PROCEEDINGS OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. Vol. L. FROM MAY 1914, TO MAY 1915. BOSTON: PUBLISHED BY THE ACADEMY 1915 I - GRE :en 3 o ' in 2 «^R ED Ml > f ,^> - 1 400 wave length Figure 1. b00 nized as color-blind by simple tests, so that while one may define an average normal color-vision, from which large variations are rare, it is clear that the relations of the color sensations are subject to con- siderable variability. It is the purpose of this paper to classify such variations with reference to their bearing on the general color sense of the individual and to point out such of the more conspicuous ab- normalities as have been detected in tests of color-sense. The facts will be stated in terms of the ordinary trichromatic theory for the sake of simplicity. How far the observed facts regarding the typical color-sensation curves may be complicated by aberrancies of color perception referable to the cortex alone, and to what degree the independent violet sensation postulated by Burch (loc. cit.) may be BELL. — TYPES OF ABNORMAL COLOR VISION. 0 involved with the residuum of the red and green sensations, the yellow- ing of the lens, and variations of macular pigmentation, are matters to be considered when the simpler facts of sensation can be better co- ordinated. The relations of the three fundamental color sensations of the Young- Helmholtz theory, at least rest on a sound experimental basis and it is well understood that ordinary cases of color blindness imply an easily measurable deficit in one of these sensations. In the normal or average eye the three fundamental sensations are related in a certain normal manner which may be schematically repre- sented as R, G, B, in which each of the sensations has its typical average value. Simi- larly the ordinary case of red blindness may be written — R, G, B indicating a deficit from the normal value of the red sensation. To be rigorous one should give R a coefficient indicating the relative deficit of the red vision from its normal which may be anything from an amount just recognizable as a variant from normal to 100%. For example a certain case of partial red blindness examined by the writer would have been expressed -.64R, G, B. And similarly one may set down as the variants from normal involving change in a single color sensation curve the following R, G, B, (1)+R, G, B, (2) R.+G, B, (3) R, G,+B, (4) -R, G, B, (5) R,-G, B, (6) R/ G,-B, Of these (4), the — R type, is the ordinary case of "color blindness"; (5) is the rather rare green blindness of which typical cases are reported by Abney (Proc. Roy. Soc, Vol. 83 A); (6) is the still rarer blue blind- ness (Abney, Colour Vision, p. 73). Of the plus variants (1) is the plus red, the first of the type detected, (Rayleigh, loc. cit.). Burch (Physiological Optics, p. 119) cites several instances of (2). The plus blue variation is apparently very uncommon but Burch cites a case 6 PROCEEDINGS OF THE AMERICAN ACADEMY. (Phil. Trans., 199, B, p. 250) which appears to be a good example. There seems to be no intrinsic reason why plus variations from the normal should be less frequent than the minus variations, and they probably are not so in fact, the apparent reason being the wrong diag- nosis likely to be made with the ordinary method of testing. Thus (1) and (5) are quite certain to be confused in the worsted tests most commonly employed, likewise (2) and (4) while plus or minus varia- tions in the blue unless very marked would almost certainly escape detection. The spectroscope and the color mixing apparatus give the only reliable methods of testing for minor variations, and the writer has used in his own experiments a simple form of spectroscopic test which may be worth describing here. The chief test is in principle the converse of Rayleigh's, and consists in matching a synthetic yellow and a syn- thetic blue-green, of the same hues as the spectral colors corresponding to the red-green and blue-green junctions for the normal eye, by shifting a pure spectrum which occupies the lower half of a slit in the focal plane of the eyepiece while the synthetic color occupies the upper half. The apparatus is shown in diagram in Figure 2. The basis is a simple constant deviation spectroscope mounted in a capacious wooden box to avoid stray light. The prism P is mounted as usual on a turntable b, rotated by the milled head D with a screw bearing on a steel plane on the turntable. On the screw shaft is a wide pinion /, engaging a narrow rack ending in a pointer g, moving over the scale h. The rack works under the turntable freely through guides. The main slit, S, has the usual collimating lens c, of 4 cm. diameter and 15 cm. focus. The observing telescope 0, of about 4 cm. diameter and 35 cm. focus has a compound eyepiece slit e, a slider with an adjustable slit and a clear aperture for viewing the spectrum. Long screws k, h, position the slider so that when slipped to the right the slit can be brought any- where in the spectrum, and when slipped to the left the field is wholly or partly clear. Beyond the turntable is a second collimator with adjustable slit S' and lens c' 12 mm. in diameter. This ranges over the prism P which is 25 mm. thick and the beam from c' is turned into the upper part of 0 by the mirror m. A small 60 degree prism can also be placed in front of c' to furnish a reference spectrum. Condensing lenses L, V direct the light from sources /, V upon the slits. In using the apparatus the filter i is placed in front of S'. For synthetic yellow this is made of opposed wedges of cobalt and selenium BELL. — TYPES OF ABNORMAL COLOR VISION. 7 glass, which by adjustment of S', L' and V can be made to give a pretty good match to the normal eye with pure spectral yellow, brought to the same luminosity by the main slit. The patient is then, the spec- trum having been widely displaced by turning D, required to bring it back for a match. A very slight degree of red blindness causes him to match the synthetic yellow with a green, while a plus red or minus .1 W *l = Ug Figure 2. green color-abnormality will produce a reddish match. Filter i is then replaced by a synthetic blue-green, produced by cobalt chloride in acetone solution combined with a uranine filter, and the test re- peated. Here a green blind observer would match with blue and a blue blind case with green. This blue-green junction supplements the other in the diagnosis. Finally for further evidence of -f- or — red. 8 PROCEEDINGS OF THE AMERICAN ACADEMY. and blue sensations, the red and violet end points are determined after resting the eye. This requires care in keeping the slit width and illumination constant and in resting the eye for ten minutes or so be- fore the test to approach a steady condition of adaptation. The two junction point filters should be modified by neutral tint glass if needed, so that one need not adjust their luminosity with the slits, but may be able to pass quickly from one standard filter to the other. Both directions of moving the spectrum should be tried to eliminate fatigue effects. This method gives quick and certain qualitative diagnosis of any of the cases of simple color aberration (1) to (6). The settings at the red-green and blue-green junctions instantly disclose even a very slight variation in color sense and the end point readings in conjunc- tion show at once whether this variation is due to weakness or abnor- mal strength of red or blue sensations. Proceeding further in the analysis of variations one must recognize the probability of variants in which two of the three color sensations are abnormal instead of one as in (1) to (6). These fall into three groups as follows: two sensations weak; two sensations strong; one weak and another strong. (7)_R,_G, B (8) -R, G,-B (9) R,-G,-B Also (10) +R,+G, B (11) +R, G,+B (12) R,+G,+B and finally (13) -R,+G, B (14) -R, G,+B (15) R,-G,+B (16) R,+G,-B (17) +R, G,-B (18)+R,-G, B These twelve variations are less easy of diagnosis than (1) to (6) since they depend on more complex quantitative relations. Take for example (7). Here the red-green junction may be abso- lutely normal, but the blue-green junction will yield a bluish match showing either weak green or strong blue. The red end point, or for that matter the blue end point, tells the story. Case (8) can be dis- BELL. — TYPES OF ABNORMAL COLOR VISION. 9 tinguished from case (2) by the end points, and so on, assuming that the abnormalities are not vanishingly small. The red end point gives fairly definite information but the blue end point is less satisfactory. It is so much modified at times by varia- tion in pigmentation of the macula and by yellowing of the lens as to be somewhat confusing. In the old the lens may be so altered in color that the solar H and K lines cannot be seen. As to pigmentation a case is cited by Abney (Researches in Colour Vision, p. 349) in which much of the blue end of the spectrum was absorbed. Such cases are sepa- rated from a genuine — B case by their giving, with R and G normal, a normal blue-green junction. It is pertinent to inquire in how far these twelve binary variations actually occur. The ordinary cases of color blindness reported have not been so tested as to show them easily. The writer has never noted them personally in congenital color blindness, but one (7) is typical of color fatigue due to the mercury-arc and may easily be detected, as found by Williams and the writer (Electrical World, Sept. 2, 1911). A case reported by Edredge-Green (Colour Blindness, p. 154, F. A.) probably belongs to this type, since with a considerably shortened red spectrum his red-green junction was toward the green and he classified violet, blue, and bluegreen together. Type (8) probably corresponds to a case described by Burch (Phil. Trans., 199, B, p. 250, XVII). Of the next group there is much difficulty in obtaining definite in- formation since for example R,+G,4-B and the ordinary — R, G, B could be distinguished only with some difficulty and would certainly escape ordinary tests. Any case in which some of the ordinary mis- takes of the red blind are made with the confusion colors, while the ordinary end points are retained should be looked into carefully. A plus sensation will rarely be detected by the end points unless the abnormality is very marked. Burch's fatigue tests (Phil. Trans., 191, B, p. 1 et seq.) used to supplement the junction and end point tests probably will prove to give the clearest diagnosis of this group. Lu- minosity tests might be useful since there is evident increase in general sensibility but on account of difficulties due to adaptation and the uncertainty of readings, the experiments are troublesome unless with experienced observers. The next group (13) to (18) is easier to deal with and more examples may be found in the literature. (13) is well shown by Burch (Phil. Trans., 199, B, p. 240, VII) in a case of marked but not complete red- blindness with slightly hypernormal green. Type (14) is also clearly 10 PROCEEDINGS OF THE AMERICAN ACADEMY. described in Burch's very next case (loc. cit. p. 241, VIII), and (15) is also described in the same paper as case XII. To (16) should prob- ably be referred a case described by Edridge-Green (Colour Blindness, p. 140, C. A.) in which the red end point was normal, and the blue con- siderably shortened while the ordinary yellow was encroached upon by the green and the blue-green junction shifted towards the blue. The remaining two types of this group do not appear in any recorded cases examined by the writer. (17) and (9) might easily be confused, as also (18), with some degrees of ordinary green blindness. Finally there must be recognized a group of abnormalities in which all three primary sensations are affected. In the notation here used one may have +R, +G, +B and — R, — G, — B, as well as the normal R, G, B. In other words some persons undoubtedly have a generally strong color sense, and others a generally weak color sense, in each case without peculiarities. From each of these types obviously may spring a group of color variants with a single abnormality, correspond- ing to the (1) to (ft). In these there is simple variation of one sensation with a general sensibility graded up or down. Likewise there will be groups corresponding to variations, -4- or — , of two color sensations in the same direction, giving simple binary variations graded up or down from (7, 8, 9) and (10, 11, 12). If one sensation remain 4" or — , with the other two abnormal relatively in opposite directions, there results a group like (13-18) but starting from a different plane of sensibility; and, since the 4- and — are referred to the normal as the datum point, the types are sometimes sharply marked. This group is, in effect made up of ternary color aberrations in which all three primary sensations show abnormal values. It comprises the following types. (19) +R,+G,+B, (23) -R,-G,-B, (20) 4-R,+G,-B, (24) -R,+ G,-B, (21) +R,-G,-}-B, (25) -R,-G,+B, (22) +R,-G,-B, (26) -R,4-G,+B, Of this ternary group several of the types are to be found more or less clearly described in the literature. (21) for example, is substantially Burch's Case XIII, (Phil. Trans., 199, B, cit.) where red and blue sensations were abnormally strong with marked deficiency in green. A rather clear case of (23) is described by Edridge-Green (Colour Vision, p. 158, G. A.) Here the spectrum was clearly shortened at both ends, especially the red, while some of the color matches indicated •\veak green sensation as well. The patient evidently had a general BELL. — TYPES OF ABNORMAL COLOR VISION. 1 1 low degree of color sense with particular weakness of red sensation. (24) corresponds with a description by Burch (Physiological Optics, p. 119, of a case of predominant green sensation so marked that vision was almost monochromatic, which makes it probable that the red and blue sensations were weakened. Indeed it seems likely that great exaggeration of one sensation may be associated with weakness of one or both the remaining sensations. (25) seems to agree well with a case cited by Edridge-Green (Colour Blindness, p. 203) as examined by Sir Win. Ramsay. In this case there was remarkable exaggeration of the blue, and degradation of the other sensations, so that vision was almost monochromatic. All the color abnormalities here noted are such as belong to the simple trichromatic theory assuming that the several color sensation curves retain their shapes and their normal position in the spectrum, varying only in area. So little is known of the mechanism of color vision that one cannot even predicate whether shifts and changes of shape are or are not likely to take place. Indeed these could hardly be differentiated from other variations except they chanced to be very marked indeed. Even the interesting case described by Abney and Watson (Proc. Roy. Soc, 89, A, p. 232) as showing a shift of the green sensation toward the red should be tested by the junction and end points and by Burch's fatigue method before forming a final judg- ment. If this shifting, or a change of shape in the sensation curve should prove real, still further classes of variants would be formed, but how- ever that may be, the mere variations of sensation curve area which are known to take place must give rise, assuming a certain relation between them as normal, to the definite groups of color variants here noted. Of the 26 abnormal types of congenital color vision in this list 16 are fairly represented in recorded cases. Seven of the remaining 10 are types having two sensations + and thus varying from a simple deficit of the remaining sensation 'only in the degree of luminosity of the other two. The best method of differentiation here seems to be careful study of the end points, and fatigue tests. The remaining three involve abnormal blue vision combined with abnormal green vision, both of which separately seem to be relatively rare. Whether they are so in fact is somewhat dubious since with the commoner tests all the smaller variations in the blue are likely to be missed or merged in variations of pigmentation or color in the lens, while certainly most of the -{- G types are placed with the more familiar — R. In all the 12 PROCEEDINGS OF THE AMERICAN ACADEMY. study of minor variation in color sensations the color fields ought to be more thoroughly investigated than is usual. In conclusion the following list shows the tabulation of all types of abnormality here considered, those which the writer has observed or found recorded being denoted by an asterisk. Simple Binary Ternary (1)+R, G, B* (7)-R,-G, B* (19) +R,+G,+B (2) R,+G, B* (8) -R, G,-B* (20) +R, + G,-B (3) R, G,+B* (9) R,-G, B (21) +R,-G,+B* (4) -R, G, B* (io) +R,+G, B (22) +R,-G,-B (5) R,-G, B* (ii) _|_r} g,+B (23) -R,-G,-B* (6) R, G,-B* (12) R,+G,+B (24) -R, + G,-B* * (13) -R.+G, B* (25) -R,-G,+B (14) -R, G, + B* (26) -R,+G,+B (15) R,-G,+B* (16) R,+G,-B (17) + R, G,-B (18) +R,-G, B The writer will be grateful for notes on any of the missing types in the table which may have escaped notice in the very scattered literature of this intricate subject. A study of these types inevitably leads to the question as to whether any remedial measures can help the victims of abnormal color vision. Within restricted limits the answer may be affirmative. The method which has to be followed is precisely that which has already been tried with considerable success in modifying the color of artificial illumi- nants to obtain normal daylight values of color viewed by them. An ordinary gas flame, for example, is in effect partially blue-blind and the normal eye will see colored objects under such a light very much as the partially blue blind would see them in daylight. The necessary correction has been found to be the interposition of absorbing media which reduce the green and red elements in the same degree as the de- ficit of the blue element in the source. The penalty of doing this is the loss of considerable luminosity. The selective screens for this purpose are highly effective subject to this limitation. By a process exactly analogous it should be possible to provide a certain proportion of the partially red blind with spectacles which would give them at least an approximation to normal color vision, although at the expense of con- BELL. — TYPES OF ABNORMAL COLOR VISION. 13 siderable luminosity, in amount depending on the extent of the red sensation deficit. Those in whom one sensation is nearly or quite ab- sent are of course beyond the chance of help, since balance would require an almost complete obscuration of the remaining sensations, but the theory of the correction rests on a substantial basis and can be put into practice in not too severe cases of partial color deficiency. The method to be followed would be substantially that of Abney in obtaining the sensation curves of the individual and the problem then would resolve itself into making approximate corrections to reduce the curves as nearly as possible to normal relations. In bright light the corrected vision would then show colors in approximately their true relations, though somewhat dulled. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 2.— May, 1914. CONTRIBUTIONS FROM THE CRYPTOGAM IC LABORATORIES OF HARVARD UNIVERSITY No. LXXIII. . LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. By Roland Thaxter. CONTRIBUTIONS FROM THE CRYPTOGAM IC LABORATORIES OF HARVARD UNIVERSITY. No. LXXIII. LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. By Roland Thaxter. Presented May 13, 1914. Received April 1, 1914. During the past eight years I have obtained from various sources a considerable number of Laboulbeniales parasitic on beetles belonging to family Chrysomelidae. The first which came under my notice was found on a species of Lactica near Buenos Aires, and was included in my recent paper on Argentine Laboulbeniales.1 The forms con- sidered in the present Contribution have been obtained on alcoholic material, from various regions in the Tropics, which I owe to the kindness of numerous correspondents ; or have been collected by my- self in Trinidad; while a considerable number are derived from the dry material in the collections of the Museum of Comparative Zoology at Cambridge. In this connection I desire to acknowledge my great indebtedness to Mr. W. M. Mann for the privilege of examining the insects collected by him in Brazil during the Leland Stanford Univer- sity Expedition in 1911, to the Rev. Geo Schwab, Mr. C. S. Banks, the late Prof. Kellerman, and others, who have been so kind as to have collecting done for me: as well as to Mr. F. C. Bowditch for numerous determinations, and to Mr. Samuel Henshaw for freedom to examine the Museum collections and for other favors. In June, 1912, a paper was published by Spegazzini on Argentine Laboulbeniales, in which several new species parasitic on this group of beetles are included. Of these one, a species very common on members of the genus Lema, is referred by him to Sphalcromyces: but since its structure corresponds irt all respects to that of a typical Laboulbenia, it should undoubtedly be removed to this genus. The three remaining forms considered by this author, are placed by him in a new genus, Laboulbenidla, which is said to be distinguished from Laboulbenia by the fact that cells III and IV of the last mentioned genus are here replaced by a single cell, and that cell VI, the 'stalk- 1 These Proceedings, 48 (1912). 18 PROCEEDINGS OF THE AMERICAN ACADEMY. cell' of the perithecium, is absent. Having had an opportunity to examine abundant material of these species, as well as of others be- longing to the same type, I am unable to follow Spegazzini in making this separation; since in all cases I find that cell VI, as well as the usual basal cells of the perithecium, are present and variably developed, as in Laboulbcnia; and the fusion of cells II-IV appears to be alto- gether too insignificant a character to form the basis of a new genus. It is true, however, that this replacement, or fusion, is characteristic of various forms parasitic on Chrysomelidae, and in most cases appears to have become a fixed condition. In other cases, however, the normal type is found and does not vary; while in still others both may be associated in the same species. I have called attention to the last mentioned condition in Part II of my monograph, and as will be seen by reference to fig. 11 of PI. XIV, have figured a variety of L. decipiens in which, although the 'Laboulbeniella' type predominates, the typical number and arrangement of the cells of the receptacle also occur. I have been disinclined, and I think rightly, to give generic value to variations in the cell numbers, especially of that portion of the receptacle in Laboulbcnia, cells III-V and the insertion-cell, which corresponds to the base of the primary appendage in such genera as Corethromyces. Such departures from the normal type are seen in a majority of the aquatic species of Laboulbcnia, in L. proli- ferous, L. variabilis and a number of the forms which occur on Clivinae,. in all of which a multiplication of the cells in this region has been effected, instead of a reduction, as in the present instance. I have therefore placed in the genus Laboulbcnia not only such of the chry- somelid forms as correspond exactly to the type, or in which the 'Laboulbeniella '-condition occurs only occasionally, but also those in which cells III and IV are normally replaced by a single cell (desig- nated as cell III + IV). Another type is also included, illustrated by the single species L. partita, in which, on certain hosts, the number of cells in the receptacle may become normally multiplied through the secondary division of the subbasal cell, a condition not previously observed except in abnormalities. Although as will be seen a great majority of the chrysomelid para- sites belong to Laboulbcnia, two other genera are represented by well marked forms; Dimcromyces contributing four species from Mexico, the West Indies and the Straits Settlements; while seven species of Ceraiomyces are included, six of them parasitic on 'flea beetles' from the West Indies and Brazil, the seventh a very peculiar form from. Kamerun and Madagascar. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 19 Dimeromyces Homophoetae nov. sp. Male individual amber-yellow. Receptacle consisting of three or four cells each of which may bear an antheridium: the primary appendage two celled, the basal cell shorter and broader, separated by a constriction from the distal which terminates in a long sharp spine and may often become one or more times septate, the terminal cell proliferating distally to form an antheridium which thus appears to be borne on a long several celled stalk on which the spine is lateral. Antheridia two to five, the stalk well developed, rather slender; the venter rather abruptly distinguished, though relatively narrow and slightly shorter than the nearly straight stout neck which tapers but slightly above its somewhat enlarged base. Total length to tip of appendage 60 /x; to tip of antheridium 80 lx, of proliferous antheri- dium 112 /x; normal antheridium including stalk about 35-40 X 6 lx. Female individual: receptacle suffused with amber-brown below, distally amber-yellow; consisting normally of four cells obliquely superposed, terminated by a two-celled primary appendage, the terminal cell of which is narrower than the basal and about as long; sometimes more or less inflated at its base, and ending in a long straight sharp spine: the basal cell becoming rather deeply suffused and extending upward against the base of the lower appendage which is somewhat broader than the sub-basal cell from which it springs, and slightly geniculate: the third cell giving rise to the normally single perithecium, the fourth to a second somewhat smaller append- age; the two appendages slender, simple, tapering, somewhat diver- gent on either side of the perithecium, which is subfusiform with no clearly defined stalk; the stalk-region hyaline, the rest of the peri- thecium amber-brown, the tip distinguished by two successive in- dentations below the hyaline three-lobed apex, the lateral lobes of which are symmetrical and smaller than the much more prominent median lobe. Spores 32 X 3.5 jjl. Perithecium, including stalk- portion, 100-190 X 20-35 it. Total length to tip of primary append- age 70 lx; to tip of perithecium 140-250 lx. Appendages, longest, 90-110 ix. On Homophoeta aequinoctialis Linn., No. 1577, Guatemala, on inferior pro thorax; No. 2066, Grenada, W. I., on antennae, and No. 2475, Port of Spain, Trinidad, W. I. The specimens from Guatemala are somewhat larger than those from Grenada, but correspond in all other respects. The species appears to be more nearly allied to D. Forficulac than to any of the other described forms. 20 PROCEEDINGS OF THE AMERICAN ACADEMY. Dimeromyces Aulacophorae nov. sp. Male individual: hyaline with purplish brown shades. Receptacle consisting of three to four very obliquely superposed cells terminated by a simple appendage, the basal cell of which is long and slightly inflated, bearing distally a three or four-celled terminal portion from which it is separated by a rather deep constriction associated with a conspicuous blackened septum. Antheridial branches one to three in number arising unilaterally, one from each cell of the receptacle; the stalk cell narrower below, suffused, rather long; the antheridium hyaline, its basal cells rather large and long; the body rather narrow, not symmetrically related to the rather broad long nearly isodiametric neck, the apex of which is nearly truncate. Receptacle 32 X 10 /x exclusive of foot; basal cell of appendage 16 X 6 ix, the distal part 30-40 X 4 p. Antheridium including stalk 30-40 X 5-6 /x, the stalk sometimes 11 ix long. Female individual: purplish or amber-brown. Receptacle consist- ing of usually six or seven obliquely superposed cells; flattened, ex- cept the terminal one which is separated from the basal cell of the terminal appendage by a horizontal septum; the subterminal cell producing the solitary perithecium; all the rest, except usually the small basal cell, giving rise to appendages which form a unilateral series: basal cells of the lateral appendages short, somewhat inflated and curved upward, bearing one to rarely four simple hyaline or slightly suffused straight or flexuous elongate branchlets, which for the most part taper but slightly and are distinguished at the base by a conspicuous broad blackened septum and constriction: the terminal appendage similar to that of the male, except that its basal cell often bears two branchlets distally. Perithecium relatively very large, hyaline or yellowish below, distally more or less suffused with purplish brown, straight or less often curved, slightly broader just above the short hardly distinguishable stalk, distally tapering rather rapidly to the rather broad apex which, in anterior view, is symmetrically three lobed, the middle lobe prominent and broader. Perithecium when well developed 175-250 X 24-28 fx, sometimes smaller (100 X 18 n). Spores 32 X 3 /x. Receptacle about 65 X 20 /x. Basal cell of primary appendage 20 X 6 .5 fx. Longer appendages 130 X 3.5 fx. On the elytra of Aulacophora postica Chap., Perak, Straits Settle- ments. M. C. Z., No. 2510. The material of this species, although sufficiently abundant, is not THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 21 in very good condition, there being no perfect individuals. It is well distinguished by its enormous perithecia and by the development of secondary branches from the basal cells of the secondary appendages. It seems to be more nearly related to D. Homophoetae than to any other species, the conformation of the apex of the perithecium being somewhat similar, as well as the long-stalked antheridia, but it is otherwise very distinct. Dimeromyces Hermaeophagae nov. sp. Male individual: nearly hyaline. Receptacle consisting of two superposed cells, the basal larger, laterally related to the foot; the subbasal giving rise to the single slender antheridium, the stalk-cell and basal cells of which form a relatively long stalk below the narrow only slightly enlarged venter, which is about as long as the rather stout outcurved neck. Primary appendage consisting of a basal cell nearly as long as the subbasal cell of the receptacle and bearing terminally a two-celled slightly inflated portion of about the same length, from which it is separated by a clearly defined dark septum. Total length to tip of appendage, 35 n; to tip of antheridium 50 ju. Antheridium-stalk (stalk- and basal cells) 16 fx; venter and neck 18 n; appendage 17 ft. Female individual: nearly hyaline or faintly yellowish. Perithe- cium arising from the third cell of the receptacle, its stalk-cell small, hardly distinguishable, its form rather elongate, tapering slightly, the tip distinguished by a very slight elevation; the spreading funnel-shaped apex distinguished by a constriction. Receptacle four-celled, the basal slightly larger, with inferior lateral small foot; the second and fourth bearing secondary appendages the basal cells of which are rather stout and long, and distinguished from the taper- ing several-celled terminal portion by a distinct dark septum which does not reach as far as the tip of the perithecium. Primary append- age like that of the male, stouter. - Perithecium, exclusive of stalk- cell, 60-70 /x. Secondary appendages 60-70 At. Primary appendage 20-25 fx. Total length to tip of perithecium 75-90 p. On antennae of Hermaeophaga insularis Jac, No. 2066, Grenada, B. W. I. (Brues). This species seems most nearly allied to D. rninutissimus and differs from all other known species in the peculiar funnel-shaped apex of the perithecium. 22 PROCEEDINGS OF THE AMERICAN ACADEMY. Dimeromyces Longitarsi nov. sp. Male individual: hyaline or faintly yellowish; receptacle consisting of three obliquely superposed cells, the two upper bearing antheridia, and subequal, the basal as long as these two combined; the distal bearing terminally the unicellular appendage, which is twice as broad as the base of a hyaline usually straight subulate process that terminates it and nearly equals it in length. Antheridia normally two, the stalk-cell broader than long; the rather stout venter some- what longer than broad, abruptly distinguished from the rather stout neck which is of about the same length and distally bent abruptly outward. Total length to tip of spinous process 60-64 /jl; to tip of distal antheridium 70 n, the foot included. Appendage, including spinous process, 14-15 fi. Basal cell of receptacle 18 /jl. Antheridia 22 X 2 /*. Female individual: tinged with yellowish, the perithecium deeper, faintly tinged with amber-brown, bent inward basally and distally, rather long and narrow, slightly broader distally below the paler tip, which is rather clearly distinguished above a slight constriction most prominent on the inner side; the apex distinguished by an often deep constriction, its base inflated to form rounded prominences above which it is compressed, asymmetrical, tapering to a blunt point: the stalk-cell small subtriangular, free only externally. Receptacle consisting of three obliquely superposed cells, the two upper subequal, angular, the basal longer; primary appendage as in the male, a minute cell distinguishable at the base of the spinous process: secondary appendage single, its basal cell similar to the subbasal cell of the receptacle from which it arises and with which it is obliquely associated ; the rest of the appendage simple, slender, whip-like, tapering; seldom extending beyond the tip of the perithecium. Perithecium 80- 120 X 20-25 ix. Secondary appendage 85-100 yu: primary appendage, including spine, 25 [x. On the elytra of Longitarsus testaceus Mels., Fayetteville, Arkansas No. 1801; of L. subcinctus Har., No. 2455 and of Apkthona Deyrollei Baly, No. 2454, Port of Spain, Trinidad, B. W. I. This species is most nearly related to D. Homophoctae from which it is distinguished by its unicellular primary appendage and single secondary appendage, as well as by various other points of difference. The material from Arkansas appears to differ in no respect from that obtained in Trinidad. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 23 Laboulbenia Bruchii (Speg.). Sphaleromyces Bruchii Speg., Cont. al Est. d. 1. Laboulbeniomycetas Argentinas; Ann. d. Mus. Nat. d. Hist. Nat. de Buenos Aires, XXIII, p. 195, with figure, 1912. This form, which is very common on various species of Lema in Tropical America, has been referred to Sphaleromyces by Spegazzini. Its structure, however, is that of a typical Laboulbenia, and the number and arrangement of the cells of its receptacle are both normal. Although the structure is sufficiently clear in younger individuals, cells II and III usually become very deeply suffused, except along their inner edges, and are indistinguishable from cell IV, the variable pro- longation of which forms the curious spur-like termination regarded by Spegazzini as a development from cell II, and as similar to that which arises from the distal cell of the two-celled receptacle of Core- thromyces, in which it is a development from this cell only. This characteristic varies very greatly in different individuals of the present species, the spur in many cases being but slightly developed, or at least far less prominent than it is in the typical form represented by the figures of Spegazzini. The species is a very striking and variable one, closely allied to the three following forms which occur on the same host genus, and in the characteristic development of cell IV resembles L. producta of my second Monograph (Plate LXIV, fig. 13). The longitudinal dehiscence of the perithecium, which is given by Spegazzini as a distinguishing character of this species, must be regarded as an accidental splitting, which is not infrequently seen in dried material that has been taken from museum specimens and suddenly swelled by mounting. Material has been examined from the following sources. No. 1643, on Lema sp. Guatemala, (Kellerman) ; No. 1774, on L. Sallei Jac. Mexico (Biologia Coll.); No. 1775, on L. Albini Lac, Mexico (Bio- logia Coll.); No. 1776, on L. dimidiaticornis var., Mexico, (Biologia Coll.); No. 2212, on L. gracilis Jac, Para, Brazil (Mann): Nos. 2476-2477, on several species of Lema, Port of Spain, Trinidad. Laboulbenia Papuana nov. sp. Receptacle short and subtriangular, the basal cell nearly hyaline, except distally and along its posterior margin; short, abruptly broader distally, subgeniculate ; its base clasped by a bluntly pointed 24 PROCEEDINGS OF THE AMERICAN ACADEMY. upgrowth from the foot on either side, which is black, contrasting and slightly oblique: cell II much smaller, flattened, dirty olivaceous, extending upward anteriorly and separated by a slightly oblique partition from cell VI; which is smaller, concolorous and separated by a strongly oblique septum from the basal cells of the perithecium, which are relatively large, clearly defined and paler dirty yellowish: cells II I- V forming a clearly distinguished, somewhat darker trans- lucent grey olive-colored region, the inner walls of which are nearly vertical, but curve abruptly outward where they are in contact with cell II: cell III larger than cell II, but somewhat similar in shape, except for its curved base, separated from cell IV by a strongly oblique curved septum; cell IV nearly as large as cells II and III combined, externally concave, projecting beyond the insertion-cell to form a broad rounded prominence distally slightly compressed; cell V well defined, triangular, externally convex. Insertion-cell clearly defined, translucent. Basal cell of outer appendage about as long as broad, distally much broader, and bearing a terminal series of three radially arranged branches, themselves once branched above their basal cells; the outer curved outward and externally more deeply suffused with blackish brown externally at the base; the branchlets curved more or less strongly inward, distally hyaline, with olive brown suffusions below, seldom reaching to the tip of the peri- thecium. Perithecium relatively long, curved slightly outward, wholly free above its basal cells; the inner half rich brown, sometimes contrasting with the often much paler dirty yellowish brown outer half, which is concolorous with the long compressed slightly darker, not abruptly distinguished tip, the concave outer margin of which is abruptly much darker; the lips small but well defined. Perithecia 100-125 X 25-28 //. Appendages, longest 110 jjl. Receptacle includ- ing protrusion 85-100 X 50-60 n, exclusive of foot. Total length, including foot, 200-228 //• On the elytra of Lema sp., New Guinea, M. C. Z. No. 2511. This species is so closely related to L. Bruckii that I have hesitated to separate it specifically, and it may prove to be merely a well marked variety when a large series becomes available for examination. The type material includes a half dozen specimens in good condition, all of which show the characteristics above described. Laboulbenia rhinoceralis nov. sp. Receptacle short and stout, subtriangular, the basal cell larger than the subbasal, longer than broad, hyaline becoming tinged with THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 25 olivaceous; cells II and III subequal; cell IV forming a short blunt prolongation external to and beyond the insertion-cell; cells II-IV becoming almost or quite opaque and indistinguishable, except along their inner margins; cell V relatively large and rounded, suffused with olivaceous brown, as is cell VI, which lies obliquely below it, is of about the same size, and is separated by a deep indentation from the outer lower basal cell of the perithecium immediately above it, which is quite hyaline, bulging asymmetrically outward and separated from the cell above it by a deep indentation. Insertion -cell rather thick, black; lying horizontally in the deep depression formed between the base of the perithecium and the projecting termination of cell IV. Outer appendage deeply suffused at the base and externally, curved outward, consisting of usually two larger basal and subbasal cells; the former giving rise to a subterminal inner branch, and the latter to a subterminal inner and two or three terminal short branches, the outer black and abortive; the basal cell of the inner appendage nearly as large as that of the outer, bearing a branch on either side which is very similar to the outer appendage and externally suffused; all the branches rather short and stout, more or less suffused about the base. Perithecium wholly free, the upper basal cells forming a very short stalk, relatively large, long and narrow; the venter hardly inflated, opaque or nearly so; the tip translucent, not distinguished from the venter, except by a clean cut transverse line of demarcation; the hyaline apex subtended externally by two superposed long hyaline slightly outcurved horn-like appendages, the lower an extension of a laterally misplaced lip-cell, the upper a subterminal projection from the outer of the three remaining lip-cells which surround the sulcate pore; the latter turned slightly inward. Peri thecia 90-120 X 20-25 fx, its horn-like appendages about IS X 6 /z. Spores 35 X 3.5 /x (meas- ured in perithecium). Receptacle average 52 X 28 it. Appendages longer 52 p.. Total length to tip of perithecium 125-175 /j,. On the elytra of Lema gracilis Jac, No. 2212, Para, Brazil (Mann), on Lema sp., Port of Spain, Trinidad, No. 2477; on Lema sp., Suriname, No. 2480 (Rorer). A very peculiar species distinguished from its near ally, L. Bruchii, by the peculiar horn-like processes which subtend the apex. The lower of these processes is formed by the abnormal termination or the left posterior series of wall-cells which, instead of forming a lip- cell, bends abruptly outward as it traverses the tip, crossing the series external to it and projecting as a free appendage. The two horns are sometimes malformed and somewhat misplaced, but are usually well developed and symmetrically placed one above the other; 26 PROCEEDINGS OF THE AMERICAN ACADEMY. the whole tip thus armed strongly suggesting the head of a two- horned rhinoceros. The species was common in the vicinity of Port of Spain, but individuals were found only in the depressions near the bases of the elytra. The receptacle is twisted one quarter in relation to the perithecium, in most specimens; so that, when the latter lies flat, the receptacle is usually viewed edgewise. Laboulbenia Hottentottae nov. sp. Receptacle rather slender, sometimes slightly geniculate between cells II and III; cell I usually quite hyaline; cells II— III becoming more or less deeply suffused, or nearly opaque; cell II sometimes abruptly broader than cell I, but always shorter; separated from cell VI by a horizontal, from cell III by a very oblique partition; cells III and IV subequal, separated by a very oblique partition; cell V narrow, triangular, nearly hyaline; cell VI suffused, distinguished above and below by an indentation, obliquely separated from the cells above, which form a broad almost stalk-like base to the perithecium. Insertion-cell suffused, but not blackened, rather thick. Basal cell of outer appendage somewhat longer than broad, brown, giving rise to a short hyaline erect subterminal branch on the inner side; the sub- basal cell colored like the basal, somewhat longer; the rest of the appendage hyaline, few-celled, short; basal cell of the inner appendage much smaller than that of the outer, concolorous; producing a branch on either side, each usually once branched; the branches sometimes exceeding the perithecium in length, hyaline, except the brownish basal cells. Perithecium wholly free, rather long and slender, often nearly symmetrically inflated, deep rich brown, tapering evenly distally; the tip hardly if at all distinguished, darker along the inner side; the apex blunt, the lip-edges subhyaline about the pore, some- times slightly oblique outward; a slight projection usually visible next the pore. Perithecia, exclusive of basal cells, 90-125 X 18-25 ju. Receptacle 90-110 X 25-32 fx. Appendages, longest 120 yi. Total length to tip of perithecium 160-200 ix. On elytra etc. of Lema Hottentotta Lac, Zanzibar (M. C. Z.): crowded near tips of elytra. This species usually has a somewhat falcate or slightly curved habit, and is rather slender in form. Although apparently allied to L. Bruchii, its appendages and receptacle separate it at once from any of the forms of that species. The material available is abundant and in good condition. