Vol. 37 PROCEEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. Vol. XXXVII. FROM MAY, 1901, TO MAY, 1902. BOSTON: PUBLISHED BY THE ACADEMY. 1902. SSttibrrsitg $3rcss: John Wilson and Son, Cambridge, U.S.A. CONTENTS. j €i Page I. The Possible Significance of Changing Atomic Volume. By Theodore William Richards 1 II. Preliminary Diagnoses of Neiv Species of Laboulbeniacae. — IV. By Roland Thaxter 19 III. The Law of Physico- Chemical Change. By Gilbert Newton 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 Spectrum of Hydrogen. By O. II. Basquin .... 159 VII. The Standard of Atomic Weights. By Theodore William Richards 175 VIII. Stuilies on the Reactions of Limax maximus to Directive Stimuli. 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 Neighborhoo!»7 i CM IV CONTENTS. 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 Hyparrhenae. 2. The Variation of Some Boreal Carices. By M. L. Fernald 445 XVIII. Apatite from Minot, Maine. By John E. Wolff and Charles Palache 515 XIX. A Description of Epidote Crystals from Alaska. By Charles Palache . 529 XX. On the Specific 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 A nne- lid Rhynchobolus dibranchiatus. By Adele Oppenheimer 551 XXII. The Composition 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 Safford 654 Horace Elisha Scudder 657 Joseph Henry Thayer 661 John Fiske 665 James Bradley Thayer 679 Officers and Committees for 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. —Jink, 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 well 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. It' 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 OP 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 liquid 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 NordenskjiJld are too seriously complicated by uncer- tain assumptions to liave much value. (See Ostwald's Lehrbuch, I. 850 (1891), for these and similar considerations.) RICHARDS. SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 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 iuvolved in the study of even a simple series of cases of chemical compression, the facts concerning 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 grains oxygen. Density of metal. Density of oxide. Space oc- cupied by giveu weight of metal. 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 +11.00 Hg 200.00 13.59 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 . . . . 112.3 8.67 6.5 12.95 19.7 + 6.75 Zn . . . . 65.4 6.9 5.6 9.5 14.5 + 5.0 Mg .... 24.36 1.74 3.4 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 carbon, accon ing to posi ... 4.' ' to 12.0 In liquid oxygen at —119° and i )0 atm. (s] ). gr. = 0.6, 5). . • O = 24.5 c.c. In liquid oxygen at —181° and ] . . . O: = 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 material 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 place when substances combine with oxygen. It is evident that in some cases the product occupies considerably more space thau 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 OF CHANGING ATOMIC VOLUME. 7 variable affinities, an approximate idea could be obtained concerning the other from these data concerning atomic and molecular volume. A slight uncertainty is caused also by the possible varying intensity of the u 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- I tstwald, The Chemometer, Z. phys. Cheni. 15, 399 (1894). 8 PROCEEDINGS OF THE AMERICAN 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 C dt = P dc, in which P is the internal stress against which the heat-energy is doing work, G the molecular heat 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 inference, opposes all other forms of expansion.* It is the inward tendency, the opposite to the driving tendency f or fugacity.J 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. % Lewis. RICHARDS. — SIGNIFICANCE OP CHANGING ATOMIC VOLUME. 9 oxygen the atomic critical volume, the contractions are as follows : 14.7 -f 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. p (200X0.139) _... , " = (14.7 X 0.000179) = 106'000 megadynes Per square cm. (65 4x0 392) Pzn = (9.5 x 0.000087) = 310'000 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 Burnstein, 1894. 10 PROCEEDINGS OP THE AMERICAN ACADEMY. Metal (in order of boiling point). Boiling point 700 rn.ni. Heat capacity (,mayers per gram) C Cubic coefficient of expansion. Energy quotieut P_ cat 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°^ = 1400° A 1400°-!- = 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 0.0000230 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. KICHAliDS. 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 should be more easily overcome by rising temperature, a prediction which agrees with facts. Thus there appears to be 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 eliini- 12 PROCEEDINGS OF THE AMERICAN ACADEMY. Molecular Volumes of Chlorides. 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 |Hg. . 100. 14.00 . 5.42 7.30 25.5 +18.2 Hg.. 200. 14.00 7.10 14.00 33.2 +19.2 |Cu . • 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 . . 56.2 8.67 3.7 6.47 24.8 18.33 i 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 II . . • • 1.01 0.07 1.27 14.1 (?) 28.9 fl4.7 Combined with ca Liquid chlorine at 22.8 -80° (boili ng point, 1 60 mm.) (s] a. gr. = 1.66 21.5 +80° (sp. | ;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 (1897). RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 13 Molecular Volumes or 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 1 Hg . . . \ Cu . . . Tlie hydroxide is exceedingly unstable. It is doubtful if the hydroxide exists. The hydroxide cannot be dried without decomposition. \ Co . . . \ Cd . . . \ Mg . . . \ 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 Hvdroxvl i" nrcranin nomnoiinds +12 ( I Hy droxyl in I13 'drogen di oxide (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 course 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 OP THE AMERICAN ACADEMY. cobalt, nickel, zinc, and magnesium sulphates,* but undoubtedly others exist. In a large majority of cases when an electrolyte is dissolved in water, the sum 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 ivhen 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 sejiarating 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 electrolytic 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 * Thonisen, Thermoehemische Untersuchungen, I. 45 (1882). MacGregor, Trans. Roy. 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. phys. Cliem., 15, 79 (1896)) ascribe this contraction to "Electro- striction." t Richards, Jour. Phys. Chem., 4, 385 (1900). See specially p. 391. RICHARDS. SIGNIFICANCE OF 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, Townsend, 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. * Proc. 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, SG. § 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, suggests 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 might 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 Hoff, 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 accompany 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 experimental 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, but 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. CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF HARVARD UNIVERSITY. — XL VII. PRELIMINARY DIAGNOSES OF NEW SPECIES OF LABOULBENIACEAE. — IV. By Roland Thaxter. Received May 6, 1901. Presented May 8, 1901. Additional material illustrating the well-marked generic type de- scribed in a former paper as Mbnoicomyces renders necessary some modification of the original diagnosis, as well as the separation of several species in a second nearly allied genus, which I have called Eumonoico- myces (E. Papuamis being taken as the type), that is well characterized not only by constant differences in the structure of the peculiar anther- idium, but also by reason of certain differences in gross habit which are constant in normal forms of all three of the known species, one of which, E. invisibilis, was formerly placed by me in Mbnoicomyces. EUMONOICOMYCES nov. gen. Receptacle consisting of a basal and subbasal cell ; the latter producing terminally a sterile appendage and laterally a fertile branch (abnormally more than one) the axis of which is coincident with that of the receptacle from which it is not distinguished and consists of a series of superposed cells which may bear a sterile appendage, an antheridium, or an anther- idium and a perithecium ; the three terminal cells usually bearing these organs in the order mentioned. The antheridia consisting of a single stalk-cell, and a single, often obscure, basal cell; the body of the antherid- ium consisting of a series of numerous antheridial cells in four (?) vertical rows which extend obliquely inward and upward, emptying into a com- mon cavity, and replace entirely the two tiers of wall-cells and the anther- idia of Monoicomyces ; the terminal cells growing upward directly to form four unequal sterile terminal appendages, similar to those of Monoicomyces. 22 PROCEEDINGS OF THE AMERICAN ACADEMY. Eumonoicomyces Papuanus nov. sp. Nearly or quite hyaline. Basal cell of the receptacle small, usually triangular ; the subbasal cell terminating in a short appendage distin- guished by a dark basal septum, and sometimes once branched. The fertile branch not differentiated from the receptacle, consisting of three, rarely two cells similar to the subbasal cell, obliquely superposed; the lowest bearing normally a short, hyaline or faintly brownish, erect, sterile appendage, similar to that of the subbasal cell ; the middle cell bearing a single antheridium, and the upper an antheridium and a stalked perithe- cium. The autheridia rather stout, broader distally ; the stalk-cell small and short; the antheridial cells very numerous — thirteen to fifteen usually visible in optical section — the terminal appendages of the usual type, short or seldom longer than the antheridium. Perithecium rather long and sometimes slender ; the venter inflated ; the distal portion tapering gradually and symmetrically to the blunt, nearly truncate apex ; the rather short tip hardly distinguished above a slight elevation ; the stalk-cell variable in length, rather slender, seldom more than half as long as the perithecium ; the basal cells rather large and broad, not dis- tinguished from the venter. Spores about 35 X 3/x. Perithecia 80- 120 X 32-40^, the stalk-cell 35-75 x 15^. Antheridia including stalk-cell and without appendages 35 X 18 fi. Total length to tip of perithecium 150-290^. On all parts of a small pale species of Oxytelus. Ralum, New Pome- rania. Berlin Museum, No. 1011. Eumonoicomyces Californicus nov. sp. Resembling E. Papuanus in general habit. Basal cell of the recep- tacle short, stout, geniculate, with a dark brown suffusion extending from the foot half-way up its convex margin ; the subbasal cell bearing distally a long appendage consisting of a short hyaline basal cell, separated by a dark septum from a second cell above it, which is dark brown and bears two long, slender, one-celled, erect branches, brown below, becoming hyaline distally. The fertile branch not distinguished from the receptacle and consisting of three, sometimes more, very obliquely superposed cells similar to the subbasal cell : the lowest bearing a sterile appendage like that which terminates the receptacle; the middle cell usually bearing an antheridium, and the npper an antheridium and a perithecium. Anther- idium short-stalked, with a more or less well-defined median constriction, resulting from an inflation of the cells which bear the terminal append- THAXTER. NEW LABOULBENIACEAE. 23 ages. The latter very long, brown, extending beyond the tip of the peritheciura. Perithecium short and stout, the venter inflated, the much shorter neck-like distal portion abruptly distinguished, the apex blunt, the stalk-cell usually rather short and stout. Perithecia 75 X 25 ix, the stalk-cell 20 X 18 fx. Sterile appendages, longest 150 ^u. Appendages of antheridium 100^. Total length to tip of perithecium 150 p. On Oxylelus sp. Berkeley, California. MONOICOMYCES Thaxter. The characters which may be considered to separate this genus from Eumonoicomyces are as follows : — The stalk of the antheridium consists of two cells placed side by side ; the body of the antheridium consists of two tiers of wall-cells, from each of which an inner antheridial cell is separated ; the subbasal cell of the receptacle bears normally more than one heterogeneous fertile branch. o ■ Monoicomyces Echidnoglossae nov. sp. Subbasal cell of the receptacle somewhat smaller than the basal cell, bearing a terminal appendage the basal cell of which is as long, or nearly as long as the receptacle and often distally enlarged ; the axis above it consisting of a curved series of several cells, externally opaque, black, hyaline along the inner margin, each cell giving rise from its inner side to a hyaline simple branchlet, much as in the appendage of Laboulbenia cristata. Fertile branches usually two, sometimes one or three, arising from the subbasal cell of the receptacle, and consisting of a single short basal cell which bears directly a perithecium (in some cases more than one) and an antheridium. Antheridium relatively large, the stalk-cells somewhat longer and narrower than the basal cells ; the cells of each of the middle tiers distally more or less prominent, the rounded, almost papillate elevations thus formed from the upper tier more prominent than those from the lower tier : the distal cells proliferous externally and dis- tally, thus forming an outer crown of shorter appendages of very unequal length, which surround the usual inner series. Perithecium becoming greatly and asymmetrically inflated below, and tapering rather abruptly to the slightly distinguished, rather short, bluntly pointed tip ; the stalk- cell variably developed. Perithecia 100-125 X 45-55^, the stalk- cells 40-80 x 15 ft. Antheridia 75-100 /j, the sterile appendages 50-75 li. Total length to tip of perithecium 220-250 fx. On the inferior surface of the thorax of Echidnoglossa Americana Fau- vel. Vera Pass, Colorado. Leconte Collection. 24 PROCEEDINGS OF THE AMERICAN ACADEMY. Monoicomyces furcillatus nov. sp. Receptacle consisting of two small cells which are hardly distinguish- able owing to a general blackish brown suffusion ; producing on either side a stout blackened prolongation, the two forming a nearly symmetri- cal fork-like structure, the prongs of which are slightly curved inward, and slightly divergent. From near the base of these outgrowths and between them arise, apparently from single basal cells on both sides, single stalked perithecia and antheridia. The antheridia rather long and slender, their detailed structure not determinable in the types. The perithecia long and slender, straight, symmetrical, pale yellowish, slightly inflated toward the base, tapering gradually to the blunt apex. Spores about 40 X 3 ^. Perithecia 135 X 27^. Outgrowths from the recep- tacle 110 X 12 fi. Near the tip of the abdomen of Aleochara repetita Sharp. Panama. Sharp Collection, No. 1095. Of the three individuals obtained one only is in fair condition, and none have antheridia in which the details of structure can be made out. Owing to the suffusion and great reduction of the receptacle it is further impossible to determine the exact origin of the remarkable fork-like outgrowths, or the other structures which arise from it. The form is a most peculiar one and recognizable without diffi- culty ; yet, until further data are obtained concerning it, its generic position cannot be certainly determined, although it seems at least more closely allied to Monoicomyces, in which it is provisionally placed, than to any other known type. Monoicomyces Aleocharae nov. sp. Pale amber, shading to amber brown. Receptacle, together with the foot and the basal cell of the terminal appendage, forming a heart-shaped body, blackened below, bearing terminally a median, rigid, slender, almost wholly opaque, black branch, abruptly distinguished from its broad basal cell : the subbasal cell of the receptacle small, triangular when viewed side wise, giving rise to two fertile branches, the short small basal cells of which give rise at once each to two secondary branches and an anther- idium ; the branchlets proliferous and forming an axis of usually three cells, the lower bearing an antheridium, and each of the two upper an antheridium and a perithecium ; there being thus sixteen antheridia and eight perithecia, in fully and symmetrically developed specimens, which form a dense, spreading, fan-like tuft, the antheridia being in general posterior in position, overlapping one another between the black sterile THAXTER. NEW LABOULBENIACEAE. 25 appendage and the perithecia. Antheridium distally broadened and truncate, elongate ; the stalk-cells about equal and about one half the length of the body of the antheridium or somewhat longer than this ; the basal cells unequal ; the cells of the two middle tiers, and their antheridia, clearly distinguishable ; the terminal cells forming four unequal, rounded prominences, the upper inner angle of each cell separated by an almost vertical septum to form the four " guard cells," that terminate in papillate prominences just below which they proliferate to form the characteristic, erect, sterile appendages, all four of which do not always develop; the sterile appendages relatively short, two to three-septate, tapering to a blunt point, distinctly inflated above the slightly constricted base. Peri- thecium relatively large, straight or slightly curved, somewhat inflated below, tapering gradually to the rather short, moderately well distin- guished tip ; the apex bluntly rounded, the basal cells relatively small ; the stalk-cell variably developed, its distal end usually somewhat broader than the basal cells collectively, sometimes more than half as long as the body of the perithecium. Spores about 50-55 X 4-5 ft. Perithecia 130-185 x 35-55 ^ the stalk-cell 35-100 X 18-25^. Antheridia 70- 75 x 22 /j, its appendages 45-50 p. Receptacle about 35 x 28 p. Greatest general length and width of largest individual 350 X 300 ^. On Aleochara rujipes Boh. Derema, Usambara, East Africa. Berlin Museum, Nos. 844 and 845. EUHAPLOMYCBS nov. gen. Receptacle consisting of two cells, the upper bearing a free stalked antheridium and a stalked perithecium. Antheridium conical, consisting of a single stalk-cell followed by a basal cell from which is separated a group of smaller cells some of which (two or four ?) extend upward and inward to form antheridial cells : above these follow three external marginal cells, the lowest of which lies beside the antheridial cells; the uppermost succeeded by a conical chamber terminating in a pore, and extending downward along the inner sides of the marginal cells to form a cavity into which the antheridial cells empty. Perithecium resembling that of Haplomyces and having two ascogenic cells. Euhaplomyces Ancyrophori nov. sp. Receptacle small, the basal cell somewhat longer, nearly hyaline, tapering to the relatively small foot; the subbasal cell becoming pale amber brown. Antheridium, including its short stalk-cell, about as long 26 PROCEEDINGS OF THE AMERICAN ACADEMY. as the receptacle, becoming pale amber brown, tapering to a pointed apex. Perithecium becoming pale amber brown, relatively large, thick walled, considerably and abruptly inflated above the basal cells, somewhat asymmetrical, tapering rather evenly to the blunt apex; the stalk-cell long, thick walled, slightly curved, nearly hyaline, distally somewhat broader, not distinguished from the basal cells. Spores about 40-45 X 3.5 fi. Perithecia 180-200 X 72-82 /* ; the stalk-cell 110-120 X 28-30 /a. Antheridium including the stalk-cell 55-65 /x. Total length to tip of perithecium 360 fi. On the superior surface of the abdomen of Aneyrophorus aureus. Dumfriesshire, Scotland. Sharp Collection, No. 1091. Eucantharomyces Xanthophaeae nov. sp. Perithecium (not fully mature) straw colored, somewhat asymmetrical, almost symmetrically and but slightly inflated from base to apex; the tip short, well distinguished ; the lip-cells rounded, and slightly inflated, forming a knob-like termination, one of them protruding in the form of a slight tongue-like projection beyond the others : the stalk-cell about as long as the receptacle, from which it projects at an angle, being more- over turned at the same time a little to one side. The cells of the recep- tacle subequal, lying side by side, the basal one extending to the base of the stalk-cell of the perithecium, with which it is in contact. Appendage relatively large, the stalk-cell subtriangular, somewhat larger than the basal cell which is wholly overlapped externally by the well defined and distally somewhat inflated marginal cell; the antheridial cells in four tiers of seven, six, five and four cells respectively; the discharge-tube long and curved outward. Spores about 36 x4ju. Perithecia 165 X 50 fj., the stalk-cell 46 X 20 p. The appendage to tip of discharge tube 120 fj., the antheridium proper 55 X 30 /x. Total length to tip of peri- thecium 290 fx. On the right inferior margin of the prothorax of Xanthophaea vittata Dej., Australia. Berlin Museum, No 973. Dichomyces bifidus nov. sp. Basal cell slightly enlarged, pellucid, tinged with brown, about as long as broad : the lower tier, and more or less of the middle tier, opaque ; the marginal cells of the latter forming a bluntly rounded, sometimes almost obsolete projection on either side, hardly extending above the THAXTER. — NEW LABOULBENIACEAE. 27 venter of the short, stout, short-necked antheridia : the upper tier relatively large, more or less crescent-shaped according to the degree of lateral development, edged externally with blackish brown, more broadly below, the brown area punctate ; the cells about thirty-one in the larger individuals, the marginal ones forming a rather slender series, which may curve abruptly upward nearly to the middle of the perithecia, or assume a more divergent* habit ; the perithecigerous area horizontal, pro- ducing normally four perithecia, three appendages arising between the two middle ones and one between each of the others, the external cells bearing appendages as usual which vary in length. Perithecia rather long and slender, hyaline or faintly yellowish brown, conspicuously tinged with purplish brown below the perfectly hyaline tip, the anterior lip-cells forming a pointed projection, the posterior ones forming each a relatively large ear-like appendage which tapers to a pointed apex, and is slightly curved, the two diverging from one another at an angle of about 50°. Spores about 38 X 2.5 fx. Perithecium without appendages 126 X 25/x.; the appendages 14^. Receptacle 220-350 X 120-165 /a. Total length to tip of perithecium 300-330 /x. Appendages 20-80 fx. Ou the abdomen of (?) Philonthus sp. Ralum, New Pomerauia. Berlin Museum, No. 1013. Dichomyces Belonuchi nov. sp. Receptacle relatively large and long : the distal tier relatively small, consisting of from eleven to thirteen short cells, slightly suffused, the median cells little longer than the rest, the series forming slight, rounded, sometimes almost obsolete lateral projections on either side of the peri- thecia : the basal cell small, partly transparent : the lower and middle tiers not distinguished, uniformly opaque • a portion of the middle cell, and sometimes the tips of other cells in the middle tier, more or less translucent, the marginal cells ending in a slight rounded prominence below the base of the antheridium. Perithecia normally two, evenly suffused with pale reddish brown, rather long and slender, tapering throughout, the conformation of the lip-cells much as in D. furciferus. Spores about 30 X 3 ll. Perithecia 75-80 X 18-20 /x. Receptacle 108-126 X 54-58,1/. Total length to tips of perithecia 185-200 /x. On the abdomen of Belonuchus fuscipes Fauvel. New Guinea. Sharp collection, No. 1090. 28 PROCEEDINGS OP THE AMERICAN ACADEMY. Dichomyces Australiensis nov. sp. Receptacle usually rather loug and narrow, the basal cell relatively large, hyaline or slightly suffused; the margins of the lower tier usually continuous with those of the middle one, the marginal cells deep blackish brown or quite opaque, the middle cell hyaline or translucent throughout, its lower third often punctate : the middle tier consisting of about nine cells, slightly suffused with pale reddish brown externally, more or less edged with deep blackish brown; the terminal cells forming a free rounded projection on either side, extending as high as about the middle of the rather large antheridia, the tips of which may reach to the bases of the perithecia : the upper tier nearly hyaline, consisting normally of from eleven to thirteen subequal cells, the terminal ones extending but slightly higher than the bases of the perithecia, which are normally two in number, rather deeply suffused with purplish brown throughout ; the apex hyaline, the posterior lip-cells producing each a relatively large bluntly pointed appendage, the two diverging nearly at right angles to the axis of the perithecium, becoming slightly recurved, the distance from tip to tip about twice the diameter of the perithecium. Appendages nearly as long as the perithecia. Perithecium 60-70 X 16-20/*, its appendages 18/*. Receptacle 90-100 X 42-48/*. Total length to tip of perithecium 160-170 /*. On the superior surface of the abdomen of Quedius riificollis Grav. Sharp Collection, No. 1102. Dichomyces Mexicanus nov. sp. General habit much like that of D. prhiceps, generally rather long and slender. Basal cell hyaline, the lower tier relatively long and narrow, broadly edged externally with black ; the median cell hyaline, or only the marginal cells slightly suffused with smoky brown : the middle tier dis- tinguished from the lower by a slight prominence, hyaline, seven to nine celled; the marginal cells protruding but slightly on either side; the antheridia brownish, short, stout, blunt pointed : the upper tier relatively very long, sometimes twice as long as the middle tier, consisting of from nine to eleven cells ; the marginal cells protruding but slightly on either side, very much as in the middle tier. Perithecia normally two, about as long as the distal tier and concolorous with it, or somewhat darker, rather stout, tapering but slightly; the tip rather abruptly distinguished, broadly truncate with a slight median projection ; the posterior lip-cells giving rise each to a long horizontal appendage, which becomes recurved, THAXTER. NEW LABOULBENIACEAE. 29 is bluntly pointed and somewhat narrower toward the base, the distance from tip to tip often twice the diameter of the perithecium. In a few specimens the receptacle and perithecia are somewhat evenly suffused with smoky brown. Perithecia 75-85 X 25-30 jx, the appendages 18- 22 ix. Receptacle 165-200 X 55-70 /x. Total length 235-275 fx. On the inferior surface of the abdomen of Philonthus atriceps Sharp. Jalapa, Mexico. Sharp Collection, No. 1112. Specimens, apparently normal, sometimes occur in which the tips of the perithecia are blunt and unmodified. Dichomyces Homalotae nov. sp. Form short and stout. Basal cell geniculate, more or less suffused : the lower tier more or less, sometimes wholly, suffused with reddish brown ; the margins darker, more or less translucent, without contrasts, the outline somewhat uneven, the transition to the middle tier indicated by a distinct prominence: the middle tier consisting of from nine to (rarely) thirteen cells, hyaline or subhyaline, with slight lateral suf- fusions ; the marginal cells ending in a slight hyaline rounded projection, seldom extending higher than the venter of the somewhat suffused curved antheridia : the upper tier relatively small, the cells subequal, hyaline, asymmetrical, owing to the development of but one perithecium ; the appendages often equalling, or exceeding the perithecium in length. Perithecium characteristically short and stout, inflated below, sometimes oval, tapering somewhat abruptly distally, to the rather broadly truncate, or slightly rounded unmodified apex. Spores 33 X 3 /x. Perithecia 65-75 X 25-30 /a. Receptacle 70-90 X 40-55/1. Total length 125- 165 fx. On all parts of Homalota sordida Marsh. Fresh Pond, Cambridge. First observed by Mr. Bullard. Peyritschiella Xanthopygi nov. sp. Basal cell of the receptacle very small, or hardly distinguished from the foot : the first tier consisting of three subequal cells without appendages, the middle one somewhat shorter than those on either side of it : the second tier asymmetrical, consisting of three subequal median cells, the margins of the two outer free below for nearly half their length and coincident with the margins of the tier below, the appendiculate " margi- nal " cells, about three to five on either side, separated from them as usual by oblique septa ; the first on the right bearing the large, slender, pointed, nearly straight purplish antheridium : the upper tier consisting 30 PROCEEDINGS OF THE AMERICAN ACADEMY. of about fifteen or more cells, the series distally concave, rising abruptly upward on either side above the base of the perithecium and bearing the usual appendages. Perithecium solitary at the right of the median (primary) appendage, almost symmetrically inflated from base to apex, dull purplish ; the tip slightly darker, hardly distinguished ; the apex truncate, sometimes slightly spreading; the lip-cells hardly projecting. Perithecia 115-150x34-42^. Receptacle 200 X 65-70 p. Total length to tip of perithecium 310-360 /x. On the abdomen of Xanthopyyus Solskyi Sharp. Sharp Collection, No. 1158. Nearly allied to P. Amazonica, from which it differs principally in the form of the perithecium. Chitonomyces occultus nov. sp. Short and stout, becoming suffused with somewhat smoky amber brown. Lower portion of the receptacle deeper brown, the basal cell relatively large, broad distally ; the subbasal cell broad and flattened ; the lower cell of the distal portion rather large and but slightly over- lapped by the subterminal cell, which may bulge slightly below the terminal cell, the latter being thus turned so as slightly to overlap the perithecium. Perithecium short and stout, its upper third or less free, darker brownish externally ; the tip bent outward, tapering rather abruptly to the slightly irregular apex, its outer half or less suffused with dark brown. Spores about 22 X 2.5 xi. Perithecium 60 X 20 xi. Receptacle to tip of distal cell 90 /x. Total length to tip of perithecium 100 ft. In the median marginal depression of the right elytron of Onemidotus sp. Lake Eustis, Florida. Chitonomyces psittacopsis nov. sp. Nearly hyaline. Receptacle rather slender, the basal cell several times as long as the squarish subbasal cell ; the cell above the latter nearly equalling it in size and separated by an oblique septum from the lowest of the marginal cells, which are all subequal ; the terminal appendiculate cell of the usual form, relatively large and long, without any distinct basal enlargement; the tip of the lower appendiculate cell curved slightly outward. Perithecium relatively very large, long, slender, usually curved sidewise throughout, the upper half tapering very slightly to the curiously modified, clear black contrasting tip, which resembles the partly open beak of a parrot ; a larger upper recurved mandible-like pro- THAXTER. — NEW LABOULBENIACEAE. 31 cess being separated from a second, that resembles a lower mandible, by a hyaline area which includes, and extends back from, the pore ; the lower lip-cells translucent, but suffused with brown in such a way as to suggest a tongue-like process projecting slightly between the " mandi- bles." Spores very numerous, completely filling the cavity of the perithecium, greatly attenuated, 85 X 2.5 /a. Perithecium 200 X 30 jx. Receptacle to tip of distal cell 140 /a. Total length to tip of perithe- cium 290-300 fi. On the posterior legs of Laccophilus sp. Lake Eustis, Florida. Chitonomyces Bullardi nov. sp. Straw colored becoming tinged with pale amber brown. Basal cell of the receptacle monstrously developed, about as long, sometimes twice as long, as the remainder of the plant, its axis coincident with that of a distal, variably developed, blunt, tooth-like, free posterior projection, near the base of which the subbasal cell and the remainder of the plant project backward at an angle of about 45° , or less, to the axis of the basal cell, the separating septum being vertical or nearly so ; the subbasal cell small and flattened : the lower marginal cell of the distal portion of the recep- tacle subtriangular, short and broad ; the lower appendiculate cell above it relatively large ; the subterminal cell larger than the lower marginal cell, curved inward so that the terminal appendiculate cell projects from it obliquely inward against the perithecium. Perithecium four fifths or more free, relatively large and stout, distinctly inflated below, taper- ing to the tip, which is characteristically modified through the presence of a large claw-like subterminal dark amber brown external projection, the distal half of which is somewhat abruptly recurved, like the upper mandible of a parrot, over the small hyaline incurved 4-papillate apex, which is immediately subtended on the inner side by a small, erect, dark amber brown, tooth-like process, the blunt tip of which alone is free. Appendages slender and extending to or beyond the tip of the perithecium. Spores about 20 X 2.5 /x. Perithecium average 70-75 x 30-32 ft not including the hook-like appendage, which is 25 /x to its upper margin. Receptacle : basal cell to tip of prolongation 90-220 X 15- 22 fx, the portion above to tip of distal cell 48 /x. On the right inferior anterior margin of the prothorax of Cnemidotus 12-punctatus Say. Glacialis Pond, Cambridge. The most singular species of the genus, discovered by Mr. Charles Bullard, to whom I take pleasure in dedicating the species. 32 PROCEEDINGS OF THE AMERICAN ACADEMY. Chitonomyces Hydropori nov. sp. Receptacle nearly hyaline, the subbasal cell flattened, many times smaller than the basal cell, slightly inflated and distinguished from the cells above and below by slight constrictions ; the two cells above sub- equal, the posterior somewhat broader, and separated from the lower marginal cell of the distal portion by an oblique curved septum, which overlaps its upper fourth ; the subterminal marginal cell often nearly as long as the lower, the narrow upper half or more of which it overlaps. The lower appendiculate cell rather small, the upper terminal one of the typical form, relatively rather long, distinguished by a slight constriction, the appendage extending beyond the tip of the perithecium. Perithecium relatively large, its upper half or more free, distally broader, the outer margin nearly straight with a slight subterminal rounded elevation below the abruptly rounded projecting outer brownish lip-cells ; the apex other- wise flat, broad, bent outward so as to be slightly oblique, the inner margin below it bulging and curved throughout. Spores 55 X 4/*. Perithecium 98-108 X 25 /a. Receptacle to base of perithecium 80 //, to tip of terminal cell 150 /a. Total length to tip of perithecium 185 yu,. On the mid-elytron of Hydroporus modesties Aube. Cape Neddock, Maine. Mr. Bullard. Chitonomyces Orectogyri nov. sp. Dull purplish, the cells thick walled and marked by faint transverse striations. The basal cell of the receptacle very small and hardly dis- tinguishable, owing to an abrupt curvature just above the foot ; the sub- basal cell relatively large, distally narrowed, nearly the whole upper half of its posterior margin covered by a relatively large triangular cell, from which it is separated by a nearly vertical septum ; this triangular cell is in contact distally with the ascigerous cavity and the base of the lowest marginal cell ; the latter is very long, extending upward, its narrow extremity ending without enlargement opposite the blackened base of the inner appendage, lying between the latter and the tip of the perithecium; the lower appendiculate cell well defined, about two thirds as long as the subterminal cell, which projects slightly above and bears the free terminal appendiculate cell, which is hyaline, about equal to the lower in length, its inner margin nearly straight, its outer margin curved abruptly inward to the base of the obliquely distinguished, blackened, narrow, erect ter- minal portion, from which the appendage has been broken in the types. Perithecium relatively large, of nearly equal diameter throughout ; the THAXTER. NEW LABOULBENIACEAE. 83 tip broad with a bluntly rounded apex ; a short erect contrasting brown prominence formed by the left posterior lip-cell, toward the base of which the inner (anterior) lip-cells are curved iu a characteristic fashion, so as partly to overlap it. Spores about 75 X 5 \x. Perithecium 125 x oG ft. Receptacle 250-270 /*. Total length to tip of perithecium 255 jx. On the superior surface of the tip of the abdomen of Orectogyrus specular is Aube. Africa. Berlin Museum, No. 606. DIOICOMYCES nov. geu. Male individual consisting of four superposed cells, the upper of which is a simple antheridium bearing a subterrainal discharge tube. Female individual. Receptacle ending distally in a peculiarly modi- fied sterile cell, corresponding to the upper spore-segment: the subbasal cell producing a single perithecium laterally, and separated from the sterile terminal cell by a second small cell. Perithecium free, stalked ; the ascogenic cell single, the spores more or less obliquely once-septate, and of two kinds corresponding to the sexes. Dioicomyces Floridanus, formerly referred provisionally to Amor- pkomyces, must be transferred to this genus ; since, although the male is unknown, the female has the typical characters which distinguish the genus very clearly from its near ally. D. obliqueseptatus on Myrmed&nia (?) sp. must also be removed from Amorphomyces, on account of its obliquely septate spores, and should with little doubt be included in the present genus; although it is evident, from comparison with abundant material of the species described below, that the specimens, both females, from which the original description was made, are more imperfect than was at first supposed, and should not have been used as types. The peculiar sterile cell is present in neither of these ; but, since they corres- pond in all other respects to the generic type, may be assumed to have been broken off. No free spores are available in either, although an ex- amination of the spore mass within the ascus seems to show that they present the same variation in size which characterizes the species described below. Dioicomyces Anthici nov. sp. Male individual. Form slender, of nearly the same diameter through- out, the basal cell half the total length of the individual to the tip of the discharge tube ; the third cell nearly square, the subbasal about as large as the terminal antheridial cell, which ends in a distal blunt projection ; the discharge-tube arising laterally below the tip, projecting upward from VOL. XXXVII. 3 34 PROCEEDINGS OF THE AMERICAN ACADEMY. a broadened base, slightly divergent from the main axis, slender, about as long, or a little longer than, the body of the antheridial cell. Length to tip of antheridial cell, including foot, 50 fx : to tip of discharge-tube GO^c. Width 8 fi. Female individual. Often more or less strongly curved, the terminal sterile cell bluntly pointed, slightly curved, brownish ; the basal cell becoming narrower below, the upper septum convex ; tinged with brown posteriorly as is the rest of the receptacle : the subbasal cell very small, subtriangular ; separated from the terminal sterile cell by a somewhat smaller triangular cell. Stalk-cell of the perithecium hyaline, long, often about the same diameter throughout; the thick wall becoming gradually thicker distally : the perithecium slightly inflated, faintly brownish ; the short, stout, broad, blunt tip slightly distinguished, and nearly symmetri- cal ; the lip-cells forming an unbroken outline, without protrusions. Spores (male) 40x4/i, (female) 60 X 6 jx. Perithecium 100-110 X 35-45 /a, the stalk-cell 75-115 x 18 /x. Receptacle including foot 35 x 1*2 /a, the sterile terminal cell 18-25 X 7-9 fx. Total length to tip of perithecium 185-220 /x. On Anthicus fioralis Linu. Fresh Pond, Cambridge. On A. Califor- nicus Laf. California (Lecoute Collection). Dioicomyces onchophorus nov. sp. Male individual similar to that of D. Ant hid, slightly smaller. Female individual. Usually strongly curved, especially at the base of the stalk-cell ; similar to D. Anthid ; the receptacle, sterile cell, and the stalk of the perithecium, relatively smaller. Perithecium dirty brown, one of the lip-cells protruding in the form of a well defined, lateral, finger-like, erect, straight, or slightly curved, blunt-tipped, cou- colorous process ; an irregular anterior elevation or angular prominence is also more or less well defined above the middle of the perithecium. Spores (male) 35 x 4/x, (female) 45 X 5 /x. Perithecia to tip of pro- jection 125-140 X 40-45 fx, the stalk-cell 90 p. Total length to tip of perithecium 210-230 fx. Usually on the basal half or at the base of the left elytron of Anthicus floralis Linn. Fresh Pond, Cambridge. Dioicomyces spinigerus nov. sp. Male individual similar to that of D. Anthici, much smaller, the ex- tremity less prominent, or almost horizontal, the discharge tube some- THAXTER. NEW LABOULBENIACEAE. 85 what more slender, and more often erect. Total length including foot 40 X 6.5 fx; to tip of discharge-tube 47 /x. Female individual. Receptacle relatively small, tinged with dirty yellowish, edged with brown to the tip of the small terminal sterile cell. Perithecium dirty yellowish and relatively large, considerably and more or less symmetrically inflated, above and including its basal cells, to the base of the tip, which is bent abruptly outward at right angles to the axis of the perithecium; the apex broad, blunt, the lip-cells hardly projecting: a unicellular brown, straight or slightly curved, spine-like process, which tapers to a blunt point, projects upward at an angle of about 45° from the middle of the outer (anterior) .margin of the perithecium ; and a slight elevation is also more or less distinct between its base and that of the tip ; the stalk-cell relatively short, becoming rapidly narrower toward its base. Spores (male) 26 X 4 /x, (female) 40 X 6 /x. Perithecia including basal cells 125 X 50 fx, the spinous process 55 /x, the stalk-cell 36-40^. Receptacle to tip of sterile cell about 45 [x. Total length to tip of perithecium about 185 fx. On Anthicus Jloralis Linn., with the last two species, more commonly on the inferior surface of the abdomen. Fresh Pond, Cambridge. Teratomyces Zealandica nov. sp. Receptacle with a distinct distal obliquity, opaque with the exception of a hyaline area just above the foot, the margins straight, the distal por- tion relatively narrow, the base relatively broad, the suffusion involving the bases of the appendiculate cells which are relatively numerous and narrow and more or less suffused with brownish yellow. Appendages sometimes scanty, but slightly divergent, concolorous throughout, nearly hyaline or pale yellowish ; the basal cells of the larger branches rela- tively slender, the external branchlets and numerous beak-like cells hardly more deeply colored. Perithecia relatively large, long, rather slender, slightly inflated throughout, the blunt tip more or less abruptly distin- guished ; the stalk-cell very short or almost obsolete, hidden by the appendages; the basal cells relatively small and not distinguished from the body of the perithecium. Spores about 50 X 2.5-3 fi. Perithecia 150-180 X 20-28 fx, basal and stalk-cells together about 35 /x. Longest appendage 180 /^. Receptacle 75-125 X 15-18 (base) 22-30 /x (distally). On Quedius insolitus Sharp. Dunedin, New Zealand. Sharp Collec- tion, No. 1099. 36 PROCEEDINGS OF THE AMERICAN ACADEMY. Teratomyces petiolatus nov. sp. Receptacle nearly symmetrical, almost wholly black, slender below, expanding rather abruptly distally ; the appendiculate cells relatively large and long, translucent, brownish yellow, subtended by a slight en- largement. Appendages numerous, spreading, the larger ones consisting of a very large colorless or brownish basal cell, which bears a series of branchlets externally and several branches terminally ; the branchlets usually short, and two-celled, the distal cell usually long, beak-like and clear purplish brown, the lower cell hyaline or light brown and in the lower branchlets usually bearing long-necked antheridia: the terminal branches with several short branchlets of a similar character. The smaller shorter appendages ahout the bases of the larger ones, mostly dark purplish brown, with many beak-like cells. Perithecia usually several, large, symmetrical, purplish brown ; the tip short, rather narrow and abruptly distinguished ; the basal cells relatively very large, forming a portion of the stalk sometimes half as long as the perithecium proper ; the stalk-cell stout and elongate. Perithecia 185-225 X 45-50 /a, the basal cell 100-150 x 10//., the stalk-cells 180-300 /*.. Receptacle about 150 /a. Appendage, longest 175, longest basal cells 110 //.. On Quedius sp. Greymouth, New Zealand. Sharp Collection, No. 1103. Teratomyces insignis nov. sp. Receptacle usually quite opaque, long, slender ; the outline unbroken and nearly straight, tapering evenly to the slightly geniculate base, which is nearly hyaline just above the foot: the margin of the suffused area distally strongly oblique, especially before maturity ; the appendiculate cells small, becoming brownish. The appendages numerous, spreading, the larger ones hyaline or nearly so, consisting of a large elongate basal cell, which bears two or ihree small remote antheridial branches exter- nally ; and terminally, as a rule, two large branches placed side by side (one of which may be wanting) sometimes associated with one or two sub- terminal smaller branchlets, the basal cells of which are dark contrasting brown : the terminal branches hyaline with branchlets like those of the basal cell ; the branchlets, however, more numerous, contrasting, brown, simple or branched, many having characteristic beak-like terminations, while others are blunt tipped, with oblique septa. The smaller peripheral appendages more or less crowded around the bases of the larger ones, with conspicuous and numerous beak-like terminations. The antheridia with long curved necks. Perithecia usually several, brown, long and THAXTER. — NEW LABOULBENIACEAE. 37 slender, straight, very slightly inflated near the base, with a slight sub- median enlargement ; tapering throughout to the short, truncate, well distinguished tip : the basal cells rather small, concolorous ; the group narrower than the stalk-cell and separated from it by a horizontal sep- tum : the stalk-cell very large, usually elongate, often inflated and thick walled. Spores about 50 X 4 jx. Perithecia including basal cells 240- 275 x 40 (u, the stalk-cell 150-325 X 25-85 /x. Appendages, longest 225,0.. Receptacle 100-185 X 14 (base) X 55 (distal end). Total length to tip of perithecium largest, 800 /x. On abdomen of Qaedius nov. sp. New Zealand. Sharp Collection, No. 1159. ACOMPSOMYCES nov. gen. Receptacle two-celled, bearing an antheridial branch terminally and a single perithecium laterally. Antheridium consisting of several super- posed cells from which single simple antheridia are borne directly. The perithecium borne on a stalk, the lumen of which becomes continuous with that of the ascigerous cavity. Acompsomyces Corticariae nov. sp. Receptacle narrow below, distally enlarged, hyaline ; the subbasal cell • small. Basal cell of the appendage brown, distally narrowed to the base of the appendage proper, which is brown, and consists of three sym- metrical cells, the upper smaller, becoming a terminal antheridium, the lower bearing several antheridia somewhat irregularly. Perithecium brown, rather abruptly distinguished from the short hyaline stalk ; the tip very broad and darker ; the lip-cells forming four hyaline-tipped, nearly symmetrical papillae, which terminate four corresponding ridges. Spores about 30 X 2 u. Perithecia 90 x 26 jx, the stalk 15 /x. Recep- tacle 25 /x. Antheridial appendage, above stalk-cell, and including terminal antheridium, 40 «. On elytron of Corticaria sp. Berkeley, California. STICHOMYCES nov. gen. Receptacle consisting of two cells, the upper bearing one or more stalked perithecia laterally, and an antheridial appendage terminally. The appendage consisting of several superposed cells, the lowest sterile, or having one or two opposite lateral perithecia; those above it bearing opposite lateral branchlets distally, the series ending in a terminal sterile 88 PROCEEDINGS OP THE AMERICAN ACADEMY. branch. Antheridia simple, flask-shaped, free, borne in small groups on short branchlets. Stichomyces Conosorriae nov. sp. Dull amber brown. Receptacle and appendage undifferentiated, the basal cell of the former small, triangular in outliue ; the subbasal cell about as broad as long, and similar to the cells of the appendage, bearing distally and laterally a single perithecium, sometimes two, which are then paired on opposite sides of the cell, like the antheridial branchlets. Ap- pendage consisting of five superposed subequal cells slightly longer than broad, the basal one sterile, or rarely (abnormally) producing one or two perithecia as in the subbasal cell below it : the three cells above slightly larger, the upper angles separated by oblique septa to form small cells on either side, which bear short one or few celled antheridial branchlets ; the terminal cell somewhat smaller, bearing a simple terminal several- celled branch in addition to the lateral branchlets, all of which appear to be sterile. Antheridia with broad necks grouped in twos or threes. Perithecium darker brown, more or less symmetrically inflated ; the tip hardly modified; the basal cells collectively broader and nearly as long as the stalk-cell. Spores 35 X 2.5 fx. Perithecia 85 X 25 /x, the stalk- cell 36 x 1 t /x. Total length to tip of the appendage proper 150 «, the terminal branch 150 fx, the antheridial branchlets about 20 /x. Total length to tip of perithecium 185-200 ft. On Conosoma pubescens Payk. Belmont and Waverly, Mass. First observed by Mr. Dullard. Rhachomyces Oedichiri nov. sp. Receptacle strongly curved, rather short, the lower cells especially more or less suffused with clear brown, the basal cell slender, the cells of the main axis above it successively larger, about ten to twelve in all. Appendage hardly ever reaching to the tip of the perithecium; the shorter margin alone subulate and straight, the rest appressed, denser toward the base of the perithecium, where they form a tuft which does not wholly surround it, curved slightly outward, somewhat attenuated; tips abruptly recurved or subhelicoid. Perithecium somewhat inflated, hyaline, with the exception of several longitudinal dark brown marks at the tip, the base concealed by the appendages. Spores 36 X 4 m. Perithecia 90- 1 10 X 30-35 (i. Total length to tip of perithecium 220-250 /x. Long- est appendages about 90 u. On Oedichirus nov. sp. Rio de Janeiro, Brazil. Sharp Collection, No. 1154. 'I Hi XTKIi. — NEW LA BOULBENIACEAE. 39 Rhachomyces Glyptomeri nov. gp. Receptacle slender, dirty translucent brown, the main axis coi of about seven cells (below the lower of the two perithecia which are present in the type; : the appendages -lightly divergent, large and long, opaque brown, flexed inward near their hyaline, somewhat more Blender extremities, and extending beyond the tips of the perithelia. Perithecinm short-stalked, -trongly curved, slightly inflated, hyaline, -oiled with brown- ish, the dps well distinguished, blackish brown and obliquely truncate. Perithecia, including basal and stalk-cells, about 185 / 41 /v.. Receptacle to base of lower perithecinm 100 / 15 /*. Appendage-, long 60/* or more. On tip of abdomen of Glyptomerta cavicolus MulL Carniola, Austria. Sharp Collection. No. 1111. Rhachomyces Dolicaontis nov. sp. Form elongate. Cells of the main axis of the receptacle- twenty to thirty-five, more or less dirty brownish, banded with dark blackish br< below, while the more slender proximal cells are usually opaque ; the axis of nearly equal diameter throughout and nearly -traight above about the eighth cell; each cell containing distally one, the axis cells two, roundish or oblong brown bodies ''possibly thickenings of the walls; which the stigmata of an insect larva. The appenda* .hat divergent, opaque, except a narrow upper hyaline margin, short, stiff and numerous ; those external more slender, slightly curved and sharply pointed ; th between somewhat stouter and longer, with -lightly recurved tips; th about the base of the perithecium, which they do not conceal, but slightly longer and few in number. Perithecinm -hort-stalked, slightly more or less symmetrically inflated, dull brown, minutely punctate or irrarmlar, not uniformly suffused ; the tip with darker shades, the blunt apex hyaline. Spores 66 / 5 a. Perithecia 150-200 X 42-60/*, including the basal and stalk-cells. Larger appendages 90-110 /t, smaller about 7o/y.. Total length 600-1100/*, the- average diameter about 30-35//. On all parts of Dolicaon Lathrobioidei Casteln. Cape of Good If Africa. Sharp Collection. No. 1146. Berlin Museum, No- 833 and 842. Sphaleromyces Quedionuchi nov- Perithecium relatively small, translucent, tinged with amber brown, straight, very slightly almcrst symmetrically inflated ; the tip hardly dis- 40 PROCEEDINGS OF THE AMERICAN ACADEMY. tinguished ; one of the lip-cells forming a blunt, terminal, irregularly curved, hyaline, sometimes abruptly distinguished projection, below the base of which arises on the inner side a tongue-like outgrowth externally and basally blackish brown, the broad rounded hyaline end of which is curved against or across the base of the terminal outgrowth; the stalk- cell small, the basal cells collectively larger, and separated from it by a very oblique septum. Basal cell of the receptacle long, black, obconical, the narrow base translucent ; the subbasal cell small, nearly triangular. Appendage consisting of five very obliquely superposed cells, the two lower nearly equal, the cells ahove successively smaller, but equal in length ; the branches which are once or twice branched and extend about to the middle of the perithecium, arising from the whole surface of their inner margins, the terminal cell soon destroyed. Spores 55 X S /x. Perithecia 135 X 36/a. Basal cell of receptacle 120 fx. Appendage without branches 55 //.. Total length to tip of perithecium 290-310 jx. On the abdomen of Quedionuchus impunctus Sharp. San Andres, Vera Cruz. Sharp Collection, No. 1105. Sphaleromyces Chiriquensis nov. sp. Almost uniformly translucent dirty amber brown. Perithecium very large and crowded with spores, long, with a very slight general inflation, the base narrower, tapering abruptly at the short tip : one of the lip-cells forming an erect, median, straight, hyaline, cylindrical or slightly in- flated, nearly truncate terminal projection, which is subtended by a posterior or partly lateral, somewhat larger, spine-like, slightly diver- gent, deep black brown, nearly straight or slightly outcurved pointed outgrowth, its tip nearly on a level with that of the median projection : the basal cells collectively slightly larger than the short stalk-cell, and not distinguished from the base of the perithecium. Basal cell of the receptacle very large, tapering throughout from the broad distal to the narrow basal end, paler than the small, flattened, deeper brown subbasal cell. The appendage consisting of a relatively large basal stalk-cell, which is slightly longer than broad, and partly united to the stalk-cell of the perithecium; above are four short successively smaller cells, their septa slightly oblique, the three lower bearing branches as usual, which may branch once above their basal cells, the branchlets brown, erect, rigid, closely aggregated ; the uppermost cell paler, with a terminal branch. Spores 50 X 2 /x. Perithecia 220-250 X 40-48 fx, to tip of median projection, the subterminal process 25 X 7 p; the stalk-cell 35 X 25 p. Receptacle 240 X 40 jx, the basal cell 220 fx. Total length to THAXTER. NEW LABOULBENIACEAE. 41 tip of perithecium 500-600 //.. Appendage without branches, including stalk-cell, 75 p. On the tip of the abdomen of Quedius flavicaudus Sharp. Volcan de Chiriqui, Panama. Sharp Collection, No. 1157. Sphaleroniyces Indicus now sp. Perithecium relatively very long and large, yellowish, very slightly inflated toward the base, tapering very gradually to the broad, blunt tip which is subtended by a truncate, conical lateral projection ; the stalk- cell relatively short. Receptacle relatively small, the two cells nearly equal, the upper bearing the stalk-cell of the perithecium terminally and the basal cell of the appendage laterally ; the latter overlapping it to its base. Appendage consisting of four superposed cells, the basal (stalk- cell) small, triangular ; the two cells above it larger and longer, bearing short antheridial branches from the upper inner angles ; the terminal cell smaller, subcorneal, bearing a small terminal branchlet. Spores about 44 X 4 /a. Perithecium 290-340 X 45 ft, the stalk-cell 72 /x. Receptacle 55^. The appendage 125 /a. On the upper surface of the tip of the abdomen of Pinophilus (near "P. rufipennis"). Malabar, India. Sharp Collection, No. 1151. Corethromyces Latonae nov. sp. Perithecium reddish brown with a purplish tinge, often straight, or externally concave, slightly inflated ; the lip-cells forming a small short, slightly bent, nearly cylindrical, truncate, or papillate terminal projection, which is rather abruptly distinguished ; the secondary stalk-cell, and the basal cell above it, bulging outward more or less prominently, and separated by a rather conspicuous irregular indentation : the stalk-cell small and squarish. The basal cell of the receptacle asymmetrical ; its anterior margin straight and perpendicular, the posterior slightly curved and oblique ; its distal margin oblique with a posterior protrusion ; its slender base translucent, but otherwise opaque, the opacity involving a portion of the small flattened subtriangular subbasal cell. The appendage consisting of a series of about five successively smaller hyaline cells, the lowest greatly flattened ; the series above, the distal cells of which soon disappear, often turned outward so as to become almost horizontal in position, giving rise from their inner sides to numerous hyaline branches, which may be more or less copiously branched. Spores about 35 X 2 fx. Perithecium 90-105 X 20-25 ^, the stalk and basal cells together 20- 42 PROCEEDINGS OF THE AMERICAN ACADEMY. 