetylene flame set d, up in the axis of the other collimator at a corre- sponding distance, and viewed through a circular x/.. aperture c, 5 mm. in diameter, cut in a metal screen interposed between the flame and the slit and as A near the former as practicable. The acetylene flame was adopted as a comparison standard for the fol- (2, lowing reasons : — lAfinnn---^ l. it possesses I " U U U u--''''^ a continuous spec- trum, brighter in the less refrangible regions than that of anv other controllable source of liojit. 2. Tlie radiating material is finely di- vided carbon, presumably of a character Figure 9. ^ot unlike that of the surface of the untreated rod. 3. The acetylene fl ime is the result of the combustion of a definite fuel (C2H2) burning under reasonably constant conditions. It is prefer- able in this regard to any of the ordinary gas or candle flames in which the fuel is of an undetermined and more or less variable character. 4. When supplied with gas under constant pressure, an acetylene flame of the type used in these experiments, that, namely, obtained by means of a burner composed of a single block of steatite, is more nearly constant in its intensity and color than any other flame with which I am acquainted, with the exception of that of the Hefner lamp. It is indeed questionable whether the latter is superior to acetylene in this respect, and its comparative weakness in the blue and violet renders it very un- desirable as a comparison source in spectrophotometry. Determination of the Temperature of the Acetylene Flame* Concerning tlie temperature of the acetylene flame, varying and in- compatible statements are in existence. The temperature of combustion * The results of these experiments on tlie temperature of the comparison flame were separately communicated to the American Physical Society ou February 24, 1900, and were published in the Physical Review, X. 234. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 89 of this gas, according to Le Chatelier,* would be, when burned in air, 2100° to 2420°. Measurements with Le Chatelier's pyrometer, on the other hand, made by V. B. Lewes,! g^ive temperatures lower than those of ordinary gas flames. Lewes found for the obscure zone 459,° for the edge of the luminous zone 1411,° and for the region near the summit of the luminous zone 1517°. Sraithells, | upon the appearance of the data given by Lewes, described a series of experiments for the purpose of showing that the temperature of the flame reaches, in point of fact, very much higher values than those given by that author, and that in many portions it is higher than the melting point of platinum. It can be easily shown by inserting wires of platinum into the flat acetylene flame obtained from any one of the forms of burner usually employed, that while the thicker wires remain unmelted, those of very small diameter are readily fused. I found, for example, that a wire havine a diameter of 0.0<»82 cm. became fused at the end with the for- mation of a distinct globule, before the metal had penetrated the outer luminous layer of the flame, whereas wires of 0.01 cm. or of larger diameter remained unmelted. The experiments of Waggener § show that there are portions of the flame of the Bunsen burner in which it is possible to melt platinum, while MacCrae, 1| working with a platinum- rhodium element, found for the hottest region in the Bunsen flame 1725°. It will be seen from the experiments to be described in this paper, that MacCrae's determination, which was made with wires having a diameter of 0.02 cm., is not incompatible with the observations of Waggener and others. Smithells, in the paper just cited, describes the melting of platinum wires having a diameter of 0.01 cm., in various parts of the outer sheath of a flat flame of illuminating gas. Pellissier, 1[ in com- menting upon Lewes's measurements, refers to experiments in which minute wires of platinum, made by Wollaston's method of silver plating, drawing, and subsequent dissolving of the silver coating, when thrust into the flame of a candle, melted instantly. I have not been able to find other printed reference to these observations and do not know with whom they originated. An attempt to repeat the experiment with a Wollaston wire having a diameter of 0.0011 cm. resulted in the ready * Le Chatelier, Comptes Rendus CXXL 1144 (1S95). t Lewes, Chem. News, LXXI. 181 (1805). J Smithells, Journal of the Chemical Society, LXIX. 1050 (1895). § Waggener, 1. c. II MacCrae, Wiedemann's Annalen, LV. 97. t Pellissier, L':fcclairage a I'ace'tylene (Paris, 1897), p. 186. 90 PROCEEDINGS OF THE AMERICAN ACADEMY. fusion of the wire by the flame. An examination of the remaining portions under the microscope showed that the metal had been melted down into clean, well-rounded beads, and had not been consumed by oxidation or any other chemical reaction. Smithells's contention that the temperature of flames cannot be obtained directly from the indications of a thermo-element because of the loss of heat by conduction and by dispersion from the surface of the latter, so that the portions submerged in the flame never arrive at the temperature of the surrounding gases, is well founded. Lewes and likewise Waggener recognized this fact, and in their measurements made use of wires of different sizes. The apparatus which I employed for the determination of the temper- ature of the acetylene flame has already been described (see Figure 6). The method was similar to that used in the calibration of the thermo- elements. The electromotive force of the elements, as these were gradually brought into the flame, was measured by means of the potentiometer previously employed in the calibration of the thermo- elements and subsequently in the determination of the temperature of the carbon rods. It consisted of a sensitive galvanometer of the d'Arsonval type and an accurately adjusted resistance box containing coils ranging from 50,000 ohms to 1 ohm. A large Clark cell of the old Feussner type was mounted in series with the resistance box. The thermo-element, the galvan- ometer, and a subsidiary re- sistance of 10,000 ohms were looped around a portion of the resistance box, the ratios being varied until complete balance was secured. The electrical connections are shown in Figure 10. The type of standard cell selected for this work is subject to considerable errors from diffu- sion lag. It has, however, the advantage of being capable of furnishing a much larger amount of current than the small types of cell, in which diffusion lag is avoided, without appreciable loss of electromotive force. Two of these cells were placed side by side in a thick-walled inner room which CELL FlGtTRE 10. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 91 had been constructed for the purpose of securing uniform temperature for the standard clock of the physical laboratory, and other similar apparatus. The range of temperature in this room fluctuated through- out the entire investigation be- tween 18°C. and 19°C. The ranofe was so small and the variations occurred so gradu- ally that no changes of electro- motive force of a size which it was necessary to consider in these measurements could have arisen other than those included in the usual correction for temperature. The two cells were compared with each other from time to time by setting them in opposi- tion to one another in circuit with a sensitive galvanometer and noting the deflection pro- duced. It was found that although one of them was sup- plying current to the 100,000 ohm circuit of the potentiome- ter, during the times when it was necessary to close the key of that circuit, the difference of electromotive force between the used and unused cell was always very small, never more than a few hundred thousandths of a volt. At the end of the entire set of measurements, the difference was 0.00006 volts. The absolute electromotive force of these cells was checked by comparison with Clark cells of the H form and of the test-tube form, constructed in this department in 1S98. As a result of these comparisons it was found that the electromotive force of the cell used in the potentiometer might be taken at 1.430 volts at 18.° "^S'x^ MELTING f/y^ 1600° PT. OF PT. 1400° If 1200° f 1000° 1 800° o 600 400° 200° 6 mm 4mm Figure 11. 92 PROCEEDINGS OP THE AMERICAN ACADEMY. The wires selected for the four junctions to be used in the experiment upon the acetylene fiame were measurtd under a microscope wath micrometer stage. Their diameters were as follows : — Junction I. " 11. " III. " IV. Diameter 0.01996 cm. " 0.01598 cm. " 0.01089 cm. " 0.00821 cm. Readings were first made with junction I. (diameter 0.01996 cm.). The flame was set at a distance of 6 mm. from the face of the junction, and the potentiometer was balanced. The flame was then moved step- wise nearer and nearer, and tlie potentiometer rebalanced at each step until the face of the junction coincided with the edge of the luminous mantle at a point just above the apex of the inner non-luminous zone. The rise of temperature indicated by the potentiometer readings is shown in curve a (Fig. 11), the data for which as well as for the other curves in that figure are contained in Table II. TABLE XL Temperatures indicated by thermo-junctigns I., 11., III., and IV. at various DISTANCES FROM THE MEDIAN PLANE OF THE ACETYLENE FLAME. Junction I. J unction II. Junction III. Junction IV. Distance. Temp. Distance. Temp. Distance. Temp. Distance. Temp. 5.62 mm. 185° . . . 5.42 mm. 165° 4.63 mm. 233° 3.91 mm. 370° 3.65 mm. 353° 4.82 mm. 183° 4.11 mm. 406° 2.85 mm. 760° 8.33 mm. 508° 3.21 mm. 657° 2.55 mm. 1168° 2.09 mm. 1128° 2.90 mm. 595° 2.03 mm. 1278° 2.12 mm. 1411° 1.66 mm. 1229° 2.30 mm. 989° 1.50 mm. 1598° 1.86 mm. 161.3° 1.30 mm. 1367° 1.93 mm. 1822° 118 mm. 1685° 1.70 mm. 1667° 1.07 ram. 1382° 1.68 mm. 1385° 0.894 mm. 1724° 1.54 mm. 1705° 0.850 mm. 1467° 1.40 mm. 1513° 0.566 mm. 1747° 1.30 mm. 1738° 1.09 mm. 1617° 0.238 mm. 1759° 1.025 mm. 1771° 0..320 mm. 1715° 0.00 mm -0.29 mm. 1775° Molten. 0.780 0.800 mm. mm. Molten. Molten. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 93 The increase of temperature as the flame approaches the junction is srradual at first; but at a distance of about O.-i cm. from the median plane, the curve suddenly becomes steep. It is probable that this distance measures the thickness of the layer of non-luminous gas which surrounds the visible flame. Outside of this region, the junction is heated almost altogether by radiation. As soon as it penetrates the column of moving gas, however, heat is brought to it principally by convection. Before the surface of the luminous mantle is reached the curve shows indications of approaching a maximum. Upon pushing the flame still nearer to the junction so that the latter penetrated the luminous region, an accumulation of lampblack began to form upon the wire, with fall of temperature ; a process so rapid that at the end of two minutes a button of carbon several millimeters in diameter is formed. This is finally torn loose from the wire by its own weight; whereupon the deposition of a new mass begins. I attempted by watch- in c the breakinor away of the carbon from ihe wire, which occurred at regular intervals, to determine the temperature of the wire before the coating of carbon had begun to show itself again. The highest temper- ature which it was possible to observe in this way was neai'ly one hundred decfrees below that in the luminous layer, and it was obvious from the movement of the galvanometer needle that the junction was being rapidly cooled by the deposition. Junction II. (diameter 0.01598 cm.) was now substituted for Junction I., and a similar set of readings were made. This junction, as had been anticipated, showed higher temperatures. It was found possible, owing to the small diameter and consequently high temperature of the wire, to penetrate further into the flame before the deposition of carbon began, so that measurements with the junction actually within the luminous layer could be made. The general form of the curve, as will be seen by inspection of the figure (curve b) is the same as that obtained with Junc- tion I. After penetrating the luminous mantle to a small fraction of a millimeter, carbon began to gather upon this junction likewise, with lowering of temperature, as in the case of Junction I. The attempt to read temperatures immediately after the dropping of the accumulated carbon showed that the highest temperature which could thus be ob- served was again about one hundred degrees below the temperature of the luminous mantle. It was clear in this case, as before, from the rapid fall of temperature already going on, that this reading has no significance. Similar readings with Junction III. (diameter 0.0108 cm.) gave a third curve of the same type as those plotted from the reading made with I. 94 PROCEEDINGS OP THE AMERICAN ACADEMY. and II., but the temperatures were higher throughout. With this junc- tion it was found possible to penetrate to the centre of the flame without the deposition of carbon, the temperature of the wire being apparently too high to permit the formation of soot. Upon pushing through the median plane of the flame to the second luminous mantle, the junction was melted. This result was not unexpected, since the temperature of the junction at the first luminous mantle reached 1750°, so that a rise of twenty-five degrees of temperature would suffice to produce fusion. The wire when pushed through the flame in the manner just described is heated for greater and greater distances back from the junction until the losses of heat at the junction are sufficiently diminished to raise the tips of the wires to the melting-point. With Junction IV. (diameter 0.0082 cm.), a fourth curve, similar in form to the preceding ones and with still higher temperatures, was ob- tained. This junction was fused at a distance of 0.075 cm. from the core of the flame, and of 0.037 cm. from the edge of the first luminous mantle. It was easy to observe in the enlarged image upon the plate of the microcamera the melting away of the platinum wire, while the platinum-rhodium alloy was still unaffected, and while contact was still unbroken. A satisfactory observation of the electromotive force of the thermoelement at the melting-point of platinum was thus obtained. This reading (0.018236 volts) differs from the value found in my calibration of the thermo-junctions used in this investigation (0.018262 volts) by a quantity of (0.000026 volts) less than the errors due to changes in the electromotive force of the standard cell. If the latter reading be taken to correspond to 1775°, the former indicates 1773°. Beyond this point, it was impossible to make direct observations of temperature ; but the form of this and the preceding curves were so closely allied that I felt no hesitation in extending the curve d to the core of the flame. This has been done by means of dotted lines in the figure. Curves a and b have been extended in the same manner. In order to form an estimate of the temperature which would have been reached by a thermo-junction of negligible cross-section, provided such a junction could have been obtained which was capable of registering tem- peratures above that of the melting-point of platinum, the ordinates of the four curves, «, b, c, and d were taken for the coi-e of the flame, for the plane of the luminous mantle, for a plane distant 0.07 cm. from the core, and for a plane 0.10 cm. from the core. These readings were plotted and curves were drawn through them as shown in Figure 12; relative cross-sections of the wires being taken as abscissae, the temperatures as NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 95 1800 1600 1400 1200 V 1 CENTER 0.7^^£\ V ^ X 1 » 100 200 300 CROSS-SECTION OF WIRES Figure 12. 400 ordinates. If these curves could be extended to the Hue representing zero cross-section, the temperatures indicated by the points in which each of them cuts that line would give the temperature of the portion of the flame to which the curve corresponds. There is a considerable element of uncertainty in extrapolation even over so short a range as this : but it is obvious from the character of the curves lying within the limits of observation, that each of them trends upward, and it seems highly prob- able that they all meet the line of zero cross-section at a temperature not far from 1900°. The fact that the curves cut this line at nearly the same temperature would seem to indicate that the distribution of tempera- tures from the centre of the flame outward for a distance of about 1 mm. is a nearly uniform one. It would perhaps be unwise to attempt to draw any more definite con- clusion from the probable trend of these curves; but I have ventured to extend them in the manner shown in the figure, so that the curve for the region 1 mm. from the centre of the flame reaches the zero of abscissae about, twenty degrees above that for the centre of the flame, i. e. at 1920°, and. the intermediate curves at temperatures lying between them. I regard this as an extreme treatment of the case, and allude to it only to indicate that, in accordance with common belief, the highest temperature 96 PROCEEDINGS OF THE AMERICAN ACADEMY. may be found in the outer non-luminous layer of the flame, but that it is unlikely that the difference amounts to more than twenty degrees. The point of intersection referred to above lies neaily one hundred degrees above tlie highest temperature recorded by even the smallest of the thermo-elements, and it is safe to infer that nearly all previous attempts at the measurement of flame temperatures must, for lack of correction of the erroi', due to loss of heat through the wire, be regarded as much too low. The junction IV. is, so far as I am aware, the smallest in cross-section that has been used in such work. With larger wires, tlie correction for loss of heat would be even greater, except in cases where, as in the observations made by Smithells, and by Waggener, the precaution was taken to immerse an extended portion of the wires within the flame. Temperature of Other Flames. For the purpose of comparison, I measured in a manner analogous to that just described, the temperature of the luminous flame of ordinary illuminating gas and the flame of a candle. The gas flame employed for this purpose was obtained from a lava tip rated at one cubic foot and giving a flat flame of the upual form. The image of this flame, when viewed upon the ground-glass screen of my camera, was found to be comparatively ill- defined and unsteady ; but although the outlines of the luminous sheath were much less clearly marked than in the case of the acetylene flame, they were discernible. Owing to the continual motion of the flame, due to the small velocity of the gas i-suing from the jet, no attempts were made to plot curves of temperatures outside the flame. All readings were made with the Figure 13. . . , * ., , . junction as nearly as possible in contact with the outer surface of the luminous sheath, at a point in the brightest por- tion of the flame. This position is approximately indicated by the letter X in Figure 13. The four junctions already described were mounted, one after another, in such a position that the flame could be moved up until they came into contact with the sheath at the point indicated. The temperatures of the junctions when in that position are given in tlie following table TABLE III. Junction I. 1385° Junction III. 1609° 11. 1484° IV. 1670° NICHOLS. THE VISIBLE RADIATION FROM CARBON. 97 These values having beeu plotted with relative cross-sections of the ires as abscissae, and temperatures as ordinates, were found to lie 1800 1600 1400 1200 N ^^ ^^£> \ *^ 1 100 200 300 CROea-SECTION OF WIRE Figure 14. 400 upon a smooth curve {g) as shown in Figure 14. This curve, when ex- tended to the line corresponding to zero cross-section, gave for the tem- perature of the flame 1780", a temperature sufficient to account for the success of Smithells's experiment, already described, in which platinum wires of small diameter were melted in the outer sheath of such a flame. I found it easy, by holding a wire of the size used in junction IV. in a plane parallel to that of the flame, and moving it gradually toward the latter to verify his statement. The wire was readily melted. It was not thought necessary to make further experiments upon this flame. The region selected was, so far as one could judge from the brightness of the luminous sheath, the hottest portion of flame. My measurements upon this region would lead to the conclusion that the luminous sheath of ordinary gas flames is at least one hundred and twenty degrees lower than the corresponding region in the acetylene flame. Luminous flames of ordinary illuminating gas would perhaps repay further study, but owing to the fact that such gas is an ever varying mixture and that it is burned under conditions of pressure, etc., such as to give a fluctuating character to the flame, the problem would have at VOL. XXXVII. — 7 98 PROCEEDINGS OP THE AMERICAN ACADEMY. best an indefinite character from which studies of acetylene are free. In the latter case we have to deal with a definite fuel, and the velocity of the jets of gas from the burner is sufficient to give a high degree of sta- bility to the flame. The candle would seem an even less satisfactory subject of study in these respects than illuminating gas, but the fact of the melting down of Wollaston wire, the verification of which I have briefly described in an earlier paragraph of this paper, seemed to discredit so completely the low values commonly given that I decided to redetermine its tempera- ture by the method already described. The fact that the flame of a candle, mounted upon a fixed stand, would move steadily downward as the material of which it was com- posed burned away, made it convenient, without any serious modifications of my apparatus, to explore the temperature of the luminous sheath throughout the entire length of the flame. It was only necessary for this purpose to mount a candle upon the steel bar in the position previ- ously occupied by the acetylene flame, and when it had reached such a length that the level of the rim of the cup lay below the level of the junction, to move the candle toward the latter by means of the microm- eter screw until the junction began to be submerged in the luminous sheath of the flame. It was then easy by a series of slight adjustments of the flame to explore with the junction the entire surface of the lumi- nous sheath from base to tip, measuring temperatures from time to time, and determining the position by means of the height of the junc- tion above the rim of the candle cup. The latter observations were readily made by means of the image of the candle upon the ground glass of the camera. Explorations of the candle flame in the manner described were made with Junctions II. and IV., and the results obtained showed a degree of consistency much greater than the fluctuating char- acter of the source under observation had led me to expect. Both sets of observations showed a maximum of temperature in the same region : that lying just above the tip of the interior dark zone of the flame. Readings were made by watching the movements of the candle flame and securing a balance of the potentiometer at times when the face of tlie junction was as nearly as possible in contact with, but not deeply submerged within, the luminous layer. Whenever the wire plunged to any considerable depth beyond the luminous surface, deposition of soot occurred with lowering temperature, and it was necessary to withdraw the junction into the non-luminous regions outside and to wait until the deposit had been burned off, before proceeding with the readings. In NICHOLS. — THE VISIBLE RADIATION PROM CARBON. 99 computing the actual temperatures of the luminous sheath of the flame from these readings, I contented myself with the following rough ap- proximation. The maximum temperatures shown by Junctions II. and IV. were plotted upon the same diagram used for the luminous gas flame. These temperatures were 1281° and 1546°; values which, as will be seen by inspection of Figure 14 (c), lie much below those of the corresponding readings for the luminous gas flame, but in such positions as to make it easily possible to draw through them a curve analogous in form to that obtained for the latter. Such a curve would cut the line of zero cross-section at about 1670°, which may, I believe, be taken as the approximate temperature of the hottest portions of the luminous sheath of the candle flame. Estimates of this temperature by the prob- ably less accurate methods of drawing a straight line through the points in question and taking the point in which this line cut the line of zero cross-section to be the temperature of the flame, and estimates based upon the assumption that the true temperature is as many degrees above the temperature indicated by Junction IV. for the candle as it is for the gas flame, would lead to values respectively twenty-four degrees and forty degrees lower than that obtained by the method which I have adopted. I believe that the temperature just given (1670°) is much closer to the truth than that obtained under either of the other assump- tions. Estimated temperatures for other portions of the luminous sheath were made by assuming that the correction to be applied to the readings obtained with Junction IV. would be the same in all positions. These values are given in Figure 14 which may serve in place of an ordinary table. The portions of the flame to which each reading refers are more readily indicated by giving such a diagram of the flame than in any other way. The fact that, in the case of the acetylene flame and the ordinary gas flame, tliis method gives values high enough to account for the melting of platinum, but leads to an estimate of the temperature of the candle flame which is about one hundred degrees below the melting-point of that metal, would seem, at first sigh., to throw the procedure into serious doubt. My experience with the method has, however, been such as to make an error of one hundred degrees in the estimation of the candle- flame tempei'ature seem highly improbable. Messrs. Lummer and Pring- sheim, in a recent communication to the German Physical Society,* give an estimate of the temperature of candle flames based upon a relation * Lummer and Pringsheim, Verhandlungen der deutschen physikalischen Gesellschaft, 1899, p. 214. 100 PROCEEDINGS OF THE AMERICAN ACADEMY. which they have established between the position of the maximunn in the energy curve of the spectrum of a source of light and its temperature. Assuming the radiating substance in the flame to have the properties of a black body, they find this temperature in the case of the candle flame to be 1687°, a value seventeen degrees above that which I have given. To account for the fusion of Wollaston wire in the flame of a candle, one might consider the possibility of the existence in such a flame of layers of gas the temperature of which is much above the surrounding regions, and that these layers may be so thin that it would not be possi- ble to submerge the thermo-junction completely in them. In such a case the junction would give a value approximate to the average of the tem- peratures of the gases with which it was brought into contact. Before assuming this structure of the flame, which really has nothing to support it save the necessity of accounting for the apparent discrepancy whicli I have just pointed out, it seemed wise to consider, on the other hand, whether the melting-point of the Wollaston wire was necessarily that of pure platinum. Such wires would naturally be made of ordinary com- mercial metal, the melting-point of which might vary considerably from that of the purer platinum used in the determination of melting-points. It is likewise readily conceivable that in the process of drawing within the silver coating, a certain amount of silver might be worked into the pores of the platinum and not be removed by the subsequent action of the nitric acid. The determination of the melting-i^oint of even such minute wires is fortunately a simple matter by means of the form of thermo-element used in the calibration experiments already described. It is only necessary to wrap a piece of the wire to be tested around the junction, as shown in Figure 15, to cut it off so that the end of the loop extends slightly (about 0.05 cm.) beyond the face of the junction ; and having mounted the junction .„ ,, in the usual manner, to move the acetylene Figure 15. ' up to it by means of a micrometer screw. I performed this experiment with a piece of the same Wollaston wire which I had succeeded in melting in the candle flame, and found its melting-point, as indicated by the electro-motive force of the junction, to be 1674°. To test the question whether this very low melting-point was due to the presence of silver undissolved by the nitric acid, a piece of the same wire was left in the acid for twelve hours, after which the NICHOLS. THE VISIBLE RADIATION FROM CARBON. 101 melting-point was again tested in the manner just described. The result of this determination was 1687°. The latter reading was, I think, too high, since subsequent examination under the microscope showed that the loop of the wire behind the junction had been melted so that the junction was probably a few degrees too hot. It may safely be concluded from these determinations that the melting-point of the Wollaston wire was at least one hundred degree.s lower than that of pure platinum. Method of Checking the Constancy of the Acetylene Flame. To secure as complete a check as possible upon the constancy of the flame, the following method, based upon the assumption that so long as the radiation from the flame remained constant, its light-giving power I ,. II if!! FlGUKE 16. would not vary, was employed. A diaphragm {d, Figure 16) similar to that interposed between the slit and the flame, and having an aperture of the same size, and mounted on the opposite side of the latter and a thermo- pile/), was placed at a distance of about lo cm. from this opening. A second diaphragm, d' , with an intervening air space, served to cut oflT, iu large part, the radiation from the heated metal. Two thin sheets of glass forming the sides of an empty cell c, of the kind used in the study of absorption spectra, etc., were placed between the cone of the thermo- pile and the second diaphragm ; so that only those rays from the flame which were transmitted by the glass fell upon the face of the pile. The thermopile was connected with a sensitive d'Arsonval galvano- meter g, the circuit being kept permanently closed ; and a double metallic shutter s, which could be raised or lowered so as to open or close the opening in the diaphragm next to the flame, was so mounted that it could be readily operated by an observer at the telescope of the galvanometer. When a reading of the radiation from the flame was to be made, the zero point of the galvanometer was noted, and this shutter was raised during the short interval of time necessary to bring the needle, which was not strongly damped, to its first turning point. The shutter was 102 PROCEEDINGS OF THE AMERICAN ACADEMY. then immediately closed in order to prevent further heating of the face of the thermopile. This throw of the galvanometer was taken as an indication of the intensity of the flame. It was found that the thermopile would cool sufficiently within two minutes to admit of the repetition of the reading. These observations were taken by an assistant simultaneously with each setting of the spectrophotometer, the intention being to reject any spectrophotometric readings made at a time when the flame showed marked deviation from its standard intensity, and to reduce the readings to a uniform flame intensity under the assumption that for the small range of variation occurring from reading to reading, the change in the brightness of the flame would be proportional to the variations of this galvanometer read- ing from the mean of the whole set. In point of fact it was found that the flame rarely varied from the mean in the course of a set of observa- tions by more than one per cent. From day to day, indeed, its intensity was usually within the limits stated above. Occasionally a larger varia- tion was detected. None of these variations in the course of the present investigation reached values so great as to lead me to liesitate to apply the correction already referred to, and all the observations described in this paper have been reduced to a constant flame intensity by means of a correction factor obtained from the readings of the galvanometer. Control and Measurement of the Temperature of the Carbon Rod. The carbon rod, having been brought to the desired degree of incan- descence by means of the current from a storage battery, was held at a constant temperature by varying the resistance placed in the battery circuit. The indications of the thermo-element inserted in the rod were noted by means of the potentiometer. The cells used in the measure- ment of the temperature of the carbon rod were the same as those em- ployed in the calibration of the thermo-elements and in the study of the temperature of the acetylene flame. The potentiometer having been balanced by looping the circuit con- taining the thermo-element around a sufficient portion of the resistance box to balance its current against that of the Clark cells, a condition which was indicated by the reduction of the galvanometer deflection to zero, the current was maintained at such a value as to hold the carbon at a constant temperature during the time necessary to complete meas- urements of the intensity of eight different portions of the spectrum, ranging from the extreme red to violet, with the corresponding portions of the spectrum of the flame. In order to insure the maintenance of this NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 103 constant temperature in tbe rod, an assistant made repeated observa- tions with the potentiometer and readjusted the resistance in the battery circuit whenever necessary. Excepting at very higli tempera- tures, where the rod was subject to rapid disintegration, it was rarely necessary to make any adjustment during the progress of a single set of observations. Readings of the current flowing through the carbon and of the full of potential between its ends were made at the beginning and end of each experiment. Spectrophotometric Observations. It was my expectation, in planning this research, that whatever might prove true as to the character of the radiation from gray carbon, the distribution of energy in the spectrum from black carbon would change in such a manner with increasing: incandescence as to become nearly or quite identical with that of the various luminous gas flames at tempera- tures corresponding to the temperature of the glowing carbon iu those flames. I had also hoped, among other things, to be able to bring about a degree of incandescence approaching that of the acetylene flame itself, before the usefulness of the thermo-eleraent as a means of measurinjj the temperature failed because of the melting of the platinum wire, and in this way to obtain a check upon my previous measurements of that flame ; and at the same time to be able to determine the temperature of any given luminous flame in which the incandescent material consists of carbon particles by ascertaining the temperature of the carbon rod for which its surface had a spectrum corresponding in distribution of energy to that of the flame. It will be seen from inspection of the curves to be discussed in a subsequent paragraph that this expectation was far from being realized, and that the distribution of energy in the spectrum of the carbon rod, instead of approaching that of the acetylene flame as the temperature of the rod increased, took on an entirely unexpected character. Even at low temperatures, that is to say up to about 1100°, the change in the spectrum was not of the comparatively simple character which had been anticipated, and shortly after passing the temperature of 1100°, unlooked for complications in the results arose. The energy in the yellow of the spectrum which from the beginning had been increasing at a relatively more rapid rate than either in the red or at the blue end, became so great as to give the distribution curve a form entirely contrary to expectation. I was very slow to believe in the integrity of these results, and nearly 104 PROCEEDINGS OF THE AMERICAN ACADEMY. a year was spent in repetitions of the measurements before I could con- vince myself that the {phenomenon was a genuine one. Measurements taken upon a great number of different rods and at different times showed the same result, however, and I was finally forced to the con- clusion that the radiation from the carbon rods showed a much more complicated law of distribution than had been anticipated, and that a sort of selective radiation occurred such as to render the establishing of any simple relationship between the curve of distribution and tem- perature out of the question. The hope of being able to make direct temperature measurements up to the melting-point of platinum was also disappointed. While the carbon rods at comparatively low temperatures showed a fair degree of stability under the action of the current, they appeared to undergo a decided change of behavior at about 1400°, and before that temperature a rather rapid disintegration, showing itself by a change of resistance, manifested itself. This effect appeared to be similar to that which shortens the life of the filauieuts of incandescent lamps when these are subjected to a large amount of current. It appears, moreover, that at these high temperatures the carbon tends to combine with the metals of the thermo-element, affecting the electromotive force very much as the vapors in a furnace have been found to do. The therrao-elements inserted in the rod begin, in consequence of this action, to fail of their purpose. It was found that after exposure to temperatures much above 1400°, the electromotive force corresponding to even lower temperatures was considerably below the normal. I was consequently compelled to abandon the attempt to measure directly temperatures above this point, although it was possible to bring the rods to a higher degree of incan- descence for a length of time sufHcient to perform the spectrophotometric observations. In order to obtain at least an approximate estimate of these temperatures, I made use of the fall of potential between the terminals of the rod, and also of the current of the heating circuit ; and by extending these curves, which, throughout the range of measured temperatures were found to be nearly straight, to the high temperatures which I wished to estimate, to obtain some idea, even if not an exact one, of the latter. In expressing the results of the photometric measurements already described, I have made use of two forms of curve. One set of curves, in accordance with the nomenclature proposed in my original paper on the visible radiation from platinum, and later adopted by Paschen and other writers, I may call isotherms. These curves give in terms of the NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 10 O J^oihsTl^ 't- fuUk^ *od ^<^^ / 1 ^ uc£ I / • / / / ,• fJO" • —• ^" • ^"^ - :r. , — . — — — • - < • / ^ ^**- •J> Figure 17. •7A corresponding wave lengths of the comparison source (in this case the acetylene flame), the relative distribntion of energy in the visible spectrum from the carbon rods. The other curves, which I have termed isochroms, indicate the rise in the energy of any particular wave length of tlie visible spectrum, with increase of temperature. Each of these curves, taken by itself, is entirely independent of the nature of the light of the comparison source, but the absolute relation of such curves to one another can only be obtained when we know the distribution of energy in the spectrum of that source. By means of the isocliroms, it is, however, possible even without this knowledge to compare the rise in intensity of any single wave length of the spectrum with increasing temperature. The set of curves shown in Figure 17 are plotted directly from obser- 106 PROCEEDINGS OF THE AMERICAN ACADEMY. vations upon a black (untreated) carbon at temperatures ranging between 795° C and 1055° C. In this diagram abscissae are wave lengths and adocI'y>.Oi^Ji,k*,.i^^e.c„^ei Co^> l/y^y^y too^ /a //ao" 'k/^ •7- Y i I I I .If. kiZ 'A y- — f I I I I I I I 1 L_ / / / — y- / I I / ~i — r / / —7 — T / / y ^^' / / y A / / / ^■ _r ----ir^ ■ I I gDO"' JLo / / f / / f / 1 1 t / / ; / / / / / t 4 / / / f 1 / ; / / / J / / / / / / / J / / / / • / / / > 1/ 0 ■' J / ^ y y y y / / ^^^ .-^ "— - -1 }^'c io ^o ^^ ^ / / tUaTtf^ CC^i-' y / -i^ / -/- y -A / / / / / /ti-oa' /J 00° /Zoo /Ooa 900' ^ Figure 20. •/A point at which the yellow regions of the spectrum possess an ordinate o-reater than that of the extreme red or of the blue or violet. At a tern- perature about 300° below that of the acetylene flame, then, the spectrum of the carbon rod was relatively weaker in the red, stronger in the yellow, and weaker again in the shorter wave lengths than the spectrum of the flame. There is no reason to suppose tliat had it been possible to heat the rods to the temperature of the flame itself the law of increase of intensity for the various wave lengths would have undergone such radical modifications to bring the two spectra at that temperature into identity. 110 PROCEEDINGS OF THE AMERICAN ACADEMY. Spectro photometric Measurements upon Rods with Treated Surfaces. In order to compare the radiation of rods of black surface with those the surfaces of whicii have acquired a gray coating by treatment in hydrocarbon vapor, rods were mounted in the usual manner, and after the exhaustion of the air from the metal box, gasoline vajDor was allowed to enter until the atmosphere surrounding the rod was saturated. The Figure 21. rod was then brousiht several times to a \\\s\\ state of incandescence for a few seconds at a time, by which means the entire surface became coated with a gray deposit of carbon similar to that obtained by tlie treatment of incandescent lamp filaments. The metal box was then again pumped out and spectrophotometric measurements similar to those already de- scribed were made upon the radiation from the treated surface. It was thouo-ht that as the result of this treatment the carbon rod"^ would stand NICHOLS. THE VISIBLE RADIATION FROM CARBON. Ill a more prolonged exposure at high temperatures, and that thus it might be possible to extend the measurements beyond the point reached with the rods of black surface. This was found to be the case. As has already been indicated in a previous paragraph, the indications of a thermo-junction at these high temperatures was subject to serious suspicion. I was obliged to content myself, therefore, with estimations of / ^■^ ••, -^^ • /4^0 U 1 1 ! / • / t 1 1 « /FiS 'i?) / / / / / / / / 100 1 1 r / 1 1 1 1 / / to / f 1 .---"»' • / / /• / f y'^ / -i'-i iO S -"" • • f J :'.^-"' /^^i J^ . <»• '•^ ^* . » — ' '*- .^'"' IfOS -4 Figure 22. • '> the temperature based upon the difference of potential between the ter- minals of the rod. Fortunately the relation between the electromotive force and the temperature up to 1400° was of such a character that but little error was to be feared in extrapolating. The relation between electromotive force in volts and temperature is shown in Figure 21. From this curve temperatures above HOC were determined. 112 PROCEEDINGS OF THE AMERICAN ACADEMY. The work upon treated carbons was confined chiefly to high tempera- tures, a sufficient number of readings within tlie range already explored with the untreated carbons being taken to show that the distribution of intensities at the lower temperatures did not differ materially from that in the spectrum of the former. The set of isotherms given in Figure 22 will suffice to indicate the general character of the re^ults. It will be seen that in this case, as in that of the untreated carbon, the concavity of the curve between .Q/j and the red end of the spectrum is well marked at 13G5° ; and that at 1515° there was a well-pronounced maximum at about .65,M. The greater stability of the treated carbon made it possible to obtain consistent measurements on a number of rods at temperatures above 1500° and to establish beyond doubt the t^orm of the curves. It is obvious that for the study of the spectrum of incandescent carbon at this and higher temperatures the conditions would be much more favorable in the case of the incandescent lamp than with rods mounted in a large vacuum chamber like tliat used iu tlie present investigation. Lamp filaments in the process of manufacture are brought by thorough carbonization into a condition to withstand permanently much higher temperatures than the rods at my disposal were capable of doing. There is as yet, it is true, no direct means of determining the tempera- ture of the lamp filament ; but the curve for the relation of electromotive force to temperature (Fignre 11) is of such a character as to lead us to expect that comparisons of the spectra of incandescent lamps, in which electromotive forces were used as a criterion of the deajree of incan- descence, would at least enable us to confirm the existence of the remarkable phenomenon brouglit out by the present experiments and to extend observations of it to still higher temperatures. Mr. Ernest Blaker has, since the completion of the measurements described in this paper, compared the visible spectrum of lamps with treated fihiments, and of lamps the filaments of which before exhaustion had been coated with lampblack, with the spectrum of the acetylene flame. His measurements confirm very completely those which I have described in this paper, and contribute important evidence in favor of the existence of this anomaly in the law of distribution of intensities in the spectrum of glowing carbon. Theoretical Aspects of the Foregoing Data. The efforts of stuflents of radiation have of late yeai's been directed particularly to the testing of the various formulae by means of which the mathematical physicists have attempted to express the intensity of NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 113 radiation as a function of wave lengtli and temperature. The equation reached from quite ditFerent points of view by Wien * and by Planck.f in particular, has been the subject of exhaustive discussion and of experimental tests. To this end Pascheu t determined with the bolo- meter the distribution of energy in the infra-red spectra of various bodies from 15° C to 1300°. The materials thus subjected to measure- ment were oxide of copper, platinum, lampblack, and graphitic carbon. The range of wave lengths explored extended from 9.2// to 0.7^. Luramer and Pringsheim § made similar determinations upon the ideal black body, and Liimmer and Jahnke || finally repeated these measure- ments in the case of the black body and of platinum. Wanner,ir working with Paschen, made careful spectrophotometric measurements of the visible radiation from the ideal black body. To test the applicability of the Wien-Planck formula to these measurements, the equation is given the form, — log /= 71 — 72 ^; in which 71 = ^og {c, X~^), = — lo 9 xf; 9k' 9ii'" 9 V 9 xj/ 9xlf 9 i/' 9k ' 9 fi 9 V = 0 This is the equation of an (n — l)-flat. The equation involves h parameters but they are connected hjh — 1 equations. Two consecutive (n — l)-flats of the system intersect in an {n — 2)-flat whose equations are ^ = 0, B= 0. Three consecutive (n — l)-flats of the system intersect in the (n — 3)- flat, ^ = 0, ^ = 0, C = 0, where 0 is the determinant B, with A replaced by B. The equation of the aS'„_i is found by eliminating the parameters between the equations of tlie (n — 2)-flats and the equations connecting the parameters. The equations of the other spreads are derived in a similar manner. The system of related spreads is of the same character as before. 2. Muhidl relations of connected loci. Let us consider more in detail these connected loci. We will use F,^ to denote a i-flat of the 1-fold infinite system of ^--flats. Two consecu- 124 PROCEEDINGS OP THE AMERICAN ACADEMY. tive F„_{s intersect ia an i^„_2, three in an i^„_3, r in an I\_r, n — 2 in an F2 or plane, n — I in an Fi or line, ?i in an Fq or point. There is a 1-fold infinite system of these F„_2S which are generators of aS'„_j, a 1-fold infinite system of i^„_3's, generators of S,^_2, a 1-fold infinite system of lines generators of S2, the developable surface. Through any F„_2 there pass two consecutive -^„_i's, through any F„_^ there pass three consecutive i^„_i's, through any Fq, n consecutive F„_^'s. Through any i^„_3 there pass two consecutive i^„_2's, through any F„_i there pass two consecutive i^„_3's and three consecutive i''„_2's, and so on. We may then reverse this process and start with the curve of the system. Through any two consecutive points of the curve there passes a line, an F^, through any three consecutive points an osculating plane, an F2, through any four consecutive points an osculating 3-flat, an F^, through any n — consecutive points an osculating (n— l)-flat, an F^_^* That these operations may give unique results this curve must lie in the n-fold space and in no flat space of a less number of ways. If the curve lie in a ^'-flat, where k ^ n — 1, all the ^-flats through ^ -f 1 con- secutive points coincide and definite (k -f l)-flats are not determined at all. By a theorem of Clifford, such a curve must be of an order as great as n.f This theorem has been generalized by Veronese.l Let us consider any curve in ?i-fold space whose equations are, = 0, X = 0, . . . . V' = 0, a restricted system equivalent to h — 1 independent equations. The equations of the tangent at any point P' of this curve are linear equa- tions whose coefficients are functions of the n non-homogeneous co- ordinates, x', y', . . . . v'. The same thing is true of the equations of any of the osculating flats at the point P'. The osculating (n — l)-flat is given by a single equation, the coefficients of which are functions of these n quantities x', y', . . . v'. If we regard these as n parameters they are connected by the equations, ,^' = 0, x' - 0, . . . . .^' = 0,§ * We shall say a A-flat osculates a curve if it contains k + 1 consecutive points of it. Killing, loc. cit. t ClifEord, Classification of Loci ; Mathematical Papers, pp. .305-331. t Veronese, Behandlung der projectivisclien Verhaltnisse der Eaume von ver- schiedenen Dimensionen durch das Prlncip des Frojicirens und Schneidens, Mathematische Annalen XIX. ^ ' = (x', >/', . . . v'), etc. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 125 » a restricted system equivalent to re — 1 independent equations. We have then the case of an (n — l)-flat whose equation involves n para- meters connected by w — 1 independent relations ; this is equivalent to the case of a single equation containing one arbitrary parameter. TVe may, in general, consider the system of developables as given by an (« — l)-flat whose equation contains a single arbitrary parameter or /' parameters connected by X; — 1 equations.* 3. The tangent (n — \)-Jlats that are common to w — \ (n — l)-spreads envelop a developable. The equation in homogeneous coordinates of any (n — l)-flat may be written x = ay + fiz-{-....-{-yw. This equation involves n independent parameters ; if we connect them by any n — 1 independent equations we shall have the equation of an (n — l)-flat that contains but a single independent parameter, so that the 1-fold infinite system of (k — 1) -flats represented by it envelop a developable. The tangent (n — l)-flat at any non-singular point of a developable S„_i contains the generating F'„_2 through that point and touches the S„_i all over this flat, t We may speak of this developable Sn_i as enveloped by its tangent i^,_i's. If then we impose on an arbitrary (n — l)-flat any conditions that give rise to w — 1 independent equations between the coefficients in its equation, the (?2 — l)-flat will envelop a developable 'S'„_i. Let U= 0 be the equation of an (n — 1) -spread. The equation of the tangent (n — l)-flat at any ordinary point P' is 9U' 9U' 9U' ^ dx' dy' dw' If we impose on the equation of the arbitrary (yi — l)-flat the condi- tions that it shall be this tangent {n — l)-flat, the coefficients in the two equations must be proportional. We must have then 9U[ 9U>_ 91P 9 x' ^= 9 y' = . . . . 9to' — la y From these equations by means of the equation U = Q, * Salmon, Geometry of Three Dimensions, p. 286. t KiUing, loc. cit. 126 PROCEEDINGS OF THE AMERICAN ACADEMY. we may eliminate the coordinates of P' leaving a single equation in a, /3, . . . . y. For an (n — l)-flat to be tangent to an (w — l)-spread, one relation between the coefficients that enter into their equations must be satisfied. We conclude then that the (n — l)-fl.ats that touch n — 1 (« — l)-spreads envelop an *S'„_i. Let us consider only those tangent (?i — l)-flat8 to an (n — 1)- spread that touch it at the point of an (« — 2) -spread that lies on it. Let U=0 be the equation of the (n — l)-spread and let U= 0, F- 0, . . . , a restricted system equivalent to two independent equations, be the equa- tions of the (n — 2)-spread on it. We derive now the equations — la y and U' = 0, V = 0, ... If we eliminate the parameters from these equations there remains a restricted system equivalent to two independent equations in the coefficients a, /?,... y. For an (?2 — l)-flat to be tangent to an (n — l)-spread at a point of an (n — 2)-spread on it requires two con- ditions between the coefficients in the equation of the (n — l)-flat. These two conditions may be used as part of the n — 1 conditions that connect the coefficients of an (n — l)-flat that envelops a developable 'S'„_i. We have then the theorem that the (n — l)-flats that are tangent to p (n — l)-spreads at the points of p (n — 2)-spreads that lie one on each (n — l)-spread, and are tangent to a other (?z — l)'flats, where n — l = 2p-fcr, envelop a developable. In a similar manner for an (n — l)-flat to be tangent to an (n — 1)- spread at a point of an (n — 3)-spread that lies on it imjjoses three con- ditions on the coefficients that enter into the equation of the (ti — l)-flat. To be tangent to the (n — l)-flat at a point of an (?i — 4) -flat on it requires four conditions, etc. To be tangent to an (n — l)-spread at a point of a curve that lies on it requires n — 1 conditions between the coefficients, which is just sufficient to make the (« — l)-flat envelop a developable. We have then the general theorem that the (n — l)-flats that are tangent to p {n — l)-spreads at points of p (n — ^)-spread3 that lie one MORENO. — ON RULED LOCI IN W-FOLD SPACE. 127 on each, tangent to cr (n — l)-spreads at points of cr (n — k -\- l)-spreacls that lie one on each, tangent to t (n — l)-spreads at points of t (n — 2)- spreads that lie one on each, and finally tangent to v other (n — 1)- spreads, where p, cr, . , . t, v, are non-negative integers connected by the relation w— l=;^.p + (^— 1)o-+.... + 2t + v, envelop a developable »S'„_i. Similar cases occur in three-fold space where we have the tangent planes that are common to two surfaces enveloping a developable surface as do the tangent planes to a surface at the points of a curve' on that surface.* 4. Some additional properties of developables ; sections. Other properties of an »S'„_i may be deduced by regarding it as the envelope of an (n — l)-flat whose equation involves a single parameter.! Through any point in space can be drawn a definite number of tangent i^„_i's to the Sn^y For substitute the coordinates of the point in the equation of the variable {n — l)-flat and there is a certain finite number of values of the parameter that satisfy the equation. Any i^„_i of the system meets its consecutive i^„_i in a definite i^„_2, a generator of S^-^ whose equations are, Any three consecutive -F„_i's meet in a definite -P„_3, a generator of *S';^2> whose equations are, , ^ 9A ^ 9^A ^ ^ = ''9X = ''9^^ = '' Any n — 1 consecutive jP„_i's meet in a definite line Fi, a generator of S2, whose equations are, ^ = 0,^ = 0,. ..^^, = 0. Finally, any n consecutive i^„_/s meet in a definite point of the curve of regression of »S'3. The equations of the Fq are, * Salmon, Geometry of Three Dimensions, p. 547. t Salmon, Geometry of Three Dimensions, p. 289 et seq. 128 PROCEEDINGS OF THE AMERICAN ACADEMY. In general « + 1 consecutive F„_j's do not have any common inter- section, for the w + 1 equations, 9A ^ d^A ^ have no common solutions. If we regard these equations as homo- geneous in the w + 1 coordinates we may form their resultant, and the values of the parameter that cause this determinant to vanish, give special points where w + 1 consecutive F^-^s, intersect. These points are cusps on the curve ^i. Reciprocally there will, in general, be a finite number of i^„_i's that go through w + 1 consecutive points of *S'i. Veronese has shown that a curve in w-fold space has 3 n singularities which are connected by 3 (w — 1) relations, an extension of the Pluecker- Cayleyan characteristics of a twisted curve in tliree-fold space.* In this we have assumed that the variables that enter into the equation of the enveloping {n — l)-flat cannot be expressed in terms of fewer than w + 1 independent linear functions of the variables alone. If they could be expressed in terms of v such linear functions, where v < «, the developable *S„_i is a conoid with an {n — v)-way head, a case to be con- sidered later. The developable S^ of the series is ruled by {k — l)-flats, F^_^^. The S^, where 2 < ^ < n — 1 can be given by means of its enveloping F^ whose equations involve a single parameter. The n — k equations of the i^4 must however be of the form 9A S"-*-M as we have previously seen. Even the S^ may be represented in this manner. Any (n - l)-flat ^ = 0 cuts the S^_^ in a developable (n — 2)-spread, for it cuts the system of F„_^s, in a system of (n — 2)-flats that intersect consecutively in {n — 3)- flats. We may see this in another way. By means of this new equa- tion we can eliminate one variable from the equation of the enveloping (n _ l)-flat. The resulting equation in n variables may evidently be considered as the envelope of an {n — 2)-spread in a new (n — l)-fold space. The {n — l)-flat cuts any S^ of the system in a (^ — l)-way * Veronese, loc. cit. ; Killing, loo. cit. p. 197 et seq. MORENO, — ON RULED LOCI IN W-FOLD SPACE. 129 developable. In general any r-flat where r ^ n — ^ + 1 cuts any ♦S'^. in a developable (k -\- r — K)-spread. Any i^„_j of the system cuts the >S'„_i in an {n — 2)-spread, and the Fn_2 that it has in common with the consecutive i^„_i appears twice in the intersection, so that the proper (ii — 2)-spread is of order less by two than the order of 5'„_j. This {n — 2) -spread is also a developable. An i^,_2 is met by the consecutive i^„_2 in an F,^_?, ; it is met by any other i^„_2 in an (n — 4)-flat. In general, where 4 ^ w, there are a 2-fold infinite system of these (« — 4)-fliits and their locus is an (« — 2)- spread which is a double spread on Sn-v I"^ the case of cones and conoids this double spread may be of fewer than » — 2 ways. - Thus in four-fold space the planes which join a line to the successive points of an irreducible conic form a three-way developable. This developable is a conoid and the one-way head is the only multiple locus on the conoid. In three-fold space cones are the only developable surfaces that do not possess a proper double curve, if we call the cuspidal curve a double curve. In general there is a double curve distinct from the cuspidal curve. We will assume that we have the general case of a developable and not a cone or conoid. The total double spread on aS'„_j consists in general of two parts, aS^.s and 2„_2i where 2^2 is the locus of the 2-fold infinite system of {ii — 4)-flat3 arising from the intersection of non-consecutive i^„_2's, while -S'„_2 is the locus of the 1-fold infinite system of {n — 3)-flats arising from the intersection of consecutive i^„_2'3. Any three non-consecutive i^,_2's intersect in an (n — 6)-flat ; there are in general a 3-fold infinite system of such {n — 6)-flats whose locus is an (n — 3) -spread, a triple spread on aS„_2' Any {n — 6)-flat is the intersection of three {n — 4)-flats of 2„_2 and any such (n — 4)-flat con- tains a 1-fold infinite system of such {n — 6) -flats. This 1-fold infinite system of (n — 6)-flats does not, in general, fill out the {n — 4)-flat, for this would require a 1-fold infinite system of them. The total triple spread on »S',i_j consists in general of two parts /S„_3 and 2„_3 where 2„_3 is the locus of the 3-fold infinite system of (w — 6)-flats. We can supply a similar mode of reasoning to the spreads of higher multiplicities on S,^_^. The spreads *S'„_2, aS^.^, ... are developable, but 2„_2, 2„_o, ... are not developable. 5. Special case where the parameter enters rationally. Let us illustrate this theory by the case of the developable which is the envelope of the (ri — l)-flat, a f" -f m h f"-i + \m {in — 1 ) c T'^ -1- . . . . = 0, 9 130 PROCEEDINGS OP THE AMERICAN ACADEMY. where t is a variable parameter, a, b, c, . . . are linear functions of the coordinates that are not expressible in terms of any v linear functions of the coordinates where v ^ n, and m is an integer which is not less than n, the number of ways of the space. Two consecutive i^„_/s intersect in the F„_2, ar-'+(m - 1) 5 r-2 + l^?-iII|!!Liil)c r-« + . . . . + e = o, Jr-i+ (m - 1) cr-2+ . . . + et -\-f— 0. The elimination of the parameter from these equations gives the equa- tion of 'S'^.j. The result is the discriminant of the original equation placed equal to zero ; the order of S^_.^ is then 2 {ni — 1).* Three consecutive F,^_^% intersect in the i^„_3, a r-2 + (m — 2) i <'"-» +.... = 0, 5r-2 + (m — 2) c r-'' + . . . . + e =r 0, cr-2+ -{. et +/= 0. The equations of /S'„_2 are found by eliminating the parameter from these equations. The result is a restricted system equivalent to two inde- pendent equations ; the order of the system, i. e., the order of »S'„_2 is 3 (m— 2).t Similarly k consecutive -^„_i's intersect in the F^, given by the k equations, b r-*+i ■{- {m — h + \) e T"* +.... = 0 -\-et+f=Q. The elimination of the parameter from these equations gives a restricted system equivalent to ^ — 1 independent equations, the equa- tions of 'S'„_;.+,. The order of *S'„_i.+j is seen to be {h -\- \) (m — k). Lastly the intersection of n consecutive i^„_i's is the point, Fq, given by the equations, a r-"+'' + {m — n-\-\)b T"" +.... = 0 b r-"+i + (m — n+\) c r-" +.... = 0 -\.et+f=0. * Salmon, Higher Algebra, art. 105. t This is the condition that the three equations have a common root; Salmon, Higher Algebra, art. 277. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 131 The elimiuation of the parameter from these equations gives a re- stricted system equivaleut to n — 1 iudepeudent equations, the equation of aS'j whose order is n (m — n -\- 1). We can find the equations of those exceptional points where n -\- I consecutive i^„_i's intersect iu a point, if we eliminate the parameter from the n -{- 1 equations a r-" + (/« — n) b"'-"-^ +.... = 0 b r-" + (m — n) c"'-"-^ +.... = 0 +et+f=0. The result is a restricted system equivalent to « independent equa- tions; it is of order (n + 1) [m — n), which is the number of such points, cusps on Si- We may verify this result by forming the resultant of these (« -f 1) equations. If we eliminate the variables from these equations we have a determinant of order n -\- 1. If we expand this result t enters to the degree (n + 1) (m — n) so that there are (n + 1) (m — n) values of t that cause this resultant to vanish. These values of t give the special points in question.* Any double point on *^„_j must lie on two i^„_2's. We may find the equations of the total double spread on »S'„_i, by expressing the conditions that the equations of an i^„_2 regarded as equations in the parameter, have two roots in common. These conditions are f (I) a, (m - 1) b, i ^ '- c, a, {771 — 1) b, e b, (/7l — 1) c, b, ("« — 1) e,/ = 0, * For n = 3, these results agree with those of Salmon, Geometry of Three Dimensions, p. 296. Neither the results there nor these hold when the system has stationary (n — l)-flats. t Salmon, Higher Algebra, art. 275. 132 PROCEEDINGS OF THE AMERICAN ACADEMY. where there are 2 (m — 2) rows and 2 m — S columns. This restricted system is of order ^ (2m — 3) {2 m — 4). The double spread repre- sented by these equations consists of two distinct parts, »S„_2 and 2„_2. The order of 2„_2 must be, ^(2m — 3)(2 m — 4) — 3 (m — 2) = 2 (m — 2) (m — 3). A triple point on S„_i must lie on three i''„_2's. We may find the equa- tions of the total triple spread on *S'„_i by expressing the conditions that the equations of the F„_2 have three common roots. These conditions are expressed by means of a rectangular system similar in form to (I), in which however there are only 2 (?« — 3) rows and 2 m — 4 columns. The order of the restricted system is ^ (2 m - 4) (2 m - 5) (2 m - 6). This triple spread consists of two distinct parts, S„_s and 2„_3. The order of 2„_3 must be 1 2 -^(2m-4) (2m-5)(2m-6)-4(m-3)r=-(m-3)(m-4)(2m-l). In like manner we can find the equations of the total ^-tuple spread on *S„_i, by expressing the conditions that the equations of the F„_i have k roots in common. These conditions are expressed by means of a rectangular system similar to (I), in which, however, there are only 2 {m — k) rows and 2 m — k — 1 columns. This is a restricted system equivalent to k independent equations, of order ^ (2 m — ^- — 1) (2 m — k — 2) . . . . (2 m — 2 k). This spread consists of two parts, /S„_j and 2„_t; the order of the latter is _L (2 m - /5; - 1) (2 m - ^ - 2) (2 m - 2 ^^ - (^- + 1) (m - k). The total {n — l)-tuple curve on S^_i is given by means of a restricted system similar to (I), in which, however, there are only 2 {in — n ■{- 1) rows and 2 m — n columns. We have then a restricted system equiv- alent to w — 1 independent equations whose order is ^— -: (2m-n) (2 m - w - 1) . . . (2 m - 2 w -f 2). {n — 1) I MORENO. — ON RULED LOCI IN W-FOLD SPACE. 133 The order of the curve 2 is, ^ (2m — w) (2m-n — 1) (2 m — 2 w + 2) — n(m — w + 1).* (n-l)\ The equations of all the «-tuple points on /S„_i are given by means of a rectangular system similar to (I), in which, however, there are only 2 (w — 7i) rows and 2 m — n — 1 columns. They form a restricted system equivalent to n independent equations, whose order is 1 n — (2 m — n — I) (2 m — n — 2) . . . . {2 m — 2 n) ; this is the number of n-tuple points. The number of the n-tuple points other than the cusps on Si, are — (2 ?« — w — 1) (2 m — n—2) (2 m — 2 7i) — {71 + 1) (m — n). These points necessarily lie on 2i ; they are either n-tuple points on 2i, or else they are ?i-tuple points on the combined curves *S'i and 2i. In three-fold space the double curve on the developable may have tripl points on it ; it can have no double points off of the cuspidal curve. If m = n, then the order of Si is n, and there are no cuspidal points on the curve ; this is the rational normal curve of Veronese. f The order of S,^_i in this case is 2 (n — 1) ; no developable S„_x can be of lower order unless it is a cone or conoid, for no curve of lower order than n can lie in the n-fold space without at the same time lying in a space of fewer than n ways. Let us consider the case where m = p < w, where p is an integer. Any J9 + 1 consecutive i^„_i's intersect in an Fn_p_i whose equations are ' 9t ' 9tp If we use two homogeneous parameters X and fi instead of the single parameter t, these equations may be written * For n = S, this result agrees with that in Salmon, Geometry of Three Dimen- sions, p. 296. t Veronese, loc. cit. 134 PROCEEDINGS OF THE AMERICAN ACADEMY. g^-0 ^-^ -0 ?!^_o in which form the parameter no longer appears. Any p + 1 consecutive i^„_i's intersect in the same i^„_p_i as any other consecutive p -\- \ ; i. e., all the -F„_i's of the system contain the same F^_p_-i^. Any p-flat that does not meet this i^i_p_i cuts »S'„_i in a developable (/> — l)-spread of order 2 {p — 1). This developable {p— l)-spread of order 2 (/> — 1) lying in a ;j-flat is exactly similar to the case in /j-fold space where m = n. The curve at the base of this system is of order p\ it is the rational normal curve of p-fold space. Hence we may derive this system by joining by lines all points of a developable {p — l)-spread of order 2 (p — 1) in a j9-fold space, to all points of an (n — p — l)-flat that does not meet the p-flat that contains the {p — l)-spread. Xwi + juWgi respectively, so that A (1) + /n (2) represents a point on the line (12), i. e., the line joining (1) and (2). "We denote the result of substituting the coordinates of the points (1) or (2) in Uhj fJi, and Uo respectively. We use the symbols / 9 9 9 \ \ d Xi dx^ dtoi) (9 9 9 \ \ a X " d y 9w) / 9 9 9 \ \ 9 X.2 9 y-i 9w^j (9 9 9 x" A*2 Wi^ix^^ h ^2 -^ h • . . + ^2 ::: Ui. \ 9 Xi, oyi 9iOil In the last case the operator is to be applied Tc times to Ux. Now A (1) + jLt (2) is a point on the line (12), if it is also a point of the {ii — l)-spread, it must satisfy the equation of the spread. Substitute the cooi'dinates of A (1) + /x (2) in £7 and we have A- U, + A-i i, A2 L\ + ^^' ^, l\ + .. . , . . -\- —, ^."' Ui = 0. m ! The m values of A : ju that satisfy this eq^iation determine the m points where the line (12) meets the {n — l)-spread. If the point (1) lies on the spread then Ui = 0. If the line (12) meets the spread twice at the point (1), then Z7i = 0, A, Ui = 0. 138 PROCEEDINGS OF THE AMEEICAN ACADEMY. The equation of tl^e locus of all the lines that meet the spread twice at (1) is A C^i = 0. From the analogy of three-fold space, this locus of lines is called the tangent {n — l)-flat to the {n — ])-spread, at the point (1).* At each point of an {n — l)-spread there is in general a unique tangent (n — I)- flat. A j9-spread is given by the equations, V=0, w=o, a restricted system equivalent to n — p independent equations. In a similar manner the equations of the locus of all lines that meet the jt)-spread twice at any non-singular point ( 1 ) are, A ?7i zzr 0, A Fl = 0, Since these equations are linear we may select any n — p that are inde- pendent and the rest are superfluous.! We have then a jo-flat which from analogy is called the tangent p-flat to the /^-spread at the point (I). At any point of a /(-spread there is in general a unique tangent p-^att We define a tangent r-flat at a given point of the jO-spread where r < p as an r-flat that lies in the tangent p-flat at that point and con- tains the point. If r > p, we define a tangent ?--flat at a given point as an r-flat that contains the tangent p-i\at at that point. The locus of tangent lines then to a />-spread is simply the locus of tangent jo-flats to the spread. The locus of tangent planes, 3-flats, . . . , (p — l)-flats is this same locus. If then there are developables that arise from a jo-spread, where 1 < /) their number is not so great as n — p — 1, for * This proof is given in Dr. Story's Lectures on Hyperspace. t Some of these equations may be satisfied identically ; this will be the case when (1 ) is a multiple point on any of the [n — l)-spreads, but not a multiple point on the /^-spread. I Dr. Story, Lectures on Hyperspace. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 139 the tangent lines, tangent planes, tangent 3-flats, . . . , tangent jo-flats all have the same locus. The planes through two consecutive lines, the 3-flats through two consecutive planes, etc., the jo-flats through two consecutive {p — 1) -flats all have this same locus possibly of a certain multiplicity. b. Intersections of consecutive tangent Jiats. We shall show further that {p -f l)-flats cannot in general be passed through two consecutive tangent p-flats, for such ^-flats do not in general have (^ — l)-flats in common. Tangent j9-flats at consecutive points 71 of a jt)-spread where 1 ^ jo ^ - do intersect in points at least. Let F=0, a restricted system equivalent to n — p independent equations be the equations of the jo-spread. Let P' = (x', y, . . . ) and P" = (x' + dx', y' + dy', . . . ) be consecutive points of the spread. The tangent j9-flats at these points are d X' d y 9V' 9V' and A£7"=Aj/' + .(^rfx' + ^rfy + ....)=0, /5' V 9^ V \ All of these equations being linear, only n — p equations in each set can be independent. In general, 2 (n — p) equations for such a value of p have no common intersection. In the present case the resultant of any n + 1 equations of the combined systems vanishes for any consecutive points P' and P" on the ^-spread, so that no more than n equations of the combined systems can be independent. Hence tangent j9-flats at con- 140 PROCEEDINGS OF THE AMERICAN ACADEMY. secutive points of a ^-spread intersect in a point at least. Tangent planes at consecutive points of a surftice in w-fold space intersect at least in points. These tangent planes do not generally intersect in lines unless the surface lies in a space of three ways. Let us take p to repre- sent the tangent plane at any point P of the surface and take p', p", J)'", ... to represent the tangent planes at the points P', P", P'", . . . consecutive points of an infinitesimal closed curve about P. If p and p' intersect in a line they determine a three-flat. If the consecutive tan- gent planes intersect in lines, then p" has a line in common w^ith both p and p' and so p" lies in this three-flat. In a similar manner it can be shown that p', p", p'" . . . , all the tangent planes consecutive, to p lie in the same three-flat with it, i. e. a unique three-flat is determined at each point of the surface that contains the tangent plane at the point and all the tangent planes consecutive to it. Since however this three-flat is determined by any two of these tangent planes, the three-flats corre- sponding to P and P' any two consecutive points are the same. Take now any curve through P that lies on the surface. Since the three-flats corresponding to any two consecutive points of the curve are the same, it follows that tiie three-flats corresponding to all the points of this curve are the same. If we take a different curve through P the same thino; is true of the points of it. The three-flats corresponding to all the points of these two curves are the same since they are all the same as the three-flat corresponding to P. From this it follows that the whole sur- face and all of its tangent planes lie in the same three-flat. Hence if in general all the tangent planes consecutive to any tangent plane of a surface lie in the same three-flat with it, then the whole surface lies in this three-flat. In the same way it may be shown that if in general all the tangent planes consecutive to the tangent plane at any point of a surface lie in the same four-flat with it that the whole surface lies in this four-flat. Hence in ?i-fold space not only do the consecutive tangent planes of a surface not intersect in lines, but all the tangent planes consecutive to any tangent plane do not lie in the same four-flat with it. c. 77^6 locus of the intersections of the tangent plane at any point of a surface ivith the consecutive tangent planes. In a four-fold space let the surface be given by F=0, MORENO. ON RULED LOCI IN Jl-FOLD SPACE. 141 a restricted system equivalent to two inde^Dendent equations. Tlie tangent planes at P' and P", any two consecutive points, have for their equations 9U> 9U' d x' 3 y 9V' 9 V AV' = x'^+y%^ + .... = 0, 9 x' d y' and /52 U' 9'^ U' \ Let us take the first two equations in each set to be independent, then the rest are superfluous. Since P' and P" are points of the surface, U' =0 F' =0 9U' c' x' 9V' V" = V + ^dx' + = 0, d x' From these three sets of equations we derive "" \9x'-' ^ 9x'9v'^ +....; + u, X fd'V , , 5-F' , , \ 9 x' 9 y -^r—r dx' + . . . . = 0, 9x' 9V' dx' These four equations are homogeneous in the five differentials dx', d >/', . . . We may take one of these differentials to be zero and eliminate the other four. We have 142 PROCEEDINGS OP THE AMERICAN ACADEMY. X 9''U' x Ti-^y 9^U' X 9^V' ■ X' 1 + ^ 9 x' 9y' 9W 9x' 9y' 9W 9x' 9V' + '"" 9 9'U' 7 + x x' 9 y' 9^V> 9 x' 9 y 9x' 9W 9U> 9y' '-'-' 9V' _ 9y' ' ' ' = 0. This determinant and its derivatives vanish for the point P', therefore the locus is a quadratic three-way cone with its vertex at P'. This cone is intersected by the tangent plane at P' iu a pair of straight lines which is the required locus. If a point cc, ?/, . . . , be taken on either of these lines, we have three independent equations just sufficient to deter- mine the ratios of the four differentials ; i. e., just sufficient to determine the consecutive point P", so that the tangent plane at this consecutive point will intersect the tangent plane at P' in the point selected. That these two consecutive tangent planes have no further intersection may be further shown by forming the equation of the plane that goes through their common intersection and through both the points P' and P". The equations of this plane are A" V . AU' - A" U' . A F =0, A' V" . AU" — A' U" . AV" = 0. These equations in general represent a definite plane so long as P' and P" are not coincident. It would be of interest to examine the motion of the point of inter- section along these lines as the point P" circles about the point P', and to see whether at any time the consecutive tangent planes intersect in one of these lines. These lines are not inflexional tangents to the surface ; lines meeting the surface in three consecutive points do not generally exist in a space of more than three ways. For such lines would have to satisfy both AU' = 0, A F' = 0, and A" U' = 0, A^ V = 0, MORENO. — ON RULED LOCI IN W-FOLD SPACE. 143 These equations, however, in general have only the point P' counted a multiple number of times in common. In general, then, in a space of more than three ways a surface is so twisted that there are no lines that meet the surface three times at a given point. This proof is easily extended to a surface in a space of more than four ways. d. The spreads thai arise by considering the junctions of the consecutive tangent flats. Consider now any surface in n-fold space. Draw the 2-fold infinite system of tangent planes. Pass a four-flat through every two consec- utive planes and there is a 3-fold infinite system of four-flats, form- ing in general a seven-spread. Each four-flat is met by the infinity of consecutive four-flats in the same plane. We may pass six-flats through every two consecutive four-flats. There is a 4-fold infinite system of six-flats constituting a ten-spread. This system of ruled loci in no wise resembles the system of developables we derived from a curve. Starting with a surface we cannot derive a system of develop- ables in the same manner as when we start with a curve. The same is true if we start with any jo-spread where 2 "^ p. Only in case the p-spread lies in a (p -f l)-flat do consecutive tangent p-flats intersect generally in {p — l)-flatsj the only exception is in the case the/;-spread is a curve. II. Loci derived from an (w — 2)-flat whose Equation INVOLVES A Single Arbitrary Parameter. 7. Description of the loci. Let us consider next the system of loci represented by an (n — 2)- flat whose equations involve a single arbitrary parameter. The parame- ter may enter rationally or irrationally. If it enters rationally we n suppose it to enter to as high a degree as - in each equation. Let the equations of the flat be ^ = 0, ^ = 0. In these equations we suppose further that the linear function of the coordinates that appear as coefficients of the various powers of the param- eter cannot be expressed in terms of fewer than « -f 1 linear functions of the coordinates. Eliminate the parameter from these equations and 144 PROCEEDINGS OF THE AMERICAN ACADEMY. we derive the equation of an (n — l)-spread S„_p which is ruled by the system of (« — 2)-flats, F ^s* Two consecutive i^„_2's intersect in an (« — 4)-flat, whose equations are, The elimination of the parameter from these equations gives a re- stricted system equivalent to three independent equations. The locus is an (n — 3)-spread ruled by the F„_iS. *S„_3 is a double spread on S„_i. Three consecutive i^„_2's intersect in an (n — 6) -flat ^„_6, whose equa- tions are, If we eliminate the parameter from these equations we derive a restricted system equivalent to five independent equations. The locus is an (n — 5)-spread *S„_5, ruled by the i^„_6's. S,,_^ is a triple spread on *S'„_j and a double sjjread on S„_s . Similarly r consecutive i^„_2's intersect in an (n — 2 r)-flat i^„_2r5 whose equations are, On the elimination of the parameter we derive a restricted system equiv- alent to 2 r — 1 independent equations. The locus is an (n — 2 r + 1)- spread, *S„_2r + i> ruled by the i^„_2r's. S„_2r + i is an r-tuple spread on S„_-^ ; it is a multiple spread on other spreads of the system. Two distinct cases arise according as n is odd or even. If n is odd, n — 1 then — - — consecutive i^„_2's intersect in a line, Fi, whose equations are, * From now on we shall use 5^ to denote the A:-spread of this system. MORENO. — ON RULED LOCI IN n-FOLD SPACE. 145 n-3 ^ 9 A 9'^' A ^.f-.- n-3 9^' A ' ' «— 3 9k^ ^.^o,. n—'i 9'^ B 9\^' ^ = 0,^ = 0,.. .^;:^, = 0. If we eliminate the parameter from these equations we derive a restricted system equivalent to n — 2 independent equations. The locus is a surface /S'g ruled bj the -Fi's ; it is an ( — - — J-tuple surface on S^^.^. Consecutive i^i's do not in general intersect for the n -\- 1 equations ^ = 0, ^- = 0, . . . — —^ --= 0, ^^ 9x^ have not in general any common solutions. If we regard these m + 1 equations as homogeneous in the n -\- \ coordinates and form their result- ant, the values of the parameter that cause it to vanish will give points where consecutive lines meet. The equations of these points may be formed by eliminating the parameter from the n + 1 equations, which gives a restricted system equivalent to n independent equations. These points are double points on ^'2 and f — - — | -tuple points on S„_x. If n is even then — consecutive i^„_2's intersect in a point Fq, whose At equations are, A = 0 9k ^ = 0, ^ = 0, . . . , -^^= 0, 5/V 2 ^^ 9 XT The elimination of the parameter from these equations gives a restricted svstem equivalent to n — 1 independent equations. The locus is a curve 10 146 PEOCEEDINGS OF THE AMERICAN ACADEMY. Si, which is an f - j-tuple curve on *5„_i. There are not in general sta- tionary points on ^S^, for the « + 2 equations . . 9A . 9'^' A ii+i 9B ^ 9^B ^='''3J = ''---'^='>' have not in general any common solutions at all. If the equation of the (n — 2) -flat involve k parameters connected by k — 1 equations, the properties of the derived system of loci is the same as in the case just discussed. 8. Mutual relations of the derived loci. Two consecutive i^„_2's intersect in an i^„_4, three in an F„_^, r in an Fn-iri — H — ^"^ ^^ -^1' ^^ ^ 's ^^^1 <^'' o ^" ^'^ -^0 if " is even. Tliere is a 1-fold infinite system of each kind of flats. The i^„_2's are generators of Sn_x, the i^„_4's of *S'„_g, the F^_2,'!?> of »S'„_2,.+i. Let us consider the case where n is odd. Through any F^^_^ pass two consecutive i^„_2's, w — 1 through any F^-^t pass r consecutive F„_2S, through any Fi pass consecutive F,^_2^- Any F,,^^ contains two consecutive F„_iS, three con- n — 1 . secutive F„_eS, — - — consecutive i^i's. Any i^„_2r contains two consecu- tive i''„_2(r+i)'s5 any two consecutive i^„_2/s determine one -F„_2(r_i)'s. "We may then reverse the process and start with S^-, which lies in the space of n ways but in no flat space of a less number of ways. Through each two consecutive i^i's of this surface pass three-flats i^g's, these i^s's will generate a four-spread «S'„_4. Through each two consecutive i^g's pass five-flats; this can be done as the i^,_3's intersect consecutively in i^i's. These five-flats will generate a six-spread S,^. Finally, through each two consecutive F^_^9, pass i^„_2's ; these F,,_2^ generate an (w — l)-spread S„_i. If we start with the system of (ti — 2)-flats we come down finally to the surface, or starting with the surface we may work back to the system of (n — 2)-flats. If n is even, through any F,^_^ pass two consecutive F„_2S, through any Fn-2.r pass T cousecutive i^n^o's, through any Fq pass - consecutive i^^a's. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 147 H Any i^„_2 contaius two consecutive Fj^_^Sj three consecutive F^_i% - con- It secutive F^%. Any -F^.or contains two consecutive -?^„_2(r+i)'s and any two consecutive i^„_2r's determine one i^„_2(r-i) except in the case that r = -. "We cannot then start with a curve and retrace our steps ; two consecutive points of the curve S^ do not determine uniquely a plane of the system. The FJ% of the system in general intersect consecutively in the points of S-^. Starting with such a system of planes we may retrace our steps. Through any two consecutive planes of the S^ we may pass a four-flat. These four-flats are generators of ^S's. Through any two consecutive F^^ we may pass six-flats ; they are the generators of S-j. Finally through any two consecutive i^_4's pass {n — 2)-flats ; they are generators of »S'„_i. We may retrace our steps only in case we do not begin with aS'i. 9. Director curves of the ruled (n — V)-sj)read. Let the equation of such a ruled {n — l)-spread S^_x be <^ = 0. We shall show that the equations of the generating flats of the spread may be represented by linear equations involving a single parameter. The equation in homogeneous coordinate of an arbitrary (ii — 2)-flat in w-fold space may be written X = ai z -\- ^i s -\- . . . . + yiW y = ao z + /32 s + ...• + 72 w. In this form the equations of the (n — 2) -flat, which we may call the (n — 2)-flat^-6, involve 2 (ti — 1) independent arbitrary parameters. These parameters must be connected by 2 (n — I) — 1 equation to make A B a generator of such an (n — l)-spread. "We wish to connect these parameters in such a way that A B will be a generator of the *S'„_i in question. The equations of a curve on ^ are <^ =z 0, C7i = 0, ZZs = 0, . . . U„_o = 0. If we eliminate the coordinates between these equations and the equa- tions of ^ 5 we derive a single equation in the 2 (n — V) parameters. This resulting equation is the necessary and sufficient condition for A B to meet the curve. In a similar way we may derive 2 (« — 1) — 1 such conditions and make A B meet 2 (« — 1) — 1 curves on ^. If from these 2 (n — 1) — 1 equations and the equations of ^ 5 we elimi- 148 PROCEEDINGS OP THE AMERICAN ACADEMY. nate the parameters, we derive a single equation in the variables alone. It is the locus of all the (n — 2)-flats that can be drawn to meet the curves in question, and so it necessarily includes all the generating flats of (f). It includes possibly other flats besides the generators of <^, but in this case the general locus will break up into several components, and one component is cJ3. This is the case in three-fold space. The spreads Ui, f^, . . . £4-2 i^^J ^^ each case be taken to be flats ; then the director curves are plane curves. These are the director curves of (j); any or all of these curves may be plane, or they may be twisted to any extent permitted by the space. Any 2 n — 3 curves in n-ioh\ space may be taken as the director curves of a ruled (n — l)-spread. In three- fold space any three curves plane or twisted may be taken as the director curves of a ruled surfiice. In four-fold space, any five curves plane or twisted may be taken as the director curves of a ruled three-spread. In this case the generating planes intei'sect consecutively in the points of a sixth curve ; so in four-fold space any five curves completely determine a sixth. In five-fold space seven curves plane or twisted may be taken as the director curves of a four-spread ruled by three flats. In six-fold space nine curves determine a five-spread ruled by four-flats. Consecu- tive four-flats intersect in planes and these in turn intersect consecutively in points. So in six-fold space nine curves determine a tenth. 10. Multiple loci on the ruled (n — \)-spread. Any generator of the (n — l)-spread is an (n — 2)-flat i^„_2 ; it is met by any other generating F„_2 in an {n — 4)-flat. If then 4 ^ w every generator is met by every other generator. If n = 3, any generator is met by only m — 2 other generators, m being the order of the surface.* For 4 ^ n, any F^_2 contains a single infinity of (n — 4)-flats where it is met by the other i^„Vs. These are evidently double flats on »S'„_i. On *S„_i there are in general a 2-fold infinite system of such (n — 4)-flats constituting a double (n — 2)-spread, 2„_2 on S„_i. In general, then, any (n — l)-spread *S'„_i ruled by {n — 2)-flats i^,Vs has on it such a double (n — 2)-spread 2„^2 ruled by the 2-fold infinite system of (n — 4)-flats. 2„_4 has on it all those (n — 4)-flats, F^_i& that arise from the intersec- tion of consecutive F^^^^s. These F„_iS generate *S'„_3, which therefore lies on S„_2 and forms but an infinitesimal part of it. Any three F^^^^ intersect in an (« — 6) -flat; there are in general a 3-fold infinite system of such (w — 6) -flats constituting an (n — 3)- * Salmon, Geometry of Three Dimensions, p. 427. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 149 spread 2„_"„ a triple spread on S„_i. S„^s li^s on 2,^_3, and constitutes but an infinitesimal part of it. If ti is sufficiently great there is a quad- ruple (n — 4)-spread 2„_4 ruled by the 4-fold infinite system of (>i — 8)- flats arising from the intersections of four i^„_2's. S,^_j lies on aS'„_5. We can go on in this manner until we reach a limit due to the narrowness of the space. If n is odd we have finally an ( — - — j-tuple ( — - — J- /n — 1\ . . spread ruled by the ( — - — j-fold infinite system of lines that arise from n — I the intersection of — - — generating F,^_2^- There may be further an — - — j-tuple I — - — j-spread made up of the I — - — j-fold infinite re -f- 1 system of points that are the intersection of — - — generating i^„_2's, an /« -f 3\ , /« — 3\ , , , , /2 — 3,,, . ^ . ( — - — j-tuple ( — - — j-spread made up of the — - — fold infinite n + 3 system of points that are the intersections of — -- — generating i^„_2's, etc., but these spreads do not always occur. In special cases the 2,j_2, n ■\- \ or some component of it, may be of greater multiplicity than — - — • ii In three-fold space a ruled surface generally has on it a double curve. This double curve, or some component of it, may, however, be of greater multiplicity than two. It is to be observed that aS'„_5 lies on 2^2- lu three-fold space this means that consecutive generators of a ruled surface, if they intersect at all, must intersect in points of the double curve. If n is even we have finally an ( - j-tuple ( - j-spread 2„ that is made up of the ( - j-fold infinite system of points that 71 arise from the intersection of - generating i^„_2's. There may be an {—■\-\ J-tuple f - — 1 j-spread 2„ whose points are points of inter- •)\ f n \ ( n \ section of - -f 1 generating F,^_^s, an ( - -f 2 j-tuple ( - — 2 j-spread 2„ whose points are points of intersection of - -f- 2 generating i^„_2's, etc., though these spreads may not always be present. 150 PROCEEDINGS OF THE AMERICAN ACADEMY. 11. Special case where the parameter enters rationally. Let us consider the special case where the parameter enters rationally. Let the equation of the generating (n — 2)-flat i^„_2 be A = at^ + b t^-^ + c <^-2 + .... = 0, B=a't'^-]-b' f"-^ + c' r-2 + = 0, where a, b, c, . . . , a', b', c', . . . ; are linear functions of the coordinates that cannot be expressed linearly in terms of fewer than n -\- 1 linear functions of the coordinates. If we eliminate the parameter from these equations, we have the equation of the S„_i ruled by the i^„_2's ; it is of order I -\- m. It is more convenient in what follows to use two param- eters, X and fjL, that enter homogeneously into the equations. Two consecutive generators intersect in the F^_^ whose equations are ^^ = 0,^-^ = 0,^-^=0,^^=0. 5 A 9 fx. 9 X. 9 fx The elimination of the parameter from these equations gives a re- stricted system equivalent to three independent equations the locus is S,^__^, whose order is 2 (/ - 1) + 2 (m - 1) = 2 (Z + m - 2). The order is found by expressing the conditions that the four equations have a common root. The locus of the intersections of three consecu- tive F„_2S is a locus of F„^qS ; the equations of this locus are found by eliminating the parameters from the equations, ' fX cJ fX 9k^ ' 9X9 11 ' 9i-^ 9X^ ~ ' 9x9ii~ ' 9fx-' ~ This gives a restricted system equivalent to five independent equations ; it represents *S'„_5, whose order is 3 (Z -f m — 4). The r-tuple spread »Svj_2^^_i on Sn_\ is represented by the equations that result from eliminating the parameters from the equations, 3'-^^ o,/44-=o,...,r4=o, 9X'-' '9X'-'9ix ' '9 IX 5 A'--^ ~ ' 9x'-'9fx -"'•••' 5^-1 - "• MORENO. — ON RULED LOCI IN W-FOLD SPACE. 151 The equations then are of S,^_2r+i foi'ni a restricted system equivalent to 2 ?• — 1 iudepeudent equations whose order is r {I -\- m — 2 7-4- 2). As we have seeu, there are two cases according as n is odd or even. If 71 is odd we come down finally to an ( — - — |-tuple surface S„. The equations of S^ are found by eliminating the parameters from the equations n-3 H-3 n— 3 n-3 — ^'' »-5 — ^) • • • J n~S — ^> n-3 n-3 n-3 9^ B_ 9^'B 9^ B n-3 — ^> n-5 — ^5 • • • 5 n-:i — ^• 9X ' 9 ^ ' 9 fj. 9 jj. ~ The equations of S2 form a restricted system equivalent to « — 2 inde- 71 — 1 pendent equations, whose order is — - — (I -\- 771 — 7i +3). There are also f — - — j-tuple points FqS> on ;S'„_i, though in general n + 1 — - — consecutive i^„_2's do not intersect. If we form the resultant of the n -\- 1 equations n— 1 n— 1 n— 1 n-l — "> ,j-3 — ^) • • • J n-1 — ^> 5a. ^ 9 X.' 9 fJI. 9 fX ^ n—1 «— 1 n— 1 9^'B_ 9"'B 9'^- B _^ n-l — ^i n-3 — ^> • • • J n-l — ^> 9X^' 9x:^'9fJi 9fji''' we have a determinant of the (n + l)-st order, in which the parame- n -\- 1 ters enter to the degree — - — (I -{- tti — ti -\- 1). There are then 71 -{■ I — - — (Z 4- OT — « -f 1) values of the parameters that cause this determinant to vanish, and so this is the number of points F^. We can find the equations of these points by eliminating the parame- ters from these n -\- 1 equations. The result is a restricted system equivalent to 71 independent equations. The order of the system is n + I - — - — (I + m — n + 1). This is another proof of the number of points Fq on S„_i. 152 PROCEEDINGS OF THE AMERICAN ACADEMY, In case n is even we have finally the (- j-tuple curve whose equations are found by eliminating the parameters from the equations, n-2 n-4 9X'''9fJi n-2 n-2 9'^' A _ 9'^' A — ^, • • • t „-2 ■ 9 [X^ n-2 9'^' B n— 2 n— 2 n-2 — ^' « 4 — *-'? • 9X^' 0, 0. 5 A ^ (9/x n The order of the restricted system is ~ (I + m — n + 2), the order of «Si. We find the equation of the double spread 2„_2 on /S',,^!, by imposing on the equations of the generating i^„_2 the conditions that they have two common roots in the parameter. These conditions are,* (H) a, h a, h, a', b>, c', «/, b', = 0 where there are I -\- m — 2 rows and I -\- m — 1 columns. This is a restricted system equivalent to two independent equations ; the order of the system is h (l + rn — I) (I + m — 2). On 2„_2 must be aS„_3. We find the equations of 2„_3 by expressing the conditions that the equations of the generating flat have three common roots in the parameter.! The result is a restricted system similar in form to (II), in which, however, there are only Z + ?« — 4 rows and I + m — 2 columns. This restricted system is equivalent to three independent equations, and its order is ^ {I -\- m - 2) (/+/« — 3) (I + m — 4). The equations of 2„_^ are found by expressing the conditions that the equations of the generating (n — r)-flat have r roots in common. By an extension of the previous method we derive a restricted system of the same form as (II), in which, however, there are only I + m — 2 (r — 1) rows and I -{- ?n — (r — 1) columns. This is a restricted system equiva- * Salmon, Higher Algebra, Art. 275. tibid., Art. 285. MORENO. — ON RULED LOCI IN n-FOLD SPACE. 153 lent to r independent equations, the order of the system is — (^ + m — r + 1) (/ + m — r) . . . . (Z + m — 2 r + 2). Whether n is odd or even we have finally a curve 2i of multiplicity n — 1, whose equations are found by expressing the conditions that the equations of the generating (w — 2) -flat have n — 1 roots in the parameter in common. We derive a restricted system of the same form as (II) in which however there are I -\- m — 2 (w — 2) rows and I -\- m — (n — 2) columns. The order of this system is -. -. (n - 1)1 (l+m — n+2) (l+m — n+ I) . . . . (I + m — 2n + 4). This curve has w-tuple points on it whose equations are found l)y expressing the con- ditions that the equations of the generating (« — 2)-flat have n roots in common. We again have a restricted system of the same form as (II), in which, however, there are Z + m — 2 (ti — 1) rows and I -\- m — n + 1 columns. The order of this system is — - (I -{- m — n -{- 1) (I -{- m — ?^) . . . . (I -{■ tn . 2 n -{- 2), which is the number of points in question. P'or n = 3 these formulae for the order agree with those given in Salmon.* A very special case is where the parameter enters only linearly in oi.e of the equations of the generating (/i — 2)-flat. Let the equations of the fiat be B=a' r + b' t'"'^ +.... = 0, where we make the same suppositions regarding a, b, a', b', . . . , as before. The S^^i in this case is a ruled spread with m sheets through the (?^ — 2)-flat, whose equations are a = 0,b = 0; it has no other multiple locus on it at all. Consecutive generating F„_2S of the system intersect in the flat, whose equations are, 9 B d t All the F„_iS of the system lie in the same (n — 2)-flat ; they generate a developable (n — 3) -spread *S''„_3 in this flat. *S''„_3 is the section by this flat of the developable (n — l)-spread enveloped by the (n — l)-flat B. Consecutive generating F^?, of S,i_i intersect in generating ^„_4's of * Salmon, Geometry of Three Dimensions, p. 428. 154 PROCEEDINGS OF THE AMERICAN ACADEMY. S'„_s. By means of an (?i — 3)-way developable lying in an (w — 2)-flat and two arbitrary curves we can generate a ruled (u — Ij-spread by taking all the (/t — 2) -flats that can be drawn through the enveloping (« — 3)-flats of the developable so as to meet both curves. We have seen that the section of an (n — l)-way developable by an (n — l)-flat gave an (?? — 2) -way developable of the same nature, so here the section of an (n — l)-spread ruled by (n — 2)-flats b}' an (n — l)-flat gives an (n — 2)-spread of the same nature as the (n — 1)- spread. III. Loci derived from an (n — ^')-flat whose Equations INVOLVE a Single Ahbitrary Parameter. 12. Description of the derwed loci. We shall comj^lete the general theory by considering the locus of the 1-fold infinite system of (« — ^-j-flats, where 2 ^ k whose equations all coutaia a single arbitrary parameter. Let the k equations of the flat be A = 0, B = 0, . . . , (7=0. The equations of the locus of these i^„_t's are found by eliminating the parameter from these equations. The result is a restricted system equivalent to ^^ — 1 independent equations. The locus is an {n — k -{- l)-spread /S^.j^, ruled by the F„^^'s. Any two consecutive i^„_t's intersect in an (n — 2 k)-^-a.t i^„_2i whose equa- tions are 9A 9B A = 0,^ = 0,B=0/^ = 0,.... If we eliminate the parameter from these equations, we derive a restricted svstem equivalent to 2^—1 independent equations. The locus is an (71 — 2 /t + l)-spread S„^2k+i ruled by the i^„_2i's ; it is a double spread on S„_^. Any three consecutive i^„_2*'s intersect in an {n — 3 X-)-flat F,^^ whose equations are, The elimination of the parameter from these equations gives a restricted system equivalent to 3 ^' — 1 independent equations. Their locus is an (ii — S k + l)~spread ruled by the F,,_o^'s.. aS^.^j+i is a triple spread on MORENO. — ON RULED LOCI IN W-FOLD SPACE. 155 The equations of the locus of the intersections of r consecutive i^,_t's are found by eliminating the parameter from the equations case we come This gives a restricted system equivalent to rk — 1 independent equa- tions. The locus is an {n — rh ^ 1 )-spread ruled by the i^„_ri's, it is an r-tuple spread on »S'„_4_^i. There are k cases according as « = 0 (mod ^•), n = 1 (mod Ic), . . . , n = yl- — 1 (mod k). In the first case we come finally to a curve Sx which is an ( , j -tuple curve on ^S^.^+i. In the second down finally to a system of lines F^% which are generators of a ruled surface S.^. In the last case we come down finally to a ^'-spread ruled by {k — l)-flats. There are on Sj^ in general special points where two con- secutive -F/,._i's intersect. 13. Multiple loci on the spread; mutual relatiotis of the system of spreads. »S^,_i-i-i has on it in general multiple loci that arise from the intersection of non-consecutive F„_,^'s. Any F„_,, intersects every other F„_f. in an (« — 2 k)-i\at ; there is in general a 2-fold infinite system of such (n — 2 Z,')-flats constituting a double (71 — 2 k + 2)-spread 2„_2i+2 on S„_^^i. Evidently S,j_2k+i li^s on 2„_2t-i-2- -^"J three F„_iJs intersect in an (n — 3 Z,')-flat ; there is a 3-fold infinite system of such (?^ — 3 ^)- flats, they constitute in general a triple (n — 3 ^' + 3)-spread 2„_3i.|_3 on 'S,i-k-+i- '^n-3k-+i I'^s on ^nsk+r,' ^"7 '" consccutive F„_f.'s intersect in an (« — r ^)-flat ; there is an r-fold infinite system of such (n — r ^^)-flats in general, constituting an r-tuple (n — r k + r)-spread 1„_^f.^^ on -S^.^.+i, on which lies S„_y,^_^i. Finally the locus of the intersection of any a F„_i.'s where a is the n greatest integer in j is an a-tuple [n — a (k — l)]-spread 2„_a,j_i, on iS„-i:+i ; it is ruled by the a-fo!d infinite system of (n — a ^)-flats. The question arises, When, in general, do these double loci cease to exist? The double spread is in general an (w — 2 ^ -|- 2)-spread 2„_2i4.2. To have a continuous locus of double points we must generally have 156 PROCEEDINGS OF THE AMERICAN ACADEMY. _ _ « + 1 n — 2 k -\- 2 ^ X ov k :^ — For values of k that satisfy this condition there is in general a continuous locus of double points. If » -4- 2 Li there is in general only a finite number of double points on the locus. If w - 2 ^' + 2 < 0, or /fc > ^-^^ Zi there are in general no double points on the locus. If there enter into the equations of the generating (« — Z,-)-flat p parameters connected by p — 1 equations the properties of the system of related loci will be similar to those of the system just described. Any two consecutive -^„_i's intersect in an F,^^2^. while through any ^n-ik P'^.ss two consecutive -^„_i.'s. Any three consecutive F^_^^ intersect in an -F„_-5i while through any i^,_3i. pass two consecutive i^„_2i's and three consecutive F^^g-'s. Any two consecutive F„_,.^'s determine in general one Fn_f.fr-i)' An exception may occur if r = a the greatest integer in -• Thus, if n = 0 \mod k), two consecutive points of Si do not determine a {k -\- I) -flat where 2 ^ k. If n = 1 (mod k), two consecutive lines of So do not determine a (k + l)-flat, except in the case k = 2. In the last case, however, where n = ^- — 1 (mod k), two non-intersecting (k — l)-flats do determine a (2 ^ — l)-flat. Only in this last case can we retrace the steps if we come down to the last spread. We can always retrace the steps if we do not come down to this last case. 14. Director spreads of the ruled spread. The equation in homogeneous coordinates of any (n — ^•)-flat, 2 "^ k, may be written x = ais + I3it -^ . . . . + yiw, t/ = a2S + /Sit -}-....+ yot^, z = a^S i- (3kt +....+ YkW. In this form the equations of the flat contain k (n — k -\- 1) independent parameters. These parameters must be connected by^(w — ^+ 1)— 1 equations for this (n — ^)-flat to be a generator of such a ruled (?2 _ ^ -f l)-spread. Any curve is given by the equations MORENO. — ON RULED LOCI IN W-FOLD SPACE. 157 • • • • a restricted system equivalent to 7i — 1 independent equations. If we eliminate the coordinates between the equations of the flat and curve, we derive a restricted system equivalent to ^ — 1 independent equations in the parameters alone. These are the conditions that must be satisfied for the (n — l-)-flat to meet the curve. In a similar way we may derive a restricted system equivalent to k — p independent equations in the parameters alone which are the necessary and sufficient conditions for tlie (» — ^•)-flat to meet a certain p-spread where 1 ^ jo ^ ^- — 1. We may have then curves, surfaces, . . . , or ;o-spread8 where 1 < jo < ^ — 1 for the director loci of a ruled (n — k + l)-spread. The numbers of loci of each kind that must be taken are A, /x, . . . v, p, namely, non-negative integers chosen to satisfy the equation \{k—l) + iM(k — 2)+ + v.2 + p.l=k{n-k+l)-l. If we consider a group of one or more points as a director locus of the spread, we have to select integers to satisfy K . k + \ {k — 1) + . . . . + p . 1 = k (n — k + 1) — 1. We may apply this to special cases. The director loci of a ruled surfece in three-fold space are three curves. We may take one curve and a group of K points, in which case the ruled surface is reducible and has for its components k cones whose vertices are the k points and whose common base is the curve in question. In four-fold space the director loci of a ruled surface may be five surfaces, three surfaces and one curve, or one surface and two curves. The ruled surface in each case consist- ing of all the lines that can be drawn to meet all the director loci. In the same space the director loci of a three-spread ruled by planes may be taken to be five curves. If the director loci be all taken on any »S'„_t_,.i, then the locus of all the (n — ^)-flats that can be drawn to meet these director loci will include as one of its components the *S'„_j.+i in question ; it may or may not have other components. There are several special cases illustrative of these methods that can be worked out in still greater detail. Some of these I hope to make the subject of another jmper. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 6. — Skptember, 1901. THE ARC SPECTRUM OF HYDROGEN. By O. II. Basquin. With Two Plates. Ikvestigations on Light and Heat made and published wholly or in part with Appropriations FROM the RuMFORD Fu.ND. MARINE BIOLOGICAL LABORATORY. Received /^^A Accession No. '--.../.}y..>J>.Z.... Given by 4«?^?r?^vrr..<< X 3 q: I- o UJ Q. CO o IT < LiJ I H z O < GQ w s° 00 Ik * V w w s° 00 (O * Ctf 5°' oo tt) **« w 5:° : # a> I 5 Z) cr I- o UJ Q. CO o IE < UJ I H %^ So ou CD tf cv? go. CO ^ i4^.. ***Ho book Of pamphlet is to be removed from the Iiab- oratory without the permission of the Trustees. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE STANDARD OF ATOMIC WEIGHTS. By Theodore William Richards. Received July 27, 1901. The long continued discussion concerning the relative advantages of hydrogen and oxygen as standards of the numerical values of chemical combining weights seems to need yet another word. In spite of the fact that an international committee has decided by a large majority in favor of oxygen, the opposing arguments have not been put to rest. The latest paper on this subject is by Erdmann,* the well known champion of the old unit value for hydrogen and the new value for every other atomic weight. The paper consists mainly of a partial reply to an earlier paper by Brauner.f The weight of the argument in these papers seems to be distinctly on Brauner's side, but it is not my purpose to recapitulate all the arguments which these gentlemen and others have advanced. $ I wish rather to call attention to a few points which do not seem to have received the attention which they deserve. The first of these concerns the question of fact. What element has served as the actual standard of comparison in a plurality of cases ? The question is easily answered by referring to Clarke's valuable compilation. § Evidently hydrogen in combination has been weighed accurately only in the cases of water and the ammonium salts. The atomic weights of zinc, aluminum, iron, nickel, cobalt, and gold have been determined by * Zeitschrift fiir anorg. Chera., 27, 127 (1901). t Zeitschrift fiir anorg. Chem., 26, 186 (1901). J A recent recapitulation of many of the arguments on each side may be found in the report of the American Chemical Society's hranch of the International Committee, published in the Journal of the American Chemical Society, February, 1901, p. 44 of the Proceedings. § F. W. Clarke, A Recalc. of the At. Weights, Smithson. Misc. Coll., The Con- stants of Nature, Part V. (1897). 178 PROCEEDINGS OP THE AMERICAN ACADEMY. measuring or weighing the hydrogen which they displace or to which they correspond, but the results of different experimenters are far from concordant. All other elements beside these eight have been referred to hydrogen only with the assistance of oxygen. On the other hand, oxygen has been used as the direct standard of reference in countless cases. The determination of oxygen in the chlo- rates, bromates, and iodates may be considered as the starting-point for the calculation of Ag, K, Na, CI, Br, and I, and through them of very many others. Into this remarkable series of experiments, executed in great measure by Stas, the value of hydrogen enters only in the case of ammonic salts. If the atomic weight of nitrogen were certain, we should indeed have here a direct basis of comparison, but unfortunately the value for this element may be as much as 0.05 per cent, or even more, in error. The direct practical determination of the exact com- position of ammonia gas, either by analysis or synthesis, has not yet been accomplished. The value for nitrogen depends largely upon the analysis or synthesis of nitrates, thus making oxygen the essential stand- ard of reference in this case also. The other elements which have been determined more or less accurately by reference to oxygen are as follows : H, C, Cu, Ca (through the carbonate), Pb (through the nitrate), Zu, Cd, Hg, Tl (through the nitrate), Sn, P, As, Sb, Bi, Mo, U, W, Se, Te, Mn, Fe, Ni, Co. If one adds to these all those which are connected less directly with oxygen through the halogen and silver values and the sulphates, all the chemical elements are included in the list. Thus an overwhelming majority of elements is referred more directly to oxygen than to hydrogen. Erdmann points out in his recent paper that there are possible causes of error in some of the methods used by Stas for the analysis of chlo- rates. Unfortunately he does not touch upon the very important ques- tion of the percentage effect of these causes of error. It is undoubtedly true that in these cases, as well as in every other case, absolute accuracy was not attained. No analytical method is wholly free from the possi- bility of error, and hence it is vain to expect that any table of atomic weights should be perfectly trustworthy. When the accuracy of Stas has been exceeded in actual fact, it will be time to forsake his results for the newer values. Erdmann suggests that silver be chosen as the standard of reference, and the susgestion is one which has some advantasies. On the other hand the tendency which this metal has to absorb oxygen has cast a sus- picion over some of the work in which it was used. A further objection RICHARDS. — THE STANDARD OF ATOMIC WEIGHTS. 