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 27 Laboulbenia Braziliensis nov. sp. Receptacle often straight and narrowly wedge-shaped, sometimes slightly curved and less regular, but tapering more or less regularly from summit to base; hyaline, becoming yellowish or tinged with brown, deeply along the posterior margin especially immediately below the insertion-cell; cell III longer than cell IV which is abruptly prominent below the insertion-cell, sometimes forming a rounded projection beyond it: cell V relatively large, sometimes as large as cell IV, and in contact with cell III: cell VI relatively very large, exceeding cell III in length. Insertion-cell thick and rather narrow; basal cell of the outer appendage rather small somewhat rounded, tinged with brown externally, separated by an oblique blackened septum from a distal and external furcate branch, within which one or more additional erect branches arise, not thus separated; basal cell of the inner appendage much smaller, also pale brownish, giving rise to branches on either side which are usually once branched, and, like those of the outer, are rather stout hyaline or faintly brownish, erect, slightly tapering, seldom reaching beyond the tip of the peri- thecium. Perithecium deep rich brown becoming opaque or nearly so, wholly free; the base of the venter somewhat narrower than the basal cell-region below it, the outer margin nearly straight, the inner convex; the tip bent outward, not distinguished except on the inner side, the apex symmetrically rounded or almost truncate; the lip- edges broadly hyaline, contrasting. Perithecia 130-158 X 40-48 /x. Receptacle, average, 175 X 52 /x. Appendages, longest, 160 /x. Total length to tip of perithecium 350-380 /x. On a chrysomelid allied to Wedionychus. Rio de Janeiro, Brazil, M. C. Z. 'Mrs. Munro,' No. 1786, on the legs and elytra. This species seems to be very well distinguished from any of the other species on Chrysomelidae. The host is a stout chrysomelid, the elytra dark bluish black, with a red margin all around. More than twenty mature individuals and numerous younger specimens have been examined, in which the measurements seem unusually constant and the variations in other respects slight, except that in some specimens cell IV protrudes in a fashion which recalls less well developed individuals of L. Bruchii. 28 PROCEEDINGS OF THE AMERICAN ACADEMY. Laboulbenia idiostoma nov. sp. Receptacle evenly suffused with olive-brown, somewhat darker distally, short and compact, relatively small; cell I slightly larger than cell II and nearly triangular, or symmetrically pointed distally between cells III and VI; cells III and IV subequal, the latter forming a rounded prominence distally, which turns the insertion-cell so that it is very oblique, or even vertical, in position, the appendages being thus turned so that they cross the base of the perithecium obliquely, or at right angles; cell VI rounded and prominent, the basal cells of the perithecium also small and bulging, especially externally. Peri- thecium relatively large, long, straight or but slightly curved, often somewhat broader distally, rich purplish brown, almost opaque, free; the tip abruptly attenuated, indented externally, and hyaline distally, the apex prominently bilobed, the lobes rounded and symmetrical when viewed anteriorly or posteriorly. Appendages relatively long, straight or symmetrically curved; the outer appendage simple, its basal cell large, externally convex, its distal septum broad and black- ened; the basal cell of the inner appendage half as large; a group of antheridial and sterile branchlets arising on either side, which may be branched near the base so as to form a tuft in which about six of the branchlets are apt to be sterile and project across the base of the perithecium; all the sterile branchlets subcylindrical, rigid, rather remotely septate, sometimes furcate near the blunt tip ; the antheridia relatively large and long, with a narrower base below the rounded venter, usually in pairs, and sometimes on long branchlets. Peri- thecia, average, 122 X 30-35 m- Receptacle 70-85 X 35-42 /x- Ap- pendages, longest, 200 ix. Total length to tip of perithecium, average 175 M- On antennae of Haltica Jamaicensis Fab. Ennery, Hayti (Mann), No. 2491. A very distinct species observed only on the antennae of its host. The peculiar tip of its perithecium is not unlike that of L. leptostoma Speg. Laboulbenia fuliginosa nov. sp. Receptacle and appendages dirty yellow olive-brown; the former of normal form and structure, more deeply suffused with age; cells IV and V often subequal ; cell III slightly larger than cell VI ; cells I and II of nearly equal length; the whole tapering more or less regularly to THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 29 the base. Insertion-cell broad and thick; basal cell of the outer appendage externally more deeply suffused and slightly convex, separated by an oblique blackened septum from its outer branch which is short, submoniliform, and usually four-celled; a second branch arises within the outer, its basal cell about equal to -that of the outer, but bearing two branchlets, radially placed ; consisting of four or five short cells like those of the outer branch, extending usually not more than two thirds the length of the perithecium, towards which, like the outer, they are usually slightly bent; basal cell of the inner appendage slightly smaller than that of the outer, bearing a branch on either side consisting of a single cell terminated usually by a pair of antheri- dia, which may also be associated with one or two short stout branch- lets like the outer. Perithecium free, except its basal cells, becoming quite opaque; convex on both sides, more abruptly so externally; tapering distally to the rather narrow tip; the apex sometimes slightly apiculate; the lip-edges hyaline, or translucent. Perithecia (above basal cells) 100-125 X 40-48 /x- Spores about 55 X 5.5 p. Recepta- cle 150-200 X 45-52 fx. Longest appendages 90 m (usually broken). Total length to tip of perithecium 60-90 ll. On the elytra and under surface of Haltica plebeia Oliv. No. 1785, Hayti (M. C. Z.); on Haltica sp. Cuba, (M. C. Z.), No. 1784; and 1787; No. 1770, on Haltica amethystina Oliv., Vera Paz, Biologia Coll. on H. Jamaicensis Fab., No. 2491. Ennery, Hayti (Mann); No. 2506, Jamaica. This is a very ordinary looking species, of more or less uniform dark, dirty olive-brown color, apparently very common on its hosts in Hayti and Cuba. It is perhaps as nearly allied to L. partita as to any of the other species on Chrysomelidae, but never appears to de- viate in structure from the ordinary type of the genus. The material is usually poor, even on hosts preserved in alcohol, and the outer branch of the appendage is seldom found in adults. Laboulbeni Halticae now sp. Dull olivaceous, the perithecium and distal portion of the receptacle somewhat darker. Receptacle normal, or occasionally cells III and IV replaced by a single cell, slender, but little broader distally; cells I and II subequal, or I slightly longer; cells III and IV subequal; cell V reaching down to, or nearly to, cell III and sometimes equaling it in size. Insertion-cell thick, deeply suffused, but not opaque: 30 PROCEEDINGS OF THE AMERICAN ACADEMY. basal cell of outer appendage large, longer than broad; its subbasal cell slightly smaller, and normally bearing two long branchlets, both simple, or the outer once branched : basal cell of the inner appendage very small, bearing a branch on either side which may be simple or once branched and bearing scanty antheridia; all the branchlets becoming tinged with olivaceous, especially at the base and externally, the longest sometimes twice as long as the perithecium or even longer. Perithecium four fifths or more free, rather narrow, the venter but slightly inflated; the tip hardly distinguished, broad; the apex broad, rounded or subtruncate, externally unevenly oblique, hyaline about the pore, beside which one of the lip-cells usually forms a distinct, though minute prominence. Perithecium 70-90 X 25-30 ll. Re- ceptacle 85-125 X 25-30 ll. Appendages, longest, 150 /jl; in one young specimen 227 /jl. Total length to tip of perithecium 125-210 fx, average 175 ju. On Haltica sp. Kamerun (Schwab), No. 2449 (type): on Systena Dcyrollei Boh., Port of Spain, Trinidad, No. 2467. The specimens from Kamerun and Trinidad do not appear to differ essentially. The species is not distinguished by striking peculiarities, but does not seem referable to any described form. The material is abundant and in good condition. A small percentage of the specimens from Kamerun are of the ' Laboulbcniclla' type, cells III and IV being replaced by a single cell. This does not seem to be the case, however, in the material from Trinidad. Laboulbenia Nodostomae nov. sp. Short and stout. Cell I slightly longer than cell II which is slightly longer than broad, its anterior margin strongly convex; cell III broader than long, shorter than cell IV; cell V small triangular, cell VI some- what smaller than cell II; cells II-V dirty yellow, deeply tinged with brown, the rest' dirty yellow; the walls, only, tinged with brown. Insertion-cell broad thick and blackish; appendages almost or quite hyaline. Basal cell of the outer appendage somewhat longer than broad; bearing distally two simple branches, obliquely related, the outer stout tapering, elongate and incurved; basal cell of the inner appendage about half as large as that of the outer, producing a single simple short stout branch on either side, each with one or two antheri- dia at the base. Perithecium a little less than one third free, rather short and stout, dark blackish olive, paler below, and subterminally; THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 31 the tip deep black, short, broad, abruptly distinguished; the lip- edges broadly hyaline, contrasting; the apex more or less rounded, two indistinct papillae above the external pore. Perithecia .60-65 X 25 ijl. Spores as long as venter, about 40 X 4 ju. Receptacle 80 X 35 /x. Appendages, longest 175 ix. Total length to tip of perithecium 130/1- On tip of the elytron of Nodostoma sp., Mindanao, Philippines, No. 2386, received through the kindness of Mr. Oakes Ames. An insignificant species very similar to some of the forms on Carabi- dae allied to L. flagellata. Laboulbenia Philippina nov. sp. Receptacle varying in length from the variable elongation of cell II; hyaline, becoming tinged with straw-yellow; cells I and II relatively large, of about the same diameter, cell II often far longer; cells III, IV and VI subequal and subisodiametric; cell V very small, triangular. Basal cells of the perithecium hyaline, well defined, contrasting with the venter; that lying externally above cell VI usually prominent; venter rich contrasting translucent purplish brown; slightly, often symmetrically, inflated; the tip more or less well defined, rather abruptly so externally where a narrow margin is deeply suffused; otherwise quite hyaline, except for a black patch which subtends the rather prominently rounded inner lip-cell; the lip-edges hyaline, outwardly oblique. Appendages wholly hyaline, becoming yellowish; the basal cell of the outer appendage giving rise to an outer and an inner branch; the basal cell of the inner ap- pendage much smaller, producing a usually simple branch on either side; all the branches rather stout, elongate, somewhat divergent or even slightly recurved, slightly tapering. Insertion-cell contrasting with all the cells about it. Perithecium about five sixths free, 85-100 X 28-35 fx. Spores 50 X 3.5 /x. Receptacle 100-225 X 38^2 y.. Appendages longest 210-420 fx. Total length to tip of perithecium 150-335 li. On the elytra and legs of a chrysomelid near Rhembastus: No. 2451 Manila, Philippines (Banks). Very like some forms of L. polyphaga, and distinguished from related forms on Chrysomelidae by its often elongate form, hyaline or evenly pale yellow color, its stout elongate concolorous appendages and deeply suffused contrasting perithecium. 32 PROCEEDINGS OF THE AMERICAN ACADEMY. Laboulbenia Oedionychi nov. sp. T Receptacle normal, hyaline, becoming faintly tinged with olivace- ous, especially distally where it is indistinctly punctate; cells I and II subequal, relatively large, the remaining cells small; cell III slightly larger than cell IV; the outer margin of the latter curved evenly. out- ward and downward from the insertion-cell; cell V triangular, small, not in contact with cell IV. Insertion-cell black contrasting, rather thick, not very broad. Outer appendage almost invariably simple, slender, divergent, horizontal or recurved, long, slender and slightly tapering, often geniculate at the base in the region of the subbasal cell ; which, like the basal, is more or less tinged with blackish olive extern- ally, and is often prominent distally on the inner side: basal cell of the inner appendage somewhat smaller than that of the outer, producing a short, usually simple, branch on either side, each bearing a single antheridium near the base. Perithecium united to cells IV and V at its base, transparent olivaceous, usually straight; the venter long, narrow, slightly and evenly inflated; the tip slightly distinguished, very slightly bent outward, broad, more deeply blackened below the hyaline lip-edges; the rather coarse lips outwardly oblique. Peri- thecia 80-85 X 20-24 p. Spores 48 X 4 p.. Receptacle 90-140 X 28 /jl. Appendage, longest, outer 175-230 p, the inner, 35-80 /z. Total length to tip of perithecium 140-210 /x. On the elytra of Oedionychus nov. sp., No. 2415 and 2450, Manila, Philippines (Banks). Abundant material of this species in perfect condition has been examined. The species like L. Halticae to which it is allied, is not unlike some of the many forms allied to L. polyphaga and L. flagellata which occur on Carabidae. Specimens from the legs (No. 2450) of the same host are somewhat smaller, the outer appendage more deeply blackened externally, both the basal and subbasal cells bearing dis- tally on the inner side an erect hyaline branch; the receptacle short, cell I longer than cell II; the perithecium more deeply suffused. Laboulbenia Hermaeophagae nov. sp. Receptacle normal, faintly punctate, olivaceous, darker distally; the basal cell paler or hyaline below, narrow, somewhat longer than the subbasal; cells III and VI subequal, the latter strongly convex externally; cell IV prominent below the insertion-cell; cell V rounded THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 33 or irregularly quadrangular, its base resting on cell II; all the cells distinguished from one another by more or less distinct indentations, owing to the convexity of their margins which may be pronounced. Insertion-cell thick and deeply suffused. Outer appendage consisting of a divergent series of three cells, successively smaller and externally more deeply suffused with blackish olive, the terminal one bearing distally a pair of short branchlets radially placed; the basal and subbasal each bearing a stout subterminal s'mple branch on the inner side; basal cell of the inner appendage much smaller, bearing a branch on either side which may be once branched ; all the branchlets rather short and stout, never reaching to the tip of the perithecium. Peri- thecium wholly free, almost subfusiform, the small but prominent basal cells forming an indistinct stalk, often hyaline and contrasting with the deep olive brown venter above; which is evenly inflated, more strongly convex externally, but sometimes almost symmetrical, tapering slightly to the truncate apex which is surmounted by a pair of minute prominences. Perithecia, average, 80 X 25 fx. Spores 50 X 5 fx. Receptacle 70-80 X 30 n. Appendages longest 70 //. Total length to tip of perithecium 150-175 //. On tips of elytra of Hermaeophaga sp., No. 2466, Port of Spain, Trinidad. Several specimens of a species very similar to this, were obtained on a species of Hermaeophaga from Jamaica. The cells of the recepta- cle in this form bulge more prominently than in the type, but there is otherwise slight difference between the two. The perithecium ap- pears to be more often twisted about one fourth, so that the appear- ance of the apex as above described is that of an anterior or posterior view. Laboulbenia Manobiae nov. sp. Receptacle uniformly hyaline tinged with yellow, normal in struc- ture; cells I and II subequal relatively large, somewhat more than twice as long as broad; cells III, IV and VI subequal and subiso- diametric, the latter, as well as the large external basal cell just above it, bulging prominently. Insertion-cell broad, rather thin and black. Basal cell of outer appendage somewhat longer than broad, externally somewhat suffused, bearing a stout simple branch subterminally which projects outward; its basal cell, except distally, deeply suf- fused, the remaining cells nearly or quite hyaline; a second similar but wholly hyaline branch arising terminally: basal cell of the inner 34 PKOCEEDINGS OF THE AMERICAN ACADEMY. appendage somewhat smaller, bearing one or two hyaline branches similar to those of the outer; on either side the external one is sub- tended by a short stiff characteristically blackened branchlet: all the branches stout, hyaline, elongate, tapering but slightly. Perithecium nearly free, rich blackish brown, the suffusion involving part of its basal cells; rather symmetrically inflated, a contrasting paler region just below the well distinguished rather broad deeply suffused tip; the lips rather coarse and prominent, the two inner lips bearing dis- tally a well defined papilla. Perithecium 75 X 25 fi. Appendages about 140 n. Receptacle 70-80 X 28 ju. Total length to tip of perithecium 145 /x. On the tips of the elytra of Manobia abdominalis Jac, M. C. Z., No. 2505. Although this species represents a somewhat ordinary type of the genus, it differs from others that are known, through the presence of a short black subulate branchlet which subtends the stout external branch of the inner appendage on either side. The branches of the appendage are unusually stout, almost hyaline, and diverge almost horizontally in the two types, which are in good condition. Laboulbenia partita now sp. Receptacle very variably developed; elongate, or short and stout, the structure normal, or often abnormal through the secondary divi- sion of cell II, which may be replaced by a series of from two to rarely ten or often nine superposed cells, many of which may be distinguished, singly or in pairs, by slight constrictions ; the series of about the same diameter throughout, except the terminal cell which may rarely be once or twice longitudinally divided ; the distal portion of the receptacle, cells III- VI, usually normal, rarely of the " Laboulbariella-type," the whole hyaline and abruptly contrasting with the dark perithecium, of more or less suffused, with yellowish brown, especially at the mar- gins of cells III-IV; cells III and VI usually subequal, cell IV pro- truding below the black, well defined insertion-cell. Appendages variable, the basal cell of the outer slightly longer than broad, some- what inflated and externally suffused, bearing distally one to three branches, usually two, radially placed the basal cell of the outer often suffused externally, bearing distally usually two or three short simple branchlets radially placed, blunt and hyaline; basal cell of the inner appendage much smaller than the outer, bearing a branch on THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 35 either side which may be multiplied by successive branching so as to form a rather dense tuft, none of the branchlets extending beyond the tip of the perithecium. Perithecium free, erect, straight, deep slightly olivaceous brown above its contrasting basal cells, the tip bent slightly outward ; lip-cells hyaline, tipped by two minute papillae. Spores about 40 X 3.5 fx. Perithecia, suffused part, average 75-85 X 32 fx. Appendages, longest, 85 fx. Receptacle, average, 135 X 25 fx, (85-175 //)• Total length to tip of perithecium 140-250 fi. On Nisotra dilecta Dej. and Nisotra sp. Kamerun, German W. Africa, (Schwab) usually on elytra: On N. Chapuisi Jac, Mada- gascar, M. C. Z., No. 2504. The abnormal septation of cell II is more common than the normal type on N. dilecta while on the second species, a uniformly steel blue form, it is comparatively rare. Specimens in which the septation is pronounced might well be mistaken for a species of Misgomyces. Speci- mens also occur having the simplified structure of " Laboulbeniella" as separated by Spegazzini. The material from Madagascar includes only the normal type and the individuals are smaller and less well developed. Laboulbenia Dysonichae (Speg.). Laboulbeniella Disonychae Speg., Contr. al Est. d. 1. Lab. Argent. p. 188. 1912. This species has been made the type of a new genus Laboulbeniella by Spegazzini, which he based on the fact that cells II and IV are replaced by a single cell. As I have already pointed out above, this character seems to me too trivial to form the basis of a new genus, for the reasons mentioned. It appears, however, to be the normal condi- tion in many of the chrysomelid forms and is found in all the following species, as well as occasionally in several of those above described, as for example in L. Halticae. L. Tucumanensis described by Spegaz- zini on a similar host, which is said, to possess stouter perithecia, does not appear to differ in any essential respect from the present form, as far as can be determined from the figures and description of the author. Material of this species has been examined from Mexico, Biologia Coll., No. 1768 on Disonycha figurata Jac, and was obtained by my- self in Trinidad on D. austriaca Schf., Nos. 2474, 2474b and 2474B, from the vicinity of Port of Spain and from Sangre Grande. It is 36 PROCEEDINGS OF THE AMERICAN ACADEMY. distinguished by its very slender and long appendages, which, although they are only about 4 n in diameter, may reach a length of more than 300 jit. In the specimens examined, the diameter of the perithecium varies from 21-35 /x. In the following descriptions all of which, except that of L. Podontiae, relate to forms of the " Laboulbeniella" '-type, the cell which replaces cells III and IV in the receptacle is spoken of as "cell III -f- IV." Laboulbenia arietina nov. sp. Receptacle relatively small, much shorter than the perithecium; olive brown, except the basal cell which is pale and slightly larger than the subbasal; cell III + IV about as long as cell II and half as wide; cell V minute; cell VI well developed, obliquely placed. Insertion- cell olivaceous, small, not deeply blackened. Appendages similar to those of L. Disonychae, the small bases of the outer and inner, opaque, prominent and persistent; giving rise to slender branches two or three times successively branched, olivaceous, their lower septa dark, bent rather abruptly toward and across the base of the perithecium and more or less circinate about it. Perithecium wholly free, relatively long and large, bent toward the appendages, dark brown, the base and tip paler olivaceous; the tip not otherwise distinguished; the apex oblique and prominent, externally oblique; one of the inner lip cells extending upward to form an erect blunt hyaline tipped appendage, its base concolorous with the dark olivaceous apex. Perithecia 100- 140 X 20-25 /jl; the terminal appendage 18-25 jj.. Receptacle 60- 100 X 24-28 it. Appendages longest about 150-175 fx. Total length to tip of perithecium 160-240 ll. On the elytra of Disonycha recticollis Jac, No. 1843, Guatemala, Kellerman; and of D. austriaca Schf., No. 2474b, Port of Spain, Trinidad. The four individuals of this peculiar species which have been ex- amined correspond in all respects; the Mexican being only slightly larger than the Trinidad specimens. It is very closely allied to L. Disonychae with which it occurred, but is at once dist:nguished by the terminal appendage of its perithecium. Laboulbenia Podontiae nov. sp. Receptacle usually small and short, but variable; dull dark brown, the basal cell conspicuously paler dirty yellowish or yellowish brown, THAXTER.— LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 37 relatively large, sometimes nearly as long as the rest of the receptacle; cells II and VI subequal in length; cell II usually broader; cells III and IV often about equal their septa oblique, their external margins convex; cell V small, extending to cell III; cell VI and the basal cell above it, externally convex. Insertion-cell free, rather thick, black, pointed above. Basal cell of the outer appendage rather deeply suffused with olive-brown, somewhat long and narrow; bearing distally, or distally and externally, a series of two or three branches, similar, radially arranged with blackened basal septa; their basal cells broader distally, short and stout and bearing one to three second- ary branches in a similar fashion, this branching being variably re- peated; the cells of these branches and branchlets similar, hyaline, with distal external suffusions; the ultimate branchlets few-celled, hyaline, curved toward the tip of the perithecium which they barely reach; all the septa of the partly suffused cells deeply blackened: basal cell of the inner appendage about half as large, becoming pushed somewhat sidewise and bearing distally a series of two or three branches radially arranged, or slightly oblique, which are similar to those of the outer appendage. Perithecium arising opposite the inner upper angle of cell III; concolorous with the receptacle, or more olivaceous; usually rather strongly curved, and tapering from near the base to the rounded apex; which is usually narrow, but hardly differentiated mostly long and slender, slightly enlarged at the apex, the lip edges not prominent, the inner hyaline: the wall-cells indicated by dark lines, the longitudinal ones having a spiral tendency sometimes lacking, so that the apex may be seen in anterior or posterior view and appear broad and subtruncate. Perithecia 70-100 X 18-20 jj.. Spores very slender, the distal half about as long as the basal, attenu- ated to a fine point bent abruptly sidewise, about 55 X 3 /x. Recepta- cle 70 X 24-28 /jl; larger form 100 X 28 fx. Appendages about 70 m- Total length to tip of perithecium about 140-160 /*; the larger type sometimes 230 yu. On the elytra of Podontia lutea Oliv., No. 2507, Hong Kong; No. 2508 on P. 14-punctata Linn., Himalayas, both in M. C. Z. Although the material of this species is abundant, no specimens are in perfect condition, the appendages apparently breaking very readily. It varies very greatly in size and form, many pigmy individuals occur- ring near the middle and base of the elytra, in depressions of their surface. In these small stout forms the receptacle is compacted and reduced, cell I forming a short hyaline stalk; cells III and IV promi- nent at the side; while the rest are hardly distinguishable from the base of the stout, small perithecium. The material from P. 14-punc- 38 PROCEEDINGS OF THE AMERICAN ACADEMY. tata is in part similar to that from P. lutea, but one specimen of the latter species bears a distinctly larger, rather slender, straight form, in which the twist of the wall cells of the straight perithecium is more distinct; so that its tip is nearly always seen at right angles to the normal position, and appears broad and flattened and quite unlike the more typical form, which occurs on other specimens of the same species. The form is most nearly related to L. orientalis, the funda- mental characters of its appendages being very similar. The latter may prove to be longer than above indicated when perfect specimens become available for examination. Laboulbenia Diabroticae nov. sp. Perithecium relatively large, its basal cells and basal wall-cells concolorous with the receptacle, dirty yellowish, the rest rich trans- lucent brown, except the hyaline outer half of the apex, the right anterior lip-cell forming distally and externally a more or less distinct truncate projection, its fellow usually shorter and rounded. Recep- tacle variable, stout, sometimes short, sometimes elongate through the elongation of cells I and II; cell III + IV relatively small, bulg- ing somewhat externally; cell VI nearly as large as cell III + IV, sometimes larger; the basal cells of the perithecium distinct above it; all the cells distinguished by more or less evident constrictions. Insertion-cell nearly opaque, as are the bases of the appendages; basal cell of the outer appendage bearing a double row of close set radially disposed branches; which may be twice branched, hyaline within or deeply suffused throughout, some or all of their tips bent abruptly outward or sidewise, or strongly recurved, the curved por- tion tapering to a blunt point; the branches of the inner appendage similar to those of the outer; the branchlets as a whole successively longer from without inward, seldom reaching to the tip of the peri- thecium, the septa oblique. Perithecium 100-225 X 20-28 fx. Spores about 50 X 5 li. Appendages, longest 120-140 fx. Receptacle to insertion-cell, longest, 265 fx; average 175 X 35 (x. Total length to tip of perithecium 300-390 /x. On elytra of Diabrotica Fairmairei Baly (Types), No. 1771, Bio- logia Coll., Jalapa, Mexico: of Diabrotica sp., No. 2471, Port of Spain, Trinidad: on legs of Diabrotica sp., No. 1641, Los Amates, Guatemala, (Kellerman). This well marked species varies considerably in the dimensions of THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 39 its perithecium and receptacle. In the Mexican material the latter is comparatively short and stout, while the former is much elongated ; but in the Guatemala material the reverse is the case. What appears to be an immature condition of the same species was also found on a species of Luperodes from Porto Velho, Amazon, collected by Mr. Mann, but none of the specimens have developed perithecia. The hooked terminations of the branches in this form are somewhat dif- ferent from the ordinary type. Laboulbenia Monocestae nov. sp. Receptacle relatively very small and compact, the basal cell usu- ally quite hyaline, often curved, as large as the remainder of the re- ceptacle combined; cell II and III + IV deep contrasting translu- cent brown, the former very broad and short, obliquely separated from cell I as well as from cells III + IV and VI; which is obliquely placed, subtriangular, hyaline or partly suffused; cell III + IV mostly suffused, broad and short, externally prominent; cell V very small, triangular, its upper surface partly free between the base of the peri- thecium and the insertion-cell. Basal cells of the perithecium hya- line and contrasting, as are the lower external wall-cells of its main . body; which is elongate, relatively very large, more or less curved toward the appendages, dark rich brown, hardly inflated, tapering very slightly at the broad apex; which is subtruncate or slightly rounded; the lip-edges slightly suffused. Insertion-cell thick, nar- row, opaque and indistinguishable from the externally blackened basal cell of the outer appendage, which is variably developed through proliferation that takes place distally from the inner side and results in a variably developed crest-like series of from three to eight radially placed branches, each usually once, less often twice branched, ex- ternally blackened as are the outer branchlets, except distally; the lower septa all suffused ; all the branchlets curved toward or past the perithecium, rather stout, slightly, tapering: basal cell of the inner appendage brown, erect, longer than broad, bearing distally a pair of short branches usually consisting of a single cell terminated by a pair of antheridia. Perithecia 85-125 X 25 fi. Receptacle 50-55 X 25-30 ix. Appendages, longest, 175 ju. Total length to tip of peri- thecium 140-175 ijl. On the legs of Monocesta atricornis Ok., Manaos, Amazon, (Mann) No. 2221. 40 PROCEEDINGS OF THE AMERICAN ACADEMY. A species well distinguished by its contrasting coloration, minute receptacle and large dark perithecium, which is characteristically hyaline externally at the base. The material is abundant and in good condition and does not seem to vary towards any of the varieties of L. Homophoetae which is its nearest ally. Laboulbenia armata nov. sp. Hyaline becoming faintly olivaceous, except the basal cell. Recep- tacle much smaller than the perithecium, the hyaline basal cell larger than the rest of the receptacle, from which it is separated by a hori- zontal septum; cell II about as large as cell III + IV, rounded, separated by symmetrical and oblique septa from cell III + IV and cell VI, which is small and somewhat oblique; cell V small, lying opposite the insertion-cell, against the base of the perithecium, the inner half of which it forms. Insertion-cell narrow, opaque and in- distinguishable from the basal cells of the appendages. Basal cell of the outer appendage small, quite opaque, longer than broad; producing a terminal and a subterminal inner branch, each usually once branched; the outer branchlet of the terminal branch short, curved outward, externally blackened; the other branchlets rather ' long, slightly flexuous and tapering; basal cell of the inner appendage very small, rounded, prominent, hyaline, free, bearing a short branch of two or three small cells on either side. Perithecium diverging from the appendages, relatively large long and hardly inflated, wholly free; the tip well distinguished on both sides, darker; the apex paler, surmounted by an outcurved, purplish, tooth-like external or subla- teral process, formed by one of the lip-cells; the other lip-cells hyaline, somewhat prominently rounded and subtending this process on the inner side; the blackened insertion of the trichogyne usually distinct on the left side of the purplish brown tip. Perithecium 120-125 X 24-30 £i; the horn-like process about 12-14 /i long. Receptacle 70-80 X 25 At. Appendages, longest, 175-210 n- Total length to tip of perithecium 175-210 n. On the elytra of Oedionychus sublineatus Jac, No. 1772. (Bio- logia Coll.) Teapa, Mexico. The appendages of this species are fundamentally similar in the origin and arrangement of their branches to those of L. Homophoetae, but the form is otherwise quite peculiar. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 41 Laboulbenia Homophoetae (Speg.). Laboulbeniella Homophoetae Speg. Cont. al Est. d. 1. Laboulbenio- mycetas Argentinas, p. 191. The material of this species studied by Spegazzini appears to have been in very bad condition ; but although it is not possible to form an accurate idea of the appendages from the figures given, there can, I think, be little doubt that the forms which I have assembled under this name are correctly referred. The species is the commonest one which is found on Chrysomelidae, with the possible exception of L. Bruchii, and inhabits a considerable variety of hosts on which it is subject to many variations. In all cases the basal cell of the outer appendage proliferates one to several times distally from the inner side, producing a variable number of branches which are almost in- variably once branched above their basal cells in a characteristic fash- ion, and which are very variably developed as to length, number, curvature etc. The size, development, and color of the receptacle and perithecium also vary very greatly; but viewing the series of variations as a whole, I have been unable to discover sufficient grounds for even varietal separation, and have concluded to assemble all the forms having this type of appendage under a single name, although I have separated one type, L. cristatella, which appears to be sufficiently constant, and in which the branches of the outer appendage are always simple. Although the position of growth in this last men- tioned form does not appear to affect the character of individuals, it produces a marked effect in the case of most of the varia- tions of L. Homophoetae, in which individuals growing on the under surface of the host are usually characterized by a distinctly more luxuriant development, especially of the appendages, the branches of which are apt to be more numerous, longer, and stouter than in indi- viduals which are found on the elytra, although the longest individuals seen, measuring 500 /j. to the tip of the perithecium were taken from the extremities of the elytra. This is especially marked in the very abundant material obtained from Systena 5-littera. Individuals from this host growing on the inferior surface, develop a fan-like series of stout incurved branches; while on the elytra a nondescript type is found, with scanty slender and irregularly curved branches; and the same is true to a somewhat less marked degree in individuals obtained from corresponding positions on species of Homophoeta, although the forms on these hosts present minor differences. Of all 42 PROCEEDINGS OF THE AMERICAN ACADEMY. the variations which have been examined that which occurs on Asphaera nobilitata in Trinidad is the most striking, and would undoubtedly be referred to a distinct species were there not variations which occur on other species of the genus which approach so closely to the type form that even a varietal separation seems undesirable. This Trinidad form is very large, and grows either on the elytra or at the base of the anterior legs of its host, its color is paler than that of individuals from other species of Asphaera. The perithecium is distinguished by an often well developed neck-like base formed from the lower tier of wall-cells, and is usually bent abruptly outward from the appendages. The latter are very stout and long. Larger specimens have the following measurements: perithecia 225 X 35 fx; appendages 480 /jl; receptacle 280 X 40 /x; total length to tip of perithecium 400 ju. In this and several other forms the cells, of the receptacle, especially, contain a distinctly yellow or orange proto- plasm, the color of which is apparently due to the peculiar yellow juices which fill the bodies of many of the Chrysomelidae. The hosts on which forms referable to L. Homophoetae have been found are as follows: (a) Homophoeta sp., No. 2475b and H. aequinoctialis Linn., No. 2475, Port of Spain, Trinidad: on H. 6-gutta'a Say, No. 1791, Brazil; (b) Systena sp., No. 1640, Los Amates, Guatemala (Kellerman); on S. basalts Jac, Nos. 2489 and 2490, Hayti (Mann): on S. 5-littera Linn.; Nos. 2469 and 2470, Port of Spain, Trinidad; No. 2479, Suriname (Rorer); No. 1769, Teapa, Mexico (Biologia Coll.). (c) Psylliodes sp., No. A+, Jamaica (Brues). (d) Disonycha sp. No. 1843, Guatemala (Kellerman); on D. recticollis Jac, No. 1769, Costa Rica (Biologia Coll.) and No. 1642, Guatemala (Kellerman). A dark form with numerous short rather slender curved appendages hardly ever reaching to the tip of the perithecium, their inner margins conspicuously indented at the septa. (e) Oedionychus sublineata Jac, Teapa, Mexico, No. 1772, (Bio- logia Coll.). A paler form, straight, with few straight appendages, the largest specimen measuring 500 /x to the tip of the perithecium. (f) Monocesta atricornis Clk., No. 2221, Manaos, Amazon, (Mann). A small dark form with few very long scanty appendages, the recepta- cle small, the perithecium bent abruptly against the appendages which may reach 425 n in length, although the total length to the tip of the perithecium is only about 120 /jl. (g) Lactica scutellaris Oliv., No. 1754, Balaclava, Jamaica, W. I. A form similar to that on (f) but with straight perithecium. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 43 (h) Asphaera nobilitata Fab., No. 2472, Port of Spain, Trinidad; A. transversofasciata Jac, Bugaba, Mexico, (Biologia Coll.), No. 1773; A. elegantissima Schf., No. 2218, Rio Madero, Amazon (Mann); A. Siebcrsii 111., No. 2211, Para, Brazil (Mann). Laboulbenia cristatella nov. sp. Hyaline, becoming suffused with olivaceous brown. Receptacle small; cell I larger than cell II, which is somewhat roundish, its margins more or less convex; cells III + IV much smaller than cell II; cell V small and narrow, often partly free above; cell VI small, flattened, and oblique. Insertion-cell narrow, opaque, indistinguish- able from the basal cell of the outer appendage. Basal cell of the outer appendage black below and externally, broad and quite hyaline above, bearing externally and distally a series of branches radially placed; the outer (lowest) branch furcate, its basal cell obliquely hyaline within, externally black, the two branchlets broadly blackened externally, except distally, the outer wholly so at the base; the re- maining branches always simple, stout, usually tapering somewhat toward the base and apex, broadly blackened externally, except distally; usually curved toward and beyond the perithecium, forming a crest-like series which exceeds the latter in length: basal cell of the inner appendage very small, brown, bearing a short simple branch on either side both two-celled, the lower cell deeply suffused, the upper hyaline, separated from it by a dark septum and bearing usually a pair of relatively large long antheridia, sometimes only one. Peri- thecium not quite free, straight, becoming dark olive brown, very slightly inflated; the tip broad, well distinguished, blackened distally, especially on the inner side; the apex with broad, rounded, rather prominent lip-cells slightly oblique inward; the outer hyaline, the inner deeply blackened, except the narrowly hyaline papillate promi- nent edge. Perithecia 60-76 X 18-22 ft. Receptacle 50-64 X 22- 28 m- Appendages longest 125 /x- .Total length to tip of perithecium 100-140 (i. On inferior surface of Haltica scutellata Oliv. No. 2473, Port of Spain, Trinidad (Type). On Asphaera Siebersii 111. No., 2233, Para, Brazil, (Mann). On elytra of Lactica nigriceps Boh., Para, Brazil, (Mann). The above description is drawn from the Trinidad material, which is abundant and in good condition. The material from Brazil is in 44 PROCEEDINGS OF THE AMERICAN ACADEMY. both instances somewhat smaller, the branches of the appendages mostly shorter, hardly reaching to the tip of the perithecium and usually swollen, rather than tapering at the tip. The species is very closely allied to L. Homophoctae from which it is distinguished by the simple branches of its outer appendage, by its small size and other minor differences. It may prove however, to be merely a variety of L. Homophoctae. Laboulbenia funebris nov. sp. Dull olivaceous, becoming deeply tinged with brown. Perithecium homewhat less than one half free, becoming almost opaque, except for a hyaline area on the inner side just below the deeply blackened ex- tremity; the lip-cells hyaline about the pore, turned somewhat out- ward; the outer more prominent, rounded, tipped by minute papillae: the outer margin directly continuous with that of the receptacle, hardly convex, bent inward abruptly at the tip; the inner straight or slightly convex. Receptacle symmetrically broader from below up- ward; the basal cell hyaline below, subtriangular; the subbasal cell somewhat longer, separated from cells III + IV and VI, which is relatively large, by somewhat oblique septa; cell III + IV rather large, cell V very minute, translucent, all the upper portion of the receptacle deeply suffused, the cell-boundaries becoming hardly distinguishable, and concolorous with the perithecium. Insertion- cell broad and thick, wholly and deeply suffused; the appendage consisting of a single outer, simple, yellowish olive, rather stout tapering, but slightly divergent outer branch of six or eight cells, relatively stout; the basal cell of the inner appendage bearing two shorter, smaller, simple branches, of usually not more than three or four cells, the subbasal bearing distally a single antheridium. Perithecium 75-80 X 25 /x. Spores 45 X 5 ju. Appendage, longest 140-150 /z. Total length to tip of perithecium 125-160 /z, greatest width 35 /x. On the elytra of species of tHaltica. Mus. Comp. Zool. No. 1790, (no locality); No. 1841, Guatemala, (Kellerman). In general appearance this ordinary looking form is not unlike the smaller specimen of L. rigida figured in my first Monograph the appendages being very similar. It also resembles some forms of L. vulgaris and of L. polyphaga but cells III and IV are always re- placed by a single cell. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 45 Ceraiomyces. * More than a dozen species of this type are now available for com- parison and an examination of them indicates that the genus is so closely allied to Laboulbenia that it may possibly have to be united with it eventually; although for the present, at least, it seems more convenient to retain the name. The cell spoken of in the original description as the "stalk-cell of the appendage," which corresponds to cells III to V in Laboulbenia, is, in some of the species, closely united to the perithecium, as in the West Indian forms described below; and it is therefore necessary to modify the original diagnosis based on two species in which this cell was quite free. Since the type may be regarded as corresponding to a reduced form of Laboulbenia, it has seemed best to refer to this cell as "cell III" of the receptacle; it being understood, however, as has been formerly pointed out, that not only this cell, but the three corresponding cells in Laboulbenia above alluded to, belong strictly to the appendage. The latter, in the species described below, is, for the most part, greatly reduced; its cells becoming more or less obliterated, the antheridia alone being distinctly visible. In some young individuals, however, the funda- mental structure is very like that of the most simple types in Laboulbenia; there being outer and inner cells which give rise to corresponding sets of branches, both of which always bear antheridia. It may be mentioned further that all of the following species are char- acterized by possessing a normal foot, and in no instance penetrate the host by means of a haustorium. Ceraiomyces Epitricis now sp. Basal and subbasal cells of the receptacle subequal, nearly hyaline, the former slightly suffused with brown just above the foot, the two together not quite as long as the perithecium; cell III clearly defined several times as long as broad, of nearly the same diameter throughout, concolorous with the perithecium. Appendage consisting of a small basal cell obliquely inserted on a dark basal septum and bearing on the inner side two large antheridia subtended by minute cells; and externally a single antheridium, less often two, subtended by a larger cell; the antheridia becoming slightly suffused with brown. Perithe- cium three fifths or more free above the insertion of the appendage, translucent brown, except the small clearly defined flattened stalk-cell; 46 PROCEEDINGS OF THE AMERICAN ACADEMY. the basal cells very small, but clearly defined ; the lower third united to cell III; the inner margin above it vertical, straight as far as the insertion of the trichogyne, above which the tip bends inward more or less distinctly; the outer margin abruptly bent opposite the inser- tion of the appendage, forming a considerable angle, so that the body appears to be bent inward ; the portion of the margin above this angle running straight to the hardly distinguished tip; the somewhat com- pressed hyaline apex subtended externally by a distinct rounded hyaline prominence; the pore terminal; the lip-cells not prominent. Perithecium 80-90 X 32 ju. Basal and subbasal cells of receptacle 50-70 X 16 ju. Appendage, including antheridia, 30-32 fx. Cell III, 28 X 7 ju. Total length to tip of perithecium 140-160 ju. On elytra of Epitrix convexa Jac, No. 2462, Port of Spain, Trini- dad. In general form this species most nearly resembles C. Chaetocne- mae from which it is easily separated by the form of the perithecium and the peculiar external prominence which subtends its apex. Ceraiomyces obesus nov. sp. Cells I and II faintly brownish, distinguished by a constriction; the former more than twice as large as the latter, its lower half nar- rowed to the foot; cell III concolorous with the perithecium, united to it throughout, and extending nearly to its middle. Appendage arising from an oblique insertion, marked by a dark septum, hyaline, consisting of two or three very small hardly distinguishable cells bearing usually two inner and one outer antheridium. Perithecium somewhat more than half free above the insertion of the appendage, arising obliquely and externally from cell II, which it almost conceals when not viewed laterally, its outline almost symmetrically long-oval : uniform rich translucent brown, tapering to the rather broad, blunt, slightly oblique apex; the hyaline lip-edges bearing each a minute but distinct papilla, and subtended by darker shades. Perithecium 106-112 X 52-60 /x. Appendage including antheridia 18 fx. Recepta- cle, cells I-II, 52 X 18 ju; cell III, 36 X 10 ju. Total length to tip of perithecium 140-160 ju. Near base of anterior legs of Epitrix convexa Jac, Port of Spain, Trinidad, No. 2464. This species is distinguished by its relatively very large, nearly symmetrically oval perithecium, the axis of which is at a considerable angle to that of the receptacle, when viewed laterally. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 47 Ceraiomyces minisculus nov. sp. External margin, from tip of foot to apex, almost an arc of a circle, the corresponding opposite margin almost straight except for the slight protrusion of cell III. Basal cell of the receptacle triangular, about as broad as long, yellowish; the subbasal cell flattened distally, oblique below the base of the perithecium with which it is concolorous and from which it is hardly distinguishable; cell III longer than the portion of the receptacle below it, very narrow and hardly distinguish- able from the body of the perithecium. Cells of the appendage minute, only one being distinguishable, and bearing two relatively large brownish antheridia, the outer spinose externally below its neck. Perithecium somewhat less than half free above the insertion of the appendage, relatively large, stout, very deep brown, barely translu- cent, the apex blunt, the hyaline lip-edges subtended by blackish shades. -Perithecium 70 X 26 /x. Cells I— II, 18 /x long by 21 xx broad; cell III, 30-32 X 4 /x. Appendage, including antheridia, 22 xx. Total length to tip of perithecium 90-95 ax. On antennae of Chaetocnema nana Jac, No. 1755, Balaclava, Jamaica, W. I. This minute species is most nearly related to C. obesus from which it differs in the structure of its receptacle, and the form and position of its perithecium. The appendage is so reduced that little remains beside the antheridia. Ceraiomyces dislocatus nov. sp. Cells I and II nearly hyaline or becoming faintly yellowish, the former about five times as long as it is broad, abruptly enlarged above the small pointed foot, distally bent abruptly inward; the septum separating it from cell II thus more or less oblique and sublateral, marking a constriction, and giving to this part of the receptacle a more or less distinctly geniculate habit; cell II roughly isodiametric, bulging slightly externally, small, separated obliquely from the base of the perithecium; cell III relatively broad and distinct, concolorous with the perithecium. Appendage seated on a dark, somewhat oblique septum, hyaline; its two or three cells very small and indis- tinguishable at maturity; bearing two inner and one or rarely two outer slender faintly brownish antheridia. Perithecium more than half free above the insertion of the appendage, deeply suffused with 48 PROCEEDINGS OF THE AMERICAN ACADEMY. blackish brown, darker below the apex, the outer margin broken by a slight basal, a median and a subterminal rounded elevation; the latter, together with a corresponding elevation on the inner side, rather clearly distinguishing the tip which is bent distinctly toward the appendage; the anterior (inner) and left lip-cells more prominent, somewhat dis- placed by a slight twist, separated by furrows, terminating in minute flattish hyaline papillae; the other two lip-cells shorter and rounded, so that the apex is asymmetrical. Perithecium 80-90 X 35 yi. Cell I 50-85 X 15 m; cell II about 17 X 18 \i\ cell III 24-28 X 7 \x. Ap- pendage, to tips of antheridia, about 25 /jl. Total length to tip of perithecium 125-175 ji. On the mid-inferior surface of the abdomen of Chaetocnema minuta Mels., No. 2460; Port of Spain, Trinidad. A species very clearly distinguished by its geniculate receptacle, and distinctive perithecium. Ceraiomyces Trinidadensis nov. sp. Cells I and II hyaline; the former abruptly bent, more than twice as long as the subtriangular subbasal cell which is obliquely separated from the base of the perithecium and from cell III; which is clearly defined, concolorous with the perithecium, bulging slightly below the nearly horizontal, relatively broad insertion of the appendage. Ap- pendage relatively large, the two cells of the outer branch hyaline, distinct, subequal, bearing usually two large antheridia which equal them in length. Perithecium translucent, blackish olive-brown, rather narrow, nearly symmetrical in outline, its upper half, or some- what less, free above the insertion of the appendage; tapering dis- tally to the broad subhyaline extremity, which is rounded and slightly sulcate and but slightly asymmetrical; the stalk- and basal cells hardly distinguishable. Perithecium 80-88 X 28 /x- Cell I, 28-35 X 18 /x; cell II, 18 /x; cell III, 28 X 10 ju. Appendage, including an- theridia, 35 fi. Total length to tip of perithecium about 125 fi. On the legs of Epitrix convcxa Jac. ; No. 2459, Port of Spain, Trinidad. Though this species is not distinguished by any single striking peculiarity, it differs distinctly from any of the others by the form of its perithecium which ends in a broad blunt hyaline apex. It is most nearly related to C. Chactocnemae, a larger more slender form. THAXTER. — LABOULBENIALES PARASITIC ON CHRYSOMELIDAE. 49 Ceraiomyces Chaetocnemae nov. sp. Straight or but slightly curved, relatively long and slender. Cells I and II hyaline, becoming tinged with pale reddish yellow; cell I often somewhat elongate, usually somewhat more than twice as long as the subbasal cell, from which it is separated by a nearly horizontal septum; cell III concolorous with the perithecium, well distinguished. Insertion of the appendage somewhat oblique, blackened, the latter bearing two inner antheridia and one outer, the necks of which are subtended by a conspicuous spine. Perithecium slightly less than two thirds free above the insertion of the appendage; becoming dark blackish olivaceous; the stalk- and basal cells hardly distinguishable, rather long and narrow, tapering distally; the tip becoming distin- guished by slight subtending elevations; the lips tending to turn slightly outward, two of them bearing minute flattened papillae which project above the otherwise rather bluntly rounded, slightly sulcate apex. Perithecium 90-116 X 38-42 \i. Spore 52 X 4 /z. Cells I-II, 60-122 X 22-25 y.. Cell III, 38-42 X 8-10 p.. Appendage 30 \i. Total length to tip of perithecium 160-250^. On the elytra of Chaetocnema sp., No. 2248, Amazon, Mann, on C. minuta Mels. No. 2460, 2461, Port of Spain, Trinidad: on Epitrix lucidula Har., No. 2457, and E. convexa Jac, No. 2458, Port of Spain. Although varying considerably in size, this species is much larger than any of the others which occur on Chrysomelidae, with the excep- tion of C. Nisotrae. It appears to be quite rare and usually not more than one or two individuals are found together on a single host. A form apparently not separable from this species was also found in Port of Spain on a single individual of Scolochrus sp. Ceraiomyces Nisotrae nov. sp. Comparatively large, short and stout. Receptacle dirty brownish yellow throughout, obscurely punctate above the basal cell, which is short and abruptly bent, its upper half abruptly twice as broad ; cell II hardly longer than broad and but slightly larger than the stalk-cell (cell VI of Laboulbenia), which lies just above it; cell III hardly extending above the perithecial cavity, and lying opposite the stalk- and basal cells, which are clearly defined and, like it, dirty yellowish brown. Insertion of the appendage slightly oblique, its basal cell almost wholly suffused with dark brown; basal cell of the outer branch 50 • PROCEEDINGS OF THE AMERICAN ACADEMY. usually bearing two branchlets, one two-, the other one-celled, each terminated by a very long slender antheridium; the inner branch single as a rule, consisting of a rather elongate cell terminated by an antheridium; the antheridia seated on blackened septa, below which a brown suffusion extends downward. Perithecium relatively large, distally somewhat broader; free except its basal and stalk-cells, deeply suffused with dark brown, faintly translucent; the external margin straight, or usually slightly concave; the inner convex and curved inward abruptly to form the tip, which is usually twisted somewhat less than one quarter; so that the outer lip, which is modi- fied to form a brown, rounded projection, subtended on either side by curved ear-like processes, is usually almost lateral in position ; the rest of the apex almost symmetrically rounded, somewhat inflated, sub-hyaline, contrasting with the basal portion of the tip which is concolorous with the body of the perithecium. Perithecium 100-125 X 35^0 /x. Spores 40 X 4 p.. Cells III about 50 X 22-24 /*. Cell III, 24-28 X 8-10 //. Total length to tip of perithecium, average 175 p, longest 200 fx. Appressed along a ridge parallel to the outer margin, usually of the left elytron, of Nisotra sp., No. 2481, Kamerun, West Africa (Schwab): on Ar. Chapuisi Jac, Madagascar, M. C.Z., No. 2504. The differences which separate this species from all other forms are so great that they need hardly be pointed out, the peculiar outgrowths of the lip-cells being in themselves sufficient to distinguish it. The Madagascar material, although inhabiting a smaller and very differ- ent species of the host-genus, corresponds in all essentials with speci- mens from Kamerun. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 3. — June, 1914. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE DEMAGNETIZING FACTORS OF CYLINDRICAL RODS IN HIGH, UNIFORM FIELDS. By B. Osgood Peirce. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. THE DEMAGNETIZING FACTORS OF CYLINDRICAL RODS IN HIGH, UNIFORM FIELDS. By B. Osgood Peirce. t Presented by E. H. Hall, March 11, 1914. Received March 5, 1914. Any one who has been compelled to measure the permeability of iron under high excitations, by experiments upon relatively short rods exposed to strong magnetizing fields, must have had occasion to notice that, under these circumstances, the corrections for the effects of the self -demagnetizing forces are often very small. In the case of an ellipsoidal specimen, it is possible to predict the phenomena which one encounters in practice,1 and although it is not easy to make long ellipsoidal test rods with accuracy, there is a sufficiently close analogy between the two cases to make the general conclusions reached for ellipsoids applicable to the cylindrical rods usually employed in the laboratory.2 It is well known that if an ellipsoid of soft, magnetizable material and of fixed, constant susceptibility, k, were placed in a uniform magnetic field, H, it would become uniformly magnetized by induction and that the components of the field within it would be HJ ( 1 + 2irabcleKo) , HJ ( 1 + 2wabckL0) , H / ( 1 + 2rabckMo) , where a, b, c, are the lengths of the semiaxes, Ao = Jo (H-a)3/2. (.?+&) 1/2- (p+c)W (1) and Lq, Mo, have corresponding values. t Deceased January 14, 1914. iRayleigh, Phil. Mag., 22, 1886; Maxwell, Vol., II; Webster, Elect, and Mag., §§ 192, 196; Peirce, N. P. F.; Yosida, Tokyo, Proc, 3, 8, 1906; Mallik, Phil. Mag., 14, 1907; 15, 1908; Daniele, N. Cimento, 2, 6, 1911; H. E. J. G. duBois, Deutsch. Phys. Gesell., Verh. 15, 8, 1913. 2Ewing, Phil. Mag., 176, 1885; Tanakadate, Phil. Mag., 26, 1888; H. E. J. G. duBois, Phil. Mag., 29, 1890. Wied. Ann., 46, 1892; Rossler, Elektro- technische Zeitschrift, 14, 1893; Mann, Dissertation Berlin, 1895. Phys. Rev., 3, 1896; Ascoli e Lori, Rendic. R. Acad. d. Lincei, 3: 2, 1894; 6: 2, 1897; J. L. W. Gill, Phil. Mag., 46, 1898; Morin, Eel. Electr. 15, 1898; Holborn, Sitzungsbericht d. Akad. Wiss. zu Berlin, 1, 1898; Benedicks, Wied. Ann., 6, 1901; Bihang Svenska V.-Akad. Handlinger, 27, 1902; H. E. J. G. duBois, Wied. Ann., 7, 1902; Gumlich, Elektrotechnische Zeitschrift, 22, 1901; 30, 1909; Peirce, These Proceedings, 44, 1908; Am. Journal of Science, 28, 1909; Shuddemagen, These Proceedings, 43, 1907; Peirce, Ibid., 49, 1913. 54 PROCEEDINGS OF THE AMERICAN ACADEMY. If two of the semiaxes (b, c) were equal, and if the third axis had the direction of the outside field, H, which had been chosen also for the direction of the a; axis, the field in the ellipsoid would agree with H in direction, and we might write, where e2 = (a2-62)/a2 = (a?-c?)/a2. The ratio of the intensity of the field, H', within the ellipsoid to that of the exciting field, H, would be 1 (l+2irabckK0) ^ Table I shows the numerical values of a3ivo and of 1 + 2TabckKo for several different values of the ratio m = a/b. TABLE I. TO a3 • Ko l+2wabckKo 30 6.198 1 + 0.0433/; 40 6.771 1 + 0 .0266/c 50 7.215 1 + 0.0181/c 60 7.575 1 + 0.0132A; 80 8.150 1 + 0.0080& 100 8.597 1 + 0.0054& 140 9.270 1 + 0.0030& 200 9.983 1 + 0.0016& Even though it be not possible to realize these conditions exactly in practice, and a relatively slight departure from a truly ellipsoidal form in the testpiece may alter the conclusions appreciably, yet the measurements of several observers who have used such nearly ellip- soidal rods as they were able to procure, show a fairly close agreement with this theory, and we shall find it instructive to examine the numeri- cal results obtained by applying it in the cases of one or two kinds of soft iron and steel to be bought in the market. Some time ago, Mr. J. Coulson and I examined with great care a long rod of soft Bessemer steel in a uniformly wound solenoid of 20904 turns, 4.85 meters long, as well as shorter specimens of the same material between the poles of a massive soft iron yoke. Table II gives very approximately for this steel and for various values of H, the values of the susceptibility; of the fractional increase in the PEIRCE. — DEMAGNETIZING FACTORS OF CYLINDRICAL RODS. 55 induction, B, due to an increase of one unit in the exciting field, H, in the metal; and of the fractional change in B due to a change in H of one percent of its own value. These quantities are denoted by k, X, Zf respectively. TABLE ; ii. H k X z 30 38.3 0.00558 0.0017 40 30.1 0.00386 0.0016 50 24.9 0.00277 0.0014 60 21.3 0 .00227 0.0014 80 16.5 0.00155 0.0013 100 13.6 0 .00128 0 .0013 120 11.0 0 .00108 0.0013 160 9.0 0.00082 0.0013 200 7.4 0 .00067 0 .0013 300 5.2 0.00046 0.0013 400 4.1 0.00032 0.0013 500 3.3 0.00024 0.0012 800 2.2 0.00014 0.0011 1000 1.7 0.00011 0.0011 1500 1.1 0.00005 0.0008 2000 0.9 0 .00004 0 .0009 2500 0.7 0.00004 0.0010 (5000) (0.34) (0.00004) (0.0019) From the numbers in the last column of Table I, and those in the second column of Table II, it is easy to compute the ratio of the intensities of the magnetizing field {H') in the metal, and the external exciting field (H), for different values of m. The results of this pro- cedure for a/b = 30, a/b, = 50, and a/b =100, appear in Table III. TABLE III. H' H'/H, if a/b = 30, H'/H, if a/b =50, H'/H, if a/b =100 30 0.377 0.591 0.828 40 0.435 0.648 0.861 50 0.482 0.689 0.882 60 0.521 0.718 0.897 80 0.584 0.770 0.918 00 0.630 0.803 0.932 56 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE III — Continued. H' H'/H, if a/b = 30, H'/H, if a/b = 50, H'/H, if a/b 120 0.666 0.826 0.941 160 0.720 0.862 0.955 200 0.758 0.880 0.962 300 0.816 0.914 0.973 400 0.850 0.933 0.978 500 0.876 0.943 0.982 800 0.913 0.962 0.988 1000 0.932 0.970 0.991 1500 0.955 0.981 0.994 2000 0.963 0.984 0.995 2500 0.970 0.987 0.996 (5000) (0.985) (0.994) (0.998) a oo A comparison between the figures given in this table and the values of Z in Table II shows that, in the case of an ellipsoidal rod only 30 diameters long, the density of the flux of magnetic induction through the metal when the exciting field is as high as 2500 gausses, is not so much as one third of one per cent less than the corresponding flux density for an infinitely long rod. When the ellipsoid is 50 diameters long, the flux density for 2500 gausses does not differ by so much as one eighth of one per cent from the flux density in an infinitely long speci- men under the same excitation, and only an extremely good determina- tion of B is correct within this fraction when the value of B is above 25000. It is interesting to note that if, under excitations above, say, 2500 gausses, we may assume the intensity of magnetization, J = kH, to be constant, so that B — H is constant; dB/dH is unity and f— •-777) increases somewhat with H. In the case of the Bessemer steel mentioned here, where 1^ = 1694, Z is 0 .00190, for H = 5000, while Z is 0 .00484, if H is 20000. Table IV gives results obtained by Mr. Coulson and myself from a long series of tests upon a special brand of Norway Iron unusually permeable at high excitations. PEIRCE. — DEMAGNETIZING FACTORS OF CYLINDRICAL RODS. 57 TABLE IV. * H. h. z. (H'/H) so (H'/H)m 400 4.4 0.0010 0.841 0.922 500 3.5 0.0009 0.869 0.940 GOO 2.9 0.0006 0.S89 0.950 700 2.4 0.0005 0.909 0.957 soo 2.2 0.0004 0.913 0.961 900 1.9 0.0004 0.926 0.965 1000 1.8 0.0005 0.931 0.968 1500 1.2 0.0006 0.951 0.978 2000 0.9 0.0008 0.962 0.984 2500 0.7 0.0010 0.970 0.9S7 In the case of this iron, the flux density, under an excitation of 2500 gausses, would be less than for an infinitely long rod, by about one third of one per cent, for a/b = 30, and, by about one eighth of one per cent, for a/b = 50. It has long been known that, although cylindrical rods of soft iron do not become uniformly magnetized when they are exposed longi- tudinally to uniform magnetizing fields, yet they behave in many other respects much like the ellipsoidal pieces which are more easily subjected to analysis. A glance at the B vs. H curves obtained thirty years ago by Ewing from an iron wire 0.158 cms. in diameter and originally 47.5 cms. long, shows that under very high excitations the flux through the central cross section of a comparatively short piece of this wire would have been much the same as the corresponding flux through a speci- men several hundred diameters long, but -the demagnetizing factor in the case of such a rod seems to be a function of both the diameter and the length and not a function of the ratio of the two alone, and although at low excitations the numbers given by DuBois and by Shuddemagen are most useful, it is not easy to compute with certainty just how long a specimen must be in order that the flux through its meridian section may be assumed to be unaffected by the nearness of the ends of the rod. It happens that Mr. John Coulson and I, who have been studying the maximum value of / in different kinds of iron, have had occasion to determine the magnitude of the influence of the ends of some rods which we have been using in fields of 2500 gausses and upwards, and we have found that we might have used much shorter test pieces and a much less massive solenoid than we have 58 PROCEEDINGS OF THE AMERICAN ACADEMY. employed in our work. Some of our observations are recorded briefly here in the hope that they may prove useful to other experi- menters. Figure 1 shows the general arrangement of the apparatus used in making the measurements described in this paper. Figure 2 indicates the forms of three of the several standards of mutual inductances which we used for calibrating the galvanometers. For a complete discussion of the apparatus used throughout this work reference is made to a preceding paper,3 since the apparatus used for both investi- gations was essentially the same. Our method of work was not new in any particular, but the necessity of using heavy currents and, therefore, of taking care of the heat equivalent of many kilowatts in our circuit, and the use of ballistic galvanometers with periods so long that a reversal of current in the highly inductive circuit could be accomplished before the galvano- meter coil had moved appreciably from its position of rest, introduced many difficulties which could be overcome only after much anxious experimentation. The large solenoid with which most of our work at high excitations was done, was made of about 300 kilograms of triply covered No. 10 copper wire wound uniformly, with great care, by Mr. George W. Thompson, the mechanician of the Jefferson Laboratory, upon a massive brass spool, 186.2 centimeters long, in inside measurements. There are two coils, one of 8117 turns in 14 layers, and the other, of slightly different wire, of 5872 turns in 10 layers. The field intensity in the centre of the solenoid when a current of one ampere passes through the first coil is 54.71 gausses, while at a point fifty centi- meters from the centre on the axis, the intensity is 54.60 gausses. A current of one ampere sent through both coils in series creates a field of 94.19 gausses at the centre of the coil. This solenoid was repeatedly tested for leakage between the turns by means of a very carefully made test coil without iron, but we were never able to detect any evidence of fault. For low excitations, we sometimes used a somewhat longer solenoid wound with No. 14 wire. The test pieces were first packed in fine iron filings in a pipe closed at the ends by caps. This was placed horizontal and perpendicular to the meridian upon supports in a furnace where it was exposed to several hundred gas jets driven by a power compressor. The dimen- 3 Peirce, These Proceedings, 49, 1913. -3— -2~ G1N- Figure 1. Shows diagrammatically the general arrangement of some of the apparatus used in making the observations described in this paper. m % g 'i au M D [HI l\ Figure 2. Three standards of mutual inductance. 60 PROCEEDINGS OF THE AMERICAN ACADEMY. sions of the test pieces were obtained by aid of a set of gauges which had been tested against two comparators, one by Zeiss. The test rods received first a very thin coat of varnish and then the test coil of triply silk-covered copper wire which was in turn varnished and then heated in a stream of hot air until the whole was thoroughly dried. Usually two test coils were wound upon each rod and their indications compared, lest an injury or imperfection in one might escape notice. Our first experiments were not so carefully carried out as the later ones, but they pointed to the same general conclusions. I need mention only two of them. In the first, we tested a rather short piece of cold-rolled shafting 1.269 cms. in diameter. This had origi- nally a length of 79 diameters, but was cut shorter by steps to 63, 47, 32, 24, and 16 diameters, respectively. In an exciting field of 1280 gausses, the fluxes through the central section of the specimen seemed to be as 176, 175, 175, 175, 175, and 175. The second experiment was made upon a rod of Norway Iron 1.110 cms. in diameter and successively 150, 130, 110, 70, and 30 diameters long. In this case the value obtained for the flux through the central section at the last step differed by less than one eighth of one per cent from the average value for the other steps, and as it happened this small difference was in excess. The truth is that all the values agreed within the small accidental error to be expected in the work. The magnetizing field had an intensity of 2700 gausses. We were at first puzzled by a phenomenon which sometimes affected our results by a small fraction of one per cent. After a long day's work when the originally long rod under examination had been cut down, by a succession of steps, to a short one, and the resistance of the circuit had become a little greater than at the outset on account of the heat set free in it, we often found the same flux at very high exci- tations through the central section of our specimen which a slightly greater current had caused in the longer piece in the morning. This was not caused by a rise of temperature in the test piece because a vigorous flow of water of practically constant temperature was sent through the tube of the solenoid all day. It was not due to a change of sensitiveness in the ballistic galvanometer, as frequent calibrations showed. It seems to be true that if a rod of soft iron of any length be repeat- edly magnetized in a very strong field, in the one direction and in the other, alternately, a very slightly weaker field will eventually suffice, after it also has been many times reversed, to magnetize the iron as strongly as the original one. PEIRCE. — DEMAGNITIZING FACTORS OF CYLINDRICAL RODS. 61 We thought it possible that we might avoid this difficulty by using at the same time a long piece and a short piece, cut freshly from a single rod, but experiment seemed to show that we could not expect the same permeability in two pieces obtained in this way and that the difference might easily be as much as one per cent at some excitations. We believe, however, that we have reduced the error in our conclusions due to the effect just mentioned to a very small fraction. All our work, which lasted more than two months, pointed to the same results, and I need mention only a few representative experi- ments. They convinced us that in our determinations of the satura- tion values of the magnetization in different kinds of iron and steel, we might safely use much shorter test pieces than those which we had employed before. Experiment A was made upon an annealed piece of Bessemer rod 0.635 cms. in diameter. The original length was 158 diameters, but this was cut down successively to 61, 31, and 18 diameters. At an excitation of 2600 gausses where B was 23530, the average of the fluxes of magnetic induction through the central sections of the various pieces, differed by less than one sixth of one per cent from an3r one of the individual values, and from the last value by a wholly inappreciable fraction. Experiment B was made upon a Bessemer rod 0.795 cms. in diameter. The lengths of the pieces were 150, 100, 60, 40, and 20 cms. For H 1320, the flux through the central section of the shortest piece seemed to be about one fifth of one per cent lower than the average of the corresponding fluxes for the other pieces. At 1850 gausses and 2700 gausses, however, there was no such difference. For H 2570, B was 23700. Figure 3 shows some B-H curves for the pieces at low excitations where the effects of the presence of the ends of the rods are very apparent. In Experiment C, we treated a somewhat stouter Bessemer rod. Its diameter was 0.879 cms. Its length was originally 164 diameters, but this was shortened by steps to 124, 100, 75, 45, and 24 diameters. At 2500 gausses the value of the flux through the centre of a piece only 19 cms., or 24 diameters, long,ldid not differ by so much as one tenth of one per cent from the mean of the fluxes for all the lengths under this excitation, where B was 23550. At an excitation of 1710 gausses, B was 22700, and it was not possible to prove that the shortest piece had a less flux than the others. Some of the results of our observations for this experiment are tabulated in Table V. H is the value that the field would have inside the solenoid if the iron were Figure 3 represents the B-H curves for four lengths of the same material, (experiment B). The curves OP, OQ, OR, and OS correspond to specimens of lengths 150, 60, 40, and 20 cms. respectively, plotted on an arbitrary scale. One unit on the Y axes corresponds to a B of 6000 gausses; and one unit on the X axes to a field H of 12.17 gausses. EXCITING FIELD 200 H Figure 4 shows the B-H curves for two of the specimens used in experiment C. These curves OA and OE are plotted from Table V, for m = 164 and m = 24. PEIRCE. — DEMAGNETIZING FACTORS OF CYLINDRICAL RODS. 63 > w 5 < II g CQ oooooooooooooccooooooccco cooxcoaoonoooocoooHHiQionooio C'^OTfO'l'NOX^^N^OcDOCOtDOONCOaiMtDin HHC)(MC0C0Mi0NONi0tDNN000000(»OiHH01(NN tq co co © co Cl©cOiO>COCCffiOt)ffiOOOCCOOOCO HHHT-tNCJ^OXOH^lONroOHN-HOOOl II g 03 COOOOOOOOOOOOCO © ©■HH©O©i-i©CiTtO00©"'*i©CD* CD CD © b- 00 CO i— It— 1 t-H t—i t— Ii- IHH C^ S3 C^COOOOOcDCiCNOOOcO©©©© lONO-HCOTt^N^OMMOOCO i-i 1— 1 T— 1 r}* II g 03 O© 0©©0©0©0©©C © © OOOOMON00OOlN*tD30 © rfit>oo©i-H(McoTtH»ocD©r^r^oo co tea r^t^c©©©iot^ ClcO'J'MiOiOOOOSO'HOOOO ior^oo©i^co©T-HcDco(M©co© © H H H CI (M Tfl LO N -H « T*l i—l i— 1 Tf IN rH II s 03 © © o © © © © © ©© © © o © © O^OOflOMCNMNCCO b- OiO»O©t^t^000000©©©©i-H'-H^H(M'O-'ICO S3 OCMiOOMCOOOOiO ©r^©co©^io©GC©cot^t^i-H>o©©©oio©0©© r-H(MCO»O»Ot^©t^'#00iM'*lCO»O©t^GC©CO©00'-HCO'#©iO'*1© rtrHi-iHiMN't00rtCxlC0'<) = lcT«, (1) where k and q are constants. For a single molecule of an ordinary gas the value of R is about 137 X 10-18. I assume that R for an electron has a very much smaller value than this at low temperatures. Whether any metal really satisfies the conditions indicated by (1) through any great range of temperature may well be doubted; but, 4 The "law of equipartion of energy," a law more familiar, perhaps, in the breach than in the observance, doubtless requires that electrons acting as gas particles among other gas particles of a different class shall attain the same mean translators energy as the latter, provided the two classes of particles remain distinct from each other in their encounters. But if electrons collide with metal atoms containing or made up of electrons, and if during a collision it frequently or usually happens that the electron enters an atom and stays there, displacing another electron, there seems to be no reason for supposing that the mean translatory energy of the free electrons will equal that of the atoms. 5 Let us, for one gram of electrons, write pv = R'T. Then, taking m as the mass per electron and c as the "velocity of mean square," we have p = $ mm2 = R'T + v = R'T mn. From these relations we get p = n{R'm)T = nRT, an expression which will be used frequently hereafter, and cy.(RT)l. This proportionality must replace in this paper the simpler relation, cxT1', which holds for an ordinary gas. This substitution is highly important. For example, if p of equation (1) is 1, so that Rs.T, we have cccT, and so §mc2. (2) When a metal is heated under ordinary conditions, — that is, at constant pressure with increase of volume, we have as the temperature coefficient of K = J*L 1 fdFA eft J_ fdF{\ ap KdT='' K\d8JTdT+ K\dTj6 h dF2 cl8 Jw-*pr~fih P /sw t n Tf„_, 0_3) /0, + R-l8-df'T +K'F2(-S){v-ip-i)Ti " ^ (3) 6 For example, see p. 303 of Tunzelmann's Electrical Theory. 