25 fj.. Receptacle 110 X 50 (distal end) X 10 /x (base). Total length to tip of perithecium 225-250 /x. On the legs and abdomen of Latona Spinolae Guer. Bogota, Colum- bia. Berlin Museum, No. 834. Corethromyces Stilici nov. sp. Perithecium amber colored, with a faint brownish or reddish tinge, somewhat irregular in outline through a spiral twist in the wall-cells, which are distinguished from one another by slight furrows ; slightly inflated toward the base, tapering to the broad blunt apex ; the tip not at all distinguished ; the basal and stalk-cells well developed, hyaline, the latter bent abruptly upward from its insertion. Basal cell of the re- ceptacle small, hyaline on the anterior side just above the foot, but otherwise blackish brown or opaque, bulging posteriorly above the foot ; distally and posteriorly pi'oliferous to form a straight, black, blunt finger- like outgrowth, which lies external to the appendage ; the subbasal cell nearly hyaline, subtriangular, separated from the basal cell by a very oblique septum. Appendage hyaline, consisting of a nearly free and nearly isodiametric stalk-cell, above which are three or four cells which produce a close tuft of hyaline brauches on the inner side. Spores about 30x3^. Perithecia 80-85 x 22 /x, its stalk-cell 30 X 18 p. Recep- tacle 25 fx, the outgrowth 55 X 7 /x. Appendage, including branches, 50 /x. Total length to tip of perithecium 150 ai. On the abdomen of Stilicus sp., Interlaken, Switzerland. On Stilicus ruftpes Germ., Berlin Museum, No. 836. Europe. Ceratomyces spinigerus nov. sp. Bright amber brown. Perithecium paler anteriorly, about twenty- eight wall-cells in each row; narrower at the base, the lower half bulging anteriorly, tapering distally where it is rather strongly curved away from the antheridial appendage : the tip hyaline, prominent, obtuse, about half as long as the curved tooth- or spine-like one-celled deep amber brown appendage, which arises below and beside it. Basal cell of the receptacle large, long, mostly curved, broader distally, opaque ; the portion above it relatively small and narrow, concolorous with the perithecium. The appendage erect, slightly divergent, stiff, long, slender, rather remotely septate, but the basal cell often broader than long, about seven-celled, tapering distally. Spores 90 X 4 /x, in one small specimen 165 x 4.5 /x. Perithecia 425-500 X 70-95^, the appendage 45-50 tt. THAXTER. — NEW LABOULBENIACEAE. 43 Receptacle 1 75-220 /x, the basal cell 150-170 /*. Antheridial appendage 200-325 fx. On the inferior anterior margin of the thorax near the base of the right elytron of Tropisternus apicipalpis Cast. Jalapa, Mexico. Sharp Col- lection, No. 1178. Ceratomyces procerus nov. sp. Rather pale amber brown. Perithecium very elongate, of nearly equal diameter throughout, the wall-cells in each row more than sixty in number ; the conformation at the tip similar to that in O. confusus ; the perithecial appendage erect, short and stout, consisting of about ten cells, distally curved outward, tapering from its broad base to the bluntly pointed tip. Appendages (broken) and receptacle much as in C. con- fusus. Perithecium 800-850 X 65 /x, its appendage 125 /x. Total length to tip of perithecium more than one millimeter. On the inferior surface of the abdomen (near the middle) of Tro- pisternus sp. San Fidelio, Brazil. Museum of Comparative Zoology, Cambridge, No. 1338. Ceratomyces curvatus nov. sp. Amber brown. Perithecium relatively large, inflated toward the base; the distal half up to the perithecial appendage of about equal diameter throughout ; about forty cells, more or less, in each row of wall-cells ; the configuration at the tip very similar to that in C. confusus, the tip itself more prominent, the apex more pointed ; the perithecial appen- dage about nine-celled, the distal half pale, curved or recurved, broader below, shorter and stouter. Receptacle much as in C. confusus, the basal cell black, the further suffusion somewhat less extensive. Appendage consisting of about six or seven cells, tapering distally, rather short. Spores about 70 X 4 /x. Perithecia 500-615 X 75 [x (below) X 60 /x (distally), the appendage 150^. Total length to tip of perithecium 600-700 (i, to tip of antheridial appendage about 250 /x. On Tropisternus Caracinus N. on inferior surface of abdomen near the tip. Caracas? Berlin Museum, No. 1057. Ceratomyces Mexicanus nov. sp. Dark amber brown. Perithecium with a slight submedian inflation ; distally broad, the outer margin turning abruptly inward distally to the inconspicuous retracted tip, which lies close at the base of the perithecial appendage, and is externally subtended by irregular inconspicuous papil- 44 PROCEEDINGS OF THE AMERICAN ACADEMY. late protrusions : the basal cell of the appendage slightly divergent, several times as long as broad ; the external margin straight, the inner strongly concave with a median blackish suffusion; the rest of the appen- dage slightly curved, about eight or nine-celled, tapering slightly and diverging strongly above the basal cell. The antheridial appendage and the receptacle much as in C. mirabilis. Spores 85 X 5 fi. Perithecia 400-175 x 110-125 fi, the appendage about 290 //, its basal cell 70 X 26 and 36^. Total length to tip of perithecium 550-640 p. On the left inferior margin of the abdomen of Tropistemus nitidus Sharp, Sharp Collection, No. 1177, and of T. chalybeus Cast., British Museum, No. 772, Oaxaca, Mexico. Ceratomyces Braziliensis nov. sp. Dark amber brown. Perithecium somewhat inflated just above the constricted base, the upper two-thirds broad and of about the same diameter throughout; about forty-five wall-cells in each row, the tip small, short, rather narrow, abruptly hunched externally, the hyaline lips turned abruptly toward the base of the perithecial appendage, which consists of a basal cell hardly differentiated from the wall-cell below it, though somewhat longer, the portion above it erect, slender, stiff, slightly curved outward, tapering but little, the subbasal cell bearing a charac- teristic basal enlargement which projects toward the lip-cells and lies just above them. The appendage and receptacle much as in C. mira- bilis. Perithecium 650 X 95 ju (basal) X 87 ^ (distal). Appendage 185 ix, or more. Total length to tip of perithecium 800 p. On inferior thorax of Tropistemus nitens Cast. var. Rio de Janeiro. Sharp Collection, No. 1181. KAINOMYCES nov. gen. "Receptacle much as in Zodiomyces, broad and flattened ; consisting of a single basal cell and typical foot, above which the successive cells become variably divided by longitudinal septa into transverse cell-rows or tiers : the distal portion more or less definitely distinguished and con- sisting of superposed cells, the lowest of which alone become longitu- dinally divided, all producing laterally antheridial (?) branches : several of the tiers immediately below this appendiculate portion growing out laterally at right angles to the main axis of the receptacle on one or both sides to form "perithecial branches" consisting of superposed cells and terminated by solitary perithecia. The perithecium of peculiar THAXTER. — NEW LABOULBENIACEAE. 45 form, with six wall-cells in each row in addition to the lip-cells ; the base of the trichogyne persistent in the tbrui of a peculiarly modified unicellular appendage. It has proved impossible from an examination of the available material of this extraordinary form, to determine the character of the antheridia; yet there can hardly be any doubt as to its true position among the " Exogenae " near Zodiomyces, Euzodiom^ces, and Ceratomyces, its dis- tal appendiculate portion being evidently homologous with the "appen- dage " of the last-mentioned genus. Kainomyces Isomali nov. sp. Receptacle variably developed below the distal appendiculate portion, sometimes very broad, often much narrower : the cells above the basal cell becoming broader and flattened, and soon divided longitudinally by one or more septa, nearly hyaline and broadly edged wholly or in part below, especially on the posterior side, with contrasting brownish black, which may involve the whole of the cell, except the transverse septa; the blackened area usually characteristically indented above, and some- times involving all but the uppermost tiers. Perithecial branches vari- ably developed, the free portion curving upward, and consisting of from about twelve to thirty-five superposed hyaline cells, which are more or less flattened, usually separated by slight constrictions, the distal one similar to the others and followed directly by the basal cells of the perithecium. Perithecium becoming tinged with pale amber brown, usually short, stout and suboblong, often not distinguished from its basal cells ; the distal end abruptly rounded, the pore subtended by a tooth-like outgrowth, half as long as and paler than the trichogynic appendage, which bears a slight resemblance to a duck's bill, is dark clear brown, somewhat narrower distally and pale tipped, broader toward the base, where it is abruptly constricted and hyaline. Spores about 30 X 3.5 jte. Perithecia 72-80 X 40-50 ^ exclusive of trichogynic ap- pendage, which measures 28-32 X 11 fi. Perithecial branch 100-253 p. Receptacle 150-220 X 40 60 p. Antheridial branches about 50 p. Total length to tip of perithecium 250-460 ft. On Isomalus Conradti Fauvel. Derema, Usambara, East Africa. Berlin Museum, Nos. 847-848. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 3. —Junk, 1901. THE LAW OF PHTSICO-CHEMICAL CHANGE. By Gilbert Newton Lewis. THE LAW OF PHYSICO-CHEMICAL CHANGE. By Gilbert Newton Lewis. Received April G, 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 formula; arc 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 = RT, (1) if P represents pressure; v, molecular volume; R, the gas constant; T, the absolute temperature. VOL. XXXVII. — 4 50 PROCEEDINGS OF THE AMERICAN ACADEMY. 4. Every solution diluted indefinitely approaches a limiting condition in which n v = R T, (2) if II 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 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, dQ = dP(V1-V2), where P represents the pressure and Vl and V.2 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 _ pi — vt) dp ' T~ dT ' in which p represents vapor pressure ; Q, the total heat of vaporization of one gram-molecule ; and vx and v2, the molecular volumes of vapor and liquid respectively. Transposing the equation gives an expression for the change of vapor pressure with change of temperature, d T (», - v2) T W 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 r2 is negligible compared with vu and therefore approximately, t'i — V2 = Vi. LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 51 Second, that the vapor obeys the gas law, RT i\ — P These two equations substituted in (4) give the familiar equation, d In p _ Q dT ~ RTZ (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 Poyntiug,* i£ = % (6) dP vx in which p represents vapor pressure ; P, total pressure ; v.2 and vh mo- lecular volumes of liquid and vapor respectively. When, therefore, the 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 * Phil. Mag., (5) XII. 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 5 Figure 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 v2. (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, so that none of the liquid evaporates. The piston C moves down on account of the expansion, dv2, of the liquid. (2) All the liquid is evaporated at temperature T -f d T, C moving to B, and A moving up to furnish the volume, vv (3) The temperature is again brought to T; the pressure on A to p. A moves down on account of the contraction di\. (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 : — Wl = Pdv2, W2 = -P(v2 + dv2) + (p + dp) Oi + dvj, W3 = — p dvu Wi = Pv2 — pvv LEWIS. — THE LAW OF PHYSICO-CIIEMICAL CHANGE. 53 The total amount of work gained, the sum of these terms, is equal to the total amount of heat transformed into work, that is, Wt+ IF2+ Wz + Wi = dQ = ^dT, from equation (3). Adding the terms we obtain, vidP = j.dT> or writing so as to express the constancy of P, 9TjP~VlT' ( (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 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, ( y^ j = — , from equation (6), therefore, it 7) Substituting for -r— from equation (4), Tfr-vjy vJ-\9TjP'0T \9TJP vxTy 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, Q \9T )P- RT2 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 utility 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.f represented by the symbol if/ and defined by the following conditions : — 1. The fugacity of a molecular species 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 quantity, 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 PIIYSICO-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 in the introduction it is easy to derive the following, which is a rigorous statement of Henry's law, namely : The 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 II 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, if/ = P n. (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 Ili of the saturated solution determined. Then by diluting this solution in contact with vapor of X the limit px of the distribution ratio may be found and so the product px IIx. So for another solvent we may find the product p2 n2 ; for a third, ps H3, 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 II, 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 if/ 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 fugacity 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), /cHn_n\ _Q_ \ 9T )P R T2' in which II 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, {-JT-)P = RT* aud VJT-)P = RT» °r COmbimng> Qx - Q, (9) 1t no 91au2 9T RT1 Qx — Q2 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 II2, 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 &, RT\u^, -, w3 = (P + d P) (v - dv) - (n + d n) 0' - dv<), Wi = Pdv. Writing the sum equal to zero, vdP— v'dU = 0, or expressing in the equation the constancy of T, (3n\ v_ \dPJT~ v<' (12) 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, n v' from equation (2). Combining this equation with (12) we obtain From equation (8), t/r = p II. Therefore In \p = In II + In p, and \JP~)*~~ \9P Jt LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 59 since p is constant at constant temperature. Hence equation (13) becomes /9 In i/A v \~9~p~ )T=ln (14) Subtracting two such equations we obtain an equation for two phases, r Sln^ *H 9P Vl — Vj 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) Qlfi> 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, —p~ = — (Si — S2), where St and S2 represent the entropy of the first and second states respectively. Substituting in equation (11) and transposing the constant R, we obtain, 9RTln ^2 9T = _ (Sl _ S.2). (1G) In equation (15) R T is constant, and may be transposed, bringing the equation into the form, *» 9RT\n*r± «^2 9P J T = vi — y2- (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 OP 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 we substitute / and H for /and 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 {dR Tin & ^2 I 91 J r,r> F7 H <18> and further, of the equation for a single phase, This equation would mean that if the fugacity is a function of a number of energy intensities, I, /', /", etc., the rate of change in the quantity .R Tlu.il/, with a change in one of the intensities alone, is equal to the corresponding capacity. In other words, this equation, if true, expresses a law so far reaching that it embraces every possibility of the change of state of any simple substance under all conceivable conditions. Let us examine the validity of this equation for all cases in which the escaping tendency can be shown to be influenced by the intensities of various energies. The influence of pressure is given in equation (14), which may be written, and therefore conforms to equation (19). * These quantities have been hitherto called the factors of energy, and their product has been written equal to the quantity of energy concerned. I believe that this part of the theory is absolutely unjustified by the facts, and that it has been the chief cause of the hostility which has been shown to a conception which is valuable in research and has proved a veritable boon in the pedagogical treat- ment of energetics. I hope soon in another paper to discuss this whole question, especially in the light of the results of the present paper. Meanwhile we may speak of intensity and capacity as the dimensions of energy, signifying that their product has the dimensions of energy. LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 61 The influence of temperature is expressed for two states simultane- ously in equation (1G), which conforms to equation (18) except for the minus sign. This slight difference might be explained away, but a much weightier difficulty confronts us when we attempt to split equation (1G) into two equations, each expressing the influence of temperature upon the fugacity for a single phase, in the form, (9R Tlnif,\ v 9 T / = -& This equation is in general not true, notwithstanding the fact that we may choose arbitrarily the zero of entropy. If for each temperature this zero could be chosen arbitrarily it could be so chosen that the equa- tion would be true, but as a matter of fact the entropy is in all cases a determinate function of the temperature, and the zero chosen for one tem- perature must be retained for all. We must conclude, therefore, either that the general equation (19) is false, or that entropy is not the capacity dimension of heat. To make the latter conclusion would appear too arbitrary were it not that other considerations lead also to the suspicion that entropy has been too hastily chosen as the capacity in question. In fact, the equation, d Q = TdS, for the heat absorbed in a reversible process, corresponding to the general equation for change of energy, dE — Id H, is the only argument for the consideration of entropy as the capacity dimension of heat. This argument would apply equally well to any other quantity, h, such that d Q = ± Td h ; in other words, such that dh = ± d S. It is interesting, therefore, to determine whether there is, in fact, a quantity which fulfils this condition and also the condition 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,* S=S0 f- GP\n^-R\n^. * See Clausius, Warmetheorie, I. p. 214, third edition. 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, \p = P, and therefore , (9RT\u^\ {9RT\nP\ h = \~-rr^)P = \--^T-)rRlxlP' (22) We see, therefore, that the value of /* 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 __1 _ and from equation (22), d h = R d In P, hence, for constant temperature, dh = — dS, (23) and the condition is satisfied. The value R In 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, — /?2 == iJ-2 — *^1* If we choose as the second state the vapor of the substance at such a low pressure, P2, that the vapor may be regarded as a perfect gas, h2 = R In P2, from equation (22), and the last two equations give, h1 = Ss-Si + BlnP* (24) in which *^2 represents the entropy of the vapor at pressure P2. 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), namely, 9T 02 — Oj, 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 P2. By the aid of equation (24) we may therefore write *p2 ~\ hi-fi In P2. According to (22) 9T and the last two equations give by addition \ 9T )rK 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 = ^ + E]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, & = ^ + fllnf, (25a) in which i|/ 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 o- and a surface tension t. The change in surface of the drop with a change in its content expressed in gram-molecules, that is, — — , has been an called the molecular surface, and we may designate it by s. If the quantity dn 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 tela, 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 of dn gram-molecules is equal to t d cr + P (d v0 — d v), where dv0 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, II and II0, 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 II0, and (3) passes out of solution into the large mass. The three steps yield the following amounts of work, in which d vj and d v' represent the volumes occupied by the amount d n in solution at the osmotic pressures II0 and II, respectively. Wi = Udv' - Pdv, W2 = dnRT\n^> W3 = Pdv0-Il0dv>. 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{dv0-dv) + Udv'-U0dv0' + dnRTln — = tda+ P(dv0-dr). Now from equation (2), II0 d vj = II d v', U^ if/ and, as on page 55, Therefore RTlu^ = t^ = ts. (26) This is the general equation connecting fugacity and surface tension at constant temperature and pressure. If t is variable we may differentiate, \p0 and s being constant, obtaining dR Tlnif/ = sdt, or expressing the constancy of T and P, fdRT\xxxb\ C-srf )„...=* (27) This equation completely confirms the validity of equation (19) as applied to surface energy and corresponds to equations (20) and (21). An important form of energy which we have not yet discussed is electrical energy, whose dimensions are potential, and quantity of elec- tricity. If these be represented by i? and e, respectively, in any case where the fugacity is influenced by the electrical potential, we should have the equation, (-^L.=* (28) There are in fact a number of cases in which the potential may be shown to have an effect upon the escaping tendency, the most important being that in which the potential influences the fugacity of the ions. The following equation has been amply proved experimentally, and thermo- dynamically is shown to be rigorously exact on the assumption that the ions form an ideal solution. e 77 = R T In n + K, in which tt is the potential at which equilibrium is established between an electrode and its ions at the osmotic pressure II, if e is the charge of one gram-ion and K is at constant temperature and pressure a character- istic constant of the electrode. In other words, II is the osmotic pressure of the ions which will be in equilibrium with the electrode when the VOL. XXXVII. — 5 66 PROCEEDINGS OF THE AMERICAN ACADEMY. potential ir is established. Since we are discussing an ideal solution this osmotic pressure is proportional to the fugacity of the ions. That is, from equation (8), \p = p II, and € 77 = R T In ijf - R Tin p + K. Differentiating at constant temperature and pressure we obtain the equation, (9RT\nxp\ V Sir Jt,p,... which is equation (28). Equations (20), (21), (27), and (28) comprise all cases in which fugacity is known to depend upon the intensity of any form of energy. The identity of these equations with equation (19) gives the highest degree of probability to the supposition that the latter equation expresses an exact law of nature and one possessing such universality as few others possess. For this equation expresses the condition for any con- ceivable change of state of any simple substance. Moreover, it will be shown in the paper which is to follow this, that equation (19) not only applies to chemically simple substances but, with a slight generalization in the meaning of the symbols which it contains, applies to mixtures as well, and further that it applies not merely to physical processes but also to all chemical processes,* so that this law becomes the general law of physico-chemical change. Finally, it will be shown that the adoption of the two functions \p and R Tlnif/, which possess such peculiar importance, will remove many obstacles in the search for the fundamental principles of energetics, in which already so much progress has been made by the work of Helm, of Ostwald, and of other investigators. I shall therefore offer in the last section of this paper a further explanation of fugacity as a tangible, physical quantity. V. The Fugacity of Imperfect Gases. The vapor pressure is determined for many substances and capable of direct or indirect determination for all. Moreover the fugacity of a sub- * In the further extension of this theory, analogy will be seen between the conception of fugacity and the driving tendency of chemical reaction as used by T. W. Richards (These Proceedings, 35, 471 ; Jour. Phys. Chem., 4, 385 (1900)). It is a pleasure to recall how much I owe to the many conversations full of assist- ance and encouragement which I had with Professor Richards during the early development of the theory of fugacity or escaping tendency. LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 67 stance is the same as that of the vapor in equilibrium with it. It is important therefore to know what relation exists in general between thi fugacity of any gas or vapor and its pressure. Figure 3. If a section of the isothermal of any vapor is plotted on the P V dia- gram (Figure 3) we obtain a curve such as M M', which, according the third law stated in the introduction, approaches asymptotically I hyperbola N N', whose equation is, P v = RT. Let us determine the value of if/ for any point M of the curve. Tl variation of if/ with P is given by equation (20), which may be written for constant temperature, d R T In if/ = v d P. Between the two points M and M' we find by integration RT V J M I- d p. Now if the lines of constant pressure L M N and L' M' N' are drawn, I v dP is equal to the area M M' L' L, and this is equal to the area 68 PROCEEDINGS OF THE AMERICAN ACADEMY. L N N' L' minus the area M M' N' N. The former area is equal to P R Tin—, and if the latter be designated by A we have the equation, RT\n^ = RTln^- A. (29) Now if the point M' is moved in the direction of greater volume, equa- tion (29) holds true continuously, and therefore is true if M' is taken at infinite volume. But at infinite volume *' = P', and therefore R T\m}, = R TlnP-A^, (30) if Am represents the total area bounded by the line M N and the curves M M' and N N', each produced to infinity. This equation may be written, RTln^ = -Aa,OT\*^ = -^i,oT $ = Pe=£, (31a) where e is the base of natural logarithms. The deviation of the fugacity from the gas pressure is, therefore, dependent upon the area A^. The case that has been chosen in which the curve M M' lies within N N' is of course the common one. For gases of the opposite type, hydrogen and helium, the formulae will be, R Tln^ = + A„ andi/, = Pe^ (31b) We see at once that for all known gases and vapors except hydrogen and helium the escaping tendency is less than the gas pressure ; for these two, greater. The determination of the value of the fugacity at any pressure involves the estimation of the area Av . This must be done by integrating the most exact empirical equation of the isotherm of a s;as between the pressure in question and the pressure zero. This method has the disadvantage of all extrapolation, but the value thus obtained may be checked by using a second empirical equation of another form and recalculating A^. If the two results coincide the value obtained will in all probability be very near the true value of A^. In conclusion it may be remarked that equation (29) applies to the isothermal of all substances, not merely to gases, and can be frequently of use. For example, if it is possible to pass continuously from vapor to liquid along an isothermal, it is evident that in passing from a saturated vapor to its liquid, LEWIS. THE LAW OF PHYSICO-CHEMICAL CHANGE. 60 Heat, mai»e ahtj published wholly oa ra part with Appropriation-* PROM THE Bl -U. THE VISIBLE RADIATION FROM CARBON.* By Edward L. Nichols. Presented May 8, 1901. Received May 15, 1901. The law of radiation has for a long time been considered by physicists as a subject of high interest, and numerous investigations looking to the establishment of a general relation between radiation and temperature have been made both from the theoretical and the experimental stand- point. The earliest attempts to determine incandescence in its relation to temperature were made with platinum. Draper f in 1847 made observations upon a wire of that metal heated by an electric current. The temperatures were determined from the expansion of the wire. ZolIner$ in 1839 compared the light emitted by incandescent platinum with the heat evolved. E. Becquerel,§ who made an extensive study of visible radiation from various solids at high temperatures, used thermo- elements of platinum and palladium, calibrated by reference to melting points with the air thermometer. A partial separation of the rays was effected by means of colored screens. Becquerel found that opaque bodies, such as lime, magnesia, platinum, and carbon, at the same temperature had very nearly equal emissive powers, a conclusion vigorously contested by his contemporaries, but ex- plained, in the light of later work, by the fact that the -lowing bodies were enclosed in a long earthen tube. The conditions for ideal blackness were thus approximately fulfilled. He likewise made photometric obser- vations upon wires electrically heated and found the' light to increase much more rapidly than the emitted heat. Although some of Becquerel's results were at fault, particularly his estimation of temperature above the melting point of gold, his work is especially noteworthy in that he employed many of the methods to which. * An investigation carried on in part by means of an appropriation from the Rumford Fund. Read at the meeting of the American Association for the Advance- ment of Science in New York, June 27, 1900. t Draper, Philosophical .Magazine, XXX. 345 (1847). | Zollner, Photometrische Untersuchungen (1859). § Becquerel, Annales de Chimie et de Physique, (3), LXYII. 17 (1863). 74 PROCEEDINGS OF THE AMERICAN ACADEMY. iti the hands of later investigators, our knowledge of the laws of incan- descence is due. He established the direct proportionality of the loga- rithm of the intensity of radiation to the temperature and pointed out the possibility of optical pyrometry. In 1878 Crova* used the Glan spectrophotometer in the comparison of various sources of light, such as candles, gas flames, the lime light, the arc light, and sunlight, and proposed au optical method for the measure- ment of temperatures. In 1879 f I published the results of a series of measurements made in this manner upon the visible radiation from platinum at various tempera- tures. At that time, the measurement of high temperatures by means of thermo-elements, of platinum and platinum-rhodium, or platinum-ind- ium, had not been developed, audj the determination of the temperature from the change of resistance of the metal was, as has been previously pointed out by Siemens, a matter of great uncertainty on account of the varying performance of different samples of platinum. This difficulty, which was due to the impurities contained in the metal, has since been largely overcome, and platinum thermometry has, through the study of Callendar and others, been advanced to the position of au operation of precision, but at that time I was forced to content myself in the investi- gation just referred to with an expression of temperature of the glowing platinum in terms of its increase of length. Work upon the incandescence of carbon was first taken up in a serious manner after the development of the incandescent lamp. Schneebeli,$ in 1884, made some observations upon the total radiation and candle power of the Swan lamp. He made no estimation of tem- peratures. In the same year Schumann § published his very complete spectro- photometric comparison of the various incandescent lamps in use in Germany. Lucas, || in 1885, heated arc-light carbons in vacuo, estimated their temperature from the current employed, and measured the light given in carcels. I shall refer to his work in some detail later. In 1887 H. F. Weber U began his studies of the spectrum of the in- * Crova, Comptes Rendus, LVII. 497 (1878). t Nichols, Ueber das von gliihendem Platin ausgestrahlte Licht. Gottingen, 1879 ; also American Journal of Science, XVIII. 446 (1879). t Schneebeli, Wiedemann's Annalen, XXII. 430 (1884). § Schumann, Elektrotechnische Zeitschrift, V. 220 (1884). || Lucas, Comptes Rendus, C. 1451 (1885). IT Weber, Wiedemann's Annalen, XXXII. 256 (1887;. NICHOLS. THE VISIBLE RADIATION FROM CARBON. 7.', candescent lamp. He found that the first light to appear was not that of the region nearest the red end of the spectrum, but corresponded in wave length to the region of maximum lumiuosity, and that at these low tem- peratures the spectrum was devoid of color. Stenger* in the same year corroborated Weber's observations and offered what has since b< received as the proper explanation of the phenomenon. In 1889 I published in collaboration with W. S. Franklin f a series of spectrometric comparisons of incandescent lamps maintained at various degrees of brightness. No attempt was made to determine temperatures. In 1891 II. F. Weber t read a paper at the Electrotechnical Congress in Frankfurt on the general theory of the glow-lamp. By means of numerous measurements through a wide range of incandescence made upon lamps with treated and untreated filaments, constants were estab- lished for his empirical formula for the relation of radiation and tempera- ture. The infra-red spectrum of carbon has, since the appearance of the incandescent lamp, likewise been subjected to measurement. Abney and Festing § in 1883 published curves for the distribution of energy in the spectrum of such lamps from measurements male with the thermopile. In 1894 I compared, with the help of the same instrument and a highly sensitive galvanometer, the infra-red spectra of lamps with black and gray filaments. || Of late years attention has been devoted especially to the problem of the law of radiation from an ideal black body, and various formulae have been proposed by means of which the rise of radiation of any single wave length upon the one hand, and of the total radiation on the other, may be expressed as a function of the temperature. Interesting as this phase of the problem is from the point of view of theoretical physics, it is perhaps even more important to know the relation between temperature and radiation for actual surfaces. Apparatus and Outline of Method. I propose in the present paper to describe an attempt to measure the temperature of carbon rods rendered incandescent by the passage of an * Stenger, Wiedemann's Annalen, XXXII. 271 (1887). t Nichols and Franklin, Am. Jour, of Science, XXXVIII. 100 (1880). | Weber, Bericht des internationalen Flektroteehniker-congresscs zu Frankfurt am Main, p. 49 (1891); also Physical Review, II. 112. § Abney & Festing, Philosophical Magazine, (5) XVI. 224 (1833); also Pro- ceedings of the Royal Society, XXXVII. 157 (1884). II Nichols, Physical Review, II 260 (1894). 76 PROCEEDINGS OF THE AMERICAN ACADEMY. electric current, and to make spectropliotometric comparisons of the visible radiation from their surfaces with the corresponding wave lengths m the spectrum of an acetylene flame. The carbons used for this purpose were produced by the well-known process of squirting a semi-fluid carbonaceous paste through a cylindrical opening. They were straight cylindrical rods 10 cm. in length, and 2 mm. in diameter. Still larger rods would have been preferable, but I was unable to obtain any of greater diameter than the above that were capa- ble of withstanding the temperatures to which it was necessary to heat thetn. The rods were mounted horizontally in a massive metal box 40 cm. in length, 20 cm. wide, and 20 cm. in height. This box, which was made especially for this investigation, had openings at the ends, through which, by means of air-tight plugs, the terminals of the carbon could be introduced. Through one of these plugs, likewise, the platinum and platinum-rhodium wires of the thermo-element, by means of which the temperature measurements were made, entered the box. In one of the vertical sides of the box was a row of five circular plate-glass windows, which could be removed for cleaning, through which the carbon could be seen and the spectropliotometric observations couM be made. Other openings in the top of the box and through the opposite sides served to connect it with a mercury air pump of the Geissler type and for the introduction of manometers for the measurement of pressure. A vertical cross-section of this part of the apparatus is shown in Figure 1. Attempts 7o jnanom&tci- To fiumjo Figure 1. NICHOLS. — THE VISIBLE RADIATION FROM CARBON i i to locate, by a variety of methods, the hot junction of the thermo-element, by means of which the temperature of the surface of the roils was to be measured, in such manner that it would assume the temperature of that surface, made it only too clear that herein lay one of the chief difficulties of the investigation. It was found that such a junction, however small its size, and however carefully it might be brought into contact with the surface of the rod, would not take even approximately the temperature of that surface ; and recourse, after the failure of numerous other expedients, was had to the following plan, which although far from being free from objection, was found to be upon the whole the most reliable, and to give, when properly carried out, the most definite and satisfactory result. By means of a drill made for the purpose from the smallest obtainable size of steel sewing-needle, a minute hole was bored radially at a point upon the surface of the rod lying within the field of view of the spectro- photometer. This hole had an approximate diameter of 0.03 cm. It extended to a depth equal to about one half the radius of the rod and was conical in form. Platinum and platinum-rhodium wires to he used for the thermo-element were drawn to a diameter of 0.0 1G cm., and their free ends having been. laid together side by side, were fused in the flame of the oxyhydrogen blowpipe so as to form a junction. This junction, which after the action of the blowpipe took the shape of a small bead of the combined metals, was trimmed down into conical form, until it would just enter the hole in the side of the rod, care being taken that the entire junction was beneath the surface. The wires leading from this junction were next sealed into a glass tube of about 2 mm. bore, through the interior of which they were carried from end to end, care being taken that they should be nowhere in contact. They were held in place by fusing the glass around them at either end of the tube. This tube was inserted through an opening in the plug a (Figure 1) carrying one terminal of the rod, and there made air tight by means of cement. One end of the carbon rod was then inserted in a clamp attached to the inner face of the plu"-, and the wires at a distance of about 1 cm. from the junction were bent downward at right-angles, so as to bring the junction into position for insertion into the hole in the rod, and to hold it there when inserted by the slight but sufficient spring-action of the wires themselves. This arrangement of the junction and rod is indicated in Figure 2. Figure 2. 78 PROCEEDINGS OF THE AMERICAN ACADEMY. The introduction of the thermo-element having been successfully car- ried out by the method just described, it was possible to insert the plug, carrying the rod and thermo-junction with it, into the end of the box and to secure it in place ; after which the free terminal of the rod was introduced between the jaws of a strong clip attached to the opposite plug (b, Figure 1). This operation had to be performed through the open windows in the side of the box. These were then screwed rightly iuto place, and the box was ready for the exhaustion of the air. This method of measuring the temperature of the surface, to be suc- cessful, involved the fulfilling of several rather difficult conditions and the application of an important correction. To bore into the material of a carbon rod carrying a current in the manner described, necessarily dis- turbs more or less the flow of the current ; and the changes of resistance thus introduced are likely to bring about decided changes of tempera- ture in that neighborhood. In some instances this became obvious when the rod was heated, the temperature being higher near the hole than else- where. Indeed, it was often possible to note this effect with the eye on account of the increased incandescence of the region in question. In all such cases the mounting was rejected. It was found possible, however, to so nearly compensate for this loss of carbon by the introduction of the platinum junction that no difference in the incandescence of the surface could be detected by the closest observation ; and since differences of temperature which cannot be detected by the eye will be negligible in spectrophotometric work, this was taken as the criterion of a satisfactory mounting of the thermo-junction. Measurements were attempted only when this condition was fulfilled. It is likewise obvious that there is danger from the contact of the two wires of the thermo-junction with the sides of the hole in the rod. A branch circuit for the passage of the current is thus formed which includes the galvanometer coils, thus im- perilling the integrity of the readings of the electromotive force. This could be obviated only by having the wires touch the rod at points in an equipotential surface, and the fulfilment of this condition was determined by the reversal of the current through the rod and the absence of any effect of such reversal upon the galvanometer. Another and more serious objection to the method, and one which could only be met by the introduction of a correction, lay in the fact that even with the smallest wires which could be used for a thermo-element a certain amount of heat would be carried away by conduction through the metal ; so that the junction would never reach the full temperature of the surfaces with which it was in contact. I was at first inclined to think NICHOLS. THE VISIBLE RADIATION FROM CARBON. 79 that this correction would be a small one, but attempts to measure in a similar manner the temperature of the acetylene flame indicated that the loss of heat from this source was by no means to be neglected. These attempts are described in a subsequent section of this paper. The numerical value of this correction was accordingly determined by direct experiment in the following manner. Thermo-elements drawn from the same pieces of wire but differing considerably in diameter were prepared. These were inserted two at a time in holes on opposite sides of a carbon rod and the rod was brought to incandes- cence by means of the current. The temperatures reached by these junctions were compared by means of the potentiometer, and a curve was plotted showing the relation between the cross-section of the wire in the thermo-element and the temperature of the junction. This curve, extended in the direction of decreasing cross-section, served to indicate l*oo° /loo0 ' 00 1 oo J oo * oo Relative Cross-sections. Figure 3. with at least a fair degree of accuracy the temperature which would have been reached by a thermo-element of zero cross-section placed in contact with the surface to be measured. The difference between this temperature and that reached by a junction of any desired size gave the correction which was to be applied. The correction, as will be seen by inspection of the curve, Figure 3, is a very large one, amounting, even in the case of the smallest wires which it was found practicable to use, to 80 PROCEEDINGS OF THE AMERICAN ACADEMY. about 85°. The result of the calibration agreed, however, so well with similar experiments made by placing thermo-j unctions of various sizes in the non luminous outer envelopes of the acetylene flame, of the ordinary gas flame, and of the flame of the candle, that I feel warranted in placing much dependence upon them. The correction is not of the same size in the various cases, but the differences are such as one would expect from the nature of the flames. This method of correcting for the loss of heat in a thermo-junction was first employed by Waggener * in his investigation of the temperature of the flame of the Bunsen burner. I became acquainted with his research only after the completion of my experiments. Calibration of the Thermo-Elements. All our estimates of very high temperatures may be said to rest in one way or another upon extrapolation. Tne upper limit of usefulness of the air thermometer has been found to lie in the neighborhood of 1.300.° At this temperature Erhardt and Schertel, t in their admirable but little known research upon the melting-points of alloys of silver, gold, and platinum, were obliged to abandon direct determination ; and, at about the same temperature, Holborn and Wien and Holborn and Day I in their latest studies upon thermo-electric thermometry found that the indications of the air thermometer, even when constructed of the most refractory of modern porcelain, began to be erratic. We have, it is true, the investigations of Violle § upon the melting-points of the metals of the platinum group; but these, it must not be forgotten, are based upon an assumed value for the specific heat, and this assumption is equivalent to the extrapolation of the curve of the variation of the specific heat with temperature. The observed values, by means of which this value was determined, all lie far below those of the melting- points of the metals in question. It is necessary, therefore, in spite of the accumulation of indirect evidence of their approximate accuracy, to hold in reserve the assignment of absolute values of these melting-points until by some means as yet unthought of we shall be able to obtain direct experimental data. In the meantime, they afford us the best present available basis for a temporary scale, our confidence in the * Waggener, Wiedemann's Annalen, LVIII. 579 (1896). t Erhardt and Schertel, Jahrbuch fur das Hiittenwesen in Sachsen, 1879, p. 154. \ Holborn and Day, American Journal of Science, VIII. 1G5 (1899). § Violle, Comptes Rend us, LXXXIX 702, 1879. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 81 approximate accuracy of which must rest upon the fact that the melting- points for palladium, platinum, etc., as given by Violle arc found to lie upon what may reasonably be supposed to be an extension of the curves experimentally determined for lower temperatures by means of the air thermometer. As for the various formulae for the variation of electro- motive forces of thermo-elemeuts with the temperature, we must not lo si'dit of the fact that they are simply analytical expressions for experi- mentally determined relations, and that the extension of them to temper- atures lying far beyond the experimental range is not to be regarded as more trustworthy than the extention of a curve by graphical methods. Under these circumstances I decided to content myself with the pro- visional acceptance of the following values for the melting-points gold, palladium, and platinum, namely : — Gold, 1075° C Palladium, 1500° C Platinum, 1775°C, and to ascertain as accurately as possible the electromotive force given by the thermo-elements used at these points. It was thought that b\ drawing a curve through them, and reading intermediate temperatures from this' curve, the values obtained would be as close as our present knowledge of the subject will admit. The platinum, platinum-rhodium wire used for my elements was obtained, as has already been state I. from Heraeus in Hanau and was supposed to be of the same stock as that employed by Ilolboru and Wien. The fact that the electromotive force given by these thermo-elements when exposed to the temperature of melting platinum agreed very closely indeed with that obtained 1»\ extrapolation of their data seems to indicate that the metals were identi- cal with those used by them. Exhaustive studies at the hands of Le Chatelier,* of Barus,t and ol Holborn and Wien. t and others have led to the conclusion that whenevei thermo-elements consisting of platinum on the one hand, and ol the alloys of that metal with iridium, rhodium, or any other metals of platinum group on the other, are to be used in the measurements of * Le Chatelier, Comptes Rendus. CII. (1860) 819; Journal de IV VI. 26 (1887) ; also Mesure des Temperatures fclevees [Paris, 1000), Chapter VI. t Barus, Bulletin of the U. S. Geological Survey No. 54 ; also American -lour nal of Science, XLVIII. 336. t Holborn and Wien, Wiedemann's Annalen, XLVIT. 107 (1892); LV1 560 (1895). VOL. XXXVII. — 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 manufactured 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 Ilolman, 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 from 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. The acetylene flame em pi »yed 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 a), which, with increasing gas pressure meet without uniting, each being deflected, by impinging upon the other, into a vertical plane (Figure 4 b). 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 calibration has been separately described in a contribution to the Lorentz Jubilee Volume. The Ha cue, 1900. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 83 ure 4 c), in which the two cylindrical 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 readied, there is oreat 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 ima^e of it, viewed edgewise, upon a screen, rarely amount to more than .1 mm., and in an especially protected place, 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 G), along which it may be Figure 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, «C~J Figure G. upon the ground-glass screen of which instrument, at a distance of abut two meters, an enlarged image of the flame is focussed. The platinum and platinum-rhodium wires to be tested are drawn down to a 84 PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 7. 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 o 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 joining the two wires is considerably less in 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 necessary to do after each obser- vation, in a few moments. The junction is rigidly mounted upon the steel bar with 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 meking 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, where it is clearly visible under the illumination of the acetylene flame, which 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 the heating of the junction a potentiometer of the 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 out. Such a strip is looped into the angle of the V and drawn snugly into place, the free ends being 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 arouud the junction. The thermo-junction carrying the loop having been mounted, in the manner described, in the 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 from 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 fiven sample of metal is excellent. It is desirable 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 bet urn 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, ami to make a new junction of tin; 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 meltiDg 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 in 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. On 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 ouch 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-junction 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 /too0 ^^ 0 /*: 0 L 0 r 0 0 IZ^O* ^r 0 ^r 0 *r * ^ 0 ^ 0 ^ 0 * too0 dp / s f /4* f 0 V +00* r * 60 00 10 ooo 1 *■ OOO It OOO Figure 8. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 87 excess of oxygen, and even where the metal to be melted is platinum itself, fusion occurs before the luminous portion of the flame, the action of which upon the thermo-electric properties of the junction is to be feared, has been reached. It is well-known that a junction, the perform- ance of which has been vitiated by exposure to the vapors of a thane or furnace, can be restored to its original condition by immersion in an oxydizing flame. In this method of calibration the junction is continually subject to such oxidation as is necessary to preserve it. Thus one of the sources of error which it has been found most difficult to guard against in the use of the furnace is altogether avoided. Figure 8 contains the calibration curve of the thermo-elements used in this investigation, and likewise, for purpose of comparison, a curve repro- duced from Waggener's paper and extrapolated by him from data given by Holborn and Wien. It will be seen that while the curves are not identical they are of the same character, and that the differences are not greater than experience would lead us to expect in the case of different thermo-elements, even where these are from metals of the same manufac- ture. It is not a question of absolute electro-motive forces, but of the form of the curves, since what we need is a criterion by means of which to determine whether temperature readings based upon Violle's values for palladium and platinum are in reasonable accord with those obtained by the extension of the curve of Holborn and Wien. The Spectrophotometer . The spectrophotometer used was a copy of the instrument designed by Lummer and Brodhun for the Imperial Institute in Charlotteuburg. It consists of a one-prism spectroscope with two collimator tubes, placed at right-angles to each other, as shown in Figure 9. Each of these tubes carries a slit the width of which is regulated by means of an accurate micrometer screw with a drum head divided into one hundred parts. By estimating tenths of a scale division, the width of the slits could be esti- mated to one one-thousandth of a revolution. The essential feature of this photometer consists in the Lummer-Brod- hun prism D, placed between the objective lenses of the two collimators, and the dispersing prism in such a position that the beam of light from one of the tubes is transmitted directly to the latter, while that from the other tube is bent to 90° by total reflection. The instrument was set up with collimator A in such a position that a portion of the surface of the incandescent rod lying nearest to the point at which the thermo-eleinent had been inserted formed a field of illumination for the slit at a distance 88 PROCEEDINGS OP THE AMERICAN ACADEMY. of about 25 cm. Tod r-id, Kct A The region under observation was limited by means of a vertical diaphragm d, 5 mm. in width, which was 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 up in the axis of the other collimator at a corre- sponding distance, and viewed through a circular aperture c, 5 mm. in diameter, cut in a metal screen interposed between the flame and the slit and as near the former as practicable. The acetylene flame was adopted as a comparison standard for the fol- D l c A 1I> the less refrangible lowing reasons : — 1. It possesses a continuous spec- trum, brighter in regions than that of ^ Figure 9. any other controllable source of light. 2. The radiating material is finely di- vided carbon, presumably of a character not unlike that of the surface of the untreated rod. 3. The acetylene fl ime is the result of the combustion of a definite fuel (C2rl2) 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 constaut in its intensity and color than any other fkime 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 the temperature of the acetylene flame, varying and in- compatible statements are in existence. The temperature of combustion * The results of these experiments on the temperature of the comparison flame were separately communicated to the American Physical Society on 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 24200. Measurements with Le Chatelier's pyrometer, on the other hand, made by V. B. Lewes, f give 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°. Smithells, $ 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 having a diameter of 0.0082 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, || 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, If 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 CXXI. 1144 (1895). t Lewes, Chem. News, LXXI. 181 (1895). \ Smithells, Journal of the Chemical Society, LXIX. 1050 (1895). § Waggener, 1. c. || MacCrae, Wiedemann's Annalen, LV. 97. If Pellissier, L'ftclairage a l'acetylene (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 au 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 THERMO JUNCTION 10,000 OHMS. 110,000 OHM8. CELL Figure 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 range 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 II form and of the test-tube form, constructed in this department in 1898. 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.° 1600° MELTING PT. OF PT. iff'' 1 1400° 11/ ^ 1200° iff ' 1000° 800° o 600 400° 200° 6 mm 4 mm Figure 11. 92 PROCEEDINGS OF THE AMERICAN ACADEMY. The wires selected for the four junctions to be used in the experiment upon the acetylene flame were measured under a microscope with micrometer stage. Their diameters were as follows : — Junction I. " II. " III. " IV. Diameter 0.0199G 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 the 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 nonduminous 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 II. Temperatures indicated by thermo-junctions I., II., 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° 3.33 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. 1613° 1.30 mm. 1367° 1.93 mm. 1322° 118 mm. 1685° 1.70 mm. 1667° 1.07 mm. 1382° 1.68 mm. 1385° 0.894 mm. 1724° 1.54 mm. 1705° 0.85C 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 mm. 0.300 mm. Molten. Molten. NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 93 The iucrease of temperature as the flame approaches the junction is gradual at first: but at a distance of about 0.4 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- ing the breaking away of the carbon from the 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 nearly one hundred decrees 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, wilh 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 OF 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 mautle, 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 iu 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 (0.0182G2 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, a, b, c, and d were taken for the core 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 CARBOX. 95 1800 1600 1400 1200 V ^C^ ■4^ 100 200 300 CROS8-SECTION OF WISES FlGDRE 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 flume, 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 OP 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 nearly one hundred degrees above the 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 error, 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, the correction for loss of heat would be even greater, except in case3 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 Hat flame of the usual 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 tic following table : — TABLE III. Junction I. 1385° Junction III. 1009° II. 1484° IV. 1070° NICHOLS. — THE VISIBLE RADIATION FROM CARBON. '••7 These values having been plotted with relative cross-sections of the ires as abscissae, and temperatures as ordinates, were found to lie 1800° \ 1600 n \ X ^V£j« (£} 1400 K X(o; 1200 \ — ^ 100 200 300 400 cross-section of wire Figure 14. 