179 to silver lies in the fact that it cannot be directly used in the demonstra- tion of Avogadro's rule. Moreover, one is in doubt as to the value to assign to this element, supposing that it should be selected as the stand- ard. According to Erdmann's earlier argument^, logically followed out, one should make silver 100.000, but this would cause hydrogen to be less than unity. If silver is taken as 107.11, hydrogen would be 1.000 at the present time, but what it might be in the future no one can predict, since hydrogen is compared with silver at present only in a roundabout fashion. Hence each of these assumptions would bring with it a further disadvantage besides that attending the immediate inconvenience of using new values. The most important argument used by the minority is the pedagogic one. It is contended that the uneven value for hydrogen, 1.0075, com- plicates the explanation of the very important rule of Avogadro. If this were true, it would indeed be worthy of consideration, but according to my experience there is no difficulty in the matter. For some time I have abandoned the comparison of specific gravities as a means of demonstrating Avogadro's rule. I have used instead the densities of gases and vapors, — that is, the actual weights of a litre of the several substances at 0°C, or at 273" C or at 546°C. This seems to be a more successful method, probably because density has concrete dimensions, and is not a numerical abstraction as specific gravity is. 1.97 X The student at once comprehends the equation of ratios -^— r = — • If the exact experimental values for the densities of the two gases are given, the solution of this equation gives the student not only the ob- served molecular weight of carbon dioxide, but also an insight into the extent of the actual deviations from Avogadro's rule. Since the intro- duction of this method of presentation, I have had far less troul)le, and far more successful examination results, than were formerly obtained. The student usually learned by heart the old rule, " The molecular weight equals twice the specific gravity," without understanding it. Because the density-method would serve equally well with any gas used as a standard, the pedagogic argument against H = 1.0075 seems to me illusory. The argument just discussed has led the Committee of the German Chemical Society to an action which seems to me exceedingly unfortu- nate,— namely, the publication of two tables of atomic weights. This action has already been criticised by Kiister and others. Either table alone, supported by suitable weight of opinion, would have been vastly 180 PROCEEDINGS OF THE AMEKICAN ACADEMY. better than two. The mistake is especially to be regretted because the eminent committee in question has previously acted with so much wisdom and ability. It seems to me that by far the most important questions which have been raised in the whole discussion are the questions of uniformity and permanence of usage. These were indeed the prime objects of the foun- dation of the German Committee in the first place. Nothing could be more destructive to accurate calculation than a changeable standard of measurement ; and yet this very uncertainty marks the present state of affairs. I cannot but think that every one should accept the standard of refer- ence upon which any considerable majority of representative chemists agree, since the matter is rather a question of convenience than a ques- tion of principle. In the first place I preferred O = 16.000 primarily because so much valuable work, both in analytical and in physical chem- istry, has already been calculated upon this basis, and because of the effect of a possible change in the oxygen-hydrogen ratio. At pres- ent a still more important reason for preferring this standard exists, namely the action of the International Committee, consisting of some of the most prominent chemists of many countries, appointed for the ex- press purpose of voting upon this question. This Committee, by a large majority, decided to call oxygen exactly 16.000. I cannot avoid the belief that until a yet more representative body of chemists is appointed by international co-operation, or until the present committee reconsiders its vote in parliamentary fashion, the present verdict of this committee should rule the chemical world. Unless chemists are prepared to ac- cept such a ruling, the appointment of an international committee is a waste of time. Representative government in civil affairs would be impossible if the minority refused to act in accordance with the decision of the majority. Does not the same principle apply to scientific rulings ? Of course intelligent discussion is always desirable — the restriction applies to action and not to speech. Before the action of the International Com- mittee the situation might have been called one of scientific barbarism, but at present it may be called one of scientific rebellion. Formerly new determinations of atomic weights made at Harvard were expressed in publication both upon the basis O = 16.000 and upon the basis O = 15.879, because the question had not been decided by representative vote. In future, out of respect to the action of the International Committee, only the former standard will bu used in this RICHARDS. — THE STANDARD OF ATOMIC WEIGHTS. 181 Laboratory. If an adequate internationally representative body of chemists should in the future decide that some other standard is better, immediate change of practice will be made to suit the new decision. One regrets that so much time should have been spent in discussing a matter which involves no fundamental principle, but is simply a question of form and of convenience. The subject matter of the present paper may be summed up in the following sentences. It is pointed out that oxygen has actually served as the experimental standard of reference in a great majority of cases, that a great bulk of valuable work has already been published on the basis O = 16.000, and that the use of this standard involves no impor- tant didactic difficulties. It is further contended that the decision of the representative International Committee is in itself an important rea- son for adopting this standard, and that uniformity of usage is more important than any of the special advantages claimed by either side in the discussion. Seal Harbor, Mt. Desert, Maine, July 22, 1901. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 8.— October, 1901. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 127. STUDIES ON THE REACTIONS OF LIMAX MAXIMUS TO DIRECTIVE STIMULI By Peter Frandsen. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 127. STUDIES ON THE REACTIONS OF LIMAX MAXIMUS TO DIRECTIVE STIMULI. By Peter Frandsen. Presented by E. L. Mark. Received September 3, 1901. II. Introduction .... Thigmotaxis .... Material and Methods Results Geotaxis Methods ... Operations and Results CONTENTS. Page 185 187 187 188 190 190 191 Summary of Part II . III. Phototaxis Methods Operations and Results Summary of Part III Bibliography . . . Page 205 206 208 209 225 226 Introduction. The following studies were made at Harvard University during the fall and winter of 1898-99. The problem was proposed by Dr. C. B. Davenport and the investigation carried on under his immediate direc- tion. I wish here to acknowledge my indebtedness to his many sugges- tions and helpful criticisms throughout the year. In connection with the preparation of the manuscript for publication, I am under obligation to Dr. E. L. Mark for many kindnesses. The behavior of any organism toward artificial stimulation is prob- ably always largely dependent on its normal environmental condi- tions. The long action of those conditions, assisted, perhaps, by the animal's own efforts, conscious or unconscious, to adapt itself to them, finally results in certain habits and instincts. The process of adaptation being extremely slow, organisms are strongly averse to great or sudden changes in their environment and incapable of adjusting themselves to them. As a rule, then, we should expect animals to seek those condi- tions of light, heat, moisture, and other physical and chemical influences which are most in accordance with those to which they are normally subjected. 186 PROCEEDINGS OF THE AMERICAN ACADEMY, The most easily observed responses of animals are naturally those which find their expression in locomotion. The number of stimuli which may influence locomotion are, of course, numerous, but of these a certain limited number play much the lai'ger part. If we had an accurate knowledge of the relative weight of these diflferent forces, we might pre- dict with certainty the path any animal would follow under certain given conditions. An experimental study of the different stimuli ought at least to enable us to find out which ones do operate, and perhaps to establish certain general laws regarding them and the biological tendencies which impel the animal to respond. The present paper is a study of the locomotor responses of the slug Limax maximus to three kinds of stimuli, — those of touch, gravity, and light. In connection with these studies new problems have constantly arisen, some of which have been cursorily considered, many others merely alluded to, so that the work is far from being complete. The term " geotaxis " has been used to designate the influence of gravity on locomotion. Interesting and careful studies have been made on the geotaxis of numerous Protista by Schwarz ('84), Aderhold ('88), Massart ('91), and Jensen ('93). These investigations clearly show a geotactic response in the nnicellular organisms studied. The kind of response varies according to other conditions, such as those of light, heat, density of medium, chemical influences, etc., and may also differ in indi- viduals of the same genus under apparently like conditions. Massart ('91, pp. 161-162) found that, when a number of Spirilla were put into a vertical tube, one group collected in the upper part and another at the lower part. He also found (p. 164) that Chromulina woroniniana was negatively geotactic — that is, moved upward, or in a direction opposite to that of the pull of gravity — at 15° to 20° C, but positively geotactic at 5° to 7° C. Jensen's work also showed the important influence of other agents in modifying geotaxis. Loeb ('88, pp. 7-8) found that cock- roaches preferred the steepest side of a box whose four sides were inclined at different angles ; that is, they are negatively geotactic. He also dis- covered that a number of other Metazoa were geotactic. In a certain way, the present paper is a continuation of a recent study made by Dr. C. B. Davenport and Miss Helen Perkins on geotaxis in the slug. Davenport and Perkins ('97, p. 105) discovered that the intensity of the animal's geotactic response was directly proportional to the sine of the angle of deviation from the vertical, and hence *' varied directly as the active component of gravity." In the third section of their paper, the question, " What determines whether the head end of FRANDSEN. — REACTIONS OP LIMAX MAXIMUS. 187 the slug shall be directed up or down ? " was raised and considered. The results showed that certain individuals appeared to have a fairly marked positive geotaxis, for, when placed on an inclined glass plate, such animals swung the head-pole of the axis toward the earth ; but others showed as strongly marked a tendency to move away from the earth, and a few seemed indifferent as to whether they went up or down. Their experiments showed further that there was, apparently, no inherent tendency in individual animals to move either to the right or to the left, so that the difference in geotactic response could not be explained as due to differences of an inherent tendency of this kind. The effect of a slight initial impulse given to the head of the animal indicated that the thigmo- tactic, or contact, stimulus imparted to the animal in handling might, to some extent, modify its response to the stimulus of gravity. But Davenport and Perkins did not reach any definite, satisfactory answer to the main question. It was to test their observations by a larger number of experiments, and, if confirmed, to explain them by further experimentation, that the present investigation was undertaken. In the first place, I wished to find out whether certain individuals, if put on an inclined glass plate, always responded to the pull of gravity by directing the head end up and moving away from the earth, and whether certain other individuals always did the contrary. If this proved to be true, then it was my main problem to seek the reason for it. Is the force which makes some slugs go up, others down, and still others indifferent to the attraction of gravity, a purely accidental one, — is it a physical force, or is it what we may call a psychical peculiarity, which varies in different individuals and in the same individual at different times ? As a preliminary to the main problem, I first made a series of experiments on the animal's thigraotaxis, — its response to contact- and pressure-stimuli. By virtue of its thigmotaxis, an animal moves either toward or away from the agent which comes in contact with it, just as its geotaxis is expressed in a movement toward or away from the earth, in response to the attraction of gravity. I. Thigmotaxis. Material and Methods. — The animal used in all the following experi- ments was Limax maximus, which is fairly abundant in the greenhouses about Cambridse. Material was obtained from several different green- houses and kept in a large closed tin box, the bottom of which was covered with moss kept moist, so as to afford an environment as much like the customary one as possible. Fresh cabbage leaves constituted the 188 PROCEEDINGS OF THE AMERICAN ACADEMY. animal's main food. The cannibalistic tendencies of the slug, together with an unavoidable deterioration due to repeated handling, necessitated a frequent renewal of the animals. The methods used in the experiments were simple. The slug was placed on a circular glass plate set horizontally in the bottom of a cuboidal wooden box which was made impervious to light and covered with a thick, black clotli. Precautions were taken to avoid thermal and chemical influences by keeping the box at as equable a temperature as possible and by wiping the plate free from slime before each test. The tests were made only when the animal had definitely oriented itself and was moving ahead in a straight line. Two series were made. In the first series the dorsal tentacle was touched gently with the forefinger. The box was then immediately covered with the black cloth. Observa- tions were made after the lapse of 20 to 30 seconds and the position of the animal noted. The right and left tentacles were touched alternately. Results. — The following Table (I.) gives the results of a number of experiments on ten different animals. TABLE I. Kesponse to Thigmotactic Stimulation of the Tentacles. Number of Trials. Animal No. Total Number of Trials. — + 0 1 7 2 3 12 2 11 3 3 17 3 8 3 1 12 4 4 3 3 10 5 7 2 0 9 6 6 0 2 8 7 10 2 2 14 8 16 4 2 22 9 18 1 5 24 10 22 1 4 17 Totals . . 99 21 25 145 FRANDSEN. — REACTIONS OF UMAX MAXIMUS, 189 The column headed with the minus sign shows the number of times the animal responded by moving away from the source of stimulus ; the one headed with the plus sign, the number of times it moved towards that source ; and the zero column, the number of times there was no response. I found that the animal would respond very definitely and precisely to stimuli two or three times in succession by immediately retracting the tentacle touched and moving away from the stimulating influence. After the third trial, however, it either refused to change its direction of loco- motion or else moved directly towards the source of the stimulus. If a respite of a few seconds before the next stimulation was then permitted, the animal would again give a precise negative response for two or three trials, and then, as before, it desisted. Out of the total 145 tests, there was a negative response in two thirds of the trials. The remaining trials — one third of the whole — were about equally divided between the positive responses and refusals to respond at all. Sometimes five or six tests were made in quick succession, so that the total negative response is rather less than it would have been if a rest had been given in each case after three tests. Out of the 21 cases of direct positive response, 15 were cases where the right tentacle was touched, and the remaining 6 were due to stimulation of the left tentacle. Similar, but more marked, differences between the results of stimulating the right and the left tentacles were observed in other experiments. This suggests that either the right tentacle may be less sensitive to stimuli, or that its coun- terirritancy may be more readily aroused. There is, however, a third possible cause. The animal may have an innate tendency to go to the right, and, if so, this tendency may diminish to some extent the force of the stimulating agent when it impinges on the right side of the animal, and correspondingly increase the response when the stimulus is directed upon the left side of the animal. Something further will be said about this point in a later part of the paper. A few thigmotactic experiments were next made on the sides of the animal posterior to the head. The right and left sides were touched alternately. The results are given in Table 11. Phenomena like those observed in stimulating the tentacles are seen here, and they also agree with similar observations by Davenport and Perkins ('97, p. 109.) After two or three trials, the animal begins to show resistance, and if the finger is held against its side, will sometimes try to displace the finger by pushing against and curling the body around it. The frequency of the negative response is here somewhat less marked than in the preceding experiments, which is as we should expect, owing 190 PROCEEDINGS OF THE AMEEICAN ACADEMY. to the greater sensitiveness of the tentacles as special tactile organs. In these experiments every one of the minus and zero results was due to stimulation of the right tentacle. TABLE II. Response to Tiiigmotactic Stimulation of the Sides of the Body. Animal No. Number of Trials. Total Number of Trials. + 0 1 2 3 11 8 17 3 6 5 3 2 4 17 16 26 Totals . . 36 14 9 59 These facts clearly prove that, under ordinary circumstances, the slug is negatively thigmotactic. In our consideration of the animal's responses to other stimuli, we shall have to take this into account, as causing occasional vagaries, and therefore endeavor to eliminate it as much as possible from the experiments. II. Geotaxis. What determines whether the head end of the slug shall be directed up or down ? Methods. — The same apparatus was used as in the preceding experi- ment. A circular glass plate was employed so that the animal could be rotated into any desired position without the necessity of its being handled. The plate was set in a box at an angle of about 45° with the horizon. In each test the animal was so placed on the plate that the long axis was horizontal, different sides being directed downward in different trials. At first the experimentation consisted mostly of watching the animals in order to obtain some clue for further work. Later, rough sketches of the pigment patterns of the individual animals were made, so that it was possible to identify individuals with certainty ; the same animal could then be subjected to experiments at different times and the difference in results noted. The methods used in working out particular FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 191 questions will appear as these questions are considered. As the same number of experiments were not made on each animal studied, I have, for the sake of comparison, estimated in each case the geotaxis in per cents. This percentage is obtained by dividing the number of positive or negative responses by the total number of reisponses. The nearer the geotaxis percentage approaches 100 the more precise has been the kind of response. No fixed time was allowed to elapse between successive tests, but in'each test the observation was made at an interval of from 30 to 60 seconds after covering the box. Operations and Results. — The first question investigated was whether particular animals exhibited a decisive positive or negative geotaxis. A number of tests were, therefore, made on each of several selected indi- viduals. The results obtained were like those of Davenport and Perkins ('97, p. 108) ; that is, certain animals showed a very marked positive geo- taxis ; others, an equally decided negative tendency ; and a few, perhaps one animal out of 12 or 15 where 10 or more tests were made, were apparently geotactically indifferent. The occasional irregularities in the responses of individual animals were easily seen to be due to influences other than pure gravity, such as jarrings of the plate, influence of contact in putting the animal on the plate, and to the influence of light admitted in lifting the cover of the box. Frequently, upon the raising of the cloth to make an observation, the animal would retract its tentacles, as if dazzled by the sudden inflow of light, and at the next observation it would be seen to have altered its response. Naturally, this question next arose, Is the response the same on different days? In Table IV. (p. 195) are given the results with a num- ber of animals experimented on to test this point. These are numbers 2, 7, 8, 22-25, 27. Number 2 was positively geotactic on two days and negative on another day. A similar variation is seen in the case of slugs 7 and 22. In the case of all the rest, however, there is a very marked constancy. The ninth (last) column in the table indicates the condition of the animals at the time of experimentation. We see from this that on the days of difi^erent response, the animals were in somewhat unlike conditions, which may account for the irregularity of response. The significance of this will be dealt with later. The important matter here is, that the animals, when in the same condition and under the same circumstances, have a fairly constant geotaxis from day to day. One of the most marked cases is that of number 24. This animal was experimented on at different times for a period of three weeks. During this period, it was always active and in good condition, and, as the 192 PROCEEDINGS OF THE AMERICAN ACADEMY. table shows, at all times, exhibited nearly the same percentage nega- tive geotaxis. At the last trial made, it responded irregularly, and so slowly, — at one time not changing its position for thirty minutes, — that I had to give up the attempt to obtain a series. This was often the case with other individuals after a few definite responses. Tests were then made on the geotaxis of the same individuals at different times of the same day. Considering the slug's normal en- vironment, it would not be surprising if, for instance, it should show an upward tendency in the evening and a downward geotaxis in the day- time. Its nocturnal habits and dislike of daylight might give it a dif- ferent geotactic instinct at night from that of the daytime. I insert here a table (in.) giving the results of a few experiments bearing on this point. As the table shows, the response is pretty constant at different TABLE in. Geotaxis of three Individuals at Different Times in the Day. Number of Trials. Animal No. Time of Day. ^ Geotaxis. Condition of Mucus. + 1 8.00 A.M. 5 2 +71.4 Good 1.30 P.M. 6 3 +66.6 Rather Dry 8.30 P.M. 7 4 +63.6 Tail Dry 2 1.30 P.M. 16 1 +94.1 Good 7.00 P.M. 9 18 -66.6 Rather Dry 7.00 P.M. 12 5 +70.5 Fair 10.00 P.M. 6 3 +66.6 Fair 3 7.00 A.M. 3 8 -72.7 Fair 1.30 P.M. 0 5 -100. Fair times of the same day. The one exception is number 2. That it was negative on one evening at 7 p. m., may be explained by the fact that its condition was not good. Moreover, on another evening at the same time the animal had become positively geotactic. From the observations recorded in Tables III. and IV., it is plain that the geotactic response is not due to purely accidental factors, but can FRANDSEN. — REACTIONS OP LIMAX MAXIMUS. 193 be explained only by some marked difference between the individual animals. The first thought is that differences in response are due to a difference in size, and the facts seem to give some support to that ex- planation. Most of the positively geotactic individuals were found among the small and medium-sized animals, and nearly all the negative animals were of large size. ^Moreover, the few indifferent individuals were of medium size. This, however, was not an invariable rule. Small animals were sometimes negatively geotactic and, occasionally, a larjre slug would migrate earthward. A second, clearly important, factor is the condition of the animal's mucus. As shown by the preceding experiments, animals, positively geotactic when normal, became negatively geotactic when lacking in an abundance of sticky slime ; e. g. animal 2, Table III., and animals 2 and 7, Table IV. On the other hand, in one instance (22 b), a nega- tive animal, when extremely sticky, went downwards. Abundant, sticky mucus is evidently connected with a downward migration, and dryness seems to force the animal to take an upward direction. But these facts are not enough to explain all responses. For sometimes two animals of nearly the same size and in equally good condition gave different geotactic responses. We must look for other differences. It will, however, be necessary first to refer briefly to the form and external appearance of the slug. ~-ta.v. Figure 1. Outline of Limax maxiinus. mtl. a., anterior edge of mantle ; mtl. p., posterior edge of mantle; a. to mtl. p., anterior region of body ; 7iitl. p. to p., posterior region ; oc, eye ; ta. d., dorsal tentacle ; ta. v., ventral tentacle ; of. puL, pulmonary orifice. The slug, if we except the respiratory opening on the right side of the body, is externally bilaterally symmetrical. It has no external shell. There are two pairs of tentacles, — a dorsal pair bearing the eyes and a smaller ventral pair. The mantle extends from the neck, ventrally, to near the edge of the foot. Posteriorly, it forms a prominent fold, as indicated in the figure, which may be used to separate the body into an anterior and a posterior region. Observations of the animal VOL. XXXVII. — 13 194 PROCEEDINGS OP THE AMERICAN ACADEMY. reveal that it has very different degrees of control over these two regions of the body. In locomotion, the head end of the body, back as far as the respiratory opening, is freely swung about from side to side and determities the axis of orientation of the animal. Over the posterior region, the animal seems ordinarily to have very imperfect control. The relation between the two regions is crudely that of a span of horses to a chain of wagons which they are pulling. When the horses change direction, the wagons come only slowly around into posi- tion one after the other, and there is likely to be some slipping in the process, especially if it takes place on a down grade. In watching the slug, I saw that the adhesion of the anterior region appeared consider- ably greater than that of the posterior. When the animal gets dry, it does so first at the posterior region. The tip of the tail is the part first to lose its clinging power, and it may curl up dorsally as a result of the drying process. If an animal which is thus beginning to deteriorate in its supply of mucus be put on a glass plate and the plate raised into a vertical position, the slug will move along and desperately cling to the plate with the anterior part of its body. The posterior region will gradually swing downward as a result of the pull of gravity, and, in consequence, the animal's head will eventually be directed upward. From this, we are justified in concluding that the same principle will operate, although to a considerably less degree, in the animal's normal condition. A hasty examination showed that there was a good deal of variation in the proportions of the two regions in different individuals. As a crude and easy way of estimating these proportions, I measured the length in millimeters of the anterior region from the tip of the head to the jjosterior fold of the mantle, and similarly the length of the pos- terior region from that fold to the tip of the tail.* The results from 27 animals thus measured are given in Table IV. The individuals (Table IV.) are arranged in a series, beginning with those in which the two regions are most nearly of the same length and ending with those in which the disproportion is greatest. In animal No. 1, the length of the anterior region is 83.3 per cent (column 8) of the posterior ; that is, the ratio is almost one to one. In No. 25, the anterior region is only 45 per cent as long as the posterior, or less than half its length. The fifth column in the table gives the geotaxis of individuals in per * The measurements were made when the animal was extended and moving aoross the plate. The amount of elongation varies a good deal, but the regions retain pretty closely their relative proportions. FRANDSEN. REACTIONS OF LIMAX MAXIMUS. 195 TABLE IV. Summary of Geotactic Results. 'Sei Animal se No. 01 et iesofOb- rvations Number of Trials. % Geo- taxis. Length of Anterior Region in mm. Length of Ratio of Ant. Posterior j to Post. Re- Region in gion in per mm. cents. Condition of Animal. 1 Ditfer- it Days. + — 1 , , 10 0 +100. 20 24 83.3 Good. 2 a 6 3 + 66.6 18 22 82. Fair. 2 b 5 13 - 72.2 18 22 82, Dry. 2 c 12 5 + 70.5 18 22 82. Good. O . 6 0 +100. 6.5 8 81. Good. 4 . 6 1 + 85.7 17 21 81. Good. 5 . 5 2 + 71.4 24 30 80. Good. 6 . 7 1 + 87.5 11 15 73. Good. 7 a 0 4 -100. 26 40 65. ■? 7 b 9 6 + 60. 26 40 65. Rather dry. 7 c 7 3 + 70. 26 40 65. Slow. 7 d 0 2 -100. 26 40 65. Tail slips. 8 a 12 6 + 66.6 ■2 7 7 Good. 8 b 17 1 + 94.4 7 1 ? Good. 9 . 0 6 -100. 21 33 63.6 Tail slips. 10 . 2 8 - 80. 20 32 62. Mucus watery. 11 . 14 3 + 82.3 21 34 61.8 Good. 12 . 6 0 +100. 27 44 61. Good. 13 a 5 12 - 70.5 17 25 61. Active. 13 b 3 8 - 72.7 17 25 61. Active. 14 ■ 9 3 + 75. 20 33 60.5 Good. 15 1 8 - 88.8 24 40 60. Fair. 16 0 10 -100. 28 50 56. Good. 17 6 14 - 70. 30 55 54.5 Good. 18 8 3 + 72.7 30 56 53.5 Extrem'ly sticky. 19 0 8 -100. 23 43 53.5 Fair. 20 1 5 -83.3 17 32 53. Good. 21 4 12 - 75. 21 40 52.5 Good. 22 a 7 8 - 53.3 41 79 52. Sticky. 22 b 8 5 + 61.5 41 79 52. Very sticky. 2.3 a 5 9 - 64.2 18 36 50. Good. 23 b 6 10 - 62.5 18 36 50. Good. 23 c 0 5 -100. 18 36 50. Good. 23 d 0 4 -100. 18 36 50. Good. 24 a 3 15 - 83.3 27 54 50. Good. • 24 b 3 14 - 82.3 27 54 50. Good. 24 c 2 19 - 90.5 27 54 50. Good. 24 d 4 19 - 82.6 27 54 50. Good. 24 e 3 14 - 82.8 27 54 50. Good. 25 a 7 17 - 70.8 21 44 48.8 Good. 25 b 4 14 - 77.7 21 44 48.8 Good. 25 c 0 12 -100. 21 44 48.8 Dry. 26 , 3 15 - 83.3 7 7 45. Good. 27 a 0 14 -100. 32 71 45. Good. 27 b 1 5 - 83.3 32 71 45. Good, 196 PROCEEDINGS OP THE AMERICAN ACADEMY. cents. The table includes those animals which were fairly active in response but does not give individuals obviously unable to respond because of a lack of slime secretion. The positively geotactic animals, with two exceptions, are all found in the upper half of the table and almost all the negative animals in the lower half. Supposing other conditions the same, we can say that those animals in which the ratio of anterior to posterior regions is as 2 : 3, or greater, will be positively geotactic. Those between the ratios of 2 : 3 and 3 : 5 will be more uncertain in their geotaxis, which will depend largely on the combina- tion of other conditions. Finally, those in which the ratio is less than 3 : 5 will almost invariably be negatively geotactic. The nearer one gets to the extremes, the greater the accuracy of prediction. This pre- diction, it is understood, applies only to animals tested on the glass plate. An examination of the ninth column shows that the few cases of nega- tive geotaxis occurring in the positive half of the table are probably due to a deficiency in the second most important factor affecting the geotaxis ; namely, the condition of the slime secretion of the animal. This secretion may be deficient either (1) in quantity, as in the case of slug 2 b ; or (2) in quality, as was the case with slug 10. Of the two cases of positive geotaxis occurring in the negative half of the table, the first, that of slug 18, is easily explained as due to an extraordinary tenacity of the mucus. Moreover in this, and more markedly in the case of slug 22 b, the slugs were very large and rather slow in their movements. Slug 22 b, instead of moving ahead actively, like most slugs when in good condition, often swung its head toward the earth without any fore- ward movement, and hence did not give the pull of gravity the most favorable opportunity to work on the posterior region of its body. This connects itself with a general observation on all the animals. When active, they are usually very precise and uniform in their responses. If stupid, slow, and averse to movement, — a condition in which the best of them sometimes get, — they will either obstinately refuse to move, or else, keeping the posterior region firmly fixed, will swing the head end toward the earth. Sometimes such a slug will slowly move in a circle, first down then up, and finally curl itself up, like a dog by the fireplace, and apparently go to sleep. This peculiarity may be connected with the food conditions of the animals, as will be shown in a set of experiments to be given later on. The two most important factors in determining the geotaxis of indi- vidual slugs are, therefore : first, the proportion of the anterior (mantle- covered) and posterior (uncovered) regions of the body ; secondly, the FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 197 character of the slime secretion of the animal. If accurate measure- ments were made of the two regions of the body, we might obtain ex- actly the relative weights of these two factors. By means of a spring balance, the effectiveness of the mucus in counteracting gravity could be ascertained with a fair degree of accuracy. A large number of such observations in connection with geotactic tests might, finally, enable us to state precisely what combination of the two factors — weight of regions and strength of mucus — would be necessary to make an animal positively or negatively geotactic. I have made no such calcu- lations, and it would perhaps not be worth the trouble. The suggestion is instructive, however, as indicating the possibilities of predicting, with a certain degree of exactness, a phenomenon which seems at first sight to be entirely haphazard. Perhaps perfect mathematical exactness would, however, never be possible in this case, for, as I shall show a little later, other factors of importance probably enter in to modify the results. However, these too are not out of the reach of precise definition. Certain slugs are negatively geotactic because gravity pulls the pos- terior region of the body down faster than it does the anterior region. Since in all slugs the posterior region somewhat exceeds in length the anterior, we should expect all animals to respond in the same way, pro- vided gravity acted in only a mechanical way. But about the same number of slugs go down as go up. Therefore, there must be some other factor, such as an inherent tendency, impelling these positive slugs to seek the earth. But if so, is it not probable that all slugs have this inherent tendency to move towards the earth, the tendency being obscured in the negative slug by the superior force of the me- chanical difficulties to be overcome ? The fact that positive slugs, when deficient in means of resisting the pull of gravity, — that is, when dry, — assume a negative geotaxis, shows that the inherent tendency is sometimes obscured. If this hypothesis is true, then we ought to be able, by diminishing the force of gravity, or better, by increasing the animal's powers of resisting the disproportionate pull on the posterior region, to make the negative animals become positive. Similarly, if this mechanical difficulty of adhesion is the cause of negative geotaxis, we ought, by increasing it, to be able to compel positive animals to be- come negative. The first end may be attained by substituting for the glass plate a wooden one, which will presumably offer the animal a better chance of adhesion. The second end may be reached by substi- tuting for the glass plate one which has been coated with vaseline or 198 PROCEEDINGS OP THE AMERICAN ACADEMY. a similar substance. Both ends may also be attained, to a certain extent, by increasing or decreasing the angle of inclination of the plate. An examination of the tables given by Davenport and Perkins ('97, p. 103) shows that the largest average number of negative responses occurred when the glass plate was vertical ; that is, when the mechanical diffi- culties were greatest. There is a gradual decrease in this average (and a corresponding increase in the average number of positive re- sponses), as the angles of inclination of the plate with the horizon were diminished from 90° to 60°, 45°, and 30° successively. At the still smaller inclinations of 22^°, 15°, 7°, and 0° (i.e., horizontal), however, there is on the whole an increase in the average number of negative responses, though this is quite irregular. Since the proportion of anterior to posterior region of the animals experimented on is not known, we cannot tell how far this factor may have been the cause of this irregu- larity in the sense of the response. I have made a few experiments by varying for the same individual the angle of inclination of the plate. The animals were all in good condi- tion throughout the experiments. The results — given in Table V. — show a decided increase in negative geotaxis with increase in the angle of inclination. TABLE V. Per Cent of Geotaxis at Different Angles of Inclination of the Support. Animal No. Angle of Inclination. Number of Trials. ^ Geotaxis. Condition of Animal. + — 1 1 2 2 3 3 45° 90° 45° 70° 45° 90° 8 0 ■ 7 8 2 0 2 14 1 3 8 10 + 80. -100. + 87.5 + 72.7 - 80. -100. Good. Good. Good. Good. Good. Good. The most striking case is the complete reversal of geotaxis, seen in the first aninial experimented on. FRANDSEN. REACTIONS OF LIMAX MAXTMUS. 199 Still more conclusive results were obtained by the substitution of wood or vaselined glass surfaces for the clean glass plate. In order to make sure that the animal's power to hold on varied with different surfaces, and to determine approximately the relative strength of the adhesion, Dr. Davenport suggested the use of a delicate spring balance, such as are used in weighing letters. The animal was placed on a horizontal glass plate. When it had oriented itself, and was moving forward, the pan of a letter balance was held against the side of the animal and gradually increased pressure exerted until the animal was made to sli]) along the plate. The maximum reading (in ounces) on the indicator was noted. Then the same animal was placed on a wooden plate and a similar test made under like conditions of movement and activity. The same was done on the vaselined plate. A number of such tests were made on each individual. In order to avoid possible differences in results due to a gradual de- terioration in the condition of the animal, the sequence of the surfaces was varied in the successive sets (three) of trials so that each surface was once employed for the first experiment of a set. This method proved fairly satisfactory and gave in some instances very striking results. TABLE VI. Amount of PniiSSURE required to dislodge the Slug from Different Horizontal Surfaces. Animal No. Wood. Glass. Vaselined Glass. 1 1.8 ounces 1.5 ounces .23 ounces 2 1.25 ounces .67 ounces .34 ounces 3 3.16 ounces 2.16 ounces 1.55 ounces 4 4.33 ounces 2.55 ounces 1.55 ounces 5 3. ounces 1.16 ounces .50 ounces 6 5.7 ounces 3 50 ounces 1.52 ounces The results recorded for each individual are the averages of three trials on each of the surfaces used. The table shows a considerable differ- ence in the degree of adhesion to the different surfaces. In the last four cases the animals were all very large. They were in excellent condition, having just been captured, and secreted a sticky slime in large quantities. 200 PROCEEDINGS OF THE AMERICAN ACADEMY. After being on the vaselined surface, there was a noticeable decrease in the power to hold on to the glass or wood, due probably to the vaseline which still adhered to the animal. Regarding these cases as typical of all slugs, we can say that the wooden surface affords a condition nearly twice as favorable as that of the glass plate for the exhibition of an inter- nal tendency. The vaselined surface, on the contrary, is only about half as fixvorable as the glass plate ; that is, it doubles the obstacles. As a general rule, owing to the irregularities of other iniiuences, the differ- ence between the different surfaces would be, probably, somewhat less. For active, well-conditioned animals, however, we have no hesitation in concluding that the ratios obtained from these cases are fairly rejjresentative. Having thus established the fact that the character of the surface does modify the animal's power to attach itself, I next give a table (VII.) showing the results of a series of experiments on twelve different individ- TABLE VII. Geotaxis of the Slug on Different Surfaces. Animal No. Ratio of Anterior to Posterior Parts iu '^. Plate at Inclination of 45^. ^Vooden Plate. Glass Plate. Vaselined Glass Plate. 1 No. of Trials. % Geotaxis. No. of Trials. Geotaxis. No. of Trials. % Geotaxis. + — + — + — 1 61. 9 8 + 53. 0 5 -100. 0 5 -100. 2 7 5 0 +100. 6 5 + 54.5 0 9 -100. 3 52. 5 0 +100. 1 3 - 75. 0 5 -100. 4 47. 7 0 +100. 1 8 - 88.8 0 slips 0 5 76. 5 2 + 71.4 5 1 + 83.3 1 3 - 75. 6 50. 7 3 + 70. 2 8 - 80. 0 slips 0 7 66.6 9 1 + 90. 1 9 - 90. 0 slips 0 8 83.3 5 0 +100. 10 0 +100. 4 6 - 60. 9 56. 9 1 + 90. 0 10 -100. 0 0 0 10 61. 5 1 + 83.3 5 1 + 83.3 1 5 - 83.3 11 53. 8 0 +100. 1 5 - 83.3 0 slips 0 12 53.5 6 0 +100. 7 2 + 77.7 2 slips 0 FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 201 uals. The geotaxis of each animal was tested on three different sur- faces, — the glass plate, a circular wooden plate, and a glass plate coated with vaseline. Care was taken to have other conditions as nearly as possi- ble the same. Circular plates were employed so that the animal could be rotated into a horizontal position without beiug touched by the hand. In several cases a series was made on an animal using the glass surface ; the animal was then transferred to a wooden plate and the same number of trials made ; the same individual was then put back on the glass plate and as many more tests were made ; finally, it was returned to the wooden plate and an equal number of observations made. The same thing was tried alternating between glass and vaselined surfaces. The second column shows what per cent of the length of the posterior region of the animal's body its anterior region is, as previously defined. A comparison of the columns " % Geotaxis " under the different con- ditions at 'once shows, in nearly every case, a marked difference in the geotactic response with the three kinds of surfaces. The same number of trials was not always made on a given animal under the different con- ditions, so that the comparisons are not always on exactly the same basis. The results, however, prove pretty conclusively that all animals have an inherent tendency to move- toward the earth. On the glass plate, the animals moving upward and downward are about equal in number, the rea-^ons for which we have already given. On the wooden plate, which affords the best of the three surfaces for adhesion, all the animals have become positive. A vaselined surface offers still greater difficulties to positively geotactic responses ; it compels the positively geotactic animals to become negative (Nos. 2,5, 8, 10). Some animals are utterly unable to adjust themselves to this extraordinary condition, especially if not en- dowed with the power of secreting excellent mucus. These animals either vainly cling with the anterior end of the body to the plate, while the poste- rior region slips downward, thus directing the animal up, or they roll off the plate altogether as soon as it is placed in an inclined position. For this reason some of the animals negatively geotactic on the glass plate gave no geotactic response when they were placed on the vaselined surface. These facts, then, conclusively answer in the affirmative our second ques- tion. All slugs have a tendency to move toward the earth. Now the question naturally comes up, Can we not assist this tendency in those animals which are negatively geotactic on a glass surface by bringing some other stimulus — light, for example — to bear upon them ? This slug is negatively phototactic to strong light, as the third part of this investigation will show. By exposing the animals to sti'ong light, can 202 PROCEEDINGS OF THE AMERICAN ACADEMY. we not make the desire for darkness cooperate with the inherent positive geotactic tendency to such an extent that the two together will over- come all mechanical difficulties and cause the animal to move downward ? The following table (VIII.) answers this question in the affirmative. TABLE VI 11. Geotaxis of Slug on Glass Plate at an Angle of 45° influenced (1) by Gravity alone, and (2) by Gravity and Strong Light. Animal No. Size. Gravity alone. Gravity -|- Influence of Strong Light. No. of Trials. % Geotaxis. No. of Trials. ^^ Geotaxis. + — + - 1 2 3 4 5 6 Big Big Big Big Medium Small 0 0 1 0 3 0 17 14 7 5 9 5 -100. -100. - 87.5 -100. - 75. -100. 8 7 2 2 4 0 8 5 2 4 4 5 + 50. + 58.3 ± 50. + 66 6 ± 50. -100. These experiments were carried on in the evening. The animal was first tested on a glass plate at an angle of 45° in the dark, in the ordinary way. Then it was placed on a horizontal glass plate and strong lamp light thrown directly upon it for a few seconds. In most cases it imme- diately gave a negative response to the light. When definitely oriented, the plate was again placed in the box at an angle of 45° and the box covered with a black cloth. Two or three geotactic observations were then taken, and the animal again exposed to strong light. The expo- sure to light was repeated about three times in the course of ten observa- tions. The table shows that the influence of light has been to change a condition of strong negative geotaxis to one of indifference. The only exception is No. 6, which seemed little affected by the light. I hope to make a fuller study of the combined action of light and gravity later. It has been said that all slugs have an innate tendency to move toward the earth. Now, this tendency is probably due to the environment and habits of the animal. The slug, we know, is nocturnal in its habits. In the nighttime, it is actively moving about in search of food. In the day- time, it is inactive and seeks concealment, which is of course accora- FRANDSEN. — REACTIONS OP LIMAX MAXIMUS. 203 plished by moving toward the earth. In hunting for food, it must naturally do some climbing. These facts lead us to expect a possible difference between the geotactic response of the nighttime and that of the daytime. My experiments in this matter, however, gave inconclusive results. But the animals experimented on were not in their normal en- vironment. There was no light and little change in temperature to assist the instinct, if it exists, in divining night from day. Moreover they did not have to seek food, for it was constantly supplied them. Such being the case, the instinct of concealment would be the main environmental influence on the animal, and this impels it toward the earth. These experiments have shown, then, that when the mechanical con- ditions are favorable, most animals exhibit a positive geotaxis. This is as we should expect. There were, however, a few exceptions. A few animals went up when all the factors enumerated seemed to point to the probability of a downward movement, and there were also a few animals which went down when the mechanical difficulties were such as should have impelled them upward. As previously noted, the upward-moving animals sometimes displayed an unusual amount of activity, and the ex- ceptional cases of positive geotaxis in the negative group were those of animals usually slow and stupid. As the effort was constantly made to select only fairly active animals in good condition for producing mucus, there were not many of these exceptions. Knowing the habits of the animal, we may naturally associate its activity with its food condition. The question then comes up, Does the state of the animal's nutrition affect its tendency to move toward the earth ? Does a poorly nourished animal respond to the stimulus of gravity differently from a well-nour- ished individual ? To get an answer to this question, four animals were put into a small box which contained nothing but moist earth. The slugs were kept there for three days, and a series of geotactic tests was then made upon them. Two of the four individuals were inactive, and so un- satisfactory in response that no series was obtained. The other two were rather restless, but precise in response. All the animals were then returned to the box and supplied with fresh cabbage leaves. The next morning another series of geotactic stimuli was given. The rather meagre results given in Table IX. are perhaps not worth very much, since only one individual (No. 1) out of the four resjjonded well in both cases. The ratios given in the second column (Table IX ) indicate that slugs Nos. 1 and 2 belong with those of the positive half of Col. 8, Table IV. I unfortunately neglected to control these experiments by observing the geotaxis before the animals were deprived of food. In 204 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE IX. Comparison of Responses of Individuals when poorly nourished and avhen well nourished. Animal No. Proportionate Ratio of Anterior to Posterior Region. Poorly nourished. Well nourished. No. of Trials. ^ Geotaxis. No. of Trials. 1% Geotaxis. + — + — 1 2 3 70. GO. 56. 3 1 0 9 8 0 -75. -88.8 0 7 4 12 2 1 6 +77.7 +80. +66.6 both instances (Nos. 1 and 2) the animals were rather dry, and they were not noticeably different in this respect after being well fed. No. 2 was less active and less precise in response after it had had plenty of food. I think these experiments too few to warrant laying much stress upon them, but I have given them here because they at least point in the direction of what we might reasonably expect, since the natural desire of the animal to escape from its narrow prison and the impulse to seek food would both tend to make it go up, if given the opportunity. Another element which may alter the slug's inherent geotaxis is probably the state of fear. This element may be combined with the impulse to seek food, as is perhaps the case in the instances just given, or it may operate by itself. Animals which had just been captured were al- ways kept in a small tin box. The captured animals would thrust them- selves between the box and lid, which was not perfectly tight, in their endeavors to escape, and they had to be frequently pushed back. When they were transferred to the large box mentioned at page 187, it was always found that they had all collected in the upper part of the smaller box. This may have been solely for the purpose of getting air, but such animals put on a glass plate were exceedingly active and restless^ and usually exhibited a decided negative geotaxis. I have not made any care- ful set of experiments to find out whether these negatively geotactic animals afterwards became positive. In one instance, I confined over night in a small flower-jar a slug (not a freshly captured one) which had shown a very decided positive geotaxis. In the morning it was found at the top of the jar, and, when placed on a glass plate, showed great activ- ity, as though it sought to escape. In every one of the tests which I then made, it responded negatively. From these few observations, it FRANDSEN. — REACTIONS OP LIMAX MAXIMUS. 205 would seem that fear, by impelling the animal to escape from captivity, may alter its geotatic response. Such freshly captured slugs, moreover, which seem unusually restless and excited, respond more capriciously to the stimulation of light, as some later experiments will show. Summary of Part II. The results of the foregoing experiments warrant the following con- clusions : — 1. On an inclined glass plate ^ all slugs give a geotactic response. 2. Certain slugs give a decided positive, others a markedly negative geotactic response; a few are somewhat indifferent. 3. The geotaxis of animals kept in confinement does not vary much on different days, nor at different times on the same day. 4. The occasional vagaries in the responses of individual animals are' to some extent due to thigmotactic and phototactic influences. 5. The different geotactic response, on a glass ^jlate, of different indi- viduals is due mainly to two factors : (a) The quantity and quality of the slime secreted, which is a very important factor ; (b) the relative pro- portions of the length of the anterior and the posterior regions of the animal's body. All the conditions being the same, it is this factor which " determines whether the head end will be directed up or down." 6. If the ratio of length of anterior to posterior region of body is 2 : 3, or more, and the mucus is of good quality and sufficient quantity, the slug will be positively geotactic. 7. If the ratio is 3 : 5, or less, the animal will usually migrate upward, and the nearer the ratio approaches 1 : 2 the more apt is the slug to respond negatively. 8. In a small number of individuals, in which the ratio lies between 2 : 3 and 3 : 5, the response will depend largely on the condition of the mucus and cooperation of other factors. 9. All slugs have a natural tendency to move towards the earth. This tendency is masked in the animals which are negatively geotactic on a glass plate by the greater pull of gravity on the disproportionately larger and heavier posterior region of the animal. 10. The general downward tendency may vary normally at different times of the day, owing to the animal's habit of remaining in concealment in the daytime and feeding at night. 206 PROCEEDINGS OF THE AMERICAN ACADEMY. III. Phototaxis. The influence of light on the direction of locomotion has heen very generally noticed among organisms, even the mostly widely separated. The swarm spores of many algae, desmids, and other lowly organized plants, are as truly responsive to light stimuli as are crustaceans or verte- brates. According to the character and direction of the stimulating light rays, two kinds of light responses have been distinguished. Photo- taxis is the response with reference to the direction of the rays of light. The organism moves in the path of the ray, either positively (toward) or negatively (away from it). The response to different intensities of light from which the directive force of the rays has been eliminated is known as photopathy. A photopathic animal is one that selects, out of a series of uniformly increasing intensities of light, a limited field of a certain intensity. Some animals, like butterflies and fresh-water Entomostraca, are strikingly positively phototactic to diffuse daylight ; others, such as the earthworm and the leech, are as pronouncedly negative. The kind of re- sponse (positive or negative) may be different in closely allied forms and in different stages of development of the same species. For example, butterflies are attracted by strong sunlight, while moths are repelled by it. The adult house fly is positively phototactic to daylight ; its larva, negatively (Loeb, '90, pp. 69-77, 81-83). The phototactic sense has been shown in some forms to change with different intensities of light. Thus, Famintzin ('67) found that swarm spores positively phototactic to a certain intensity of light became negative to a light of greater intensity. The same phenomenon has been found true of various flagellates, desmids, diatoms, oscillariae, etc. Wilson ('91, p. 414) found that Hydra fusca was attracted by diffuse daylight and repelled by strong sunlight. Finally, the moth's liking- for candlelight and aversion to daylight is well known. The fact that many organisms are photopathic — that is, have a preference for light of a certain intensity — makes it probable, in connection with these observed variations in phototactic responses, that, for most organ- isms, there is an optimum intensity to which they will respond posi- tively. This optimum will vary widely in different species, probably according to the habits and the usual environment of the species. In- habitants of sunny pools or the open air will have an optimum of rela- tively high intensity ; those which dwell in the ground or in shady places FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 207 will have a correspondingly lower optimum. May it not be that every organism will respond positively to a certain range of light intensities and negatively to another range of intensities which is greater ? The nature of the phototaxis may sometimes be gradually changed by organisms becoming acclimated to new conditions. Verworn ('89, pp. 47-49) found that a culture of the diatom Navicula brevis, which ordinarily is negatively phototactic to very weak light, became positively phototactic when reared for several weeks near a window. Groom und Loeb ('90, pp. 166-167) found that young Nauplius larvae of Ealanus which were at first positively phototactic to daylight became negatively phototactic later in the day, probably as the result of the accumulated effects of this exposure. The character of the light responses, as was the case with geotaxis, depends also to a certain extent on other external conditions, such as those of temperature, the states of density and pressure, and various chemical influences. Polygordius larvae, when gradually cooled from 16.5° C. to 6° C, were found by Loeb ('93, pp. 90-96), to change from a negative to a positive phototaxis. Like results were obtained by him from Copepoda. When the temperature was raised from 6° C. to 16° C, the animals again became negative. Increasing the density of sea-water by the addition of sodium chloride produced a change from a negative to a positive response, thus acting like diminished temperature. Engelmann ('82, pp. 391-392) showed the apparent phototactic response of chlor- ophyllaceous ciliates to be really a chemotactic attraction for oxygen, which chlorophyll can produce only in the light. These facts make it important in any study of light response to consider other possible influ- ences, and above all to take account of the strength of the stimuli used. Davenport and Perkins ('97) found that the slug (Limax maximus) responded with marked precision to the varying stimuli of gravity at different angles of inclination of the glass plate. The precision of re- sponse varied correlatively with the force of gravity. In fact, the paral- lelism was almost perfect. The question naturally rises, Is there a similar parallelism between other stimuli and their responses ? A very little experimentation shows that the slug is extremely sensi- tive to light. We have already seen how light may enter in to modify the action of gravity. Casual observation shows that the response is in most cases negative, — the animal moves away from the source of light. Owing to its method of locomotion, the slug is easily experi- mented on. Itmovesslowly and deliberately. In regard to its responses to light, the following questions suggest themselves : (1) Are all indi- viduals negatively phototactic to artificial light ? (2) Does the precision 208 PROCEEDINGS OP THE AMERICAN ACADEMY. of response vary correlatively with the intensity ? (3) Within what limits of intensity is the animal responsive ? (4) Does the kind of response vary at different intensities ? (5) Is there a difference in the sensitiveness to light of the two sides of the animal's body ? (6) In what part, or parts, of the animal's body does the sensitiveness reside? (7) How does the animal move when in the dark and deprived of all stimu- lating influences ? These various problems came up gradually as the work progressed and were considered in turn. Other interesting studies have suggested themselves in the course of the investigation, but there has not been time to go much beyond a consideration of the questions above proposed. The experiments performed were all phototactic ; that is, they were studies of the response of the slug to the direct rays of light. MetJwds. — The methods used were simple. For light, the standard candle and the ordinary small Christmas candle, of a one fourth candle power, were employed. The candle was placed in a box 50 cm. (20 inches) high and having a bottom 12.5 cm. (5 inches) wide and 20 cm. (8 inches) long. It could be raised or lowered to any desired position by means of an adjustable stage inside the box. A circular opening in the middle of one of the broad sides of the box 2 cm. (f inches) in diameter permitted the light to pass out. This opening was covered by a piece of oiled paper, so as to give a well-defined uniform source of light. During the experiment the box was closed by a lid. The intensity of the light was varied by altering the distance between the box and the animal. Additional thicknesses of paraffined paper were also employed when it was desired to greatly diminish the intensity of the light. The animal was put on a circular glass plate which rested horizontally on a support, and the box was raised so that the centre of the light opening was in the same horizontal plane as the body of the animal. The movement of the slug from its original position was measured in degrees in the following manner. A circle of the same size as the glass plate was described on a sheet of thin paper and divided by radii into 72 sectoi's of 5° each. This sheet was pasted to the under side of a second circular glass plate (of the same size as the first), on which also a heavy base line was drawn, corre- sponding with a diameter of the circle. This second plate was so placed that the centre of the source of light was on a line perpendicular to the base line at its middle point. The slug was put on the first glass plate, which could be rotated so as to bring the animal into any desired position with reference to the base line. The experiments were carried on in a dark room provided at one end with a hinged window which could be easily FRANDSEN. REACTIONS OF LIMAX MAXIMUS. 209 and quickly thrown open. The window was covered with a thick, black cloth, so that, when closed, external light was almost completely shut off. Unfortunately, it was impossible, owing to the position and nature of the room used, entirely to equalize all conditions. The temperature was not the same from day to day and varied somewhat in different parts of the room. Generally, it was so hot and close that it was necessary to leave an opening between the sashes, and this of course created a slight draft and produced irregularities of temperature. No account was taken of the varying humidity of the atmosphere, a factor which may have some- what influenced the animal's locomotion. Moreover, as the room was not perfectly light-tight, there were feeble light stimuli in addition to the artificial ones used. However, all these imperfections were but slight, and, since they entered more or less into all the experiments, could not greatly alter the relation between the results, which was the main thing sought in the investigation. Other unestimated possible influences were the nutrition of the animal and such slight thigmotactic stimuli as could not well be avoided. The strength of the different intensities of light used was measured by moving a piece of paper, the centre of which was oiled, between a light of known intensity and the light whose intensity it was desired to know, until the oiled spot on the paper was not distinguishable from the rest of the paper. The distance from this point to each source of light was then measured. Since the intensity varies inversely as the square of the dis- tances, it is an easy matter to calculate the relative strengths. This method is accurate enough for all ordinary purposes. Operations and Results. — In beginning any experiment, the slug, as soon as it had definitely oriented itself, was rotated into such a position that the axis of its body coincided with the base line, and its head was at the centre of the disk. The window was then immediately closed and the time noted. At the expiration of 45 seconds, the window was thrown open and the animal's position instantly noted. The extent of positive or negative migration was at first ascertained by finding the length of the arc stretching from the base line to the radius which was parallel with the axis of the slug's body. Any movement into the half of the circle toward the source of light was called positive ; any movement into the other half, negative. It would occasionally happen that an animal would at first move into the positive half of the circle and then turn away from the light. In this case the axis of orientation made a negative angle with the base line, although the animal itself lay in the positive half of the circle. Later, in the course of the experiments, the positive or VOL. XXXVII. — 14 210 PROCEEDINGS OP THE AMERICAN ACADEMY, negative movement of the animal vras measured by taking the radius which passed midway between the two tentacles, vfiihowi regard to the position of the body axis. A comparison of the two methods showed but little difference in the results. The animals only occasionally made these irregular responses, first in a plus and then a minus direction. As a rule, the migration was unequivocal after the head end had oriented itself to the stimulus. Experiments were made with 18 different intensities of light, each constituting a " series." Six successive observations were made on each individual (3 with the right side exposed ; 3 with the left), and from 8 to 14 animals were employed in each "series." i.e., at each intensity of light, making a total of from 48 to 84 observations at each candle power used. A summary of the results for each of 18 such " series " is given in Table X. The first column gives the number of the series ; the second, the intensities of light. This intensity is expressed in terms of the standard candle power at a distance of one meter. The next column (3) shows the total positive migration of the (8 to 14) animals experimented with. Column 4 similarly gives the total negative migration. Column 5 repre- sents the average arithmetical angular deviation from the original posi- tion due to phototactic stimuli, effected in a period of 45 seconds by all the slugs, without regard to the positive or negative character of the individual phototaxis. This average was obtained by adding together the average phototactic responses (whether plus or minus) of each individual of the series and dividing the result by the number of animals. The average plus or minus phototactic response (algebraic average) for each series (column 6) was obtained by getting the difference between the sums of all the plus and all the minus movements of each series and dividing this difference by the number of tests (observations) made. Column 7 gives the number of positively phototactic animals in each series; column 8, the number of negative animals; column 9, the num- ber of indifferent animals ; and column 10, the total number of individ- uals employed in each series. The sequence of the series is not the same as that of the experiments, but is based on gradually diminishing light intensities. I did not determine the possible influence of the heat of the candle for each of the series, but in one series of experiments in the dark (18J), a candle, covered (to shut out the light) with an opaque paper of the same thickness as the paraffined paper, was left burning at a distance of 30 cm. (intensity .676 C. P.). A casual glance at the table at once answers the first of the questions proposed in the statement of the problems (pp. 207-208). All slugs are FRANDSEN. — REACTIONS OP LIMAX MAXIMUS. 211 not negatively phototactic. At the strongest intensity of light used, two animals exhibited a positive phototaxis, — they moved toward the stinm- TABLE X. Responses of the Slug to Light. 1 2 3 4 5 6 7 8 9 10 No. of Series. Intensity of Light. Total Phototactic Mi- gration in Degrees. Average Response in Degrees in a Period of 45 Minutes. No. of Animals. Arithmet- rical Sum. Algebraic Sum. + — + 2 6 0 0 Total. 1 .076 330 2155 45.5 -38. 8 2 .382 625 2772 40. -25.5 2 12 0 14 3 .169 440 2430 27.5 -25.5 2 11 0 13 4 .042,4 625 1330 26. -11.7 2 8 0 10 5 .010,5 250 1165 17.6 -15. 2 8 0 10 6 .004,7 830 1140 16.1 - 5.1 O 7 0 10 7 .001,69 405 760 9.1 - 6. 3 6 1 10 8 .000,754 695 595 13. + 1.4 7 5 0 12 9 .000,424 1145 895 17. + 3.5 6 4 2 12 10 .000,260 823 345 14.5 + 7.9 7 3 0 10 7a .001,69 365 480 4.6 + 1.7 4 7 0 11 8a .000,754 845 345 11.8 + 8.3 7 3 0 10 9a .000,424 985 130 14.7 +14.2 9 1 0 10 10a .000,260 740 435 11. + 4.2 8 4 0 12 11 .000,022 1395 55 22.3 +22.3 10 0 0 10 12 .000,009,6 630 515 8.6 + 2. 7 3 0 10 13 .000,003,35 865 255 13. +10. 8 2 0 10 14 .000,002,00 800 170 10.5 +10.5 9 0 1 10- 15 .000,001,26 850 415 11.1 + 7.2 7 3 0 10 16 .000,000,185 1375 145 24. +20.5 7 3 0 10 17 .000,000,018,8 445 370 8.9 + 1. 6 4 0 10 18a Darkness. 1440 1290 3.6 + 1.2 10 8 2 20 186 " with candle heat. 475 635 8.7 - 3. 3 6 0 10 212 PROCEEDINGS OF THE AMERICAN ACADEMY. lating light rays. Here, then, arises another problem, similar to the one treated of in the first part of this paper, viz., What determines whether a particular slug shall be positively or negatively phototactic ? In the first series of experiments — in fact throughout this whole set — the animals used were about equally divided between large, small, and medium-sized individuals. The two positive animals in series 1 were both of large size. They were very active. The only peculiarity wherein they seemed to differ from other individuals was in the unusually sticky character of the slime. Whether there is any correlation between this fact and the liking for strong light, I am not prepared to say. It is possible — and certain observations seem to indicate that it is highly probable — that the food conditions of the animals have some influence on their responses to light, as they were shown to have on their responses to gravity. The psychic state of the animal is also to some extent, I think, a factor. Freshly caught slugs when put on a glass jilate some- times acted as if in great fear. They displayed unusual activity and were very erratic in their movements. If forcibly checked or held, they made strenuous efPorts to escape. The great activity of the posi- tive individuals indicates a possible state of fear. One animal in par- ticular seemed highly abnormal. Several times it moved directly toward the circular field of light and even placed its tentacles against the oiled paper which covered the opening. This was the only individual in the whole course of the experiments which exhibited a response like that of moths. No definite set of experiments was planned or carried out in regard to this matter. As we run down column 5, we see that the average arithmetical response varies quite strikingly at the different intensities. The first seven series show a gradual decrease in the average response as the strength of the light is diminished. Although not so regular, there is also a gradual decrease in the degree of negative response on the part of these seven groups of animals, as shown by the average algebraic sums of their responses (column 6). Owing to the constant dying off and deterioration of the stock, it was found impossible to use the same set of animals in all the different series of experiments. Moreover, this was not desirable, for the reason that an animal which is constantly experimented on gradually loses its sensi- tiveness, and thus its responses become untrustworthy. Not knowing the factors which determine the kind of phototaxis, it was of course impossible to make a uniform selection in this respect. We see, how- ever, that the number of negative animals (column 8) is less at the FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 213 weaker intensities than at the stronger. When we come to series 8 of the table, we meet with a uew condition of affairs. Instead of a still further decrease in the amount of deviation, there is a sudden slight in- crease, from 9.1° to 13°, and a reversal in phototaxis for the series from an average response of — 6° to + 1.4°. The number of positive indi- viduals has increased from 3 to 7. It was because of this striking: change that it was thought best to repeat this series and the three suc- ceeding ones on another set of animals. The absolute positive or nega- tive migration was this time taken without regard to the position of the body axis. Sei'ies la, 8a, 9a, and 10a are hence taken at the same intensities as 7, 8, 9, and 10 respectively. These repeated sei'ies indi- cate as strongly as the first set that an intensity of .001,69 C. P. very nearly marks the lower limit of negative phototaxis in the slug. Some- where near a candle power of .000, 75-4, lies an intensity which attracts about as many animals as it rej^els and in about the same degree. That is, the average phototaxis (algebraic sum) is zero. Below this intensity, there is more attraction than repulsion, and hence there is an average in- crease of migration toward the light. The table shows that the average positive response increases to some extent correlatively with the diminution of the light intensity, up to a certain point. This point, according to the results here obtained, is the intensity of .000,022 C. P., where the average movement toward the light, in a period of 45 seconds, was through an angle of 22.3°. As we go below this intensity, there is again a falling off in the strength of the positive response, which dimin- ishes, however, with a good deal of irregularity until absolute darkness is reached. These facts will become more apparent from the study of their graphic portrayal in the curve here given. The continuous line represents the curve as plotted from the results of Table X., column 6 ; the dotted line, the curve of responses as one may assume theoretically it would have been, could all of the conditions other than intensity of light have been equalized. The abscissae here represent the logarithms of the intensities of light + 10. Beginning with darkness on the left end, there is a constant increase of intensity as we move toward the right. The sines of the angles of response are marked off" on the ordinates. Remembering that the left represents a region of weak intensity and the right a region of strong light, that all points above the line x x' are points of positive response and all points below it of negative response, we can understand the significance of the curve. In the region of strong light, the curve lies far below the line X x', but gradually rises toward and finally crosses it, as the light 214 PEOCEEDINGS OF THE AMERICAN ACADEMY. CURVE OF RESPONSES TO LIGHT. ^-* -" ■>. J 1 1 &y -' A s K 1 y / \ 1 \ ■> 4 / y \ \ \ \ \ 9a t \ \ / / V \ o / \ 'V V \ / / \ ' 1 _J \" \m-/ \J^ / v \ V y / / .^15 \ t / 1 ' 1 1 \ \ / \ 1 1 f \ lOa • \ / / \ ' -] 7 a / 17 / , 1 1\ 1 \ 8"l \ 1 3 4 5 ( 5 7 \ 8 ? 10 \ ,-\ "1 7 \ \ I \ \ \ \ \ 4 fy \ \ >/ \ \ / \ \ \ 5 \ \ \ \ \ \ , \ \ \ y \ \ A 2 3v — "T \ 1 1 ^ \ 1 ', 1 \ t 6 *• il . _.. 7 Figure 2. Curve of Responses to Licht. AUc.isme arc lofraritlnms of liglit intensities plus 10 ; ordinates are sines of angles of responses multiplied by 10. FRANDSEN. — REACTIONS OF UMAX MAXIMUS. 215 diminishes in strength. Then there is a gradual increase in positive reaction, which reaches its height in a response of +22.°3 at a .000,022 C. P., and then falls toward the zero line as we approach darkness. There is some irregularity in the negative region, but on the whole the rise is gradual. In the region of positive response, there is a consider- able lack of regularity, especially marked by the interpolation of one series (12) of very low response between the two series of greatest response. These series intermediate between Nos. 11 and 16 represent later experiments than the two series bearing those numbers. Having obtained such a marked positive response at two widely separated in- tensities of light, it was thought desirable to get other intermediate series. Hence, the order of the series as arranged in the table, on the basis of gradually diminishing light intensities, does not, as already stated, represent tlie order in which the series were obtained in my experiments. While the slugs, thus far, had, on the whole, been in good active condi- tion, they were not so in these intermediate series. Although a fresh supply was obtained, all the animals seemed much more stupid and irresponsive than usual. Some of them refused to move, when put on a plate, and many of those that did, responded in a very half-hearted way. The cause of this unusual lack of activity, I could not discover. It may be that a slight change in the food of the animals, which I made at this time, was partly responsible. At any rate, instead of obtaining responses intermediate in amount between those of series 11 and 16 as might have been expected, the results were as have been given. Series 12 was the last one taken. In this, the animals wei'e noticeably more stupid and irresponsive than in any of the preceding experiments. It is very evident from these results, I think, that the precision of response will vary to some slight extent from day to day. The negative responses — those to strong intensities of light — will not be as variable at different times as the positive responses — those to weaker stimuli — as the curve shows. The varying thermal conditions of the room, already mentioned, may have been in part a cause of this irregularity. Furthermore, an animal that has had plenty of food is likely to be stupid and slow in movement and is more apt than a hungry one to seek darkness and concealment. On the other hand, a hungry, active slug will probably ex- hibit positive phototaxis in a most marked and sometimes abnormal degree, as was the case occasionally with the positive animals at the strongest li^-ht intensities. Besides this individual variation, there is, I think, a general variation for all slugs from time to time, for reasons imperfectly knowUj which will find its expression in curves of different heights. 216 PROCEEDINGS OF THE AMERICAN ACADEMY. Thus the less responsive animals of the intermediate but later series mentioned fall into a less prominent curve, as is indicated by the shorter dotted line in the diagram. The curve of positive response approaches, but never actually reaches, the zero line. Even in darkness there is a slight positive migration. This series (No. 18a) represents the average of two series of experiments, one of 54 and the other of 66 deter- minations, each taken at different times during the investigation. This slight positive response — speaking of it as positive with reference to the position of the source of light in the preceding series (17) — may be inde- pendent of conditions of light and due to several causes. As mentioned before, the thermal conditions of the room were not uniform, conse- quently the positive response may have been a response to heat. The movement was away from the window and hence might be ex- plained as a negative response to the repeated inflowing of daylight, when the window was thrown open to make observations. In the last few experiments an opaque screen was put up between the animal and the window. In these cases the average of the responses was slightly negative, so there is some reason to suppose that it was in part the posi- tion of the window in the previous experiment that determined the slight positive migration. The actual phototactic responses to the candle light in the positive half of Table X. would then be the observed responses minus this small positive movement in the dark. The actual negative responses to the strong intensities would be the observed responses plus this increment. In series 18b the box was placed at a distance of 30 cm. (C. P. 0.676) with the light burning, but the opening was cov- ered with a piece of black paper to shut out the influence of the light while leaving that of heat. The small average response of —3.0 may possibly be regarded as a thermotactic one, and, if so, will have to be deducted from the negatively phototactic response to this intensity of light. For intensities less than the 0.676 C. P., the response to the heat would be correspondingly less. We can now answer the second and fourth questions (pp. 207-208) by saying, — that the precision of the phototactic response does, on the whole, vary correlatively with the intensity of the light, and that the kind of phototaxis (positive or negative) is not the same for different intensi- ties of light. The slug gives a negative phototactic response to strong light, a positive one to weak intensities, and is neutral to an intensity somewhere between the extremes. A few individuals were tested successively at different light intensities in order to find out with what precision an individual's phototaxis might vary with a change of intensity. FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 217 TABLE XI. Responses of Individuals to Different Intensities of Light. Animal No. Intensity. Response. Intensity. Response. Intensity. Response. 1 2 3 .382 C. P. .382 C. P. .382 C.P. -36.° -39.° -42.° .169 C. P. .169 C.P. .169 C. P. -34.° -14.5° -31.° .067 C. P. .067 C. P. .067 C. P. -27.°5 -10° -23.° In all these cases, there i? seen to be a gradual diminution in the degree of response as the intensity of light diminishes. Again, from an animal which responded negatively to a certain intensity of light, a positive response could be got by weakening the light sufficiently (Nos. 2 and 3, Table XII.), and a positive animal could be made to give a negative response by using stronger light (No. 1, Table XIL), as the following instances show. TABLE XIL Responses of Individuals to Different Intensities of Light. No. Intensity. Response. Intensity. Response. Intensity. Response. Intensity. Response. 1 ,382 C.P. +41.° Strong Light. -22.° 2 .676 C.P. -15.° .0424 C.P. +35.° 3 .169 C.P. -37.° .0188C.P. - 2.°5 .0067 C.P. -32.° .0047 C.P. +36.° No. 3, Table XIL, shows a less regular response than any of the other animals. From a response of — 37° it drops to one of —2.5°, and, under the influence of a still lower intensity of light, it again rises to a marked negative response of —32.° At a still lower intensity, it gives a striking positive response of +36°. Here, however, we have well illustrated in particular individuals the law laid down for all slugs, — that they are negatively phototactic to strong intensities of light, the precision of re- sponse varying correlatively with the intensity of the stimulus ; that to weak intensities they are positive ; and that to a certain intermediate intensity they are neutral. A glance at the intensity column (Table X.) shows that the slugs are 218 PROCEEDINGS OF THE AMERICAN ACADEMY. responsive to a very wide range of intensities. They would probably continue to respond negatively to still stronger light, until the light became strong enough to kill the animal. They respond positively to a light (series 16) less than one three millionth part as intense as the strongest intensity experimented with. The response to the weakest intensity used (series 17) is less than the positive migration in the dark. Hence we cannot speak of this as a phototactic response. This attenua- tion of light was so weak that I could not be sure I saw it myself, and had constantly to reassure myself by approaching it. The slug is evi- dently sensitive to a very minute degree of light. Where does the slug's sensitiveness reside? The first and most natural answer is, that the eyes are the important organs. The matter was tested on five different individuals. The normal phototactic response was first taken with a .676 candle power. Then the dorsal tentacles, bearing the eyes, were snipped off with scissors and the animal again experimented on. The results are given in Table XIII. TABLE XIII. Effect of Amputation of Tentacles. Animal No. Normal Phototactic Response. Response after Amputation of Dorsal Tentacles. Ventral Tentacles also Amputated. 1 -70.° +41.° 2 -26.0 - 3.° -44.° -29.° +7.° 4 -53.0 +16.° 5 -G5.° + C.° As soon as the operation was performed, the stumps were retracted, as the tentacles are when stimulated by touching, or by strong light. After a moment or two, the animal again rolled out the stumps and began moving forward in perfectly normal fashion, as though nothing had happened. The only observable difference was a perhaps slightly in- creased activity. This table (XIII.) shows a striking effect of the amputation on the phototactic response. In some cases, the animal deviated but very little either positively or negatively from its original position, but kept on moving ahead in a straight line. In other cases, the amputation seemed to cause a change from a strongly negative to a FRANDSEN. — REACTIONS OF UMAX MAXTMUS. 219 more or less positive response. In the case of animal No. 3, removal of the eyes did uot seem to altogether prevent, though it considerably reduced, the negative response. Thereupon, the ventral tentacles were also amputated and the result then was a slight positive response. Since there is probably some shock to the nervous system by the amputation, these results ought to be corroborated by other experiments where the eyes are covered over with some substance to shut off the rays of light. This, I have not yet succeeded in doing satisfactorily. The experiment of removing only one of the ocular tentacles was tried on two different animals with the following interesting results. TABLE XIV. COMPAEISON OF EfFECT OF AMPUTATION OF RiGHT AND LeFT DoRSAL Tentacles. Animal No. Normal Phototactic Response. Response after Amputation of Right Tentacle. Left Tentacle. 1 2 -70.° -55.° -27.° +3.0 In the case where the right tentacle was removed, the animal still responded negatively with considerable precision. Amputation of the left tentacle, in the case of No. 2, on the other hand, resulted in a slight positive phototaxis. While these two cases by themselves have little, if any, significance, taken in connection with facts now to be discussed, they seem to indicate a greater degree of sensitiveness to strong light on the part of the left side of the animal's body than the right. It will be remembered that our thigmotactic experiments pointed to a possible asymmetry in the sensitiveness of the right and left tentacles of the slug. Do we find a similar asymmetry in the responses to light? Table XV, gives the responses of right and left sides respectively for the 18 series. Column 1 gives the number of the series, column 2 the in- tensities of light, columns 3 and 4 the total angular migrations in a positive and negative direction for the series when the right side was exposed to the light, and the fifth column the algebraic average (positive or negative) phototactic response of the right side. Similarly, the next three columns, 6, 7, and 8, give the responses of the left side. Column 9 represents tlie total movement of the series in degrees to the right. This result was obtained by adding the total positive responses of the right side (column 3) 220 PROCEEDINGS OP THE AMERICAN ACADEMY. TABLE XV. Comparison of Responses of Eight and Left Sides to Light. I 1 O 6 1 2 o o 4 5 6 7 8 9 10 11 Intensity of Light. Responses of Right Side in Degrees. Responses of Left Side in Degrees. Total Movement in Degrees to < •3 8 + — Average Photo- taxis + or- + — Average Photo- taxis + or- Right. Left. .676 305 770 -19. 25 1385 -57. 1690 795 2 .382 2-50 1056 -19. 375 1716 -82. 1966 1431 14 3 .169 425 595 - 4.3 15 1835 -46.8 2260 610 13 4 .042,4 255 355 - 3.3 370 975 -20. 1230 725 10 5 .010,5 65 730 -22. 185 435 - 8. 500 915 10 6 .004,7 295 805 -17. 535 335 + 6.7 630 1340 10 7 .001,69 250 500 - 8.3 155 260 - 3.9 510 655 10 8 .000,754 280 330 - 14 415 265 + 4.1 545 745 12 9 .000,424 530 645 - 3. 615 250 -10. 780 1260 12 10 .000,260 435 245 + 6.3 388 100 + 9.6 535 633 10 la .001,69 250 210 + 1.2 115 270 - 5. 520 325 11 8« 000,754 410 165 + 8.1 435 180 + 8.5 590 600 10 9a .000,424 380 75 +10. 605 55 +17. 435 680 10 10a .000,260 560 230 + 9. 180 205 - 0.7 765 410 12 11 .000,022 955 0 +31.7 440 55 +12.7 1010 440 10 12 .000,009,6 160 275 - 3.8 470 240 + 7.6 400 745 10 13 .000,003,35 460 120 +11.7 405 135 + 9. 595 525 10 14 .000,002,0 410 90 +10.7 390 80 +10.3 490 480 10 15 .000,001,26 895 320 + 2.5 455 95 +12. 490 775 10 16 .000,000,185 915 40 +29. 460 105 +12. 1020 500 10 17 .000,000,018,8 210 215 - 0.2 235 155 + 2.6 365 450 10 18a 186 Darkness " with candle heat 1220 155 240 495 +16. -10. 220 820 1050 140 -13.8 + 7. 2270 295 460 815 20 10 Tot als 9570 8506 7808 10321 19891 16314 (( less 18a & 186 8195 7771 7268 9131 17326 15039 FRANDSEN. REACTIONS OP LIMAX MAXIMUS. 221 and the total negative responses of the left side (column 7), — these responses being necessarily right-hand movements. The total movement in degrees to the left (column 10) was likewise obtained by adding the total negative responses of the right side and the positive responses of the left side. Column 1 1 gives the total number of animals used in each series. In the region of negative phototaxis, the total positive and negative angular migrations, and the average negative phototaxis of all the series (1-7, inclusive) when the right and left sides respectively were turned toward the light, were as follows. TABLE XVL Sum of the Responses of Right and Left Sides when Phototaxis IS Negative. Side turned toward Light. Total Angular Migration. Average Negative Phototaxis. + - Right. Left. 1845.° 1660.° 4811.° 6941.° 13.°1 23.°4 This shows on the whole a less sensitive right side, or, to put it differently, a more marked negative phototaxis of the left side. How is it when the animals become positively phototactic? Table XVII. gives the average positive response of the right and left sides for series 8 to 18, including series 7a, 8a, 2a, and 10a. TABLE XVII. Sum of Responses of Right and Left Sides when Phototaxis is Positive. Side turned toward Light. Total Angular Migration. Average Positive Phototaxis. + — Right. Left. 6350.° 5608.° 2960.° 2190.° 7.°68 7.°75 Here an asymmetrical response is less strongly marked. The left side, however, appears on the average to be somewhat more strongly attracted toward the light. The results prove that the asymmetry in response of the right and left sides cannot be wholly due to a tendency to move toward 222 PROCEEDINGS OF THE AMERICAN ACADEMY. the right, for, if this were so, we should expect an average positive response of the right side as much greater than that of the left side, as the average negative response of the left is greater than that of the right side, for both these would mean a greater movement to the right. These facts curiously suggest that the right and left sides are attuned to slightly different intensities of light. Is this possibly due to ancestral habits of life in which environment, acting unequally on the two sides, produced this difference ? The results obtained for the right and left sides from the experiments in darkness (series 18a) are rather puzzling. If the responses are due to some uncontrolled directive stimuli of the kind already suggested, it would seem that the two sides had given opposite responses. As these experiments represent two series taken at different periods, it is the more surprising that they should both show this peculiarity. Again, in the responses to weak candle heat (series 186) the left seems to have been positively, and the right side negatively affected. So far as is known, there was no unequal operation of stimuli on the two sides. Related to this matter is the question, — Is there any tendency on the part of all slugs to move either to the right or to the left? Individuals were noticed which seemed to have a marked tendency to continue moving toward the right, and there were others which seemed to be as strongly biassed toward the left. Not many seemed entirely indifferent. The total movement of all the slugs in the region of negative response (series 1-8, Table XV.) toward the right side was 8786° (col. 9), and to the left 6471° (col 10). In the positive region (series 8-18, Table XV.), the total migration toward the right side was 8540° (col. 9), and to- ward the left 8568° (col. 10). Thus, there seems to have been con- siderably less migration toward the left in the range of negative responses, but only a slightly greater movement toward the left in the region of positive response. In all the 17 series, there was a mi- gration towards the right of 17,326°, and towards the left of 15,039°, That is, there appears on the whole to have been a slightly greater average movement for all slugs toward the right than there has been toward the left. What do we find to be the case with the animals experi- mented on in the dark? Out of the 120 determinations made on 20 animals in the dark (series 18«), the amount of right-hand movement was 2270° and the left-hand movement only 460°. That is, there was nearly five times more migration toward the right than there was toward the left. In series I8b, however, there seems to have been a marked pre- ponderance of movement toward the left. From the foregoing exjieri- FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 223 ment?, it seems pretty clear that there is a difference in the sensitiveness of the right and left sides. There is also some indication of a slightly greater average tendency to move to the right. But a further study of the undirected movements of slugs in the dark is needed. Studies have been made by several observers on the undirected move- ments of a number of different animals, chiefly ants and other insects. In all animals experimented on, there appears to be a tendency to travel in loops or constantly widening spirals. Man, when he loses his way, travels in a circle. Some interesting observations have been made by George and Elizabeth Peckham ('98, pp. 211-219) on the sense of direction in the solitary wasps. When the wasp starts out from its nest, it flies quite around it and gradually circles farther and farther away in a constantly enlarging spiral, sometimes recrossing its path a number of times. The authors' observations show that this action is to enable the wasp to familiarize itself with its surroundings, so that it can find its way home when it so desires. The similar phenomenon observed in other insects, such as ants, is, no doubt, for the same purpose. Davenport ('97, pp. 278-279) in his experiments on Amoebae found that, when their movement was undirected by any external stimulus, they tended to travel in curious spiral loops. Pouchet ('72, pp. 227-228) made obser- vations on the movement of larvae of Musca (Lucilia) caesar in the dark. There is a striking contrast between the paths given by him of the un- directed movements and those made in response to the stimulus of light. The tendency to travel in a gradually widening spiral has also been observed by the writer in young frog and toad larvae — before the develop- ment of mouth and eyes — when they are dislodged from the support to which they are clinging. Most of the following experiments on the slug were made in a room about 12 feet square. The floor was sometimes covered with cardboard or paper, but in other experiments was left bare. Heavy curtains were hung in front of the windows and light shut out as completely as possible. The experiments were conducted at night, and the temperature of the room was nearly, if not quite, constant. A slug was put on the floor in the centre of the room and left to itself for two or three hours, sometimes longer. By means of the mucous secretion, which hardened into white, shiny flakes, the exact path of the animal could, in most cases, be easily followed. This path was roughly reproduced by pencil on paper. A num- ber of these paths are given in Figures 3-22, much reduced from the actual space covered. The series here given includes all the animals experimented on, with the exception of three individuals which did not 224 PROCEEDINGS OP THE AMERICAN ACADEMY. Much reduced copies of the tracks made by slugs (Limax maximus) in the dark. dx., right-handed loops ; s., left-handed loops. FRANDSEN. — REACTIONS OF LIMAX MAXIMUS, 225 give auy characteristic paths. Two of the three moved only a short dis- tance in wavy lines without recrossing their paths, and were in poor condi- tion, for they did not go far, and shortly died. One extremely active little individual moved ahead in a straight line quite across the floor, a distance of eight or ten feet. With these few exceptions, it will be seen that there is a very marked tendency to travel in loops. In general, the loops varied in size from a couple of inches in diameter to two feet and sometimes more. The animal generally makes a circle soon after starting out, and then may travel for some distance before again recrossing its tracks. The individuals which did the most looping also showed a tendency, by gradually swinging away from the starting point, to make larger and larger circles. ISTos. 7, 8, 11, 13, 14, 16, 17, 19, and 22 all showed this tendency. The smaller individuals usually make the smaller loops, but this is not always the case. Although the paths made by different animals have a very different appearance, they all show the same general looping tendency. It will at once be noticed that all curves are not in the same direction. Some are right-handed loops, others are left-handed, and two cases, Nos. 10 and 12, contain loops of both right and left hand character, or at least indicate a tendency to the formation of such loops. As a rule, however, the individual shows a marked con- stancy in the character of the loops made. Disregarding the two cases in which there were both right and left hand loops, we have ten individuals with a tendency to circle to the right and eight individuals with just as marked a tendency to circle to the left. This does not indicate a very great preponderance of individuals travelling to the right. If the total space travelled over by all individuals be considered, I think it might show, on the average, a more marked swerving to the right than does a counting of right and left circling individuals, but I have not measured the distances carefully enough to speak confidently on this point. The evidence thus far accumulated in regard to an asymmetrical response of the right and left sides to artificial stimuli points to a greater sensitive- ness of the left side, which is perhaps correlated with a slight average tendency to move toward the right side more than to the left. Summary of Part III. These studies on the light responses of Limax maximus seem to estab- lish the following points : — (1) The animals are markedly phototactic. (2) There are individual differences in phototaxis, as there are in geotaxis. VOL. XXXVII. — 15 226 PROCEEDINGS OP THE AMERICAN ACADEMY. (3) To strong light, slugs, on the average, give a strong negative response. (4) The degree of response gradually diminishes with the reduction in the strength of the stimulus. (5) There is a certain strength of light which appears neither to repel nor attract the slug. This may be said to be a neutral stimulus. (6) Reduction of the intensity of the light beyond the neutral point changes the phototaxis from negative to positive. (7) The positive response becomes stronger up to a certain degree of intensity. (8) It then gradually diminishes with decreasing intensity until abso- lute darkness accompanied by no response is reached. (9) Slugs are responsive to light stimuli covering a wide range of intensities. (10) The principal organ of response is probably the eye. (11) The response is unsymmetrical on the part of the right and left sides of the animal's body. The right side is not as sensitive to stimuli as is the left. On the whole the right side moves through a slightly greater arc in a period of 45 seconds than does the left. (12) In the dark, other directive stimuli being eliminated, the slug tends to travel in a spiral of gradually increasing radius, though almost invariably producing one or more loops. Some slugs make right-hand loops, others left-hand ones ; there is a slightly greater tendency to right-hand circling. These responses of the slug to touch, gravity, and light-stimuli empha- size tlie fact that it is an animal's normal environmental conditions which chiefly determine its general response to artificial stimuli. The variations in precision and character of this general response are mainly dependent on certain internal factors, such as the food conditions of the animal, its fear of an enemy, and desire to escape captivity. Bibliography. Aderhold, R. '88. Eeitrag zur Kenntnis richtender Krafte bei der Bewegung niederer Or- ganismen. Jena. Zeit. Bd. 22, pp. 310-342. Davenport, C. B. '97. Experimental Morphology. Part T. pp. xiv. -r 280. New York. Davenport, C. B., and Perkins, Helen. '97. A Coiitributiou to the Study of Geotaxis in the Higher Animals. Jour, of Physiol. Vol. 22, pp. 99-110. FRANDSEN. REACTIONS OP LIMAX MAXIMUS. 227 Eugelmanu, T. "W. '82. Ueber Liclit- uud Farbeuperceptiou uiederster Organismea. Arcli. f. ges. Physiol. Bd. 29, pp. 3S7-400. Pamintzin, A. "67. Die Wirkung des Lichtcs uud der Dunkelheit auf die Vertlieiluiig der Cliloropliyllkdrner in den Blattern von Mniura sp. (?) Jalirb. f. wiss. Bot. Bd. 6, pp. 49-54. Groom. T. T., und Loeb, J. "90. Der. Heliotropismus der Nau])lien von Balanus perforatus uud die peri- odischen Tiefenwanderuugen pelagischer Tiere. Biol. Ceutralbl. Bd. 10, pp. 160-177. Jensen, P. '93. Ueber deu Geotropismus uiederer Orgauismen. Arch. f. ges. Pliysiol. Bd. 53, pp. 428-480. Loeb, J. '88. Die Orientieruug der Thiere gegen die Schwerkraft der Erde (Thierischer Geotropismus). Sitzber. phys.-med. Gesell. Wiirzburg. Jahrg. 1888. pp. 5-10. Loeb, J. '90. Der Heliotropismus der Thiere und seiue Uebereinstimmung mit dem Heliotropismus der Pflanzen. 118 pp. Wiirzburg : G. Hertz. Loeb, J. '93. Ueber kiiustliche Umwandluug positiv heliotropischer Tliiere in negativ heliotropische und umgekehrt. Arch. f. ges. Physiol. Bd. 54, pp. 81-107. Massart, J. '91. Recherches sur les orgauismes inferieurs. III. La sensibihte a la gravita- tion. Bull. Acad. roy. Belg., ser. 3, torn. 22, pp. 158-167- Peckham, G. W., and Elizabeth G. '98. On the Instincts and Habits of the Solitary Wasps. Wisconsin Geol. and Nat. Hist. Survey, Bull. No. 2 (Sci. ser., No. 1), 1898, pp. iv. + 245. 14 pis. Pouchet, G. '72. De rinfluence de la lumiere sur les larves de dipteres privees d'organes exterieurs de la vision. Rev. et Mag. de Zool., ser 2, torn. 23, pp. 110-117, 129-138, 183-186, 225-231, 261-264, 312-316, pis. 12-17- Schwarz, F. '84. Der Eiufluss der Schwerkraft auf die Bewegungsrichtung von Chlamido- mouas und Euglena. Ber. deutsch. bot. Gesell. Bd. 2, Heft 2, pp. 51-72. VerTvorn, M. '89. Psycho-physiologische Protisten-studieu. viii. + 218 pp. 6 Taf. Jena : Pischer. Wilson, E. B. "91. The Heliotropism of Hydra. Amer. Nat., Vol. 25, pp. 413-433. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVn. No. 9. — November, 1901. THE ALGAE OF JAMAICA. By Frank Shipley Collins. MARINE BIOLOGICAL LABORATORY. Received ik'^^..//^.^. Accession Nfo. /. 0 ..^./.. Given by L^'^>r>-.^^..<^.<^^ pamphlet is to be removed fpom tbe Iiab" OPQtOPy uaithout the pepmission of the Trustees. THE ALGAE OF JAMAICA. By Frank Shipley Collins. Presented October 9, 1901. Received October 15, 1901. The earliest reference to the algae of Jamaica, and very nearly the earliest reference to the algae of America, appears to be by Sloane ; * in the chapter on submarine plants 43 species are named and described, amono- which, however, are a few aquatic phanerogams, and a considerable number of corals ; of the remainder most are too vaguely described to be now identified, but by the help of the plates, we can give with fair cer- tainty the modern names for four. Vol. I. p. 57, PI. XX. Fig. 2, Corallina opuntioides, ramulis den- sioribus, et Jills magis sinuatis atque corrugatis, is Halimeda Opuntia. P. 58, PI. XX. Fig. 3, Corallina major, nervo crassiore fuciformi, inter- nodia breviora nectente, White Bead Bandstring dicta, is Cymopolia bar- bata. P. 61, PI. XX. Fig. 9, Fucus minimus denticulatus triangularis, is Bryothamnion triangulare. P. 58, PL XX. Fig. 6, Fucus marinus vesi- cidas habens membranis extantibus alatas, is Turbinaria trialata. P. 58, PL XX., Corallina minima capillacea, is probably our present Corallina capillacea, but neither plate nor description is characteristic enough to make this certain. P. 51, PL XVIII., Corallium album pumi- lum nostras, seems to be some species of Lithothamnion. The other de- scriptions are too uncertain to hazard any identifications. A few algae are mentioned by Browne,t apparently mostly copied from Sloane ; some plants undoubtedly belonging to the genus Sargassum are mentioned, and from the description of the great floating masses, S. bacciferum is undoubtedly meant, but it is jjrobable that other species are included under this name. Lunan % gives seven species of algae, as follows, p. 157-158 : * A voyage to the Islands Madera, Barbados, Nieves, S. Cristophers and Jamaica, by Hans Sloane, M.D., London, 1707. t The Civil and Natural History of Jamaica, by Patrick Browne, M.D., 1756. % Hortus Jamaicensis, by John Lunan, 1814. 232 PROCEEDINGS OP THE AMERICAN ACADEMY, Fucus turbinatus = Turbinaria trialata. " natans = Sargassum bacciferum, at least in part. " acinarius. " vesiculosus. " triqueter. Ulva pavonia = Padina sp. " Lactuca. After this date, except for an occasional reference in some general work, we find nothing until Murray's West India list.* In this are in- cluded references to Sloane and Browne, and several species are added from specimens in the British Museum, collected by Chitty ; in a few cases, however, these are species so little to be expected in tropical regions, that it seems as if there must have been some displacement of labels. The total number of Jamaica species mentioned in Murray's list is surprisingly small, if we consider the size of the island, and that it has been so long a comparatively thickly settled English colony. It would be hardly fair to compare it with the Maze & Schramm Guade- loupe list, t for it is not improbable that half the species in the latter, certainly more than half the new species, will ultimately be relegated to synonymy or to the catalogue of indeterminables. As an iust:ince of this, see the genus Gracilaria; 57 species are given by Maze and Schramm under Gracilaria and Plocaria ; 15 of these are species whose previously known distribution would lead one to expect them in Guadeloupe ; of 5, the previous record would make their occurrence here unlikely ; the remaining 37 are new species, with scanty description or none at all. Any one at all familiar with Gracilaria will recognize what this means. But as compared with Puerto Rico, for which Hauck's list t gives 92 species against 31 Jamaica species in Murray's list, the disproportion is so great that it might seem as if there must be some special conditions at Jamaica to impoverish the marine flora. Within the past few years the writer has had the opportunity of ex- amining three collections of algae from this island, that show quite con- clusively that this is not the case, and that there is every reason to * Catalogue of the Marine Algae of the West Indian Region, by George Murray. Journal of Botany, Vol. XXVII. p. 224. 1889. I Algues de la Guadeloupe. 2d Edition. Maze' & Schramm, Basse Terre, 1870-77. t Meeresalgen von Puerto-Rico, von F. Hauck. Engler's Botanische Jahrbiicher, Vol. IX. p. 30, 1888. COLLINS. THE ALGAE OP JAMAICA. 233 suppose that the flora of the islaud is in no way inferior to similar regions. The first collection was made by Mrs. Cora E. Pease of Maiden, Mass., and her sister, Miss Eloise Butler of Minneapolis, Minn. In July, 1891, they collected at Port Antonio and points in its vicinity ; and some collecting was done at other ports, where the steamer touched for a few hours. In 1894 Morant Bay was visited in July, with a visit to Borden and Annotto Bay the first of August, followed by Orange and Hope Bays and Port Antonio, where the greater part of August was spent. In June, 1900, short visits were made to Ora Cabessa, Rio Novo, Runaway Bay, and Rio Bono; June 21 to 27 was spent at Montego Bay; June 29 to July 1 at Kingston ; and the time to July 18 was spent at Manchioneal, Port Morant, Hope Bay, Port Antonio, St. Ann's Bay, and Port Maria, in the order named. The second collection was made by the late Dr. J. E. Humphrey, in March and April, 1893, mostly at or near Kingston, but also near Port Antonio ; a few specimens in Dr. Humphrey's herbarium were collected by R. P. Bigelow at Kingston in July, 1891. In 1897 Dr. Humphrey made a second visit to Jamaica ; on August 1 6 he was attacked by the island fever, and died two days later. Among the collections made that year is a large amount of material of shell boring algae, of which he hoped to make a thorough study on his return ; unfortunately no one has been able to take up this task, and only such notes as Dr. Humphrey made at the time of collecting have been available for this list. The third collection, received when this paper was practically ready for publication, was made near Kingston, May 3, 1901, by Dr. J. E. Duerden, who at that time was collecting corals for the Museum at Kingston. By the kindness of Dr. William Fawcett, Director of the Museum, arrangements were made whereby two lai-ge cans of algae pre- served in formalin were forwarded to the writer. Of the 47 species which were included, six were not represented in the other and larger collections. In the following list the abbreviation P. & B. has been used for the first named collection, H. for the second ; where the specimens had a number in the Humphrey herbarium, the number is given here ; notes on station, depth of water, etc., have been copied; and Dr. Duerden's name is given for the third collection. Of one species, not included in either of these collections, I have received specimens from F. Borgesen, col- lected by O. Hansen. Many Jamaica algae have been distributed in the two sets of exsiccatae. 