7 See footnote, p. 69. HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 71 This quantity, as a whole, must have a negative value, if it is to accord with the experimentally known facts; but as to the signs of its separate terms there may be some question. It seems plain that the first term is negative and that the third term is positive. The second term, if there were no evidence to the contrary, I should take as positive, and at first I did so take it, believing that I had experimental ground, as well as a priori ground, for this belief. The experimental ground proved not to be good footing, and I am now inclined to the opinion that this term is negative, for reasons which will pres- ently appear. The fourth term evidently has the sign of its factor (v — ^ p — |). Now according to my discussion of the Thomson effect (see equations (15)— (21)) this factor is probably positive in many metals, and, as the third term of ap is obviously positive, we reach the conclusion that, in these metals at least, the negative value of the tem- perature coefficient ap cannot be accounted for if the electric conduc- tion within these metals is solely, or even mainly, by means of the (B) electrons. We are thus led to attach especial importance to the first term in the value of K, as given in equation (2), and to the first two terms in the values of ap, as given in equation (3) . 1 r)F In seeking further light on the term y? r-~, the sign of which has thus far been left in doubt, we naturally turn to such experiments as show the effect of increased pressure on the electric conductivity of metals. We have at command the data for calculating, in the case of several metals, approximately what the temperature coefficient of the conductivity would be if heating occurred with such increase of pressure as to keep the volume of the metal constant. If we call this coefficient av, and if we assume that we can find an expression for it by merely dropping from the value of ap the two terms which contain the factor dS-hdT, we have o, = ^~+~-F2(5)(v-ip-i)T^^. (3a) In liquid mercury, according to the experiments of Barus,8 the value of av is positive; but in the solid pure metals, so far as I know, it is negative and, though numerically less 9 than ap, not very much less. If, then, equation (3a) is a correct expression for av, it appears that the 1 dFi • term j? -^j, is negative, since the second term, as we have seen, is probably positive. 8 Bulletin of the U. S. Geol. Survey, No. 92 (1892), p. 75. 9 See the Appendix to this paper for discussion of this matter. 72 PROCEEDINGS OF THE AMERICAN ACADEMY. The Thermodynamic Point of View. The greater part of my argument from here on will lie in a thermo- dynamic treatment of thermoelectric action, and in the course of it I shall make free use of the fact, which I have pointed out in previous 10 papers, that the ordinary thermoelectric diagram, representing "thermoelectric heights" as functions of temperature, is in reality a temperature-entropy diagram. Following ordinary engineering prac- tice, I shall take the temperature coordinate as vertical and the en- tropy coordinate as extending horizontally toward the right. Putting aside for the present the consideration of part (A) of the electric current, I shall discuss part (B) at some length as if it existed alone, returning to the treatment of (A) later. Several years ago I discussed the analogy which exists between the cycle described by water in the circuit of a heating system, or in the circuit of a steam engine, and the cycle described by electricity in a thermoelectric circuit. The motion of the water in each of the cases referred to is, of course, due to heat, but heat alone would not main- tain circulation. The application or expenditure of the heat must be managed or maneuvered by agents which do none of the net work of the cycle. In the case of the steam engine this control is given by a system of valves or checks which permit movement in one direction but not in the other. In the heating system, valves and checks may be dispensed with, gravity exercising what in chemistry would be called the catalytic function of maintaining the desired action, circu- lation, at the expense of heat. In the thermoelectric circuit we must look for some agency to perform a like service. Thus, if we have a detached piece of copper with one end at temperature T and the other at a lower temperature T' , a state of equilibrium exists within it such that there is no electric flow along the metal; it is the same with a detached piece of iron wire having its ends at the same temperatures, T and T'; but, if we join the warm end of the copper to the warm end of the iron and the cold end of the copper to the cold end of the iron, we find that a current of electricity flows from copper to iron at one junction and from iron to copper at the other junction. It is quite evident that, if we had to do with electric potential only, in the ordi- nary sense of the term, either there would be no flow on bringing the wires into circuit or there would be flow in the same direction at both 10 For example, These Proceedings, 46, 649 (1911). HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 73 junctions. Let us therefore consider carefully what may be the nature of the equilibrium which exists in a detached piece of wire having a temperature gradient.. The Boltzmann Aerostatic Equation. I shall make use of the idea that each metal exercises a specific "intrinsic" attraction for electrons. Helmholtz long ago assumed such an attraction n for electricity in discussing the "double layer" at the surface between different substances. Several years since I made the suggestion that this attraction might be a function of the tempera- ture of the metal. More recently O. W. Richardson 12 has made use of the Boltzmann formula w "' = e-RT (4) in dealing with the forces exerted upon electrons by electrical charges or by the attracting metal atoms. In this formula "wi is the con- centration of the electrons at a point .4 and n2 that at a point B," and " W is the work done in taking an electron from .-1 to B and R is the gas constant in the equation pv = R9[— RT], reckoned for a single electron." I feel greatly indebted to Professor Richardson for his discussion of this matter, and when I took up the question now before us I expected to use his ideas and conclusions, except in so far as they might be modified by my assumption that R for an electron is less than R for a gas molecule. I have, however, upon close examination of the matter, been forced to the conclusion that, in applying formula (4) to a discussion of the Thomson effect, involving of course a difference of temperature between the two points .4 and B, he has fallen into error. Boltzmann gives the equivalent of the formula in question under the heading Aerostatilc,13 and it is very easily derived, as follows, for an atmosphere of uniform temperaturean equilibrium: II This at least is my interpretation of certain passages in his papers; for example, the following sentence from an article in the Monatsbericht d. k. Akad. d. Wiss. zu Berlin, Nov. 3, 1881, S. 951 : "Soil in einen Leiter, (lessen Potential (elektrostatisch gemessen) p und dessen galvanische Constante A- ist, ein neues Quantum Elektricitat dE eingefuhrt werden, so ist dazu die Arbeit (p~k) dE nothig." 12 Phil. Mag.; Vol. 23 (1912), pp. 263-278. 13 Gastheorie, Vol. I, § 19. 74 PROCEEDINGS OF THE AMERICAN ACADEMY. Let I = height above the earth's surface, p = density of the gas, p = pressure " " g — gravity acceleration, R'= gas constant for unit mass, T = absolute temperature. dp p Then — ln=9P = ^Wt> whence — = - Wj,^ and so log p = - ^,1 + log k, __£*_ or p = ke R'T, where k = pressure at the earth's surface. Then for any two points A and B, with pressures 2>i and p%. respec- tively, and molecular concentrations n\ and n2 respectively, we have ^ — — = e R'T = e R'T Pi n\ In this equation W is the work of lifting unit mass from h to ^ against the pull of gravity. If we wish to deal with a single molecule of mass m, we can write Z* = — = e R'mT = e RT Pi fh which is the Boltzman equation as used by Richardson. Thermoelectric Equilibrium in a Detached Wire (with consideration of (B) electrons only). In dealing with the free electrons in a metal unequally heated we have a case somewhat like the one just discussed but considerably more complicated. In place of g we must now put// the resultant of attractions and repulsions per gram of free electrons, this resultant being called positive when it is directed along the path of diminishing I, and we must consider /' as a variable. In place of R' for a gram of gas we must put R' for a gram of free electrons, and take R' as a varia- ble according to equation (1). Moreover T is now to be taken as a variable along /. We shall Avrite /? = dT -r- dl, and shall treat /3 as a variable. HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 75 Now in place of the equation — = — -jjrf dl we have p R'T R'$ T' But p = R'Tinn, and so dp _ dR' dn dT _ f dT ~p : : ~R ~w + ~f ~~ ~ W$ ' Y' dR' , dn ( f , AdT whence W + ^ = ~ (lTp+ 1JT> or, if we multiply both R' and /' by m, and so get R and / for a single electron, dR dn- ff \dT _ When we observe that /, /?, and i? are all variables, the integra- tion of this equation appears at first to present difficulties. But two of our fundamental assumptions, expressed in equation (1), give Rn = k Tq, where A- and q are constants, and the only wav to make 7/ this equation agree with equation (5) is to have the factor ( v*--. + 1 a constant. Thus we get by the integration of (5) Rn = JcT~(rp + 1) =1cT«, (6) and so n2 /r-M (7) In dealing with our detached piece of wire I shall use F to indicate virtual potential for a single electron, — that is, the total potential due to attractions and repulsions of electric charges together with the attractions of the metal atoms,1* as exerted on a single electron. If the distance I is measured from the cold end of the wire, we have * dF , a dT f dF J = Yj, ancl P = -JT> so tnat q = -Jf- (8) We have seen that equation (6) is a necessary consequence of equations (1) and (5). As (1) expresses merely certain fundamental 14 If the assumption of an attraction of the metal for the electrons, as a function of temperature, were omitted, the word virtual as applied to the potential would be omitted. 76 PROCEEDINGS OF THE AMERICAN ACADEMY. assumptions, our only question here is whether (5) is necessarily true. Examination shows that it involves the assumption, not explicitly made thus far, that the free electrons in unequally heated metal tend toward equality of gas-pressure, that the difference dp, between two isothermal planes differing by dT, must be balanced, if we are to have equilibrium, by the force /, applied to every free electron between the planes. This assumption, which implies that the free electrons tend to the condition n1R1Tl = n2R2T2, (9) where the subscripts (1) and (2) refer to any two parts of the metal, is by no means a matter of course when we are dealing with a gas permeating narrow passages where differences of temperature exist. It is well known that, if a thin partition pierced only by a very small hole separates two bodies of an ordinary gas, one at temperature T\, the other at temperature To, the condition of equilibrium between the two bodies of gas is not equality of pressure, but pvr-pz — Ti*S- T2* , or, since p\\ p2: : n\T\\ n2T2, »i7\* = n2T2K That is, there is a certain tendency of the gas from the cold chamber to the warm chamber, which must in the end be balanced by superior pressure in the warm chamber.15 Going to the case of electrons, for which we assume R to be a varia- ble, we have as the law of equilibrium under thermal effusion alone mWtf = n2(R2T2)K (90 16 or, since p = nRT, p cc (RT)K 15 Maxwell, toward the end of his memoir on Stresses in Rarefied Gases, says, "The passage of gases through porous plates, as was shown by Graham, is of an entirely different kind from the passage of gases through capillary tubes, and is more nearly analogous to the flow of a gas through a small hole in the thin plate. "\Yhen the diameter of the hole and the thickness of the plate are both small compared with the length of the free path of a molecule, then, as Sir William Thomson has shown, any molecule which comes up to the hole on either side will be in very little danger of encountering another molecule before it has got fairly through to the other side. "The finer the pores of a porous plate, and the rarer the gas which effuses through it, the more nearly does the passage of a gas through the plate corre- spond to what we have called effusion." etc. 16 For, another way of stating the condition of equilibrium in the case of thermal effusion is, that the momentum of the particles per cu. cm. shall be the same at one place as at another. If we take c as the "velocity of mean square," this condition gives riiCi = 112C2, and we have already seen, in the footnote on p. 69, that c v V. (15) If, on the other hand, we go through the argument regarding a from the point of view of thermal effusion, as expressed in (6'), where (/ + 13) = -RQ + 1. 82 PROCEEDINGS OF THE AMERICAN ACADEMY. and (3)-(3), and assuming that we have to do with free electrons, electrons (B), only, we should have to conclude that p is 1. To determine the algebraic sign of a we must look to the relative magni- tude of p and p. According to equation (15), p being 1, we have 0, if ^<3; >3. From (15') we should get 0, if v<4; a = 0, if v = 4; a<0, if i>>4. Turning back now to equation (2), and assuming that we have to do with (B) electrons only, we get as the specific conductivity Kb=kbFo(8)T^-^ + ^, where Fi (8) is a factor which increases with rise of temperature. Accordingly, Kb must increase with rise of temperature, unless "<2(p+1)> — that is, unless v< 1, if p= 1. But we have just seen that, in order for a metal to have a negative and proportional to T, v must be greater than 3, and so v — \{p + 1)>2, which will make Kb propor- tional to some power of T higher than the second. Metals commonly represented by straight lines on the thermoelectric diagram, with ) is the amount of poten- tial energy which an electron gains in being freed from an atom. Let$ = kvT*, where kv and -k are constants, hv being negative and ir 19 The (B) electrons may be regarded as individuals which have dropped out of the (A) class by going astray from the short path leading from one atom to the next atom. HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 85 probably so. Accordingly we get, as the total energy of our - electrons at temperature T of the metal, B~ljr(^T+r+*) + i(^T+r) (17) = I(| + X^RT+ l+\ (!_«)#. In looking for the amount of heat energy which is absorbed from the metal by our - electrons in their passage from T to T + dT through e the metal, we must remember that x is a variable, increasing, accord- ing to my assumption, with rise of temperature. We have (IE adT = jfdT, whence a = e [_2 If {RT) + df (XRI) + dT + dT ~ ^rr} (18) It may be well just here to inquire whether the (B) electrons, which we have found to be inadequate when taken alone, are needed at all, — whether the (A) electrons acting alone would serve our purpose. Let us accordingly assume, for the moment at least, that v and x are each equal to zero. That part of F which is dependent on the free electrons will also be zero in this case, while the other part of F, the part depending on the attraction of the atoms as a function of temperature, will be included in , provided (— <£) is now defined as the gain of potential energy of an electron in being taken from an atom in the metal to a point outside the metal. Accordingly we get from (18) a = I [jT (1 + p) T" + '^Tiw~ n] (19> The first term within the brackets is + , according to our assumption regarding R as a function of T. In the second term the factor h^ is — , as we have seen before, but the factor w is also — , if, as seems probable, $ diminishes numerically with rise of temperature. We seem, then, with (19) to have no provision for negative values of a, such as, we know, occur in metals. 86 PROCEEDINGS OF THE AMERICAN ACADEMY. Returning, then, to equation (18) and putting x=kxTK, (20) with kx and k as positive constants, we get e L 2 + t,Tf'-« kjcv (k + tt) r<« + *- « (21) If we take the point of view of thermal effusion, according to which dF 4- dT= - R (| + ^ + v), we get from (18) 1 a = - e kr {l + p-v)T»+ kxkr (1+K + p) Tl* + "> (210 + kvirT(« ~ 1) - ftjfe, (* + tt) T ^ + - ~ 1) • Neither equation (21) nor equation (21') would permit us to have a strictly proportional to T; but we are not sure that a is strictly proportional to T in any metal. If the terms beyond the first in the second member are small compared with this first term, we may have approximately straight lines on the thermo-electric diagram, — that is, have a nearly proportional to T, if p = 1. Moreover, the presence of (— v) in the coefficient of this first term provides for possible negative values of a, if the first term is really the dominating part of this quantity. Of the other terms, the second and third are positive, according to the assumptions already made, while the fourth may be negative, if tt, which is supposed negative, can be numerically greater than k. I shall assume, for the present at least, that kx is very small, thus making the second and fourth terms very small. To make kx small is to make x small, so that I am here assuming that the greater part of the electric conductivity is due to the (^1) electrons. This assumption accords well with what we know in regard to the temperature coefficient of conductivity. For even with equation (21) we cannot get a negative value of cr proportional to T, a condition approached very closely by several metals, without making p = 1 and v greater than 1, so that the K^ term in the value of the conductivity, equation (2), will still increase with rise of temper- ature. The Ka term in (2) must apparently he the prevailing term, at least so far as the temperature coefficient of conductivity is con- cerned, in some metals, if not in all. HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 87 It is to be observed that the very important part played by v in the equations (21) and (21') does not imply that n, the number of free electrons per cu. cm. of the metal, is so large as to be of the same order of magnitude as the number of atoms per cu. cm. The value of {dF -5- (IT), by way of which v gets into the equations in question, is not dependent upon the absolute value of n at any place, but upon the ratio of the n of one temperature to the n of another temperature. Thus it is possible for a comparatively small number of free electrons to have a great effect upon a, by way of the (A) electrons which are subject to the (dF -r dT) established by the (B) electrons. As to the term Ayr T(-w~ :) in equation (21) and (21'), although we are hardly at liberty to assume kv to be small in comparison with kr, t, which we suppose to be negative, may be small, and the factor T^~ 1) is less than T~l. It seems not unlikely, then, that this term is small compared with the Tp term. If we are satisfied that equations (21) and (21') accord in a general way with the known phenomena of the Thomson effect, we must next inquire whether either of these formulas will give a good quantitative account of the Thomson coefficient a as found by experiment in certain metals. Let us consider lead, with a = 0, very nearly; cobalt, with r» > or dn = dn n\ — no -ni — Ro ni — no Ri - Ri (24) (25) ni — no For equilibrium of condition of the slice in. question, the thickness of which we shall call dl, we must, if we disregard thermal effusion and assume that the free electrons, as a gas, tend to uniformity of pressure, have the difference between the electron gas-pressures at the two faces equal to the pull of the virtual potential gradient on all the free electrons in the slice. This consideration, with the reflection that p, the gas pressure of the electrons, is n R T, leads to the equation dp=T(^dl=-n(^dl, (26) dl dl whence dF= - TR— - TdR. (27) Substituting for R and dR from (24) and (25), we get dp =_2T Ri- R2 ^ _ f r _ Ri - RA dn^ ni — no \ iii — no J n 90 PROCEEDINGS OF THE AMERICAN ACADEMY. whence F2 - Fx = T R*m ~ Rm log * + 2T (R, - R2). (29) th — rii no If i?i is equal to R2, this reduces to the familiar form F2-Fl= RTlog -, or - = e «r the Boltzmann equation which we have called (4). The condition for gas-pressure equilibrium in case of thermal effusion, being p = (RT)1- X a constant, becomes now, in the iso- thermal bridge passing from M\ to M2, p = R* X a constant. If there were no electrical complication, the condition for equilibrium in this bridge would be d f p\ _ 1 dp p dR _ dl \&) " R~i~dl ~ 2ffi~dT '' ' or , p dR dp=2li' (See eq. (10)) The actual condition for equilibrium is , p dR dF „ dp-2li=-n~didl> whence, as p = nRT, we get Td{nR) T dF 1 ~ — dl= — ndR — n ^r dl, dl 2 dl (26') and so dF= - TR—-1 TdR. (27') n 2 Substituting for R and dR from (24) and (25) we get dF=-l T ^=*-» dn -T(fr- m) ^^ - (28') 2 Tli — 7*2 Wi — tl2 n whence p TR2ni-Rin2 n1+3 ni — w2 w2 2 This differs from (29), which was obtained without the hypothesis of 3 thermal effusion, only in having ^, instead of 2, as the coefficient of HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 91 the last term, from (29) If i?i = R2, this last term disappears and we have as F2 — Fi RTlog-. J n2 The difference of virtual potential expressed by equation (29) applies to the (A) electrons as well as to the (B) electrons; for it is to be remembered that, even when we have been dealing with a tem- perature gradient, the rate of change of F has depended not at all upon x, though the Thomson effect was found to be a function of x, as the Peltier effect doubtless will prove to be. The Peltier Effect: — Referring to equation (17) we see that, when e electrons pass reversibly at temperature T from A/\ to Mo, the gain of total energy of these electrons, which must be equal to the amount of heat energy absorbed by the electrons from the metals at the junc- tion, is 2e e e 3 + 2.n 2e e (1— a*)*i (30) Substituting for (F2-Fx) from equation (29), we get T Q = 1 >h . T R2ni — Ritio, H • - - log - e ni — n* n» + (1— .r2)*2 — (1— .n)$i (31) This is the Peltier effect heat at the junction of temperature T. With thermal effusion equation (30) would hold unchanged, but (31) would become Q=T (.r, R2 - xi R,) + - e e + 1 (l-a-2)$2-(l i?2 »i — Ri no ni — ?i2 - Xi) i (31') The Volta Effect: — It is evident that the equilibrium which we are discussing between two metals at their junction is of the mobile type, the superior gas-pressure of the electrons in one metal maintaining a movement of individual electrons from this metal to the other, while the superior "virtual potential" of the second metal has become great enough to maintain an equal movement of other individual electrons 92 PROCEEDINGS OF THE AMERICAN ACADEMY. from this metal back to the first, the case being pretty closely analo- gous to the equilibrium between a liquid and its saturated vapor. A still closer analogy, perhaps, is found in the equilibrium of an isother-' mal atmosphere over some part of the earth. Individual particles in the upper strata are falling toward the earth under the pull of gravity, but their places are taken by equally numerous molecules projected upward by heat energy from the denser layers below. The question now to be considered is, whether our "virtual" poten- tial-difference, (F2-F1) for the electromagnetic unit charge, is the e same thing as the Yolta potential-difference, which quantity has been the subject of a vast amount of arguing and experimenting for more than a century. In approaching this question let us write -(F2-F1) = 8V=8aV+8cV, (32) e where 8av is that part of - (i*W*i) which depends on the difference of specific attraction of the two metals for the electrons, and 8CV is the part which is due to the difference of electric charge of the two metal-;. To give my conception of the Yolta potential difference I shall describe an experiment which, if we could work with perfectly clean metals in a vacuum or in a gas absolutely inert, would be easy to carry out, but which, failing this exceedingly difficult condition, must be regarded as imaginary. In Figure 3 let M2 be a plate of metal connected with two quadrants gyu M* M. fyg.4. of an electrometer, E, and with a distant plate, Mi, of another metal, both Mi and the quadrants being grounded. For simplicity let us suppose that the quadrants and all connecting wires are of metal (2). There is, accordingly, no difference of potential between M2 and the quadrants in Figure 3, but the potential of M2 exceeds the potential of Mi by the amount, positive or negative, which we call 8V. HALL. — ELECTRIC CONDUCTIOX AND THERMOELECTRIC ACTION. 93 In Figure 4, M2, disconnected from the electrometer but still con- nected with the grounded A/\ by the wire ic2, is brought very near to Mi, so that the two act as the plates of a condenser. The difference of potential between them is still <5I\ but M2 now acquires a considerable charge, Q. The two plates are next disconnected, and M2 is then re- moved to its first position, out of range of the condenser action of Mi, and is connected with the quadrants, now insulated from the ground, as * in Figure 5. The charge Q dis- . tributes itself over Mo and the quad- /To r.5. rants, .but, as the capacity of this combination is much less than that of M2 when near Mu the potential now exceeds that of Mi by the amount AT = 8a I' + N 5C V, the value of N being greater the less the distance between M2 and Mi in Figure 4. If we assume, as we shall do for convenience here, that the capacity of the quadrants is negligible compared with the capacity of M2 by itself, we take the capacity of M2 when near Mh as in Figure 4, to be A7 times the capacity of M2 by itself. After grounding M2 and the quadrants for a moment, thus reducing their excess of potential over Mi to the original 5F, we bring Mo again to the same position as in Figure 4 and again connect it with Mi by means of wire of metal (2) ; but now through a part of this wire flows a H M, M, F,g.Z current, so that by a potentiometer arrangement, indicated in Figure 6, we can make the Mi end of the wire exceed the M2 end of it by a differ- ence of potential 8P. If we make 5P such that the difference of potential between M2 and Mi in Figure 6 is 8a V + (8C V 4- N), the charge on Mo will be precisely what it was after M2 and E were grounded from the condition shown in Figure 5; that is, when M2 is separated from Mi in Figure 6 and is afterward brought to the position and con- 94 PROCEEDINGS OF THE AMERICAN ACADEMY. nection of Figure 7, its potential excess above Mi will be 8V, just as it was before the last approach of the two plates. Now in Figure 6 the Mi end of the connecting wire, being of metal (2), is at potential 8V above M\. Accordingly we have whence 8 V — 8 P = 8a V + 8CV -8P= 8a V+ (8C V -^ N), N . „ (33) 8C V = N-l 8P As 8P is easily measured, and as N can be made large, we have here indicated a definite, even if not at present entirely practicable, method of measuring 8V. This is the Volta potential difference, chemical action excluded. It is evident that the experiments just described would not give the value of 8a V or even show whether such a difference of potential, due to differential attraction of the metals for the electrons, really exists. If it does not exist, if 8aV = 0, the Volta potential difference is our 1 {FrF0. e But, according to equation (30), - (F2-Fi) does not account for the e whole of the Peltier effect heat, so that, even if 8aV = 0, the Volta effect is not so related to the Peltier effect that the value of one can be inferred from the value of the other. Thcrmo-elcctromotivr-forcc of a Complete Circuit. A/WV^ — '-(T) Fig. 8 If we have a complete circuit of M\ and M2, we may think of its total, or net, electromo- tive force as measured by means of a potenti- ometer, and we may with advantage have this potentiometer ap- plied as in Figure 8,. having contact with M i only, an isothermal stretch of this metal being joined to M2 at the T' end. The measurement here suggested HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 95 is strictly analogous to measurement of the e. m. f. of a galvanic cell in open circuit. Our preceding discussion suggests two expressions for this net e.m.f. of the circuit. On the one hand, since we begin and end with the same metal, Mi, at the same temperature, 7", the difference of F between these two terminals must be independent of the specific attraction of Mi for the electrons, and must therefore represent the charge-difference of potential, the difference of potential in the ordi- nary sense, between the terminals. Accordingly we have for the open circuit of Fig. 8, B T E -if*- e ''Bmi~R^logr± + 2{Ri-B*) 7li — Tin, W2 > + 1-f>-(1 + rf-J (34) r e R'2n'i — R'm'i , n\ , , , . 7 log — 4- 2 (R i - R 2) n\ — n'2 " n-2 -(1 + r^KK1 + if> Equation (34'), from (16') and (29'), for the case of thermal effusion, would differ from (34) only in having, as the first term within the brackets containing v, | instead of 1, and in having f instead of 2 as the coefficient of the (R\-Ro) and (Ri'-R/). The other way of getting an expression for E is to integrate dQ from A to B in Figure 8, assuming now that a current, due to the thermo- electromotive-force, is flowing in the circuit, with sufficient resistance between A and B, at the low temperature part of the cycle, to absorb there practically all the work done by this current, the resistance of the rest of the circuit being negligible in comparison. But, if we perform this integration, we find that the expression obtained for E reduces to precisely what we already have in (34) or in (34'), as of course it should. If R were a constant and the same for both metals, and if vi were equal to v2, we should get from each of these equations E= [(T- T) Rlog-. (35) That is, E would be simply proportional to (T-T'); but in order that this relation may hold we must have the representative lines of the two metals, on the temperatuVe-entropy diagram, the same distance 96 PROCEEDINGS OF THE AMERICAN ACADEMY. apart at every temperature, which is equivalent to saying that the Thomson effect coefficients, 1? 1950° 1790?25 Lead 327° 1.92 1.032 675° 716° Mercury —39° 4.22 1 036 735° 236° Potassium 60° 1.61 1 024 174° 160° Rubidium 38° 1.37 1.023 109° 126° Sodium 98° 1.51 1.015 210° 171° Thallium 300° 1.90 1.043 780° 768° Tin 232° 2.15 1.027 700° 638° Zinc 420° 2.19 1.04? 800° 1220° In some cases tr and /„ were obtained by calculation, in others by a graphical process which is illustrated in Figures A and B. It is evident that the extrapolations indicated by the dotted extensions of the curves in these Figures are extremely hypothetical, and there was, perhaps, no good a priori ground for expect- ing that tr and /„ would prove to be even of the Fi$.A same order of magnitude. 0: c t 25 If Vl-h Vs = 1.03. 100 PROCEEDINGS OF THE AMERICAN ACADEMY. That they are, in many cases, pretty nearly the same appears to be a fact of some significance, though this significance may be at present obscure. In explanation of and apology for the very marked dis- agreement of these two hypothetical temperatures in the case of bismuth, and in illustration of the degree of precision needed in the data used, I will say that, if (Vi -f- V$) for bismuth were taken as 0.98, /„ would be — 235°; and if the ratio were taken as 0.99,f,wouldbel7°. Evi- dently the precise deter- mination of (Vi -¥• Vs) in a crystalline substance like bismuth is very difficult. In drawing curves like those of Figures A and B, I sometimes ignored the course of the curve for the solid just below the melting point, for the reason that for some metals there was a rapid change in the curvature here, as if the melting were already incipient. Although one can hardly study the table here given without being convinced that the change of volume in fusion is very closely connected with the change of resistance, and is in some large measure the cause of it, examination of the known phenomena of conduction in the solid state shows that we cannot account for changes of resistance by con- sideration of changes of volume only. For example, the following Table Y, the second, third and fourth columns of which are taken from an article by E. Griineisen,26 shows by comparison of the fourth and fifth columns that increase of volume is not a very important fac- tor in the increase of resistance which accompanies rise of tempera- ture at constant pressure in the metals here exhibited. 26 Bericht. d. Deutschen Physikalischen Gesellschaft, Heft 6, S. 198 (1913). HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 101 TABLE Y. For 0° C. Pure metals 1 2 3 4 5 v\dT Jp 1 Idv \ ~t>\dp) T cm.2/kg w\dT J P w\dpl 1 cm.-/kg w \dT J v Al. 70X10"8 133 X10"8 40X10"4 43X10"7 37.7X10"4 Ni. 40 " 56 " 60 " 16 " 59 Cu. 45 " 75 " 43 " 22 " 42 Ag. 54 " 90 " 40 " 39 " 37.7 " Cd. 90 " 210 " 40 " 100 " 35.7 Pt, 27 " 40 " 39 " 20 " 37.6 Au. 40 " 59 " 40 " 30 " 38 Pb. 88 " 210 42 150 " 35.7 " The method by which the numbers of column 5 are found may be shown by an example. We have for aluminium (1) Coef. of cubical expansion = 70 X 10-6. (2) " " compressibility = 133 X 10"8. .'.No. of atm. (cm2 kg) to keep v const, during 1° heating = 70 -T- 1.33 = 52.5. f3) Compression coef. of resistivity = 43 X 10~7. .". Decrease ( — dw/w) of resistivity caused by 52.5 atm. = 43 X 10-7 X 52.5 = 226 X 10-6. (4) Temp. coef. (p const.) of resistivity = 40 X 10~4. (5) Temp. coef. (v const.) of resistivity = 40 X 10-4 — 226 X 10-6 = 37.7 X 10-4. From the data given by Barus27 the following statement for liquid mercury is derived: 27 Bulletin of the U. S. Geol. Survey, No. 92, 74 (1892). 102 PROCEEDINGS OF THE AMERICAN ACADEMY. (1) (2) (3) (4) (5) 180 X 10-6 300 X 10-8 8 X 10-4 300 X 10"7 -10 X 10"4 The negative sign of the value of (5) indicates, as Bams points out, that in liquid mercury " the immediate electrical effect of rise of tem- perature, ... .is a decrement of specific resistance." Whether a like statement would hold true of other metals in the liquid state we have, so far as I am aware, insufficient data to deter- mine. Summary. 1. It is pointed out that thermal capacity of the electrons seems to be a necessary condition for thermoelectric action. 2. It is assumed that, through a considerable range of temperature, the number of free electrons per cu. cm. of a metal is represented by the formula n = kn T", where kn and v are constants, T being absolute temperature, and that R, of the equation pv = RT, "reckoned for a single electron," is represented by the formula R = krTp, where kr and p are constants, R being less, at ordinary temperatures, for an electron than for a gas molecule. 3. Electric conduction is supposed to be maintained in part by free electrons, (B), acting very much like gas molecules in the intera- tomic spaces of the metal, and hi part by other electrons, (A), which pass directly from atom to atom, perhaps during collisions, without taking part in the gas-pressure action of the (B) electrons. 4. Formulas are obtained for the specific conductivity and the Thomson effect coefficient of a metal, as these properties would be if dependent entirely on the free electrons; and it is found that these two expressions are either incompatible with each other or in disac- cord with observed facts. Argument leads to the conclusion that the free electrons are necessary for the phenomena of thermo-electric action but play an unimportant part in electric conduction. 5. Expressions are found for the Peltier effect and for the difference of "virtual" potential at the junction of two metals, virtual potential being due in part to electric charge and in part to the specific attraction of metals for the electrons. In this connection the Volta effect is discussed. 6. Inspection of the formula obtained for the net e.m.f. of a thermo- electric circuit shows this total to be dependent on the 7"s, n's, e's and p's of the system and not upon any specific attraction of metals for the electrons. HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 103 7. An Appendix gives data relative to change of volume and change of electric resistance in the melting of metals. It is a general, if not an invariable, rule that change of resistance in melting is of the same sign as change of volume. An attempt is made at a quantitative comparison of these two changes. 8. Attention is called to the fact, first pointed out by Barus, that in liquid mercury rise of temperature without change of volume would bring a decrease of resistance. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 5. — October, 1914. ON THE THEORY OF THE RECTILINEAR OSCILLATOR. By Edwix Bidwell Wilson. ON THE THEORY OF THE RECTILINEAR OSCILLATOR.1 By Edwin Bidwell Wilson. Introduction. Planck's rectilinear oscillator is of great importance in theoretical physics. To grant this it is not necessary to assert a belief in the physical existence of the oscillator, much less to assert Planck's belief in such existence. The Carnot engine may not exist; but the concept has proved so fruitful as to be fundamental in the general field of thermodynamics. The (perfect) semipermeable membrane may be a figment of the imagination; but, in special fields in thermo- dynamics, reasoning based on the membrane is of crucial impor- tance. And in that branch of thermodynamics which deals with radiant energy, the oscillator has held the position of cornerstone. Moreover, as in the case of the Carnot engine and semipermeable membrane, there does exist in physics a (more or less imperfect) prototype of the oscillator — the radiator or resonator of Hertz and his followers in radiotelegraph}-. In addition to the thermodynamic importance there is an interest attaching to the oscillator as the simplest model of the atom. Hypo- thetical models of the atom vary greatly; some are founded on statical configurations, others on dynamic equilibrium, some call for a number of corpuscles per atom comparable with the atomic weight, others for a number far greater than this, some represent the positive charge as widely spread out with the negative corpuscles imbedded in it, others concentrate the positive charge at a point. It is not neces- sary to take the oscillator very seriously as a model of an atom; all that is useful is to observe that by its means energy is absorbed and emitted and that thus it performs the functions of matter in establish- ing a temperature equilibrium in a closed field of radiant energy. The object of this article is to make some comments on the equation which defines the motion of the ^oscillator. These comments are obvious at first sight to any one who examines the differential equa- tions used in the theory of the oscillator, but as I cannot find them in the literature, I venture to print them at this late day. 1. The differential equations. Let us consider first some of the 1 Read to the Academy at its Stated Meeting, March 11, 1914. Received June 16, 1914. 108 PROCEEDINGS OF THE AMERICAN ACADEMY. prime facts or hypotheses underlying the analysis. These supposi- tions are as follows: 1°. The oscillator executes in the main a simple harmonic motion. This leads to the statement of the (approximate) equation i+««-ft • a) where x is the coordinate defining the state of the system. The basic reason for this assumption is that it is desirable for the oscillator in its function of emitter of energy to be as simple as possible, that is, to emit monochromatic radiation of a definite frequency; for our customary analysis resolves heterogeneous radiation into monochromatic elements. (If we wish to assume that the oscillator consists of a widely spread uniform positive charge at rest and of a concentrated negative charge vibrating to and fro through the center of the positive charge, we may obtain a model of the oscillator which satisfies the condition that the force on the moving particle shall be proportional to the displacement ; for if a particle moves within a uniform sphere and if the elemental attraction follows the Newtonian law, the resultant force is proportional to the distance of the particle from the center of the sphere.) 2°. The motion of the oscillator is not affected by frictional re- sistance. This leads to (or corresponds with) the omission of a possi- ble corrective term proportional to the velocity dx/dt in (1). Perhaps the best reason for omitting frictional terms is that there seems to be no necessity for complicating the mathematical equations or physical hypotheses by admitting friction. In the Hertz radiator there is frictional dissipation of energy due to the resistance of the circuit; in the idealised oscillator the resistance would naturally be omitted. 3°. The motion is damped by the emission of energy. If the form of (1) appropriate to the principle of energy be used, that is, the integrated form, the undamped motion would be characterized by the equation 'dx^ I)1***-' . - i dt>+™ = o, and the damping would then be inserted by a change to the form d (!)'+„_ c_2jr;M or — dt dx\2 = - 2F, (2) where F is the rate of radiation. WILSON. — RECTILINEAR OSCILLATOR THEORY. 