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 flumes is at least one hundred and twenty degrees lower than the corresponding region in the acetylene /lame. 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 VOL. XXXVII. — 7 98 PROCEEDINGS OF 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 caudle 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 eutire surface of the lumi- nous sheath from base to tip, measuriug 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 the 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 FROM 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 »as flame. These temperatures were 1281° and 154G0; 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 position? 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. TIi 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, this 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 sight, 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'temperature seem highly improbable. Messrs. Lurnmer 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 pliysikalischen Gesellschaft, 1899, p. 214. 100 PROCEEDINGS OF THE AMERICAN ACADEMY. which they have established between the position of the maximum 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 which 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-point 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 juuction in the usual manner, to move the acetylene 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 Figure 15. 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 conclude 1 from these determinations that the melting-point of the Wollaston wire was at least one hundred degrees 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 dd Ifll Figure 16. would not vary, wras 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 p, was placed at a distance of about 15 cm. from this opening. A second diaphragm, d' , with an intervening air space, served to cut off, in 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 (lame 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 Dot strongly damped, to its first turning point. The shutter was 102 PROCEEDINGS OF THE AMERICAN ACADEMY. then immediately closed in order to prevent further heatiug 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 spectrophotometry 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 hesitate 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 pf 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 the rod, an assistant made repeated observa- tions with the potentiometer and readjusted the resistance in the battery circuit whenever necessary. Excepting at very high 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 fall of potential between its ends were made at the beginning and end of each experiment. Spectrophotometry Observations. It was my expectation, in planning this research, that whatever might prove true as to the character of the radiation from gray carbon, Lhe 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 in 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-element as a means of measuring 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 aide 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 questiou. 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 filaments 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 thermo-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 svas 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 sufficient to perform the spectrophotometric observations. In order to obtain at least an approximate estimate of these temperatures, T 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. 105 ^oTfu*-u*4 • / / • ' / 1* / / - — ^ / / / r« ?J0° •- • • 0 r~i--- — — • ~ 0 _ — — — »J • • ^. poo' •J> Figure 17. •7/*- corresponding wave lengths of the comparison source (in this case the acetylene flame), the relative distribution of energy in the visible sprctrum from the carbon rods. The other curves, which I have termed tsochroms, indicate the rise in the energy of any particular wave length of the 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 isochroms, 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 tbis diagram abscissae are wave lengths and -*f- Zoo" /r //oo" ''It- I •fo- \7af* T ! i i ~/ T / / K / / / / / 1 L. / / / / L I I I I I I i I — 7 — T >s. ji >A —t I I I I'tOto ! +■ / $00' fooe /ooo° Figure 18. IIOO' ordinates are ratios of the brigbtness of the spectrum of tbe carbon rod in each region to that of the corresponding region in the spectrum of NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 107 the acetylene flame. A noteworthy fact exhibited by means of these curves is the relatively rapid increase of intensity in the middle of the spectrum. In passing from 930° to 1055° the brightness of wave length .7C p, increases 5.3 times ; that of .70 p, 7.2 times ; that of .60 p, 13.5 times, and that of .50 p o>dy 9 times. We have here the beginnings of a process which becomes more marked in its effects as higher temper- faocA £*7**<7 (frca^ca c ce*>. ■^xn+4 (.0 (cvuy U&J aM. , *ua*&<~ -CjHu+iA V t 1 1 1 t ! , ' / / / t / i i 1 1 i 1 1 ¥0 / 1 1 / / i ' / i / ' / / / / i / / / / i / / / / // t / / / / io / / / i / / / t * i i » f / / / / 4 / / / / t 4 / / / / '/. > ' / / / / / i / / ' \S j / f ^* y y • * / y * y y * y y / y y * / / ■ss-^. ■6o. y- ■JfS-f*. IOOO" nOQa /lOO° /ZOO' Figure 19. atures are attained. From 1100° upwards it was found much more difficult to obtain satisfactory readings. The carbon rods which I had brought from Paris for this investigation would not stand prolonged heating and it was necessary to replace them frequently. 108 PROCEEDINGS OF THE AMERICAN ACADEMY. In order to bring the observations upon the various rods to a common scale, isochroms from the readings for each rod were plotted. The gen- eral character of these curves is shown in Figure 18, in which the isochroms corresponding to the isotherms of Figure 17 are given. From the ordinate at 1000° of the isochrom for .G/.i, which for convenience was taken as unity for the entire set, a reduction factor was obtained by means of which all the curves for all the carbons were brought to the same scale. A new set of isochroms was then plotted for each of the wave lengths .75^, .70^, .65^, .60^, .55//, .50(i, and .45^, in the drawing of which all the obser- vations upon the rods were used. While this method did not bring the various sets of observations into perfect agreement, the results were sufficiently definite to indicate with a close degree of approximation the trend of these curves for temperatures up to 1400°. The result of this compilation for the wave lengths just mentioned is shown graphically in Figure 19. From these curves in turn, isotherms for the temperatures 900°, 1000°, 1100°, 1200°, 1300°, and 1400° were plotted. These curves are given in Figure 20. Had the law of increasing intensities throughout the spectrum with rising temperature been that anticipated at the begin- ning of this investigation, the trend of the isochroms would necessarily have been such as to bring all the curves together at a common point corresponding to the temperature of the acetylene flame. In other words, if the spectrum of the acetylene flame were identical throughout with that of the carbon rod at the same temperature, the isotherm of the spectrum of the rod at that temperature would be a horizontal line. It is obvious, however, that if the wave lengths of the middle of the spectrum should continue to increase faster than the red and the violet, a condition would presently be attained in which the ordinate of the isotherm would be greater in the yellow or green than at either end of the spectrum. We see indications of the approach of this condition in the diagram of iso- chroms (Figure 19), from which it is evident that the curves for .65/i and .60/i would cut each other and would cut the curve for ,70ft at some tem- perature not far above 1400° ? whereas the isochroms for the shorter wave lengths would not be likely to cut the curves for the red until some much higher temperature had been reached. The curves in Figure 20 show the nature of this unexpected development of the spectrum in a somewhat different aspect. It will be seen from this figure that the growth in the extreme red so far lags behind that of the full red, and this in turn behind that of the orange, and this in turn behind that of the wave length .6^, that at 1400° the isotherm, instead of being convex to the base line throughout, actually becomes convex. 1 NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 109 have indicated by means of lighter lines the form of curve which might have been expected had the type of isotherm which exists at lower tem- peratures been maintained. Ahove 1400° it was found impossible to obtain consistent readings on account of the rapid disintegration of the carbon rods ; but I was ahle to satisfy myself after repeated trials that at temperatures not far above 1500° this change in the character of the isotherms had progressed to the y^O fac^~ /3oo° lOoa" 9oom 9- FlGURE 20. /A point at which the yellow regions of the spectrum possess an ordinate greater than that of the extreme red or of the blue or violet. At a tem- 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 Maine. There is no reason to suppose that 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. Spectrophotometric Measurements upon Rods with Treated Surfaces. In order to compare the radiation of rods of black surface with those the surfaces of which 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 vapor was allowed to enter until the atmosphere surrounding the rod was saturated. The Figure 21. rod was then brought several times to a high 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 the 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 thought that as the result of this treatment the carbon rods 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 ol / i •/ -^ • /¥Q / / 1 1 1 / 1 J / / t © /Fff Vj : i /CO t 1 :/ / t 1 1 1 1 1 / i $ / / / 60 i / / / / f ,.--"»"■ • S / / • / s r / ,'' ;3K D -2.0 • 9j S S * f •>•-' * * • -""■ ~ " = -::: ^~~~' IIOS° -• ,t>IL .6 ii. Figure 22. ./ ix 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 1400° 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 the 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 results. It will be seen that in this case, as in that of the untreated carbon, the concavity of the curve between .6^ and the red end of the spectrum is well marked at 1365° ; and that at 1515° there was a well-pronounced maximum at about .65^. 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 form 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 that used in the 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 (Figure 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 decree of incan- descence, would at least enable us to confirm the existence of the remarkable phenomenon brought 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 filaments, 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 students of radiation have of late years 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 length and temperature. The equation reached from quite different points of view by Wien * and by Planck, f /= Cl A-5 e-Ar' in particular, has been the subject of exhaustive discussion and of experimental tests. To this end Paschen $ 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/t to 0.7(«. Luiumer and Pringsheim § made similar determinations upon the ideal black hotly, and Lummer and Jahnke || finally repeated these measure- ments in the case of the black body and of platinum. Wanner,! 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 7= -vi — y» y> in which yi = log ( We see also that $„_g is a triple spread on *S',i_1 ; Killing calls it doubly stationary. Finally, St is an (ft — l)-tuple curve on £„_! ; it is a multiple curve on all the other spreads of the system. J If the equation A = 0 contains k arbitrary parameters connected by k — 1 equations <£ = 0, x = 0, ^ = o, * Killing, Nicht-Euklidische Raumformen, p. 195 et seq. t Puchta calls the S„—i the most general developable spread in w-fold space. Puchta, Ueber die allgemeinsten abwickelbaren Riiume, ein Beitrag zur mehrdi- mensionalen Geometric Wien. Berichte, CI. % Killing, loc. cit. MORENO. — ON RULED LOCI IN 71-FOLD SPACE. 123 we can, theoretically, solve these equations for k — 1 of the parameters in terms of the remaining one, so that this case is the same as the previ- ous one. The actual elimination may be avoided. Let the parameters be A, fjL, .... v. Differentiate totally all the equations, 9 A 9A^ JAr1 -7TT- « A + -pr- dfl + a A 9 9 v 4> dv = 0 d\ + ^dfJL + + -^ dv = 0 From these we may eliminate the differentials, 9 A 9 A 9 A B = 9 A 9 (i 9 9 9 A 9 (i 9 v 9 I 9 v 9 i[/ 9 ^ c/A 9 [i 9 $ 9 v = 0 This is the equation of an (n — l)-flat. The equation involves k parameters but they are connected by k — 1 equations. Two consecutive (n — l)-flats of the system intersect in an (n — 2)-flat whose equations are A = 0, B = 0. Three consecutive (re — l)-flats of the system intersect in the (re — 3)- flat, A = 0, B = 0, C=0, where 0 is the determinant B, with A replaced by B. The equation of the £„_! is found by eliminating the parameters between the equations of the (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. Mutual relations of connected loci. Let us consider more in detail these connected loci. We will use Fk to denote a &-flat of the 1-fold infinite system of £-flats. Two consecu- 124 PROCEEDINGS OF THE AMERICAN ACADEMY. rive i'Vi's intersect in an Fn_s, three in an Fn_3, r in an Fn_r, n — 2 in an F.2 or plane, n — 1 in an F1 or line, n in an F0 or point. There is a 1-fold infinite system of these i^,_2's which are generators of £„_!, a 1-fold infinite system of Fn_3s, generators of Sn_2, a 1-fold infinite system of lines generators of S2, the developable surface. Through any Fn_2 there pass two consecutive F^s, through any F„_3 there pass three consecutive -F„_i's, through any F0, n consecutive F^s. Tlirough any Fn_z there pass two consecutive F„_2's, through any F„_4 there pass two consecutive -Fn_3's and three consecutive F„_2S,&nd 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 Fu through any three consecutive points an osculating plane, an F2, through any four consecutive points an osculating 3-flat, an F3, through any n — consecutive points an osculating (n — l)-flat, an Fn_v* 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 h + 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 ra.f This theorem has been generalized by Veronese.^ Let us consider any curve in n-foh\ space whose equations are, 0 = 0, x = 0, . . . . if, = 03 a restricted system equivalent to n — 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, . . . . ip' = o,§ * We shall say a /t-flat osculates a curve if it contains k + 1 consecutive points of it. Killing, loc. cit. t Clifford, Classification of Loci; Mathematical Papers, pp. 305-331. i Veronese, Behandlung der projectivischen Verhaltnisse der Baume von ver- schiedenen Dimensionen durch das Princip des Projicirens und Schneidens, Mathematische Annalen XIX. § , y', . . . v>), etc. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 125 a restricted system equivalent to n — 1 independent equations. "We have then the case of an (n — l)-flat whose equation involves n para- meters connected by n — 1 independent relations ; this is equivalent to the case of a single equation containing one arbitrary parameter. We may, in general, consider the system of developables as given by an (» — l)-flat whose equation contains a single arbitrary parameter or k parameters connected by k — 1 equations.* 3. The tangent (n — \)-flats that are common to n — 1 (n — V)-spreads envelop a developable. The equation in homogeneous coordinates of any (n — l)-fiat may be written x = ay-\-j3z-\-....J!-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 (n — 1) -flats represented by it envelop a developable. The tangent (n — l)-flat at any non-singular point of a developable S,^ contains the generating Fn_2 through that point and touches the *S'„_1 all over this flat, t We may speak of this developable Sn_! as enveloped by its tangent i^-i's. If then we impose on an arbitrary (n — l)-flat any conditions that give rise to n — 1 independent equations between the coefficients in its equation, the (n — l)-flat will envelop a developable Sn_i. Let IT= 0 be the equation of an (n — 1) -spread. The equation of the tangent (n — l)-flat at any ordinary point P' is 9U< 3U> 9U> A If we impose on the equation of the arbitrary (n — 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[ 9U< 9 x' = 9 y' = . . . . 9 w' — la y From these equations by means of the equation W = Q, * Salmon, Geometry of Three Dimensions, p. 286. t Killing, loc. cit. 126 PROCEEDINGS OF THE AMERICAN ACADEMY. we may eliminate the coordinates of P' leaving a single equation in a, (5, .... y. For an (n — l)-flat to be tangent to an (?i — l)-spread, one relation between the coefficients that enter into their equations must be satisfied. We conclude then that the (n — l)-flats that touch n — 1 (n — l)-spreads envelop an Sn_1. Let us consider only those tangent (n — l)-flats to an (n — 1)- spread that touch it at the point of an (n — 2) -spread that lies on it. Let £7=0 be the equation of the (n — l)-spread and let U=0, V=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 9U' 9 IP 9U' 9x' =. 9 y' = . . . . 9 to' — la y and IP = 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, (3, ... y. For an (n — 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„-v 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 cr other (n — l)-flats, where n — 1 = 2 p -\- cr, 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 imposes three con- ditions on the coefficients that enter into the equation of the (w — l)-flat. To be tangent to the (n — l)-flat at a point of an (n — 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 {n — 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 — &) -spreads that lie one MORENO. — ON RULED LOCI IN W-FOLD SPACE. 127 on each, tangent to o- (n — l)-spreads at points of cr (n — k -f l)-spreads 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 n — 1 = k. p + (k — 1) o- + •••• + 2 t + v, envelop a developable Sn_v 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 devehpables ; sections. Other properties of an Sn_x 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^n-j's to the Sn_v 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 Fn_x of the system meets its consecutive F„-\ in a definite Fn_2, a generator of Sn_t whose equations are, „ = o,fi = <, Any three consecutive i^-^s meet in a definite Fn_z, a generator of *^„_2, whose equations are, . 9 A PA . A==0>9X=°>W=0- Any n — 1 consecutive 2?TB_1's meet in a definite line Fx, a generator of $2, whose equations are, . n 9A 9->A ^ = 0,_=:0,. ..^=0- Finally, any n consecutive i^_1's meet in a definite point of the curve of regression of S2. The equations of the F0 are, . . 9A 9^A * Salmon, Geometry of Three Dimensions, p. 547. t Salmon, Geometry of Three Dimensions, p. 289 et seq. 128 PROCEEDINGS OP THE AMERICAN ACADEMY. In general n + 1 consecutive Fn_^s do not have any common inter- section, for the n + 1 equations, have no common solutions. If we regard these equations as homo- geneous in the n -f 1 coordinates we may form their resultant, and the values of the parameter that cause this determinant to vanish, give special points where n + 1 consecutive F^s intersect. These points are cusps on the curve Si. Reciprocally there will, in general, be a finite number of Fn_^a that go through n + 1 consecutive points of S^ Veronese has shown that a curve in n-fold space has 3 n singularities which are connected by 3 (n — 1) relations, an extension of the Pluecker- Cayleyan characteristics of a twisted curve in three-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 n + 1 independent linear functions of the variables alone. If they could be expressed in terms of v such linear functions, where v < n, the developable »Sn_1 is a conoid with an (n — v)-way head, a case to be con- sidered later. The developable Skoi the series is ruled by (k — l)-flats, Fk_r'a. The Su, where 2 < k ^ n — 1 can be given by means of its enveloping Fk whose equations involve a single parameter. The n — k equations of the Fk must however be of the form , n 9A n dn~k~xA n as we have previously seen. Even the Sx may be represented in this manner. Any (n — l)-flat B = 0 cuts the £„_, in a developable (n — 2)-spread, for it cuts the system of Fn_i& 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 (?i — 2)-spread in a new (n — l)-fold space. The (n — l)-flat cuts any Sk of the system in a (i — l)-way * Veronese, Ioc. cit. ; Killing, loc. cit. p. 197 et seq. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 129 developable. In general any r-flat where r > n — k + 1 cuts any Sk in a developable (k + r — w)-spread. Any Fn_x of the system cuts the Sn_x in an (ft — 2) -spread, and the Fn_2 that it has in common with the consecutive Fn_l appears twice in the intersection, so that the proper (ft — 2)-spread is of order less by two than the order of Sn_v This (ft — 2)-spread is also a developable. An Fn_o is met by the consecutive Fn_2 in an Fn_^ ; it is met by any other Fn_2 in an (n — 4)-flat. In general, where 4 < n, there are a 2-fold infinite system of these (ft — 4)-flats and their locus is an (n — 2)- spread which is a double spread on Sn_v In the case of cones and conoids this double spread may be of fewer than n — 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 S,^ consists in general of two parts, Sn_2 and 2„_2, where 2„_2 is the locus of the 2-fold infinite system of (ft — 4)-flats arising from the intersection of non-consecutive F^s, while Sn_2 is the locus of the 1-fold infinite system of (ft — 3)-flats arising from the intersection of consecutive F„_2s. Any three non-consecutive Fn_2s 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 Sn_2. Any (ft — G)-flat is the intersection of three (ft — 4)-flats of 2„_2 and any such (n — 4)-flat con- tains a 1-fold infinite system of such (ft — 6)-flats. This 1-fold infinite system of (ft — 6)-flats does not, in general, fill out the (ft — 4)-flat, for this would require a 1-fold infinite system of them. The total triple spread on S,,^ consists in general of two parts *S,(_3 and 2„_3 where 2„_o is the locus of the 3-fold infinite system of (ft — 6)-flats. We can supply, a similar mode of reasoning to the spreads of higher multiplicities on Sn_v The spreads Sn_2, Sn^, . . . are developable, but 2„_2, 2„_^, . . . arc 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 (« — l)-flat, a tm + mb r-1 + i m (m — 1 ) c P~\ -f . . . . = 0, 9 130 PROCEEDINGS OF 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 F^s intersect in the Fn_2, ar-i+ (m _ j) br-2+ O-1) ' |m~2)cr-8+ . . . . + e = 0, - 1 bfa~1+ (m — 1) ctm~2+ . . . + et +f= 0. The elimination of the parameter from these equations gives the equa- tion of Sn_v The result is the discriminant of the original equation placed equal to zero ; the order of *S'„_1 is then 2 (m — 1).* Three consecutive Fn_^s intersect in the Fn_& a r~2 + (m — 2)b tm-3 +.... = 0, btm~2 + (m — 2) c tm-' +.... + 0 = 0, ctm~2+ + et +/= 0. The equations of Sn_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 Sn_2 is 3 (m- 2).f Similarly k consecutive Fn_^s intersect in the Fk, given by the k equations, a fn-*+i + (m — k+ 1) b tm~k +....= 0 b r-&+1 + (m — h + 1) c r~* +.... = 0 + 0*+/=O. The elimination of the parameter from these equations gives a restricted system equivalent to k — 1 independent equations, the equa- tions of Sn_k+y The order of Sn_k+l is seen to be (k + 1) (m — k). Lastly the intersection of n consecutive Fn_^s is the point, F0, given by the equations, a r-"+1 + (m — n + l)b tm'n +.... = 0 b r-n+1 + (m — ii+l)c tm~n +.... = 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 elimination of the parameter from these equations gives a re- stricted system equivalent to n — 1 independent equations, the equation of Sx whose order is n (m — n -f 1). We can find the equations of those exceptional points where n -f- 1 consecutive Fn_xs intersect in a point, if we eliminate the parameter from the n + 1 equations a tm~n + (m — n) bm~n-1 +.... = 0 b t"1-" + O — n) c'"-"-1 + .... = 0 + et + f=0. The result is a restricted system equivalent to n 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 (« + 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 tnat cause this resultant to vanish. These values of t give the special points in question.* Any double point on Sn_x must lie on two i^_2's. We may find the equations of the total double spread on £„_!, by expressing the conditions that the equations of an Fn_2 regarded as equations in the parameter, have two roots in common. These conditions are t a, (m - 1) b, i ^j '- c, (I) a, ('» - 1) 6, b, (m — 1) h, (m — \)e,f * 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 OP THE AMERICAN ACADEMY. where there are 2 (m ■— 2) rows and 2 m — 3 columns. This restricted system is of order | (2w — 3) (2 m — 4). The double spread repre- sented by these equations consists of two distinct parts, Sn_2 and 2n_2. The order of 2n_2 must be, J (2 m — 3) (2 m — 4) — 3 (m — 2) = 2 (m — 2) (m — 3). A triple point on Sn_i must lie on three Fn_2's. We may find the equa- tions of the total triple spread on Sn_1 by expressing the conditions that the equations of the Fn_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 (m — 3) rows and 2 m — 4 columns. The order of the restricted system is ~ (2 m - 4) (2 m-b) (2 m- 6). This triple spread consists of two distinct parts, Sn_3 and 2n_3. The order of 2„_3 must be 1 2 -^(2m-4) (2m-5)(2m-6)-4(m-3)=-(m-3)(m-4)(2m-l). o I o In like manner we can find the equations of the total &-tuple spread on Sn_u by expressing the conditions that the equations of the JFn_i have Jc 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 — h — 1 columns. This is a restricted system equivalent to k independent equations, of order -r~j (2 m — k — 1) (2 m — h — 2) . . . . (2 m — 2 k). This spread consists of two parts, Sn_k and %n_k\ the order of the latter is JL (2 m — k—\)(2m-k-2) (2 m — 2 k)- (k + 1) (m — k). The total (n — l)-tuple curve on #„_! is given by means of a restricted system similar to (I), in which, however, there are only 2 (m — n + 1) rows and 2 m — n columns. We have then a restricted system equiv- alent to n — 1 independent equations whose order is (2 m — n) (2 m - n — 1) . . . (2 m - 2 n + 2). (n - 1) MORENO. — ON RULED LOCI IN W-FOLD SPACE. 133 The order of the curve 2 is, — - (2 m — n) (2m — n — 1) (2 m-2n + 2) — n(m — n+ 1).* (n — 1)1 The equations of all the w-tuple points on Sn_x are given by means of a rectangular system similar to (I), in which, however, there are only 2 (jn — n) rows and 2 m — n — 1 columns. They form a restricted system equivalent to n independent equations, whose order is —. (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 m) ; n ! this is the number of w-tuple points. The number of the rc-tuple points other than the cusps on Sx, are — (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 n) — (n + 1) (w — n). These points necessarily lie on Si ; they are either n-tuple points on 2i, or else they are n-tuple points on the combined curves Si 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 Sx is n, and there are no cuspidal points on the curve ; this is the rational normal curve of Veronese. f The order of Sn_x in this case is 2 (n — 1) ; no developable Sn_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 < n, where p is an integer. Any p -\- 1 consecutive Fn_i& intersect in an Fn_p_i whose equations are . A 9 A n 9pA . If we use two homogeneous parameters X and /x instead of the single parameter t, these equations may be written * For n = 3, this result agrees with that in Salmon, Geometry of Three Dimen- sions, p. 296. t Veronese, loc. cit. 134 PROCEEDINGS OF THE AMERICAN ACADEMY. in which form the parameter do longer appears. Any p -f 1 consecutive i^_i's intersect in the same Fn_p_1 as any other consecutive p -f 1 ; i. e., all the -Fn_i's of the system contain the same Fn_p_x. Any p-flat that does not meet this Fn_p_l cuts S^_x in a developable (p — l)-spread of order 2 (p — 1). This developable (p — l)-spread of order 2 (p — 1) lying in a p-flat is exactly similar to the case in n-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 p-fold space, to all points of an (n — p — l)-flat that does not meet the p-flat that contains the (p — l)-spread. Sn_1 is a conoid of (n — 2)-flats with an (n — p — l)-way head. The generating Fn_2's of Sn_i arise from the junction of the (« — p — l)-way head with the generating (p — 2) -flats of the (p — 1) -spread. The generating Fn_s's of Sn_2 arise from the junction of the (n — p — l)-way head with the system of generating (p — 3)-flats of the (p — 2)-spread, and so on. Any conoid ruled by a 1-fold infinite system of c+ — o, /+(m-1)c + ("-1H°'-2)rf+.,.. = o. The points of intersection of three generators of the system are given by the equations MORENO. — ON RULED LOCI IN tt-FOLD SPACE. 135 (m-l) (m-2) e, (m — 1) d, c, e, (in — 1) of, Q - 1) Qi» - 2) /, (m — l)e, g- -f/, = 0. /, O - 1) «f • where there are 2 (m — 2) rows and 2 m — 2 columns For t = 0 we have the particular (n — 2)-flat e = 0,f=0. The next consecutive generator has for its equations, e + 8t . d= 0 f+8t.e=0 The intersection of the two consecutive generators is the (n — 3)-flat whose equations are e = 0, /= 0, d= 0. This Fn^ does not generally lie on the total triple spread for one of the equations of that system, namely (m — 1) (m — 2) c (m — 1) d, (m — 1) (m - 2) d, (m — 1) e, f, = 0. is not generally satisfied when the equations of the i^,_3 are satisfied. The points that satisfy both these systems of equations are evidently points on two consecutive generators and at the same time points on three generators. 136 PROCEEDINGS OF THE AMERICAN ACADEMY. If there is a linear relation between f, e, and d, then these two consec- utive generators intersect in an (n — 2)-flat, i. e., they are coincident and we have a stationary generator of the system. If then « = 0, /=0 is the equation of a stationary generator of the system. The equation of the developable Sn_i in this case is (— 1H—2), 2! /, 0, 0>d,(B>-l)(w-2)c 2! 0, d, 0, 0. "We see that / is a factor of the left member of this equation. When this factor is thrown out, the residual or proper developable is of a degree less by one than before. The orders of the multiple loci pre- viously given are also reduced, they only holding when there are no stationary ^_1,s in the system. By means of Veronese's formulae we see that when there are /3 stationary F„_,'s the order of the A-way developable is reduced from (m — X + 1) (m — n -\- X) to (?i — A -f- 1) (m — n + X) — (n — X) (3. 6. Tangent flats to a ^-spread where 2 < p. a. Definitions. We have treated up to this point the various developables that arise from a curve in ra-fold space. We shall show now that similar develop- ables do not arise from the consideration of the tangent flats of spreads of more than one way. MORENO. ON RULED LOCI IN W-FOLD SPACE. 137 Let £7=0 be the equation of an (n — 1) spread of order m. We shall use the points (1), (2), A (1) + fi (2) to denote the points whose coordinates are xx, yx, . . . wx, x2, y2, . . . w2, and \ xx -{- p x2, \yx -\- py., , . . ., Xwx -j- \iw2, respectively, so that A (1) + ft (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 U by Ux, and U2 respectively. We use the symbols ( 9 9 9 \ Tt A2 Ux = x, - h y, -, h • • • + »i n — Ux, V 9 Xi 9xx die J ( 9 9 9 \ A U = [x2 — + y2 7r- + . . . + w2 ^—) Uj \ a x 9 y dw) f 9 9 9 \ rT A U2=[X yr— + ^ h • . • + «> ^ Us, \ 9x2 9y2 9w2J (9 9 9 \k ^k2Ux~(x2^ h y2 ■= h • • • + «>2 s — tfi- \ 9xx J 9yx <9wv In the last case the operator is to be applied h times to f^. Now A (1) + /i (2) is a point on the line (12), if it is also a point of the (n — l)-spread, it must satisfy the equation of the spread. Substitute the coordinates of A (1) + p (2) in Z7and we have A"' Ux + A-1 M A2 Ux + ^T/i- A22 0i + . . . u"1 . . . + —. A2ra Ux = 0. m I The m values of A: /u that satisfy this equation determine the m points where the line (12) meets the (n — l)-spread. If the point (1) lies on the spread then t71==0. If the line (12) meets the spread twice at the point (1), then Ux = 0, A2 Ux = 0. 138 PROCEEDINGS OF THE AMERICAN ACADEMY. The equation of the locus of all the Hues that meet the spread twice at (1) is A Ux = 0. From the analogy of three-fold space, this locus of lines is called the tangent (n — l)-flat to the (n — 1) -spread, at the point (1).* At each point of an (n — l)-spread there is in general a unique tangent (n — 1)- flat. A ^-spread is given by the equations, V=0, W=Q, a restricted system equivalent to n — p independent equations. In a similar manner the equations of the locus of all lines that meet the jo-spread twice at any non-singular point (1) are, A Ux = 0, AV1=0) A Wl = 0, Since these equations are linear we may select any n — p that are inde- pendent and the rest are superfluous. t We have then a ^?-flat which from analogy is called the tangent p-flat to the p-spread at the point (1). At any point of a ^-spread there is in general a unique tangent p-fl&t.t We define a tangent r-flat at a given poiut of the jo-spread where r < p as an r-flat that Jies in the tangent />-flat at that point and con- tains the point. If r > p, we define a tangent r-flat at a given point as an r-flat that contains the tangent ;>flat at that point. The locus of tangent lines then to a ^-spread is simply the locus of tangent p-flats to the spread. The locus of tangent planes, 3-flats, ...,(/> — l)-flats is this same locus. If then there are developables that arise from a jo-spread, where 1 < p 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 p-spread. t 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 ^>-flats through two consecutive (p — l)-flats all have this same locus possihly of a certain multiplicity. b. Intersections of consecutive tangent flats. We shall show further that (p -f l)-flats cannot in general be passed through two consecutive tangent p-flats, for such p-^&ts do not in general have (p — 1) -flats in common. Tangent ^o-flats at consecutive points fi of a j9-spread where 1 < p < - do intersect in points at least. Let ft v=o, a restricted system equivalent to n — p independent equations be the equations of the p-spread. Let P' = (x1, y', . . . ) and P" = (xr + dx', y' + dy', . . . ) be consecutive points of the spread. The tangent jo-flats at these points are 9 x' 9 y' 9 V 9 V dx dy and A U" = A U< + x / 9 x 9 y' 9 V 9 V 9x' dy' and LW, = AU, + x(^dxl + J^LiW + . ..) + .. .. = <>, (9'2 V 92 V \ A V" = A V + x ~ dx> + ^-p^ dy' + ....+.... = 0 \9 x'~ 9 x' d y' I 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 V =0 U"= U' + ^jdx' + = 0, d x 9 V V" = V + %^dx> + = 0, dx From these three sets of equations we derive (92 U' 9'2 U' \ x[jx^ dx' + 9*9y-< dy' + ' ' ' 'J + * * • ' = °' (d2 V 92 V \ x\9^dx' + d*w?d* + • • • ■) +■ • • • = °' 9J^dx> + .... = 0, 9x' 9 V ?rTrfar' + .... = 0. dx' These four equations are homogeneous in the five differentials dx', d i/', . . . We may take one of these differentials to be zero and eliminate the other four. We have 142 PROCEEDINGS OF THE AMERICAN ACADEMY. 92U> ;^^ + y 9x12 92V X X 1 + 9 92W 9 x' 9 y' 92V> + 9x' 9y 9U' 9x> 9V< Jx1 7 + x X 92U< 9 x' 9 y' 92V 9 x' 9 y' 92U> 9y'2 92V> 9U> 9y> 9 V 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 PL This cone is intersected by the tangent plane at P' in a pair of straight lines which is the required locus. If a point x, y, . . . , 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 .&U> - A" U' . A V = 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 A U> = 0, A V = 0, and A2 U> = 0, A2 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 that arise by considering the junctions of the consecutive tangent flats. Consider now any surface in rc-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 ^-spread where 2 < p. Only in case the ©-spread lies in a (p + l)-flat do consecutive tangent p-flats intersect generally in (p — l)-flats; the only exception is in the case the w-spread is a curve. II. Loci derived from an (n — 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 - iu each equation. Let the equations of the flat be .4 = 0, .5=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 n + 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 (ti — l)-spread Sn_v which is ruled by the system of (n — 2)-flats, F n_2s.* Two consecutive Fn_2's intersect in an (?i — 4)-flat, whose equations are, ^ = 0,^ = 0^=0,^ = 0. 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 Fn_f&. Sn_s is a double spread on S^_x. Three consecutive Fn_2's intersect in an (ti — G)-flat Fn_6, whose equa- tions are, . 9 A 9" A A = °>-9^ = °> 9X>=°> 9B_ 9*B_ If we elimiuate 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 F„^s. Sn_5 is a triple spread on Sn_1 and a double spread on Sn_s . Similarly r consecutive FH_2s intersect in an (n — 2 r)-flat Fn_2r, whose equations are, A A 5 A A 9r~1A A „ A 9B A 9r-xB A On the elimination of the parameter we derive a restricted system equiv- alent to 2 r — 1 independent equations. The locus is an (« — 2 r + 1)- spread, Sn_2r + V ruled by the Fn_2r,s. S„_2r + i is an r-tuple spread on aS^j ; 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 Fn_2s intersect in a line, F1} whose equations are, * From now on we shall use Sk to denote the ^-spread of this system. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 145 . . 9 A 9^'A n ^ = 0,^ = 0,.. .-==,= 0, B ft 3B-a ^B ft B-0'ax-0'---s-T¥-°- If we eliminate the parameter from these equations we derive a restricted system equivalent to n — 2 independent equations. The locus is a surface S2 ruled by the Fx's ; it is an ( — - — j-tuple surface on aS^. Consecutive i^'s do not in general intersect for the n -\- 1 equations 0, ^ = o,|i = o;. n— 1 9'*'A 9\2 B=0,3,f=0,. a A n—l 9* B a— i 5 A"2" o, have not in general any common solutions. If we regard these n -f 1 equations as homogeneous in the n + 1 coordinates and form their result- aut, 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 S2 and ( — - — j-tuple points on Sn_x. If n is even then — consecutive Fn_2'$ intersect in a point F0, whose equations are, . n 9 A 9**A A A = 0, -=- = 0, . . . , — -j= 0, 2a 5 A" n=2 2" 5 = 0,^ = 0,. ..,^=0. ° A 9 A 2- The elimination of the parameter from these equations gives a restricted system equivalent to n — 1 independent equations. The locus is a curve 10 146 PROCEEDINGS OF THE AMERICAN ACADEMY. Si, which is an [ - J-tuple curve on Sn_i. There are not in general sta- tionary points on >$i, for the n + 2 equations n+l .9 A 9'2'A A = 0, ^— = 0, . . . , — ^r= 0, pass Fn_2s ; these Fn_2s generate an (n — l)-spread Sn_i. If we start with the system of (n — 2)-flats we come down finally to the surface, or starting with the surface we may work back to the system of (ti — 2)-flats. If n is even, through any Fn_± pass two consecutive Fn_2s, through any 71 Fn_2r pass r consecutive Fn_2s, through any F0 pass - consecutive F^_2s. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 147 Any Fn_o contains two consecutive F„_4's, three consecutive i^„_6's> o con- secutive FqS. Any F„__2r contains two consecutive -^fTn_2(r+i)'s and any two consecutive I,n_2r,s determine one FH_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 Si do not determine uniquely a plane of the system. The i'Vs of the system in general intersect consecutively in the points of Sv Starting with such a system of planes we may retrace our steps. Through any two consecutive planes of the Sa we may pass a four-flat. These four-flats are generators of S5. Through any two consecutive B^s we may pass six-flats ; they are the generators of S7. Finally through any two consecutive i^_4's pass (n — 2)-flats ; they are generators of Sn_t. We may retrace our steps only in case we do not begin with Sv 9. Director curves of the ruled (n — \)-spread. Let the equation of such a ruled (n — l)-spread Sn_x be 0 = 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 (?i — 2)-rlat in n-fold space may be written x = ax z + fix «+.... + 71 w y — a2 z + /?2 s + . . . . + 72 w- In this form the equations of the (n — 2)-flat, which we may call the (n — 2)-flat AB, involve 2 {n — 1) independent arbitrary parameters. These parameters must be connected by 2 (n — 1) — 1 equation to make A B a generator of such an (n — 1) -spread. We wish to connect these parameters in such a way that A B will be a generator of the Sn_i in question. The equations of a curve on <£ are <£ = 0, Ui = 0, u2 = o,... un_2=o. If we eliminate the coordinates between these equations and the equa- tions of A B we derive a single equation in the 2 (n — 1) 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 (n — 1) — 1 curves on . If from these 2 (n — 1) — 1 equations and the equations of A B 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 . 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 <£. This is the case in three-fold space. The spreads U^ U2, . . . Un_2 may in each case be taken to be flats ; then the director curves are plane curves. These are the director curves of <£; 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 w-fold 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 surface. 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 intersect 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 — V)-spread. Any generator of the (ii — l)-spread is an (n — 2)-flat Fn_2\ it is met by any other generating Fn_2 in an (n — 4)-flat. If then 4 < n 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 Fn_2 contains a single infinity of (n — 4)-flats where it is met by the other Fn_2s. These are evidently double flats on &„_!• On &„_! there are in general a 2-fold infinite system of such (n — 4)-flats constituting a double (?i — 2)-spread, 2„_2 on Sn_x. In general, then, any (n — l)-spread Sn_x ruled by (n — 2)-flats Fn_2s 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^s that arise from the intersec- tion of consecutive i^,_2's- These i^./s generate Sn_s, which therefore lies on 2n_2 and forms but an infinitesimal part of it. Any three Fn_2s intersect in an (n — 6)-flat; there are in general a 3-fold infinite system of such (n — 6) -flats constituting an (?i — 3)- * Salmon, Geometry of Three Dimensions, p. 427. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 149 spread 2„_3, a triple spread on S,^. Sn_5 lies on 2„_3, and constitutes but an infinitesimal part of it. If n is sufficiently great there is a quad- ruple (n — 4) -spread 2„_4 ruled by the 4-fold infinite system of (n — 8)- fhits arising from the intersections of four Fn_2's. Sa_7 lies on Sn_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 f — - — j-tuple ( — - — )- spread ruled by the f — - — Wold infinite system of lines that arise from n — 1 the intersection of — - — generating i^4_2's. There may be further an ( — - — j-tuple ( — - — j-spread made up of the ( — - — j-fold infinite system of points that are the intersection of — - — generating F^s, an fn + 3\ , fn — 3\ , , , , n — 3 , , , . „ . I — - — j-tuple I — - — j-spread made up of the — - — fold infinite system of points that are the intersections of — - — generating -F„_2's, etc., but these spreads do not always occur. In special cases the 2„_2, or some component of it, may be of greater multiplicity than — - — • M 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 Sn^ lies on 2„_2. In 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 2n that is made up of the ( - j-fold infinite system of points that n arise from the intersection of - generating Fn_.?s. There may be an I - + 1 j-tuple f - — 1 j-spread 2„ whose points are points of inter- section of - + 1 generating i^,_2's, an ( - + 2 j-tuple ( - — 2 j-spread n 2n whose points are points of intersection of - + 2 generating Fn_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 Fn_2 be A = a tl + b t1'1 + c tl~2 + = 0, B = a' r + b' r_1 + c> r~2 + .... = o, 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 £„_! ruled by the -F„_2's ; it is of order I -\- m. It is more convenient in what follows to use two param- eters, A and fx, that enter homogeneously into the equations. Two consecutive generators intersect in the Fn_4 whose equations are 9 X 9 jx 9 X 9 /x The elimination of the parameter from these equations gives a re- stricted system equivalent to three independent equations the locus is £n_3, whose order is 2 {I— 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 Fn_2's is a locus of F„_e's ; the equations of this locus are found by eliminating the parameters from the equations, 3"-A 0^L_03M_0 ix a [x 9 A2 ' ' 9X9fx ' 9r2 92B _ 92B 92 B _ 9X2 ~ ' 9\9fi~ ' 9fx2 ~ This gives a restricted system equivalent to five independent equations ; it represents Sn_s, whose order is 3 (I + m — 4). The r-tuple spread Sn_2r+i on £„_! is represented by the equations that result from eliminating the parameters from the equations, 9" A r*A 3^ ir-1 — U> CI vr-2 Cl .. — U' * • * ' O ..r-1 U> 9X"'1 " ' 9kr~29fx ' ' * "'5 /• 9r~'B 9r^B 9r~1]3-o 9X^ ~ ' 9xr~29,x - u' • • • ' ^ " MORENO. — ON RULED LOCI IN W-FOLD SPACE. 151 The equations then are of Sn_or+1 form a restricted system equivalent to 2 r — 1 independent equations whose order is r (/ -f- m — 2r + 2). As we have seen, there are two cases according as n is odd or even. If n is odd we come down finally to an f — - — J-tuple surface S. The equations of S2 are found by eliminating the parameters from the equations n-3 n-3 n-3 9~*'A_ 9'*' A 9~*'A n=3 — ^' n-5 — O, . . . , n_3 — 0, 9X'2' QK'V'Qfi d/ir n-3 n-3 n-3 n-3 — ^, n-S — "»•••} n-3 — 0. 2 A"2"" , 9\'* dp 9fiY The equations of $2 form a restricted system equivalent to n — 2 inde- n — 1 pendent equations, whose order is — - — (I + m — n 4-3). Li There are also f — — J-tuple points jP0's on Sn_u though in general n 4- 1 — - — consecutive Fn^2's do not intersect. If we form the resultant of the n -f- 1 equations n-l n— 1 52~J rt 9^'A —^i = 0, — ^ = 0, . 3 A 2 9 k 2 9 ft n—l n—1 5A.2 3 A. 2 5 //. n-l J w-l - = 0, n-l 9'^ B 3/x 2 = 0, we have a determinant of the (w + l)-st order, in which the parame- ters e n + 1 n 4- 1 ters enter to the degree — — — (l 4- m — n -\- 1). There are then (I + m — n -\- 1) valujs of the parameters that cause this Ld determinant to vanish, and so this is the number of points F0. We can find the equations of these points by eliminating the parame- ters from these «4 1 equations. The result is a restricted system equivalent to ii independent equations. The order of the system is ii 4- 1 — - — (I 4- m — ii 4- 1). This is another proof of the number of points F0 on Sn_i. 152 PROCEEDINGS OF THE AMERICAN ACADEMY. In case n is even we have finally the f — J-tuple curve whose equations are found by eliminating the parameters from the equations, n-2 3-~ A n-2 — 2 A"2 n-2 9^'A o» -^— = o, . 9\2'9/x n-2 ST A • • 5 n-2 — UJ 5 fX.'2 n-2 9^'B n-2 9 k2' n 9^' B o, n< = o, . 5a2 9 /ji. n-2 9 ft 2 « The order of the restricted system is - (I + m — n + 2), the order of 8V. We find the equation of the double spread 2„_2 on *S'„_1, by imposing on the equations of the generating Fn_2 the conditions that they have two common roots in the parameter. These conditions are,* a, b, c =0 b, .... (") a, a' b', e', < V, where there are I -\- m — 2 rows and I -\- m — \ columns. This is a restricted system equivalent to two independent equations ; the order of the system is \ (J + m — 1) (I -\- m — 2). On 2„_2 must be Sn_o. We find the equations of 2„_g 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 I + m — 4 rows and / + m — 2 columns. This restricted system is equivalent to three independent equations, and its order is \ (I + m — 2) (/ + m -3) (1+ m — 4). The equations of 2„_r 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 -\- m — (r — 1) columns. This is a restricted system equiva- * Salmon, Higher Algebra, Art. 275. tlbid., Art. 285. MORENO. — ON RULED LOCI IN W-FOLD SPACE. 153 lent to r independent equations, the order of the system is — - (I + m — r ! r + 1) (Z + m — r) . . . . (Z -f m — 2 r -f- 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 (n — 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 (n — 2) rows and I + m — (n — 2) columns. The order of this system is — V ; * (n - 1)1 (Z+ m — n + 2) (Z + m — n + 1) . . . . (I + m — 2 n + 4). This curve has M-tuple points on it whose equations are fouud by expressing the con- ditions that the equations of the generating (n — 2)-flat have n roots in common. We again have a restricted system of the same form as (II), in which, however, there are I -\- m — 2 (« — 1) rows and I -f- m — n + 1 columns. The order of this system is — - (I -\- m — n -\- 1) (I + m — n) . . . . (I + m . 2 n + 2), which is the number of points in question. For 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 one of the equations of the generating (n — 2)-flat. Let the equations of the flat be A = a t + b = 0, B = a' tm + V r-1 + . . . . = 0, where we make the same suppositions regarding a, b, a', b', . . . , as before. The Sa_t in this case is a ruled spread with m sheets through the (n — 2)-flat, whose equations are a = 0, b = 0 ; it has no other multiple locus on it at all. Consecutive generating -F„_2's of the system intersect in the flat, whose equations are, 9 B a = Q,b = 0,B= 0, V- = 0. at All the F^s of the system lie in the same (« — 2)-flat ; they generate a developable (n — 3)-spread «S'„_3 in this flat. S'n^> is the section by this flat of the developable (n — l)-spread enveloped by the (n — l)-fl;it B. Consecutive generating F^'a of Sn^ intersect in generating -F„_4's of * Salmon, Geometry of Three Dimensions, p. 428. 154 PROCEEDINGS OF THE AMERICAN ACADEMY. ff=o> case we come This gives a restricted system equivalent to r k — I independent equa- tions. The locus is an (n — rk -f l)-spread ruled by the Ftl_rk%, it is an r-tuple spread on Sn_k+1. There are k cases according as n = 0 (mod k), n = 1 (mod £), . . . , n = k — 1 (mod k). In the first case we come finally to a curve St which is an ( y- j-tuple curve on S„_k+l. In the second down finally to a system of lines F^s which are generators of a ruled surface S2. In the last case we come down finally to a ^-spread ruled by (k — l)-flats. There are on Sk in general special points where two con- secutive Fk_i's intersect. 13. Multiple loci on the spread; mutual relations of the system of spreads. Sn-k+\ nas on it m general multiple loci that arise from the intersection of non-consecutive Fn_ks. Any Fn_k intersects every other Fn_k in an (n — 2 £)-flat ; there is in general a 2-fold infinite system of such (« — 2 £)-flats constituting a double (n — 2 k + 2)-spread 2„_24+2 on Sn-k+i- Evidently Sn_2k+1 lies on 2n_2fcf2- Any three Fn_k'B intersect in an (n — 3 £)-flat ; there is a 3-fold infinite system of such (n — 3 k)- flats, they constitute in general a triple (n — 3 k + 3)-spread 2n_3A.+3 on 'S'n-A+i- Sn_Sk+1 nes on %n-sw Any r consecutive Fn_k's intersect in an (n — r k)-i\at ; there is an r-fold infinite system of such (n — r£)-flats in general, constituting an r-tuple (n — r k + r)-spread 2„_rjbfr on S„_k+U on which lies Sa^rk+V Finally the locus of the intersection of any a Fn_k's where a is the n greatest integer in T is an a-tuple [n — a (k — l)]-spread ln_a ll_1) on n^^- there are in general no double points on the locus. If there enter into the equations of the generating (n — £)-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 Fn_k's intersect in an Fn^2k while through any Fn__<2k pass two consecutive F„_^a. Any three consecutive Fn_ks intersect in an Fn^,k while through any F„_ok pass two consecutive Fn_2ks and three consecutive Fn_ks. Any two consecutive Fn_rks determine in general one Fll_k(r_l). An exception may occur if r = a the greatest n integer in -=• • Thus, if n = 0 ^mod k), two consecutive points of ^ do rC not determine a (k + l)-flat where 2 < k. If n = 1 (mod k), two consecutive lines of S-2 do not determine a (k + l)-flat, except in the case k — 2. In the last case, however, where n EE k — 1 (mod k), two non-intersecting (k — l)-flats do determine a (2 k — 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 = ai s + & t + . . . . + yx w, y = a2 * + (3o t + . . . . -f y2 w, z = akS + (3kt +.... + ykW. In this form the equations of the flat contain k (n — k -f 1) independent parameters. These parameters must be connected hy k(n — k + 1)— 1 equations for this (n — £)-flat to be a generator of such a ruled (n — k -f- l)-spread. Any curve is given by the equations MORENO. — ON RULED LOCI IN W-FOLD SPACE. 157 x = °, • t • • a restricted system equivalent to n — 1 independent equations. If we eliminate the coordinates between the equations of the flat and curve, we derive a restricted system equivalent to k — 1 independent equations in the parameters alone. These are the conditions that must be satisfied for the (n — &)-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 the (n — &)-flat to meet a certain ^-spread where 1 < p < k — 1. We may have then curves, surfaces, . . . , or ^-spreads where 1 < jt> < & — 1 for the director loci of a ruled (« — k + l)-spread. The numbers of loci of each kind that must be taken are A, p., ... v, p, namely, non-negative integers chosen to satisfy the equation A (k — 1) + ix (k — 2) + . . . . + v . 2 + p ■ 1 = k (n — k + 1) — 1. 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 + A (k — 1) + . . . . + p ■ 1 = k (n — k + 1) — 1. We may apply this to special cases. The director loci of a ruled surface 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 Sn_k+1, 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 Sn_k+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 paper. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVU. No. 6. — September, 1901. THE ARC SPECTRUM OF HYDROGEN. By O. II. Basquin With Two Plates. Investigations on Light and Heat made and published wholly oe in part with Appropriations FROM THE RllMFORD FUND. THE ARC SPECTRUM OF HYDROGEN. By O. H. Basquix. Presented by C. R. Cross. Received June 8, 1901. The Problem. The arc spectra of those elements which are gases at ordinary tem- peratures and pressures have not been extensively studied. Their spark spectra, however, are easily obtained, and were among the first to be in- vestigated. The general impression prevails, therefore, that these ele- ments do not possess arc spectra. On the other hand practically all the so-called "hot stars" and all the "new stars" possess the more impor- tant lines of the hydrogen spectrum. Although our knowledge of what is going on in the arc and in the spark is very crude and unsatisfactory, yet it is, to the average mind, much easier to imagine a star as being in a condition similiar to that of the arc, rather than in one similar to that of the electric spark. It has seemed worth while, therefore, to search for the more important lines of hydrogen in the arc spectrum. This is the problem of the following investigation. Historical. Liveing and Dewar* examined the carbon arc in an atmosphere of hydrogen and saw "the fairly bright" C line of hydrogen, also "a faiut diffuse band " at the position of the F line of hydrogen. They obtained these two lines also by allowing small drops of water to fall into the arc in air.f They found the F line usually obscured by continuous spectrum, becoming visible at intervals only, when, from some variation in the work- ing of the arc, the continuous spectrum was less brilliant. Crew and Basquin t incidentally noticed these two lines of hydrogen while work- ing with the rotating metallic arc in an atmosphere of this gas. * Proc. Roy. Society, 30, 156 (1880). t Ibid., 35, 75 (1883). t Proc. Amer. Acad., 33, 18 (1898). VOL. XXXVII. 11 162 PROCEEDINGS OF THE AMERICAN ACADEMY. Apparatus. In searching for these lines I have employed the rotating metallic arc » wh"h s'one to nse chemically pnre electrodes having httle or no rhemical reaction with the gas employed. In this arc, then, one my exne the gas to give off its characteristic radiations with greater m- ensi v han "n one where the gas may enter into chemtcal compounds W re a temperatnre is reached at which it becomes lum.nou. Tins ar enables one also to select snch metals as do not have strong hues m the neighborhood of the lines sought for, while in the spectrum of the carbon arc there arc few spaces not already ocenpied by lines of carbon or of an Tie rotating arc, one electrode, either a disc or a rod of meUjl rotates npon an axis, making abont 700 rotations per minute, while the o her electrode has a slow movement of translation toward U-».. f rotation The rotation not only prevents the excessive heating and weTdtng together of the electrodes, bat it throws the hot gases to one Tide o° thai the arc has the appearance of a small fan. The part of the tne tl separated from the poles is very free from continuous SPTnTe apparatus used in these experiments the arc is enclosed in a brass box or ■ « hood," having a volume of about 1* litres and being corn- el ivly .as-tight. The light from the arc issues through a long bras LTdosed with a lens at the outer end ; the lens thus forms part of the S of the hood, but is so far removed from the arc that it receives »m- parativel, little of the deposit sometimes formed inside the hood, and hence remains clean. lnnT,0[! -f _t A stream of gas enters the hood at one stop-cock and leaves ,t at another- a third cock is provided for nttachment to a manometer A - 1th the hood is not absolutely gas-tight, the purity of the gas inside preserved in these experiments, partly by the small excess of pres- Tre i id tie hood above that outside, and partly by the fresh supply of ;ue gas constantly running through the hood. The hydrogen used w generated electrolytically, and varied in quantity from 10 to lo hues ^ThTspectra have been examined both visually and P»bical,y by means of a small plane grating spectroscope and by means of a large concave grating spectroscope. * Crew and Tatnall, Phil. Mag., 38, 379 (1894). BASQUIN. — THE ARC SPECTRUM OP HYDROGEN. 