234 PROCEEDINGS OF THE AMERICAN ACADEMY. Phycotheca Boreali-Americana, issued by Collins, Holden and Setchell, and Phykotheka Universalis, issued by Hauck and Richter : references to these are given under the respective species, with the abbreviations P. B.-A. and P. U., and the numbers. The Humphrey collection includes 25 fresh water algae, the Pease and Butler collection 9 ; only two species are common to both. If we com- pare the marine species * in these two collections, we find that of the whole number, 215, only 72 occur in both; 143 are found in one and not in the other. A natural inference from this would be that the field was by no means exhausted, and that more species might be expected. In Murray's list four species are given, which are omitted here : Gymnogongrus furcellatus, Phyllophora Brodiaei, Liagora viscida, and Plocamium coccineum, the first on the authority of Wright, the others of Chitty. Probably a misplacement of labels has occurred. Tables have been prepared, comparing the marine flora of Jamaica with the floras of New England, Great Britain, the northern coast of Spain, the coast of Morocco, the Canary Islands, and Puerto Rico, lists having been published of these regions of sufficient extent to make a comparison of interest.f Some of these regions having been more thoroughly explored than others, too much importance should not be given to the total number of species in any region ; the relative proportion of the different classes is of more weight, while the number of species common to two regions * In making up tliese statistics, named varieties and forms have been counted the same as species. t Tlie data of tiiese tables are from the following works : — Preliminary List of New England Marine Algae, by F. S. Collins, Ehodora, Vol. II. p. 41, 1000. A Revised List of the British Marine Algae, by E. M. Holmes andE. A. L. Bat- ters, Annals of Botany, Vol. V. p. 63, 1892. Note Preliminaire sur les Algues Marines du Golfe de Gascogne, par C. Sauva- geau, Journal de Botanique, Vol. XL, 1897. Les Algues de P.-K.-A. Schousboe, par E. Bornet, Memoires de la Societe' Na- tionale des Sciences Naturelles de Cherbourg, Vol. XXVIII. p. 165, 1892. Plantes Cellulaires des lies Canaries, par C Montagne, Paris, 1840. Crociera del Corsaro alle Isole Madera e Canarie ; Alghe, per Antonio Piccone, Genova, 1884. Contributions a la Flore Algologique des Canaries, par Mile. A. Vickers, An- nales des Sciences Naturelles, Series 8, Botany, Vol. IV., 1897. Meeresalgen von Puerto-Rico, von F. Hauck, Eugler's Botanische Jahrbiicher, Vol. IX. p. 30, 1888. In addition to the published lists of the Canary Islands, some species have been included from the collection of the author. COLLINS. — THE ALGAE OP JAMAICA. 235 indicates the affinities of the floras. The tables are useful merely as showing general tendencies, not exact relations. Exactness would be possible only when the districts compared had been explored and studied to the same extent, with the same care and under the same conditions, a thing practically impossible. Table No. I. shows the distribution, in the districts named, of each species found in Jamaica ; Table No. II. summarizes by classes the total number of species for each of the seven regions, — it represents less the probable richness of each region, than the extent to which it has been explored. A tolerable test of thoroughness of exploration is often found in the proportion which the Schizophyceae bear to the whole number. Being insignificant, usually microscopic plants, they are quite overlooked by the non-scientific collector. Where the knowledge of a region de- pends on collections made by a non-scientific collector, or by a collector who, however competent in other departments, is not specially an algolo- gist, the red algae constitute a larger, the blue-green a smaller proportion of the whole. The Puerto Rico collection, and in great part the Canary collection, were made by non-algologists ; the Morocco was made by a skilled al- gologist, but before much was known of the lower algae, or microscopes perfected so that they could be suitably studied. The Biscay collection was the work of one man, a trained algologist, studying the plants on the spot ; while the lists for New England and Great Britain cover the most thoroughly studied parts of the world, and the work of generations of botanists. The proportion of Schizophyceae, as shown by Table No. III., follows these conditions fairly well. In the New England list it is ex- ceptionally large, as that list included a number of species, normally fresh water, which were found growing with marine forms, but which usually would not be included in a marine flora. The totals in all parts of the Great Britain list are increased by the fact that in that list the naming of forms is carried out more fully than in any of the others ; the percentage, however, is but little affected by this. It is noticeable that in the first five floras, which might be grouped as warm water floras, the red algae constitute over half the whole list, while in the two northern they are less than half, New England, the most arctic in character though not in latitude, having only 37 per cent. Puerto Rico and Jamaica, the most southern, have the highest percentage of green algae, 27 and 28, respectively, they being in the region of the Siphonaceous plants. The Canaries have less of this element, but more than the region farther north. The low percentage of green algae 236 PROCEEDINGS OF THE AMERICAN ACADEMY. in the Biscay region is noticeable, but not easy to account for. The high percentage of brown algae in New England and Great Britain is due to their northern latitude, these plants becoming increasingly preva- lent as we go from the equator to the poles ; in actual arctic waters they constitute the most conspicuous element of the flora. Table No. IV. shows the number of species common to the flora of Jamaica and the other floras respectively ; No. V. shows the per cent of each class of the Jamaica flora which is found in each of the other floras ; No. VI. the per cent of each of the others found in Jamaica. A thor- oughly explored country shows a larger per cent in No. V., a smaller per cent in No. VI. than a region less known, but certain general deductions can be made. The Puerto Rican flora is closely allied to the Jamaican, 69 percent being common to the latter; further exploration would proba- bly increase rather than reduce this. The Canaries come next, and it is noticeable that the percentage in Table No. V. is nearly the same in green, brown, and red algae. In Table VI., which is perhaps the one best show- ing the relationships, the common elements in the European floras grow regularly less as the distance increases, only 8 per cent of the flora of Great Britain being found in Jamaica. The Schizophyceae seem to vary least in different regions, the other classes coming, Chlorophyceae, Rhodophyceae, Pliaeophyceae, the com- mon per cent of the latter being surprisingly small outside of Puerto Rico and the Canaries. It is worth noting that Jamaica and the Canaries have 66 species in common, being 30 per cent of the former and 24 per cent of the latter ; while New England and Great Britain, at about the same distance, have 258 in common, being 60 per cent for the former, 35 for the latter. This merely illustrates the general rule that beginning almost identical, in the Arctic Ocean, the floras of the two shores of the Atlantic diverge increasingly as we go south. There are, however, a few species common to Jamaica and the Canaries which have not apparently been found on the mainland of either continent ; these probably represent an actual communication between the two. Of the 34 fresh water algae, all but 2 are found in Europe, quite in conformity with the rule that the fresh water algae of the two continents, though separated by salt water, in which they cannot exist, are much more alike than the marine algae, inhabiting the two shores of the Atlantic. COLLINS. THE ALGAE OP JAMAICA. 237 The island of Jamaica is situated in the Caribbean Sea, between lat. 17.40 and 18.30 N. and between long. 76.10 and 78.28 W. from Green- wich. The land vegetation is distinctly tropical in character, though the high land of the interior, and the steady sea breezes of the eastern coast, make the climate more comfortable than might be expected from the latitude. The marine flora is also of a tropical character, as is shown by the number of species of the Dictyotales, and of green algae of the Caulerpaceae, Codiaceae, Valoniaceae, and Dasycladaceae, as also by the absence of any representative of the I/aminariaceae. Coral abounds all along the shore, and the coral reefs are often richly overgrown with algae. The following notes by Mrs. Pease give an idea of the character of the shore and the conditions for collecting algae ; occasionally throughout the list that follows similar notes by Mrs. Pease on special localities or forms will be inserted, enclosed, like this, in quotation marks. " The island of Jamaica is scalloped with beautiful little bays or har- bors, and a description of one will apply to nearly all of them. The semi- circular shores of these bays, about which the little villages cluster, are usually low for only a very short distance back from the water ; then they rise abruptly into steep hills or mountains. From one to several small rivers empty into each of these bays; the shores are often of 'tufa,' a porous rock, very trying to a pedestrian, but sometimes relieved by little stretches of sandy beach. . . . " At Port Antonio, which was visited at each of our trips, the harbor is varied by having a small island lying at its entrance, and by a bold point of land running out to break the shore into two little scallops instead of one, one of the bays being barred by a coral reef, the other having a very narrow channel for the entrance of vessels. This reef was the best collecting ground at this place; the water was shallow for quite a distance, and on jagged rocky bottom, the water about waist deep, we found a very luxuriant growth. Caulerpa clavifera grew like little clusters of green grapes, in big soggy masses ; there were great clumps of the encrusted algae, Halimedas, Amphiroas, Galaxauras, Cymopolias, etc. ; these continued up towards the shore, and with them upon the rocks were those green, warty, potato-ball-like Dictyosphaerias, Padina, Colpomenia sinuosa, and Anadyomene stellata. Still nearer the shore, the water flattened out to nothing, and the bottom was sand, like pow- dered shell. Corallina still grew here, but the others dropped out, and Caulerpa ericifolia and C. plumaris covered the bottom, as club mosses grow in the woods. We searched here in vain for a lonsr time for Peni- 238 PROCEEDINGS OF THE AMERICAN ACADEMY. cillus, and only at our last visit I noticed, in water barely deep enough to cover them, peculiar little mounds in the sand ; brushing off the tops of these revealed the Penicillus capitatus, as abundant as seedling ever- greens in a neglected Maine pasture lot. Not far from here, on a stone wall at the edge of a gentleman's garden, the ribbon Ulva, U. fasciata, streamed out into the water, quite filling it for a distance of about a meter. It grew here, on a very limited area, on each of our visits, but we found it nowhere else on the island. . . . " Morant Bay is larger, and has a comparatively long stretch of sandy beach, but the surf comes in so heavily that seaweeding is very difficult. Annotto Bay is somewhat unusual, the land for some distance from the sea being low and swampy, with sluggish rivers entering the sea by several mouths, but the sandy pebbly shores retained the usual beautiful curve. Montego Bay has a group of small atolls overgrown with man- grove trees, surrounded with shallow water. Kingston has a fine large harbor, enclosed by a long, narrow, sandy arm. On the outside of this, deep water species were often washed ashore. . . . " The conditions under which one must collect algae in the tropics are somewhat different from those for collecting in the North, where we have the rise and fall of the tide at intervals of a few hours, alternately laying bare and covering the algae on the rocks. At Jamaica many weeds grow on rocks so situated as to be alternately bared and covered by the wash of the waves at intervals of a few minutes. Many of the Polysiphouias, Gelidiums, Gracilarias, etc., are generally found under these conditions. Padina and the Galaxauras occur at these stations, but the finest growth of Padina that we saw was at Montego Bay, from a road passing over a bluff, directly on the edge of the sea, down into which one could look and see Padina growing like a field of gray morning- glory blossoms set upon stones in the shallow, rather quiet water. Near by were patches of Zonaria variegata, like red-brown morning glories. " Much of our collecting was done from boats, rowed by two or three strong, experienced boatmen. We would be rowed out to the shallow places overgrown with grass, the water even there being to our waists, then jump from the boat into the water, and fish about for seaweeds. We always wore bathing suits and boys' thick hip rubber boots. On the reefs or by the ledges the waves were often strong enough to take us off our feet. Then we would cling closely together, one holding on to the other, while the latter plunged for the seaweeds. Even then we would sometimes be washed away from our footing. The boatmen would be busy keeping the boat from the rocks, and stood ready to assist us back COLLINS. — THE ALGAE OF JAMAICA. 239 into the boat, often with great difficulty. Most of the Caulerpas were collected in this way, at places some distance from the shore. Even when the plants grew near land, often the shores were so precipitous that one to reach them must use a boat." In the list that follows, the arrangement practically follows that of Die Natilrlichen Pllanzentamilien of Engler and Prantl, but the names of orders, fiirailies, etc., are not given ; these are shown later in Table I., giving the comparison of the marine flora of Jamaica with the floras of other regions ; the few fresh water algae are included in their appropriate positions in the general list, and the fact of their being fresh water plants is noted by a star prefixed to the name. General List. Chrooooccus turgidus (Kuetz.) Naeg. Among various fresh water algae, forming a scum on a small roadside brook at the base of a cliff, near the baths, Bath, July, 1900, P. & B. P. B.-A., No. 751. Among marine algae, near Kingston, Duerdeu. *Gloeocapsa quaternata (Breb.) Kuetz. Roadside, Bath, July, 1900, P. &B. Chroothece Richteriana Hansg. Among other algae, in small quantity, Montego Bay, P. & B. Xenococcus Schousboei Thuret. On Spermothamnion Gorgoneum, Kingston, July, 1900, P. & B. *Oscillatoria anguina Bory. In still water. Roaring River, near St. Ann's Bay, March, 1893, H. O. Corallinae (Kuetz.) Gomont. In a pellicle on coral rock. Port An- tonio, March 27, 1893, II. Among other algae, near Kingston, Duerden. *0. formosa Bory. In still water. Roaring River, near St. Ann's Bay, March, 1893; Castleton, April, 1893, H. *0. princeps Vauch. In mats in stream, St. Ann's Bay, March, 1893, H; Bath, July, 1900, P. & B. *0. princeps forma purpurea n. f. Trichomes and stratum a bright purple, otherwise like type. Forming a stratum on a roadside brook, near the baths, July, laOO, P. & B. P. B.-A., No. 753. *0. proboscidea Gomont. In a pool by "Wag Water," and in stream from reservoir, Castleton, April, 1893, H. *0. tenuis Ag. In company with 0. princeps forma purpurea, Bath, July, 1900, P. & B. *Phormidium Retzii (Ag.) Gomont. In tufts on plants, Rio Cobre, Bog Walk, April, 1893, H. 240 PROCEEDINGS OF THE AMERICAN ACADEMY. Lyngbya aestuarii (Mert.) Liebm. In mats on stones, Kingston, April, 1893, H; Port Antonio, July, 1891, P. & B. Near Kingston, Duerden. L. confervoides forma violacea n. f. lu company with L. ma- juscula, Mancbioneal Bay, July, 1900, P. & B. Differing from the type only in color. L. majuscula Harv. Forming a film on marine algae, Port Antonio, March, 1893, H. Same locality, July, 1891, P. & B. Forming exten- sive tufts on muddy bottom, near the mouth of a small stream, Mancbio- neal Bay, July, 1900, P. & B. *L. putalis Mont. Morant Bay, July, 1900, P. & B. *L. versicolor (Wartm.) Gomont. Marine Garden, Kingston, H. P. B.-A., No. 54. Symploca hydnoides Kuetz. var genuina Gomont. On rocks in shallow water, in small patches, not abundant, Montego Bay and Mancbioneal Bay, 1900, P. & B. S. hydnoides var. fasciculata (Kuetz.) Gomont. With var. genuina, P. & B. *Plectonema Nostocorum Bornet. Among Gloeocapsa quaternata, Bath, July, 1900, P. & B. *P. Wollei Farlow. Morant Bay, Aug., 1894, P. & B. Roaring River, H. P. B.-A., No. 55. *Schizothrix coriacea (Kuetz.) Gomont. In tufts on sides of lily tanks, Botanic Garden, Castleton, April, 1893, H. *S. Mexicana Gomont. On rock in " Wag Water," Castleton, April, 1893, No. 399, H. Microcoleus chthonoplastes (Fl. Dan.) Thuret. In turfs of algae, St. Ann's Bay, March, 1893, H. M. tenerrimus Gomont. In company with M. chthonoplastes, March, 1893, H. *M. vaginatus (Vauch.) Gomont. On moist rock, Rio Cobra, Bog Walk, April, 1893, H. *Nostoc commune Vauch. In crusts on sandy soil. Constant Spring, April, 1893, No. 365, H. *N. microscopicum Carm. On steps into reservoir. Constant Spring, April, 1893, No. 361, H. The specimens are sterile, so that the deter- mination is somewhat in doubt. *N. verrucosum Vauch. On rocks in "Wag Water," Castleton, April, 1893, H. No. 362, H., from trough in running water, Castleton, April, 1893, is probably the same species. *Cylindrospermum muscicola Kuetz. On sides of basin, Constant COLLINS. — THE ALGAE OF JAMAICA. 241 Spring; on sand at edge of river, Castleton, Ai^ril, 1893, No. 364, H. Hormothamnion enteroraorphoides Grunow. In shallow water, St. Ann's Bay; on coral reef, Navy Island, July 25, 1897, H. P. B.-A., No. 56. Near Kingston, Duerden. *Scytonema Arcaiigelii Born. & Flah. On moist rocks by spring, Castleton, April, 1893, H. S. conchophilum Humphrey ms. In old conch shell, Port Antonio, March, 1893, H. Kingston, June, 1897, li; Producing slight, gray, pustular roughenings of outside of shell, Mastigocoleus testarum occur- ring on inside of same shell. Filaments 5-8 fx. diam., irregularly branched, branches single or gemi- nate, tips rounded, cells two thirds to two times as long as broad, 2.7- 4.5 /A diam., pale bluish when separate. Heterocysts globose or slightly elongated, 5 /u, diam., rarely two or three together, intercalary. Sheath rather thin, deep yellow, homogeneous ; when old, rough outside, hyaline and thin at growing tips. J. E. Humphrey. *S. crispum (Ag.) Bornet. On sides of trough, Constant Spring ; in basin, Kingston, April, 1893, H. P. B.-A., No. 60. *S. densum (A. Br.) Bornet. In turfs, moist places, Port Antonio, April, 1893, H. *S. Hofmanni Ag. On steps of Court House, Port Antonio, April, 1893, H. *S. Javanicum (Kuetz.) Bornet. On flower-pot in garden, Castleton, April, 1893, H. *S. ocellatum (Dillw.) Thuret. On old palm stems, Castleton, April, 1893, H. *Hapalosiphon fontinalis (Ag.) Bornet. On rock, "Wag Water," Castleton, April, 1893, H. Mastigocoleus testarum Lagerh. In old shells, Kingston, 1897, H. Calothrix aeruginea (Kuetz.) Thuret. On Dasya arbuscula, Montego Bay, June, 1900, P. &B. C. confervicola (Roth) Ag. On various algae, Port Antonio, March, 1893, H. C. Contarenii (Zan.) Born. & Flah. On wreck on beach. Port Mo- rant, March, 1893, H. *C. fusca (Kuetz.) Born. & Flah. Among Gloeocapsa quaternata, Bath, 1900, P. & B. *C. Juliana (Meneg.) Born. & Flah. On stones in stream, Roaring River, St. Ann's Bay, March, 1893, H, VOL. xxxvn. — 16 242 PROCEEDINGS OF THE AMERICAN ACADEMY. C. pilosa Harv. On Bostrychia tenella, Port Antonio, Aug., 1894, 1^. & B. Dichothrix penicillata Zan. On Cymopolia barbata, Port Maria, H. On Dictyota dicbotoma, P. & B. P. B.-A., No. 62. *Gloeotricbia natans (Hedw.) Rab. Under Nympbaea leaves, Botanic Garden, Castleton, April, 1893, H. *Spirogyra decimina (Muell.) *Kuetz. Mancbioneal, July, 1900, P. & B. Tbe spores agree with this species, and as far as can be judged from dried specimens, the vegetative characters. A sterile Spirogyra from Bath has the same dimensions of cells, but cannot be specifically deter- mined. Ulva fasciata Delile. In dense masses just below water mark, but only in one limited locality, Port Antonio, July, 1891, P. & B. P. B.-A., No. 221. Near Kingston, Duerden. U. Lactuca var. rigida (Ag.) Le Jolis. Port Antonio, Aug., 1894; Kingston, Montego Bay, June, 1900, P. & B. Near Kingston, Duerden. Enteromorpha erecta (Lyng.) J. Ag. Port Antonio, April, 1892, P. & B. E. flexuosa (Wulf.) J. Ag. Port Antonio, July, 1891 ; Runaway Bay, July, 1900; washed ashore, Manchioueal Bay, July, 1900, P. & B. Near Kingston, Duerden. E. intestinalis (L.) Link. Port Antonio, washed ashore, July, 1894, P. & B. E. prolifera (Muell.) J. Ag. Runaway Bay, Montego Bay, Mancbi- oneal, on stones; also in fresh water at Bath, on stones in river, 1900, P. & B. *Stigeoclonium tenue (Ag.) Rab. No. 366, H., locality not given. Diplochaete solitaria n. g. & sp. Frond epiphytic, consisting of a single cell, with thick, transparent wall, and bright green contents, spherical or flattened, the outline as seen from above round or slightly oval ; two hairs arising from each cell, usually opposite, and from points on the under surface quite near the edge. Cell 25-30^ diameter, half this diameter being occupied by the wall ; hairs 4-6(U diameter, slightly tapering, straight. On Laurencia obtusa, near Kingston, Duerden. This minute plant was observed on a specimen of Laurencia, after it had been mounted for the herbarium, so that nothing is known as to its development, but it seems so distinct from any described genus of the Chaetophoraceae as to require a new name. COLLINS. — THE ALGAE OF JAMAICA. 243 Pringsheimia scutata Reinke. On Laurencia obtusa, near Kingston, Duerden. *Mycoidea parasitica Cunningham. On leaves of various plants, Roaring River, March, 1893, Nos. 324 & 325; Bath, 1897, H. P. B.-A., No. 763. Chaetomorpha brachygona Harv. Port Antonio, July, 1891 ; Man- chioneal Bay, Rio Bono, 1900, P. & B. Forming dense mats on bottom of Kingston Harbor, April, 1893, No. 369, H. Near Kingston, Duerden. Hardly distinct from C. cannabina of Europe. C. clavata (Ag.) Kuetz. Washed ashore, Port Antonio, P. & B. St. Ann's Bay, March, 1893, No. 329, H. A rather slender form. C. aerea (Dillw.) Kuetz. "Washed ashore, Port Antonio, Aug., 1894, P. & B. C. Linum (Fl. Dan.) Kuetz. Kingston Harbor, Aug., 1891, R. P. Bigelow. Manchioneal, in company with C. brachygona, Morant Bay, June, 1900, P. & B. The plant from Morant Bay has very moniliform filaments, up to .4 mm. diameter, the cell wall thin, color light green, articulations one to two diameters ; perhaps a distinct species. C. Linum var. brachyarthra Kuetz. Port Antonio, July, 1891, P. & B. C. Melagonium (Web. & Mohr.) Kuetz. ? Growing in mud near the mouth of a river, Manchioneal, July, 1900, P. & B. Quite like the northern form usually known as C. Picquotiana, but possibly not distinct from C. Linum. Cladophora fascicularis Kuetz. Port Antonio, July, 1891 ; Montego Bay, Manchioneal, 1900, P. «fe B. ; Port Antonio, Feb., 1893, No. 179, H. Generally distributed, usually growing on pebbles in mud in shallow water. C. crystallina (Roth) Kuetz. Ora Cabessa, June, 1900, P. & B. C. fuliginosa Kuetz. In turfs, Port Maria, No. 298, H. Morant Bay, Annotto Bay, etc., P. & B. Apparently common everywhere ; usually known as Blodgettia confervoides. C. Hutchinsiae (Dillw.) Kuetz. Port Antonio, July, 1891, P. & B. C- intertexta n. sp. Filaments 200-3o0jU diam., articulations one to three diameters, usually one and one half to two ; sparingly branched, branches naked or with short, usually secund ramuli ; terminal cells blunt, rounded. Tufts densely matted, prostrate. The plant forms dense masses on the bottom of pools, creeping over the coral sand and broken shells ; the upright branches are usually sim- ple, and the plant resembles an entangled mass of some coarse Chaeto- 244 PROCEEDINGS OF THE AMERICAN ACADEMY. morpha rather than a Cladophora, but occasionally the free branches have a series of secund, two or three-celled ramuli, issuing one from each articulation. In the entangled mass more branching of this character will be found, also long normal branches in no definite order. The habit of C. intertexta is much like that of C. repens (J. Ag.) Harv., but the filaments are two or three times as large as in that species, and the color is a light green, somewhat whitish in drying, instead of the dull olive green of C. repens ; the latter has, moreover, a vaguely dichotomous branching, and articulations many times — according to Harvey, even twenty times — the diameter. C. herpestica (Mont.) Kuetz. has fila- ments of about the same size as C. intertexta, but it has long articula- tions, up to fifteen diameters, and irregular branching, with the upper branches fasciculate. Found along the shore near Manchioneal, July, 1900, P. & B. P. B.-A., No. 818. C. trichocoma Kuetz. Manchioneal, July, 1900, P. & B. Gomontia polyrhiza (Lagerb.) Born. & Flah. In old shells, coral and bones, Kingston, 1897, H. Bryopsis Harveyana J. Ag. In tufts on stones, Kingston Harbor, April, 1893, No. 367, H. B. pennata Lamour. In tufts on rocks, Apostles' Battery, Kingston Harbor, April, 1893; Port Maria, March, 1893, No. 297, H. A single specimen. Port Morant, July, 1900, P. & B. Caulerpa cupressoides var. typica Weber. On sandy bottom, Navy Island, Port Antonio, March, 1893, No. 188, H. ; Port Antonio, P. & B. P. B.-A., No. 79. C. cupressoides var. Turneri Weber. Port Antonio, P. & B. P. B.-A., No. 765. C. cupressoides var. mamillosa (Mont.) Weber. Among eel-grass, at about one meter depth, Montego Bay, July, 1900, P. & B. Including forma typica and forma nuda. P. B.-A. No. 765. Near Kingston, Duerden. C. cupressoides var. ericifolia (Turn.) Weber. Port Antonio, July, 1891, P. & B. C. pinnata forma Mexicana (Sond.) Weber. Montego Bay, July, 1900, P. &B. C. plumaris forma longiseta (J. Ag.) Weber. Forming dense mats in mud in shallow water. Port Antonio, July, 1891, P. & B. P. B.-A., No. 27. Near Kingston, Duerden ; very luxuraint, the erect fronds 20 cm. high. COLLINS. — THE ALGAE OF JAMAICA. 245 C. plumaris forma brevipes (J. Ag.) Weber. Port Antonio, July, 1891; Montego Bay, July, 1900, among eel-grass at about one meter depth, P. & B. P. B.-A., No. 7 06. P. U., No. 672. Near King- ston, Duerden. C. prolifera (Forsk.) Lamour. Washed ashore, not common, Port Morant, July, 1900, P. & B. C. racemosa var. clavifera (Turn.) Ag. Port Antonio; Port Morant, at about one meter depth, July, 1900, P. & B. In tufts on rocks, Kingston, April 8, 1893. No. 370, H. P. B.-A., No. 767. C. racemosa var. clavifera forma macrophysa (Kuetz.) Weber. On coral reef, Port Antonio, 1894 & 1900, P. & B. Near Kingston, Duerden, passing insensibly into var. clavifera. P. B.-A., No. 870. C. taxifolia (Vahl) Ag. Washed ashore. Port Morant, July, 1900. Annotto Bay, 1894, P. & B. Chitty. P. B.-A., No. 768. C. verticillata J. Ag. In tufts on coral rocks. Port Antonio, Feb. 27, 1893, No. 181, H. Near Kingston, Duerden. C. verticillata forma charoides (Elarv.) Weber. Kingston, June, 1900, P. & B. Forming fine moss-like mats in soft mud near Man- grove swamp, at depth of about one meter. Near Kingston, Duerden. Peuicillus capitatus Lam. Port Antonio, Montego Bay, Mancliioneal, nearly buried in coral sand, 1900, P. & B. Port Maria, No. 294, H. Sloane. P. B.-A., No. 271. P. U., No. 523. Near Kingston, Duerden. P. dumetosus (Lamour.) Decsne. Annotto Bay, washed ashore, Manchioneal, July, 1900, P. & B. Specimen without locality, H. P. B.-A., No. 769. "■ Penicillus dumetosus grew in some abundance in a pool near Man- chioneal. The pool was narrow, with precipitous tufa walls, which towards the sea closed over the pool in an arch, through which the waves broke heavily. The Penicillus grew among eel-grass, in muddy soil, covered by a coating of powdered shell and coral. With it were P. capitatus, Avrainvillea longicaulis, and Halimedas. The P. dumetosus looked like miniature groves of carefully trimmed evergreen trees, gray green in color." Rhipocephalus Phoenix (Ell. & Sol.) Kuetz. Port Morant, a single specimen washed ashore, July, 1900, P. & B. Avrainvillea longicaulis (Kuetz.) Murray & Boodle. Montego Bay, June, Manchioneal, July, 1900, P. & B. P. B.-A., No. 770. Avrainvillea nigricans Decsne. Singly in shallows, Port Maria, March 17, 1893, No. 270, H. Manchioneal, July, 1900, P. & B. P. B.-A., No. 771. 246 PROCEEDINGS OF THE AMERICAN ACADEMY, " Avrainvillea longicaulis at Montego Bay grew imbedded in mud among eel-grass in shallow water, near a small island consisting of man- grove swamp. It was discovered by the sense of feeling as we were dredging in the mud among the eel-grass roots for Caulerpa. We were continually feeling through the thick soles of our rubber boots a sensa- tion as of stepping on drowned kittens. It proved to be the curious fleshy fronds of Avrainvillea, somewhat resembling a downy, dirty, swollen XJdotea, often full of worms and other small animals. Avrain- villea grew also at Manchioneal, in an enclosed salt water pool, in eel- grass with Penicillus dumetosus, rooted in a clean bottom of powdered shells and coral ; but on the rocks bordering the pool was another species, A. nigricans, with short stems, and tops not so flabellate, resembling in shape our stemmed pufF-balls." Udotea conglutiuata (Sol.) Lamour. Closely set on bottom, Port Maria, March 17, 1893, No. 269, H. U. flabellata Lamour. On sandy bottom, Port Antonio, March 3, 1893, No. 202 ; Port Maria, March 17, 1893, No. 268, H. On muddy bottom, Port Antonio, July, 1894; washed ashore, Moraut Bay, P. & B. Halimeda Opuntia (L.) Lamour. In dense tufts. Port Maria, March, 1893, H. Port Antonio, July, 1891, P. & B. Near Kingston, Duerden. Sloane. Growing similarly to the preceding species. H. tridens (Ell. & Sol.) Lamour. In tufts, St. Ann's Bay, March 23, 1893; Port Maria, March 17, 1893, PL Port Antonio, July, 1891, growing in shallow water, in soil composed of broken shells and coral. Near Kingston, Duerden. It is impossible to distinguish H. incrassata (Ell.) Lamour from H. tridens. In any considerable collection typical forms of each and a series of intermediate forms are to be found. H. Tuna (Ell. & Sol.) Lamour. In dense tufts, shallows, Port An- tonio, March 10, 1893, No. 235, H. Codium adhaerens (Cabr.) Ag. Port Antonio, Aug., 1894, P. & B. Specimen without locality. No. 293, H. C. tomentosum (Huds.) Stack. In immense tufts. Port Maria, March 17, 1893, No. 266, H. Port Antonio, July, 1891 ; Kingston, July, 1900, P. & B. Near Kingston, Duerden. Washed ashore in large quantities, nearly everywhere. P. B.-A., No. 168. Valonia aegagropila Ag. On rocks in shallows, Port Maria, March 20, 1893, No. 296, H. Montego Bay, July, 1900, on rocks in shallow water, P. & B. P. B.-A., No. 772. V. ventricosa J. Ag. On rocks in shallows. Port Antonio, March 11, COLLINS. — THE ALGAE OF JAMAICA. 247 1893 ; Port Maria, March 20, 1893, No. 295, H. On rocks in shallow- rough water, Montego Bay, June, 1900, P. & B. "Fronds smooth and transparent, as if made of thin green glass." V. verticillata Kuetz. On rocks in shallow water, Port Morant, Manchioneal, July, 1900, P. & B. Siphonocladus membranaceus (Ag.) Bornet. Growing in mats on rocks, near shore, Port Antonio, Aug., 1894 ; Runaway Bay, June, 1900, P. & B. Near Kingston, Duerden. S. tropicus (Crouan) J. Ag. "Washed ashore, Morant Bay, July, 1894, P. & B. Dictyosphaeria favulosa (Ag.) Decsne. On rocks in shallows. Port Antonio, March 3, 1893, Nos. 205 & 271, H. On coral reef, Port Antonio, July, 1891, P. & B. P. B.-A., No. 124. Chamaedoris anuulata (Lam.) Mont. Washed ashore, Morant Bay, July, 1894, P. & B. Microdictyon umbilicatum (Velley) Zan. In dense tufts. Port Anto- nio, Feb. 27, 189.3, No. 174, H. Anadyomene stellata (Wulf.) Ag. In tufts on rocks. Port Antonio, Feb. 27, 1893, H. Similar localities, Port Antonio, July, 1891 ; Kings- ton, Port Morant, July, 1900, P. & B. P. B.-A., No. 169. Acetabularia crenulata Lamour. Port Antonio, Annotto Bay, Aug., 1894 ; Rio Novo, June, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 125. " At Annotto Bay Acetabularia and Dasycladus grew in water nearly to our shoulders, not very rough, on cobble stones, the two species grow- ing together like minute forests covering the stones." Dasycladus clavaeformis (Roth) Ag. In tufts on rocks, Port Maria, Apr. 19, 1893, No. 285, H; Annotto Bay, with the preceding species; on pebbles washed ashore, St. Ann's Bay, 1900, P. & B. P. B.-A., No. 170. Botryophora occidentalis (Ilarv.) J. Ag. In salt pools, Palisadoes, Kingston Harbor, April 10, 1893, No. 386, H. Port Antonio, Aug., 1894, P. & B. Neomeris dumetosa Lamour. Kingston Harbor, on mangrove roots, July, 1900, P. & B. "Looking like small green worms." Cymopolia barbata (L.) Lamour. In tufts on stones, St. Ann's Bay and Port Maria, March, 1893, H. On coral reef, Port Antonio, Annotto Bay, 1891 & 1894, washed ashore ; Kingston, Port Morant, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 28. P. U., No. 674. Sloane. 248 PROCEEDINGS OF THE AMERICAN ACADEMY. Many specimens agree with the descriptiou of C. Mexicana J. Ag., but all intermediate forms occur, and often the same individual will agree with one species in one part of the frond, with the other in other parts. E. Mitchellae Harv. ? Kingston, March, 1893, Nos. 141, 142,372, H. Not exactly like the type of this species, the plurilocular sporangia being longer and sometimes clavate. Possibly E. Duchassaingianus Grunow. Striaria attenuata (Ag.) Grev. Montego Bay, June, 1900, washed ashore on sandy beach, P. & B. S. attenuata var. ramosissima (Kuetz.) Hauck. With the type, June, 1900, P. & B. Colpomenia sinuosa (Roth) Derb. & Sol, On coral rocks, Port Anto- nio, March 8 and 23, 1893, Nos. 153 and 212; Port Maria, March 17, 1893, No. 273, H. Anuotto Bay to Port Antonio, in shallow water, Aug., 1894, P. & B. Hydroclathrus cancellatus Bory. On coral rocks, Port Antonio, Feb. 10, 1893, No. 234, H. Cutleria sp. A single specimen, attached to a frond of Udotea flabel- lata, seems to be the Aglaozouia form of some Cutleria, but in the absence of fruit it is indeterminable. The frond consists of radiating articulate filaments, united laterally, and varying much in diameter. Turbinaria trialata Kuetz. Washed ashore, Port Antonio, March 8, 1893, No. 211 ; in tide pools, Port Maria, March 16, 1893, No. 249, H. Washed ashore, Port Antonio, July, 1891 ; Montego Bay, July, 1900, P. & B. P. B.-A., No. 774. T. vulgare, Sloane, is undoubtedly this species. Sargassum bacciferum (Turn.) Ag. Washed ashore. Port Maria, March 18, No. 248, H. Sloane, Chitty. S. lendigerum (L.) Kuetz. Washed ashore, Port Antonio, July, 1891, P. & B. In tufts in tide pools. Port Maria, March 17, 1893, No. 292, H. S. platycarpum Mont. Washed ashore. Port Antonio, July, 1891, P. & B. Same locality, March 8, 1893, No. 210, H. P. B.-A., No. 775. S. vulgare Ag. Washed ashore, Port Maria, March 18, 1893, No. 247, H. The references to Sloane and Chitty are doubtful, and some other form may have been referred to under this name. S. vulgare forma ovata n. f. Washed ashore, Montego Bay, June, 1900, P. & B. P. B.-A., No. 776. Leaves thick, dark, ovate to subor- biculate, coarsely and sharply, sometimes doubly toothed, usually slightly oblique at the base. The branching is dense, the leaves numerous and COLLINS. — THE ALGAE OF JAMAICA. 249 of form and thickness mentioned above ; otherwise it agrees with typical S. vulgare. S. vulgare var. foliosissimum (Lamour.) J. Ag. Washed ashore, Port Antonio, July, 1891, P. & B. Spatoglossum Schroederi (IMert.) J. Ag. Two specimens only, washed ashore on sandy beach with high surf, near lighthouse, Kingston harbor, July, 1900, P. & B. Chitty. Stypopodium lobatum (Ag.) Kuetz. "Washed ashore. Port Maria, March 10 and 19, Nos. 231 and 286; St. Ann's Bay, March 23, 1893, No. 311, H. Annotto Bay, July, 1891 ; Moutego Bay, June, 1900, P. & B. P. B.-A., No. 777. " Stypopodium lobatum grew in magnificent clumps of two sorts, one with the frond narrowly divided and heavily marked with dark bars, mak- ing the plant resemble bunches of turkey feathers ; the other with fronds of broader divisions and not so prominently barred. The first mentioned form grew deeper down in the water, so deep as to have to be pulled off by the boatmen by means of a long handled boat-hook. The two forms were plainly distinguished as they grew in the water." Gymnosorus variegatus (Lamour.) J. Ag. Kingston, Montego Bay, 1900, P. & B. P. B.-A., No. 778. " Gymnosorus variegatus grew with Padina, which it resembled in manner of growth, being in shape like clusters of short-stemmed morning glory flowers. It formed a covering to the rocks nearer shore than the Stypopodium, the water being about knee deep. G. variegatus is reddish brown in color, Padina gray, Sargassum and Turbinaria rich yellow brown ; Dictjota a darker brown with less yellow ; Stypopodium gen- erally grayish brown with dark markings. The conti'asting colors were very rich in the water." Padina Durvillaei Bory. On rocks, Port Antonio, Feb. 28, 1893, No. 173, H. Port Antonio, July, 1891 ; Ora Cabessa, Montego Bay, 1900, P. & B. Near Kingston, Duerden. The P. Pavonia of Murray and earlier lists is probably this species. Dictyopteris delicatula Lamour. In tufts on rocks. Port Maria, March 19, 1893, H. Washed ashore, Annotto Bay, Aug., 1894; Hope Bay, Kingston, 1900, P. & B. P. B.-A., No. 485. D. Justii Lamour. Washed ashore, Port Antonio, July, 1891 ; Morant Bay, Annotto Bay, Aug., 1894; Kingston, 1900, P. & B. In tufts on rocks, Port Maria, March 17, 1893, No. 264, H. Chitty. D. plagiogramma Mont. Annotto Bay, July, 1894, washed ashore, P. & B. Chitty. 250 PROCEEDINGS OF THE AMERICAN ACADEMY. Dictyota Bartayresiana Lamour. Washed ashore in mats, Port Anto- nio, March, 1893, Nos. 154, 194, 229, H. Port Antonio, July, 1891 ; on rocks in shallow water, Kingston, Montego Bay, Manchioneal, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 579. Found in both broad and narrow forms, at nearly all the localities, often appearing like two distinct species. D. cervicornis Kuetz. Washed ashore, Port Antonio, Aug., 1894, P. & B. Near Kingston, Duerden. D. ciliata Ag. In tufts on rocks. Port Maria, March 16, 1893, Nos. 246 and 287; Port Antonio, March 10, 1893, No. 230, H. Washed ashore, Montego Bay, Ora Cabessa, Manchioneal, 1900, P. & B. P. B.-A., No. 779. All three kinds of fruit are represented in the specimens dis- tributed in the Phycotheca Boreali- Americana, the plants being collected at the same time. All are similarly arranged, occupying the whole of the fertile segments, except a narrow strip at the margin. The male plants are mostly old and battered, as if the antheridia were produced somewhat earlier in the season than the other kinds of fruit. " Dictyota ciliata at Montego Bay, June 23, 1900, grew on boulders near a precipitous rocky shore in water more than waist deep. It formed large round clumps. The water being very clear here, the hairs on the edge of the frond were so conspicuous as to easily distinguish in the water this form from other Dictyotas. The rocks in this locality were beauti- fully draped with the Dictyota, robust plants of Turbinaria in large thick masses, a Sargassum with rounded leaves, and Stypopodium in magnifi- cent clumps." D. dentata Lamour. Washed ashore, Port Maria, March 17, 1893, No. 265, H. Port Antonio, July, 1891, P. & B. On rocks in rough water, one meter or more deep. P. U., No. 669. Some specimens have the tips of the branches so finely divided as to seem ciliate. D. dichotoma (Huds. ) Lamour. Kingston Harbor, July, 1891, R. P. Bigelow. On rocks, Port Antonio, July, 1891 ; Montego Bay, June, 1900, P. & B. Chitty. D. divaricata Lamour. In various places, 1900, P. & B. Near Kings- ton, Duerden. Connected by intermediate forms with D. Bartayresiana. D. fasciola (Roth) Lamour. Washed ashore, Port Antonio, July, 1891 ; Rio Novo, June, 1900, P. & B. Dilophus alternans J. Ag. Port Antonio, July, 1894, P. & B. D. Guineensis (Kuetz.) J. Ag. On flat rocks washed by the waves, in company with Gelidium rigidum, Montego Bay, Rio Novo, June, 1900, P. & B. COLLINS. — THE ALGAE OF JAMAICA. 251 Dictyerpa Jamaicensis n. g. & sp. Frond filiform, 1-3 mm. diam. up to 2 dm. long ; consisting of two layers of cells, an inner layer of large, colorless, cylindrical cells, about three diameters long, symmetrically arranged : an external monostromatic laver of brown rectangular cells from one to three diameters long, in distinct longitudinal series. Branch- ing di- or trichotoaious, with occasional irregularly placed lateral branches, mostly at wide angles, each branch ending in a large, depressed-hemi- spherical cell, by whose division the growth of the branch proceeds. Tufts of very fine, rust-colored or colorless confervoid rhizoidal filaments at irregular intervals on the frond. Fructification ? Washed ashore, Manchioneal, July, 1900. P. B.-A., No. 780. Though evidently belonging to the Dictyotaceae, this plant differs from any genus of the family yet described, in having the frond terete throughout. Many Dictyotaceae have prostrate rooting filaments from which the erect fronds arise, but in all species found in Jamaica this pros- trate growth is quite insignificant in comparison with the plant in ques- tion. It was found washed ashore in two places, in considerable quantity, and in no case shows any indication of fructification, or of producing erect flattened fronds. It may seem hazardous to give it a generic name, but as it is a plant of quite distinct habit, and cannot be now identified with any named form, it seems to require at least a provisional name. As washed up on the beach, it appeared like rolled and twisted strings. The dried plant is quite black in color, and under a hand lens shows closely set constrictions, probably due to the large interior cells being of uniform length, and terminating at the same level, as in the frond of Polysiphonia. These constrictions are lost when the frond is remoistened. Goniotrichum Humphreyi Collins. On woodwork of wreck, St. Ann's Bay, March 2i, 1893, No. 316, H. P. B.-A, No. 421. " Frond filamentous, solid, gelatinous, occasionally forking or dividing into several branches, the terminal portion consisting of a single sei'ies of cells ; the older part containing numerous cells, irregularly placed near the surface of the filament; lateral branches abundant, simple, issuing nearly at a right angle, composed of a single series of cells." Tliis de- scription is copied from the label of P. B.-A., No. 421. G. elegans (Chauv.) Le Jolis. Among other algae, on Laurencia obtusa, near Kingston, Duerden. Chantransia Saviana (Menegh.) Ardiss. Among other algae, on Laurencia obtusa, near Kingston, Duerden. Liagora Cheyneana Harv. Washed ashore. Port Maria, March 17, 1893, No. 281 ; Port Antonio, March, 1893. No. 186, H. 252 PROCEEDINGS OF THE AMERICAN ACADEMY. L. decussata Mont. Washed ashore, Hope Bay, July, 1891, and Aug., 1894, P. & B. Very abundant in 1894. P. B.-A., No. 89. The finest species of the genus, with fronds in shape of a fir tree, sometimes over a meter in length. Apparently confined to the islands on the two sides of the Atlantic. L. elongata Zan. Hope Bay, July, 1891 ; Montego Bay, July, 1900, P. & B. L. pulverulenta Ag. Washed ashore, Manchioneal, July, 1900, P. & B. L. valida Harv. In large tufts, Port Maria, March 17, 1893, No. 283; Port Antonio, March 10, 1893, No. 240, H. Hope Bay, Orange Bay, Montego Bay, 1891 and 1900, P. & B. Under No. 687, P. B.-A., a form was distributed as L. tenuis, which it now seems better to regard as L. valida. It is difficult to see how the two species can be distin- guished, when one has a large number of specimens. Harvey's name, being the older, must be maintained. Galaxaura cylindrica (Sol.) Decsne. Port Antonio, Morant Bay Manchioneal and elsewhere, common, P. & B. Near Kingston, Duerden. Sloane. Chitty. P. B.-A., No. 134. G. lapidescens (Sol.) Lamour. In large tufts, Port Antonio, March 10, 1893, No. 239, H. Annotto Bay, Port Antonio, July, 1891 ; Mon- tego Bay, on rocks, June, 1900, P. & B. Chitty. Not so common as other species of the genus. G. marginata (Ell. & Sol.) Lamour. On stones at tide-mark. Port An- tonio, March 10, No. 145 ; March 21, No. 241, H. Port Antonio, An- notto Bay, Montego Bay, Manchioneal, 1900, P. & B. Common, growing very densely on rocks. G. obtusata (Ell. & Sol.) Lamour. Port Antonio, July, 1891 ; Port Maria, July, 1900, P. & B., in company with other species of the genus. G. rugosa (Sol.) Lamour. In large tufts. Port Antonio, March, 1893, No. 131, H. Port Antonio, July, 1891 ; Rio Novo, Rio Bono, Montego Bay, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 133. P. U., No. 510. Sloane. Usually washed ashore on beaches. Wrangelia Argus Mont. Montego Bay, June, 1900, forming soft mats on rocks, P. & B. Specimen without locality, H. Gelidium coerulescens Crouan. Port Antonio, July, 1891 ; July, 1900, P. & B. P. B.-A., No. 783. By the kindness of Dr. Bornet this plant has been compared with authentic specimens from Guadeloupe, and it is the plant referred to by Maze & Schramm, Algues de Guadeloupe, p. 199. Whether it is the COLLINS. — THE ALGAE OF JAMAICA. 253 plant of Kuetzing, Tab. Phyc, Vol. XVIII. PL 56, from New Caledo- nia, is not certain, G. crinale (Turn.) J. Ag. Port Antonio, July, 1900, with G. coeru- lescens, P. & B. G. rigidum (Vahl) Ag. Port Antonio, July, 1891; Montego Bay, June, 1900, P. & B. P. B.-A., No. 784. Appears to be the form known as var. radicans (Bory) J. Ag. G. supradeconapositum Kuetz. Morant Bay, July, 1894, P. & B. No. 227, no locality, H. The identification of this form is from a specimen from Fajardo, Puerto Rico, received from Hauck. If G. crinale were taken in a broad sense, it might include this form. Catenella Opuntia var. pinnata (Harv.) J. Ag. Manchioneal, July, 1900, P. & B. Forming a thin greenish coating on small stones iu shal- low water, on muddy bottom near the mouth of a small river. P. B.-A., No. 792. Agardhiella tenera (J. Ag.) Schmitz. Morant Bay, July, 1894; Mon- tego°Bay, June, 1900, P. & B. Solieria chordalis (Ag.) J. Ag. "Washed ashore, Port Antonio, July, 1891. P. & B. Eucheuma echinocarpum Aresch. Montego Bay, a few small plants, June, 1900, P. & B. Gracilaria Blodgettii Harv. "Washed ashore, Montego Bay, June, 1900, P. tSt B. ; only a few specimens, some of which show a tendency to pass into G. confervoides. G. caudata J. Ag. Port Antonio, Aug., 1894, P. & B. G. cervicornis (Kuetz.) J. Ag. "Washed ashore, Morant Bay, July, 1894; Manchioneal, July, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 787. Some of tlie plants are quite like Mediterranean specimens of G. armata. The Florida plant described as G. armata by Harvey in the Nereis Boreali-Americana seems to be different, and has not been found in Jamaica. G. compressa (Ag.) Grev. Annotto Bay, Aug., 1894, P. & B. G. confervoides (L.) Grev. On small stones, St. Ann's Bay, March 23, 1893, No. 312, H. "Washed ashore, Borden, July, 1894; Montego Bay, Manchioneal, 1900, P. & B. Near Kingston, Duerden. Common and variable. G. cornea J. Ag. "Washed ashore, Rio Bono, June, 1900, P. & B. G. Curtissiae J. Ag. "Washed ashore, Annotto Bay, Aug.. 1894, P. & B. 254 PROCEEDINGS OF THE AMERICAN ACADEMY. G. damaecoruis J. Ag. Annotto Bay, Aug., 1894; Mauchioueal, July, 1900, P. & B. P. B.-A., No. 788. G. divaricata Harv. In short tufts, Navy Island, Port Antonio, March, 1893, Nos. 155 and 228, H. Port Antonio, July, 1891 ; Port Morant, Rio Bono, June, 1900, P. & B. P. B.-A., No. 789. Generally dis- tributed but nowhere common. G. Domingensis Sond. Mauchioneal, June, 1900, P. & B. Found only in a very limited station, in large tufts on rocks about one meter depth, in rough water; very luxuriant plants, showing beautiful shades of violet. By J. G. Agardh this is considered as merely a form of G. multipartita var. polycarpa. Imperfectly developed specimens have some resemblance to that variety, but well developed plants are quite different; the habit reminds one rather of Laurencia pinnatifida. All three kinds of fruit were found in the Manchioneal specimens, the cystocarps and tetraspores as usual in this genus, the antheridia in crypts, as described by Thuret for G. confervoides. The description of G. Krugiana in Hauck's Puerto Rico list is quite suggestive of some of these specimens. G. ferox J. Ag. Washed ashore, Morant Bay, Julj^, 1894, P. & B. G. multipartita (Clem.) J. Ag. Port Antonio, July, 1891 ; Port Mo- rant. Montego Bay, Ora Cabessa, Manchioneal, 1900, P. & B. No. 380, no locality, H. Near Kingston, Duerden. Chitty. P. B.-A., No. 885. G. Wrightii (Turn.) J. Ag. Annotto Bay, Aug., 1894; Montego Bay, June, 1900, P. & B. A few plants only. The fresh frond is very stout and densely branched, and not at all compressed ; it shrinks much in drying, and herbarium specimens give the idea of a flattened frond. Hypnea divaricata Grev. In large tufts on rocks in shallow water, Montego Bay, Manchioneal, 1900, P. & B. H. musciformis (Wulf.) Laraour. On stones at tide mark, Port An- tonio, March, 1893, Nos. 147 and 223 ; St. Ann's Bay, March 24, 1893, No. 320, H. Near Kingston, Duerden. Common everywhere, P. & B. Chitty. H. Valentiae (Turn.) Mont. Annotto Bay, Aug., 1894, P. & B. The species is here taken in the same sense as by Hauck, Hedwigia, 1887, Heft 1, to include H. nidifica J. Ag. and H. fruticulosa Kuetz. ; forms corresponding to both of these occur at Annotto Bay. Cordylecladia irregularis Harv. Annotto Bay, Aug., 1894, P. & B. Near Kingston, Duerden. COLLINS, — THE ALGAE OP JAMAICA. 255 Some of the plants from each locality have tetraspores, which appear not to have been previously reported. They are arranged much as in C. erecta, except that they are at the ends of short lateral branches, instead of terminal on the larger branches ; the modified portions of the branches being ovate or subspherical rather than lanceolate. One of the Kingston specimens has cystocarps, which are spherical and external on the branches, as in other species of the genus. Cordylecladia Peasiae n. sp. Fronds slender, filiform, arising from a more or less distinct crustaceous base, dichotomously divided, with oc- casional scattered or secund ramuli, usually quite short. Tetraspores cruciate, in the somewhat swollen and darkened tips of the branches and ramuli, immersed in the cortical layer. Cystocarps globular, sessile along the main branches. Color purplish brown, changing into whitish or greenish ; substance rigid. Somewhat resembles C. erecta, which is, however, a smaller plant, much less branched, and having the receptacles for tetraspores larger and of different shape. C. conferta and C. Andersoniana have the tetra- spores in densely tufted special lateral branches. C. irregularis is stouter, with hollow stems and with oval or subspherical lateral branches for the tetraspores. In C. furcellata the tetraspores are borne in branches resem- bling the vesicles of Chrysymenia uvaria. C. heteroclada has a flat frond, and C. Huntii is unrecognizable from the description of Harvey. Manchioneal, July, 1900, P. & B. P. B.-A., No. 791. Chrysymenia halymenioides Harv. Washed ashore, Morant Bay, July, isk, P. & B. Champia parvula (Ag.) Harv. Moutego Bay, Port Maria, 1900, P. & B. Caloglossa Leprieurii (Mont.) J. Ag. Among Bostrychia, just above water level. Port Antonio, July, 1900, P. & B. Asparagopsis Delilei (Ag.) Lamour. In tree-like tufts, Navy Island, March 10, 1893, H. Laurencia cervicornis Harv. Annotto Bay, Aug., 1894 ; washed ashore, Kingston, July, 1900, P. & B. L. implicata J. Ag. Morant Bay, July, 1900, P. & B. L. obtusa (Huds.) Lamour. In tufts on rocks. Kingston Harbor, Apr. 8, 1893, No. 376 ; no locality. No. 224, H. Port Antonio, July, 1891 ; on rocks, Montego Bay, June, 1900, P. & B. Near Kingston, Duerden. Chitty, L. papillosa (Forsk.) Grev, In tufts on rocks, Kingston Harbor, Apr. 8, 1893, H. Port Antonio, Kingston, Montego Bay, Manchioneal, Port 256 PROCEEDINGS OF THE AMERICAN ACADEMY. Maria, P. & B. Near Kingston, Duerden. Closely covering ledges in rather shallow water, also washed ashore. Chitty. L. perforata Mont. Densely carpeting rocks in shallow water, Mon- tego Bay, July, 1900, P. & B. P. B.-A., No. 794. L. tuberculosa var. gemmifera (Harv. ) J. Ag. Washed ashore. Mo- rant Bay, Annotto Bay, 1894 ; Ora Cabessa, July, 1900, P. & B. Choudria Baileyana Harv. Hope Bay, July, 1900, P. & B. No. 336, no locality, H. C. dasyphylla (Woodw.) Ag. Washed ashore, Port Antonio, July, 1891 ; Montego Bay, June, 1900, P. & B. C. tenuissima (Good. & Woodw.) Ag. Washed ashore, on sandy beach, Montego Bay, June, 1900, P. & B. Acanthophora Thierii Lamour. Common on rocks in Kingston Har- bor, Port Maria, Nos. 176, 195, 278, 377, H. Port Antonio, July, 1891, P. & B. Near Kingston, Duerden. Digenea simplex (Wulf.) Ag. In tufts on rocks. Port Maria, March 16, 1893, No. "252 ; on stones in shallows, St. Ann's Bay, March 30, 1893, No. 334, H. Washed ashore, Orange Bay, 1894; Manchioneal, July, 1900, P. & B. Near Kingston, Duerden. Polysiphonia cuspidata J. Ag. In tufts on piles at beach, Port Maria, March 16, 1893, No. 251 ; on stones in shallow water, St. Ann's Bay, March 30, 1893, No. 335, H. Port Antonio, Aug., 1894, covering rocks in shallow water; Manchioneal, Port Morant, 1900, P. & B. P. ferulacea Suhr. In dense tufts on rocks and eel-grass, Rio Novo, June, 1900, P. & B. Near Kingston, Duerden, a slender, long-jointed form. P. Havanensis Mont. On mangrove roots, Port Antonio, March 8, 1893, No. 214; on other algae, Kingston Harbor, Apr. 8, 1893, Nos. 374b, 375, H. Washed ashore, Montego Bay, Port Antonio, 1900, P. & B. Near Kingston, Duerden. P. Havanensis var. Binneyi (Harv.) J. Ag. Port Antonio, July, 1891, P. &B. P. Pecten- Veneris Harv. On other Florideae, Port Maria, March 17, 1893, No. 276, H. P. secunda (Ag.) Zan. On other algae, Kingston Harbor, Apr. 8, 1893, No. 374, H. Washed ashore, Borden, Morant Bay, 1894, P. &B. P. subulata (Duel.) J. Ag. Washed ashore, Montego Bay, June, 1900, P. & B. Only two specimens collected of this species, which has not before COLLINS. — THE ALGAE OF JAMAICA. 257 been reported from America. These agree well with specimens from the Mediterranean. The range of this species, as previously known, has been from the English Channel to Spain, the northern shore of the Mediterranean and the Adriatic. Lo{)hosiphonia obscura (Ag.) Falk. Covering stones in shallow water, Manchioneal, July, 1900, P. & B. Bryothamnion triangulare (Gmel.) Kuetz. In great tufts in pools, Port Maria, March IG, 1893, Nos. 254 and 277, H. Washed ashore, Annotto Bay, Aug., 1894; Ora Cabessa, June, 1900, P. & B. Chitty. P. B.-A., No. 95. B. Seaforthii (Turn.) Kuetz. Washed ashore, Port Antonio, July, 1891 ; Kingston, July, 1900, P. & B. Bostrychia tenella (Vahl) J. Ag. Port Antonio, on rocks reached only by spray, July, 1891, and 1894 ; Manchioneal, similar locality, July, 1900, P. & B. P. B.-A., No. 796. B. Mazei Crouan. In dense tufts on rock, Port Antonio, Feb. 23, 1893, No. 158, H. B. Moritziana var. intermedia J. Ag. On rocks, shore of island. Port Antonio, Aug., 1894, P. & B. " The Bostrychias grew upon rocks and ledges, usually above water, but dashed by spray." Murrayella periclados (Ag.) Schmitz. On mangrove roots, Port An- tonio, March 8, 1893, No. 215; in dense tufts on wood, St. Ann's Bay, March 24, 1893, H. Manchioneal, July, 1900, P. & B. P. B.-A., No. 795. Amansia multifida Lamour. Washed ashore, Morant Bay, Annotto Bay, July, 1894 ; Rio Bono, Rio Novo, Kingston, 1900, P. & B. P. B.-A., No. 94. P. U., No. 708. Dasya arbuscula (Dillw.) Ag. Washed ashore, Montego Bay, July, 1900, P. & B. D. Gibl)esii Harv. Washed ashore, Port Antonio, Aug., 1894, P. & B. D. mucronata Harv. Washed ashore, Morant Bay, July, 1894, P. & B. Heterosiphonia Wurdemanni (Bailey) Falk. On Gelidium rigidum, No. 276, H. Annotto Bay, Aug., 1894, P. & B. Dictyurus occidentalis J. Ag. Annotto Bay, Aug., 1894; Kingston, near the lighthouse, July, 1900, P. & B. Always washed ashore, never in large quantity, usually only a fragment here and there. P. B.-A., No. 797. VOL. XXXVII. — 17 258 PROCEEDINGS OF THE AMERICAN ACADEMY. Halodictjon mirabile Zan. Washed ashore, St. Ann's Bay, March 30, 1893, H. Spermothamnion Gorgoneum (Mont.) Bornet. On Codium tomento- sum, Port Antonio, Aug., 1894; Kingston, July, 1900, P. & B. Port Antonio, Feb. 27, 1893, No. 175 a, H. P. B.-A., No. 441. " Both cystocarps and polyspores have been found in Jamaica speci- mens ; in the former the spores have thick cell walls and are arranged as in Spermothamnion ; the involucre is only slightly developed. The polyspores are quite numerous, in an ovate or subspherical mass, occu- pying not more than half the diameter of the large, hyaline sporangium." Note from label of P. B.-A., No. 441. S. Turneri var. variabile J. Ag. On Bryothamnion Seaforthii, Kings- ton, July, 1900, P. & B. Callithamnion byssoideum var. Jamaicensis Collins. In dense tufts on rocks, Port Antonio, Feb. 27, No. 170, H. P. B.-A., No. 443. " This plant has the divided cystocarps, with conical lobes, characteris- tic of C. byssoideum ; antheridia and tetraspores also agree ; but the habit is strikingly different, everything being condensed, the branches relatively shorter and stouter, and very densely set, the terminal ramuli often arranged more like C. corymbosum. It may possibly be the same as C. Hypneae Crouan in Maze & Schramm, Algues de Guadeloupe ; the name must be considered as provisional, awaiting comparison with authentic specimens of the latter." Note from the label of P. B.-A., No. 443. C. corymbosum (Eng. Bot.) Lyng. On Codium tomentosum, Port Antonio, Aug., 1894, P. & B. Haloplegma Duperryi Mont. Washed ashore, Morant Bay, Annotto Bay, Orange Bay, 1894; Kingston, July, 1900, P. & B. Only a few fragments at each place. Crouania attenuata (Bonnem.) J. Ag. On Cryptonemia crenulata, Morant Bay, July, 1894, P. & B. In small tufts, Navy Island, March 10, 1893, H. Antithamnion Butleriae n. sp. Fronds erect, ecorticate, simple or with a few branches, which may be dichotomous, alternate, or occasion- ally opposite, diameter near base about 30^, cells 3-6 diameters, walls tliick. The lower portion of the frond or branch is naked ; above that each cell bears normally a pair of ramuli, issuing at about two-thirds the height of the cell ; the lowest ramuli are simple, subulate, of from two to six cells about as long as broad; sometimes by the suppression of a ramulus the branching is apparently alternate ; fiirther up the frond these COLLINS. THE ALGAE OP JAMAICA. 259 ramuli are compounded with similar smaller subulate ramelli, appearing first on the lower side of the ramulus. The upper pinnae have from each cell of the rachis a pair of ramelli which touch each other laterally, so that the pinna forms a continuous triangle. At the ti[)s of the branches the cells are much shorter than those below, and the triangular compound pinnae are in contact, giving a linear outline to the whole. Color a rich rose. On Bryothamnion Seaforthii, Kingston, July, 1000, P. & B. From A. pteroton (Schousb.) Bornet it differs in the more densely branched pinnae, with ramelli on both sides, or on the lower only. From Ptilothamnion micropterum (Mont.) Bornet it differs by the absence of the apparent bifurcation of the pinua. Callithamnion microptilum Gru- now has much shorter articulations in the main branches, and less dense pinnules, which also are alternately more and less developed, as in some species of Ptilota. In the absence of fruit it is impossible to determine that the plant in question may not, when fruit is found, have to rather bear the name of Ptilothamnion Butleriae. Spyridia aculeata Kuetz. Washed ashore, St. Ann's Bay, March 30, 1893, No. 337; in tufts, Port Antonio, March 10, 1893, No. 228, H. S. filamentosa (Wulf.) Harv. In dense tufts, Port Antonio, March 10, 1893, No. 222, H. Port Morant, Kingston, Montego Bay, Man- chioneal, P. & B. Probably common everywhere. Chitty. Ceramium byssoideum Harv. Washed ashore, Port Antonio, July, 1891, P. & B. C. clavulatum Ag. Port Maria, Nos. 275 and 301 ; Port Antonio, No. 183, H. Morant Bay, Manchioneal, Kingston, Montego Bay, P. & B. Common everywhere and very variable. C. fastigiatum Harv. Washed ashore, Port Antonio, July, 1891 ; Ora Cabessa, Rio Bono, Rio Novo, June, 1900. C. gracillimum Harv. On rocks, Apostles Battery, Kingston Harbor, Apr. 10, 1893. H. C. nitens (Ag.) J. Ag. Washed ashore, Port Antonio, July, 1891 ; INIanchioneal, Montego Bay, 1900, P. & B. C. tenuissimum (Lyng.) J. Ag. On eel-grass, St. Ann's Bay, March 24, 1893, No. 318, H. Port Antonio, July, 1891; Manchioneal, Mon- tego Bay, 1900, P. & B. P. B.-A., No. 798. The Montego Bay speci- mens are small, connecting the type with the following variety. C. tenuissimum var. pygraaeum (Kuetz.) Hauck. On Laurencia obtusa, near Kingston, Duerden. P. B.-A., No. 896. A very small form, hardly visible to the naked eye, but in full tetrasporic fruit. 260 PROCEEDINGS OF THE AMERICAN ACADEMY, Halymeiiia Floresia (Clera.) Ag. Washed ashore, Montego Bay, June, 1900, P. & B. Grateloupia filicina (Wulf.) Ag. Morant Bay, on rocks washed by the waves, but not really under water, July, 1894; Rio Bono, Rio Novo, July, 1900, P. & B. In tufts on wood, St. Ann's Bay, March 24, No. 419; Kingston Harbor, Apr. 8, 1893, No. 381, H. "The Grateloupia gathered in 1900 was lying in coarse, black, dry, rigid tangle on the beach, totally unlike the Grateloupia found in 1894 at Morant Bay, growing on a big boulder on shore washed by heavy surf. At the latter locality, when the water was over the plants they floated out like fine, greenish-brown hair ; as the water receded the plants fell back on to the rock, covering it like a soft jelly. From the habit of the two forms, one would never suspect that they were the same species." G. dichotoma J. Ag. Near Kingston, Duerden. Fronds broader than usual in this species as found in the Mediterranean or at the Cana- ries, but otherwise the same. G. prolongata J. Ag. Near Kingston, Duerden. Agreeing well with Agardli's description, and with the form from California which passes under this name. Cryptonemia crenulata J. Ag. Morant Bay, Annotto Bay, and coast towards Port Antonio, washed ashore and growing on "sea-fans," July and Aug., 1894; Kingston, July, 1900, P. & B. Cruoriella Armorica Crouan. On stones and shells, Annotto Bay, July, 1891, P. & B. Peysonnellia Dubyi Crouan. On corals, Port Maria, March 17, No. 283; Port Antonio, Feb. 23, 1893, No. 161, H. P. rubra (Grev.) J. Ag. On rocks, Port Maria, March 19, 1893, No. 291, H. Hildenbrantia Prototypus Nardo. On coral rock. Port Antonio, Feb. 23, 1893, No. 161 ; Port Maria, March 20, 1893, No. 300, H. Melobesia farinosa Lamour. On Dictyota, etc.. Port Antonio, July, 1891, P. & B. On various algae, near Kingston, Duerden. M. Lejolisii Rosanoff. On various algae and eel-grass, P. & B. M. membranacea Lamour. On various algae, P. & B. M. pustulata Lamour. On Gracilaria Domingensis, P. & B. Lithothamnion incrustans Phil. On rocks, Port Maria, March 16, 1893, No. 258, H. Montego Bay, July, 1900, P. & B. L. Lenormandi (Aresch.) Foslie. On shells. Port Antonio, P. & B. Amphiroa charoides, Lamour. Port Antonio, July, 1891, P. & B. In tufts on bottom. Port Antonio, March 2, 1893, H. COLLINS. — THE ALGAE OF JAMAICA. 261 A. debilis Kuetz. Port Antouio, July, 1891, P. & B. In tufts on rocks, Port Antonio, Feb. 27, No. 177 ; Kingston Harbor, Apr. 8, 1893, No. 382, H. Near Kingston, Duerdeu. A. fragilissima Lamour. Growing like a moss on coral reef and sand near shore, in shallow water, Port Antonio, July, 1891, P. & B. Murray gives this species on authority of a specimen by Sloane, but as he also refers to Farlow, Anderson & Eaton, No. 15, it is probable that Sloaue's specimen is rather A. debilis. The plant distributed under No. 15 was originally labelled A. fragilissima, but a revised label was after- wards issued, as A. debilis. Corallina capillacea Harv. Annotto Bay, Aug., 1894, P. & B. In dense tufts, Kingston Harbor, Apr. 8, No. 383 ; Port Maria, March 17, 1893, H. P. B.-A., No. 150. C. Cubensis Mont. Annotto Bay, Aug., 1894, P. & B. In dense tufts, Port Maria, March 16, 1893, No. 256, H. C. pumila (Lamour.) Kuetz. On Turbinaria trialata, Port Antonio, July, 1891 ; on Stypopodium lobatum, Montego Bay, June, 1900, P. & B. P. B.-A., No. 799. C. rubens L. In dense tufts, Port Maria, March 16, 1893, No. 257, H. On rocks, Port Morant, July, 1900, P. & B. P. B.-A., No. 800. Sloane. Chitty. C. subulata Ell. & Sol. Kingston, Feb., 1896, 0. Hansen. Sloane. 262 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. Comparison of Marine Floras of Jamaica and Other Regions. CLASS SCHIZOPHYCEAE. Family Chroococcaceae. Chroococcus turgidus Chroothece Richteriana Family Chamaesipliouaceae. Xenococcus Schousboei Family Hormogoneae. Oscillatoria Corallinae Lyngbya aestuarii confervoides f. violacea .... majuscula Symploca hydnoides " var. fasciculata . . Microcoleus chthonoplastcs tenerrimus Hormothamnion enteromorphoides . . Scytonema concliopliilum Mastigocoleus testarum Calothrix aeruginea confervicola Contarenii pilosa Dichothrix penicillata CLASS CHLOROPHYCEAE. Family Ulvaceae. Ulva fasoiata Lactuca var. rigida Enteroniorpha erecta flexuosa intestinalis prolifera Family Chaetophoraceae. Diplochaete solitaria Family Mycoideaceae. Pringslieirtiia scutata s + + + o + + + •f + + + + + + + + + + + + n + + + + + + + + + + + + + + + + + M "Si is + + + + + + + + + + + + + + + + •t + COLLINS. — THE ALGAE OP JAMAICA. 263 TABLE I. — continued. Family Cladophoraceae. Chaetomorpha brachygona clavata aerea Linum " var. bracliyarthra IMelagonium f. typica Cladophora crystallina fascicularis fuliginosa Hutchinsiae intertexta trichocoma Family Gomontiaceae. Gomontia polyrhiza Family Bryopsidaceae. Bryopsis Harveyana pennata Family Caulerpaceae. Caulerpa cupressoides var. typica . ~. . . " var. Turneri . . . " var. mamillosa . . " var. ericifolia . . . pinnata f. Mexicana plumaris f. longiseta " f. brevipes prolifera racemosa var. clavifera " " " f. macrophysa taxifolia verticillata " f. charoides Family Codiaceae. Penicillus capitatus dumetosus Rhipocephalus Phoenix Avrainvillea longicaulis nigricans Udotea conglutinata flabellata Halimeda Opuntia tridens Tuna Codium adhaerens tomentosum 3 + + + ce a + + + + + + + + + + + + n c s + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 264 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. — continued. Family Valoniaceae. Valonia aegagropila ventricosa verticillata Siphonocladus membranaceus . . . . tropicus Dictyospliaeria favulosa Chamaedoris annulata Microdictyon unibilicatum Anadyomene stellata Family Dasycladaceae. Acetabularia crenulata Dasycladus clavjieformis Botryophora occidentalis Neoineris dumetosa Cyraopolia barbata CLASS PHAEOPHYCEAE. Family Ectocarpaceae. Ectocarpus Mitcbellae Family Striariaceae. Striaria attenuata " var. ramosissima . . Family Encoeliaceae. Colpomenia sinuosa Ilydroclathrus cancellatus Family Fucaceae. Turbinaria trialata Sargassum bacciferum lendigerum platycarpum vulgare " var. foliosissimum . . . " f. ovata CLASS DICTYOTALES. Family Dictyotace^e. Spatoglossum Schroederi Stypopodium lobatum Gymnosorus variegatus Padina Diirvillaei Dictyopteris delicatula 6 s o a o o § to PQ d 1 + + + + + + + + + + + + + + + + + + f + + + + + + + + + ! a C8 + + + COLLINS. — THE ALGAE OF JAMAICA. 265 TABLE I. — continued. Family Dictyotaceae. — continued. Dictyopteris plagiograrama Justii Dictyota Bartayresiana cervicornis ciliata dentata dichotoma divaricata fasciola Dilophus alternans Guineensis Dictj'erpa Jamaicensis CLASS RIIODOPHYCEAE. Family Bangiaceae. {roniotriclium Humphreyi eiegans Family Helminthocladiaceae. Cliantransia Saviana Liagora Cheyneana decussata elongata pulverulenta valida Family Chaetangiaceae. Galaxaura cylindrica lapidescens marginata obtnsata rugosa Family Gelidiaceae. Wrangelia Argus Gelidium coerulescens critiaie rigidum supradecompositum Catenella Opuntia var. pinnata Family Rhodophyllidaceae. Agardhiella tenera Solieria cliordalis Euclieuma ec;liinocarpum a .'d o "3 o 2 o o o 2 o 1 2 fM o y n o iz; + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 26G PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE l. — contmued. Family Sphaerococcaceae. Gracilaria Blodgettii caudata cervicornis conipressa confervoides cornea Curtissiae damaeconiis divaricata Domingensis ferox multipartita Wrightii Hypnea divaricata muscifortnis Valentiae Family Rhodymeniaceae. Champia parvula Cordylecladia irregularis Peasiae Chrysymenia halymenloides .... Family Delesseriaceae. Caloglossa Leprieurii Family Bonnemaisoniaceae. Asparagopsis Delilei Family Rhodomelaceae. Laurencia cervicornis implicata obtusa perforata papillosa tuberculosa var genimifera . . . Chondria Bailevfiua dasypliylla tenuissima Acanthophora Thierii Digenia simplex Polysiphonia cuspidata ferulacea Havanensis " var. Binneyi .... Pecten- Veneris A 3 + + + + + + + + + + + a o + + + + + + + + + + + + + + + + + n O a t8 + + + + + + + + + + + + + + + + + + + + + COLLINS. THE ALGAE OP JAMAICA. 267 TABLE l. — ro!)tin>ied. Family Rhodomelaceae. — continued. Polysiphonia secunda subulata Lophosiplionia obscura Bryotliamnion Seaforthii triangulare Bostrycliia tenella JMazei Moritziana var. intermedia .... Murrajella periclados Amansia nuiltifida Dasya arbuscula Gibbesii , niucronata HeterosipliDiiia Wurdemanni , Dictyurus occidentalis Haiodictyon niirabile Family Ceramiaceae. Spermotliamnion Gorgoneum , Turiieri var. variabile Callithamnion byssoideum var. Jamaicensis . corymbosum Haloplegiiia Duperryi Crouania attenuata Antitliamnion Butleriae Spyridia aculeata filanientosa Ceramiiim byssoideum clavulatum fastigiatum gracillimum nitens tenuissimura " var. pygmaeum Family Grateloupiaceae. Halymenia Floresia Grateloupia filicina difliotoma prolongata Cryptonemia crenulata Family Squamariaceae. Cruoriella Armorica Feysonnellia Dubyi rubra pj 3 CM + + + + + + + + a + + + + + + + + + + S + + + + + + + + + + + + + + « + + + + + + + + « O + + + + + + + + + + + + + S3 "So p + + + + 268 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE I. — continued. Family Corallinaceae. Hildenbrantia Prototypus . . . . Melobesia farinosa Lejolisii meinbranacea pustulata Lithothamnion incrustans . . . . Lenormandi Corallina capillacea Cubensis pumila rubens subulata Amphiroa charoides debilis fragilissima o + + + + + (A + + + + + S + + + + §> n + + + + + + + n o + + + + + bo S + + + + 4- + TABLE II. SOMMART OF MaRIXE FlORAS, ARRANGED BY CLASSES. Jamaica. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae Chlorophyceae Pliaeophyceae ) Dictyotales ) Rhodophyceae Total 19 62 29 114 2 25 16 49 7 62 61 156 24 59 75 237 34 33 80 173 66 130 193 346 75 88 118 153 224 92 286 395 320 735 434 COLLINS. — THE ALGAE OF JAMAICA. 269 TABLE III. Percentage by Classes in each Flora. Jamaica. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae 8 2 3 6 11 9 17 Chlorophyceae 28 27 21 15 10 18 20 Phaeopliyceae ) Dictyotales ) 13 17 21 19 25 26 26 Rhodophyceae 51 54 55 60 54 47 87 TABLE IV. Common to Jamaica in other Floras. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae Chlorophyceae Phaeoph\ceae ) Dictyotales ) Rhodophyceae 2 17 11 33 4 17 8 36 5 13 2 31 6 7 2 27 9 14 3 29 10 10 3 21 Total 68 65 51 42 55 44 TABLE V. Percentage of Jamaica Flora common to other Floras. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae Chlorophyceae Phaeopliyceae ) Dictyotales ) Rhodophyceae 11 28 38 29 22 29 27 31 26 22 7 27 32 12 7 23 47 23 10 25 53 16 10 18 Total 28 30 23 19 25 19 270 PROCEEDINGS OP THE AMERICAN ACADEMY. TABLE VI. Percentage of other Floras common to Jamaica. Puerto Eico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae Clilorophyceae Phaeophyceae ) Dictyotales ) Rhodophyceae 100 68 69 72 57 29 13 22 21 23 3 13 18 21 3 15 14 11 2 9 13 11 3 14 Total 69 24 14 11 8 10 Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. iS'o. lU. — Novemukk, lUOl. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. MODIFICATIONS OF HEMPEUS GAS-APPARATUS. By Theodore William Richards. MARINE BIOLOGICAL LABORATORY. »■ • ■* . Received . . . .)?^^.^-tr^' ./ /^^. ^. Accession No. /SsS/, - ^ Given by '-^^..C:^-<.t^ir^_.,o,c^^^^^ Place, ***rlo book ot. pamphlet is to be t-emoved from the Iiab- oratory without the permission of the Trustees. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. MODIFICATIONS OF HEMPEL'S GAS-APPARATUS. By Theodore William Eichards. Received October 2G, 1901. Presented November 13, 1901. The object of this paper is the description of some simple devices which make possible the accurate analysis of gases with a minimum of special apparatus. I. Absorbing Pipette. The essential feature of Hempel's method is the use of simply con- structed vessels distinct from the measuring burette for the purpose of ab- sorbing successively the various constituents of a gaseous mixture. Hempel used for this end a modification of Ettling's gas pipette, which answers the purpose admirably ; but of course many other combinations of apparatus might be used. The simplest is perhaps a bulb or wide tube inserted over liquid contained in a bottle. In order to prevent the access of air into this bulb from below, it is well to make the lower part of the tube somewhat narrow, and to bend it upward. If desired, the capillary serv- ing to admit the gas may be bent downwards and then upwards, as it is in the Hempel pipette; but with intelligent use of the pinchcock this pre- caution is not necessary. A satisfactory form of the apparatus is illus- trated in Figure 1. Fifty cubic centimeters is quite enough gas for analysis, if a suitably narrow burette is used for measurement, hence the receiving bulb of the pipette (A) need not exceed seventy-five cubic centimeters in capacity. The bottle (C) should be capable of holding one hundred and fifty cubic centimetres in this case. The " compound pipette " of Hempel may be imitated by the addition at B of another bottle containing water and a levelling funnel, or the same object may be attained merely by connecting to the outlet B a flex- ible rubber bulb, such as a child's toy balloon. VOL. XXXVII. — 18 274 PKOCEEDINGS OF THE AMERICAN ACADEMY. For solids, the stem D of the pipette may be made of wider tubing, closed at the bottom with a perforated stopper. A small tube bent upwards may be inserted in this per- foration, if especial precaution against incoming air is desired. An explosion-pipette could be made of similar apparatus, with the addition of a stopcock just below the bulb A and the usual conducting wires. The pipette for fuming acid might be made with a ground-glass joint instead of a stopper to connect bulb with bottle. In that case the bottle should be pro- vided with a suitable side tube on the neck, bent upwards. The method of using these pipettes will be understood without difficulty by any one familiar with the Hempel apparatus. II. Measuring Apparatus. The most serious cause of error in Hempel's ordinary apparatus is due to the possible change of temperature. This is considerably greater than the probable error in reading ; for a single degree Celsius causes an error of 0.5 per cent of the total volume of gas measured under ordinary conditions, while the volume is easily read within 0.05 per cent. Hence, unless much greater care than usual is taken to pre- serve constant temperature, the reading of the volume is unnecessarily precise. But Hempel's ingenious arrangements for maintaining constant conditions in a 100 c.c. burette are so large as to be inconvenient for students' use in cramped quarters. For these reasons I have often used somewhat smaller volumes, which may be surrounded with an envelope of water without producing thereby an unwieldy combination. An ordinary 50 c. c. burette, inverted and pro- FlGURE 1. RICHARDS. — MODIFICATIONS OF HEMPEL's GAS-APPARATUS. 275 vided with a levelling bulb or funnel, answers very well as a measuring instrument. The burette may even be used in its usual position, if it is provided above with a smooth rubber stopper with a single hole for the capillary connecting-tube. Of course the stopper is always pushed pre- cisely into a definite position, indicated by a carefully made mark on the burette. There is little risk of displacing this stopper if it is firmly wired into place. In any case of course the ungraduated space at the upper extremity must be carefully calibrated. An especially made 50 c. c. in- strument, graduated all the way to the capillary tube at the top, is more convenient, although no more accurate than the inverted burette. For convenience in cleaning, it is Avell not to have both ends of the burette drawn down to small diameter. The small size of the burette makes it easily possible to provide tlie water jacket which is so essential for accu- rate work, and both burette and pipette may be supported upon the ordi- nary iron ring stand. III. Practical Operation. Of course the precautions usually necessary in gas analysis must be used in all the operations with this apparatus. For example, due time must be allowed for the running down of the liquid from the moistened walls. Asain, care must be taken that the same amount of gas, at definite pressure (as small an amount as possible) is always left in the connecting capillary tubes. In order to make sure that no air- bubbles are caught, it is well to draw out the ends of the tubes in the manner illustrated in the diagram, which indi- cates two successive stages of the glass blowing, as well as the finished and con- nected nipple. The object of blowing the small bulbs is to render the bore of the portions drawn out as large as that of the rest of the tube. While the apparatus thus constituted was devised primarily for use in an emer- gency, it has several advantages over the Hempel apparatus. It dispenses with the necessity of calibrating the whole length of a new burette, it m WM 276 PROCEEDINGS OP THE AMERICAN ACADEMY. is very iuexpensive, and it occupies but little space. Each student may possess a complete set of apparatus, and every one knows the value from a pedagogic standpoint of such a possibility. A furtlier advantage lies ia the fact that the pipette is easy to fill and to clean ; and a precipitate in the liquid is not apt to clog its working. The short straight capillary brings an obvious gain of speed in transferring. Moreover, because of this speed, and the fact that the pressure during transferreuce is always from the outside inward, the danger of loss by leakage is considerably less than it is with Hempel's apparatus. It is well known that in a rubber tube an internal pressure may cause leakage, while an external jsressure tends to stop small outlets by causing the rubber tube to be pressed more closely together. On the other hand, the calculation is less obvious, because the volume taken is not just a hundred cubic centimeters ; and somewhat more care must be used to prevent the access of air into the pipette from below while shaking. A little practice enables one to shake thoroughly the liquid in the bulb without much agitation in the bottle if the movement is hinged about the point D ; hence the danger is slight. Another slight difficulty is the possible leakage of the absorbent around the stopper of the pipette bottle, — an unpleasant occurrence which has no effect upon the accuracy of the method. In presenting for general use any new instrument one must record its practical working in the laboratory. Everybody knows that plausible Analysis of known Mixtures of Air and Carbon Dioxide. Volume COj taken. Volume Air taken. Volume Air found. Error. c.c. c. c. c. c. c.c. 1G.95 32.02 32.01 -0.01 18.45 32.21 32.12 -0.09 12.20 42.20 42.20 ±0.00 20.00 32.00 32.10 +0.10 14.90 37.60 37.60 ±0.00 13.00 34.50 34.48 -0.02 16.50 36.50 36.55 +0.05 Excess of positive ovt >r negative err ors, 0 03. RICHARDS. — MODIFICATIONS OF HEMPEL'S GAS-APPARATUS. 277 inventions do not always stand the test of indiscriminate use. Accordingly a large class in gas analysis has been asked to use the new devices, with favorable outcome. The pipette and burette were tested as follows. A definite amount of air was run into the burette, and the volume measured with the usual care. Pure carbon dioxide was then run in from a generator, and the gain in volume was noted. This known mixture of air and carbon dioxide was run over into the new pipette, and after suitable shaking the residual air was returned to the burette and measured. These figures, taken at random from among the results of the class, agree with one another as well as could be expected ; and since the posi- tive deviation balances the negative, there is no constant error. No trouble was experienced as to manipulation. I am much indebted to Mr. Bisbee, the assistant, and to the gentlemen of the class in gas analysis, for their kindness in carrying out the practical trial of the apparatus. Cambridge, May 3, 1901. Proceedings of the American Academy of Arts and Sciences, Vol. XXXVII. No. 11. — January, 1902. THE PARAMETRIC REPRESENTA TION OF THE NEIGH^ BORHOOD OF A SINGULAR POINT OF AN ANALYTIC SURFACE. By C. W. M. Black. MARINE BIOLOGICAL LABORATORY. Received ^^l.^ y/^^:^, Accession No. / P^.'^ f^.,. Given by '<^.->:^r^.^<^^<>:^*=(r,a)+Cx(r,cr)+ ] V (b) * .Journal de mathematiques pures et appliquees, 4th Series, Vol. VIII. (1892), p. 385. 282 PROCEEDINGS OP THE AMERICAN ACADEMY. and the neighborhood of the original point is represented by the neigh- borhood of the curve <^(r, cr)=0, C=0, (c) on the surface ^ (t, (T, 0 = 0. 3) The neighborhood of the curve (c) is included in the domains of a finite number of points which are a. regular points of the curve (c), the domain of each being repre- sented by a single jiower series T=p(cr,0; (d) h. critical points of the curve (c), the domain of each being repre- sented by an equation of the form ^ + pi(cr, 0 r^-^ + + ^^-l(cr, 0 ^ + p^ (cr, 0=0; (e) c. points at an infinite distance on the curve (c), the domain of each being represented by an equation of form (d) or (e) in the variables T], o"!, 1], where T 1 T 1 ' p (u, v) 1 y = ,l;p(u, V) V p = 1, 2, p, (A) where «/)p, \pp, Xp ^'"^ analytic in the arguments (it, v) throughout a cer- tain region ; further for each set of values of (x, y, z), the values (0, 0, 0) excepted, there corresponds for at least one value of p a pair of values (m, v) lying within the region in which the functions 4>p, i//p, Xp <^^^ con- sidered, and for any value of p for which this is the case, there corresponds no second pair of values. To the set of values (0, 0, 0) corresponds at least one, and in general an infinite number of pairs of values {u, v) for every value of p. 2. Explanation of Symbols. The symbol (x, y, z, )„ indicates, in the expression in which it appears, the total collection of terms of degree n in the arguments taken together, which belong to that expression. 288 PROCEEDINGS OF THE AMERICAN ACADEMY. A functional sign expressed by means of a letter will always represent an analytic function. Tiie symbol E {x, y, z, ) will always represent a function which is analytic at the point (0, 0, 0 ) and for which ^ (0, 0, 0 ) ^ 0. If written with a subscript, as E^ {x, y, z, ) it represents a particular function of the class ; if without a subscript, it represents a general function of the class ; so that two functions E {x, y, z, ) both expressed by the same symbol, need not be equal to each other. B. — The Transformations. 3. The equation F(x,y,z) = Q can be transformed to the form ^ (^, -n, 0 = a, j7. 0». + (^, V, 0«.+i + - 0 where 1) m > 2, 2) the polynomial contains the term ^'", a, ri, i)„. = c^ a, v) 3) the points in which the curves corresponding to the irreducible factors of ff> (f, r}) cut the line at infinity shall be distinct from each other and from the point in which the line f = 0 cuts that line. To do this, we first make the transformation X = U + a, :=! V + b , Z T=: w -\- c , thus obtaining ^(^, I/, z ) =/(«, '', ■?<'•) = (u, v, w),„ + {u, V, w),„+y + Here, m > 2, the singularity now being at the origin. Next we make a linear homogeneous transformation with non-vanishing determinant, V = a.i+ /3.r, + y.^V (1) with the result : f(u, V, w) = ($, rj, 0 = (t\ V, 0,„ + (^, V, 0,«+i + = 0 . For this equation, conditions 2) and 3) can be secured, as is readily seen by a proper choice of the coefficients in transformation (1). BLACK. THE NEIGHBORHOOD OF A SINGULAR POINT. 289 The surface == 0 corresponds in the neighborhood considered, point for point, to the surface F = 0, and thus it is only necessary to prove the theorem for 4> =^ 0. We may assume that of the irreducible factors* of there are none of degree lower than m vanishing at the point (0, 0, 0), for otherwise each of such factors could be treated separately by the methods here used, and the results combined. This provision excludes the case in which one of the variables has equal roots for all values of the other two in the neighborhood of the point (0, 0, 0). 4. The quadratic transformation ^ = ~a v^v (2) reduces 4> ($, -q, () to the form = r ^ (I, V, 0 (3) where, an arbitrarily large positive number V having been chosen at pleasure, S can be so determined that the function /, 0 = r [(f, V, i)», + c(f, ^, i),„+i + ^' (I, V, i)»<+2 + ]. We now proceed to the proof that the function 4> (f, t/, ^) is analytic within the above limits. Let ^ (f, r/, 0 = 2 A,j, e rj'C, i+j + k>m, and suppose it to be convergent when .^\ ^ h ! % < h, \v\ < h, Ul < /* A > Si. Then, for the general term, we have J/ being a positive constant. By transformation (2) * For the definition and the fundamental properties of the irreducible factors of an analytic function of several variables, which vanishes in a point, cf. Encyclo- padie der matheniatischen Wissenschaften, IL B. 1, Nr. 45. voi>. XXXVII. — 19 290 PROCEEDINGS OF THE AMERICAN ACADEMY. and Now choose S so that V S ^ hi. Then, when the absolute value of the general term of series becomes ■ ^ < ^ Accordingly, the series is convergent when and it represents an analytic function for these values of the arguments. 5. The family of lines tangent to the surface ^ {$, t^, 4) = 0 at the point (0, 0, 0) forms a cone that cuts the plane ^ = 1 in the curve <^ (f, 7]) = 0. If the line rj/^ = /S, $/C = a. (a and (3 being finite) is one of this family, then the point $ ^^ a, t] =^ ^, I = 0 of the surface (f, r], t,) = 0, (3) is at most a singular point of order m of that sur- face, and its neighborhood corresponds to a portion of the neighborhood of the singular point of the original surface {i, rj, 0 = 0. In fact, cut the surface ^ a, v,o = o by the plane rj-l3C=0. Then the curve of intersection C will have a multiple point at (0, 0, 0) and the equations of the tangents to C at (0, 0, 0) will be C cr=l,2, s?, 'Q which satisfy the condition To deal with the points for which a, /3 would be infinite, cut the surface by the plane The equations of the tangents to the curve of intersection at (0, 0, 0) are ^^A T=l, 2, t1) = 0, T = 1, 2, ti (t? Vi)f take out all terms not containing rji, so that i>i (i, Vi) = n (^ — a^) -f 7/1 1//1 (^, Tji), fii + + ft, = m. Then make the transformation ^-a. = 4 (6') and we have 4) {$, ^, 0 = r [t/ i' (4 + a, - a^.T"' + V^^ a., Vi)+Cx (i.^ Vi^ 0] (r';= 1 = ^"'ff. (I., Vu 0 = 0 (7) BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 293 where g^ has a term in ^'^'^ free from 7/1 and ^, since a^ — a^, ^ 0. So there are near the point (0, 0, 0) /i,^ values off satisfying the equation g^ = 0 for every pair of values of 771 and ^ in the neighborhood of the point 7;i = 0, ^ = 0. Now, for any such set of values of $ , t^i, ^, different from the set (0, 0, 0), satisfying the equation g — 0, there is a corresponding set of values of f, 77, ( satisfying the equation 4> ($, rj, ^) = 0, their coordinates being connected by the relations (2), (6), and (6'), which are equivalent to the required relation (4). Also by considering s _ the other factors of 11 ($ — a^)'^'^, we get (s — 1) other equations of form (7), the corresponding coordinates being connected by relations of form (4). No two points (f, rj, ^), (|', rj', tj) of T (distinct from (0, 0, 0)), de- rived from points (f^, 77^, ^j) (f^„ tj^, ^2) lying respectively in the neigh- borhoods of the singularities which are given by two distinct equations can be the same. For suppose ^ = 4^' = ^: (f<, + a^) = 4 (4' + «a') ^ == C = Ci =C. Then we must have 4 + a = 0 must also have equal roots at the corre- sponding points, and this case has been excluded. So as each equation ^r = 0 has near the point (0, 0, 0) ^ values of ^ ? in general distinct, for each pair of values of 7/1 and ^, and as 2 // = m, the collection of equations 9^ = ^^ 0-= 1, 2, s, has within sufficiently small limits as many different roots as the equa- 294 PROCEEDINGS OF THE AMERICAN ACADEMY. tion $ = 0, and thus represents the latter equation within the corre- sponding limits, i. e., when or K|?, K=Crj. (8) Then, by the same method of treatment as above, putting t, for "rj and 7} for ^, and taking 13 = 0, we derive a set of surfaces ffA^r^V,t) = 0, T=l, 2, t;) : Now, for the infinite roots of we put the equation into the form (i,a) -, 1, ^ ) - 0. \ rj So the equation «^(l, 0 = 0 is such that its roots for | = 0 are the same as the ratios of the infinite roots of the equation and by 3, 3) these ratios are all finite. BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 295 C. — The Number of the Neighborhoods, ti, t.^, t^, REQUIRED TO REPRESENT T IS FiNITE. 6. In the foregoing paragraph it has been shown that the neighbor- hood of each tangent line to the surface $ = 0, at the singular point can be mapped on the neighborhood of a (regular or singular) point of the surface y = 0. We now proceed to show that the whole neijihborhood o T: Kl < 8, h| (f, rj) has no multiple factors. Case II. — This polynomial has multiple factors. Theorem: T/ie neighborhood T can be completely covered by a finite number of regions 7\, T^, T^, which overlap each other and which are mapped respectively on the following regions ty, to, t^: In Case I: 1) the region t^, i = 1, 2, k, consists of the neigh- borhood of a singular point of the surface y*' = 0 ; 2) the extent of each of the neighborhoods ti, t^, t^ having been arbitrarily determined, the regions tj, J =: k + 1, v, then consist of regidar regions of surfaces g^^ = 0. In Case II : 1) the region ^;, V = 1, 2, k, consists of the neigh- borhood of a singidar point of the surface ^''' = 0 ; 2) the extent of each of the neighborhoods {K + e,)\(\, where h^ is the distance to the furthest point in the r;-plane for which the equation has a critical point, and if e^ is first chosen arbitrarily small, 83 can be determined not zero. Now consider the neighborhoods of the critical points of the curve Hi v) = 0. In these, however small we take the 8, all the remainder of a circle in the ^-plane including all the values for which the curve ^ = 0 has critical points can be covered with circles such as were determined for the domains of the regular points above, these circles overlapping the circles about the singular points and not reaching out to these points in any case. Let the radius of the large circle be G where G^ > 1 , G> h2-\- 62. Then, if we take for 84 the smallest value of any 8j or S, the develop- ments within these circles together with the neighborhoods of the set of new singular points will represent all points of the original neigh- borhood for which Finally, taking for 8 the smallest of the three quantities 82? S3, S^, the BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 299 whole set of functions thus determined will represent all points of the orififiual neighborhood for which hl<3, Kl and we have the surface $,' + 2t^3 - ? - Cvis - i^'v = 0, whence i, = ^^2L-li + ^VcW + H'-^- In a similar way, from the other root, $, = ^''^'^^^'-h^CW + H'-^' (c) (d) In (c) and (d), for the radical is taken only that branch which becomes + 2i for zero values of the arguments, and the function is seen to be analytic for sufficiently small values of rj when C = V < 1 - f 1 ; aud similarly when l'?l = > 1 + e. Thus, in the ry-plane, we have by the formulas (a), (b), (c), (d) covered two small circles about the points 1 and —1 corre- sponding to developments (a) and (b), and all of the region outside of a circle of radius (1 + e), corresponding to devel- opments (c) and (d). We must now obtain further formulas so as to fill up the remaining unshaded region. BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 301 Consider the point $ = -1, ^ = 0. Let f = fs — 1 and we have whence ^5 = ^^-i'V/r-4?+4. (e) 2 In the same way, about the point we have the function ^-2 4 = ^ + i'^r-47?^+4 (f) In (e) and (f), for the radical we take only that branch which becomes + 2 for zero values of the argument, and for sufficiently small values of $ the functions are analytic when Again, consider the point f = 2 Vl - »■ , ^ = 1 + 22. Let I = ^- + 2 Vl - *■ , ^ = r},+ l-\-2i, and we have whence ^7 ^-^'^^~"~^+iVl6-16i + ^^^ 4,^,^-8 (1 + 20.?,. (g) For the corresponding point f=:_2\/l -i, ^ = l + 2^, we have the formula ^8 = ^^^ g '"^^-iVie - 16t + ^' - 4,782 _ 8(1 + 2i)r,,. (h) In (g) and (h), for the radical we take only the branch which becomes + 4 Vl — ^ for zero values of the arguments, the same value of the radical \/l — i being taken in all cases. These functions are analytic for sufficiently small values of ^ when 1^7 I = 1^8 I < 2 — C7 . Also, considering the corresponding points of 302 PROCEEDINGS OF THE AMERICAN ACADEMY. for which ^ = - 1 + 2i, ^= 1 - 2z, r;= - 1 - 2i, we have evidently similar re- gions for each. Then, by taking the c's all small enough, we cover the whole unshaded re- mainder of the ^-plane by five circles within each of which there is a development as required. The sets of parametric form- ulae, derived by using the inter- mediate transformations, are V rj = V Vw (y — m) -f 1 , Tj = — V Vu (v — u) + 1 , V = $ = -(u'^v + Vu*v' + iu^ — 4), V, ^ = -(u'^U — V"*V2 +42^2—4), y] = v. ^ = uv i = uv from ?/. i = V2(^i-Vii'-4:V-'-^ 4), i = '^{ii+Vu^-^v^ + 4), rj = uv, ^ = u ' 2^ 2^ r} = ic(v + 1 + 2/), ^ = u u - Vl6 — 1 6 ^• + m2 _ 4 y2 _ s (^1 ^ 2t) y ), 7) = u{v + 1 i- 2i), ^=u (a) (b) (c) («) (0 (g) 00 with three more sets similar to (g) and (h). Cask II. — The polynomial (f>(e, ^) contains multiple factors. Here, any points which are common to two different irreducible factors of (ft (f, rj), or are critical points of a single irreducible factor, will be critical points of the curve <^(i;^) = o, [ BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 303 and all such points, a finite number in all, will be treated like the critical points of the previous case. But also any point on a multiple factor is a critical point of the curve, and further treatment is needed for such points. Suppose f = a, r? = yS is a regular point of a factor <^i ($, r/) of mul- tiplicity r, i. e. of the irreducible factor whose rth power is equal to i(^) v) ^"^ "°t a point of any different factor of (ji($, -q). Then, in the corresponding equation of form (7), g^ will contain a term ^'^ as the lowest term in ^"^ free from rji and ^, and by Weierstrass's Theorem * we can develop the function about the point in the form C + P^ (vi^ 0C+ + Pr (vi, Ol ^(C' vu 0 = 0. (9) These functions P;,(vi, 0' X= 1, 2, r, are shown by a method similar to that used for the functions in Case I to be analytic within a region \vi\{x, y) have the form in the neighborhood of the point X = 0, y = 0, ^{x,y) = [x+p{y)YE{x,y), (/?) where p (y) is analytic at the point y = 0, and p (0) — 0. The function ^ (x, y, z) shall be analytic at the point (0, 0, 0), but shall not be divisi- ble by X + p(y) at that point. Consider a region for which \y\ <, h, and let h be chosen a) less than the radius of convergence of the Taylor's series which represents the function p (y) developed about the point y = 0, and h) sufficiently small, so that the points (x = p (y), y) will lie in the region in which E(x,y) is analytic and different from zero. Then the part of the neighborhood of the curve x + p(y)--=0, z = 0, which lies on the surface ^{x,y, s) = 0 can be transformed, by means of quadratic transformations of the type BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 305 on a finite number of regions ti, T2, t , which fall into two categories : — 1) the region Ti(i ■= \, 2, k) is the neighborhood of a singular point of order < m ; 2) each of the neighborhoods of 1) having been determined arhitrarily small, the region tj ( i ^= k -\- 1 , v) is then a regidar piece of an analytic surface, represented in its whole extent by a single set of para- metric formulae of the type {A). By the neighborhood of the curve x+p(y) = 0, 2 = 0, is meant the set of points (x, y, z) satisfying the relation \y\ \y\< h, |^|i (xj, y, z). By means of a transformation with non-vanishing determinant, $1 can be thrown into the form : *i (xi, y, z) — 2 (xo, y, 20) = 9o(y)a:2"'' + qi(y)xr-'^-2 + + g„n(.i/)-2"^ + ^2(^2, y, ^2) = 0 (ri) where ^o (y) ^ 0. Consider first the points of the circle \y\ < h at which ^o (y) =■ ^5 if such exist. Each one of these points y^, (i = 1, 2, k) is a singu- lar point of ^2 = 0 of order not greater than m, and its neighborhood l^il \^\<^ may be chosen arbitrarily small. Surround each of these points in the circle \y\ = h hj A circle of arbitrar- ily small radius c'. We now proceed to consider the region about an arbi- trary point a of the circle \y\ < h not lying in any of the regions just cut out. Let yi^y — a and let 4>2 then be written in the form *2 (a;25 y^ ^2) = ^2 (a^2, yz, ^2) = 70(^2)3^2'"' + 9i (^2) a^2"' ~' 2:2 -f + q„,^ (^2)^2"'' + ^2_0^2, ^2, ^2) = [xs'"! -F ri(y.^x.'"-^z.^ + -f r„.^ (3^2) ^2'"^ ^ (^^2) + ^2 (•-'^2,^2, ^2) = 0. ' (,6) 3. Apply to the function ^2 the quadratic transformation X2 — 'l'3'^2- * Here, for the first time, a quadratic transformation of the type that trans- forms but a single variable is employed. Such transformations do not occur in Kobb's analysis. They appear to be indispensable. BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 307 Let the result be written as follows : — C2'"i{[x3"'i + ri(y2)a:3"'i-' + + r,„,(9/r,)]E(i/^)-{-Z2Fs(x3,i/o,Z2)} =0.(k) From this last equation we deduce the following theorem : — AH points of the surface O = 0 m the neighborhood of the curve are mapped upon a finite number of new neighborhoods which are 1) neighborhoods of singular points of degree ^ m, which neighbor- hoods may be taken arbitrarily small ; 2) neighborhoods of new multiple curves on surfaces constituted like the surface ^ (x, y, z) = 0 of the lemma, the values of m thus arising never exceeding the original m of the lemma. By the same kind of reasoning as in § 1, 5, we show namely that for any one of the above values of a, the corresponding value of y^ being in or on the circle of convergence of the Taylor's development about the point z.2 = 0 of the function ^a(2/2)> A. = 1, 2, mi, all points of the surface $0 = 0 i» the neighborhood of the curve 4>{^,y) = ^, 2 = 0, are represented by points in the neighborhoods of points of the curve xz'^ + ri (2/0) Xg" -1 + + r„,^ (yo) = 0 , Zj = 0 , on the surface $3 = 0, i. e. if such a value of y is b, so that the corre- sponding value of y, is (b — a), and if the roots of the equation xr^ + n (6 - a) X,"'-' + + r,„^ (b-a) = 0 (/x) are ai, 02, a„, then points of the surface $2 =^ 0 for which ^2! < 8, l^ol < 3, !/ = b, are connected with the points of the surface (k) by the relation x^ = z„{x^ + a^), y„ = b — a, o- =1,2, m^. Further, if we limit y^ to a circle not reaching out to the nearest point for which qo(y.,) vanishes, we have an upper limit for a^- as a root of the equation (fx), and thus by taking ^2 and x^ small enough we can make X2 as small as we please. Then the transformations (8) and (Q still 308 PROCEEDINGS OP THE AMERICAN ACADEMY. secure a limit for the values of x and 2, and thus we have represented a neighborhood of the curve (f>(x,y) = 0, « = 0, on the surface ^ (x, y» 2) = 0 as required. Now, however small the neighborhood we shut off about the points in the region |^| < h for which qo(y) vanishes, since the results estab- lished above would hold also in a circle of radius hi > h, but still less than the radius of convergence of the series for p (t/) in (/3), we can fill up the remainder of the circle of radius h with circles within which go (y) does not vanish, these circles overlapping at all points the bounda- ries of the excepted neighborhoods and not reaching up to the excepted points. Within each of these circles we have a development of type (k). Consider one of these new circles. We want to consider the neighborhood of the curve «^3 (^8' ^2) = ^a"* + n (2/2) ara™ -1 + + r^^iy^) = 0. (v) If this is a multiple curve of the mi-th order and nii < m, we have reduction. Moreover, if nii = m, but iCs"' + ^1(^2) a^s"!-' + + r„^(yz) ^ [^3 + Pz(.y^)T^^ we also have reduction. We need consider, therefore, only the case that a^s'i + n (y2)a:3'"i-' + + ^m, (^2) = [a^s + />3 (^2)]'"', > , ,-. mi = m, ) and show that this case can repeat itself at most but a finite number of times. 4. Suppose the function {x,y) = 0, 2 = 0, on the surface ^{x,y,z) = 0. In fact, the first lot of points excepted, those for which in equation (yi) 9o (y) vanishes, are along the line X2 = 0, 22 = 0, which is connected with the original curve by the one-to-one transfor- mations (8) and (^). Also so long as the multiple curve does not break up into simpler curves, the neighborhoods corresjiond, and when this reduction takes place we can cut out the neighborhoods of the points common to all of the resulting curves by cutting out neighborhoods along the original curve for the same values of y. C. — The Reduction of the Original Singularity. The transformations hitherto considered, when applied to the original surface ^ (^, r], C) = 0, make it possible to map the neighborhood of the point (0, 0, 0) of that surface on a finite number of regions which are of two classes : — BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 311 1) neighborhoods of singular points of transformed surfaces ; 2) regular pieces of transformed surfaces. The pieces of class 2) lead at ouce to representation by means of para- metric formulae of type (A). The singular points of class 1) are all of lower order than the original singularity except in one case, and it is this case that it remains to consider in §§ 3, 4. The case can pre- sent itself at the outset only if the polynomial (i, rj, ^),„ is the product of m linear factors in ^, rj, ^, all vanishing for a single set of values of the arguments $, tj, ^ not all zero. Geometrically, the tangent cone, (t) v^ Om = 0? of the surface (^, 77, ^) = 0 at 'the point (0, 0, 0) con- sists of m planes having a common line of intersection. It is found necessary to distinguish two sub-cases according to whether the planes themselves are not all coincident, or are all coincident. To sum up, then, we already have reduction in all cases except when ■we are led to singular points in class 1) of the particular type just described. §3. A. — The Singular Points of Special Type. 1. In the special case in which the function (^, 77, Om is composed of m linear factors, each vanishing for all points on a common line, it is possi- ble to reduce the singularity by means of a finite succession of quadratic transformations together with certain additional transformations. We consider two cases : — Case A. — The m linear factors of ($, -q, ^)„, are not all equal. Case B. — The m linear factors of (f, r/, ^)„j are all equal. 2. Case A. — (|, -q, ^),„ is composed of m linear factors not all equal. The surface can be expressed in the form 4>(|, rj, 0 = (i, V\> + (f, V, 0.«+i + = 0 (13) where ($, rf)^ contains terms in both f" and rf". If the surface were in a form f(u, V, w) = (u, V, iv)^ + (u, V, w)„+i + = 0 with the condition that the m linear factors of (m, v, w)^ all vanish for the line u = ato, V = ftw, we could make the transformation 312 PROCEEDINGS OF THE AMERICAN ACADEMY. and all the resulting linear factors would have to vanish when ^ = 0, ^ = 0, and so not contain ^. Also by a linear homogeneous transformation in ^ and r; we can se- cure the presence of terms in ^ and rp, and in such case every linear factor of ^15 0)m would have its linear factors all equal, but these are the factors of (|i, 171)^. Also the common point of intersection of the lines BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 313 in which the plane ^ = 1 cuts the planes corresponding to these factors is at a finite distance. We have now the conditions 2) and 3) of § 1, 3, and are ready to apply the transformations giving ^i (iu Vi^ 0 = C' [(li, Vu 1)- + C(li. Vu l).+i + ] = 0. (17) Now if f] = y2, 7/1 = 8oj is the common point for which the m factors of (li> Vi) ^)m vanish, then the substitution ^2 = ?1 — 72 J V2 = Vl ~ ^2i gives a group of mth degree terms in ^^ and r]^ exactly corresponding to the terms of ($, t])„. So in the successive collection of terms of the mth degree, the terms of (i, r])„ are always carried over with merely a change of subscript, and thus we never introduce the condition of m equal linear factors. Accordingly so long as the degree of the singular point is not reduced, the intermediate transformations are of the type thus securing the succession of transformations (14). 4, The succession of transformations in 3 will lead to the relation e^L (^„ r,^ 0 ^^ + ^{U V^^O ^'"-'"' ^ = Ji(yj,^)$0 (18) where Combining transformations (14) we have the relations ^ = 71^+72^^ + + 7.^' + ^"$.) r) = 8U+ 82^' + + 8,C + ^"7?. \ ^^^^ As $ contains both ^^ and rj"' terms, we can develop by Weierstrass's Theorem. a>(^, rj, 0 = [e"+p,(v, oe'-' + +Pn.{v,o:iM^, v, o] ^(i, V, 0 = [r + qid. Ov""' + + qm(i, 0]^2(l, V, 0 As the function E-, (f, -q, ^) contains a constant term, when the first trans- formation of (14; is made, the factor C" must come out of the , ^^ for ^^, (/x = 1,2, v), where the *'s are derived successively in the same way as the $'s. At each stage the <> factor must contain alL the terms of lowest degree in the corresponding (except for a constant multiple), and no lower terms ; for, otherwise, either there would be lower terms in the product by the corresponding £J factor on account of its constant term, or the required terms would not be present. Now, by (19), Also $=i^'«>'$,; (22) and, combining with (21), we have || = r-||". (23) But as $ has no multiple factors vanishing at (0, 0, 0) (see § 1,3), we have the relation L(^, rj, 0* + M{^, >?, 0 fl = Ri-n, 0 ^ 0. (24) Then, substituting for f and t] from (19) on the left side of equation (24) and using the relations (22) and (23), we have the required relation (18). 5. If V is taken large enough the transformations (14) will lead to the relations ^(^., vr, 0^" + M.{^., v., 0 ^ = ^ Iv^ + -h(OJ^J^(v^, 0, (25) p.{i., v., 0*^ + (26) where ^viL, V^, 0 = ^.(f., V^; 0^1 i^r, ^., 0 = ^^(^"^ v^, 0J^2(i., v^, 0- (27) We consider the effect of the transformations (14) on R in (18). Ex- press it in the form Riri, 0 = ^'[{V, On + (V, On+l + ] = i'^iV, 0. where S(v, 0) ^ 0. If (rj, C)n contains no term in rj, the first transformation of (14) will al- low the factor C to be taken out of S, leaving behind a constant term, and thus securing the form (25) at once with BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 315 qi=P •{■ n, ri = 0. Next, suppose (t], ^)„ does contain terms in rj, but no term in rj", i. e. we can express it in the form where (tj, ^)„_r_s contains terms in both 7]"~''~' and ^-^' and 5 > 0. Then if any transformation is applied, there can be divided out of (77, ^)„ the factor ^" leaving behind as the term of highest degree one in f]"''. This cannot be cancelled with any term from another part (rj, C)n+i> foi" ^^J term from this would have as a factor ^' after the C" has been divided out. As long, tlien, as the rj variable does not enter to the highest degree in the expression corresponding to (?;, ^),j if n > 0, the degree of the S factor is decreased with each transformation, while the exponent of ^ outside may be in- creased. Accordingly, by a finite number of transformations, we re- duce the S factor either to an £ function or to an expression in which the 7] variable enters to the highest degree in the collection of terms of lowest order. In the former case we have the form required. In the latter case, suppose for convenience that this condition holds for the function S (rj, C)- By Weierstrass's Theorem we develop in the form S(v, 0 - Iv" + niOv"-' + + r„(0:\E(r], 0 =^T(r],OE(r,,0- (28) Consider the n factors of T(r], Q, T(r,, Q = Ulrj + S,(02. (29) A X If the factors are not all equal, pair them off, so that in each pair there will be two different factors, leaving a number of equal factors : Now, for each pair, we have the relation ^. + P.iv, oi^' = L^O $ 0, (31) drj since the two factors are unequal. Then, by the same reasoning as used 316 PROCEEDINGS OP THE AMERICAN ACADEMY. in 4, the succession of transformations (14) which leaves the degree of T unchanged will secure for equation (31) a form The left side of the equation is divisible by ^^ and so the right side must be, V < X, and we have an upper limit for y, the number of transformations which leave the factor N^. of the second degree, and as a result leave the func- tion T of the nth degree. So, unless the function T{rj, C) in (28) is composed of ?^ equal factors of form Lv + ^ (OT, (32) the transformation of (14) will finally reduce its degree. Then, by ap- plying the same reasoning to the resulting function, we see that finally the function corresponding to S(r}, ^) either becomes an J^ function or has besides the JiJ factor a factor of form (32), thus securing the form (25) if we divide out the factor ^("•-D", The condition (26) is secured by using on the second equation in (20) the same kind of reasoning as applied in 4 and 5. Then we take for V the larger of the two values required to secure conditions (25) and (26). C. — Further Transformations. 6. A transformation ^V = iw — Wg (0 ) .ggs Vv = rj„ — 0)1 (^) ) applied to the surface ^.