109 The modification of the equation is thus based directly on the principle of energy. The form in which F is thrown depends some- what on the point of view. If the oscillator is considered as a Hertz dipol and the ordinary solution for the electromagnetic field set up by this radiator at large distances from its center is obtained, we find by the application of Poynting's theorem that a certain amount of energy is radiated off per period and, in particular, that the amount is proportional to the square of the acceleration. Then the equation, written for a com- plete integrated period T is / J to -*££-» where a(t0-\-(nJrl)T) — aito+nT) = 0. There is nothing at all to 2 Planck, Vorlesungcn iibcr die Theorie der Warmestrahlung, first edition, 110 (1906). Abraham, Theorie der Elektrizitat, second edition, 70 (1908). Rudenberg, Annalen der Physik, 25, 346-466 (190S). (In his second edition. Planck introduces the quantum hypothesis early and omits this derivation of the equation of the oscillator.) 110 PROCEEDINGS OF THE AMERICAN ACADEMY. suggest that the function a(t) has a negligible effect upon the motion. It therefore follows that (4) or the equation _ + jft. - „ _ = o, (5) obtained therefrom by discarding the factor dx/dt, is at best only approximate. Concerning the degree of approximation we may perhaps be willing to admit that the error is always extremely small ; but we should be very chary about admitting that the error is neces- sarily small relative to the terms retained. That (5) is only an approximate result is clearly brought out by Planck in his derivation, but the clearness is somewhat obscured by a footnote referring to Abraham's derivation in a manner which implies, though it does not state, that the latter proof is exact. Abra- ham gives in the first instance essentially the proof which we have given above. He goes on, however, to show by a discussion of the physical dimensions of the terms that the equation (5) is the only possible one. What he really proves is that under certain hy- potheses (5) is the only possible linear equation of the form (pxii» v div d¥+kx=^^W The physical dimensions are equally well satisfied by the non-linear equation dx It — 4- /'27- df + A X 12 ,\ 2 ( m) = °' (6) which follows naturally and immediately from (2), that is, from the principle of energy, provided it is assumed that the rate of radiation is proportional at each instant to the square of the acceleration, instead of merely proportional thereto when integrated over a complete period, and which would arise from the equation in integrated form, provided one were willing to apply to it directly the reasoning which is applied after an integration by parts. Lorentz has also derived (5) by a method which throws emphasis on the approximate nature of the result.3 That he regards the equa- tion with some suspicion may be inferred from his statement of ;i later date4: Eine Gleichung "die iibrigens den Mathematikern noch manche Frage darbote." 3 See, for example, his Theory of Electrons, 251, (1909). 4 Physikalische Zeitschrift, 11, 1250 (1910) It was this remark which so strengthened my own suspicions as to lead me to take up the question some time ago. WILSON. — RECTILINEAR OSCILLATOR THEORY. Ill The calculation of the instantaneous rate of radiation of energy from a moving electron, as contrasted with the integrated rate hitherto used, has been carried out by a number of authors in different ways. The rate is almost universally found proportional to the square of the acceleration when the square of the velocity is negligible relative to the square of the velocity of light.5 The mathematical statement of this result is contained in (6), and this equation therefore might more properly be taken as representative of the motion of the oscil- lator than the equation (5), — provided, of course, that we are willing to use the electron model of the oscillator. A comparison of (5) and (6) will throw some light on the legitimacy of the approximations used in deriving (5). The terms to be com- pared are dx d3x . (d2x\2 -^M and M [d¥ On the supposition that the oscillator executes in the main a simple harmonic motion, the signs of the two terms are the same. But the phases of the magnitudes are very different; for the first term is a maximum as the particle passes through the position of equilibrium and vanishes in the positions of extreme elongation, whereas the second term is a maximum in the extreme positions and vanishes in the position of equilibrium. The average magnitudes of the terms are the same, but it is difficult to see how two terms of equal average magnitude could be more different than these two in their effect upon the equation of motion. We shall now discuss the two forms (5) and (6), the first rather briefly, because it has been tolerably well treated, the second more in detail, because it seems to have been neglected. 2. Discussion of (5). As we have to deal with cubic equations and their (approximate) solutions, it is necessary to determine the order of magnitude of the coefficients and it is desirable to put the equations into their simplest form. If m is the mass of the vibrating particle, c the charge in electrostatic units, c the velocity of light, and if we adopt the customary coefficient for the radiation term, we have 5 For two different lines of deduction see J. J. Thomson, Electricity and Matter, chap. 3 (1904), and Wilson and Lewis, The Space-time Manifold of Relativity, These Proceedings, 48, 389-507 (1912), with especial reference to p. 480. A. Macdonald in his Electric Waves, 75 (1902), finds a steady rate of radiation from the oscillator. 112 PKOCEEDINGS OF THE AMERICAN ACADEMY. m dll + k2r\ _2td^-Q df-+kX 3c3tf*3-U or m dx dt — + k2x 2e2 + 3c (PxV dt2) 0. As numerical values we may assume e = 4.7 10-10, m = 9 lO"28, Hence c= 3 10 10 2 e2 = 6 10 -'.21 3 mc3 Substitute t = ar and choose a2F = 1 d2x dr2 + x-6k 10-24 Then d?x d? 0 and ~d2x , + 6M0-^Y=0. Now ft = 2tc/\, where X is the wave length. The observed range of X in the spectrum is from 10~5 to 3 10~2 with X about 5.5 10~5 in the center of the visible spectrum. The range for the coefficient of the last term in the equations is therefore from about 10~7 in the ultra- violet to about 4 10-u in the infra-red with 2 10-8 for the value near the middle of the range of visibility. The numerical forms of the equations are therefore d2x 5 + x d?x d? 0 and with dx dr 'd?x dr2 + x + K r/-.r dr2 = 0 (5') (6') 10-7 > k > 4 lO- ii or 2 10-8 the latter being taken as a sort of standard value. (It is not necessary to make the special assumptions involved in the electron model of the oscillator if we desire merely to determine the order of magnitude of k. If (5') be replaced by d2x dx -d?+KJr+X o, (7) WILSON. — RECTILINEAR OSCILLATOR THEORY. 113 which is nearly equivalent to it, since x and d2x/dt2 are nearly equal, the amplitude of the motion is seen to suffer a reduction in the ratio during n complete oscillations. We may now use experiments on the distinctness of interference fringes for different path-lengths to obtain an estimate for k, and we find that 2 1CH is an entirely reasonable value. See Abraham, loc. cit.) The complete solution of (5') will be of the form x= d eaT + c~0T (C2 cosyr -1- C3 shm), where a,—/? ±71 are the roots of the cubic r°- + r - k r3 = 0. The root a is positive and of great magnitude, approximately 1/k, say, | 108. As Planck says, this root has no physical significance.6 This means that for every determination of the constants C\, C,2 C3, the value of C\ must vanish and the solution of the equation reduce to x = p-/3r (C2 cosyt + C3 shvyr). It is certainly unfortunate that we are forced to discard so arbi- trarily one root of an equation which we have labored so carefully to establish. Moreover, as the solution of the equation now depends only on two constants, the elimination of these constants by differ- entiation will give an equation of the second order which accounts satisfactorily for the phenomenon as far as its mathematical side is concerned. This equation, which is almost identical with (7), con- tains a friction term, it is true, and is unsatisfactory physically be- cause of this fact. But there is no real reason for considering it as less satisfactory than (5') which has a physically meaningless root and which moreover, while ostensibly allowing for radiation on a physical basis, actually requires the rate of radiation to be maximum where there is a general agreement that it should be minimum, and minimum where it should be maximum. 3. Discussion of (6). We turn next to the equation (6') and, for the sake of brevity, write it as Kp+ vf+ vx= 0, (8) / and v designating respectively acceleration and velocity when the 6 If we make clear the assumption of the quasi-stationary state as a prelimi- nary condition in our approximations which lead to the equation, the large root is sure to be inadmissible by virtue of our assumption. 114 PROCEEDINGS OF THE AMERICAN ACADEMY. unit of time is the fraction \/(2irc) of the second. This equation differs very minutely from (5') or (7), but there is no reason to believe that the motion denned by the equation should resemble very closely the motion defined by those. As the integration of the non-linear equation of the second order is not simple, we shall first examine the equation to find certain elementary qualities of the solution. A. When the velocity vanishes, the acceleration also vanishes. B. When the acceleration vanishes, either the velocitv or the displacement vanishes. C. In the neutral position x = 0, either the acceleration vanishes or the acceleration and velocity satisfy the relation kj + v = 0. D. Arbitrarily assumed (initial) values of the acceleration and position determine the velocity, and similarly values of the accelera- tion and velocity determine the position, but assumed values of the velocity and position allow the acceleration either of two values j- v 1 ,— — Ik Ik E. Values of v and x which make v'2 — 4kvx negative are not ad- missible. Hence if x is positive, v must either exceed 4/a- or be nega- tive; and if x is negative, v must be positive or less than 4.kx (alge- braically) . F. The case of x positive and v greater than 4kx leads to a point d'arrM. For under these conditions / is negative, no matter which sign is taken before the radical, and the velocity must be decreasing as x increases; when v becomes equal to 4/cr, the acceleration becomes imaginary, and so does the motion. The same arises under the case of x negative and v less than 4/c.r. G. The case x positive and v negative also leads to a point d' arret. For under these conditions if the negative sign is taken with the radical, then / is negative and the magnitude of v is increasing as x diminishes toward zero, the particle will reach the origin with a definite velocity and pass through to the negative values of x where it falls under the case F; and if the positive sign is taken with the radical, so that / is positive, the particle is slowing down, and we have to consider two possibilities, first where the particle reaches the origin before its velocity vanishes and where the argument just given will then again be applicable, second where the particle comes to rest before reaching the origin only to start on again with a negative / and fall under the first supposition of this case G. A similar discussion may be given for the hypothesis x negative and v positive. (There WILSON. — RECTILINEAR OSCILLATOR THEORY. 115 is a special case in which the particle just comes to rest at the origin, remaining there in a sort of unstable equilibrium.) The consequences of this discussion of the second type of equation — the equation (6) founded on the radiation formula generally adopted — may be formulated in the unsatisfactory statement that, except for two special possibilities, the motion runs into a point d'arret where at a certain time and in a certain position, with a definite velocity and acceleration neither of which vanishes, the motion suddenly becomes imaginary. This is very disconcerting; it is at direct variance with our accepted notions of what happens in mechanical or electrodynamic systems. It is also a consequence that the oscillator governed by equation (6) cannot oscillate. Unfamiliar as this result may sound to those who have a feeling that a slight change in the differential equation introduces only a slight change in the motion, we must nevertheless admit the result and de- velop the contrary feeling that a slight change may entirely alter the type of motion. This fact has been brought out by Borel in a paper just printed 7 wherein it is shown that the equation ir + x2 = or 4- A/, no matter how small the constant X, does not define an oscillatory motion, nor does the motion approach the oscillatory type as X ap- proaches zero. Any one might admit that, in the course of a long time, \t would become important and the type of motion be changed; but this is not the true explanation, for, no matter how small the constant X, the motion departs from the simple harmonic type from the time t = r/2, that is, after executing a quarter oscillation. 4. The integrals of (6). We shall now turn to the integration of the equation The first thing we shall treat is motion from a position of rest. In 7 Borel, Annali di Matematica (3), 21, 225, (1913). The equation of Borel corresponds to a constant radiation of energy. The solutions of the equation do not exhibit the point d'arret, but are continuous. It has seemed to me, notwithstanding the publication of Borel's paper, and perhaps even on account of it, that the printing of my own results would be of interest. The comments on Borel's paper, which he prints as a footnote to a brief account of his results in his new book, Introduction Geom6trique a Quelques Theories Physiques, 107 (1914) appear less applicable to the results of our present work. 116 PROCEEDINGS OF THE AMERICAN ACADEMY. this case v and/ are both zero. Let us therefore assume a solution for a: as a series x = a(l 4- clt3 + 0r4 4- 7t5 + . . .) in r. The equations for the determination of the coefficients are 36a2/c 4- 3a = 0, 144a/3/c + 18a2 + 4/3 = 0, (144/32 + 240a7> + 60aj3 4- 5? = 0, . ., . Hence or a = 0, 0 = 0, 7 = 0,... 11 11 a=~TFT> 0=7Tr5>" 7= — 12k' ^ 64k2' ' 3840k3'' Thus one solution for x is .r = a, the particle remains at rest in the initial position, and the other solution is / t3 r4 llr5 \ X=aV1~l^+64K2-3840^+----> (9) the particle moves with an acceleration toward the origin, as was foreseen under G above. If this solution in series is valid, that is, if the series converges, it is at any rate of no value for purposes of calculation unless r is exceed- ingly small, that is, for intervals of time which are very small com- pared with the period of monochromatic light (r = 2ir). The value of the series is first to show how the motion starts and second to show that there is a possibility of motion, that is, that there is a solution of the equation other than the solution x — a with the given initial conditions. In discussing this question we shall follow the method given by Picard.8 Let the equation (6') of the second order be written as two simul- taneous equations of the first order, namely, ..^Y+.fe+.W £ — 0. do) Kdr ) \dr ' J dr These may be expressed in solved form as dx dv v 1 y- = v, -j- ' ^v2 — 4kvx. at (It 2k 2k The fundamental theorem on the existence of integrals fails for those 8 E. Heard, Traite d'Analyae, 3, chap. 3. WILSON. — RECTILINEAR OSCILLATOR THEORY. 117 values of the variables for which two values of the derivatives become equal. In this case the failure is when v2 — 4kvx = 0. This equation factors, and there are therefore two surfaces v = 0, v = 4kx in the space (v, x, t) which are singular in the sense that the funda- mental existence theorem fails. Of these surfaces one, namely, v = 0, satisfies the differential equa- tion (6') and is therefore singular also in the sense that it is the envelope of particular solutions. It is possible to put. the particular solutions in evidence. For let x be positive so that v <. 0. Intro- duce a new variable v = — z2 and let the sign of z be so chosen that 2 increases with r. We have then the equation n dz z2 — 2z^- = dr 2k Vz4 + 4:KZ2X. In cancelling the variable z the double sign goes out. For since / is decreasing with r (see G above) and since , dv - dz f = -T- = — 2z -r, dr cLt it follows that dz/dt is positive. We therefore have to integrate the equations dz z . 1 ,— dx . rfr = 4« + 4k V4K* + *2' dT=-Z~> with the initial conditions z = 0, x = a < 0, to obtain the particular solutions which are tangent to the singular solution v = 0. For these equations the existence theorems are applicable. As a solution exists, it must be (9) which we found by undetermined coefficients. The other singular solution v = 4/c.r is not singular in the sense that it is enveloped by particular solutions but in the sense that it is a cusp locus for particular solutions- (see Picard, loc. cit.). Without following Picard through the individual steps of the work we may write down the result. If vo and xo are two values satisfying the relation v = 4/c.r at r = to, the solution may be expanded into the form x = xo + a (r0 — r) + /3 (r0 — r)1 + y (to — t)2 + 8 (t0 — t)§ + . . . v = vo + a' (to - t) + p (to - t)* + y' (to - t)2 + 8' (r0 - t)= + . . . 118 PROCEEDINGS OF THE AMERICAN ACADEMY. Now let us take the case a-o>0, /o = — »o/2k. The constant /3 is zero, and x = Xo — v0 (t0 - t) — j- (to - r)2 + 8 (r0 — r)5 + , «o 4k 5 8 = «o + ;T.(to-t) + ^ S(r0-r)' + ... The value of 5, which does not vanish, may readily be found, if desired. This solution brings out the fact very clearly that the motion runs into a point d'arret. The curve, to be sure, has a cusp, but the expan- sion is in powers of VTo — r, which means that the time cannot exceed r0. If we could imagine that time satisfies the same possibilities of reversal of direction as space, we could interpret this cuspidal motion, but as time can flow only in one direction, the motion must be inter- preted as having a point d'arret. This does not mean that the two parts of the geometric locus cannot be interpreted, but that they must be representative of two different motions terminating in the same point d'arret. We may indeed trace the motion back from the point d'arret along the two branches. We have v 1 , J = — ^r =*= n~ "v^2 — 4jcVX. 2k Ik The acceleration is negative for both signs before the radical; x has increased up to .To at t = to and v has decreased to v0. In following the motion backward through time we find that x decreases and v X /A-) 1 T -a (+)/ Figure 1. increases. For the motion with the positive sign before the radical the retardation is less than for the motion with the negative sign. Hence in going backward, the former motion gives larger values of x WILSON. — RECTILINEAR OSCILLATOR THEORY. 119 and smaller values of v than the latter motion for the same value of to — t. When the (+) motion passed the origin, the acceleration was zero; when the (— ) motion passed the origin, the acceleration was negative and twice as large as at the cusp. The (+) motion may be traced back to a point where the particle comes to rest for a certain negative value of x; this corresponds to the solution (9), and the motion may be traced still further back, the velocity and retardation increasing all the while. The (— ) motion may likewise be traced back through the origin x = 0, the velocity and retardation increasing. The curve which shows roughly the relation between x and r is given in Figure 1. If we call the curve which corresponds to the posi- tive sign x — « 0; but the acceleration becomes imaginary when — vr3 — 4k, and the motion has a point d'arret. Motion away from the center does not have this peculiarity. The real interest of our work lies, however, not in the critique of current "demonstrations," nor in a tour de force integration of a 12 See, for instance, J. Fleming, Principles of Electric Wave Telegraphy, chaps. 3, 5 (1906). 13 J. J. Thomson, On the Structure of the Atom, Phil. Mag. (6) 26, pp. 792- 799, Oct. 1913. WILSON. — RECTILINEAR OSCILLATOR THEORY. 127 certain differential equation, nor in pointing out that the integration of the equation leads to a physical point d'arret, but in the general inferences or alternative inferential possibilities of importance to physical science which the discovery of the point d'arret may suggest. It is clear that we shall not have to abandon the statement of physi- cal problems in terms of differential equations possessing mathemati- cally continuous solutions in order to introduce into physics discontinu- ities even more startling than those introduced by the adherents of cur- rent theories of quanta. The statement of simple cases of rectilinear motion in equations of the second degree and second order has led to cusps in the space-time locus and, by virtue of the irreversibility of time, to physical discontinuities. (Such a conclusion could hardly be drawn from Borel's work, for his equation led to no point d'arret.) If we regard the existence of the point d'arret as inconceivable, we must look about for a method of doing away with it. One possi- bility is to accept literally the method of calculation employed by J. J. Thomson as cited above, namely, to regard the motion of the electric charge as determined by an ordinary equation of mechanics, which omits altogether the reaction of the radiation, and to compute the radiation subsequently. This would mean that the radiant energy did not come out of the field or motion (potential and kinetic energy) of the system but was a phenomenon inherently arising when charges moved. 14 This would be a shock to those who have implicit confidence in the conservation of energy as now generally understood, but would, not perhaps be so serious to those who take the position of Ritz15: La localisation de l'energie doit done etre comptee au nombre des con- ceptions logiquement inutiles (et peut-etre parfois nuisibles) de la theorie . . . Dans le cas le plus general du rayonnement eleetromagne- tique, la conservation de l'energie n'est plus une loi, mais une con- vention. Another method of escape would be to deny the accuracy of the law that the radiation is proportional at each instant to the square of the acceleration. The law is indeed only an approximation to the general form given by Abraham and Heaviside (with the apparent assumption of the quasi-stationary state) and proved by Lewis and me (on the basis of the principle of relativity) to be rigorously true for the point electron moving with any velocity and acceleration,16 — for with the 14 This may remotely suggest Bateman's double-barreled gun in his Corpus- cular Radiation, Phil. Mag. (6) 26, pp. 579-585, Oct. 1913. 15 Gesammelte Werke, pp. 343, 345. 16 Wilson and Lewis, loc. cit., (5). 128 PROCEEDINGS OF THE AMERICAN ACADEMY. usual definitions of field and energy the law becomes merely a geometric theorem in four dimensional non-Euclidean geometry. It is reason- able, however, to suppose that the use of the general form of the law could not remove the difficulty; for the point d'arret arises under conditions of relatively minimal velocity. Moreover, a qualitative discussion of the equation which arises under the general law indicates17 that the difficulty is not removed. It is tolerably clear that we cannot avoid the point d'arret and main- tain simultaneously the point electron, ordinary mechanics, and ordi- nary electromagnetic theory. This conclusion may be welcome to the school that follows Bohr in abandoning both mechanics and electro- magnetic theory18 as hitherto understood even when transformed as suggested by the principle of relativity. And we certainly do not wish to imply that this abandon may not work out satisfactorily. The conservative, however, will naturally try to work out of the present difficulty by abandoning the point electron, especially as elec- trons are generally supposed to have magnitude. It is a bit hard to see why the assumption of a very small finite size for the electron must fundamentally vitiate the reasoning which leads to the law of the square of the acceleration; but we shall not go into this question, because we are not acquainted with any derivation of this law which does not in some form practically assume the electron to be a point. Moreover, the work of Lorentz and Ritz, starting with a distributed electron and introducing approximations based on the assumption of small velocities and accelerations, establishes a reaction proportional to the rate of change of the acceleration and thus leads on mechanical principles to a law of radiation (at any rate to a loss of mechanical energy) propor- tional to the (scalar) product of the velocity and rate of change of accele- ration. And it is interesting to note that this reaction and rate of change of energy is actually independent of the size or shape assumed for the electron, that is, may be assumed to hold for the point electron. Howeverso apologetic one may be in regard to (16), that equation seems somewhat less in need of apologies than (15) or its derivation from (15) in integrated form. Massachusetts Institute of Technology, Boston, Mass, May, 1914. 17 Just what assumptions in non-Newtonian mechanics should be made to treat this problem it is perhaps difficult to state, and consequently the question is here left as a qualitative judgment of the author. 18 N. Bohr, Phil. Mag., (6) 26 (1913) a series of three articles On the Constitu- tion of Atoms and Molecules, pp. 1, 476, 857. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. G. — January, 1915. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. PLANCK'S RADIATION FORMULA AND THE CLASSICAL ELEC TROD YNA MICS. By David L. Webster. Investigations on Light and Heat published with Aid from the Romford Fund. CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY. PLANCK'S RADIATION FORMULA AND THE CLASSICAL ELECTRODYNAMICS. By David L. Webster. Presented by G. W. Pierce. Received, December 1, 1914. Introduction. As Poincare : has pointed out, Planck's formula for black body radiation, or any other formula giving only a finite amount of energy per unit volume in the radiation field, involves the assumption of some discontinuities in the process of absorption and emission. Thus Planck assumes that while an oscillator may absorb energy continuously, it may radiate only when the energy is an integral multiple of h v, and that if it does then radiate, all its energy is radiated at once. This assumption, being inconsistent with the classical electrodyna- mics, involves the abandonment of the explanations that the classical system gives of many phenomena. Its explanation of inertia, for example, depends directly on the theorem that every part of an ac- celerated electron will radiate electric forces proportional to its accel- eration, and that these forces, acting on other parts of the electron, produce the force of inertia, proportional and opposite to the acceler- ation. This explanation must be abandoned if we make Planck's assumptions, which deny the existence of these forces in most cases. Likewise, according to the retarded potential theorem, the classical explanations of all phenomena of the propagation of light through matter may be put entirely on the basis of continuous re-radiation from vibrating electrons, whose energy in many cases never reaches the value h i>, because the amplitude of a forced vibration is so small unless the frequency is near that of resonance. Although light phe- nomena other than scattering are not ordinarily treated in this way, any method derived from the classical field equations must necessarily be equivalent to any other, and any assumptions that make one of these methods give wrong results must necessarily do the same for all. Therefore, if Planck's assumptions are true, all such explanations must be abandoned, and we must create a whole new theory of optics. 1 Journal de Physique, (5) 2, p. 1 (1912). 132 PROCEEDINGS OF THE AMERICAN ACADEMY. It might be supposed that we could remedy this defect by assuming the existence of two classes of oscillators, the first obeying the classical laws and the second obeying Planck's assumptions, and in that way account for both optical and thermal phenomena. This hypothesis, however, does not seem tenable. For although the classical oscillators would do their best to account for other light phenomena, they would tend to give Rayleigh and Jeans's radiation law (which any system obeying the classical dyna- mics must give) rather than Planck's. Or, in terms of Planck's deri- vation, their entropy, computed from the thermodynamic probability, would be different from that of his Oscillators because their distribu- tion on the energy diagram would be different. Hence the radiation law would be different also, if any noticeable percentage of these oscillators were present. Moreover, Jeans's law, which they would tend to make the radiation obey, gives an intensity whose ratio to Planck's becomes infinite rapidly as XT diminishes. Thus an ex- tremely small percentage of classical oscillators would give large devi- ations from Planck's law, while the Planck oscillators would not give the well known relations between absorption and dispersion, and other optical laws that are explained by the classical theory. Moreover, unless the percentage of each class of oscillators for each frequency were exactly the same for every substance at each tempera- ture the distribution of energy in the spectrum of a cavity would depend on the substances contained in its walls. Such a result is well known to be contrary to the second law of thermodynamics. As Planck 2 says, the assumptions he makes are not the only ones that can lead to his law of radiation. The object of the present investigation is therefore to see whether the abandonment of the classical electrodynamics and its explanations of these and other phenomena is really necessary, and if it is not so, to find a mechanism giving both heat radiation and optical phenomena, and at the same time consistent with other phenomena as far as possible. The con- clusion is that it is not necessary, and that the formula can equally well be derived from other assumptions, inconsistent with the classical mechanics only as applied to the internal structure of the electron, and consistent with the classical electrodynamics and its explanations of many phenomena; and, moreover, this explanation is based on a mechanism which has been shown by Parson 3 to be very useful in 2 "Heat Radiation," English translation by Masius, 154 (1914). 3 Not yet published. webster. — planck's radiatiox formula. 133 explaining chemical affinities, and which has other advantages over Planck's oscillator and most other models of the quantum. Planck's Assumptions. The basis of the derivation of Planck's formula is Boltzmann's relation between entropy and probably, which Planck puts in the form S = k log IF where S is the entropy and k is the gas constant reckoned for a single molecule, and IP is the "prob- abilitv," considered as the number of ways in which the svstem can be arranged so as to be indistinguishable from its present form. In applying this law to a system of similar molecular oscillators, two arrangements are considered indistinguishable if they give equal num- bers of oscillators in each of certain groups, any group, the nth, being- defined by the condition that the energy of every oscillator in it must lie between (n — 1) h v, and n h v. For this rule to be a real criterion of indistinguishability, we must have the density of their representative points of the energy scale constant through each one of these inter- vals and changing abruptly on going from one interval to the next. These assumptions, as Planck shows, give for the mean energy of the oscillators in the nth group the value f n — - J h v. By setting the entropy equal to its maximum value consistent with a given total energy, he finds for the probability that a given oscillator will be in the nth group the value w„ = 017" where a = r-= ^-f— and 2 t, — J\ h v 2 E — N h v „ . 7 = 9 pi at l~ ' E being the total energy of N oscillators.4 Now to obtain a law of distribution of energy in the black body spectrum, it is necessary to have some law of emission and absorption for the oscillators. To keep in touch with the classical electrodyna- mics, he assumes that an oscillator absorbs energy as that system would require if one might neglect reradiation entirely; but to ob- tain the discontinuities required, he assumed, not the classical law of emission, but that the oscillator can emit only when the representative point reaches the boundary of one of these intervals, and that, if it does emit, it must emit its whole energy, n h v. With these assumptions, he proves that the energy of such an oscillator, exposed to radiation of continuously distributed frequencies, will increase at a constant rate, thus insuring the constancy of the density of points in each interval ; and he obtains the proper reduction of their density from one interval to the next by assuming that the 4 Planck, 1. c, § 139. 134 PROCEEDINGS OF THE AMERICAN ACADEMY. probability tj that the oscillator will emit when its energy reaches the 1 77 value n h v is given by the formula - - = pi, where p is a constant, V and / is the intensity of the electric vibration per unit interval of frequency. That is, the stronger the light, the more likely the oscilla- tor is to go on accumulating energy. The value of p is obtained by setting the mean energy thus found approximately equal, for ex- tremely large values of /, to the value it would have if the oscillator radiated as demanded by the classical theory. This is a new assump- tion, independent of the previous ones, and based on the experimental fact the Rayleigh's law of radiation is true for large values of X T. The next step is to identify the distribution of points thus found with that obtained above from entropy considerations, and thus find / in terms of v and T, and from I the energy density per unit frequency interval, 8tt^3 1 u c3 kT -. — 1 Assumptions of the Present Theory. The starting point of the present theory is Parson's magneton, a ring of negative electricity of a diameter perhaps xV that of a hydrogen atom, revolving on its axis with a velocity of the order of that of light. This has been proposed by Parson as a substitute for the classical electron, and has given good results in the explanation of chemical affinities. These magnetons are supposed by Parson to be free to move in a sphere of continuously distributed positive electricity, in which, as he shows, they have a strong tendency to group themselves in eights, thus giving the foundation of the periodic table of the elements. A detailed discussion of their groupings and the surprising way in which they explain not only the table, but also the exceptions to its rules, and many other chemical phenomena, will be found in his paper. Inquiring into what may be expected of the vibrations of the mag- neton, we find a state of affairs somewhat more complex than in the classical electron theory. For we have not only the attraction of the positive electricity through which it moves, and the electrostatic repulsions of the other magnetons, both tending to make its equili- brium stable, but also the magnetic attractions of the others, tending to make it less stable, and perhaps still other repulsions by them, proportional to some inverse power of the distance higher than the second, and therefore having a strong tendency to promote stability. The combined effect must, of course, be a stable equilibrium. WEBSTFR. — PI ANCK'S RADIATION FORMULA. 135 Moreover, as possible modes of vibration, we have not only a rigid displacement of the magneton as a whole, but also a disturbance of the flow of electricity around it, that may give electrical oscillations. These may be thought of as superposed on the continuous flow just as they would be in the case of a large ring of wire, heavily charged with negative electricity and at the same time carrying a current around the ring and performing electrical oscillations which may dis- place the centre of charge to any point in its plane. The displacement of the center of mass of the magneton during these oscillations might be anything, depending on how the charge was distributed and on what changes of thickness of the ring might be caused by the changes in distribution of its charge. We shall assume here, purely for con- venience, that the center of charge and the center of mass move together. We shall also assume that any number of these waves may be superposed without disturbing one another, except by electro- static action, as in the case of the ring of wire. Let us now consider a magneton whose geometric center is dis- placed in the plane of the ring by a distance £', and whose center of charge and mass is displaced relative to the ring by a distance £", or in all a distance £ = £' + (•". We shall divide the intra-atomic forces acting on it into the following five classes : (1) The resultant of the attraction of the positive electricity through which it moves and the repulsions of the other magnetons, equal to — /£, and acting on the electricity itself, rather than on the rest of the structure; (2) The resultant of the magnetic attractions and all non-electro- static repulsions between them, equal to — /'£' and applied to the structure of the ring; (3) The internal forces of the magneton, giving a force — /"|" on the electricity and +/"£" on the ring; (4) The force of inertia,— m — -} due to radiations caused by the at- acceleration of the electricity, and acting on it; 2 e2 d3 £ (5) The damping force + - -= — f due to radiation, equal for o c* dr d£ simple harmonic motions depending on sin wt to — g -j where g=3?"- d£" (6) Another damping force — g" ~~ due to an assumed tendency (76 136 PR< CEEDINGS OF THE AMERICAN ACADEMY. of the internal mechanism of the magneton to transfer energy from the oscillation of the electricity on it to the steady current around it. /, /', and /" are assumed to be constant, and we shall assume the equilibrium of the ring under the action of (2) to be so stable that for visible and ultraviolet frequencies, the motion of the center of charge is due chiefly to the oscillation of the electricity on the ring, and very little to the motion of the ring as a whole. In the infra-red, the motion of the atom itself will, of course, change the whole character of the oscillation. This plan does not agree entirely with Parson's assumptions, which make the magnetons interchange their positions in the atom rather freely; but I doubt if this is a serious difficulty, since even with these assumptions, a strong collision, with its accompanying distortion of the positive sphere, might easily cause considerable changes in their arrangement. The damping force (6) is contrary to the laws of the classical mechan- ics as applied to the internal structure of the magneton. But this conflicts with no experimental facts, and, as we have seen, we must expect a violation of these laws somewhere in the absorbing and emit- ting system. The mechanism of this transfer cannot be ordinary electromagnetic induction, because simple considerations of symmetry show that the mutual inductance between these oscillations and the steady current is zero. The energy transferred from the oscillations, according to these assumptions and others to be made below, will be found very small compared to the whole magnetic energy of the magneton, which is of the order of magnitude of mc2. (This value will be discussed in more detail in a subsequent paper showing why we cannot expect the magnetic properties of the magneton to be detected by experiments on cathode rays or photo-electrons.) Therefore the increase in the veloc- ity of the steady current that is given by this energy must be very small compared with the original velocity, and so will not interfere with the explanation of chemical phenomena by the magnetons. Neglecting the electrostatic influence of neighboring molecules, we may say that all the above forces on the electricity must balance, and so must all those on the ring. This gives the equations, (1) -fS-f' £" -ml-gk- f k" + rEf = 0 (2) - r r + r r = o. Combining these, we obtain webster. — planck's radiation formula. 