163 Observations of Hydrogen Lines. The arc spectra of the following metals in hydrogen have been ex- amined : Aluminium, copper, magnesium, coin-silver, sodium, tin, and zinc. With the exception of sodium the arc of each metal shows to the eye very clearly the Ha and ILj lines of hydrogen, and in most of them the H? line comes out with the small instrument very clearly, and in- distinctly with the large one. The H5 line shows only rarely, and then to the eye rather indistinctly. The IIa line is quite sharp and well de- fined, unless the electric current through the arc is unusually great ; it has much the same appearance as the zinc line at 6363. The other three are always broad, hazy, and ill-defined. On the photographs taken with the large spectroscope H^ and IIV usually show very plainly, always excepting the spectrum of metallic sodium, while H5 shows in spectra of tin, silver, and copper. On photographs taken with the small spectroscope -these lines show more sharply, on account of the very much smaller dispersion, and the photo- graphs of tin show the next hydrogen line, He quite clearly. Not hav- ing found the hydrogen lines in the metallic sodium arc (using copper as stationary electrode), I tried it in dry hydrogen also, thinking that in some way the water vapor might have affected the appearance of the hydrogen lines, but I have been unable to detect any of the hydrogen lines in that arc in any way. None of these lines excepting Ha is sharply defined. A wide space in the middle of each line has fairly uniform intensity, shading off gradu- ally and uniformly to each side. The following table gives a rough estimate of widths, in Angstrom units, of these lines as they appear on the photographic plates, the middle of the shading being taken as the edfre of the line. Line. Ha Hy Hs IIe faint, same general width. It will be noticed that these lines, with the exception of TTai are exces- sively wide, and I think it is for this reason alone that I have been unable to photograph the still weaker hydrogen lines of Balmer's series. imum width. Minimum width. Mean width 6 4 5 65 13 31 44 14 26 32 12 20 164 PROCEEDINGS OF THE AMERICAN ACADEMY. They may appear upon the plates, but are so wide and so faint that they cannot be detected upon the general shading of the plates. That these lines are not merely spark lines introduced into these arc spectra by the supposed spark at the breaking of tbe current through the rotating arc is shown, first, by the fact that they were first observed in the carbon arc, and, second, by the fact that I have seen Ha and Hp quite clearly in the magnesium metallic arc, when the poles were not rotating. The lines produced in the stationary arc have much the same character as in the rotating arc, but there is a large amount of continuous spectrum, appearing as a background, in the case of the stationary arc, so that it would be difficult to photograph the hydrogen lines in this way. These lines in the arc seem to be due to hydrogen, and not to water vapor coming from the hydrogen generators.* This is shown by the fol- lowing two experiments : (1) I passed the stream of hydrogen through concentrated sulphuric acid and phosphorus pentoxide ; and even after the stream of dry gas had. been running through the hood for three hours, I found the Ha line as bright as it was in the damp hydrogen coming directly from the generators. (2) In place of the current of dry hydro- gen, I passed through the hood a stream of air bubbling through warm water, so that this air was charged with moisture to about the same degree as the moist hydrogen coming directly from the generators. In this case I was not able to detect the faintest trace of the Ha line. Magnesium poles were used in both the above experiments. Other Methods. I have examined some of these metals in commercial ammonia gas, such as is used in refrigeration. In this gas the hydrogen lines come out with nearly the same intensity as in hydrogen when copper or aluminium electrodes are used; no hydrogen lines are seen in the sodium arc in ammonia, although the arc works well, and when tin electrodes are used in ammonia a black dust collects in the atmosphere about the arc to such an extent as to shut off practically all the light within thirty seconds after starting the arc. From the standpoint of convenience and safety, the ammonia gas is much to be preferred to hydrogen. The copper arc in coal gas shows the Ha line very clearly, but the other hydrogen lines are not distinguishable on account of the multitude of comparatively strong carbon lines which the coal gas furnishes in this part of the spectrum. * Trowbridge, Phil. Mag., 50, 338 (1900). BASQUIN. THE ARC SPECTRUM OP HYDROGEN. 165 Following the suggestion of Liveing and Dewar, above referred to, I have tried the rotating metallic arc in air, playing a very small jet of water upon the rotating electrode. In this manner the silver arc works rather more poorly than usual, and resembles a rapid series of small explosions. The hydrogen lines come out clearly, but are rather weaker and more diffuse than in the hydrogen atmosphere. The copper arc works well in an atmosphere of steam, much better than in hydrogen. The hydrogen lines are nearly, if not quite, as strong in steam as in hydrogen. The electrodes of the arc are slightly oxidized and have very beautiful colors. In making this experiment a slight alteration was necessary in the hood of the arc. The window through which the light issues is usually as far away from the arc as possible, but it was moved for this experiment so as to be as close to the arc as pos- sible. It was placed at the inner eud of a brass tube projecting into the hood, in order that the heat of the surrounding steam and hot air, as well as that of the arc itself, might prevent condensation of steam upon the surface of the window. CHEMICAL ACTION IN THE ARC IN HYDROGEN. Historical. Crew and Basquin * have sought to eliminate the radiations due to chemical causes in the electric arc by using chemically pure metallic electrodes and enclosing the arc in an atmosphere of hydrogen or nitro- gen. They interrupted the current through the arc about 110 times per second and examined the light of the arc while the current was null. They found in the rotating metallic arc in air " a luminous cloud " per- sisting for several thousandths of a second after the current through the arc had ceased, but they found no such luminous effect in an atmosphere of hydrogen or nitrogen. This seems to show that the cloud is due to chemical action going on in the gases after the electric current has stopped, and that in hydrogen the chemical action is too feeble to be noticed in this way. Liveing and Dewarf found a magnesium "line" at 5210, making its appearance in the arc spectrum only upon the introduction of hydrogen or coal gas into the arc. Professor Crew t gives a number of lines ap- pearing in the iron arc in hydrogen and not appearing in the arc in air. * Proc. Amer. Acad., 33, 18 (1808). t Proc. Roy. Society, 30, 96 (1880). t Phil. Mag., 50, 497 (1900). 1G6 PROCEEDINGS OF THE AMERICAN ACADEMY. Hydrogen-metal Flutings. With the exception of tin, every metal thus far examined in the rotating metallic arc in hydrogen gives a characteristic set of spectrum Hues which are not found in the arc in air. Inasmuch as compounds of hydrogen with some metals are known, I have, in lieu of a better hypoth- esis, supposed that these lines are due to such compounds formed in the arc. No new isolated lines, surely due to hydrogen, have been found. The following description takes up the metals in the order of the relative intensities of these flutings. Tin. No fluting has been discovered due to a combination of tin and hydro- gen. There are four lines of intensity \ on Rowland's scale, at ap- proximately 3715, 3841, 4245, and 4386, which have not yet been identified. These may be weak tin lines not listed, or weak impurity lines. The deposit which is formed in the hood enclosing the arc is very small in amount and of a greenish color, and consists of very small globules. If this deposit is heated upon platinum foil in a Bunsen flame it quickly glows, and thereafter has a slate color ; and if this powder is placed in hydrochloric acid it dissolves when heat is applied and gives off bubbles of gas. If the dark powder, after the first heating, is reheated on foil in the flame, it glows again, apparently at a higher temperature than before, and then becomes a very white powder, both of which ex- periments go to show that the original powder is not metallic tin but is possibly some combination of tin and hydrogen. Coin Silver. This metal gives a delicate fluting with first head at 3333.86 and run- ning toward longer wave lengths. There are only about fifty lines in this fluting, and they have an average intensity rather less than h on Rowland's scale. Copper. This metal gives a rather open fluting, having the head at 4279.77 and running toward the longer wave lengths. The number of lines in this fluting is about sixty, and they are individually stronger than those of the coin-silver fluting. This fluting makes its appearance also when an atmosphere of ammonia or of steam is used. The deposit formed inside the hood is rather small in amount and of a brown color. The following table gives the wave lengths of the hydrogen-copper flutings : — BASQUIN. — THE ARC SPECTRUM OF HYDROGEN. 167 Wave lengths. 4279.77 4280.72 4281.25 4281.85 4282.48 4283.38 4284.15 4285.26 4287.58 4290.25 4293.45 4294.86 4296.98 4298.55 4300.92 4302.63 4305.24 4307.07 4309.98 4311.89 4315.12 4317.07 4820.68 4322.74 4324.59 4320.61 4328.77 4331.38 Intensity. Remarks. >vave lengths. Intensity. Remarks. 2 head. 4332.98 1- 1 4335.20 1+ 1+ ghost of 4275? 4339.80 1- 1+ 4341.98 1+ i 2 4347.06 1- 1+ 4349.13 1+ \ 4354.59 1- 1+ 4356.73 1+ 1 + 4364.68 1+ 1 + 4373.01 1+ 1+ 4381.70 1 + 1- 4382.92 2 hazy 1+ 4384.74 1- 1- 4390. very indistinct, 1+ 4390.85 1+ 1 + 4400.30 1+ 1+ 4405.04 1- 1 + 4410.12 1+ 1 4413.09 1 2 1 + 4420.42 1+ 1 4421.59 1- 2 slight shading toward 4430.94 1 1- [blue. 4436.48 1 1 4447.18 i 1+ 4453.30 i 1 4158.03 i 1+ 4465.01 i i j hazy. 4477.15 i Aluminium. The aluminium arc in hydrogen gives a beautiful fluting with first head at 4241.26 and running toward longer wave lengths. This fluting ap- pears equally well in an atmosphere of ammonia. The following table gives the wave lengths and intensities of the principal lines : — lengths, ^tensities. Remarks. lengths. Intensities. Remarks. 4241.26 3 1st head. 4218.09 2 4241.75 3 4249.68 2 4242.41 2 4250.34 1 4243.10 2 4251.44 2 4243.94 3 wide. 4253.26 2 4245.32 4 4255 22 2 4246 58 3 4257.35 1+ 4217.58 1 4259.71 3 wide, 2d head 1C8 PROCEEDINGS OF THE AMERICAN ACADEMY. ■\Vave lengths Intensities- Remarks. lecths Intensities. Remarks. 4261.18 3 4315.57 3 4261.77 3 4320.63 3 42G2.59 3 4326.00 5 4263.50 3 4331.91 2 4264.58 3 4338.37 2 4265.80 3 4345.34 1 4267.24 3 4353.38 2 4268.86 3 4354.13 4270.68 3 4355.17 4272.72 3 4356.64 4274.98 5 impurity here. 4361.30 4277.70 4 impurity here. 4362.21 4280.67 4 4363.50 4283.94 4 436518 2 4287.30 2 3d head? 4367.21 2 4287.75 3 4368. i 2 4289.91 3 4369.67 2 4290.68 2 4371.49 i 2 4292.01 2 4372.54 • 1 4294.31 3 4375.18 \ 4296.99 2 4375.97 1 4298.10 3 4379.19 1 "2 4302.08 3 4379.90 i 4302.65 1 4388.23 1 4306.34 3 4393.42 1 4310.82 3 M 4399.19 &.GNESITJM. 1 impurity superposed. 4th head. The magnesium arc in hydrogen gives the three flutings discovered by Liveing and Dewar * in the magnesium-hydrogen spark, with first heads at 5618, 5210, and 4849, and running toward the shorter wave lengths. The fluting at 5210, which is the cme showing the plainest on my photo- graphs, is made up of such very fine lines near the heads that the princi- pal head appears like a line by itself; but farther away from the heads the lines seem to become stronger and to overlap one another, so that many of these lines are much stronger than the head itself and their distribution seems quite irregular. I mention this more particularly because it is characteristic of the hydrogen-zinc and hydrogen-sodium flutings de- scribed below. I have noticed that in the spark, the intensity of the magnesium flutings is greatly increased with respect to that of the "b" group by the introduction of inductance in series with the capacity * Proc. Roy. Society, 32, 189 (1881). BASQUIN. — THE ARC SPECTRUM OP HYDROGEN. 169 shunted about the induction coil. The deposit iu the hood enclosing the magnesium arc in hydrogen is quite plentiful, has a dark slate color, decomposes water at ordinary temperature, giving alkaline reaction, and oxidizes rapidly on heated platinum. Zinc. The zinc arc in hydrogen gives a collection of lines between 4300 and 4050, having an average intensity from 2 to 4, and not found in the arc in air. This appears to be a set of flutiugs of complicated structure having heads less distinctly marked than usual and running toward the shorter wave lengths. The semi-opaque deposit formed in the atmos- phere of the hood is so considerable that a current of not more than about four amperes can be used. This deposit is dark brown in color, gives alkaline reaction in water, but does not decompose it enough to form bubbles even when heated. It dissolves completely in sulphuric acid, forming a clear solution, and rapidly oxidizes on heated platinum. Sodium. The sodium spectrum was obtained by using metallic sodium as the cooler rotating electrode and copper as the stationary one. As above mentioned, there is not the slightest trace of any of the hydrogen lines to be detected in this spectrum either visually or on the photographs, but there is a strong series of lines between 5000 and 3800, resembling the hydrogen-magnesium series in character. This is probably a complicated fluting of heads less clearly marked than usual and running toward the shorter wave lengths. A compound of sodium and hydrogen is already well known. The formation of the semi-opaque deposit in the atmos- phere of the hood is so considerable that the arc can be run only about five minutes at a time. I have not tried the sodium arc in air. The sodium spectrum obtained in hydrogen is itself quite interesting. All the sodium lines given by Kayser and Runge* come out very clearly, but the principal interest centres about the D lines, which are very in- tense, and so wide as to cover all the region between them. "When observed visually their reversals change in width quite rapidly. At first these reversals may be quite narrow black lines, and then they quickly widen and blot out the whole of the bright field between them. The width of the two lines taken together is about 150 Angstrom units, though the photographic plates are stained for a much greater width. * Kayser & Runge, Weld. Ann., 41, 302 (1890). 170 PROCEEDINGS OF THE AMERICAN ACADEMY. The strongest copper lines show only very faintly, the weaker ones not at all. Correlation of Effects. In the metals arranged in the order given above (tin, silver, copper, magnesium, aluminium, zinc, and sodium) the following relations hold roughly : — (1) The set of lines characteristic of the spectrum of each metal in an atmosphere of hydrogen is stronger than that of the preceding metal of the series ; (2) the hydrogen lines appearing in the spectrum of the me- tallic arc of each metal are stronger than in that of the succeeding metal of the series ; (3) the general working of the metallic arc is worse for the metals at the first of the series than for those at the end. Briefly stated, the intensities of the hydrogen lines coming out in the spectra of various metals are roughly inversely proportional to the intensities of the char- acteristic flutings of those metals. GENERAL EFFECTS OF THE HYDROGEN ATMOSPHERE. Historical. Liveing and Dewar * found the carbon arc to work badly in hydrogen, and to give spectral lines of different relative intensities than in air. Professor Crew | has given quantitative measurements of the changes of intensities for the metallic arc spectra of magnesium, zinc, and iron. The general effects of the hydrogen atmosphere may be summarized thus : — (1) The arc works poorly in hydrogen. (2) The intensity of the whole spectrum is greatly reduced in hydrogen. (3) Those metallic lines which belong to the series of Kayser and Eunge are uniformly reduced in intensity. (4) Other lines are reduced in intensity but not uniformly. (5) Certain lines supposed to belong to the spark spectrum make their appearance in the arc in hydrogen. Discussion. The radiations of the electric arc are generally admitted to be due to three causes, — electrical, chemical, and thermal. The chemical cause must depend upon the electrical cause in some way, for the chemical cause * Proc. Roy. Society, 33, 430 (1882). t Phil. Mag., 50, 497 (1900). BASQUIN. — THE ARC SPECTRUM OF HYDROGEN. 171 cannot originate the arc, and the chemical cause follows the electrical in point of time, as is shown by the " luminous cloud " of Crew and Basquin above referred to. The thermal cause also must depend upon the electri- cal cause in some way. It probably depends upon it directly, but in any event, it is a function of it through the chemical cause, for all chemical reactions either take in heat or give off heat. Let us consider two arcs which are alike except that a larger current runs through the first than through the second. Since the secondary causes of radiation go hand in hand with the electrical cause we may expect the first arc to have a spectrum which is uniformly brighter from one end to the other than that of the second arc. With the exception of a slight variation probably clue to conduction losses, this is just what is always observed and confirms the secondary character of the chemical and thermal causes of radiation. If these causes were not dependent upon the electrical cause, we might possibly get an arc which would give only a flame spectrum or an arc which would give only a spark spectrum. Let us now suppose that we run the same current through both the similar arcs, and suppose that in some way we reduce the chemical action going on in the second arc. What difference may we expect to observe in them ? A reduction of the chemical action necessarily involves a reduction of the temperature of the arc, because the chemical reaction in the arc in air is exothermic, We have then an arc of lower temperature. If it is a stationary arc it will be shorter and will go out more frequently. If it is rotating it will have a smaller flame and work more poorly. All of which is amply verified by experiments in hydrogen. But we may expect this reduction of chemical action to have certain effects upon the spectrum. If all the lines of the spectrum of this arc were functions of the electrical cause alone, then there would be no re- duction in intensity of any part of the spectrum when the chemical action is reduced. Professor Crew estimates from 5 to 100 times as the reduc- tion in intensity caused by the hydrogen atmosphere. The electrical cause alone can account, then, for only a small part of the radiation. The secondary causes play very important parts. If all the lines of the spectrum of this arc were the same function of the causes of radiation, then all the lines of the spectrum would be uniformly reduced in intensity upon the reduction of chemical action. Experiment shows this hypothesis to be too broad, but the lines belong- ing to the series of Kayser and Runge are uniformly reduced in intensity, so that it is probable that these lines are all the same function of the causes of radiation. 172 PROCEEDINGS OF THE AMERICAN ACADEMY. Of the other lines, those which are reduced more in intensity than the series lines, must be less intimately related to the electrical or thermal causes of radiation than are the series lines. Let us agree that the average intensity of the spectrum of the arc in hydrogen is only one fifth of its intensity in air, and let us agree that the electrical cause of radiation remains practically constant with constant current and voltage although the general intensity of the arc is greatly reduced by the hydrogen atmosphere, then it follows that of the total radiation, that fraction which must be attributed to the electrical cause alone, is relatively five times as great in hydrogen as it is in air. Any line, therefore, which is a function of the electrical cause alone, should have in hydrogen five times the relative intensity that it has in air. It seems quite likely that this may account for the appearance in hydrogen of numerous strong spark lines, not found in the arc in air. The appearance of the spark lines in hydrogen is not confined to the rotating arc; the magnesium spark line at 4481 appears clearly in the stationary metallic arc in hydrogen but not in air. The above explana- tion for the appearance of these lines makes it probable that the electri- cal cause of radiation is not zero in either atmosphere. In the rotating arc the current is interrupted about twenty-five times per second when the rotating electrode is a rod, instead of a disc, of metal, and this spark at the breaking of the current may account, in part, for the appearance of these spark lines in hydrogen. But we may in- quire why this spark should partake any more of the nature of the true spark in hydrogen than in air. The reduction of the chemical action in the arc reduces the temperature and conductivity of the gases between the poles in hydrogen, and it occurred to me that this action may affect the appearance of the spark lines in either of two ways : — 1 . It may be that a gas which is in the hot condition of the arc in air cannot give off spark lines; the arc spectrum may be characteristic of this condition of the gas and may have nothing to do with electrical action, and so, in this state, would give off only arc lines if a spark were passed through it. 2. It may be that the conductivity of the gases in air is reduced so slowly at the breaking of the current in the rotating arc that the voltage of break never rises high enough to make a true spark. In either of these cases, in hydrogen, the hot gases are largely absent, owing to reduction of chemical action, and give opportunity for the spark to appear. In order to test the first suggestion I arranged an electrical circuit as BASQUIN. — THE ARC SPECTRUM OF HYDROGEN. 173 shown in the diagram. The dynamo furnishes a direct current of 110 volts, and when the switch was closed the current simply passed through the arc and the resistance in series. The arc was stationary, one electrode was carbon and the other a zinc rod. The induction coil used is a duplicate of the one designed by Professor Rowland to give a short SWITCH SPARK Figure 1. spark but a very powerful discharge ; an alternating current of 110 volts, 6 amperes, was run through the primary, without an interrupter. The condenser used has a capacity of fa microfarad. It will be noticed that the spark can take place only by passing in succession the two gaps marked "arc" and "spark." The spectroscope is adjusted to observe phenomena at "arc" gap. In performing this experiment I first turned on the spark and set the cross-hairs of the eyepiece of the 10-ft. concave grating upon the zinc spark line at 5895, between the D lines of sodium. The spark was turned off and the arc turned on. The spark lines no longer appeared, but came out instantly when the spark was again started along with the arc ; both arc and spark were now running through the gap marked " arc " and the spectroscope showed both arc and spark lines. Now while both currents were on, the arc current was turned off ; the arc spectrum dis- appeared, but the spark spectrum persisted with apparently the same intensity as before and without an interval of darkness. This experiment shows that the first suggestion is not true ; that the arc spectrum is not characteristic of the condition of the gases in the arc, and makes it highly probable that the electrical cause of radiation is not zero. In order to test my second suggestion above, I short-circuited the spark gap shown in Figure 1. The spark line appeared as before in the spark, but disappeared as soon as the arc current was made ; the arc and the spark discharges were both passing through the arc as before ; I had 174 PROCEEDINGS OF THE AMERICAN ACADEMY. simply cut out the " spark " gap, but the spark line could not be seen when both currents were on. Now when both currents were on I broke the arc circuit, and nothing at all could be seen in the spectroscope ; neither the arc nor the spark lines remained, although the spark current was still passing. After remaining at the eyepiece of the spectroscope about one second I began to see traces of the spark lines, and then they soon came out with their usual brightness, and the spark discharge which had been silent during that second of darkness assumed its usual noisy character. This experiment shows that the gases of the arc do not furnish enough resistance to the passage of a high voltage alternating current to cause the discharge to assume the character of a spark for a full second after the breaking of the arc current. This seems to confirm the second suggestion above, to the effect that the conductivity of the gases de- creases so slowly on the breaking of the arc current in air as to give rise to no very high voltage, and so accounts for the non-appearance of the spark lines in the rotating arc in air. These two experiments throw an interesting light upon the nature of the spark. The spark at the arc gap in these experiments seems to be due to neither the current nor to the voltage, but to some kind of an im- pulse furnished by the sudden rush of electricity across the auxiliary " spark " gap. In the second experiment, above described, the spark lines do not all seem to come out at the same time. I hope in the near future to be able to arrange an automatic apparatus for making and breaking the currents and an adjustable occul ting-screen which will enable one to photograph the spectrum of the spark at definite intervals of time after the arc current is broken. A series of these photographs will probably furnish an interesting story of the development of the spark spectrum. Physical Laboratory, Northwestern University. INDEX TO PLATES. Plate I, Figure 1. Tin arc in hydrogen, 1st order. Plate I, Figure 2. Upper part, copper arc in hydrogen, 1st order. Lower part, copper arc in air. Plate I, Figure 3. Tin arc in hydrogen, 1st order. All lines are second order except Ha at 6563. Plate I, Figure 4. Copper arc in hydrogen, 2d order, showing hydrogen-copper fluting and the Hy line. Plate II, Fig ore 1. Aluminium arc in ammonia, 2d order, showing hydrogen- aluminium fluting. Plate II, Figure 2. Middle, magnesium arc in hydrogen, showing hydrogen- magnesium fluting at 5210, 1st order. Outside, magnesium arc in air. Plate II, Figure 3. Upper part, zinc arc in hydrogen, 1st order, showing hydro- gen-zinc lines. Lower part, zinc arc in air. Plate II, Figure 4. Sodium (and copper) arc in hydrogen, 1st order, showing hydrogen-sodium lines. LLl h < S' I en £, ^ <* «5. CO u. 3' ♦ ro cr (- o LU a. I 02 03 2 tr I- O LU Q- CO o or < LU I 00 <0 3° 00 (0 * 00 CO * cv CO to <** %° a) _> ^ l^ 5° 03 CO <* a ro° ., anterior region of body ; mtl. 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 determines 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 posterior 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 across the plate. The amount of elongation varies a good deal, but the regions retain pretty closely their relative proportions. FRANDSEN. — REACTIONS OP LTMAX MAXIMUS. 195 TABLE IV. StJMMART OF GeOTACTIC RESULTS. Sei Animal se No. oi ei •iesof ( rvatioi )b- Number of Trials, is taxis. Length of Anterior Region in mm. Length of Posterior Region in mm. Ratio of Ant. to Post. Re- gion in per cents. Condition of Animal. ) Diffe it Days r- " + — 1 , 10 0 +100. 20 24 83.3 Good. 2 a 6 3 4- 0(5.0 18 22 82. Fair. 2 b 5 13 - 72.2 18 22 82, Dry. 2 c 12 5 + 70.5 18 22 82. Good. 3 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. 0 7 1 + 87.5 11 15 73. Good. 7 a 0 4 -100. 26 40 65. 7 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 t 7 7 Good. 8 b 17 1 + 94.4 i 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 • > 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. 23 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 (1 4 19 - 82.6 27 54 50. Goo.l. 24 e 3 14 - 82.3 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. 20 3 15 ■ - 83.3 7 ■2 45. Good. 27 a 0 14 -100. 32 71 45. Good. 27 b 1 5 - 83.3 32 71 45. Good. 19G PROCEEDINGS OF 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 geo tactic 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 iu 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 OF 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 80° 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. Number of Trials. Animal No. Angle of Inclination. % Geotaxis. Condition of Animal. + 1 45° 8 2 + 80. Good. 1 90° 0 14 -100. Good. 2 45° 7 1 + 87.5 Good. 2 70° 8 3 + 72.7 Good. 3 45° 2 8 - 80. Good. 3 90° 0 10 -100. Good. The most striking case is the complete reversal of geotaxis, seen in the first animal experimented on. FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 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 slip 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 Tricssure 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 ou 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 favorable as the glass plate ; that is, it doubles the obstacles. As a general rule, owing to the irregularities of other influences, 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 representative. 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 in %. Plate at Inclination of 45 D. Wooden Plate. Glass Plate. Vaselined Glass Plate. No. of Trials. % Geotaxis. No. of Trials. n % ■ 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 QO O — oo.o 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 being 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 strong 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 VIII. 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 -f- Influence of Strong Light. No. of Trials. % Geotaxis. No. of Trials. »j0 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 accom- FRANDSEN. — REACTIONS OF 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, aud 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 responded 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 Kesponses of Individuals when poobly nourished and when well nourished. Animal No. Proportionate Ratio of Anterior to Posterior Region. Poorly nourished. Well nourished. No. of Trials. % Geotaxis. No. of Trials. °10 Geotaxis. + — + - 1 2 3 70. 60. 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 OF 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 plate, 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 OP THE AMERICAN ACADEMY. III. Phototaxis. The influence of light on the direction of locomotion has been 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 OP LIMAX MAXIMOS. 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 Balanus 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. It moves slowly 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 OF 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. Methods. — 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. (£ 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 sectors 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 orieuted 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 tvith 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 OF THE AMERICAN ACADEMY. negative movement of the animal was measured by taking the radius which passed midway between the two tentacles, without 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 (186), 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 stiinu- 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 Pho gration i ;otactic Mi- i 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 .676 330 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 .001,09 405 7G0 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 la .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 9« .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 .000,009,6 030 515 8.6 + 2. 7 o o 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 plate 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 efforts 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 new 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. Series 7a, 8a, 9a, and 10a are hence taken at the same intensities as 7, 8, 9, and 10 respectively. These repeated series 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 .000,754, lies an intensity which attracts about as many animals as it repels 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 PROCEEDINGS OF THE AMERICAN ACADEMY. CURVE OF RESPONSES TO LIGHT. *■**" *-. '{ 1 6S y \ s / / \ \ \ * / \ ' \ h / / \ \ \ \ \ . / \ \ \ ? a / \ \ \/ ► / / \ '( 2 / t / 14. \ / \ 1 t 1 1 > 1 : V J \ 3 a t 1 \ U. VI 1 ?\ D 1 \ J 1 I 1 i 1 \ \ 1 / / / I If )a* J \ / i 7 a / 1 , 7 i i 1 1\ -- \ 2 3 4 5 5 7 8 3 10 --1 , 7 ' \ i \ \ i \ i \ 4 2 ^ ■^ / \ 5 \ \ 3 \ \ * \ \ \ 4 \\ : ?* \ i 5 \ \ i l i 1 6 ii 7 Figure 2. Curve of Responses to Light Abscissae are logarithms of light intensities plus 10 ; ordinates are sines of angles of responses multiplied by 10. PRANDSEN. — 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 the 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 beeu given. Series 12 was the last one taken. In this, the animals were 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 light intensities. Besides this individual variation, there is, I think, a general variation for all slugs from time to time, for reasons imperfectly known, 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 caudle 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 saving, — 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 OV 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.° -14.6° ::i.° .067 C. P. .067 C. P. .067 0.1'. -27.°5 - 10° -23.° In all these cases, there if 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 XII.), as the following instances show. TABLE XII. 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.° o .676 C.P. -15.° .0424 C.P. +35.° 3 .169 C.P. -37.° •0188C.P. - 2.°5 .0067 C.P. -32.° .0047 C.P. +30.° No. 3, Table XII., 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 phototaetic 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 OP 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.° - 3.° o o -44.° -29.° +7.° 4 -53.° +16.° 5 -65.° + G.° 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 LIMAX MAXTMUS. 219 more or less positive response. In the case of animal No. 3, removal of the eyes did not 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 probahly 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. Comparison 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.° 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 the 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 OF THE AMERICAN ACADEMY. TABLE XV. Comparison of Responses of Right and Left Sides to Light. 1 CO JV 0) o 6 m l 2 o O 4 5 6 7 8 9 10 11 < °i & s a o H Intensity of Light. Responses of Right Side in Degrees. Responses of Left Side in Degrees. Total Movement in Degrees to + — Average Photo- taxis + or — + — Average Photo- taxis + or — Right. Left. .676 305 770 -19. 25 1385 -57. 1690 795 8 2 .382 250 1056 -19. 375 1716 -32. 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 - 1.4 415 265 + 4.1 545 745 12 9 .000,424 530 645 - 3. 615 250 -10. 780 1260 12 10 .000,200 435 245 + 6.3 388 100 + 9.6 535 633 10 la .001,69 250 210 + 12 115 270 - 5. 520 325 11 8a 000,754 410 165 + 8.1 435 180 + 8.5 590 600 10 9a .000,424 380 75 +10. 005 55 +17. 435 680 10 10« .000,200 560 230 + 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 .000,001,26 395 320 + 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. 220 320 1050 140 -13.8 + 7. 2270 295 460 815 20 10 Totals 9570 8506 7808 10321 19891 16314 " less 18a & 186 8195 7771 7268 9131 17326 15039 FRANDSEN. — REACTIONS OF 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 riglit and left sides respectively were turned toward the light, were as follows. TABLE XVI. 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. 1815° 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 la, 8a, da, 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 18b) 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 G471° (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 18a), the amount of right-hand movement was 2270° and the left-hand movement only 4 G0°. That is, there was nearly five times more migration toward the right than there was toward the left. In series 18b, however, there seems to have been a marked pre- ponderance of movement toward the left. From the foregoing experi- FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 223 ments, 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 bv 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. Figttres 3-22. Much reduced copies of the tracks made by slugs (Limax maximus) in the dark. dx., right-hauded loops ; s., left-handed loops. FRANDSEN. — REACTIONS OF UMAX MAXIMUS. 225 give any 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. Nos. 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. xxxvn. — 15 226 PROCEEDINGS OF 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 the 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. Beitrag zur Kenntnis rich tender Krafte bei der Bewegung niederer Or- ganismen. Jena. Zeit. Bd. 22, pp. 310-342. Davenport, C. B. '97. Experimental Morphology. Part I. pp. xiv. + 280. New York. Davenport. C. B., and Perkins, Helen. '97. A Contribution to the Study of Geotaxis in the Higher Animals. Jour. of Physiol. Vol. 22, pp. 99-110. FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 227 Engelmann, T. W. '82. Ueber Liclit- unci Farbenperception niederster Organismen. Arch. f. ges. Physiol. Bd. 29, pp. 387-400. Famintzin, A. '67. Die Wirkung des Lichtes und der Dunkelheit auf die Vertheilung der Chlorophyllkorner in den Bliittern von Mnium sp. (?) Jahrb. f. wiss. Bot. Bd. 6, pp. 49-54. Groom, T. T., und Loeb, J. '90. Der Heliotropismus der Nauplien von Balanus perforatus und die peri- odischen Tiefenwanderuiigen pelagischer Tiere. Biol. Ceutralbl. Bd. 10, pp. 160-177- Jensen, P. '93. Ueber den Geotropismus niederer Organismen. Arch. f. ges. Physiol. Bd. 53, pp. 428-480. Loeb, J. '88. Die Orientierung 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 seine Uebereiustimmung mit dem Heliotropismus der Pflanzen. 118 pp. Wiirzburg : G. Hertz. Loeb, J. '93. Ueber kiinstliche Umwandlung positiv heliotropischer Thiere in uegativ heliotropische und umgekehrt. Arch. f. ges. Physiol. Bd. 54, pp. 81-107. Massart, J. '91. Recherches sur les organismes inferieurs. III. La sensibility 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. Fouchet, G. '72. De l'influence 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 Einfluss der Schwerkraft auf die Bewegungsrichtung von Chlamido- monas und Euglena. Ber. deutsch. bot. Gesell. Bd. 2, Heft 2, pp. 51-72. Verworn, M. '89. Psycho-physiologische Protisten-studien. viii. -f- 218 pp. 6 Taf. Jena: Fischer. "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. XXXVII. No. 9. — November, 1901. THE ALGAE OF JAMAICA. By Frank Shipley Collins. 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, among 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, ramidis den- sioribus, et Jills magls sinuatis atque corrugatis, is Halimeda Opuntia. P. 58, PI. XX. Fig. 3, Corallina major, nervo crassiore fuciformi, inter- nodla breviora nectente, White Bead Bandstring dicta, is Cymopolia bar- bata. P. 61, PI. XX. Fig. 9, Fucus minimus denticulalus triangularis, is Bryothamnion triangulare. P. 58, PI. XX. Fig. 6, Fucus marlnus vesi- culas habens membranis extantlbus alatas, is Turbinaria trialata. P. 58, PI. XX., Corallina minima capillacea, is probably our present Corallina capillacea, but neither plate nor description is characteristic enough to make this certain. P. 51, PI. 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,! 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 probable 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. t Hortus Jamaicensis, by John Lunan, 1814. 232 PROCEEDINGS OF 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, f 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 instance 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. t Algues de la Guadeloupe. 2d Edition. Maze & Schramm, Basse Terre, 1870-77. | Meeresalgen von Puerto-Rico, von F. Hauck. Engler's Botanische Jahrbiicher, Vol. IX. p. 30, 1888. COLLINS. THE ALGAE OF 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 Mo rant 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 Manchioueal, 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 16 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. Tlie 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 large 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. IL, 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 : Gyrnuogongrus 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, aud Puerto Rico, lists having been published of these regions of sufficient extent to make a comparison of interest.! 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 these statistics, named varieties and forms have been counted the same as species. t The data of these tables are from the following works : — Preliminary List of New England Marine Algae, by F. S. Collins, Rhodora, Vol. II. p. 41, 1900. 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 Pre'liminaire 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 Socie'te 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- nates des Sciences Naturelles, Series 8, Botany, Vol. IV., 1897. Meeresalgen von Puerto-Rico, von F. Hauck, Engler'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 OF 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. Tbe Puerto Rico collection, and in great y>art 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. iii the Biscay region is noticeable, but not easy to account for. Tbe 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 tbe 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, Phaeophyceae, 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 showu 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 Lamiuariuceae. 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 long 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 Polysiphonias, 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^jdown 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 OP 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 Natiirlichen Pflanzenfarnilien of Engler and Prantl, but the names of orders, families, 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 positious in the general list, and the fact of their being fresh water plants is noted by a star prefixed to the name. General List. Chroococcus 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, Duerden. *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. Aun'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, II. *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, 19.00, 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 O. 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. confervoid.es forma violacea n. f. In company with L. ma- juscula, Manchioneal 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, Manchio- neal Bay, July, 1900, P*. & B. *L. putalis Mont. Morant Bay, July, 1900, P. & B. *L. versicolor (Wartm.) Gomont. Marine Garden, Kingston, II. P. B.-A., No. 54. Symploca hydnoides Kuetz. var genuina Gomont. On rocks in shallow water, in small patches, not abundant, Montego Bay and Manchioneal 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 " AVag Water," Castleton, April, 1893, No. 399, H. Microcoleus chtbonoplastes (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 (Vaucb.) Gomont. On moist rock, Rio Cobre, Bog Walk, April, 1893, II. *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 OP JAMAICA. 241 Spring; on sand at edge of river, Castleton, April, 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 Arcangelii Born. & Flah. On moist rocks by spring, Castleton, April, 1893, H. S. conchophilum Humphrey ms. In old conch shell, Port Antouio, March, 1893, H. Kingston, June, 1897,11; Producing slight, gray, pustular roughenings of outside of shell, Mastigocoleus testarum occur- ring on inside of same shell. Filaments 5-8 /x diam., irregularly branched, branches single or gemi- nate, tips rounded, cells two thirds to two times as long as broad, 2.7- 4.5 fx diam., pale bluish when separate. Heterocysts globose or slightly elongated, 5 /x 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, 1S93, H. *Hapalosiphon fontinalis (Ag.) Bornet. • On rock, " Wag Water," Castleton, April, 1 893, 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. XXXVII. — 16 242 PROCEEDINGS OP THE AMERICAN ACADEMY. C. pilosa Harv. On Bostrychia tenella, Port Antonio, Aug., 1894, P. & B. Dichothrix penicillata Zan. On Cymopolia barbata, Port Maria, H. On Dictyota dichotomy P. & B. P. B.-A., No. 62. *Gloeotricbia natans (Hedw.) Rab. Under Nymphaea leaves, Botanic Garden, Castleton, April, 1893, H. *Spirogyra decimina (Muell.) Kuetz. Mauchioneal, July, 1900, P. & B. " The 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 Jobs. 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, Mauchioneal 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, Manchi- 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/* 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, II. 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. Mauchioneal, 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, Mauchioneal, 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, Mauchioneal, 1900, P. & 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 200-350^ 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 OP 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 (Lagerh.) 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. hi 43 C8 o DQ .2 o o >> Eh n s o FH o C8 Eh a Pm u a s o fc + + + + + + + + 1 T + + + + + + + + + + + + + + + + + + + + + + + + + + TABLE II. Summary of Marine Floras, arranged by Classes. Jamaica. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. 60 130 193 346 New England. Scbizophyceae Chlorophyceae Phaeopbyceae ) Dictyotales ) Khodopli3'cene 19 02 29 114 2 25 10 49 7 62 61 156 286 24 59 75 237 34 oo 80 173 75 88 118 153 Total 224 92 395 320 735 434 COLLINS. — THE ALGAE OF JAMAICA. 269 TABLE III. Percentage by Classes in each Flora. Jamaica. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Scliizophyceae 8 2 3 6 11 9 17 Chlorophyceae 28 27 21 15 10 18 20 Phaeophyceae ) Dictyotales ) 13 17 21 19 25 20 26 Rhodophyceae 51 54 55 60 54 47 37 TABLE IV. Common to Jamaica in other Floras. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New Englaud. Scliizophyceae Chlorophyceae Phaeophyceae ) 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 63 65 51 42 55 44 TABLE V. Percentage of Jamaica Flora common to other Floras. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Scliizophyceae Chlorophyceae Phaeophyceae ) Dictyotales ) Rhodophyceae 11 28 38 29 28 22 29 27 31 26 22 7 27 32 12 7 23 47 23 10 25 53 10 10 18 Total 30 23 19 25 19 270 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE VI. Percentage of other Floras common to Jamaica. Puerto Rico. Canaries. Morocco. Biscay. Great Britain. New England. Schizophyceae Chlorophyceae Phaeophyceae ) Dictyotales ) Rliodophyceae 100 68 69 72 57 29 13 22 21 23 3 13 18 21 3 15 14 11 2 9 11 3 14 Total 69 24 14 11 8 10 Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. Xo. 10. — Xovembek, IDOL CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. MODIFICATIONS OF HEMPEVS GAS-APPARATUS. By Theodore William Richards. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. MODIFICATIONS OF HEMPEL'S GAS-APPARATUS. By Theodore William Richards. Received October 26, 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 PROCEEDINGS 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- Figure 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. Au 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 well 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 the 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 dowu of the liquid from the moistened walls. Again, care must be taken that the same Hvf 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 Figure 2. the Hempel apparatus. It dispenses with the necessity of calibrating the whole length of a new burette, it UkJ lU 276 PROCEEDINGS OP THE AMERICAN ACADEMY. is very inexpensive, aud 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 further advantage lies in 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 transference 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 pressure 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 C02 taken. Volume Air taken. Volume Air found. Error. c.c. c. c. c. c. c. e. 10.95 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 .GO ±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 ne*v 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 carrving 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. THE PARAMETRIC REPRESENTATION OF THE NEIGHBORHOOD OF A SINGULAR POINT OF AN ANALYTIC SURFACE. By C. W. M. Black. Presented by W. F. Osgood. Received September 9, 1901. INTRODUCTION. A. — Outline of Kobe's Treatment of the Problem. The problem of the representation, by a finite number of parametric formulae in two variables, of the neighborhood of a singular point of an algebraic surface is considered and alleged to be solved in an article " Sur la theorie des functions algebriques de deux variables," * by Gus- tav Kobb. A brief outline of Kobb's method follows : — 1. Treatment of the Original Singular Point. 1) Let the equation of the surface be written in the form F(x,y,z) = 0, where F is a function of the three independent variables x, y, z analytic in the point x = a, y = b, x = c. The function F is transformed by means of a change of axes to the form * (6 V, 0 = (6 V, Om + (6 V, Om+l + = 0 (a) where the expression (£, 17, 'Qn is a homogeneous polynomial of degree n, the resulting surface (a) having the singular point considered at the origin, while the function (£, 77, £),„ is of a form convenient for later treatment. 2) By the quadratic transformation £ = t£ , 7] = a'C, $ (£ rj, 0 = tT [(r, a, 1)„, + t (r, (T,o-) + ZX(T, (r)+ ] (b) * Journal de mathe'matiques pures et applique'es, 4th Series, Vol. VIII. (1892), p. 385. 282 PROCEEDINGS OF THE AMERICAN ACADEMY. and the neighborhood of the original point is represented by the neigh- borhood of the curve 0(t,o-)=O, f=0, (c) on the surface * (r, cr, 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 power series t = V (er, 0 I (d) b. critical points of the curve (c), the domain of each being repre- sented by an equation of the form t" + ^(tr, 0 tm_1 + + /V-iO, 0 r + ?m 0, 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 Tj, cti, 7], where - = Tj , - = crx , £ is reducible, but contains no multiple factors, the same selec- tion of points holds as in a, but there may occur a singular point of order m. c. If contains multiple factors, all critical points of the curves cor- responding to any factor, together with all points of intersection of two different factors, are first taken, then all points of class 3) c, these being possibly singular ; finally, a finite number of regular points of the several curves corresponding to the different factors of <£, these last points being possibly singular points of the surface. In this case, there may occur a number of singular points of order m. 2. Treatment of Points Determined in 1. The same treatment as in 1 is applied to each of these points and to each of the corresponding BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 283 resulting points in turn, so long as they are singular. If after a finite number of such processes, all the resulting points are regular, then by combining the results it is assumed that the neighborhood of the origi- nal point is represented by the domains of a finite number of regular points, and so by a finite number of parametric formulae as desired. 3. Proof that a Finite Number of the Processes of 1 will be Sufficient to make all Points in 2 Regular. Starting with the surface f(u, v, w)=0, (f ) in which the singular point considered is at the origin, the transfor- mations in 1, 1) and 2) are combined in the form u = (out + fro- + yOn v = (a2T + /?2o-+72)£>- (g) W= (a3r + fi3o- + y3)0 We can assume that y-2 + 0 , y8 4= ° by making, if necessary, upon / (it, r, w) a suitable homogeneous linear transformation. Then the next set of transformations, in 2, can be expressed in the form r=(a1'r1 + /Vo-! + y/Ki ) = [y3 y3' y3" y3M + (r,, w) m (j) under the substitution (i). Let the given sur- face be f =: u2 — 2uw — v2 + 2vw + uvw — vw2 — uw2 + wz = 0. (k) Here, X (v, w) = (4 + w2) (w — v)2. The curve (u, v) = u2 — 2u — v* + -2v = 0 * Annali di matematica, Series 2, Vol. XXVI. (1897), p. 219. t Cf. Levi, 1. c, p. 224. \ Cf. Levi, 1. c, pp. 225-G. BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 285 has a singular point at u = 1, V = 1. So the first transformation is i; = (o- + 1) £ V (1) which, applied to (k), gives £2 (r2 - o-2 + to-0 = 0 (m) and x(t.,«,)=£2o-2(£2+4). (n) Now the set of transformations to which Kobb is naturally led in this case is the following : — * T = Ti & O" = 0^ & £ = £j *"l = T2 £2 0"l = 0"2 £2 £l — £2 whence T = TV C, O- = OY £/> £ = £r- But this substitution in (11) gives x (v, w) = Vr+2 — , 5 1 — O" and the resulting series converges only when | o- 1 < 1. 7. From geometrical considerations we should not expect the quad- ratic transformation used to resolve the singularity in all cases. In ordinary space the transformation £ = t£, rj — cr£, will transform in a one-to-one manner, without change of the £ coordinate, all points except those in the £ = 0 plane. Now in the surface from (m), t2 - a' + t(t£ = 0, all points in the £-axis are singular, and whatever the reduction that may be secured for the origin, there will be within the neighborhood of the origin points whose singularity is not reduced. The same consider- ations would be seen to apply if we had any space curve as a singular line. Levi, in the article previously mentioned, does not attempt a proof of the entire proposition, but directs his work toward establishing by geometrical considerations the reduction of the singularity, making ex- ception, however, of certain cases,* which are closely related to the one considered in 7. Having thus considered the failure of Kobb to establish the proposi- tion even for the general case of an algebraic surface, we shall, in the im Grossen, the limit to the number of points taken being determined by finding the extent of tbe domain of each ; while the developments about the later points giye relations im Kleinen, as far as the first point is concerned. * Cf. Levi, 1. c. p. 227. Cf. also a second paper by Levi, Atti R. Ace. Sci. Torino, Vol. XXXIIL, 5 Dec, 1897. BLACK. THE NEIGHBORHOOD OP A SINGULAR POINT. 287 present article, supply the deficiency, and treat at once the more general case of an analytic surface, i. e., the case that the function F (x, y, z) is not merely a polynomial, but is any analytic function which vanishes at the point (a, b, c.) § 1 A. — The Fundamental Theorem. 1. The theorem, the proof of which forms the subject of this article, is the following. Theorem: Let F (x, y, z) be a function such that 1) F (x, //, z) is analytic in the three independent variables in the neighborhood of the point x = a, y = b, z = c ; 2) F(a, b, c) = 0; 3) (— \ =(9~) =( — ) =0- \dzj[a.b,c) \5y/(a.6,c) \dzj[a,b,c) then we can represent all values of (x, y, z) satisfying the equation F(x,y, *)=0 and lying in the neighborhood of the point (a, b, c) : \x — a | < S, \y — b\<8, \z — c\<$> by a finite number of parametric formulae of the following type : x = p (u, v) 1 y = «0 y p = 1, 2, p, (A) z = Xp(?/' v) J where t/>p, if/p, \p are analytic in the arguments (u, 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 (u, v) lying within the region in which the functions gm < gn, 3 4* ??{*»**- Accordingly, the series is convergent when \l\ (f, ??, £) = 0 at the point (0, 0, 0) forms a cone that cuts the plane £ = 1 in the curve $ (£, 77) = 0. If the line -q/t, = /?, £/£ = a, (a and /? being finite) is one of this family, then the point £ = a, -q = ft, £ = 0 of the surface <1> (£, 77, £) = 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 ($, rj, £) = 0. In fact, cut the surface * (6 * 0 = 0 by the plane »7-/3£=0. Then the curve of intersection C will have a multiple point at (0, 0, 0) and the equations of the tangents to C at (0, 0, 0) will be v-j3£=0) > cr = 1, 2, s < m. * Cf. Stolz, Allgemeine Arithmetik, Vol. I. p. 293. BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 291 Now, the transformation (2) being made, the points of the region T: |*| < 8, h|< 8, |C|<8, which lie in the neighborhoods of the lines > cr = 1, 2, 5, can, with the exception of the point (0, 0, 0), be transformed in a one- to-one manner on the neighborhoods of the points (0, 0, 0) of a set of surfaces 9« (£r> VU 0 = ° . Or = 1, 2, S , the coordinates being connected by the relation r (4) *=£foi + /?> S By the neighborhood of the above line is here meant the set of points (£, 7/, £) which satisfy the condition |*-«**|<«|C|, h-£C|:S«|C|, ICK8- To deal with the points for which a, /? would be infinite, cut the surface 4> (£ r/, 0 = 0 by the plane C = o. The equations of the tangents to the curve of intersection at (0, 0, 0) are f- t=1, 2, « ($, rj) contains the term $ m by 3, 2). Apply the transformation V-P= *7i, (6) whence (3) takes the form * (6 v, 0 = C" Oi (I vi) + t Xi (?» ft> 0]. In (j>x (£, tij), take out all terms not containing rju so that _ « _ ^a _ 01 (£ *h) = n (£ — a„) + 77 1 i^ (£, ??!), (U! + + ^ = m. , £') of T (distinct from (0, 0, 0)), de- rived from points (£ffl rjv Q (^„ %, £2) lying respectively in the neigh- borhoods of the singularities which are given by two distinct equations 9, = °, = 0 must also have equal roots at the corre- sponding points, and this case has been excluded. So as each equation g = 0 has near the point (0, 0, 0) p values of £ , in general distinct, t for each pair of values of rji and £, aud as 2 /j. = m, the collection of equations ga = 0 , o- = 1 , 2, 8 , has within sufficiently small limits as many different roots as the equa- 294 PROCEEDINGS OF THE AMERICAN ACADEMY. tion 4> = 0, and thus represents the latter equation within the corre- sponding limits, i. e., when |£| U or |*-a,{|l) = 0, t= 1, 2, < = 0, at the singular point can be mapped on the neighborhood of a (regular or singular) point of the surface g = 0. We now proceed to show that the whole neighborhood 'b' T: |*| <*, hl (£, 77) has no multiple factors. Case II. — This polynomial has multiple factors. Theorem: The neighborhood T can be completely covered by a finite number of regions Tu T.2, Tv, which overlap each other and which are mapped respectively on the following regions tx, f2, tv: In Case I: 1) the region t{, i = 1, 2, k, consists of the neigh- borhood of a singular point of the surface gw = 0 ; 2) the extent of each of the neighborhoods tx, t.2, tK having been arbitrarily determined^ the regions tfi j — k + 1, v, then consist of regular regions of surfaces g = 0. In Case II : 1) the region tit i = 1, 2, k, consists of the neigh- borhood of a singular point of the surface g{i) = 0 ; 2) the extent of each of the neighborhoods tx, t.2, tK having been arbitrarily determined, the regions fj,j = K + 1, v, then consist of regions of surfaces g'j) = 0 defined as follows ■' omitting the index j throughout, we write 9 (£., Vv 0 = [£ + ft (Vv 0 C + + pr(Vv Ol^d,, Vv 0, where pe (r^, £) is analytic throughout a region M (f, 77) contains no multiple factors. Here, the equation 296 PROCEEDINGS OP THE AMERICAN ACADEMY. can have multiple values of $ only for a finite number of values of 77, these being the values for which the equations * = 0, ^ = 0 have common roots, and by the condition 3, 3) none of these values of r) become infinite. Now we consider all such values of -q V = cr, r = 1, 2, /, for which the equation, considered as an equation in J,, *(?,}) = <> has multiple roots. Deal with each of these as in 5, cr taking the place of /3 in (6) ; then, in equation (7), some of the // 's will, in general, be greater than unity, i. e. some of the equations g ■=. 