(^., /i., 0 = 0 in 5 will secure a form in which the singularity will be reduced by either 1 ) a further succession of transformations as in 3, 2) the method of the Lemma, § 2. Let us consider here the case in which either rj or r, in (25) and (26) is zero. Then in one of the equations a further succession of trans- formations of type (14) will not change the power of ^ as a factor on the right ; and if there are /x such further transformations, the reasoning BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 317 of 4 shows that the left side becomes divisible by ^""-Hf*. So we have either (m — 1) fi < qi or {tn — l)fj, < q^ and thus an upper limit for fi, the number of transformations which leave the order of the singular point unchanged. Now, to consider the transformation (33), we see that it is a one- to-one transformation by which the surface remains analytic near the origin, w^ (Q ^^^ wo (() contain no constant term, for otherwise the factor rjv + wi (Q or f;, -f c,)2 (0 could be combined with the £J factor. Then the transformation (33) leaves the £ factors still £J factors, and the factors vanishing at the origin still vanishing there. Also, it is easily seen that this transfor- mation leaves the terms of type ((, •>/),„ still in the part (tV, -q^, Om' Further, if the function $„(^^, 7y„, t,) goes over into X{^y, rji,, I), we have 9^_9X _ 9X91; _ 9X 9^v 9 $v 9^v 9iu 9 $v and similar conditions hold for the partial derivative with reference to r)y. Accordingly, if by the transformation (33) „(fi., rji,, C) goes over mto il{$v, rjv, C) ^^ replace equations (25), (26), and (27) by A(f., v^, l)HCu ^., 0 + Q. Cs, ^v, 0^= ^ e^ECU 0. (35) d-qv ^(l.-* ^n 0 = ^(fv» !?„ ^)ExQv, -qv, 0 = H{!ty, 7]^,, OE^i^u, -qv, 0- (36) Now, in a further succession of transformations of type (14) on the surface Cl (^„, yji,, Q = 0, if tliere enters either a y or a S not 0, then on the right side of equation (34) or (35) the only factor remaining outside of the E factor is a power of ^, and we must finally have a reduction as shown above. So it is only in the case in which all the y's and 8's of the later transformations are 0 that we are not already sure of reducing the singularity. Now if in O (|i,, qy, Q there is any term of degree less than m in if^, and rjy combined, such a succession of transformations must reduce this term to a degree less than m and thus reduce the singularity. 318 PROCEEDINGS OP THE AMERICAN ACADEMY. For suppose such a term to be aljrjj'l'', where /+ g < m. Then, by a succession of p transformations such as defined, we have ^y = ^i'$v+p-, V''='Q'-nv+p, (derived from form of (19) when all y's and 8's are 0). Substituting this in the expression above we get But we must divide out of this C^'', so that we have left the term " t v+p Vv+P *= This term could not combine with any other derived in a similar way, for if we had another term 6 J-^t;^^*", we should get 7 >/ 9 c-k+plf+g—m) 0$y+pVu+pC and this would not combine with the other unless k = h. Now, if the degree of the singular point is not reduced, we must have for the sum of the exponents f+ 9 + h + p(f+ g — m) ^m or (p + l)(m -f—g)S h, and SiS m > f -{- g h + 1^ m —/— g thus securing an upper limit for p, the number of transformations which leave the term and the singular point of the ?«th order. So it is only in the case in which all terms of Vl (tV, y]v, 0 ^^^ ^^ degree not less than m in I" and 7]^ together that we do not have a re- duction of singularity by the succession of transformations of type (14). But, in this exceptional case, we have the conditions of the Lemma of § 2, where in equation (6) we take the singular line being ^. = 0, 1 = 0. There is in Q (IJ,, rj^, ^) a term in H,*", and so the expression go (y^ does not vanish when ^2 = 0. Accordingly, within a neighborhood about this point, we can break up the singularity by the methods of BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 319 § 2. Further, since the expression (J„, 7;„),„ is not composed of m equal factors, the part ^o(0)a:2"H + ^i(0)a:2'"i-iz + + qm,{0)z^^^ from {6) which corresponds to (^^, rjy) is not composed of m equal factors, and the resulting curve in (k) x.,^'h + ri(^,)a;3"h-i + + r,„^(y„) = 0 has not in equal roots when y., = 0. So a single transformation of the kind in § 2, 3, reduces the singularity in the neighborhood considered here. 7. The neighborhood of the original singular point is mapped upon a finite number of neighborhoods of simpler points. At every stage the function (f^, 17^, ^)„ contains the terms of the type (^, ?;),„ found in the original equation (13). So there is but one singular point of the m-th order in the finite region of the 7;^-plane. Further, the equation {$^, 1, ^),„ z=: 0 for the value ^ = 0 cannot have in equal roots since (f, yj)^ is not a perfect m-t\\ power of a linear factor. Accordingly, the transformation corresponding to (8) in § 1, 4, cannot produce a singular point of the /«-th order. So, at each step, the neighborhood of the singular point is represented by a number of regions as in § 2, C, in which but one of the points of class 1) is of the mth order. Further, the extra transformations (33) carry the neighborhood of the singular point over into that of the new point. So, by combining all the representations, as the singularity is finally reduced, we have the original neighborhood mapped upon a finite number of regions as in § 2, C, in which all points of class 1) are of order lower than m. § 4. A. — The Singular Points of Special Type (continued). 1. Case B. — The m linear factors of (^, rj, £,),„ are all equal. The surface can be expressed in the form ^(i, V, 0 = It + P2{v, 0^-' + +p,niv> 0] ^i^, V, 0 = X(^,r],O^(i,vU)^0, (37) where, in X, $'" is the only term of degree m. If it were in the form /(m, V, w) = (all + (3v + yw)"' + (u, v, w)„+i + = 0, as one of the three numbers, a, (3, y, is not zero, suppose a = 0. 320 PROCEEDINGS OF THE AMERICAN' ACADEMY. Then by a linear homogeneous transformation V = V w = w we secure the form f{u, V, w) =f(u, V, w) — U'" + (/7, V, T<,-)„,+i + By Weierstrass's Theorem we can express this in llie form f{u, V, w) = [i?' + p, (v, w) u"'~^ + + p,„ {v, w)'] E{Ji, V, w). (38) Now, in the expression 7>^(y, w), A = 1, 2, m there is no term of degree less than A + 1, for otherwise on account of the constant term in the ^factor, there would have to be present in^" a term of degree ^ m containing v or w. Make in (38) the transformation M + ,^ ^1 iv W) = $\ V = 7] >■ As jOi {y, w) contains no term of degree less than 2, by the considera- tion above, y goes over into form (37). B. Thk Quadratic Transformation. 2. The transformation applied to $ {$, t], C) secures the form (^, V, i) = C"^(l I 0 = C"lr + ^^(1, V, 01 (39) Here the curve ^ (i, rj) = 0 becomes |"' — 0, and so, applying the Lemma of § 2 to a circle in the v^-plane however large, we have within it but a finite number of singular points to treat further. But one such circle is needed, for by taking it large enough we can deal with all of the 1^-plane outside of that circle by the transformation So we need to consider for further treatment only a finite number of points along the line t = 0, and the point at infinity. BLACK. — THE NEKJHBORHOOD OP A SINGULAR POINT. 321 3. The quadratic transformations to be used are of two types 1) $^ = $n+iC^, ^,a = (^^i+i + S^+i) ^Mi (40) 2) 1^ = $^+iv^, i^ = (^,.+1 + ^)^+i)Vn' (41) In a succession of transformations of type (14) we see that yi = 0, since the first set of points is taken on the line f = 0. Further, sup- pose after the substitution rj — 8i = rji'm ^ oi (39) the expression (f, Vl Om contains terms besides the J™ ; then it cannot be composed of m equal linear factors, for that would require a term containing f""^ ; but no such term can arise from the factor X of (37), and, on the other hand, it could not be the product of a term from X by a non-constant term of the ^ factor, for then, on account of the constant term of the -E factor, there would have to be present in <5 a term of degree lower than m. So as soon as the function corresponding to <^ of $ contains more than the »ith power of the $ variable, the function corresponding to (f, rj, t,)„^ is no longer the product of m equal linear factors, and we have one of the cases treated earlier. The same considerations apply to the transformations corresponding to type 2), since, when the transformation which deals with the infinite region is introduced, the first one of that order is of form Accordingly, the most general succession of transformations here is one in which groups of types 1) and 2) alternate. We shall call them the t, and rj types respectively, and when a change is made from one type to the other, we shall speak of it as a reversal of type. We shall treat the subject in two cases, first supposing that there is no reversal of type in the succession of transformations used, and later supposing that reversals of type occur. C. — Succession of Quadratic Transformations in which THERE IS NO REVERSAL OF TyPE. 4. After a sufficient number of quadratic transformations the surface can be reduced to the form [(C + ?^*^^(^- 0C~'+ • • • + ?;^'''^(^- 0']E{^.. v^, 0, (42) VOL. XXXVII. — 21 322 PROCEEDINGS OF THE AMERICAN ACADEMY. while all later transformations can be taken of the type i^ = in+lC, Vf^ = •7^+1 C (43) After V transformations of type (40), since there can be no interchange of terms among the coefficients of the different powers of the $ variables in the A' factor of (37), the surface will take the form [C + P-2AV^, 'C)C' + + Pm^^^^^ 0] ^(t., v., 0 = 0. (44) Now by the same reasoning as used for the function H in § 3, 5, if v is taken large enough, the coefficients of the powers of $t, in A^ will all be of the type s = 2, 3, m. For any one of the functions >7,. + v(0 there is a determinate succession of transformations of type which will leave it of the same degree after the I is divided out, all others reducing the degree at once , i. e., if » 1?^ + >' (0 = ■^M + Cll ^ + ^^2 r + > we must take etc. So, unless the factors ■rii' + V, (0, s = 2, 3, m are all equal, Ave must have finally some coefficient of a power of ^^ with the •>7„ present only in the E factor, and by taking v large enough we come to a point where all the factors f]^ + v,(0> s == 2, 3, . . . . . m, are equal, some of them possibly having zero exponents. Tlieu we use the transformation -qv + Vs (0 = Vy (45) BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 323 and arrive at the form (42) required. Now any further transformation of type (40) in which the 8 is not zero will leave the rj variable present only in the E factors, so that the general term (after the first) of the function Xv is of type r^^(^".,OC~*' ^--=2,3, m. Suppose, after this, there are p transformations of type (40). Then the corresponding term after the factor ^™'* has been divided out is and if this is of degree not less than m, as it must be if we are not to secure reduction, we have m — s -\- q^ — ps > m or p S J ~ s thus securing an upper limit for the number of transformations of type (40) which do not give reduction of singularity. Accordingly, after the form (42) is reached, it is only when all later 8's are zero that we are not sure of reduction.* 5. A sufficient number of transformations of type (43) applied to (42) secures either 1) reduction of singularity, or 2) the condition that for some term (the rth) of the X factor s = 2, 3, m. If, for any term a transformation of type (43), after the factor C™ has been divided out, yields decreasing the exponent of ^ by r — p^. This decrease takes place at every such transformation, and thus the exponent of ^ must finally be * We do not lieed to consider the possibility of liaving all the coeflBcients of the powers of |^ lower than the m-th vanish, for then the function X^ would have m equal factors 1^ and this case has been excluded. Pr < Pi r — s 9l < 9i r s 324 PROCEEDINGS OP THE AMERICAN ACADEMY. reduced to a value q' ^ less than r — p^, in which case the sum of the exponents of the three variables, p^-\- q\^- in — r, is less than m and reduction ensues. So it is only in the case in vphich for every term p,>s, s = 2, 3, m, that we are not sure of reduction. Suppose the number of transforma- tions after this point to be n. Then we get for the new exponent of t, qs + n{p, — s). Now by taking n large enough we can make the quotient " {Ps - ■s) + qs s iy "■"" s have the lowest value for the term in which — is lowest, while if this is the same for two or more terms, we can make the fraction above lowest for the one in which — is lowest. Accordingly, by a finite number of transformations of type (43) we secure the condition that p — y p . . . Q . ^-^ and so — is lowest in the same term in which — is lowest. r r 6. A succession of transformations of type ^M = Wi^, (46) followed by a succession of type secures the surface with condition 5, 2) in the form ^pi^.p, Vp> 0 = ^p(fp. Vpi V)E{Ep, r)p, 0 = [C+<'C''^('/p'OC' + --- + <'"^''"^('7p'0]^(^p.'7p,0 y ^4g^ where for some particular term in Xp, the rth, Pr q, — ns > 0, or 1'- 1 < 7i < £f. s s So the term for which — is least is among those first reached in which the new exponent of ^ is lower than s. In the same way we show that, by applying a succession of transfor- P mations of type (47), the term for which — is least is among the first lot reached for which the new exponent of rj^ is less than s. But, by P Q condition 2) in 5, - and — were least in the same term. So we secure ' s s the surface in form (48). 7. A further succession of quadratic transformations of type (43) as applied to the surface in form (48) will reduce the singularity. This follows at once by the reasoning in the first part of 5. D. — Succession of Quadratic Transformations in which THERE ARE REVERSALS OF TtPE. 8. A succession of transformations in which there is a sufficient num- ber of reversals of type will secure a surface of type (42). If there is but a finite number of reversals, after the last one we are in the same position as at the start in 4, and the succession of trans- formations which follows, not having any reversal of type, will enable us to secure the condition derived by the method of 4. So we need here to consider only the possibility of an indefinitely large number of reversals of type. In equation (37) consider any one of the coefficients Pr(v,0 = tPriU) = tl{ri,On, + (77,On,+l + ] where p^ (rj, 0)^0. A transformation of type (40) will give for p^ a function from which we 326 PROCEEDINGS OF THE AMERICAN ACADEMY. take out the factor ^"'', the other factor being of degree less than n^ unless the part (17, ^)nr has n^ equal linear factors. For, if and not all the linear factors are equal (or linearly dependent), then the substitution gives tlr C n {ap-rji + ttpSi — /3p) p = \ and leaves an absolute term in any factor for which apSj 4^ /3p, thus securing in the product of the factors terras of degree less than n^. Also the degree might be lowered on account of terms in some later part as (r/, Qnr+k- But, if all the factors of (77, Qn,- are equal (or linearly dependent) and 81 is taken so as to satisfy the condition o-pOi = Pp, p := 1, 2, n,. , then after the factor C^ is divided out, we have left but one term in rj^''^ which cannot cancel with any term from another part of the function, as all later terms have as a factor some power of ^. Accordingly a suc- cession of transformations of type (40), if it does not reduce the degree of the part not divisible by ^, must leave a term in 77 "^ Now when the reversal of type is first made, the e of (41) is zero, as is seen by con- sidering the use of transformation (8) § 1, 5, Then we take out a factor 7] "'■ and leave a constant term. So a succession of transformations which contains reversals of type must reduce the degree of the function /),. (possibly to zero), except for factors taken out which are powers of the 7] and I variables. Accordingly, by a succession of transformations containing a sufficiently large number of reversals of type, the coefficient p^ must be reduced to the type 9. All further transformations to be considered may be taken of the types 4 = ^f*+i ^1 '?/^ = •7m+i ^' (49) BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 327 For if a transformation of type (40) or (41) in which the S or c is not zero were used, we should have in all the coefficients of X^ in (42), out- side of the £J factor, only powers of one variable. Suppose it to be ^ ; then, by means of a succession of transformations of type (46), we can reduce some term to a form in which the exponent of C is less than r, and thus secure a reduction of singularity. 10. A sufficiently long succession of transformations of types (49) and (50), applied to surface of type (42), unless it first secures reduction of singularity, will secure the condition that, for some term (the rth), s = 2, 3, m. r s Consider the two terms Any transformation of type (49) leaves the p^ and pt unchanged, and increases the qs hy Ps — s, qt " Pt — t. Any transformation of type (50) leaves the q, and q^ unchanged, but increases the Ps by q, — s, Pt " qt — t- Represent q, — r r = 2, 3, m, (51) So, for each transformation of type (49) the K^ is increased by the IT,., and for each transformation of type (50) the 11^ is increased by the K,.. We shall show that finally we must have one of two conditions «) n, > n„ K. > K„ b) n, < n,, K, < K,. Suppose, at any stage, neither of these conditions holds, and we have, for example, n, > n„ K, < K,. (52) 328 PROCEEDINGS OF THE AMERICAN ACADEMY, Then, for a transformation of type (49), supposing the new K's to be K/, K/, we have K/ = Ks + n„ K/ = K, + n„ and so K/ - KJ = Kt- Ks - (n. - n,) < K, - K,. Also, for a transformation of type (50), if the new II's are IT/ 11/, we have n/ = n, + K„ n/ = n, + K„ and IT/ - n/ = n, - n, - (k, - k,) < n, - n,. So when a condition of type (52) holds, any transformation applied will reduce the difference of either the II's or K's, if in fact it does not change the sien of the difference. Further, the reduction is each time by a value not infinitesimal, for it is at least 1 j st, as is seen by con- sidering the values of K;. and IT,, in (51). So the succession of trans- formations of whatever kind must finally reduce the difference of either the it's or the K's to zero, or change its sign, and then we secure either condition a) or b). When one of these conditions has once been secured, any further transformation will not change it; for, in condition a), a transformation of type (49) will add at least as much to the K^ as to the K,, and so retain the inequality of the same order, and similar conditions are seen to hold in the other cases. Also, as one of the conditions a) or b) must hold finally, whatever the pair of values s and t, we shall have some value as ?■ such that n, < n„ K, < K„ s = 2, 3, m. from which follows the required condition '' ' ' L s=2,3, m. r ~ s J 11. The method of G, applied to the surface resulting from the treat- ment of 10, will secure the result of 6. It may be that already either p, < r or q, < r, but in such a case the number of transformations of BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 329 type (46) or (47) can be considered zero, while in the other case we have exactly the initial conditions of 6, the result of which then can be secured in any case whatever. 12. In the case of surface (48) any succession of transformations of types (49) and (50) will finally reduce the degree of the singular point. Consider the term m — r Any transformation of type (49) adds to the exponent of ^, jo,. — r, and as pr < r, the exponent of ^ is reduced. In the same way we see that any transformation of type (50) reduces the exponent of the rj variable. So in any case, by virtue of the reduction of degree, we must have finally either p,^ i-t;^<<^z«?^r. ^il^^^ Place, *** Ho book OP pamphlet is to be removed fpom the Iiab- opatopy uiithout the pepmission of the Tpustees. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A NEW INVESTIGATION CONCERNING TPIE ATOMIC WEIGHT OF URANIUM.* By Theodore William Richards and Benjamin Shores Merigold. Presented December 11, 1901. Received December 19, 1901. Introduction. Our knowledge of uranium dates from the year 1789, when it was first recognized as an element by Klaproth. It can by no means, therefore, be classed with the new elements, nor is it of great rarity. Nevertheless, comparatively few determinations of the atomic weight of this element have been made, and of these, one only has been carried out with the degree of accuracy necessary in work of this kind. During the fifty years following the discovery of uranium a number of atomic weight determinations were made by Berzelius, Arfvedson, Schonberg, Mar- chand, and Rammelsberg. This early work is now of historical interest only, for the results vary widely, and in some cases are of such a nature as scarcely to be considered quantitative, in the modern sense of the word. For example, Rammelsberg obtained results varying from 184 to 234, calculated upon the modern basis. In 1841 Peligot discovered that the substance then known as uranium was not an element, but an oxide. This discovery, while it did not impair the value of the analytical work previously done, necessitated a recalculation of the numerical value of the atomic weight. The new value was 120, and this remained practically unchanged during the next thirty years. When the periodic classification of the elements was first suggested, uranium, with the atomic weight 120, was one of the elements for which there was no place. From a study of the properties of uranium and its compounds, Mendeleefi" declared that the atomic weight * The greater part of the work described in this paper was presented to the Faculty of Arts and Sciences of Harvard University by B. S. Merigold, as a thesis for the degree of Ph.D., in June, 1901. 366 PROCEEDINGS OF THE AMERICAN ACADEMY. of uranium was probably 240 instead of 120.* The question was not definitely settled until Zimmermann, in 1885, carried out the suggestions of Mendeleeff, and by specific heat and vapor density determinations confirmed the higher value.f Owing to the wide variations in the published results, the atomic weight of uranium has long been considered one of the least satisfactorily determined of the atomic weight values. A glance at the results thus far obtained is sufficient to show the need for further work in this line. A complete resume of the older work upon the subject is to be found in Clarke's recent work on the atomic weights, t The following table summarizes those investigations which seem to possess even a little quantitative value : — Less Inaccurate Previocs Work on the Atomic Weight of Uranium. O =r 16.000 1841 Peligot §— Analysis of Green Chloride 240. ± 1842 Ebelmen II — Combustion of Oxalate 238. ± 1843 Wertheim TT — Double Acetate of Sodium and Uranium 239. ± 1846 Peligot** — Combustion of Oxalate and Acetate . . 240. ± 1886 Zimmermann ff — Reduction of Oxide, UsOg to UO2 . 239.6 1886 Zimmermann H — Ignition of Double Acetate . . . 239.5 The work of Ebelmen, Wertheim, and the early work of Peligot is neces- sarily of little weight in assigning a probable value to the atomic weight of uranium. lu some cases the material used was impure, and in others the methods of analysis were faulty. Consequently it is not surprising to find differences of whole units in the individual determinations of each series. Peligot's later determinations from the oxalate is perhaps the best of the early work. His material was carefully purified, and his method is far preferable to the work of Ebelmen and Wertheim. By combustion * Annalen der Chemie u. Pharmacie, Supp. Vol. 8, 178 et. seq. t Annalen der Cliemie u. Pliarmacie, 216, 1. } A Recalculation of the Atomic Weights, by F. W. Clarke, Smithson. Misc. Coll., Constants of Nature, Part V. (1897), 263. § Compt. Rend. 12, 735. Ann. Chira. Phys. (3) 5, 5 (1842). II J. prkt. Chem. 27, 385 (1842). 1 Ibid., 29, 209 (1843). ** Compt. Rend., 22, 487 (1846). tt Ann. d. Chem., 232, 299 (1886). Jt Ibid. RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 367 analysis he determined the ratio between uranium oxide and carbon dioxide. Thus he eliminated the error involved in weighing a crystal- lized salt which would probably contain more or less included water. The principal sources of error are the questionable use of combustion analysis in atomic weight investigations, and the possibility of unoxidized carbon remaining in the uranium oxide. His best results vary from 239.4 to 241.1. The work of these chemists, though a great improvement over the attempts of Rammelsberg and the other early workers, leaves much to be desired, and does little more than give an approximate idea of the probable value of the atomic weight of uranium. Zimmermann's investigation of the ratio between the oxides UO., and UsOg was much more carefully carried out, and is the only work thus far published that is worthy of serious consideration. Using carefully purified material, and giving attention to detail, Zimmermann oxidized the lower oxide by means of a stream of oxygen, and observed the gain in weight. His results for the atomic weight varied from 239.49 to 239.76, an extreme difference of 0.27, or 0.11 per cent. The average was about 239.6. The chief probable cause of error in this method is the difficulty which is always exjDerienced ip forming a more voluminous solid from a less voluminous one. Uranous oxide has a specific gravity of 10.2, while the " Urauoso-uranic" oxide has a specific gravity of only 7.3. The great increase of volume which occurs when the higher oxide is formed must tend to protect particles of the lower oxide from the action of the oxygen. Hence the gain in weight will be too small, and the apparent atomic weight of the metal too large.* It is clear that a very small deficiency in the weight of the higher oxide must cause a great increase in the apparent atomic weight. Moreover, any incompleteness in the reduction by which the lower oxide was prepared, or any retention or occlusion of gases within this oxide, would also tend to raise the apparent atomic weight. Hence one is inclined to believe, even without further evidence, that Zimmermann's result for uranium must be too high. A new determination of the atomic weight of uranium has recently been made by J. Aloy.f The method employed differs materially from any previously used in uranium work. The values obtained are derived * Compare Richards and Baxter, These Proceedings 34, 351 (1898). Ztsch. anorg. Chem. 21, 251 (1899). t Comptes Rendus, 132, 551 (1901). This work is discussed rather fully here, since it is too recent to have been included in Clarke's book. 368 PROCEEDINGS OF THE AMERICAN ACADEMY. from the ratio between the weight of nitrogen and that of uranous oxide contained in crystallized nranyl nitrate. Uranyl nitrate was purified by repeated crystallization. A quantity of the pure nitrate, the weight of which need not be known, was put into a boat, and the boat surrounded by a section of platinum tube, to prevent loss of material. The whole >\'as placed in a combustion tube between spirals of reduced copper. One end of the combustion tube was connected with a carbon dioxide generator, and the other with an absorption apparatus containing a con- centrated solution of potash. After sweeping the air out of the apparatus with a current of carbon dioxide, the nitrate was heated so long as evolution of nitrogen occurred, the temperature being finally raised to red heat. The reduced copper was kept at red heat throughout the operation. When it was certain that no more nitrogen was evolved, the green oxide remaining in the boat was reduced by hydrogen to uranous oxide and weighed. The nitrogen was transferred to a measuring tube reading to tenths of a cubic centimeter. From the ratio of the weight of this volume of nitrogen to the weight of the oxide, the atomic weight is calculated. The following are the results of the eight determinations given : — Atomic Weight of Uranium. N = 14.04 Volume of nitrogen, 15.25 cc. Atomic wt. of uranium, 239.3 33.5 239.4 38.0 239.6 52.5 239.5 81.25 239.4 125.0 239.5 151.2 239.4 165.0 239.4 Average 239.4 This method has the merit of simplicity, and does not involve the weight of the crystallized salt. There are, however, several sources of possible constant error that have not been taken into account. When crystallized uranium nitrate is heated, it first melts in its water of crystal- lization. As in all similar cases, it requires the very greatest care to prevent spattering while the crystal water is being driven off. It was undoubtedly as a precaution against loss of material in this way that Aloy used his j^latinum tube. By the time the crystal water is expelled, the fused mass has hardened into a solid cake, changing in color from yellow to orange, and finally to the green of urano-uranic oxide, UsOg. This method of preparing the green oxide from pure uranyl nitrate RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OP URANIUM. 369 was used in the work to be described in the following pages. It was invariably found, however, that during the decomposition of the dried nitrate, and the subsequent oxidation, the oxide first produced forms a protecting crust, as it were. This prevents, or at least very materially retards, the decomposition of the material within the interior, even when the temperature is maintained for several hours at red heat. On the outside, the material had the appearance of being completely converted to oxide. On powdering the lumps, however, and again heating, there was in every case a further evolution of nitric fumes. Moreover, nitrogen itself is often retained by oxides prepared in this way.* It seems thus extremely probable that the quantities of nitrogen measured by Aloy were in every case too small. Obviously, until this point is definitely settled, Aloy's results must be regarded with more or less suspicion. It has been pointed out that reduction is usually much more complete than oxidation. t During the reduction of an oxide, there is formed, perhaps, by the removal of a portion of the oxygen, a kind of skeleton framework, giving to the remaining substance a porous structure which enables the reducing gas to penetrate farther into the interior of the mass, until reduction is complete. Owing to this action, it is probable that when the green oxide of uranium is finally reduced by hydrogen, all the nitrogen is expelled, and the final product is pure uranous oxide. Consequently, the weight of uranous oxide used in the calculation is probably nearly correct, the principal error being in the volume of nitrogen . Aside from this special objection to the use of this method in its application to uranium, there is the general objection to the use of such a method where great accuracy is desired. The exact measurement of small quantities of gas offers considerable opportunity for error, especially, when, as in this case, the gas is first to be transferred from the collect- ing to the measuring apparatus. When the volume or weight of a gas is involved in an atomic weight investigation, it is customary to work with as large volumes as possible, thus reducing to a minimum the effect of the errors inevitably connected with the measurement of the gas. The exact measurement of a volume no larger than 165 cubic centimeters, even, — the largest volume measured by Aloy, — is a matter of considerable experimental difficulty, while with the smaller volumes, 15, 33, and 38 cubic centimeters, errors of at least 0.1% are * Richards and Rogers, These Proceedings, 28, 200 (1893) ; also Richards, Ibid. 33, 399 (1898). t Richards and Baxter, loc. cit. VOL. xxxvii. — 21 370 PROCEEDINGS OP THE AMERICAN ACADEMY. not only possible, but extremely probable. A difference of one tenth of one per cent in the volume of nitrogen makes a difference of 0.3 in the value of the atomic weight. The errors of collection and transference of the gas are more likely to result in reading too small rather than too large volumes, giving too high values for the atomic weight. From these considerations, it is evident that Aloy's results are at least somewhat doubtful. Aloy gives notice of his intention to apply this method to the determination of other atomic weights, but it is to be hoped that before doing so he will clear up some of the doubtful points in connection with the process. As carried out in this investigation, the method certainly is not a valuable addition to the methods of atomic weight determination. From the earlier results Clarke computed the value 239.6, while the German Committee recommend 239.5. Both figures are practically identical with Zimmermann's figures. The investigation herein described was undertaken with the hope that by increasing the experimental basis of our knowledge of the subject, we might be able to reduce to somewhat narrower limits our present uncer- tainty in regard to the real value of this constant. Preliminary Work upon the Preparation, Properties, and Methods of Analysis of Some Uranium Compounds. In view of the well known advantages of the halogen compounds for accurate analysis, when these compounds can be prepared and weighed in a state of purity, — it seemed desirable to use a halogen compound as the basis of a determination of the atomic weight of uranium. Of the four chlorides of uranium known to exist, none can be pre- pared in a state of purity that is beyond question. Green uranous chloride, UCI4, which results from passing dry chlorine over a mixture of uranium oxide and carbon at red heat, is easily converted to the pentachloride, UCI5, by further action of chlorine at high temperatures. There can be no positive evidence that the green chloride would not contain some of the pentachloride, and if the attempt is made to prepare the pentachloride from the green chloride, it is equally difficult to be sure that the conversion is complete. The trichloride, UCI3, is made by reduc- ing the tetrachloride with hydrogen, and here agaia it is difficult to be sure that the tetrachloride is completely reduced. Uranyl chloride, UO2CI2, cannot be prepared in the dry state. It is extremely probable, then, that any of the chlorides will contain larger or smaller quantities of a higher or lower chloride. It may be RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 371 observed, in this connection, that Zimmermann used the chlorides in his vapor density determinations, and his analyses show good agreement. This does not show conclusively, however, that his material was free from small, but fairly constant quantities of higher or lower chlorides as impurities. Ou the other hand, bromine forms with uranium only three distinct compounds: the tribromide, UBrg ; uranous bromide, UBr4; and the oxybromide, or uranyl compound, UO.iBro. The tribromide can be produced only from the tetrabromide by the action of reducing agents. Uranyl bromide, UOaBr.,, has been certainly formed only in solution, resulting in hydrated crystals. It has never been definitely obtained in an-hydrous form. Zimmermann made many attempts to form the penta- bromide, corresponding to the pentachloride, by passing bromine at high temperatures over sublimed uranous bromide. Every attempt gave negative results, showing tliat at temperatures up to the subliming point of uranous bromide higher bromides cannot exist. Since higher bromides are non-existant under the conditions prevailing in the forma- tion of the tetrabromide, the objections to the use of the tetrachloride are not applicable in the case of uranous bromide. The investigations of Zimmermann * have shown that the tetrabromide can be formed in an apparently definite state. It seemed probable, therefore, from the literature on the subject, that in uranous bromide we had a compound well suited to the purposes of our investigation. The method of preparation followed at first was essentially that described by Zimmermann.* In an apparatus constructed wholly of glass, a mixture of dry nitrogen and bromine vapor was passed over a mixture of the green oxide of uranium, UsOg, and pure carbon. The air was first thoroughly swept out of the apparatus by a current of nitrogen, and the oxide was heated to a high temperature. When the bromine vapor was passed in, uranous bromide formed, and sublimed in brilliant crystalline j^lates of a brownish color. After cooling in a current of nitrogen, the sublimate was transferred to a weighing bottle. At this point, however, unexpected difficulties arose, owing to the rapid oxidation of the bromide. Uranous bromide is extremely deliquescent, and forms with water and oxygen the oxybromide, with liberation of hydrobromic acid. Consequently, when exposed to the moist air of the laboratory even for the short time required for removing the sublimate from the combustion tube, the bromide loses its brilliant lustre, and * Annalen der Chemie, 216,3. 372 PROCEEDINGS OP THE AMERICAN ACADEMY, assumes a dull, greenish yellow appearance, due to formation of the oxy- salt. If not protected from further action of moist air, the salt liquifies completely in a surprisingly short space of time. In an attempt to change the coating of oxybromide back to the normal salt, recourse was had to the method which has been used suc- cessfully in many atomic weight investigations carried on in this labora- tory. The salt was transferred to a platinum boat and placed, with a weighing bottle of suitable size, in a glass bottling apparatus.* A stream of dry hydrobromic acid gas was then passed over the bromide at a temperature just below the subliming point of the salt. This treat- ment, however, fails to restore the original brilliant appearance of the freshly sublimed bromide. The yellow color of the oxybromide still remains. Apparently the oxybromide, once formed, cannot, by this method, be reduced to the normal uranous bromide. In the previous investigations upon zinc, magnesium, nickel, and cobalt, in which this method of converting oxy-salts to the normal com- pounds has been used, the presence of even minute quantities of oxy-salt was made known by the opalescence of the" solutions on account of the insolubility of these salts. With uranium, however, this method of detecting the presence of uranyl bromide cannot be used, for the oxy- bromide of uranium is even more soluble than uranous bromide. The analysis of uranous bromide presents further difficulties. All uranous salts reduce silver nitrate. When a solution of silver nitrate, slightly in excess of the calculated amount, is added to a solution of uranous bromide, the silver bromide first precipitated is probably mixed with metallic silver; for if the silver bromide is filtered off, and the filtrate set aside, finely divided metallic silver soon separates. If a large excess of silver nitrate is added to the uranous bromide, a brilliant purple precipitate is obtained. It is possible that the precipitate may be a mixture of finely divided metallic silver and argentic bromide, or perhaps of normal argentic bromide and the long sought sub-bromide. Although this is an interesting phenomenon, it was not considered advisable to interrupt the research at this period for the length of time necessary for an investigation. The addition of nitric acid prevents the formation of this colored precipitate, but owing to the danger of the loss of bromine, this is not au advisable expedient. Of course it is possible to determine the bromine by first precipitating the uranium and adding silver nitrate to the filtrate, but this introduces * For a description of this apparatus, see These Proceedings, 32, 59. RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 873 a complexity of operations incompatible with the degree of accuracy requisite iu an atomic weight investigation. On account of these formidable difficulties in the preparation and analysis of pure uranous bromide, it was thought best to search for some compound which offered fewer obstacles. It will be seen that this search was vain, although it required many mouths. In view of the great tendency of uranous bromide to oxidize, under ordinary conditions, the use of uranyl bromide seemed to offer the simplest solution of the problem. Anhydrous uranyl bromide has never been prepared in a pure state. In the prepai'ation of uranous bromide, if the nitrogen used contains a little oxygen, or if traces of moisture are present, there is formed, in addition to the uranous bromide, a yellow powder, very different in appearance from the brown color of finely divided uranous bromide. This powder has been assumed by various investigators to be the oxybromide. Owing to the fact that it is always mixed with uranous bromide, an analysis has never been obtained. There seemed to be, however, some basis for belief that under suitable conditions of temperature, moisture, and oxygen supply, it might be possible to obtain anhydrous uranyl bromide entirely free from the uranous compound. With this end in view, the green oxide, without any admixture of carbon, was heated in a stream of bromine, also iu a current of hydrobromic acid. In each case there was apparently no action whatever other than a partial and gradual reduction to the black oxide. This slight reducing action is probably not due to the gases used, in the sense of being peculiar to them, for Zimmermann has shown that this reduction takes place whenever the green oxide is heated in a current of inactive gas such as nitrogen or carbon dioxide. * Both moist and dry gases were used. Mixtures of these gases and air were also tried, at different temperatures. The green oxide was then reduced by hydrogen to uranous oxide, UO2, and this was then treated with various combinations of dry and moist bromine vapor, hydrobromic acid, and air, at various temperatures. Again the results were negative. Under these conditions the bromine did not combine to the slightest extent with the uranium. Since combination fails to take place, even in the presence of considerable quantities of oxygen, there is naturally some cause to doubt that the light colored powder above mentioned is really an oxybromide. Possibly it is, after all, uranous bromide in a different state of aggregation. * Log. cit. See also Richards, These Proceedings, 33, 423 (1898). 374 PROCEEDINGS OF THE AMERICAN ACADEMY, The hydrated uranyl bromide is more easily obtained. The green oxide was reduced by hydrogen to uranous oxide, suspended iu water, and heated with bromine on the steam bath. After driving off the excess of bromine, uranyl bromide remains in solution. The solution may be evaporated to the consistency of a thick syrup, and even under the best conditions the yield of crystals is very small. Moreover, it is almost impossible to wash the crystals free from the mother liquor, since they are extremely soluble in water and alcohol, and ether decom- poses the compound, setting free bromine. Hence uranyl bromide was abandoned. Of the iodine compounds of uranium, the iodate alone seemed promis- ing. This compound has been prepared and described by A. Ditte,* who assigns to it the anhydrous formula U02(I03)o. The iodate was prepared by us as follows : — To a solution of uranyl nitrate, containing much nitric acid, was added a solution of iodic acid, prepared by warming finely powdered iodine with nitric acid of specific gravity 1.50. Both solutions were heated to boiling before mixing. Uranyl iodate is precipitated as a yellow, finely crystalline salt, but slightly soluble in water at ordinary temperatures. At 100°, however, if some nitric acid is added, it is possible to obtain a solution containing ten grams of iodate to the litre. On cooling, 2.5 to 3.0 grams of iodate crystallize out. By recrystalliziug a few times, in sufficiently large vessels, it is possible to obtain a compound in a high state of purity. The method of preparation described above is that recommended by Ditte, Although Ditte's course of procedure was carried out as ex- actly as possible, the compound obtained differed from that which he describes. Instead of being anhydrous, it contained one molecule of water. Inasmuch as Ditte's statement of the amount of nitric acid ■which he used is extremely vague, different concentrations were tried, from a solution slightly acid up to one containing twenty-five per cent of strong nitric acid. In every case the hydrated compound was obtained. Ditte did not recrystallize his compound, but our recrystallized product was identical with that which was only once precipitated. The analysis given is the average of ten concordant analyses of material prepared from both hot and cold solutions. Both recrystallized iodate and that precipitated only once are represented. The method of analysis is described below, * Annales de Chimie et de Physique, 6th Series, 21, 158 a890). RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 375 Analysis of Urastl Iodate. p, , Calculated for • U02(103),H,0. Uranous oxide 42.54% 42.34 % Iodic acid 54.84 54.84 Water (by difference) 2.62 2.82 100.00% 100.00% In determining the composition of the iodate, a weighed quantity of the substance was used, and the percentage composition by weight cal- culated in the usual manner. For an atomic weight determination, however, any method which involves the original weight of a salt crystallized from solution as a factor in the calculation must of course be avoided on account of the ever present possibility of included mother liquor. It was necessary, then, to determine directly the ratio of iodine to uranium, or to uranium oxide. To determine the uranium, advantage was taken of the behavior of the iodate on ignition. When heated, the iodate is decomposed, water, oxygen, and iodine being given off, leaving uranium oxide. The process was carried on in an ordinary combustion tube of hard glass, a current of dry air being passed through the tube. Since Zimmermann has shown that the green oxide under- goes partial reduction at high temperature unless in an atmosphere of oxygen, * a stream of oxygen was finally passed through the tube. The oxide was then cooled in an atmosphere of oxygen. Treated in this way, the decomposition of the iodate is not complete. Some iodine always remained in the oxide, even when the heat was maintained for thi'ee hours at a temperature just below the softening point of the com- bustion tube. To correct for this amount of iodine, the oxide was weighed, dissolved in dilute nitric acid, and the iodine precipitated as argentic iodide. The amount of iodine found in this way varied from 0.1% to 1.0% of the total iodine, according to the duration of the period of ignition. Iodine was determined in another sample of material exactly similar to that used for the uranium. The method was, briefly, reduction of the iodate by sulphurous acid, and precipitation with silver nitrate. Stas has shown that silver iodate can be converted completely and with- out loss into silver iodide by the use of sulphurous acid.f and the same * Annalen der Chemie u. Pharmacie, 232, 287 (1886). t Untersuchungen iiber die Gesetze der chemischen Proportionen iiber die Atomgewichte u. ihre gegenseitigen Verhaltnisse, J. S. Stas. Aronstein's transla- tion, p. 69. 376 PROCEEDINGS OF THE AMERICAN ACADEMY. method applies equally well to uranium iodate. The iodate was sus- pended in 200 c.c. of water acidified with 20 c.c. sulphuric acid, cooled in ice to 0°, and pure sulphur dioxide was passed in until the solution smelled strongly of this reagent. The flask was then removed from the ice and shaken occasionally. From three to four hours is required before complete reduction takes place and the last traces of iodate go into solution. When completely reduced, silver nitrate is added, and heated to 60° in order to cause the more coherent deposition of the jjrecipitate.* Thus it was found possible to convert the insoluble iodate into soluble iodide without loss of iodine. In this way the ratio of uranium oxide to iodine may be determined, regardless of the presence of occluded water in the iodate used, provided that the amount of water occluded be exactly the same in each of the samples. It would obviously be more satisfactory to determine both uranium and iodine in the same sample, provided a sufficiently simple method could be found. The following method was found to fulfil the required conditions fairly well. A quantity of the iodate was placed in a boat in a com- bustion tube, to one end of which was attached, by a ground glass joint, a weighed U-shaped tube. The free end of this tube was drawn out and fused to a smaller tube which dipped into a solution of sulphurous acid. On heating the iodate in a stream of air and oxygen, the salt was decom- posed and the iodine was carried over and condensed in the U-tube, which was packed in ice. The small quantity of iodine vapor not con- densed was collected in the sulphurous acid and precipitated as silver iodide. The heating was continued for an hour after no more iodine could be seen coming off. The end of the U-tube was then sealed by fusing off the small tube, and the other end was closed by a ground glass stopper immediately after disconnecting from the combustion tube. In this way about ninety-nine per cent of the total iodine was weighed directly as free iodine. Of course the small amount of iodine remaining in the oxide after ignition had to be determined separately, as already described. By this method the amount of iodine found was practically identical with that found by the sulphurous acid method. In determining the iodine present in the oxide after ignition, it has been assumed that the iodine is present as iodide. Although it is hard * When silver iodide is precipitated in the presence of sulphurous acid, the supernatant liquid does not become clear enough to filter even after several days, unless heated to 60°. Vide Stas, " Untersuchungen," p. 69. RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 377 to believe that at the temperature employed any of the iodine can exist as iodic acid, it is impossible to prove the point experimentally. The uncertainty in regard to this point renders the use of the method inadvis- able where the greatest possible accuracy is desired. Hence none of these analyses have any significance as a basis for computing the atomic weight of uranium. Besides the bright yellow, slightly soluble iodate, we prepared a paler yellow, more soluble, and more highly hydrated salt, which suffers transi- tion quickly into the earlier compound at a high temperature and more slowly at a low temperature. Double iodates with sodium and potas- sium were also prepared. Some of our observations were inconsistent with the published record concerning the subject ; but in spite of our desire to clear up the uncertainty and to study the rather intei-esting transition phenomena, we abandoned the iodates because none of them gave promise of a precise basis for the determination of the desired atomic weight. The next compound investigated was the oxalate, which has the com- position UOoCoOi' SHoO. Owing to the comparatively slight solubility of this compound it can be obtained in a state of great purity by a few crystallizations. The best method of analysis is that of dry combustion, the carbon dioxide being absorbed in potash in the usual manner. The uranium is left in the combustion tube as the green oxide, UgOg, and consequently can be compared directly with the weight of carbon dioxide obtained. This obviates the necessity of using the weight of the oxalate as a factor in the calculation of the atomic weight, and so eliminates the error due to included water. As already mentioned, this method has been used by Klbelmen and Peligot in their determination of the atomic weight of ura- niura. There is in this method a possible source of error, difficult of detection and correction, but none the less dangerous, in the possibility that the uranium oxide may after combustion still retain traces of carbon. Moreover, it became evident, after a few analyses had been made, that combustion analysis, as ordinarily conducted, is an exceedingly question- able method where great accuracy is desired. The great difficulty in obtaining absolute " blanks " is well known. Our experience amply confirmed the observations of Mabery,* Auchy,t and others in regard to * Inaccuracies in the Determinations of Carbon and Hydrogen of Combustion, C. F. Mabery, Journal Am. Chem. Soc, 20, 510 (1898). t George Aiichy, Journal Am. Chem. Society, 20, 243 (1898). 878 PROCEEDINGS OP THE AMERICAN ACADEMY. the loss of water and possibly of carbon dioxide from the ordinary form of potash bulbs. We also found a single sulphuric acid tube entirely insufficient to absorb all the water. Clearly, then, if we were to use this method, an elaborate investigation of the form of apparatus, method of procedure, and limits of error, was absolutely imperative. The use of the oxalate, however, did not seem sufficiently promising to warrant the necessary expenditure of time. After thus investigating the uranium compounds which seemed likely to furnish a suitable basis for an atomic weight determination, anhydrous uranous bromide, in spite of its disadvantages, seemed most likely to fulfil the necessary requirements. As already mentioned, this compound oxi- dizes with the greatest ease on exposure to moist air. It was necessary, therefore, to devise apparatus which should preclude any possibility of bringing the sublimed bromide in contact with the air of the laboratory until it had been collected and weighed. After much experimenting with different forms of apparatus, the ibllowing method was adopted. Preparation and Collection of Pure Uranous Bromide. The mixture of urano-uranic oxide and carbon was placed in a porce- lain boat within the larger of two " telescoping " porcelain tubes. The portion of the tube containing the oxide was heated in a Fletcher furnace, and after thoroughly sweeping out the apparatus with dry nitrogen, a mixture of dry nitrogen and bromine vapor passed over the oxide. The sublimed bromide collected near the inner end of the smaller porce- lain tube. The very efficient and elaborate desiccating apparatus which served so well in the work on the atomic weights of cobalt and nickel, was very kindly given by Dr. Baxter for use in this investigation.* This apparatus , with slight modifications, was used for drying the nitro- gen and bromide, and was connected by a ground glass joint with the porcelain combustion tube. With this apparatus traces of air diffused through the annular joint between the porcelain tubes, forming a coating of oxide on the inner tube.f In the case of uranium, the oxide is found to be copiously mixed with the sublimate also. This diffusion of air takes place even when the outer end of the inner porcelain tube is nearly closed, thus making a considerable outward current within the tubes. * For a full description of this apparatus see There Proceedings, 33, 124 (1897). + In the case of cobalt and nickel this oxide was easily removed by subsequent treatnoent, but in the present case removal was impossible. RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 379 In order to obviate the difficulty aud exclude air a glass jacket was slipped over the joint between the tubes. The construction and use of this jacket will be made clear by reference to the accompanying drawing. v-^v^-^v^. y,t!K»aStMtaiiK!«5^J^jMS!51 p H Section of Subliming and Bottling Apparatus. A, outer porcelain tube fitted with ground glass joint B ; C, inner porcelain tube with ground-glass stopper D ; E, boat containing oxide and carbon ; F, furnace ; G, glass jacket; H, H, H, H, packing of asbestos wool; I, weighing bottle; L, tube for admitting nitrogen, sliding within tube M through rubber connection N, and carrying at its end stopper 0 of weighing bottle ; P, sublimate ; R, rod for removing sublimate. The jacket was drawn down at the ends, so as to fit the porcelain tubes A and C as well as possible, and the spaces between the tubes and the jacket were packed tightly with asbestos wool. This packing makes a joint sufficiently tight to withstand a pressure equal to that of eight or ten centimeters of water. The jacket was provided with a long tube, M, within which slid a second tube, L, connection being made by means of the short piece of rubber tubing, N. To the end of the inner tube was attached, by platinum wires, the stopper, 0, of the weighing bottle. The outside diameter of L was very little less than the inside diameter of M, thus leaving very little space between the walls of the two tubes. For this reason, and also on account of the length of the tube M, — about fifteen centimeters, — there was little danger of bromine diffusing up in sufficient quantities to attack the rubber connection, N. Even if this were the case there could be no possibility of contamination of the sub- 380 PROCEEDINGS OF THE AMERICAN ACADEMY. limate thereby, since there was always a constant outward pressure of bromine during the sublimation. The outer end of L was connected with the nitrogen supply of the desiccating apparatus. All glass joints and stop-cocks were lubricated with syrupy phosphoric acid. The method of procedure was as follows : In the porcelain boat, E, was placed an intimate mixture of urano-uranic oxide and pure carbon, the carbon being about twenty per cent of the weight of the mixture, thus insuring a large excess of carbon. The apparatus was then thor- oughly swept out by nitrogen, which enters at B and L simultaneously. After the air was completely expelled, the combustion tube was grad- ually raised to a high temperature by the blast lamp. Heating in a current of nitrogen was then continued for three hours at least, some- times longer, in order to insure complete removal of all traces of air and moisture. During this and subsequent operations, the outlet of the stopper D of the inner tube was nearly closed by asbestos wool, thus maintaining a constant and considerable pressure within the apparatus, and hindering the diffusion of air. After this preliminary heating in nitrogen, bromine vapor was passed in through B. During the first trials of the apparatus it was our practice to keep a slow current of nitrogen passing in at L during the sublimation. This kept the jacket entirely free of bromine, a very slow current of nitrogen being sufficient to keep any bromine from passing between the walls of the porcelain tubes. It was found, however, that traces of air diffused through the permeable asbestos packing, and were of course carried into the combustion tube by the current of nitrogen, forming on the inner tube a coating of oxide, and contaminating the sublimate. In order to avoid this, the nitroiren was shut off from L sometime before turning on the bromine. After turning on the bromine, the jacket slowly filled with dilute bromine vapor. While the greater part of the sublimate collected within the inner tube, a little collected between the walls of the two tubes, almost sealing the annular space. This sublimate, which collected on the outside of the inner tube, is a valuable indicator of the condition of the subli- mate witliin. In the presence of mere traces of oxygen the lustrous brown color of the urauous bromide gives place to a dull yellow color easily distinguishable. Comparatively small quantities of oxygen form a coating of black oxide. When the sublimation is conducted according to the method described, the outside of the inner tube is free from any traces of the supposed oxybromide or of oxide, thus showing that no appreciable quantity of moist air could have reached the innermost portions of the sublimate. The best proof of the purity of the sublimate is of course RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 381 found in the agreement of analyses of substance formed under various conditions of bromine supply. After the bromine had been run for about one and a half hours, the sublimate was cooled for three hours in a current of nitrogen. "When the tubes were thoroughly cold, nitrogen was finally passed into the jacket through L, iu order to sweep out any traces of bromine that might still remain. The inner tube, containing the sublimate, was then carefully drawn out until the inner end reached a position over the mouth of the weighing bottle, indicated in the diagram by the dotted line. This can be done without seriously disturbing the asbestos pack- ing, a rapid current of' perfectly dry nitrogen being admitted meanwlule through L. By means of the glass rod, R, the sublimate was pushed out of the tube and dropped into the weighing bottle, I. The tube L, carrying the stopper, was then pushed down and the stopper in- serted. The stopper was held by the platinum wires so lightly that after pushing it into place the tube L could be withdrawn, leaving the stopper inserted in the bottle. Thus uranous bromide was sublimed, collected, and bottled up in an atmosphere of dry nitrogen ready for weighing, without once coming in contact with the air of the laboratory. That the apparatus is effective for the purpose intended, and capable of producing material of constant composition, was shown by the first rough analyses of uranous bromide, which yielded 57.41, 57.41, and 57.42 per cent bromine respectively. These analyses were made with material that had not been purified, but served to show the constancy of composition of the sublimate ; for not only was the length of time occupied in the sublimation varied, but in one case the sublimate was cooled in bromine instead of in nitrogen. Of course if an appreciable amount of an oxygen compound were formed, by diffusion of air or moisture, there would almost certainly be discrepancies in the results, since it is hardly conceivable that under the varying conditions exactly the same quantities of oxy-salt should be formed each time. Because the specific gravity of uranous bromide was unknown, the fol- lowing determinations were made : 2.0328 grams of the salt displaced on one occasion 0.3332 gram of kerosene at 21°, and at another trial 0.3322 gram. The kerosene had been redistilled, and only the high boiling portion was used. The density of the kerosene at 21°, referred to water at 4°, was 0.7919. Hence the specific gravity of the uranous bromide was (1) 4.830 and (2) 4.846, giving as the mean 4.838. This value was used in reducing the observed weights of bromide to the vacuum standard. 382 PROCEEDINGS OF THE AMERICAN ACADEMY. During the weighing in the final analyses, the bromide of uranium was still surrounded by an atmosphere of pure dry nitrogen in the tightly stoppered weighing bottle. Since this bottle had been full of dry air when it was first weighed, a small correction had to be applied on this account. The difference in weight between 6.70 cubic centi- meters (the interior volume of the weighing bottle) of air and the same volume of nitrogen at 20° C. is 0.000265 gram. Of this nitrogen a gram of uranous bromide displaced -rw, = 0.206 cubic centimeters, or 0.24 milligram, while the brass weights used in weighing the bromide displaced 0.145 milligram of air. Hence in vacuum a gram of uranous bromide would weigh 0.265 + 0.24 — 0.145 = 0.36 milligram more than the observed weight, while two grams would weigh 0.265 + 2(0.24 — 0.145) = 0.46 more than the observed weight. All the weights given in the tables are corrected in this way to the vacuum standard. Methods of Analysis. By the use of these devices we were able to prepare and weigh pure uranous bromide in a definite state. There still remained, however, the problem of devising a suitable method of analysis. As previously men- tioned, all uranous compounds reduce silver nitrate, making impossible the usual method of procedure in halogen determinations. The method of precipitating the uranium and determining bromine in the filtrate involves too much danger of loss of material in the multiplic- ity of operations. The most satisfactory solution of the problem seemed to be to oxidize the compound to the uranyl salt, provided this could be done without loss of bromine. Nitric acid is of course effective as an oxidizing agent, but the oxidation is accompanied by loss of bromine. After much experimenting, hydrogen dioxide was found to be the most suitable oxidizer. From neutral solutions of uranium compounds, hydro- gen dioxide precipitates a hydrated peroxide of uranium. If the solution is slightly acid, this precipitation is prevented and the uranous compound completely oxidized to the uranyl state. The weighed sample of uranous bromide was dissolved in considerable water — at least 400 cubic centi- meters of water to each gram of bromide. The bottle containing the bromide was opened by means of a suitable glass fork, either below the water or just above the surface, so that it could be instantly submerged, and thus avoid loss of hydrobromic acid by the action of moist air. The calculated volume of a standard solution of pure hydrogen dioxide was then diluted to about 100 c.c, one cubic centimeter of pure dilute sul- RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 383 phuric acid was added, and the mixture was slowly i"un into the solution of uraiious bromide. The green color of the uranous salt soon changes to the yellow color characteristic of uranyl com[)ounds. On adding the first few cubic centimeters of the dilute hydrogen dioxide solution, a greenish white precipitate came down. Addition of more of the acid dioxide solution redissolved it, and the resulting solution was perfectly clear. This peculiar hydrolytic action is due to the acid, and not to tlie hydric dioxide, lor the same reaction occurs if dilute sulphuric acid alone is added to the solution. * The explanation of this interesting phenomenon, which is just the opposite of what might have been expected, is, undoubtedly, that the bromide is already hydrolyzed to a great extent by merely dissolving in water. The hydrate is probably in solution in the colloidal state. Evi- dence of this is found in the fact that if the clear aqueous solution of uranous bromide is allowed to stand exposed to the air, a hydrate gradu- ally separates, giving to the solution a cloudy, murky appearance. After two or three days this precipitate disappears, giving place to a clear yellow solution of oxybromide and hydrobromic acid. The addition of sulphuric acid coagulates the colloid before it can all be converted into uranyl salt. In order to be sure that no bromine or hydrobromic acid is lost by this method of oxidation, the following experiment was made. 0.5 gram of bromide was dissolved in 250 c.c. of water, 50 c.c. of dilute sulphuric acid (1 :10) was added, and the hydrogen dioxide solution was run in. This was done in a closed flask, similar in construction to a gas washing bottle. A current of air was drawn through the bottle and then through starch solution containing potassium iodide to see if bromine is liberated. Not the slightest trace of blue color appeared in the starch solution, even after adding a large excess of hydrogen peroxide and allowing it to stand over night. A test for hydrobromic acid was sought in a similar way, by drawing the air through a solution of silver nitrate, again with nega- tive results, as was to have been expected. These experiments show conclusively that uranous bromide can be oxidized completely by hydro- gen dioxide, without loss of bromine. Silver nitrate, in moderately concentrated solutions, is not acted upon by a three per cent solution of hydrogen peroxide. Consequently a con- siderable excess of the latter reagent could do no harm. Nevertheless care was taken never to add more than the calculated amount of hydro- gen dioxide. Moreover, the solution of hydrogen dioxide used contained only one per cent of this reagent, and this was diluted ten times before 384 PROCEEDINGS OP THE AMERICAN ACADEMY. adding to the bromide solution, thus reducing to a minimum the possi- bility of too vigorous oxidation, with consequent liberation of bromine. After the oxidation, bromine was precipitated by pure silver nitrate in the usual manner. This precipitation was conducted in an Erlenmeyer flask fitted with a ground glass stopper. The silver bromide was col- lected on a Gooch crucible, and dried in an electrically heated drying oven. Of course the asbestos shreds carried away in washing the silver bromide were collected by passing the filtrate and wash water through a fine filter, and their weight was added to that of the silver bromide. The bromine determination was carried on in orange colored light. It was found in the work upon cobalt and nickel that the porcelain tube is attacked by bromine vapor at the high temperature employed during the sublimation, with the result that sodium bromide was always present in the sublimate. In these investigations this impurity was de- termined by the reduction of the bromide to the spongy metallic state by means of hydrogen, and extraction by water.* A somewhat similar method was tried with uranium. Since hydrogen reduces uranous bro- mide only to the tri-bromide, the bromide was ignited in a current of air and the resulting oxide leached with water. It was found to be impos- sible to oxidize the bromide completely. A little uranous bromide invariably remained and was washed out with the alkali. Both dry and moist air was tried, also ignition in steam, but in every case uranium was washed out in considerable quantity. Precipitation of the uranium by hydrogen dioxide was next tried, but it was found impossible to precipitate the uranium completely. The rather unsatisfactory method of determining the sodium in the filtrate from the bromine precipitation, or in a new sample of uranous bromide as nearly similar as possible, after removing the uranium with ammo- nium sulphide, appeared to be the only available method. The filtrate and wash waters from the bromine precipitation were evaporated in platinum to small bulk, and the uranium and excess of silver precipitated by pure colorless ammonium sulphide. This reagent precipitates uranium completely. The filtrate was then evaporated to dryness, the ammonium salts expelled by ignition, and the residual sodic nitrate converted to the sulphate and weighed as such. Of course these operations were all con- ducted in platinum vessels. This method of work is not wholly satisfac- tory, on account of the complexity of operations involved, but it seems to be the only practical method. * These Proceedings, 34, 329, 359 (1899): RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 385 Purification of Materials. As the source of uranium, commercial " chemically pure " uranium acetate was used.* This was first converted to the chloride on account of the greater solubility of this compound, — by precipitation as ammonium uranate and redissolving iu dilute hydrochloric acid. To the hot and slightly acid solution, pure sulphuretted hydrogen was added to satura- tion. The free acid was then neutralized with amnionic hydroxide, a slight excess of the alkali was added, and more sulphuretted hydrogen was run in. In this way some uranyl sulphide was precipitated, in order to sweep down with it any colloidal sulphides of the higher groups which miglit otherwise escape removal. The excess of sulphuretted hydrogen was boiled off, and after standing over night the supernatant liquid was decanted through a washed filter. The next step depended upon the fact that uranium remains in a solution of the double carbonate of ammonium and uranium, iu the presence of an excess of ammonium sulphide, while all the other members of the aluminum and iron groups are thrown down by this reagent. Consequently ammonic hydrate and ammonium carbonate in slight excess were added to the filtrate, forming the double carbonate. If the solu- tions are concentrated, the double carbonate is precipitated when more than a slight excess of ammonic carbonate is used. This happened in some cases, when it was necessary to redissolve the precipitate in dilute hydrochloric acid and again add ammonic carbonate in more dilute solution. About fifty grams of carbonate per litre was found to give the best results. Ammonic hydroxide was then added to the hot solution, and sulphuretted hydrogen iu excess. After standing over night the solution was filtered. In several of the more concentrated solutions, a considerable quantity of the salt crystallized out. These crystals were worked up separately, as they were probably purer than the solution. On boiling the solution to decompose the excess of ammonium sulphide, some of the ammonic carbonate was decomposed, causing the precipita- tion of some uranium sulphide. This precijjitate was discarded, as it might have contained iron, or other analogous metals which had previ- ously escaped precipitation. Dilute hydrochloric acid in slight excess was added, and the carbon dioxide was expelled by boiling. The free acid was then almost neutralized with pure ammonic hydroxide, and * This method of uranium purification, with some modifications and additions, is similar to that employed by Zimmermann. Annalen der Chemie u. Pharmacie, 232, 299. VOL. xxxvii. — 25 386 PROCEEDINGS OP THE AMERICAN ACADEMY. pure ammonic su]phhydrate added in excess. The color of the result- ing precipitate of uranium sulphide varies greatly with the temperature, lu warm solution it was at first reddish brown, while that precii)itated in the cold varied from bright red to brownish yellow. On washing, all turn black, the sulphide being decomposed into uranous oxide and sul- phur. After thorough washing the resulting mixture of oxide and sulphur was ignited in a porcelain dish, the green urano-uranic oxide being the product. The oxide was then dissolved in a platinum dish in redistilled nitric acid, evaporated, and recrystallized from nitric acid solution. Uranyl nitrate does not crystallize well from aqueous solution, but it was found that if a little nitric acid is added, it crystallizes readily in fairly large monoclinic prisms. This recrystallization was repeated ten times from acid solution, and finally twice from aqueous solution. Finally the pure nitrate was converted to the oxide by ignition in platinum. A second sample, used in the preliminary series, was prepared by repeated fractionation of the mother liquors of the first sample. Since this work was carried out. Sir William Crookes * has published the account of several methods by which he was able to prepare specimens of uranyl nitrate which were not radio-active. The radio-activity of uranium has hitherto been supposed to be characteristic of this element. Crookes has shown, however, that this is not the case, but that the active element can be separated by treatment with ether, by fractional crystallization, or by treatment with excess of ammonium carbonate. Unfortunately none of the pure oxide prepared for this investigation remained, hence it is impossible to test directly its radio-activity. Since two of Crookes's methods were used in purifying our material, viz. the ammonium carbonate treatment and fractional crystallization, it is highly improbable that our oxide was radio-active. In repeating Crookes's work with nitrate made from some of the same material used in pre- paring our best nitrate, it was found that a sample of the ^/i/i!A crystalliza- tion gave no trace of action on twenty-four hours exposure to a quick photographic plate. The material used in this experiment had not been submitted to the ammonium carbonate treatment. "When it is con- sidered that the material used for our atomic weight determinations was first put through the carbonate process, — in itself sufficient to remove the radio-active element, — and then was recrystallized twelve times as nitrate, it would seem that our pure oxide must have been free from all radio-active material. * Proceed. Lond. Royal Soc, 66, 409 (1900). RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 387 There is another phase of this subject that deserves to be considered, namely, the possible effect of radio-active matter, even if present, upon the atomic weight value. The purest specimen of radium or "polonium" 3'et obtained has consisted of a mixture containing ^^robably little more than fifty per cent of the active element, as nearly as could be estimated. This highly impure material, however, possesses 8,000 times the radio- activity of uranium. The radio-active power of the pure material is undoubtedly very much greater than that of the impure mixture. Con- sequently the quantity of ratio-active substance necessary to give to uranium the comparatively slight degree of activity that it possesses must be exceedingly minute. Giesel has recently shown * that a quantity of radium so small that it cannot be detected by sulphuric acid is sufficient to affect a photographic plate. Crookes also says on this point, " Con- sidering my most active UrX does not contain sufficient of the real material to show in the spectrograph, yet is powerful enough to give a good impression on a photographic plate in five minutes, what must be its dilution in compounds which require an hour, a day, or a week to give an action ? " f Even in the ordinary active uranium compounds it is most unlikely that the active element — if indeed it is an element — could possibly be present in quantity sufficient to exert any influence whatever upon the atomic weight of uranium. Pure carbon was obtained by ignition of sugar. Large, clear crystals of the best " rock candy " of commerce were ground up in a porcelain mortar and ignited at low heat in a platinum dish as long as organic gases were given off. The resulting charcoal was then powdered in an agate mortar and ignited in a hard glass combustion tube ; first in a stream of pure, dry nitrogen, and finally in a stream of bromine vapor. In this way the carbon was freed from any impurities which might, if present, be acted upon during the sublimation and contaminate the sublimate. Owing to the presence of undecomposed carbohydrates, or possibly of water, most of the bromine was converted into hydrobromic acid. Heatin? in bromine was continued until acid fumes ceased to be given off. Finally, the carbon was again heated in a current of dry nitrogen. Five grams of carbon, thus prepared, left no visible or weigh- able residue after combustion in oxygen. The method of bromine purification was essentially identical with that used in many other atomic weight investigations in this laboratory, and has * Berichte der deutschen chemischen Gesellschaft, 33, 3569 (1900). t Proceed. Lond. Royal Soc, 66, 422 (1900). 388 PROCEEDINGS OF THE AMERICAN ACADEMY. been proved by long experience to be the most efficient and satisfactory. Commercial, " pure " bromine was partially freed from chlorine by shaking with a fifteen per cent solution of potassic bromide. One fourth of the bromine was then converted to calcic bromide by running it slowly into milk of lime in the presence of a large excess of ammonia. The calcic bromide solution was filtered and concentrated by evapora- tion, and the rest of the bromine was added to it. A little zinc oxide was then added, and after standing over night the bromine was distilled, nearly free from chlorine. Most of the iodine is removed as zinc iodate. After redistilling the bromine, iu order to remove any calcium bromide that may have spattered over in the first distillation, it was con- verted into hydrobromic acid by slowly dropping it into a mixture of red phosphorus and hydrobromic acid. The red phosphorus was at first washed free from chlorides. The hydrobromic acid, containing some free bromine, was distilled. The free bromine liberates any iodine which may have escaped the zinc oxide. The first portion of the distil- late, containing free bromine and iodine, and organic matter, was rejected, and so was the last portion, which may have contained traces of arsenic. The hydrobromic acid was then converted into bromine by distilling over pure manganese dioxide previously treated with sulphuric acid and washed. One half the bromine is obtained by the manganese dioxide alone. As soon as no more bromine comes off, a little redistilled sul- phuric acid is added, and the rest of the bromine was obtained. It was then redistilled several times, rejecting the first and last portions, and finally dried over pure phosphorous pentoxide. The silver precipitation also presents no new features, except, perhaps, its somewhat unusual thoroughness. Partially purified silver was dis- solved in nitric acid, diluted, and precipitated with pure hydrochloric acid. After thorough washing the chloride was reduced by invert sugar and sodic hydrate which had been purified by electrolysis. The metallic silver was thoroughly washed, dissolved in nitric acid, and again precipi- tated as chloride and reduced. It was then dried and fused on charcoal ; the lumps of silver were cleaned with sand, dissolved in pure nitric acid, diluted to a volume of two litres, and again precipitated with pure hydro- chloric acid. The resulting chloride was then digested on the steam bath with aqua regia, washed, and once more reduced by invert sugar and sodic hydrate. After drying, it was fused on pure sugar char- coal. The buttons of silver were cleaned with sand, and then puri- fied electrolytically, a small portion being dissolved in nitric acid to serve as the electrolyte, and the rest serving as anode material. The RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 389 crystals of electrolytic silver were then dried over potash and fused in vacuo on a boat of pure lime. The buttons of silver thus obtaiiit-d were treated with nitric acid to remove the surface, dried, and kept over potash. A second sample was obtained by fusing in vacuo electrolytic silver which had been prepared from the silver bromide obtained in Dr. Baxter's work upon cobalt, which was known to be very pure. Hydric dioxide was purified as follows : To a solution of the ordinary commercial peroxide prepared for medicinal use, was added a solution of baric hydroxide, which had been purified by recrystallization. The pre- cipitated baric dioxide was washed until a nitric acid solution of the same showed no trace of halogen. It was then added to pure dilute sul- phuric acid, and the resulting solution of hydric dioxide was filtered and distilled in a partial vacuum. The solution thus obtained showed no trace of halogen, and left no visible residue on evaporation in platinum. Ammonium sulphide was made from pure ammonia, which had been redistilled in platinum, and pure sulphuretted hydrogen. It left no visible residue on evaporation in platinum. Hydrochloric and nitric acids were redistilled in a platinum still, and throut^hout the work platinum vessels were used wherever possible. Water was twice redistilled, once over alkaline potassic permanganate, and again over acid potassic sulphate from a Jena glass flask, a block-tia condenser and Jena glass receiver being used. The Results of the Analyses of Ueanous Bromide. The method of analysis has been already fully described. The analyses recorded in the first series were made by adding an excess of silver nitrate to the solution of uranyl bromide. From the ratio of the observed weights of urauous bromide to argentic bromide, the molecular weight of uranous bromide was calculated, that of argentic bromide being assumed to be 187.885. From the results obtained from this preliminary series the weight of silver necessary to precipitate the bromine in one gram of uranous bromide was calculated. In the subse- quent determinations the exact weight of silver required was weighed out, as nearly as possible, and dissolved in pure nitric acid with suitable precautions to avoid loss. The exact end point was reached by standard hundredth normal solutions of argentic nitrate and hydrobromic acid, by means of the nephelometer.* After determining the end point a slight excess of argentic nitrate was always added, and the weight of the total * Richards, These Proceedings, 30, 385 (1894). Z. anorg. Chem., 8, 269 (1895). 390 PROCEEDINGS OF THE AMERICAN ACADEMY. argentic bromide determined. Tlius from each of these analyses two distinct ratios were obtained as a basis for the calculation of the molecular weight of uranous bromide, — the ratio of uranous bromide to argentic bromide, and that of uranous bromide to silver. As would naturally be expected from the complexity of operations involved, determinations of the sodium in the filtrates from the argentic bromide gave unsatisfactory results. The large quantity of filtrate and wash waters had to be evaporated to small bulk, the uranium precipi- tated, and the sodium determined in the residue. It seemed advisable to make a series of separate analyses for sodium only, and use the average percentage of sodium found as a constant correction. This method was used in the work upon cobalt and nickel.* Accordingly three alkali determinations were made, wholly in platinum, the material not coming in contact with glass at any time except during the original collection and weighing of the sublimed bromide. The sub- limate was dissolved in pure water, in a platinum dish, and the uranium was precipitated with pure ammonium sulphide. The ammonium sul- phide was freshly prepared for each analysis, wholly in platinum. It left no residue on evaporation in platinum. The precipitated sulphide was digested on the water bath to expel most of the excess of ammonium sulphide, filtered through a platinum funnel, and the filtrate and wash water evaporated to small bulk in a platinum dish. The sodium bro- mide was then converted to sodium sulphate and weighed. The follow- ing table contains the data and result : — No. . Weight of Uranous Bromide. Weight Sodic Sulphate obtained. Equivalent Weight of Sodic Bromide. Per cent Sodic Bromide. grams. gram. gram. 1 1.656 0.00092 0.00133 0.081 2 2.629 0.00143 0.00207 0.079 3 1.407 0.00121 0.00175 0.124 Average . 0.095 The average of these three determinations, 0.095, per cent, is practically identical with the amount of sodic bromide found in the cobalt and nickel work, which was 0.10 per cent. The porcelain tubes used in this inves- * These Prcoeedings, 34, 339, 365 (1899). RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 391 tiwation were of the same manufacture as those used in the nickel and cobalt work, and since the method of preparation of the three bromides was practically the same, probably the quantity of sodium extracted from the tubes by the action of the hot bromine vapor was the same, — on the average^ — in all three cases, and not far from 0.10 per cent. Conse- quently, in calculating the following results, this value was used as a constant correction. The effect of applying the correction is to raise the calculated atomic weight about two tenths of a unit. Of course by this method the quantity of sodic bromide calculated will vary somewhat from the exact quantity present, in individual determinations. The arerage result, however, will undoubtedly vary but little from the result obtained if the alkali could be determined in each sample. It certainly is very much nearer the truth than the results to be obtained by the cumber- some method of determining the alkali in the filtrate from each precipita- tion of argentic bromide. Analvsis No. 2 was rejected on account of contamination of the uranous bromide by shreds of asbestos from the packing of the jacket, and No. 4 was not used because the combustion tube cracked during sublima- tion, rendering probable the formation of some oxy bromide. The silver required in analysis No. 6 was determined for practice preparatory to the final series, being 0.9087 gram when all corrections were applied. It is not included in the table, since its nature was essentially preliminary. As usual, all weighings were reduced to the vacuum standard. While all THE ATOMIC WEIGHT OF URANIUM. O = 16.000 ; Ag rr 107.93 ; Br = 79.955. First Series (preliminary). UBr4 : 4AgBr. No. of Analysis. Total Weight of Uranous Bromide + So- dium Bromide in vacuo. Weight of Uranous Bromide corrected for NaBr. Total Weight of Silver Bromide in vacuo. Weight of Silver Bromiile corrected for NaBr. Parts of Ura- nousBromide equiv. to 100 parts Argen- tic Bromide. Atomic Weight of Uranium. 1 3 5 6 grams. 2.20795 1.44321 1.40639 1.17607 grams. 2.2058 1.4418 1.4050 1.1749 grams. 2.97391 1.94272 1.89355 1.58396 grams. 2.9699 1.9401 1.8910 1.5818 grams. 74.272 74.316 74.299 74.276 238.36 238.69 238.56 238.39 Average 74.289 238.50 392 PROCEEDINGS OP THE AMERICAN ACADEMY. Second Series. UBr4 : 4AgBr. No. of Analysis. Weight of Uranous Bro- mide + Sodic Bromide in vacuo. wt. of Ura- nous Bromide corrected for Sodic Bromide. Total Weight of Silver Bromide in vacuo. Weight of Silver Bromide corrected for NaBr. Parts of Ura- nous Bromide equiv. to 100 parts Argen- tic Bromide. Atomic Weight of Uranium. 7 8 9 grams. 1.80174 1.06723 1.85698 grams. 1.7999 1.0662 1.8551 grams. 2.42588 1.43713 2.50009 grams. 2.4226 1.4352 2.4967 grams. 74.296 74.290 74.302 238.54 238.50 238.59 Average 74.296 238.54 Third Series. UBr^ : 4Ag. No. of Analysis. 10(7) 11(8) 12(9) Weight of Uranous Bromide with all Corrections. grams. 1.7999 1.0662 1.8551 Weight of Sil- ver in vacuo (not corrected for Sodic Bromidf). grams. 1.39365 0.82559 1.43817 Weight of Silver with all Corrections. grams. 1.3918 0.8245 1.4342 Wt. of Uranous Bromide corre- sponding to 100 grams Silver. grams. 129.322 129.315 129.347 Atomic Weight of Uranium. 238.49 238.46 338.60 Average 238.52 Average of all determinations . . Average of six final determinations 238.52 238.53 the weighings were actually made to the hundreths of a milligram the final corrected data are rounded off to the nearest tenth of a milligram, since the deviations of the results show that the hundredths could have had no significance. The extreme difference between the highest and the lowest values in the preliminary series is 0.33 unit, in the second series 0.09 unit, and in the third series 0.14 unit. At first sight these variations seem large, but their relative magnitude appears smaller when the great molecular weight of uranous bromide, 558.34, is taken into consideration. Thus the extreme percentage error of the preliminary series is 0.06, while those of the last two series are only 0.016 and 0.024 per cent respectively. RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 393 The so-called " probable error " of the average atomic weight computed from the six analyses numbered 7 to 12 inclusive, if each is given the same weight, is O.Olo. That is, according to the theory of least squares, the atomic weisht of uranium should be between 238.515 and 238.545. The magnitude of the maximum deviations in these two final series is, moreover, about as large as would have been expected from known ana- lytical uncertainty. The observed variation in the amount of sodic bromide, for which a constant correction had to be applied, would account for three quarters of it, and the rest, corresponding to less than the tenth of a milligram in the weighings, might easily be due to unavoidable errors of weighing or manipulation. Further evidence of the trustworthiness of the figures is to be found in the comparison of the amounts of silver used in analyses 10, 11, and 12, with the corresponding amounts of argentic bromide, found in analyses 7, 8, and 9. This comparison is given in the following table, which gives the weights of silver corresponding to 100.000 parts of argentic bromide. Weight of AgBr in vacuo. Weight of Ag ia vacuo. Quotient x 100 = per cent of Silver in Argentic Bromide. grams. 2.42588 1.43713 2.50009 grams. 1.39365 0.82259 1.43617 57.449 57.447 57.445 A St verage 57.447 as found 57.445 The result not only verifies the mechanical work, but affords evidence that the pi-ecipitate must have been pure argentic bromide. Clearly, then, the analysis is as accurate as need be. Further repetition of the process might reduce the so-called " probable error," but could not change the average by a significant amount. In the present state of the question, the method seems to have been carried as far as expediency demands. It is worth while to inquire whether or not the method may conceal some source of constant error beyond the reach of the experimental precautions detailed above. Such an error could hardly have occurred 394 PROCEEDINGS OF THE AMERICAN ACADEMY. during the analysis ; for every step of this procedure was verified by confirmatory evidence. If a flaw existed, it must have been in the purity of the original substance. Since the observed atomic weight is lower than the former results, it is important to examine into only those possible irregularities which could have had the effect of lowering the apparent value. The probable impurities tending to lower the atomic weight are, first, sodic bromide ; second, hydrobromic acid ; third, free bromine ; fourth, uranic pentabromide ; and fifth, an unknown metal with a lesser equiva- lent. The first impurity was found to be present, its amount was deter- mined, and a suitable correction was applied. The second could not have been formed during the sublimation of the uranous bromide, because com- pounds of hydrogen were scrupulously excluded. If formed by the action of water after the sublimation, the atomic weight would have appeared too high — for moist uranous bromide emits hydrobromic acid instead of absorbing it. The third impurity, free bromine, could hardly have been imprisoned or absorbed by the sharply crystalline salt to any appreciable extent, since the concentration of the bromine vapor in the issuing gases was but small. The evidence in regard to the absence of pentabromide is fiiirly conclu- sive, although somewhat indirect. All attempts by many investigators to form this compound have failed, in spite of the recognized existence of the corresponding chlorine compound. It seemed possible, however, that while this compound is not formed at high temperatures, lower temperatures might permit the addition of the extra bromine. Accord- ingly the jireparations used in Analyses 7, 8, 10, and 11, were cooled in a current of dilute bromine vapor, instead of in pure nitrogen. The presence of a comparatively small amount of pentabromide would make a very decided difference in the quantity of bromine found. Hence the essential agreement of the average result of these analyses, 238.50, with the average result of all the others, 238.52, is good evidence of the absence of uranium pentabromide. "With regard to the fifth possible impurity nothing can be said except to point out the many operations involved in the purifications. These seem to point toward probable purity ; but it is nevertheless to be re- gretted that lack of time prevented the analysis of many different fractions of material, prepared in varying ways. The presence of oxybromide would of course cause low bromine anal- yses, and too high an apparent atomic weight. Therefore this possible cause of error need not be considered, even if the oxybromide had ever RICHARDS AND MERIGOLD. ATOMIC WEIGHT OP URANIUM. 395 been made in the absence of water. In the light of all these consid- erations, there would seem to be no good reason to question the purity of our bromide. On comparing the result of this investigation, 238.53, with that of Zimmermann's, 239.59 (the only previous work worthy of serious consid- eration), the difference of over a unit seems at first to be one of great magnitude. The percentage difference (0.45%) is however smaller than many a difference which often has been passed by unheeded in small atomic weights, such as those of magnesium or aluminum. This point illustrates the difficulty of obtaining results with high atomic weights which can satisfy the cursory reader. Nevertheless, such a difference is far too great to pass unchallenged. It seems highly probable that the greater part of it is due to the previously discussed sources of inaccuracy in Zimmermann's method, — especially to the difficulty of wholly re-oxidizing the lower oxide. The failure to oxidize half a per cent of the uranous oxide, involving an error in the weight of only 0.017 per cent of the total weight of the substance, would account for the discrepancy. Heuce it seems not unlikely that the atomic weight of uranium is really as low as 238.53. Nevertheless, the question cannot be looked upon as conclusively settled. Certainty can be obtained only by the application of a new method, radically different from the two just com- pared. Our experience of nearly four years of varied work seems to indicate that the search for such method will not be an easy one. The many degrees of quantivalence of uranium and the unsuitable properties of its compounds combine to render the problem one of unusual difficulty. When face to face with a problem of this kind one cannot but admire Stas's wisdom in selecting chiefly univalent elements with powerful affinities in order to prove the constancy of the atomic weights. The result of our analyses of uranous bromide may be summed up iu the following words: If oxygen is taken as 16.000, and bromine as 79.955, the atomic weight of uranium appears to be not far from 238.53. Cambridge, Mass., U. S. A. 1897-1901. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 15. — February, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. II. — THE PROBABLE SOURCE OF THE HEAT OF CHEMICAL COMBINATION, AND A NEW ATOMIC HYPOTHESIS. By Theodore William Richards. lNrE3TIOA.TI0NS ON LiGHT AND HeAT MADE AND PUBLISHED WHOLLT OR IN PART WITH APPROPRUTIONS FROM THE EOMFOED FuND. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. IL — THE PROBABLE SOURCE OF THE HEAT OF CHEMICAL COMBINATION, AND A NEW ATOMIC HYPOTHESIS. By Theodore William Richards. Presented January 9, 1901. Received January 14, 1901. I. Presentation of the Facts. In a paper first presented to the American Academy of Arts and Sciences in May, 1900, then revised and printed in the Proceedings a year later,* certain interesting facts concerning the significance of chang- ing atomic volume were pointed out and emphasized. It was shown that the contractions and expansions occurring in liquids and solids during chemical reaction are related to the affinities concerned, as nearly as we can estimate those affinities. A greater affinity seems to produce a greater contraction, if the compressibilities concerned are equal. It seemed possible that this idea might have very fundamental and far reaching applications as to matters of fact, and might lead moreover to a somewhat new conception of the atomic hypothesis. Many such applications have already been tested with plausible results. The complete detailing of the ramifications of this idea would need the compass of a book ; in the present paper the attempt will be made merely to sketch the relations of a single side of the question. In the paper already referred to the suggestion was made that the heat of chemical reaction might be traceable to the work done by chemi- cal affinity in compressing the substances concerned. The discussion below will show the close relationship which exists between these facts. The most serious diflaculty in the way of determining the relationship is the extreme scarcity of data concerning compressibility. Obviously * These Proceedings, 37, 1 (June, 1901). 400 PROCEEDINGS OF THE AMERICAN ACADEMY. the compressibility of a compound contains too many possible variables to form at once the certain basis of exact reasoning ; and among elements only mercury, lead, copper, and iron in the uncertain form of steel, seem to have been even crudely stvidied.* The problem is moreover compli- cated by the fact that the coefficient of compressibility diminishes as the pressure increases. The work which is needed in order to compress a given substance to a given extent can only be computed accurately when the varying com- pressibility through the whole range is known ; and since the pressures involved in the present question are clearly many thousands of atmos- pheres, the precise solution of the problem seems to be a distant matter, although by no means impossible. By a process of approximation some light may be obtained, however. If one selects a single series of compounds, such as the chlorides, it is obvious that a large part of the compressibility throughout the series should correspond to the compressibility of the chlorine. In those cases where the compressibility of the metal is smallest, the change of volume would be due almost solely to the compression of the non-metal. In view of these considerations, the first approximation should be obtained by comparing the actual contractions taking place during the formation of amounts of substance containing the same weight of chlorine with the heat evolved in each case. The starting point in each case is liquid chlorine, having a molecular volume of about 50 (or an atomic volume of about 25) at 20°. The heat of formation of the chloride is usually given in tables of data as starting from chlorine gas, under atmospheric pressure ; hence the latent heat of evaporation and expan- sion of tbe chlorine should be subtracted fi"om the usual values in order to institute a precise comparison. f However, these quantities cannot be large in proportion to the heat of combination with the metal, and they * Landolt and Bornstein, Pliys. Cliem. Tab., pp. 268, 278 (1894). Unless otherwise stated, all data used in this paper were taken from this admirable book of tables. t The latent heat might be approximately calculated from the data of Knietsch (Landolt and Bornstein, p. 80 (1894)) as follows : — _ RT^dP 8.32 X (293.5)2 X 0-19 „„ ,^„ . , on r; ^ ^ PdT ^ 6 (52 X 1 ^ ' -■ ' ^^ kilojoules, between 20° and 21° C, for the evaporation of one gram-molecule. The wide deviations from the gas-law exhibited by chlorine render the calculation very uncertain. It is enough, however, to show that the value is relatively small. The heat absorbed on expansion must also be in doubt on account of the same deviations. RICHARDS. — SOURCE OF CHEMICAL HEAT. 401 would apply equally in each case ; hence in the first approximation the usual values for the heats of combination may be given without affecting the argument. The table of data herewith collected compares the contraction which takes place when two gram-atoms of chlorine combine with some other substance, and the heat evolved during the operation. Comparison of Contractiox with Heat of Formation involved in THE Synthesis of Chlorides. Metal. Atomic Volume of Metal. Atomic Vol. Metal -f- M times Atomic Vol. Chlorine. Molecular Volume of Chloride. Difference or Contraction. Contrac- tion corre- sponding to 2 Atoms Chlorine. Heat of Formation corre.spond- iug to 2 Atoms Chlorine. (Kilojoules.j Lithium 11.9 36.9 20.9 16.0 32.0 784 [Carboniv] 3.4 103.4 96.5 6.9 3.5 99 Sodium . . 23.7 48.7 27.2 21.5 43.0 816 Magnesium 13.3 63.3 43.9 19.4 19.4 632 Potassium . 45.5 70.5 37.8 32.7 65.4 872 Calcium 25.3 75.3 50.0. 25.3 25.3 760 Iron" . . 7.1 57.1 42.6 14.5 14.5 343 Nickel . . 6.7 56.7 50.4 (?) 6.3 6.3 312 Cobalt . . 6.7 56.7 44.2 12.5 12.5 320 Copper . . 7.1 57.1 44.1 13.0 13.0 216 Zinc . . . 9.5 59.5 49.6 9.9 9.9 407 Strontium . 34.5 84.5 51.9 32.6 32.6 772 Silver . . 10.3 35.3 26.5 8.8 17.6 123 Cadmium . 13.0 63.0 46.5 (?) 16.5 16.5 390 Barium . . 37.0 87.0 53.9 33.1 OO -1 OO. 1 815 Mercurj-ii . 14.7 64.7 50.0 14.7 14.7 223 Thallium . 17.2 42.2 34.1 8.1 16.2 406* Lead . . . 18.2 68.2 48.1 20.1 20.1 346 The parallelism of the heat of reaction and the contraction which results from it, is obvious from the table and the accompanying diagram, VOL. XXX vii. — 26 402 PROCEEDINGS OF THE AMERICAN ACADEMY. 100 200 300 400 500 600 700 800 900 kj. 10 20 30 40 50 GO 70 cubic centimeters. Li -= ^ ^ — -— ^ C ^ ■^^ ---^ Nil M ^ ]> ^ r ■ "- Mg ^ ..^^ ^ \, Iv ^ -^ / Ca / / ,— - ^ ^ he / / r Ni \ \ Co .. / ( Cu 1 \ Zn -^ "v^ "~" ^ &r -5 ^ ^ — ■ ■ — ■ Ag 7 ^^ ^^ Cd S \ s ' ■ ^ Ba .^ ^ ^ . — - — Hg \ ^ I'l \ V / J- ■ Pb RICHARDS. — SOURCE OF CHEMICAL HEAT. 403 which represents graphically the results recorded in the table. The ele- ments are arranged in the order of their atomic weights, and both sets of data are drawn as abscissae, because this method of treatment will facili- tate later comparison, and because it obviates certain irregularities due to periodicity. Each division stands for ten cubic centimeters of contraction on the left hand curve, and a hundred kilo joules of heat-energy on the right hand curve. The correspondence is obviously too close to be the result of chance. One is forced to believe that a fundamental relationship exists between the two phenomena. In these curves the compressibility is ascribed wholly to chlorine, and that of the other substance is neglected ; but when the latter is large, it also must enter into the problem. Unfortunately our data concerning compressibility are unusually limited ; but approximate calculations, based upon such as are known or may be guessed, show that at least some of the irregularities in the parallelism may be ascribed to this source. We may thus formulate the following law : The work needed for the compression involved in the formation, of one solid or liquid by the combi- nation of two others is approximately proportional to the heat evolved. While the general tendency of the law is manifest, and a correction for individual compressibilities would undoubtedly make it more so, there are nevertheless several exceptions to be explained. These may arise from several causes ; in the first place, many specific gravities of solids are known only approximately ; * in the next place, it is important that the same modifications of each substance should enter into each calcu- lation. A plausible explanation has been found even for the excep- tionally wide deviation exhibited by argentic chloride ; but this point will not be dwelt upon now, since it is being submitted to the test of experiment. The relation may be further illustrated by a table giving the data for a few bromides, and of course many other data might also be given. In order to eliminate as much as possible the contraction of the metal, it is well to choose for comparison a common non-metal possessing a compara- tively large coefficient of compressibility, hence both chlorine and bromine serve well. As a final example, the case of a single metal combining with several * See Richards, These Proceedings, 31, 163 (1895); also Ostvvald, Zeitschr. phys. Chem. 3, 143 (1889). 404 PROCEEDINGS OF THE AMERICAN ACADEMY, non-metals may be cited. Potassium is chosen in this last case because it is probably among the most compressible of metals. COMPAEISON OF CONTKACTION WITH HeAT OF FORMATION INVOLVED IN THE Synthesis of the Bromides. Metal. Atomic Volume of Metal. Atomic Vol. Metal + n times Atomic Vol. Bromine. Molecular Volume of Bromide. Difference or Contraction. Contrac- tion corre- sponding to 2 Atoms Bromine. Heat of Formation corresp'd'g to 2 Atoms Bromine. Sodium 23.7 49.2 34.2 15.0 30.0 718 Potassium 45.5 71.0 44.2 26.8 63.6 796 Calcium . 25.3 76.3 60.1 16.2 16.2 648 Zinc . . . 9.5 60.5 53.4* 7.1 7.1 318 Strontium. 34.5 85.5 58.4* 27.1 27.1 659 Cadmium . 13.0 64.0 56.9 7.1 7.1 315 Barium 37.0 88.0 62.2* 25.8 25.8 711 Comparison of Contraction with Heat of Formation involved in the Synthesis of Potassic Halides. Halogen. Atomic Volume of Halogen. Sum of At. Vols, of Metal and Halogen. Molecular Volume of Salt. Difference or Contraction. Heat of Formation of2Mols. Chlorine . Bromine . Iodine . . 25.0 25.5 25.7 70.5 71.0 71.2 37.8 44.2 53.8 32.7 26.8 17.4 850-1-t 796 670 When the more obvious experimental errors have been considered, two important questions at once suggest themselves : Does this propor- tionality signify equality, or is some of the energy of compression stored as potential energy and not manifested as heat ? Again, if this equality exists, is it always exact, or is it modified by subordinate secondary effects ? * Tliese values are calculated from very accurate determinations of specific gravity made recently in this Laboratory. See These Proceedings, 31, 168 (1895). t Approximately corrected for heat of evaporation and expansion. RICHARDS. — SOURCE OF CHEMICAL HEAT. 405 These questions cannot be answered at present. The total amount of work done in any case cannot be computed without a knowledge of the compressibility of the substances involved throughout the total range of volume, as has already been said. Unfortunately no suitable data exist 10 20 300 30 400 500 600 700 800 kilo joules. 40 50 60 cubic centimeters. 2NaBr 2KBr CaBro ZnBro SrBrg CdBro BaBro 2C1K 2BrK 2IK ^ ^ \ ^^^ -^ .--> y y ^ ■^ ^ ^ ~^ ^^ ^ ^^ ^ ^ -^ V "^i. ~^ -^ * V * * « ■».^ \ \ % 'y \ \ \ \ / / / / ^ ^ / V capable of satisfying the conditions of the problem. Before long I hope to present such data, and to formulate answers to both questions ; for the present the following unsatisfactory approximation is suggested as being better than nothing. From the study of many allied data I have been able to form an ap- proximate evaluation of the compressibilities of sodium and chlorine. 