137 (3) m I + | g + f/+/f, , } £ + { f + f/+^, } £ = « K, This equation, being of the standard form for forced harmonic motion with damping, shows at once that the classical theory of the propagation of light through matter is reproducible from this model. For, if the electric force is inclined obliquely to the plane of the mag- neton, the component in the direction perpendicular to this plane will produce practically no effect, on account of the immobility of the charge of the magneton in this direction. Other magnetons, being tipped in other directions, will supply the mobility that is lacking in the one we have considered. In the infra-red, where the vibrations of atoms as a whole begin to be of importance, we must superpose the motion of the sort con- sidered above on that of the atom itself. Since each atom has in general very little magnetic moment, it must have magnetons (espe- cially in the groups of eight) turned in all directions. Therefore some of them will always be vibrating with a motion of the center of charge relative to the ring. Their rates of absorption, however, cannot be found from this equation because in a solid or liquid the vibrations of the atoms as a whole will be governed chiefly by collisions with other molecules, while in a liquid or gas the rotation of the molecules will change the direction of the axis of vibration continually and thus prevent the accumulation of large amplitudes. Therefore the rates of absorption are much less than this equation would indicate, as soon as we get to frequencies such influences become noticeable. That this occurs to some extent even in the visible spectrum at ordi- nary temperatures is indicated by the readiness with which absorption of most visible light generally produces heat rather than other effects, such as photo-electric currents or chemical changes, and also by the well known widening of absorption lines by pressure. The fact that such influences may result in a transfer of a certain amount of energy from the vibrations to molecular motions rather than to the steady current of the magnetons, is, as we shall see, entirely immaterial for the derivation of Planck's law, since this derivation depends on con- siderations of probability that are unchanged by this transfer. Since each high frequency magneton exposed to radiation will execute a steady vibration, it must store up energy at a constant rate. Likewise at low frequencies, since the oscillations themselves are inde- pendent of the amount already stored, however much they may be affected by molecular motions, the rate of storing will, on the average, 138 PROCEEDINGS OF THE AMERICAN ACADEMY. be constant. This result, which is attained in Planck's theory by the prohibition of all re-radiation or external influences, is quite necessary for the derivation of his law. This accumulation of energy, moreover, must continue until the energy stored in the oscillator reaches some integral multiple of h v, so that even at the shortest wave lengths or lowest temperatures it must always be able to attain the value h v at least. At longer wave lengths or higher temperatures, the oscillator will accumulate many quanta. It is, therefore, important to see how this energy will affect its properties. If the oscillator is the classical electron,5 the energy must all be stored in its vibration, so that for an amplitude £o to hold a quantum, we must have the energy l , y , , h COO 2 ZTV or \ 2 7T m c This value, being proportional to VX, will be greatest for the longest waves for which the oscillator may safely be assumed to be an electron in a non-vibrating atom. Since the values of the Zeeman separations lead to this assumption certainly throughout the visible spectrum, we may apply this forumla for X = 8000 A finding £o = 3.1 A. Comparing this with the distance between carbon atoms in diamond, found by W. H. and W. L. Bragg 6 to be 1.52 A, we find that the length of the whole vibration would have to be over four times the diameter of the atom. This is another serious difficulty in the way of Planck's theory. For even if the oscillation consists of all the electrons in the atom mov- ing together, so that the amplitude required is reduced in proportion to the square root of their number, the distance which the group may go before some of them get outside the atom is also greatly reduced. Moreover if the positive sphere is not absolutely uniform in density, the distance they can go before the frequency of vibration is changed is even less. 5 Planck does not specify the charge or mass of the oscillator: this paragraph therefore starts with the most plausible assumption as to its nature. 6 Nature 91, 557 (1913). WEBSTER. — PLANCK'S RADIATION FORMULA. 139 If one could assume without conflict with measurements of the Zeeman effect that the atom itself takes an appreciable part in the motion at such frequencies, then the amplitude required for this energy would be less than what we have found. In this case, however, the electron would have to be able to distinguish carefully between the part of the atom's energy that it could include in the quantum and the part due to heat motions and vibrations with other frequencies. There is, furthermore, another difficulty caused by the fact that the transfer of energy to heat motion of the molecules would increase rapidly with the amplitude of the oscillator, so that the rate of increase of the vibratory energy would diminish, rather than remain constant as it must for Planck's law. These difficulties are all avoided by the magneton, because of its storing its energy in its steady current, and thus making the oscillation, as we have noted above, independent of the amount already stored. The smallness of the increase of the steady current that is required for this is evident from the fact that mc2, which gives the order of magnitude of the magnetic energy, is 7.9 X 10~7 erg, while even at lOOOA, where the oscillator practically never holds more than one quantum, the quantum is only 2 X 10~11 erg. Another point that is as necessary for the derivation of Planck's law as a satisfactory method of absorbing and storing the energy is a satisfactory law of emission. For this Planck assumes p. 153, "that the emission does not take place continuously, as does the absorption, but that it occurs only at certain definite times, suddenly, in pulses, and in particular we assume that the oscillator can emit only at the moment when its energy of vibration, U, is an integral multiple » of the quantum of energy, e = hv." Just how a sudden pulse can have a definite frequency is difficult to imagine, and is not stated in his book. The experimental facts, moreover, are against the assumption that the emission is absolutelv instantaneous. For Fabry and Buisson,7 have found that the path difference for interference observable in spectrum lines from the inert gases at low temperatures is often a very considerable fraction of a meter, and in the case of Krypton, with the tube immersed in liquid air, the path difference for wave length 5576 A is 53 cm. or 950000 wave lengths. These path differences, moreover, are given within the limits of experimental error by Schonrock's formula derived from the kinetic theory, on the assumption that the light of each oscillator is really monochromatic and that the width of 7 C. R. 154, 1224-7 (1912;, or J. de Phys. 2, 5, 442-64 (1912). 140 PROCEEDINGS OF THE AMERICAN ACADEMY. the line is due only to the Doppler effect. Thus we may conclude that in such cases, at least, the time required for an emission is really quite considerable, and that Planck's assumption of practically in- stantaneous emission must be abandoned. One way to evade this difficulty in the derivation of Planck's law is to assume that the radiation takes place at a constant rate until the whole energy, n h v, is emitted. This, however, is easier said than done; and one would be strongly tempted to look for some other radiation law, if Planck's had not been so well confirmed by direct experiments, not only those quoted in his book (p. 169) but also those published more recently by Coblentz,8 and indirectly by the appear- ance of his constant h is the laws of so many other phenomena, such as specific heats and photo-electric effects. This constant rate of radiation cannot be obtained by making the effect of the vibrating charge on the ether suddenly become some con- stant multiple of that which the classical theory would give, because it is well known that any such law would make the amplitude die out exponentially, rather than linearly, and approach a finite value, rather than zero. For the same reason, it cannot be obtained by having the absorbed energy stored as potential energy of an electron transferred from one equilibrium position in the atom to another, and re-emitted when the electron is jarred out of the latter position and falls back, with oscillations, into the former. Such models, moreover, would also be open to the objection to Planck's oscillator, that, to give a single quantum, they require too great an amplitude of vibration. Another serious difficulty for such models of the oscillator is the fact that an essential point in the derivation of the law is the assump- tion that an oscillator may acquire an amount of energy that is any integral multiple of the quantum before it radiates. This applies, for example, to Bohr's atom, in which the transition from one equili- brium position to another makes the electron give out just one quan- tum, and the transitions between all other such positions will give different frequencies. Still another point where such models are apt to be insufficient is in the explanation of photo-electric phenomena. For if, in the "lower" equilibrium, the electron is in a region of positive potential, and in the "higher" one it is either in such a region or removed to infinity, then, when it escapes from the higher position, it will either not leave the atom at all or else leave with an infinitesimal velocity. The only way 8 Bull. Bur. Stan., Jan. 15 (1914). webster. — planck's radiation formula. 141 for it to obtain the kinetic energy hv—W0 indicated by experiments such as those of Richardson and Compton 9 is to have the higher posi- tion in a region of negative electrostatic potential, that is, to have the electron vibrate toward a mass of negative electricity without being thrown to one side of the path by the repulsion. This seems distinctly difficult to accomplish, and I do not know that it has ever been done. To account for Planck's law and other experimental results, there- fore, we are driven to the unpredictable and unsatisfactory assumption that when the energy stored in the magneton reaches any integral multiple of h v, the internal mechanism of the ring may start another oscillation, larger than the absorbing one, and that this emitting oscillation will maintain a constant amplitude, deriving its energy in some way from the steady current-, until the excess energy stored in the magneton has been radiated, and its total energy is reduced to a standard amount. The probability 77 of starting to radiate at any particular multiple of h v is the same as in Planck's theory. To be sure that this mechanism is not, like Planck's, too big for the atom, we may calculate the amplitude of the emitting oscillation that is required to emit the energy faster than it is absorbed. Rewriting equation (3) in the more condensed form (4) >»£ + bk + k£ = eEk = cE0 cos wt where b and k are abbreviations for the coefficients in (3), we may evaluate the rate of absorption for the frequencv v = — as (5) R„ = eKi In using this equation (5) we are implicitly assuming that all the work done by the electric force goes into energy stored by the magneton, and we are therefore neglecting its extremely small re-radiation. Solving (4) for the case of a steady vibration, and substituting in (5), we obtain he2E02a>o2b R„ where co0 ' 'm J" m? (coo2"— co2)2 + &2co2 We may replace E02 now by Idv and integrate with respect to v to obtain the rate of storing energy by the magneton. In this integra- 9 Phil. Mag. 24, 575 (1912). 142 PROCEEDINGS OF THE AMERICAN ACADEMY. tion, w may be replaced by coo except in the expression (co02 — co2) 10. Performing the integration in this way, one obtains for the rate of absorption by vibrations in the £ direction only, the value (6) f'7=/^ v 4 m independent of coo or b. To see what amplitude is required to emit as fast as this, we may use the well known equation for the rate of emission, e2 1 4 t 2 i^co04|o2. For the limiting case, let us set this« equal to U and thus find the least permissible amplitude, £o- Thus 3c3/ ?o" — 4 m coo4 Inserting the value coo = 2itp and r 3 2 7T2 h v3 1 3c: 3 hv kT , e — 1 we have >_ 1 A 1 (6) / / \ \ < / f \ ' \ /B I ft \ \ / / \ \ / \ 1 A \ \ / 1 / \ 1 \ 1 \ 1 \ 1 V \ s / \ / / u "v. U 0 i j A UPERE TURNJ Figure 2. Magnetization curve, OBA, for the electromagnet J which at the outset is in a neutral state. Each horizontal division is 100 Ampere-turns and each vertical division is 100,000 Maxwells. The ordinates of the dotted curve represent the slopes of the magnetization curve, with each vertical division equal to 200 -. . - • M Ampere-turn Further Facts Regarding Electromagnet J. — We may add to the foregoing discussion, of the characteristics of the electromagnet J the results of a series of hysteresis cycles obtained some years ago. An outline of this magnet is shown in Figure 1. It weighs about 300 kilograms: the core has a square cross-section of 156 square centimeters area, and was built from varnished sheets of soft iron 156 PROCEEDINGS OF THE AMERICAN ACADEMY. about one third of a millimeter thick. The exciting coil consists of 1394 turns of well insulated copper wire. Figure 3. The ordinates of the boundary of the shaded area represent 104o,(:T) for E = 10, r = 1, and n = 100. The curve OPQ, shows the theoretical form of the corresponding current curve. TABLE III. T 104 fi ( T) X 0 0.151 0.000 50 0.324 0.123 100 0.605 0.336 150 1.477 0.790 200 2.629 1.887 250 3.519 3.477 300 3 . 710 4.612 400 3.467 8.157 500 3.042 11.404 600 2.800 14.318 700 2.727 17.058 800 3.085 19.884 900 4.370 23.489 950 7.800 26.279 PEIRCE. ESTABLISHMENT OF CURRENT IN COIL. 157 It is difficult to obtain an accurate hysteresis diagram for trans- formers containing massive iron cores, by the "step-by-step" ballistic method, with a short period galvanometer. Although, eddy currents may be nonexistent the time-lag of magnetization necessitates the use of a long period instrument, when ballistic methods are employed. The galvanometer used throughout these experiments was of the d' Arson val type, and had a period of about four minutes. The accuracy of the ballistic method was tested by comparing the results, thus obtained, of a corresponding hysteresis cycle for an excitation of MAXWELLS. 10,000 AMPERE TURN Figure 4. Hysteresis diagrams for the core of the electromagnet J. 1812 ampere turns, with a series of results reduced from oscillograph records. Throughout the comparison the agreement lay within a tenth of one per cent, and this may be considered close since it is not always possible to make a large mass of iron travel exactly the same magnetic journey twice. Computation of Current Growth on Reversal of E. M. F. — Figure 4 shows a series of hysteresis diagrams for the electromagnet J obtained by decreasing and reversing the exciting current step by step after maximum excitations of 1812, 5370, and 10880 ampere-turns. The results of measurements of the flux changes in the core for the 158 PROCEEDINGS OF THE AMERICAN ACADEMY. first of these cycles are given in Table IV. The next diagram, Figure 5, show's the slopes of the curve corresponding to Table IV, as a function of the strength of the exciting current. From equation (4) it will be seen that the march of current on reversal of e. m. f. may be obtained. If the slope for any point of the flux curve is multiplied by n2/l08 (E-ri), the result is the value of dt/di, for the reversed current curve, when the constant voltage E is applied to the exciting coil and reversed, where the coil consists of n turns of wire with resistance r ohms. Figure 5 exhibits dt/di for E = 19.5, r = 15, and n = 1394. UJ s r\ w \ / / 0 TENTH S OF A MPERE 3. Figure 5. If now the area X, underneath the curve, Figure 7, from z = 0 to x — i, for a number of different values of i, be measured in terms of the unit square of the figure; this area expresses the time required for the reverse current to attain the strength i. Table V contains a few values of X which were measured with a planimeter, and from which the desired reverse current curve, shown in Figure 7, was plotted. PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 159 di dt V A 1 ] \ \ \ / / / V 0 0 TENTHS OF AMPERES. Figure 8. The value of di/dt for a reverse current in the coil of the magnet J when i? = 19.5 and r = 15. Figure 7. The full curve, OP, shows the rate of increase of the flux of magnetic induction through the core of the magnet J while a reverse current of 1.3 amperes is being established in the exciting coil of 1394 turns. The current curve is shown on an arbitrary scale by the dotted line. 160 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE IV. Flux on Gradually Decreasing and Reversing Exciting Current. Ampere Turns Flux in Thousands of Maxwells Ampere Turns Flux in Thousands of Maxwells 1812 1371 -131 772 1394 1351 -148 734 1255 1340 -181 552 1031 1316 -234 332 809 1285 -294 22 474 1211 -392 -465 392 1186 -474 -661 294 1148 -809 -1010 234 1121 -1031 -1128 181 1099 -1255 -1214 148 1070 -1394 -1265 131 1060 -1821 -1371 000 953 TABLE V. i x/io i x/io 0.05 0.057 0.50 1.750 0.10 0.115 0.60 1.875 0.15 0.494 0.70 1.985 0.20 0.878 0.80 2.088 0.25 1.141 0.90 2.188 0.30 1.325 1.00 2.294 0.35 1.471 1.10 2.412 0.40 1.579 1.20 2.682 PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 161 PART II. SECONDARY CLOSED. Theory. — In an iron core built up of varnished sheets of metal there is usually a noticeable amount of magnetic leakage, but in a toroidal core made of one piece of varnished, very fine, soft iron wire, upon which two transformer coils are uniformly and closely wound, the leakage is generally negligible and we may assume with a close ap- proximation to the truth, that if the coils consist of wi and n2 turns respectively, and if the resistances of their circuits are n and r2, the excitation of the core in ampere turns is at any time, T = niii + Ttyk and if N is the flux of magnetic induction through the core, the corre- sponding fluxes through the two circuits are niN and n2N respectively. Let N be determined experimentally at many points of a journey from one magnetic state of the core to another by a given path, and let the results be plotted in the form of a curve, the unknown equation of which may be written in the form N = <& (T7). Let the slope of this curve be obtained at a large number of points so as to give the values of dN/dT or ^f {T) for many values of T, then it is possible to predict the form of a building up curve for a current in the exciting coil which will carry the core over a part, or the whole, of the magnetic path for which we know the values of N as a function of T. The current equations are wi dN ■ . . El-w'-dT = ri'll> (5) ih dN . . ~ 10* ' ~dt = r* ' * (6) whence Ein^ = n® • n ■ i\ — rii • r2 • U, (7) wi • r2 • T -f- W22 • Ex . *i = 9 i 2 » y°) ■Wi ' T\ ' T — Hi • U2 • Ei m2 • r2 + w22 • n rii dN dT ?n2 • r2 • Ex — nx • r, • r2 108 dt dt m2 • r2 + rtf • n (9) (10) 108 {ni2 • r2 • Ei — rii • rx ■ r2 ■ 1) 162 PROCEEDINGS OF THE AMERICAN ACADEMY. If now ft (T) be accurately plotted against T, the area under this curve from T\ to Ti is equal to the time in seconds which elapses while the excitation is growing from T\ to T2. If a large number of these areas be measured by aid of a planimeter, it is easy to give a graphical representation of T (and therefore of ii and i2) in terms of t, and we may expect the current curves thus obtained to correspond closely with the oscillograph records for the same case. If r2, r2, m, n\, and E\ are all increased in a given ratio X, the quantity ft ( T) and therefore, dt, will be increased in the same ratio. Application to Transformer with Fine Wire Core. — It will be instructive to apply the foregoing theory to a certain transformer (DN), in which magnetic leakage and eddy currents were negligible. This transformer was constructed in the form of a toroid, about 41 centimeters mean diameter, the core of which was made of about 25 kilograms of fine, soft, varnished iron wire. After the core of the transformer had been thoroughly demagnetized the magnetic flux through the core, due to an ascending series of steady currents in the exciting coil, was determined. The results of the long series of measurements, which were taken with a slow period ballistic galvanometer, are given in Table VI. The full curve, OK, Figure 8, reproduces the table graphically: one vertical unit corresponds to fifty thousand maxwells, and one horizontal unit to a thousand ampere- turns. The ordinates of the dotted curve exhibit, on an arbitrary scale, the corresponding slopes of the other. A few values of the slope,. dN/dT, are given in Table VII. From the foregoing theoretical discussion, and the numbers given in Tables VI and VII, it is always possible to predict under fixed condi- tions the growth of the excitation in the core, the march of the current in the primary and secondary coils, and the manner of increase of the flux of magnetic induction in the core of the transformer in question. It will be seen from equation (11), when E = 10, n2 = 1000, n\ = 100, r-i = 10, and n = 1, that if the slope of any point of the curve, OK, is multiplied by 11/104 (1000- T), the result is the value of ft (T) for the given value of T. A few values of ft (T) are shown in Table VIII. If now ft (T) be plotted as a function of T, and the area from T = 0 to T = T\, for a number of different values of T be measured in terms of the unit square of the figure, this area gives the time in seconds for the excitation in the core to attain the value T. The curve, VWSZ, bounding the shaded area (Fig. 9), reproduces the first two columns of Table VIII graphically; that is, ft (T) as a function of T. For convenience 104ft (T)/5 was taken as the vertical PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 163 unit, and 100 ampere-turns as the horizontal unit. In consideration of the units here chosen the growth of the excitation in the core (in ampere-turns) would be given by the equation JfTi U(T)dT o (12) Therefore, it is clear that the area, between the limits of T = 0 and T = jTi, divided by 20 gives the time in seconds for the excitation to grow from 0 to TV The third column of the table contains a number 1 1 i ! H 5 INDUCTION. K f 1 ! S j L < I j z i pi r- r- P • 200.000 1 (1 II - «| Up V 1 \ 50.000 1 \ ' / \ 0 20 DO AMPERE TURNS. Figure 8. Magnetization curve for the finely divided core of the trans- former (DN) which at the outset is in a neutral state. The dotted curve represents, on an arbitrary scale the slopes of the other. 164 PROCEEDINGS OF THE AMERICAN ACADEMY. of areas, found by mechanical integration, for different values of T and the next column the corresponding time in seconds which the excitation took to rise from 0 to T. The curve OBLP shows graphi- cally the increase of the excitation as a function of the time. TABLE VI. Flux of Magnetic Flux of Magnetic Ampere Turns Induction (JV) through the Core Ampere Turns Induction (N) through the Core in Hundreds of in Hundred^ of Maxwells Maxwells 23 10 600 2910 42 20 700 3032 87 50 800 3124 100 52 1000 3259 200 240 1200 3348 232 445 1400 3406 257 879 2000 3516 294 1520 2630 3602 300 1548 3000 3644 316 1733 3500 3690 400 2372 4160 3740 500 2736 TABLE VII. Ampere Turns (T) dN/dT Ampere Turns (T) dN/dT 000 35 600 142 100 76 700 103 200 510 800 79.4 220 700 1000 53.9 240 1742 1200 36.2 260 1670 1400 30.5 280 1338 1600 20.5 320 950 1800 18.7 360 748 2000 13.6 400 552 3000 10.9 500 251 4000 4.8 PE1RCE. — ESTABLISHMENT OF CURRENT IN COIL. 165 We may now determine the march of the current in the primary and the secondary coils of the transformer, for the given values of Ei, nh n2, n, and r2. Substituting in equations (21), and (22) we get. ii = T+ 104 1100 ' 103 «2 = 1100 (13> for any given T. Table VIII, columns five and six, contain values of ii, and i2 corresponding to the value of T which is given in the first column. Figure 10: the curve PRH shows graphically the march of z o < o X LJ / / / z / w , L^ £. / 1 \ V / t i , —— 0 2( 0 4C 0 « )0 a 0 1 T WENTIE THS 0 " SECO NDS. Figure 9. The ordinates of boundary of the shaded area represent 10* £2 (T)/5, E = 10, m = 100, n2 = 1000, r, = 1, and r2 = 10, the abscissas correspond to 100T. The curve OLP shows the manner of growth of the excitation in the core of the transformer (DN), as a function of the time. the current in the primary coil; and the curve SEC, bounding the shaded area at the bottom of the figure, the manner of decay of the current i2 in the secondary. It will be seen from the figure that i\, the current in the primary, builds up very rapidly at the start, but before reaching its maximum value it remains for a comparatively long time almost exactly parallel to the time axis. During this time the indication of an amperemeter in the circuit does not change per- ceptibly, and yet the flux of magnetic induction through the core is increasing at a very nearly constant rate. The shaded area, bounded by the curve PRH and its asymptote KD, which is a measure of the 166 PROCEEDINGS OF THE AMERICAN ACADEMY. induction flux, is constantly growing. If the core of a transformer is very large the building-up time may be a minute or more, and the phenomenon may then become very striking. The curve ONM (Fig. 10) represents graphically the flux of mag- netic induction through the core as a function of the time. One vertical unit of the figure corresponds to thirty thousand maxwells, and one horizontal unit to a twentieth of a second. A hysteresis diagram for the transformer under investigation is shown in Figure 11. The cycle corresponds to a maximum excitation TABLE VIII. Ampere Turns io4fi(r) Area t ii i. 00 0.385 0.000 000 9.092 -0.909 50 0.550 0.037 0.002 9.136 -0.864 100 0.929 0.123 0.006 9.182 -0.818 150 2.700 0.268 0.013 9.230 -0.773 200 7.013 0.692 0.035 9.273 -0.727 230 15.500 1.232 0.062 9.301 -0.700 250 26.300 2.169 0.108 9.320 -0.682 270 22.500 4.093 0.205 9.338 -0.664 300 17.950 5.313 0.266 9.365 -0.636 350 13 . 100 6.866 0.343 9.411 -0.591 400 10.120 7.988 0.399 9.458 -0.545 500 5.522 9.444 0.472 9.547 -0.454 600 3.905 10.297 0.515 9.636 -0.363 700 3.777 11.037 0.552 9.727 -0.273 800 4.367 11.814 0.596 9.800 -0.182 900 7.095 12.886 0.644 9.910 -0.091 950 12.980 13.786 0.689 9.957 -0.045 980 30.300 14.933 0.747 of 4200 ampere-turns, and the results of measurements of the flux changes in the core for this cycle are given in Table IX. From what has been explained already, and the data given here one can predict with accuracy the characteristics of the core, and the current curves for this transformer, for any practical case within the limits of the above excitation. PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 167 Figure 10. Transformer (DN): The curves, PRH and SEC, deduced from theoretical considerations, indicate the march of the current in the primary and secondary coils respectively. The increase of the flux of magnetic induction, through the core, with the time is shown by the curve ONM. s X < aofi 000 K/ 1 1 000 p B 0 2000 AMPERE TURNS. 4000 A J IPigture 11. Hysteresis diagram for the core of the transformer (DN). 168 PROCEEDINGS OF THE AMERICAN ACADEMY. TABLE IX. Flux of Magnetic In- Flux of Magnetic In- Ampere Turns duction through the Core .in Hundreds of Ampere Turns duction through the Core in Hundreds of Maxwells Maxwells (Up) 1410 +3406 000 -3380 2190 +3580 203 -3241 3310 +3670 238 -2938 4200 +3750 262 -2321 (Down) 303 + 866 4000 +3730 317 + 1276 3500 +3698 339 -1700 3000 +3667 360 +2030 2500 +3635 386 +2248 2000 +3603 422 +2482 1500 +3571 502 +2752 1000 +3531 685 +3048 500 +3482 1050 +3282 000 +3380 It is evident from the foregoing discussion that if eddy currents are nonexistent in the core of a transformer, a fair approximation to the form which the characteristic curves will have under any given cir- cumstances can be made if one has an accurate statical hysteresis diagram of the core for the range required. That is, one can predict with accuracy the form of the current curves, the growth of excitation and flux of magnetic induction in the core of a good transformer. Harvard University, Cambridge, Mass. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 8. — February, 1915. CONTRIBUTIONS FROM THE T. JEFFERSON COOLIDGE, JR., CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF PRASEODY- MIUM. THE ANALYSIS OF PRASEODYMIUM CHLORIDE. By Gregory Paul Baxter and Olus Jesse Stewart. CONTRIBUTIONS FROM THE T. JEFFERSON COOLIDGE, JR., CHEMICAL LABORATORY OF HARVARD COLLEGE. A REVISION OF THE ATOMIC WEIGHT OF PRASEODY- MIUM. THE ANALYSIS OF PRASEODYMIUM CHLORIDE. By Gregory Paul Baxter and Olus Jesse Stewart. Presented January 13, 1915. Received December 29, 1914. CONTENTS. Page. Introduction 171 The Purification of the Praseodymium Material 174 The Purity of the Praseodymium Material 177 The Absorption Spectrum of Solutions of Praseodymium Salts . . 179 The Preparation of Praseodymium Chloride 180 The Purification of Silver and Reagents 181 The Drying of Praseodymium Chloride 182 The Method of Analysis 189 Results and Discussion 191 Introduction. Not many years ago the atomic weight of neodymium was investi- gated in this laboratory by the analysis of the anhydrous chloride.1 Since considerable success was met both in preparing pure material and with the analytical method employed, the twin element praseo- dymium was investigated in a similar fashion ; for, from the results of the earlier investigations upon praseodymium, it can readily be seen the value of its atomic weight is far from certain. After Auer von Welsbach 2 first separated the old didymium, he determined the atomic weights of the constituents by Pmnsen's method of converting oxide to sulphate. Apparently the results were 1 Proc. Amer. Acad., 46, 213 (1911); Jour. Amer. Chem. Soc, 33, 1; Zeit. anorg. Chem., 70, 1. 2 Sitzungsb. Akad. Wiss. Wien, 92, 317 (1885). 172 PROCEEDINGS OF THE AMERICAN ACADEMY. interchanged in publication, as Brauner has suggested, for the lower value 140.8 was assigned to neodymium. Next Brauner,3 in 1898, starting with material purified by Shapleigh by crystallization of the double ammonium nitrate, continued the process of crystallizing this salt until neodymium was completely eliminated, then removed a trace of lanthanum by fusion with potas- sium nitrate, extraction of the praseodymium oxide with ammonium nitrate, and fractionation with ammonia and oxalic acid. By both the analysis of the oxalate and synthesis of the sulphate thirteen results were obtained between 140.84 and 141.19, with an average of 140.95. Jones,4 in the same year, further purified double ammonium nitrate furnished by the Welsbach Light Company by crystallization until the neodymium content was about 0.06 percent, as determined by comparison with neodymium solutions of known concentration. Cerium was removed by the basic nitrate process, and traces of lan- thanum by further crystallization of the double ammonium nitrate. Spectroscopically only a trace of lanthanum and no cerium could be detected. The oxalate was converted to trioxide by ignition in air and then in hydrogen, and after being weighed the oxide was converted to sulphate. Twelve determinations between 140.38 and 140.54 give an average of 140.46. Scheele 5 also purified material first by crystallization of the double ammonium nitrate, next by extracting the black oxide with ammonium nitrate, and then by precipitation of the oxalate. In a final series of determinations oxalate was converted to trioxide in a current of hydrogen, and the oxide in turn to sulphate. From the ratio of tri- oxide to sulphate five values between 140.48 and 140.61 resulted. In 1901 Brauner 6 confirmed his earlier work by four different methods, using similarly purified material. By igniting weighed quantities of octahydrated sulphate to the black oxide and correcting for the oxidizing power of the oxide as determined iodimetrically, he obtained from the ratio Pr203 : P^SO^ 8 H20 two results, 141.13 and 141.04. Weighed amounts of carefully dehydrated sulphate were then converted to oxide in the same way, yielding the values 140.96 and 140.94. Air-dried oxalate was weighed and ignited, and 3 Proc. Chem. Soc, (1898) 70. 4 Am. Chem. Jour., 20, 345 (1898). 5 Zeit. anorg. Chem., 17, 310 (1898). 6 Proc. Chem. Soc. (1901) 65; Abegg, Handb. d. anorg. Chem., 3 (1) 263 (1906). BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 173 the oxidizing power of the oxide was determined. Other weighed portions of oxalate were oxidized with permanganate. The ratio Pr203 : 3C2O3 gave the average result 140.98. Finally, weighed amounts of oxalate, the praseodymium content of which had been found as above, were ignited to black oxide and this in turn to trioxide in hydro- gen. The trioxide was changed to sulphate by solution in nitric acid and evaporation with sulphuric acid. Excess of acid retained by the salt was found by titration. In eight experiments the ratio Pr203: Pr^SO^ yielded an average value 140.96. The mean of the four methods is 140.97, which is essentially identical with the result of Brauner's earlier work. Auer von Welsbach 7 next published the results of three determina- tions by the Bunsen method, without details, 140.64, 140.50, 140.56, average 140.57. Finally Feit and Przibylla 8 purified praseodymium material from neodymium by crystallization of the double magnesium nitrate, and from lanthanum by crystallization of the nitrate from nitric acid solution. The higher oxide, prepared by ignition of the oxalate, was dissolved in standard sulphuric acid and the oxygen evolved was measured, as well as the excess of sulphuric acid. The oxygen evolved was subtracted from the weight of the black oxide before computing the atomic weight from the relation of trioxide to sulphuric acid used. The average result of three experiments is 140.54. Thus it can be seen that while the investigations of Jones, Scheele, von Welsbach, and Feit and Przibylla indicate a value for the atomic weight of praseodymium between 140.5 and 140.6, that of Brauner, which was carried out with equal or greater care, and with material of undoubted purity, points to a value at least as high as 140.9. The International Committee upon Atomic Weights has chosen the lower figure, and recommends the value 140.6. The various difficulties likely to be met in carrying out the methods used in the earlier determinations have been many times discussed, and a resume of the situation is given in the paper by Baxter and Chapin on the atomic weight of neodymium.9 It is worth pointing out that in addition to the dangers there mentioned, methods involving the use of praseodymium oxide are subject to error from the tendency of this substance to form a higher oxide of somewhat uncertain com- 7 Sitsungsb. Akad. Wiss. Wien, 112, 1037 (1903). 8 Zeit. anorg. Chem., 50, 258 (1906). 9 Loc. cit. 174 PROCEEDINGS OF THE AMERICAN ACADEMY. position. While ignition in hydrogen causes reduction to the trioxide, yet it is not easy to make certain that no higher oxide is retained in the lower one. On the other hand the analysis of the anhydrous chloride served so satisfactorily with neodymium that it seemed worth while to apply the same method to praseodymium. The results amply justi- fied our expectations. The Purification of the Praseodymium Material. Through the great kindness of Dr. H. S. Miner of the Welsbach Light Co., Gloucester City, N. J., we were fortunate enough to secure as a starting point about 10 kilograms of praseodymium ammonium nitrate containing about 50 per cent, of the corresponding lanthanum and cerium salts as well as a small proportion of neodymium. Since one of the most rapid and effective methods of freeing praseodymium from the closely related elements, lanthanum, cerium, neodymium, and samarium, is the fractional crystallization of the above salt, this method of purification was chosen. According to Auer von Welsbach,10 the bases separate in the order, lanthanum, cerium, praseodymium, neodymium, samarium, terbium and yttrium earths. The salt was crystallized in the usual way, that is, a concentrated, hot solution containing a small amount of nitric acid was allowed to cool and deposit the excess of salt, a period of 24 hours being allowed to secure equilibrium between the crystals and liquid. The separation of crystals and liquid was not completed by centrifugal drainage, be- cause the labor and time involved in this operation are not repaid by any considerable increased speed of purification. The details of the crystallization are shown in the diagrams on pages 175 and 176. In any given series of crystallizations a lower number always indicates a less soluble fraction. A line not connecting an end fraction with any fraction in a subsequent series indicates rejection. This crystal- lization was begun by Mr. W. H. Whitcomb, continued by Mr. B. W. Grimes and Mr. C. C. Wallace and completed by Mr. Stewart. In the early part of the crystallization it became obvious that the original material consisted largely of the lanthanum salt, the least soluble fraction quickly becoming essentially colorless. At the same time the neodymium absorption bands, which were readily visible in the original material, rapidly strengthened in the extreme mother liquor. When this mother liquor was reduced to a volume of about 20 cc, fraction 63, its absorption spectrum was examined visually in 10 Sitzungsb. Akad. Wiss. Wien, 112, 1043 (1903). BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 175 a Hilger wave length spectroscope. The only absorption bands which could be detected were those of praseodymium and neodymium. No sign of any of the samarium bands could be seen. Photography of the SEKIC3 A ' li V K ei ei Sf et m ' si X *i ?e H '<¥ .'* X '°i • g/m *r ** T a tl I ,-• it /*J N 'i 4 ' >H V XXX ^ ,*>. 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From the diagrams it can be seen that the number of fractions rapidly increased from the outset to a fairly se/ves MO 1807 8. 9, 10 II 1832 >J j(( 35 M> 1. _ y '^f7. /* s&. ,b^ ** p\ ,m *f ps. „**, ,*>7 &8 *? >v ,?/, .. ves* "si p* es ,*i> 6? bb 09 St? pi 9\ 93 94 9$ '$6, 97, } isoe V to //, /i '13 iZ yS fb\ ■- /l9Jk 35 3«j i? >e '-1 /&S9 60 '«/ '" •VAT9 60 '«/ 6< 6$ 64 65 "6(i '»«i h,s &> 597 fta a? )o a/ p. NCODYMtUM, E TCr* J2 IJ IV IS 16 n J8 19 £0 21 22 23 2.4 2S 2$ 27 29 29 30 183/ 7 38 '39 4b '41 fix, 43 44 45 filb *7 4J) 49 So Si Si 's\t si> JJr IBS* '-'■ 74 ?s 7$ 7i *e >9 f&ise/ & M_fi\ ,2, e\_& ,J-_."I&. ~'907 ay*' fi3 fit fit fifi. *>7 >*> M ?A 7'. M 7j r* _7s /* xi 7a 7s. eo ei si e,« si sj at, 7obt\ /roes a ■ po ,3. V df> 7 K ^» V« » i/>^ N '*W /*. -,J /*. /* '8. /». „•*« .■*'. 24. M >* .rr^* (»? fi* ?» 30 ^' 3* 33 39 35 36 >> 2/38 2133 flO, .•" .42 43 ?* ,43 ,-3* .-37 4$ 49 SO » S3 5,J >0 ,5.5 ,56 5"7 SB 59 60 67 6J 6$ W6A S**/^- -*** *« ^e «? ?o w 7^ ?j ?« ?J" 7* *? 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V 2/ 22 23 24 25 2b >/ . = . ■- dn j. d< di u ^t d^ ^i .i._ iu 'w "^jA W ■>i «i £/(? 