0 will have for the lowest terms in £ alone exponents greater than 1. For such as have their /x = 1, there are regular points. The others will afford singular points unless they have terms of the first degree in either ^ or £. Surround these points by neighborhoods 141 < 8, \m\<*, |CI<*» i. e. |?-aj<&, \V-Cr\ < J, \t\< 8, which are to be considered later. Now let t] = b be any value for which the equation <£ (?, V) = o has not equal roots. Then the equations g = 0 of (7) each have a term in £ to the first degree, free from -qx and £, and thus the points of the surface g = 0 lying in the neighborhood of the point $a = 0, rjx = 0, £ = 0, can be represented by a power series So, in this case, we have m developments $,=£rO&i©i 7i | < h ~ e' £ is an analytic function of £ throughout the region Also consider the surfaces in 5. Here also we have m regular points of surfaces, and as a result m functions of the form These, by the same method of proof as above, are seen to be analytic when III < *i-*, \v\ < **, where A is the nearest point in the 4-plane for which the equation has multiple roots for £, i. e. the smallest value of £ for which the equation (?, 1, ?)m = 0 has equal roots for $. But this is the smallest value of - for which the V equation a 1, i) = 0 * Cf. Briot et Bouquet's The'orie des fonctions elliptiques, § 28. The proof of continuity there given for polynomials in two variables will apply with very slight mollifications to analytic functions of any number of variables. Cf. further Jordan's Cours d'analyse, I. § 206, § 258. 298 PROCEEDINGS OF THE AMERICAN ACADEMY. regarded as an equation in £/r], has equal roots. Thus — is the largest value of t) for which the equation has a critical point. So the functions are analytic and give all points of the original neighborhood for which I- < hi — «n \v\ < 82> or for which / > jt^— = t + rrr1 — \ = ** + «*» f*> = r)» thus securing the limits \v\ < Sai Ul < S3, U| > (^ + e2)|4l, where A2 is the distance to the furthest point in the r/-plane for which the equation has a critical point, and if e2 is first chosen arbitrarily small, 83 can be determined not zero. Now consider the neighborhoods of the critical points of the curve *(?, v) = 0. In these, however small we take the 8, all the remainder of a circle in the 77-plane including all the values for which the curve cf> = 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 > h, + e2 . Then, if we take for 84 the smallest value of any ^ or S", the develop- ments within these circles together with the neighborhoods of the set of new singular poiuts will represent all points of the original neigh- borhood for which Finally, taking for 8 the smallest of the three quantities $2, 83, o4, the BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 299 whole set of functions thus determined will represent all points of the original neighborhood for which h| < 8, |C|< 5. The new set of singular points may or may not be all of degrees lower than ?n, but if they are we have simplified the problem ; we have reduc- tion, as we shall say, borrowing a term frequently used in the theory of algebraic invariants of a linear transformation ; and if not, the further treatment will be considered later. D. — An Example. Before taking up Case II, however, we consider an example in which the degree is reduced by one quadratic transformation, and the para- metric representation (A) is at once secured. Let the surface be The transformation secures for the equation corresponding to (3) *(6^0 = P + ?-l-?C = O. Here 0 (£$ = ? + ?-l and the critical points are 1=0, 5=1, ?=0, , = -l. Let and we have Hence Also let and we have d = €> Vi = V ~ l t ^2 + ^2+2t7i-^C=0. m = -i + Vti(t-&) + i- (a) £2 = l> f]i = V + ! > In (a) and (b), only that branch of the radical is taken which becomes + 1 for zero values of the arguments. 300 PROCEEDINGS OF THE AMERICAN ACADEMY. Again, we make the transformation and derive the surface Here and for the value £ = 0 we have the roots ? = * j I = — **• Let $3=1 — i, and we have the surface L2 + 2*& - e - ?V& - i?V = 0, 1 + h ^/?t?2+4|=2-4. whence £3 = 2 In a similar way, from the other root, (c) (d) In (c) and (d), for the radical is taken only that branch which becomes + 2 i for zero values of the arguments, and the function is seen to be analytic for sufficiently small values of q when CI '/ < i - « i ; and similarly when V \v\ = > 1 + e. Thus, in the ^-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 till up the remaining unshaded region. BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 301 Consider the point Let £ = £5 — 1 and we have &2- 2 & + ?-&£+ £=0, whence ^ = ^-2-i^-^+4. (e) In the same way, about the point £=1, ^ = 0, we liave the function £ 6= — + W£2-4?+4 (f) In (e) and (f), for the radical we take only that branch which becomes -f 2 for zero values of the argument, and for sufficiently small values of f the functions are analytic when | rj | < 1 — e2 . Agaiu, consider the point Let 1 = & + 2 Vl - i , ^ = -77 + 1 + 2*, and we have ^72 + 4 yi^^7 4-7 + Vl2 + 2 (1 + 2 1) 777 - £7£ - 2 vT^?£ = 0, whence j^-4^1-*-^ 1^16-16^+^-4^-8 (l + 2^7. (g) For the corresponding point 4r=-2A/l -i, ^ = l + 2», we have the formula 4 Vl — * + £ & = 2 ^ - £ Vl6 - 16* + ? - 4 V - 8(1 + 2t)%. (h) In (g) and (h), for the radical we take only the branch which becomes + 4 V4 — i 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 I *77 | = 1 17s | < 2 — e7 • Also, considering the corresponding points of 302 PROCEEDINGS OF THE AMERICAN ACADEMY. for which ^ = -1 + 2*, V= 1-2*, V= -1-2/, we have evidently similar re- gions for each. Then, by taking the e'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 £ = UV, 7] — v \/u (v — u) + 1 , £ = uv , r) = — v y/u (y — u) + 1 , $ = -(u2v + a/mV-F 4w2 — 4), v $ = ~(u2v — V«*4»a + 4w2— 4), 7] = V, ( = uv from u U ^z=^(u-V"2-4t;2+4), ^ = -(«+V"2-4r2 + 4), rj — uv, £ = a f] = uv, t, = u 00 (b) (c) (<*) (e) (0 u £= -( u + Vl6 — 16/ + u2-4v2-8(L + 2i)v ), v = u (v + 1 + 2 1) , $ M )#=!( M _ Vl6 - 16t + w2 — 4u2- 8(1 + 2%)v ), (g) 00 with three more sets similar to (g) and (h). Case II. — The polynomial <£(£, rj) contains multiple factors. Here, any points which are common to two different irreducible factors of <£(£, rj), or are critical points of a single irreducible factor, will be critical points of the curve *(£v) = o, BLACK. — THE NEIGHBORHOOD OP 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 I = a, 7] = P is a regular point of a factor fa (£, rj) of mul- tiplicity r, i. e. of the irreducible factor whose rth power is equal to i(£> v) an(* not a P°int of any different factor of <£(£, rj). Then, in the corresponding equation of form (7), g will contain a term £r as the lowest term in ifa free from ^ and £, and by Weierstrass's Theorem * we can develop the function about the point in the form PC + pi fa OC + + Pr (*» 0 1 E(^ Hi 0 = o. (9) These functions Pk(vi, 0' X = l, 2, r, are shown by a method similar to that used for the functions in Case I to be analytic within a region hi| y) + »*(*i y> z) — o, (a) <£(*, y) = 0 is a multiple curve ; let (x, y) have the form in the neighborhood of the point x = 0, y = 0, (x,y) = [x+p(y)]'»JE(x,y), (/?) where p (y) is analytic at the point y = 0, and p (0) — 0. The function ty (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 b) 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,tf, z) = 0 can be transformed, by means of quadratic transformations of the type x =■ xz, BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 305 on a finite number of regions ru t2, t , which fall into two categories : — 1) the region rt(i = 1, 2, k) is the neighborhood of a singular point of order < m ; 2) each of the neighborhoods of 1) having been determined arbitrarily small, the region ts (i = k + 1 , v) is then a regular 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, s = 0, is meant the set of points (cc, y, z) satisfying the relation \y\j (a?!, y, z) = x1mE(xu y) + zipx(xu y, z) = 0. (y') Here, the function E (xu y) is analytic and different from zero in the neighborhood of any point xx = 0, y = y0, (\y0 | < h), which corresponds to the neighborhood of the point x0 = p (y0), y0, and lience E (xx, y) is analytic throughout a region including in its interior the region l*i I < e> \y\ < h> if the positive quantity € is suitably chosen. A similar remark ap- plies to the analytic character of the function \px (xu y, z), and hence ! (xu y, z) is an analytic function of its three arguments throughout a region including in its interior the region l^i I < e> |y| < A» 1*1 < s- Now express equation (y') in the form *i(*n y? z) = 2p,..(y)^ir2s + F(x1} y, z) = 0, (e) where 0 < r + s = mi < m, vol. xxxvii. — 20 806 PROCEEDINGS OP THE AMERICAN ACADEMY. ml being the lowest degree of any term in xt and z together, and F(xuy, z) including all terms of degree higher than m^ in the two variables xu z. Each coefficient pr3 (y) may be divisible by a power of y, yl. In that case, however, nti must be less than m, for the term in x™ is present in $a (a^, y, z). By means of a transformation with non-vanishing determinant, xx = ax x2 -f /?! z2 ) Z = a2 X2 + Pi Z2 ) 4>j can be thrown into the form : *i (*i> V, z) = $2 fa, y, z2) = 9o(y)^mt + qi(y)x2'n-1z, + + qmi(y)z2"h + F,(x2, y, z2) = 0 (,) where q0 (y) =j= 0. Consider first the points of the circle \y\ < h at which q0 (y) = 0, if such exist. Each one of these points y{, (i = 1, 2, «) is a singu- lar point of 2 = 0 of order not greater than /«, and its neighborhood |*i|<«i |y-y*|<«, M.2 then be written in the form $2 (*2, y, *2) = *2 (*2> Vi, *2) = 02)*2mi + q~i{ydx™l~l z* + + qMj (y-i)z,n\ -f F2(x2, y,, z2) = [*."•« + nbtixt-i-1* + + rmJy2)l.2'"qF(y2)+F2(x2,y2,z2) = 0. (6) 3. Apply to the function 2 the quadratic transformation X2 =^ x$ z2. * 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 Ivobb's analysis. They appear to be indispensable. BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 307 Let the result be written as follows : — <£2(x2, y2, 22) = z2'"xl + rl(i/2)xzmi-1 + + rm{y2)]E(y2) + z2F&(xz,y2,z2)} =0.(k) From this last equation we deduce the following theorem : — All points of the surface = 0 in the neighborhood of the curve (x,y) = 0, 2i = 0, 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 (a:, y, z) = 0 of the lemma, the values of in 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 y2 being in or on the circle of convergence of the Taylor's development about the point z2 = 0 of the function rx(V2)> A=l, 2, r/h i\y2j> k — i, ±, /«!, all points of the surface <£2 = 0 in the neighborhood of the curve (x,y) = 0, sz = 0, are represented by points in the neighborhoods of points of the curve *3m' + rx (yjx^-1 + + r,% (y2) = 0 , z2 = 0, on the surface 4>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 a^K + n (b - a) x3m~l + + rmi (b - a) = 0 (p) are ux, a2, a,„ then points of the surface 4>2 — 0 for which |*«| < 8, K| < 8, y — b, are connected with the points of the surface (k) by the relation x2 = z, (xo + av) , y, — b — a, a = 1, 2, mx. Further, if we limit y.2 to a circle not reaching out to the nearest point for which qo(y2) vanishes, we have an upper limit for a„ as a root of the equation (u), and thus by taking z2 and xa small enough we can make x2 as small as we please. Then the transformations (8) and (£) still 308 PROCEEDINGS OF THE AMERICAN ACADEMY. secure a limit for the values of x and 2, and thus we have represented a neighborhood of the curve (x, 20 = 0, « = 0, on the surface $ (a:, y, z) = 0 as required. Now, however small the neighborhood we shut off about the points in the region \y\ < h for which q0(y) vanishes, since the results estab- lished above would hold also in a circle of radius hx > h, but still less than the radius of convergence of the series for p (y) in (/3), we can fill up the remainder of the circle of radius h with circles within which g0 (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 & (*» ft) = *3mi + rx (y2) xzm -1 + + rmi(y2) = 0. (v) If this is a multiple curve of the mx-th. order and mx < m, we have reduction. Moreover, if mx = m, but «."» + rx(y2)xzm^ + + n„,(y2) 4= [>a + />3(y2)]"\, we also have reduction. We need consider, therefore, only the case that *3m' + rx (j^W^1 + + rmi(ya) = [x, + PsCya)]"1!, > , ,. mx = m, > and show that this case can repeat itself at most but a finite number of times. 4. Suppose the function <£3(x3, y2) has the form (v'). Apply to the surface 3 (xs, y2, z2) = 0, (k), the transformation xs + p3(yz) = xi> and reduce the result to the form ^O^ y» z*) = x^Efa) + 22-^4(^4) yt, 22) = (0). (o) If any term in z2Fi(xi, y2, z2) is of degree in xi and z2 together less than mu it appears at once that we have a line of lower order. So we assume there are no such terms. Also, as the coefficient of a;4mi does not vanish identically in y2 (in fact, not at all) no transformation of BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 809 type (£) is needed, and after collecting all terms of the mrth order we make at once the substitution and proceed in the same manner as before if the degree is not reduced. For convenience, we suppose the succession of multiple curves of the same order to begin with that on the surface 4> = 0, and use a nota- tion independent of that hitherto employed. Our successive transformations are of the type x —pi (y) = *i (»■) xv-x-pv(y) = x whence x - px (y) +p*(y)z + pz(y)z'x+ + pv(y)zv~1 + x/. Q>) Develop the function in (y) by Weierstrass's Theorem : (x,y) = 0, z = 0, on the surface ®(x,y, z) = 0. In fact, the first lot of points excepted, those for which in equation (77) q0 (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 (0- Also so long as the multiple curve does not break up into simpler curves, the neighborhoods correspond, and when this reduction takes place we can cut out the neighborhoods of the points common to all of the resulting curves uy 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 3> (f, rj, £) = 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 once 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 (£, rj, Qm is the product of m linear factors in £, rj, £, all vanishing for a single set of values of the arguments $, rj, £ not all zero. Geometrically, the tangent cone, ($, rj, £)„, = 0, of the surface (£, rj, £) = 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 Ttpe. 1. In the special case in which the function (£, rj, £)m 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 (|, rj, £)m are not all equal. Case B. — The m linear factors of (£, rj, £)m are all equal. 2. Case A. — (£, rj, £)m is composed of m linear factors not all equal. The surface can be expressed in the form *(6 rj, 0 = (ft rj)m + (ft rj, Qm+1 + = 0 (13) where (£, 77),,, contains terms in both $"1 and r/"1. If the surface were in a form f(u, v, w) — (u, v, io)m -I- (u, v, w)m+1 + = 0 with the condition that the m linear factors of {u, v, w)m all vanish for the line u = aw, v = (iw, we could make the transformation ^ — u — aW, rj — V — /?«>, £ = W, 312 PROCEEDINGS OP THE AMERICAN ACADEMY. and all the resulting linear factors would have to vanish when £ = 0, 77 = 0, and so not contain £. Also by a linear homogeneous transformation in £ and rj we can se- cure the presence of terms in £"* and rf1, and in such case every linear factor of <£ (f, rj), which here is (£, rj)m itself, will contain $ and thus secure condition 3) of § 1, 3. B. — Quadratic Transformations. 3. The succession of surfaces and corresponding quadratic transfor- mations which are applied to the new singular points as found, so long as they do not reduce the degree, can be written in the form ^ (14) Apply to the surface (13) the transformation f = £i£i 7 = 7i£> and we have *(£, r;, o = r"[(^ >?om + £&, ti, i)m+i + ] = r[&, 7i)»K«A(^,7i» 0] as) = r*i(ii,7i, 0- As we assume the transformation does not reduce the degree of the singular point, there can be no term of degree less than m in the part ^(iu 7u £) and as all terms of this contain £, when we put the expres- sion in the form *, Hi, VI, 0 = (*1. 7l, Om + (*„ 71, 0-+1 + (16) we will secure reduction by another quadratic transformation unless ($v 7i» Om is tne product of w linear factors with a common line of intersection. In this case the factors cannot be all equal," for then (£i> Vi> 0)m would have its linear factors all equal, but these are the factors of (£1} rji)m. 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 (&, *, 0 = C" [(& vi, 1). + C(fi. vu i)m+i + ] = 0. (17) Now if f] = y2, r;x = S2, is the common point for which the m factors of (li> t)u l)m vanish, then the substitution & = fi — y2> % = vi ~ ^2> gives a group of with degree terms in £2 and 770 exactly corresponding to the terms of (£, rj)m. So in the successive collection of terms of the wth degree, the terms of (£, rf)m 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 vh = s ~~ vi-i ' vr ~ \ — , + M(U Vv,£) tf-*» 9^ = B(V,£)$0 (18) where **(£,, >to 0 = &*(£», Vv, l)E(Jsv, yv, 0- Combining transformations (14) we have the relations £ = yi£ + y2£2 + + y,P + P&\ v = s1z + 82f+ + 8vz» + e>Vv] *(6 v, 0 = C"**(t» n» 0 As contains both £m and rjm terms, we can develop by Weierstrass's Theorem. *(*, * 0 = [£" + j»i(* OF''1 + +Pm(v,Q]Ei(e, v, 0 *(6 * 0 = Df + ?i(& 0vm~l + + ?„(*, 0]^(£, v, 0 = * (^ 17, 0 ^2 (6 V, 0- ' As the function i£, (£, 17, £) contains a constant term, when the first trans- formation of (14yi is made, the factor £"• must come out of the , and a (20) 314 PROCEEDINGS OF THE AMERICAN ACADEMY. similar result is true for all of the succeeding transformations. So in the first part of (14) we could write for <£, ^ for 3>M, (^ = 1, 2, v) where the 's are derived successively in the same way as the 3>'s. At each stage the $ factor must contain all the terms of lowest degree in the corresponding

Also (22) = £,mv®v; and, combining with (21) , we have 9® _ £(m -l)v 9<5>v 9£v (23) But as has no multiple factors vanishing at (0, 0, 0) (see § 1,3), we have the relation L($, v, 0* + M& V) 0 || = R(v, 0 + 0. (24) Then, substituting for £ and 77 from (19) on the left side of equation (24) and using the relations (22) and (23), we have the required relation (18). 5. If v is taken large enough the transformations (14) will lead to the relations A(fe v„ 0** + mv($v, Vv, 0 %r = ?l O* + <»i(QT*fi(v» 0, (25) PAiv, v» Q*v + Qv&, vv, 0p- = M£ + ^(m^{U 0, (26) vrjv where 0. Then if any transformation is applied, there can be divided out of (77, £)n the factor £" leaving behind as the term of highest degree one in rf*~*. This cannot be cancelled with any term from another part (77, £)„+i, for any term from this would have as a factor tf after the £" has been divided out. As long, then, as the ?7 variable does not enter to the highest degree in the expression corresponding to (77, £)„ if n > 0, the degree of the S factor is decreased with each transformation, while the expouent of £ outside may be in- creased. Accordingly, by a finite number of transformations, we re- duce the S factor either to an E 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 £(77, £). By Weierstrass's Theorem we develop in the form S(?h 0 = It + niOv"-1 + + rn(0]£(v, 0 = T(v,0E(V)0- . (28) Consider the n factors of T(rj, £), 2?(^0 = n[, + fx(0]. (29) A=l 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 : fr! + «ta(0] [*+**«)]} {Lv+sth(.Q]tv+suA(01}bi+s»(Qy- (so) Now, for each pair, ^=[? + ^(0]D» + **(o:i, we have the relation Nk+Pk(V,i:)9~k = Lktt)$0, (31) at] since the two. factors are unequal. Then, by the same reasoning as used 316 PROCEEDINGS OF 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 £v, and so the right side must be, v = ^> and we have an upper limit for v, the number of transformations which leave the factor Nk of the second degree, and as a result leave the func- tion T of the rath degree. So, unless the function T(rj, £) in (28) is composed of n equal factors of form bi + s (0?i (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], 'Q either becomes an E function or has besides the E factor a factor of form (32), thus securing the form (25) if we divide out the factor £<"»-i)»\ 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 & = £-<»2(0j (33) i)v — y]v — oja (£) ) applied to the surface iu 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 rx or r2 in (25) and (26) is zero. Then iu 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 OP A SINGULAR POINT. 317 of 4 shows that the left side becomes divisible by £(m-1)M. So we have either (m—l)/x„(£„, -qv, £) goes over into X(£v, rjv, £), we have 9®v _9X _9X9lv _9X 9 £ v 9i„ 9 £„ 9£v 9 $v and similar conditions hold for the partial derivative with reference to 7/v. Accordingly, if by the transformation (33) <&„(£„, Vv, £) goes over into £2(£„, rjv, £) we replace equations (25), (26), and (27) by 1 v Lv(iV} £, t)X(l, Vv, 0 + MvQvi yv, 0— - = frvSiEfa 0, (34) 9tv Pv(l, vv> QBQ„ £,, £) + &<&, Vv, 0-J?= ^~^E($V, 0, (35) 9rjv Q(|*» Vv> 0 = XQv* Vi"> CAlC?** V"> 0 — &(€vj t]v, O-^aClfj Vv, 0- (36) Now, in a further succession of transformations of type (14) on the surface f2 (£„, Vi>> £) — 0, if there enters either a y or a 8 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'a and S's of the later transformations are 0 that we are not already sure of reducing the singularity. Now if in £2 (f„, r),,, £) there is any term of degree less than m in £„ and -qv 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 aljrjjt,h, where /+ g < m. Then, by a succession of p transformations such as defined, we have L = £,p$v+p, V" = £pyv+pj (derived from form of (19) when all y's and S's are 0). Substituting this in the expression above we get a?v+PV,,+p£ But we must divide out of this £mp, so that we have left the term n t} J yh+piZ-hg-m) "^v+pVv+p^ This term could not combine with any other derived in a similar way, for if we had another term b$* rjg £\ we should get 7 >/ 9 yk+p{f+g—m) o?v+pvv+P£ 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+g + h + p(f+g — nij^rn or (p + 1) (m — /— g) ^ h, and as m > f + g h + 1^ »» — /— g thus securing an upper limit for p, the number of transformations which leave the term and the singular point of the mth order. So it is only in the case in which all terms of Q (£„, r/v, Q are °f degree not less than m in £" and rjv 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 (0) we take lv = a?a, Vv = z-i, t = y-i, the singular line being ^ = 0, |„ = 0. There is in D, (£„, rjv, £) a term in £vm, and so the expression q0 (y2) does not vanish when y2 = 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 (f„, rjv),n is not composed of m equal factors, the part q0(0)xami + qx{0)x^-lz + + ?«h(0)si"i from (6) which corresponds to (£„, nv) is not composed of m equal factors, and the resulting curve in (k) *3CTl + niy^x^-1 + + rmi(j/2) = 0 has not m equal roots when y2 = 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 (£M, rj^, *£),„ contains the terms of the type (£, rj)n found iu the original equation (13). So there is but one singular point of the m-th order in the finite region of the 77^-plane. Further, the equation (^, 1, Qm = 0 for the value £ = 0 cannot have m equal roots since (£, v)m is not a perfect m-th. power of a linear factor. Accordingly, the transformation corresponding to (8) in § 1, 4, cannot produce a singular point of the m-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 (f, rj, £)m are all equal. The surface can be expressed in the form *(& v, 0 = [F + Pn(a, Of-2 + + Pm(r,, 0] #(6 v, 0 = X(£,v,0£&vU) = 0, (37) where, in X, $'" is the only term of degree m. If it were iu the form f(u, v, w) = (ail + (3v + yw)m + (it, v, w)m+1 + = 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 u = au + (3v + yW v = v w = w we secure the form f(u, v, w) =f(u, v, w) — um + («, v, w)m+l + By Weierstrass's Theorem we can express this in the form f{u, v, w) = \um + p, (v, w) u"1-1 + + pm (v. w)-] E{u, v, w). (38) Now, in the exjjression pK(v, 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 i£ factor, there would have to be present in^a term of degree < m containing v or w. Make in (38) the transformation u + r* Pi (v w) v w As pi (v, w) contains no term of degree less than 2, by the considera- tion above, f goes over into form (37). B. The Quadratic Transformation. 2. The transformation £ = i£> v — v& applied to (£, 77, £) secures the form *(*, v, 0 = *"•*(£ v, 0 = £*[?" + £*(!, v, 01 (39) Here the curve Q, ij) = 0 becomes |m = 0, and so, applying the Lemma of § 2 to a circle in the y^-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 ^-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 $ = 0, and the point at infinity. BLACK. THE NEIGHBORHOOD OF A SINGULAR POINT. 321 3. The quadratic transformations to be used are of two types 1) £p =s &+1&4 Vn = Ofo+1 + VrO &u (40) 2) in — in+iVnt Cm = (&+1 + ef.+i)Vn' (41) In a succession of transformations of type (14) we see that yx = 0, since the first set of points is taken on the line |" = 0. Further, sup- pose after the substitution q — 8X = ^ in of (39) the expression (!, 171 Qm contains terms besides the £m ; then it cannot be composed of m equal linear factors, for that would require a term containing fm_1 ; 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 E factor, for then, on account of the constant term of the E factor, there would have to be present in a term of degree lower than m. So as soon as the function corresponding to of 4> contains more than the mih power of the £ variable, the function corresponding to (£, 77, £)„, 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 £ and q 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 op Quadratic Transformations in avhich THERE IS NO REVERSAL OF TYPE. 4. After a sufficient number of quadratic transformations the surface can be reduced to the form -,v + • • • + vv VOL. XXXVII. 21 [(C + ~<2&E(n»> 0 C"2 +■■•■• + % ?vE(ji*, i)] m» i, 0> (42) 322 PROCEEDINGS OF THE AMERICAN ACADEMY. while all later transformations can be taken of the type £M = £y+lL rjy. = Vn+iC (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 X factor of (37), the surface will take the form [C + v» (v* 0 C2 + + P™ (Vv, 0] * (&, to 0 = 0. (44) Now by the same reasoning as used for the function R in § 3, 5, if v is taken large enough, the coefficients of the powers of £„ in Xv will all be of the type s = 2, 3, m. For any one of the functions there is a determinate succession of transformations of type Vy = £(Vn+l + S = 2, 3, m, are equal, some of them possibly having zero exponents. Then we use the transformation np + v.OO^n, (45) BLACK. — THE NEIGHBORHOOD OF 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 -q variable present only in the E factors, so that the general term (after the first) of the function Xv is of type pUfayQC-, s = 2,3, m. Suppose, after this, there are p transformations of type (40). Then the corresponding term after the factor £mp has been divided out is 9%+{ m—s)p—mp jg, on. gm— s 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 -f <7s — Ps = m or p < — » ~ 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 S'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. r ~~~ s ) If, for any term a transformation of type (43), after the factor £'" has been divided out, yields „Pr yQr+Pr—r jfi / y\ j.m-r decreasing the exponent of I by r — pr. This decrease takes place at every such transformation, and thus the exponent of £ must finally be * We do not need to consider the possibility of having all the coefficients of the powers of £„ lower than the m-th vanish, for then the function Xv would have m equal factors £„ and this case has been excluded. 324 PROCEEDINGS OF THE AMERICAN ACADEMY. reduced to a value q'r less than r — pr, in which case the sum of the exponents of the three variables, pr + q'r + m — r, is less than m and reduction ensues. So it is only in the case in which for every term ps> 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 £ 9s + n(Ps~ *)• Now by taking n large enough we can make the quotient n (P* - *) + 9s 7) ™— S have the lowest value for the term in which — is lowest, while if s 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 V — T V . Q — and so — is lowest in the same term in which — is lowest. r r 6. A succession of transformations of type & = |M+i£, (46) followed by a succession of type £1 = ^+117, (47) secures the surface with condition 5, 2) in the form J. (48) where for some particular term in Xp, the rth, Pr qs — ns > 0, or Si— I °) ^ °- A transformation of type (40) will give for pr a function from which we 326 PROCEEDINGS OF THE AMERICAN ACADEMY. take out the factor C, the other factor being of degree less than nr unless the part (7/, £)nr has nr equal linear factors. For, if nr (V> t)nr — n (aprj — jB pt) pr=l and not all the linear factors are equal (or linearly dependent), then the substitution V = C(vi + Si) gives fir C II (apr/x + dp^ — /3p) P = l and leaves an absolute term in any factor for which apSj 4= /3P, thus securing in the product of the factors terms of degree less than nr. Also the degree might be lowered on account of terms in some later part as (77, £,)nr+k- But, if all the factors of (7/, £)«,. are equal (or linearly dependent) and 8j is taken so as to satisfy the condition aP^i = fip, p = 1» 2, «r, then after the factor C is divided out, we have left but one term in rj1nr, 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 rj Br, 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 pr (possibly to zero), except for factors taken out which are powers of the r/ and £ variables. Accordingly, by a succession of transformations containing a sufficiently large number of reversals of type, the coefficient pr must be reduced to the type 9. All further transformations to be considered may be taken of the types in = t».+\yi, £m = C+1^7- (50) BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 327 For if a transformation of type (40) or (41) in which the 8 or c is not zero were used, we should have in all the coefficients of Xv in (42), out- side of the E 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 £ 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. 17„ K, > Kt, b) Us n„ K, < Kt. (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,' = K, + ITS, K/ = K, + IT,, and so K/ — K/ = K, — Ks - (n, — nf) < K( - Ks. Also, for a transformation of type (50), if the new El's are Uj IT/, we have UJ = n. + K„ uj = Ut + K„ and IV - uj = us-ut- (k, - k.) < n3 - n,. So when a condition of type (52) holds, any transformation applied will reduce the difference of either the ITs or K's, if in fact it does not change the sign 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 Kr and IT,, in (51). So the succession of trans- formations of whatever kind must finally reduce the difference of either the II'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 Ks 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 «) or b) must hold finally, whatever the pair of values s and t, we shall have some value as r such that n,. < ITS, K, < K„ s = 2, 3, m. from which follows the required condition Pr KPs r ~~ z s 9r<91 2, 3 m. 11. The method of 6, applied to the surface resulting from the treat- ment of 10, will secure the result of 6. It may be that already either pr < r or qT < r, but in such a case the number of transformations of BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 829 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 tlie case of surface (48) any succession of transformations of types (40) and (50) will finally reduce the degree of the singular point. Consider the term Any transformation of type (40) adds to the exponent of £, pr — 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 77 variable. So in any case, by virtue of the reduction of degree, we must have finally either Pr (£, rj), to the points of intersection of two such curves, and to the points of class 1) in § 2, 1. In the third group place all singular points derived in a similar way from those of the second group, etc. Suppose n to be the number of the last group in which there are singular points. From what we have proved, n must be finite. The neighborhood of a point in the wth group is represented by the neighborhoods of a finite number of regular points, together with a finite number of regular regions, and so by a finite number of parametric formulae of type (.4). The neighborhood of a point in the (ra — l)st group is represented by the neighborhoods of a finite number of points of the ?ith group, together with a finite number of regular regions, however small the neighborhoods of the singular points are taken ; but as the neighborhood of any point in the wth group is represented by a finite number of parametric formulae of type (A), the same follows for any point of the (n — l)st group, using the intermediate transformation to get the parametric formulae. This reasoning can be carried on until the original singular point is reached, since the mapping of the neighborhood of the original point upon a finite number of regions of classes 1) and 2) applies to each of the later singular points also, and then furnishes the step by which we know that we can always pass from the (y + l)st to the vth group. Thus we have the coordinates £, rj, £ of the surface expressed in parametric formulae of the desired type, the parameters being in general coordinates of points of some simple surface. Then by using the intermediate transformations connecting x, y, z with $, rj, £, we represent the first set of coordinates in the desired form. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 12. — December, 1901. CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF HARVARD UNIVERSITY. — XLVIII. A PRELIMINARY ENUMERATION OF THE SOROPHOREJE. By Edgar W. Olive. ♦ CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF HARVARD UNIVERSITY. — XLVIII. A PRELIMINARY ENUMERATION OF THE SOROPHOREiE. By Edgar W. Olive. Presented by Roland Thaxter. Received November 9, 1901. Owing to unavoidable delay iu the publication of a monograph of the Acrasieae and their allies which the writer has in preparation and for which figures have already been drawn, the following preliminary synopsis, which includes all the known forms and which will be sup- plemented as soon as possible by the more extended paper, has seemed advisable. This investigation was undertaken some years since at the suggestion of Professor Thaxter, and a majority of those species that I have myself studied have been kept under observation in pure cultures for a long period, so that the constancy of the characters distinguishing them has been definitely determined. As far as I am aware only one member of the group has been heretofore reported from America, although certain of them are very abundant in laboratory cultures. Of the European representatives several remain unknown except through the original diagnoses, which are unfortunately, in a majority of cases, meagre and unaccompanied by figures. A comparison of the conditions presented by the individuals which constitute the so-called fructifications of these organisms indicates that the term spore cannot be properly applied to them in all cases. In the genera Sappinia and Guttulinopsis the individuals, even in mature fructifications, are merely slightly contracted and hardened, secreting no definite wall. At germination such resting individuals, therefore, gradu- ally assume the form of a vegetative amoeba without casting off a spore wall of any kind. In order to distinguish these bodies from true spores, such as occur in a majority of the genera, as well as from the transi- tory resting conditions of isolated vegetating amoeba? which were first characterized as " microcysts " by Cienkowsky, the term pseudospore is 334 PROCEEDINGS OF THE AMERICAN ACADEMY. here employed, since it expresses with sufficient exactness the actual conditions. It will be noted further that in characterizing the Acrasieae as a whole, emphasis has been laid on the fact, usually overlooked in accounts of these organisms, that the vegetative stage ends before the pseudo- plasmodium condition begins. The latter, therefore, is a phenomenon con- nected not with vegetation but with fructification, and is by no means homologous with the plasmodium of true Myxomycetes; nor is it com- parable to the vegetative net-plasmodium of the Labyrinthuleae. I have followed Zopf, moreover, in characterizing as a " net-plasmo- dium " the peculiar form of association occurring in the Labyrinthuleoe, although it appears to be doubtful whether, in all cases at least, the con- dition thus distinguished represents a true fusion, or whether the relation is merely one of contact. SOROPHOREtE Zopf. Amcebas of the usual irregular myxamceba form or more or less reg- ular and spindle-shaped, never possessing a swarm spore stage, forming either a pseudoplasmodium or a net-plasmodium ; resting bodies borne in sessile or stalked sori, which are either naked or imbedded in a gelatinous matrix. ACRASIEiE Van Tieghem. Saprophytic, usually coprophilous, organisms, having two definitely recurring stages, — a vegetative period, in which independent myxamoebaa crawl about by means of amoeboid movements and undergo multiplication by division ; and a fructifying period, in which the myxainccbse typically aggregate into colonies called pseudoplasmodia and form either spores or pseudospores, held together by a mucus substance, and borne in stalked or sessile naked masses, or sori. SAPPINIACE^E. Myxamcebas comparatively large, with lobose pseudopodia. The resting sta^e consisting either of a single encysted individual or of many individuals encysted in masses at the ends of projections of the substratum. This group is included here only provisionally, since the amoeba? normally become encysted singly, thus forming microcysts, and do not show the characteristic phenomenon of aggregation, or colony formation. The aggregations which, it is true, often occur at the distal ends of OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE.E. 335 small projections above the surface of the substratum, are not due to any chemotactic stimulus such as must be assumed to cause the formation of true pseudoplasmodia, but, although they may perhaps suggest the possible beginnings of such conditions, are probably accidental, resulting rather from a tendency of the arnoebaj to seek drier situations at the period of fructification. SAPPINIA Dangeard (1896). Characters of the order. Sappinia pedata Dangeard. Le Botaniste, 5 Ser. p. 1-20. 5 Figs in text. 1896. Amoeba? forming resting conditions of three kinds : " amibes pedicel- Ices," in which they are transformed into a pear-shaped body without definite wall raised above the substratum by a stalk of about equal length ; " hjstes pedicelles" in which they are similarly modified but which form a definite wall about the oval body; and '' spores," in which groups of individuals become encysted at the ends of projections from the substratum. On dung of horse, cow, dog. France ; Russia; Massachusetts ; Indiana. At least two species of this genus appear to be common on various kinds of dung in this country, but owing to the fact that Dangeard gives no measurements I have been uncertain which of them should be referred to S. pedata. In both forms resting bodies comparable to the aggregated "spores" occur, as well as u amibes pedicellees" although I have not as yet observed the definitely walled "kystes" which Dangeard appears to distinguish from them. The larger and more frequent of the American species, which I have assumed to beloDg to S. pedata, has the following measurements : stalk of the "amibes pedicellces" 30^-125^, head 30^-60^ long; rounded individuals (" spores ") of the aggregations 20^-50^ in diameter. GUTTULINACEvE Zopf. Myxamoebse either limax-shaped, without pseudopodia, or of the ordinary form with rounded or lobose short pseudopodia. The sori, irregular in shape or spherical, sessile or stalked, consisting of either spores or pseudospores. GUTTULINOPSIS nov. gen. Myxamceba3 having lobose pseudopodia. Sori sessile or stalked, com- posed of pseudospores, those of the stalk usually slightly elongated. 336 PROCEEDINGS OP THE AMERICAN ACADEMY. Guttulinopsis vulgaris nov. sp. Sori usually stalked, sometimes sessile, about 150^-500/* in height X 150//.-4.CKV broad. Fructifications varying in color from whitish to dirty yellowish according to the character of the substratum and the dry- ness of the sorus. Pseudospores usually irregularly spherical, about 4/z- 8p in diameter. On dung of horse, cow, pig, mouse, etc. Cambridge, Mass ; Alabama j Indiana ; Maine ; Porto Rico. This form, which has conspicuous fructifications so large that they may be readily seen with the naked eye, lias been met with very fre- quently on fresh cultures of various kinds of dung. Although Guttulina aurea Van Tieghem may prove to be identical with the ahove species, the fact that, according to the original description, it possesses resting bodies which are characterized as " spores," having a golden yellow color, renders it improbable that the two forms are the same. Guttulinopsis stipitata nov. sp. Sori yellowish white, long stalked, the stalk composed of individuals similar to those of the head. Sorus about 1 mm. -1.2 mm. high; the stalk about 800/a long, the head 250/* in diameter. Pseudospores spher- ical, 3^-5^ in diameter. On dung of dog. New Haven, Conn. This species, the largest representative of the genus, has been met with but once, and is founded on a mounted specimen and dried material collected at New Haven some years ago by Dr. Thaxter. Guttulinopsis clavata nov. sp. Sori yellowish white when young, comparatively long-stalked, the stalk composed of a column of slightly elongated individuals surrounded by mucus. The stalk-cells held within the peripheral mucus adhere together after the deliquescence of the pseudospores of the head, forming at the apex a rounded or conical columella of elongated adherent cells. Sorus about 400iu-800iu in height, the stalk about 170^-250//. long, the head I00(u-400iu in diameter. Pseudospores of the head somewhat broadly oval, 3//.-4/A X 6// - 7/a, or spherical, then 4^-5//. in diameter ; those of the stalk about 3fi-Ofi X 7/j-10ix. On dung of dog. Cambridge, Mass. ; Indiana. This distinct species is frequently met with in fresh cultures of the dung on which it has its habitat. The base of the stalk is often imbedded OLIVE. — PKELIMINARY ENUMERATION OP THE SOROPHORE^E. 337 in an abundant mucus, which is especially noticeable when it swells after being placed in water. GUTTULINA Cienkowsky (1873). Myxamcebre limax-shaped, without pseudopodia. Sori irregular in shape or spherical, sessile or stalked, composed of spores which have a definite protective cell-wall. The cells of the stalked forms somewhat differentiated in shape. Guttulina rosea Cienkowsky. Trans. 4th Session of Russ. Nat. at Kazan, 1873. ' ' Sori short-stalked and rose-colored ; head IQQfx long, supported upon a stalk of about equal length. Spores of the head spherical ; those of the stalk closely laid and wedge-shaped." On dead wood. Russia. Known only from the original description above quoted. Guttulina protea Fayod. (Copromyxa protea Zopf.) Bot. Zeit., 11, p. 167-177. 1 Plate. 1883. Sori l-3mm. high, sessile or short-stalked, of somewhat irregular form, yellowish white, with crystalline lustre. Spores 9/aX14u; hyaline, colorless or slightly yellowish, more or less oblong or oval, bean-shaped, or almost triangular in outline. On dung of horse and cow. Germany. This form, which is known only from Fayod's original description, is retained under its original name, notwithstanding the fact that it has been separated by Zopf under the name Copromyxa on the ground that the " myxamcebae undergo no differentiation into stalk and head cells, whereas in Cienkowsky's form, there is a slight differentiation." The fact that certain species of Guttulinopsis show both stalked and sessile forms in the same culture diminishes the importance of the stalk as a character of generic value and justifies the resumption of the original name given by Fayod. Guttulina aurea Van Tieghem. Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. " Guttulina aurea has its fruit pedicelled and resembles closely G. rosea, but differs in color. The spores spherical, Ap.-6fA, golden-yellow. Upon dung of horse." France. 338 PROCEEDINGS OP THE AMERICAN ACADEMY. Guttulina sessilis Van Tieghem. Bull, de la Soc. Bat. de France, XXVII. p. 317. 1880. " Fruit sessile ; a simple droplet of pure white, resting directly on the substratum. Spores oval, colorless, aggregated in a sphere and cemented, as in the preceding species, by a gelatinous substance ; 4/a X 8/t. On the integument of beans in a state of decay." France. Guttulina aurea and G. sessilis are known only from the original descriptions above quoted. DICTYOSTELIACEiE Rostafinski. Myxamcebce possessing slender elongated pseudopodia. Sori consist- ing of spherical masses of spores or of a chain of spores ; stalked, the stulks composed of distinct parenchyma-like cells with cellulose walls. ACRASIS Van Tieghem (1880). Spores concatenate, terminating an erect simple filament, consisting of a single row of superposed cells. Acrasis granulata Van Tieghem. Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. Spores spherical, with a slightly roughened or granular wall, having acuticularized external portion of deep violet color ; 10^-15^ in diam- eter, often unequal in the same chain, the chain varying much in the number of component spores and cells. On a culture of beer yeast. France. Known only from the original description. DICTYOSTBLIUM Brefeld (1869). Sori stalked ; the stalk simple or only occasionally bearing irregularly disposed branches ; luxuriant fructifications frequently gregarious. Sori spherical, or subglobose. Dictyostelium mucoroides Brefeld. (Ceratopodium elegans Sorokin.) Abh. d. Senck. Nat. Ges., VII. p. 85-108. PI. I-III. 1869. Sorus and stalk white, or when old, yellowish ; the fructifications varying in height from 2-3 mm. to 1 cm. or more. Spores oval or elongated ellipsoid, 2A/x-S^ X 4/x-6/x. OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE.E. 339 On the dung of various animals, such as horse, rabbit, clog, guinea pig, grouse, etc. Also found on cultures of yeast, paper, fleshy fungi, etc., in a state of decomposition. Germany, Russia, common in America. This very common species is extremely variable in the size of its spores and fructifications. The limits of the spore measurements as given by Brefeld in his original description have been therefore somewhat increased. Dictyostelium sphserocephalum (Oud.) Sacc. and March. {Hyalostilbum sphcerocephalum Oudemans.) Aanw. Myc. Nederl., IX.-X. p. 30. PL IV. 1885. Sorus white; when old, yellowish or greenish-white. Stalk frequently very long and luxuriant, varying from 2 mm. to 1.5 cm. Spores oval, rarely spherical, or sub-inequilateral, 3^-5/x X 5/a-IO/a. Dung of mouse, (common), rat, bird, toad, deer, turtle, muskrat, etc. Belgium ; Cambridge and Boston, Mass. ; New Hampshire ; Florida ; Pennsylvania ; Liberia. In the above description the limits of the measurements of spores and of the length of stalks are greater than those given by Marchal, by whom the maximum length of the spore is stated as 8^ and that of the stalk as 5mm. The measurements of the fructifications are certainly more variable than indicated by Oudemans. This species was founded by Marchal from the fact that the spores differed in size from those of Dictyostelium mucoroides, which he states to be only about one-half as large. As will be seen by the measurements given above, this difference is by no means as great as indicated ; and, although the present arrange- ment is retained for the present, it may prove desirable to unite these two variable species. Dictyostelium roseum Van Tieghem. Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. " Spore mass spherical, of a bright rose color. Spores elongated oval, 4/x X Sp.. On the dung of various animals ; especially on rabbit dung, in company with Pllobolus micros'porus.'n France. Dictyostelium lacteum Van Tieghem. Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. "The mass of spores forms a milk-white drop at the summit of a stalk which I have always seen composed of a single row of cells. Spores 340 PKOCEEDINGS OF THE AMERICAN ACADEMY. colorless, spherical, very small, 2[x-3fi in diameter. This form has been met with several times on decaying agarics." France. Neither of the two ]5receding forms have been found in American cultures, hence the writer can add nothing to our knowledge concerning them. Dictyostelium brevicaule now sp. Sorus white ; stalks 1-3 mm. high. Spores oval, 3/^-4/j. X 4//-7/Z or rarely spherical and 3^-4//. in diameter. Dung of sheep and goat. Cambridge, Mass. A small, erect fructification, quite constant in the possession of a short rather rigid stalk bearing a sorus of comparatively large size and very different in aspect from the long, luxuriant, frequently flexuous, fructifi- cations of D. mucoroides and D. sphcerocephahcm. Throughout the four years that this species has been kept growing in laboratory cultures, it has retained its original distinct characters. Dictyostelium purpureum nov. sp. Sorus and stalk purplish or violet ; when mature, almost black. Spores oval, rarely somewhat inequilateral, 3/*.-5/x X 5/x-Sfx. Dung of mouse, toad, cow, horse, sheep, muskrat. Cambridge, Mass.; Indiana ; Florida. This distinct species, well-marked by its color, was collected in Aug- ust, 1897, in Crawfordsville, Indiana, on mouse dung cultures, and in October of the same year by Dr. Thaxter in Eustis, Florida, on toad dung. Both forms have been cultivated ever since in the laboratory, with no particular precautions as to the dissemination of the spores, and it is not impossible that the fructifications which appeared at Cambridge on sub-strata other than the two just mentioned represent laboratory escapes. Dictyostelium aureum nov. sp. Mature sori light to golden yellow, 1.5mm. -4mm. high. Spores oval, or frequently inequilateral, 2.5^-3^ X Ofi—Sfi. Mouse dung from Porto Rico. This species, communicated by Dr. Thaxter, is quite well defined through the color of its fructifications, but especially so by its myxamcebse and its manner of growth. It matures very slowly on a horse dung de- coction or on other media especially favorable for the rapid development of the common species ; while the myxamoeboe, instead of possessing the OLIVE. — PRELIMINARY ENUMERATION OF THE SOROPHORE^. 341 usual form with elongated, sharp pseudopodia, are in general irregularly lobed and nodulated, even when growing under normal conditions. Such irregular shapes are similar to those assumed by the rnyxamcebre of other species when they are growing under such abnormal conditions as are furnished by an insufficient water supply. POLYSPHONDYLIUM Brefeld (1884). Sori spherical, borne terminally on primary and secondary stalks, the latter branching in whorls from the main axis ; the fructification occa- sionally simple as in Dictyostelium. Whorls varying in number from 1-10, and the number of branches in each whorl from 1-6. Polysphondylium violaceum Brefeld. Schimmelpilze, VI. p. 1-34. PI. I, II. 1884. Sori and stalks purplish or dark violet, varying in height from about ^cm.-2cm. ; sori about 50/x.-300^u in diameter. Spores elongated oval, 2.0/i.-5/x X 6ix-8fx. On dung of horse, bird, sheep, toad, muskrat. Italy, Maine, New Hampshire, Massachusetts, Florida. The limits of spore measurements as given by Brefeld have been in- creased here as in other instances. The form growing on bird dung, brought by Prof. F. O. Grover from Center Ossipee, N. EL, and the Massachusetts form on the dung of muskrat, seem to correspond very closely to the type description. The spores of the Maine and Florida forms are somewhat smaller, while the general aspect of the fructifica- tions is different in that they are more delicate and less luxuriant and the sori have a less diameter than those of the type. These differences, however, seem hardly more than varietal. Polysphondylium pallidum nov. sp. Sori and stalks white, the sori about 50/^-80/x in diameter. Spores oval, 2.5/x-3/x X 5^-6.5/^, or occasionally spherical, about 7fx-8fi in diameter. On duug of ass, rabbit, muskrat. Liberia, Africa ; Arlington and Stony Brook, Mass. This delicate species is well characterized by the small size of its sori. In an interesting specimen, found by Mr. A. F. Blakeslee on muskrat dung, luxuriant fructifications showed that some of the branches them- selves bore several whorls of branchlets. That this doubly verticillate 342 PROCEEDINGS OF THE AMERICAN ACADEMY. character was not constant, however, was proved by growing the form on a sterilized nutrient medium, on which the fructifications showed simply the normal method of branching. Polysphondyliura album nov. sp. Sori and stalks white, the sori 100^. to 200^ in diameter. Spores oval, 2.5^-3/x X 4^-5.6^. On dung of toad from Eustis, Florida. Although the two forms above described have some features in com- mon, their gross characters are such as to justify their being placed in separate species. The sori of P. album are not only larger but are usually more numerous in a whorl, hence its fructifications are more conspicuous ; moreover, the stalks of this species are rather constantly weak at the base, so that the fructifications lie close to the substratum in a characteristic fashion. CCENONIA Van Tieghem (1884). Sorus globular, borne at the summit of a stalk which is dilated into a sort of cupule, in which the sorus is supported. Ccenonia denticulata Van Tieghem. Bull, de la Soc. Bot. de France, XXXI. p. 303-300. 1884. Sorus yellowish; stalk colorless, 2-3 mm. high, having a dilated base and expanding at the summit into a cupule which is finely toothed at its edges ; each peripheral cell of the stalk bearing a tooth or papilla on its exposed side. Spores Q^-S/j. in diameter, with yellowish cell walls. On decaying beans. France. This remarkable form, so far as I am aware, has not been met with since it was originally described by Van Tieghem. LABYRINTHULEiE Cienkowsky. Organisms having two definitely recurring stages, — a vegetative stage in which spindle-shaped or rarely spherical amoebae, bearing usually bipolar filiform pseudopodia singly or in tufts, may be either isolated or combined by the union of the pseudopodia into colonies forming net-plas- modia; and a fructifying stage, in which aggregations of individuals, com- parable to pseudoplasmodia, form spores borne in stalked or sessile sori. OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE^E. 343 Saprophytic or parasitic organisms living on dung, or on alga? in fresh or salt water. LABYRINTHULA Cienkowsky (1867). Amoeba? spindle-shaped, colorless, or colored by means of yellow fat bodies. Spores borne in formless masses, producing one to four amoeba? at germination. The species of this genus have thus far been observed only by the authors cited. Labyrinthula vitellina Cienkowsky. Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867. Amoebae containing orange-red coloring matter, which turns blue with iodine. Spores oval or spherical, 12^ in diameter, producing four amoeba? at germination. Living on sea-weeds growing on piles in Odessa harbor, Russia. Labyrinthula macrocystis Cienk. Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867. Colorless or feebly yellowish. Spores spindle-shaped, 18^-25^ long, imbedded in a hyaline substance ; the contents producing four amoeba? at germination. Living on alga? growing on piles at a higher elevation than L. vittelina, only submerged by the surf. Russia. Labyrinthula Cienkowskii Zopf. Beitriige zur Pliys. u. Morph. niederer Organismen, II. p. 36-48, Taf. IV, V. 1892. Sori colorless, naked. Spores at germination producing only one or at most two amoeba?. Living in fresh water, parasitic on Vaucheria. Germany. DIPLOPHRYS Barker (1868). Amoeba? spindle-shaped or nearly spherical, with yellowish oil globules. Fructification (in D. stercorea) a definite stalked or sessile sorus. Diplophrys Archeri Barker. Quart. Jour. Mic. ScL, VII. p. 123. 1868. Individuals nearly spherical or broadly elliptical, 4^-5^ in diameter, bearing at almost opposite poles a tuft of filiform pseudopodia ; the pro- 344 PROCEEDINGS OP THE AMERICAN ACADEMY. toplasm containing an oil-like refractive globule of an orange or amber color. Fructification unknown. Living in fresh water. Ireland, Germany, Pennsylvania and New Jersey (Leidy). In this provisional arrangement, I have followed Cienkowsky in refer- ring this species to the Labyrinthulese, although I regard it as improbable whether Diplophrys Archeri and D. stercorea should be included in the same genus. The aggregations of the vegetating amcebce of D. Archeri seem to be an association of the young iu groups, the colonies being formed by successive division of the individuals ; and there is nothing definite known concerning a resting stage. Diplophrys stercorea Cienkowsky. Archiv. f. mikr. Anat, Bd. XII. p. 44. PI. VIII. 1876. Individuals lens- or spindle-shaped, about 4^-6^ long, bearing at both ends several pseudopodia, almost bilaterally symmetrical. In the interior a nucleus, one or two contractile vacuoles and a yellow pigment body. Both the isolated and united individuals of the net-plasmodium finally becoming aggregated to form without change of shape pseudospores borne in sori, which are usually stalked, sometimes sessile. On dung of horse, cow and porcupine. Russia; Cambridge, Mass.; Intervale, New Hampshire. This species has been met with twice in American cultures, and so far as I am aware, with the exception of D. Archeri, is the only repre- sentative of the Labyrinthuleae which has been found in this country. A form, which is probably the resting condition of Cldamydomyxa laby- rinthuloides Archer, has been found growing in the cells of sphagnum, at Kittery, Maine, by Professor Thaxter. As Archer and others have pointed out, however, it is very doubtful whether this peculiar organism should be included in the Labyrinthuleae. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 13. — January, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE DECOMPOSITION OF MERCUROUS CHLORIDE BY DISSOLVED CHLORIDES: A CONTRIBUTION TO THE STUDY OF CONCENTRATED SOLUTIONS. By Theodore William Richards and Ebenezer Henry Archibald. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. THE DECOMPOSITION OF MERCUROUS CHLORIDE BY DISSOLVED CHLORIDES: A CONTRIBUTION TO THE STUDY OF CONCENTRATED SOLUTIONS. By Theodore William Richards and Ebenezer Henry Archibald. Received November 23, 1901. Presented December 11, 1901. Introduction. Long ago Miahle observed that a concentrated solution of common salt acts upon calomel with the formation of small amounts of mercuric chloride.* Many years afterwards, one of us,f without knowing of his work, rediscovered this reaction, and found that the fluctuations in the potential of the " normal calomel electrode " of Ostwald, are due to ita disturbing influence. At that time it was shown that the reaction is much diminished by dilution, and hence that a decinormal solution is far better as an electrolyte than a normal solution. The "decinormal electrode," thus recommended for the first time, has since come into common use. It was shown also that neither light nor oxygen are important causes in effecting the decomposition, but that the reaction is much furthered by increase of temperature. No attempt was made at the time to fathom the matter, but a suggestion was made that the reaction might be due to the catalytic action of the ionized chlorine of the dissolved chloride. The investigation of the problem which was at that time promised has now been continued, and the object of this paper is to show that while the second condition of this suggestion seems probable, the first does not hold. Another example is thus afforded of the frequently recurring circum- stance of the removal of a reaction from its classification among catalytic phenomena after better acquaintance with its nature. * Miahle, J. Pharm., 26, 108; Ann. Cliim. et Phys. (3), 5, 177 (1842). t Richards, These Proc, 33, 1 (1897) ; Z. phys. Ch., 24, 39. 348 PROCEEDINGS OF THE AMERICAN ACADEMY. The method employed was to treat calomel with solutions of chlorides of various concentrations for varying times, and to determine the extent of the reaction by determining the amount of mercury dissolved. Preparation of Materials. Mercury already very pure was thoroughly freed from the possible presence of substances with greater solution-tension by treatment with sulphuric acid and potassic dichromate, and subsequent spraying through ten per cent nitric acid. Calomel was resublimed at as low a temperature as possible, and thoroughly washed with water and with the solution to be used in each particular case. One of us had previously shown that the source of the calomel is immaterial.* Sodic chloride was precipitated by pure hydrochloric acid from a saturated solution of the so-called " chemically pure " salt. It was then twice recrystallized from water, and thoroughly dried to drive off any possible traces of acid. Pure calcic nitrate was made by many recrystallizations ; this was converted into carbonate, and the carbonate converted again into chloride. Several recrystallizations freed this chloride from every trace of the nitrate or of ionized hydrogen. Baric chloride was crystallized first from a solution strongly acid with hydrochloric acid, and subsequently from aqueous solutions by precipitation with pure alcohol. It also was wholly neutral to methyl orange. Cadmic chloride was made by dissolving the pure metal in pure acid and recrystallizing twice. The salt was dried thoroughly in order to make certain of the absence of ionized hydrogen, which is less easily detected in this case. Hydrochloric acid itself was purified by redistillation, the purest acid of commerce serving as the starting-point. Apparatus and Method of Analysis. It was necessary to digest the mixtures for long periods of time at a constant temperature. For this purpose they were placed in large test-tubes of sixty cubic centimeters capacity arranged to rotate tran- sit-fashion in an Ostwald thermostat after the manner suggested by Schroder. f In the case of the weaker solutions several of these tubefuls were used for each analysis, but with the stronger solutions fifty cubic centimeters sufficed. The tubes were corked with rubber stoppers * Richards, loc. cit. t Richards and Faber, Am. Ch. J., 21, 168 (1899). The thermometer used to register the temperature was of course suitably verified. RICHARDS AND ARCHIBALD. CONCENTRATED SOLUTIONS. 349 which had previously been boiled with dilute alkali and scrupulously rubbed and washed. Into each tube was placed a large excess of calomel, about a decigram of mercury, and fifty cubic centimeters of one of the solutions of chlorides. After a slight shaking, the settled precipitate was always covered upon standing with a layer of gray partially reduced material, which settled more slowly and hence gave more opportunity for reduction. When the equilibrium was completed by prolonged shaking, this gray material was mixed evenly throughout, and no longer appeared on the surface of the precipitate. Thus the absence of a gray film on settling was a rough guide to the completion of the reaction. After five or six hours of agitation in the thermostat at 25.° ± 0.05° one of the tubes was opened, its contents filtered, and the dissolved mer- cury determined analytically. At intervals of an hour successive tubes were similarly treated, and after seven or eight hours no change was found in any case. Evidently a state of equilibrium is soon attained, and the reaction cannot be called catalytic. The values given below are of course the values corresponding to this maximum. In this paper no evidence is given concerning the size of the grains of calomel. Ostwald * has recently shown that this may be an important factor in determining the concentration of a saturated solution, and hence in fixing the basis of the present equilibrium. Concerning this point it need only be said that while the absolute extent of solubility may vary with the size of the grains, the relative results, upon which alone the conclusions of this paper are founded, are not affected. This is the case because the same preparation of calomel was used in every instance. Moreover, since the calomel was sublimed and since it is notoriously difficult to powder, the individual diameters could not have been very small, hence a value approximating that corresponding to a flat surface must have been obtained. A number of experiments indicated that the mercury salt thus dis- solved was in the mercuric rather than in the mercurous state. The visible deposition of mercury during the reaction is alone almost enough to prove this. Moreover, neither permanganate nor bichromate suffered more than the faintest trace of reduction upon addition to a solution which contained much dissolved mercury. The minute trace of decolor- ization which was observed was no greater than that produced by a solu- tion of mercurous chloride in pure water. On the other hand, small * Zeitschr. phys. Chem., 34, 495 (1900). 350 PROCEEDINGS OP THE AMERICAN ACADEMY. amounts of stannous chloride gave plentiful white precipitates of calomel. In all cases except that of cadmium, the mercuric salt in solution was determined as sulphide. The black precipitate produced by hydrogen sulphide was collected on a Gooch crucible, washed with alcohol, carbon disulphide, and again with alcohol, and finally dried at 100°. Satis- factory agreement between parallel analyses, which were almost always made in duplicate, was obtained. In the tenth-normal solutions of sodic chloride the amount of mercuric chloride was too small to be collected, hence it was determined colorimetrically by comparison with known solutions of similar dilution. The following table explains itself. The last-column contains an arbi- trary ratio which is an index of the changing relationship between the amounts of mercuric chloride formed and the amounts of sodic chloride present. The values in the third column were calculated from those in the second ; and the values in the fifth column from those in the third and fourth. Mercuric Chloride found in Solutions of Sodic Chloride. No. of Exp. ( a Sa Wt. of Solution taken. grm. 64.5 66.1 65.9 80.3 75.4 83.0 73.8 80.3 58.7 69.7 Vol. of Solution. 62.0 63.5 61.1 74.5 68.8 75.7 64.6 70.3 49.4 58.8 Wt. of HgS found. m.g. 2.2 2.3 6.8 8.2 11.4 12.6 21.1 22.8 27.2 32.5 Wt. of HgCI., in 1 Litre of Solution. grm. 0.0041 Mean Wt. of HgClj in 1 Litre. grm. 0.0041 0.041 0.129 0.194 0.380 0.643 C Cone, of NaCl Solution in Equiv. Grams. equiv. 0.10 1.00 2.00 2.50 3.80 5.00 1000 -c Milligrams Hgi\>. The tribromide can be produced only from the tetrabrotnide by the action of reducing agents. Uranyl bromide, U02Br2, 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 that 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 conqjouud 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, U308, 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 plates 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 OF 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 lar^e 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 an 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. 373 a complexity of operations incompatible with the degree of accuracy requisite in 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. Jt 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 preparation 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 in 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 reduciug 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, U02, 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. * Loc. cit. See also Eichards, 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 urauous oxide, suspended in 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)2. 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 recrystallizing 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 (1890). RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 375 Analysis of Uranyl Iodate. Found. Caleul:itril for U02(I03),1IJ>. 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 three 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 liber 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 contiuued 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 OP 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 interesting 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 UO2C2CV 3H20. 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, U308, 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 Ebelrnen and Peligot in their determination of the atomic weight of ura- nium. 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. Maberyt Journal Am. Chera. Soc, 20, 510 (1898). t George Auchy, Journal Am. Chem. Society, 20, 243 (1898). / 378 PROCEEDLNGS OF 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 confound 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 following method was adopted. Preparation and Collection of Puke 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 treatment, but in the present case removal was impossible. RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 879 In order to obviate the difficulty and 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. 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 carhon ; 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, O, 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 nitrogen 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 within. In the presence of mere traces of oxygen the lustrous brown color of the uranous 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 OP 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, in 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 meanwhile 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. 0002(35 gram. Of this nitrogen a gram of urauous bromide displaced - - = 0.206 cubic centimeters, or 4.84 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 Jthe 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- EICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 883 pluiric acid was added, and the mixture was slowly run into the solution of uranous bromide. The screen color of the uranous salt soon changes to the yellow color characteristic of uranyl compounds. 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 the hvdric dioxide, for 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 hydropen 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 OF 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 in 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 might 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 iu a solution of the double carbonate of ammonium and uranium, in 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 amnionic 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 amnionic 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 in excess. After stauding 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 precipitate 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 Cliemie u. Pharmacie, 232, 299. vol. xxxvn. — 25 38G PROCEEDINGS OF THE AMERICAN ACADEMY. pure amnionic sulphhydrate added in excess. The color of the result- ing precipitate of uranium sulphide varies greatly with the temperature. In warm solution it was at first reddish brown, while that precipitated 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 fifth 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" yet obtained has consisted of a mixture containing probably 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 quautity 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. Heating 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, in 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 bromiue, 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 EICHARDS 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 obtained 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. Ilydric 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 throughout 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-tin condenser and Jena glass receiver being used. The Results of the Analyses of Uranous 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 uranous 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. Cliem., 8, 269 (1895). 390 PROCEEDINGS OF THE AMERICAN ACADEMY. argentic bromide determined. Thus from each of these analvses 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 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 tigation were of the same manufacture as those used in the nickel and cohalt 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 average 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. Analysis 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 oxybromide. 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 = 107.93 ; Br = 79.955. First Series (preliminary). UBr4 : 4AgBr. No. of Analysis. Total Weight of Uranous Bromide + So- dium Bromide iu vacuo. Weight of Uranous Bromide corrected for NaBr. Total Weight of Silver Bromide in vacuo. Weight of Silver Bromide 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 OF 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. grams. 74.296 74.290 74.302 Atomic Weight of Uranium. 7 8 9 grams. 1.80174 1.06723 1*85698 grams. 1.7999 1.0662 1.8551 grams. 2.42588 1.4:3713 2.50009 grams. 2.4226 1.4352 2.4967 238.54 238.50 238.59 Average . .... . 74.296 238.54 Third Series. UBr4 : 4Ag. No. of Analysis. 10(7) 11 (8) 12(9) Weight of Uranous Bromide with all Corrections. 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 0.015. 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 iu 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 The result not only verifies the mechanical work, but affords evidence that the precipitate 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 n 9-4 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 fairly conclu- sive, although somewhat indirect. All attempts by many iuvestigators 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 preparations 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 AXD MERIGOLD. — ATOMIC WEIGHT OF 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. Hence 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 in 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. Investigations on Light and Heat made and published whollt or in part with Appropriations prom the rcmford fund. 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. 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 h}rpothesis. 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 difficulty 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 studied.* 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 from 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, Phys. 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 . Q = PdT ~ 6.62 X 1 = Joules, or 20.5 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 Contraction with Heat of Formation involved in the Synthesis of Chlorides. Metal. Atomic Volume of Metal. Atomic Vol. Metal -f 11 times Atomic Vol. Chlorine. Molecular Volume of Chloride. Difference or Contraction. Contrac- tion corre- sponding to 2 Atoms Chlorine. Heat of Formation correspond- ing to 2 Atoms Chlorine. (Kilojoules.) Lithium 11.9 36.9 20.9 1G.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 TO too 50.0 2-3.3 25.3 760 Iron11 . . 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 33.1 815 Mercury11 . 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 OP THE AMERICAN ACADEMY. 100 200 300 400 500 600 700 800 900 kj. 10 20 30 40 50 60 70 cubic centimeters. Li C Na Mg K Ca Jbe Mi \ Co Cu , / Zn Sr Ag C'd Ea Hg Tl 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 kilojoules 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, 1G3 (1895); also Ostwald, 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. Comparison of Contraction 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 53.6 796 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-J-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 ? * These values are calculated from very accurate determinations of specific gravity made recently in this Laboratory. See These Proceedings, 31, 163 (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 20 300 400 500 600 700 800 kilojoules. 30 40 50 00 cubic centimeters. 2NaBr 2KBr CaBr2 ZnBr2 SrBr, CdBr2 BaBr., 2C1K 2BrK 2IK ***«. \ \ \ t \ % ■ . \ > \ 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 OP 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. The 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 inherent in the problem — the presumption is strong that the chief source of the heat of chemical 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 effect 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 OF CHEMICAL HEAT. 407 17.66, 17.1, and about 14.1 respectively. The first small contraction is attended with an evolution of 0.65 kilojoules, 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 respective 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 fabric. 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 resideut 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, aud 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 difficultv 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 larked ; 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 regards 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 consistency. 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 consideration 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 III. Summary. The contents of the paper may be divided into two parts : In the first part is set forth an approximate generalization 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. (a) 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 magnitude 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. (/) 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 FROM 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 HARVARD COLLEGE. ON THE ACCURACY OF THE IMPROVED VOLTAMETER. By 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, coulometer 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, 123 (1899). f The word " voltameter " 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 in 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 X^ Figure 1. — Porous Cup Voltameter (§ actual size). A, glass hook for supporting anode. B, glass ring for supporting porous cup. C, silver anode, centimeters; they were pro- D, porous cup. E, platinum kathode. vided with lips. A crucible exposes a smaller surface of liquid to the impurities of the atmosphere, and gave in our experiments a more evenly distributed deposit than a bowl. RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 417 The anodes were bars 5xlXl 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 niffht. 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 washing. As has been said, the crucibles were dried at 100°. It was subse- quently shown, in agreement with the results of Lord Rayleigh and Mrs. 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 work upon copper, — one which has served also for many determinations of atomic weights. Its results with small objects may he depended upon to within ^ milligram. All weighings were made by double substitutions, a similar vessel being used as a tare, and the weights were of course carefully standardized. Since the question con- cerned 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 OF 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 Porous Cup Voltameter. No. of Experiment. Voltameter I. Weight of Silver. Voltameter II. Weight of Silver. Difference. Percentage Difference. 2 Q O 4 5 6 7 8 9 grams. 2.43744 2.69691 2.36193 2.14900 1.65485 2.31480 2.22258 2.67264 grams. 2.43749 2.69713 2.36196 2.14913 1.65490 2.31500 2.22260 2.67268 milligram. 0.05 0.22 0.03 0.13 0.05 0.20 0.02 0.04 per cent. 0.002 0.008 0.001 0.006 0.003 0.009 0.001 0.002 0.004 There is of course nothing in this table to show whether the figures represent the weight of silver which ought 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 current 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 diffusion-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 begins to be manifest. The same error begins to show itself when the viscosity of the solution is diminished 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 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. oh. Ges., 20, 197 R (1887). 420 PROCEEDINGS OP THE AMERICAN ACADEMY. zinc nitrite. The N03' 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, f 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, Phys. Rev., X, 169 (1000). t Paweck, Zeitsch. fur Berg. u. Huttenwesen, 46, 570 (1898) ; Winkler, Ber. d. d. ch. Ges., 32, 2192 (1899). RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 421 second lost 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. In the table the weights of the iguited precipitates are given. TABLE III. Comparison of Porous Cup Voltameter with Wire Gauze Voltameter. No. of Experiment. Weight of Silver in Porous Cup Voltameter. Weight of Silver deposited on Gauze. Difference. Percen tage Difference. 13 14 grams. 2.10326 2.31237 grams. 2.10344 2.31234 milligram. +0.18 -0.03 per cent. +0.00!) -0.001 Average € 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 fact 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 voltameter 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 OP THE AMERICAN ACADEMY. Average deviation of two porous cup voltameters in series = ± j^-j*^ Difference caused by sealing bottom of cup = — looooo Difference caused by use of zinc anode = ± lofnjoo 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 (1899). t Phil. Trans., 186 A, 633 (1895). RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 423 pare the nitrite, we had recourse at first to a method used by Proust.* lie 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 ceut 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 iu 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 and nitrite was extracted TABLE IV. Standard vs. Voltameter with Solution Saturated with AgN02. No. of Experi- ment. Type of Voltameter containing Nitrite. Wei prh t of Silver in Standard. Weight of Silver iu Vol- tameter con- taining AgN02. Difference. Percentage. Difference. 16 17 Standard. Filter paper volt. grams. 2.27944 2.30276 grams. 2.28011 2.30539 milligrams. 0.67 2.G3 per cent. 0 030 0.114 * Journ. de Physique, March, 1806, 211 ; also Nicholson's Journal, 15 : 378. 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 the 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 boiling water. The great bulk of nitrate may then he 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 hut 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 jjorous cup (16), 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 bo 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 N03- ion into the nitrite ion N02~ and ox3rgen, 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 carried from 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- itv is the nitrate ion ; its deionization would make possible the form- ation of the nitrite ion anil oxygen, which might at once oxidize the silver plentifully present.* The reaction might be written thus: — N08 + 3Ag = Ag + + N02- + Ag20. 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 f 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, 031 (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. When the solution is dilute and neutral, oxygen and hydroxy], 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 carried out of the solution through their agency with the formation again of argentic oxide, or even oxygen 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 ? Hellvvig f in a recent paper has shown that the weak silver ion in the presence of the strong N03~ ion tends to strengthen itself by taking up a molecule of some other undissociated substance, as AgCl, A"I, A"Br, or AgCN. He has proved also that the solution actually contains ions like Ag2I+, since on electrolysis the iodine accumulates at the kathode, and disappears from the anode. In 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 turned 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 fail with its basic load to the bottom of the kathode vessel. There the complex ion (possibly Ag3Of) 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, Wied. Ann., 67, I (1899). t Zeitschr. anorg. Cliem., 25, 157 (1900). 426 PROCEEDINGS OF 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, tains the results : — TABLE V. The following table con- Standaed vs. Standard saturated with Ag20. No. of Experiment. Weisht of Silver in Standard. Weight of Ag Standard with Ag20. 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 ion heavier than Ag+. Since this has been formed directly RICHARDS AMD HEIMROD. — THE IMPROVED VOLTAMETER. 427 from the oxide, it probably contains Ag20, and may be assumed to have the formula already given, Ag30+. 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 Ag20, but afterwards acidified. No. of Experiment. Weight of Ag in Standard. Weight Ag from Sol. with Ag20+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 Ag7NOn 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. Cliem., 12, 89, 180 (1896) ; 24, 305 (1900). t Mulder and Heringa, Ber d. d. ch. Ges., 29<, 583 (189G). 428 PROCEEDINGS OF 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 Rayleigh, 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 on Platinum and on Silver. No. of Experiment. Weight of Deposit on Platinum. Weight of Deposit on Silver. Difference. Percentage Difference. Weight of Anode. 23 24 25 26 grams. 2.26680 2.17215 2.18071 2.11134 grams. 2.26672 2.17250 2.18100 2.11162 milligram. -0.08 4-0.35 4-0.29 4-0.28 per cent. -0.003 4-0.016 4-0.013 40.013 grams. 2 4.5 6.7 8.8 Mphyi ... . 4-0.010 There is an undeniable surplus when the deposit is made on silver. The main question now arises, — Is this effect due to the anode solution, or is it an irregularity which would come equally from pure argentic nitrate ? The answer to the question is easily determined by means of our porous cup ; a comparison of deposits made iu a standard voltameter on a silver and a platinum kathode .gave the following results: — RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 429 TABLE VIII. Standard Method on Platinum and on Silver. No. of Experiment. Weight of Deposit on Platinum. Weight of Deposit on Silver. Difference. Percentage Difference. 27 28 grams. 2.69700 2.25769 grams. 2.69674 2.25770 milligram. 0.26 0.01 per cent. -0.009 +0.000 The only difference is now in the opposite direction ; and this was due to known experimental error. In experiment 27 a small loss of silver particles in the wash-water from the silver cell produced the difference of 0.009 per cent. It is highly probable that but for this accident, the deposit on silver would have been equal to that on platinum, as it is in No. 28. These results permit us to draw two conclusions. First, it is not the greater inclusion of silver salt in the crystals which increases the total weight when the kathode is silver. Otherwise 27 and 28 should have grown heavier in the same ratio. Secondly, it is the anode solution again which is responsible. The increase in the deposit on a silver surface indicates the existence of silver in the solution in a supersaturated state ; and this existence shows that there must be present some complex gradually dissociating, with metallic silver as one of its products. If this is the case, we should ex- pect to find that an oxidizing environment would be capable of removing this cause of inaccuracy, while substituting another easily removed by nitric acid. As a matter of fact, Schuster and Crossly * have shown that deposits made in vacuo are heavier than when made in air; again those made in an atmosphere of air are heavier than when made in oxy- gen. Of course it is understood that in all three cases the anode was only wrapped in filter paper. The solution usually contained fifteen per cent of silver nitrate, but sometimes as much as thirty per cent. They used the solution over and over again, thereby accumulating the irregular compounds. Under reduced pressure (about " 1 J inch"), the deposits exceeded those made in air by about 0.04 per cent, while the lat- ter exceeded those in oxygen by 0.04 per cent more. Myers, f who re- peated these experiments, found the difference between deposits in air and in vacuo to be as much as 0.10 per cent for 20-40 percent solutions. * Proc. Roy. Soc, 50, 350 (1802). t Wied Ann., 55, 291 ff. (1895). 430 PROCEEDINGS OF THE AMERICAN ACADEMY. In an atmosphere of nitrogen an excess of .05 per cent in the deposit was observed. Our own experiments in the same direction verify the results of these experiments, and need not be recorded here. Putting aside for the moment the question concerning the nature of the irregular compound which can thus be partly oxidized out of exist- ence, it seemed worth while to discover if an oxidizing a. Clark) ; Lansing (L. H. Bailey, no. 262) ; Alma (C. A. Davis): British Columbia, Mts. east of Adams Lake (Dawson, hb. Geol. Surv. Can., no. 30,520) : Washington, Seattle (C. V. Piper, no. 1106). Var. disjuncta. — Figs. 118 to 120. —Tall and lax, 3 to 8 dm. high: spike elongated, flexiioas, 0.5 to 1.5 dm. long ; the 5 to 8 oblong- ovoid to cylindric spikelets 6 to 12 mm. long, all hit the terminal remote, the lowermost 2 to 4 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 OP SECTION HYPARRHENAE. 489 most swamps or on wet shores from Newfoundland to Michigan, Ohio and Pennsylvania. The following uumbered specimens belong here — Prince Edward Island, Brackley Point (J. Macoun, 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) — J. Macoun, hb. Geol. Surv. Can. : Massachu- setts : Framiugham {E. G. Smith, no. 628) : Connecticut, South- incton (L. Andrews, no. 590) : Ontario, Cache Lake (J. 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, flat, 1 to 2.5 mm. ivide, shorter than or equalling the culms : spike 1 to 6 cm. long, of 3 to 6 more or less remote or approximate spikelets S 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, fig. 848. G. curta, var. brunnescens, Pers. Syn. ii. 539. G. canescens, var. alpicola, Wahlenb. Fl. Lapp. 232 ; Bailey, Proc. Am. Acad. xxii. 143, & in Gray, Man. ed. 6, 618; Macoun, 1. c. 124; Howe, 1. c. 37. G. Gebhardii, Hoppe Car. Germ. 30. Vignea Gebhardi, Reichb. Fl. Exc. 58. G. canescens, j3, Torr. Ann. Lye. N. Y. iii. 393. C. 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. C. vitilis, Fries, Mant. iii. 137 ; Anders. Cyp. Scand. 58, t. 4, fig. 38 ; Boott, 111. iv. 219 ; Fl. Dan. xvii. t. 2973. C. Buckleyi, Dewey, Am. Jour. Sci. xlviii. 143, t. Dd, fig. 104. G. sphaerostachya, Dewey, 1. c. xlix. 44, t. Ee, fig. 110. G. 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. C. 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 OF THE AMERICAN ACADEMY. Europe. June-Aug. On alpine summits becoming more rigid and browner than in sheltered situations. ++ -H- Perigynia 4 to 5.5 mm. long, distinctly less than half as broad. = Leaves very narrow (1 to 2.5 mm. broad) : spikelets lanceolate : perigynia 1 to 1.3 mm. wide. 33. C. bromoides, Schkuhr. — 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 2 to 6 approximate or slightly scattered spiikelets 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 oblong pointed scale. — Riedgr. Nachtrag. 8, t. Xxx, fig. 17G; Willd. Sp. iv. 258; Schwein. & Torr. Ann. Lye. N. Y. i. 300 ; Torr. 1. c. 391 ; Carey in Gray, Man. 539 ; Chapm. PL 533; Boott, 1. c. ii. 82, t. 227; Bailey, Proc. Am. Acad. xxii. 146; Macoun, 1. c. 114 ; Britton, 1. c. 354, fig. 857 ; Howe, I. 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.1 May-July. = = Leaves broader (2 to 5 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 G or 7) 3- to 12-flowered spikelets 5 to 12 mm. long, the upper sub- approximate or scattered, the lowest very remote, usually subtended by an elongate slender bract : beak about one-half as long as the obscurely nerved 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 6touter 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.1 May-Aug. * * Perigynia entirely smooth at the tip (exceptional forms of C. canescens might be looked for here ; and very rare individuals of C tenuiflora might be sought in the preceding section). -t- Perigynia oblong or ovate-oblong. ++ Perigynia 3 to 4 mm. long, uerved : 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. loug, mostly exceeding the very narrow (0.7 to 2 mm. broad) pale green leaves : spikelets subglobose, 3- to 10-flowered : perigynia 3 to 3.4 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. — Kougl. 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. Fl. 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; Macouu, 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 (31acoun, 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. sparsiflora, Olney (C. Deweyana, var. sparsiflora, Bailey) is a distinct species, probably C. laeviculmis, Meinsliausen, 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 Elomjatae. 492 PROCEEDINGS OP THE AMERICAN ACADEMY. = = Spikclets remote, the uppermost strongly divaricate-pedunculate ; the lower- most subtended by a long leaf-like bract : perigynia beaked. 36. C. trisperma, 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, Proc. 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 appressed ascending 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 (31. 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. h- •*- Perigynia broadly elliptic to suborbicular : spikes mostly tinged with brown. ++ Terminal spikelet with conspicuous clavate 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 and/ree/y 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. — CARrCES OP SECTION HYPARRHENAE. 493 1.5 to 5.5 cm. long, of 2 to G ovoid or broad-oblong spihelets ; the lower 5 to 12 mm. long, the terminal, including the clavate sterile base, 1 to 1.8 cm. long : perigynia 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 yellotvish brown orbicular to ovate blunt scales. — Willd. ex. Schkuhr, Riedgr. 50, t. S, no. 6G, & Spec. iv. 227 ; Wahlenb. Kougl. 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. Nat. Hist. i. 135; Gray, Man. ed. 3, Addend, xcvii : Boott, 1. c. iv. 211; Fl. Dan. Suppl. 13, t. 103; Bailey, Proc. Am. Acad. xxii. 115; Macoun, 1. c. 125 ; Britton, 1. c. 351, fig. 849 (as to babital sketch). — Brackish marshes, northern Scandinavia. Damp usually brackish soil, coast of southern Labrador : Anticosti Island, and Kamouraska, Saguenay, Rimouski, and Gaspc Cos., Quebec : locally southward along the coast in New Brunswick at Shediac, Westmoreland Co., and Back Bay, Charlotte Co. (J. Brittain, herb. Geol. Surv. Can. nos. 30,421 & 30,420); Whale Cove, Grand Manau 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 (Redfield) ; Wells (Blake): reported from Alaska.1 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 flaccid 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 spihelets; the lower If. to 9 mm. long, 3 or If. 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 1.0 mm. broad, nearly or quite equalled by the ferrugi neons ivJiite-edgcd ovate acutish scales. — 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. 494 PROCEEDINGS OF THE AMERICAN ACADEMY. Spec. iv. 251; Schkuhr, Riedgr. Nachtr. 24, t. Aaa, fig. 97; Anders. 1. c. 62, t. 4, fig. 31 ; Torr. 1. c. 39G; 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; Meiushausen, Acta Hort. Petrop. xviii. 325. — Arctic regions of both hemispheres, extending south in America along the coast of Labrador to Quebec, Bonne Esperance {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. b. 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 8 mm. wide) leaves : spike from cylindric to globose, 1 to 2.5 cm. long, with 3 to 6 ascending spikelets mostly larger than in the last : perigynia brown or reddish-brown, 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. Calif, ii. 233 ; Bailey in Coulter, Man. Rocky Mt. Reg. 395, & Proc. Am. Acad. xxii. 145 ; Britton, 1. c. 353, (fig. uncharacteristic) ; Meinsh. 1. c. C. leporina, 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. C. parviflora, Gaud. Etr. Fl. 84, ace. to Boott. C. 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-Aue. *&■ ++ ++ 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. — Culms 1.5 to 3.5 cm. high, stiff, usually overtopping the erect narrow (1 or 2 mm. tcide) PERNALD. — VARIATIONS OF BOREAL CARICES. 495 leaves: the globose or ovoid spikelets 4 t° 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. 14G, & Fl. Lapp. 230; Schknhr, Riedgr. 51, t. Ii, fig. 97; Hoppe & Sturm, Car. Germ. t. 6; Hook. Fl. Bor.-Am. ii. 214; Reichenb. Ic. Fl. Germ. viii. t. 204, fig. 542 ; Anders. Cyp. 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. Nacht. t. FfF, fig. 129, not L. C. Carltonia, Dewey, Am. Jour. Sci. xxvii. 238, t. U. fig. 64 ; Torr. 1. c. 393. C. marina, 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 Brainerd, no. 172): British Columbia, Glacier (Ezra Brainerd); Kicking Horse Lake (J. Macoun, hb. Geol. Surv. Can. nos. 28; 49; 30,410; 30,411; 30,412). July, Aug. II. — 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 a 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/perns 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 which there is a solitary simple in- florescence (or true spike), as C. (jy hoc rates 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 spilcelet seems not inappropriate to the normal inflorescence of such species. 496 PROCEEDINGS OP THE AMERICAN ACADEMY. to Bear Lake, Mackenzie & British Columbia, south to Maine, Vermont, central and western New York, and Utah. The Scandi- navian material examined lias been referred to the true C. aquatilis by Andersson, Fries, Laestadius, and Wickstrom, and it agrees well with Lauge'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. But. 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 m. 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 perigynia. — Maine, Fort Fairfield and Orono (M. L. Fernald, nos. 136, in part, 395) : New York, Pen Yan & Junius (Sartwell) ; -Dexter (G. Vasey) ; Jefferson Co. (Crawe)', Niagara Falls ( W. Boott): Ohio (Sullivant): Michigan, Pecke Isle, Detroit River ( C. F. Wheeler) : Manitoba, English River (Sir John Richardson).1 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 English Hirer has 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 northern river, however, was consistently 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). PERNALD. VARIATIONS OP BOREAL CARICES. 497 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. Ban's). 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 bluut. — Northern Europe, Greenland. Newfoundland {La Pylaie) ; Packs Harbor {A. C. Wag/tome, 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 Lapiand 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 spiudle- vol. xxxvi. — 32 498 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 European 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 plant 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. pihdifera. 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 G. Emmonsii. In place of the misapplied name, C. varia, Professor Bailey proposed for the plant which had long borne that name the new appellation G. communis, giving no suggestion that the plant has close affinity to the common G. pihdifera 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 G. varia Muhlenb. conjungitur ; quo modo autem G. variam a C. pihdifera. distinguam, neque ex descriptione neque ex speciminibus eruere possum." 1 Schlech- tendahl discussing specimens in the Willdenow herbarium which he took for C. varia was unable to point out any character to separate it from C. pihdifera .- " Species haec vero simillima C. puhdiferae et uti nobis fere videtur eadem." 2 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.3 This plant, the true C. varia (C. Emmonsii, Dewey) is readily distinguished from C. pihdifera by its much more slender habit, very narrow leaves and smaller-bodied longer- beaked perigynia. 1 Drejer, Rev. Crit, 55. 2 Linnaea, X. 262. 3 See Bailey, Mem. Torr. Club., I. 40. PERNALD. VARIATIONS OP 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. [6V. communis, Bailey], differt spicis confertis, plurifloris, subinde apice masculis, e viridi-purpureo variegatis ; perigyniis enerviis, rostello semper recto breviore bidentato ; basi styli persistente abruptecompresso- deflexa ; culmo incurvo, basi vagiuis foliorum pallide ferrugineis tecto ; foliis viridibus."1 In discussing C. varia \_C. com munis, Bailey] he said : " A C. pilulifera differt inflorescentia laxa ; spicis plus minus re- motis, laxifloris, saepe paucifloris ; perigyniis subinde nervatis, rostro nunc excurvato, bihdo ; 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. communis 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 Egglestou'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; 1 111., II. 96. 2 Ibid. 98i 500 PROCEEDINGS OF THE AMERICAN A CAD EM Y. Wheeler's specimens from Grand Ledge, Michigan ; Macoun's 1876 material from Quesnelle, British Columbia, with specimens of C. piluli- fera from Berne, Switzerland (Seringe) ; Stockholm, Sweden (Andersson) ; Finland (Simming) ; the Grosser Pfalzberg, Austria (Haldcsy,no. 1064), and St. Petersburg, Russia ( Turczaninow) ; 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 of 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 spikelets 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 longibracteata 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 1 and Dr. Boott'2 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. pilvlifera. 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. pilulifera 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 often 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. variety as ''enerviis vel basi plus minus nervatis pallidis." The length, i Trans. Linn. Soc, II. 191. 2 111., II. 96. FERNALD. VARIATIONS OF BOREAL CARICES. 501 Table of Measurements of European Carex pilulifera and the Smaller Form of American C. communis. European Specimen. Collector. Length of Jnlloresceuee in mm. c ~ 3 ■=> 3.3 ■U.f. ^ °B a a, Number of pistillate Spikelets. «M 3 o » 3 — iS.S §.- » a. 02 0 ggts t M a Length of Perigynia in mm. Length of Beak iu mm. Strombacka, Sweden . . Lauren 12-18 6-8 2-:! 4.5-6 4.5-7 3.4 0.6 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. Schulz 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 9-1 G 2-4 5-9 3-9 2.8 0.7 Kyffhauser (Mt.), Germ'ny 17-22 11 6-8 6 3.0 0.7 Grosser Pfalzberg, Austria Ilalacsy, 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 20 0.7 I'jis.ila, Sweden .... Tuckerman 25 10 4 6-8 9 3.0 0.8 Snowdori, Wales . . . J. Ball 18 6.5 3 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 15-10 4-8 o 5-7 7-15 3.2 0.8 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 5-6 5-10 3.0 0.7 Grand Ledge, Mich. . . Wheeler 18-10 8 3 5-6 6-9 3.3 0.8 Mt. Mosalamoo, Vt. . . Brainerd 17-23 8 3 4-0 7-12 2.4 0.8 EastMt., Middlebury, Vt. Eggleston, no. 434 17-24 9-11 2-3 5-6.5 5-13 2.6 0.9 Willoughby Mt., Vt. . . Faxon 13-26 6.5-10 1-2 4-6 8-12 3.0 0 7 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. 4807'' 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 3.1 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 . . 10-30 3.5-18 1-4 4-9 5-15 2.4-3.3 0.7-1.0 502 PROCEEDINGS OF 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 European specimens. On the other hand, the straight style supposed to characterize the American plant is clearly represented by Lange in his plate of C. pihilifera, var. longibracteata. 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 Tuckerman 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. pihilifera has likewise been maintained as a character separating that plant from the American 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 C. jrihilifera, the leaves were originally described as '"bright green." The length of the stamiuate 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. 10G4 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 from 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 OP 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 European plant. * The length of the lower bract, emphasized in the descriptions of C. pilulifera, 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. pilulifera 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. pihdi- 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. pedicellata. The American plants, then, should be called C. PiLULiFKRA, L. Cidms 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; Reichb. Ic. Fl. Germ. viii. t. 260 ; Boott, 111. ii. 96, t. 283. C. filiformis, Pol. PI. Palat. ii. 581 ; Vahl, Fl. Dan. vi. t. 1048; not L. C. Bastardi- 504 PROCEEDINGS OF THE AMERICAN ACADEMY. ana, DC. Fl. Fr. vi. 293. C. varia, Authors, incl. Boott, 111. I. c. 97, in part, not Mulil. C. varia, var. pedicellata, Dewey, Am. Jour. Sci. xi. 163, in part. C. varia, var. minor, Boott, I.e. t. 289. C. communis, in part, and var. Wheeler i, Bailey, Mem. To it. 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, Lange. 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. — Ilaandb. Dansk. Fl. G21, & Fl. Dan. xvii. 12, t. 3050; Kneucker, Allgem. Bot. Zeitschr. (1898) 128. C. varia, Authors, in part, incl. Boott, 1. c. t. 288, not Muhl. C. varia, var. pedicellata, 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 Georgia: rare and local in northern Europe. ( Iarex 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 aud 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 sufficient 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. pilulifera, 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. pilulifera in northern Europe as well as in America is frequently found with dark red scales, especially when growing in 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 PERNALD. — VARIATIONS OF BOREAL CARICES. 505 conspicuous elongated stolons, while C. pilulifera (C. communis) is caespitose, with short assurgent basal shoots. As may be implied, varieties of C. pennsylvanica based upon color of the spikelets are quite as inconstant 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 New 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 Rep. 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. Enum. PL Berol. Suppl. 63; Kunze, 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) — M. L. Fernald; Cambridge (F. S. Bunker); Glassface Mt., Rumford, July 13, 1890 (/. C. Parlin) : New Hampshire, Barrett Mt., New Ipswich, June 5, 1896 (M. L. Fernald) : Vermont, Chipman 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 {E. $ C. E. Faxon); Wilmington, May 14, 1899 (E. F. Williams): 506 PROCEEDINGS OF THE AMERICAN ACADEMY. Rhode Island, Cumberland (S. T. Olney) : Connecticut, Southington, June 4, 1899 (C. H. Bissell) ■ Fairfield, June 23, 1901 (E. H. Eames, no. 168) : Michigan, Detroit, May 22, 1864, June, 1860, May 9, 1858 (Wm.Boott): Virginia, Harper's Ferry, May 7, 1881 (John Donnell Smith): North Carolina, Broad River, May. 1841 (Rugel according to Kunze, 1. a). 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. pihtlifera and C pennsylvanica, C. umbellata, Schkuhr, pre- sents considerable variation in the length and breadth of its leases 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 loug-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 G. nigro-marginata, and on the other to C. deflexa. 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 C. deflexa, C. umbellata may best be distinguished by an examination of the scales. In 0. umbellata the scales are nearly or quite as long as the subtended perigynia, while in C. deflexa they are distinctly shorter. FERNALD. — VARIATIONS OF BOREAL CARICES. 507 The most marked tendencies of C. umbeUata are C. umbellata, Schkuhr, Riedgr. Nachtr. 75, t. "Www, fig. 171 (C. umbeUata, 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 (J. 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 unusual in the Montanae. Var. brevirostris, Boott, 111. ii. 99, t. 294. Periirynia 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. fy C. E. Faxon) : New Hampshire, Mt. Willard, and Bald Mt., Franconia (E. 3? C. E. Faxon). Carex vaginata and C. saltuensis. C. vaginata, Tausch, Flora (1821) 557 (C. vaginata, var. alto-caulis, 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 ; Blaine, 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. Andersson. 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/dberg), 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 CARICES. 509 mature fruit no difference is apparent between plants from Christiauia, 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, Britton) with no constant vegetative or morphological character and witli 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. vaginata 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 in. — Mt. Albert (J. A. Allen): Maine, Mt. Kineo (T. C. Porter et al) : New Hampshire, Mt. Washington (Wm. Oakes et at): Colorado, Rocky Mts., alt. 8,385 m. (E. L. Greene in Exsicc. Olney) ; South Park (J. 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. Macoun) : 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 Fail-field (nos. 140, 2029), Blaine (no. 2028), Mars Hill — M. 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) ; Port Huron (C. K. Dodge): Saskatchewan (Bourgeau) : Assiniboia, Assiniboine River (J. Macoun) : Albekta, Bow River (J. Macoun) : Colorado, Rocky Mts., alt. 2460 m. (E. L. Greene in Exsicc. Olney) ; Twin Lakes (/. 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 (tSandberg, 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. " " glomerate, 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 " " cumulate, 472. " glomerate, 481. " sparsiflora, 452, altocaulis, 507, 508, 509. approximate, 494. aquatilis, 495, 496, 497. X stricta, 496. " var. cuspidate, 497. " elatior, 496. " epigejos, 497. " sphagnophila, 497. " " virescens, 497. arcta, 458, 459, 466, 486. argyrantha, 452, 478. arida, 167. 479, 481. 464, 472. 453, 480. Carex atlantica, 454, 456, 457, 458, 485. Bastardiana, 503. Bebbii, 449, 462, 478. Bicknellii, 450, 451, 463, 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. 0, 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, 489. capillaris, 509, 510. FERNALD. — CARICES OP SECTION HYPARRHENAE. 511 Carex capillaris, var. elongata, 509. Carltonia, 495. cinerea, 487. communis, 497, 498, 499, 500, 501, 502, 503, 504, 505. var. Wheeled, 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. cj'peroides, 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. " ormantha, 465, 483. elachycarpa, 467, 492. elongata, 453, 487. Emmonsii, 498. exilis, 453, 460, 465, 482, 495. " var. androgyna, 482. " " squamacea, 482. festiva, 474. festucacea, 450, 451, 404, 475, 477. var. brevior, 464, 474, 477. " mirabilis, 473. " tenera, 474. filiformis, 503. foenea, 449, 451, 452, 462, 464, 472, 478. var. ft 450, 451, 477. " y, 476. " (?) ferruginea, 451, 477. " perplexa, 452, 464, 478, 480. " sparsiflora, 480. " (?) subulonum, 476. furva, 494. Gebhardii, 453, 459, 489. glareosa, 4(50, 493. Carex gynocrates, 453, 460, 465, 482, 495. var. monosperma, 482. lieleouastes, 459, 467, 494. helvola, 492. interior, 454, 457, 458, 465, 485, 493. var. capillacea, 465, 485. Kunzei, 486. Lachenalii, 494. laeviculmis, 491. lagopina, 406, 487, 494. lagopodioides, 408, 469. var. cristata, 472. " mirabilis, 473. " moniliformis, 469. '• scoparia, 468. lapponica, 488. Leersii, 483. leporina, 449, 462, 464, 468, 479, 494, 495. var. bracteata, 472. Liddoni, 469, 471. lucorum, 505. marina, 495. mirabilis, 450, 462, 403, 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. Wlieeleri, 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. " longibracteata,498,499, 500, 502, 503, 504. " pallida, 498, 500. pinguis, 481. pratensis, 471. " var. furva, 452. 512 PROCEEDINGS OF TIIE AMERICAN ACADEMY. Carex praticola, 452, 401, 462, 404, 471. Redowskiana, 482. remota, 490. Richardi, 487. saltuensis, 507, 508, 509. sax umbra, 504. scirpina, 458, 485. scirpoidea, 457,458, 185 seirpoides, 453, 454, 455, 157, 458,485. scoparia, 447, 448, 449, 400, 461, 463, 467. " var. condensa, 401, 4G8. " lagopodioides, 468. " minor, 447,448,449, 470. " moniliformis, 449, 461, 4G8, 169. " muskingumcnsis, 467. seorsa, 458, 460, 465, 486, 491. siccata, 401, 469. silicea, 463, 404, 476. gparsiflora, 453, 480. sphaerostachya, 489. stellulata, 454, 455, 156, 483. 7, 485. " var. angustata, 455, 484. " conferta, 485. " scirpina, 457, 485. " seirpoides, 457, 485. " sterilis, 485. sterilis, 453, 454, 455, 456, 457, 405, 483, 484. 0, 484. var. aequidistans, 484. " angustata, 484. " cephalantha, 484. " excelsior, 455, 458, 484. straminea, 447,41s, 450, 451, 462, 403, 171, 477. " var. alata, 476. " " aperta, 451, 475. " brevior, 450, 451, 476, 477. " " chlorostacliys, 472. " Crawei, 450, 451, 175. " cristata, 472. " " cumulata, 472. Carex straminea, var. echinodes, 463, 474. " ferruginea, 451, 477. " festucacea, 477. " foenea, 472. " intermedia, 472. " invisa, 475. " Meadei, 475. " minor, 474. " mirabilis, 473. " moniliformis, 476. " Sclikubrii, 477. " silicea, 470. " tenera, 474, 475. " typica, 477. syclinocephala, 464, 481. tenera, 1 18, 450, 451, 403, 474, 475. " var. invisa, 403, 474, 475. " " major, 175. " Richii, 463, 464, 474, 475, 476. " " suberecta, 477. tenuiflora, 460, 480, 491. tribuloides, 449, 450, 461, 468. var. Bebbii, 478. " cristata, 472, 473. " moniliformis, 419,468, 169. " reducta, 449,461, 168, 469, 474. " " turbata, 461, 469. trisperma, 466, I Tuckormani, 449. umbel lata, 506, 507. var. brevirostris, 507. " tonsa, 507. " vicina, 560, 507. vaginata, 507, 508, 509. " var. alto-caulis, 507, 508. varia, 498, 499, 500, 503, V 1 " var. minor, 499, 503, 504. " " pedicellata, 504. vitilis, 458, 459, 189 xerantica, 462, 464, 479. Vignea Gebbardi, 489. stellulata, 483. FERNALD. — CARICES OP SECTION HYPARRHENAE. 513 EXPLANATION OF PLATES.1 Plate I. Carex muskingumensis : Fig. 1, spike; Fig. 2, perigynium. C. sc.oparia: 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 : ¥\g. 8, spike. C. siccata : Figs. 9, 10, spikes ; Fig. 11, perigynium. C. Craivfordii : 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. 30, 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. Bicknel/ii : Figs. 37, 38, spikes ; Figs. 39, 40, perigynia. C. slllcca: Fig. 41, spike; Fig. 42, perigynium. C. alata : Fig. 43, spike ; Fig. 44, perigynium. C. alata, \&v.ferruginea : 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.focnea : Fig. 54, spike ; Fig. 55, perigynium. C.foenea, var. pcrplexa : 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, vor,. xxxvu. — 33 514 PROCEEDINGS OP 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. 113, perigynium. C. canescens : Fig. 114, spike; Fig. 115, perigynium. C. canescens, var. subloliacea : Fig. 116, spike ; Fig. 117, perigynium. C. canescens, var. disjuncta : Figs. 118, 119, spikes ; Fig. 120, perigynium. ('. brunnescens : 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. 130, 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, 139, spike; Fig. 140, perigynium. C. heleonastes: Fig. 141, spike; Fig. 142, perigynium. Fernald — Carex § Hyparrhen yparrhenae. Plate Fernald — Carex g Hyparrhenae. Plate II. Fernald — Carex § Hyparrhenae. Plate ill. Fernald — Carex § Hyparrhenae Plate IV. Fernaid — Care* § Hyparrhenae V A Plate V. 1 1-1 Yf 11-2 . Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 18. — March, 1902. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. — X. APATITE FROM MINOT, MAINE. By John E. Wolff and Charles Palache. With a Plate. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM.— X. APATITE FROM MINOT, MAINE. By John E. Wolff and Charles Palaciie. Presented December 11, 1901. Received February 7, 1902. In the summer of 1901, while prospecting for tourmaline or other gem minerals on the farm of Mr. P. P. Pulsifer in Minot, Maine, a pocket was opened in the granite containing the material here described. It was first brought to our notice by Mr. C. L. Whittle, formerly of this Department, and the whole was subsequently acquired by the Harvard Mineralosrical Museum. This find is noteworthy for the unusually rich purple color of the crystals, and the purity, crystalline perfection, and abundance of the material, which comprises about two thousand loose crystals or frag- ments of crystals with a total weight of over a kilogramme, and about a dozen large groups of crystals on the matrix. Of the loose crystals about three hundred show at least one perfect termination, five hundred are slightly less perfect, and the rest imperfect or fragmentary. Paragenesis. The apatite was found in a single cavity in pegmatitic granite, the walls of which appear to have been lined with crystals of quartz, ortho- clase, and lepidolite, with which in smaller amounts were albite, musco- vite, and cookeite. The quartz crystals range from small dimensions up to a height and thickness of 15 cm. They show the common quartz forms only, the positive and negative unit rhombohedrons and the prism, and are nota- ble chiefly as presenting in a very striking manner the evidence of two periods of growth. Wherever broken and whether large or small, the crystals show a core of glassy, light to dark smoky quartz ; surrounding this is a surface layer of white opaque quartz from 1 to 3 mm. in thickness, crystallographically continuous with the smoky quartz, but on many of the face*, especially those of the rhombohedrons, composed of 518 PROCEEDINGS OF THE AMERICAN ACADEMY. a multitude of small parallel crystals which give the surface a pitted appearance. A thin section cut across this boundary showed under the microscope that the outer opaque layer was in crystallographic continuity with the inner part, but the line between them was sharp, the opaque layer con- taining very abundant liquid and obscure solid inclusions and showing faintly a division into libres or columns perpendicular to the surface. The appearance pointed to a second period of quartz deposition rather than to an alteration of quartz previously formed. The evidence of the secondary deposition of the white quartz was rendered stronger by the occurrence in several places between the two layers of a thin de- posit, not more than 1 mm. thick, of tiny muscovite crystals, or of a double layer of muscovite and cookeite. The apatite crystals are often deeply embedded in the white quartz and seem to have developed in part pari passu with this material ; but at no place does the apatite appear to penetrate the smoky quartz. The lepidolite is in part in confused lamellar aggregates, in part in quite definite hexagonal prismatic crystals with somewhat rounded basal terminations. The interior of these crystals is of the characteristic pale lilac color of lepidolite, but their surfaces are everywhere covered by a uniform layer of pale greenish-white muscovite about 1 mm. in thickness. The cleavage of the lepidolite and of the bordering musco- vite is absolutely continuous, but the boundary between them is sharp and plane, showing that the muscovite represents, not an alteration of lepidolite, but a later parallel growth of the new and isomorphic mineral, a sort of secondary enlargement. Sharply bounded lepidolite crystals without the muscovite border are sometimes enclosed in the smoky quartz, showing that these two minerals were of contemporaneous growth. The orthoclase, a pale flesh-colored variety, and the albite, colorless, in thin plates showing albite twinning, are small in amount, and their relations to the smoky quartz show that they belonged to the same period of growth with it. Cookeite occurs quite abundantly on some of the specimens as crusts or clumps of scales or platy crystals of a greenish-white color. It is similar in appearance to the muscovite, but is slightly darker in color, less pearly in lustre, and readily distinguished by its reactions before the blowpipe. The cookeite appears to have been formed at several periods of mineral growth in the cavity. It is seen occasionally as above stated in thin layers between the outer white quartz layer a»d the coating of WOLFF AND PALACHE. APATITE FROM MINOT, ME. 519 muscovite ; more frequently it forms an irregular layer on the lepidolite- muscovite crystals, showing, however, no parallelism with them ; and it is rarely included in, and in small amount deposited upon, the apatite crystals. In no case does the cookeite appear to have heen formed at the expense of any of the minerals previously formed in the cavity, which are perfectly fresh and free from alteration. The apatite is implanted upon the quartz crystals and upon the lepido- lite-muscovite crystals or the cookeite which covers them. As stated above the apatite is embedded at times in the white quartz layer in which it leaves sharp moulds when broken out, it having maintained its crystal form despite the interference of the quartz. Finally a third generation of quartz in minute crystals is found as- sociated with the cookeite, and rarely implanted upon the apatite crystals. To briefly recapitulate the facts relating to the paragenesis of this deposit we may say that we find : First, the crystallization of the smoky quartz, lepidolite, orthoclase, and albite, the normal constituents of the granite, to form the walls of the cavity. Second, the crystallization of muscovite, coating smoky quartz crystals in part and the lepidolite crystals wholly. Third, the crystallization of cookeite, coating muscovite, wholly or in part. Fourth, the simultaneous crystallization of apatite and white quartz, the latter confined to enlargement of smoky quartz crystals. Fifth, a second period of cookeite formation, accompanied by a final deposition of quartz. Crystallography.* The apatite crystals are in general of pronounced prismatic habit, the average size being about 1 cm. in height and 0.5 cm. in diameter. Crystals larger than this are, however, common, the largest measuring nearly 3 cm. in height and diameter. Crystals smaller than the average, which are also numerous, tend to assume a more or less rounded habit by nearly equal development of prismatic and terminal planes. The crystals are geuerally so implanted upon a terminal face that one end has developed freely, and the fact that over three hundred loose crystals with complete single termination and prism zone were * By C. Palache. 520 PROCEEDINGS OF THE AMERICAN ACADEMY. obtained from the collection shows how prevailing is this habit of growth. Occasionally the attachment to the matrix is by a prism plane* and then both terminations are developed. The forms observed were as follows, the letters used being those of Dana: c (0001), m (10T0)), a (1120), h (2130), z (3031), y (2021), *(10Tl), r (1012), w (7073), s (1121), ii (2131), ^ (3121). Four crystals were carefully measured on the two-circle goniometer and the same forms found on all. The results of measurement of the better developed forms agreed so well among themselves that it seemed worth while to calculate the axial ratio from the better readings, and this was done, using the forms y, x, r, and s. The following table shows the average angle to the base from each of these, the ratio calculated for each crystal, and the average ratio obtained : Angle from No. of d.* Angle from No. of d.* 0001 to 2021. Faces. 0001 to 1012. Faces. Cryst. 1 . . 59° 29' 5 3' Cryst 1 . 23° 00' 6 1' tt 2 . . 59° 29f 5 2' tt 2 ' 23° 00' 5 5' U Q 'J . 59° 30i' 6 3' tt 3 . 23° 00' 3 0' it 4 . . 59° 28J' Angle from 0001 to loll. 5 3' tt 4 . 22° 59f Angle from 0001 to 1121. 4 Cryst. 1 . . 40° 18' 6 3' Cryst 1 . 55° 45' 6 1' it 2 . . 40° 19' 5 5' ti 2 . 55° 46' 6 3' it O . 40° 19' 5 6' tt O . 55° 46' 4 it 4 . . 40° 18' 5 2' it 4 . 55° 45' 0 4' Crystal 1, from 23 measurements, p0 = 0.848307 Crystal 2, from 21 measurements, p0 = 0.848739 Crystal 3, from 18 measurements, p0 = 0.848753 Crystal 4, from 20 measurements, p0 = 0.848148 Average from 82 measurements, p() = 0.848476 or a : c = 1 : 0.734800 Angle calculated from p0 = 0.848476, 0001 to 2021 59° 29' 22" 0001 to 10T1 40 18 50 0001 to 10T2 22 59 19 0001 to 1121 55 45 59 Two types of combinations may be distinguished among these crystals. One of these is represented in figure 1, and consists essentially of the * d is the difference in minutes between largest and smallest readings for faces of any form. WOLFF AND PALACHB. APATITE FROM MI NOT, ME. 521 prism of the first order and the base, the edges modified by narrow plaues of the forms a, s, r, x, and y. Crystals of this type are not uncommon and often show double terminations. They merge, however, by slight gradations into the second type, more characteristic for the locality, shown in figures 2 and 3. Here the pyramidal planes become more prominent and the most notable feature is the simultaneous occur- rence of the right and left third order pyramids, giving the appearance of the normal dihexagonal pyramid. The different forms may be characterized as follows : c (0001) always present, generally large, brilliant, and plane giving perfect reflections. m (10T0) always present, generally dominant, brilliant, and generally plane but sometimes faintly striated vertically. a (1120) generally present but narrow and commonly dull from deep striatiou, the striae vertical and bounded by faces of adjoining plaues of m. Occasionally the striations stop abruptly in the centre or near the boundaries of a face as shown in figure 3, or they may be wholly lacking, in which case the face is brilliant and "fives 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., 3.159 at 2 0°C. A. Apatite from Minot, Maine. B. Calculated to 100. J. Apatite from Ceylon, Jannasch and Locke, loc. cit. , p205 RO F-OH, 1 3.42 0.57 1.5 5.13 0.85 or, CasP8[F.OH]012. * 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. Fluorine 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 iu the current of air to complete decolorization, and determining the loss of weight. Optical Properties. f .- 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 J and for this purpose a glass prism was selected having the index reNa r= 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 c determined by the millimeter screw reading to six seconds. The boun- * Zeit. anorg. Chemie, 7, p. 154; also Jannasch, Praktischer Leitfaden d. Gewichts 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 obtaiued : WNa = 1.63353 wLi= 1.63067 0,-6 = 0.00191 w — e = 0.0020 cNa= 1.63162 €Li= 1.62865 The crystal was then heated to 320° C. or until decolorized and the indices again determined as follows : a>Na == 1.63346 eNa =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 («) red- dish purple, perpendicular to e (to) 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 whicli 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 in the optic angle apparatus : 2ENa = 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 coloring 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)01.2 as also deduced by Jannasch from the analysis quoted above. Rammelsberg t explained the low content of fluorine (and chlorine) in certain apatites as due to removal of these elements * Annales des Mines, VII. 10, 1870, 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 Koksckarow (Ref. 2) extended this statement, holding that the normal angle c to x 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 sj^ecific 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 support the supposed relations. His table has been republished by several authors with slight modifications (Dana, Syst., 1892, 7G4-, 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 x 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 Baumhauer'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 the 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 there- fore omitted from the table below. WOLFF AND PALACHE. — APATITE FROM MINOT, ME. 527 Table of Physical and Chemical Characters of Apatite. Locality 1 Comba di Compare ) Robert, Piedmont ) 2 Achmatowsk . . . 3 Laacher See . . . 4 Rothenkopf, Tirol . _ ( Zillerthal, Tirol 6 Tirol .... 7 Ala, Piedmont 8 Kirjabinsk . . 'Jumilla, Spain tt tt 9 i Angle 0001 (' to 1011 O / // 40 4 0.7284 40 G 21 0.7294 40 G 21 0.7294 40 10 46 0.7313 40 10 40 0.7313 40 13 30 0.7325 40 11 48 0.7318 40 13 37 0.7326 10 \ Knappenwand, Tirol 40 1 11 Tirol (tale schist) 12 Sulzbachthal, Tirol . 13 Berg Blagodat . . 14 Nordmarken . . . , r S St. Gotthard . . 15 < 16 Tavetsch .... 17 Floitenthal . . . 18 Schwarzenstein . . 19 Vestana (Mn. apatite) 20 Hiddenite Mine, N. C. 21 Turkistan .... 22 Tokowaja, Urals . . Elirenfriedersdorf 5 26 40 16 10 0.7337 •1 40 16 10 40 17 40 17 40 17 40 17 40 17 40 17 20 40 17 45 40 18 10 40 18 22 40 18 22 24 Pisek 40 18 25 25 Elba 40 18 48 26 Minot, Me 40 18 50 27 Zwiesel (Mn. apatite) . . . 28 Ilmen Mts 29 Sudjanka River . . ... 0.7337 0.7340 0.7340 0.7340 0.7340 0.7340 0.7341 0.7343 0.7345 0.7346 0.7346 0.7346 0.7348 0.7348 Sp. Or. w-t CI 3.120 0.51 . . . 3.202 3.1495 .00435 .0044 0 085 absent 1.54 3.126 trace . . . 3.235 .00448 .0042 0.557 . . . 3.153 ( 3.132 ) 3.200 .0026 3.197 3.2154 3.225 0042 3.199 3.201 3.212 3.211 3.094 0.24 0.47 0.028 0.03 0.20 0.21 trace trace trace 0.01 absent absent trace 1.98 3.54 3.G3 3.58 0.028 3.74 3.64 lief. 2&18 Q o 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 3.159 .0020 absent 4.20 2 & 18 o ... o 2.27 5 3.56 15 ... 16 2.38 3.169 3.216 3.178 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. Baumhauer, Zeit. f. Kryst, 18, 31, 1890. 5 Hoskyns-Abrahall (Inaug. Diss. 1889), Abs. Zeit. f. Kryst., 21, 389. 6 Heusser, Pogg. Ann., 87, 468, 1854. 7 K. Zimanyi, Zeit. f. Kryst., 22, 331, 1893. 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. Akad. 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, Rendie. R. Ace. Lincei, Roma, 4 (2), 259, 1895. 17 Sandberger (Hilger),.N. J. Min. 1885, 1, 171. 0 18 Pusyrewsky, Verb. k. k. Mineral. Gesell. St. Petersburg, 1859-1860 (cited by Baumhauer, No. 4 above). 19 Latterman, Rosenbusch, Mik. Pliys., I. 409, 1892. Weibull, Geol. For. Forh., Stockholm, 20, 63, 1898. 20 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 exists between the specific gravity and the chlorine content. Nos. 2 and 9, from Achmatowsk and Jumilla, having about 0.5 per cent cblorine, 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. — XI. A DESCRIPTION OF EP1DOTE CRYSTALS FRO 31 ALASKA. By Charles Palache. With a Plate. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM.— XI. A DESCRIPTION OF EPIDOTE CRYSTALS FROM ALASKA. By Charles Palache. Presented by John E. Wolff, January 8, 1902. Received February 7, 1902. The ejtidote crystals described in this paper were sent to the Harvard Mineralogical Laboratory for crystallographic study by Mr. W. C. Plart of Manitou, Colorado, to whom we wish to express our thanks for the generous supply of material placed at our disposal. This material is from a new locality for the mineral and is remarkable for the size and unusual habit of the crystals ; it therefore seemed well worthy of description. According to Mr. Hart the epidote is found at Sulzer, Prince of Wales Island, Alaska. It is in the close vicinity of a body of copper ore and is further associated with garnet, albite, magnetite, and quartz. The coun- try rock of the region is limestone, which is cut by numerous igneous dykes, and it seems probable that the deposit is the result of contact metamorphism of the limestone by the dyke rocks, resembling closely in this respect the epidote occurrence with copper ore in the ,Seven Devils Mts. in Idaho.* The specimens at hand consist of several loose crystals and a mag- nificent cluster of large crystals implanted on massive epidote. The only associated mineral is quartz in small clear crystals of later formation than the epidote. The epidote is very dark green to greenish black in color, but oil- green and translucent in thin crystals or where bruised or cracked. The larger crystals are in the form of nearly square tables, which measure as much as 5.5 cm. each way and 3 cm. in thickness. In the smaller crystals the tabular habit is less pronounced and the mineral sometimes assumes the ordinary prismatic habit parallel to the b axis. The crystals are not * Compare Am. J. Science, VIII, 1899, 299. 532 PROCEEDINGS OF THE AMERICAN ACADEMY. infrequently doubly terminated. In the large group to which reference was made about twenty of the tabular crystals are found on a surface measuring about 15 by 20 cm., several of the crystals over 3 cm. on an edge, and attached by an edge in such fashion as to present an appear- ance altogether foreign to epidote. The crystals are frequently twinned according to the ordinary law for epidote, twinning plane the orthopin- acoid. Measurement of numerous crystals proved the presence of some tweuty-six forms as shown in the following list. The smaller crystals were measured on the two-circle goniometer and most of the faces gave excellent reflections. For the large crystals contact measurements were used, and these, with a study of zonal relations made determinations of forms fairly certain. A few forms were thus found that were not observed on the smaller crystals. Two forms new for epidote are marked with an asterisk. c(001), b (010), a (100), u (210), z (110), o (011), e (101), i (T02), N (304), r (T01), 1 (201), n (Til), a (212), F (154), Z (232), (121), 8 (T41), E (T51), q (221), O (544),* j (755),* X (322), y(2ll), R (111), * (113). 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 but 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 (011) 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 poor in forms and free from striation as compared with most crystals of epidote. r (T01) 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), (353), c/> (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 hy 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.

and 8 were determined solely by contact measurements ; Z and <£ by contact measurements and zonal relations. q (221) often present, sometimes large, always dull. O (o44), j (755), X (322), y (211), and R (411) 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. O was measured on three crystals (two of them twins) with six faces as follows : Measured. Quality. Calculated (010 as pole). 544 Crystal No. 4, " 5, -42° 04' 42 57 p 38° 30' 39 11 poor fair 42° 07' 42 07 p 39° 33' 39 33 137 06 38 58 fair 137 53 39 33 " " 6, —42 13 -137 37 39 20 39 19 good good -42 07 -137 53 39 33 39 33 136 48 39 18 fair 137 53 39 33 Average -'-± I _42° 07' 39° 33' -42° 37' 39° 06' or 180 — c/> ) 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 : * Biliang t. K. Sv. Vet. Akad. H. Stockholm, 12, No. 2, 1886. 534 PROCEEDINGS OP THE AMERICAN ACADEMY. 755 Measured.

p 142° 00' 66° 08' 141° 47' 66° 20' 322 y (211) and R (411) were the commonest forms of this series and were well determined by measurem ;nt on several crystals. * (513) present only on one crystal (figure 7) as a small face. Several of the above forms are lacking in the Winkeltabellen of Goldschmidt, and as the various values there given have been calculated for each of them they are given in the following table, which also includes two forms for which certain values were found to be incorrectly stated in the Tabellen : No Letter Symb.

> . . f79 ¥ 413 63 34 53 31 50 27 3102 46 04 20 58 T.2113 0.6019 1.3525 83 F 454 19 17 67 18 38 18 66 06 T7 44 60 33 0.7897 2.2570 2.3914 84 O 544 3129 64 43 47 53 6101 28 11 50 27 1. 1060 1.8057 2.1176 85 J 755 35 39 65 46 52 20 6101 32 07 47 49 12955 1.8057 2.2224 86 X 322 38 13 66 29 54 53 6101 34 34 46 05 1.4220 1.8057 2.2983 The drawings show the extremely variable habit of the crystals. Figure 1 represents perhaps the commonest type, a tabular twin crystal, the two individuals entirely symmetrical to the twinning plane * Mem. Acad. Lincei. 4, 380, 1887. t Correction, Winkeltabellen, p. 130, line 32 from above, col. 10. \ Correction, Winkeltabellen, p. 131, line 12 from above, wbole line. PALACHE. EPIDOTE CRYSTALS FROM ALASKA. 535 and so developed as to present no re-entrant angles. Here as in all the twin crystals the reversal of direction of the striations on 010 in the twinned crystal is the easiest means of recognizing the composite nature of the group. Figures 2 and 2a are orthographic projections of the same crystal on the orthopinacoid and the clinopinacoid respectively. They represent the largest crystal studied in natural size, and show how irregularly the two twinned crystals are sometimes united — in this case an imperfect penetration having taken place. The upper surface of this crystal is bounded by cleavage planes parallel to c where the crystal was broken from its matrix. The remaining figures (3 to 7) are orthographic projections on the clinopinacoid. Figure 3 is another tabular crystal in which the larger portion of the crystal is a single individual. Rarely such tabular crystals are untwinned. Figures 4 and 5 are two very symmetrical twin crystals, both pris- matic parallel to the axis b and doubly terminated. They show many of the less common forms and the re-entrant angle between two faces of n which is not common on these crystals. Figure 6 is a type of the untwinned crystal, prismatic parallel to axis b, the usual epidote habit. It is a left-hand termination. Many of the smaller crystals are of this habit with varying development of the planes of n and u. Figure 7 is a small crystal of prismatic habit but quite unlike any other found in its terminal planes. In conclusion it may be said that this Alaska epidote ranks among the finest occurrences of American crystallized minerals, and is only sur- passed in the size, beauty, and complexity 6f its crystals by the epidote from the Knappenwand in the Tyrol. MlNERALOGICAL LABORATORY, HARVARD UNIVERSITY, January, 1902. Palache. — Epidote Crystals. 5>-b u a 2 a Proceedings of the American Academy of Arts and Sciences. Vol. XXXVII. No. 20. — March, 1902. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XL. ON THE SPECIFIC HEAT AND HEAT OF VAPORIZATION OF THE PARAFFINE AND METHYLENE HYDROCARBONS. By Charles F. Mabery and Albert H. Goldstein. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — NO. XL. ON THE SPECIFIC HEATS AND HEAT OF VAPORI- ZATION OF THE PARAFFINE AND METHYLENE HYDROCARBONS. By Charles F. Mabeky and Albert II. Coldstein. Received February 10, 1902. Presented February 12, 1902. Since 1819, when Dulong and Petit, on the basis of their work on thirteen of the chemical elements, announced the law that atoms of all elementary bodies possess the same capacity for heat, or that the specific heats of the elements vary inversely as their atomic weights, the specific heats of the elements have been important physical constants. With some exceptions, the constant 6.54 represents the product of the atomic weight into the specific heat. Later work showed that this law could be extended to compounds. In 1831, Neumann discovered that compounds, with analogous composition have the same specific heat. Or in a series of compounds with analogous composition the specific heat varies inversely with the molecular weight. These laws apply to approximately forty ele- ments and to solids only at temperatures much below their melting points. The specific heats of many organic compounds have since been deter- mined, and although no law has been stated, it is evident that, in certain homologous series of organic compounds, a condition exists in some of these series analogous to the law of Neumann. For instance, deter- minations have been made on a few of the alcohols with the following results * Ethyl alcohol 0.680 Iso-propyl alcohol 0.5286 Iso-butyl alcohol 0.5078 Iso-amyl alcohol 0.49,'] 2 That the variations on certain homologous series so far as they have been observed do not conform to a general law, is shown by the follow- ing series, in which the specific heats increase with increase in molecu- lar weights : 540 PROCEEDINGS OF THE AMERICAN ACADEMY. Methyldichloracetate 0.3202 Ethyldichloracetate 0.33S4 Propyldicbloracetate 0.3506 In general, the data on specific heats of organic compounds are meagre and not concordant. For the same substance the results of different observers seldom agree in the third decimal place ; they often do not agree in the second, and even in the first place (see tables of Landolt and Bornstein). These variations are probably due to the fact that spe- cific heat is materially affected by impurities in the substance, and the temperatures at which it is taken. Then, furthermore, the details of the determinations demand very careful attention to insure concordant results. In the determinations of the hydrocarbons to be described in this paper, it was found that impurities depressed the specific heats very considerably. Although the paraffiue series of hydrocarbons offers the best field for study of an homologous series, very little has been done in the direction of ascertaining the specific heats of these bodies. In a study of distillates separated from Pennsylvania petroleum, by Bartoli and Stracciati,* the specific heats of the following hydrocarbons were determined : Hexane C,,IIU .5042 16°-37° Heptane C7H16 .4869 16°-37° Octane . C8H1S .5111 12-19° Decane V. io ' l-L' .5057 14°-18° Tetradecane ^ 1 1 1*30 .4995 Hexadecaue ^H.l'oi .4963 l.V -22° The inference derived from these results was that the specific heats of these hydrocarbons were remarkably constant. No data could be found relating to the specific heats of the methylene hydrocarbons CnIL„, nor those of the series still poorer in hydrogen. With the greatly extended uses of crude petroleum and refined distillates for fuel, in gasoline and oil engines, accurate information concerning specific heat and heat of vaporization is greatly desired. Having in hand a great variety of hydrocarbons of the various series, which have been prepared in as pure form as possible, and numerous inquiries having been received for more complete information concerning these physical properties, it seemed advisable to make some determin- ations of these constants. The hydrocarbons of the series CnH2n+2, were obtained from Pennsyl- vania petroleum, those of the other series from California petroleum. *Gazz. Cliim., 1885, 417-445. MABERY AND GOLDSTEIN. — SPECIFIC HEATS OP HYDROCARBONS. 541 Each hydrocarbon had been separated by a long process of distillation, and purified, by treatment with sulphuric acid, sodic hydrate, and drying over sodium. The determinations were made in a Bunsen ice calorimeter, to which was attached a capillary side tube 70 centimeters long, and the bore of such size that 1 centimeter contained 0.0579 grams of mercury. To maintain the temperature at 0°, the calorimeter was placed in a jar ot ice-water with an excess of ice, and this jar was placed in another jar and the space between filled with cotton. The calorimeter was filled with air-free water and dry mercury, and the inside film of ice, 2 to 3 millimeters thick, was formed by evaporation of ether by an air blast within the inner tube. Approximately 2 grams of the hydrocarbon was placed in a small glass stoppered tube of thin glass, whose heat equiva- lent was determined. The tube and hydrocarbon were heated to 50°, in a larger tube placed in a beaker of water, kept at this temperature for at least 15 minutes, then transferred by a thread to the calorimeter, ^ith care this could be done without loss of heat by radiation. The contraction of the mercury column was from 15 to 25 centimeters. This method can be used for the paraffine hydrocarbons from C6H14 to C16H34, the limit at which the hydrocarbons remain wholly liquid at 0°. After obtaining the water constant of the apparatus, three to six de- terminations of each hydrocarbon were made at the temperatures 0° and 50°, with results given in the following table : Boiling Points. Specific Heat C6H14 68 .5272 C7Hli; 91 .5005 CrH1G 98 .5074 Cs"18 125 .5052 (- ".("20 151 ' .5034 ^10 "22 162 .4951 ^10^22 172 .5021 ^llH24 195 .5013 V12"26 214 .4997 C13H2S 226 .4986 ^uHso 242 .4973 ^15 "82 260 .4966 ^16"34 275 .4957 Commercial Gasoline .5135 Crude Ohio Petroleum .4951 542 PROCEEDINGS OF THE AMERICAN ACADEMY. The following table gives the specific heats obtained from the series of methylene hydrocarbons : Boiling Points, o Specific Heat. V-/6tli2 68 .5062 C7H14 98 .4879 ^sH16 119 .4863 t^Hxs 135 .4851 ^10 H2o 160 .4692 QuH22 190 .4819 C12H24 212 .4570 Ci3H2(; 232 .4573 ^14^28 244 .4531 ^15^30 263 .4708 It appears from these results that there is a uniform decrease in specific heat with increase in molecular weight. Furthermore the normal hydro- carbons, such as heptane, C7H16, B. P. 98°, and decaue, C10H22, B. P. 172°, have higher specific heats than their isomers, such for example as isoheptane, C7H1G, B. P. 91°, and isodecaue, C10II22 B. P. 162°. The same variation also appears in the methylene series, with high values for certain members that probably indicate different structural relations. It is further interesting to observe the materially lower values given by the methylene hydrocarbons as compared with the values for the parafnne hydrocarbons. Whether this be due to greater compactness in the methylene molecule or to some quality of its ring structure, it would be interesting to ascertain. Perhaps the falling off in specific heat with increasing molecular weight will appear to better advantage when arranged as ordinates on a curve with the molecular weights as abscissae. Only those compounds are given on the curve that are known to be normal, although, of course, this is not known with reference to the higher members. The different values of the isomers heptane and decane is shown on the shorter curve. This uniform decrease in specific heat with increasing molecular weight in the series CnH2n+.2, suggest a constant relation analogous to the law of Neumann. If the constant K be expressed in terms of the specific heat multiplied by the molecular weight and the product divided by the number of atoms in the molecule, the specific heats found for the hydrocarbons of this series give the following values for the constant : MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 543 » K. 2.26 2.21 2.21 2.22 2.23 2.23 2.23 2.24 2.23 2.24 2.23 A similar curve drawn for the specific heats of the methylene hydro- carbons, so far as they were determined, show also a regular variation. The constant K, for the methylene hydrocarbons calculated from the determinations, shows a somewhat higher mean value than that of the paraffine hydrocarbons : Hydrocarbon. Mol. Wt CeH14 86 C7H16 100 C8H18 114 LgM.j,) 128 ^10 ^22 142 ^11 H24 156 ^12^-26 170 ^13^28 184 C14H30 196 C15H32 210 C16H34 224 The constant, therefore, CnHn2_|_2» 1S «•««« Sp. Heat. No. Atoms .5272 20 .5074 23 .5052 26 .5034 29 .5021 32 .5013 35 .4997 38 .4986 41 .4973 44 .4966 47 .4957 50 fdrocarbon. Mol. Wt. Sp Ileat. No. Atoms. K. M5U12 84 .5062 18 2.26 C7H14 98 .4879 21 2.28 CsH16 112 .4863 24 2.37 C0H18 126 .4851 27 2.27 C„H22 154 .4819 33 2.25 Ci5H30 210 .4708 45 2.20 The values for the specific heats of both hexane and hexamethylene are higher than should be expected from the results on the other members of the series. These hydrocarbons were well purified, except it seems probable that the distillates contaiued certain proportions of both. Determinations were also made of the specific heats of a series of hydrocarbons separated from the high boiling portions of Pennsylvania petroleum. This series is under examination to establish its composition and relations to series, separated from heavy petroleums from other fields. These hydrocarbons were cooled to — 10°, and filtered to remove so far as possible the solid hydrocarbons with which they are associated in Pennsylvania petroleum. They have been shown to be members of the series CnH2n. A more detailed description of these bodies will be presented in a subsequent paper, which is now in preparation. 544 PROCEEDINGS OF THE AMERICAN ACADEMY. The following values were obtained for the specific heats of these hydrocarbons : B. P. Sp. Heat. CigH32 173 .4723 Cl8 "36 202 .4723 ^20 "40 223 .4706 C23"46 260 .4612 C»4"48 272 .4586 From data obtained with the paraffine hydrocarbons, there is no opportunity to compare the specific heats, although the sudden drop from the last member examined of the series CnH2n+2, C16H34, specific heat .4957, to the first member of the last series above in which the solid hydrocarbon C16H32 had been removed by cooling and filtration, specific heat .4723, shows a marked difference in structure. This rela- tion appears in the longer curve in the table. Comparing the last member of the series CnH2n from California oil C15H30, specific heat .4708, with the hydrocarbon C16H82, specific heat .4746, it appears that the series CnH.2a from Pennsylvania petroleum is a continuation of the same series from California petroleum. Unfortu- nately the higher members of the series from California petroleum were not available for comparison. But results already obtained as to the com- position, specific gravity, refractive index, &c, are in accord with the specific heats. The specific heat was also determined in several hydro- carbons of the series CnH2n_2, and the series CnH2n_4, which had been separated from Texas petroleum with the following results : Series CnH2l, — 2- B. P. 50 mm. Sp. Heat. K. ^14"26 127 .4447 2.15 CisHog 142 .4439 2.15 CicH3t) 162 Series CnH2D B. P. 50 mm. .4426 -4- Sp. Heat 2.14 C21H38 218° .4560 C25"46 273° .4650 The latter results cannot be accepted as reliable, for the quantities of the hydrocarbons were very small, and the oils began to crystallize at 0°. There is no doubt that the specific heats of these hydrocarbons are smaller than those of the preceding series. MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 545 To convey a clear idea of the variation in hydrocarbons in the same series, and also to show the differences between the different series, the results are brought together on the following coordinate table : .520 8 6 4 2 .*SIO 8 1 In /y ?n ^ 6 £•« Hi. 1 f k£7 Hh 4 XC sl\ ,8 2 ^Q 0 i f .500 ///. (h Oj -*< i, h '24 8 SV ^U -- Hi 6 •iss 6 (14 Hi 4 *%C <>H 22 1 IS a J -xCi //' JJ ?. .490 8 6 £7 Hi, 4 X^ •J/ 'IS 2 480 ^ C i ' Ui 8 \ "X 6 \ >s. s. CV o£ iVAj A) 4 S >s _ ~- f"' //j. 2 V ^■C ' IH )i .470 *1 C/i H J >(?) KC2 c H 4-0 8 \ 6 \ \ 4 \ \ 2 \ .460 C 2 irt 46 \ 8 c 2-t JU N 6 4 ?, .450 8 6 C, ?/ zr, -2 (1 ItX Ail 4 V k"' Vic ? ^c J 6 ! /■ \a 440 ft 80 100 120 140 160 180 200 220 240 260 280 300. 320 340 Mo/ ecu far Weight VOL. XXXVII. — OO 546 PROCEEDINGS OF THE AMERICAN ACADEMY. The regular variation in members of the series CnH2n+2, appears in its curve, and the differences in what are known to be isomeric forms in the same series. It is further interesting to observe the continuation of the curve representing the members of the series CnH2n from the curve con- taining the members of the series CnH2n from California petroleum. The lower values in the series CnH2n_2 from Texas petroleum form a char- acteristic curve near the base of the table. The specific heat was determined in the following crude oils from various fields : Specific Gravity. Specific lleat Pennsylvania 0.8095 .5000 Berea Grit 0.7939 .4690 Japanese 0.8622 .4532 Texas (Lucas well) 0.9200 .4315 Russian 0.9079 .4355 Wyoming 0.8816 .4323 California 0.9600 .3980 Texas 0.9466 .4009 Ohio .4951 Commercial Gasoline .5135 These values show that the specific heat of the crude oils is an im- portant property from a practical point of view. It also appears that there is no close agreement between specific heat and specific gravity. Pennsylvania oil stands at the head, and Berea Grit with a much larger proportion of volatile constituents is next. Of the heavier oils it appears in general that the specific heats are much lower, but with no definite relation. It would be interesting to ascertain the specific heats of the less volatile constituents of petroleum from different fields, including the solid hydrocarbons. This would require observations at different tem- peratures, and it would add to the interest of the data if all determina- tions could be made within a wide range of temperatures. Heats of Vaporization of Hydrocarbons of the Paraffine and Methylene Series. Since it had been found that a boiling point constant can be calculated from the absolute boiling point, and latent heat of evaporation, which may be used as a basis of a method for the determination of molecular weights, more complete knowledge of the latent heat of evaporation or MABERY AND GOLDSTEIN. —SPECIFIC HEATS OF HYDROCARBONS, 547 heat of vaporization of liquids at their boiling points has become of great importance. FYorn a practical point of view, the greatly extended use of crude petroleum and its constituents can only be economically con- tinued with the aid of further information concerning the heats of vaporization. Numerous inquiries from persons interested in these directions attest an appreciation of further knowledge on this subject. In 1885 the following law was proposed by Dudley, on the heats of vaporization of members of a homologous series.* " In any homologous series the heat of vaporization in a unit of volume of the vapor, under the same conditions of temperature and pressure, is proportional to the density and also to the abso- lute boiling point." This gen- eralization was based on data selected from determinations of the heats of vaporization of the formiates, acetates, propionates, butyrates, isobutyrates, alcohols, and aromatic hydrocarbons. With numerous members of the different series of hydrocarbons at hand, it was our intention to determine the latent heat of the Series ^n"^'2n4-2^ ^n 2n' ^n 2n 1* But the only apparatus available was constructed of glass, which E~ would not withstand the high tem- peratures necessary in determina- tions of thehydrocarbons with high boiling points, and the time was too limited to permit of the construc- tion of a metallic apparatus. For the apparatus used, we are indebted to the kindness of Professor Kahlenberg of the University of Wisconsin, who allowed us to use the * Journ. Am. Chem. Soc , Vol. XVII., No. 12. 548 PROCEEDINGS OF THE AMERICAN ACADEMY. form devised by him, before he had published his description which appeared in the Journal of Physical Chemistry, April, 1901. This apparatus is an ingenious modification of Berthelot's method, in which the suhstance is heated and volatilized by means of an electric cur- rent within the body of the liquid, thus avoiding errors due to external heating. Through the kindness of Professor Kahleuberg and Profes- sor Trevor we are able to show in this connection the form of this apparatus. In the publication referred to, the apparatus is described as follows : " The retort consists of a tube 17 centimeters long and 5.5 centimeters in diameter, into the bottom of which is fused a tube which fits into a con- denser with a ground glass joint. At the other end of the inner tube are two large lateral openings. Glass tubes pass through the cork at the top, and into these are fused the ends of the spiral of platinum wire. This spiral consists of about 40 centimeters of fairly stout platinum wire, to the ends of which are welded short heavy jjieces of platinum rod, and these rods are in turn fused into the glass tubes. Long, rather heavy copper wires pass down into the glass tubes, at the bottom of which they are connected with the ends of the platinum rods by means of a few drops of mercury. The calorimeter is covered with a heavy piece of asbestos board and the retort is enclosed in asbestos and cotton batting." A current from eight to ten amperes, regulated by a rheostat, gave suf- ficient heat to vaporize from 20 to 30 grams of the oil in from 5 to 6 minutes. The calorimeter, about 2500 cubic centimeters capacity, was made of thin nickel-plated sheet copper. It was elliptical in form, to conform to the shape of the condenser, and was provided with a cop- per stirrer. The capacity of the calorimeter was reduced, as shown in the figure, by bending closer together the glass tubes leading from the body of the condenser. Temperatures were taken on a Beckman thermometer. The water equivalent of the calorimeter, condenser, stirrer, and ther- mometer were found to be 185 grams, practically the same value as the equivalent calculated from the weights and specific heats of the parts of the apparatus. As mentioned above, this form of the apparatus is limited in this work by the fact that when oils of boiling points higher than 125° are volatil- ized, the sudden change in temperature at the water line of the condenser is so great that glass will not stand it. The following results were obtained with a few members of the series CnH2n+2, as the mean of several observations : 4 MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 549 Boiling Point. Heat of Vaporization in Calories. o Hexane, C6H14 68 79.4 Heptane, C7H1(J 98 74. Octane, C8H18 125 71.1 Determinations were also made on the methylene hydrocarbons that could be volatilized in this form of apparatus : Hexamethylene, C6H12 Dimethylpentamethylene, C7HU Methylhexamethy lene, C7 H14 Dimethylhexamethylene, C8'H16 These results indicate a rapid falling off 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. Boiling Point. Heat in Calories 68-70 87.3 90-92 81. 98 75-7 118-119 71.7 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 POLTCHAETOUS ANNELID RHYNCHOBOLUS D1BRANCH1ATUS. By Adele Oppeniieimer. With Six Plates. 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 RHYNCHOBOLUS DIBRANCHIATUS. By Adele Oppenheimer. Presented by E. L. Mark, April 13, 1898. Received February 15, 1902. The proboscis of Rhynchobolus dibranchiatus was described by Elders ('64-68, p. 670) as "short, thick, club-shaped, with small egg-shaped papillae (compare Plate 1, Fig. 1), and was divided by him (p. 678) into two parts, the " Russelrohre," or sheath of the proboscis, and the " Kiefertriiger," or bearer of the jaws. Before eversion the " Russel- rohre " is anterior to the " Kiefertriiger," but when the proboscis is everted (Fig. 1) the latter is anterior. The " Keifertriiger " may be subdivided, as Ehlers suggested, into three regions, which in the non- everted state are respectively anterior, middle, and posterior: (1) the anterior has none of the small egg-shaped papillae ; (2) the middle region is that supporting the four jaws; and (3) the posterior is, as a rule, not everted, it is the region of the four glands (gl.) of the jaws and the remainder of the proboscis following the glands. The boundary between " Kiefertriiger " and "Russelrohre" is marked, ac- cording to Ehlers, by the place of attachment to the proboscis of four partial diaphragms, called by him " Lappen " (Fig. 1, hnn.). When cross sections of the -everted proboscis are made in the region of the four partial diaphragms (Fig. 2), one encounters in succession in passing from the surface toward the centre (1) a cuticula (eta.) ; (2) an epithelial layer ie'th.); (3) a connective-tissue layer (tis. co'nt.), in which are embedded eighteen longitudinal nerves (n. lg.), and a nerve plexus; (4) a region composed of eighteen longitudinal muscles (mu. lg.) ; (5) a sheet of circular muscles (mu. crc.) ; (6) a fascia or peritoneum (pi'tn.) 554 PROCEEDINGS OF THE AMERICAN ACADEMY. lining the body-cavity ; then in the body-cavity the four partial dia- phragms ; and finally that part of the proboscis which has not been everted. This consists of nearly the same kinds of layers arranged in the reverse order, namely a peritoneum, circular muscles, longitudinal muscles, nerves, connective tissue, and cuticula. The epithelial layer directly beneath the cuticula is not mentioned as such by Ehlers. Since it apparently undergoes an interesting metamor- phosis, it is worthy of further study. From the underlying connective-tissue layer eighteen projections of connective tissue pass radially inward between the eighteen longitudinal muscles to the region of the circular muscles. Where the radial projec- tions are continuous with the outer circular portion of the connective tissue the eighteen longitudinal nerves (n. Ig.) are seen cut crosswise. (Compare PI. 2, Fig. 10.) Concerning the structure of these longitudinal nerves I have nothing to add to what Ehlers ('64-68, p. 696) has already pointed out. They are evidently surrounded by a protecting connective tissue, within which lie what are apparently nerve fibres. In preparations fixed in vom Rath's picric-osmic-platinic chloride-acetic mixture, the nervous plasm is flocculent and has shrunken away from the nerve sheath. From these longitudinal nerves, fibres pass out (PI. 2, Fig. 10) to form the peripheral nerve plexus, which is embedded in the connec- tive tissue occupying the space between the longitudinal muscles and the cuticula. Other nerve fibres (n. r.) starting from the plexus pass radially inward, skirting the longitudinal muscle (Fig. 10); yet appar- ently they do not innervate the muscles, for I have seen no nerve fibre pass through the sheath enclosing the muscle. Still other radial nerve fibres (n. ?'.') can be followed from the longitudinal nerves passing through the middle of the radial connective-tissue projections toward the centre of the sections as far as to the membrane immediately superficial to the circular muscles (PI. 1, Fig. 2 ; PI. 2, Fig. 10). In the anterior region, where the four partial diaphragms, the " Lappen " of Ehlers, are at- tached to the wall of the proboscis, radial nerve fibres occupying the same relative position as those marked in other regions n. r! can be traced into these four pendent structures. Ehlers says concerning these " Lappen " (p. 686) : " By means of a fold it [the fascia wdiich invests the surface of all these parts] forms the four ' Lappen,' which are attached at the boundary between ' Riisselrohre ' and ' Kiefertrager ; ' these ' Lappen ' therefore possess the fine tense membrane on both sur- faces ; between lies a fibrous tissue, which is apparently identical with OPPENIIEIMER. RHYNCHOBOLUS DIBRANCHIATUS. 555 the subcuticular tissue of the sheath of the proboscis, with which, more- over, it is evidently continuous. This tissue . . . consists of a fibrous network, in the meshes of which lie ganglion cells." Further on (p. 696) he says : " The ganglion cells between the leaves of these ' Hautlappen ' lie in a single layer and are surrounded by strands of fibres, so that they lie as it were in the meshes of such a net made up of bundles of fibres ; however, it seems to me very doubtful whether these strands of fibres which make the meshes are all of nervous nature ; on the contrary I believe that the greater mass of this fibrous tissue is identical with that which lies under the chitinous cuticula of the ' Russelrohre ' and forms the sheath of the longitudinal nerves." If I understand Ehlers correctly (he has no figures showing these histological conditions), I do not entirely agree with him concerning the structure of the " Lappen." Within the peritoneum I find connective tissue, ganglion cells, and also cells not mentioned by Ehlers (PI. 2, Figs. 7, 8). These last have an epithelial character; they form, indeed, the main bulk of the lobe, as appears both in material prepared in the vom Rath mixture and in two haematoxylin preparations made from material fixed respectively in corrosive sublimate and in sublimate- acetic. The " Fasergewebe " of Ehlers I consider nervous in large part. Almost all of the fibres (Fig. 8) surround, not the ganglion cell, as one might infer from his description, but its nucleus, and pass out at one pole of the cell body to the longitudinal nerves of the proboscis. Finally, nerve fibres from the longitudinal nerves and from the pe- ripheral nerve plexus can be traced out peripherally into the small papil- lae which are thickly distributed over the surface of the " Russelrohre." Through the kindness of Mrs. Margaret Lewis Nickerson, who sug- gested to me the subject of the present paper, I was able to begin my study of the distribution of the sensory papillae of the proboscis on a preparation of the cuticula already made by her. The cuticula had been prepared by a method which was first employed by Mrs. Nickerson. All my subsequent preparations of the cuticula of other individuals were secured by the same method, which was as follows: The worm, after being narcotized in a mixture of sea-water and alcohol, was placed in a ten per cent solution of common salt until it was evident that its skin was loosened from the body. A cut was then made through the cuticula along a longitudinal line of the body, and the animal placed in tap- water. After the salt had been thoroughly washed out, the worm was cut transversely into pieces short enough for the cuticula to be mounted conveniently on a slide. The cuticula was next peeled off with needles 556 PROCEEDINGS OP THE AMERICAN ACADEMY. and floated upon glass slides. These preparations were ready for study as soon as they were dry. The whole surface of the proboscis, except the part which is most anterior in the usual state of eversion (Fig. 1), is covered with conical or thirnble-shaped papillae, which are arranged on the summit of transverse folds (PI. 5, Figs. 32, 33). In general the axes of the papillae are per- pendicular to the surface of the proboscis, or are directed outward and either slightly backward or slightly forward. The rows of papillae are as a rule separated from each other by regular intervals, but sometimes there is an anastomosis (Fig. 32) of the folds from which these organs project. The folds follow one another closely, and there are one or two rows of papillae to each fold. At the posterior part of the everted proboscis the transverse rows are divided into eighteen longitudinal groups (Fig. 33); the interspaces correspond to the position, of the eighteen longitudinal nerves. Otherwise the arrangement and frequency of these organs is the same from the anterior to the posterior end of the jiroboscis, and there is no other evidence of special grouping in any part. The papillae are more or less ovoid or conical. On a proboscis about o^- mm. in diameter at the anterior end, they were found to be about 80 [jl in height and about 35 /x in diameter at the thickest part. The cuticula of the proboscis passes over each papilla, but is here re- duced to about two-thirds the thickness it has elsewhere. The cuticula of the posterior face of each papilla is coarsely corrugated. The ridges are most clearly seen in preparations of removed cuticula (PI. 6, Fig. 34), or in sections stained in Kleinenberg's haematoxylin (PI. 1, Fig. 6 ; PI. 3, Fig. 13). Though varying in number in different papillae, the ridges show considerable regularity of form and arrange- ment, for the outlines produced by them are always rather sharply bent in a region corresponding with the middle of the posterior face of the papillae, so that the surface view of that face shows a series of V-shaped outlines, like the longitudinal section of a nest of funnels, the apices of the V's being directed toward the base of the papilla. Sometimes, however, there is an anastomosis of the folds (PI. 3, Fig. 13). Elders (p. 679) says of this species of Rhynchobolus that the cuticula of the papillae has " fine folds, which, like those of the gills, occur in spiral lines, surround- ing the papilla, or more rarely, standing out as sharply projecting ridges." Concerning the gills he says (p. 676) : " The chitinous cov- ering possesses at fairly regular intervals furrows which pass around the circumference spirally ; their significance probably consists in their laying the gill into definite folds when it collapses and withdraws into OPPENIIEIMER. — RIIYNCHOBOLUS DIBRANCHIATUS. 557 the parapodial pouch." Whatever may be the condition in the case of the gills, the furrows of the papillae do not encircle those organs, for I have found that they exist on the posterior face of the papilla only. That the function of the furrows of the papillae is similar to that sug- gested by Ehlers for those of the gills, namely to determine the place of folding when the organs are retracted, may well be questioned, for there is no evidence that the papillae are ever retracted ; there are no muscles to effect contraction, nor have I ever found the organs in a retracted condition. The papillae have been studied in sections fixed in a mixture of corrosive sublimate and acetic acid and subsequently stained in Klein- enberg's haematoxylin ; in sections fixed in corrosive sublimate and stained iu iron haematoxylin ; in preparations fixed in vom Rath's ('95, p. 282) picric-osmic-platinic chloride-acetic mixture (to which tap- water was sometimes added) ; and in methylen-blue preparations. The sections stained in iron haematoxylin I prepared, through the kindness of Professor Lloyd, in the laboratory of the Teachers College, Columbia University. The living substance of the papillae appears to consist of either four or five cells, which are, to judge from the nuclei, of two kinds. Two of the nuclei (PI. 1, Fig. 3 ; PI. 3, Fig. 16, nl. ba.) found in the papillae are basal in position and larger than the others ; the remaining two or three (ill. ax.) are nearer the apex of the papilla and also usually more nearly axial in position (PL 1, P'igs. 3, 4 ; PI. 2, Figs. 9a, 9b, 1 1 ; PI. 3, Figs. 1G, 17 ; PI. 4, Figs. 2G, 28, 30). The boundaries of the two cells to which the two basal nuclei belong cannot be made out by any process that I have employed. In preparations made with vom Rath's mixture, the protoplasmic con- tents of the papilla are distinctly vacuolated. The vacuoles are also seen with nearly equal distinctness in the methylen-blue preparations, but not quite so clearly in sections stained with iron haematoxylin or with Kleinen- berg's haematoxylin. The vacuoles are merely clearer, usually roundish, regions, which stand out distinctly, in contrast to the deeply stained granu- lar or fibrous surrounding substance, and are quite variable in size, as is to be seen in PI. 3, Figs. 18, 20; PI. 4, Figs. 22, 25, 29. I believe that some of the more elongated vacuoles and the clusters of the more rounded ones in the region of the central nuclei (Figs. 22, 29), and perhaps a lighter coloring of the axial region of the papilla (PI. 1, Fig. 4 ; PI. 2, Fig. 11), gave rise to the following opinion expressed by Ehlers (p. 679) : " There lies under the chitinous covering a thin sheet 558 PROCEEDINGS OP THE AMERICAN ACADEMY. of finely granular substance, which in the papilla appears to surround a narrow cavity, and there is connected with this sheet a thick layer of fibrous tissue." Connective-tissue fibres pass from the connective tissue of the pro- boscis into the papillae (PL 1, Fig. 4; PL 2, Fig. 11 ; PL 3, Figs. 12, 19, 20 ; PL 4, Fig. 27) ; as a rule, these could not be traced more than half-way to the apex of the papilla, but sometimes the contents of the papilla, in great part or entirely, looked fibrous (PL 1, Fig. 4 ; PL 3, Figs. 12, 15, 19). These fibres of the papilla are, as Ehlers says, in close connection with a finely granular substance. There is a particu- larly dense and deeply stained layer of this finely granular substance immediately under the cuticula (PL 1, Figs. 3, 4; PL 2, Fig. 11 ; PL 3, Fig. 16; PL 4, Fig. 30) ; it surrounds not a cavity, but a central re- gion in which there is a little granular substance and in which there are many vacuoles. At one point of the base of the papilla, where the connective tissue enters (PL 1, Fig. 4; PL 2, Fig. 11), and again at one point near the apex, apparently in the region of the sensory termination of the papilla (PL 4, Fig. 30c), there is a break in the dense layer of finely granular substance. Of the two basal nuclei (nl. ba.) one is near the anterior, the other near the posterior face of the papilla (PL 2, Fig. 96). They are sphe- roidal or ellipsoidal, and contain small irregularly scattered chromatin granules in large numbers ; but in preparations stained in haematoxylin (PL 1, Fig. 3; PL 2, Figs. 9/>, 11 ; PL 3, Figs. 16, 17) they appear less deeply colored than the remaining nuclei. The more distal nuclei (nl. ax.) are more elongated, being ellipsoidal or spindle-shaped. They present an elliptical outline whether seen in sections perpendicular to the axis of the proboscis (PL 1, Pigs. 3, 4 ; PL 2, Fig. 11 ; PL 4, Fig. 30c), in longitudinal sections of the pro- boscis passing through the axis of the papilla (Fig. 28), or in sections perpendicular to the axis of the papilla (PL 2, Fig. 9a; PL 3, Figs. 16, '17). The outline may be more or less pointed at one end, and is more nearly circular in the sections perpendicular to the axis of the papilla than in those parallel to the axis. The deeply staining granulations of the distal, or axial, nuclei are larger and not less numerous than those of the basal nuclei ; and it is perhaps for this reason that the first-named nuclei appear more deeply stained than the basal ones. The gran- ulations of the axial nuclei are also more evenly distributed. Both kinds of nuclei have a clearly defined nuclear membrane. In the prep- arations fixed in sublimate-acetic and stained in Kleinenberg's haema- OPPENHEIMER. — RHYNCHOBOLUS DIBRANCHIATUS. 