406 PROCEEDINGS OF THE AMERICAN ACADEMY. If one accepts these guesses, and imagines that the compressibilities decrease with decreasing volume according to the usual approximate law, one arrives at the conclusion that an amount of work equivalent to the heat of combination of sodium and chlorine would correspond to a change of volume in the system not far from the observed change of volume. Tlie outcome is complicated by the fact that even in ele- ments, but especially in compounds, there may be superposed several grades of compressibility. This can be explained hypothetically as fol- lows : When the molecule is composed of two atoms, the highly com- pressed portion of each atom at the point of chemical union should have a much smaller coefficient of compressibility than the slightly compressed remainder of the molecule. If the molecule is polymerized, there will probably be yet other grades of compressibility in the various parts. The only object of a calculation so uncertain as this is to show that the heats of formation are of the same order of magnitude as the work involved in the compression. In spite of the inevitable difficulties in the way of interpretation — difficulties which seem to be irdierent in the problem — the presumption is strong that the chief source of the lieat of clievtical combination is the work performed in compressing the material. Since the heat of reaction is known to represent only approximately the free energy of the reaction, while the compression may really represent the affinities at work, one would hardly expect the relation to be exact. The generalization is a question of fact ; it does not necessarily involve any atomic hypothesis, and can be regarded as uncertain only on account of the uncertainty of the data at present accessible. It is my intention to carry out the experimentation necessary to place the law on a more stable basis. In the same way any other manifestation of attraction or affinity, such as cohesion or adhesion, should have a compressing effi,'ct and therefore evolve heat. The superficial and limited nature of these phenomena would ordinarily prevent any appreciable rise in temperature. In some cases, however, as in the adsorption of liquids and gases by porous ma- terial exposing a large surface, such a heating effect has been actually observed. Thus the essential difference between water of crystallization and adsorbed water is that the former penetrates the mass, while the latter is merely superficial. It is obvious, moreover, that the same considerations apply to solidifi- cation and change of allotropic form. For example, liquid phosphorus, yellow phosphorus, and red phosphorus have at 44° the atomic volumes RICHARDS. SOURCE OP CHEMICAL HEAT. 407 17.66, 17.1, and about 14.1 respectively. The first small contraction is attended with an evolution of 0.65 kilojoulcs, and the second larger one with the evolution of 114 kilojoules of heat energy. In those cases where there is a transition from a more compressible union to a stabler, less compressible one, involving more work of compression, solidification would involve increase of volume, as in the case of water. II. A Plausible Interpretation. It becomes now an interesting question to determine, if possible, the mechanism by which this work is converted into heat. One is reminded at once of the compression of a gas, where the work of compression re- appears quantitatively as heat energy. But the compression under con- sideration differs from the other in detail, because in the present case the attraction of the two substances for one another seems to be the cause of their mutual compression ; and this mutual compression takes place not from the outside, but throughout the whole substance. Those who shun the atomic hypothesis and consider substance only in the mass, will rest contented without further attempt at interpretation ; but those who hold that the hypothesis is a useful tool, to be thrown aside when newer invention has devised a better one, will be tempted to go further. The case, considered hypothetically, seems to be this : "When two dif- ferent atoms possessing mutual affinity approach one another, they are drawn closer than they can be to their lespective fellows, and in the process evolve heat. The " repulsion " which is often supposed to sur- round an atom, and prevent it from touching any other, seems to be par- tially overcome by the potential energy of affinity. But of what nature is this '* repulsion " ? Ordinarily it is assumed to be due to the frequent impacts of a hard atom in the centre of the space; but no evidence is afforded of the existence of a free space. Indeed, it seems inconceivable that solids should retain their structure, or should be capable of retaining gases or liquids, if they are so loosely built up. A pile of sand would be stable compared to such a fabi'ic. The present research points to quite a different interpretation of the facts. The space occupied by a solid seems to have a chemical signifi- cance as well as a physical one; it seems, indeed, to be as essential a property of the material as any other property. Since the significance of the total volume is a chemical one, the " free space " around each indi- vidual atom must also have a chemical as well as a physical significance. 408 PROCEEDINGS OF THE AMERICAN ACADEMY. In other words, we have no right to imagine that the space is " free " or that there is a hard particle in the centre ; the shell is as essential an attribute of the atom as the centre. But how are we to account for heat vibration, if the atom is supposed to fill the whole space ? This question is important ; but before answering we must consider some of the con- sequences of this form of compression. Let us imagine two highly elastic spheres ; for example, two very thin- walled india-rubber balls filled with gas. Imagine these to be drawn together by a powerful attraction resident throughout themselves. When they come in contact, each will compress the other and evolve heat in the process. They will remain bound together and distorted, unless some force separates them. If the shell of an atom is elastic and compressible, it is only reasonable to suppose that the interior is also. In that case the whole substance of both of two combining atoms will suffer distortion from the mutual attraction of every part of their substance ; and the con- centration of those constituents in each atom which cause the affinity will thus be increased in the half nearest the other atom. The supposition that the affinity comes from within will cause here an essential divergence from the actual conditions in two balls filled with gas, in which the gas is distrib- uted equally throughout. As a consequence, the opposite half which is not combined will lose some of it attractive constituents, and should then have less tendency to unite with the new substances than it had before its union with the first atom. This plausible influence agrees with the well-known facts of " false equilibrium " and the nascent state ; in fact, it would account in general for the permanence of slightly stable compounds. By the process of hypothetical reasoning given above, one concludes that the whole substance of the atom may be elastic. In that case heat vibration might consist simply in alternate condensation and rarefaction of the medium within the shell, started by the momentum of impact. This would continue indefinitely, unless the vibration were imparted to other substances possessing less. Such internal rarefaction and condensation might well tend to distend the atom if any portion of the atom were held by another. Thus, it is evident that there is no difficulty in imagining internal vibration in an atom which is packed on all sides closely with other atoms, or in explaining the mechanism of the thermal expansion of solids and liquids upon that basis. The chief reason for imagining a small hard particle with a large free space around it is therefore removed. Two other reasons for retaining the conception of the old atom may be RICHARDS. — SOURCE OF CHEMICAL HEAT. 409 urged ; one, the continuity of the liquid and gaseous state, and the other, the porosity of solids. In answer to the first, attention may be called to the fact that the con- tinuity of the liquid and gaseous condition exists actually only at the critical pressure ; below that point they are, as a matter of fact, discon- tinuous and very different. Perhaps the critical pressure is simply the point where the gas molecules at the critical temperature are pressed into actual contact. The compressibilities of very compressed gases are, in fact, of the same order of magnitude as those of liquids. Porosity is usually only manifest under very great pressure, which might be enough to compress the atoms into smaller space, and thus open orifices which previously did not exist. From these considerations it seems to me that the new kinetic concep- tion of the solid and liquid state has no disadvantages which the old conception does not possess, while it has many advantages which the old theory has not. But it is not the intention of the present paper to enter into the detail of so large a question. I hope that in the next few years I may be permitted to study and report upon the possible consequences of the significance of changing atomic volume. In the preceding paper and the present one, the following phenomena have been suggested as capable of a new and plausible interpretation if atoms are considered as capable of altering their volume through a wide range ; namely, the heat of chemical reaction, adsorption, adhesion, and cohesion ; ordinary solution ; electrolytic solution ; electrolytic dis- sociation ; the passage of electricity through solids, liquids and gases ; the nature of cathode rays (and probably also X rays and radium) ; the laws of Faraday and Dulong and Petit ; false and true equilibrium ; heat capacity and thermal expansion ; quantivalence ; stereo-chemistry and crystal form ; and the critical phenomena. Following papers will be devoted to a development, quantitative where possible, of these applications, as well as of many others. Unless further study reveals discrepancies, which have hitherto been concealed, I expect to be able to show : — 1. That the conception is not inconsistent with the two laws of energy. 2. That it conflicts with none of the quantitative conclusions of the atomic hypothesis, nor with the kinetic theory of gases, if heat be assumed to be due to mechanical energy operating upon atomic inertia. 3. That it is able to interpret the actual deviations of gases from the gas law better than any other theory, retaining the essential import of 410 PROCEEDINGS OF THE AMERICAN ACADEMY. the equation of van der Waals, and modifying this equation only as regai'ds the changeability of a and b. 4. That it is consistent with the varying specific heats of substances in the solid, liquid, and gaseous states. 5. That with the help of this theory such physical properties as ten- acity, ductility, malleability, and coefficient of expansion assume for the first time a conceivable consisteney. 6. That upon it may be based a definition of the essential influences of chemical change and equilibrium. 7. That the variable compressibility of atoms furnishes a plausible explanation for many of the phenomena of quantivalence, including even the feeble affinities holding water of crystallization and other so-called molecular combinations. 8. That it explains all the tridimensional relations of material, such as stereochemistry and crystal form, at least as well as any other theory. 9. That with the proviso that electrical energy is a rhythmic mani- festation of energy, — tending to repel itself and therefore to keep upon the surface of material which is susceptible to it, and hence to expand a free atom, — many of the electrical and magnetic phenomena of matter become more conceivable. 10. That the effect of light in hastening the attainment of chemical equilibrium, and the possibility of storing and emitting light energy possessed by material, may be interpreted in a similar way. 11. That the careful considei'ation of all these and other facts leads to a somewhat new conception of the relation between gravitation and chemical affinity, as well as between matter and luminiferous ether. This conception involves simply an antithesis of contracting and expand- ing tendencies, and is thus founded entirely upon an energetic basis. 12. That the idea is capable of throwing light upon the periodic sys- tem, and the genesis and permanence of the elements. 13. That it may be applied even to such astrophysical problems as the cause of the sun's heat. This is a large program ; some of it is already in manuscript, and more must await further exact experiment. The program is given here only to call attention to the wide possibilities of the consistent introduction of the conception of atomic compressibility into chemistry and molecular physics. The present paper is only one step in the direction indicated. It is nevertheless an important step, for it adds approximate quantitative evidence to the previously given qualitative evidence concerning the significance of changing atomic volume. RICHARDS. — SOURCE OF CHEMICAL HEAT. 411 in. Summary. The contents of the paper may be divided into two parts : In the first part is set forth an approximate generahzation which rests upon facts alone. This part of the paper can be overthrown only by the proof that the facts upon which it rests are erroneous. In the second part of the paper a plausible hypothetical interpretation of the facts is given. This part of the paper stands ready to share the fate of all hypotheses, — namely, to retire into oblivion if it is not capable of aiding the discovery of truth. In brief, the chief points touched upon may be summed up as follows : — I. (rt) It has been shown that the contraction exhibited during chemical combination is in many cases approximately proportional to the heat evolved. (b) Upon correcting the results for known differences of compressibility, the approximation becomes closer. (c) An approximate calculation of the work which would probably be involved by the compression of a gram-atom each of sodium and chlorine into the space occupied by a gram-molecule of salt showed this work to be of the same order of maijnitude as the actual heat of formation. (d) From these facts and calculations the inference is drawn that the heat of chemical reaction is chiefly due to the energy required for the compression which takes place in the reaction. (e) Possible corrections are pointed out. (f) An explanation is given upon the same basis of the mechanism of the heat of adsorption, adhesion, and change of allotropic form. II. (a) While the evidence is not exact, it affords a strong presump- tion in favor of the hypothesis of compressible atoms. The possibly far- reaching effect of this simple and plausible hypothesis upon chemical theory is pointed out. (b) There is given a list of the especially prominent aspects of the question which will form the subjects of immediate experimental and theoretical study in this Laboratory. Cambridge, Mass., U. S. A. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 16. — April, 1902. CONTRIBUTIONS BMIOM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. ON THE ACCURACY OF THE IMPROVED VOLTAMETER. By Theodore W. Richards and George W. Heimrod. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVAUU COLLEGE. ON THE ACCURACY OF THE IMPROVED VOLTAMETER. Bv Theodore William Richards and George William Heimrod. Presented February 12, 1902. Received January 29, 1902. Introduction. In a recent preliminary paper * it was shown that the disturbing in- fluences in the common silver " voltameter " (or better, coulometei- f) are due to the concentrated liquid which falls from the anode. In order to avoid the inaccuracy thus caused, it was suggested that the anode be surrounded by a fine-grained porous cup, which is capable of preventing this heavy liquid from reaching the kathode. The weight of silver deposited by a given current in such a voltameter was found to correspond very closely to the amount of copper deposited at the same time in a copper voltameter shielded as much as possible from all discoverable sources of error ; hence it seemed probable that the new voltameter gives the true value of the electrochemical equivalent of silver. In a matter so important as this, however, it seemed advisable to ob- tain much more information concerning the constancy and trustworthiness of the new instrument, as well as to discover if possible the mechanism of the phenomena which rendered the older form untrustworthy. The investigation described below was undertaken with these objects. I. The Constancy of the Porous Cup Voltameter. The first problem was to determine if two instruments in series would always give identical results; in other words, to find if the new voltam- eter is always consistent with itself. * Richards, Collins, and Heimrod, These Proceedings, 35, 12.3 (1899). t The word " voUameter " was devised before electrical dimensions were understood. It is moreover too much like the universally used and suitable word " voltmeter." Now that the former instrument is placed upon a firm basis of accuracy, it may appropriately receive also an accurate name ; and it is hoped that the new word "coulometer" may replace wholly the anachronism. 416 PROCEEDINGS OP THE AMERICAN ACADEMY. Nine such duplicate experiments were made. The first of these was a crude trial, and need not be recorded ; the eight others are given iu the following table. The apparatus employed was precisely like that described in the pre- vious paper. For the sake of easy reference, the description is repeated below. Small cylinders of Pukal's porous ware (Berlin), suitable for osmotic pressure experiments, were used to enclose the anode in order to prevent the heavy anode-solution from reaching the kathode. These vessels were 50 millimeters high and — J A ^ 20 in diameter ; their walls were not much over one milli- meter in thickness. Their impurities were removed by boiling with nitric acid and thorough washing with water. Before being used they should be carefully searched and tested for cracks or imperfec- tions. They were suspended in the solution by means of a platinum wire hung upon *a glass hook, which insulated the wire from the electric connections. By means of a siphon, or a small pipette with a rubber top, the liquid within the cup was always kept at a lower level than that without, so as to prevent outward filtration. The kathodes consisted of large crucibles weighing only GO grams, although they were capable of holding 120 cubic centimeters ; they were pro- vided with lips. A crucible exposes a smaller surface of liquid to the impurities of the atmosphere, and gave in our expeiuments a more evenly distributed deposit than a bowl. -«^ FiGDRE 1. — rOKOUS CuP VOLTAMETER (I actual size). A, glass hook for supporting anode. B, glass ring for supporting porous cup. C, silver anode. D, porous cup. E, platinum kathode. RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 417 The anodes were bars 5x1x1 centimeters of the purest silver, sup- ported by silver wires and not enclosed in filter paper ; and the electro- lyte usually contained ten grams of pure, freshly prepared argentic nitrate in a hundred cubic centimeters of solution. The manipulation was simple. The platinum crucibles were cleaned, dried at 160°, and weighed after three or four hours' cooling in a large desiccator kept in the balance-room. In order to prevent leakage during the electrolysis, the several stands were insulated by separate glass plates, and all the connections were air lines. The apparatus was protected, as in the earlier experiments with copper, by a miniature house with walls of fine cotton cloth, which helped to exclude dust. When the current was broken, the electrolyte was removed, the silver was rinsed twice with water, a third filling with water was allowed to stand in the cru- cible for two or three hours, and a fourth one remained in it over night. The wash-waters were collected and filtered if the silver showed any tendency to break off. In such cases a Gooch crucible was employed to collect the particles ; and a very small filter, afterwards burned, served to catch the minute flakes of asbestos detached from the mat. On the next morning the crucibles were washed once more, rinsed twice with pure alcohol, and finally dried and weighed as before. This method of treatment gave opportunity for the diffusion of mother liquor from the intricate recesses of the crystallized mass, while it did not run the risk of dissolving silver which may attend the use of boiling water for w.ishing. As has been said, the crucibles were dried at 1G0°. It was subse- quently shown, in agreement with the results of Lord Rayleigh and INIrs. Sidgwick, that a red heat is needed to drive off all the included liquid from the silver crystals ; but since the amount included is fairly constant, this fact does not interfere with the availability of the uncorrected data for the present purpose of comparing one weight of silver with another. Weighings were made upon the balance which served for the weigh- ings in the earlier woik upon copper, — one which has served also for many determinations of atomic weights. Its results with small objects may be depended upon to within ^^ milligram. All weigliings were made by double substitutions, a similar vessel being used as a tare, and the weishts were of course carefully standardized. Since the question con- cerued merely the comparison of silver with silver, the results were not at first corrected to the vacuum standard. The results show that the average difference between the weights of the silver deposited in two crucibles placed in series was less than the tenth of a milligram, or only about four parts in one hundred thousand. VOL. XXXVII. — 27 418 PROCEEDINGS OP THE AMERICAN ACADEMY. Considering the size of the platinum vessels weighed, this average agree- ment is all that could be expected ; hence the test of the constancy of the apparatus seems to have been satisfactory. TABLE I. Test of the Constancy of the Pokous Cup Voltameter. No. of Experiment. Voltameter I. Weight of Silver. Voltameter II. Weight of Silver. Difference. Percentage Difference. grams. grams. milligram. per cent. 2 2.43744 2.43749 0.05 0.002 3 2.69691 2.69713 0.22 0.008 4 2.36193 2.36196 0.03 0.001 5 2.14900 2.14913 0.13 0.006 6 1.65485 1.65490 0.05 0.003 7 2.31480 2.31500 0.20 0.009 8 2.22258 2.22260 0.02 0.001 9 2.67264 2.67268 0.04 0.002 Mean differs >nce . . . . 0.09 0.004 There is of course nothing in this table to show whether the fieures represent the weiglit of silver which ouglit to have been deposited by the quantities of electricity employed. It may be that the error of the old voltameter was merely reduced, and that a small constant error still re- mained. The most probable cause of such a remaining error seemed to be the possible diffusion or migration of the heavy anode-liquid through the bottom of the porous cup, in spite of the fact that it was continually removed by means of a pipette or siphon. In order to prevent this, the bottom and a few millimeters of the sides of a porous cup were filled with melted paraffin, which effectually sealed the pores. The upper part of the sides only served to allow the passage of the electricity. A tenth comparison showed that a curient which deposited 1.83370 grams of silver in this cup deposited 1.83375 grams in the ordinary porous cup coulometer. This difference is no greater than a possible experimental error; hence we may conclude that the effect of the diffusion is impercep- tible. It will be shown later that the substance which causes the chief RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 419 irregularity of Lord Rayleigh's voltameter is probably a heavy complex ion ; hence it is not surprising that both the migration-rate and the ditfusion-rate of the impurity is small. On the other hand, when the porous cup is too coarse-grained or too large, or when the anode solution is allowed to rise too high and thus filter through, the effect of the diffu- sion betrins to be manifest. The same error begins to show itself when the viscosity of the solution is diminislied by increasing temperature, as we showed in the preceding paper. If now the formation of ionized silver at the anode is attended by such disturbing side reactions, it is reasonable to assume that a remedy may be found in the use of an anode of some other metal. For this purpose zinc seemed to offer peculiar advantages ; it possesses only one degree of quantivalence, and has so great a solution-tension as to avoid the possi- bility of contaminating the deposit of silver at the kathode. A zinc rod (so-called " C. P.") served as the anode in the following two experiments, and it was surrounded by a ten per cent solution of zincic nitrate prepared from the same material by solution in nitric acid (standing for a week over zinc), filtration, and crystallization. The kathode solution consisted of a ten per cent solution of argentic nitrate, as usual. TABLE II. The Effect of a Zinc Anode. No. of Experiment. Wt. of Silver in Ordinary Porous Cup Voltameter. wt. of Silver in Voltameter with Zinc Anode. Difference. Percentage Difference. 11 12 grams. 2.69702 2.36195 grams. 2.69688 2.36209 milligram. -0.14 +0.15 per cent. -0.005 +0.006 Average error .... 0.01 0.001 A peculiar reaction was observed during this electrolysis. The zinc rod was covered with a copious white flaky precipitate, and a marked test for nitrite was observed in the supernatant solution.* Thus the ionization of the zinc is attended with the formation of basic salt and * See also Senderens, Comp. Rend., 104, 504 ; also Ber. d. d. ch. Ges., 20, 197 R (1887). 420 PROCEEDINGS OP THE AMERICAN ACADEMY. zinc nitrite. The NO3' ion must have been decomposed into NO.,' and oxygen. This same reaction takes place when silver serves as an anode in its nitrate solution, although to a much smaller extent. In spite of the irregularities just described, the deposition on the kathode proceeded in a perfectly regular manner, and the figures show that as much silver was deposited in one cell as in the other. Still another means of testing the porous cup voltameter was found in its comparison with a device which eliminates the porous cup wholly, but which nevertheless keeps the anode solution quite away from the cathode. This device consists in placing the anode at the bottom of a tall beaker filled with a concentrated solution of argentic nitrate (200 grams of the salt in a litre of solution), and arranging the kathode in the upper part of the vessel.* The anode solution becomes heavier and remains around the anode, while the kathode solution becomes lighter and rises to the surface. In order to prevent this dilution around the kathode from diminishing too much the concentration of the contiguous liquid, it is well to sink the kathode at least two centimeters below the surface. A circular disk of platinum wire gauze,t six centi- meters in diameter, was used as the kathode, since many holes in gauze permitted the ready escape upward of the impoverished electrolyte. The gauze was bent around a stout circular platinum wire, and the disk was stiffened by four radial wires, and was hung rigidly from the centre. The vertical distance between this kathode and the anode was about seven centimeters. The anode consisted of a plate of pure silver, and its platinum connecting wire was protected from the solution by an enclos- ing glass tube. The chief trouble encountered in manipulating the voltameter thus constructed is the danger of losing fine crystals of silver from the flexi- ble gauze. In the two experiments described below every precaution was taken to avoid this source of error, and it is believed that no appre- ciable weight was lost. Another disadvantage of the gauze is the fact that metals deposited upon it are very apt to include minute quantities of electrolyte because of the interstices arising from its woven structure. Even silver deposited in a crucible contains some included mother liquor, and that deposited on the gauze contains much more. In the two experiments given below, the first deposit on the gauze lost 0.42 milligram on gentle ignition in a large porcelain crucible, and the * Merrill, Pliys. Rev., X, 169 (1000). t Paweck, Zeitsch. fiir Berg. u. Hiittenwesen, 46, 570 (1898) ; Winkler, Ber. d. d. ch. Ges., 32, 2192 (1899). RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 421 second lo.st 0.72 milligram, while the two crucible deposits lost respec- tively 0.20 and 0.24 milligram. These losses, accompanied by audible decrepitation, must have been due to retained electrolyte. lu the table the weights of the ignited precipitates are given. TABLE IIL Comparison of Porous Cup Voltameter with Wire Gauze Voltameter. No. of Experiment. Weight of Silver in Porous Cup Voltameter. Welsh t of silver deposited on Gauze. Difference. Percentage Dillereuce. 13 14 grams. 2.10326 2.31237 grams. 2.10344 2.31234 milligram. +0.18 -0.03 per cent. +0.009 -0.001 Average e rror . . . . +0.08 +0.004 The gauze kathode thus showed an average surplus of less than a tenth of a milligram. But even this slight error is explicable, for it is clear that the argentic nitrate held by the electrolyte must have left silver nitrite or silver behind on heating. If we assume that the temperature of ignition was enough wholly to decompose the electrolyte, the average loss of 0.57 milligram would correspond to a residue of about 0.1 milli- gram, while the corresponding residue from the weaker solution used in the porous cup voltameter could not have exceeded 0.02 milligram. The difference between these two figures is exactly equal to the observed difference between the gauze voltameter and the porous cup voltameter, so that the two may be said to give precisely identical results. An important point connected with this experiment is the f\xct that the kathode surface available for deposition on the gauze had an area of less than half that on the inside of the large crucible. Hence the current density in the gauze voltameter must have been over twice that in the standard. There has thus been accumulated a convincing array of evidence indi- cating that the porous cup A^oltameter affords a means of depositing the amount of silver which really corresponds to the quantity of electricity sent through it. The numerical averages may be summed up in a brief table as follows : — > 422 PROCEEDINGS OF THE AMERICAN ACADEMY. Average deviation of two porous cup voltameters in series = ± y^^^ Difference caused by sealing bottom of cup = — jq^^^ Difference caused by use of zinc anode = ± ioo]ooo Difference (corrected) between gauze voltameter and cup voltameter ±0 The agreement of these results is as close as could be expected, since the discrepancies do not exceed the possible experimental error. With Lord Rayleigh's method, when two precisely similar voltameters are compared, Kahle * and Rodger and Watson f have shown that an ac- curacy of 6 or 7 parts in 100,000 can be obtained. On the other hand, the least variation of size of kathode or anode, or of any other condition, causes large deviations which may amount to ten times as large an error. In our experiments given above, the most radical changes of method were introduced, without affecting the results. Among the efficient forms of apparatus described above, the porous cup voltameter with a silver anode is the most convenient. Hence for the further purposes of this paper it will be chosen as the standard method. II. The Separate Effect of each Anode Irregularity. It is obvious from the study of earlier work that more than one irreg- ularity exists at the anode in a silver cell ; and the separation and iden- tification of the individual effect of each irregularity became a matter of considerable interest. The outcome was instructive as an example of the multitude of hidden minor influences which so often modify the ob- vious outcome of chemical experiment. Qualitative testing revealed not only acid, but also nitrite, in the anode liquid ; and in those cases where the anode is very small, some experi- menters have indicated the formation of highly oxidized compounds of silver. Moreover, the singular crystalline silver dust which forms around the anode demands an explanation. In order to solve the prob- lem, of course an obvious available method was to introduce artificially each impurity in turn into the pure liquid around the kathode in the porous cup voltameter, and study its effect on the gain in weight of the kathode. The first impurity to be investigated was the nitrite. In order to pre- * Wied. Ann. N. F., 67, 22 (1809). t Phil. Trans., 186 A, G33 (1895). RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 423 pare the nitrite, we had recourse at first to a method used by Proust.* He has found that on boiling an argentic nitrate solution with finely di- vided silver, the nitrite is produced in quantity. In repeating this ex- periment, powdered silver reduced from purest silver chloride by the Stas method was boiled in a ten per cent argentic nitrate solution. Nitrite was indeed formed, but a very fine film of crystallized metallic silver was formed on the surface ; a complication which seemed to point towards the existence of a reaction similar to the solution of copper in cupric sulphate. But it was found that pure silver nitrite in neutral silver nitrate solution likewise deposits a fine silver mirror on exposure to the light; hence the silver in both cases must be supposed to result simply from the decomposition of the nitrite. The solution boiled with silver was filtered through a Gooch crucible, and after cooling was em- ployed in a voltameter with a porous cup. The solution containing the nitrite deposited 2.27945 grams of silver, while pure argentic nitrate in another standard voltameter deposited 2.27944 grams, a difference of only 0.01 milligram. (Exp. 15.) Evidently the nitrite present had no effect at the kathode ; and the liquid in an ordinary voltameter could hardly contain more nitrite than this solution which had been boiled with metallic silver. In order to pursue the matter further, however, we prepared silver nitrite from pure potassium nitrite and silver nitrate.f Pure potassic hydrate was neutral- ized with nitric acid ; the nitrate was re-crystallized and fused in a silver crucible, and the resulting mixture of nitrate aud nitrite was extracted TABLE IV. Standard vs. Voltameter with Solution Saturated with AgN02. No. of Experi- ment. Type of Voltameter containing Nitrite, Weight of Silver in Standard. Weight of Silver in Vol- tameter con- taining AgNOo. Difference. Percentage, Difference. 16 17 Standard. Filter paper volt. gram.s. 2.27944 2..30276 grams. 2.28011 2.30539 milligrams. 0.G7 2.63 per cent. 0030 0.114 * .Journ. de Physique, March, 1806, 211 ; also Nicholson's Journal, 15 : 878. This reference has evidently been lost, since no text-book, including; Dam- mer, gives it, although all mention Proust's observation. After a long search through tlie journals published in Proust's days, the reference was rediscovered. t Victor Meyer, Liebig's Ann., 171, 23 (1874). 424 PROCEEDINGS OF THE AMERICAN ACADEMY. with boilino- water. The great bulk of nitrate may tlien be removed by one crystallization. If to the mother liquor is added a solution of ar- gentic nitrate, the argentic nitrite will precipitate at once as a thick yellow paste. This is washed and re-crystallized from hot water, until the color has changed to white. The pure nitrite was dissolved in a nitrate solution to saturation, and this was employed, first, with a porous cup (IG), and second, with a paper-wrapped anode (17). The results show that a saturated solution of nitrite really has the effect of increasing the kathode deposit. Since the increase due to a paper-wrapped anode over the weight found with a porous cup would have been from 0.04 to 0.08 per cent, the nitrite caused an increase of about the same amount in each case. But this increase happens only when the solution is saturated with nitrite ; hence it is interesting chiefly as a limiting effect, and can hardly be im- portant in solutions of nitrite as dilute as those formed spontaneously around the anode. The formation of nitrite is evidently the result of the breaking up of the IsOg" ion into the nitrite ion 1^0.~ and ox3'gen, and the latter is probably taken up by the silver in forming one of the oxidized compounds to be discussed later. It is not at all surprising that this side reaction should take place to a small extent. The current is normally cariied fi'om the anode to the solution by the formation of the silver ion from the metal ; but a slight tardiness in this reaction (which might be named " physico-chemical in- ertia") would result in assistance from the anions in the neighborhood. They would seek to adjust the potential by discharging their negative electricity on the anode. Of course the most plentiful anion in the vicin- ity is the nitrate ion ; its deionization would make possible the form- ation of the nitrite ion and oxygen, which might at once oxidize the silver plentifully present.* The reaction might be written thus: — NO3 -H 3Ag = Ag + -f NO2- -f Agp. Thus the electrolysis of a strong solution of argentic nitrate might be predicted to result, in the neutralization of a previously acid solution — a prediction which agrees with the fact discovered by Rodger and "Watson t with thirty per cent solutions of argentic nitrate. It is pos- sible that a higher oxide also would be found if the anode were small. * The probable presence of silver in supersaturated solution around the anode will be shown later. 1 Rodger and Watson, Phil. Trans., 186 A, G31 (1895). RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 425 But Kahle * found that in weaker solutions acid is produced instead of being removed, and we have verified his results. Clearly this must be due to yet another irregularity. Wlien the solution is dilute and neutral, oxygen and hydroxyl ions are both present in appreciable amount, ac- cording to modern electrochemical interpretation. Their greater ease of deionizatian would compensate for their relatively small concentration, and traces of negative electricity might be cai-ried out of the solution through their agency with the formation again of argentic oxide, or even oxveren gas. The reaction would, however, leave an excess of ionized hydrogen (acid) in solution, a state of affairs not paralleled in the case of the nitrite. This would explain the phenomena in question. But would not the argentic oxide at once dissolve in the simultaneously formed acid, and thus form argentic nitrate again? Or, in other words, does argentic oxide form with silver an oxide-complex of any degree of stability? Hellwigtin a recent paper has shown that the weak silver ion in the presence of the strong NOs" ion tends to strengthen itself by taking up a molecule of some other undissociated substance, as AgCl, Agl, AgBr, or AgCN. He has proved also that the solution actually contains ions like Agol"*", since on electrolysis the iodine accumulates at the kathode, and disappears from the anode. lu order to find if argentic oxide could in a similar way associate itself with the silver ion, we boiled very pure argentic oxide with a concen- trated solution of argentic nitrate, and filtered the solution hot. Upon "being diluted with cold water this solution yielded a white precipitate, which tui-ned gray upon standing. The precipitate was soluble in dilute nitric acid, hence it could not have been an argentic halide ; besides, every precaution had been taken to exclude the halogens. The com- pound precipitated on dilution must, therefore, be silver hydroxide or a basic salt; and a basic complex must have existed in solution. It is by no means inconceivable that this complex, although finally de- composed by acid, should not yield at once to its action. In the meantime the acid, diffusing at a far more rapid rate than the heavy complex, would have partly left the immediate neighborhood of the anode, and hence the heavy solution around the latter would fall with its basic load to the bottom of the kathode vessel. There the complex ion (possibly AgjO^) would be capable of transferring electricity as well as any other ion, and upon deionization would deposit over three times the weight of material * Kalile, Wicd. Ann., 67, 1 (1899). t Zeilsclir. aiiorg. Cheui., 25, 157 (1900). 426 PROCEEDINGS OP THE AMERICAN ACADEMY. contained in the silver ion carrying the same quantity of electricity. Part of this material would be in the form of oxide, and would therefore cause dark spots on the surface of the kathode, — spots which have actually been noticed by other experimenters. This interpretation serves to explain also the very high results ob- tained by Lord Rayleigh in the presence of argentic acetate. The possibility of forming slightly dissociated acetic acid would prevent any considerably accumulation of ionized hydrogen, and the oxide-complex would grow in concentration without hindrance. This explanation seems more plausible than the provisional one suggested by Lord Ray- leigh, — namely, that the acetate itself might be carried down with the silver. In order to submit these interpretations to the test of experiment, electrolyses were conducted with solutions saturated with argentic oxide. Kahle, Patterson and Guthe, and others, have likewise carried out such electrolyses, showing that the deposit is as a matter of fact too great ; but our trial is easier to interpret, because by means of the porous cup all anode complications were excluded, and the result of experiment gives the effect of argentic oxide alone. Three trials were made, in which a given current of 0.25 ampere as usual was run first through a standard porous cup voltameter, and then through a cell precisely similar except that the kathode solution in the latter was saturated with the argentic oxide. The following table cou- tains the results : — TABLE V. Standard vs. Standard saturated with AggO- No. of Experiment. Weizht of Silwr in Standard. Weight of Ag Standard with Ag.,0. Difference. Percentage Difference. 18 19 20 grams. 2,30276 2.34799 2.21379 grams. 2.30449 2.34887 2.21489 milligrams. 1.73 0.88 1.10 per cent. 0075 0.037 0.050 Mean 0.055 The solution after boiling with silver oxide thus really contains, there- fore, some iou heavier than Ag+. Since this has beeu formed directly RICHARDS AMD HEIMROD. THE IMPROVED VOLTAMETER. 427 from the oxide, it probably contains Ag.^O, and may be assumed to have the formula already given, AgaO"*". Thus the preceding interpretation is confirmed. The next question which arises concerns the permanence of this com- plex in the presence of acid. In order to test this, a solution of argentic nitrate was saturated with argentic oxide, and then treated with a slight excess of nitric acid. After a short time, perhaps an hour, electrolyses were made with this solution in series with the standard, as usual. TABLE VI. Standard vs. Standard saturated with Ag^P, but afterwards acidified. No. of Experiment. Weight of Ag in Standard. Weight Ag from Sol. with Ag,0+HN03. Difference. Percentage Difference, 21 22 grams. 2.34799 2.21379 grams. 2.34836 2.21361 milligrams. +0.37 -0.18 per cent. +0.016 -0.008 The results are somewhat less regular than usual, but clearly most if not all of the oxide-complex had been removed by the acid. Thus, while the complex is capable of existence in a neutral solution, the speed of its reaction with acid results in its decomposition in a short time, as would be expected. It is possible that this oxide-complex is not the only one capable of being formed at the anode. Kahle, Sulc,* Mulder and Heringaf and others, present evidence showing that with a small anode, where both silver and nitrate ions would be less available for transferring electricity, a highly oxidized compound having some such formula as AgyNOu may be formed. This compound is capable of dissolving in acids, forming a brown solution ; and it may be responsible for the colored rings which Kahle has noticed from old acid solutions. The fact that after boiling with metallic silver such solutions cease to yield colored rings is evidence that the foreign compound is a highly oxidized substance. In spite of the fact that the nitrite, the oxide-complex, and the per- * Sulc, Z. anorg. Chem., 12, 89, 180 (1896) ; 24, 305 (1900). t Mulder and Heringa, Ber d. d. ch. Ges., 29^, 583 (1896). 428 PROCEEDINGS OP THE AMERICAN ACADEMY. oxide-complex, may explain many of the irregularities observed during the electrolysis, they cannot explain them all. The chief questions re- maining to be answered concern the cause of the high results which are still to be obtained when all the preceding causes of irregularity have been eliminated, as well as the mechanism of the formation of the plentiful " anode dust." A number of facts point to the conclusion that some other complex compound exists in the electrolyzed liquid which is capable of deposit- ing metallic silver upon a silver surface. Among others is the well known fact that a pure silver kathode receives a larger deposit with a given current than a platinum kathode in the old Lord Rayleigh vol- tameter. It seemed to be worth while to test once more this relation, in order to confirm the results of Lord Eayleigh, Kahle, and others, and also to discover if a pure argentic nitrate solution in the porous cup voltameter would give like results. The following tables record the results of our experiments. In the first place we repeated Kahle's ex- periments, using an anode protected only by filter paper. TABLE VII. Filter Paper Voltameter os Platinum and on Silver. No. of Experiment. Weight of Deposit on Platinum. Weigtit of Deposit on Silver. Difference. Pprrentac>^ //^^:€', Accession No, /K /^v , Given by ^--^^^j v. c. t:,-£^« Place, ■i^fd^'-i^. ***No book OP pamphlet is to be removed tpom the Liab- OPQtopy uiithout the pepmission of the Tpustees. Coxjyright, 1902, By the President and Fellows OF Harvard College. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. New Series. — No. XXII. By M. L. Fernald. Presented May 8, 1901. Received January 31, 1902. I. — THE NORTHEASTERN CARICES OF THE SECTION HYPARRHENAE. The Carices of Koch's subgenus Vigneae, with its sections Acroar- rhenae and Huparrhenae of Fries, have always perplexed the systematist, and by the general student they have as a rule been ignored or vaguely referred to such characteristic species as Carex straminea or C. echinata. Recently, however, the generally widening interest in sys- tematic botany has brought together in Carex, as in other groups, a large mass of material ; and an attempt to identify these specimens has made it necessary to study in great detail the minuter but tolerably con- stant characteristics of the fruiting plants. In general, the classification of Carices has always been based upon characters in the inflorescence ; and although the detailed study of the perigynia (or utriculi) has been the final resort of the specialist, an attempt has been made in our manuals to separate species as much as possible upon the more obvious characters of the inflorescence. Thus Carex scoparia is described in the two current manuals as having the spikelets (spikes) "all contiguous or bunched" or "usually aggre- gated ; " while in only one of these works is Boott's var. minor given recognition, and there as a mere dwarf variety. Yet in plants which are undoubtedly C. scoparia the spikelets are often scattered, forming a loose moniliform spike ; and the northern plant described by Boott as var. minor has a distinct range and unique habitat, while its minute thick-bodied perigynia distinguish it at a glance from the more southern species with which it has been associated. The case of Carex scoparia is only one of many in which the attempt to rely upon superficial characteristics has led us to confuse plants 448 PROCEEDINGS OP THE AMERICAN ACADEMY. which are genetically very distinct. Consequently, as stated, an attempt has been made to get at a more satisfactory basis for classification by studying the characteristics of the perigynia, which, naturally, are sub- ject to less variation than is the superficial aspect of the inflorescence as a whole. But since variations in texture and nerving, which are per- fectly evident upon comparison of specimens, are extremely difficult to render clear in descriptions, it has been found advisable to employ as the primary basis of division, at least in the groups here discussed, the actual or proportional measurements of the perigynia or the achenes. Even this method of careful measurement may sometimes prove mislead- ing, but in most species the perigynia vary within certain clearly defined limits, and it is only the very exceptional individual which will not fit the system here proposed. And, although in rare cases a species thus presents perplexing forms in which the perigynia are not characteristic, many attempts to classify the members of this group have convinced the writer that by actual measurement alone can we safely identify plants of such strong outward resemblance as Carex straminea, G. scoparia and C. tenera, or C. alata and C. albolutescens. As a result of these studies it has been found desirable to treat many plants in a manner somewhat different from that in any current synopses of the genus, and in some cases a study of the original descriptions and specimens has brought the writer to conclusions very different from those generally accepted by American caricologists. Some of these points are of slight significance, others of fundamental importance ; and, since it is inadvisable to complicate the synoptic treatment of the species with detailed discussions as to the identity and synonymy of different forms, the more important questions may be here discussed. Carex scoparia, Schkuhr, presents little difficulty, as the original figure is unmistakable. The species has, however, been made to harbor plants of very different aspect ; and a study of the fruiting characters shows these to fall into three groups with marked and constant char- acteristics. C. scoparia, itself, has the perigynium very thin and scale- like, with the wings so strongly developed as to minimize the apparent thickness of the body. This plant in its different forms is of broad range south and west of the Gulf of St. Lawrence. The other two species which have been included with Carex scoparia have the narrower subulate or elongate-lanceolate perigynia so little winged as quite to lack the scale-like character seen in that species. The best known of these two plants is the form described by Francis Boott as C. scoparia, var. minor. The material from which Boott's FERNALD. — CARICES OF SECTION HYPARRHENAE. 449 plate was drawn was collected by Tuckerman at the base of the White Mountains ; and since it is necessary to distinguish the plant by a new specific name (minor having been used too often as a varietal name to be eligible) and since there is already a Carex Tuckermani, it is a pleasure to commemorate the explorations and generous services of the Crawford family, familiar to a lung generation of visitors to the White Mountains. This plant with which their name now becomes associated is common in northern New England and about the Great Lakes, thence extendius far northward. The other plant with narrow thick perigynia is more puzzling. In the dark brown color of its broad scales it is unlike the other forms which have been referred to Carex scoparia. In fact, by different students it has been referred with doubt to C. tribuloides, C. lepornia, and C. foenea as well. Yet in its perigynium it resembles only Boott's C. scoparia, var. minor. This tall dark-spiked plant, which is common in the region of Orono, Maine, has been collected by Professor Lamson- Scribner and by the writer, but it seems to be unknown from other regions. This fact immediately suggests that it may be an introduced form, but a careful search through Old World material and descriptions fails to show anything to which it can be referred. It is, therefore, here treated as a local species, taking the name of the town from which all our material has been collected. One other form of the scoparia group should be specially mentioned since, by an unfortunate misinterpretation, it has already caused needless confusion. This is Carex scoparia, var. moniliformis, Tuckerman. A specimen in the Gray Herbarium from Tuckerman himself, is without question a slender-spiked form of C. scoparia. The variety was so treated by Francis Boott, in whose table 368 it is well represented. Yet in his Preliminary Synopsis of the genus Professor Bailey treated it without question as identical with his own C. tribuloides, var. reducta ; and Professor Britton, following his lead, has since made the new com- bination, C. tribuloides, var. moniliformis (Tuckerman) Britton, for a plant very different from that to which the varietal name was originally applied. Carex tribuloides, Wahl.,has been clearly treated by Professor Bailey.^ C. Bebbii, Olney, however, which by him is reduced to a variety of that species, seems to be as well marked as other members of the subgenus, and it is here given equal rank witli them. In its shorter, broader, and 1 Mem. Torr. CI., I. 54. VOL. xxxvii. — 29 450 PROCEEDINGS OP THE AMERICAN ACADEMY. thicker perigynia it is more nearly related to C. straminea and its allies. So, likewise, C. cristata^ Sclivveiii., is reinstated as a species, since its tolerably constant habit and its shorter, firmer perigynia place it as near C. straminea as to C. tribuloides. The diverse plants which have been treated by various authors, now as distinct species, now as forms of Carex straminea, fall into groups which are, in the main, fairly free from complexity. The attempt to separate these forms by color-characters has naturally led to much con- fusion, for plants which in bright sunlight have a strongly marked ferrugineous tendency, in shade are often quite green. The shape, size, nerving, and texture of the perigynia, however, show that almost with- out exception the species proposed by Willdenow, Schkuhr, Torrey, Schweinitz, Dewey, and other early students of the group were based on permanent characters. To treat all these well marked and constant forms as varieties of one species is adding confusion rather than clearness to our interpretation of the genus, especially when several of them are as closely related to other well recognized species. The ideutity of Willdenow's Carex straminea was settled by Professor Bailey^ in 1889, and a recent examination of Willdenow's material by Dr. J. M. Greenman has verified Professor Bailey's conclusions. C. albolutescens, Schweinitz, is now well understood, as are likewise C. mirabilis^ Dewey, C. tenera, Dewey, C. BicknelUi, Britton (C. straminea, var. CVat<;ei, Boott), and (7. a/afa, Torrey. But C. festucacea, Schkuhr, C. straminea, var. brevior, Dewey, and C. foenea, var. j8, Boott, seem to have been less clearly understood. Schkuhr's Carex festucacea, according to the original description, was a plant with about eight spikelets subapproximate or in a loosely cylindric spike, and the species is so represented in Schkuhr's figure. It is likewise well represented by Dr. Boott, who apparently had a clear conception of the species, in his table 386. Schkuhr's C. straminea, which we now know to be different from Willdenow's plant of that name, was an extreme form of C. festucacea with fewer spikelets, and until recently it passed as the type of the species ; i. e., C. straminea (tyjnca) of Boott and others. This plant, however, was called by Dewey G. straminea, var. brevior, and under that name it has lieeu treated by Professor Bailey. He includes with it, though, the C. festucacea of Schkuhr, a plant which, though closely related, is of rather marked appearance and of more limited range. More recently Dr. Britton, in 1 Mem. Torr. CI., I. 21. FERNALD. — CARICES OP SECTION HYPARRHENAE, 451 restoring to specific rank C. festucacea, has included in it Dewey's C. straminea, var. hrevior, and in tlie Illustrated Flora he figures the latter plant under the former name. But the late Dr. Eliot C. Howe, in his admirable ti-eatment of the New York Species of Carex, has recognized both plants, thus following the general treatment of Francis Boott and other earlier writers and at the same time clearing the names festucacea and hrevior from the confusion which has recently surrounded them. Carex foenea, var. /? of Boott has had a peculiarly unsettled history. When Francis Boott described and figured the plant as a variety of O. foenea, the latter name applied to O. albolutescens, Schweinitz, not to the true C. foenea of Willdenow. It was Boott's opinion, then, that the slender brown-spiked plant of the interior was a phase of what we now know without much doubt to be G. albolutescens. In the fifth edition of the Manual Dr. Gray took up C. foenea, var. /3 as C. foenea, var. ( ?) ferruginea ; and later the plant was distributed by Olney as a variety of Dewey's G. tenera ((7. straminea, var. aperta, Boott). In his Preliminary Synopsis in 1886, Professor Bailey reduced it to synonymy under G. straminea, Schkuhr (not Willd.), and later in his Critical Studies of Types he treated this plant along with G. festucacea, Schkuhr, and C. straminea, var, Grawei, Boott ( G. BicknelUi, Britton) as iden- tical with C. straminea, var. hrevior, Dewey ( C. straminea, Schkuhr, not Willd.). Subsequently, however, he has taken out of his C. stra- minea, var. hrevior, two plants, which he treats as parallel varieties, var. Grawei, Boott, and yhv. ferruginea {C. foenea, var. y8, Boott); and at the same time he has discussed as a species G. albolutescens, Schweinitz (C foenea of authors, not Willd.). This course has greatly cleared the group from its former confusion ; but it is unfortunate that while separating C. albolutescens specifically Professor Bailey should have attached C. foenea, var. j3 to the slender usually flexuous-spiked G. straminea, whose identity he had already so carefully worked out. G. foenea, var. /3 in its stiff habit, its strongly appressed broad-ovate peri- gynia, and the lexture of its leaf-sheaths, is quite unlike that species, but is very close to G. albolutescens with which it had been placed by Francis Boott. In these characters, likewise, it is equally close to G. alata, Torr., while its perigynia and the occasional awn-tips of the scales are so like those of the latter species as to place it nearer to that than to the former plant. The two species, Garex foenea, Willd., and G. adusta, Boott, have already been discussed and very clearly settled by Professor Bai- 452 PROCEEDINGS OP THE AMERICAN ACADEMY. ley. ^ But his own C.foenea, var. perplexa has proved very puzzliiio- to students of the group. In the original description of this variety at least two distinct species are referred to, while the words " head erect or nearly so " have proved misleading for a plant with more flexuous spikes (heads) than ordinarily occur in the type of the species. Dr. J. M. Greenman has kindly compared with Willdenow's original material various plants passing in America as Carex foenea, and he has furnished the writer with detailed camera-drawiuss from Willdenow's material. From these comparisons there seems no doubt that the origi- nal O. foenea was, as Professor Bailey has already stated, the smallest form of the species, with 4 to 9 spikelets in a suberect linear-c^lindric spike. This is the plant subsequently described by Tuckerman as C argyrantha and figured by Boott in his table 382, fig. 2. Professor Bailey's Oarex foenea, var. perplexa was based on Boott's table 380 and a portion of table 382 (presumably fig. 1), upon Olney's C albohUescens (E^xsicc. fasc. 1, no. 8), as well as his G. ulbolutescens, var. sparsijlora (fasc. V. no. 11). Now, the perigynia of good Carex foenea are strongly and conspicuously nerved on both faces, and the spikelets are pale green or silvery brown. The first part of var. pei-- plexa (Boott's table 380) shows a perigyniuin quite nerveless or only faintly short-nerved on the inner face ; the second component (table 382, fig. 1) is the characteristic large form of C.foenea with crowded spikes of large spikelets; the third (C. albolutescens of Olney) is, as represented by two sheets in the Gray Herbarium, a form between the large state and the small typical G. foenea ; while the fourth component (C. albolutescens^ var. sparsiflora, Olney — at least the New Brunswick plant) in habit as well as in the nerveless inner face of the perigynium closely matches the first cited plate (Boott's table 380). From the fact that yar. perplexa was proposed as a variety of G. foenea it is probable that its author had in mind the coarse form represented by Boott's table 382, fig. 1, and in the present treatment of the group it has seemed advisable to retain that name for the large plant. Olney's Carex albolutescens, var. sparsiflora is represented in the Olney Herbarium by two different plants. One of these, from Oregon, is the dark-spiked form of C. praticola which has been described as C. pratensis, var. furva, Bailey. The other, from Kent Co., New Bruns- wick, the northeastern plant which is identified with Boott's table 380, is much more closely related to G. adusta, Boott, than to C. foenea, Willd. 1 Mem. Torr. CI., I. 24. FERNALD. CARICES OF SECTION HYPARRHENAE. 453 From the former species it differs constantly in its more slender habit and flexuous elongated spikes of clavate-based spikelets, as well as iu smaller achenes. It is a plant of broad range from Labrador to British Columbia, creeping south to the coast of New England and the mountains of New England and New York. Since its varietal name, sparsijlora, is preoccupied in the genus, another specific name is here proi^osed in reference to the characteristic color of the mature inflorescence. The other large group of the Ihjpnrrhenae which has been treated by recent authors as the subsection Elongatae contains plants of two markedly different tendencies. One group is characterized by strongly divergent thin-edged perigynia which are spongy at base. The other group has ascending plump or plano-convex perigynia which are rarely thin-edged and are without conspicuously spongy bases. Mr. Theodor Holm, who has recently studied some of the members of the first group, includes with them Carex gynocrates and C. exilis, which by most other authors have been placed in the Dioicae. The texture and aspect of the perigynia seem to justify the treatment proposed by Mr. Holm and formerly for G. exilis by Francis Boott;^ and for the group thus con- stituted Mr, Holm suggests the name Astrostachyae.^ The other group, with ascending blunt-edged perigynia, may well retain the subsectional name Elongatae, since the characteristic species, C. elongata, C. hrunne- scens (C Gebhardii), C. canescens (C. curta), etc., were originally included in it by Kunth. Mr. Holm, in the paper cited, takes exception ^ to Professor Bailey's recent treatment* of Carex echinata, C. sterilis, and C scirpoides, on the ground that that author had been more controlled by the original specimens of Willdenow and of Schkuhr than by the original diagnoses. That Willdenow's original descriptions do not accord well with Pro- fessor Bailey's conclusions there can be no doubt; and when we are told by Professor Bailey that C. sterilis and C. scirpoides are identical, and when he says "the figures of both C. sterilis (fig. 146) and C. scir- poides (fig. 180) in Schkuhr's ' Riedgraser ' are unequivocal,"^ we find it indeed difficult to understand his observations. An examination of Schkuhr's figures shows his G. sterilis (fig. 146) to be a coarse plant with sharp-pointed ovate scales and broad-ovate cordate perigynia with distinct beak shorter than the body. Schkuhr's G. scirpoides (fig. 180), on the other hand, is represented with broad-oblong or elliptical blunt 1 Boott, 111., I. 17. 2 Holm, Theo., Am. Jour. Sci., Ser. 4, XL 205-223. 3 Holm, 1. c, 212. * Bailey, Bull. Torr. CI., XX. 422. 5 Bailey, 1. c, 424. 454 PROCEEDINGS OP THE AMERICAN ACADEMY. scales and deltoid-ovate obscurely short-beaked perigynia. These fio-ures of Schkuhr's agree very well with his descriptious. Furthermore, they agree equally well with Willdenow's diagnoses, for these latter were essentially the same as Schkuhr's. Professor Bailey further states that G. sterilis and 0. scirpoides are identical with the common American plant which he had formerly treated as G. echinata, var. microstachys, a plant with lanceolate or narrowly ovate slender-beaked perigynia ; and for this aggregate he takes up the name G. sterilis. After thus bunching three very different species as G. sterilis, he separates from " our so-called Garex echinata " two plants, G. atlantica and G. interior, with " ample specific characters." Through the kindness of Dr. J. M. Greenman the writer has been able to examine camera-drawings of Willdenow's original material ; while from Professor Carl Mez he has received fragments from the original material of Schkuhr. The drawings of the Willdenow mate- rial of both Garex sterilis and G. scirpoides, and the Schkuhr specimens of G. scirpoides agree with the original diagnoses. Dr. Greenman has, further, compared critically specimens sent him of the different Ameri- can forms with Willdenow's plants and with authentic specimens of C. stellulata, Gooden. (C. echinata, Murray). The identification thus made of these forms, leads to a conclusion very different from that published by Professor Bailey. These results may best be stated by discussing separately the three clearly cut species which have been so unfortunately confused. Garex echinata, Murray (C. stellulata, Gooden.). This sj^ecies was long considered a boreal plant of broad range, and it was so treated by Torrey, Tuckerman, Dewey, Carey, and other early students of American Carices. Francis Boott distinctly implied that the European species occurs in British America, saying: "I have not seen specimens which I can satisfactorily refer to the European C. stellulata, south of the British provinces of North America." ^ Yet Professor Bailey has interpreted this to mean that " Francis Boott questioned if the Ameri- can plant is the same as the European G. stellulata (or G. echinata) ; " and in "eliminating the European species from our flora," he says: " Definite specific characters of separation are obscure, and yet I am convinced that they exist. The American plant is habitually taller than the European, the scales are sharper and usually longer, the perigynia are more strongly nerved and more attenuated or conical, 1 Boott, III, I. 56. FERNALD. — CARICES OF SECTION HYPARRHENAE. 455 and above all, it is far more variable. . . . There are probably no species common to both countries, except those which are hyperboreal and occur through the Arctic regions of both hemisphei'es, being found in Greenland." ^ Then Professor Bailey defines his conception of the " habitually taller " American plant with " sharper " scales, etc., etc., including in it forms varying from the low slender Carex steUulata, var. augustata, Carey, with '' narrowly-lanceolate perigynia tapering into a long . . . beak,"- to the tall (often nearly 1 m. high) coarse C. sterilis, Willd., with broad-ovate perig}Dia, and the slender C. scirpoides, Schkuhr, with thick scarcely beaked often nerveless deltoid-ovate perigynia and elliptic blunt scales. The two latter constituents of this aggregate apparently do not occur outside North America and if they are included with the other American representative of C. echinata as one species, it is of course easily said that the American plant is taller or shorter, coarser or more slender than the European ; and certainly a species so constituted is " far more variable." When, however, we eliminate from the complex Carex sterilis of Pro- fessor Bailey's treatment the true C. sterilis and C. scirpoides, there is left a plant characterized by slender culms and leaves, the perigynia barely half as broad as long, and tapering to a slender conspicuous beak which is often nearly as long as the body. This is the C. echinata or C. steUu- lata of American authors and it includes as formal variations the very slender var. angustata^ Carey (C. echinata, var. microstachys, Boeckeler), and the tall C. sterilis., var. excelsior, Bailey, while a very coarse varia- tion with rather better defined characteristics is C. echinata, var. cepha- lantha, Bailey. This American species with the narrow perigynia has been compared many times by the writer with European C. echinata in a vain attempt to find some point of distinction. Specimens collected by Godet at Lignieres on the River Cher in central France are inseparable from Mortens' material from Sitka, and, again, Japanese specimens collected by Chas. Wright and by Maries are identical in their slender perigynia with Newfoundland plants. In order, however, to test still further the specific value of the American plant a portion of Allen's Labrador mate- rial was forwarded to Dr. Greenman at Berlin, and he was asked to compare it, along with other American forms, with Willdenow's types 1 Bailey, Bull. Torr. CI., XX. 423. - Carey in Gray, Man. 544. 45(3 PROCEEDINGS OF THE AMERICAN ACADEMY. and with other authentic European specimens of the group. In reply Dr. Greenman writes of this specimen : " No. 4. Differs from the original C. sterilis, Willd., in the following characters : («) narrower, more gradually acuminate and longer beaked perigynium ; (b) more oblong achene, which is less narrowed at the base. To me, however, your No. 4 is a perfect match for Carex stellu- lata in herb. Willdenow, and for European C. echinata, Murr. I am quite unable to make any distinction between them. The perigynial characters are exactly the same." Extreme difficulty is experienced, then, in attempting to distinguish the American Carex echinata from Old World material. The range of the American plant, too, from Labrador to Alaska, and southward in the mountains, immediately places the species in the hyperboreal flora from which Professor Bailey, at least by inference, would exclude it. In view of these two facts there seems, then, as Mr. Holm has already indicated, good reason to consider both the American and the European plant C. echhiata, Murr. Carex sterilis, Willd. This plant has already been sufficiently defined in the discussion of Willdenow's original description and of Schkuhr's figure. The writer has, however, examined with much care camera- drawings of Willdenow's material made by Dr. Greenman and fragments of Schkuhr's material generously sent by Professor Carl Mez. The Willdenow plant, which alone is of final importance, proves to be iden- tical with the large species of the Atlantic seaboard recently described as C. atlantica. The fragment sent by Professor Mez from the Sclikuhr herbarium is, however, from cultivated material, and is only a form of C. echinata with narrow perigynia quite unlike those shown in Schkuhr's figure and in the Willdenow plant as further shown by Dr. Greenmau's report of his critical comparisons in the Willdenow herbarium. Besides No. 4, the Labrador Carex echinata, two other forms were sent to Dr. Greenman for comparison with C. sterilis. No. 1 is C. echinata, var. cephalantha, Bailey, collected by Dr. C. B. Graves at Waterford, Connecticut, May 27, 1896. No. 2 is characteristic C. at- lantica, Bailey, collected by Dr. G. G. Kennedy at Ponkapog, Canton, Massachusetts, July 12, 1899. Of these two plants Dr. Greenman writes : "No. 1. This differs from C. sterilis, Willd., in the following charac- ters : (a) longer inflorescence, more remote and slightly longer spikelets ; {h) longer and more prominently beaked perigynium ; (c) achene less narrowed at the base. FERNALD. — CARICES OP SECTION HYPARRHENAE. 457 "No. 2. I am quite unable to distinguish this plant from the original of C. sterilis, Willd. It has the same broad-ovate, short-acuminate or short-beaked perigyuium, and the same achenial characters, that is, the achene is rather conspicuously narrowed below. The characters of the inflorescence are the same, except as to color. The Willdenow plant is more brownish : this, however, may be due, at least to a certain extent, to age." From Willdenow's original description, from Schkuhr's description and fi'nire, and from Dr. Greenman's examination and drawings of the Willdenow plant, there seems no question, then, that Carex atlantica, Bailey, is the true C. sterilis, Willd. Carex scirpoides, Schkuhr. The characters of this species, likewise, are sufficiently stated in the discussion of Schkuhr's and Willdenow's characterizations. Material from the Schkuhr herbarium received through Professor Mez is identical with camera-drawings made by Dr. Green- man from Willdenow's plant. These accurately agree, also, with Schkuhr's fig. 180. This species, was, furthermore, correctly inter- preted by Sartwell, Carey, and Boott, and it is well represented as C. stellulata, var. scirpoides in Boott's Illustrations, t. 146 .** Sartwell's No. 36 and Boott's plate are the only exact citations given by Professor Bailey for his C. interior, and his description of the so-called new species accords well with those of Willdenow and of Schkuhr. In distinguishing C. interior from C. scirpoides, Bailey says that the former has " greenish- tawny spikes," while the latter is "fulvous;" and he furthermore de- scribes Schkuhr's C. scirpoides, "as the plate plainly shows," with "long-beaked broad-winged perigynia." How such a statement and such conclusions could have been made is very puzzling. There can be no question, however, that the figure of Schkuhr's C. scirpoides as interpreted by Dewey, Schweinitz, Torrey, Sartwell, Carey, Francis Boott, Holm, and other students of the genus, is the same as Boott's table 146** upon which, in part, C. interior was founded. The name Carex scirpoides, Schkuhr, so long attached to this plant, was published in 1805, but it cannot, unfortunately, be retained for the species, since in 1803 Michaux published C. scirpoidea, the well known dioecious plant of extreme boreal and alpine regions. The next clearly defined name for the plant seems to be C. interior, although, as originally intended by its author, that name was supposed to apply to a species very distinct from C. scirpoides. Tuckerman , it is true, published in his Enumeratio Methodica the name C. stellulata, var. scirpina, citing C. scirpoides, Schkuhr, as a synonym. On a preceding page, however. 458 PROCEEDINGS OF THE AMERICAN ACADEMY. in an unfortunate endeavor to latinize one of Michaux's names, he had substituted 6'. scirp'ina for C. scirjjoidea,, Michx., not C. scirpoides, Schkuhr. This unfortunate citation of "C. scirpina" as a pure synonym of Michaux's C. scirpoidea attaches to that name a decided element of indefiniteuess. It is, therefore, wiser to take for the plant of Schkuhr and of Willdenow the more clearly defined name, C. interior. One other plant of the Astrostachyae has been the source of much con- fusion in the treatment of New England species of this group. Unlike Carex eclmiata, 0. sterilis, and G. interior, the perigynia of this plant are broadest at the middle, thence tapering to a narrow base. In aspect the plant is strikingly like the largest form of C. canescens, but its thin- edged strongly recurved perigynia place it clearly in the Astrostachyae. The species is not uncommon from eastern Massachusetts to Delaware and central New York, and in New England herbaria it has recently jaassed variously as C. atlantica, C. interior, C. canescens, var. vulgaris, C. sterilis, var. excelsior, &c. From notes left by the late William Boott it is apparent that he recognized in some of Chas. Wright's Connecticut material an undescribed form, but evidently he never described the plant. A portion of the original material of the late Dr. Eliot C. Howe's Carex seorsa, generously furnished the writer by Professor C. H. Peck, agrees in every regard with the perplexing New England plant, and under that name the species should now be known. The members of the Elo7igatae, as here interpreted, offer less difficulties than the other species of the Hyparrhenae, and special discussion is needed only of the forms which have been at various times associated with Carex canescens. These plants present two marked forms in their perigynia : in one plant, C. arcta, the perigynium is broadest at the rounded or subcordate base ; while in C. canescens and C. hrunnescens ( C. vitilis. Fries) the perigynium is nearly elliptic in outline, being broadest near the middle. Carex arcta of Francis Boott was originally published by him as C. canescens, var. polystacliya, but in his latest treatment of the plant he considered it a distinct species. As stated, its perigynial character is very constant. Furthermore, its rather limited strictly American range and unique habit quickly separate it from most forms of C. canescens. C. canescens, var. oregana, Bailey, said to differ from var. polystacliya in having the " head larger and more dense . • . becoming brownish," has identical perigynia with that plant, and the spikes (heads) are green or brownish, as are those of the eastern plant, a character dependent on age and exposure to light. FERNALD. — CARICES OP SECTION HYPARRHENAE. 459 Carex canescens^ L., is characterized by its glaucous color and strongly appressed-ascending elliptic pointed perigynia tapering very gradually to the short beak. Another plant, G. brunnescens, Poir. (C. canescens, var. alpicola, Wahl., C. canescens, var. vulgaris, Bailey), is usually bright green, and the few loosely spreading-ascending perigynia are rather abruptly contracted to a definite serrulate-based beak. This plant is common in dry soils throughout the boreal sections of America and Europe ; while the glaucous G. canescens is a species of very wet situations. Under various names, G. vitilis, Fries, C. Gehhardii, Hoppe, etc., G. hrunnescens has been treated as a species, and as often again as a variety of G. canescens. An examination of much material shows its characters to be essentially constant, and, though the plant superficially resembles small forms of G. canescens, its claim to specific rank rests upon a number of definite characters, "When Garex arcta and G. brunnescens are removed from C. canescens, there remains a species characterized by its glaucous foliage and ap- pressed scarcely beaked perigynia. This species presents in America three noteworthy variations. The true G. canescens, L., of northern Europe has the spikes 2.5 to 5 cm. long, of 4 to 7 oblong-cylindric to narrowly obovoid spikelets 0.6 to 1 cm. long. This plant occurs in Arctic America coming south to northern New England and New York, the Rocky Mts., and Vancouver. Rare in the eastern United States and Canada, the typical form of G. canescens has been misinterpreted by recent American students, although the species was very clearly discussed by Francis Boott. The American plant which has passed as true G. canescens is, however, strikingly different in aspect, and consequently the typical plant has more than once been published as a local American variety — var. dubia, Bailey, and var. robustina, Macoun. Another form of Garex canescens common to northern Europe and America is var. svbloliacea, Laestadius. In this plant the spike is usually rather shorter than in typical G. canescens, the less approximate globose or short-oblong few-flowered spikelets are only 4 to 7 mm. long, and the smaller perigynium is nearly or quite smooth. In its smooth perigynium this plant approaches G. heleonastes, which, however, has larger spikelets and perigynia and quite lacks the distinctive glaucous aspect of G. canescens. The var. suhloliacea, which is commoner in northern New England than is the true C. canescens, also simulates G. brunnescens ; but it is very canescent and the perigynia otherwise as in true G. canescens are essentially smooth, while in the greener G. 460 PROCEEDINGS OP THE AMERICAN ACADEMY. bnmnescens they are distinctly beaked, of more membranous texture, and usually with serrate margins. The commonest form of Carex canescens in North America is the plant mentioned without name by P"'rancis Boott and figured by him in his Illustrations, IV. table 49 G. This unique American form, which in essential characters is like true C. canescens, differs in its elongated in- florescence, 5 to 15 dm. long, at least the lower spikelets very remote. The plant seems to have been generally treated by American authors as typical C. canescens^ and no published name is available for it. The following synopsis presents tlie characters and ranges of the northeastern Hyparrhenae as now understood by the writer. In its preparation he has studied the material in the Gray Herbarium and the herbarium of the New England Bot9,nical Club ; as well as the hundreds of sheets in the herbarium of the Geological Survey Department of Canada, kindly placed at his disposal by Mr. James M. Macoun ; those of the Olney Herbarium of Brown University, made accessible to him by Mr, J. Franklin Collins; and a series from the Fairbanks Museum at St. Johns- bury, Vermont, rich in forms of the scoparia group, specially accumulated by the director. Dr. T, E, Hazen, for detailed study, and then generously forwarded to the writer. He has also been greatly assisted by the use of material from the private herbaria of the Honorable J. R. Churchill ; President Ezra Brainerd ; Doctors C. B. Graves, J. V. Haberer, G. G. Kennedy, and C. AV. Swan ; and Messrs, Luman Andrews, C, H. Bissell, Walter Deane, E. L, Rand, W. P. Rich, and E. F. Williams. The identification of dubious species of Willdenow and of Schkuhr has been facilitated by the cooperation of Dr. J, M. Greenman while at the Royal Botanical Museum in Berlin, and by Prof. Carl Mez of the University of Halle ; and authentic material of the late Dr. E. C. Howe's Carex seorsa has been generously furnished by Prof. C. H. Peck. HYPARRHENAE, Fries. Staminate flowers scattered or at the base of the uniform spikelets (only in exceptional individuals and in the often dioecious G. gynocrates and C. exiUs the entire spikelet staminate). Key to Species.^ * Perigynia with thin or winged margins, -t- Perigynia ascending, the tips only sometimes wide-spreading or recurved, not spongy at base, the margins whiged at least toward the beak. 1 The perigynial characters are here based on study of mature plants. In gen- eral the perigynia at the tip of the spikelet are less characteristic than those nearer the middle ; and, if possible, the latter alone should be used in critical comparisons. FERNALD. — CARICES OF SECTION HYPARRHENAE. 461 •w Bracts wanting or setaceous, if broad at most twice as long as the spike. = Plant strongly stoloiiiferous ; culms rising from an elongated root- stock : perigynium firm, 5 to ti mm. long (4) C. siccata. = = Plant not strongly stoloniferous ; culms solitary or in stools. a. Perigynia less than 2 mm. broad. 1. Perigynia 5 mm. or more long. O Perigynia 7 to 10 mm. long: spikelets oblong-cylindric, pointed, 1.5 to 2.5 cm. long (1) C. muskingumensis. O O Perigynia shorter (or, when exceptionally 7 mm. • long, in shorter spikelets). + Perigynia half as broad as long, plump, nerveless or obscurely short-nerved on the inner face (21) C.aenea. + + Perigynia one-third as broad as long. X Perigynia thin and scale-like, scarcely distended over the achenes, distinctly nerved on the inner face, and promi- nently exceeding the subtending scales. § Leaves at most 3 mm. wide : spikelets 3 to 9, glossy brown or straw-colored, pointed. Spike oblong-ovoid or subcylindric, with ascending approximate spikelets (2) n- long, 1.3 mm. broad,\erj narrowly winged above. — Dry fields, thickets, open woods, and gravelly banks. Maine, Orono, about 1870 (F. Lamson-Scribner), June 28, 1890, June 30, 1891, July 3, 1897 (M. L. Fernald). = = Perigynia 1.5 to to 2 mm. broad, ovate-lanceolate, 4.5 to 6.5 (average 5) mm. long. 7. C. PRATICOLA, Rydberg. — Figs. 17, 18. — Culms smooth and slender, 3 to 6 dm. high, overtopping the smoothish flat (2 to 3.5 mm. broad) leaves ; spike slender, Jlexuous, moniliform, the 3 to 7 silvery brown mostly remote pointed spikelets few-Jlowered, 7 to 1.7 mm. long, mostly long-clavate at base ; perigynia nerveless or minutely short-nerved on the inner face, equalling the ovate-lanceolate acutish or blunt scales. — Mem. N. Y. Bot. Gard. i. 84; Britten, Man. 226. (7. pratensis, Drejer, Rev. Crit. Car. Bor. 24; Fl. Dan. xiv. 8, t. 2368; Bailey, Proc. Am. Acad. xxii. 147 ; Britton, in Britt. & Brown, 1. c. 354, fig. 858 ; not Hose. C adusta, var. minor, Boott in Hook. Fl. Bor. -Am. ii. 215, & 111. iii. 119, t. 383. C. Liddoni, in part, of authors, not Boott. — Open woods, clearings, and prairies, Labrador to Saskatchewan and British Columbia, south to Nova Scotia, Aroostook County, Maine, Lake Superior, and North Dakota ; also in Greenland. June-Aug. 472 PROCEEDINGS OP THE AMERICAN ACADEMY. * * Mature perigynia distinctly more than one-third (.44 to .75) as broad as long. t- Perigynia one-fifth to one-third (.19 to .34) as thick as broad (rarely thicker in C. mirahilis). ++ Mature perigynia 3 to 4 mm. long (very rarely longer in C mirahilis and C. albolutescens). = Mature perigynia with roseate-spreading tips. 8. C. CRISTATA, Schweinitz. — Figs. 19 to 21. — Culms 1 m. or less high, harsh above : leaves soft and jlat^ S to 1 mm. broad., often equalling the culms, sheaths loose : spike usually dense, linear -cylindric or oblong, of 6 to 15 globose closely flowered greenish or dull-brown spikelets 0.5 to 1 cm. long. — Ann. Lye. N. Y. i. 66 ; Schwein. & Torr. Ann. Lye. N. Y. i. 315, t. 24, fig. 1 ; Dewey, 1. c. 44 ; Boott, 1. c. 117, in part ; Gray, Man. ed. 5, 579; Boeckeler, 1. c. 115; Howe, 1. c. 41. O. lagopodioides, var. cristata, Carey, 1. c. 545. G. straminea, var. cristata, Tuck. 1. c. 9, 18. C. tribuloides, var. cristata, Bailey, Proc. Am. Acad, xxii. 148, in Gray, Man. ed, 6, 620, & Mem. Torr. CI. i. 55 ; Macoun, 1. c. 130. C cristatella, Britton, 1. c. 357, fig. 865. — Swales and wet woods, western New England to Pennsylvania, "Virginia," Mis- souri, Saskatchewan, and British Columbia. June- Aug. = = Mature perigynia witli ascending tips. a. Plant stout and stiff: spikes stiff and upright ; the gray-green mostly approx- imate spilielets with appressed firm perigynia. 9. C. albolutescens, Schweinitz. — Figs. 22 to 24. — Culms 2 to 8 dm. high : leaves erect, long-pointed, pale green, 2 to 5 mm. wide, shorter than the culms : spike linear-cylindric to subglobose, with or without elongated bracts, of 3 to 30 (sometimes compound) conic-ovoid to subglobose spikelets 0.6 to 1 cm. long : perigynia 2 to 3 mm. broad, rhombic-ovate to suborbicular, lolth a short deltoid firm greenish tip. — Ann. Lye. N. Y. i. 66; Bailey, Bull. Torr. CI. xx. 422 (inch var. cumidata) ; Britton, 1. c. 359, fig. 873; Howe, 1. c. 43. C. foenea. Ell. Sk. ii. 533 ; Schwein. & Torr. 1. c. 315 ; Carey, 1. c. 546 ; Boott, 1. c. 118 (excl. vars.), t. 375; not Willd. C. straminea, \a,v. foenea, Torr. Ann. Lye. N. Y. iii. 395 ; Bailey, Proc. Am. Acad. xxii. 150, & in Gray, Man. ed. 6, 622 ; Macoun, 1. c. 132. C. straminea, var. intermedia. Gay, Ann. Sci. Nat. ser. 2, x. 364. C. leporlna, var. bracteata, Liebmann, Mex. Halv. 76. G. straminea, var. chlorostachys, Boeckeler, 1. c. 118. G. straminea, var. cumidata, Bailey, Mem. Torr. FERNALD. — CARICES OF SECTION HYPARBHENAE. 473 CI. i. 23, & in Gray, 1. c. — Damp or even very dry soil, principally on the coastal plain, New Brunswick to Florida, Texas, Mexico, and Central America; rarely inland to Bear Mt., Livermore, Maine (Kate Furbish) ; Mt. Monadnock, alt. 925 m., New Hampshire {R. M. Harper) ; Tagbkanick Range, Columbia Co., New York {L. H. Hoysradt) ; also from Lake Huron to Manitoba. July-Sept. b. Plant not very stiff : the bright green or brownish spikelets witli spreadhig or ascending (not appressed) perigynia. 1. Leaves 2.5 to C mm. wide : culms 0.3 to 1.5 m. high. 10. C. MiRABiLis, Dewey. — Figs. 25, 26, — Culms very loose and smooth; leaves soft and thin, the sheaths rather loose : spikelets 4 to 12, greenish, subglobose or ovoid, 5 to 9 mm. long, mostly approximate in an oblong spike ; pei-igynia with divergent tips. — Am. Jour. Sci. xxx. 63, t. Bb, fig, 92; Boott, 1. c. 117 (under C. cristata), t. 374; Howe, 1. c. 46. C. straminea^ var. mii'abilis, Tuck. 1. c. 9, 18; Bailey, Proc. Am. Acad. xxii. 150, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 358. G. festticacea^ var, mirabilis, Carey, 1. c. 545. C cristata, Kunze, Car. t. 44, figs. «, e, and y (colored), not Schwein. C. cristata, var. mirabilis, Gray, Man. ed. 5, 580. C. lagopodioides, \ ax. mirabilis, Olney, Exsicc. fasc. ii, no. 9. C. tribuloides, var. cristata., Macoun, 1. c. 130, in part, not Bailey. — Dry banks, open woods, or even moist copses, central Maine to Manitoba, south to North Carolina and Missouri. June, July. Var. perlonga- — Fig. 27. — Spikelets scattered in a moniliform spike. — New Hampshire, dry thicket, Barrett Mt., New Ipswich, June 5, 1896 (J/. L. Fernald): Vermont, Little Notch, July 9, 1901 {E. Brainerd) : Massachusetts, Stoneham, June 5, 1887 {F. S. Collins) ; Oak Island, Revere, July 5, 1891 (IF, P. Rich); Beaver Brook Reservation, July 6, 1894 (C. W. Swan) ; Sharon, June 17, 1896 (W. P. Rich) : Connecti- cut, dry open woods, Southington, June 17, 1900 (C. H. Bissell) : New York, Binghamton, June 29, 1871 (Wm. Boott); Sacondago River (J. V. Haberer) : Michigan, Grosse Isle, June 30, 1867 {Wm. Boott) ; open swales, Lansing, June 8, 1886 (Z. H. Bailey., no. 283, in part) : Illinois, Marion Co. (M. S. Behb). Var. tincta. Spike of 3 to 7 ovoid approximate brotcn-tinged spike- lets : scale hmcn with a pale margin. — New Brunsavick, banks of St. John River, July 4, 1899 {J. Macoun, Herb. Geol. Surv. Can. no. 22) : Maine, Fort Kent, June 16, 1898 (no, 2158), Masardis, June 6, 1898 (no, 2159), Ashland, June 13, 1898 (no. 2160), Fort Fairfield, 474 PROCEEDINGS OF THE AMERICAN ACADEMY. July 12, 1893 (no. 165), Foscroft, June 25, 1894, Dover, June 28, 1894, Orono, July 6, 1891, — all coll. AT. L. Fernald ; Sangerville, July 17, 1896 {G. B. Fernald, no. 176): New Hampshire, between Marshfield and Fabyans, July 6, 1878, Bethlehem, June 20, 1887 {E. ^ C. E. Faxon); Wbitefield, July 3, 1896 {W. Deane) : Vermont, St. Johnsbury, June 21, 1901 {T. E. Hazen, no. 206). Resembling north- western forms of the polymorjihousyes^iVa group, but not satisfactorily referable to any of them. 2. Leaves 0.5 to 2 mm. wide : culms 3 to 7 dm. high : spikelets remote or at least distinct in a monihform or linear-cylindric spike. 11. C. STRAMINEA, Willd. — Figs. 28, 29. — Culms very slender, smooth except at summit : spikelets 3 to 8, yellow-brown, or rarely green, ovoid or subglobose, 4 to 8 mm. long, usually forming jlexuous spikes : perigynia with ascending inconspicuous tips ; the inner faces 3- to 5-nervcd or nerveless. — Willd. in Schkuhr, Riedgr. 49, t. G, fig. 34; Bailey, Mem. Torr. CI. i. 21, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. fig. 868 ; Howe, 1. c. 44. C. straminea., var. minor, Dewey, Am. Jour. Sci. xi. 318, t. N, fig. 45 ; Torr. 1. c. 395. C. festucacea, var. tenera, Carey, 1. c. 545. G. straminea, var. tenera, Boott, 1. c. 120, t. 384 (except perigynia from Olney) ; Gray, Man. ed. 5, 580 ; Macoun, 1. c. 132. — Meadows, or occasionally on dry banks or in open woods. New England to BritIsh Columbia, Kentucky and Arkansas. June- Aug. Var. eohinodes. — Fig. 30. — Tips of the slightly longer perigynia divergent and conspicuous. — Ontario, Wyoming, June 24, 1901 {J. Macoun, Herb. Geol. Surv. Can., no. 26,624) : Michigan, Detroit, July 20, 1867 {H. P. Sartwell), June 26, 1870, and June 22, 1873 {Wm. Boott): Iowa, Ames, 1872, Spirit Lake, June 21, 1881 (/. C. Arthur). Superficially resembling C. t7'ibuloides, var. reducta. ++ ++ Mature perigynia more than 4 mm. long (very rarely shorter in exceptional individuals of C. tenera, var. invisa, and C. festucacea, var. brevior). = Perigynia elongate-ovate, about half as broad as long (suborbicular in var. RicMi). 12. C. tenera, Dewey. — Figs. 31, 32. — Culms slender and flexuous, sharply angled, smooth except at summit, 3 to 9 dm. high: leaves shorter than or rarely exceeding the culms, very ascending, 1 to 2.5 mm. broad: spike slender, moniliform (or on late culms more or less con- gested), of 3 to 9 broadly ovoid brownish spikelets 8 to 12 mm. long, with FERNALD. — CARICES OP SECTION HYPARRHENAE. 475 or without subtendinf; elongated bracts : perigynia ascending or rarely spreading, distinctly aboitt 10-nerved on either face, 4-S to G (cwei'age 5.2) mm. long ; scales lauce-attenuate or aristate. — Am. Jour. Sci. viii. 97, & ix. t. C, fig. 9 ; Britton, 1. c. fig. 870. C. straminea, var. aperta, Boott, 1. c. 120, t. 385 ; Gray, Man. ed. 5, 580 ; Bailey, Proc. Am. Acad. xxii. 152, & in Gray, Man. ed. 6, 622; Macoun, 1. c. 133; Howe, 1. c. 45. C. tenera, var. major, Olney, 1. c. no. 15. G. straminea, var. tenera, Bailey, Bot. Gaz. x. 381, & Mem. Torr. CI. v. 94. — Brackish or fresh marshes, mostly near the coast, Gulf of St. Lawrence to Delaavare and Iowa ; also in British Columbia, Yellow Head Pass (Spi-eadboroiigh, Herb. Geol. Surv. Can. no. 20,871). June- Aug. Var. INVISA, Britton. — Figs. 35, 36. — Lower; with spiJcelets 5 to 8 mm. long, and perigynia 4 to 5 (average 4.5) mm. long. — Britton, 1. c. 358. C. straminea, var. invisa, W. Boott, Bot. Gaz. ix. 86 ; Bailey, Proc. Am. Acad. xxii. 152, & in Gray, JNEan. ed. 6, 622 ; Howe, 1. c. — Range of the species and too often intergradiug with it ; mostly in dry soil or even in pure sand. Var. Richii. — Figs. 33, 34. — Perigynia 4 to 5 mm. long, with suborbicular bodies abruptly contracted to slender conspicuous loosely ascending or spreading beaks. — Massachusetts, Reading, June 14, 1883 {G. E. Perkins) ; Fresh Pond, Cambridge, June 8, 1887 ( TF. Deane) ; near Spot Pond, and north end of Doleful Pond, Stoneham, May 30, 1894, near Bear Hill, Stoneham, June 5, 1894 ( Wm. P. Rich) ; Amherst (^. Tuckerman): Connecticut, Newington, May, 1879 {Ghas. Wright). In its elongate loose brown spikes and subulate- or awn- tipped narrow scales clearly an extreme form of G. tenera, although the perigynia when well developed suggest those of G. festucacea. = = Perigynia with broadly ovate to suborbicular bodies, more than half as broad as long. a. Perigynia 5.7 to 7.7 mm. long. 13. C. BiCKNELLii, Britton. — Figs. 37 to 40. — Culms comparatively stout, 4 to 9 dm. high, smooth except at summit : leaves ascending, rather short and firm, 2 to 4.5 mm. broad : spike of 3 to 7 silvery brown or greenish ovoid obovoid or subglobose approximate or slightly remote spikelets 8 to 14 mm. long: perigynia ascending, the tips becomitig con- spicuous, broadly wing-margined, when mature almost translucent and with about 10 nerves on either face. — Britton, 1. c. 360, fig. 874. G. stra- minea, var. Grawei, Boott, 1. c. 121, t. 388 ; Bailey, Bull. Torr. CI. xx. 422 ; Howe, 1. c. G. straminea, var. Meadei, Boott, 1. c. t. 389 ; Gray, 476 PROCEEDINGS OF THE AMERICAN ACADEMY. Man. ed. 5, 581. G. straminea, var. hrevior, Bailey, Mem. Torr. CI. i. 22, in part, not Dewey. — Dry or rocky soil, eastern Massachusetts to Manitoba, New Jersey, Ohio, and Arkansas. May-July. b. Perigj'nia at most 5.5 mm. long. 1. Spikelets whitish or silvery-brown, mostly scattered in a flexuous moniliform spike. 14, C. siLiCEA, Olney. — Figs. 41, 42. — Oalms slender, stiff", smooth except at summit, 3 to 8 dm. high : leaves erectish, shorter than or equalling the culms, usualli/ glaucous, 2 to 4.5 mm. wide, often be- coming involute : spike of 3 to 12 usually remote conic-ovoid usually clavate spikelets 1 to 1.5 cm. long: perigynia strongly oppressed, firm and opaque, 4 to 5 mm. long, 2.2 to 3 mm. broad, short-beaked, broad- winged, the body distinctly 3- to 5-nerved on the inner, 6- to 12-nerved on the outer face. — Proc. Am. Acad. vii. 393 ; Bailey, Mem. Torr. CI. i. 24, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 358, i]g. 869 ; Howe, 1. c. 44. G. straminea, var. moniliformis. Tuck. 1. c. 9, 17 ; Bailey, Proc. Am. Acad. xxii. 151 ; Macoun, 1. c. 133. G. adusta, Carey in Gray, Man. ed. 2, 516, not Boott. G. foenea, var. y, Boott, 1. c. 118, t. 377. G. foenea, var. (?) subulonum, Gray, Man. ed. 5, 580. G. straminea, var. silicea, Bailey, Carex Cat. 4. — Sand and rocks near the sea, Prince Edward Island to New Jersey. June-Aus. *o- 2. Spikelets green or brownish, approximate or only slightly remote in a mostly upright spike ( C. tenera, var. Richii, with moniliform flexuous spikes might be looked for here). O Sheath of tlie leaf green and strongly nerved nearly or quite to the narrow subchartaceous auricle : perigynia appressed-ascending : achenes mostly oblong. 15. C. ALATAj Torr. — Figs. 43, 44. — Culms rather stout, smooth except at summit, 0.5 to 1 m. high : leaves mostly short and harsh, 2.5 to 4.5 mm. wide: spike oblong or ovoid, of 3 to 8 compact green or finally dull-brown conic-ovoid to oblong spikelets 8 to 15 mm. long : perigynia firm and opaque, orbicular or obovate, 4.3 to 5.5 mm. long, 2.8 to 3.7 mm. broad, broad-winged, very faintly nerved 'or nerveless, much broader than the lance-subulate usually rough-awned scales. — Ann. Lye. N. Y. iii. 396 ; Boott, 1. c. 118, t. 378 ; Gray, Man. ed. 5, 581 ; Britton, 1. c. 359, fig. 872 ; Howe, 1. c. 45. G. straminea, var. alata, Bailey, Carex Cat. 4, Proc. Am. Acad. xxii. 150 & in Gray, Man. ed. 6, 622. — Marshes and wet woods. New Hampshire to Michigan and Florida, mostly near the coast. June, July. FERNALD. — CARICES OF SECTION HYPARRHENAE. 477 Var. ferruginea. — Figs. 45, 46. — Slender : the 3 to 5 irregularly clustered spikdets tawny or ferrugineous from the first : perigynia oimte, 4 to 5 mm. long, 2.3 to 2.8 mm. broad : scales lance-ovate, mostly awnless, — G. foenea, var. y8, Boott, 1. c. 118, t. 376. C. foenea, YSiY.'i ferruginea, Gray, Man. ed. 5, 580. G. tenera, var. suberecta, Olney, Exsicc. fasc. ii. no. 16. C. straminea, vzx. ferruginea, Bailey, Bull. Torr. CI. xx. 421. — Ohio to Michigan, Illinois, and Iowa. 0 O Sheath with a thin barely nerved or nerveless pale band extending down from the membranaceous auricle : perigynia spreading-ascending : achenea suborbicular. 16. C. festucacea, Schkuhr. — Figs. 47, 48. — Gidms stiff, 0.5 to 1 in. high : leaves stiff., erect, shorter than the culms, 2 to 4 mm. wide : spike narrowly oblong, rarely ovoid, of 5 to 10 distinct or rarely approx- imate subglohose or broadly ovoid-conic yellow-brown or green-brown as- cending spikelets 7 to 12 mm. long : perigynia broad-ovate to suborbicular, 4 to 5.5 mm. long, 2.7 to 3.5 mm. broad, strongly 7- to 15-nerved on the outer, nerveless or faintly nerved on the inner face : scales blunt. — Schkuhr in Willd. Sp. iv. 242, & Riedgr. Nachtr. 23, t. Www. fig. 173 ; Dewey, Am. Jour. Sci. viii. 96 ; Schwein. & Torr. 1. c. 316 ; Torr. 1. c. 394; Carey, 1. c. 545; Britton, 1. c. 359, in part. C. straminea, var. festucacea, Tuck. 1. c. 9, 18 ; Boott, 1. c. 120, t. 386 ; Macoun, 1. c. 132; Bailey, Mem. Torr. CI. v. 94, in part ; Howe, 1. c. G. straminea, Bailey, Proc. Am. Acad. xxii. 149, in part, not Willd. G. straminea, var. brevior, Bailey, Mem. Torr. CI. i. 22, in part, not Dewey. — Dry or rocky soil, Maine to Manitoba and Pennsylvania. June-Aug. Var. brevior. — Figs. 49 to 51. — Lower (rarely more than 0.6 m. high), and more slender .- spikelets 3 to 6, approximate or subapproxi- mate. — G. straminea, Schkuhr, Riedg. Nachtr. 23, t. Xxx, fig. 174; Schwein. & Torr. 1. c. 314 ; Carey, 1. c. 546 ; Torr. 1. c. 395 ; Boott, 1. c. 121, t. 387 ; Bailey, Proc. Am. Acad, xxii, 149, in part ; not Willd. in Schkuhr, Riedgr. 49, t. G. fig. 34, & in herb. G. straminea, var. brevior, Dewey, Am. Jour. Sci. xi. 158 ; Bailey, Mem. Torr. CI. i. 22, in part, & in Gray, Man. ed. 6, 622 ; Howe, 1. c. G. straminea, var. Schkuhrii, Gay, Ann. Sci. Nat. ser. 2, x. 363 ; Tuck. 1. c. 8, 17. G. straminea, var. typica, Gray, Man. ed. 5, 580; Macoun, 1. c. 131. G. festucacea, Britton, 1. c. 359, in part (including fig. 871), not Schkuhr. — Commoner than the species, extending to British Columbia, Arkan- sas, &c. May-July. 478 PROCEEDINGS OF THE AMERICAN ACADEMY. •t- -t- Perigynia two-fifths to one-half (.40 to .50) as thick as broad. ++ Tips of the perigynia distinctly exceeding the scales : spilces short, compact, ovoid or short-oblong, brown : perigynia 3 to 3.5 mm. long. 17. C. Bebbii, Olney. — Figs. 52, 53. — Culms rather slender, 2 to 6 dm. high, smooth except at tip : leaves mostly shorter, ascending hit not stiffs 1.75 to 4.5 mm. wide : spikes 1 to 2 cm. long, of 3 to 12 globose or ovoid-oblong ascending spikelets 5 to 8 mm. long : 2)erigynia narrowly ovate, inostly dull brown and loosely ascending, faintly few-nerved or nerveless, 1.5 to 2 mm. broad: scale oblong, bluntly acuminate. — Exsicc. fasc. ii, no. 12, as nomen nudum. C tribuloides, var. Bebbii, Bailey, Mem. Torr. CI. i, 55 & in Gray, Man. ed. 6, 620 ; Britton, 1. c. 356; Howe, 1. c. 42; Cratty, Bull. Lab. Nat. Hist. Univ. la., iv. 359, t. 8. — Low ground, Newfoundland to western Massachu- setts, central New York, Illinois, the Rocky Mts., British Columbia, and northward. June-Aug. ++ t-c Tips of the perigynia nearly or quite equalled by the scales : perigynia more than 3.5 mm. long (sometimes shorter in the slender-spiked silvery green C. foenea). = Perigynia With strong nerves the entire length of the inner face (very rarely nerveless). a Spike loose and elongated, green or silvery-brown. 18. C. FOENEA, Willd. — Figs. 54, 55. — Culms slender and lax, smooth except at tip, 3 to 9 dm. high : leaves soft and loose, pale green or glaucous, mostly shorter, 2 to 4 mm. broad : spike linear-cylindric or moniliform, erect or flexuous, of ^ to 9 globose or ovoid clavate-narrowed appressed-ascending spikelets 6 to 10 mm. long : perigynia ovate, 3 to 4- mm. long, 1.8 to 2.2 mm. broad, appressed-ascending, finally a little spreading. — Enum. 957 ; Bailey, Mem. Torr. CI. i. 25, & in Gray, Man. ed. 6, 621 ; Macoun, 1. c. 377 ; Britton 1. c. 357, fig. 867 ; HoM^e, 1. c. 43. G. argyrantha. Tuck, in Herb, distr. (1859). C. adusta, Boott, 1. c. 119, in part, t. 382, fig. 2, not Boott in Hook. Fl. Bor.-Am. ii. 215. C. albolutescens, var. argyrantha, Olney, Exsicc. fasc. i. no. 9. C. adusta, var. argyrantha, Bailey, Carex Cat. 2. — Dry woods and rocky banks, Maine to British Columbia and Maryland. July. Var. perplexa, Bailey. — Figs. 56, 57. — Coarser, and often taller: spikes heavier, mostly nodding, the 6 to 15 spikelets larger, 1 to 1.7 cm. long, the terminal ones often crowded : perigynia 3.5 to Jf.Jf mm. long. — Mem. Torr. CI. i. 27, in part, & in Gray, Man. Ed. 6, 621 ; Britton, FERNALD. — CARICES OP SECTION HYPARRHENAE. 479 1. c. ; Howe, 1. c. 44. C. adiista, Boott, 111. iii. 119, in part, t. 381, 382, fig. 1 ; Gray, Man. ed. 5, 580; Macouu, 1. c. 129, in part (excl. syn.) — Commoner than the species. Newfoundland to Manitoba and Virginia. June- Aug. b. Spike with approximate or subapproximate brown or ferrugineous spikelets. 19. C. leporina, L. — Figs. 58 to 60. — Culms stiff and ascending, 2 to 8 dm. high : leaves mostly short and rather firm, 1.5 to 4 min. broad : spike from subglobose to cylindric, of 3 to 6 obovoid to oblong- ovoid ascending spikelets 8 to 1.4 mm. long: perigynia 3.8 to 4.5 mm. long, 1.8 to 2.3 mm. broad, ascending. — Sp. 973, & Fl. Suec. ed. 2, 326 (excl. cit. Fl. Lapp.); Wahl. Fl. Lapp. 228; Reich. Ic. FI. Germ. viii. t. 211 ; Anders. Cyp. Scaud. 63, t. 4, fig. 26; Boott, 1. c. iv. 190; Bailey, Proc. Am. Acad. xxii. 152, & in Gray, Man. ed. 6, 622; Britton, 1. c. 356, fig. 864; Meinsh. Acta Hort. Petrop. xviii. 324. G. oralis, Good. Trans. Linn. Soc. ii. 148; Eng. Bot. t. 306; Vahl. Fl. Dan. vii. t. 1115; Host, Gram. i. 39, t. 51; Willd. 1. c. 955 j Schkuhr, 1. c. 20, t. B, fig. 8. — Europe and Asia : Newfoundland, shores of Quiddy Viddy Lake, Aug. 2, 1894 {Robinson ^ Schrenh) : Nova Scotia, Yarmouth, July 22, 1896 {E. Brainerd) : Maine, low, rocky pasture, South Berwick, June 23, 1898 (/. C. Parlin, no. 959); hillside pastures. East Parsonsfield, July 4, 1900 (J. F. Collins ^ M. L. Fernald) : New Hampshire, dry hillsides, Alstead, July 9, 1901 {31. L. Fernald) ; Gap Mt., Troy, June 13, 1898 {E. L. Rand Sf B. L. Robinson, no. 508) : Massachusetts, Essex Co., Aug. 23, 1881 ( W. P. Conant); Long Island, Boston Harbor, July 6, 1871, July 1, 1873 {Wm. Boott); Nobscot Hill, Framingham, June 14, 1901 {M. L. Fernald) ; Purgatory Swamp, Dedham, June 23, 1878 {E. ^ C. E. Faxon) : New York, slopes of Bald Mt., north of Fulton Chain, Herkimer & Hamilton Cos., Aug. 12, 1895 (/. V. Baberer, no. 1103) New Jersey, ballast ground, Camden, 1878 {Isaac Burk). Doubtless introduced at the latter station, but perhaps indigenous northward. = = Inner face of perigynia nerveless or only slightly nerved at base (excep- tional individuals of C. leporina might be sought here). a. Ellipsoidal spikelets brownish-white : the appressed perigynia golden-yellow at base. 2f ?0. C. xerantica, Bailey. — Figs. 61, 62. — Culms stiff", scabrous above, 3 to 6 dm. high : leaves short, mostly near the base, 2 or 3 mm. broad : spike linear-cylindric^ of 3 to 6 distinct ascending spikelets 8 to 480 PROCEEDINGS OP THE AMERICAN ACADEMY. 13 mm. long: perigynia 4 to 4.8 mm. long, 2 to 2.3 mm. broad. — Bot. Gaz. xvii. 151; Britton, 1. c. 355, fig. 859. — Open prairies, western Manitoba and adjacent Assiniboia. July. b. Obovoid spikelets brownish or ferrugineous : the loosely ascending perigynia dark green or brown when mature, 1. Spike loose and fiexuous ; spikelets mostly long-clavate at base, the lowest remote : acliene 1.5 (1.3 to 1.7) mm. broad. 21. C. aenea. — Figs. 63 to 66. — Culms smooth and wiry, but more or less Jlexuous at tip, 0.25 to 1.2 m. high : leaves much shorter, rather soft and flat, 2 to 4 mm. broad : spike loosely cylindric or ynoniliform, of 3 to 12 spikelets 0.8 to 2.5 cm. long (in luxuriant plants often peduncled or compound): perigynium 4 to 5 mm. long, 1.9 to 2.7 mm. broad. — C. adusta, Boott, 1. c. iii. 119, in part, t. 380, not Boott in Hook. Fl. Bor.-Ara. ii. 215. C albolutescens, var. sparsijlora, OIney, fasc. V. no. 11, in part (as nomen nudum), not C. sparsijlora Fries. G. adusta, var. sparsijlora, Bailey, Carex Cat. 2 (as nomen nudum) ? 0. foenea, var. perplexa, Bailey, Mem. Torr. CI. i. 27, as to syn. , in part. 0. Joenea, var. sparsijlora, Howe, 1. c. 44. — Open woods, dry banks, or rarely in low ground. Labrador, without station, Aug. 23, 1896 (Spreadborough, Herb. Geol. Surv. Can. no. 13,354) : Ungava, East Main E., 1892 {A. H. D. Ross, Herb. Geol. Surv. Can. no. 30,582) : Newfoundland, Grand Lake, Bay of Islands, Aug. 6, 1897 {A. C. Waghorne): Quebec, Riviere du Loup, July 23, 1861 (Wm. Boott), Aug. 2, 1896 (in. Brainerd): Calumet, June, 1891 {J. M. Macoun, Hb. Geol. Surv. Can. no. 16,535) : New Brunswick, Kent Co. (J. Fowler, in Olney, Exsicc. fasc. v. no. 11, in part): Maine, Fort Fairfield, 1881 {Kate Furbish)-, Milford, June 30, 1864 (/. Blake); Orono, July 7, 1892, July 3, 1897, June 8, 1901 {M. L. Fernald) ; Mt. Desert Island, numerous stations (Rand, Faxon, Williams et al.) : New Hampshire, Franconia, June 23, 1888 (F. S; G. F. Faxon) ; Crawford Notch, July 16, 1895 (G. G. Kennedy): Vermont, East Mt., Middlebury, June 23, 1882, Moosalamoo Mt., Salisbury, July 5, 1901 (E. Brainerd) ; MASSACHUSfeTTS, Mt. Wachusett, June 27, 1878 (Win. Boott) : New York, base of Stony Creek Mt., June 29, 1899 (Rowlee, Wiegand Sf Hasti?igs) : Ontario, near Michipicoten, July 26, 1869, Cache Lake, July 12, 14, 1900 (/. Macoun); Lake Victoria, Sept. 12, 1901 (F. Brainerd) : Michigan, Isle Royale (JI. Gillman) : Athabasca, Methy Portage (Sir John Richardson, fide Boott, 111. t. 380) : Alberta, Banff, Rocky Mts., July 10, 1891 (/. Macoun, Herb. FERNALD. — CARICES OF SECTION HYPARRHENAE. 481 Geol. Surv. Can. no. 16, 536) : British Columbia, Beaver Creek, Selkirk Mts., July 13, 1885 (no. 10,797) ; Kicking Horse Lake, Aug. 11, 1890 (no. 30,603); Revelstoke, May 19, 1890 (no. 30,604) — ^. Macoim, Herb. Geol. Surv. Can. 2. Spike dense and stiff, erect ; spikelets full and rounded at base, mostly approximate : achene 2 (1.8 to 2 1) mm. broad. 22. C. ADUSTA, Boott. — Figs. 67 to 69. — Culms smooth, stiffli/ erect, 2 to 8 dm. high : leaves usually shorter, 2 to 5 mm. broad : spike ovoid to cylindric^ usually subtended by a stiff rather prominent bract, of 3 to 15 simple or compound spikelets 6 to 12 mm. long : perigynia 4 to 5 mm. long, 2 to 3 mm. broad. — Boott in Hook. Fl. Bor.-Am. ii. 215, 6 111. iii. 119, in part, t. 379 ; Bailey Mem. Torr. CI. i. 24, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 357, fig. 866. C. albolutescens, var. glomerata, Olney, Exsicc. fasc. v. no. 10. 0. adusta^ var. glomerata, Bailey, Carex Cat. 2, Bot. Gaz. ix. 139, & Proc. Am. Acad. xxii. 149. C. pinguis, Bailey, Bull. iii. Geol. and Nat. Hist. Surv. Minn. 22 ; Macoun, 1. c. 129. — Dry woods, rocky banks and recent clearings, Newfoundland to Mount Desert Island, Maine, west to Minnesota, AssiNiBOiA, Saskatchewan, and Keewatin. June-Sept. §§ Cyperoideae. Bracts leaf-like and much prolonged, forming a conspicuous involucre. 23. C. stchnocephala, Carey. — Figs. 70, 71. — Culms smooth, 2 to 6 dm. high : leaves soft, ascending, 2 to 4 mm. wide ; bracts unequal^ the lowest longest.^ 1 to 2 dm. long : spikelets 4 to 10, oblong, 8 to 15 mm. long) forming a dense ovoid or oblong spike : perigynia lance-suhdate, 5 mm. long, barely 1 mm. wide, firm, slightly nerved or nerveless. — Am. Jour. Sci. Ser. 2, iv. 24, & in Gray, Man. 545 ; Boott, 111. i. 46, t. 118 ; Bailey, Proc. Am. Acad. xxii. 153; Macoun, 1. c. 121 ; Britton, 1. c. 360, fig. 875 ; Howe, 1. c. 46 ; Cratty, Bull. Lab. Nat. Hist. Univ. la., iv. 363, t. 9. C. cyperoides, Dewey, Am. Jour. Sci. Ser. 2, iii. 171, not L. — Meadows, ditches, and wet sandy soil, locally from central New York to the Ottawa River (Canada), Iowa, Saskatch- ewan, and British Columbia. July, Aug. Astrostachyae, Holm. Monoecious or dioecious, the spikelets often purely staminate or purely pistillate, or with the flowers variously mixed. Bract not sheathing, if present short and filiform. Perigynia horizontally spreading or reflexed at maturity, spongy at base., glabrous, nervose, distinctly pointed or beaked, with thin margins and bidentate apex. VOL. XXXVII. — 31 482 PEOCEEDINGS OF THE AMERICAN ACADEMY. * Spikelets terminal and solitary (rarely one or two secondary ones below) : plants usually dioecious. -1- Culms filiform or setaceous, solitary or few from filiform creeping stoloniferous rootstocks. 24. C. GTNOCRATES, Wormskiold. — Figs. 72 to 77, — Culms 0.6 to 3 dm. high, mostly exceeding the setaceous leaves: spikelets 0.5 to 2 cm. long, some staminate and linear or linear-lanceolate, with oblong mostly blunt-poiuted scales ; others staminate above, with 1 or more pistillate flowers below; others oblong, strictly pistillate, with 6 to 12 rather plump subterete, but thin-edged strongly nerved conic-beaked periyynia. — Wormsk. in Drejer, Rev. 16; Fries, Mant. iii, 134, & Sum. 222 Anders. Cyp. Scand. 71, t. 3, fig. 8; Kunze, Car. 123, t. 31, fig. 1 Carey, in Gray, Man. ed. 2, 509 ; Boott, 111. iv. 143, t. 459, 460 Bailey, Proc. Am. Acad. xxii. 142, & in Gray, Man. ed. 6, 617 Macoun, 1. c. 109; liowe, 1. c. 49 (incl. var. monosperma, Peck) Holm, 1. c. 209. C. Redowskiana, Bailey, Mem. Torr. CI. v. 89 Britton, 1. c. 340, fig. 815 ; not C. A. Meyer, according to Meinshausen Acta Hort. Petrop. xviii. 305. C. dioica, Schwein. & Torr. 1. c. 293 Dewey, 1. c. Ser. 1, x. 283; Carey, in Gray, Man. 537; not L G. monosperma^ Macoun, in Bailey, Carex Cat. 3, nomen nudum 0. alascatia, Boeckeler, Engler's Bot. Jahrb. vii. 277, ace. to Bailey — Swamps and bogs, Labrador to Alaska, south mostly in Thuya swamps to Restigouche Co., New Brunswick ; Aroostook and Piscataquis Cos., |klAiNE ; Herkimer, Yates and Genessee Cos., New York ; Alleghany Co., Pennsylvania ; and Alcona and Oscoda Cos., Michigan ; in the Rocky Mts. to Colorado : also in northern Europe and Asia. June, July. t- ■*- Culms stouter, rigid, forming strongly caespitose stools without stolons. 25. C. ExiLis, Dewey. — Figs. 78 to 83. — Cidms wiry, 2 to 7 dm. high, usually much exceeding the j?/(/b7-/« stiff leaves : spikelets mostly solitary, 1 to 3 cm. long, staminate, or pistillate, or with the flowers variously situated : perigynia ovate-lanceolate, with serrulate thin mar- gins^ strongly convex on the outer, Jiattish and few-nerved or nerveless on the inner face. — Am. Jour. Sci. xiv. 351, t. Q, fig. 53 ; Carey, 1. c. 538; Boott, 111. i. 17, t. 47; Bailey, Proc. Am. Acad. xxii. 142, & in Gray, Man. ed. 6, 617 ; Macoun, 1. c. Ill ; Britton, 1. c, 340, fig. 816 ; Howe, 1. c. 38 ; Holm, 1. c. 207. C. exilis, var. squamacea, Dewey, 1. c. fig. 54. C exilis, var. androgyna, Dewey, in Wood, Class-book, ed. FERNALD. — CARICES OF SECTION HYPARRHENAE. 