2/5 constant number between 20 and 25. In series 174 a spectroscopic examination of the more soluble fractions showed that fraction 3478 contained a very small quantity of neodymium, the absorption band at BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 177 520 being faintly visible. The proportion of neodymium in this frac- tion we estimate to be at least as small as 0.05 percent. In fraction 3476 the same neodymium band could scarcely be detected. At this point fraction 3474 was removed for analysis, since it seemed likely that this fraction was as pure as any in the series 174. The fractions 3475-3480 were rejected. Fractional crystallization was then con- tinued in a similar way with the remaining fractions, except that while the extreme crystal fractions were occasionally rejected to re- move cerium and lanthanum, no fractions were rejected from the more soluble end. When the extreme fraction at this end became very small, it was set aside to be added to a subsequent similar one, and the fractionation then continued. After 41 more series of crystalliza- tions the process was discontinued because very careful spectroscopic examination of the extreme mother liquor, fraction 4383, in saturated solution with a 10 cm. layer showed no sign of the neodymium absorp- tion band X 520. The quantitative examination of selected fractions was then undertaken. Those chosen were 3474, 4383, 4381, 4379, 4377, 4374, 4371 and 4368. Since the less soluble fractions beyond 4368 were believed to contain cerium, they were rejected. In fact, an analysis of fraction 4368 showed it to contain about 0.4 of one percent of this element, a proportion, however, which is hardly per- ceptible in the atomic weight. The Purity of the Fractions of Praseodymium Material. The purity of the fractions in the final series was determined as follows: In neither fraction 3474 nor the more soluble fractions of the last series, 4383 and 4381, could any of the neodymium absorption lines be detected, either visually with a Hilger wave length spectro- scope or by photography with a Hilger quartz spectrograph of the Fery type. With the latter instrument photographs were made with various depths of solution and with widely varying exposures, but the results were less satisfactory than the visual ones. In order to find out what proportion of neodymium could be detected in praseodymium material, measured portions of a standard solution of neodymium ammonium nitrate were added to weighed portions of the double ammonium nitrate of fraction 4367, which was as free from neody- mium as any. By using concentrated solutions and a 10 cm. layer it was found that 0.05 percent of neodymium could be detected with ease through the absorption band X 520, and it was evident that the sensi- 178 PROCEEDINGS OF THE AMERICAN ACADEMY. tiveness of the method could have been increased still further if necessary. Since even 0.05 percent of neodymium would raise the atomic weight of praseodymium by only 0.002 unit, it is obvious that the purity of the material so far as neodymium is concerned is amply sufficient. Attempts were made also to detect neodymium by means of the spark spectrum between copper electrodes with the quartz specto- graph, but the absence of strong neodymium emission lines at points in the praseodymium spectrum which are comparatively free from lines prevents this method from being at all satisfactory. At the other end of the series the detection of cerium was under- taken. Since lanthanum ammonium nitrate is even less soluble than the corresponding cerium salt, the absence of cerium in the praseo- dymium material is sufficient proof of the absence of lanthanum also. In the spark spectrum of cerium fortunately there is a strong line of wave length 306 located at a point in the praseodymium spectrum which is comparatively free from lines. By photographing the spec- trum of the spark, between copper electrodes, of praseodymium mate- rial originally free from cerium (fraction 4380) but diluted with known percentages of cerium, it was found that the limit of detection of cerium in this way lay between 0.5 and 1.0 percent. Assuming the atomic weights of cerium and praseodymium to be 140.3 and 140.9 respectively, one percent of cerium, if in the trivalent condition, would lower the atomic weight of praseodymium by 0.006 unit. Such a difference is difficult to detect by the method which we are using for the determination of the atomic weight of praseodymium. Upon photographing the spark spectra of the extreme fractions 4361, 4364 and 4368 (the most impure analyzed), it was found by comparison that the first fraction of the three was rich in cerium, the second con- tained much less, and fraction 4368 contained no more at any rate than 1 percent. Because of the uncertainty in estimating proportions of impurity from the intensity of the spectrum lines, fractions 4365, 4368, and 4371 were further tested for cerium as follows: The solution was precipitated with an excess of sodium hydroxide and the precipitated hydroxides were washed several times. Carefully scrubbed chlorine gas was next passed into the solution in order to dissolve the prase- odymium hydroxide. The residual eerie hydroxide was dissolved and the process was repeated. The second residue was collected upon a filter paper, washed and ignited. Then the dissolved praseo- dymium was precipitated as oxalate and ignited to oxide which was BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 179 weighed. In this way fraction 4365 was found to contain 2.5 percent, fraction 4368, 0.4 percent and fraction 4371, 0.1 percent of cerium. Besides the small and unimportant percentage of cerium in fractions 4368 and 4371, which were analyzed, the rapid falling off of the cerium percentage is worth noting. The Absorption Spectrum of Praseodymium Chloride. The absorption spectrum of praseodymium chloride prepared from fraction 4181 was measured in the region of the visible spectrum by means of a Hilger wavelength spectroscope, provided with an extra dense prism and achromatic lenses. The accuracy of measurement with this spectroscope was not far from 0.1 h/j, even for the longer wavelengths. Of the four broad absorption bands shown by con- centrated solutions, only the one in the yellow visibly resolves into two narrower ones as the dilution increases. The wavelengths of the middle of each band at the lowest concentration at which it could be plainly seen are given below, together with observations by some other observers.11 Praseodymium nitrate was found to give an exactly similar absorption spectrum. Baxter and Stewart Aufrecht Auer Bohm (1914) (1904) (1903) (1902) 597 595.5 596 587 590.1 592-587 589.6 481.5 482.0 482^81 481.2 469 468.9 470.6^66.2 469.0 443.5 444.0 447.8-440.3 444.0 Photographs of the absorption spectrum also were taken with a Fery quartz spectrograph. When the source of illumination was a Nernst filament, no absorption bands beyond the visible region could be found with any exposure or any" concentration of solution. When the spark from " Nichrome" wire was employed, however, it was found that the light is completely cut off at from X 280 to X 270 according to the concentration of the solution, and that the solution is opaque up to the extreme limit of the spectrograms, about X 210. In these spectro- 11 Kayser, Handb. d. Spectr., Ill, 440. 180 PROCEEDINGS OF THE AMERICAN ACADEMY. grams there were noticeable at certain concentrations very faint minima of absorption in the middle of all three bands in the blue. These minima could be seen over a considerable range of concentration in all three cases but the particular concentration at which they were most marked was different for the three bands. Measurements were made of the position of these minima with a comparator and the cadmium spark spectrum as a standard, and the minima were found to coincide with the centres of the absorption bands observed with the most dilute solutions both visually and in the spectrograms. The ultraviolet absorption bands at 354 and 353 reported by Forsling 12 and the one at 346 given by Exner 13 correspond to strong absorption bands of neodymium. As we could not find the least trace of these bands in the spectrograms, it seems probable that they were produced by neodymium impurity. The Preparation of Praseodymium Chloride. Each fraction of double nitrate investigated was converted to chloride as follows: The salt was dissolved, and the solution, after dilution to about two liters, was filtered. A considerable quantity of nitric acid was added, the solution was heated to boiling and prase- odymium oxalate was precipitated by an excess of oxalic acid. After the precipitate had been thoroughly washed by decantation, it was collected upon a disk of filter paper in a large porcelain Gooch crucible, and dried in an electric oven at 105°. In order to change the oxalate to oxide it was heated to dull redness in a platinum boat in an elec- trically heated porcelain muffle. Care was taken that the temperature should not be high enough to vaporize platinum from the boat into the oxide.14 The black oxide was next dissolved in a quartz dish in a large excess of nitric acid which had been distilled through a quartz condenser, and the oxalate was reprecipitated from dilute solution by adding a solution of twice recrystallized ammonium oxalate. After thorough washing, the oxalate was collected, dried and ignited as be- fore. The chloride was now prepared by dissolving the oxide in a quartz dish in hydrochloric acid which had been distilled through quartz. Free chlorine was expelled by heating on an electric stove, 12 Kayser, loc. cit. 13 Ibid. 14 See Baxter and Chapin, Jour. Amer. Chem. Soc, 33, 16 (1911). BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 181 and the salt was crystallized three or four times from concentrated solution by "salting out" at 0° with hydrochloric acid gas made by boiling the fuming solution and conducting the gas to the solution through a quartz tube. The crystals were each time centrifugally drained and rinsed in platinum Gooch crucibles.15 The product was preserved in quartz in a vacuum desiccator over fused potassium hydroxide. The Purification of Silver and Reagents. The greater part of the silver used in this work was prepared by Mr. W. H. Whitcomb for an investigation upon the atomic weight of neodymium, which will be published shortly. No innovations were made in the processes of purification which have been frequently described in papers from the Harvard Laboratory. These processes were in brief as follows: Crude silver was dissolved in nitric acid, and the chloride precipitated with a large excess of hydrochloric acid. The precipitate, after being washed, was dissolved in ammonia and reprecipitated with nitric acid. Then the silver chloride was reduced with sodium hydroxide and sugar, and the metal was fused on charcoal before a blast lamp. The metallic buttons were cleansed by scouring and etching, dissolved in distilled nitric acid, and the metal repre- cipitated with ammonium formate made from distilled ammonia and formic acid. After thorough washing the product was again fused on the purest lime before a blast lamp. Electrolytic deposition, with silver nitrate as the electrolyte and with a dissolving anode of the pure silver buttons, followed and the electrolytic crystals were fused in a current of electrolytic hydrogen on a pure lime boat. Adhering lime was removed by etching with nitric acid, and the buttons were washed with water and ammonia, dried, and heated to about 500° in a vacuum. The silver was preserved over potassium hydroxide in a desiccator. In some of the later analyses the silver used had been purified exactly as described above by Mr. F. L. Grover for work upon the atomic weight of lead, or by Dr. H. C. Chapin for the investigation upon neodymium. In Analyses 1 and 2 silver nitrate was employed which had been freed from chloride by repeated crystallization. This material was 15 Baxter, Jour. Amer. Chem. Soc, 30, 286 (1908). 182 PROCEEDINGS OF THE AMERICAN ACADEMY. prepared by Dr. Grinnell Jones for work on the atomic weight of phosphorus.16 In the preparation of reagents the precautions usual in exact work were taken. The ordinary distilled water of the laboratory was twice redistilled, once from alkaline permanganate and once alone, through block-tin condensers. Hydrochloric and nitric acids were distilled through quartz condensers, in the case of the hydrochloric acid the first and last running being rejected, in the case of the nitric acid two distillations being carried out, the first third being rejected in each distillation. Nitric acid distilled in this way does not contain more than the merest trace of chlorine, if the original acid is nearly free from the latter element. Quartz or platinum utensils were employed wherever glass would have introduced objectionable impurities, and electrical heaters were used whenever the products of combustion of illuminating gas were to be avoided. In the crystallization of solids centrifugal drainage was always used to assist in the mechanical removal of mother liquor from crystals, except in the fractional crystallization of the praseo- dvmium material where it would have been of little assistance. The Drying of Praseodymium Chloride. The drying of the chloride for analysis was effected according to the recommendations of Matignon 17 and in very much the same way that neodymium chloride was dried by Baxter and Chapin, except that while the neodymium salt was not fused, and hence retained a trace of water, which was subsequently determined, the praseodymium chloride was rendered anhydrous by fusion. Bearing in mind the earlier experience with neodymium chloride, that the dehydration of the salt must be made as complete as possible before the actual fusion occurs, in order to prevent the formation of basic salt, the salt was caused to lose its crystal water by a process of efflorescence in a current of dry nitrogen and hydrochloric acid gases at gradually increasing temperatures. Richards 18 has pointed out that a hydrated salt may be freed from moisture much more effectively in this way than when melting is allowed to take place. We found the transition tem- 16 Proc. Amer. Acad., 45, 137 (1909); Jour. Amer. Chem. Soc, 31, 298. l7Compt. rend., 134, 427 (1902). 18 Zeit. physik. Chem., 46, 194 (1903). BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 183 perature of the heptahydrate 19 to be 1110 but when the salt is heated in a current of hydrochloric acid gas, the melting point is somewhat lowered. Therefore until a very considerable proportion of the water had been expelled, the temperature was kept below 100°. The temperature was then raised to about 165° where the last molecule of crystal water begins to evaporate, according to Matignon,20 and when the salt was essentially anhydrous it was gradually heated to about 350°. During the latter part of the heating only hydrochloric acid was passed through the tube. The aluminum block oven 21 which had been used for heating the salt up to this point was now replaced by a sleeve which could be heated electrically and the salt was first heated to dull redness for a few minutes and then quickly to its fusing point, which Matignon 22 states to be 818°. The platinum boat with the salt was placed in a quartz tube which formed part of the "bottling apparatus" 23 containing the weighing bottle with its stopper in which the boat originally had been weighed, and the bottling apparatus was connected with systems for the pro- duction of pure dry hydrochloric acid, nitrogen, and air. The hy- drochloric acid gas was generated by adding C. P. concentrated sulphuric acid to C. P. fuming hydrochloric acid, and the gas was dried by passing through five towers filled with beads moistened with con- centrated sulphuric acid which had previously been heated nearly to its boiling point. Nitrogen was prepared by Wanklyn's method of saturating air with ammonia and passing the mixture over hot copper gauze. The excess of ammonia was removed by dilute sulphuric acid, and the nitrogen was further purified and dried in towers containing glass beads moistened with silver nitrate solution, fused potassium hydroxide, concentrated sulphuric acid, and phosphorus pentoxide. Nitrogen made in this way invariably contains a small proportion of hydrogen,24 owing to catalytic decomposition of the excess of ammonia in the copper tube, but this gas would do no harm in the present instance. Air was purified and dried by reagents similar to those used for purifying the nitrogen. The apparatus was constructed wholly of glass with either ground or fused joints, except at the beginning of the air and nitrogen apparatus. By means of stop-cocks any one of the 19 Matignon found 105°. Loc. cit. 20 Loc. cit. 21 Proc. Amer. Acad., 44, 184 (1909); Jour. Amer. Chem. Soc, 31, 206. 22 Compt. rend., 140, 1340 (1905). 23 Richards and Parker, Proc. Amer. Acad., 32, 59 (1896). 24 Dr. R. C. Wells first pointed out this fact. 184 PROCEEDINGS OF THE AMERICAN ACADEMY. three gases could be delivered to the bottling apparatus at will. This apparatus is identical with that used by Baxter and Hartmann 25 for the drying of cadmium chloride, and by Baxter and Grover 26 for the drying of lead chloride. After the fusion of the neodymium chloride, the hydrochloric acid was displaced by nitrogen and the nitrogen in turn by air. Then the boat and contents were transferred to the weighing bottle, which was allowed to stand in a desiccator near the balance for some hours before being weighed. A solution of praseodymium chloride which has been fused in this way, sometimes contains a small amount of insoluble glistening particles, practically invisible unless examined in a strong light in a vessel whose curvature magnifies their apparent size. A similar difficulty was met by Baxter and Chapin in the preparation of pure anhydrous neodymium chloride. Under unfavorable conditions, which will be described shortly, the amount of this insoluble material may be considerably augmented, but when prepared under the most favorable conditions the salt dissolves rapidly without leaving even a trace of insoluble matter. Even when a small amount of insoluble material is formed, a clear solution is usually obtained after a day or two. The conditions under which the extent of the difficulty is too small to have an appreciable effect upon the results, have been found to be very careful preliminary dehydration of the salt, and a very short period of fusion. These conditions were maintained in the preparation of all of the specimens of material which were analyzed, but only in Analyses 5, 6, 9, 10, 16, 24, 25, 30, 31, 38 and 39 was the solution of the salt absolutely clear at the start. Many experiments were carried out, however, first, to find out the nature of the insoluble matter, and second, to discover the extent of the difficulty. At the outset there seemed to be three possibilities as to the nature of the substance. The most probable one was that the sub- stance is a basic chloride, but it was possible that it might be either an insoluble allotropic form of the trichloride or a lower chloride, i. e. praseodymium dichloride. The fact that prolonged fusion of the salt invariably resulted in the formation of relatively large amounts of insoluble material seemed to point toward one of the last two explana- tions, although there seems to be no certain evidence of the existence of such compounds in the case either of praseodymium or of other rare earths. 25 Jour. Amer. Chem. Soc, 37, 113 (1915). 26 Investigation not yet published. BAXTER AND STEWART. PRASEODYMIUM CHLORIDE. 185 In order to find out the composition of the insoluble substance, amounts large enough to be analyzed were prepared by dehydrating the crystals with the usual care, and then fusing the salt for periods from one-half hour to one hour in a current of dry hydrochloric acid gas. The product was then treated with water, and as soon as the soluble portion of the salt had dissolved, the insoluble residue was col- lected upon a small weighed platinum-sponge Gooch crucible, dried and weighed. The residue, which was distinctly crystalline, did not change in appearance during the drying, so that it is improbable that its composition was appreciably altered during this treatment. The praseodymium content of the residue was then determined by dissolv- ing the residue from the crucible in dilute hydrochloric acid, precipitat- ing the base with ammonium oxalate, collecting the precipitate upon a filter, and igniting in a weighed platinum boat. The weight of the black oxide Pr40; was checked by igniting the residue in a stream of hydrogen and reweighing. The weights of oxide obtained in two experiments correspond very closely to the weight which should be obtained, assuming the residue to be praseodymium oxychloride, PrOCl. About 6 grams of anhydrous salt were used in each experi- ment. Period of Fusion 1 11 35 min. 60 min. Wt. of Insoluble Residue 0.2002 gm. 0.0131 gm. Wt. of Pr407 Observed 0.1760 " 0.0117 " Wt. of Pr40, Calculated from PrOCl 0.1757 " 0.0115 " Wt. of Pi'407 Calculated from PrCl3 0.1366 " 0.0090 " Wt. of Pr407 Calculated from PrCl2 0.1597 " 0.0104 " Wt. of Pr203 Observed 0.1700 " 0.0114 " Wt. of Pr203 Calculated from PrOCl 0.1715 " 0.0112 " The composition of the residue was further checked by determining the chlorine content. Residues were collected and weighed as above, and then after solution in dilute nitric acid, the chlorine was precipi- tated as silver chloride, collected and weighed. During the solution of the residue the crucible and contents were placed in a closed tube through which a current of air was passed into a solution of ammonia, so that in case chlorine was liberated during the solution, it would be 186 PROCEEDINGS OF THE AMERICAN ACADEMY. caught in the ammonia. The results of the chlorine determinations check closely those of the praseodymium determinations. Period of Fusion I ii 60 min. 60 min. Wt. of Insoluble Residue 0.0146 gm. 0.0111 gm. Wt. of AgCl Observed 0.0110 " 0.0079 " Wt. of AgCl Calculated from PrOCl 0.0109 " 0.0083 " Wt. of AgCl Calculated from PrCI3 0.0252 " 0.0193 " Wt. of AgCl Calculated from PrCl2 0.0198 " 0.0150 " Since it is obvious that, if the oxychloride is formed from the tri- chloride, a loss in weight must occur, further experiments were carried out to discover whether during the formation of the larger amounts of insoluble residue, when the fusion is prolonged, the loss in weight of the salt corresponds to the weight of residue produced. In these experiments the hydrated salt was first very carefully dried, then quickly fused and weighed. During this treatment little if any in- soluble material is formed. Then the boat with the salt was returned to the quartz tube, and after the apparatus had been thoroughly swept out with dry hydrochloric acid, the salt was brought to the fusing temperature, which was maintained for one hour in every case. After the salt had been reweighed, the insoluble residue was determined as previously described and a few tenths of a milligram of salt which sublimed from the boat to the quartz tube were dissolved in water, the solution was evaporated and the residue was heated and weighed. The weight of sublimed material was of course added to the weight of the fused salt before determining the loss in weight during fusion. Period of Fusion I ii 60 min. 60 min. Loss on Fusion 0.0063 gm. 0.0034 gm. Wt. of Insoluble Residue Observed 0.0234 " 0.0111 " Wt. of Insoluble Residue Calcu- lated as PrOCl 0.0220 " 0.0119 " Wt. of Insoluble Residue Calculated as PrCl2 0.0376 " 0.0203 " BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 187 These experiments agree very satisfactorily with those in which the praseodymium and chlorine were actually determined, in indicating beyond question that the insoluble residue is the oxychloride. The surprising feature of these results is that the amount of insol- uble matter increases with the period of fusion instead of decreasing or even remaining constant. The obvious conclusion is that some source of oxygen exists in the fusion atmosphere. To be sure, in the first of the experiments for the determination of the insoluble residue a tiny hole was discovered in one of the fused joints of the hydrochloric acid apparatus, and in this experiment the weight of insoluble residue was found to be about ten times as large as in the subsequent experi- ments. Fortunately the defective joint was a comparatively new one, and could have affected only four of the fusions of the salt for analyses. The Analyses involved are Nos. 12, 13, 14, 15, 34, 35, 36 and 37. The hole was excessively small, however, and it is not at all certain that any real difficulty was produced. It seemed possible that the hydro- chloric acid gas might contain air, originating in the reagents used for generating the gas, or possibly from incomplete sweeping out of the purifying train. By passing the hydrochloric acid gas into water under an inverted tube after the apparatus had been thoroughly swept out, we found that it actually did contain a trace of air. We tried in some experiments to avoid the first difficulty by passing the hydrochloric acid gas through a hydrochloric acid solution of cuprous chloride before it entered the drying towers, and in order to avoid the second difficulty the apparatus was swept out even longer than before previous to the fusion of the salt, but neither of these remedies seemed to have any effect upon the formation of the basic salt. Another source of oxygen might be moisture. However, concentrated sul- phuric acid has been found by Morley 27 to be a very effective dry- ing agent. One liter of gas passed over concentrated sulphuric acid retains only 0 . 003 mg. of moisture. In order to make sure that the hydrochloric acid was really as dry as this, the gas was passed for several hours through a U- tube cooled with alcohbl and solid carbon dioxide. A very small amount of white solid was condensed in the tube, presumably a hydrate of hydrochloric acid. But even on the assumption that all of the moisture is removed from the gas by the salt during the fusion, it seems impossible that the residue should have formed wholly from moisture contained by the acid gas. Still another possibility was that the quartz tube was attacked by the acid gas to yield moisture and a chloride of silicon. This point was tested by 27 Am. J. Sci., 30, 141 (1885). 188 PROCEEDINGS OF THE AMERICAN ACADEMY. drying and fusing the salt in a platinum tube instead of in a quartz tube, but even under these conditions the insoluble residue was formed. We are still somewhat uncertain as to the cause of the for- mation of the basic salt during prolonged fusion, although incomplete preliminary drying is invariably the cause when the fusion period is short, but we are inclined to the opinion that the difficulty is due to a trace of air in the hydrochloric acid gas. Since we were unable to avoid the formation of the insoluble material in every case, in two experiments in which the salt was dried as for analysis and then fused for a short period, the insoluble residue was collected and weighed. The results of these experiments follow. As before, about 6 grams of anhydrous salt were used in each experiment. Period of Fusion 0.5 min. 4.0 min. Wt. of Insoluble Residue 0.0001 gm. 0.0010 gm. In order to discover whether the basic salt dissolves to an appreci- able extent, in experiments with three separate portions of material which had been collected, dried and weighed upon a platinum-sponge crucible, about a liter of water was allowed to flow slowly through the crucible during the course of an hour. The crucible and contents were then dried and reweighed. The losses in weight per liter of water were 0.9, 0.5 and 0.3 mg. While these figures are undoubtedly some- what less than the real solubility in water, they are probably far greater than the solubility in dilute praseodymium chloride solution. This explains the extreme slowness with which a mere trace of the basic salt dissolves in the solution of the neutral salt and supports the conclusion that the quantity of basic salt present in the material fused for a short time is very small. In preparing the salt for the actual analyses the period of fusion was less than one minute, so that the weight of residue certainly must have been considerably less than 1 mg. But since even as large a propor- tion as 1 mg. of oxychloride in 5 gm. of salt, if it dissolves eventually, would raise the apparent atomic weight of praseodymium by only 0.028, we feel that little danger is introduced by not attempting to apply any correction for the residue. In a research upon the atomic weight of neodymium carried out immediately at the conclusion of this research, similar evidence was obtained as to the nature of the insoluble neodymium compound which forms under essentially the same conditions. baxter and stewart. — praseodymium chloride. 189 The Method of Analysis. After the salt had been fused and weighed, the boat was transferred to a glass-stoppered Erlenmeyer flask and treated with about 500 ee. of pure water. In eleven of the analyses the salt dissolved immedi- ately leaving an absolutely clear solution. In the remainder of the analyses, after the bulk of the salt was in solution, by close inspection a small quantity of the insoluble basic chloride could be seen. On allowing the flask to stand for a considerable period, 24 to 48 hours in general, this basic salt disappeared, and in a few instances gentle heating was used to accelerate its solution. When the solution was clear, it was transferred quantitatively to the 3 or 4 liter glass-stop- pered Erlenmeyer precipitating flask. The rinsings of the weighing bottle were added and the solution diluted to a volume of from 1200 to 1500 cc. In the mean time a quantity of pure silver as nearly as possible equivalent to the praseodymium chloride was dissolved in nitric acid, in a dissolving flask provided with a column of bulbs to prevent loss by spattering while the metal was dissolving. After diluting the solution of silver nitrate, it was heated to eliminate nitrous acid, and then further diluted to about the same volume as the praseo- dymium chloride solution. The silver nitrate solution was poured into the chloride solution, both being cold, in small portions with con- tinual gentle agitation. When the silver nitrate had been completely transferred to the precipitating flask, the flask was stoppered and gently shaken to insure thorough mixing, and allowed to stand for several days with occasional shaking. Then.it was cooled with ice- water in order to lower the solubility of the silver chloride, and after standing for a day in the ice-bath, portions of the mother liquor were tested for excess of silver or chloride by adding to separate portions equal amounts of 0.01 normal chloride and silver solutions and com- paring the opalescences in a nephelometer. If a deficiency of either chloride or silver was found, this deficiency was made up by adding 0.01 normal silver or chloride solution. The amount of either added, expressed in the silver equivalent, is given in the tables of results under the heading "Silver added or subtracted." When equilibrium had been reached, 0.05 gm. of dissolved silver nitrate for each liter of super- natant liquid was added to render the silver chloride less soluble. After the solution had been allowed to stand for at least a day, usually much longer, at room temperature, the precipitate was washed many times by decantation with a solution containing 0.05 gm. of silver nitrate per liter, and several times with ice-cold water, and transferred with cold water to a large weighed platinum-sponge Gooch crucible. 190 PROCEEDINGS OF THE AMERICAN ACADEMY. The crucible with its contents was dried for at least 12 hours in an electric air-bath at 160°, cooled in a desiccator and weighed. The crucible had originally been dried in exactly the same way. In order to find out how much moisture had been retained by the dried silver chloride, the greater part of the salt was transferred to a porcelain crucible which was weighed. Then the crucible was heated to the fusing point of the silver chloride and reweighed. The loss in weight is assumed to represent residual moisture. On an average 0.004 percent of moisture was found, a proportion which is in accord with earlier experience in the Harvard laboratories. The solubility of silver chloride in the filtrate and silver nitrate wash waters, which both contained 0.05 gm. of silver nitrate per liter, was computed from the solubility products as found by Kohlrausch 28 at 20° and 25°, 1 X 10'10 and 1.7 X 10"10 respectively. At 20° the solu- bility in 0.0003 normal silver nitrate solution is 0.05 mg., at 25° 0.08 mg. per liter. The former correction was used during the colder months when the laboratory was maintained at about 20°, the latter correction in four analyses which were completed in summer. The total correction in most cases fell between 0.2 and 0.3 mg. The silver chloride dissolved in the aqueous rinsings as well as that ob- tained by rinsing the precipitating flask with ammonia was determined by comparison with standard solutions of chloride in a nephelometer, the usual precautions being taken to secure uniformity of precipita- tion. As in earlier researches it was found desirable to dissolve in ammonia the cloud of silver chloride in both the standard solution and that being analyzed, and then to reprecipitate with nitric acid. Corrections were of course applied for any chloride introduced in order to compensate for excess of silver, and also for the standard chloride solution added to the portions which were tested in the com- parison, for these portions were always returned to the precipitating flask. The latter quantity amounts to 1 .328 mg. for each test which was made in the comparison. Because of the comparatively large size of this correction, the standard silver and chloride solutions were made up, preserved, and measured with great care. Weighings were carried out on a No. 10 Troemner balance, sensitive at least to 0.02 mg. In order to avoid difficulties from changes in atmospheric humidity and density, the receptacles containing the salts were always weighed by substitution for counterpoises as nearly as possible like the objects both in material, volume, and external surface. The balance case was provided with a small amount of radio-active 28 Zeit. physik. Chem., 64, 167 (1908). BAXTER AND STEWART. — PRASEODYMIUM CHLORIDE. 191 material to dissipate electrical charges produced during the transfer- ence of the objects to the balance pans. The weights were standard- ized to hundredths of a milligram by the method described by Richards.29 Vacuum corrections were applied as follows: Vacuum Correction Specific Gravity Per Gram Weights 8.3 PrCl3 4.020 30 +0.000154 AgCl 5.56 +0.000071 Ag 10.49 -0.000031 Results and Discussion. In order to show that no considerable error occurred owing either to occlusion by silver chloride or from loss of silver chloride in solution, the ratio between the silver used and the silver chloride obtained has been calculated in the eighteen pairs of analyses for which the data are available. Analyses 3 and 21 4 and 23 5 and 24 6 and 25 7 and 26 8 and 28 9 and 30 10 and 31 11 and 33 12 and 34 13 and 35 14 and 36 15 and 37 16 and 38 17 and 40 18 and 41 19 and 42 20 and 43 Average Ag:AgCl 0.752573 0.752711 0.752628 0.752597 0.752723 0.752660 0.752644 0.752671 0.752735 0.752784 0.752716 0.752610 0.752587 0.752647 0.752664 0.752637 0.752685 0.752630 0.752661 29 Jour. Amer. Chem. Soc, 22, 144 (1900). 30 Determined at 25° by Mr. C. F. Hawkins, not yet published, found 4.017 at 18°. Compt. rend., 140, 1340 (1905). 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Then the coefficient k will represent the angle which 0Q makes with OP. To find the equation of a line joining two points, we will take as the defining property of the line the fact that the area of the triangle formed by any three of its points is zero. Let Qi(.i*i, yi), Q2OT2, 2/2) be two fixed points and Q (x, y) be any point on the line joining them, then QQ1Q2 = OQQ1+ 0QQ2 - OQ2Q1. Using the formula for area this becomes x xj \x x2J \x2 xj or (x - Xi) {yi - y2) = (y - iji) Oi - .t2). That is the equation of the straight line is of the first degree. 204 PROCEEDINGS OF THE AMERICAN ACADEMY. The coordinates of a line will be the dual of the coordinates of a point and therefore will be the numbers corresponding to the points in which the line cuts/ and OP. The angle between two lines will be the difference between the numbers corresponding to the points in which it cuts /. The number corresponding to the point in which the line, ux + vy = w, cuts /is Hence the angle between the lines u2x2 + v2y2 = w2, is (2) 9 = ^ ~ ** V1V2 Curvature. Using the ordinary definition of curvature we can now d erive the expression for the curvature, in this geometry, for a curve V = fix). The tangent at the point (xi, yi) is y - yi = f 0) 0 - xi), and the tangent at the near by point (.1*1 + dx, y\ + dy) is, y — yi— dy = f (xi + dx) {x - xx - dx). The angle between the tangents is then //(.r1 + ^)-/'(.r2). Hence dividing this by the element of arc we have for the curvature, v / (x) + f" (x) dx + f" Or) dx* +••••-/' fo) „.. K== : dx ~j {X)- From this we see at once that the curves of zero curvature are straight lines. The curves of constant curvature are defined by the differen- tial equation, *y 1. dx* - k That is the curves of constant curvature are (4) y = ^a-2 + ci.r + c2. This curve is then the analog of the circle in the euclidean plane. It MOORE. — MINIMUM GEOMETRY. 205 is a conic tangent to the line/ at the point F. In the minimum plane this is the curve which Study calls the parabolic circle. Area. The line area of the triangle whose vertices are the points (*i, Vi), O2, 2/2), (*b, yz), is 2/1 - 2/2 y\ 2/3 Oi — .r2) (.r3 — .Ti) = - .r2 a* — U'3_ (2/30-1 - 2/1*3) + (2/1*2 — 2/2-Tl) + (2/2*3 - 2/3*2) = 1 2/1*1 1 2/2*2 1 2/3 *3 which agrees with the ordinary formula for area. The angle area is 1 (*i — *a) (*2 — *s) (*3 - a-i) 1 2/i*i 1 ?/2 *2 1 2/3*3 That is, Line area = angle area multiplied by the product of the three sides. The curvature of the parabolic circle circumscribing the above triangle is 1 2/i *i 1 2/2 *2 1 2/3*3 — . = 2 X Angle area = 2 X line area -£- abc. (*1 — *2) (*2 — XZ) (*3 — *l) This agrees with the curvature of a circle in euclidean geometry except for a factor 2. This is due to the definition of area but there seems to be no need to complicate the formula just to make a closer agreement. The condition for a point of inflection is the same here as in ordinary geometry, d2y dx2 = 0. Collineations of the plane. We -saw from the definition of distance that the sides and angles of a triangle are in a measure independent. In fact if the vertices are moved along the lines which join them to the point F the sides are not changed in length while the angles can be made to vary from zero to infinity. We should then expect to find collineations which leave distance invariant and change angle and vice versa. If distance is to be preserved both the point F and the 206 PROCEEDINGS OF THE AMERICAN ACADEMY. line / must be left invariant and X\ — x2 must be transformed into x\ — x\. Therefore the collineations which do this are, yx = a2x + b2y + c2. These transformations, as we shall see multiply angle by a constant, therefore there is a four parameter group of transformations which leave distance invariant and multiply angle by a constant. The five parameter group of collineations, *> = to + J* y1 = a2x + b2y + c2, is a magnification for both distance and angle. The ratio of magnifi- cation for distance is at once seen to be 61. Since distance and angle are dual conceptions, there is a four parameter group of collineations which leave angle invariant and multiply distance by a constant. We could have taken the equations in angle coordinates and then the transformations leaving angle invariant would have had a form exactly similar to (5). Similarity transformations do not exist in this plane in the same sense that they exist in the euclidean plane for if the sides of a triangle are left invariant the angles are not necessarily left invariant. If we apply the transformation (5) to the two lines, uix + viy = 0, u2x + v2y = 0, the angle between the transformed lines becomes, 1 fu\ u2y h \vi v2t Hence by these transformations angle is multiplied by 7-. The 02 collineations which preserve both distance and angle are the trans- formations of the three parameter group, x1 = x + Ci, yl = a2x + y + c2. If we apply the transformation (6) to the above two lines, the angle between the transformed lines becomes, MOORE. — MINIMUM GEOMETRY. 207 Then the subgroup of the similarity group which preserves angle are those for which b\ = b^. The transformations which preserve distance and reverse angle are x1 = x + a, y1 = a2x — y -f c2. Those which preserve angle and reverse distance are, x1 = — x +' Cjj ij1 = a2x + y + c2. Those which reverse both distance and angle are, X1 = — X + Ci, yl = a-ix — y + c%. In this geometry instead of having the ordinary similarity trans- formations we have two kinds, one which multiplies distance leaving angle invariant and one which multiplies angle leaving distance invariant. There is a three parameter group of motions leaving both invariant. We have also the "umlegung" which reverses distance and the dual which reverses angle. Since the distance between two points is the same as the distance between any other two points, one on each line joining the two given points to the point F, the question arises, what are the most general analytic transformation of the plane into itself which will preserve distance. In the first place / and F must be invariant. Let the transformation be, x = f(x\ if), y = g(x\ yx). If it preserves distance, ds = dx = ~x dx1 + -^ dy1 = dx1. Hence, dy1 U' dx1 Therefore f(x\ yl) is independent of y1 and must have z1 with coeffi- cient unity, that is, / = a;1 -f- a, and ^(a:1, yl) is any arbitrary function. We will take g so that in a 208 PKOCEEDINGS OF THE AMERICAN ACADEMY. given region the transformation will be (1,1), that is in the angle between two lines through F a branch of a curve will go into a single branch with ends on the lines through F into which the boundaries of the angle transforms. By such a transformation the curves, u(x + a) + vg(x, y) = w, can be transformed into straight lines. So far then as length is con- cerned these curves could be taken for straight lines and angle defined accordingly. The whole geometry would then be the same. In this character this geometry differs very much from ordinary geometry. Case II. The second kind of geometry discussed in A. P. G. had for funda- mental system a line/ and a point F not on it. In this geometry angle and distance are so related that any three parts of a triangle determine it. A transformation then which preserves distance must also pre- serve angle and there is no separation of these groups as in Case I. The general definitions of distance are the same here as before. There is a metric example here, however, which will serve to make it more concrete. Let the line / be the line at infinity. The distance here defined then becomes equal to the area of the rectangles of which BF is one diagonal and A one vertex. The properties of distance can then be verified in this metrical case. Distance has the following properties : AB = AC if BC meets AF on /. That is the locus of points equi- distant from a given point is a straight line. This line can be any line of the plane, however, instead of a line through F as in Case I. The distance from a point A, not on/, to a point P of /is infinite if F does not lie on AP. If F does lie on AP the distance is indeterminate. The distance from a point A to a point on AF, not on /, is zero. Distance is a- directed quantity, that is if a positive direction is assigned for one line of the plane a positive direction is assigned for each line of the plane. A construction was given for measuring on any line beginning at an assigned point, a distance equal to a given distance. From these most all properties of distance can be derived. Angle was defined as the dual of distance and with reference to the same fundamental system. Angle then has the following properties: MOORE. — MINIMUM GEOMETRY. 