559 toxylin, I have seen a nucleolus in the basal nucleus only, and here only occasionally (PI. 3, Fig. 16; PI. 4, Fig. 24). Sometimes, though rarely, there are in a basal nucleus two larger granulations (PI. 2, Fig. 11 ; PI. 4, Fig. 30c), which may perhaps be entitled to rank as nucleoli. In preparations stained in iron haematoxylin and in those fixed in vom Rath's mixture the nucleolus is regularly seen with great distinctness near the ceutre of the basal nucleus (PI. 2, Fig. 9b ; PI. 4, Fig. 26-28). The nucleolus is not infrequently sur- rounded by a light area. From the different effects produced on the two kinds of nuclei by haematoxylin and by methylen blue, it is fair to conclude that the cells to which the basal nuclei belong are very different from those of the apical nuclei, and that they have nothing to do directly with the nervous system. They are evidently indifferent subcuticular cells, which probably have the same functions as the cover cells of more com- plicated sensory organs. The central elongated nuclei found in haematoxylin preparations, judging from their position, evidently correspond to the two or three spindle-shaped cell bodies which appear in methylen-blue preparations. " I have not succeeded," says Pollers (p. 690), " in finding proof posi- tive that there are nerves in the fibrous tissue which enters the papilla from the common subcuticular layer." What Ehlers was unable to find, I have, by the use of improved histological methods, succeeded in demonstrating with entirely satisfactory clearness. The spindle- shaped cells are evidently nerve cells of sensory function. For, on the one hand, the basal end is connected with one of the eighteen longi- tudinal nerves of the proboscis by a nerve fibre passing to that nerve, either directly or, through the intervention of the peripheral nerve plexus, indirectly; and on the other hand the peripheral end tapers toward the apex of the papilla, where it terminates in a sensory structure, the precise nature of which it is difficult to make out. Each of the sensory cells of the papilla has the form of an elongated spindle tapering at its free end to a delicate fibre-like structure, and continuous at its basal end with a fibre traceable to a nerve trunk. This spindle-shaped enlargement, or cell body, lies in the axis of the papilla and about midway between its base and apex. An exception to this rule regarding the position of the cell body is seen in Figure 20 (PI. 3), where the cell seems to have a basal position. I am, how- ever, in doubt as to whether the sensory cells in this case are actually basal in position, or whether the appearance may not be due to an 560 PROCEEDINGS OF THE AMERICAN ACADEMY. accidental staining of parts adjacent to the nerve fibres, — a sort of extravasation, — accompanied by a failure to stain on the part of the real cell body and the more distal portions of the sensory cell. The spindle-shaped enlargement is sometimes stained uniformly, but more often the staining is irregular and blotchy ; in some cases a nucleus is to be distinguished near the middle of the cell body in the widest part of the spindle, which it almost completely fills. In one case (PI. 3, Fig. 14) the nucleus was sharply differentiated from the cell body, which was not at all blotchy, but distinctly fibrous and sparsely granular. From the distal end of the spindle-shaped cell body there passes off a fibre that, I believe, breaks up into a number of fibrils, each of which seems to me to end iu a disc (PI. l, Fig. 5 ; PL 3, Fig. 14). In Fig- ure 31 (PI. 4), the fibrils are quite clearly recognizable ; in Figures 25 and 29 (PI. 4), though distinguishable, they are not so evident. The terminal discs (PI. 3, Fig. 18; PI. 4, Figs. 25, 29) may, it is true, be artefacts ; but the frequency of their occurrence and the similarity of their appearance seem to me to be arguments against that supposition. Sometimes the blue is deposited in great amount around this bunch of fibrils (PI. 3, Figs. 12, 15, 18 ; PI. 4, Fig. 29), but in other cases it has failed entirely to stain the portion of the sensory cell that is distal to the spindle-shaped enlargement. On the other hand, there are cases in which the peripheral part of the distal portion of the sense cell has been differ- entiated by staining in haematoxylin (PI. 2, Fig. 11, not well brought out in the figure). In the case in which I have seen fibrils with their terminal discs most distinctly (PI. 3, Fig. 14), the discs at the ends of the fibrils are at the surface of the papilla outside the cuticula ; in other prepara- tions, the fibrils seem not to pass through the cuticula, but to end at its deep surface. It is probable that in most cases the cuticula has been artificially separated from the protoplasmic mass of the papilla, and that normally the fibrils pass to the surface of the papilla. The connection of the cell body with one of the eighteen longitudinal nerves of the proboscis is often to be traced on a single thick section. The process which the cell body sends centripetally either joins a longi- tudinal nerve directly, or enters the peripheral nerve plexus, which in turn joins the longitudinal nerve (PI. 2, Fig. 10; PI. 3, Fig. 19). The basal end of each of the two or three cell bodies of the papilla seen in methylen-blue preparations (PI. 3, Figs. 12, 14, 20; PI. 4, Figs. 23, 25, 29) is prolonged into a slender nerve fibre. While the fibre be- longing to one of the cells of a papilla bends to the left when it joins OPPENHEIMER. — RHYNCHOBOLUS DIBRANCHIATUS. 5G1 the nerve plexus, that belonging to another cell of the same papilla may bend to the right, as is to be seen in Figures 10 (PI. 2), 12, and 19 (PL 3). Occasionally the fibres twist around each other, and there is sometimes to be found an appearance which suggests anas- tomosis of these fibres, but focusing shows that in a great number of such cases the fibres cross without touching each other ; in still other cases (PL 3, Figs. 12, 19) the blue staining is not confined to the fibres, and this makes the following out. of the fibres more difficult. The condition shown in Figure 15 (PL 3), which seems to be an ex- ception to the rule that the basal end of each spindle-shaped cell body tapers into a nerve fibre, is probably the result of the well-known capriciousness of methyleu-blue staining. In no case have I seen a nerve fibre arise from an abruptly rounded basal end of one of these sensory cells, but the cell body seems always to taper gradually into the nerve fibre. There are, however, quite a number of cases in which the inner end of the .cell body does not simply taper into a single nerve fibre, but iu which it is prolonged into a few processes which ultimately unite to form the fibre (PL 4, Figs. 23, 25). These nerve fibres on their way to the longitudinal nerves often show at intervals those characteristic swellings, or varicosities, which have been so frequently figured in recent works on nerve fibres treated either by the methylen-blue or the Golgi methods. Summary. The papillae of the proboscis of Rhynchobolus are sensory organs. They are considered to be sensory on the following grounds: — 1. The papillae are well differentiated organs. 2. They are found over almost the entire surface of the everted proboscis. 3. They are elevated above the surrounding surface. 4. The cuticula which passes over each papilla is reduced to about two-thirds the thickness it has elsewhere on the proboscis. It should be mentioned that the cuticula of the posterior face of each papilla is coarsely corrugated, but the significance of this wrinkling is unknown. 5. There are two or three spindle-shaped cells in a papilla, each of which terminates — either below the cuticula or more probably at the very apex of the papilla — in what is clearly a sensory structure, and each of these cells tapers gradually at its base into a nerve fibre. These VOL. XXX VI i. — oG 562 PROCEEDINGS OF THE AMERICAN ACADEMY. nerve fibres are connected either directly or indirectly — through the in- tervention of a peripheral nerve plexus — with the eighteen longitudinal nerves of the proboscis. G. There are two basal nuclei that belong to cells which probably have the function of cover cells. It remains to be said that there enter each papilla besides nerve fibres, connective-tissue fibres. These latter are found in close connection with a finely granular substance, of which there is a particularly dense and deeply staining layer immediately under the cuticula. Standing out in contrast to the deeply stained granular or fibrous surrounding substance are the clear, generally rounded vacuoles. If there is any differentiation in function between papillae, it is not correlated with any pronounced difference in structure. Bibliography. Ehlers, E. '64-68. Die Borstenwiirmer (Annelida chaetopoda) nach systemati- schen und anatomischen Untersuchungen dargestellfc. Leipzig, xx + 748 pp., 24 Taf. Rath, O. voni '95. Zur Cunservirungstechnik. Anat. Anzeiger, Bd. 11, No. 9, pp. 280- 288. EXPLANATION OF PLATES. Abbreviations. coel. Coelom, body-cavity. eta. Cuticula. cta. + e'th. Cuticula and epithelium. gl. Gland. gnu. Jaw. linn. Lemniscus. mu. crc. Circular muscle. mu. Ig. Longitudinal muscle. n. crc. Circular nerve. nl. ax. Axial nucleus. nl. ba. Basal nucleus. n. Ig. Longitudinal nerve. n. r. Radial nerve fibre skirting longi- tudinal muscle. 11. rf Radial nerve fibre passing directly to the membrane superficial to the circular muscles. pap. Papilla. pi'tn. Peritoneum. tis. 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 proboscis showing: (1) the sheath of the proboscis; (2) the bearer of the jaws and its subdivision; and (3) the lemniscus (Imn.), which marks the boundary between (1) and (2). Narcotized in a mixture of sea-water and alcohol; fixed in Muller's fluid; stained with Beale's ammonia carmine. X circa 11. Fig. 2. Cross section of the partially everted proboscis in the region of the four lemnisci (Imn.), showing, among other things, a diagrammatic representation of the papillae and the connection of their sensory cells with the circular and the longitudinal nerves, and also the nerve fibre (n. r.') passing to the membrane which invests the circular muscles. Chloroform, methylen 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 the 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, methylen blue, Bethe's ammonium molybdate for invertebrates. X 650. Fig. 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 together with one of the basal nuclei. Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 585. Oppenheimer.- Sense Organs] Pl.a ■ PLATE 2. Fig. 7. Portion of cross section of proboscis, showing structure of lemniscus. Sea-water and alcohol, vom Path's mixture. X 200. 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 the two sections, and shows the form and position of the three axial nuclei ; Figure 96 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 haematoxylin. Fig. 10. Portion of the cross section of an everted proboscis, showing one of the eighteen longitudinal nerves (n. Ig.) cut crosswise, the peripheral nerve plexus, the union of the centripetal processes from the sense cells with the longitudinal nerve (in the case of the third papilla from the upper margin of the Figure, one of the two nerve fibres bends to the left when it enters the nerve plexus, the other to the right), a radial nerve (n. r.) following the surface of the longitu- dinal muscle (this is sketched in from an adjacent section), and another radial nerve (n. r.') passing directly to the 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. Oppenheimer- Sense ., i :hobolus. <«£?••. ■Ai 7 ■ , PLATE 3. Figs. 12, 14, 15, IS, 19, 20. Prepnrations made by use of chloroform, methylen blue, and Bethe's ammonium molybdate for invertebrates. Figs. 13, 16, 17. Prepared by use of sea-water and alcohol, sublirr.ate-acetic, Kleinen berg's haematoxylin. Fig. 12. Papilla from cross section of proboscis, showing connective-tissue fibres passing into the papilla; deep coloration of terminal fibrils; the nerve fibres bending in opposite directions where they enter the nerve plexus. X 080. Fig. 13. Papilla from cross section of proboscis, showing corrugations of posterior face of papilla, and the outline of one of the basal nuclei. X 460. Fig. 14. Papilla from sagittal section of proboscis; the two sensory (axial) cells, their peripheral terminations, and their proximal nerve-fibre prolonga- tions stained blue. T lie nucleus of one of the sensory cells more deeply stained than the cell body. Cuticula distended and detached from substance of the papdla by treatment. X 710. Fig. 15. Papilla from cross section of proboscis, showing deeply stained axial body, from winch a single peripheral, deeply stained process extends to the apex of papilla, where it terminates in a specialized and stained area ; the contents of the papilla in great part fibrous. X 1020. Fig. 1(5. 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 throughout ; their distal prolongations have a more or less spiral course and terminate in a cluster of discs at the apex of the papilla. 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 (?) ; the basal end of each sensory cell is prolonged into a slender nerve fibre. X G82.5. OppENHEiMERr Sense Organs Rhynchobolus. k /■j M- 76 ■ /; \ J7 20 / 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 chloroform, 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, Miiller's fluid, Beale's ammonia carmine. Fig. 23. The nuclei of the two sensory cells distinguishable 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 070. 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. 20. Cross section of a small papilla, showing a nucleolus in each basal nucleus. Sea-water and alcohol, vom Rath'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 alcohol, vom Rath's mixture. Fig. 28. 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-30<7. 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 Oj i ' ■ PLATE 5. Fig. 32. From a photograph of the cuticula of the proboscis stripped by 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. Fig. 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. iSiine of the eighteen longitudinal columns of papillae are shown. X 18 5. Oppenheimer. -Sense Organs Rhynchobolus. Plate 5. ■ >Vhi! ■•« tM *\ '1- -^ S? ->"N >>v .*, <& r«»> #*v •* *-*,* ^^>«»^«,f ^«R# ^ <*>5i« 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. — XLI. THE COMPOSITION OF PETROLEUM. By Charles F. Mabery. ON THE HYDROCARBONS IN PENNSYLVANIA PETROLEUM WITH BOILING POINTS ABOVE 216°. Aid in the Work described in this Paper was given bt the Academy from the C. M. Warren Fund for Chemical Research. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF CASE SCHOOL OF APPLIED SCIENCE. — XLI. THE COMPOSITION OF PETROLEUM. By Charles F. Mabery. ON THE HYDROCARBONS IN PENNSYLVANIA PETROLEUM WITH BOILING POINTS ABOVE 210°. 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 CnH2n + 2. Concern- ing the constituents with higher boiling points very little is known. Pelouze and Cahours t collected distillates to which they gave the fol- lowing formulas : — 216°-218° 236°-240° 255°-2G0° 280° C13H03 Cj4 H30 CiBrl82 Ci6H34 From paraffine the following hydrocarbons have been separated (Beil- stein's Handbook) : — 212°-215° 230°-235° 252°-255° 273°-275° Ci3H23 C14H30 (_/15H32 Ci6H34 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. 121. t Ann. China. Phys. (4), 1, 5 (18G4). 566 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 hulk 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 uncontaminated 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 the 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°-138° 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 : — Ci3H28 C14rl30 Ci5H32 C16H34 L17H3(5 124°-126° 136°-138° 156°-158° 174°-176° 188°-199° 0.22 0.26 0.43 0.37 0.43 per. cent. Ci8H38 C19H40 C20H42 ^2i"44 199°-201° 210°-212° 230°-232° 242°-244° 0.40 0.60 0.27 0.23 per. cent c G8 PROCEEDINGS OF 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 : — 56°-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 OP 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 760 mm. and with the mercury column all within the vapor : — 224° -225° 225°-226° 226°-227° 227°-228° 228°-229° Grams, 4 28 20 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 300o-301°. The hydrocarbon dodecane C12H26 was identified in the fraction 214°-216°.* Tridecane, C13H2S. 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. C02 and 0.2028 grm. H20. Calculated for C13HM. 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 C13H28. distillation of Russian petroleum, air accidently admitted caused such a violent explosion that 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 of0°.82. II. 1.2502 grm. of the oil and 33.3631 grms. benzol gave a depression of r.oio. III. 1.496 grm. of the oil and 32.9131 grms. benzol gave a depression of 1°.205. Calculated for Found. Cl3H28. I. II. III. 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 CX3H28- Found. 61.94 61.44 JlJonochlortridecane, C13H27C1. — 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 mouochloride. 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 mouochloride : — 0.1920 grm. of the oil gave 0.1273 grm. AgCl. Required for Ci3H2-Cl. 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 C13U2jCl. 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. 571 Tetradecane, Ci4H30. The fraction 142°-143°, collected after the twenty -fourth distillation, gave as its specific gravity, after drying over sodium, 0.7848. Alter 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°.718. Calculated for Found. CmHjo. I. II. 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. C02 and 0.2024 grm. H20. Calculated for C14II30. 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. C02 and 0.1970 grm. H20. Calculated for CUII30 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 difficult 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 0,41130. Found. 66.54 66.36 572 PROCEEDINGS OF THE AMERICAN ACADEMY. Monochlortetradecane, C14Ho9Cl. — 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 C^IL^Cl. 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., which 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 CnH^Clj. 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 C14H28C1S. Found. 267 264.3 Pentadecane, C15H32. The specific gravity of the fraction 158°-159° (50 mm.) dried over sodium was found to be 0.8U54 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 aud 23.2679 grms. benzol gave a depression of 1°.37. Calculated for Found. C15H3l. I. II. 212 211 212 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. C02 and 0.1919 grm. 11,0. II. 0.1608 grm. of the purified oil gave 0.5002 grm. C03 and 0.2198 grm. H20. Calculated for Found. C„H32. I. II. C 84.92 85.21 84.87 H 15.08 14.80 15.20 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 C15H32. Found. 71.15 70.49 Dichlorpentadecane, C15H30C12. — 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 C^HjuCIj. 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 C10H30C12. Found. 281 283.2 Hexadecane, C16H34. 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 OF THE AMERICAN ACADEMY. 276° under 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. C1(,H.34- 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 sulphuric acid (II.), and in a third portion purified with fuming sulphuric acid (III.), with the following results : — I. 0.1477 grm. of the oil gave 0.4600 grm. C02 and 0.1973 grm. H20. II. 0.1454 grm. of the oil gave 0.4522 grm. C02 and 0.1986 grm. H20. III. 0.1454 grm. of the oil gave 0.4516 grm. C02 and 0.1971 grm. H20. Calculated for i. Found. II. in. 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 Cir,HM. Found. 75.750 75.555 Dichlorhexadecane, C16H33C12. — 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 C10H3,C12. 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 C16H3,Clj. Found. 295 295 MABERY. — THE COMPOSITION OP 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 shown above, the original distillate has the composition of the series CnH2ll+2. Heptadecane, Ci7H36. 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 preseuce 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. CJ7H36. 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. C02 and 0.2044 grm. H20. II. 0.1491 grm. of the oil gave 0.4641 grm. C02 and 0.2014 grm. H20. Calculated for ^17^36. Found. I. II. c 84.96 84.94 84.87 H 15.04 14.80 15.01 576 PROCEEDINGS OP THE AMERICAN ACADEMY. Monochlorheptadecane, C17H35C1. — 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 grin. AgCl. Calculated for C^H^Cl. Found. CI 12.92 13.21 On cooling a portion of the distillate 188°-189° to —10°, it formed a pasty mass from which 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, CnH2n+2, it did not seem worth while to make any further exami- nation of the filtered oil. OCTODECANE, C18H38. 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 of0°.53. II. 0. 9926 grm. of the oil and 23.2544 grms. benzol gave a depression of 0°.84. Calculated for Found. CjgH^. I. IL 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. 0.1423 grm. of the oil gave 0.4435 grm. C02 and 0.1915 grm. H,0. II. 0.1513 grm. of the oil gave 0.4702 grm. C02 and 0.2054 grm. H20. III. 0.1524 grm. of the oil gave 0.4727 grm. C02 and 0.2064 grm. H20. Calculated for C 18^38- i. Found. 11. in. 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, C18H37C1. — 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 C18H37C1. 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. Kraff t * gave 28° as the melting point of octodecane, which he obtained from stearic acid; but his octodecane boiled at 2 14°. 5 under 50 mm. pressure. The specific gravity of the solid hydrocarbon was * Ber. deutsch. chera. Gesellsch., XV. 1703 (1882). vol. xxxvu. — 37 578 PROCEEDINGS OF THE AMERICAN ACADEMY. 0.7830 at §£, and 0.7816 at %. Krafft gave 0.7768 as the specific grav- ity of C18H38 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 C18H37C1. Found. 288.5 291.5 This molecular weight, showing that the hydrocarbon boiling at 300° is octodecane, does not agree with Krafft'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 C18H38, the size of the molecule could not be determined. Krafft looked upon the hydrocarbon boiling at 303° as having the formula Ci7H36. 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 C]8H38. 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. C02 and 0.1954 grm. FLO. Calcul ^18^30- ated for ^18^38- 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 CnHn2 and Hna •/2n+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 C18H36 : — Calculated for Found 82.90 84.96 82.60 A combustion of the solid hydrocarbon gave proportions required for the series CnH2n+2 : — 0.1564 grm. of the substance gave 0.4883 grm. C02 and 0.2083 grm. H20. Calculated for Cl8H38. 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. ^18^38- I- !*• 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 Cl8H33. Found. 84.96 84.53 NONODECANE, C19TT lo- 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 210°-212° 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 of0°.575. II. 1.1418 grm. of the oil and 36.2175 grms. benzol gave a depression of 0°.505. Calculated for Found. C19H,0. 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. C02 and 0.1994 grm. H20. II. 0.1591 grm. of the oil gave 0.4976 grm. C02 and 0.2132 grm. H20. Calculated for 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 C19H40. Found. 89.55 88.68 The results on the composition of the distillate 210°-212° 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, !£, and 0.7781 at |£. A determination of its molecular weight gave a value required for the hydrocarbon Ci9H40. 1.4011 grm. of the solid and 26.66 grms. benzol gave a rise of 0°.496. Calculated for C19H40. Found. 268 271.6 MABERY. — THE COMPOSITION OP PETROLEUM. 581 The melting point of the solid was found to be 33°-34° corresponding to the melting point, 32°, that Krafft 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 C19H3S. 0.1495 grm. of the oil gave 0.4715 grm. C02 and 0.1928 grm. H20. Calculated for C^H^. Found. 85.70 86.00 14.30 14.33 A determination of the molecular weight confirmed the formula: — 2.5445 grins, of the oil and 24. G3 grms. benzol gave a rise of 0°.994. Calculated for Ci3H38. 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 C^Hjg. 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 Krafft 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°. 582 PROCEEDINGS OF THE AMERICAN ACADEMY. The boiling point of tridecane has been variously stated at 219°, 216° and 212°-2lo°. But neither of these temperatures can be accepted as the boiling point of tridecane since its molecular weight is fouud to be that of the hydrocarbon boiling at 225°-22G°. 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 Cahours, 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 CnH2ll is liquid even at low tem- peratures, of higher specific gravity, and another is composed of solid hydrocarbons, of the series CnH2n+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 C2oH42 ; 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, C2iH44, and Liquid Hydrocarbon, C2iH42. From Distillate 230° -232°, 50 mm. Larger quantities of distillates amounting to 200 grams collected at 230°-232°, for the most part at 230°-23 1° • 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. CO., and 0.1968 grm. H20. Calculated for CnILn C,,HW. 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 C21H42. 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. C21II4;, C21H44. 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 OP THE AMERICAN ACADEMY. Calculated for C2IH42. 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 CnH2n. 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. C02 and 0.1778 grm. H20. Calculated for 0^11^. 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. C02 and 0.1898 grm. H20. Calculated for C21H,2. 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 C21H4J. Found. 294 299 docosane, c22h46, and llquid 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 Cj2H44 C22II1(.. c 85.70 85.16 H 14.30 14.84 MABERY. THE COMPOSITION OP PETROLEUM. 585 I. 0.1538 grm. of the oil gave 0.4800 grin. C02 and 0.1992 grms. H,0. II. 0.1560 grm. of the oil gave 0.4874 grm. C02 and 0.2024 grm. H20. III. 0.1362 grm. of the oil gave 0.4257 grm. C02 and 0.1788 grm. H20. Found. I. II. III. 85.09 85.21 85.25 14.40 14.42 14.59 The molecular weight 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 grms. of the oil and 21.91 grms. benzol gave a rise in boil- ing point of 0°.9566. Calculated for Found. C22IIU. I. II. 308 313.4 311.3 The index of refraction was found to be 1.454 and the molecular refraction : — Calculated for CKH41. 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. After 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 CnH2n+2. 0.1521 grm. of the solid gave 0.4721 grm. C02 and 0.2021 grm. H20. Calculated for Found. c 85.70 85.16 85.13 H 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. C02 and 0.1937 grm. H20. 0.1411 grm. of the oil gave 0.4419 grm. C02 and 0.1819 grm. H20. Calculated for C^H^. 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 C22Ha. 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, C23H48, and Liquid Hydrocarbon, C23H46. From Distillate 258°-260°, 50 mm. After the nineteenth distillation, 175 grams collected at 258° -2 60°, 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 OF 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. C02 and 0.1945 grm. H20. Calculated for 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 CnH2n, 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, C23H48, 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 CnH2n+2 : — 0.1515 grm. of the substance gave 0.4710 grm. C02 and 0.1989 grm. H20. Calculated for C^H^. 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 C^H^. Found. 324 327 588 PROCEEDINGS OF THE AMERICAN ACADEMY. The filtered oil gave as its specific gravity at 20°, 0.8569. It gave percentages of carbon and hydrogen required for the series CnFI2n: — 0.1504 grm. of the oil gave 0.4711 grm. C02 and 0.1945 grm. H20. Calculated for 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 C^H^. Found. 322 325 The index of refraction was found to be 1.4714, from which was cal- culated the molecular refraction : — Calculated for C23II48. Found. 105.87 105.31 TETRACOSANE, Co4H50, AND LlQUID 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 CnH2n. 0.1539 grm. of the oil gave 0.4769 grm. C02 and 0.2000 grm. H20. Found. 85.35 14.54 Calculated for C24H,8 C^H^. c 85.70 85.21 H 14.30 14.79 MABERY. — THE COMPOSITION OF PETROLEUM. 589 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°.G096. Calculated for C^H^. 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 Co4II18. Found. 110.47 109.75 Specific gravity of the oil at |§°, 0.8582. The solid separated by filtration melted at 48°. Krafft'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 Krafft 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 CnH2n+2. 0.1433 grm. of the solid gave 0.4479 grm. C02 and 0.1895 grin. H20. Found. 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^H^,. 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 Calculated for Cnli^n. ^24^50* 85.70 85.23 14.30 14.77 590 PROCEEDINGS OF THE AMERICAN ACADEMY. was cooled to 0°, filtered at the same temperature, 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 51°-52°. It is therefore evident that this distillate consists chiefly of one solid hydrocarbon, Co4H50i 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. C02 and 0.2107 grm. H20. Calculated for C^Hjj. 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 C^H^. Found. 364 362 A determination of the index of refraction gave 1.4725, which cor- responded to the molecular refraction : — Calculated for C26H52. 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 CnH2n+2. MABERY. — THE COMPOSITION OF PETROLEUM. 591 0.1534 grm. of the substance gave 0.47S7 grin. CO., and 0.2006 grin. ILO. Calculated for C^IIjj. 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, C27HC2. 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. C02 and 0.2033 grm. H20. Calculated for C^H^. 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 and 24.2827 grms. benzol gave a rise of 0°.416. Calculated for C2SHM. Found. t 366 364 592 PROCEEDINGS OF 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°. 800°-304°, 59°-G0°. 294° -296°, 58°. 302°-304°, 59°-60°. The oil filtered under pressure was very thick and viscous. Its specific gravity at 20° was 0.8G88. A combustion gave the following percentages of carbon and hydrogen : — 0.1500 grin, of the oil gave 0.4750 grm. C02 and 0.1812 grm. II20. Calculated for C27IIC2. Found. C 80.17 86.36 II 13.83 13.43 Its molecular weight at the boiling point of benzol corresponded to the formula C27IIC2. 3.650G grms. of the oil and 25.80 grins, benzol gave a rise of 0°.9G4. Calculated for C2;II52. 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 fcr Cj7HM. Found. 122 121.4 OCTOCOSANE, CagHss* AND LIQUID HYDROCARBON, C28IIC4. 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. Meltiug poiut 60°. Its specific gravity was determined as follows : — * 70°, 0.7945 80°, 0.7927 90°, 0.7911 MABERY. —THE COMPOSITION OF PETROLEUM. 593 A combustion gave the following percentages of carbon and hy- drogen : — 0.1508 grm. of the substance gave 0.4703 grm. C02 and 0.2032 grra. H20. Calculated for C28U"38- Found. C 85.28 85.07 H 14.72 14.97 The molecular weight at the boiling point of benzol corresponded to the formula C2sIl58. 3.070 grms. of the solid hydrocarbon and 26.21 grms. benzol gave a depression of 0°.7538. Calculated for C^llsg. Found. 394 399 The very thick oil separated by filtration gave as its specific gravity at 20, 0.8G94. A combustion gave percentages of carbon and hydrogen required for the series, CnII2n_2. 0.1500 grm. of the oil gave 0.4729 grm. CO, and 0.1836 grm. H.,0. Calculated for Found. Casing C;eII-n Cjg(lr^. 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 grm. 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. C28IIr4. I II. 392 396 394.4 The index of refraction was found to be 1.480, which corresponds to the molecular refractions : — Calculated for C^Hsg. Found. 127 126.78 It will be observed that the two liquid hydrocarbons last described have been shown to belong to a series CDII2a_2. 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 CnH2n_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, 0.8G94. 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 iu 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 C23H54 iu 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, 370.2, of the liquid hydrocarbon C27ll52» 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 Heneicosaue Hydrocarbon, liquid at —10° Docosane Hydrocarbon, liquid at —10° Tricosane Hj'drocarbon. liquid at —10° Tetracosane Hydrocarbon, liquid at —10° Pentacosane Hydrocarbon, liquid at —10° Hexacosane Hj-drocarbon, liquid at —10° Octocosane Symbol. C15H 32 ^16^34 Cl7HS6 ^18^38 C19H40 C2iH44 C00H44 C22H46 C23H46 ^-'23"48 ^24"48 ^24"50 C27Hg2 ^20^54 ^28^54 Boiling Point. 226° 236°-288° 256°-257° 274°-275° 288°-289° 300°-301° 210°-212°, 50 mm. 2.30°-231°, 240°-242°, 258°-260°, " 272°-274°, " 280°-2.-2°, 202°-294°, 310°-312°, " Melting Point. 10° 20° 33°-34° 40°-41° 44° 45° 4S° 53°-54° 58° G0° pressure. Much attention has been given to these determinations, espe- cially by Messrs. O. J. Sieplein and R. P. Cushing. 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. Cushing, Dr. E. J. Hudson, and O. 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 Wentworth IIigginson. Joseph Henry Thayer. By C. H. Toy. John Fiske. By Andrew McFarland Davis. James Bradley Thayer. By James Barr Ames. OFFICERS AND COMMITTEES FOR 1901-1902. LIST OF THE FELLOWS AND FOREIGN HONORARY MEMBERS. STATUTES AND STANDING VOTES. RUM FORD 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 Corresponding Secretary read letters from Frank S. Collins, accepting Fellowship; 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 Henry A. Rowland ; from the 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 -\. The Corresponding Secretary presented the Annual Report of the Council. The Treasurer presented his annual report, of which the following is an abstract : — - GOO PROCEEDINGS OF THE AMERICAN ACADEMY. General 'Fund. Receipts. Balance from last y*ear $259.50 Investments $5,344.80 Assessments 915.00 Admission fees 20.00 Sale of publications 101.01 6,380.81 6,640.31 Expenditures. 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. Receipts. 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 Medals 327.00 Publishing 266.22 Library 374.44 Miscellaneous 11.25 1,894.91 Income invested during the year and transferred to capital account 10.75 Balance ... 2,546.08 $4,451.74 RECORDS OP MEETINGS. 601 Warkkn Fund. Receipts. Balance from last year $994.57 Investments 1,332.97 $2,327.54 Expenditures. Investigations $600.00 Income invested during the year and transferred to capital account 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 dollar, 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 Academy. The Rumford Committee has given much consideration to the question introduced by Professor E. C. Pickering, of the feasibility of co-operation among the various committees in this country having in charge the administration of funds devoted to research. 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 meeting 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. RECOUDS 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 OP THE AMERICAN ACADEMY. Professor Wallace C. Sabine with Mr. Theodore Lyman, on the study of false spectra from the Rowland Concave Grating. The Committee has devoted much time to the 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 Tread well, 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 Rutherfurd, of New York, for his im- * provements in the processes and jnethods 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 Gibbs, 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. Samuel 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 ahsolute 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, 189a. Thomas Alva Edison, of Oraage, 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 by 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. ?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 (8150) 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. Mabery, 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 one hundred dollars ($100) to continue the catalogue of the Library and to purchase a catalogue-case. 608 PROCEEDINGS OF 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. I., 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. I., 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 elass 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 ex officio, and three other Fellows, one from each Class, who shall examine the Library and make an annual report on its condition and management. 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 Kumford 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. "The 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 the Kumford 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 voi.. xxxvn. — 39 610 PROCEEDINGS OF THE AMERICAN ACADEMY. Fellows must be proposed by two Resident Fellows of the section to which the proposal is made, in a recommendation signed by them, and this recommendation shall be transmitted to the Corresponding Secretary, and by him referred to the Council for nomination." 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 I. Alphetjs 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 year. ^| 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. J William Everett, for one year. ^ A. Lawrence Lowell, for two years. > Class HI. Penman W. Ross, for three years. ) Member of Committee of Finance. Eliot C. Clarke. RECORDS OF MEETINGS. 611 Rum ford 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, Wjlliam L. Richardson. The following gentlemen were elected members of the Academy : — George Frisbie Hoar, of Worcester, as Resident Fellow in Class III., 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, Mineralogy, 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 II., 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 the 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 hundred 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 Theodore Lyman, accepting Resident Fellowship ; from George E. Hale, W. W. Keen, E. H. Moore, C. O. Whitman, acknowledging election as Associate Fellows ; and from Sir Lauder Brunton, RECORDS 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, inviting 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, Felix 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 Academv: — Henry 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 Bar us 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 anniversary 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 OP MEETINGS. 615 Nine hundred and twenty-eighth Meeting. December 11, 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 pro 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 Pcr- 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 the 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 : — G16 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 III., 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 Hann, of Vienna, to be a Foreign Honorary Member in Class II., Section 1 (Geology, Mineralogy, and Ph}rsics 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 Felix 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 III., Section 4, to Class I., Section I. 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. XXIII. " A Revision of the Galapagos Flora." By B. L. Robinson. " The Probable Source of the Heat of Chemical 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 Mi not, 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 II. 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- bourg, acknowledging congratulations on the occasion of its fiftieth anniversary. The Chair announced the following deaths : — Alpheus Hyatt, Vice-President for Class II. Clarence King, Associate Fellow in Class II., Section 1. Karl Weinhold, Foreign Honorary Member in Class III., Sec- lion 2. In accordance with the Statutes, the following Councillors were appointed a committee to nominate a candidate for the office of Vice-President for Class II. : — Harry M. Goodwin, of Class I. George H. Parker, of Class II. William Everett, of Class III. 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 Delitzsch, 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 II. Samuel Rawson Gardiner, Foreign Honorary member in Class III., 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 II., 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 : — *t> 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 IT. 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 Prevalence 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 II. ; H. E. Clifford, 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 Secretaiy, 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 $2,780.94 Publishing $2,095.59 Library 1,570.08 Catalogue 95.40 3,707.07 Balance, April 30, 1902 '. ~ . 272.42 $0,827.03 Rumford Fund. Receipts. Balance, April 30, 1901 $2,540.08 Income from investments $2,514.17 Sale of publications 5.00 2,519.17 $5,005.25 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 $5005.25 622 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 Ms 4 2 4310 RECORDS OF MEETINGS. G23 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, $604.70; 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 iu aid of researches in light and heat. The following grants have been voted : — Nov. 13, 1901. One hundred dollars to Professor Henry Crew of Northwestern University, in aid of his 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. W. 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 effect 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 iu a list transmitted to him by the Committee. 624 PROCEEDINGS OF THE AMERICAN ACADEMY. The following papers, embodying the results of researches aided by appropriations from the Rumford Fund, have been printed in Volume XXXVII. 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. Arthur 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 sum 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 to 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 OP MEETINGS. 625 Report of the C. M. Warren Committee. The Committee in charge of the C. M. 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 continue 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 falling 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 expensive 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 ($750) 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 ($150) 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 re- 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 officers and committees : — ■ Alexander Agassiz, President. John Trowbridge, Vice-President for Class I. Henry P. Walcott, Vice-President for Glass II. John C. Gray, Vice-President for Class III. William M. Davis, Corresponding Secretary. & RECORDS OF MEETINGS. G27 Willtam 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. Member 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 Committee. 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 11., 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 III. Auditing 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 (Philosophy 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 III., 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 the 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 Laboulbeniaceae." — 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." Bv Anion Benton Plowman. J 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. REC0RD3 OP MEETINGS. 629 " On the Dibromdinitrobenzols derived from Paradibrom- benzol." Second paper. By C. Loring Jackson 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, //om 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 = CI) 94. Beryllium . Be = Gl 9.1 Nitrogen . N 14.04 Bismuth Bi 208. Osmium Os 190.8 Boron . . B 11.0 Oxygen (stanc lar a) O 16.000 Bromine . Br 79.955 Palladium . Pd 106.5 Cadmium . Cd 112.3 Phosphorus . P 31.0 Caesium Cs 132.88 Platinum . Pt 195.2 Calcium Ca 40.13 Potassium . K 39.14 Carbon . . C 12.001 Praseodymiur n 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 1 . Th 233. ? Indium . . In 114. Thulium ? . 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 OF 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. The 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 ma}' still be a whole unit in doubt ; but it has been retained as a compromise. The differences between the present table, that of the German Committee,! and that of F. W. Clarke, § are diminishing year by year. Nevertheless to as many as twenty-eight elements out of the seventy-seven are given values in these three tables differing among themselves by over one tenth of a per cent; namely, the atomic weights of antimony, bismuth, cerium, columbium, fluorine, gadolinium, germanium, helium, hydrogen, lanthanum, magnesium, mercury, neon, osmium, palladium, platinum, potassium, samarium, scandium, selenium, tantalum, tellurium, thorium, thulium, tin, titanium, uranium, and zirconium. To this list of uncertain elements should be added erbium, gallium, glucinum, indium, terbium, tungsten, ytterbium, upon which the three tables agree only because of lack of data upon which to base a disagreement. Thus nearly half of the elements are still in doubt by at least one part in a thousand. This circumstance is not so much a reproof to the many earnest workers upon the subject, as an evidence of the great difficulty of some of the problems involved. Three of the elements given in the list above should not properly be included among the uncertain values, namely, hydrogen, magnesium, and potassium. The first finds its way into the list because of the disregard of significant figures by the German Committee, and the second chiefly because Clarke has included in his calculation work upon magnesic oxide undoubtedly erroneous on account of the presence of included gases. || The case of potassium is somewhat peculiar; for in spite of the great wealth of data concerning this element, Clarke assigns to it the value 39.11, while the German Committee chooses 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): J Landolt, Ostwald, and Seubert, Extra insertion in Berichte d. d. ch. Ges. 1902. Heft 1. § F. W. Clarke, Journ. Am. Chem. Soc, 24, 201 (1902). || Richards and Rogers, These Proceedings, 28, 209 (1893). AMERICAN ACADEMY OF ARTS AND SCIENCES. Report op tiie Council. — Presented May 14, 1902. BIOGRAPHICAL NOTICES. Augustus Lowell Percival Lowell. Truman Henry Safford Horace Elisha Scudder Joseph Henry Thayer . John Fiske James Bradley Thayer Arthur Searle. Thomas Wentworth Higginson. C. H. Toy. Andrew McFarland Davis. 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 Nordenskib'ld, Karl Weinhold. AUGUSTUS LOWELL. Augustus Lowell was born in Boston, Jan. 15, 1830. His father was John Ainory 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 by descent — the name, originally Lowle, dating from the conquest — while the Putnams, originally Putteuham, 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 her, 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. GC6 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 sou's labors at that insti- tution of learning the sole document extant is of the Incus 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. Go7 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 living ; in his studies he collected a line 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 Watertowu 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 the 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 in 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 authority 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 in. 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 somehow 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 friendship 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. G39 On getting home he began his career in State Street, going into the counting-room of Bui lard & Lee, East Indian merchants, to learn the business. His quickuess 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, regardless 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. lie 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. G40 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, aud 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 Bigelnw Lawrence, the youngest daughter of the Hon. Abbott 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- in-law. 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. The exception occurred some time after Mr. Lawrence's death, which 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. AUGUSTUS LOWELL. G41 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 country 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 Parkman 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. xxxvn. — 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 office next his father's, and became gradually con- nected, on the one hand, with the manufacturing interests which his 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, -Tune 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 Suffolk 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 position 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- uting 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, beyond business hours, his life was now quite bucolic. The place he had bought possessed already a fine garden and two greenhouses. Iu 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 iu 044 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 foreign 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. Q-^ 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 mention 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 hut 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 terms 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 again 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 administration 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 conuected with them which speaks £4:6 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 no 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 lee- 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 world 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 much 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 el'ose. 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 :i 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. 047 almost from its start. The Massachusetts Institute of Technology was fouuded 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 scfiool 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 equally 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 the 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 invincihle 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 648 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 aud 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 Technology 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 Robert Ball informed the writer that it was in advance of anything of the kind iu Great Britain ; a belief which he had years before acted on by sending his sou 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 recog- nized at home, which means that it probably is of some importance, as the American believes firmly in the ignota pro magnifico. 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 Poly technique 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. AVhereupon 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. G4U Of the American Academy of Arts and Sciences he was made a mein- her in 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 was in thought or word or deed ; and very refreshing it is, like a cool breath of pure air in 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 brought 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 this 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 eot 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, uucomplexioned, 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 and judiciousness in its presentation. In the first place he was apt to be right, that is, to be wise. His judgment of things 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," he once said to me, " I ask a good price of the tenant and then do all the little repairs he 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 they care for their feelings. And Mr. Lowell's forte was not the silver tongue of eloquence, but the more golden gift of statement, lie 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 his 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 him 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 stagnation. Not in knowledge nor in intellect ; it was in cast of mind he differed. His preference W*as for action. Of this he never tired. To recreation he was less {riven. 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 habitation 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 misrepresentation, it is no small thing to say of a successful man of affairs that lie 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 only 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 SAFFORD. 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, foolishness; without the third, knavery. The apathy of most of us, the crankiness of a few, and the financial trickery of others, are 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 thorough education. He graduated 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. <555 obtained employment at Harvard College Observatory, where he con- tinued for nearly twelve years. He married Elizabeth M. Bradbury, of Cambridge, in March, I860, ''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. Safford'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 he 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 with the actual place of the companion discovered almost simultaneously by the younger Alvau 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 iu later years. In 18G3 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 in 1863. By means of these fundamental stars, the right as- 65Q TRUMAN HENRY SAPFORD. 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 this 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 riffht 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 Satford'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 iu 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 the 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 iu 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. xxxvn. — 42 658 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). Repub- 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 hours daily as due tn the firm for which he labored; and he then kept carefully the record of these In mis. 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 conservatory 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 ami perfect, and represented that other extreme from that celebrated collection of De Quincev 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," bnt 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 7, 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 eveu 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 nie 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 Cod." 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- 000 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 suhjects in their relations rather than in their 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 power"' (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 noblv 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. (J61 the effect of immediate surroundings. His father, so far as I can ascer- tain, was one of those Congregationalists 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 Congregationalist, 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 Wentworth 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 the 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, the 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 industr}'. 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, ami 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 that every year produced in Europe and America, and to form well-defined opinions as to its value. JOSEPH HENRY THAYER. 6QS 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 he never spoke of the attitude of the Faculty 004 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 aud 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 cheery manner gave him, even in his last years, a remarkably youthful appear- ance, and his bodily alertness was in keeping with his mental activity. His literary career extended over forty years, apparently without dimi- nution of interest. He had the great happiness 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, No'vember 26, having not long before passed his seventy-third birthday. C. H. Toy. JOHN FISKE. 665 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 had 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 Edmund 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 Middletown and was placed in a private school, after which he went to Cambridge. Meantime he seems to have browsed honic 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, ()., Regular Singular Points of a System of Floniogeneous Linear Differential Fquations 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. nexuosa, 242. intestinalis, 212. prolifera, 242. Epidote Crystals 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. II. , 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, 665-67S. Foreign Honorary Members de- ceased, — Cornu, A., 620. Gardiner, S. R., 618. Grimm, F. H., 613. Kovalevskv, 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, 253. rigidum, 253. supradecompositum, 253. General Fund, 600, 621, 625. Geotaxis, 190. Glasgow, University 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 Humphreyi, 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 Kumford 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 Rum- ford Fund to, 601 ; Radiometer, 601; Rumford Premium awarded to, 624, 628. Halimeda Opuntia, 246. tridens, 246. Tuna, 246. Halodictyon mirabile, 258. Haloplegma Uuperryi, 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, 397-111, 617. Heat of Vaporization, 537-549, 618. Heimrod, G. W. See Richards, T. W., 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, II. O., elected Resident Fellow, 618 ; accepts Fellow- ship, 620; Grant from Income of C. M. Warren Fund to, 625, 626. Hormothamnion enteromorphoides, 241. Horsley, V. A. II., 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, 620. Hydrocarbons, Paraffiue and Methy- lene, 537-549, 618. Hydroclathrus cancellatus, 248. Hydrogen, Arc Spectrum of, 159-174. Hyparrhenae, Carices of the Section, 445-495. Hypnea, divaricata, 254. musciformis, 251. Valentiae, 254: Iron, Arc Spectrum of, 028. 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, 621); 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. Kainomyces, 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. Labyrinthulesc, 342. Lacaze-Duthiers, F. J. II. 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. Libraiy, Appropriations for, 607. Library, Committee on the, Report of, 606. Limax maximus, Reactions of, 183- 227. Lithothamnion incrustans, 260. Lenormandi, 260. Loci in n-Fold Space, On Ruled, 119— 157, 612. Lophosiphonia obscura, 257. 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 Hydrocarbons, 537-549, 618. MacDonald, A., Psycho-Physicai Lab- oratory, 599. Magnesium, Arc Spectrum of, 628. Mall, F. I'., accepts Fellowship, 599. Manchioneal, 255. Mark, 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. Mastio-ocoleus testarum, 241. Melobesia farinosa, 200. Lejolisii, 260. membranacea, 260. pustulata, 260. Mendenhall, C. E., Bolometer, 601 ; Grant from Income of Rumford Fund to, 601. Mendenhall, T. C, Associate Fellow, 616. Mercurous 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. tenerrimus, 240. vaginatus, 240. Microdictyon umbilicatum, 247. Minot, Maine, Apatite from, 515- 528, 615, 617. Mislawsky, A., Fiftieth Anniversary, 614. Monoicomyces, 23. Aleocharae, 24. Echidnoglossae, 23. furciliatns, 24. Moore, E. PL, accepts Fellowship, 612. Moreno, H. C, On Ruled Loci in rc-Fold Space, 119-157, 612. Morgan, M. II., elected Resident Fellow, 616, 617. Miiller-Breslau, H., accepts Member- ship, 613. Murrayella periclados, 257. Museum of Comparative Zoology. See Zoological Laboratory. Mycoidea parasitica, 243. Neighborhood of a Singular Point, 279. Neomeris dumetosa, 247. Nichols, E. F., Grant from Income 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, 210. 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 Rhvncho- bolus dibrancliiatus, 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 Member- ship, 613. Penicillus capitatus, 245. dumetosus, 245. Pennsylvania Petroleum, Hydrocar- bons in, 5 f'Hriftflf ill' 1«* HrJH I iutWHi mm irlrwiKKiliHl lnK> K{J (Of IiiliKllrimtiini liuUUfl tf ■' • !i;K!,!-"'i !>[ t IjJ \M ! 'Srauat ulitilwtnKiiit I !HkkHk lljjljb pi I Inmw \WM\W4\M IkkIihkkm Nwlf HUH) _■■■■■ he 8P I Rtet \\M BBBBfnB "KawDi ■Oh ImW