483 1861, 750, —Bogs and meadows near the coast, or on the coastal plain, locally from Labrador and Newfoundland, to New Jersey : also summit of Smoky Mt., Cape Breton, Nova Scotia; Crystal, Maine ; Bristol and Peacbam, Vermont ; Essex and Onondaga Cos., New York ; Mer Bleue, Ontario ; Calumet, Michigan ; and reported from Hennepin and Crow Wing Cos., Minnesota. May-Aug. * * Spikelets 2 to several, the starainate flowers mostly at their bases ; plants very rarely dioecious. •♦- Perigynia broadest at the rounded or subcordate base ; the beak rough or serrulate. ♦* Perigynia .40 to .50 as broad as long, tlie slender beak conspicuous, often nearly as long as the body : scales pointed. 26. C. echinata, Murray. — Figs. 84 to 88. — Culms rather wiry^ 1 to 4 dm. high : leaves shorter than or equalling the culms, 1 to 2.5 mm. wide: spike linear-cylindric, 1 to 3 cm. long, of 2 to 6 subapproximate or slightly remote subglobose or oblong 3- to 12- flowered spikelets : ■perigynia finally yellowish, narroioly ovate, early ascending, later wide- spreading, faintly nerved or nerveless on the inner face, 3 to 4 mm. long, one-third or one-half exceeding the ovate pointed brownish scale. — Prodr. 76; Boeckeler, Linnaea, xxxix. 124; Bailey, Proc. Am. Acad. xxii. 142 ; Mem. Torr. CI. i. 57, & Bull. Torr. CI. xx. 424 ; Macoun, 1. c. 126; Richter, PL Eur. i. 150; Holm, 1. c. 212. C. muricata, Huds. Fl. Ang. 406 (1778) : Leers, Fl. Herb. 200, t. 14. fig. 8 ; not L. C. Leersii, Willd. Prodr. 28. C. stellulata, Gooden. Trans. Linn. Soc. ii. 144; Schkuhr, Riedgr. 45, t. C, fig. 14; Host, Gram. i. 41, t. 53; Schwein. & Torr. 1. c. 317 ; Reich. Ic. Fl. Germ, viii. 9, t. 214, fig. 560; Carey in Gray, Man 544; Boott, 111. i. 55. Vignea stellulata, Reich. Fl. Exc. 57. C. sterilis, Gray, Man. ed. 5, 578; Bailey, Bull. Torr. CI. xx. 424-, Britton, 1. c. 350, fig. 844: Howe, 1. c. 38 ; not Willd. — Open low ground, Labrador and Ungava to Alaska, south to Garrett Co., Maryland, Ohio, Michi- gan, Saskatchewan, and Humboldt Co., California: also in Europe and Asia. June-Aug. Extremely variable, passing by num- erous transitions to the following more marked extremes. Var. ormantha. — Fig. 89. — Spikes 2 to 6 cm. long, of 2 to 4- very remote 3- to 9-flowered spikelets, the terminal one with a clavate base 0.5 to 1 cm. long : perigynia as in the species, spreading or slightly ascending, mostly twice as long as the scales. — C. echinata, W. Boott, in Wats. Bot. Cal. ii. 237, in part. — Riiodk Island, Providence, 1846 484 PROCEEDINGS OP THE AMERICAN ACADEMY. (^Geo.Tlmrher)\ Connecticut, without locality {Ghas. Wright)] South- ingtou, June o, 1898 {G. H. BisseJl) ; Waterford, May 29, 1889 {G. B. Graves): Oregon, without locality, 1871 (E. Hall, no, 582) : Cali- fornia, bogs along Strawberry Creek, El Dorado Co., alt. 1,815 m., July 18, 1897 (K Brainerd, no. 160 [type]) ; Big Trees, Calaveras Co. (Bolander, no. 2324) ; Santa Eosa (J. M. Bigelow) ; Bluff Lake, San Bernardino Mts., alt. 2,280 m., June, 1895 {S. B. Parish, no. 3702). Var. excelsior. — Fig. 90, 91. — Tall and slender, 0.3 to 1 m. high: spike 3 to b.b cm. long; spikelets 3 to 9, distinct, only the lower- most remote, 12- to 20-Jlowered, at first oblong-cylindric, with the perigynia ascending, later subglobose, with strongly reflexed perigynia one-third longer than the scales. — G. sterilis j3, Boott, 111. i. 56, t. 146.* G. sterilis, var. excelsior, Bailey, Bull. Torr. CI. xx. 424; Howe, 1. c. — Newfoundland to Michigan and North Carolina. Var. cephalantha, Bailey. — Figs. 92 to 94. — The coarsest, form, 3 to 7 dm. high: leaves £ to 4 f^^^' broad: spike cylindric or slightly raoniliform, 3 to 7.o cm. long : the 4 to 8 broad-oblong spikelets approxi- mate or slightly remote (rarely 1 cm. apart), 15- to Jfi-jioicered : perigynia ovate, one-half as broad as long, wide-spreading or reflexed. — Mem. Torr. Cl. i. 58, & in Gray, Man. ed. 6, 618. 0. sterilis, Boott, 111. i. 55, t. 146. G. sterilis, var. cephalantha, Bailey, Bull. Torr. Cl. XX. 425 ; Britton, 1. c. ; Howe, 1. c. 39. G. sterilis, var. aequidistans. Peck in Howe, 1. c. — Newfoundland to North Carolina, Michi- gan, and British Columbia. Var. ANGUSTATA, Bailey. — Figs. 95 to 97. — Extremely slender or almost setaceous, 1 or 2 dm. high (in shade often taller) : leaves 0.5 to 1.5 mm. wide: spike 0.75 to 2.5 cm. long ; the 6 or fewer 3- to 15-fiow- ered spikelets approximate (or slightly remote in shade) : the divaricate perigynia lance-ovate or lanceolate, 2.5 to 3 mm. long, twice exceed- ing the scales. — Mem. Torr. Cl. i. 59, & in Gray, Man. ed. 6, 618. C. stellulata, var. angustata, Carey in Gray, Man. 544. G. sterilis, var. angustata, Bailey, Bull. Torr. Cl. xx. 425 ; Howe, 1. c. — Nova Scotia to Connecticut, Lake St. John, Quebec, Illinois, and Michigan. •M. ++ Perigynia about .70 as broad as long, the beak short, one-fourth to one-half as long as the body. = Tall : leaves 2.5 to 4.5 mm. broad : perigynia 2 to 3 mm. broad : scales sharp-pointed. 27. C. sterilis, Willd. — Figs. 98 to 100. — Goarse, 1 m. or less high •. leaves flat, shorter than or equalling the culms: spike 1.5 to 3.5 FERNALD. — CARICES OP SECTION HYPARRHENAE. 485 cm. long ; the 3 to 6 subglobose or ohlong-cylindric densely 15- to 50- Jlowered olive-green spikelets crowded or distinct : the thick strongly many- nerved perigynia broad-ovate, 3 to 3.5 mm. long, squarrose or with recurved tips. — Sp. iv. 208 ; Schkuhr, Riedgr. Nacht. 3, t. Mmm, fig. 146. C, stellulata, var. sterilis, Carey in Gray, Man. 544. O. stellulata, var. conferta. Chapman, Fl. 534. C. echinata, var. co7iferta, Bailey, Carex Cat. 2, Proc. Am. Acad. xxii. 143, Mem. Torr. CI. i. 58, & in Gray, Man. ed. 6, 618 ; Macoun, 1. c. 126. C. atlaiitica, Bailey, Bull. Torr. CI. XX. 425; Britton, 1. c. 350. — Bogs and damp pine-barrens, near the coast from Newfoundland to Florida, rarely inland on cold bogs, at Lake St. John, Quebec (G. G. Kennedy) ; Squapan, Aroostook Co., and northern flank (near Bell Camp) of Mt. Katahdin, Maine (Fernald) ; Adirondack Mts., Essex Co., New Yokk (Knies- kern) ; and Mt. Sorrow, Valley Forge, Pennsylvania (C. E. Smith). June, Julv. = = Low : leaves 0.5 to 2 (very rarely 2.5) mm. broad: scales blunt. 28. C. INTERIOR, Bailey. — Figs. 101 to 105. — Slender, 1.5 to 5 dm. high ; the leaves 1 to 2 (rarely 2.5) mm. broad, shorter than or exceeding the rather stiff culms : spike 1 or 2 cm. long ; the 2 to 5 spike- lets all fertile, all sterile, or variously mixed, usually subglobose, If. or 5 mm. in diameter, the terminal long-elavate at base, 5- to 15 -flowered: perigynia firm, plump, olive-green or -brown, more or less nerved or almost nerveless, broadly deltoid-ovate, obscurely short-beaked and with slightly thickened margin, 2.3 to 3.2 mm. long, 1.5 to 2 mm. broad, finally wide-spreading or recurved, much exceeding the oblong or ovate blunt scales. — Bull. Torr. CI. xx. 426 ; Britton, 1. c. fig. 846 ; Howe, 1. c. 39. C. scirpoides, Schkuhr, Riedgr, Nacht. 19, t. Zzz, fig. 180; Willd. Sp. iv. 237; Schwein. & Torr. 1. c. 317; Dewey, Am. Jour. Sci. viii. 96 ; not C. scirpoidea, Michx. C. stellulata y, Torr. 1. c. 392. C. stellulata, var. scirpina, Tuck. Enum, Meth., 9, not O. scirpina, Tuck. 1. c. 8. C. stellulata, var. scirpoides, Carey in Gray, Man. 544 ; Boott, III. i. 56, t. 146.** G. echinata, Boeckeler, Linnaea, xxxix. 124, in part, not Murray. 0. norvegica, E. P. Sheldon, Bull. Torr. CI. xx. 284, & Minn. Bot. Studies, i. 224, not "Wahl. In damp or wet soil. New Bruns- wick to Rupert Land and Vancouver Island, south to Florida and Arizona. Commonest northward and in the interior. May-July. Var. CAPILLACEA, Bailey. Stiff, culms almost setaceous ; leaves about 0.5 mm. broad, often involute : perigynia strongly 7ierved. — Bull. Torr. CI. XX. 426; Howe, 1. c. ; Britton, 1. c. 351. — New Hampshire to New York, New Jersey, and Pennsylvania. 486 PEOCEEDINGS OF THE AMERICAN ACADEMY. •1- -4- Perigynia broadest near the middle, tapering to a narrow base and a smooth beak. 29. C. SEORSA, E. C. Howe. — Figs. 106 to 109. — Culms soft, in loose stools, 3.5 to 6.5 dm. high : leaves shorter, soft, pale, 2 to 4 mm. broad : spikes 2,5 to 7 cm. long, oi 2 to 6 mostly remote subglobose or oblong 6- to 20-flowered green spikelets 3.5 to 7 mm. long, the ter- minal one usually with a long-clavate base, the lower often subtended by a setiform bract : perigynia very thin and conspicuously nerved, ellip- tic-ovate, with a very short smooth beak and a narrow suhstipitate base, 2.7 ram. long, 1.9 mm. broad, wide-spreading or recurved, much exceed- ing the acutish scales. — 48 Rep. N. Y. Mus. Nat. Hist. 40. C. canes- cens, var. vulgaris, Deane, Met. Park Fl. 95, not Bailey. — Wet woods and swamps, from Middlesex Co., Massachusetts to Suffolk and Oneida Cos., New York, south to Delaware. May, June. Elongatae, Kunth. Spikelets remote or approximate in a simple elongated or short inflorescence. Staminate flowers at the base of the spikelets. Perigynia ascending when mature, glabrous, ovate to oblong or lanceolate, plano-convex, beaked or beakless, not thin-winged. * Perigynia more or less roughened or serrulate on the upper edges (sometimes smooth in exceptional forms of C canescens ; and by exception obscurely toothed in rare individuals of C. tenuiflora). ■*- Perigynia broadest at the rounded or subcordate base. 30. C. arcta, Boott. — Figs. 110 to 113. — Pale green or somewhat glaucous : culms very soft, in loose stools, 1.5 to 6 dm. high, often over- topped by the soft flat leaves 2.5 to If mm. broad: sjnke oblong -cylindric, of 5 to 13 ovoid or oblong closely approximate or slightly remote spikelets 6 to 11 mm. long: perigynia ovate, with a rather definite beak, strongly nerved on the outer, faintly on the inner face, 2 to 3 mm. long, 1.2 to 1.5 mm. broad, somewhat exceeding the acute, often brown-tinged, scales. — 111. iv. 155, t. 497 ; Macoun, 1. c. 124 ; Britton, 1. c. 352, fig. 850. C. canescens, var. polystachya, Boott in Richards. Arct. Exped. ii. 344; Bailey, Proc. Am. Acad. xxii. 144, Mem. Torr. CI. i. 75, & in Gray, Man. ed. 6, 619. C. Kunzei, Olney, Proc. Am. Acad. viii. 406 (excl. syn.). G. canescens, var. oregana, Bailey, Mem. Torr. CI. i. 75. — "Wet woods, alluvial thickets and swales, from the larger river-valleys of Maine and Quebec, Lake Champlain, Vermont, and the Adirondack Mts., New York to Lake Nipigon, Ontario, and British Columbia, south to Michigan, Minnesota, and the coast and mountains of Washington and Oregon. June-Aug. FERNALD. CARICES OF SECTION HYPARRHENAE. 487 1- t- Perigynia broadest near the middle. ++ Perigynia 2 to 3 mm. long, fully half as broad. = Plant glaucous : spikelets oblong-cylindric to ovoid ; the strongly appressed- ascending pale perigynia slightly roughened or smooth above, tapering gradu- ally to the short obscure beak. 31. C. CANESCENS, L. — Figs. 114, 115. — Culms soft, in loose stools, 1.5 to 6 dm. high: leaves soft and flat, shorter than or exceeding the culms, 3 to 4 *'2'^' hroad: spike 2.5 to 5 em. long, of 4 to 7 oblong- cylindric to narrowly obovoid appressed-asc ending approximate or slightly remote spikelets 0.6 to 1 cm. long, the lowermost rarely 1.5 cm. apart: perigynia glaucous, ovoid-oblong, usually serrulate toward the short- pointed tip, 2.3 to 3 mm. long, 1.3 to 1.7 mm. broad, more or less nerved on both faces, somewhat exceeding the ovate pointed scale. Sp. ii. 974 ; Oeder, Fl. Dan. ii. 8, t. 285 ; Lightf. Fl. Scot. ii. 550 ; Reichb. Ic. Fl. Germ. viii. 7, t. 206, fig. 546; Anders. Cyp. Scand. 57, t. 4, fig. 39; Boott, 111. iv. 154, in part; W. Boott ex Rothrock in Wheeler, Eep. 277 ; Ett. & Pok. Phys. PI. Aust. vi. t. 515 ; Richter, PL Eu. i. 151. C. brizoides, Huds. Fl. Ang. 349, not L. C. elongata, Leers, Fl. Herb. 197, t. 14, fig. 7; Oluey ex Wats. Bot. King Rep. 365; Bailey in Coulter, Man. Rocky Mt. Reg. 394, in part ; not L. C. cinerea, Pollich, PL Palat. ii. 571. C. Richardi, ThuilL Fl. Par. (1799) 482. G. curta. Good. Ti'ans. Linn. Soc. ii. 145; Host, Gram. i. 37, t. 48; Schkuhr, Handb. iii. 347, t. 287C, fig. 13; Eng. Bot. xx. t. 1386; Kuuth, Enum. ii. 403. G. lagopina, Olney ex Wats. Bot. King Rep. 365, in part, not Wahl. G. canescens, var. dubia, Bailey, Bot. Gaz. ix. 119 & Proc. Am. Acad. xxii. 143. G. canescens, var. robustina, Macoun, 1. c. 376. — Northern Europe. In wet places, seen from the following American stations — Labrador, (Spreadborough hb. Geol. Surv. Can. no. 13,372) : Rupert Land, Lake Mistassini (J. M. Macoun, hb. Geol. Surv. Can. no. 30,511) : Maine, Fort Kent, Island Falls, and Foxcroft {M. L. Fernald, nos. 2143, 2144, 2145): New Hamp- shire, Mt. Washington and Mt. Lafayette {E. ^ G. E. Faxon) ; Crawfords {E. F. Williams) : Vermont, Eipton {Ezra Brainerd) : On- tario, Belleville & Lake Nipigon (J. Macoun, hb. Geol. Surv. Can. nos. 30,513, & 30,512) : Michigan, Alma (C. A. Davis): Colorado, Twin Lakes (J. Wolf, no. 1017); Bob Creek, alt. 3,230 m. (Baker, Earle S,- Tracy, no. 693) : Montana, Grasshopper Valley (S. Watson, no. 435) : Wyoming, without station (Parry, no. 278) ; Centennial Hills (A. Nelson, no. 1730) ; Beaver Lake (A. ^ E. Nelson, no. 6130) : 488 PROCEEDINGS OP THE AMERICAN ACADEMY. Utah, Bear River Canon, alt. 3,080 m. {S. Watson, nos. 123P & 1233); Alta, Wahsatch Mts., alt. 2,460 m. {31. E. Jones., no. 1273) : Alaska, Ounalaska (/. M. Macoun, lib. Geol. Surv. Can., no. 30,514) ; Sitka {Mertens) : Alberta, Lake Louise {E. Brainerd) : British Colum- bia, Revelstoke (nos. 19 & 30,526), Comox (no. 371), Port Henly (no. 20,500), Mt. Mark, Vancouver Isl. (no. 30,515), Beaver Creek, Selkirk Mts. (no. 30,519), Dead Man River (no. 30,522), —/o/m Macoun., hb. Geol. Surv. Can. ; Ilgacho Brook {Dawson, hb. Geol. Surv. Can. no. 30.518) ; Lulu Island, Fraser River Delta {R. B. Dixon) : Washington, upper valley of the Nesqually {0. D. Allen, no. 163). May— Aug. Var. SUBLOLIACEA, Laestad. — Figs. 116, 117. — Smaller, the short- oblong or subglobose spikelets Jfto 7 mm. long : perigynia smaller, barely 2 mm. long, smooth throughout. — Nov. Act. Soc. Sci. Ups. xi. 282 ; Andersson, Cyp. Scand. 57 ; Boott, 1. c. ; Bailey, Mem. Torr. CI. i. 66 ; Richter, 1. c. 152. C lapponica, Lange, Linnaea, xxiv. 539. G. canescens in part, of Am. authors. — Lapland. In America specimens examined from Ungava, Ungava Bay (Z. M. Turner) : Hudson Bat {Sir John Richardson): New Brunswick, South Tobique Lakes {G. U. Hay, no. 55) ; Petitcodiac {J. Brittain, hb. Geol. Surv. Can. no. 30,510) : Nova Scotia, Halifax (./ Macoun) : Maine, Orono and Southport {M. L. Fernald) : New Hampshire, Mt. Washington {Asa Gray, et al.) ; Mt. Monadnock — ledges toward summit ( W. P. Rich) : Vermont, Willoughby Lake ( W. Boott, G. G. Kennedy) ; summit of Mt. Mansfield {E. Brainerd) ; bog, Wallingford, alt. 675 m. {E. Brainerd): Massachusetts, Sharon {W. P. Rich); Washington, Berkshire Co. ( W. Boott) : New York, Fairfield {A. Gray) ; Pen Yan {Sartwell, no. 32) ; Oriskany Swamp {Kniesken) ; tamarack swamps, Herkimer Co. (/. V. Haherer) : Ontario, Ottawa (/. Fletcher, hb. Geol. Surv. Can., no. 7408) ; Hastings Co. (/. Macoun) : Michi- gan, Flint {D. Clark) ; Lansing {L. H. Bailey, no. 262) ; Alma ( G. A. Davis) : British Columbia, Mts. east of Adams Lake {Dawson, hb. Geol. Surv. Can., no. 30,520) : Washington, Seattle {G. V. Piper, no. 1106). Var. disjuncta — Figs. 118 to 120. — Tall and lax, 3 to 8 dm. high: spike elongated, Jlexuous, 0.5 to 1.5 dm. long ; the 5 to 8 oblong- ovoid to cylindric spikelets 6 to 12 mm. long, all but the terminal remote, the lowermost 2 to If cm. apart: perigynia as in the species, serrulate above. — C. canescens of most Am. authors. C. canescens, form, Boott, 111. iv. 154, t. 496. The common form in eastern America found in FERNALD. — CARICES OF SECTION HYPARRHENAE. 489 most swamps or on wet shores from Newfoundland to Michigan, Ohio and Pennsylvania. The following numbered specimens belong here — Prince Edward Island, Brackley Point (/. Ifacoun, hb. Geol. Surv. Can. no. 30,509) : New Brunswick, Serpentine River (Hay, no. 84); Chipman (Wetmore, hb. Geol. Surv. Can. no. 30,507): Nova Scotia, Boylston (C. A. Hamilton, hb. Geol. Surv. Can., no. 25,443); Baddeck (no. 20,805), Sable Island (nos. 22,076 & 23,071), Truro (no. 30,506) — /. Macoun, hb. Geol. Surv. Can. : Massachu- setts : Framiugham {£J. C. Smith, no. 628) : Connecticut, South- ington (L. Andrews, no. 590) : Ontario, Cache Lake (/. Macoun, hb. Geol. Surv. Can., no. 22,036). = = Green, not glaucous : spikelets subglobose to short-oblong, few-flowered : the loosely spreading dark green or brown perigynia serrulate at the base of the distinct beak. 32. C. brunnescens, Poir. — Figs. 121 to 124. — Very slender and lax: culms 1.5 to 7 dm. high: leaves soft, Jlat, 1 to 2.5 mm, wide, shorter than or equalling the culms : spihe 1 to 6 cm. long, of 3 to 6 more or less remote or approximate spikelets 3 to 7 mm. long : perigynia 2 to 2.7 mm. long, 1 to 1.5 mm. broad, with distinct slender beaks, loosely spreading when mature. — Suppl. iii. 286; Britton, 1. c. 351, fior. 848. G. curta, var. brunnescens, Pers. Syn. ii. 539. C. canescens, var. alpicola, Wahlenb. Fl. Lapp. 232 ; Bailey, Pi'oc. Am. Acad. xxii. 143, & in Gray, Man. ed. 6, 618; Macoun, 1. c. 124; Howe, 1. c. 37. C. Gebhardii, Hoppe Car. Germ. 30. Vignea Gebhardi, Reichb. Fl. Exc. 58. G. canescens, (3, Torr. Ann. Lye. N. Y. iii. 393. G. Per- soonii, Lange, Flora, xxv. (1842), 748 ; Reichb. Ic. Fl. Germ. viii. 7, t. 206, fig. 547. G. canescens, var. sphaerostachya, Tuck. Enum. Meth. 10, 19 ; Carey in Gray, Man. 544. G. vitilis. Fries, Mant. iii. 137 ; Anders. Cyp. Scand. 58, t. 4, fig. 38 ; Boott, 111. iv. 219 ; Fl. Dan. xvii. t. 2973. G. Buckleyi, Dewey, Am. Jour. Sci. xlviii. 143, t. Dd, fig. 104. G. sphaerostachya, Dewey, 1. c. xlix. 44, t. Ee, fig. 110. C. canescens, var. vitilis, Carey in Gray, Man. ed. 2, 514. G. canescens, var. brunnescens, Boott, 1. c. 220 (nomen nudum) ; Bailey. Mem. Torr. CI. V. 74. G. canescens, var. vulgaris, Bailey, Bot. Gaz. xiii. 86, Mem. Torr. CI. i. 66, v. 74, & in Gray, Man. ed. 6, 618 ; Macoun, 1. c. 123 ; Howe, 1. c. 37. G. brunnescens, var. gracilior, Britton, 1. c. 350. — Open woods and dry, rocky banks, Newfoundland and Labra- dor to British Columbia, south to Idaho, Michigan, and mostly in the mountains to North Carolina. Also in Greenland and northern 490 PROCEEDINGS OP THE AMERICAN ACADEMY. Europe. June-Au<^. On alpine summits becoming more rigid and browner than in sheltered situations. ++ ++ Perigynia 4 to 5.5 mm. long, distinctly less than half as hroad. = Leaves very narrow (1 to 2.5 mm. broad) : spikelets lanceolate : perigynia 1 to 1.3 mm. wide. 33. C. BROMOIDES, Scbkuhr. — Figs. 125, 126. — Very slender and lax, green., scarcely glaucous, the culms 3 to 8 dm, long, mostly exceed- ing the soft flat leaves : spike loosely subcylindric, 2 to 5.5 cm. long, of S to 6 approximate or slightly scattered spikelets 0.5 to 2 cm. long: beak of the perigynium one-half to two-thirds as long as the strongly nerved body, slightly exceeding the ohlong pointed scale. — Riedgr. Nachtrag. 8, t. Xxx, fig. 176; Willd. Sp. iv. 258; Schwein. & Torr. Ann. Lye. N. Y. i. 300 ; Torr. 1. c. 391 ; Carey in Gray, Man. 539 ; Chapm. Fl. 533; Boott, 1. c. ii. 82, t. 227; Bailey, Proc. Am. Acad. xxii. 146; Macouu, 1. c. 114 ; Britton, 1. c. 354, fig. 857 ; Howe, 1. c. 47. — Rich low woods and swamps. Nova Scotia, southern New Brunswick and central Maine to western Ontario and Michigan, south to Florida and Louisiana.^ May-July. = = Leaves broader (2 to 6 mm. broad) : spikelets ovoid : perigynia 1.6 to 1.9 mm. wide. 34. C. Dewetana, Schweinitz. — Figs. 127, 128. — Very lax, glau- cous, the culms 2 to 12 dm. long, much exceeding the soft, flat leaves : spike Jlexuous, 2 to 6 cm. long, of 2 to 5 (in very luxuriant individuals rarely 6 or 7) 3- to 12-fiowered spikelets 5 to 12 mm. long, the upper sub- approximate or scattered, the lowest very ret7iote, usually subtended by an elongate slender bract : beak about one-half as long as the obscurely neri'ed or nerveless body of the perigynium, somewhat exceeding the ovate acumi- nate or short-cuspidate pale scale. — Ann. Lye. N. Y. i. 65 ; Dewey, Am. Jour. Sci. ix. 62, t. 3, fig. 11 ; Schwein. & Torr. 1. c. 310; Torr. 1. c. 392 ; Carey, 1. c. 544 ; Boott, 1. c. i. 27, t. 70 ; W. Boott in "Wats. Bot. Calif, ii. 236 ; Bailey in Coulter, Man. Rocky Mt. Reg. 394, & Proc. Am. Acad. xxii. 146; Macoun, 1. c. 124; Britton, 1. c. fig. 856; Howe, 1. c. 36. C. remota, Richards, in Frankl. 1st Journ. ed. 2, App. 35, ace. to Boott, not L. — Rich open woods and banks. Nova Scotia and 1 Californian and other northwestern specimens referred here seem much better placed with the stouter broader-leaved C. Bolanderi, Olney. FERNALD. — CARICES OF SECTION HYPARRHENAE. 491 Quebec to Athabasca and British Columbia, south to Pennsyl- vania, Michigan, New Mexico, and Washington.^ May-Aug. * * Perigynia entirely smooth at the tip (exceptional forms of C. canescens might be looked for here ; and very rare individuals of C tenuijlora might be sought in the preceding section). t- Perigynia oblong or ovate-oblong. ■w- Perigynia 3 to 4 mm. long, nerved : culms weak, almost capillary : spikelets 2 to 4, loose, silvery -green or silvery brown. = Spikelets closely approximate in a small usually bractless terminal cluster : perigynia beakless. 35. C. TENUiFLORA, Wahlenb. — Figs. 129, 130. — Lax, the culms 2 to 6 dm. long, mostly exceeding the very narrow (0.7 to 2 mm. broad) pale green leaves : spikelets subglobose, 3- to lO-flowered : perigynia 3 to 3.Jf mm. long, 1.5 to 1.7 mm. broad, with the bluntish scarcely beaked tip smooth or rarely with one or two teeth, about equalled by the ovate or ovate-oblong white scale. — Kongl. Vet. Acad. Handl. xxiv. 147, & Fl. Lapp. 232 ; Schkuhr, Riedgr. Nachtr. 17, t. Eeee, fig. 187 ; Anders. Cyp. Scand. 59, t. 4, fig. 36; Hook. Fh Bor.-Am. ii. 214; Torr. 1. c. 392, 443 ; Carey, 1. c. 543 ; Boott, 111. iv. 144, t. 463 ; Fl. Dan. Suppl. 13, t. 167 ; Bailey, Proc. Am. Acad. xxii. 145 ; Macoun, 1. c. 122 ; Britton, 1. c. 352, fig. 851 (as to habital drawing) ; Howe, 1. c. — Cold bogs among the mountains, Scandinavia. Bogs and wet mossy woods, local, from eastern Ungava to western Keewatin and Manitoba ; south to Westmoreland and Victoria Cos., New Bruns- wick; southern Aroostook, Penobscot and Oxford Cos., Maine; Hamp- shire Co., Massachusetts ; Oneida Co., New York ; Ingham Co., Michigan ; Milwaukee Co., Wisconsin ; Chisago and Hennepin Cos., Minnesota : also on Elbow River, Alberta, and near Victoria, British Columbia {Macoun^ hb. Geol. Surv. Can. nos. 25,571 & 30,517). 1 The California material which has been referred here is C. Bolanderi, Olney, differing in its less acutely angled culm, longer spikes of more approximate usually more numerous lance-cylindric many-flowered spikelets, the lowest with or without a short bract. The northwestern C Bolanderi, var. sparslflora, Olney (C. Deweyana, var. sparsijlora, Bailey) is a distinct species, probably C. laevicuhnis, Meinshausen, Acta Hort. Petrop. xviii. 326, in its small short-beaked strongly nerved finally spreading thin-edged perigynia much nearer related to the eastern C. seorsa than to the members of the Elongatae. 492 PROCEEDINGS OF THE AMERICAN ACADEMY. = = Spikelets remote, the uppermost strongly divaricate-pedunculate ; the lower- most subtended by a long leaf-like bract : perigynia beaked. 36. C. TRiSPEKMA, Dewey. — Figs. 131, 132. — Culms almost fili- form, 2 to 7 dm. long, usually much overtopping the soft narrow (0.5 to 2 mm. wide) leaves: the 2 or 3 spikelets, 2- to 5-jlowered: the finely many-nerved perigynia 3.3 to 3.8 mm. long, 1.6 to 1.8 mm. broad, slightly exceeding the ovate-oblong pale obtuse to mucronate-acumiuate scale. — Am. Jour. Sci. ix. 63, t. 3, fig. 12; Hook. Fl. Bor.-Am. ii. 213; Schwein. & Torr. 1. c. 311 ; Carey, 1. c. 543; Boott, 1. c. i. 29, t. 74; Bailey, Froc. Am. Acad. xxii. 144; Macoun, 1. c. 122; Britton, 1. c. 353, fig. 855; Howe, 1. c. 35. — Mossy woods and bogs, Newfound- land and Labrador to Saskatchewan, south to northern Pennsyl- vania, Ohio, Michigan, and Nebraska (according to Webber), and in the mountains to Garrett Co., Maryland. Ascending to 770 m. in the New England mountains. June-Aug. ++ ++ Perigynia 1.2 to 1.5 mm. long, nerveless, with a very short broad truncate beak, or beakless : culms wiry : spikelets 3 to 5, closely flowered, in a greenish-brown or straw-colored linear spike. 37. C. elachycarpa. — Figs. 133, 134. — Tufted, the stif slender culms 3 or 4 dm. high, strongly scabrous above, longer than the soft narrow (1 to 2 mm. broad) green leaves: spike 0.5 to 1.5 cm. long; the cqjpressed asceiiding narrowly ovoid approximate or slightly remote spikelets 3 to 6 mm. long : perigynia oblong, plump, smooth and nerveless, subtruncate at base, shorter than the oblong-ovate acuminate dull-brown, green-ribbed scales. — Maine, wet sandy river bank, Fort Fairfield, June 29, 1899 {M. P. Cook, E. L. Shaw & M. L. Fernald). A unique plant, in maturity strongly suggesting an immature slender form of C. echinata, or the little-known C. helvola, Blytt, which, however, have very different perigynia. ■*- -1- Perigynia broadly elliptic to suborbicular : spikes mostly tinged with brown. ++ Terminal spikelet with conspicuous ciavate sterile base : perigynia rather abruptly contracted to the slender beak. = Spikelets mostly distinct, the lowest 4 or 5 mm. thick. 38. C. NORVEGiCA, WiLLD. — Figs. 135, 136. — Glaucous Q.ndi freely stoloniferous ; culms smooth and soft, 1 to 4.5 dm. high, mostly over- topping the soft flat rather narrow (1 to 2.5 mm. broad) leaves : spike FERNALD. — CARICES OF SECTION HYPARRHENAE. 493 1.5 to 5.0 cm. long, oi 2 to G ovoid or hroad-ohlong spihelets ; the lower 5 to 12 mm. long, the terminal, including the clavute sterile base, 1 to 1.8 cm. long : ferigynia pale, faintly nerved, 2.5 to 3.3 mm. long, 1.6 to 2 mm. broad, conic-rostrate, usually abruptly contracted to a substipitate base, about equalled by the yelloioish brotvn orbicidar to ovate blunt scales. — Willd. ex. Schkuhr, Riedgr. 50, t. S, no. 66, & Spec. iv. 227 ; Wahlenb. Kongl. Vet. Acad. Handl. xxiv. 146, &, Fl. Lapp. 233, t. 15, fig. 3 ; Anders. Cyp. Scand. 61, t. 4, fig. 29 ; Goodale in Holmes, Prelim. Rep. Nat. Hist. & Geol. Me. (1861), 128, & Proc. Portland Soc. Nut. Hist. i. 135; Gray, Man. ed. 3, Addend, xcvii : Boott, 1. c. iv. 214; Fl. Dan. Suppl. 13, t. 103; Bailey, Proc. Am. Acad. xxii. 145; Macoun, 1. c. 125 ; Britton, 1. c. 351, fig. 849 (as to habital sketch). — Brackish marshes, northern Scandinavia. Damp usually brackish soil, coast of southern Labrador : Anticosti Island, and Kamouraska, Saguenay, Rimouski, and Gaspe Cos., Quebec : locally southward along the coast in New Brunswick at Shediac, Westmoreland Co., and Back Bay, Charlotte Co. (/. Brittain, herb. Geol. Surv. Can. nos. 30,421 & 30,420); Whale Cove, Grand Manan and Fryes Island {Hay) : Nova Scotia, Baddeck, Cape Breton and Truro (/. Macoun, herb. Geol. Surv. Can. nos. 20,846 & 30,422) ; Boylston (C. A. Ham- ilton, herb. Geol. Surv. Can. no. 25,521) : Maine, Little Cranberry Isle (Redjield) ; Wells (Blake) : reported from Alaska.^ June-Aug. = = Spikelets approximate at the tip of the culm, the lowest 2.5 to 4 mm. thick. a. Plant -weak and lax, with filiform or involute leaves. 39. C. GLAREOSA, Wahlenb. — Figs. 137, 138. — Culms acutely angled, mostly curved, scabrous at tip, 1 to 3 dm. high, once and a half or twice exceeding the Jlaccid narrow (0.5 to 1.5 mm. broad) leaves : spike oblong to obovoid, 0.7 to 2 cm. long, with 2 to 4 oppressed- ascending obovoid spikelets; the lower J{. to 9 mm. long, S or ^ mm. thick, the terminal larger, including the slender sterile base, 6 to 11 mm. long : perigynia pale, elliptic or ovate, acute at base, with narrowly conic beak, faintly nerved or nerveless, 2.5 to 3 mm. long, 1.1 to 1.9 mm. broad, nearly or quite equalled by the ferrugineous white-edged ovate acutish scc/es. — Kongl. Vet. Acad. Handl. xxiv. 146, & Fl. Lapp. 230; Willd. 1 Prof. Conway MacMillan has courteously forwarded me the Minnesota speci- mens referred to C. norvegica by Mr. E. P. Sheldon (Bull. Torr. CI. xx. 284, & Minn. Bot. Studies, i. 224), and they prove to be C. interior, Bailey. I 494 PROCEEDINGS OP THE AMERICAN ACADEMY. Spec. iv. 251; Schkuhr, Riedgr. Nachtr. 24, t. Aaa, fig. 97; Auders. 1. c. G2, t. 4, fig. 31 ; Torr. 1. c. 396; Dewey, Am. Jour. Sci. Ser. 2, iv. 344; Boott, 1. c. 153, t. 494; Fl. Dan. xiv. 8, t. 2430; Bailey, Proc. Am. Acad. xxii. 146; Macoun, 1. c. 127; Britton, 1. c. 353, fig. 854 ; Meinshausen, Acta Hort. Petrop. xviii. 325. — Arctic regious of botti liemispheres, extending south in America along the coast of Labrador to Quebec, Bonne Esjierance (Allen), Watsheeshoo (St. Cyr, hb. Geol. Surv. Can. no. 16,524), and Tadousac (Kennedy)^ Saguenay Co. ; Pointe des Monts (Bell) and Grand Etang (Macoun, hb. Geol. Surv. Can. no. 30,413), Gaspe Co. : also on the coast of Alaska. June-Aug. d. Plant stiff and upright, with flat leaves. 40. C. lagopina, Wahlenb. — Figs. 139, 140. — Culms obtusely angled, mostly erect, smooth except at tip, 1 to 4 dm. high, more or less exceeding the narrow (1 to 3 mm. wide) leaves : spike from cylindric to globose, 1 to 2,5 cm. long, with 3 to 6 ascendiny spihelets mostly larger than in the last : perigynia hrown or reddlsh-broicn, from elliptic- lanceolate to broadly obovate, rather abruptly beaked, 2.5 to 3.8 mm. long, 1.5 to 1.9 mm. wide, exceeding the ovate obtuse white-margined fuscous scales. — Kongl. Vet. Acad. Handl. xxiv. 145, & Fl. Lapp. 229 ; Gay, Ann. Sci. Nat. Ser. 2, xi. 177; Drejer, Rev. 25 ; Anders. 1. c. 63, t. 4, fig, 28; Reichenb. 1. c. t. 204, fig. 543 ; Torr. 1. c. 393 ; Boott, 111. iv. 189 ; W. Boott in Wats. Bot. CaUf. ii. 233 ; Bailey in Coulter, Man. Rocky Mt. Reg. 395, & Proc. Am. Acad. xxii. 145 ; Britton, 1. c. 353, (fig. uncharacteristic) ; Meinsh. 1. c. G. leporinn, L. Spec. 973, in part (cit. Fl. Lapp.) ; Oeder, Fl. Dan. ii. 9, t. 294 ; Willd. Spec. iv. 229 ; Schkuhr, Riedgr. Nachtr. 17, in part (excl. t. Fff, fig. 129) ; Host, Gram, iv, 45, t. 80 ; Eng. Bot. Supp. iii. t. 2815. C. Lachenalii, Schkuhr, Riedgr. 51, t. Y. fig. 79. C. approximata, Hoppe, ex DC. Fl. Fr. vi. 290. G. parvijiora. Gaud. Etr. Fl. 84, ace. to Boott. G. furva, Webb, Iter Hisp. 5. — Arctic and alpine regions of Europe and Asia : Greenland : Arctic America, rarely south to Mt. Albert, Gaspe Co., Quebec, the mountains of Colorado, and northern California. June-Auff. *»• ++ ++ Terminal spikelet ovoid or subglobose, not conspicuously clavate at base : perigynia tapering gradually to the tip : culms sharply angled and harsh, upright, the 2 to 5 spikelets crowded at the tip: leaves flat. 41. C. heleonastes, Ehrh. — Figs. 141, 142. — Gulms 1.5 to 3.5 cm. high, stiff, usually overtopping the erect narrow (1 or 2 mm. wide) FERNALD. VARIATIONS OF BOREAL CARICES. 495 leaves : the globose or ovoid spikelets 4 to 8 mm. long : perigynia 2.5 to 3.5 mm. long, 1.2 to 1.7 mm. broad, brown tinged, mostly exceeding the ovate blunt scales. — Ehrh. in L. f. Suppl. 414; Wahlenb. Kongl. Vet. Acad. Handl. xxiv. 146, & Fl. Lapp. 230; Schkuhr, Riedgr. 51, t. li, fig. 97; Hoppe & Sturm, Car. Germ. t. 6; Hook. Fl. Bor.-Am. ii. 214; Reichenb. Ic. Fl. Germ. viii. t. 204, fig. 542 ; Anders. Gyp. Scand. 62, t. 4, fig. 30 ; Boott, 111. iv. 152, t. 489; Fl. Dan. Suppl. t. 31 ; Bailey, Proc. Am. Acad. xxii. 145; Macoun, 1. c. 127; Britton, 1. c. 352, fig. 852. C. leporina, Schkuhr, Riedgr. Nacbt. t. FiF, fig. 129, not L. C. Carlfotiia, Dewey, Am. Jour. Sci. xxvii. 238, t. U. fig. 64 ; Torr. 1. c. 393. C. triarina, Dewey, 1. c. xxix. 247, t. X, fig. 74; Torr. 1. c. — Bogs and mossy places, arctic and alpine Europe. Very locally in America : examined from the following stations : — Keewatin, York Factory (Sir John Richardson) : Saskatchewan, Norway House and Carlton House {Richardson) : Alberta, Lake Louise (Ezra Brai7ierd, no. 172) : British Columbia, Glacier (Ezra Brainerd) ; Kicking Horse Lake (/. Macoun, hb. Geol. Surv. Can. nos. 28; 49; 30,410; 30,411; 30,412). July, Aug. n. — THE VARIATIONS OF SOME BOREAL CARICES. Carex aquatilis. C. AQUATILIS, "Wahlenb., Kongl. Acad. Handl. xxiv. 165. — Plants 3 to 9 dm. high ; leaves 4 to 7 mm. broad : spikelets ^ slender ; the pistillate 1.5 to 5.5 cm. long, 3 to 4.5 mm. thick, the lowermost often long-attenuated and remotely flowered at base : scales dark, subacute, hardly equal- ling or barely exceeding the perigynia. — Northern Europe, Green- land. In North America from the Shickshock Mts., Gaspe, Quebec, 1 The inflorescences of Carex are simple or compound spikes, racemes, or pani- cles ; and, since in other genera of Cyperaceae, as Ci/perus and Scirpus, the ultimate spicate divisions of the inflorescence are called spikelets, that term is here adopted, for the sake of uniformity and clearness, for these ultimate spicate divisions of the inflorescence of Carex. The species in wliich there is a solitary simple in- florescence (or true spike), as C. gynocrates and C. exilis, are few in comparison with those in which the inflorescence has more than one such division. From the occurrence in those plants, however, of occasional secondary divisions of the in- florescence, the term spikelet seems not inappropriate to the normal inflorescence of such species. 496 PROCEEDINGS OF THE AMERICAN ACADEMY. to Bear Lake, Mackenzie & British Columbia, south to Maine, Vermont, central and western Neay York, and Utah. The Scandi- navian material examined has been referred to the true C aquatilis by Andersson, Fries, Laestadius, and Wickstrom, and it agrees well with Lange's representation of the plant in Flora Danica, Supplement, t. 33. This is the plant of broadest range in America. Many extreme varia- tions have been described by European authors. The identity of these is too often obscure, but some of the forms recognized by Mr. Arthur Bennett in Great Britain (Jour. Bot. xxxv. 248) are found to occur also in America. As extreme variations these plants may well be dis- tinguished, though many transitional specimens occur which render their ready separation difficult. The best marked forms are the following: Var. elatior, Bab. Man. Brit. Bot. 341 ; Bennett, 1. c. 249. — Ro- bust, 0.9 to 1.5 ra. high: leaves 5 to 8 mm. broad: pistillate spikelets stout and heavy, 3.5 to 8 cm. long, 5 to 8 mm. thick : scales dark, blunt or acuminate, about equalling or slightly exceeding the perigyuia. — Maine, Fort Fairfield and Orono (J/. L. Fernald^ nos. 136, in part, 395) : New York, Pen Yan & Junius {Sartwell) ; Dexter ((?. Vasey) ; Jefferson Co. (Craive) ; Niagara Falls (W. Boott): Ohio (SuUivant): Michigan, Peche Isle, Detroit River ( C F. Wheeler) : Manitoba, English River (^Sir John Richardson)} I have been unable to see authentic specimens of Babington's plant, but from his description and the note of Mr. Bennett, it seems probable that our large form should be referred there. The material from Orono (where the once abundant plant has been exterminated by the '' improvement " of the meadow) has been described as a hybrid, C. aquatilis X stricta^ Bailey, Bot. Gaz. xvii. 153; but there was little besides the local occurrence of the plant to suggest hybrid origin. The same very large form is shown in Crawe's New York material, as well as in Richardson's English River plant, and it is closely matched by Boott's plate 542, drawn from New York specimens. 1 Richardson's plant probably came from the river rising in Lake Sal and flowing into Lake Winnipeg from the southeast. The name Engliah River lias been applied to a district between the Saskatchewan and Athabasca Lake, and it was long used for the upper portion of Churchill River (emptying into Hudson Bay). This larger nortiiern river, however, was consistenth' spoken of by Rich- ardson in his Arctic Searching Expedition (1852), p. 62, &c., as Missinippi or Churchill River, while to the more southern river flowing from Lake Sal he ap- plied the name English River (p. 362). FERNALD. VARIATIONS OF BOREAL CARICES. 49T Var. viRESCENS, Anders. Cyp. Scand. 46; Bennett, 1. c. — Scales pale and short, mostly hidden by the closely imbricated perigynia, thus giving the spikelets a pale green color. — Northern Europe. The only American specimens seen are from Michigan, without locality {Michigan State Collection in herb. Gray) ; near Alma ( C. A. Davis). Material from Pownal, Vermont, closely approaches this variety, but has longer darker scales. Var. cuspiDATA, Laest. ex Fries, Bot. Not. (1843) 104; Bennett, 1, c. — Spikelets slender, 3 or 4 mm. thick : scales cuspidate, distinctly exceeding the perigynia. — Northern Europe. Quebec, Grand Etang, Gaspe {J. Macoun): New Jersey, Camden {C. F. Parker). The Gaspe plant is a perfect match for Lapland material from Nylander, but the New Jersey specimen shows a nearer approach to typical C. aqnatilis. Var. EPiGEJos, Laest. Kongl. Vet. Akad. Handl. (1822) 339; Bennett, 1. c. — Very slender : the leaves 2 to 3.5 mm. broad : spikelets at most 5 cm. long, 2 to 4.5 mm. thick; scales dark and blunt. — Northern Europe, Greenland. Newfoundland {La Pylaie) ; Packs Harbor {A. C. Waghorne, no. 35): Labrador, L'Anse au Loup (J. A. Allen): Quebec, Mont Louis, Cape Rosier, and Madaline River, Gaspe (J. Macoun, nos. 23, 27, 31). The material examined matches well Scan- dinavian material from Ahlberg. It is also identical with plants from Lapland distributed by Andersson as var. sphagnophila. The latter variety, however, is said by Andersson to differ from var. epigejos in its pale not dark scales. Carex pilulifera and C. communis. Carex pilulifera, L., a common species of Europe, presents three rather marked tendencies. The original plant of Linnaeus was apparently the common form with the pistillate spikelets subapproximate or slightly remote at the tip of the somewhat curved culm. This form with the lower spikelets sometimes 1 cm. apart, is represented in the Gray Herbarium by specimens from many parts of northern and central Europe. In this plant the perigynium is 2.5 to 3.5 mm. long, tipped by a short bidentate beak less than 1 mm. in length. Another phase of the plant, evidently rare in Europe, has larger more scattered spikelets, the lower often subtended by a conspicuous leafy bract ; and the larger perigynia more ellipsoid or with the longer beak equalling the stipitate spongy basal portion and thus giving the perigynia a symmetrical spindle- voL. xxxvi. — 3*2 498 PROCEEDINGS OF THE AMERICAN ACADEMY. form. This larger plant was described by Lange as var. longibracteata and later figured by him in Flora Danica, xvii. t. 3050 ; and again it has been described by Ridley and figured in Jour. Bot. xix. 97, t. 218, as var. Leesii. A third Eluropean form, var. pallida, Peterm., as shown by Reichb. Ic. Fl. Germ. viii. 26, t. 240, has the densely flowered spike- lets closely approximate in an ovoid or subglobose head. In studying this European species in connection with the well known American jjlant which has recently been called C. communis, Bailey, the writer has been baffled in every attempt to find constant distinguishing characters to separate the plants of the two continents. The form of the plant most common perhaps in America is apparently rare in Europe (var. longibracteata, Lange ; var. Leesii, Ridley), but it passes by abso- lutely promiscuous variations into a small form which can be distin- guished in none of its characters from the smaller tendency of the European C. pilulifera. By early caricologists the American plant was supposed to be Carex varia, Muhl., and under that name it passed until in 1889 Professor Bailey showed that Muhlenberg's plant was the more slender species described by Dewey as C. Emmonsii. In place of the misapplied name, C. varia. Professor Bailey proposed for the plant which had long borne that name^ the new appellation C. covimimis, giw'mg no suggestion that the plant has close affinity to the common C. pilulifera of Europe. To earlier students, however, the separation of the American and European plants of this group had presented many perplexities. Drejer stated in his Revisio that he could find no distinctions either in the descriptions or specimens : " Forsitan nostra planta rectius cum C. varia Miihleub. conjungitur ; quo modo autem C. variam a C. pilulifera distinguam, neque ex descriptione neque ex speciminibus eruere possum." ^ Schlech- tendahl discussing specimens in the Willdenow herbarium which he took for C. xmria was unable to point out any character to separate it from C. pilulifera : " Species haec vero simillima C. pululiferae et uti nobis fere videtur eadem." ^ Whether Drejer and Schlechtendahl had true C. varia of Muhlenberg or the coarser plant which so long passed under that name is not perfectly clear, although it is probable that Schlechten- dahl at least had the true C. varia.^ This plant, the true C. varia (C. Emmonsii, Dewey) is readily distinguished from C. pilulifera by its much more slender habit, very narrow leaves and smaller-bodied longer- beaked perigynia, 1 Drejer, Rev. Crit, 55. - Linnaea, X. 262. 3 See Bailey, Mem. Torr. Club., I. 40. FERNALD. — VARIATIONS OF BOREAL CARICES. 499 The coarse American plant, C. communis, Bailey, which until recently passed as C. varia, presents, however, less definite marks of specific dis- tinctness. The most careful analysis of the characters which are sup- posed to separate C. communis (C varia of authors) from C. pilulifera was published by Francis Boott, who inclined to regard the two species as separable. In his discussion of C pilulifera, Boott said : " A C. varia, Muhl. [C communis, Bailey], differt spicis confertis, plurifloris, subinde apice masculis, e viridi-purpureo variegatis ; perigyniis enerviis, rostello semper recto breviore bidentato ; basi styli persistente abrupte compresso- deflexa ; culmo incurvo, basi vaginis foliorum pallide ferrugineis tecto ; foliis viridibus." ^ In discussing C. varia [C. communis, ^aWey^ he said : " A C. pilulifera dilFert inflorescentia laxa ; spicis plus minus re- motis, laxifloris, saepe paucifloris ; perigyniis subinde nervatis, rostro nunc excurvato, bifido ; basi styli persistente recta ; vaginis foliorum purpureis." ^ When we analyze these supposed differences in the light of old speci- mens and the abundant modern ones which have accumulated since the publication of Dr. Boott's work, certain traditional marks of separation fail. The large form of the American plant figured by Boott (t. 288) as C. varia, and treated by Bailey as C. commimis and by Britton as C. pedicellata, has the spikelets more remote than in the common European form of C. pilulifera ; but a comparison of this plate with Lange's illus- tration of his C. pilulifera, var. longibracteata (Fl. Dan. xvii. t. 3050) and the figure of C. pilulifera, var. Leesii (Jour. Bot. xix. t. 218), shows that the rarest form of the European plant is not to be distinguished by the crowding of the spikelets from our larger form of C. communis. If, furthermore, we compare Boott's C. varia, var. minor (t. 289), a common plant in America, with the smaller European specimens of C. pilulifera with slightly remote spikelets, no constant difference can be found to sepa- rate them. The plant in America passes by innumerable transitions to the coarsest form (var. longibracteata) , as shown in the large middle speci- men in Boott's t. 289, but in its extreme form, as shown by the smaller specimens in that plate, the spikelets are often subapproximate. A comparison of this plate as well as scores of American specimens such as Eggleston's no. 434: from Middlebury, Vermont ; Brainerd's material from Mt. Mosalamoo, Vermont; no. 4897b of the Biltmore Exsiccatae from Craggy Mt., North Carolina ; Bailey's material of June 13, 1888, from West Harrisville, Michigan, and his no. 187 from Lansing; 1 HI., II. 96. 2 ibij. 98. 500 PROCEEDINGS OF THE AMERICAN ACADEMY. Wheeler's specimens from Grand Ledge, Michigan; Macoun's 1876 material from Quesnelle, British Columbia, with specimens of C. piluli- fera from Berne, Switzerland (Sermge) ; Stockholm, Sweden (Andersson) ; Finland (Simming) ; the Grosser Pfalzberg, Austria (^Haldcsy,\io. 1064), and St. Petersburg, Russia ( Turcznninow) ; shows conclusively that the remoteness of the spikelets is not to be relied upon in separating our smaller American material from the European plant. In the accom- panying tabulation ot" measurements from European specimens and the smaller form of the American plant it will be seen that in the length of the inflorescence and the number, length and remoteness of S2:)ikelets essentially identical conditions are found, although the European mate- rial shows a tendency to a reduction in the length of the rachis between spikelets, thus passing to the short-headed var. pallida, while the Ameri- can plant varying toward the elongated variety longihracteata shows a natural lengthening of the rachis. Dr. Boott laid stress upon the more abundantly flowered spikelets of C. pilulifera, but an examination of the European material shows that this character is maintained only in the extreme specimens with unusu- ally full spikelets. In the others many spikelets are found bearing less than ten flowers while not a few have only four or five. The presence or absence, in the American or the European plant, of staminate flowers at the tips of the pistillate spikelets is likewise a character upon which little reliance can be placed. Both Goodenough ^ and Dr. Boott ■^ noted this tendency in European specimens and in a sheet of Austrian material it is very conspicuous. In America likewise this tendency to androgy- nous spikelets occurs, but it seems to be quite as unusual as in Europe. The pale or castaneous scales of Carex communis were emphasized by Dr. Boott as opposed to the purple scales of C. pilulifera. Students of American Carices, however, are all familiar with specimens of C. com- munis from sunny or open situations in which the scales are quite as purple (or rather maroon) as in C. pennsylvanica ; and many specimens of European C. jnlulifera show quite as little color in the scales as do the commoner plants of America. The basal nerves supposed to distinguish the perigynium of C. com- munis from that of C. pilulifera are also quite as ol'teu wanting as present ; and although Dr. Boott laid stress upon this character in his comparative note, he described the perigynia of C. communis (his C. varia) as "enerviis vel basi plus minus nervatis pallidis." The length, 1 Trans. Linn. Soc, II. 191. 2 m.^ n. 95, FERNALD. — VARIATIONS OP BOREAL CARICES. 501 Table of Measurements of Eukopean Carex piluUfera and the Smaller Form of American C. communis. European Specimen. Collector. Length of Inflorescence in mm. Length of staniinate Spikeletinmm. Number of pistillate Spikelets. Length of pistillate Spikeletinmm, Distance in mm. between lowest Spikelets. Length of Perigynia in mm. Length of Beak in mm. Strumbacka, Sweden . . Lauren 12-18 6-8 2-3 4.5-6 4.5-7 3.4 0.6 Finland Simming 16-19 6-7 3-4 4 8 2.8 0.8 Stockholm, Sweden . . Andersson 17-22 10-11 2-3 7 5-7 2.7 0.7 Halifax, England . . Leyland 13-22 7-10 2-3 5.5 5-10 3.0 0.7 Dresden, Germany . . . 20 9-13 3 4-6 7.5 2.9 0.7 Halle, Germany .... A. Sehulz 18-23 8-9 4 4-8.5 9 3.0 0.8 Berne, Switzerland . . Seringe, no. 1238 17-22 10 2-3 4.5-7 3.5-7 3.0 0.8 Upsala, Sweden .... Angstrom 14-26 9-16 2-4 5-9 3-9 2.8 0.7 Kyffhauser (Mt.), Germ'ny 17-22 11 3 6-8 6 3.0 0.7 Grosser Pfalzberg, Austria Halacsy, no. 1064 14-26 7-18 1-3 3-6 3.5-6 5 2.7 0.9 Salzburg, Austria . . . Hoppe 26-32 11-13 4-5 6-11 6-9 3.0 0.7 St. Petersburg, Russia Turczaninow 18-23 9-11 2 5-7 6-9 2.9 0.7 Upsala, Sweden .... Tuckerman 25 10 4 6-8 9 3.0 0.8 Snowdon, Wales . . . J. Ball 18 6.5 O 6 6 2.9 0.8 Extremes in Europe . . 12-32 6-18 1-5 3-11 3-10 2.7-3.4 0.6-0.9 American Specimen. Keweenaw Co., Mich. . . Farwell, no. 653 10-13 4 2-3 4 5-6 3.3 0.8 Alcona Co., Mich. . . . Bailey 15-19 4-8 2 5-7 7-15 3.2 0.8 Burlington, Vt Jones & Eggleston 11-23 6-13 1-2 6-8.5 7-8 3.2 0.8 Quesnelle, Brit. Columbia Macoun 15-23 9-10 2-3 5-0 5-10 3.0 0.7 Grand Ledge, Mich. . . Wheeler 18-19 8 3 5-6 6-9 3.3 0.8 Mt. Mosalamoo, Vt. . . Brainerd 17-23 8 3 4-6 7-12 2.4 0.8 East Mt., Middlebury, Vt. Eggleston, no. 434 17-24 9-11 2-3 5-6.5 5-13 2.6 0.9 WiUoughby Mt., Vt. . . Faxon 13-26 6.5-10 1-2 4-6 8-12 3.0 07 Lake Memphremagog, Q'b. Faxon 13-29 3.5-9.5 2-4 4-8.5 7-11 3.0 0.9 Craggy Mt., No. Carolina Biltmore Herb., no. 4897'' 21-31 9-16 2-3 4-8 7-11 2.8 0.7 Orono, Me Fernald 23-36 6-13 3-4 4-9 11-12 8.1 1.0 Franconia, N. H. ... Faxon 24-39 8-11 3-4 4-9 7-15 3.3 0.8 Milwaukee, "Wis. . . . Lapham 30-35 14 3 4-7 9 3.0 0.9 Lansing, Mich Bailey, no. 187 25-39 13-18 2 4-8 11-14 3.2 0.8 Extremes in America . . 10-39 3.5-18 1-4 4-9 5-15 2.4-3.3 0.7-1.0 502 PROCEEDINGS OP THE AMERICAN ACADEMY. bending, and orifice of the beak show likewise considerable variation in Old World specimens, all of which can be matched by our plant, while the curving of the base of the style is a tendency not infrequent in American as well as E^uropean specimens. On the other hand, the straight style supposed to characterize the American plant is clearly represented by Lange in his plate of C. pilulifera, var. longihracteata. The deeper purple coloring of the lower sheaths of the American plant, a character much emphasized by authors, is not a satisfactory distinction. The color in the American plant is usually conspicuous and is pronounced by Mr. F. Schuyler Mathews a dilute maroon with no true purple tendency, but rather fading in the older sheaths to chestnut. Mr. Mathews, who has likewise examined the sheaths of European specimens, finds the same red present in them. This color of the sheaths generally fades with age, yet in specimens collected by John Ball on Snowdon, by Andersson at Stockholm in 18G0, by Lauren at Strombacka in 1855, and by Tuckerraan at Upsala in 1841 or 1842, show quite as conspicuous a red as the average American plant. The bright green color of the leaves of C. pilulifera has likewise beea maintained as a character separating that plant from the Ameiican C communis. From dried specimens alone it is impossible to make this dis- tinction apparent, although the fresh plant may sometimes show a brighter color than is often seen in C. communis. Yet in the American plant the leaves vary from a weak to a deep green, and in Bailey's var. Wheeleri, which is certainly inseparable from European specimens of G. pilulifera., the leaves were originally described as " bright green." The length of the staminate spikelet and the breadth of the leaves, two characters upon which stress is sometimes laid, were not emphasized by Dr. Boott. An examination of the accompanying table of measure- ments of the inflorescence will show that the length of the staminate spikelets is thoroughly inconstant and not concomitant with other char- acters. In fact, both short and long staminate spikelets are often found on the same individual, as shown by Halacsy's no. 1064 of the Austro- Hungarian Exsiccatae (staminate spikelets from 7 to 18 mm. long), by Fernald's no. 151 from Maine (spikelets G to 13 mm. long), and a Faxon plant fi'om Franconia, New Hampshire (spikelets from 8 to 14 mm. long). The variations in the breadth of the leaf, likewise, are very great on both continents. The young leaves at the fruiting season are naturally much narrower than the old and weather-beaten ones, which, unfortunately, are too often torn away in the preparation of attractive specimens. Measurement of the breadth of these older leaves FERNALD. — VARIATIONS OF BOREAL CARICES. 503 where present shows in the American plant a variation from 2 to 5.5 mm. and in the European from 2 to 4.5 mm. These measurements, however, include the largest American form, in which all the parts are conspicuously more developed than in the smaller American and the apparently identical Euroijean plant. The length of the lower bract, emphasized in the descriptions of C. piluUfera, var. longibracteata and var. Leesii, seems to the writer an unfortunate character to make prominent. In America, at least, this elongation of the bract accompanies no other definable character. It is a purely vegetative development which may occur either in the large form (C. varia [typical] of Boott's 111. t. 288) or in the smaller C. communis^ var. Wheeleri with shorter inflorescence and more approxi- mate spikelets. This study of the European Carex pilulifera and the American C. communis (C. varia of many authors) has led to the following con- clusions. The form of C. piluUfera of Europe with the pistillate spike- lets subapproximate or slightly remote, the lowest from 0.5 to 1 cm. apart, is also common in America, where the plant has passed generally as C. varia, var. minor ^ Boott ; C communis, Bailey, and C. pedicellata, Britton, in part ; or C. communis, var. Wheeleri, Bailey (C. pedicellata, var. Wheeleri, Britton). Another European form, the large C. ^^Huli- fera, var. longibracteata, Lange, is rare in Europe, but in America is represented by the large extreme which has passed as C. varia and later as C. communis and C. liedicellata. The American plants, then, should be called C. PILULIFERA, L. Culms 1 to 5 dm. high, usually overtopping the leaves: inflorescence 1 to 3.5 cm. long, the lowest spikelet subtended by a short and narrow or sometimes elongated broad bract : staminate spikelet from green to chestnut-brown or maroon, sessile or stalked, 3.5 to 20 mm. long; pistillate spikelets 1 to 5, loosely flowered, 4 to 11 mm. long, sessile or short-pedicelled, subapproximate or slightly remote, the lowest rarely 1.5 cm. apart: perigynia hairy, obscurely 3-angled, 2.5 to 3.5 mm. long, the body plump, obovoid or subglobose, with a more or less elongated spongy nerveless or slightly nerved stipitate base ; the beak broad, bidentate, rarely 1 mm. long, nearly or quite equalled by the green brown or reddish-brown ovate acuminate scale. — Sp. 976; Gooden. Trans. Linn. Soc. ii. 190; Schk. Riedgr. 78, t. I, fig. 39; Andersson, Cyp. Scand. 30, t. 7, fig. 82; Eeichb. Ic. Fl. Germ. viii. t. 2G0 ; Boott, 111. ii. 96, t. 283. C. Jilifurmis, Pol. PI. Palat. ii. 581 ; Vahl, Fl. Dan. vi. t. 1048; not L. C. Bastardi- 504 PROCEEDINGS OP THE AMERICAN ACADEMY. ana, DC. Fl. Fr. vi. 293. C. varia, Authors, incl. Boott, 111. 1. c. 97, ia part, not Muhl. C. varia^ var. pedicellata^ Dewey, Am. Jour. Sci. xi. 163, in part. C. varia, var. minor ^ Boott, 1. c. t. 289. C. communis^ in part, and var. Wheelei-i, Bailey, Mem. Torr. CI. i. 41. C. pedicellata, in part, and var. Wheeleri, Britton, Mem. Torr. CI. V. 87, 88. — In dry soil, New Brunswick to British Colombia, North Carolina, Ohio and Wisconsin: common in Europe. Passing gradually to Var. LONGiBRACTEATA, Langc. Coarser ; the inflorescence often 5 to 8 cm. long, the usually fuller and longer pistillate spikelets remote, the lowest 1.5 to 4 cm. apart : perigynia larger, more ellipsoid or spindle-form, with longer beak. ^ — Haandb. Dansk. Fl. 621, & Fl. Dan. xvii. 12, t. 3050; Kneucker, Allgem. Bot. Zeitschr. (1898) 128. C. varia, Authors, iu part, incl. Boott, 1. c. t. 288, not Muhl. C. varia, var. pedicellafa, Dewey, 1. c, in part. C. saxumbra, F. A. Lees, Jour. Bot. xix. 25. C. pilulifera, var. Leesii, Ridley, Jour. Bot. xix. 98, t. 218. C. communis, Bailey, 1. c. in part. C. pedicellata, Britton, 1. c. in part. — New Brunswick to Iowa and Gkorgia : rare and local' in northern Europe. Carex pennsylvanica. Carex pennsylvanica, Lam., is one of the widest-distributed of the North American Carices, and as one of the earliest-flowering it is per- haps better known to the general botanist than any of the other species. In the length and breadth of its leaves, the comparative height of its culm, etc., the plant shows considerable variation, and many formal varieties have been based upon these characters. But since they are all of a purely vegetative nature, often produced in a colony of the species by changes of ecological conditions, none of these variations seem to the writer of sufiicient constancy to merit recognition as more than trivial forms. The color of the spikelets, also, a character too commonly relied upon to separate C. pennsylvanica from the closely related C. pihdifera, L. (C communis, Bailey), is not to be accepted as final, since C. pennsylvanica, ordinarily characterized by dark reddish brown scales, may often have them pale or even straw-colored when growing in deep shade. Furthermore, C. pihdifera in northern Europe as well as in America is frequently found with dark red scales, especially when growing iu very sunny or exposed situations. The simplest means of distinguishing C. pennsylvanica from its nearest common ally is in its stoloniferous character-, for when well developed the plant produces FERNALD. VARIATIONS OF BOREAL CARICES. 505 conspicuous elongated stolons, while C. pilidifera (C. communis) is caespitose, with short assurgent basal shoots. As may be implied, varieties of C. pennsijlranica based upon color of the spikelets are quite as inconstaut as are those based upon the length or breadth of the leaf, or other purely vegetative tendencies. In the character of its perigynia, however, C. pennsylvanica presents three marked variations which, from the material examined, seem to belong to well marked geographic areas. These forms of the plant are : C. PENNSYLVANICA, Lam. Diet. iii. 388. Strongly stoloniferous ; the slightly caespitose small stools with reddish bases : leaves soft, com- paratively narrow, 1.5 to 3.5 mm. broad, 0.5 to 5 dm. long, shorter than, equalling, or often exceeding the slender culms : pistillate spike- lets 1 to 4, globose or ovoid, loosely flowered, approximate or more or less remote, the lowest rarely peduncled, often subtended by a narrow leafy bract : scales usually maroon or red-tinged, rarely pale : perigynia from subglobose to obovoid, puberulent, the short bifid beak one-fourth to one-fifth as long as the body : staminate spikelet clavate, 1 to 2 cm. long, sessile or short-stalked, usually reddish, rarely straw-colored. — In dry or sandy soil from Cumberland Co., Maine, to Alberta, south to Georgia and Neav Mexico. It is impossible to say from the original description whether this or the following variety was intended by Lamarck, but the commonest form of the species has been accepted as typical since it was so considered by Boott, Kunze, and other classic writers on the genus. The varieties and forms described by Peck (46 Kep. N. Y. Mus. Nat. Hist. 51 ; 48 Rep. 76) appear to be vegeta- tive states due largely to different degrees of light and exposure. Var. lucorum. Perigynium puberulent or glabrate, with a con- spicuous slender beak nearly or quite as long as the body. — C lucorum, Willd. Euum. PI. Berol. Suppl. 63; Kuoze, Car. 153, t. 39; Boott, 111. ii. 98, t. 291, in part. — Maine to Michigan and "Arctic America," and in the mountains to North Carolina. Maine, Orono, May 31, 1890, June 4, 1898 (no. 2006) — J/. L. Fernald; Cambridge {F. S. Btmker) ; Glassface Mt., Rumford, July 13, 1890 (/. C. Parlin) : New Hampshire, Barrett Mt, New Ipswich, June 5, 1896 (M. L. Fernnld) : Vermont, Chipraan Hill, Middlebury, May 30, 1897, Burlington, June 16, 1898 {E. Brainerd) ; Pownal, May 29, 1898 {J. R. Churchill) : Massachusetts, Spot Pond, Stoneham, May 29, 1855, Maiden, June 11, 1861, Medford, May 21, 1865, Blue Hills, Milton, June 3, 1870 (Wm. Boott); Purgatory Swamp, Dedham, May 26, 1878 (F. ^ C. F. Faxon); Wilmington, May 14, 1899 {E. F. Williams): 506 PROCEEDINGS OF THE AMERICAN ACADEMY. Ehode Island, Cumberland (S. T. Olney) : Connecticut, Soutliington, June 4, 1899 (C. ^ Bissell) -, Fairfield, June 23, 1901 (K H. Eames, no. 1G8) : Michigan, Detroit, May 22, 18G4, June, 1860, May 9, 1858 (Wm. Boott) : Virginia, Harper's Ferry, May 7, 1881 (John Donnell Smith): North Carolina, Broad River, May, 1841 (i?^<^6? according to Kunze, 1. c). The long slender beak of the perigynium and its essentially northern and montane range suggest that further knowledge of the plant may show it to be well distinguished from C. -pennsylvanica. No other character has yet been found by which it can be recognized, and occasional individuals show transitions in the elongation of the beak. Var. VESPERTINA, Bailey, Mem. Torr. CI. i. 74. Rather coarser than the species : the usually very dark staminate spikelet peduncled : peri- gynia more coarsely hairy, almost hirsute. — The northwestern form, from the Cascade Mts. of British Columbia to Oregon and Van- couver Island. Carex umbellata. Like C pilulifera and C. pennsylvanica, C. iimhellata, Schkuhr, pre- sents considerable variation in the length and breadth of its leaves and in the length of its culms and peduncles. As in those species, likewise, these purely vegetative characteristics in C. umbellata seem to accompany no fixed characteristic of the perigynia, nor any special geographic areas ; and too often the long-peduncled spikelets of the so-called var. vicina may be found on portions of a clump which is otherwise good C. um- bellata. As in the related species just discussed, however, C. umbellata presents at least two geographic tendencies seemingly characterized by constant differences in the perigynia. A third form, of which we as yet know too little, has the perigynia glabrous, thus breaking through one of the distinguishing marks of the Montanae. Carex umbellata is related on the one hand to 0. nigro-inarginata, and on the other to C. dejlexa. From these two it is usually distinguished without difficulty, but occasional specimens occur which are perplexing. The writer has found that in such cases the best means of distinction between C. umbellata and C. nigro-marginata is offered by the thickness of the perigynia. In C nigro-marginata the mature perigynia vary from 1.3 to 1.6 mm. in thickness, while in mature C. umbellata they are from 1.7 to 2.4 mm. thick. From doubtful forms of G. dejlexa, C. umbellata may best be distinguished by an examination of the scales. In G. umbellata the scales are nearly or quite as long as the subtended perigynia, while in G. dejlexa they are distinctly shorter. FERNALD. — VARIATIONS OP BOREAL CARICES. 507 The most marked tendencies of C. umbellata are C. UMBELLATA, Schkulir, Riedgr. Nachtr. 75, t. \^vfw, fig. 171 {C. umhellata^ var. vicina, Dewey, Am. Jour. Sci. xi. 317 & x. t. D, fig. 13). Low and conspicuously caespitose, forming dense mats : leaves rather stiff, 0.5 to 4.5 dm. long, 1 to 4.5 mm. wide : culms mostly very short and crowded at the base of the leaves, or some elongated, rarely even to 2 dm., and bearing both staminate and pistillate, or staminate spikelets alone: pistillate spikelets 1 to 4, ovoid or oblong, 0.5 to 1 cm. long, sessile or on short or occasionally elongate-capillary peduncles : perigynia plump, stipitate or substipitate, puberulent, 3.2 to 4.7 mm. long ; the slender beak nearly or quite as long as the ellipsoid-ovoid to subglobose or pyri- form body, and about equalled by the ovate acuminate green or purple- tinged scale: staminate spikelets subsessile or peduncled, 6 to 12 mm. long. — Dry sandy or rocky places, Prince Edward Island to central Maine, west to Saskatchewan and British Columbia, and south to New Jersey, District of Columbia, and Indian Territory. Var. tonsa. Similar, but with the perigynia glabrous or merely puberulent on the angles of the long beak. — Maine, Streaked Mt., Hebron, June 2, 1897 (./. A. Allen) : Connecticut, rocky wooded slope of Lantern Hill, North Stonington, May 30, 1901 (C. B. Graves). A plant with identical glabrous perigynia is figured in Boott, 111. ii. t. 293, from specimens collected at Methy Portage, Athabasca, by Sir John Richardson. This and the New England plant represent a tend- ency uuusual in the Montanae. Var. brevirostris, Boott, 111. ii. 99, t. 294. Perigynia rather smaller, the broad beak short, about one-third as long as the plump short- hairy body. — The commonest form from Saskatchewan to Vancou- ver Island, south in the mountains to California and New Mexico : also Maine, Fort Kent, Ashland, Masardis, Island Falls and Foxcroft {M. L. Fernald, nos. 2111, 2112, 2113, 2114, 2115); summit of Sargent Mt., Mount Desert Island {E. 8^ C. E. Faxon) : New Hampshire, Mt. Willard, and Bald Mt., Franconia (E. S^ C. E. Faxon). Carex vaginata and C. saltuensis. C. vaginata, Tausch, Flora (1821) 557 (C. vaginata, var. alto-cauUs, Dewey, Am. Jour. Sci., Ser. 2, xli. 227. C. saltuensis, Bailey, Mem. Torr. CI. i. 7. C. altocaulis, Britton, in Britton & Brown, 111. Fl. i. 326, fig. 773). The American plant was long considered by Francis Boott 508 PROCEEDINGS OF THE AMERICAN ACADEMY. and other caricologists identical with the European ; but in 1866 the New York plant was distinguished by Dewey, on account of its tall slender culm, narrow leaves and loose spikelets as var. alto-caulis. In 1889, however, Professor Bailey raised the American plant to specific rank as C- saltuensis, separating it from the European C. vaginata " by its much more slender and less caespitose habit, narrower leaves and less conspicuous sheaths, its alternately-flowered spikes, and its much smaller, less inflated, and conspicuously nerved perigynium." And Dr. Britton, following Professor Bailey's lead in treating the plant as strictly American, has taken up for it Dewey's varietal name as altocaulis (not alto-caulis). That American specimens from the deep swamps of western New York, Ontario and Michigan are more slender than some European specimens there can be no doubt; but in northeastern Maine, where the plant is a common species of arbor-vitae swamps, it varies greatly in these characters. Individuals growing in excessive shade are naturally taller and more slender than those in bright light ; and the spikelets vary indiscriminately from the slender alternate-flowered tendency sup- posed to characterize the American plant to the dense-cylindric form said to distinguish the European. The height of the European plant, too, is often as great as that of the American, while our own plant sometimes fruits when scarcely 2 dm. high (Mt. Albert, Quebec — Allen ; lilaine, Maine — Fernald). A speci- men from Christiania collected by Blytt is 5 dm. high, while the extreme height given by Dr. Britton for his C. altocaulis is 2 feet (6 dm.). The breadth of the leaf, likewise, is as variable on one continent as on the other. Both Dewey and Bailey have maintained that the European plant is broader-leaved ; yet a specimen from Fries collected in Jemtland (Sweden) has leaves from 1.5 to 1.75 mm. wide, while the broadest leaves seen on the European plant are those of a Lapland specimen (5 mm. wide) from N. J. Anderssou. In the American plant the leaves vary from 1.5 mm. wide (Blaine, Maine) to 5 mm. (Montreal). The variation in the density of the spikelet in the American plant has been already mentioned. In Europe the same variation occurs, speci- mens from Jemtland (A/(lbe>-g), Lapland (^Andersson) and Finland {Lehmann) having the spikelets as loosely flowered as in the most extreme American form. Nor are the differences assigned by Professor Bailey to the perigynia maintained in mature specimens. Young individuals of the American as well as the European plant have the nerves poorly developed, but in FERNALD. VARIATIONS OP BOREAL CAKICES. 509 mature fruit uo difference is apparent between plants from Christiania, Norway, and Aroostook Co., Maine. The sheath, said by Professor Bailey to be " less conspicuous " in the American plant, is 4 cm. long, by 2.7 mm. wide in one of Macrae's Montreal specimens, fully as conspicuous as in the best developed European material. There is, then, no reason why the American Carex saltuensis, Bailey (C. altocaulis, Britten) with no constant vegetative or morphological character and with a broad range from northern Labrador to the Mackenzie River, northern New England, New York, the Great Lakes and the upper Rocky Mts., should be treated as distinct from C. vaginala of Greenland, northern Europe and Asia. Carex capillaris. C. capillaris, L. Sp. 977. The Linnaean plant was the low plant of the Scandinavian mountains, described as a span high. This plant, well represented in the Gray Herbarium by European specimens from Andersson, Holmgren, Hoppe, Lehmann, Tuckerman, and others, varies in height from 3 to 25 cm., the spikelets being subapproximate or scarcely remote, the lower at most 2 cm. apart. This dwarf plant occurs likewise in Greenland and northeastern Asia. It has been ex- amined from the following regions in America — Labrador, Dead Islands (J. A. Allen) : Newfoundland, without locality (La Pylaie) ; Middle Arm, Bay of Islands {A. C. Waghome) : Quebec, dry stony ground, near summit — 1,150 m. — Mt. Albert (J. A. Allen): Maine, Mt. Kineo (T. C. Porter et cd) : New Hampshire, Mt. Washington (Wm. Oakes et al): Colorado, Rocky Mts., alt. 3,385 m. {E. L. Greene in Exsicc. Olney) ; South Park (/. Wolfe, no. 1059); Clear Creek, Georgetown, alt. 2,615 m. {H. N. Patterson, no. 144, in part): Utah {S. Watson, no. 1261) : Wyoming, La Plata Mines {E. Nelson, no. 5260). Var. elongata, Olney, in herb. & in Rothr. Prelim. Rep. Wheeler PI. 53 (as nomen nudum). Tall, 2 to 6 dm. high, forming loose stools : pistillate spikelets remote, often 6 or 8 cm. apart. — Mossy woods and sphagnum-swamps. Rupert Land, Lake Mistassini {J. M. Macouri) : Newfoundland, Coal River, Bay of Islands (A. C. Waghome, no. 24) : Quebec, Ste. Anne des Monts and Little Metis (J. A. Allen) : New Brunswick, Drury's Cove, St. John (Wm. Boott): Maine, Fort Fairfield (nos. 140, 2029), Blaine (no. 2028), Mars Hill — J/: L. Fernald : New York, Otter Creek, near Cortland (S. N. Cowles) : 510 PROCEEDINGS OP THE AMERICAN ACADEMY. Ontario, Bruce Co. {J. Macoun) : Michigan, Point de Tour ( Wm. Boott) y Port Huron (C. K. Dodge): Saskatchewan (Bourgecm) : AssiNiBOiA, Assiuiboiue River (J. Macoun) : Alberta, Bow River (J. Macoun) : Colorado, Rocky Mts., alt. 2460 m. {E. L. Greene in Exsicc. Oluey) ; Twin Lakes {J. Wolfe, no. 1060 [type]) ; Clear Creek (Parry, no. 386, Patterson, no. 144, in part) : Utah, Aquarius Plateau (L. F. Ward, no. 484) : Idaho, Lake Pend d'Oreille {/Sandberg, Mac- Dougal S^ Heller, no. 751). A plant confined in the East to arbor- vitae swamps at low altitudes, and in its tall lax habit and very distant spikelets hardly suggesting the dwarf alpine G. capillaris with approxi- mate spikelets. Somewhat similar specimens in the Gray Herbarium from Salzburg, Austria, suggest that the same form may be present in Europe. INDEX TO SPECIES. Carex adusta, 451, 452, 464, 476, 478, 480, " var. argyrantha, 478. " " glomerata, 481. " minor, 471. " sparsiflora, 480. aenea, 461, 462, 464, 480. alascana, 482. alata, 448, 450, 451, 463, 476. " var. ferruginea, 463, 477. albolutescens, 448, 450, 451, 452, " var. argyrantha, 47 " " cumulata, 472. " " glomerata, 481. " " sparsiflora, 452, altocaulis, 507, 508, 509. approximata, 494. aquatilis, 495, 496, 497. " X stricta, 496. " var. cuspidata, 497. " elatior, 496. " " epigejos, 497. " " sphagnophila, 497. " " virescens, 497. arcta, 458, 459, 466, 486. argyrantha, 452, 478. arida, 467. 479, 481. 464, 472. 453, 480. Carex atlantica, 454, 456, 457, 458, 485. Bastardiana, 503. Bebbii, 449, 462, 478. Biclinellii, 450, 451, 468, 475. Bolanderi, 490, 491. " var. sparsiflora, 491. brizoides, 487. bromoides, 465, 490. brunnescens, 453, 458, 459, 460, 466, 489. " var. gracilior, 489. Buckleyi, 489. canescens, 453, 458, 459, 460, 466, 486, 487, 488, 491. j8, 489. var. alpicola, 459, 489. " " brunnescens, 489. " disjuncta, 466, 488. " dubia, 459, 487. " oregana, 458,486. " polystachya, 458, 486. " robustina, 459, 487. " " sphaerostachya, 489. " subloliacea, 459, 466, 488. " " vitilis, 489. " vulgaris, 458, 459, 486, 469. capillaris, 509, 510. FERNALD. CARICES OF SECTION HYPARRHENAE. 511 Carex capillaris, var. elongata, 509. Carltonia, 495. cinerea, 487. communis, 497, 498, 499, 500, 501, 502, 503, 504, 505. " var. Wheeleri, 502, 503, 504. Crawfordii, 461, 469. " var. vigens, 462, 470. cristata, 450, 462, 469, 472, 473. " var. mirabilis, 473. cristatella, 472. curta, 453, 487. " var. brunnescens, 489. cyperoides, 481. deflexa, 506. Deweyana, 465, 490. " var. sparsiflora, 491. dioica, 482. echinata, 447, 453, 454, 455, 456, 458, 465, 483, 485, 492^ " var. angustata, 465, 484. " " cephalantha, 455, 456, 465, 484. " conferta, 485. " excelsior, 465, 484. " " microstachys, 454, 455. " " orniantha, 465, 483. elaoliycarpa, 467, 492. elongata, 453, 487. Emmonsii, 498. exilis, 453, 400, 465, 482, 495. " var. androgyna, 482. " " squamacea, 482. festiva, 474. festucacea, 450, 451, 464, 475, 477. " var. brevior, 464, 474, 477. " mirabilis, 473. " tenera, 474. filiformis, 503. foenea,449, 451, 452, 462, 464, 472, 478. var. /8, 450, 451, 477. " 7, 470. " (?) ferruginea, 451, 477. " perplexa, 452, 464, 478, 480. " sparsiflora, 480. " (?) subulonura, 476. furva, 494. Gebhardii, 453, 459, 489. glareosa, 466, 493. . Carex gynocrates, 453, 460, 465, 482, 495. " var. monosperma, 482. heleouastes, 459, 467, 494. helvola, 492. interior, 454, 457, 458, 465, 485, 493. var. capillacea, 465, 485. Kunzei, 486. Lachenalii, 494. laeviculmis, 491. lagopina, 466, 487, 494. lagopodioides, 408, 469. " var. cristata, 472. " mirabilis, 473. " moniliformis, 469. " " scoparia, 468. lapponica, 488. Leersii, 483. leporina, 449, 462, 464, 408, 479, 494, 495. " var. bracteata, 472. Liddoni, 469, 471. lucorum, 505. marina, 495. mirabilis, 450, 462, 463, 472, 473. " var. perlonga, 462, 473. " tincta, 462, 473. monosperma, 482. muricata, 483. muskingumensis, 461, 463, 467. nigro-marginata, 506. norvegica, 466, 485, 492, 493. oronensis, 462, 471. ovalis, 479. pallida, 469. parviflora, 494. pedicellata, 499, 503, 504. var. Wheeleri, 503, 504. pennsylvanica, 500, 504, 505, 506. " var. lucorum, 505. " vespertina, 506. Persoonii, 489. pilulifera, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506. var. Leesii, 498, 499, 503, 504. " " Iongibracteata,498,499, 500, 502, 503, 504. " pallida, 498, 500. pinguis, 481. pratensis, 471. " var. furva, 452. 512 PROCEEDINGS OF THE AMERICAN ACADEMY. Carex praticola, 452, 461, 462, 464, 471. Redowskiana, 482. remota, 490. Richardi, 487. saltuensis, 507, 508, 509. sax umbra, 504. scirpina, 458, 485. scirpoidea, 457, 458, 485. scirpoides, 453, 454, 455, 457, 458, 485. scoparia, 447, 448, 449, 460, 461, 463, 467. " var. condensa, 461, 468. " " lagopodioides, 468. " minor, 447, 448, 449, 470. " " moniliformis, 449, 461, 468, 469. " " muskingumensis, 467. seorsa, 458, 460, 465, 486, 491. siccata, 461, 469. silicea, 463, 464, 476. sparsiflora, 453, 480. spliaerostacliya, 489. stellulata, 454, 455, 456, 483. 7, 485. " var. angustata, 455, 484. " conferta, 485. " scirpina, 457, 485. " " scirpoides, 457, 485. " " sterilis, 485. sterilis, 453, 454, 455, 456, 457, 458, 465, 483, 484. /3, 484. " var. aequidistans, 484. " " angustata, 484. " " cephalantha, 484. " excelsior, 455, 458, 484. straminea, 447, 448, 450, 451, 462, 463, 474, 477. " var. alata, 476. " " aperta, 451, 475. " brevior, 450, 451, 476, 477. " " chlorostachys, 472. " Crawei, 450, 451, 475. " " cristata, 472. " " cumulata, 472. Carex straminea, var. echlnodes, 463, 474. " ferruginea, 451, 477. " " festucacea, 477. " foenea, 472. " " intermedia, 472. " invisa, 475. " Meadei, 475. " minor, 474. " mirabilis, 473. " " moniliformis, 476. " Sclikuhrii, 477. " silicea, 476. " " tenera, 474, 475. " typica, 477. sychnocephala, 464, 481. tenera, 448, 450, 451, 463, 474, 475. " var. invisa, 463, 474, 475. " major, 475. " Richii, 463, 464, 474, 475, 476. " " subereeta, 477. tenuiflora, 466, 486, 491. tribuloides, 449, 450, 461, 468. var. Bebbii, 478. " cristata, 472, 478. " " moniliformis, 449,468, 469. " reducta, 449, 461, 468, 469, 474. " turbata, 461, 469. trispernia, 466, 492. Tuckermani, 449. umbellata, 506, 507. var. brevirostris, 507. " tonsa, 507. " vicina, 506, 507. vaginata, 507, 508, 509. " var. alto-caulis, 507, 508. varia, 498, 499, 500, 503, 504. " var. minor, 499, 503, 504. " pedicellata, 504. vitilis, 458, 459, 489. xerantica, 462, 464, 479. Vignea Gebhardi, 489. stellulata, 483. FERNALD. — CARICES OP SECTION HYPARRHENAE, 513 EXPLANATION OF PLATES.i Plate I. Carex muskingumensis : Fig. 1, spike; Fig. 2, perigynium. C. scoparia : Fig. 3, spike ; Fig. 4, perigynium. C. scoparia, var. condensa : Fig. 5, spike. C. tribuloides : Fig. 6, spike ; Fig. 7, perigynium. C. tribuloides, var. reducta : Fig. 8, spike. C siccata : Figs. 9, 10, spikes ; Fig. 11, perigynium. C. Crawfordii: Fig. 12, spike ; Fig. 13, perigynium. C. Crawfordii, var. vigens : Fig. 14, spike. C. oronensis : Fig. 15, spike ; Fig. 16, perigynium. C. praticola : Fig. 17, spike ; Fig. 18, perigynium. C. cristata : Fig. 19, spike ; Figs. 20, 21, perigynia. C. albolutescens : Figs. 22, 23, spikes ; Fig. 24, perigynium. Plate II. C/mirabilis : Fig. 25, spike ; Fig. 26, perigynium. C. mirabilis, var. perlonga : Fig. 27, spike. C straminea : Fig. 28, spike ; Fig. 29, perigynium. C. straminea, var. echinodes : Fig. 80, spike. C. tenera : Fig. 31, spike ; Fig. 32, perigynium. C. tenera, var. Richii : Fig. 33, terminal spikelet ; Fig. 34, perigynium. C. tenera, var. invisa : Figs. 35, 36, spikes. C Bicknellii : Figs. 37, 38, spikes ; Figs. 39, 40, perigynia. C. silicea: Fig. 41, spike; Fig. 42, perigynium. C. alata : Fig. 43, spike ; Fig. 44, perigynium. C. alata, xax./erruginea : Fig. 45, spike ; Fig. 46, perigynium. Plate III. C.festucacea : Fig. 47, spike ; Fig. 48, perigynium. C.festucacea, var. brevior : Figs. 49, 50, spikes ; Fig. 51, perigynium. C. Bebbii : Fig. 52, spike ; Fig. 53, perigynium. C.foenea: Fig. 54, spike; Fig. -55, perigynium. C.foenea, var. perplexa : Fig. 56, spike ; Fig. 57, perigynium. 1 The plates illustrating this synopsis were prepared by Mr. F. Schuyler Mathews from characteristic specimens. The figures of the spikes represent life-sized individuals, while those showing the inner faces of the perigynia are four times as large as in nature. VOL. XXXVII. — 33 514 PEOCEEDINGS OF THE AMERICAN ACADEMY. C. leporina : Figs 58, 59, spikes ; Fig. 60, perigynium. C. xerantica : Fig. 61, spike ; Fig. 62, perigynium. C. aenea : Figs. 63, 64, spikes ; Figs. 65, 66, perigynia. C. adusta : Fig. 67, spike ; Figs. 68, 69, perigynia. C. sychnocephala : Fig. 70. spike ; Fig. 71, perigynium. Plate IV. C. gynocrates : Figs. 72, 73, 74, 75, spikes ; Figs. 76, 77, perigynia. C. exilis : Figs. 78, 79, 80, 81, 82, spikes ; Fig. 83, perigynium. C. echinata : Figs. 84, 85, 86, 87, spikes ; Fig. 88, perigynium. C. echinata, var. ormantha : Fig. 89, spike. C. echinata, var. excelsior : Figs. 90, 91, spikes. C. echinata, var. cephalantha : Figs. 92, 93, spikes ; Fig. 94, perigynium. C. echinata, var. angustata : Figs. 95, 96, spikes ; Fig. 97, perigynium. C. sterilis : Figs. 98, 99, spikes ; Fig. 100, perigynium. C. interior : Figs. 101, 102, 103, spikes ; Figs. 104, 105, perigynia. C. seorsa : Figs. 106, 107, spikes ; Figs. 108, 109, perigynia. Plate V. C arcta. Figs. 110, 111, 112, spikes ; Fig. 118, perigynium. C. canescens : Fig. 114, spike; Fig. 115, perigynium. C. canescens, var. suhloliacea : Fig. 116, spike ; Fig. 117, perigynium. C. canescens, var. disjuncta : Figs. 118, 119, spikes ; Fig. 120, perigynium. C. bnmnescens : Figs. 121, 122, spikes ; Fig. 123, 124, perigynia. C. bromoides : Fig. 125, spike ; Fig. 126, perigynium. C. Deweyana : Fig. 127, spike ; Fig. 128, perigynium. C tenuijiora : Fig. 129, spike ; Fig. 180, perigynium. C. trisperma: Fig. 131, spike; Fig. 132, perigynium. C. elachycarpa : Fig. 133, spike ; Fig. 134, perigynium. C. norvegica : Fig. 135, spike ; Fig. 136, perigynium. C.glareosa: Fig. 137, spike; Fig. 138, perigynium. C. lagopina: Fig, 189, spike; Fig. 140, perigynium. C. heleonastes : Fig. 141, spike ; Fig. 142, perigynium. Fernald — Carex § Hyparihenae. Plate Fernald — Carex § Hyparrhenae. Plate Fernald — Carex § Hyparrhenae. Plate ill. Fernald — Carex § Hyparrhenae. Plate IV. Fernald — Catex § Hypanhenae. Plate V. l-l Wn2 Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. IS. — March, 1902. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — X. APATITE FROM MINOT, MAINE. By John E. Wolff and Charles Palache. With a Platk. MARINE BIOLOGICAL LABORATORY. Received J^^J^.//^'^=^.^ Accession No. ' ^ ^^ /..'. Given by ^^f>yr?< 0.1586 1.82 F . . . 2.38 2.40 0.1263) 1.03 Loss at 320° 0.04 0.04 Less 0 = F . 100.33 1.00 101.00 1.00 100.58 0.90 99.33 100.00 99.68 Sp. gr., 8.159 at 2 [)°C. A. Apatite from Minot, Maine. B. Calculated to 100. J. Apatite from Ceylon, Jannasch and Locke, loc. cit. Hence, P-205 RO F-OH, 1 3.42 0.57 1.5 5.13 • 0.85 or, Ca5P3[F.OH]Oi2. * By J. E. Wolff. t Calculated as OH = 0.55 per cent OH. 524 PROCEEDINGS OF THE AMERICAN ACADEMY. by Jannasch and Locke, * namely solution in nitric acid with addition of mercuric oxide, precipitation with ammonia and determination of phos- phoric acid, most of the lime and the other bases in the precipitate, while the rest of the lime and the alkalies were determined in the first filtrate. Water was determined directly by fusion with plumbic oxide mixed with potassium di-chromate. Pluorine was determined by the method of Fresenius, that is by heating the finely powdered mineral, mixed with previously ignited quartz, in a flask with strong sulphuric acid and absorbing the SiF4 in weighed tubes with the prescribed precautions. From the total weight obtained there was subtracted a correction for the general gain in weight of the absorption tubes due to the action of the air current on the rubber connections; etc., which had been previously determined by experiment. The process was continued for five hours or to a con- stant weight. Chlorine was absent. The mineral was soluble without residue in nitric acid. At about 320° C, the purple color disappears and the mineral becomes colorless or faintly yellow ; this change is accompanied by some decrepitation, by phosphorence, and the production of a vapor (in part water ?) which is deposited in drops on the walls of the tube ; there is also a petroleum- like odor. The loss of weight accompanying this change was deter- mined by gently heating three grammes of the mineral in a bulb tube in a current of dry air, weighing, and heating again cautiously in the current of air to complete decolorization, and determining the loss of weight. Optical PROPERTiES-t For the determination of the indices of refraction one of the best clear crystals was used, having a deep purple color and a brilliant basal plane. The determination was made with the Abbe crystal refractometer by the differential method t and for this purpose a glass prism was selected having the index n^^ = 1.6326, for which the boundary of total reflec- tion was carefully determined and the telescope clamped. The apatite crystal was then placed with its base on the glass hemisphere of the apparatus and the angular difference in the boundaries for w and e determined by the millimeter screw reading to six seconds. The boun- * Zeit. anorg. Chemie, 7, p. 154; also Jannasch, Praktischer Leitfaden d. Gewiclits Analyse, p. 259. t By J. E. Wolff. t C. Viola, Zeit. Krystall., 30, p. 438, and 32, p. 311. WOLFF AND PALACHE. — APATITE FROM MINOT, ME. 525 dary lines were sharp and the readings generally good. From the average of a large number of readings the following values were obtained : w^-„ = 1.G3353 ojLi = 1.63067 t^_c = 0.00191 a,-€ = 0.0020 £jj,==: 1.63162 eLi= 1.62865 The crystal was then heated to 320° C. or until decolorized and the indices again determined as follows : wj,.^ = 1.63346 ej,, = 1.63165 w — c = 0.00181 The change in the bi-refringence and in both indices is within the limits of error. The pleochroism is strong and the ray vibrating parallel to c (c) red- dish purple, perpendicular to c (w) deep violet blue. In converging light the thick clear crystals show on the basal plane a marked bi-axial character with the vertical axis the acute (negative) bisectrix and a division of the base into six sectors, in each of which the axial plane is parallel to a prism of the second order (or perpendicular to a lateral axis). These sectors come out clearly with the sensitive tint of the gypsum plate ; while some are almost perfect, others merge together and overlap at the centre of the crystal. The angle of the optic axes in one of these sectors was measured iu the optic angle apparatus : 2E,-, = 20°, but it appears to vary in different sectors of the same crystal. These phenomena of apparent orthorhombic symmetry were described and fig- ured by Mallard * for the violet apatite from Schlaggenwald, but appear to be even more distinct in the Maine apatite. While driving off the colonng matter destroys the pleochroism the anomalous bi-axial characters are not affected. Conclusion. The Minot apatite is a pure fluor-apatite with a fluorine content lower than that necessary for the formula Ca5F(P04)3 and indicating Groth's formula Ca5P3(F.OH)Oi2 as also deduced by Jannasch from the analysis quoted above. Rammelsberg f explained the low content of fluorine (and chlorine) in certain apatites as due to removal of these elements * Annales des Mines, VIL 10, 1876, p. 147. t N. J. M., 1897, 2, p. 38. 526 PROCEEDINGS OF THE AMERICAN ACADEMY. by a process of alteration, and therefore, according to him, all such apatites are altered. The freshness of the Minot material makes such a supposition inapplicable here. The axial ratio of the Minot apatite is the largest and the birefrin- gence the lowest recorded for the species. It was interesting to see what data existed for a comparison between fluorine or chlorine content and the axial ratio, specific gravity, and birefringence. The normal angle c to x and also the specific gravity of apatite have been held by numerous observers to diminish with increasing chlorine content. G. Rose (Ref. 3 below), the first to discover the fluorine and chlorine in apatite, stated as the result of his studies that the angles and specific gravity were alike in all apatites of like composition, but that the reverse of this statement was not proved. Von Kokscharovv (Ref. 2) extended this statement, holding that the normal angle c to a; of all chlorine-containing apatite was somewhat less than that of pure fluor-apatite. The analyses of Pusyrewsky (Ref. 18) seemed to confirm this view, and he further maintained that the specific gravity regularly decreased with increasing chlorine. Von Kokscharow (loc. cit.) incorporated the results of the last writer with his measurements and published a table showing the relations of the three values, but without comment. Baumhauer (Ref. 4) was the next to investigate the subject, and his measurements, analyses, and specific gravity determinations seemed to sujjport the supposed relations. His table has been republished by several authors with slight modifications (Dana, Syst., 1892, 764, and Weibull, Ref. 20 below).* In order more fully to test the matter a table has been prepared and is given below, arranged according to increasing values of the angle c to cc or of the axial ratio, and showing for all occurrences for which accurate crystallographic data existed, the specific gravity, birefringence, and chlorine and fluorine content so far as such data could be found. * In Baumliauer's table and in all later tables of the same kind the locality Schlaggenwald is given with c to x 40° 20', the largest value for this angle ob- served on apatite. Reference to tiie description of this occurrence by Schrauf (Ref. 8 below) showed that the measured crystals were poorly adapted to measure- ment, having curved faces ; and the average axial ratio calculated from all the measurements gave a value much lower, about 40° 17'. This locality was tliere- fore omitted from the table below. WOLFF AND PALACHE. — APATITE FROM MINOT, ME. 527 Tablk of Physic.a-L and Chkmical Characters of Apatite. Locality Comba di Compare ) Robert, Piedmont ^ Achmatowsk . . . Laacher See . . . Rothenkopf, Tirol . ( Zillerthal, Tirol Angle 0001 to 1011 o / // 40 4 40 40 40 6 Tirol .... 7 Ala, Piedmont 8 Kirjabinsk . . 'Jumilla, Spain 9 J ( Knappenwand, Tirol 40 11 Tirol (talc schist) . 12 Sulzbachthal, Tirol . 13 Berg Blagodat . . 40 14 Nordniarken ... 40 , ^ S St. Gotthard . . 40 ^M " . . 40 16 Tavetscli .... 40 17 Floitenthal ... 40 18 Schwarzenstein . . 40 19 Vestana (Mn. apatite) 40 20 Hiddenite Mine, N. C. 40 21 Turkistan .... 40 22 Tokowaja, Urals . . 40 < Ehrenfriedersdorf 40 24 Pisek 40 25 Elba 40 26 Minot, Me 40 27 Zwiesel (Mn. apatite) 28 Ilmen Mts 29 Sudjanka River . . G 21 G 21 10 46 40 10 4G 40 13 30 40 11 48 40 13 37 18 25 18 48 18 50 0.7284 0.7294 0.7294 0.7313 0.7325 0.7318 0.7326 15 26 0.7333 16 10 0.7337 16 10 0.7337 17 0.7340 17 0.7340 17 0.7340 17 0.7340 17 0.7340 17 20 0.7341 17 45 0.7343 18 10 0.7345 18 22 0.7346 18 22 0.7346 0.7346 0.7348 0.7348 Sp. Gr. M-e Cl 3.120 3.202 3.1495 0.51 0085 absent 1.54 .00435 .0044 3.126 >.2o5 trace 0.557 .00448 .0042 . . . . . • 0.24 1.98 . . . 0.47 3.54 3.153 . . . 0.028 0.03 3.63 • ■ * • . . 0.20 3.58 . . . .0026 . . . . . . 5 3.1.32 i 3.200 0.21 • • • 3.197 0.028 3.2154 . . . trace • • • 3.225 .0042 trace 3.74 3.199 trace 3.64 ( 3.201 ] 3.212 0.01 4.20 3.211 absent . . . . • . absent 2.27 3.094 ■ trace 3.56 3.159 .0020 3.169 . . . 3.216 . . . 3.178 . . . Ref. 2&18 3 4 5 6 7 4 2 8 2 9 19 5 10 4 10 10 7 11 2&3 4 12 12 4 20 13 14 5 15 16 absent 2.38 absent 2.15 trace 3.97 0.109 4.02 17 18 18 1 G. Boeris, Atti. della R. Ace. Sc. di Torino, 34, 609, 1899. 2 Kokscharow, Mat. zu Min. Russ., V. 86, 1866. 528 PROCEEDINGS OF THE AMERICAN ACADEMY. 3 G. Rose, Pogg. Ann., IX. 206, 1827. 4 H. Baumliauer, Zeit. f. Kryst., 18, 31, 1890. 5 Hoskyns-Abrahall (Inaug. Diss. 1889), Abs. Zeit. f. Kryst., 21, 389. e Heusser, Pogg. Ann., 87, 468, 1854. 7 K. Zimanyi, Zeit. f. Kryst., 22, 331, 189-3. 8 Schrauf, Ber. Acad. Wien, 62 (2), 745, 1870. 9 " " " " 42, 111, 1862. 10 Carnot, Bull. Soc. Franc. Mineral., 19, 135, 1896. 11 Flink, Bihang t. K. Sv. Vet. Aliad. H. Stockholm, 12 (2) No. 2, 42, 1886. 12 Schmidt, Zeit. f. Kryst., 7, 551, 1883. 13 Hidden & Washington, Zeit. f. Kryst, 14, 299, 1888. 14 Jeremejew & Nikolajew, Zeit. f. Kryst., 11, 389, 1886. 15 Vrba, Zeit. f. Kryst., 15, 464, 1889. 16 Artini, Rendic. R. Ace. Lincei, Roma, 4 (2), 259, 1895. 17 Sandberger (Hilger), N. J. Min. 1885, 1, 171. 18 Pusyrewsky, Verb. k. k. Mineral. Gesell. St. Petersburg, 1859-1860 (cited by Baumhauer, No. 4 above). 19 Latterman, Rosenbusch, Mik. Phys., I. 409, 1892. WeibuU, Gcol. For. Forh., Stockholm, 20, 63, 1898. ^^ } " " " " " 8, 492, 1886. One point brought out by the preparation of this table is the lack of studies of apatite in which on the same material all these characters have been determined. It is also to be noted that no crystallographic data whatever appear to have been secured on what could fairly be called a chlor-apatite, the highest chlorine content in the table being about 0.5 per cent only. Without such data it does not seem that the theory of Pusyrewsky and Baumhauer that axial ratio decreases with chlorine content can be considered as established. Moreover exceptions to that rule may be noted in the table, notably Nos. 5, Zillerthal, and 9, Jumilla. On the other hand it seems fairly safe to accept the statement that an apatite with large angle c to x (40° 17' or more) will be practically free from chlorine. The table shows that absolutely no definite relation exi.sts between the specific gravity and the chlorine content. Nos. 2 and 9, from Achraatowsk and Jumilla, having about 0.5 per cent chlorine, have specific gravity respectively 3.12 and 3.235 ; while the chlorine-free varieties have specific gravities from 3.09 to 3.22, or practically the same range. Observations on the birefringence are few, but so far as they go do not point to a definite relation to the chlorine content. Harvard Mineralogical Laboratory, December, 1901. ^ Wolff and Palache — Apatite. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 19. — March, 1902. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — XL A DESCRIPTION OF EPIDOTE CRYSTALS FROM ALASKA. By Charles Palache. With a Plate. MARINE BIOLOGICAL LABORATORY. Received j-^-^^^^:'^^ Accession No. y.-../Jl>^.7.^ Given by .4-fc-^i^r:^ v ^-■':t-«l^^ 6>ti!4 «?.^;.v> (T'^O' ^ (T41), E (T51), q (221), O (544),* j (755),* X (322), y(2ll), R (ill), * (il3). Of these forms c, a, b, u, r, and n are nearly always present and define the habit of most crystals, z, e, o, and q are also found on many crystals ; the remaining forms are rare and subordinate in development. The forms may be characterized as follows : c (001) always present, bright and unstriated, often broad. b (010) always present, always dull and striated parallel to intersec- tion with n ; generally has narrow faces. a (100) always present ; the largest face on tabular crystals; bright butt often striated faintly horizontally. u (210) always present, generally with large bright faces. z (110) generally quite subordinate to u but frequently present as a narrow face and always pitted and dull. o (Oil) bright face, generally small. e (101), i (T02), N (304), 1 (201) are infrequent forms in orthodome zone, generally narrow, bright and unstriated when they do occur. This zone is remarkably jDOor in forms and free from striation as compared with most crystals of epidote. r (TOl) always present, broad, generally striated lightly and less brilliant than c with which it is easily confused on the crystals. PALACHE. — EPIDOTE CRYSTALS FROM ALASKA. 533 n (Til) always present, often large, brilliant, and striated. The only form found in the re-entrant angles rarely found on twin crystals. a (212) present on one crystal only (figure 7) as a large, fairly bright face. F (554), Z (232), 4> (353), <^ (T21), 8 (T41), and E (T51) are pyra- mids of the zone [Til to 010]. Unimportant forms but several of them sometimes present on single crystals as shown in the drawings. F (454), a rare form for epidote, has been reported heretofore only from Pers- berg, Sweden* by Flink ; he determined it by a single bright face in two zones, no angles being given. It was found with a single face on each of two crystals and was measured as follows : Measured. Quality. Calculated.

p i54 -160° 40' 67° 21' fair -160° 43' 67° 18' (010 as pole) 128° 01' 29° 33' fair 128° 18' 29° 27' (normal position) and S were determined solely by contact measurements ; Z and <^ by contact measurements and zonal relations. q (221) often present, sometimes large, always dull. O (544), j (755), X (322), y (211), and R (ill) are pyramids of the zone [Til to 100]. Of these forms y alone is common; O and j are new to epidote and X and R are rare. 0 was measured on three crystals (two of them twins) with six faces as follows : Measured. Quality. Calculated (010 as pole). 344

f ) Crystal No. ^4, -42° 04' 38° 30' poor 42° or 39^^ '33' (( «( 5, 42 57 39 11 fair 42 07 39 33 137 06 38 58 fair 137 53 39 33 « (.( 6, -42 13 39 20 good -42 07 39 33 -137 37 39 19 good -137 53 39 33 136 48 39 18 fair 137 53 39 33 Average - or 180° ^n -42° 07' 39= ' 33' -42° 37' 39° 06' The agreement of measured and calculated angles is not very close, but the form seems assured. j was measured on two twin crystals with three faces as follows : * Bihang t. K. Sv. Vet. Akad. H. Stockholm, 12, No. 2, 1886. 534 PROCEEDINGS OP THE AMERICAN ACADEMY, Measured. Quality. Calculated. 755 0 p

6 \ \_ Cr ' h 2n (> Of NN a) 4 N \ ^»> "'L' H3. 2 N \ *-~. ^^ the mean of several observations : MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 549 Boiling Point. Heat of Vaporization in Calories. Hexane, C6Hi4 68 79.4 Heptane, C7H16 98 74. Octane, CgHig 1-25 71.1 Boiling Point. Heat in Calories. 68-70 87.3 90-92 81. 98 7o-7 118-119 71.7 Determinations were also made on the methylene hydrocarbons that could be volatilized in this form of apparatus : Hexamethyleue, CgHia Dimethylpentamethylene, C7H14 Methylhexamethylene, C7H14 Dimethylhexamethylene, CsHje These results indicate a rapid falling oflf in latent heat, with increase in molecular weight. It is to be regretted that we had not the metallic condenser, which would have enabled us to carry these observations up to include the less volatile hydrocarbons of both series. Advantage will be taken of the earliest opportunity to continue this work. The hydrocarbons used in the work described in this paper were pre- pared with assistance granted by the Academy from the C. M. Warren Fund for Chemical Research. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 21. — April, 1902. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE, UNDER THE DIRECTION OF E. L. MARK.— No. 129. CERTAIN SENSE ORGANS OF THE PROBOSCIS OF THE POLYCHAETOUS ANNELID RHTNCHOBOLUS . DIBRANC HIATUS. By Adele Oppenheimer. With Six Plates. MARINE BIOLOGICAL LABORATORY. Received ry<^^-^ ■ //.■/. f..^.!^.., Accession No. ^^ /.^'P ■. Given by i^ap. Papilla. pi'tn. Peritoneum. lis. co'nt. Connective tissue. In many figures not only the papilla is shown, but also a portion of the under- lying parts. PLATE 1. Fig. 1. Longitudinal section of the everted jjroboscis showing: (1) the sheatli of the proboscis; (2) the bearer of the jaws and its sulidivision ; and (3) the lemniscus {tinn.), wliich marks the boundary between (1) and (2). Narcotized in a mixture of sea-water and alcohol; fixed in Miiller's fluid; stained witli Beale's ammonia carmine. X circa 11. Fig. 2. Cross section of the partial!}' everted proboscis in the region of tlie four lemnisci {Imn.), sliowing, among other things, a diagrammatic representation of the papillae and the connection of their sensory cells with tlie circular and tlie longitudinal nerves, and also the nerve fibre (n. r.') passing to the membrane which invests the circular muscles. Chloroform, methyleu blue, Bethe's ammonium molybdate for invertebrates. X 14.5. Fig. 3. Papilla from a cross section of the proboscis, showing two "basal" and three "axial" cell nuclei. Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 675. Fig. 4. Longitudinal section of a papilla, from a cross section of tlie proboscis, showing the two axial nuclei and one of the two basal nuclei, also fibrous struc- tures entering the base of the papilla. Treatment the same as in Fig. 3. X 585. Fig. 5. Longitudinal section of a papilla, from a sagittal section of the proboscis, showing two sensory axial cells with peripheral sensory termination and prolongation of the basal end of each into a slender nerve fibre. Chloroform, niethylen blue, Bethe's ammonium molybdate for invertebrates. X 050. Fjg. 6. Papilla from cross section of proboscis viewed from behind, showing the corrugations of the cuticula on the posterior face of the papilla, and in optical section the two zones of living substance togetlier with one of the basal nuclei. Sea-water aud alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 5b5. OPPENHEIMERr SENSE ORGANS RhYNCHOBOLUS Plate 1 • qna. 9i >mn -.' ■nrrp m. ^1 \ 2 ; ■ f.-, Lr~^'"~# J ^ if ^ii/ V / /^' its. CO III. 'fill Ig. ■CtctAi'tk. co'e^. mu.lg:.. ' \ Imn pt'lri ::9 rim.crc. :i.Ms::e!, :';:;. SiiC PLATE 2. Fig. 7. Portion of cross section of proboscis, showing structure of lemniscus. Sea-water and alcoliol, vora Ratli's mixture. X i^OO. Fig. 8. Part of Fig. 7 enlarged. X ca. 400. Figs. 9a, 96. Sections of a papilla perpendicular to its axis. Figure 9a represents the more distal of tlie two sections, and sliows tlie form and position of tiie three axial nuclei ; Figure 9b shows the two basal nuclei. The anterior face of the papilla is directed toward the top of the plate in both cases. Sea-water and alcohol, corrosive sublimate, iron liaematoxylin. Fig. 10. Portion of the cross section of an everted proboscis, showing one of the eigliteen longitudinal nerves (n. Ig.) cut crosswise, tlie peripheral nerve plexus, the union of tlie centripetal jirocesses from tlie sense cells witii the longitudinal nerve (in tlie case of the third papilla from the upper margin of tlie Figure, one of the two nerve fibres bends to tiie left when it enters the nerve plexus, tiie otlier to the right), a radial nerve {n. r.) following tlie surface of the longitu- dinal muscle (this is sketched in from an adjacent section), and another radial nerve (n. r/) passing directly to tlie membrane which is immediately superficial to the circular muscles. Chloroform, methylen blue, Bethe's ammonium molybdate for invertebrates. X 145. Fig. 11. Papilla from a cross section of proboscis showing one of the basal and one of the axial nuclei ; there are two large granulations in the basal nucleus. The differentiation of the distal portion of the sense-cell is not well shown. Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 460. OppENKEiMERr Sense Organs Rhynchobolus. Pla-^'^'' ? .S %i# 9^ V-'^^'^^:. '%. >^u --^ &b AO.l- 3Me:;-:.,i:,>iiK: PLATE 3. Figs. 12, 14, 15, 18, 19, 20. Preparations made hy use of chloroform, methylcn blue, anil Bcthe's auinionium niolybdate for invertebrates. Figs. 13, 16, 17. Prepared by use of sea-water and alcohol, sublin.ate-acetic, Kleinen berg's haematoxylin. Fig. 12. Papilla from cross section of proboscis, showing connective-tissue fibres passing into tlie papilla; deep coloration of terminal fibrils; the nerve fibres bending in opposite directions where they enter tlie nerve plexus. X 080. Fig. 13. Papilla from cross section of proboscis, sliowing corrugations of posterior face of papilla, and the outline of one of tlie basal nuclei. X 460. Fig. 14. Papilla from sagittal section of proboscis; tlie two sensory (axial) cells, tlieir peripheral terminations, and their proximal nerve-fibre prolonga- tions stained blue. The nucleus of one of the sensory cells more deeply stained than the cell body. Cuticula distended and detached from substance of the papilla by treatment. X 710. Fig. 15. Papilla from cross section of proboscis, showing deeply stained axial body, from wiiich a single peripheral, deeply stained process extends to tlie apex of papilla, where it terminates in a specialized and stained area ; the contents of the papilla in great part fibrous. X 1020. Fig. 10. Somewhat oblique cross sections of two papillae from a cross section of the proboscis. In one papilla are two basal nuclei and a part of one of the axial nuclei ; in the other the three axial nuclei cut crosswise. X 070. Fig. 17. Cross sections of two papillae from a cross section of proboscis. In one are seen two axial nuclei, each surrounded with a clear area; in the other a basal nucleus and portions of two axial (') nuclei. X 070. Fig. 18. Papilla from cross section of proboscis. The two sensory cells are stained throngliout ; their distal prolongations iiave a more or less spiral course and terminate in a cluster of discs at the apex of the i)apilla. Vacuoles large. X 715. Fig. 19. Papilla from cross section of proboscis, showing that where the cen- tripetal fibres from two sensory cells meet the nerve plexus, one bends to the right, the other to the left. X 725. Fig. 20. Papilla from cross section of proboscis, showing the basal position of the sensory cell body f?) ; the basal end of each sensory cell is prolonged into a slender nerve fibre. X G82.5. OppENHEiMERr Sense Organs Rhynchobolus. Plate 3. /y /> /4 I --,_ Pi r' i^^ />' ;\. *i^ •(T \. \ ■.*». I / 77 Jv-^^/'] / niha.. . \ -iv. 19 ■JO ( )1 AO.del BReisel,: PLATE 4. Figs. 21-23, 25, 27, 29, 30. Longitudinal sections of papillae from cross sections of proboscis. Figs. 21-23, 25, 29. Preparations made by use of cliloroform, methylen blue, Bethe's ammonium molybdate for invertebrates. Figs. 24, 30. Preparations made by use of sea-water and alcohol, sublimate- acetic, Kleinenberg's haematoxylin. Fig. 21. Three sensory cells, two showing peripheral fibres and terminations. X 715. Fig. 22. Papilla showing a row of axial vacuoles. Sea-water and alcohol, Muller's fluid, Beale's ammonia carmine. Fig. 23. The nuclei of the two sensory cells distinguisliable from the cell body by their deeper stain. Peripheral and proximal fibres stained. X 710. Fig. 24. Basal nucleus of a papilla showing a large single nucleolus. X 670. Fig. 25. Highly vacuolated papilla, fibrils and discs of the sensory termination stained blue, the deep ends of each of the sensory cells prolonged into a few processes, which unite to form the single nerve fibre. X 700. Fig. 26. Cross section of a small papilla, showing a nucleolus in each basal nucleus. Sea-water and alcohol, vom Path's mixture. X 680. Fig. 27. Papilla showing one of the basal nuclei with large nucleolus, and the passage of connective-tissue fibrils into the papilla. Sea-water and alcoiiol, vom Path's mixture. Fig.*8. Papilla from sagittal section of proboscis, showing three axial nuclei and two basal nuclei. Sea-water and alcohol, sublimate, iron haematoxylin. Fig. 29. Papilla from cross section of proboscis, showing numerous small vacuoles, fibrils and discs of sensory termination. The basal end of each sen- sory cell is prolonged into a slender nerve fibre. X 730. Figs. 30a-30f?. Four successive sections from a single papilla. Fig. 306 shows one of the basal nuclei ; Fig. 30c, the other basal nucleus and the two axial nuclei. In the region of the apex of the papilla, there is an interruption in the cortical layer of finely granular substance, not well shown, and the region is traversed by fine fibres. X 585. Fig. 31. Fibrils from the peripheral termination of a sensory cell. Oppenheimer.- Sense Organs Rhynchobolus. Plate 4. A^de! B MeissUilti Bosltin PLATE 5. Fig. 32. From a photograph of the cuticula of the proboscis stripped bj' macera- tion (consult text, p. 555) and mounted on glass slide. The part of the figure nearest the top of the plate is toward the anterior end of the everted proboscis. To show the arrangement of the papillae in transverse rows. X 22.5. Fjg. 33. From a photograph of a preparation similar to that of Fig. 32, showing the appearance of the cuticula and attached papillae near the posterior end of the everted proboscis. Kine of the eighteen longitudinal columns of papillae are shown. X 18 5. Opfenheimer. -Sense Organs Rhynchobolus. Plate 5. ^^ li if "tM^-.^V ,v.t'fl'»A^ '-^^, ^ »r^*r >^<^ ^'ij-S* f 32 ;«*»^'*- S. 33 PLATE 6. Fig. 34. Highly magnified view of portions of four transverse rows of papillae, to show the corrugations of the flattened and dried papillae, and the circular wall and pit of the cuticula at the apex of the papilla, marking the position of the termination of the sensory cells. X 110. Oppenheimer. -Sense Organs Rhynchobolus, Plate 6. 34 Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 22.— May, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XLL THE COMPOSITION OF PETROLEUM. By Charle8 F. Mabery. ON THE HYDROCARBONS IN PENNSYLVANTA PETROLEUM WITH BOILING POINTS ABOVE 216°. Aid in the Work described in this Paper was given bt the Academy from the C. M. Warren Fo-d for Chejucal Research. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XLL THE COMPOSITION OF PETROLEUM. By Charles F. Mabery. ON THE HYDROCARBONS IN PENNSYLVANIA PETROLEUM WITH BOILING POINTS ABOVE 216°. Received March 24, 1902. Presented April 9, 1902. In a former paper* the principal hydrocarbons in Pennsylvania, Ohio, and Canadian petroleum below 216°, were shown to have the composition represented by the general formula CnHgn + a- Concern- inor the constituents with higher boiling points very little is known. Pelouze and Cahours f collected distillates to which they gave the fol- lowing formulas : — 216°-218° 236°-240° 255°-260° 280° C13H28 C14H30 U15H32 C16H34 From paraffiue the following hydrocarbons have been separated (Beil- stein's Handbook) : — 212°-215° 230°-235° 252°-255° 273°-275° C13H28 ^14^130 ^15 "32 ^leHsi So far as I am aware, these are the only allusions to the composition of Pennsylvania petroleum in these portions. It appears that the dis- tillations were made under ordinary atmospheric pressure in presence of air with no attempts to avoid decomposition under these conditions. Then, furthermore, as I have suggested in a former paper, the high specific gravity of the distillates separated by Pelouze and Cahours indicate that their distillates were obtained from Canadian petroleum. It does not appear that any attempts have been made to ascertain the molecular weights of the individual hydrocarbons. Indeed this has been * These Proceedings, XXXII. 12L t Ann. China. Phys. (4), 1, 5 (1864). 666 PROCEEDINGS OF THE AMERICAN ACADEMY. possible only within recent years since the freezing and boiling point methods for the determination of molecular weights have been known. Then it is not possible to determine the vapor densities of these hydro- carbons, because, as I have recently ascertained, even in vacuo small quantities of the hydrocarbons such as are used in vapor density deter- minations, undergo serious decomposition ; and this occurs even in oils that have been distilled many times over in bulk in vacuo. In the ear- lier work, it was evidently assumed that a few distillations under atmos- pheric pressure were sufficient to collect the individual hydrocarbons within the limits of their boiling points, sufficient at least to afford reliable data as to their composition. A glance at the small differences in percentage composition is sufficient to show that it is not possible by analysis alone of products even well purified to distinguish between homologous members of a series, although such analysis may define the series. But the chief difficulty is to obtain each hydrocarbon uncontamiuated by any admixture of its homologues or by products of decomposition. This is well illustrated by the experience of Markownikoff in separating the hydrocarbons in the Russian oil, who found it impossible to collect distillates closer than limits of five degrees on account of decomposi- tion. That the same is true perhaps in a less degree in distillates from Pennsylvania oil is evident whenever distillation is made of the higher portions under atmospheric pressure. The rank odor is evidence of cracking. Yet the constituents with higher boiling points are under the influence of vapor tension as much as the constituents with lower boil- ing points, and consequently require as prolonged distillation for com- plete or approximately complete separation. In my experience it is only possible to obtain even an approximate separation by exclusion of air and depression of boiling points. In this manner the higher hydrocarbons may be distilled any number of times with no appreciable decomposition. The only limit is the patience of the operator. But the stability of these hydrocarbons is evidently dependent on the influence of mass. Since as mentioned above, while distillation of any considerable quantity of tlie oil may be carried on indefinitely, a limited quantity cannot be volatilized even in vacuo without decomposition. Many attempts to determine the vapor density of the hydrocarbons in Pennsylvania and California petroleum by volatilization in vacuo according to the method of Lunge and Neu- berg have failed on account of cracking, even so far as the separation of sooty carbon from the members with high boiling points. MABERY. — THE COMPOSITION OP PETROLEUM. 567 In September, 1896, I set out to ascertain the composition of the principal hydrocarbons in Pennsylvania petroleum above 216° so far as they can be separated by distillation on a laboratory scale. Through the courtesy of the Standard Oil Company, I procured a barrel of crude oil from Oil City and this material has been used to separate the hydro- carbons that will be described in this paper. That this oil was an approximately average specimen of Pennsylvania petroleum, appears from its properties. A determination of the specific gravity of the crude oil at 20° gave 0.8095. A combustion of the oil dried over sodium gave the following percentages of carbon and hydrogen : Carbon, 85.80 ; Hydrogen, 14.04. Eight hundred grams distilled in the ordinary way in the following proportions : — 50°-150° 150°-200° 200°-250° 250° -300° +300° 166 88 83 100 337 Fifty -six kilos of the crude oil was distilled in quantities of 10 litres each in a porcelain still, collecting under atmospheric pressure to 200°, and within limits of 10° under a vacuum of 50 mm. to 300°, then within limits of 5°, and finally within limits of 2°. After eight distillations the following proportions collected : — 124°-126° 136°-I38° 156°-158° 174°-176° 188°-199° Grams, 125 145 240 205 240 199°-201° 210°-212° 226° -228° 242°-244° 225 335 150 130 Since the weights of these fractions represent all that came from the original crude oil, it is possible to gain a very general idea of the pro- portion of the hydrocarbons which are contained in the crude oil. But such estimation must be only approximate from the fact that any dis- tillation however thorough gives only an approximate separation, and a considerable portion of any hydrocarbon must be contained in the in- termediate distillates. The percentages of the weights are as follows : — C13H28 C14H30 C15H32 C16H34 L17H36 124°-126° 136°-138° 156°-158° 174°-176° 188°-199° 0.22 0.26 0.43 0.37 0.43 per. cent. C13H33 C19H40 C20H42 C21H44 199°-201° 210°-212° 230°-232° 242°-244° 0.40 0.60 0.27 0.23 per, cent. 568 PROCEEDINGS OP THE AMERICAN ACADEMY. In the intervals between these fractions the weights were much smaller. After the eighth distillation each fraction was agitated at first with common concentrated sulphuric acid until the acid was not much colored and then several times with fuming sulphuric acid. That the distillates consist almost entirely of the principal hydrocarbon is shown by the slight change in specific gravity by the acid treatment : — 182°-184° 0.8100 Original distillate. 0.8093 After treatment with acid. There was some loss in weight of the fraction by the acid treatment, but it was doubtless due for the most part to solution of the principal hydrocarbons in the acid. The weights of the fractions before and after treatment were as follows : — 156°-158° 174°-176° 0.805 0.8064 0.7992 0.8031 156°-158° 174° -176° 182°-186° 240 215 205 195 190 155 This solvent action has been observed in other oils with high boiling points in continuous treatment with fuming sulphuric acid, which caused a gradual loss without changing materially the specific gravity. After the purification with the acid, distillation was continued through a Hempel column filled with glass beads or broken glass, under 50 mm. within limits of one degree, until the hydrocarbons collected in consider- able quantities. After the thirtieth distillation, the hydrocarbons came together within the following limits : — 124°-126°, 142°-143°, 158°-159°, 173°-174°, 189°-190°, 198°-199°. Even after nearly continuous distillation of sixteen months, these products showed very little indication of decomposition. Leaks in the apparatus immediately cause decomposition, as shown by a disagreeable odor, and the appearance of the distillates. So long as air is excluded from the hot vapors there is no danger of decomposition. But as we found in attempting to ascertain the boiling points under atmospheric pres- sure, a single distillation in air causes a very rank odor of decomposition.* * The difference in stability of the constituents of different petroleums is shown by their behavior when air comes in contact with the hot vapors. In acci- dents that have occurred during distillation, letting in air on the hot vapors, in the case of Pennsylvania petroleum the still becomes filled with dark vapors, but in a MABERY. — THE COMPOSITION OF PETROLEUM. 569 In determining the boiling points of these hydrocarbons under at- mospheric pressure, 70 grams of the fraction 124°-126° distilled as follows, under 7 GO mm. and with the mercury column all within the vapor : — 224°-225° 225°-226° 226° -227° 227°-228° 228°-229° Grams, 4 28 26 3 3 Colored residue, 6 The portions between 225° and 227° collected almost entirely between 225° .5 and 226°.5. The fraction 142°-143° nearly all distilled at 237°-238° atmospheric pressure, the fraction 158°-159° at 256°-257°, the fraction 173°-174° at 274°-275°, the fraction 188°-189° at 288°-289°, and the fraction 198°- 199° at 300°-301°. The hydrocarbon dodecane C12H26 was identified in the fraction 214°-216°.* Tridecane, CjsH 28' The next homologue, tridecane, was sought for in the series of distil- lates that collected between 215° and 235°. After carrying these fractions eight times through a Hempel bead column a larger portion, 200 grams, collected at 221°-222°. This portion was distilled twenty- four times, when 70 grams collected, as shown above. The specific gravity of the distillate before further treatment was 0.7866, and after thorough agitation with fuming sulphuric acid, 0.7834. A combustion gave the following values for carbon and hydrogen : — 0.1506 grm. of the oil gave 0.4690 grm. CO2 and 0.2028 grm. H2O. Calculated for CijHjg. Found. C 84.78 84.94 H 15.22 14.96 The molecular weight of this oil as determined by the Beckman method at the freezing point of benzol, in the hands of different workers, corre- sponded to that of C13H2S. distillation of Russian petroleum, air accidently admitted caused such a violent explosion ftiat the thermometer was sent violently across the room and broken against the wall. * These Proceedings, XXXII. 138. 570 PROCEEDINGS OF THE AMERICAN ACADEMY. I. 1.1209 grm. of the oil and 36.3043 grms. benzol gave a depression of 0°.82. II. 1.2502 grm. of the oil and 33.3631 grms. benzol gave a depression of 1°.015. III. 1.496 grm. of the oil and 32.9131 grms. benzol gave a depression of 1°.205. Calculated for Found. CiaUjs- !• II. in. 184 184.5 181 184.9 In still further confirmation of the formula of tridecane, the index of refraction was determined, and its molecular refraction calculated. The index was found to be 1.4354 at 20*^, and the molecular refraction as follows : — Calculated for CuHja* Found. 61.94 61.44 Monochlortridecane, C13H27CI. — In the preparation of the chlorine de- rivative of tridecane, chlorine was allowed to act on the hydrocarbon in screened sunlight, over water. With care to avoid an excess of chlorine, the product consisted for the most part of the monochloride. It was fractioned in vacuo under 12 mm. several times until considerable of the oil collected at 135^-140°. This fraction gave as its specific gravity at 20°, 0.8973. A determination of chlorine gave a percentage required for the monochloride : — 0.1920 grm. of the oil gave 0.1273 grm. AgCl. Required for CijHjjCl. Found. CI 16.23 16.39 The molecular weight as determined at the freezing point of benzol corresponded to the same formula : — 0.4585 grm. of the oil and 18.35 grms. benzol gave a depression of 0°.568. Calculated for C13H27CI. Found. 218.5 216 A determination of the index of refraction confirmed the same formula; the index as determined was 1.451, corresponding to the molecular refraction : — , Calculated. Found. 65.71 66.67 MABERY. — THE COMPOSITION OF PETROLEUM. 671 TeTRADECANE, C14H30. The fraction 142° -143°, collected after the twenty -fourth distillation, gave as its specific gravity, after drying over sodium, 0.7848. After agitating with concentrated sulphuric acid, washing, and drying over sodium, it gave 0.7847. After treatment with fuming sulphuric acid it gave 0.7814; this determination, like the others, was made at 20°. A determination of the molecular weight of this fraction purified with fuming sulphuric acid gave the following result : — I. 1.1049 grm. of the oil and 36.8505 grms. benzol gave a depression of 0°.735. II. 1.052 grm. of the oil and 35.970 grms. benzol gave a depression of0°.7l8. Calculated for Found. CuUao- I n. 198 199.9 199.5 A combustion gave the following percentages of carbon and hydrogen : 0.1502 grm. of the oil gave 0.4698 grm. CO2 and 0.2024 grm. H2O. Calculated for CijIIso. Found. C 84.84 85.02 H 15.16 14.96 This specimen was purified with common concentrated acid ; another portion purified with fuming sulphuric acid gave slightly different pro- portions : — 0.1458 grm. of the oil gave 0.4532 grm. CO2 and 0.1970 grm. H.,0. Calculated for Cj^^H^ Found. C 84.84 84.76 H 15.16 15.02 The boiling point of this fraction under 760 mm. was 236°-238°. On account of decomposition when the oil is distilled in air, it is ditficult to determine the boiling point with great precision. A determination of the index of refraction of this hydrocarbon gave 1.4360, which corresponds to the following molecular refraction : — Calculated or C14H30. Found. 66.54 66.36 572 PROCEEDINGS OF THE AMERICAN ACADEMY. Monochlortetradecane, C14H29CI. — Since only small quantities of the purified hydrocarbons were available for the study of the chlorides, great care was necessary to avoid too high chlorination. Most of the hydro- carbons gave only sufficient of the chlorine derivative to verify its formula by the percentage of chlorine. The chlorine product obtained from tetradecane was fractioned in vacuo until it collected in larger quantities at 150°-153° under 20 mm. A determination of chlorine gave the following result : — 0.1966 grm. of the oil gave 0.1245 grm. AgCl. Calculated for C14H29CI. Found. CI 15.25 15.65 Its specific gravity at 20° was found to be 0.9185. The quantity of product was not enough for other determinations. Another portion of the chlorine product collected at 175°-180°, 17 mm., wliich gave as its specific gravity at 20°, 1.032. A determination of chlorine gave the value required for the dichloride : — 0.1937 grm. of the oil gave 0.2125 grm. AgCl. Calculated for Ci^HogClj. Found. CI 26.55 27.12 A determination of molecular weight at the freezing point of benzol confirmed the dichloride : — 1.3407 grm. of the oil and 19.81 grms. benzol gave a depression of 1°. 255. Calculated for C14H28CIJ. Found. 267 264.3 PeNTADECANE, C15H32. The specific gravity of the fraction 158°-159° (50 mm.) dried over sodium was found to be 0.8054 at 20°. After treatment with concen- trated sulphuric acid it gave 0.7939, and after thorough treatment with fuming'sulphuric acid it gave 0.7896. The molecular weight was determined by the Beckman method : — I. 1.050 grm. of the oil and 35.9775 grms. benzol gave a depression of 0°. 675. II. 1.3946 grm. of the oil and 23.2679 grms. benzol gave a depression of 1°.37. Calculated for Found. C,,H3j. I. II. 212 211 212 I. II. 85.21 84.87 14.80 15.20 MABERY. — THE COMPOSITION OF PETROLEUM. 573 Combustion I. was made of the unpurified distillate dried over sodium ; and combustion II., of the oil after treatment with fuming sulphuric acid : — I. 0.1440 grm. of the oil gave 0.4500 grm. CO2 and 0.1919 grm. HoO. II. 0.1608 grm. of the purified oil gave 0.5002 grm. CO2 and 0.2198 grm. H,0. Calculated for Found. V'-trjUotj. C 84.92 H 15.08 In determining the boiling point of pentadecane under atmospheric pressure, it distilled almost completely at 256°-257°. A determination of the index of refraction gave 1.4413, from which the molecular refraction was calculated : — Calculated for €,51132. Found. 71.15 70.49 Dichlorpentadecane, C15H30CI2. — "With the small quantity of the hy- drocarbon at hand, we did not succeed in limiting the action of chlorine to the formation of the monochloride. Fractioned in vacuo under 13 mm. the chlorinated product collected for the most part at 175°-180°. This product gave as its specific gravity at 20°, 1.0045. A Carius determina- tion for chlorine gave the following percentage : — 0.<1411 grm. of the oil gave 0.1462 grm. AgCl. • Calculated for CuHjdCIj. Found. CI 25.28 25.63 The molecular formula was established by a determination of its molec- ular weight : — 1.4308 grm. of the oil and 18.53 grms. benzol gave a depression of 1.336. Calculated for C15H30CI2. Found. 281 283.2 Hexadecane, CisHj^. The heap that collected at 174°-175°, 50 mm., after the thirtieth distillation gave as its specific gravity at 20°, 0.8000. After treatment with concentrated sulphuric acid it gave 0.7964, and after treatment with fuming sulphuric acid, 0.7911. It distilled almost completely at 275°- 574 PROCEEDINGS OP THE AMERICAN ACADEMY. 276° uuder 760 mm., barometric pressure. In determining the molecu- lar weight of this fraction at the freezing point of benzol, it gave the formula C16H34 : — I. 1.1507 grm. of the oil and 35.27 grms. benzol gave a depression of 0°71. II. 1.1833 grm. of the oil and 35.63 grms. benzol gave a depression of 0.715. Calculated for Found. CicH34. I II. 226 225.2 227.6 Determinations of carbon and hydrogen were made in the unpurified distillate (I.), in a portion purified with concentrated suljjhuric acid (II.), and in a third portion purified with fuming sulphuric acid (III.), vvith the following results : — I. 0.1477 grm. of the oil gave 0.4600 grm. CO. and 0.1973 grm. HgO. II. 0.1454 grm. of the oil gave 0.4522 grm. CO. and 0.1986 grm. H.O. III. 0.1454 grm. of the oil gave 0.4516 grm. CO., and 0.1971 grm. H2O. Calculated for I. Found. II. III. c 84.96 84.94 84.80 84.60 H 15.04 14.84 15.18 15.06 The index of this hydrocarbon was found to be 1.4413, from which the molecular refraction was calculated : — Calculated for CigHjj. Found. 75.750 75.555 Dichlorhexadecane, C16H33CI2. — The chlorine product obtained from hexadecane collected for the larger part at 205°-210°, under 16 mm. Its specific gravity was 1.0314 at 20'\ A determination of chlorine gave a value required for the dichloride : — 0.1477 grm. of the oil gave 0.1525 grm. AgCl. Calculated for CicHjjClj. Found. CI 24.61 24.44 This formula was also confirmed by its molecular weight : — 0. 5019 grm. of the oil and 18.21 grms. benzol gave a depression of 0°.457. Calculated for CigHsjClj. Found. 295 295 MABERY. — THE COMPOSITION OF PETROLEUM. 575 A portion of the original distillate 174°-175° was cooled to —10°, which caused the separation of a crystalline mass. It was filtered cold, but the solid remaining formed but a small part of the original oil. The specific gravity of the filtered oil 0.8005, was slightly higher than the unfiltered distillate. The quantity of the solid was not sufficient for analysis or further examination. No further examination was made of the filtered oil, for it was evident that the small amount of solid hydro- carbon could not change the composition, nor other constants, especially since, as siiown above, the original distillate has the composition of the series C„H2n+2- HePTADECANE, C17H36. The fraction which collected at 188°-190° after the 42d distilla- tion gave as its specific gravity at 20° after drying over sodium, 0.8017. After agitation with sulphuric acid it gave 0.8019, and after purification with fuming sulphuric acid, 0.8000. Under 760 mm. pressure this oil distilled almost entirely at 288°-289°, with very little residue above 289°. The small residue was badly colored from decomposition. Evidently it would not be possible to distill this oil continuously under atmospheric pressure in presence of air without serious decomposition. The formula of this distillate was established by two determinations of its molecular weight and by analysis. I. 1.4294 grm. of the oil and 25.7086 grms. benzol gave a depression of 1°.17. II. 1.4382 grm. of the oil and 25.6785 grms. benzol gave a depression of 1°.18. Calculated for Found. C17H38. I. II. 240 241.2 240.9 Analysis I. was made of the unpurified oil dried over sodium, and Analysis II. after purification with fuming sulphuric acid. I. 0.1534 grm. of the oil gave 0.4778 grm. CO2 and 0.2044 grm. HjO. II. 0.1491 grm. of the oil gave 0.4641 grm. CO2 and 0.2014 grm. H2O. Calculated for C„H36. Found. I. n. c 84.96 84.94 84.87 H 15.04 14.80 15.01 576 PROCEEDINGS OF THE AMERICAN ACADEMY. Monochlorheptadecane, C17H35CI. — The chlorine product from hepta- decane collected in considerable quantity at 175°-177°, 15 mm. Its specific gravity at 20° was found to be 0.8962. The percentage of chlorine corresponded to the monochloride : — 0.1510 grm. of the oil gave 0.0807 grm. AgCl. Calculated for CJ7H35CI. Found. CI 12.92 13.21 On cooling a portion of the distillate I88°-189° to —10°, it formed a pasty mass from vrhich a small amount of a crystalline solid was ob- tained by filtration. The solid after crystallization from ether and alcohol melted at approximately 10°. The amount of solid was not sufficient for purification or examination. The filtered oil gave as its specific gravity at 20°, 0.8035, slightly higher than the distillate before filtration. Since the original distillate showed the composition of the series, GJ^2n+2^ it did not seem worth while to make any further exami- nation of the filtered oil. OCTODECANE, CigH 38 • After the twenty-sixth distillation larger quantities of distillates col- lected between 198° and 204°, mostly at 199°-200° (50 mm). The dis- tillate l99°-200° distilled for the most part, although with considerable colored residue and bad odor, at 300°-301°, under 760 mm. After dry- ing over sodium its specific gravity was 0.8054, after agitation with sulphuric acid, 0.8035, and after purification with fuming sulphuric acid, 0.8017, at 20°. Its molecular weight was ascertained by the Beckman method at the freezing point. I. 0.9963 grm. of the oil and 36.4129 grms. benzol gave a depression of 0°.53. II. 0. 9926 grm. of the oil and 23.2544 grms. benzol gave a depression of 0°.84. Calculated for Found. 254 252.7 254.2 Combustion I. was made of the unpurified distillate dried over so- dium ; combustion II., of the oil after purification with concentrated sul- MABERY. — THE COMPOSITION OF PETROLEUM. 577 phuric acid; and combustion III., after treatment with fuming sulphuric acid. I. 0.U23 grm. of the oil gave 0.4435 grm. CO2 and 0.1915 grm. H.,0. II. 0.1513 grm. of the oil gave 0.4702 grm. CO2 and 0.2054 grm. H.^O. III. 0.1524 grm. of the oil gave 0.4727 grm. CO2 and 0.2064 grm. HoO. Calculated for I. Found. II. III. c 85.06 85.02 84.76 84.59 H 14.94 14.96 15.09 15.05 It is evident from the slight change in specific gravity after purifica- tion, and the percentages of carbon and hydrogen, that the original distillate consisted to a large extent of octodecane. Monochloroctodecane, C18H37CI. — The product obtained by the action of chlorine on octodecane, collected in greater part at 185°-190°, under 15 mm., and this fraction gave as its specific gravity at 20°, 0.9041. The percentage of chlorine corresponded to the monochloride : — 0.1482 grm. of the oil gave 0.0782 grm. AgCl. Calculated for C18H37CI. Found. CI 12.35 13.05 The results given above were obtained with the hydrocarbon that was liquid at ordinary temperatures. When it was found that crystals sepa- rated from this distillate at 3°, and that it became pasty at 0°, it was cooled to — 10°, when it became so thick it filtered only slowly. The solid after filtering was melted and again cooled and filtered, after which it was perfectly white. It was then crystallized from ether and alcohol, after which it melted at 20°. It was estimated that twenty per cent of the original oil separated as the solid hydrocarbon on cooling. It was difficult to separate the solid completely on account of the great solvent action of the oil. The filtered and pressed solid melted at 20°, and after crystallization from ether and alcohol and from gasoline, the melting point could not be raised. Kraflft* gave 28° as the melting point of octodecane, which he obtained from stearic acid; but his octodecane boiled at 214°. 5 under 50 mm. pressure. The specific gravity of the solid hydrocarbon was * Ber. deutsch. chem. Gesellsch., XV. 1703 (1882). VOL. XXXVII. — 37 578 PROCEEDINGS OP THE AMERICAN ACADEMY. 0.7830 at io, and 0,7816 at ^o. Krafft gave 0.7768 as the specific grav- ity of CigHss at 28°. A determination of the molecular weight of the purified hydrocarbon confirmed its formula : — 1.1003 grm. of the oil and 19.65 grms. benzol gave a depression of 0.941. Calculated for CigHjjCl. Found. 288.5 291.5 This molecular weight, showing that the hydrocarbon boiling at 300° is octodecane, does not agree with Kraflt's conclusion as to the formula of the hydrocarbon obtained from stearic acid. In heating stearic acid with hydriodic acid KrafFt assumed that all the oxygen is removed, leaving intact the carbon of the carboxyl, with the formation of octo- decane. But when this work was done the only means of verifying the •formula was by analysis, which was sufficient to determine the series, but not the individual members of the series. While the results of Krafft's combustions gave almost exact values for the formula CigHgg, the size of the molecule could not be determined. Krafft looked upon the hydrocarbon boiling at 303° as having the formula C17H36. The specific gravity of the oil after cooling and filtration was some- what higher than before, 0.8110 at 20°, and higher than the specific gravity of the filtered solid octodecane, 0.7830. The molecular weight of the filtered oil was the same as before filtration. 0.9904 grm. of the substance and 16.10 grms. benzol gave a depression of 1°.184. Calculated for CigHsg. Found. 254 254.6 A combustion of the liquid hydrocarbon showed some change in the proportions of carbon and hydrogen : — 0.1483 grm. of the substance gave 0.4636 grm. CO2 and 0.1954 grm. HoO. Calculated for Found. c 85.70 85.06 85.25 H 14.30 14.94 14.64 While there is a narrow difference in calculated percentages between the two formulae, the percentages found, together with the higher specific gravity, indicate that the filtered oil was a mixture of the two series C„H„2 and H„C2n+2- MABERY. — THE COMPOSITION OF PETROLEUM. 579 A determination of the index of refraction, which was found to be 1.4435, and the molecular refraction, correspond more nearly to the formula CisHgo : — Calculated for vn„„A r TT r IT Jjouna. 82.90 84.96 82.60 A combustion of the solid hydrocarbon gave proportions required for the series C^U-i^+o- — 0.1564 grm. of the substance gave 0.4883 grm. CO.j and 0.2083 grm. H.^O. Calculated for CijHjj. Found. C 85.06 85.15 H 14.94 14.80 The position in the series was shown by its molecular weight : — I. 1.9475 grm. of the solid and 25,21 grms. benzol gave a rise of 0°.7734. II. 1.9475 grm. of the solid and. 25. 28 grms. benzol gave a rise of 0°.7830. Calculated for Found. CsU-s. I. II. 254 256 253.2 The formula of octodecane was further confirmed by its index of refrac- tion. The index was found to be, at 20°, 1.440, which corresponds to the molecular refraction : — Calculated for CigHja. Found. 84.96 84.53 NONODECANE, C19H40. In the eighth distillation under 50 mm., 335 grams collected at 210°- 212° with much smaller weights on either side. After continuing the distillation twenty-seven times, a portion of the fraction 2 10° -2 12° was purified with fuming sulphuric acid ; before this treatment the oil gave as its specific gravity at 20°, 0.8274, and afterward, 0.8122. In deter- mining its molecular weight by the freezing point method the following values were obtained : — 580 PROCEEDINGS OF THE AMERICAN ACADEMY. I. 1.1039 grm. of the oil and 39.7462 grms. benzol gave a depression of 0°.575. 11. 1.1418 grm. of the oil and 36.2175 grms. benzol gave a depression of 0°.o05. Calculated for Found. C,gH,o. I. II. 268 269.5 268 Determinations of carbon and hydrogen gave values for the series T. 0.1530 grm. of the oil gave 0.4771 grm. CO2 and 0.1994 grm. HoO. II. 0.1591 grm. of the oil gave 0.4976 grm. CO2 and 0.2132 grm. H2O. Calculated for C19H33. CioHiu. Found. I. II. c 85.70 85.08 85.04 85.29 H 14.30 14.92 14.48 14.89- Analysis I. was made of the oil before purification, and Analysis II. afterward. A determination of the index of refraction gave 1.4522, which cor- responds to the following molecular refraction : — Calculated for Gyjlltf). Found. 89.55 88.68 The results on the composition of the distillate 2 10° -21 2° were ob- tained on the purified distillate without cooling to separate the solid hydrocarbon. On cooling a portion of this distillate to —10°, filtering cold and pressing the solid, 5 grams of the solid hydrocarbon, and 30 grams of the liquid hydrocarbon were obtained; the solid hydrocarbon, therefore, formed a small part of the original distillate. The specific gravity of the filtered oil was 0.8208 at 20°. The specific gravity of the distillate before cooling as shown above was 0.8122 at 20°. After crystallization from ether and alcohol, the specific gravity of the solid hydrocarbon was 0.7725, |^o, and 0.7781 at 5^0. A determination of its molecular weight gave a value required for the hydrocarbon CioHio- 1.4011 grm. of the solid and 26.66 grms. benzol gave a rise of 0°. 496. Calculated for CigH^o. Found. 268 271.6 MABERY. — THE COMPOSITION OF PETROLEUM. 581 The melting point of the solid was found to be 33°-34° corresponding to the melting point, 32°, that Kraflft found for the solid hydrocarbon distilling at, 226°. 5, 50 mm. A combustion of the oil filtered from the solid hydrocarbon gave percentages of carbon and hydrogen required for CigHsg. 0.1495 grm. of the oil gave 0.4715 grm. CO2 and 0.1928 grm. H2O. Calculated for Ciglljg. Found. 85.70 86.00 14.30 14.33 A determination of the molecular weight confirmed the formula: — 2.5445 grms. of the oil and 24.63 grms. benzol gave a rise of 0°.994. Calculated for CioHjg. Found. 266 267 The formula was further verified by its index of refraction. It gave the index 1.4515, corresponding to the molecular refraction : — Calculated for CigHjg. Found. 87.46 87.51 With the distillate 212°-214°, 50 mm., the limit is reached of the solid hydrocarbons whose molecular weight can be determined by the freezing point method on account of the crystallization of the hydrocar- bon before the benzol freezes. The molecular weights of solid higher members were determined by the boiling point method. The results described in this paper defining the physical properties and formulae of the hydrocarbons separated from Pennsylvania petroleum dif- fer in several essential particulars both from the hydrocarbons obtained by Kraflft by decomposition of the monobasic acids with high molecular weights, and those formerly reported as among the constituents of Penn- sylvania oil. It has been shown that the hydrocarbon at 196° is undecane, CnH24, and not dodecane as found by Pelouze and Cahours. Likewise the hydrocarbon at 216° proved to be dodecane and not tridecane. Since there was no method for ascertaining the molecular weights of these bodies at the time when they were separated by Pelouze and Cahours, and elementary analysis could only determine the series, it was only by analogy that the homologous members of the series could be guessed at. Since 182° was accepted at the boiling point of undecane, naturally dodecane and tridecane should fall into the heaps at 196° and 216°. 682 PROCEEDINGS OF THE AMERICAN ACADEMY. The boiling point of tridecane has been variously stated at 219°, 216° and 212°-2I5°. But neither of these temperatures can be accepted as the boiling point of tridecane since its molecular weight is found to be that of the hydrocarbon boiling at 225°-226°. The hydrocarbon tetradecane boils at 236°-238°, the same boiling point as was assigned to the tridecane separated by Pelouze and Cahours, but the specific gravity of tetradecane, 0.7812 at 20° is es- sentially lower than that found by Pelouze and Cahours, 0.809. Pentadecane, boiling point 156°-157°, is nearly the same in boiling point as the hydrocarbon separated by Pelouze and Cahours, boiling point 260°, although its specific gravity, 0.7896 at 20°, is much lower than they found, — 0.825 at 19°. The boiling point of hexadecane is not very different from that given by Pelouze and Cahoux's, but its specific gravity is considerably lower. It does not differ in boiling point materially from hexadecane which Krafft obtained by heating palmitic acid, nor from that of hexadecane, boiling point 278°, obtained by Zincke from normal octyl iodide.* Since, however, the oils obtained by freezing out the solid hydrocarbons have specific gravities considerably higher than those of the original distillates, and apparently belong to another series, as shown by analysis and refrac- tion indices, it is possible that the solid hydrocarbons held in solution in the oils have their boiling points depressed in the fractional distillation by which they were separated from the main body of the crude oil. Still, the molecular weights of the solid hydrocarbons correspond to definite formulas; for instance, from the distillate 300°-301°, atmospheric pres- sure, octodecane was separated, in a practically pure form. The less volatile portions of Pennsylvania petroleum consist of several series of hydrocarbons. The series CnHj,, is liquid even at low tem- peratures, of higher specific gravity, and another is composed of solid hydrocarbons, of the series CnH2„+2- In a former paper f it was shown that the high values assigned by Pelouze and Cahours as the specific gravity of the distillates separated by them from petroleum, indicated that their hydrocarbons were sep- arated from Canadian petroleum. The same inference is supported by the high specific gravity of the hydrocarbons separated by Pelouze and Cahours boiling above 216°, as compared with the specific gravity of the hydrocarbons separated from Pennsylvania petroleum described in this paper. * Ann. Chem. u. Pharm. 152, 15. t These Proceedings, XXXII. 171. MABERY. — THE COMPOSITION OP PETROLEUM. 583 After establishing a homologous series by analysis, evidently the only means available for Pelouze and Cahours to determine the molecular size of the hydrocarbons was to assume that a hydrocarbon constituted the chief portion of any distillates that collected in unusually large amounts, and to compute the series in unbroken order from the lower members. Several attempts were made to ascertain the presence of the hydro- carbon C20H42; but the distillates between the limits 215° and 225° were small, and in none of them did the molecular weight obtained correspond to this formula. HeNEICOSANE, C21H44, AND LiQUID HYDROCARBON, C21H42. From Distillate 230°-232°, 50 mm. Larger quantities of distillates amounting to 200 grams collected at 230°-232°, for the most part at 230°-23r- The specific gravity of the unpurified distillate was 0.8321 ; after purification it gave 0.8230. A combustion of the purified oil gave the following percentages of carbon and hydrogen : — 0.1540 grm. of the oil gave 0.4813 grm. CO2 and 0.1968 grm. HgO. Calculated for CnHgn CniH44. Found. c 85.70 85.14 85.23 H 14.30 14.86 14.32 There was evidently some loss in this analysis, but the percentages are more satisfactory for the formula C2iH42. It will be shown that this distillate was a mixture of a solid hydrocarbon with an oil of higher specific gravity. Its molecular weight was determined at the freezing point of benzol. I. 1.4807 grm. of the oil and 25.9125 grms. benzol gave a depression of 0°.949. II. 0.6845 grm. of the oil and 19.48 grms. benzol gave a depression of 0°.579. Calculated for Found. Cj,H„ C„,H,4. I. II. 294 296 295 297.4 The index of refraction of this hydrocarbon was found to be 1.4608, corresponding to the molecular refraction : — 584 PROCEEDINGS OF THE AMERICAN ACADEMY. Calculated for CjiH^j. Found. 96.66 96.91 The molecular weight and molecular refraction show that this dis- tillate is composed of a twenty-one carbon hydrocarbon, and the com- bustion and high specific gravity point to the series C^Han. A portion of the oil was cooled to —10°, filtered cold, the solid well pressed in filter paper, and crystallized from ether and alcohol. The ready solubility of these solid hydrocarbons in ether and insolubility in alcohol afford an easy means of purification. The melting point of the purified solid was 40°-41°. A combustion gave the following values for carbon and hydrogen : — 0.1353 grm. of the substance gave 0.4237 grm. CO2 and 0.1778grm. H2O. Calculated for CjiH,!. Found. c 85.13 85.39 H 14.87 14.72 The filtered oil gave as its specific gravity at 20°, 0.8424. The per- centages of carbon and hydrogen were ascertained by a combustion : — 0.1498 grm. of the oil gave 0.4724 grm. CO2 and 0.1898 grm. H2O. Calculated for CjiHjj. Found. C 85.70 85.98 H 14.30 14.08 Its molecular weight was determined at the freezing point of benzol. 0.9466 grm. of the oil and 21.01 grms. of benzol gave a depression of 0°.737. Calculated for CjiHjj. Found. 294 299 docosane, c20h46, and liquid hydrocarbon, c22h44. From Distillate 240°-242°, 50 mm. After the thirtieth distillation, 150 grams collected at 240°-242°, which gave as its specific gravity before purification 0.8341. After purification with fuming sulphuric acid its specific gravity was 0.8262. Combustions gave the following percentages of carbon and hydrogen : — Calculated for c 85.70 85.16 H 14.30 14.84 MABERY. THE COMPOSITION OF PETROLEUM. 585 I. 0.1538 grm. of the oil gave 0.4800 grm. COj and 0.1992 grms. H,0. 11. 0.15G0 grm. of the oil gave 0.4874 grm. COj and 0.2024 grm. HoO. III. 0.1362 grm. of the oil gave 0.4257 grm. COj and 0.1788 grm. H.O. Found. I. II. III. 85.09 85.21 85.25 14.40 14.42 14.59 The molecular weisrht was determined as follows : — I. 0.8367 grm. of the oil and 20.38 grms. benzol gave a depression of 0°.642. II. 2.5442 o^rms. of the oil and 21.91 grms. benzol gave a rise in boil- ing point of 0°.95G6. Calculated for Found. 308 313.4 311.3 The index of refraction was found to be 1.454 and the molecular refraction : — Calculated for CjjH^. Found. 101.27 100.7 The distillates in the vicinity of 240°, 50 mm., deposited no solid on standing at ordinary temperatures, but higher fractious all deposited solids. When cooled to 0°, the fraction 242°-254° became nearly solid. A-fter further cooling to —10°, the solid was filtered in a funnel sur- rounded with salt and ice, pressed in filter paper and crystallized from ether and alcohol. The solid melted at 43°, and further purified from gasoline, at 44°. Krafft gave 44°. 4 as the melting point of the hydro- carbon C22H46. Its specific gravity at 60° was found to be 0.7796. A combustion gave proportions of carbon and hydrogen required for the series C„H2„+2. 0.1521 grm. of the solid gave 0.4721 grm. CO3 and 0.2021 grm. HgO. Calculated for ^22344 '^"22H46. Found. c 85.70 85.16 85.13 II 14.30 14.84 14.86 586 PROCEEDINGS OF THE AMERICAN ACADEMY. The quantity of the hydrocarbon was not sufficient for a determina- tion of its molecular weight. The filtered oil gave as its specific gravity at 20°, 0.8296, a value somewhat higher than that obtained before filtration. A combustion gave the following percentages of carbon and hydrogen : — 0.1505 grm. of the oil gave 0.4717 grm. CO. and 0.1937 grm. HoO. 0.1411 grm. of the oil gave 0.4419 grm. CO2 and 0.1819 grm. HgO. Calculated for CjjH^j. Found. C 85.70 85.49 85.41 H 14.30 14.31 14.32 These proportions correspond to the formula C22H44, which is supported by the high specific gravity. The molecular weight of the filtered oil was also determined : — 1.0713 grm. of the oil and 19.60 grms. benzol gave a depression of 0°.858. Calculated for CojUa- Found. 308 312 The wide difference in specific gravity between the solid and liquid hydrocarbons at 240°-242°, 50 mm., point to different series. While the percentages of carbon and hydrogen given by analysis could not alone be depended on to prove the different series, the results of combustion with specific gravity are sufficient. The differences in theoretical com- position of the two series are 0.5 of one per cent for carbon and for hydrogen. In combustions conducted under the most favorable condi- tions and with the greatest care, the different series may be shown in well purified materials. But with so many determinations, and the ex- treme care in details of the method, while the percentages obtained are sufficiently close to indicate the series, the results are not in all cases as close to the calculated percentages as should be reached in the greater precision of a few analyses. TrICOSANE, C23H43, AND LiQUID HYDROCARBON, CasHig. From Distillate 258°-260°, 50 mm. After the nineteenth distillation, 175 grams collected at 258°-260°, 50 mm., for the most part at 260°-261°, which deposited a considerable quantity of solid hydrocarbon on standing. The specific gravity of the unpurified distillate decanted from the solid was as follows : — MABERY. — THE COMPOSITION OP PETROLEUM. 587 60°, 0.8341 70°, 0.8320 80°, 0.8310 The oil was agitated several times with concentrated sulphuric acid until the acid was not much colored, and washed with sodic hydrate and water, and finally with salt brine. On account of the high specific gravity of the oil some heavy solution such as brine or calcic chloride was necessary to separate the water and oil. The oil was dried for examination over calcic chloride and metallic sodium. A combustion of the oil gave the following percentages of carbon and hydrogen : — 0.1508 grm. of the oil gave 0.4711 grms. CO2 and 0.1945 grm. H2O. Calculated for C23H45. CjaHjg. Found. c 85.70 85.18 85.21 H 14.30 14.82 14.33 A part of the carbonic dioxide was evidently lost, but the results point to the series C^Uo^, which represents the composition of the oil, much the larger part of the distillate. A portion of the distillate was cooled to — 10°, and filtered cold to separate the crystalline solid. The solubility of the solid hydrocarbon seemed to diminish rapidly with lower temperatures, consequently a small proportion of the solid remains in the oil below — 10°. After pressing and crystallizing from ether and alcohol, the solid melted at 45°. Krafft's hydrocarbon, CgsHig, melted at 47°. 7. Two determinations of its specific gravity at 60° gave (1) 0.7894, (2) 0.7900. A combustion of the solid gave results for the series C„H2„+2 '• — 0.1515 grm. of the substance gave 0.4710 grm. CO2 and 0.1989 grm. HoO. Calculated for C03H43. Found. C 85.20 85.06 H 14.80 14.64 A determination of its molecular weight at the boiling point of benzol was made : — 1.1208 grm. of the substance and 23.08 grms. benzol gave a rise of 0°.412. Calculated for C23H4g. Found. 324 327 588 PROCEEDINGS OP THE AMERICAN ACADEMY. The filtered oil gave as its specific gravity at 20°, 0.85 G9. It gave percentages of carbon and hydrogen requii'ed for the series CaH2a : — 0.1504 grm. of the oil gave 0.4711 grm. CO2 and 0.1945 grm. HgO. Calculated for ,, . p TT p IT Found. C 85.70 85.18 85.41 H 14.30 14.82 14.36 The molecular weight was determined at the freezing point of benzol : 3.464 grms. of the oil and 26.06 grms. benzol gave a rise of 1°.0475. Calculated for CjsHjg. Found. 322 325 The index of refraction was found to be 1.4714, from which was cal- culated the molecular refraction ; — Calculated for CjjH^g. Found. 105.87 105.31 TeTRACOSANE, C24H50, AND LiQUID HYDROCARBON, C24H48. From Distillate 272°-274°, 50 mm. After the nineteenth distillation, 150 grams collected at 272°-274°, 50 mm., that became partly solid on standing. The decanted oil gave as its specific gravity 0.8448 at 20°. A part of the distillate was then cooled to —10°, and the solid filtered cold under pressure. The distillate was purified by treatment with successive portions of fuming sulphuric acid, until the acid was nearly colorless, then washed with sodic hydrate and a concentrated solution of calcic chloride, and dried over fused calcic chloride and sodium. Nearly one third of the volume was removed in purification. The purified oil then gave as its specific gravity at 20°, 0.8598, and at higher temperatures: — 60°, 0.8375 70°, 0.8366 80°, 0.8354 A combustion of the purified oil gave percentages of carbon and hydrogen required for the series CnHan. 0.1539 grm. of the oil gave 0.4769 grm. CO2 and 0.2000 grm. H2O. Calculated for C24H43 C24H5D. Found. c 85.70 85.21 85.35 H 14.30 14.79 14.54 MABERY. — THE COMPOSITION OF PETROLEUM. 689 These percentages evidently support the formula C24H48. A determination of the molecular weight of the liquid hydrocarbon gave at the boiling point of benzol a result required for C24H48. 2.0681 grms. of the oil and 25.78 grms. benzol gave a rise of 0°.6096. Calculated for CjiH^g. Found. 336 337.4 The index of refraction of the oil was found to be 1.4726, from which the following molecular refraction was calculated : — Calculated for C24H48. Found. 110.47 * 109.75 Specific gravity of the oil at |go, 0.8582. The solid separated by filtration melted at 48°. Kraflft's hydrocarbon, C24H48, melted at 51°. It gave as its specific gravity the following values : — 60°, 0.7902 70°, 0.7893 80°, 0.7875 With water at 4° these results reduce to 0.7742. The specific gravity given by Krafift to tetracosane at 4° was 0.7784, the same as that of the solid hydrocarbon which he separated from shale oil. The solid products from Pennsylvania oil show only slight variations in specific gravity. But the heavy oils show a decided increase in specific gravity with increase in molecular weight. A combustion gave percentages of carbon and hydrogen required for the series CJi2a+2- 0.1433 grm. of the solid gave 0.4479 grm. CO2 and 0.1895 grm. H2O. Calculated for ,, , C 85.70 85.23 85.25 H 14.30 14.77 14.70 The molecular weight was determined at the boiling point of benzol. Calculated for C^Q^, Found. 338 ' 337 To ascertain whether the solid which separated at ordinary tempera- tures was identical with what remains in solution, a portion of the oil 590 PROCEEDINGS OF THE AMERICAN ACADEMY. was cooled to 0°, filtered at the same temjoerature, and the filtrate cooled to — 10° and filtered under pressure at the same temperature. The three solids were carefully purified by crystallization from ether and alcohol and their melting points taken. The solid separated at ordinary temperatures melted at 48°, that separated at 6° melted at 51°-52°, and that separated at —10° melted at 5r-52°. It is therefore evident that this distillate consists chiefly of one solid hydrocarbon, C24H50, and that the oil remaining liquid at —10° belongs to a different series. PeNTACOSANE, C25H52, AND LiQUID HYDROCARBON, C26H52. From Distillate 280°-282°, 50 mm. After the fifteenth distillation, 100 grams collected at 280°-282°, 50 mm., which deposited a larger quantity of solid hydrocarbon than the lower distillates. This solid was separated from the oil and the latter was then cooled to 0° and filtered at the same temperature. The specific gravity of the filtered oil at 20° was 0.8580. A combustion gave the following values : — 0.1593 grm. of the oil gave 0.4997 grm. CO2 and 0.2107 grm. H.O. Calculated for C2fjH52. Found. C 85.70 85.55 H 14.30 14.67 The formula was established by its molecular weight, determined at the boiling point of benzol: — 3.9867 grms. of the oil and 30.19 grms. benzol gave a rise of 0°.936. Calculated for CjeHsj. Found. 364 362 A determination of the index of refraction gave 1.4725, which cor- responded to the molecular refraction : — Calculated for CjeH^j. Found. 119.87 119.12 After crystallization from ether and alcohol, from which it separated in crystalline plates, the solid hydrocarbon gave percentages of carbon and hydrogen required for the series C„H2n4-2. MABERY. — THE COMPOSITION OP PETROLEUM. 591 0.1534 grm. of the substance gave 0.4787 grm. CO2 aud 0.2006 grm. H2O. Calculated for CjgHgj. Found. c 85.25 85.09 H 14.75 14.53 A determination of its molecular weight verified the formula : — 1.7583 grm. of the substance, and 24.39 grms. benzol gave by the boiling point method a rise of 0°.5231. Calculated for C25H52. Found. 352 353.4 Melting point of the solid hydrocarbon, 53° -5 4°. HeXACOSANE, C26H54, AND LiQUID HYDROCARBON, C27H52. From Distillate 292°-294°, 50 mm. After the fifteenth distillation, 100 grams collected at 292°-294°, 50 mm., which deposited a considerable quantity of solid crystalline hydrocarbon. These crystals were filtered, pressed, and purified by crystallization from ether and alcohol. Melting point, 58°. The specific gravity of this hydrocarbon was determined as follows : — 60°, 0.7977 70°, 0.7956 80°, 0.7943 A combustion of the solid gave the following percentages of carbon and hydrogen : — 0.1508 grm. of the substance gave 0.4709 grm. COo and 0.2033 grm. H.,0. Calculated for C26H54. Found. c 85.24 85.17 H 14.76 14.98 The molecular weight was ascertained at the boiling point of benzol. 1.2754 grm. of the substance aud 24.2827 grms. benzol gave a rise of 0°.416. Calculated for C26Hg4. Found. 366 364 592 PROCEEDINGS OP THE AMERICAN ACADEMY. On cooling the original distillate to —10°, it formed a thick pasty mass. It was filtered under pressure, keeping cold. The filtered crys- tals were pressed, and crystallized from ether and alcohol. Melting point, 58°. The solids pressed out from the fractions from 288° to 302°, 50 mm., showed very slight variations in melting points. 288°-290°, 56°. 300°-304°, 59°-60°. 294°-296°, 58°. 302°-304°, 59°-60°. The oil filtered under pressure was very thick and viscous. Its specific gravity at 20° was 0.8688. A combustion gave the following percentages of carbon and hydrogen : — 0.1500 grm. of the oil gave 0.4750 grm. COg and 0.1812 grm. U.O. Calculated for C27H52. Found. C 86.17 86.36 H 13.83 13.43 Its molecular weight at the boiling point of benzol corresponded to the formula C27H52. 3.6506 grms. of the oil and 25.80 grms. benzol gave a rise of 0°.964. Calculated for C27H5J. Found. 376 376.2 The index of refraction corresponded to the same formula. The index was found to be 1.4722, and the molecular refraction: — Calculated for C27H52. Found. 122 121.4 octocosane, c28ii58, and liquid hydrocarbon, c28h54. From Distillate 310°-312°, 50 mm. After the tenth distillation 75 grams collected at 310°-312°, from which a considerable quantity of crystals collected above the oil on standing. The oil separated from the crystals was then cooled to — 10° and filtered cold under pressure. The solid was pressed and purified by crystallization from ether and alcohol. Melting point 60°. Its specific gravity was determined as follows : — 70°, 0.7945 80°, 0.7927 90°, 0.791 1' MABERY. —THE COMPOSITION OP PETROLEUM. 593 A combustion gave the following percentages of carbon and hy- drogen : — 0.1508 grm. of the substance gave 0.4703 grm. CO2 and 0.2032 grra. HoO. Calculated for CjsHsg. Found. C 85.28 85.07 H 14.72 14.97 The molecular weight at the boiling point of benzol corresponded to the formula C23H5g. 3.070 grms. of the solid hydrocarbon and 26.21 grms. benzol gave a depression of 0°.7538. Calculated for CssHjg. Found. 394 399 The very thick oil separated by filtration gave as its specific gravity at 20, 0.8694. A combustion gave percentages of carbon and hydrogen required for the series, CnHjn-g. 0.1500 grm. of the oil gave 0.4729 grm. CO2 and 0.1836 grm. H.O. Calculated for Found ^28^58 CnjU-i; CojHjj. C 85.28 85.70 86.02 85.96 H 14.72 14.30 13.98 13.60 The molecular weight was found at the boiling point of benzol. I. 2.6792 grms. of the oil and 29.85 grra. benzol gave a rise of 0°.5826. II. 1.9196 grms. of the oil and 27.98 grm. benzol gave a rise of 0°.4459. Calculated for Found. 392 396 394.4 The index of refraction was found to be 1.480, which corresponds to the molecular refractions : — Calculated for C^gS^. Found. 127 126.78 It will be observed that the two liquid hydrocarbons last described have been shown to belong to a series Caiiia-T Results already ob- voL. XXXVII. — 38 594 PROCEEDINGS OP THE AMERICAN ACADEMY. tained but not yet published indicate that the same series of hydrocar- bons constitute the less volatile portions of Canadian petroleum, and probably also of Ohio petroleum. Results already published show that the less volatile distillates from California and Texas petroleum are composed of the same series and other series still poorer in hydrogen. The unexpected appearance of the series C„H2„_2 in Pennsylvania petroleum suggests a closer relationship between this petroleum and the heavier oils from other fields, such as those in Texas and California, than was suspected. To gain further information concerning the heav- ier portions of Pennsylvania oil, we allowed three kilos of the sample from which the hydrocarbons described in this paper were prepared, to evaporate spontaneously in the air in a strong draught, but with no appli- cation of heat. At the end of thirty days there remained one kilo that gave as its specific gravity 0.8620, practically the same as that of C28H54, 0.8694. A combustion gave percentages of carbon and hydrogen re- quired for the series CnH2n_2- A distillation showed that 65 per cent of the residual oil was composed of hydrocarbons above C15H30. The com- position of these hydrocarbons will be ascertained in connection with the study of natural and commercial paraffine, which is now in progress. This interesting relation, and others between the numerous petroleums from different oil fields that have been examined in this laboratory will be presented more at length in a later paper. As a general summary of the results described in this paper, hydrocar- bons have been identified as shown in table on opposite page. It appears that the liquid hydrocarbon C2SH54 in fraction 310°-312° has the same number of carbon atoms as the solid hydrocarbon octocosane in the same fraction. In this respect the hydrocarbons in this fraction differ from those in the two preceding fractions, in each of which the liquid hydrocarbon is one carbon higher than the solid constituent. De- terminations of the molecular weights of hydrocarbons with high carbon content can only be made by the boiling-point method ; and even with the greatest care in manipulation, this method is somewhat uncertain for high molecular weights of solid hydrocarbons, for the reason that the rise in boiling points diminishes with the increase in molecular weight. With oils there is less difficulty. For instance, the molecular weight, 376.2, of the liquid hydrocarbon C27H52, given on page 592, is one of five closely concordant determinations by different persons. As an illus- tration of the care necessary in details, heating with a lamp supplied with gas from the laboratory mains is so irregular on account of variation in gas pressure that the gas must be supplied from a tank under water MABERY. THE COMPOSITION OF PETROLEUM. 595 Name. Tridecane Tetradecane Pentadecane Hexadecane Heptadecane Octodecane Nonodecane Heneicosane Hydrocarbon, liquid at —10° Docosane Hydrocarbon, liquid at —10° Tricosane Hydrocarbon, liquid at —10° Tetracosane Hydrocarbon, liquid at —10° Pentacosane Hydrocarbon, liquid at —10° Hexacosane Hj"drocarbon, liquid ;it —10° Octocosane Symbol. ^13^28 C14H30 ^17^36 C18H38 C19H40 C21H44 C22H44 ^22 "46 ^231^^46 C23H48 C24H48 ^24^^50 ^26"52 ^25"52 ^27 "52 ^^26^54 ^28^54 ^28"5S Boiling Point. Melting Point. 226° 236°-238° 256°-257° 274°-275° 288°-289° 300°-301° 210°-212°, 50 mm. 230°-231°, 240°-242°, 258°-260°, " 272°-274°, 280°-2.-2°, " 292°-294°, " 310°-312°, " 10° 20° 3.3^-34° 40°-41° 44° 45° 48° 53°-54° 68° 60° pressure. Much attention has been given to these determinations, espe- cially by Messrs. 0. J. Sieplein and R. P. Gushing. The preparation of the distillates described in this paper was begun December 1, 1896, by Mr, A. S. Kittelberger, who distilled 56 kilos of Pennsylvania crude oil. The distillations were later continued by different assistants. The following gentlemen have also aided in the purification, examination, and analysis of these hydrocarbons : Messrs. Shaw, Latimer, R. P. Gushing, Dr. E. J. Hudson, and 0. J. Sieplein. To the latter especially is due the analysis and identification of the chlorine derivatives of the hydrocarbons. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 23.— August, 1902. RECORDS OF MEETINGS, 1901-1902. A TABLE OF ATOMIC WEIGHTS. By Theodore William Richards. REPORT OF THE COUNCIL: BIOGRAPHICAL NOTICES. Augustus Lowell. By Percival Lowell. Truman Henry Safford. By Arthur Searle. Horace Elisha Scudder. By Thomas Wentwortii IIigginson. Joseph Henry Thayer. By C. H. Toy. John Fiske. By Andrew McFarland Davis. James Bradley Thayer. By Jasies Barr Ames. OFFICERS AND COMMITTEES FOR 1901-1902. LIST OF THE FELLOWS AND FOREIGN HONORARY MEMBERS. STATUTES AND STANDING VOTES. RUMFORD PREMIUM. INDEX. (Title Page and Table of Contents.) RECORDS OF MEETINGS. Nine hundred and twenty-fifth Meeting. May 8, 1901. — Annual Meeting. Vice-President Thayer in the chair. The CoiTesponding Secretary read letters from Frank S. Collins, accepting Fellowiship ; from Franklin P. Mall, ac- knowledging his election as Associate Fellow; from VI. Mark- ovnikoff, thanking the Academy for its message of congratulation ; from the Johns Hopkins University, announcing the death of Pro- fessor Henr\' A. Rowland ; from tlie Royal Lyncean Academy, of Rome, announcing the death of its President, Professor Angelo Messedaglia ; from the Royal Academy of Sciences of Turin, announcing the death of Professor Giulio Bizzozero ; from V. Pissaroff, Vice-President of the Ural Society of Natural Sciences of Ekaterinburg, announcing the proposed establish- ment of an ophthalmological hospital, and asking for gifts of works or instruments ; from Arthur MacDonald, of Washington, regarding the establishment of a Psycho-Physical Laboratory in the Department of the Interior ; from S. C. Mastick, secretary of the committee on the modification of the Federal legacy tax, announcing that the desired changes have been incorporated in the Statutes of the United States and that the committee has adjourned sine die. The Chair announced the death of William Stubbs,of Oxford, Foreign Honorary Member in Class III,, Section 3. The Corresponding Secretary presented the Annual Report of the Council. The Treasurer presented his annual report, of which the following is an abstract : -^ 600 PROCEEDINGS OF THE AMERICAN ACADEMY. General Fund. Receipts. Balance from last year $259.50 lavestments $5,344.80 Assessments . 915.00 Admission fees 20.00 Sale of publications 101.01 6,380.81 6,640.31 Expendittires. General expenses $2,461.49 Publishing expenses 2,438.82 Library expenses 1,922.33 Expenses of moving 5.00 $6,827.64 Balance 187.33 $6,640.31 RuMFORD Fund. lieceipts. Balance from last year $1,775.93 Investments . $2,640.81 Sale of publications 35.00 2,675.81 $4,451.74 Expenditures. Researches $916.00 jMedals 327.00 Publishing 266.22 Library 374.44 Miscellaneous 11.25 1,894,91 Income invested dui'ing the year and transferred to capital account 10.75 Balance .,.,.,...... 2,546.08 $4,451.74 RECORDS OF MEETINGS. 601 Warren Fund. Receipts. Balance from last year $994.57 Investments 1,332.97 $2,327.54 ExiJenditures. luvestiirations $600.00 Income invested during the year and transferred to capital accomit 451.25 $1,051.25 Balance • • • . 1,276.29 $2,327.54 Building Fund. Receipts. Balance from last year $539.52 Investments 783.02 $1,322.54 Expenditures. Income invested during the year and transferred to capital account $942.50 Balance 380.04 $1,322.54 The following reports were presented : — Report of the Rumford Committee. At the Annual Meeting of the Academy held May 9, 1900, the amount of $1,000 was put at the disposal of the Rumford Committee for the furtherance of research. From this sum grants have been made as follows : — Oct. 10, 1900: Two hundred dollars to Dr. Charles E. Mendenhall, of Williams College, in aid of his investigations upon a hollow bolometer. Oct. 10, 1900: Five hundred dollars to Professor George E. Hale, of the Yerkes Observatory, in aid of his researches in connection with the application of the radiometer to a study of the infra-red spectrum of the chromosphere. 602 PROCEEDINGS OF THE AMERICAN ACADEMY. March 13, 1901 : Three hundred dollars to Professor Arthur A. Noyes, of the Massachusetts Institute of Technology, in aid of his research upon the effect of high temperature on the electrical conductivity of aqueous salt solutions. It was furthermore voted by the Committee at its meeting of April 12, 1901, to recommend to the Academy the appropriation of the sum of five hundred dollars from the income of the Rumford Fund to Professor Theodore W. Richards of Harvard University, in aid of his research upon the Thomson-Joule Free Expansion Experiment, which recom- mendation was favorably acted upon by the Academj'. The Rumford Committee has given much consideration to t!ie question introduced by Professor E. C. Pickering, of the feasibility of co-operation among tlie various committees in this country having in charge the administration of funds devoted to researcli. It was voted by the Com- mittee that the Chairman be authorized to represent the Committee in such consideration of the subject as might be brought about. Several entirely informal conferences have taken place among representatives of such committees, and it is hoped that some general understanding may be reached which will be helpful to those engaged in research. The following recommendations have been voted by the Committee, and are now presented to the Academy for its consideration. Oct. 10, 1900, it was voted that the Committee recommend to the Academy the appropriation of one hundred dollars from the income of the Rumford Fund to aid in the cataloguing of the books in the Academy Library. March 13, 1901, it was voted to recommend to the Academy that a replica in bronze of each Rumford Medal hereafter awarded by the Academy be struck off and preserved in the Hall of the Academy. April 12, 1901, it was voted that the Committee recommend to the Academy the appropriation of one hundred and fifty dollars from the income of the Rumford Fund for the purchase and binding of the usual periodicals for the current fiscal year. At the same meeting it was voted that the Committee recommend to the Academy the appropriation of the sum of one hundred and fifty dollars from the income of the Rumford Fund for the purchase and binding of books on light and heat, said works to be purchased upon the recommendation of the Rumford Committee. At the same meetinsf it was furthermore voted that the Chairman of the Committee recommend to the Academy the appropriation from the income of the Rumford Fund of one thousand dollars for the immediate needs of the Committee in the furtherance of research. RECOKDS OF MEETINGS. 603 A wish has frequently been expressed for a complete list of persons to whom the Rumford Premium has been awarded, and to meet this desire such a list is appended to the present report. Papers embodying the results of researches conducted wholly or in part by the aid of grants from the Rumford Fund as follows have been printed during the past year in the Proceedings of the Academy. " On the Thermal Diffusivities of Different Kinds of Marble," by B. O. Peirce and R. W. Willson. " On the Thermal and Electrical Conductivity of Soft Iron," by Edwin H. Hall. " False Spectra from the Rowland Concave Grating," by Theodore Lyman. " A Study of Growing Crystals by Instantaneous Photomicrography," by Theodore W. Richards and Ebenezer H. Archibald. In accordance with a vote of the Committee passed Nov. 10, 1897, all persons receiving grants from the Rumford Fund are expected to present an annual report of the progress of their work. In response to the usual request such reports have been received from the following persons, regarding their several researches as stated below : — Mr. Arthur L. Clark, on the molecular properties of vapors in the neighborhood of the critical point. Professor Henry Crew with Mr. 0. H. Basquier, on electric arc spectra. Professor Edwin B. Frost, on the spectroscopic determination of the radial velocities of stars. Professor Edwin H. Hall, on the thermal properties of iron. Professor George E. Hale, on the application of the radiometer to the study of the infra-red spectrum. Professor Frank A. Laws, on the thermal conductivity of metals. Professor Edward L. Nichols, on the visible radiation from carbon, accompanied by a paper for presentation to the Academy embodying the result of his researches. Mr. C. E. Mendenhall, on the hollow bolometer. Professor Edward C. Pickering, on the determination of the light of very faint stars. Professor Theodore W. Richards, on (a) the photographic study of growing crystals ; (b) the transition temperatures of salts as fixed points in thermometry ; (c) the experimental study of the Joule-Thomson Effect. 604 PROCEEDINGS OF THE AMERICAN ACADEMY. Professor Wallace C. Sabine with Mr. Theodore Lyman, on the study of false spectra from the Rowland Concave Grating. The Committee lias devoted much time to tlie consideration of the desirability of an award of the Rumford Premium. The claims of several meritorious candidates have been investigated and discussed at length. As a result of these deliberations the Committee voted unani- mously on Feb. 13, 1901, for the first time, and on March 13, 1901, for the second time, that the Academy be recommended to award the Rum- ford Premium to Elihu Thomson for his inventions in electric welding and lighting. Chas. R. Cross, Chairman. Awards of the Rumford Premium, May 28, 1839. Robert Hare, of Philadelphia, for his invention of the compound or oxyhydrogen blowpipe. June 1, 1862. John Ericsson, of New York, for his improvements in the management of heat, particularly as shown in his caloric engine of 1855. May 30, 1865. Daniel Treadwell, of Cambridge, for improve- ments in the management of heat, embodied in his investigations and inventions relating to the construction of cannon of large calibre, and of great strength and endurance. Presented November 14, 1865. June 12, 1866. Alvan Clark, of Cambridge, for his improvements in the manufacture of refracting telescopes as exhibited in his method of local correction. Presented February 26, 1887. May 25, 1869. George Henry Corliss, of Providence, for his im- provements in the steam engine. Presented January 11, 1870. June 6, 1871. Joseph Harrison, Jr., of Philadelphia, for his mode of constructing steam-boilers, by which great safety has been secured. Presented January 9, 1872. May 27, 1873. Lewis Morris Rutherfukd, of New York, for his im- provements in the processes and methods of astronomical photog- raphy. Presented March 10, 1874. May 25, 1875. John William Draper, of New York, for his re- searches on radiant energy. Presented March 8, 1876. May 25, 1880. Josiah Willard Girbs, of New Haven, for his re- searches in thermodynamics. Presented January 12, 1881. May 29, 1883. Henry Augustus Rowland, of Baltimore, for his researches in light and heat. Presented February 14, 1884. RECORDS OF MEETINGS. 605 May 25, 1886. Samukl Pierpont Langley, of Allegheny, for his researches in radiant energy. Presented May 11, 1888. May 29, 1888. Albert, Abraham Michelson, of Cleveland, for his determination of the velocity of light, for his researches upon the motion of the luminiferous ether, and for his work on the absolute de- termination of the wave-lengths of light. Presented April 10, 1889. May 26, 1891. Edward Charles Pickering, of Cambridge, for his work on the photometry of the stars and upon stellar spectra. Pre- sented January 13, 1892. May 8, 1895. Thomas Alva Edison, of Orange, N. J., for his investigations in electric lighting. Presented May 13, 1896. May 11, 1898. James Edward Keeler, of Allegheny, for his applica- tion of the spectroscope to astronomical problems, and especially for his investigations of the proper motions of the nebulae, and the physi- cal constitution of the rings of the planet Saturn, by the use of that instrument. Presented June 14, 1899. May 10, 1899. Charles Francis Brush, of Cleveland, for the prac- tical development of electric arc lighting. Presented March 14, 1900. May 9, 1900. Carl Barus, of Providence, for his various researches in heat. Report of the C. M. Warren Committee. The C. M. Warren Committee recommends to the Academy the fol- lowing appropriations from the income of the C. M. Warren Fund : — To Professor C. F. Mabery, Case School of Applied Science, Cleve- land, Ohio, four hundred dollars for use in his researches on petroleum. To Professor A. A. Noyes, Massachusetts Institute of Technology, three hundred dollars for use in his investigation of a systematic pro- cedure for the qualitative analysis of the rare metals. To Professor Charles H. Herty, Athens, Georgia, one hundred and forty-five dollars for use in his research on platinum and allied metals. C. L. Jackson, Chairman. Report of the Committee of Publication. The Publishing Committee begs leave to report that there have been issued during the last academic year five numbers of Volume XXXV. of the Proceedings and the first twenty-eight numbers of Volume XXXVI., aggregating 719 pages and 11 plates. Besides this a small edition of Volume XXXIV. was reprinted, at a cost of $180, to replace losses l)y 606 PROCEEDINGS OF THE AMERICAN ACADEMY. fire in the bindery. Four numbers of the current Proceedings (62 pages and 4 plates) were printed at the cost of the Rumford Fund ($266.22). The total expenditure for printing falling on. the General Fund was $2438.82. The appropriation was $2400, and the return from sales $101.01, leaving an unexpended balance of $62.19. The Committee recommends for the coming year an appropriation of $2400, the same as in the last. For the Committee, Samuel H. Scudder, Chairman. Report of the Committee on the Library. The two most important matters relating to the Library have been the installation of a steel stack for folios by the Massachusetts Historical Society, on the same terms as the other stacks were furnished, and the commencement of a new card catalogue of subjects and authors, for which $200 was appropriated last year. About 1300 cards, covering nearly the whole of the works on mathematics and astronomy, have been type- written at a total cost of $70.62. The reappropriation of $100 and an appropriation of $100 from the income of the Rumford Fund is requested to continue this work and to purchase a catalogue case. The accessions during the year have been as follows : Vols. Parts of toIs. By gift and exchange .... 473 2027 By purchase — General Fund . 28 717 By purchase — Rumford Fund . 36 340 Total 537 3084 Last year the total number of accessions was 3224. 28 volumes and 717 parts of volumes were bought with the appropria- tion from the income of the General Fund at an expense of $339.52 ; 340 parts of volumes were bought with the appropriation from the income of the Rumford Fund for $101.48; 36 volumes of the " Fortschritte der Physik," needed to complete the set to date, for which a special appro- priation was made from the income of the Rumford Fund, have been purchased at an expense of $202.66; 698 volumes were bound at an expense of $925.41, of which $861.11 was charged to the General Fund and $64.30 to the Rumford Fund. A. Lawrence Rotch, Librarian and Chairman of the Committee on Library. P.ams. 296 Maps. 5 Total 2798 745 376 296 5 3919 RECORDS OF MEETINGS. 607 On the recommendation of the Rumford Committee, it was Voted^ To appropriate from the income of the Rumford Fund — One hundred dollars (§100) to aid in the cataloguing of the books in the Academy Library. One hundred and fifty dollars ($150) for the purchase and binding of periodicals. One hundred and fifty dollars ($150) for the purchase and binding of books on light and heat, said works to be purchased upon the recommendation of the Rumford Committee. One thousand dollars ($1000) for the immediate needs of the Committee in the furtherance of research. Voted., That a replica in bronze of each Rumford Medal here- after awarded be struck off and preserved in the Hall of the Academy. Voted, To award the Rumford Premium to Elihu Thomson for his inventions in electric welding and lighting. On the recommendation of the C. M. Warren Committee, it was Voted., To appropriate from the income of the C. M. Warren Fund — Four hundred dollars ($400) to Professor C. F. Mabeiy, of Cleveland, Ohio, for use in his researches on petroleum. Three hundred dollars ($300) to Professor A. A. Noyes, of Boston, for use in his investigation of a systematic procedure for the qualitative analysis of the rare metals. One hundred and forty-five dollars ($145) to Professor Charles H. Herty, of Athens, Georgia, for use in his research on platinum and allied metals. On the recommendation of the Committee on Publication, it was Voted., To appropriate from the income of the General Fund twenty-four hundred dollars ($2400) for publications. On the recommendation of the Committee on the Library, it was Voted, To appropriate from the income of the General Fund Olio hundred dollars ($100) to continue the catalogue of the Library and to purchase a catalogue-case. 608 PROCEEDINGS OP THE AMERICAN ACADEMY. On the recommendation of the Committee of Finance, it was Voted, To appropriate from the income of the General Fund two thousand, dollars ($2000) for general expenses. Voted, That the assessment for the ensuing year be five dollars. On the recommendation of the committee to whom certain alterations of the Statutes were referred at the meeting of December 12, 1900, it was Voted, To amend the Statutes as follows : — Ch. I., Sec. 1, first sentence. "The Academy consists of Resident Fellows, Associate Fellows, and Foreign Honorary Members." Ch. L, Sec. 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 assess- ment, not exceeding ten dollars, as shall be voted by the Academy at each annual meeting. Resident Fellows only may vote at the meetings of the Academy." Ch. I., Sec. 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 residing outside of the Commonwealth of Massachusetts. They shall not be liable to the payment of any fees or annual dues, but on re- moving within the Commonwealth they may be transferred by the Coun- cil to resident fellowship as vacancies there occur." Ch. L, Sec. 4. Omit " And " at the beginning of last sentence. Ch. II., Sec. 2, first sentence. " 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 Coun- cillors 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 succes- sive terms." Ch. II., Sec. 2, second sentence. Change " These " to " The." At end of this sentence add : " Five members shall constitute a quorum." Ch. v.. Sec. 5. " The Committee of Publication, of three Fellows, one from each Class, to whom all communications submitted to the Academy for publication shall be referred, and to whom the printing of the Memoirs and the Proceedings shall be intrusted." RECORDS OF MEETINGS. 609 Ch. v., Sec. 6. "The Committee on the Library, of the Librarian €x officio^ and three other Fellows, one from each Class, who shall examine the Library and make an annual report on its condition and management. Ch. VI., Sec. 1. Omit the second sentence. Ch. VI., Sec. 2, third sentence. ''He shall notify the meetings of the Academy, apprise officers and committees of their election or appoint- ment, and inform the Treasurer of appropriations of money voted by the Academy.'' Ch. VI., Sec. 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.*' Ch. VII., Sec. 2. Omit the words " by order of the President or presiding officer." Ch. VII., Sec. 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." Ch. VII., Sec. 4. Omit the words " on such securities as the Academy shall direct." Ch. VIII., Sec. 1. "It shall be the duty of the Librarian to take charge of the books, to keep a 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." Ch. VIII., Sec. 2. "Tlie Librarian, in conjunction with the Com- mittee on the Library, shall have authority to expend such sums as may be appropriated, either from the General or Special Funds of the Academy, for the purchase of books and for defraying other necessary expenses connected with the Library." Ch. VIII., Sec. 3. "To all books procured from the income of tlie 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." Ch. VIII., Sec. 5. Omit " And" at beginning of second sentence. Ch. VIII., Sec. 7. "The Librarian shall have custody of the Publi- cations of the Academy and shall distribute copies among the Associate Fellows and Foreign Honorary Members at their request. With the advice and consent of the President, he may effect exchanges with other associations." Cli. X., Sec. 2, first sentence. " Candidates for election as Resident VOL. XXXVII. — .39 610 PROCEEDINGS OP THE AMERICAN ACADEMY. Fellows must be proposed by two Resilient 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." Ch. X., Sec. 2, second sentence. Change "seven" to " five." Ch. X., Sec. 3. Abbreviate first sentence, as follows : "The nomina- tion and election of Associate Fellows may take place in the manner prescribed in reference to Resident Fellows." Ch. X., Sec. 6. Change first word ("each") to "a majority of any." Under Rumford Premium, change " a gold and silver medal " to " a gold and a silver medal." The annual election resulted in the choice of the following officers and committees for the academic year 1901-02 : — Alexander Agassiz, President. John Trowbridge, Vice-President for Class L Alpheus Hyatt, Vice-President for Class II. James B. Thayer, Vice-President for Class III. William M. Davis, Corresponding Secretary. William Watson, Recording Secretary. Francis Blake, Treasurer. A. Lawrence Rotch, Librarian. Councillors. Harry M. Goodwin, for one 3^ear. "j Charles R. Sanger, for two years. V Class I. George F. Swain, for three years, j George H. Parker, for one year. ^ Theobald Smith, for two years. V Class II. Robert DeC. Ward, for three years. William Everett, for one year. 1 A. Lawrence Lowell, for two years. V Class III Denman W. Ross, for three years. J Member of Co^nmittee of Finance. Eliot C. Clarke. RECORDS OF MEETINGS. 611 Ruwford Committee. Erasmus D. Leavitt, Amos E. Dolbear, Edward C. Pickering, Arthur G. Webster, Charles R. Cross, Theodore W. Richards, Thomas C. Mendenhall. C. M. Warren Committee. Charles L. Jackson, Leonard P. Kinnicutt, Samuel Cabot, Arthur M. Comey, Henry B. Hill, Robert H. Richards, Henry P. Talbot. The Chair appointed the following standing committees : — Committee of Publication. Samuel H. Scudder, Seth C. Chandler, Crawford H. Toy. Committee on the Library. Henry W. Haynes, Samuel Henshaw. Theodore W. Richards. Auditing Committee. Henry G. Denny, William L. Richardson. The following gentlemen were elected members of tlie Academy : — George Frisbie Hoar, of Worcester, as Resident Fellow in Class HI., Section 1 (Philosophy and Jurisprudence). John Fritz, of Bethlehem, Pennsylvania, as Associate Fellow in Class I., Section 4 (Technology and Engineering). Thomas Chrowder Chamberlin, of Chicago, as Associate Fellow in Class II., Section 1 (Geology, INIineralog}', and Physics of the Globe), in place of the late George Mercer Dawson. Ferdinand Freiherr von Richthofen, of Berlin, as Foreign Honorary Member in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe). Adolph Engler, of Berlin, as Foreign Honorary Member in 612 PROCEEDINGS OF THE AMERICAN ACADEMY. Class IT., Section 2 (Botany), in place of the late Jacob Georg Agardh. Angelo Celli, of Rome, as Foreign Honorary Member in Class II., Section 4 (Medicine and Surgery). Gaston Paris, of Paris, as Foreign Honorary Member in Class III., Section 4, in place of the late Charles Jacques Victor Albert, Due de Broglie. The Treasurer proposed an amendment to Chapter V., Sec- tion 2, of the Statutes. This proposition was referred to a committee consisting of the Treasurer and James B. Ames. James B, Thayer read an obituary notice of John E. Hudson. Clarence J. Blake read an obituary notice of his father, John H. Blake, and F. W. Putnam gave an account of tlie archaeo- logical work of Mr. Blake. The following papers were presented by title: — " On Ruled Loci in w-Fold Space." By Halcott C. Moreno. Presented by W. E. Story. " The Possible Significance of Changing Atomic Volume." By T. W. Richards. " The Visible Radiation from Carbon." By Edward L. Nichols. Contributions from the Gray Herbarium of Harvard Uni- versity. New Series. — No. XXII. I. " The Northeastern Car- ices of the Section Hyparrhenae ; " II. "Notes on the Varia- tions of Certain Boreal Carices." By M. L. Fernald. Contributions from the Cryptogamic Laboratory of Harvard University. — XLVII. " Preliminary Diagnoses of New Species of Laboulbeniaceae." — IV. By Roland Thaxter. Nine liundred and twenty-sixth Meeting. October 9, 1901. — Stated Meeting. The Academy met at the house of the President, Cambridge. The President in the chair. The Corresponding Secretary read letters from Tlieodore Lyman, accepting Resident Fellowship ; from George E. Hale, W. W. Keen, E. H. Moore, C. 0. Whitman, acknowledging electiou as Associate Fellows ; and from Sir Lauder Brunton, KECORDS OF MEETINGS. 613 A. V. Dicey, A. Engler, Henry Jackson, R. Koch, Miiller- Breslau, Gaston Paris, Poincare, Fr. Richthofen, acknowledging election as Foreign Honorary Members. He also read letters from the President and Fellows of Yale University, invitinsr the Academy to be represented at the celebration of the two hundredth anniversary of the founding of Yale College ; from the Natural History Society of Nuremberg, inviting attendance at the celebration of its one hundredth anniversary ; and from a committee of the Anthropological Section of the American Association for the Advancement of Science, announcing that the thirteenth session of the International Congress of Ameri- canists would be held at New York in 1902, and inviting the Academy to appoint a representative to the General Committee of the Congress. On the motion of E. S. Morse, it was Voted, To authorize the President to appoint delegates in response to these invitations. The Chair announced the following deaths : — Truman Henry Safford, of Class I., Section 1, and John Fiske, of Class III., Section 3, Resident Fellows. Joseph LeConte, of Class II., Section 1, Associate Fellow. Friherre Adolf Erik Nordenskiold, of Class II., Section 1, F^lix Joseph Henri de Lacaze-Duthiers, of Class II., Section 3, and Friedrich Herman Grimm, of Class III., Section 3, Foreign Honorary Members. On the motion of the Recording Secretary, it was Voted, To meet, on adjournment, on the second Wednesday in November. The following gentlemen were elected members of the Academy : — Henr}^ Smith Pritchett, of Boston, to be a Resident Fellow in Class I., Section 1 (Mathematics and Astronomy). William Townsend Porter, of Boston, to be a Resident Fellow in Class II., Section 3 (Zoology and Physiology). George Wharton Pepper, of Philadelphia, to be an Associate Fellow in Class III., Section 1 (Philosophy and Jurisprudence), in place of the late William Mitchell. 614 PROCEEDINGS OF THE AMERICAN ACADEMY. The President made a few remarks on the condition and prospects of the Academy. The Rumford Medals were presented to Carl Barus and Elihu Thomson. The President gave an account of the Albatross Expedition to the Tropical Pacific. The following paper was read by title : — " The Algae of Jamaica," by Frank S. Collins. » Nine hundred and twenty-seventh Meeting. November 13, 1901. — Adjourned Stated Meeting. The Academy met at the house of James Ford Rhodes. Vice-President J. B. Thayer in the chair. The Corresponding Secretary read a letter from Mrs. Cooke, presenting to the Academy a bronze bas-relief of her husband, the late Josiah Parsons Cooke, President of the Academy. Voted, That the Academy gratefully accept this gift and that the Corresponding Secretary be instructed to inform Mrs. Cooke to that effect. A letter from the National Society of Natural and Mathemat- ical Sciences of Cherbourg, requesting sympathetic souvenirs on the occasion of the fiftieth anniversary of its establishment, was referred to the Council. Letters were also read from W. T. Porter, accepting Resident Fellowship ; from George Wharton Pepper, acknowledging election as Associate Fellow ; from A. Mislawsky, of Ekaterin- burg, acknowledging the congratulations of the Academy on the occasion of the fiftieth anniversarv of his medical service ; from the Nobel Committee of the Royal Academy of Sciences of Sweden, soliciting suggestions for the award of the Nobel Prize in 1902. Percival Lowell read a biographical notice of the late Augustus Lowell. William Everett read an essay entitled '' The Malignity of Dante." A paper entitled " The Parametric Representation of the Neighborhood of a Singular Point of an Analytic Surface,'' by C. W. M. Black, was presented by title. RECORDS OF MEETINGS. 615 Nine hundred and twenty-eighth Meeting. December U, 1901. The Academy met at the Massachusetts Institute of Tech- nology. The Corresponding Secretary in the chair. In the absence of the Recording Secretary, G, F. Swain was elected Secretary jpro tempore. The Chair announced the death of Joseph Henry Thayer, Resident Fellow in Class III., Section 2. The following papers were read : — " Some Results from the Last Opposition of Mars." By Per- cival Lowell. "The Atharva Veda and its Significance for the History of Hindu Tradition and Hindu Medicine." By Charles R. Lanman. The following papers were presented by title : — " The Standard of Atomic Weights." By T. W. Richards. " Modifications of Hempel's Gas-apparatus." By T. W. Richards. " A New Determination of the Atomic Weight of Uranium." By T. W. Richards and B. S. Merigold. " The Decomposition of Mercurous Chloride by Dissolved Chlorides : a Contribution to tlie Study of Concentrated Solu- tions." By T. W. Richards and E. H. Archibald. " Apatite from Minot, Maine." By John E. Wolff and Charles Palache. Nine hundred and twenty-ninth Meeting. January 8, 1902. — Stated Meeting. The Corresponding Secretary in the chair. A letter was read from A. Celli, acknowledging his election as Foreign Honorary Member ; also, a circular inviting attend- ance at the Thirteenth Session of the International Congress of Americanists, in New York, in October, 1902. The Chair announced the death of Aleksandr Onufrijevic Kovalevsky, Foreign Honorary Member in Class II., Section 3. The following gentlemen were elected members of the Academy : — 616 PROCEEDINGS OF THE AMERICAN ACADEMY. Harry Ellsworth Clifford, of Newton, to be a Resident Fellow in Class I., Section 2 (Physics). Theodore Hough, of Boston, to be a Resident Fellow in Class II., Section 3 (Zoology and Physiology). Francis Henry Williams, of Boston, to be a Resident Fellow in Class II., Section 4 (Medicine and Surgery). Morris Hicky Morgan, of Cambridge, to be a Resident Fellow in Class HI., Section 2 (Philology and Archaeology). Edmund Beecher Wilson, of New York, to be an Associate Fellow in Class II., Section 3 (Zoology and Physiology), in place of the late George Mercer Dawson. Julius Harm, of Vienna, to be a Foreign Honorary Member in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe). Edwin Ray Lankester, of London, to be a Foreign Honorary Member in Class II., Section 3 (Zoology and Physiology), in place of the late F^lix Joseph Henri de Lacaze-Duthiers. Victor Alexander Haden Horsley, of London, to be a Foreign Honorary Member in Class II., Section 4 (Medicine and Surgery). Friedrich Delitzsch, of Berlin, to be a Foreign Honorary Member in Class III., Section 2 (Philology and Archaeology), in place of the late Friedrich Herman Grimm. Samuel Rawson Gardiner, of Sevenoaks, to be a Foreign Honorary Member in Class III., Section 3 (Political Economy and History), in place of the late William Stubbs. The Corresponding Secretary announced that Thomas C. Mendenhall had removed from the Commonwealth and that his name had again been placed in the list of Associate Fellows. Upon the recommendation of the Council, it was Voted, To transfer Percival Lowell, Resident Fellow, from Class in., Section 4, to Class I., Section 1. Upon the recommendation of the committee on amending the Statutes, it was Voted, To amend the first sentence of Chapter V., Section 2, of the Statutes to read as follows : — " The Committee of Finance, to consist of the President, Treasurer, and one Fellow chosen by ballot, who shall have full RECORDS OF MEETINGS. 617 control and management of the funds and trusts of the Academy, with the power of investing or changing the investment of the same at their discretion." A. Lawrence Lowell read a paper entitled, " Party Votes in Parliament, Congress, and the State Legislatures." The following papers were presented by title : — Contributions from the Gray Herbarium of Harvard Univer- sity. New Series. — No. XXHI. " A Revision of the Galapagos Flora." By B. L. Robinson. " The Probable Source of the Heat of Cliemical Combina- tions." By Theodore William Richards. " A Description of Crystals of Epidote from Alaska." By Charles Palache. Presented by John E. Wolff. John E. Wolff exhibited a specimen of apatite from Minot, Maine. Nine hundred and thirtieth Meeting. February 12, 1902. In the absence of the regular presiding officers, the chair was taken by Charles R. Cross. Letters were received from Theodore Hough and Morris H. Morgan accepting Fellowship ; from Edmund B. Wilson, ac- knowledging his election as Associate Fellow ; and from the National Society of Natural and Mathematical Sciences of Cher- bourar, acknowledgrinsf congratulations on the occasion of its fiftieth anniversary. The Chair announced the following deaths : — Alpheus Hyatt, Vice-President for Class H. Clarence King, Associate Fellow in Class H., Section 1. Karl Weinhold, Foreign Honorary Member in Class HI., Sec- lion 2. Li accordance with the Statutes, the following Councillors were appointed a committee to nominate a candidate for the office of Vice-President for Class TL : — Harry M. Goodwin, of Class L George H. Parker, of Class 11. William Everett, of Class HL 618 PROCEEDINGS OF THE AMERICAN ACADEMY. The following communications were presented : — "Experiments on Forms of Least Resistance to Passage through Air." By Samuel Cabot. Remarks on this subject were made by Messrs. Davis, Atkinson, Webster, Clayton, and the Recording Secretary. " What Science has not yet Accomplished in the Art of War." By Edward Atkinson. The following paper was presented by title : — ■ " On the Specific Heat and Heat of Vaporisation of the Paraf- fine and Methylene Hydrocarbons." By Charles F, Mabery and Albert H. Goldstein. Nine hundred and thirty-first Meeting. March 12, 1902. — Stated Meeting. Vice-President Trowbridge in the chair. Letters were read from Friedrich Del'itzsch, S. R. Gardiner, Julius Hann, Victor Horsley, E. Ray Lankester, acknowledging their election as Foreign Honorary members. The Chair announced the following deaths : — James Bradley Thayer, Vice-President for Class IL Samuel Rawson Gardiner, Foreign Honorary member in Class 111., Section 3. The vacancy occasioned by the death of Alpheus Hyatt was filled by the election of Henry P. Walcott, Vice-President for Class II. The following gentlemen were elected members of the Academy : — Heinrich Oscar Hofman, of Boston, to be a Resident Fellow in Class I., Section 4 (Technology and Engineering). Thomas Augustus Jaggar, Jr., of Cambridge, to be a Resident Fellow in Class IL, Section 1 (Geology, Mineralogy, and Physics of the Globe). Edward Henry Strobel, of Cambridge, to be a Resident Fellow in Class III., Section 1 (Philosophy and Jurisprudence). Herbert Putnam, of Washington, to be an Associate Fellow in Class III., Section 4 (Literature and the Fine Arts). RECORDS OF MEETINGS. 619 The Chair appointed the following Councillors to serve as Nominating Committee : — William Everett, of Class III. George H. Parker, of Class II. Harry M. Goodwin, of Class I. On the motion of the Recording Secretary, it was Voted, To rescind Standing Vote 9, ''The Annual Meeting and the other stated meetings shall be holden at eight o'clock P. M." The following papers were read : — " Biographical Notice of the late Horace E. Scudder." By- Thomas W. Higginson. " Biographical Notice of the late Joseph H. Thayer." By Crawford H. Toy. " The Formation of River Terraces." By William M. Davis. " The Spectra of Gases at High Temperatures." By John Trowbridge. The following papers were presented by title : — " Experiments on the Effect of Freezing and other Low Tem- peratures upon the Viability of the Bacillus of Typhoid Fever, with Considerations regarding Ice as a Vehicle of Infectious Disease." By William Thompson Sedgwick and Charles- Edward A. Winslow. " Statistical Studies on the Seasonal Prevalente of Typhoid Fever in Various Countries and its Relation to Seasonal Tem- perature." By William Thompson Sedgwick and Charles- Edward A. Winslow. Nine hundred and thirty-second Meeting. April 9, 1902. — Stated Meeting. The Academy met at the house of Robert Amory. The Corresponding Secretary in the chair. The following papers were read : — " Account of the Ninth Jubilee Celebration of the University of Glasgow." By William G. Farlow. 620 PROCEEDINGS OF THE AMERICAN ACADEMY. " Biographical Notice of the late John Fiske." By A. McF. Davis. The following paper was presented by title : — Contributions from the Case School of Applied Science. — XLI. " On the Hydrocarbons in Pennsylvania Petroleum with Boiling Points above 216 °." By Charles F. Mabery. Nine hundred and thirty- third Meeting. May 14, 1902. — Annual Meeting. Vice-President Trowbridge in the chair. The Corresponding Secretary read letters from Henry P. Walcott, accepting his election as Vice-President for Class H. ; H. E. Cliftbrd, H. O. Hofman, T. A. Jaggar, Jr., Edward H. Strobel, accepting Resident Fellowship ; Herbert Putnam, acknowledging election as Associate Fellow ; Madame Cornu, announcing the death of her husband, Alfred Cornu; the University of Oxford, inviting the Academy to send a repre- sentative to the commemoration of the 300th anniversary of the opening of the Bodleian Library, on October 8 and 9, 1902 ; the Royal University of Christiania, announcing the celebra- tion, in September next, of the 100th anniversary of the birth of Nicolaus Henricus Abel and inviting the attendance of dele- gates. On the motion of the Recording Secretary, it was Voted, To appoint Herbert Putnam, Associate Fellow, to represent the Academy at the Bodleian Library commemora- tion. The annual report of the Council was read by the Corre- sponding Secretary. The Treasurer presented his annual report, of which the fol- lowing is an abstract : — RECORDS OF MEETINGS. 621 General Fund. Receipts. Balance (Deficit), April 30, 1901 $187.33 Assessments $990.00 Admission fees 150.00 Sale of publications 138.78 $1,278.78 Income from investments 5,735.58 7,014.36 $0,827.03 Expenditures. General expenses $2,786.94 Publishing $2,095.59 Library 1,576.68 Catalogue 95.40 3,767.67 Balance, April 30, 1902 . '. . . • 272.42 $6,827.03 RuMFORD Fund. Receipts. Balance, April 30, 1901 $2,546.08 Income from investments $2,514.17 Sale of publications • 5.00 2,519.17 $5,065.25 Expenditures. Researches $1,800.00 Medals 474.00 ^ Publishing . 417.51 Library " 183.12 Catalogue 70.00 Miscellaneous 23.66 $2,968.29 Income invested and transferred to capital acc't, 1,715.00 Balance, April 30, 1902 381.96 $5065.25 622 PROCEEDINGS OF THE AMERICAN ACADEMY. Warren Fund. Receipts. Balance, April 30, 1901 $1,276.29 Income from investments 329.43 $1,605.72 Expenditures. Investigations $845.00 Balance, April 30, 1902 760.72 $1,605.72 Building Fund. Receipts. Balance, April 30, 1901 $360.04 Income from investments 309.51 $689.55 The following reports were also presented : — Report of the Librarian. The card-catalogue, commenced in 1900, has been continued by the Assistant Librarian, who has type-written during the past year 2770 cards, the total number of cards now being upwards of 4000. Most of the works on general science, mathematics, astronomy, physics, optics, heat and electricity are now catalogued. A catalogue-case was pur- chased for $70. Of the $200 appropriated, the total amount expended on account of the catalogue was $164.40, of which $95.40 was charged to the General Fund and $70 to the Rumford Fund. The same appro- priation that was made last year is requested for continuing this work, namely: $100 from the income of the General Fund and $100 from the income of the Rumford Fund. The accessions during the year have been as follows : — Parts of Vols. Vols. Pams. Maps. Total. By gift and exchange .... 496 2486 384 2 3368 By purchase — General Fund . 18 665 683 By purchase — Rumford Fund . 1 256 259 Total ........ 515 3406 384 2 4310 RECORDS OF MEETINGS. 623 Last year the total number of accessions was 3919. At the request of the Rumford Committee, 21 volumes on light and heat, for the purchase and binding of which $150 was appropriated from the income of the Rumford Fund, have been ordered but not paid for. The expenses charged to the Library were as follows : — Miscellaneous, which includes expenses in no way relating to the Library, $439.95 ; Binding, $G04.70; Subscriptions, $532.03, making a total of $1450.38. The usual appropriation of $1500 from the income of the General Fund is requested in addition to the customary appropriation from the income of the Rumford Fund, namely $150. A. Lawrence Rotch, Librarian. Boston, May 14, 1902. Report of the Rumford Committee. At the Annual Meeting of the Academy held May 8, 1901, the sum of $1000 was placed at the disposal of the Rumford Committee, to be expended at its discretion in aid of researches in light and heat. The following orrants have been voted : — Nov. 13, 1901. One hundred dollars to Professor Henry Crew of Northwestern University, in aid of bis research on the order of appear- ance of the different lines of the spark spectrum. Nov. 13, 1901. Three hundred and fifty dollars to Professor R. \Y. Wood of Johns Hopkins University, in aid of his researches on the anomalous dispersion of sodium vapor. Nov. 13, 1901. Sixty-five dollars to Professor A. G. Webster of Clark University, in payment of the cost of fluorite plates purchased for use in a research on the distribution of energy in various spectra. Feb. 12, 1902. Three hundred dollars to Professor Ernest F. Nichols of Dartmouth College, for the purchase of a spectrometer in furtherance of his research on resonance in connection with heat radiations. April 9, 1902. Three hundred dollars as it is or may become avail- able to Professor Arthur A. Noyes of the Massachusetts Institute of Technology, in aid of his research upon the efi^ect of high temperatures upon the electrical conductivity of aqueous solutions. At the meeting of February 12, 1902, it was voted to authorize the Librarian to purchase certain books upon light and heat as specified in a list transmitted to him by the Committee. 624 PROCEEDINGS OF THE AMERICAN ACADEMY. Tlie following papers, embodying the results of researches aided by appropriations from the Rumford Fund, have been printed in Volume XXXVIl. of the Proceedings of the Academy : — " The Visible Radiation from Carbon," by Edward L. Nichols. " The Arc Spectrum of Hydrogen," by O. H. Basquin. " The Probable Source of the Heat of Chemical Combination and a New Atomic Hypothesis," by Theodore William Richards. Reports of the progress of unfinished researches which have been aided by grants from the Rumford Fund have been received from the following persons : Messrs. Artliur L. Clark, Henry Crew, Edwin B. Frost, George E. Hale, Frank A. Laws, Charles E. Mendenhall, Ernest F. Nichols, Arthur A. Noyes, Edward C. Pickering, Theodore W. Rich- ards, Wallace C. Sabine, R. W. Wood. The following recommendations have been voted by the Committee, and are now presented to the Academy for its consideration. On February 12, 1902, it was voted to ask the Academy to appropri- ate the sum of seven hundred and fifty dollars from the income of the Rumford Fund to be expended for the construction of a mercurial com- pression pump designed by Professor Theodore W. Richards, and to be used in his research on the Thomson-Joule Effect. At the meeting of April 9, 1902, it was voted to request the Academy to appropriate the sura of one thousand dollars from the income of the Rumford Fund, for the immediate needs of the Committee in further- ance of research, and also to appropriate the sum of one hundred and fifty dollars from the same source for the purchase and binding of periodicals. At the meeting of May 14, 1902, it was voted to ask the Academy to reappropriate from the income of the Rumford Fund the unexpended balance of the amount granted at the last annual meeting, for the pur- chase and binding of books on light and heat for the Library. The Committee has considered at length the question of an award of the Rumford Premium, and at the meeting of April 9 it was unani- mously voted for the first time, and at the meeting of May 14 it was unanimously voted for the second time, to recommend tio the Academy that such award be made to Professor George E. Hale, Director of the Yerkes Observatory, for his investigations in Solar and Stellar Physics, and in particular for the invention and perfection of the Spectro- heliograph. Chas. R. Cross, Chairman. RECORDS OF MEETINGS. 625 Rkpout of the C. M. Wauuen Committee. The Committee in charge of the C. INI. Warren Fund has the honor to report that Professor Mabery and Professor A. A. Noyes have reported satisfactory progress in the work supported by grants from the Fund. Professor Herty, owing to an. unforeseen change of occupation, is unable to coniinue his work on platinum, and will return the money granted him. The Committee recommends the following grants from the C. M. Warren Fund for this year : — C. F. Mabery, of Cleveland, $300.00 for the continuation of his researches on Petroleum. A. A. Noyes, of Boston, $300.00 for the continuation of his work on the qualitative analysis of the rare elements. H. O. Hofman, of Boston, $160.00 for a research on the decomposition of sulphate of zinc. C. L. Jackson, Chairman. Report of the Committee of Publication. The Publishing Committee begs leave to report that there have been issued during the last academic year one number of Vol. XXXVI. and twenty-one numbers of Vol. XXXVII. of the Proceedings, aggregating 648 pages and 15 plates. Three numbers of the current volume (82 pp. and 2 pi.) were printed at the cost of the Rumford Fund ($417.51). The expense of printing fallino- on the General Fund was $2095.59 ; the appropriation was . $2400, and the returns from sales $138.59, leaving an unexpended balance of $443. The Committee recommends for the ensuing year the usual appropriation of $2400. An exjiensive memoir, closing Vol. XII., is in press. For the Committee, Samuel II. Scudder, Chairman. Boston, May 14, 1902. 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 expenditures during the ensuing year : — VOL. XXXVII. — 40 626 PROCEEDINGS OP THE AMERICAN ACADEMY. For general expenses, $2400 For the library, 1500 For cataloguing, 100 For publishing, 2400 On the recommendation of the Rumford Committee, it was Voted, To make the following appropriations from the in- come of the Rumford Fund : One thousand dollars (^1000) for the immediate needs of the Committee in furtherance of research ; seven hundred and fifty dollars (-1750) to be ex- pended for the construction of a mercurial compression pump designed by Theodore W. Richards, and to be used in his re- search on the Thomson-Joule Effect ; one hundred and fifty dollars (iflSO) for the purchase and binding of periodicals. Voted, To re-appropriate the unexpended balance of the amount granted at the last annual meeting for the purchase and binding of books on light and heat for the Library. On the recommendation of the C. M. Warren Committee, it was Voted, To make the following grants from the income of the C. M. Warren Fund: (1) To C. F. Mabery of Cleveland, three hundred dollars ($300) for the continuation of his re- searches on petroleum. (2) To A. A. Noyes of Boston, three hundred dollars ($300) for the continuation of his work on the qualitative analysis of the rare elements. (3) To H. O. Hof- man of Boston, one hundred and sixty dollars (-$160) for a te- search on the decomposition of sulphate of zinc. On the motion of the Corresponding Secretary, it was Voted, That the assessment for the ensuing year be five dollars ($5). The annual election resulted in the choice of the following oSicers and committees : — Alexander Agassiz, President. John Trowbridge, Vice-President for Class I. Henry P. Walcott, Vice-President for Class II. John C. Gray, Vice-President for Class HI. William M. Davis, Corresponding Secretary. RECORDS OF MEETINGS. 627 William Watson, Recording Secretary. Francis Blake, Treasurer. A. Lawrence Rotch, Librarian. Councillors for Three Years. Arthur G. Webster, of Class I. Edward L. Mark, of Class II. Arlo Bates, of Class III. 3Iember of Committee of Finance. Eliot C. Clarke. Rumford Committee. Erasmus D. Leavitt, Amos E. Dolbear, Edward C. Pickering, Arthur G. Webster, Charles R. Cross, Theo. W. Richards, Elihu Thomson. ■ C. M. Warren Comynittee. Charles L. Jackson, Samuel Cabot, Henry B. Hill, Leonard P. Kinnicutt, Arthur M. Comey, Robert H. Richards, Henry P. Talbot. The following standing committees were appointed by the Chair : — Committee of Publication. Seth C. Chandler, of Class I., Edward L. Mark, of Class IL, Crawford H. Toy, of Class III. Committee on the Library. William F. Osgood, of Class I., Samuel Henshaw, of Class II., Henry W. Haynes, of Class HI. Audiiitiy Committee. Henry G. Denny, William L. Richardson. 628 PROCEEDINGS OF THE AMERICAN ACADEMY. The following gentlemen were elected members of the Acad- emy : — Arthur James Balfour, of London, to be a Foreign Honorary Member in Class III., Section 1 (Pliilosophy and Jurisprudence), in place of the late Charles Russell, Baron Russell of Killowen. William Edward Hartpole Lecky, of London, to be a Foreign Honorary Member in Class IH., Section 3 (Political Economy and History), in place of the late Samuel Rawson Gardiner. On the recommendation of the Rumford Committee, it was Voted, To award the Rumford Premium to George Ellery Hale, of the Yerkes Observatory. James Barr Ames read a biographical notice of tlie late James Bradley Thayer. A biographical notice of the late Alpheus Hyatt, by Alpheus S. Packard, was read by the Corresponding Secretary. The following papers were presented by title : — " 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 Royal A, Porter. Presented by Charles R. Cross. " On the Multiple Points of Twisted Curves." By John N. Van der Vries. Presented by William E. Story. "Regular Singular Points of a System of Homogeneous Linear Differential Equations of the First Order," By Otto Dunkel. Presented by Maxime Bocher. Contributions from the Cryptogamic Laboratory of Harvard University. — L. "Preliminary Diagnoses of New Species of Laboulbeniaeeae." — V. By Roland Thaxter. Contributions from the Cryptogamic Laboratory of Harvard University, — LI. "On Cauloglossum transversarium (Bosc) Fries." By J. R. Johnston. Presented by Roland Thaxter. " On the Ionization of Soils." By Anion Benton Plowman, Presented by George Lincoln Good ale. Contributions from the Gray Herbarium of Harvard Uni- versity. New Series. — XXV. I. " Flora of Cocos Island of the Pacific." II. " Diagnoses and Synonymy of some Mexican Spermatophytes." By B. L. Robinson. RECORDS OP MEETINGS. 629 " On the Dibromdinitrobenzols derived from Paiadibrom- benzol." Second paper. By C. Loring Jackeon and D. F. Cal- hane. '■'■ On the Colored Substances derived from Nitro-compounds." Fourth paper. By C. Loring Jackson and R. B. Earle. " On Certain Derivatives of Picric Acid." By C. Loring Jack- son and R. B. Earle. " On Symmetrical Dinitrobenzolsulphonic Acid." By C. Loring Jackson and R. B. Earle. " On Certain Derivatives of 1, 2, 3-tribrombenzol." By C. Loring Jackson and A. H. Fiske. 630 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. Name. Symbol. Atomic Weight. Name. Symbol. Atomic Weight. Aluminium . . Al 27.1 Molybdenum . . Mo 96.0 Antimony . Sb 120.0 Neodymium Nd 143.6 Argon . . A 39.92 Neon . . Ne 19.94 Arsenic . . As 75.0 Nickel . . Ni 58.71 Barium . . Ba 137.43 Niobium . Nb = Cl) 94. Beryllium . Be = Gl 9.1 Nitrogen . N 14.04 Bismuth Bi 208. Osmium Os 190.8 Boron . . B 11.0 0.\ygen (stanc lar d) 0 16.000 Bromine Br 79.955 Palladium . Pd 106.5 Cadmium . Cd 112.3 - Phosphorus . P 31.0 Cffisium Cs 132.88 Platinum . Pt 195.2 Calcium . Ca 40.13 Potassium . K .39.14 Carbon . . C 12.001 Praseodymiur Q Pr 140.5 Cerium . . Ce 140. Rhodium . Rh 103.0 Chlorine . CI 35.455 Rubidium . Rb 85.44 Chromium Cr 52.14 Ruthenium Ru 101.7 Cobalt . . Co 59.00 Samarium ? Sm 150. Columbium Cb = Nb 94. Scandium . Sc 44. Copper . . Cu 63.60 Selenium . Se 79.2 " Didymium ' Nd + Pr 142.± Silicon . . Si 28.4 Erbium . . Er 166. Silver . . Ag 107.93 Fluorine F 19.05 Sodium . . Na 23.05 Gadolinium Gd 156. ? Strontium . Sr 87.68 Gallium Ga 70.0 Sulphur S 32.065 Germanium Ge 72.5 Tantalum . Ta 183. Glucinum . Gl=Be 9.1 Tellurium . Te 127.5 ? Gold . . . Au 197.3 Terbium? . Tb 160. Helium . . He 3.96 Thallium . Tl •204.15 Hydrogen . H 1.0076 Thorium ? . . Th 233. ? Indium . . In 114. Tlmlium 1 . Tu 171.? Iodine . . . I 126.85 Tin . . . Sn 119.0 Iridium . . Ir 193.0 Titanium . Ti 48.17 Iron . . . Fe 55.88 Tungsten . W 184. Krypton Kr 81.7 Uranium . U 238.5 Lanthanum La 138.5 Vanadium . V 51.4 Lead . . Pb 206.92 Xenon . . X 128. Lithium Li 7.03 Ytterbium . Yb 173. Magnesium Mg 24.36 Yttrium Yt 89.0 Manganese Mn 55.02 Zinc . . . Zn 65.40 Mercury . Hg 200.0 Zirconium . Zr 90.6 RICHARDS. — A TABLE OP ATOMIC WEIGHTS. 631 NOTE. The accompanying table of atomic weights is but little changed since last year. Caesium is made 132.88 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. Tlie value for caesium 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 tiie presence of included gases. || The case of potassium is somewhat peculiar; for in spite of the great wealth of data concerning tliis element, Clarke assigns to it the value 39.11, while the German Committee chooses 39.15. 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). t Richards, Journ. Am. Chem. Soc, 22, 72 (1900), also 24, 374 (1902). I 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). II Richards and Rogers, These Proceedings, 28, 209 (1893). AMERICAN ACADEMY OF ARTS AND SCIENCES. Report of the Council. — Presented May 14, 1902. BIOGRAPHICAL NOTICES. Augustus Lowell Percival Lowell. Truman Henry Safford . . . Arthur Searle. Horace Elisha Scudder . . . Thomas Wentworth Higginson. Joseph Henry Thayer . . . . C. H. Toy. John Fiske Andrew McFarland Davis. James Bradley Thayer .... James Barr Ames. REPORT OF THE COUNCIL. The Academy has lost sixteen members by death since the annual meeting of May 8, 1901 : Six Resident Fellows, — John Fiske, Alpheus Hyatt, Truman Henry Safford, Horace Elisha Scudder, James Bradley Thayer, Joseph Henry Thayer ; two Associate Fellows, — Clarence King, Joseph LeConte ; eight Foreign Honorary Members, — Marie Alfred Cornu, Samuel Rawson Gardiner, Friedrich Herman Grimm, William Edward Hearn, Aleksandr Onufrijevic Kovalevsky, Felix Joseph Henri de Lacaze-Duthiers, Friherre Adolf Erik Nordenskidld, Karl Weinhold. AUGUSTUS LOWELL. Augustus Lowell was born in Boston, Jan. 15, 1830. His father was John Amory Lowell and his mother Elizabeth (Putnam) Lowell, daughter of Hon. Samuel Putnam of Salem. Both the Lowell and the Putnam families were early settlers in the new world, the former landing in Newburyport in 1639, the latter in Salem in 1630. Mr. Lowell thus came of Puritan stock on both sides. Otherwise the parts of his inheritance differed, for the Lowells were Norman b}' descent — the name, originally Lowle, dating from the conquest — while the Putnams, originally Puttenham, were apparently Saxon. He inherited the quali- ties of his name. Mentally he was the son of his father ; as a matter of fancy as much as of fact, his mother's share in him being chiefly physical. For while in feature he looked like lier, in mind he not only resembled his father but looked up to him with a very unusual amount of reverence and esteem. The feeling doubtless was born of the fact and is note- worthy because of the common belief that capable men have had capable mothers. Yet not only in his case but in the case of his father, grand- father, and great-grandfather before him, the capacity followed the name. Indeed the family has proved a singular instance of prepotence in the male line, while the temperament has been as strikingly a maternal gift. 6S6 AUGUSTUS LOWELL. In Boston and in its immediate neighborhood his boyhood was spent. Of the winter delights of town as seen through youthful eyes we are given a glimpse in a letter written at the time to his friend, Mr. Augustus Peabody. Chief among them it would seem was coasting on the Common, and in the epistle we are informed of the existence of two coasts there: " one the big boys' coast and the other the small boys' coast ; " " but," the writer adds to fire the ambition of his friend and so induce him to come up for a visit, " the big boys do coast on the small boys' coast and the small boys do coast on the big boys' coast." The rounded accuracy of this statement, devoid of even the least suspicion of the elliptical, testifies conclusively to the writer's time of life. His father had inherited the family country place in Roxbury, which then was country indeed, innocent of bricks and mortar, of city streets and of course of railroads. Horses and carriages made sole means of outside communication. Partly from necessity, therefore, partly for pleasure, Mr. .John Amory Lowell every day drove into town to his business and with him he took his son to attend the Boston Latin School. This school, so named from teaching " small latin and less greek," was then the popu- lar school for boys of the place. To it in consequence went many well- known men, among them his lifelong friends, Mr. George A. Gardner and Mr. Thornton K. Lothrop. The " small latin " was hardly such in quantity, if one may judge by report of the approved Latin grammar of the day. Indeed education would seem to have consisted of the learning by heart — pathetically so called in such connection — of a mass of rules and their elephantine exceptions, sufficient to stagger even a Roman into speaking something else. At all events, of the son's labors at that insti- tution of learning the sole document extant is of the lucus a non kind : a petition to his Honor the Mayor and Chairman of the School Committee to allow the boys the first day of May as a holiday in which they might " enjoy the beauties of nature and a recreation and relaxation from school labors." Mr. Lowell appears heading the interesting document, which was couched as convincingly as possible by a classmate. By nature the place in Roxbury was beautiful, though one would never divine it to-day. Shorn of its fine old trees, even pared of its hills, the land is possessed now by a brewery and tenement houses. But in those days it was otherwise, as fading photographs show, and its garden was both a delight and a name. For Mr. John Amory Lowell had two pas- times, algebra and botany. His spare moments were devoted to one or the other of these pet pursuits. When he was not setting himself prob- lems he was puttering over plants. And he did both to some effect. AUGUSTUS LOWELL. 637 His algebraic propensities won him local reputation as a mathematician, and a manuscript volume upon the same, still in the family's possession, is both curious and interesting reading. As a botanist he was known not only at home but abroad, and was on terms of correspondence, not to say criticism, with botanists of his day. His botanical care was not confined to the livins: ; in his studies he collected a fine herbarium which received fully as much of his attention, and attracted attention from others. The son inherited both paternal proclivities, but both rather as deep-seated mental characteristics than as current mental traits. Mathematics he neither cared for, nor was proficient in, but he derived from his father that logical exactness of mind which is their basis. The botany bore greater fruit. His tastes for plants, including both trees and flowers, proved a very deep-seated passion. Doubtless fostered in part by his father's familiarity with shrubs — though as a boy he showed no marked symptoms of botanic zeal — the love of growing things later became his most pronounced avocation. In 1846 Mr. Lowell entered Harvard College where he spent the four years enjoined for a degree and was duly graduated in 1850. It was not then more than it is now the fashion to study, and he took his parchment void of invidious distinction. Indeed his recollections do not seem to have been specially academic, as one of the most vivid of them had to do with a certain midnight ride for illicit purposes to the Watertown arsenal. His rank in his class, if I am right, was sixteenth, just below what was at the time the BK line. He was not therefore a member of that de- servedly distinguished society of learning, but it is significant of his sub- sequent standing in the community that on the fiftieth anniversary of his graduation he was elected into it as an honorary member, an honor he never lived to receive or even know of, as unknown to the election committee he was on his deathbed at the time. In college he was neither dissipated nor lazy. His course was much like that of all his fellows, and is distinguished from the commonplace only by a comical dream with which his ancestors saw fit to favor him later on the subject, I say his ancestors advisedly as will shortly appear, and I repeat the dream partly because of its touch of humor, of which he was always fond, and partly because of its psychologic import. The gusto with which he related it at the time proves the censure implied to have been undeserved, but the atavism betrayed by it makes it worth recording. It was the family tradition that at college its scions should be students, a traditional devoir handed down from father to son, though I am not aware that tlie fathers always followed it themselves as religiously as 638 AUGUSTUS LOWELL. they inculcated it upon the sons. In consequence of his supposed neg- lect of this precept, it was perhaps not unnatural that his ancestors should disapprove and should show their disapproval. This they did iu the only way in their power — by means of a dream. For dreams are really reversions to type and are in consequence very interesting things. When we dream it is the atavic paths of which we are conscious. We think again the thoughts of our progenitors. The occasion of this visitation was the going up of his second son for the entrance examinations, and the paternal mind was naturally full of the subject. With the unimpeachable autliority of dreams he was sud- denly made aware one night that he had not done all he might in college. Profoundly stirred by the thought, the singleness of which made it pass for truth, he decided after due and weighty consideration — lasting at least a tenth of a second — to enter the university once more and go over the course again. The fact that he was middle-aged, married, and had a large family only made the resolve seem, after the manner of dreams, the more meritorious. On the strength of his already holding a degree, the college faculty consented to admit him without examination. He was thus enabled triumphantly to get iu. His action caused some comment, chiefly commendatory, such as follows an unusually pious deed. He thus became, against his will, something of a cynosure. So the first year glided by till with a speed peculiarly their own the annual examina- tions were upon him and with them the eyes of the community. Then, and someliow not till then, did he realize, to his consternation, that he had done nothing and was quite unprepared to pass. The situation was beyond words. At this awful moment he woke, — to the pleasing con- sciousness that his son, not he, would have to pass them on the morrow. Just before his graduation in 1850 his father, who was not very well, decided to go abroad with his family, including his son Augustus, in the event of needing his help. Mr. Lowell stayed with his father till the spring of 1851. In Paris he was joined by his friend and classmate, Mr. Lincoln Baylies, and there at the same time was John Felton, brother of the then president of the college, with whom the two young men fore- gathered. John Felton was something of a character and a good deal of a man, with fiery red hair on the outside of his head and much genial wit and wisdom within it. Under his guidance, philosophy, and friendsliip the two young men passed an interesting and not unprofitable winter, frequenting the theatres to pick up French. Labiche was then in his prime. In the spring the two classmates went off" to travel in Germany and Switzerland, and returned by themselves in the autumn to the United States. AUGUSTUS LOWELL. 639 On getting home he began his career in State Street, going into the counting-room of Bullard & Lee, East Indian merchants, to learn the business. His quickness of body as well as of mind here procured him a questionable distinction. From his father he had inherited consider- able athletic ability, and it was soon discovered in the office that he was fleet of foot. In consequence he was promoted to the post of messenger, with the duty of carrying the foreign business letters to the mail. Now Mr. Lee was addicted to lengthy epistles, to extreme peculiarity in com- pleting them, and to never finishing on time. As the mail was incon- siderate of their importance, he eagerly embraced Lowell's pedestrian possibilities. In consequence it soon became the regular thing for young Lowell to be seen standing, watch in hand, waiting while Mr. Lee com- pleted his last page, folded the foolscap down methodically with his large thumb, and elaborately sealed it. Meanwhile the minutes slipped by with the young man calculating if he still had time to catch the post. It was midsummer and hot. Nevertheless the human Mercury was kept standing within, reirardless of how its metallic namesake stood without. Finally when only running at his topmost speed would suffice to get the letter in he would hint that there were but six minutes more before the mail closed. " How many did you make it in last time, Augustus? " Mr. Lee would ask. " Five and three-quarters, sir, but I had to get it in the back way." *' I think you can do it this time then." And he did. This little episode occurred as regularly as mail day. After it had been cheerfully going on for some months, Mr. Bullard, who had been abroad, came home and one afternoon happened in on it. He said nothing at the time ; but when Lowell, hot and breathless, had returned once more successful he called him into his private office. , " Does what I saw this afternoon occur often, Lowell ? " he said to him. '* Every mail day, sir," the young man answered. '" It shall not occur again," he said. And it never did. With tact equal to his considerateness, Mr. Bullard, on the ground — if I am right — of preferring to do it him- self, from that day took the foreign correspondence into his own hands. Perhaps — after Balzac's phrase — this episode may be put between leads and given the air of a thought: the young man who goes quickly will go far. After two years spent with Bullard & Lee Mr. Lowell's father thought it advisable the young man should learn another line of business, — one in which the family was interested. Francis C. Lowell, the elder, who was the founder of the cotton manufactures of New England and after whom Lowell — their chief seat — was named, was the uncle of Mr- 640 AUGUSTUS LOWELL. Lowell's father. In consequence the father had come himself into con- nection with them, and it seemed well that the son should do likewise. He was therefore sent to Lowell to become practically acquainted with the running of the mills. The house in which he boarded was kept by a woman who was destined through her own exertions to no little notoriety later on. She had a sister who had a beautiful voice. This voice was one of the few alleviations of the place to the boarders, and the same voice, more ably than considerately exploited by the boarding- house keeper, proved the family's making. For the boarding-house keeper was so successful in her management that she soon became the proprietress of the Revere House in Boston, and next emerged by the help of the voice at her entertainments into one of the chief lights of Newport and New York society. Such in a nutshell was the career of Mrs. Paran Stevens. After passing a year at the mills, Mr. Lowell in 1853 became engaged to and in 1854 married Katharine Bigelow Lawrence, the youngest daughter of the Hon. Abbot* Lawrence, then recently returned from his post at the Court of St. James. Mr. Lawrence was as closely identified with the then nascent cotton manufactures of New England as was Mr. John Amory Lowell. Mr. Augustus Lowell thus found himself doubly involved in them, first by birth and then by marriage. For the two centres of the industry were the towns of Lowell and Lawrence, the one named as I have said after his father's uncle, the other after his father- in4aw. On his engagement Mr. Lawrence put him in with J. M. Beebe, Morgan & Co. Thus for the years preceding and following his marriage he was busy learning the details of what was to make Massachusetts' mercantile greatness, her manufacturing interests. With one exception, from this period to the end of his life, he was always associated in one way or another with the Lowell and Lawrence mills. He was succes- sively treasurer, that is, the executive head, of more than one of them, and president of many others. Tiie exception occurred some time after Mr. Lawrence's death, whicli happened in 1855, when Mr. Lowell entered into business ventures of his own, forming a partnership with Mr. Franklin H. Story for the pur- pose of engaging in the East Indian trade. For some years this trade was profitable, but the firm was brought to a close by the panic of 1857, for though the firm did not suffer the East Indian trade did. The friend- ship remained, and among the pleasantest incidents of the writer's boyhood was the acquaintance of this genial gentleman. By a coincidence he died only about a week before his former partner. AUGUSTDS LOWELL. 641 In 1864 the health of his wife necessitated his taking her and his family abroad. They sailed for England in May, and for the next two years and a half lived in Europe; the summers spent in travelling, the winters in Paris. To one so temperamentally prone to a busy life at home, this existence was no sinecure. With a wife at the point of death as it was thought and four young children, Mr. Lowell had his hands full. For a long time Mrs. Lowell did not gain at all. Indeed it was only during the second summer, under the treatment of a couutry doctor fortuitously encountered in the Austrian Tyrol, that she began to mend. It is instructive, if tardy, to perceive now, in view of the widespread professional ignorance on the subject, that what Mrs. Lowell was suffer- ing from was nervous exhaustion, — a disease, this, which it may be noted incidentally, Faraday, Darwin, Huxley, and Parkmau all suffered from without knowing it. Three little episodes may serve to mark these years of a search after health. The first summer the wanderers happened to be at Bonchurch in the Isle of Wight when the action between the '' Kearsarge " and the " Alabama" took place just across the channel off the coast of France. In the second they were among the first to go to that nook in the Austrian Salzkammergut, the village of Ischl, since become well known and popu- lar. In the third and last they were lodged at Schwalbach near Wies- baden, when that little watering place suddenly became one of the seats of war, and thereupon was occupied alternately by the two opposing forces, the invading Prussians and the native Hessians. Usually evacu- ation considerately took place before occupation set in ; but once by acci- dent the two interfered and a battle occurred between the rear guard of the one army and the advance scouts of the other under the very windows of the hotel. The Hessians, who had been quartered in the town, had heard of the proposed Prussian advance and had at once started to evacuate the place. But they were a little too Teutonically slow. The invaders, although Prussians and landwehr at that, were, quite to their own surprise, too quick for them ; a belated squad of Hessians had got only halfway up the hill on its way out when the Prussian cavalry was heard cantering into the town. There was no time to go on unseen when fortunately a friendly wood pile by the side of the road offered its shelter. Instantly the squad deployed behind it and waited. Five min- utes later three cavalrymen cantered past the hotel, their pistols pointed at the windows as they went by, and started unsuspiciously up the hill. The spectators in the secret stood waiting the surprise. Just as the dragoons got abreast of the wood pile the squad deployed out and fired. VOL. XXXVII. — 41 642 AUGUSTUS LOWELL. One dragoon fell on the spot, a second turned like a flash and leaped his horse over an embankment twenty feet to a road below, while the third wheeled in his tracks and came galloping wildly down the street again. All which served to relieve the watering place dulness. By the autumn of 1866 Mrs. Lowell was so far recovered that Mr. Lowell was able to return with her to the United States. It was many years before he left it again. He now took an oflice next his father's, and became gradually con- nected, on the one hand, with the manufacturing interests which hia father controlled, and on the other with the many trusts his father managed. During Mr. John Amory Lowell's subsequent absences in Europe the care of these things devolved upon his son, and with the former's increasing years the care became more and more permanent. In 1875 he was chosen treasurer of the Boott Cotton Mills. This office he held for eleven years. About the same time he was elected to suc- ceed his father on the board of the Massachusetts Hospital Life Insur- ance Company,- — -familiarly known as the Life Office, State Street's oldest, staidest, and most famous institution, whose real business has but a bowing acquaintance with its name, — and later was put upon its executive com- mittee. Of the corporation of the Provident Institution for Savings, — another financial landmark, not so deceptively named to the uninitiated, — he was likewise made a member, and eventually became its president, succeeding the Mr. Lee of epistolary fame. At this date too he began his long career upon the board of the Boston Gas Light Company, then so ably managed by Mr. Greenough, a career which ended more than twenty years later in the negotiations he conducted as its president when it became necessary to sell the property, which he did for two and a quarter times all it had ever cost. In addition to holding the offices above mentioned he was treasurer of the Merrimack Manufacturing Company, June 20-October 29, 1877 ; president of the Massachusetts Cotton Mills ; of the Massachusetts Mills in Georgia ; of the Pacific Mills ; of the Merrimac Manufacturing Company, 1887-8, 1892 to death; of the Boott Cotton Mills ; of the Lowell Bleachery : of the Lowell Machine Shop ; of the Glendon Iron Company ; and a director of the Everett Mills ; of the Middlesex Company ; of the Lawrence Mills ; of the Lowell Manufacturing Company ; of the Suffi^lk National Bank ; of the Cranberry Iron Company ; of the Plymouth Cordage Company ; besides being a trustee of the Union Trust Company of New York. This long list means even more than it usually would ; for Mr. Lowell was a director who did direct. In every concern into which he entered he very soon took AUGUSTUS LOWELL. 643 a leading part. Never seeking a place, his ability was such that he found liimself forced into position after position of responsibility. Indomitable, he was always selected to do what others agreed ought to be done but were averse to doing. For Mr. Lowell knew no such thing as shirking in the discharge of duty. He disliked the disagreeable as much as any one, but he was not weak. Of the financial jjosition he held in the down-town community it is enough commentary that seven bonds of treasurers of great corporations were found in his tins at his death, deposited with him as president. Such were the business concerns with which he was connected. But side by side with them he gave much time and thought to matters of more public interest. For many years he was a trustee of the Boston Eye and Ear Infirmary. Not simply one in name, for to him and to Mr. Brown its management was for a long time chiefly due. Ex-officio he was a trustee of the Boston Art Museum for twenty years, and a trustee of the Lowell Textile School for the four years pre- ceding his death. Of purely public functions he once performed one, that of member of the Boston School Committee in 1857-58, and from the echoes of this which have reached the writer it would seem that politics played as objectionable a part in what should have been above them then as now. Before going abroad he had had a summer place at Beverly, but attrib- utinof the loss of a child there to unhealthiness of the shore he sold it. On coming home he cast about for a country-place where he could live the year round, as being alike beneficial for his wife and his children. He found it in Brookline. His children were still young, and he took to repeating the experience of his own boyhood, driving them and himself into town every day to school and to business respectively. Out of it, beyoud business hours, his life was now quite bucolic. The place he had bought possessed already a fine garden and two greenhouses. In them he centred his affections, greenhouse and garden dividing the year between them. Two hot-houses of grapes helped to shield the latter, which lay in a hollow open to the south. Natural embankments enclosed it on the east and west, and a raised roadway, shut off from view, made artificial protection on the north. Clipped evergreens stood for sentinels along a terraced path, ending in an arbor which fringed one side of it, and a corresponding row faced them upon the slope opposite. In this shel- tered spot he spent much of his time. Pruning his shrubs, tying up his plants, and attending generally to the welfare of his flowers, he was almost as much of an inhabitant of the place as they. It was a world in 644: AUGUSTUS LOWELL, which he found infinite satisfaction. His roses were his chief delight. And fine they were — no finer than the feeling with which he showed them off. But nothing vegetal was alien to him. He would point out with almost as much zest, punctuated by a wink, a foi*eign thorn-tree, which flanked the avenue, a platted mass of thorns a foot long, the despair of squirrels and cats. His botany was of the old-fashioned kind. He did not pursue it as a science, but cultivated it as an art. His plants were rather pets than subjects for vivisection. Philosophically he was not concerned with their genealogy or relationship and disbelieved Darwinism to the day of his death. But in his intercourse with them he knew the life and the merits or demerits of each, and took pleasure in their thriving with something like affectionate interest. He behaved like a distant relative, the while stoutly denying that he was one. Indeed the relation did not seem so very distant, for he was never tired of attending to them, and took a paternal pride in their introduction to others. He would conduct you to view some bush at the moment in flower, and point out in what lay its peculiar praiseworthiness with the care of long acquaintance. Pretty much every tree upon his place — and it included some rare ones — was personally known to him. And if you strolled round with him he would talk fine print about each with you. He was constantly importing new plants and then watching them succeed. Though he made no parade of knowledge or of success, he not infrequently had plants which knew no rival in the neighborhood. A contrast this side of his life made with that of his morning down-town, where he played so prominent a part in the active affairs of men. The long list of business offices held by him might lead one to infer that his time in the city must have been fully occupied by them alone. But he was much too busy a man for such to be the. case. With all his industrial and financial concerns he found time for an equal employment in educational affairs. His ability was of the executive kind, which was as vital to the one as to the other. It thus came about that side by side with his business, and almost hand in hand with it, so practical was he in his workings, went another employment — usually only on speaking terms with the first, and then those of a beggar — the conduct of educa- tional concerns. Busy as Mr. Lowell was with purely business affairs, he was equally engaged in matters of mind. Partly the accident of birth, partly the possession of ability, placed him in positions of authority in two important educational institutions : the Lowell Institute in the first place, and the Massachusetts Institute of Technology in the second. AUGUSTUS LOWELL. 645 Of the first of these he became the trustee in 1881, on the death of his father. Even before this, however, much of the work had fallen to him. The Lowell Institute is too well known to need description, but one phase of it will bear raeution in connection with the man who for so long was its trustee. Most institutions of learning live by begging. If they happen to be possessed of presidents who are past masters in the art, they thrive ; if not so blessed, they languish. That a president should be an able intellectual director is unfortunately not so pressing a demand as that he should be a persistent, importunate, and successful beggar. In view of this fact deficits in college finances have lost their terror and surpluses are unknown, a sympathetic public being with confidence relied on to stand in the gap. Now the peculiarity of the Lowell Institute has been not only that it is not dependent upon alms-giving but that it has thriven and grown without it. Although on the one hand it has paid larger salaries than any college or kindred institution to the teacher, it has asked no fee whatever of the taught. Yet despite this liberality on both sides, its funds have more than quadrupled in amount. Part of this increase has been due to the wise terras of the endowment, part to the like wisdom of the two successive trustees. Kindred wisdom it has been in both senses, for by a provision of the testator the trustee must be of the testator's family if a fit person exist of the name. How fit Mr. Lowell was for the post this able result of his administration of the finances attests. But besides being its financial head, Mr. Lowell was its intellectual body and its executive arm as well. For the Institute is a one man power, an absolute dictatorship. Mr. Lowell was president, corporation, and treasurer all together. And the success he made of it shows ajrain the wisdom of such a rule, provided only the ruler be fit. Of his capacity as financier the property speaks ; of his ability in general adiniuistratiou the list of lecturers before the institution sufficiently betokens. At the time the Institute was founded lectures were a popular form of instruc- tion, and the object of the testator was to secure for the people of Boston lectures by the most eminent men at home and abroad, and to give these to the public free of charge. His wish has been well carried out. On the roster of the books are to be found a majority of the names which are known the world over, and almost every one of those to whose pos- sessors distance or age or language did not prove an impassable bar. America, Europe, even Asia have contributed to the list. Some of these men came more than once ; and many of them became well known per- sonally to Americans. But the fact connected with them which speaks 646 AUGUSTUS LOWELL. most for the institution and its trustee is that well-nigh without exception each came originally at his instigation. Almost all the famous foreigners in science, literature, or art who have been in this country have owed their personal introduction to it to the trustee of the Lowell Institute. Since from over seas these lecturers came, simply as a bond between countries the Institute has played uo unimportant part. Mr. Lowell's tie to science was thus rather indirect than direct, but it was none the less intimate if in a different way. By virtue of his office he was brought personally in contact with the scientists of his day, and in a most pleasant and withal domestic manner. For besides meeting them at the lectures, of which he always attended the opening one and oftener than not the whole course, he was in the habit of entertaining the lec- turers during their stay in Boston at his house at dinner, sometimes more than once. Many is the memorable evening he passed in consequence with men who have made the worhi what it is. Such personal knowledge of a man is as invaluable as it is invigorating. Even in an estimate of the mind a side light of no mean value is shed on it by intercourse with the personality. The man proves a footnote to his own writings. This advantage of glosses on the text Mr. Lowell possessed ; and in various aspects in as muph as he was thrown with these men in diverse relations. Intercourse of the sort he enjoyed more or less for nearly half a century. For, as I have said, before he became trustee he had been acting for his father, and even before that had met the lecturers at his father's house. During the second half of the nineteenth century he had thus been familiar, not only with the century's best thought, but with most of its best thinkers. And he passed away just as the century itself was drawing to a close. Coincident with holding this responsible post in educational matters of a general character Mr. Lowell filled a second position of a more direct kind and not less important. For quite as long a term as he managed the Lowell Institute was he associated with the government of the Massachusetts Institute of Technology. Entering the corporation of that institution in the early seventies, he very soon took a leading part in its policy. From that time the conduct of its affairs had been inti- mately connected with him, much more so than the public is cognizant of. For Mr. Lowell never put himself forward, having an innate aver- sion to unnecessary publicity. Even on the few occasions when it was indispensable for him to appear, he only did so, as those in his confidence are aware, after great reluctance. Mr. Lowell was identified with this phenomenally successful institution AUGUSTUS LOWELL. 647 almost from its start. The Massachusetts Institute of Technology was founded in 1861, chiefly through the instrumentality of Prof. William B. Rogers. To the same eminent mind it owed its early success. Measure of the man's executive ability in the first place, its success was in the long run the sign of his forethought in founding it. A school of technol- ogy was exactly what the American genius had demanded for many years in vain. It seems strange that no one should have heeded this unmis- takable cry of nature before; but men are prone to being thus strangely deaf, till an interpreter arises. For a century the American has been noted for his innate inventiveness and general ingenuity, and has been e(]ually noted for the untrained character of his craft. In some things this did well enough, but in the higher branches it left a good deal to be desired. To supplement natural aptitude with proper training was thus the one thing needful. To think of it was so simple a matter as to require a master mind for the thought. It was a piece of educational acumen of the highest order. And it has borne its inevitable result. But though it was destined to great and permanent success it would be contrary to common sense to suppose that the move was fully appre- ciated, from the very start. On tlie contrary, had it not been for its founder the institution would probably have gone under. After Mr. Rogers' death much came to devolve upon Mr. Lowell ; and since then, that is for the last quarter of a century, the policy of the Institute has been intimately associated with him. Elected a member of the corporation in 1873, he was chosen a member of the executive com- mittee in 1883, and was kept upon it to the day of his death. During his term of service were chosen four presidents, and I need only mention the name of General F. A. Walker, who was the longest incumbent, to suggest how wisely made these choices were. But the work of the committee did not end with the selection of the executive ; as its name implies, it was itself a part of that executive and its function was con- tinual. As the senior member of the committee Mr. Lowell's force was felt in every portion of the policy pursued. Not a measure was passed which had not been influenced by his opinion. His judicious advice was fully appreciated by General Walker. Indeed the two men were natural complements to each other, General Walker with his brilliant, engaging personality, and Mr. Lowell with his uncommon judgment and invincible determination. The position taken by the Institute under this leadership is well known. The institution has quadrupled in size, and what is far more important, has more than quadrupled in prestige. It is recognized to-day not only 6-i8 AUGUSTUS LOWELL. as the first, but as easily the first, school of technical arts in this country. To it now flock students from the farthest portions of these United States: from Oregon and Texas, from Illinois and Ohio, as well as from New York and Massachusetts. And as graduates they go back again to help develop the country. If any such institution may fairly be called national the Massachusetts Institute of Technoloo-y is the one. Nor is this all. Not confined to the limits of this continent, its fame has successfully invaded lands across the sea. It is not long since Sir Eobert Ball informed the writer that it was in advance of anything of the kind in Great Britain ; a belief which he had years before acted on by sending his son to it, who is now practising in England. The belief would seem to be spreading; for in June, 1901, examinations for admis- sion to it were held in London. Its rank would seem even to be recosf- nized at home, which means that it probably is of some importance, as the American believes firmly in the ignota pro magnijico. The post- graduate course, pursued by the ranking men of the U. S. Naval Academy at foreign institutes heretofore, is in future to be taken at the Institute. It has been the custom of the Academy since 1883 to send the first few scholars of the highest grade, the construction department, abroad to finish their education. At first it was Greenwich they went to, till the British Government ludicrously enough became sensitive to the cadets outstripping their own students and forbade them. Then the Navy sent men to the University of Glasgow, and lastly to the Ecole Polytechnique in Paris, where the recent ones have all graduated. In future it will be in Boston. Evidently the United States Government is convinced of the primacy of the Institute. What Mr. Lowell's share in this success was may best be gathered from an episode which occurred about a twelvemonth before his death. Feeling himself worn by a painful trouble which he had had for years, he was minded in a moment of acute access of it to give up active work. Accordingly he sent in his resignation to his colleagues of the corpora- tion. They refused to accept it, and the committee did their best to persuade him to reconsider his determination ; but in vain. Whereupon a memorial was drawn up, signed by every member of the corporation accessible at the time, protesting against his resignation, and begging him not to withdraw his services from the institution. Such unanimous spon- taneity of appreciation in a body of forty odd members is not common. That he was profoundly touched by this mark of confidence and esteem needs no saying. AUGUSTUS LOWELL. 649 Of the American Academy of Arts and Sciences he was made a mem- ber ill 1886. He was first the treasurer and then the vice-president. On the death of Professor Cooke, deeming it fitting that the post of presi- dent should be filled by a man of science, he secured the election of Agassiz. When the change into sections was made he became the vice- president of his section, — jurisprudence and literature. He was also a member of the American Association for the Advancement of Science from 1898; of the Massachusetts Historical Society in 1900; of the Colonial Society of Massachusetts from 1898. He died on June 22, 1901. Such, in brief, was what Mr. Lowell did. Quite as important is what he was. For the man was always behind his measures, as the whole in- cludes the part. His actions were but parcel of himself. Not always is this the case. Some men become noteworthy for what they do, while being notorious for what they are. But with him the act was outcome of the man. He said what he meant and meant what he said. In this unity lay one element of his force. To those with whom he came in con- tact this oneness with one's self made itself felt. To the world at large, which sees the works but not the workings, his hand in matters which he had brought about often escaped notice. For a certain ingrained aver- sion to publicity prevented him from putting himself forward. Nothing, however, restrained him from pushing his measures. In consequence, many as were the acts one can point to in his unusually active life, those which actuated others without appearing themselves were more ; in con- sequence also, the world remained in ignorance of the motive cause. For he acted for results ; and what is to take effect does not need to make it. Effect indeed was the very opposite of what Mr. Lowell w^as in thought or word or deed ; and very refreshing it is, like a cool breath of pure air iu the artificial heat and closeness of a crowded room, to consider such a character in these days of blatant, forth-putting mediocrity. When to seem is at a premium, and to be at a discount, it is invigorating to turn to a life which owed nothing to adventitious or meritricious aid ; a life which not only was fine, but escaped the soiling consequent upon too much mental fingering by the world at large. To be generally in evidence means a loss of that delicacy of distinction, if it means nothing more, which is for so much in beauty of character. But it means usually very much more ; it leads inevitably to a substitution of superficiality for solidity, of appearance for reality, of a sinking to a level of one's audience instead of a rising superior to applause. To say that a man owed nothing to effect is to say of him the best that can possibly be said. The natural forces with which we daily come in contact owe nothing to such cause; 650 AUGUSTUS LOWELL. on the contrary they stir us all the deeper, if we stop to think, for the very fact that they do not stir us without such thought. We are im- pressed the more by what seems superior to the impression it makes. There is, too, another merit in the absence of effect — a gain in effec- tiveness. It is the greatest compliment to a man's ability that he should succeed without seeming to do so, because it shows that all his force has been massed upon the one strategic point. We are all familiar with this when it is done of intent aforethought. As potent is the principle when the self-effacement is unconscious. The one obliteration differs from the other only in being instinctive in- stead of being thought out; and the one is as telling as the other. How- ever it be brought about, the fact that the self is effaced is proof that the work has been done well. For it shows that the result has been brousht to pass with the least expenditure of force. Personality causes friction, and evidence of self is therefore proof that force has been uselessly em- ployed. The fact that a man has succeeded in having his idea prevail without forcing himself along with it is sign of the best kind of work. Now tliis was the case with Mr. Lowell. It was so because of an un- usual combination of characteristics, a singular wedding of energy in deed with dislike of its external trappings. To an exceptional extent, therefore, Mr. Lowell's distinction lay in character. Three qualities he possessed to an unusual degree, qualities each rare enough as it is : will, ability, and integrity. He was, in the first place, a combination of force and ability as simple and as uncommon as success, which is its immediate consequence. The one is but the neces- sary premiss to the other's conclusion. If a man be originally possessed of the first he is sure eventually to possess the second. Schopenhauer's definition of the world as all will and representation certainly holds of one part of it, — the affairs of men. If the affairs consist rather in the dealing with men than nature the representation takes the form of words, and may be paraphrased as first the skill to put a thing convincingly and then the will to put it through. Mr. Lowell combined the two qualities. Will he possessed to the full. He was noted for his determination. To his lot, in consequence, fell many necessary and thankless tasks. He likewise escaped many empty honors. For where he went he worked. No one ever thought of preferring him to a post merely honoris causa. For people knew that in getting him they jjot not a figure-head, but a man who was certain to make himself felt ; not because he tried to do so, but because it was in him to do it. He entered concerns not by the postern AUGUSTUS LOWELL. 651 gate of popularity, but by the portal of inevitableness. He was chosen because he was necessary. And he stayed for the same reason. Now will is pure force, uncomplexioned, the mere dynamic outcome of the idea. Its effectiveness to any particular end depends, therefore, upon the character of the idea whose explosive force it is. With Mr. Lowell the idea owed its carrying power to two characteristics : judiciousness in itself arud judiciousness in its presentation. In the first place he was apt to be right, that is, to be wise. His judgment of thiugs within his own field was excellent. It was essentially sound. His was that uncommon sense-possession, the possession of common sense. Instinctively his mind worked correctly. It was the exact opposite of the mind of the crank, which may often hit off" a brilliant conception, but which is too unsafe to be trusted. With him no one idea ever usurped the right of way to the exclusion of others. Each had its due effect ; which fundamental balance makes the only safe foundation for superstructure. In the next place he was as shrewd as he was sound. He had a keen- ness for the essential point which almost assured success in advance. In- sisting upon what was vital, he waved less important issues to the other side. In this consists the consummation of the art of commerce with one's kind. An instance of the combined breadth and shrewdness of his business insight occurs to my mind. "When I lease a building," be once said to me, " I ask a good price of the tenant and then do all the little repairs lie wants. The price makes its impression but once; the perqui- sites repeatedly, and the latter impressions stand nearer to the falling due of the lease." Backing up his judgment was his excellence of exposition. His ideas were the more telling for being well told. His words were few and to the point. In a twinkling he would dissect a situation, and with equal terseness suggest its remedy. With ability for audience this had imme- diate effect ; with mediocrity it was rather his tact that told. His logic was too accurate for popular approval, which prefers the coloring of emotion to the lines of thought. For very few men care for truth as thev care for their feelings. And Mr. Lowell's forte was not the silver tongue of eloquence, but the more golden gift of statement. He could put a point so that it pierced perception instantly. Lastly, there was about his advocacy of his measures an impersonality as potently as it was subtly persuasive. It was not that the ideas them- selves were what one would call impersonal, but that the idea appeared by itself with so little of that aura of the personal, which in human affairs the man unconsciously throws around it, as to appear to stand alone. For 652 AUGUSTUS LOWELL. in Mr. Lowell's case it was as if he were but the mouthpiece of the idea, so heartily did he identify himself with it, and yet so single was his intent. It was the idea he thought of, not of himself. Such a condition tends in a twofold way to conviction ; first, by the sincerity of the pleading, and secondly, by the absence so far as is humanly possible, of the antagonism roused by personality. Recognition of liis ability followed any knowledge of him ; it did not, as with some men, precede it. Those qualities compounded of sociability and forth-puttingness, however unintentional, which make for instant dis- tinction among one's fellows, were not his by nature. His abilities were solid, not showy. Nor was it his bent to go out of his way in the road we all travel to make a new path. He neither courted position nor shirked it. When it once fell to him he became as it were the office. Nothing was ever done by hira for his own sake, however incidentally. He seemed simply to embody his trust. In intent he was singularly single. Indeed, in describing his action I find it difficult to convey the combination of self-obliteration and of self-sufficiency in its best sense, which he was. For the character is uncommon. One often witnesses self-abnegation. But it is usually wedded to weakness. Or, on the other hand, one sees strength associated with self-seeking. Few men are essen- tially impersonal enough to strive strenuously for the thing in itself, as if it were a person. He did. This was perhaps the stranger that his mental makeup was not of the abstract but of the distinctly concrete kind. In practical, not in theoreti- cal matters, he was great. Widely read as he was he never seemed to care to theorize. He enjoyed highly the theories of others, when they did not collide with the puritanism which, as I have said, he inherited doubly distilled. Even this was perhaps as much due to the society in which he had been brought up. He was educated before the modern movement in thought took place, and Boston of sixty years ago was even behind the rest of the world in this stirring of the waters of stajjnation. Not in knowledge nor in intellect ; it was in cast of mind he differed. His preference was for action. Of this he never tired. To recreation he was less giveia. Such as he took was of a serious kind. He was a member of the Wednesday Evening Club, of the Thursday Evening Club, and of a class dinner club ; but clubs which consist but of a local liabitation and a name he never cared to join. Loafing and he were strangers. Will and the power of representation were, as I have said, two of his attributes. But the second of these should, though it often does not, include a quality which is itself fundamental to all character, and which AUGUSTUS LOWELL. 653 Mr. Lowell possessed to the utmost — the quality of honesty. In these days, when successful financial operations so often depend upon will and 7n?'srepresentation, it is no small thing to say of a successful man of affairs that he was conspicuously honest. When to steal enough is to steal with credit, it is cheering to see business triumph attendant on unimpeachable integrity. And this was typically true of him. Honest he was by essence. Verity was of the very fibre of his being. Nor is it only of the grosser form of that attribute which has usurped the generic name of honesty of which I would speak, but of that finer sense of fair dealing which we include under the appellation of a just man. His uprightness was perfectly well known. No adversary ever questioned that. A tribute to the fact once came in an amusing manner to Mr. Lowell's ears in one of the latter years of his life. He was pass- ing through a railway station in Boston one afternoon when he chanced to overhear two men unknown to him discussing his character. It was his own name that caught his attention. " Augustus Lowell," said one, " is a hard man, but he is absolutely honest." "Yes," said the other, ''he is emphatically that." It is not often that one overhears a bit of one's own obituary during one's life, nor is made privy to concurrent testimony on the subject from both sides of a discussion. As to the hardness imputed to him, it had no foundation in fact, though it was often attributed to him by people who knew him onlj- from the outside. A cast of countenance which looked stern when in repose, and which was purely a matter of feature, was chiefly responsible for the reputation. He was quite aware of the look himself, as well as of that to which it was due. As a matter of fact he was very tender-hearted, singularly so for a man of his determination. Few suspected him of the kindnesses he was constantly doing, so unostentatiously were they performed, and almost no one credited him with the affection he felt. The complexion of his character — for will is an uncomplexioned force — may be described in one word: exactness. Accuracy of state- ment and honesty of purpose are both but facets of a crystallization of thought. A man who sees clearly must be honest by instinct if he be not dishonest by intent. There is with him no limbo of self-deception. Much of the untruth current in the world is due to an initial haziness of conception subsequently seized upon and distorted to its own ends by passion, without disquiet to the perpetrator, because unrecognized as distortion by him. Mr. Lowell was essentially exact. His nature therefore imposed honesty. He saw much too correctly either to jumble or to juggle with his thoughts. 654 TRUMAN HENRY SAFPORD. Important as the qualities he possessed are to the making of a man, they are no less so to the making of a community. And in any consti- tutional country no small part of the value of a man lies in his value as a citizen. Indirect as well as direct his influence may be, and with universal suffrage the former is apt to be the case with the best men. To be determined, discerning, and honest does not, unfortunately, in our system of supposed political equality, lead to purely civic distinction. For the choice of a popular suffrage cannot rise above its source. But if the qualities do not lead to civic distinction for their possessor they do something as enduring, — they tend to raise to his level the community of which he forms a part. For without the first attribute, nothing is possible; without the second, fi'olishness ; without the third, knavery. The apathy of most of us, the crankiness of a few, and the financial trickery of others, ai-e the several results of the absence of these qualities. Too strong a personality to be generally popular, recognition of such a character is slow. For we are all prone to praise what we like. Only when distance does away with personal perspective do men, like hills, reveal their height. Posterity gives the final judgment. For posterity judges of a man's worth unhaloed by the engaging lack of it, and sets the seal of its appre- ciation upon those who have contributed to the world's advance and incidentally to posterity's own existence. To make for this advance is the best any man can do, and to this end to be determined, discerning, and honest is one of the surest means. If a man possess these attributes he will not have lived in vain. Percival Lowell. TRUMAN HENRY SAFFORD. Truman Henry Safford was born January 6, 1836, at Royalton, Vermont. The course of his life was determined by a phenomenal ca- pacity for the mental solution of arithmetical problems, which began to display itself when he was only six years old. This faculty, which might under easily conceivable circumstances have been wasted in mere display for the amusement of the curious, fortunately attracted the attention of judicious and eminent men, and thus secured for him the advantages of a thoroueh education. He irraduated at Harvard College in the class of 1854, which he joined at the beginning of its Junior year. As a boy he had computed an almanac, and given other evidences of interest in astronomy, and capacity for it ; and immediately after his graduation he TRUMAN HENRY SAFFORD. 655 obtained employment at Harvard College Observatory, wliere he con- tinued for nearly twelve years. He married Elizabeth M. Bradbury, of Cambridge, in March, 1860, " on six hundred dollars a year," as he once told the writer of this notice; for astronomy has never been a prom- ising road to riches for young Americans insufficiently endowed with the practical turn of mind generally regarded as characteristic of their coun- trymen. He was elected Fellow of the Academy, Nov. 13, 1861. Saft'ord's position at Cambridge, if not pecuniarily advantageous, offered him in some other respects greater advantages than, perhaps, he could secure in later life ; for lie had here comparatively few hindrances to the undisturbed development of his scientific abilities. Accordingly, the results of his work soon began to make him widely and favorably known in astronomical circles. One of the most generally interesting of these investigations related to the orbital movement of Sirius. Many years before, the observed want of uniformity in the proper motion of this star had led astronomers to the belief that it formed one of a system of bodies revolving about a common centre of gravity ; its companion, or companions, as the case might be, being too faint to be visible, at least with the existing instrumental means. Still more recently, the character of the supposed revolution of Sirius had been discussed by means of its right ascensions, as observed at different times. Safford now undertook a similar discussion of its observed declinations, and after combining the result of this work with that previously found, on the supposition that only one disturbing body occasioned the observed effects, was able to indicate its direction from Sirius at the time, in excellent agreement witli the actual place of the companion discovered almost simultaneously by the younger Alvan Clark. A catalogue of the declinations of five hundred and thirty-two stars, intended for use in the government survey of the lake region, was pre- pared by SafFord during his connection with Harvard College Observa- tory, and probably marks the beginning of the geodetic work which occupied a large part of his time in later years. In 1863 he received the formal title of Assistant Observer; and two years later, upon the death of Professor G. P. Bond, he was placed in charge of the Observatory. At this time, he completed and prepared for publication Professor Bond's researches on the nebula of Orion, which appeared as Volume V. of the Observatory Annals. Volume IV. of the same series is also the work of Safford. The first part, dealing with the preparation of a list of fundamental stars for transit observations, was published iu 1863. By means of these fundamental stars, the right as- 656 TRUMAN HENRY SAFFORD. censions of five hundred and five stars were determined by observations in the years 1862 to 1865 ; the second part of the volume, containing the result of tliis work, appeared in 1878. In 1866 Safford was appointed director of the Dearborn Observatory at Chicago, which had recently been provided with the large refracting telescope, by means of which, while still in its maker's hands, the com- panion of Sirius had been discovered. This position, with which was connected a professorship of astronomy in the University, seemed to offer the fairest prospect of permanent and congenial employment to its occu- pant ; but the disastrous fire which destroyed so large a part of Chicago in 1871 deprived the Observatory of the financial support upon which its activity depended. Professor Safford, accordingly, now found it neces- sary to maintain his family by geodetic work connected with the govern- ment surveys. He had undertaken the observation of one of the zones of stars distributed among various observatories under the general system arranged by the Astronomische Gesellschaft ; but this, and other pieces of work begun at Chicago, were now necessarily laid aside. In 1876, however, Professor Safford was restored to his favorite pur- suits by appointment to the chair of astronomy at Williams College. In this position, teaching required much of his time, and of course largely impeded his attention to scientific investigation ; he also acted as libra- rian of the College, and was at times engaged in other business con- nected with its administration. It is not probable that he felt the work of instruction to be a burden ; on the contrary, he took great interest in the subject of pedagogy, which he studied theoretically as well as practically. Notwithstanding all hindrances to the pursuit of strictly astronomical research, he accomplished much in that direction during the years spent at Williamstown, devoting himself largely, as before, to the subject of accuracy in the determinations of the positions of fixed stars. One of the principal results of this work was the publication (in the Proceedings of this Academy, Volume XIX.) of a catalogue of the mean right ascensions of one hundred and thirty-three stars near the north pole ; but many other articles in scientific periodicals, particularly the Monthly Notices of the Royal Astronomical Society, attest Professor Safford's perseverance and success in scientific work during his later years. He died June 13, 1901, at Newark, New Jersey, where he was resid- ing at the time with one of his sons. A stroke of paralysis, three years previously, had put an end to his activity in science. His widow, with four sons and a daughter, survives him. Arthur Searle. HORACE ELISHA SCUDDER. 657 HORACE ELISHA SCUDDER. It is a merit of the American Academy of Arts and Sciences that it does not limit itself to one form of intellectual pursuits, as do the merely historical or scientific societies or even some which share the name of Academy. It also has the merit that it is ready to recognize the various subdivisions of each pursuit, and has a place of honor for every such department. Intellectual self-respect is to be found only in honoring every form of work in its place. It has been generally felt, I think, that no disrespect was shown to our late associate, John Fiske, when the New York Nation headed its very discriminating sketch of him with the title " John Fiske, Popularizer ;" and in speaking of another late associate who has left us, I should feel that I showed no discourtesy, but on the contrary, did him honor in describing him as Horace Elisha Scudder, Literary Workman. I know of no other man in America, perhaps, who so well deserved that honorable name ; no one, that is, who if he had a difficult piece of literary work to do could be so absolutely relied upon to do it carefully and well. Whatever it was, compiling, editing, arranging, translating, indexing, — his work was uniformly well done. Whether this is li.e highest form of literary distinction is not now the question. What other distinction he might have won if he had shown less of modesty or self-restraint, we can never know. It is certain that his few thoroughly original volumes show something beyond what is described in the limited term, workmanship. But that he brought simple workman- ship up into the realm of art is as certain as that we may call the cabinet-maker of the middle ages an artist. Mr. Scudder was born in Boston on October 16, 1838, the son of Charles and Sarah Lathrop (Coit) Scudder ; was a graduate of Williams College and after graduation went to New York, where he remained for three years engaged in teaching. It was there that he wrote his first stories for children, entitled " Seven Little People and Their Friends " (New York, 1862). After his father's death he returned to Boston and thenceforward devoted himself almost wholly to literary pursuits ; pre- pared the " Life and Letters of David Coit Scudder" his brother, a mis- sionary to India (New York, 1864) ; edited the " Riverside Magazine" for young people during its four years' existence (from 1867 to 1870) ; and published " Dream Children " and " Stories from My Attic." Becoming associated with Houghton, Mifflin and Company he edited for VOL. XXXVII. — 42 G58 HORACE ELISHA SCUDDER. them the Atlantic Monthly Magazine from 1890 to 1898, preparing for it also that invaluable index, so important to bibliographers ; he also edited the "American Commonwealth" series, and two detached volumes, "American Poems" (1879) and "American Prose" (1880). He pub- lished also the " Bodley Books " (8 vols. Boston, 1875 to 1887) ; " The Dwellers in Five Sisters' Court" (1876); "Boston Town" (1881); "Life of Noah Webster" (1882) ; "A History of the United States " for schools (1884); "Men and Letters" (1887); "Life of George Washington" (1889); " Literature in School" (1889); "Childhood in Literature and Art" (1894), besides various books of which he was the editor or compiler only. He was also for nearly six years (1877-82) a member of the Cambridge School Committee ; for five years (1884-89) of the State Board of Education ; for nine years (1889-98) of the Harvard University visiting committee in English literature ; and was at the time of his death a trustee of Williams College, Wellesley College, and St. John's Theological School, these making altogether a quarter of a cen- tury of almost uninterrupted and wholly unpaid public service in the cause of education. Since May 28, 1889, he was a member of this Academy, until January 11, 1902, when he died. This is the simple record of a most useful and admirable life, filled more and more, as it went on, with gratuitous public services and disinterested acts for others. As a literary workman, his nicety of method and regularity of life went beyond those of any man I have known. Working chiefly at home, he assigned in advance a certain number of liours daily as due to the firm for which he labored ; and he then kept carefully the record of these hours, and if he took out a half hour for his own private work, made it up. He had special work assigned by himself for a certain time before breakfast, an interval which he daily gave largely to the Greek Testament and at some periods to Homer, Thucydides, Herodotus, and Xenophon ; working always with the original at hand and writing out translations or commentaries, always in the same exquisite handwriting and at first contained in small thin note-books, afterwards bound in substantial volumes, with morocco binding and proper lettering. All his writings were thus handsomely treated, and the shelves devoted to his own works, pamphlet or otherwise, were to the eye a very conservatoiy and flower garden of literature ; or like a chamberful of children to whom even a frugal parent may allow himself the luxury of pretty clothes. All his literary arrangements were neat and perfect, and represented that other extreme from that celebrated collection of De Quincey in Dove Cottage at Grasmere, where that author had five thousand books, by HORACE ELISHA SCUDDER. 659 his own statement, in a little room ten or twelve feet square ; and his old housekeeper explained it to me as perfectly practicable " because he had no bookcases," but simply piled them against the walls, leaving here and there little gaps in which he put his money. In the delicate and touching dedication of Scudder's chief work " Men and Letters " to his friend Henry M. Alden, the well known New York editor, he says : '' In that former state of existence when we were poets, you wrote verses which I knew by heart and I read dreamy tales to you which you speculated over as if they were already classics. Then you bound your manuscript verses in a full blue calf volume and put it on the shelf, and I woke to find myself at the desk of a literary workman." Later, he says of himself, " Fortunately, I have been able for the most part to work out of the glare of publicity." Yet even to this modest phrase he adds acutely : " But there is always that something in us which whispers /, and after a while the anonymous critic becomes a little tired of listening to the whisper in his solitary cave, and is disposed to escape from it by coming out into the light even at the risk of blinking a little, and by suffering the ghostly voice to become articulate, though the sound startle him. One craves company for his thought, and is not quite con- tent always to sit in the dark with his guests." The work in which he best achieves the purpose last stated is undoubt- edly the collection of papers called by the inexpressive phrase '-Men and Letters ; " a book whose title was perhaps a weight upon it and which yet contained some of the very best of American thought and crit- icism. It manifests even more than his " Life of Lowell " that faculty of keen summing up and epigrammatic condensation which became so marked in him that it was very visible, I am assured, even in the literary councils of his publishers, two members of which have told me that he often, after a long discussion, so summed up the whole situation in a sen- tence or two that he left them free to pass to something else. We see the same quality for instance in his " Men and Letters," in his papers on Dr. Mulford and Longfellow. The first is an analysis of the life and literary service of a man too little known because of early death, but of the rarest and most exquisite intellectual qualities. Dr. Elisha Mulford, author of " The Nation" and then of " The Republic of God." In this, as every- where in the book, Mr. Scudder shows that epigrammatic quality which amounted, whether applied to books or men, to what may be best de- scribed as a quiet brilliancy. This is seen, for instance, when in defending Mulford from the imputation of narrowness, his friend .sums up the whole character of the man and saves a page of more detailed discussion by say- 660 HORACE ELISHA SCUDDER. ing, " He was narrow as a canon is narrow, when the depth apparently contracts the sides " (page 17). So in his criticism called " Longfellow and His Art," Scudder repeatedly expresses in a sentence what might well have occupied a page, as where he says of Longfellow, " He was first of all a composer, and he saw his subjects in their relations rather than in tlieir essence" (page 44). He is equally penetrating where he says that Longfellow "brought to his work in the college no special love of teaching," but '' a deep love of literature and that unacademic attitude toward his work which was a liberalizing jjower" (page 66). He touches equally well that subtle quality of Longfellow's temperament, so difficult to delineate, when he says of him : " He gave of himself freely to his in- timate friends, but he dwelt, nevertheless, in a charmed circle, beyond the lines of which men could not penetrate " (page 68). These admirable statements sufficiently indicate the rare quality of Mr. Scudder's work. So far as especial passages go, Mr. Scudder never surpassed the best chapters of " Men and Letters," but his one adequate and complete work as a whole is undoubtedly, apart from his biographies, the volume en- titled "Childhood in Literature and Art" (1894). This book was based on a course of Lowell lectures given by him in Boston, and is probably that by which he himself would wish to be judged, at least up to the time of his admirable " Biography of Lowell." He deals in suc- cessive chapters with Greek, Roman, Hebrew, Mediaeval, English, French, German, and American literary art with great symmetry and unity throughout, culminating, of course, in Hawthorne and analyzing the portraits of children drawn in his productions. In this book one may justly say that he has added himself, in a degree, to the immediate circle of those half dozen great American writers whom he commemorates so nobly at the close of his essay on " Longfellow and his Art," in " Men and Letters." " It is too early to make a full survey of the immense importance to American letters of the work done by half a dozen great men in the middle of this century. The body of prose and verse created by them is constituting the solid foundation upon which other structures are to rise ; the humanity which it holds is entering into the life of the country, and no material invention, or scientific discovery, or institutional prosperity, or accumulation of wealth will so powerfully affect the spir- itual well-being of the nation for generations to come" (p. 69). If it now be asked what prevented Horace Scudder from showing more fully this gift of higher literature and led to his acquiescing, through life, in a comparatively secondary function, I can find but one explana- tion, and that a most interesting one to us in New England as illustrating JOSEPH HENRY THAYER. 061 the effect of imnuiliate surroundings. His father, so far as I can ascer- tain, was one of those Cougregationalists of the milder type who, while strict in their opinions, are led by a sunny temperament to be genial with their households and to allow them innocent amusements. The mother was a Cougregationalist, firm but not severe in her opinions ; but always controlled by that indomitable New England conscience of the older time which made her sacrifice herself to every call of charity and even to refuse, as tradition says, to have window curtains in her house, inasmuch as many around her could not even buy blankets. Add to this the fact that Boston was then a great missionary centre, that several prominent leaders in this cause were of the Scudder family and the house was a sort of headquarters for them, and that Horace Scudder's own elder brother, whose memoirs he wrote, went as a missionary to India, dying at his post. ' Speaking of his father's family in this memoir, he says of it, '' In the conduct of the household, there was recognition of some more profound meaning in life than could find expression in mere enjoyment of living; while the presence of a real religious sentiment banished that counterfeit solemnity which would hang over innocent pleasure like a cloud " (Scud- der's Life of David Coit Scudder, p. 4). By one bred in such an atmos- phere of self-sacrifice, that quality may well be imbibed ; it may even become a second nature, so that the instinctive demand for self-assertion may become secondary until a man ends in simply finding contentment in doing perfectly the appointed work of every day. If we hold as we should that it is character, not mere talent, which ennobles life, we may well feel that there is something not merely pardonable, but ennobling in such a habit of mind. Viewed in this light, his simple devotion to modest duty may well be to many of us rather a model than a thing to be criticised. Thomas Went worth Higginson. JOSEPH HENRY THAYER. Joseph Henry Thayer was born in Boston, November 7, 1828. He graduated from Harvard in 1850, spent one year (1854-55) in the Harvard Divinity School, graduated from tiie Andover Theological Seminary in 1857, and was minister of the Crombie Street Church in Salem from 1859 to 1864 ; a part of this time, from September, 1862 to May, 1863, he served as Chaplain of the Fortieth Infantry Regiment of Massachusetts Volunteers. His career as teacher began in 1864, 662 JOSEPH HENRY THAYER. when he became Professor in the Andover Theological Seminary. Re- signing his chair in 1882, he came to Cambridge, was Lecturer in the Harvard Divinity School for the year 1883-84, and in 1884, on the death of Ezra Abbot, succeeded him as Bussey Professor of New Testa- ment Criticism and Interpretation; this position he held up to 1901. He was a member of the Harvard Corporation from 1877 to 1884. He was elected a Fellow of the American Academy of Arts and Sciences March 9, 1887, and, though not an active member, was always deeply interested in the work and fortunes of the Academy. Other societies to which he belonged are the Archaeological Institute of America, tlie American Oriental Society, and the Society of Biblical Literature. He received the degree of A.M. from Harvard, the degree of S.T.D. from Yale, Harvard, and Princeton, and the degree of Litt.D. from Dublin. Dr. Thayer chose as his field of study the grammar and lexicography of the New Testament, and his distinguished services in this department have been universally recognized in Europe and America. He brought to his task wide learning, patience in investigation, minute accuracy in details, and critical acumen. His " Greek-English Lexicon of the New Testament " will long remain a manual for students and a monument of erudition and industry. The statement on the title-page, that it is a "revised and enlarged translation" of a German lexicon (Grimm's Wilke), hardly conveys a correct impression of its character. In fact the increase of the breadth and precision of definitions, the verification of references, the addition of further references, and the construction of the New Testa- ment text from the best manuscript authorities, entailed an amount of labor almost equivalent to the production of an independent lexicon. This breadth of research and exactitude of statement characterized all his scientific work — his articles in the Bible Dictionaries of Smith and Hastings, his translation of the New Testament Greek grammars of Winer and Buttmann, and his work on the Revised Version of the New Testament. To this last he gave many years of labor, as a member of the American Committee collaborating with the English Committee, and as principal editor of the American Version (the English Version with the changes introduced by the American Committee), which by agreement with the English Committee was published last year. His reading in his chosen field was wide and critical. He found time amid pressing professional and editorial duties to keep up with the enormous mass of New Testament literature tliat every year produced in Europe and America, and to form well-defined opinions as to its value. JOSEPH HENRY THAYER. 663 He was not only singularly precise in details, he had a marked capacity for organization. He conceived large plans, and worked them out with patience and success. As early as 1864 he announced his purpose to translate Grimm — he completed the translation in Cambridge in 1885. It is mainly to him that we owe the establishment of the American School of Oriental Research in Jerusalem. Year after year he set forth the desirableness and the feasibility of such a school, and by unwearied exertions secured the indorsement of the Society of Biblical Literature and of the American Oriental Society, and the cooperation and financial support of a number of colleges, and of the Archaeological Institute of America. The school went into operation in the year 1900, and seems certain to give an impulse to Oriental study in this country, and to increase our knowledge of Oriental (especially Semitic) life, ancient and modern. Dr. Thayer was an enthusiastic teacher, ever ready to give sympathy and time to his students. He was exacting in his demands, had small patience with negligence, and refused to lower his standards on any per- sonal grounds, such as lack of previous preparation, or sickness; but he knew how to encourage and assist backward students, and to stimulate all by his own sense of the requirements of scholarship. He held firmly to the traditional New England standard of a minister's outfit, insisting on the necessity of Hebrew and Greek for the preacher. This point was the subject of debate in the Harvard Divinity Faculty for years, and the final decision made it possible for a student to take the degree of Bach- elor of Divinity without a knowledge of Hebrew or Greek, the Faculty reserving the right, however, to pass on every individual case. In point of fact, it is true, in the past thirty years at least, only one man without Greek had received the degree, and he was a Japanese, from whom crit- ical study of the Chinese classics was accepted in lieu of Greek. But Dr. Thayer, seeing that the Hebrew requirement was practically given up, believed there was danger that the Greek requirement would go the same way. Against this disposition to dispense with the original languages of the Bible he set his face steadfastly ; he lost no opportunity to protest against what he regarded as a lamentable lowering of the standard of ministerial learning. When the question was finally decided, he, of course, accepted in good faith the action of the Faculty. Accept it cordially he could not : he was not an easy-going man, willing to fall in gracefully with the opinions of the majority ; on the contrary, he took things very seriously, and, in matters that interested him, expressed him- self pointedly. To the last be never spoke of the attitude of the Faculty QG-^ JOSEPH HENRY THAYER. toward the Hebrew and Greek requirements without a word of emphatic distrust and condemnation. His thinking was notably clear-cut — he could not abide haziness. This trait, which is prominent in his scholarly work, appears also in his theo- logical views. He was not intolerant of other men's opinions ; he only held tenaciously to his own opinions, and claimed the right to define his position precisely. When he found, in 1882, that he could not sub- scribe the Andover Creed as it was then interpreted by the governing boards, he resigned his professorship in the Seminary — a sundering of old ties that gave him great pain. His own creed was distinct, yet cath- olic; he held firmly to certain principles and facts that he believed to be fundamental, and among these he gave a prominent place to scientific truth and personal experience. Born and brought up in Boston, his traditions and training were those of New England, modified, however, by travel in foreign countries, and by a wide knowledge of men and things. He was a scholar and a man of affairs, a Puritan and a man of the world. In personal intercourse he showed an engaging frankness and friendliness, and the same devotion that appears in his scholarly undertakings manifested itself in his rela- tions with his friends, for whom he was always ready to do the uttermost. He was fortunate in retaining his physical soundness and vigor up to a few months before his death. His erect carriage, alert step, and cheeiy manner gave him, even in his last years, a remarkably youthful appear- ance, and his bodily alertness was in keepirfg with his mental activity. His literary career extended over forty years, apparently without dimi- nution of interest. He had the great happmess of seeing his main under- takings brought to a successful completion — the Greek lexicon, the revision of the English New Testament, and the establishment of the Jerusalem School. At the close of the year 1900-01 he resigned his position in Harvard, and was made Professor Emeritus. The following summer he spent in Europe, and, returning to America, died in Cambridge after a short illness, November 26, having not long before passed his seventy-third birthday. C. H. Toy. JOHN PISKE. 6G5 JOHN FISKE. On the 4th of July, 1901, John Fiske, philosopher, lecturer, and historian, died at Gloucester. On the morning of the fifth, hundreds of obituary notices of this distinguished man were read in the daily news- papers from Maine to Texas, from the Atlantic to the Pacific, and even across the water in the capital of Great Britain, by a public familiar, through his ministrations on the platform, with his giant form and ruddy countenance. These preliminary notices were followed at a later date by biographical and critical articles treating of his career, more finished in style and more analytical in character, in reviews and magazines ; in weekly, monthly, and quarterly publications. Many of these were characterized by a familiarity with the details of Mr. Fiske's early life, unusual under such circumstances, but easily to be accounted for, since his biography liad been partially written during his lifetime by two competent authors. The first of these sketches, and in some respects the more complete of the two, was published by Edwin D. Mead, in the '• Christian Register," in a series of papers occasioned by an address by Mr. Fiske before the Concord School of Philosophy in 1886. The second was by the late Horace E. Scudder, and appeared in a sort of introduction to one of the editions of " The War of Independence." The striking similarity of these biographies extends even to the language used, and indicates a common origin. It is certain that Mr. Fiske himself furnished the material for Mr. Mead's sketch, and there can be but little doubt that he did the same by Mr. Scudder. This will fully explain the points of coincidence, and will also give to both the authoritative character, which neither in words claims, of being practically autobiographical. From these sketches we learn that on the 30th of March, 1842, there was born in Hartford, Connecticut, to Edmund Brewster Green and Mary Fiske Green, a son named by them Edmund Fiske Green, the greater part of whose child life was spent in Middletown, Connecticut. This ILdmund Fiske Green was our John Fiske, his name having been changed during boyhood to that borne by his maternal grandfather. At an early age the wonderful precocity of the child foreshadowed the marvellous attainments of his later years. His education was carried on first in the lower schools at Middletown and later at Stamford. Then he returned to INIiddletown and was placed in a private school, after wliich he went to Cambridge. Meantime he seems to have browsed o 666 JOHN FISKE. in a library in the family mansion, and to a great degree taught himself much that is acquired with difficulty by persons of ordinary intellect even when assisted by the best of masters. In his " Dutch and Quaker Colonies," Mr. Fiske says of James Logan : ''He was an infant prodigy; at the age of twelve his attainments in Greek, Latin, and Hebrew had attracted much notice, and he afterward obtained distinction in modern languages, mathematics, physics, and natural history." The story of Logan's precocity is fairly eclipsed by Fiske's own record, but what he says of Logan shows us what his dispassionate judgment was as to his own childhood career. Fiske's biographers recapitulate his progress from year to year. It is needless to give in full detail the story of his prodigious acquisitions. Suffice it to say, that when six years old he began the study of Latin, and at the age of seven he amused himself by reading Caesar, and found entertain- ment in such authors as Rollins and Josephus, and in the perusal of Goldsmith's Greece. The taste for history thus disclosed led him on to the works of other authors, and before he was eleven years old he had not only devoured many histories of divers peoples, but had from memory filled a quarto blank-book of sixty pages with chronological tables of events between 1000 15. C. and 1820 A. D. By the time he was thir- teen lie had read the greater part of the writings of about a dozen Latin authors, the work thus accomplished being in fact more than would be required in that line of a graduate at Harvard. Meantime, mathematics had not been neglected. Beginning with algebra at the age of eight, he had, by the time he was thirteen, gone through Euclid, plane and spher- ical trigonometry, surveying and navigation, and analytical geometry, and had made a good start in differential calculus. Until he had mastered Latin sufficiently to make use of a Greek lexicon in which the meanings were given in Latin, he could not take up Greek, a lexicon of this description being the only one at his com- mand. So trifling a discouragement as that did not long delay him. As soon as he felt competent to make use of the means at hand, he entered upon the study of Greek, and even before he obtained a modern lexicon he made considerable progress in his knowledge of the language. With the facility for study gained through the acquisition of a suitable key to the meanings of the words, he reached such proficiency, at the age of fifteen, that he could read Plato and Herodotus at sight. He began his philosophical studies at the age of eleven with Locke's " Essay of the Understanding," and at fourteen himself wrote an essay on the habitability of the planets, in which he made the point that JOHN FISKE. 667 Jupiter and Saturn, owing to their great size and slow refrigeration, are in a much earlier stage of development than Venus, Mars, and the Earth. His taste for philology led him to attack the modern languages at the age of fifteen. He began with German ; took up Spanish, in which he kept a diary ; conquered French; and then attacked Italian. At the end of six months he had read the whole of Giuccardini, with parts of Ariosto and Petrarch. He then turned his attention to Portujruese. We have followed him as a boy down to the time when he is about to leave home to go to Cambridge, What had college to offer him in the way of instruction ? It is true that in much of the work he had performed he had been without a master, and of course there was much that he might still learn, but clearly the regular curriculum would practically be merely review work for him. Nevertheless, he looked forward with yearning to the time he should spend at Harvard, knowing that he could discover avenues in which the extraordinary mental activity which had impelled him along this wonderful path of study could find exercise. We are told that until he was sixteen " he averaged twelve hours study daily for twelve months in the year." With the qualifications which will naturally suggest themselves this statement would seem probable, yet this boy who could cope with problems which present difficulties to the ordinary collegiate student, and whose learning at fifteen years of age far exceeded in many directions the standard which we should set for a cultivated man of maturity, found time for other occupations than delving in books. He taught himself to play upon the piano; participated iu out-of-door sports, and took pleasure in walking, riding, and boating upon the Connecticut. He was much interested in church and oratorio music, was a member of the church choir, and his fondness for choral music, then developed, is said to have abided by him throughout life. AVe do not find evidence that works of fiction had much attraction for him as a boy. Later in life, we know that he was fond of novels, and that the characters portrayed by the masters of fiction were as real to him as the heroes with whom he met in history. His reading at this time must have been controlled by his surroundings, and what the libraries at his command furnished we can conjecture from the list of his acquirements. He gives us a hint of what there was at hand for him to read, in addition to what might be termed '"useful books," in the following: "I remem- ber," lie says in one of his essays, " that when I was about ten years old, a favorite book witli me was one entitled ' Criminal Trials of all Coun- 668 JOHN FISKE. tries by a Member of the Philadelphia Bar.' I read it and read it, until forbidden to read such a grewsome work, and then I read it all the more." He also tells us that he had access to a few scientific books owned by a strange character in Middletown, a sort of hermit ; a dabbler in biol- ogy and geology, who led a solitary life ; immersed, apparently, in studies and speculations concerning things far above his stage of culti- vation. In the curious den — the library, workshop, and probably liv- ing room also — of this friendly recluse, among stuffed birds, mounted animals, strange creatures preserved in alcohol, specimens of fossil foot- prints from the Connecticut sandstone, and a few books on the subjects in which the owner was interested, the learned boy was admitted as a privileged guest, and here he talked with his strange companion con- cerning the surrounding objects, and from his host young Fiske bor- rowed such of the books as he cared to read. The future author of " Outlines of a Cosmic Philosophy" and "Through Nature to God," was at this time a teacher in the Sunday-school and was active at prayer-meetings. What it cost him to reach the frame of mind which could put forth these works is substantially set forth in his Cosmic Philosophy. "A person," he says, "is educated in an environment of Presbyterian theology, accepting without question all the doctrines of Calvinism. By and by his environment enlarges. Facts in science or in history, methods of induction, canons of criticism present themselves to his mind as things irreconcilable with his old creed. Hence painful doubts, entailing efforts to escape by modifying the creed to suit new mental exigencies. Hence eager study and fur- ther enlargement of the environment, causing fresh disturbance of equilibrium and renewed doubt, resulting in further adaptation. And so the process continues, until, if the person in question be sufficiently earnest and sufficiently fortunate, the environment enlarges so far as to comprehend the most advanced science of the day, and the process of adaptation goes on until an approximate equilibrium is attained between the order of conception and the order of phenomena, and scepticism, having discharged its function, exists no longer, save in so far as it may be said to survive in the ingrained habit of weigh- ing evidence and testing one's hypotheses." Elsewhere, and this time speaking in the first person singular, he refers to his early religious opinions as being based upon the fear of the " burning hell with which my childish imagination had been unwisely terrified." He entered the sophomore class at Harvard in 1860 at the age of JOHN FISKE. 669 eighteen, and was graduated in 1863. His study of the modern lan- guages, which as we have seen already comprehended nearly all those in use in ICastern Europe, was followed by an attack on the ancient tongues, Hebrew and Sanskrit ; the former before he entered college, the latter after he reached Cambridge. While in college he is said to have worked from twelve to fifteen hours each day, during vacations as well as terms, his time being divided between comparative philology, ancient and modern history, and modern literature. His philological studies at this period comprehended the Icelandic, Gothic, Danish, Swedish, Dutch, and Roumanian tongues, and an attack on the Russian. " He was but a lad of seventeen," says one of his eulogists, " when Darwin's great work appeared and aroused in him the zeal that deter- mined his mental activity for more than a score of years." Mr. Mead, in his sketch, eprieurii, 255. Calothrix aerugiiiea, 241. confervicola, 241. Calothrix Contarenii, 241. fusca, 241. Juliana, 241. pilosa, 242. Carbon, The Visible Radiation from, 71-118, 612. Carex. (For index of species, see pp. 510-512.) Carices of the Section Hyparrhenae, 445-495, 612. Carices, Variations of some Boreal, 495-514, 612. Case School of Applied Science. See Chemical Laboratory. Catenella Opuntia var. pinnata, 253. Caulerpa cupressoides var. ericifolia, 244. cupressoides var. mamillosa, 244. cupressoides var. Turneri, 244. cupressoides var. typica, 244. pinnata forma Mexicana, 244. plumaris forma brevipes, 245. plumaris forma longiseta, 244. prolifera, 245. racemosa var. clavifera, 245. racemosa var. clavifera forma macrophysa, 245. taxifolia, 245. verticillata, 245. verticillata forma charoides, 245. Cauloglossum ti'ansversarium, 628. Celli, A., elected Foreign Honorary Member, 612; accepts Member- si lip, 615. Ceramium byssoideum, 259. clavulatum, 259. fastigiatum, 259. gracillimum, 259. nitens, 259. tenuissimum, 259. teniiissimum var. pygmaeum, 259. Ceratomyces Braziliensis, 44. curvatus, 43. Mexicanus, 43. procerus, 43. spinigerus, 42. Chaetomorpha aerea, 243. brachygona, 243. clavata, 243. Linum, 243. Chaetomorpha Linum var. brachyar- thra, 243. Melagonium, 243. Chamaedoris aunulata, 247. Chamberlin, T. C, elected Associate Fellow, 611. Champia parvula, 255. Chantransia Saviana, 251. Chemical Combination, Probable Source of the Heat of, 397. Chemical Laboratory of Harvard College, Contributions from, 175, 271, 345, 363, 397, 413. Chemical Laboratory of the Case School of Applied Science, Con- tributions from, 5;37, 563. Cherbourg, National Soc. of Nat. and Math. Sci., Fiftieth Anni- versary, 614, 617. Chitonomyces Bullardi, 31. Hydropori, 32. occultus, 30. Orectogyri, 32. psittacopsis, 30. Chlamydomy xa labyrinthuloides, 344. Chondria Baileyana, 256. dasyphylla, 256. tenuissima, 256. Christiania, Royal University of, The 100th anniversary of birth o*' N. H. Abel, 620. Chroococcus turgidus, 239. Chroothece Richteriana, 239. Chrysymenia halynienioides, 255. Cladophora crystallina, 243. fascicularis, 243. fuliginosa, 243. Hutchinsiae, 243. intertexta, 243. trichocoma, 244. Clifford, II. E., elected Resident Fellow, 616 ; accepts Fellowship, 620. Cocos Island, Flora of, 628. Codium adhaerens, 246. tonientosum, 246. Coenonia, 342. denticulata, 342. Collins, F. vS., accepts Fellowship, 599 ; The Algae of Jamaica, 229- 270, 614. Colpomenia sinuosa, 248. Committee, Nominating, 617, 619. Committees elected, 610, 627; List of, 683. INDEX. 707 CoQcentrated Solutions, 345. Cooke, J. P., Bronze Bas-relief of, C14. Corallina capillacea, 261. Cubeusis, 201. pumila, 261. rubeiis, 261. subulata, 261. Cordylecladia irregularis, 254. Peasiae, 255. Corethromyces Latonae, 41. Stilici, 42. Cornu, A., Death of, 620. Council, Report of, 620, 635. Crew, H., Grant from Income of Rumford Fund to, 623. Cross, C. R., President />ro tern., 617 ; Report of the Rumford Com- mittee (1900-01), 601, (1901- 02), 623. Crouania attenuata, 258. Cruoriella Ai'morica, 260. Ci-yptogamic Laboratory of Harvard University, Contributions from, 19, 331, 612, 628. Crj^tonemia crenulata, 260. Curves, Multiple Points of Twisted, 628. Cutleria, 248. Cylindrospermum musciola, 240. Cymopolia barbata, 247. Dante, The Malignity of, 614. Dasya arbuscula, 257. Gibbesii, 257. mucronata, 2.57. Dasycladus clavaeformis, 247. Davis, A. McF., Biographical Notice of John Fiske. 620, 665-678. Davis, W. M., The Formation of River Terraces, 619. Delitzsch, F., elected Foreign Hon- orary Member, 616 ; accepts Membership, 618. Dibromdinitrobenzols, 629. Dicev, A. v., accepts Membership, 613. Dichomyces Australiensis, 28. Belonuchi, 27. bifidus, 26. Homalotae, 29. Mexicanus, 28. Dicothrix penicillata, 242. Dictyerpa -lamaicensis, 251. Dictyopteris delicatula, 249. Justii, 249. Dictyopteris plagiogramma, 249. Dictyosphaeria favulosa, 247. Dictyosteliacese, 338. Dictyostelium, 338. aureum, 340. brevicaule, 340. lacteum, 339. mucoroides, 338. purpureum, 340. roseum, 339. sphserocephalum, 339. Dictyota Bartayresiana, 250. cervicornis, 250. ciliata, 250. dentata, 250. dichotoma, 250. divaricata, 250. fasciola, 250. Dictyurus occidentalis, 257. Digenea simplex, 256. Dilophus alternans, 250. Guineensis, 250. Dinitrohenzolsulphonic Acid, Sym- metrical, 629. Dioicomyces, 33. Anthici, 33. onchophorus, 34. spinigerus, 34. Diplochaete solitaria, 242. Diplophrys, 343. Archeri, 343. stercorea, 344. Directive Stimuli, Reactions of Limax maximus to, 183-227. Dunkel, O., Regular Singular Points of a System of Homogeneous Linear Differential Equations of the First Order, 628. Earle, R. B. See Jackson, C. L., and Earle, R. B. Ectocarpus Mitchellae, 248. Engler, A., elected Foreign Honor- ary Member, 611 ; accepts Mem- bership, 613. Enteromorpha erecta, 242. flexuosa, 242. intestinalis, 242. prolifera, 242. Epidote Crvstals from Alaska, 529- 535, 617. Eucheuma echinocarpum, 253. Euhaplomyces, 25. Ancyrophori, 25. Xanthophaeae, 26. 708 INDEX. Eumonoicomyces, 21. Californicus, 22. Papuanus, 22. Everett, W., The Malignity of Dante, 614. Farlow, W. G. , Account of the Ninth Jubilee Celebration of the Uni- versity of Glasgow, 619. Federal Legacy Tax, 599. Fellows, Associate, deceased, — King, C, 617. LeConte, J., 613. Rowland, H. A., 599. Fellows, Associate, elected, — Chamberlin, T. C, 611. Fritz, J., 611. Pepper, G. W., 613. Putnam, H., 618. Wilson, E. B., 616. Fellows, Associate, List of, 689. Fellows, Resident, deceased, — Fiske, J., 613. Hyatt, A., 617. Safford, T. H., 613. Thayer, J. B., 618. Thayer, J. H., 615. Fellows, Resident, elected, — Clifford, H. E., 616. Hoar, G. F., 611. Hofman, H. O., 618. Hough, T., 616. Jaggar, T. A, Jr., 618. Morgan, M. H., 616. Porter, W. T., 613. Pritchett, H. S., 613. Strobel, E. H., 618. Williams, F. H., 616. Fellows, Resident, List of, 685. Fernald, M. L., The Northeastern Carices of the Section Hypar- rhenae, 445-495, 612; The Va- riation of Some Boreal Carices, 495-514, 612. Fiske, A. H. See Jackson, C. L., and Fiske, A. H. Fiske, J., Death of, 613; Notice of, 620, 60.5-678. Foreign Honorary Members de- ceased, — Cornu, A., 620. Gardiner. S. R., 618. Grimm, F. H., 613. Kovalevsky, A. O., 615. Lacaze-Duthiers, F. J. H., 613. Foreign Honorary Members de- ceased, — Nordenskiold,FriherreA.E.,613. Stubbs, W., 599. Weinhold, K., 617. Foreign Honorary Members elected, — Balfour, A. J., 628. Celli, A., 612. Delitzsch, F., 616. Engler, A., 611. Gardiner, S. R., 616. Hann, J., 616. Horsley, V. A. H., 616. Lankester, E. R., 616. Lecky, W. E. H., 628. Paris, G., 612. Richthofen, Freiherr F. von, 611. Foreign Honorary Members, List of, 691. Forms of Least Resistance to Pas- sage through Air, 618. Frandsen, P., Studies on the Reac- tions of Limax maximus to Directive Stimuli, 183-227. Fritz, J., elected Associate Fellow, 611. Fugacity, 54-69. Galapagos Flora, Revision of, 617. Galaxaura cylindrica, 252. lapidescens, 252. marginata, 252. obtusata, 252. rugosa, 252. Gardiner, S. R., Death of, 618 ; elected Foreign Honorary Member, 616 ; accepts Membership, 618. Gas-Apparatus, Hempel's, 271-277, 615. Gases, Fugacity of Imperfect, 66 ; at High Temperatures, Spectra of, 619. Gelidium coerulescens, 252. crinale, 2.53. rigidum, 253. supradecompositum, 253. General Fund, 600, 621, 625. Geotaxis, 190. Glasgow, Univei'sity of. Ninth Jubi- lee Celebration, 619. Gloeocapsa quaternata, 239. Gloeotrichia natans, 242. Goldstein, A. H. See Mabery, C. F., and Goldstein, A. H. INDEX. 709 Gomontia polyrhiza, 244. Goniotrichum Huinphreyi, 251. elegans, 251. Gracilaria Blodgettii, 253. caudata, 253. cervicornis, 253. compressa, 253. confervoides, 253. cornea, 253. Curtissiae, 253. damaecornis, 254. divaricata, 254. Domingensis, 254. ferox, 254. multipartita, 254. Wrightii, 254. Grants, from Income of C. M. War- ren Fund, 605, 607, 625, 626; from Income of Rumfoi'd Fund, 601, 623, 626. Grateloupia filicina, 260. dichotoma, 260. prolongata, 260. Gray Herbarium of Harvard Univer- sity, Contributions from, 445, 612, 617, 628. Grimm, F. H., Death of, 613. Guttulina, 337. aurea, 337. protea, 337. rosea, 337. sessilis, 338. Guttulinacese, 335. Guttulinopsis, 335. clavata, 336. stipitata, 336. vulgaris, 336. Gymnosorus variegatus, 249. Hale, G. E., accepts Fellowship, 612 ; Grant from Income of Ruin- ford Fund to, 601 ; Radiometer, 601; Rumford Premium awarded to, 624, 628. Halimeda Opuntia, 246. tridens, 216. Tuna, 246. Halodictyon mirabile, 258. Haloplegma Duperryi, 258. Halymenia Floresia, 260. Hann, J., elected Foreign Honorary Member, 616; accepts Member- ship, 618. Hapalosiphon fontinalis, 241. Harvard College. See Chemical Lab- oratory, Cryptogamic Labora- tory, Gray Herbarium, and Zoological Laboratory. Harvard Mineralogical Museum, Con- tributions from, 515, 529. Heat of Chemical Combination, Prob- able Source of, 397-411, 617. Heat of Vaporization, 537-549, 618. Heimrod, G. W. See Richards, T. \V., and Heimrod, G. W. Hempel's Gas- Apparatus, Modifica- tions of, 271. Herty, C. H., Grant from C. M. Warren Fund to, 605, 607. Heterosiphonia Wurdemanni, 257. Higginson, T. W., Biographical No- tice of Horace Elisha Scudder, 619, 657-661. Hildenbrantia prototypus, 260. Hoar, G. F., elected Resident Fellow, 611. Hofman, H. O., elected Resident Fellow, 618 ; accepts Fellow- ship, 620; Grant from Income of C. M. Warren Fund to, 625, 626. Hormothamnion enteromorphoides, 241. Ilorsley, V. A. H., elected Foreign Honorary Member, 616 ; accepts Membership, 618. Hough, T., elected Resident Fellow, 616 ; accepts Fellowship, 617. Hudson, J. E., Obituary Notice of, 612. Hyatt A., Death of, 617 ; Notice of, 628. Hydrocarbons in Pennsylvania Pe- troleum, 563-595, 020. Hydrocarbons, Paraffins and Methy- lene, 537-549, 618. Hydroclathrus cancellatus, 248. Hydrogen, Arc Spectrum of, 159-174. Hyparrhenae, Carices of the Section, 445-49.5. Hypnea, divaricata, 254. musciformis, 254. Valentiae, 254. Iron, Arc Spectrum of, 623. Jackson, C. L., Report of the C. M. Warren Committee (1900-01), 605, (1901-02), 625. 710 INDEX. Jackson, C. L., and Calhane, D. F., On the Dibromdinitrobenzols derived from Paradibromben- zol, 629. Jackson, C. L., and Earle, R. B., On certain Derivatives of Picric Acid, 629; On Symmetrical Dinitro- benzolsulphonic Acid, 629 ; On the Colored Substances derived from Nitro-compounds, 629. Jackson, C. L., and Fiske, A. H., On certain Derivatives of 1, 2, 3-Tribrombenzol, 629. Jackson, H., Foreign Honorary Mem- ber, 613. Jaggar, T. A., Jr., elected Resident Fellow, 618 ; accepts Fellowship, 620. Jamaica, Algae of, 229-270. Johnston, J. R., On Cauloglossum transversarium (Bosc) Fries, 628. Kainorayces, 44. Isomali, 45. Keen, W. W., accepts Fellowship, 612. King, C, Death of, 617. Koch, R., accepts Membership, 613. Kovalevsky, A. O., Death of, 615. Laboulbeniaceae, Preliminary Diag- noses of New Species of, 19-45, 612, 628. Labyrinthula, 343. Cienkowskii, 343. macrocystis, 343. vitellina, 343. Labyrinthulese, 342. Lacaze-Duthiers, F. J. H. de. Death of, 613. Lankester, E. R., elected Foreign Honorary Member, 616; accepts Membership, 618. Lanman, C. R., The Atharva Veda and its Significance for the His- tory of Hindu Tradition and Hindu Medicine, 615. Laurencia cervicornis, 255. implicata, 255. obtusa, 255. papillosa, 255. perforata, 256. tuberculosa var. gemmifera, 256. Lecky, W. E. H., elected Foreign Honorary Member, 628. LeConte, J., Death of, 613. Legacy Tax, Federal, 599. Lewis, G. N., The Law of Physico- chemical Change, 47-69. Liagora Cheyneana, 251. decussata, 252. elongata, 252. pulverulenta, 252. valida, 252. Librarian, Report of, 606, 622. Library, Appropriations for, 607. Library, Committee on the. Report of, 606. Limax maximus. Reactions of, 183- 227. Lithothamnion incrustans, 260. Lenormandi, 260. Loci in M-Fold Space, On Ruled, 119- 157, 612. Lophosiphonia obscura, 2.57. Lowell, A., Notice of, 614, 635-654. Lowell, A. L., Party Votes in Par- liament, Congress, and the State Legislatures, 617. Lowell, P., Biographical Notice of Augustus Lowell, 614, 635-654 ; Some Results from the Last Opposition of Mars, 615. Lyman, T., accepts Fellowship, 612. Lyngbya aestuarii, 240. confervoides forma violacea, 240. majuscula, 240. putalis, 240. versicolor, 240. Mabery, C. F., Grant from Income of C. M. Warren Fund to, 605, 607, 625, 626 ; On the Hydrocar- bons in Pennsylvania Petroleum with Boiling Points above 216°, 620, 563-595. Mabery, C. F., and Goldstein, A. H., On the Specific Heats and Heat of Vaporization of the Paraffine and Methylene Hydrocai'bons, 537-549, 618. MacDonald, A., P.sycho-Physicai Lab- oratory, 599. Magnesium, Arc Spectrum of, 628. Mall, F. P., accepts Fellowship, 599. Manchioneal, 255. jNIark, E. L. See Zoological Labor- atory etc.. Contributions from. Markovnikoff, V., 599. Mars, Last Opposition of, 615. INDEX. 711 Mastick, S. C, Federal Legacy Tax, 599. Mastigocoleus testarum, 241. Melobesia farinosa, 2G0. Lejolisii, 200. membranacea, 260. pustulata, 260. Mendenhall, C. E., Bolometer, 601 ; Grant from Income of Rumford Fund to, 601. Mendenhall, T. C, Associate Fellow, 616. INIercurous Chloride, The Decompo- sition of, 345-361, 615. Merigold, B. S. See Richards, T. W., and Merigold, B. S. Messedaglia, A., Death of, 599. Microcoleus chthonoplastes, 240. tenerrinuis, 240. vaginatus, 240. Microdictyon umbilicatum, 247. Minot, Maine, Apatite from, 515- 528, 615, 617. Mislawsky, A., Fiftieth Anniversary, 614. Mouoicomyces, 23. Aleocharae, 24. Echidnoglossae, 23. furcillatus, 24. Moore, E. H., accepts Fellowship, 612. Moreno, H. C, On Ruled Loci in n-Fold Space, 119-157, 612. Morgan, M. H., elected Resident Fellow, 616, 617. Miiller-Rreslau, H., accepts Member- ship, 613. Murrayeila periclados, 257. Museum of Comparative Zoology. ^ee Zoological Laboratory. Mycoidea parasitica, 243. Neighborhood of a Singular Point, 279. Neomeris dumetosa, 247. Nichols, E. F., Grant from Licome of Rumford Fund to, 623. Nichols, E. L., The Visible Radia- tion from Carbon, 71-118, 612. Nitro-compounds. Colored Sub- stances derived from, 629. Nobel Committee, Nobel Prize, 614. Nordenskiold, Friherre A. E., Death of, 613. Nostoc commune, 240. Nostoc microscopicum, 240. verrucosum, 240. Noyes, A. A., Electrical Conductivity, 602; Grant from Income of C. M. Warren Fund to, 605, 607, 625, 626; Grant from Income of Rumford Fund to, 602, 623. Nuremberg, Natural History Society of. One hundredth Anniversary, 613. Officers elected, 610, 618,626; List of, 683. Olive, E. W., A Preliminary Enum- eration of the Sorophorae, 331- 344. Ophthalmological Hospital, 599. Oppenheimer, A., Certain Sense Organs of the Proboscis of the Polychaetous Annelid Rhyncho- bolus dibranchiatus, 551-562. Oscillatoria anguina, 239. Corallinae, 239. formosa, 239. princeps, 239. princeps forma purpurea, 239. proboscidea, 239. tenuis, 239. Oxford, University of, 300th Anni- versary Bodleian Library, 620. Packard. A. S., Biographical Notice of Alpheus Hyatt, 628. Padina Durvillaei, 249. Palache, C-, A Description of Epi- dote Crystals from Alaska, 529- 535, 617. Palache, C. See Wolff, J. E., and Palache, C. Paraffine and Methylene Hydrocar- bons, Specific Heat of, 537-549, 618. Parametric Representation of the Neighborhood of a Singular Point, 279-330, 614. Paris, G., elected Foreign Honorary Member, 612 ; accepts JNlember- ship, 613. Penicillus capitatus, 245. dumetosus, 245. Pennsylvania Petroleum, Hydrocar- bons in, 563. Pepper, G. W., elected Associate Fellow, 613 ; accepts Fellowship, 614. 712 INDEX. Petroleum, Composition of, 563-595, 620. Peyritschiella Xanthopygi, 29. Peysoiiiiellia Dubyi, 260. rubra, 260. Pliormidium Retzii, 239. Phototaxis, 206. Physico-chemical Change, The Law of, 47-69. Pickering, E. C, Co-operation in Ad- ministering Research Funds, 602. Picric Acid, Derivatives of, 629. Pissaroff, V., Ophthalmological Hos- pital, 599. Plectonema Nostocorum, 240. Wollei, 240. Plowman, A. B., On the Ionization of Soils, 628. Poincare, H., accepts Membership, 613. Points, Multiple, 628. Points, Regular Singular, 628. Polysiphonia cuspidata, 256. ferulaea, 256. Havanensis, 256. Havanensis var. Binneyi, 256. Pecten- Veneris, 256. secunda, 256. subulata, 256. Polysphondylium, 341. album, 342. pallidum, 341. violaceum, 341. Porter, R. A., The Influence of Atmospheres of Nitrogen and Hydrogen on the Arc Spectra of Iron, Zinc, Magnesium and Tin, compared with the Influ- ence of an Atmosphere of Am- monia, 628. Porter, W. T., elected Resident Fellow, 613; accepts Fellowship, 614. Pringsheimia scutata, 243. Pritchett, H. S., elected Resident Fellow, 613. Psycho-Physical Laboratory, 599. Publication, Committee of. Report of, 605, 625. Publications, Appropriations for, 607, 626. Putnam, F. W., Archaeological Work of J. H. Blake, 612. Putnam, II., Delegate to Bodleian Library Commemoration, 620; elected Associate Fellow, 618; accepts Fellowship, 620. Radiation from Carbon, The Visible, 71-118, 612. Records of INIeetings, 599-628. Rhacomyces Dolicaontis, 39. Glyptomeri, 39. Oedichiri, 38. Rhipocephalus Phoenix, 245. Rhynchobolus dibranchiatus, 551- 562. Richards, T. VV., Grant from Income of Rumford Fund to, 602, 624, 626 ; Modifications of Hempel's Gas-Apparatus, 271-277, 615; Table of Atomic Weights, 630'; The Possible Significance of Changing Atomic Volume, 1-17, 397-41 1, 612; The Probable Source of the Heat of Chemical Combination, and a New Atomic Hypothesis, 397-411, 617; The Standard of Atomic Weights, 175-181, 615 ; Thomson-Joule Experiment, 602, 624. Richards, T. W., and Archibald, E. II., The Decomposition of Mer- curous Chloride by Dissolved Chlorides : a Contribution to the Study of Concentrated So- lutions, 345-361, 615. Richards, T. W., and Ileimrod, G. W., On the Accuracy of the Improved Voltameter, 413-443. Richards, T. W., and Merigold, B. S., A new Investigation con- cerning the Atomic Weight of Uranium, 363-395, 615. Richthofen, F. Freiherr von., elected Foreign Honorary Member, 611; accepts Membership, 613. River Terraces, 619. Robinson, B. L., Diagnoses and Syn- onymy of some Mexican Sper- matophytes, 628 ; Flora of Cocos Island of the Pacific, 628; Re- vision of the Galapagos Flora, 617. Rotch, A. L., Report of Librarian, 606, 622. Rowland, H. A., Death of, 599. Rumford Committee, Report of (1900-01), 001, (1901-02), 623. INDEX. 713 Rumford Fund, 600, 621; Appro- priations from Income of, 607, 624, 626 ; Tapers published by Aid of, 71, 159, 397. Rumford Medals, Presentation of, 614 ; Replicas, 602, 607. Rumford Premiinn, 703; Awards of, 604 (Complete List from 1839 to 1900 inclusive), 607, 624, 628. Safford, T. 11., Death of, 613; Notice of, 654-656. Sappinia, 335. pedata, 335. Sappiniacete, 334. Sargassum bacciferum, 248. lendigerum, 248. platycarpum, 248. vulgare, 248. vulgare forma ovata, 248. vulgai'e var. foliosissiraum, 249. Schizothrix coriacea, 240. Mexicana, 240. Scudder, H. E., Notice of, 619, 657- 661. Scudder, S. H., Report of Committee of Publication (1900-01), 605, (1901-02), 625. Scytonema Arcangelii, 241. conchophilum, 241. crispum, 241. densum, 241. Hofmanni, 241. Javanicum, 241. ocellatum, 241. Searle, A., Biographical Notice of Truman Henry Safford, 654-656. Sedgwick, W. T., and Winslow, C- E. A., Experiments on the Effect of Freezing and other Low Tem- peratures upon the Viability of the Bacillus of Typhoid Fever, with Considerations regarding Ice as a Vehicle of Infectious Disease, 619 ; Statistical Studies on the Seasonal Prevalence of Typhoid Fever in Various Coun- tries and its Relation to Seasonal Temperature, 619. Sense Organs of the Proboscis of Rhynchobolus, 551-562. Silver, Electrochemical Equivalent of, 438. Siphonocladus membranacetis, 247. tropicus, 247. Soils, Ionization of, 628. Solieria chordalis, 253. Solutions, Concentrated, 345-361. Sorophorae, A Preliminary Enumera- tion of the, 331-344. Spatoglossum Schroederi, 249. Specific Heat of Hydrocarbons, 537- 549. Spectra, Arc, of Iron, Zinc, Magne- sium and Tin, 628. Spectra of Gases, 619. Spectrophotometer, 87. Spectrophotometric Observations, 103. Spectrum of Hydrogen, The Arc, 159- 174. Spermatophytes, Diagnoses and Syn- onymy of some Mexican, 628. Spermothamnion Gorgoneum, 258. Turneri vai". variabile, 258. Sphaleromyces Chiriquensis, 40. Indicus, 41. Quedionuchi, 39. Spirogyra decimina, 242. Spyridia aculeata, 259. filamentosa, 259. Standing Committees appointed, 611, 627. Standing Votes, Amendment of, 619. Statutes, Amendments of the, 608, 616. Statutes and Standing Votes, 693. Stichomyces, 37. Conosomae, 38. Stigeoclonium tenue, 242. Striaria attenuata, 248. attenuata var. ramosissima, 248. Strobel, E. H., elected Resident Fellow, 618; accepts Fellowship, 620. Stubbs, W., Death of, 599. Stypopodium lobatum, 249. Swain, G. F., Secretary pro (em, 615. Symploca hydnoides var. genuina, 240. hydnoides var. fasciculata, 240. Teratomyces insignis, 36. petiolatus, 36. Zealandica, 35. Thaxter, R., Preliminary Diagnoses of New Species of Laboulbeni- aceae, IV., 19-45, 612; V., 628. 714 INDEX. Thayer, J. B., Death of , 618; Notice of, 628, 679-681 ; Obituary No- tice of John E. Hudson, 612. Thayer, J. II., Death of, 615 ; Notice of, 619, 661-664. Thigniotaxis, 187. Thomson, E., Rumford Medal pre- sented to, 614; Rumford Pre- mium awarded to, 607. Tin, Arc Spectrum of, 628. Toy, C. H., Biographical Notice of Joseph Henry Thayer, 619, 661- 664. Treasurer, Annual Report of (1900- 01), 599, (1901-02), 620. Tribrombenzol, 629. Trowbridge, J., The Sjiectra of Gases at High Temperatures, 619. Turbiiiaria trialata, 248. Typhoid Fever, 619. Udotea conglutinata, 246. flabellata, 246. Ulva fasciata, 242. Lactuca var. rigida, 242. Uranium, Atomic Weiglit of, 363- 395. Valonia aegagropila, 246. ventricosa, 246. verticillata, 247. Van der Vries, J. N., On the Mul- tiple Points of Twisted Curves, 628. Voltameter, Accuracy of the Im- proved, 413-443. Vries, J. N. Van der. See Van der Vries, J. N. Walcott, H. P., elected Vice-Presi- dent, 618, 620. War, Art of, 618. Warren (C. M.) Committee, Report of (1900-01), 605, (1901-02), 625. Warren (C. M.) Fund, 601, 622; Appropriations from Income of, 607, 626 ; Paper published by Aid of, 563. Webster, A. G., Grant from Income of Rumford Fund to, 623. Weinhold, K., Death of, 617. Whitman, C. O., accepts Fellowship, 612. Williams, F. H., elected Resident Fellow, 616. Wilson, E. B., elected Associate Fellow, 616; accepts Fellowship, 617. Winslow, C.-E. A. See Sedgwick, W. T., and Winslow, C.-E. A. Wolff, J. E., and Palache, C, Apatite from Miiiot, ]\Iaine, 515-528, 615, 617. Wood, R. W., Grant from Income of Rumford Fund to, 623. Wrangelia Argus, 252. Xenococcus Schousboei, 239. Yale University, Two-hundredth An- niversary, 613. Zinc, Arc Spectrum of, 628. Zoological Laboratory of the Mu- seum of Comparative Zoology at Harvard College, Contribu- tions from, 183, 551. MBL/WHO! LIBRARY lilH lAflK 5 li'l L