209 ab = ac (where xy denotes the angle between the lines x and y) if the line joining the point of intersection of b and c to F meets a on /, that is the envelope of lines making equal angles with a given line is a point. The angle which a line a, not through F makes with a line through F is infinite if a does not meet it in /. If this is the case the angle is indeterminate. Angle is a directed quantity, that is if a positive rotation is assigned around one point of the plane it is assigned around each point of the plane. A construction was given for measuring about any point, beginning at a fixed line, an angle equal to a given angle. The relations connecting distance and angle are the expressions for the angles of a triangle in terms of the sides. These are, . a+b+c a+b+c a+b+c A = -, > Jt> = — » ks — 1 • be ac ab Solved for a, b, c, these relations become, A+B + C , A+B+C A+B + C a = BC ' b= AC ' C= AB From these can be derived, a be A~ B~ C' which corresponds to the sine law of ordinary trigonometry. It should be kept in mind that distance is a directed quantity and there- fore a direction around the triangle must be assumed. Coordinate systems. Having these triangle relations it is easy to set up a coordinate system. A very simple one is an ordinary polar system consisting of a point 0 from which distances are measured and a line /, through it from which angles are measured. The coordinates are then the dis- tance from 0 and the direction 6, measured from I. This system does not have the indeterminate character of polar coordinates in the euclidean plane since a point will have just one set of coordinates. It does have the disadvantage, however, of having an indeterminate character for the points of the line OF. The coordinates of any point on this line are (0, oo), since the distance from any point to F is zero and the angle which any line makes with a line through F is infinite. 210 PROCEEDINGS OF THE AMERICAN ACADEMY. The distance between two points (pi, 0]), (p2, #2) is, d = pi — Pi + pi pi (02 — 0i). For the angle between OP2 and OPi is 02 — 0i and expressing the angle in terms of the sides of a triangle, we have, e2-dl = pl + d-p2 — p\pi which is the relation above. The equation of a straight line is, Ap0 + Bp + C = 10, which is obtained by finding the locus of a point at a constant distance from a fixed point. The angle which this line makes with / is, 0= l A+ B Hence for lines through F, A = — C. The element of arc is, ds = dp + phld. A second and for most purposes more convenient system has two points of reference. Algebraically this is very similar to cartesian coordinates in euclidean geometry but geometrically like bipolar coordinates. Let X and Y be the points of reference so chosen that 3(*i,Vi) x(o,-n r(i,o) Figure 2. the line XY does not pass through F. The coordinates of a point A is then the distances from X, Y to the point. The only indeterminate points for this system are those of the line/. For convenience we will choose the distance from X to Y to be unity. The coordinates of X and Y are (0,-1), (1, 0). MOORE. — MINIMUM GEOMETRY. 211 The distance between two points (xi, yi), (x2, y2) is d = Xi y2 — Xz 2/1. For in the triangle XPiY, fig. 2, from the triangle relations, XPx + P:X + YX xx - yi - 1 1 XPx + YX - Xl In the triangle XP2Y, XP2 + P2X + YX x2-y2-l 2 XP2 • YX - x2 Then, e = e - e- = yiX2 ~ y2Xl + X2 ~ Xl • XlX2 In the triangle XPiP2 we have, XPi + P:P2 + P2X e = XPi • P2X xi + d — x2 yix2 — xiy2 + x2 — xi — X\X2 XiX2 This solved for d gives the value above. The equation of a straight line in this system of coordinates is linear as can easily be seen by finding the locus of points equidistant from a given point, this we saw was a straight line. For measuring angles we shall take a third point of reference Z (1,-1). We will then write the equation of the straight line in the form, ux + vy = 1 . The equations of ZY, ZX and XY are respectively, x = 1, y = -1, x - y = 1. The equation of a line passing through F is y = kx. From the triangle PQZ, fig. 3, 1 + v — u u — v — 1 v — u -\- 1 PQ + QZ + ZP = uv + v + u PQ • ZP v-u+ 1 _ v-u+ 1 = U' u uv 212 PROCEEDINGS OF THE AMERICAN ACADEMY. Similarly we find ^ = v. (It is to be observed that for the angle between two lines, the one is always taken, which does not contain the point F. The other angle is the sum of two infinite angles). The angle between the lines, uix + V\y = 1, uix + v2y = 1, is P = U1V2 — u2vi. These formulas for distance and angle show the directed character of both. For the angles of the triangle X Y Z we have, X= 1, Y= 1, Z= -1, corresponding to the lengths of the sides opposite, ZY =1, XZ = 1, YX = -1. This triangle will do for triangle of reference for both distance and angle. The angle coordinates of a line are the angles which it makes Z(l,-1) f r(i,o) Figure 3. with YZ and XZ. If the equation of a line be written in the form above it will be perfectly dual and the condition that the point (x, y) be on the line (u, v) is precisely, ux + vy = 1. MOORE. — MINIMUM GEOMETRY. 213 The element of arc in this system of coordinates is, ds = xdy — ydx, and likewise the angle between two nearby tangents of a curve is da = udv — vdu, where the curve is expressed in angle coordinates. Using the definition for area as was used in Case I, it was shown in A. P. G. that here also we have two areas: Line area = a + b + c = Abe = Cab = Bac. Angle area = A + B + C =? ABc = ACb = BCa. From these formulas it is at once seen that the line area of any closed curve is equal to its length. That is for a closed curve, Line area = Length = f0 {xdy— ydx). If the curve is given in angle coordinates, Angle area = Angle sum = J~c (udv — vdu). If the equation of a curve is written in the form, y = f 0), the tangent at the point (xi,y\) is, xdy — ydx = X\dy — yxdx or dy dx ds yds If x and y are functions of s the tangent at a nearby point is or (dy d?y \ (dx , d?x \ 1 The angle between these two tangents is, j _. (dy_ d2x dx d2y\ \ds ds2 ds ds2) The angle area then becomes, (7) Angle area = Angle sum = J(| * - | g) d, 214 PROCEEDINGS OF THE AMERICAN ACADEMY. Curvature. then have Here as in case I we can define curvature as da ds We -r- _ da dy d2x dx d2y ds ds ds2 ds ds2 (8) dx dy\2 d^ (lte_ ds J ds \dy ds which is the same form as the formula for curvature in euclidean geom- etry. From (8) we see that curves of zero curvature are straight lines. If x is taken as the independent variable the differential equation of the curves of constant curvature is, d2y ( dy ^ the solution of which is, ay — c2x- = V (Cl or Kx2) (ay — ax)2 + K.r2 = a. We will call these curves of constant curvature "pseudo circles." From the equations it is seen that these are conies with respect to which / is the polar of F. The points of a curve for which K = 0, are points of inflection. Any collineation of the plane which leave / and F fixed have K = 0, as an invariant. Any conic of the form, Ai.r2 + 2A«xy + A3y2 = 1, is a pseudo circle whose curvature is, K = \ (AxA3 - A22) The line area of a triangle is the sum of the sides. As in Case I, this can be expressed as, 1 x\V\ Line Area = 1 x-2yo 1 xsyz MOORE. — MINIMUM GEOMETRY. 215 The area of any closed curve is its perimeter. The dual of this from formula (7), is Angle area = jKds. For curves of constant curvature then, Angle Area = Line area X K. The area of a pseudo circle which does not cut / that is of the curve A.r2 + 2Bxy + Cif = 1, where AC - B2 > 0 is 'y Line area = / (xdy — ydx) = / x2d (-) = / d A+»g)+o(gr 2tt, - v— where A = AC - B2. 14 2 . but p = ^ = — > hence p = ,—• The line area of the pseudo circle is 7r Vp. If the pseudo circle cuts the line/ the area is infinite. Collineations of the plane. The general collineation of the plane, which leave F and /invariant is, x1 = ax + by, yl = ex + dy. If this transformation be applied to Xi y^ — x^ y\ we have x\y\ — x\y\ = M (xiy2 — x2yi), where M = ad — be. This is then a magnification for distance. The angle between the lines, uix + viy = 1, u2x + v2y = 1, becomes u\v\ — u\v\ = ^rj (mi»2 — UoV\). 1YI The transformation then divides angle. If it is applied to a pseudo circle we have for curvature, 216 PROCEEDINGS OF THE AMERICAN ACADEMY. If the collineation is a motion ad — be = 1. These transformations are the area preserving eollineations of the plane in euclidean geometry. If ad = be = —1, the transformation is an "umlegung," that is a transformation which reverses the sign of distance. For both motion and umlegung the curvature of a curve is an absolute invariant. In this geometry rotation about a point A is equivalent to a trans- lation along the series of lines passing through the point where the line AF meets /. If the rotation is to be about a finite point that point must remain invariant. But as / and F are left invariant no other finite point can be and hence there are no rotations except identity. Parallel curves. Parallel curves are defined in ordinary geometry as the envelope of circles of constant radius having their centers on a fixed curve. In this geometry then a parallel to a given curve will be the envelope of the lines which are the loci of points at a constant distance from the points of the curve. The lines corresponding to the same point of the given curve all pass through the same point of/ and hence are parallel. That is in a set of parallels to a curve the tangents at corresponding points are parallel. The parallels to the curve /(*, y) = o, will have for equation the eliminant of f(xh Vi) — 0, xyi — yxi = a. This however is exactly the process for finding the tangential equation of the curve f(x, y) = O in euclidean geometry. Hence the parallels to a given curve have the order equal to the class of the original curve and vica versa. The parallels to the pseudo circle is the eliminant of Xi, yi between, Kx\+2Bxiyi+Cy\ = 1, xy\ — yxi = a, which is Ax2 + 2Bxy + Cy = a2 (AC - B2). This is again a pseudo circle having the same pair of tangents from F. MOORE. — MINIMUM GEOMETRY. 217 Conversely all pseudo circles having the same pair of tangents from F are parallel curves. The form of the equation shows that the parallel is the same whether a is positive or negative. Hence the lines at a distance =±= a from the points of the given curve are parallel tangents to the same parallel curve. All the lines which cut a given tangent to the curve /(a-, y) = O, at a constant angle will pass through the same point. The locus of this point will be the dual of the parallel to a given curve. If the curve is given in angle coordinates, f(u, v)=0 then the angle equation of this locus will have the same degree as the reciprocal of the given curve. The curve which corresponds to a pseudo circle is again a pseudo circle. We again have the same curve whether we take the fixed angle as ± a. It was shown in A. P. G. that if the line / is the locus of points at a distance k from P then the lines through P all make with / angles equal to t. An easy calculation will show that the parallel to a pseudo circle corresponding to the distance k and the dual corresponding to the angle 7 are one and the same curve. If we wish then to determine the point of contact of a given generator / of a parallel curve with its envelope all we need to do is to draw a line through the corresponding point of the original curve making an angle — t with the tangent line. Where this line cuts I will be the point of contact. Evolutes. In ordinary geometry the envelope of the normals of a curve is of considerable interest. Aside from the tangent the normal is the only unique line connected with a curve. Here however each line passing through a point of a curve is unique in the same sense, that is it makes a definite angle with the tangent line and there is no other line passing through this point making the same angle. Then connected with every curve there is an infinite number of involutes, that is, the envelope of lines making a fixed angle with the tangent lines. If the original curve is, /(*, y) = 0, the line making the angle k with the curve at the point (xh yi) is 218 PROCEEDINGS OF THE AMERICAN ACADEMY. (a — kyy)x + (b + kxi)y = ax\ -f- byh where d£ dl dxi , dyi a~ df df ' df . 3/ The envelope of this line subject to the condition, /Oi, yi) = o, will be the e volute. For the pseudo circle this is again a pseudo circle. In fact if the curve is of the form f(x, y) = 1, where f(x, y) is a homogeneous function of x and ?/, the order of the evolute will be the same as the order of the original curve. The dual of this set of curves is the set traced by the points on the tangent line at a fixed distance from the point of tangency. In the case of a pseudo circle these curves are again pseudo circles. The pedal curves of a given curve form another interesting configura- tion. Here for a given point there will be an infinite number of pedals depending on the size of the angle used. If we denote the given curve by C and the dual of the parallel by P and take A as the point with reference to which the pedal is taken a simple construction will show that the pedal curve is the locus of the intersections of the tangents to C with the lines drawn from the corresponding points of P through A. The point A will be a multiple point on the pedal of multiplicity equal to the class of C. Length preserving transformations of the plane into itself. We found that there was a three papameter group of collineations which left distance invariant. It is evident that there are other transformations which leave distance invariant since the distance between two points measured along various curves may be the same as if measured along straight lines. The transformation, (T) a- = G(x\ if), y = R(x\ yl), will preserve length if, = x1 dy1 — y1 dx1 from which we see that, MOORE. — MINIMUM GEOMETRY. 219 W G^" H£ - -"'• QdK _H aG dyl dyl .1 If we make the following simple transformation we can more readily draw conclusions from the above equations. I = % x2 = U t = vl X12=U\ X X Suppose the transformation (T) then becomes, u = f(u\ v1), v = g(u\ vl). Then, "* = f(%* ^ + % (hl) = Ul dvl> and the relation (9) becomes, The first equation says that g is a function of vl only. Since -, is an u integrating factor and g (v) is an arbitrary function of the solution of the differential equation we see from the second equation if written ]_ f = ul dg, that f{ul, v1) is the reciprocal of an integrating factor. We then have for the original transformation, and G2(.xa, yl) is the reciprocal of -an integrating factor. The trans- formation then is such that, 220 PROCEEDINGS OF THE AMERICAN ACADEMY. where / and g are both arbitrary functions of -. . xL By this transformation a curve of the form, «G + sH= 1, will be transformed into a straight line and the theory of distance will be the same if these curves were used for straight lines. There is then an infinite group of transformations of the plane into itself which will preserve distance and consequently will preserve angle. The foregoing is then only one of an infinite number of geometries which can be built up and which are simply isomorphic with the one here discussed. Application to Minimum Developables. The equations of a minimum developable can be written in the form, -»© + *•©• y = S (£\ + V*S' fU ( f\ + v*T g where R'1 + S'2 + T'2 = 0. u Primes denote differentiation with respect to . Then v ds= ^R"2+S"2+T"2 (udv-vdu). By a proper choice of variable the expression under the radical can be made equal to unity. In fact the change of variable is, . r d(~ U1 I \V wi r vl=~~ J (R" (R"2+ S"2+T"2)*- With this choice of variable we have, ds = udt — vdu. Since this form is the same for all minimum developables it follows that all such surfaces can be mapped on any one of them in such a MOORE. — MINIMUM GEOMETRY. 221 way that length will be preserved and in fact this can be done in an infinite number of ways.4 If we put, u = x, v = y. we will have the minimum developable mapped on the plane of A. P. G. in such a way that distance is preserved. In this depiction the genera- tors of the developable are carried into the lines through F: the imaginary circle at infinity into the line /. The cuspidal edge will be transformed into the point F. This then differs from the develop- ment of the ordinary developable on the euclidean plane since a whole curve is transformed into a point. The transformation, however, does everywhere preserve length. For lines analogous to geodesies on a minimum developable then we can take the lines which by this depiction go into straight lines. As we saw before this depiction can be made in an infinte number of ways and therefore on a minimum developable there are an infinite number of simply isomorphic geometries. The curves which we shall take as pseudo geodesies are, au -j- bv = 1. The distance between two points (wi, Vi), (u2, 02) measured on one of these lines is d = Hi V2 — U2 Vi. The angle between two lines «i u + 61 v = 1, a% u + 62 v = 1, can then be defined as, /3 = aj)2 — a2 b\, and will then be the exact dual of the distance between two points. The area of the triangle (uh Vi), (u2, v2), (u3, v3) will be A = 1 U\ Vi 1 u2 v2. 1 «3 V3 4 From the ordinary formula the curvature of a minimum developable i indeterminate. However they can all be mapped on a minimum cone (point sphere). If the curvature of a sphere be taken as the reciprocal of the radius , the curvature of the point sphere is infinite. If then we say that applicable surfaces have the same curvature, the curvature of a minimum developab le is infinite. 222 PROCEEDINGS OF THE AMERICAN ACADEMY. A pseudo geodesic curvature of a curve can be defined as for the plane and will be found to be, du d2v dv d2u ds ds2 ds ds2 where the curve is defined parametrically on terms of arc length. The pseudo geodesic circle of constant radius will be, au -f- bv = 1, And the pseudo geodesic circle of constant curvature will be Aw2 + 2Buv + Cv2 = 1, and the curvature is, T, AC - B2 Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 10.— June, 1915. SYNOPSIS OF THE CHINESE SPECIES OF PYRUS. By Alfred Rehder. SYNOPSIS OF THE CHINESE SPECIES OF PYRUS. By Au'itKi) Rioumcu. Presented, January L3, L915. Received, January L9, 1915. At ih«' Arnold Arboretum there have been growing under the name of Pyrus sinensis several quite distinct trees which always have been a puzzle as regards their taxonomic standing. In working up the Pyrus of the Wilson collection I took the opportunity to essay a determination of all the Chinese Pyrus represented in the herbarium and grounds of the Arnold Arboretum. The first task, of course, was to decide which of the different forms represents the true Pyrus sinensis of Lindley. Professor Sargent, who had always taken much interest in the ( 'hincse pear question, looked up Lindley \s type in t he Botanical Museum at Cambridge during his visit, to England last summer and came to the conclusion that, it docs not agree wbh any of the forms now cultivated as Pyrus .sinensis. He brought hack an excellent, photograph of the type specimen, which, together with Lindley's description and figure in the Botanical Register, convinced me, too, that P. sinensis of Lindley is quite different from the P. sinensis of subsequent authors, which is in most cases an aggregate of several species. To one of them belong the forms introduced some forty years ago from Japan into this country as Japanese or (hincse sand pears and which have given rise by crossing with the common pear to the Kieffer and similar forms. These Japanese pears are probably garden forms derived from u Chinese type or partly hybrids and, though differing in the fruit, are remarkably alike in foliage, as shown by an extensive collection from the Garden Herbarium of the Cornell University Experiment Station, kindly loaned by I'rofessor L. H. Bailey. Two apparently wild forms, introduced from northern China, have been cultivated at the Arnold Arboretum since L8S2, to- gether with a third form of unknown native habitat, received from Kew as P. Sinionii which I have seen in France cultivated as P. sinensis. Two other forms have been introduced by Wilson from western ( 'hina. Recently the Department of Agriculture has introduced a number of Chinese cultivated pears which exhibit a, great variety in the size, shape, color and quality of the fruits, and, to a lesser degree, also in foliage. We are obliged to the Department for a series of photo- graphs of fruits taken in China and of specimens of leaves from grafts 226 PROCEEDINGS OF THE AMERICAN ACADEMY. growing at Chico, Cal. Little, however, can be said at present about the affinity of these pears, as the material is too insufficient; the leaves are apparently from the tips of young shoots and do not show the characteristic form of normal leaves, and most of the photo- graphs fail to exhibit the important character of the persistent or deciduous calyx. We shall have to wait until these plants flower and fruit before we can attempt their classification. The following Conspectus includes all the species hitherto known from China proper. Several of these species occur also outside of the limits of China; Pyrus ussuriensis ranges into Amurland, P. Calleryana into Korea and Central Japan, P. Koehnei into Formosa and P. pashia into the Himalayas. Besides these there occur in central and eastern Asia three species which are not found in China, though closely related to Chinese species; these are P. Fauriei Schneider in Korea, P. Uyematsuana Makino in central Japan, and P. Jaque- montiana Decaisne in the western Himalayas. All these are mentioned and briefly characterized in the following Enumeration under the species to which they are most nearly related. Another group of about nine species extends from Turkestan through Persia and Asia Minor into southern and western Europe and into northern Africa, but as none of them seems to be very closely related to any of the Chinese species, they do not concern us here. There is no true Pyrus in the southern hemisphere nor on the American continent. CONSPECTUS SPECIERUM SINENSIUM. Calyx persistens. Folia argute setoso-serrata. Pomum breviter pedicellatum, subglobosum: folia orbiculari- ovata vel ovata, ut inflorescentia ab initio glabra. 1. P. ussuriensis. Pomum longe pedicellatum, ovatum; folia oblongo-ovata v. ovata ut inflorescentia ab initio plus minusve floccoso-tomen- tosa 2. P. ovoidea. Folia denticulata v. dentata dentibus non setoso-acuminatis : pomum longe pedicellatum, ovale 3. P. Lindleyi. Calyx deciduus. Folia setoso-serrata. Basis foliorum late cuneata: pomum flavum. 4. P. Brctschneideri. REHDER. — CHINESE SPECIES OF PYRUS. 227 Basis foliorum subcordata vel rotundata: pomum fuscum. 5. P. serotina. Folia argute serrulata v. dentato-serrata dentibus non setoso- acuminatis. Styli 3—1: pomum 1.5-2 cm. diam. : folia basi plerumque ro- tundata. Folia argute serrulata dentibus acutis vel acuminatis subac- cumbentibus 6. P. serrulata. Folia dentato-serrata dentibus erecto-patentibus. 7. P. phaeocarpa. Styli 2: pomum circiter 1 cm. diam.: folia grosse dentato- serrata, basi plerumque late cuneata...8. P. betulaefolia. Folia crenata vel crenato-serrata. Stamina circiter 20: folia et inflorescenta ab initio glabra. Styli 2: folia ovata, basi plerumque rotundata. 9. P. Calleryana. Styli 3-5. Folia late ovata, crenato-dentata, basi subcordata. 10. P. kolupana. Folia ovata, crenato-serrata, basi late cuneata vel rotundata. 11. P. Koehnei. Stamina 25-30: folia ovata v. oblonga, crenato-serrata, basi plerumque rotundata, ut inflorescentia tomentosa vel fere glabra: styli 3-5 12. P. pashia. ENUMERATIO SPECIERUM. 1. Pyrus ussuriensis Maximowicz in Bull. Acad. Sci. St. Petersb. XV. 132 (1857); in Mem. Sav. Etr. Acad. Sci. St. Petersb. IX. 102 (Prim, Fl. Amur.) (1859).— Regel in Gartenfi. X. 374, t. 345 (1861).- Lauche in Monatsschr. Ver. Bef'ord, Gartenb. Preuss. XXII. 318, t. 4 (1879), pro parte, quoad flores. Pyrus communis Bunge in Mem. Sav. Etr. Acad. Sci. St. Petersb. II. 101 (Enum. PI. Chin. Bor. 27) (1833), pro parte, non Linnaeus. Pyrus sinensis Decaisne, Jard. Fruit. 1. 1. 5 (1872), non Poiret, nee Lindley. — Maximowicz in Bull. Acad. Sci. St. Petersb. XIX 172 (1S73); in Mel. Biol. IX. 168 (1873), pro parte. — Komarov in Act. Hort. Petrop. XXII. 476 (Fl. Manshur.) (1904), pro parte. — Schneider, III. Handb. Laubholzk. I. 663, fig. 361 q (1906), pro parte, quoad folia. Pyrus Simonii Carriere in Rev. Hort. 1872, 28, fig. 3. 228 PROCEEDINGS OF THE AMERICAN ACADEMY. Pirus sinensis a. assuriensis Makino in Tokyo Bot. Mag. XXII. 69 (1908). Pirus sinensis a. silvestris Makino msc. ex Makino, I.e., quasi synon. Chili: "China bor.," ex herb. Bunge (Gray Herb.); Hsiao Wu- tai-shan, August 20, 1913, F. N. Meyer (No. 1232). Amurland: " montes Burejae," 1859, Maximowicz (Gray Herb.); " Amur medius," May 18, 1891, S. Korshinsky. Ussuri: without precise locality, Ma.vimoivicz (Gray Herb.). Manchuria: Khabarovsk, cultivated, August 23, 1903, C. S. Sargent. This species differs from the allied species chiefly in the short stalk of the globose fruit with persistent calyx, in the broad, often nearly orbicular, strongly setosely serrate leaves and in the lighter yellowish brown color of the branches; the flower clusters are, owing to the short stalks rather dense and hemispherical; the petals are obovate and rather gradually narrowed toward the base; the styles are distinctly pilose near the base. Pyrus ussariensis was first introduced into cultivation by Richard Maack who sent seeds to the Botanic Garden at St. Petersburg, but the tree is still rare in gardens. 2. Pyrus ovoidea Render, sp. n. 1 Pyrus chinensis Roxburgh, Hort. Bengal. 38 (1814), nomen nudum, non Pyrus sinensis Poiret; Fl. Ind.ed. 2, II. 511 (1832). Pyrus sinensis Hemsley in Jour. Linn. Soc. XXIII. 257 (1887), pro parte, non Poiret, nee Lindley — Diels in Bot. Jahrb. XXIX. 38 (1900), pro parte. — Schneider, III. Handb. Laubholzk. I. 663, fig. 364 c-d (1906), pro parte. Pyrus Simonii Hort., non Carriere. Arbor pyramidalis, 10-15-metralis, inermis; ramuli hornotini maturi purpureo-fusci v. flavo-fusci, nitiduli, vetustiores castanei, lenticellis parvis paucis conspersi; gemmae conico-ovoideae, castaneae, glabrae. Folia ovato-oblonga, rarius ovata, acuminata, basi rotun- data v. subcordata, argute setoso-serrata dentibus erecti-patentibus v. interdum accumbentibus, 7-12 cm. longa et 4-6.5 cm. lata, initio ad marginem tantum et subtus ad costam tomento floccoso fulvo cito evanescente praedita, mox glaberrima, supra luteo-viridia, lucida, subtus paullo pallidiora, maturitate chartacea et autumno colore pulchro purpureo-scarlatino et aurantiaco gaudentia, utrinsecus nervis 9-10 supra et subtus leviter elevatis; petioli graciles, 2.5-5 cm. longi, initio sparse floccoso-lanati, mox glaberrimi. Flores circiter 3 cm. diam., in racemis umbelliformibus 5-7-floris glabris v. interdum to- mento floccoso cito evanescente vestitis; pedicelli 2.5-4 cm. longi; REHDER. — CHINESE SPECIES OF PYRUS. 229 calyx lit receptaculum extus glaber; sepala e basi late triangulari- lanceolata, denticulata, intus ad basin dense lanata; petala late obovata v. late ovalia, circiter 12 mm. longa, basi subito brevissime unguiculata, glabra, alba; stamina circiter 20, dimidiam partem petalorum vix aequantia, antheris purpureis; styli 5, distincti, basi pilosi, staminibus longioribus paullo breviores. Pomum ovoideum, basi rotundatum impressum, apicem versus attenuatum calyce per- sistente erecto vel incurvo coronatum, pedunculo gracili 2-4 cm. longo insidens, flavum, punctatum, circiter 4-4.5 cm. longum et 3.5-4 cm. diam., sapore grato leviter adstringente; semina ovoideo- oblonga, compressa, 9-10 mm. longa et 6 mm. lata, castanea, nitida. Cultivated in the Arnold Arboretum under No. 4033 (received from Kew as P. Simoni), May 7 and 13, 1909, April 30, 1910, May 14, 1914, October 19, 1908, October 16, 1912 (type); Hort. Simon-Louis, Plantieres near Metz, August 24, 1911, A. Rehder (as P. sinensis). Probably also the following specimens belong to this species : Fokien : Dunn's Exped. to Central Fokien, April to June, 1905 (Hongkong Herb. No. 2595). Yunnan: Mengtze, cultivated, alt. 1500 m., A. Henry (No. 11058). This species seems to be most closely related to P. tissuriensis Maximowicz which differs chiefly in the broader orbicular-ovate or ovate leaves, in the lighter colored branches, and in the short-stalked subglobose fruit with the persistent sepals spreading. The shape of the fruit of P. ovoidea is very unusual and quite distinct from any pear I know; the fruit is exactly ovate, broad and rounded at the base and tapering from the middle toward the truncate apex, as figured by Schneider (1. c. fig. 364 d). This may, however, not be a specific character and the shape of the fruit may vary in other specimens referable to this species. The Chinese material which I have seen and which might belong here is very meagre. The Fokien specimen is in young fruit which suggests a more pyriform shape, though tapering toward the apex and showing the same kind of persistent calyx; the serration of the leaves is more minute and more accumbent. The Yunnan specimen is in flower and differs somewhat in the more copious tomentum of the leaves and of the inflorescence and in the shorter nearly entire calyx-lobes. It is not known when and whence this species was introduced. Possibly it was sent in the early sixties from northern China by G. E. Simon, or by A. David a little later from the same region or from Mongolia to the Museum in Paris and was afterwards distributed by Decaisne. 230 PROCEEDINGS OF THE AMERICAN ACADEMY. 3. Pyrus Lindleyi Rehder, nom. n. Pyrus sinensis Lindley in Trans. Hort. Soc. London, VI. 396 (1826), non Poiret; in Bot. Reg. XV. t. 1248 (1829). Lindley's Pyrus sinensis seems to have been much misunderstood, and the name has been applied to all Chinese pears characterized by setosely serrate leaves. Lindley's description, however, as well as his type specimen, of which I have a good photograph before me, show that the leaves of his species have short, rather small and not at all acuminate teeth. He certainly would have mentioned such a striking character as the setose teeth in his description, but in the description he simply says " foliis .... serratis " and in his comparison with Pyrus communis he does not mention the serration at all, which tends to show that he did not perceive much difference between the serration of Pyrus communis and that of his new species. The true P. sinensis of Lindley seems to have been lost to cultivation in Europe and in this country, for all the plants and specimens I have seen belong to species with setosely serrate leaves, and Pyrus Lindleyi rests at present only on Lindley's description and his type specimen. In the P. sinensis of most authors three species seem to have been included, two of them with persistent calyx and one with deciduous calyx. In P. Lindleyi the calyx is persistent according to Lindley's description in the Botanical Register and according to the description, probably by the secretary of the society, in the Transactions of the Horticultural Society where only the fruit is fully described and nothing said about the leaves and the tree itself, with a note that " it has been named by Mr. Lindley Pyrus sinensis." In Lindley's type specimen the leaves of the shoots are ovate, abruptly acuminate and rounded at the base, and those of the short branchlets mostly subcordate; all are closely serrate, with small appressed, acute teeth, or those of the short branchlets nearly cren- ately serrate. As much as can be judged from the photograph they appear to be quite glabrous and about 8 or 10 cm. long. Pyrus Lindleyi is possibly not a wild species, but a cultivated form. At present, however, with our incomplete knowledge of the Chinese pears, it seems best to treat it as a species. Pyrus communis Loureiro {Fl. Cochin. 321. 1790) may belong here as a synonym, as the author describes the leaves as "subintegerrima." The name Pyrus sinensis of Lindley cannot be maintained for this species on account of the older P. sinensis (Thouin) Poiret (Encycl. Meth. Suppl. IV. 452. 1816). Even though the latter species is now KEHDER. — CHINESE SPECIES OF PYRUS. 231 generally referred to Chaenomeles, it must be considered nomen- clatorially a valid name and the combination cannot be used again for another species. 4. Pyrus Bretschneideri Rehder, sp. n. Arbor mediocris; ramuli hornotini sparsissime lanuginosi, cito glabri, annotini fusco-purpurei, sparse lenticellati; gemmae ovatae, 4-5 mm. longae, perulis late ovatis manifeste mucronulatis castaneis extus margine villoso excepto glabris. Folia subchartacea, ovata vel elliptico-ovata, acuminata, basi late cuneata, rarissime fere rotundata, argute serrata dentibus initio setoso-acuminatis, demum manifeste acuminatis plerumque leviter accumbentibus, 5-11 cm. longa et 3.5- 6 cm. lata, initio utrinque laxe araneoso-lanuginosa, cito glabra, supra saturate luteo-viridia, subtus paullo pallidiora, leviter reticulata; petioli graciles, 2.5-7 cm. longi, initio sparsissime lanuginosi, cito glabri. Inflorescentia umbellato-racemosa, 7-10-flora, rhachi, pedicellis, re- ceptaculis sparse lanuginosis, mox glabris; pedicelli 1.5-3 cm. longi, bracteolis 2 subulatis circiter 5 mm. longis instructi; sepala e basi late triangulari acuminata, circiter 4 mm. longa, glanduloso-serrata, extus glabra, intus fulvo-lanuginosa; petala ovalia, apice plerumque irregulariter erosa, basi breviter unguiculata, 12-14 mm. longa et 10-12 mm. lata, alba; stamina circiter 20, petala dimidia aequantia; styli 5 vel interdum 4, stamina subaequantes, glabri. Pomum sub- globosum vel globoso-ovoideum, 2.5-3 cm. longum et circiter 2.5 cm. diam., apice cicatrice impressa calycis decidui notatum, basi subito in pedicellum 3-4 cm. longum contractum, pendens, flavum, pallide et minute punctulatum, 5- vel rarius 4-locuIare; semina obovoidea, leviter compressa, 6-7 mm. longa, castanea. Arnold Arboretum, cultivated, April 22, 1910 and October, 1908 (type, raised from seed sent by Dr. E. Bretschneider from Peking in 1882). This species seems nearest to P. ovoidea Rehder which is easily distinguished by the persistent calyx and by the more oblong-ovate leaves rounded or even subcordate at the base. In its deciduous calyx it agrees with P. jihaeocavpa Rehder, but this species differs in its smaller 3-4-celled brown fruit and the coarser serration of the more oblong-ovate leaves. Pyrus Bretschneideri may be the pear alluded to by Bretschneider (Hist. Eur. Bot. Discov. 830) as pai-li (white pear), though this name may also apply to P. ussuriensis or to P. ovoidea. 5. Pyrus serotina Rehder, sp. n. Arbor 7-15-metralis; ramuli hornotini glabri vel initio laxe villosuli, rarius tomento floccoso densius obtecti, mox glabri, annotini et vetu- 232 PROCEEDINGS OF THE AMERICAN ACADEMY. stiores purpureo- vel fusco-brunnei, sparse lenticellati; gemmae acu- tiusculae, ad 1 cm. longae, perulis ovatis acutis margine exeepto fere glabris fuscis. Folia subchartacea, ovato-oblonga vel rarius ovata, longe acuminata, basi rotundata, rarius subcordata, interdum late cuneata, arete et argute serrata dentibus setoso-acuminatis subaccum- bentibus, 7-12 cm. longa et 4-6.5 cm. lata, initio margine laxe villosa et subtus secus costam tenuiter araneoso-lanata vel fere glabra, rarius utrinque fere in tota facie tomento araneoso evanescente laxe obtecta, mox glaberrima, supra laete viridia, subtus paullo pallidiora, utrinque in sicco leviter reticulata, utrinsecus nervis 6-11 arcuatis; petioli graciles, 3-4.5 cm. longi, initio fere glabri vel plus minusve floccoso- tomentosi, mox glabri. Inflorescentia umbellato-racemosa, 6-9-flora, fere glabra vel plus minusve tomento floccoso flavescente vel canes- cente obtecta; pedicelli graciles, 3.5-5 cm. longi; sepala e basi tri- angulari-ovata, longe acuminata, 6-10 mm. longa, glanduloso-denticu- lata, patentia, receptaculum saepe fere duplo superantia, extus fere glabra vel plus minusve tomentosa, intus ad basin saltern fulvo- tomentosa; petala ovalia, 15-17 mm. longa, apice plerumque irregu- lariter erosa, breviter unguiculata; stamina circiter 20, dimidia petala aequantia; styli 5, rarius 4, glabri, staminibus fere aequilongi. Po- mum subglobosum, apice leviter impressum, cicatrice calycis decidui notatum, basi subito in pedicellum gracilem 3.3-5 cm. longum con- tractum, circiter 3 cm. diam., fuscum, pallide punctulatum; semina cuneato-ovoidea, leviter compressa, basi in stipitem contracta, 8-10 mm. longa, atro-brunnea. Western Hupeh: Hsing-shan Hsien, woodlands, alt. 1300-2000 m., May and December 1907, E. H. Wilson (No. 479a, type); same locality, May and October 1907, E. H. Wilson (No. 2977); Patung Hsien, thickets, alt. 1000-1600 m., May 1907, E. H. Wilson (No. 556b) ; north and south of Ichang, thickets, alt. 600-1300 m., April 1907, E. H. Wilson (No. 479b); same locality, October 1907, E. H. Wilson (No. 415); Changlo Hsien, thickets, May 1907, E. H. Wilson (No. 556c); without precise locality, A. Henry (No. 5299). Eastern Szechuan: without precise locality, A. Henry (No. 5875). Western Szechuan: Tachienlu, alt. 2000-2600 m., October 1908, E. H. Wilson (No. 1293). This species seems to be most closely related to P. Bretschneideri Rehder which is easily distinguished by the leaves being broadly cuneate at the base, by the smaller flowers and by the yellow color of the fruit. Its leaves resemble closely those of P. ovoidea Rehder so that it seems impossible to distinguish these two species with cer- REHDER. — CHINESE SPECIES OF PYRUS. 233 tainty without flowers or fruits; in fruit, however, the persistent calyx of the ovate yellow fruit of P. ovoidea presents a good character, and the flowers of P. ovoidea may be distinguished by the styles being pubescent at the base. Wilson's No. 2977, of which the fruit is not known, differs from the type in its broader ovate or broadly ovate leaves with more appressed teeth and may represent a distinct variety or even another species. Henry's No. 5875 has the fruit pyriform and may belong to the following variety. Henry's No. 5299 is in flower only and agrees with this species in its glabrous styles; both specimens of Henry may be from cultivated plants. This species was introduced by E. H. Wilson in 1909 and seeds were distributed by the Arnold Arboretum. According to a note received two years ago it is growing in the Botanic garden at Glasnevin. This pear and probably other brown-fruited species are called by the Chinese tang-li. Pyrus serotina var. Stapfiana Rehder, n. var. Pyrus sinensis Stapf in Bot. Mag. CXXXIV. t. 8226 (1908), quoad plautam depictam, non Poiret, nee Lindley. A typo recedit fructu pyriformi, foliorum dentibus minus adpressis, petalis satis sensim in unguiculum attenuatis. Pyrus serotina var. culta, Rehder, comb. n. ?Pyrus communis Thunberg, Fl. Jap. 207 (1784), non Linnaeus. IPyrus communis c. hiemalis Siebold in Verh. Bat. Genoot. XII. pt. 1, 66 (Syn. PI. Oecon. Jap. No. 349) (1830), nomen nudum. IPyrus communis /?. sinensis K. Koch in Ann. Mus. Lugd.-Bat. III. 40 (1866). Pyrus Sieboldi Carriere in Rev. Hort. 1880, 110, t., non Regel. Pyrus sinensis Bailey, Cycl. Am. Hort. III. 1470 (1901), pro parte, non Lindley, nee Poiret. Pyrus japonica Hort. ex Bailey, 1. c. quasi synon., non Thunberg. Pyrus sinensis /?. culta Makino in Tokyo Bot. Mag. XXII. 69 (1908).— Koidzumi in Jour. Coll. Sci. Tokyo, XXXIV. art. 2, 54 (1913). A typo recedit fructu majore pyriformi vel maliformi, foliis majori- bus latioribusque ad 15 cm. longis et ad 8-10 cm. latis. Japan: Arakawa, north of Tokyo, roadside, April 2, 1914, E. II. Wilson (No. 6541, bush 2 m.); Hatogaya near Tokyo, cultivated, April 29, 1914, E. H. Wilson (No. 6595); Tokyo, Sakurai's gar- den, April 24, 1912, K. Sakurai; slopes of Mt. Fuji, alt. 2600 m., cultivated, May 8, 1914, E. H. Wilson (No. 6668; small tree, 12-20 234 PROCEEDINGS OF THE AMERICAN ACADEMY. feet); Tsuba-kura-dake, prov. Shinano, alt. 900 m., cultivated, September 15, 1914, E. H. Wilson (No. 7497; tree 10 m. tall, fruit russet, flesh white, sweet). Besides these specimens I have seen from the Herbarium of the Cornell University Experiment Station numer- ous specimens from plants cultivated in this country under the names : Oriental Pear, Japanese Pear, Chinese Sand Pear, Madame von Siebold, Daymio, Mikado, Rikiya and Gold Rust or Golden Russet. The Japanese pear cultivated under the name "Madame von Siebold" may be considered as representing the type of this variety. It has large subglobose, somewhat depressed fruit with deciduous calyx and is well described and figured by Carriere (in Rev. Hort. 1879, 170, t.); by Ottolander in Flor. & Pomol 1877, 100, fig. 2 and in Nederl. Flora en Pomona 69, t. 21 ; by S. Morris in Am. Gard. n. ser. XIII. 87 (1892); also the figure in American Agriculturist, XXX. 462 (1871) and in Gard. Chron, ser. 2, III. 106, fig. 17, 18 (1875) belong probably here. Pyrus Sieboldi Carriere (in Rev. Hort., 1880, 110, t.) has large pear-shaped fruit with deciduous calyx, but according to Ottolander (in Flor. & Pomol., 1877, 100, fig. 3) it has a persistent calyx. "Ottolander" has an oblong fruit with deciduous calyx (Flor. & Pomol., 1877, 100, fig. 4; also in Gard. Chron, ser. 2, IV. 456, fig. 95. 1875, and ser. 3, XXVIII. 300, fig. 89. 1900). "Gold Rust" has, according to a photograph in the Cornell Garden Her- barium, a subglobose fruit without calyx. "Daymio" has a globose- ovoid yellowish fruit with persistent calyx (Nederl, Flora en Pomona, 69, t. 21, fruit at the left). "Mikado" has a broadly pear-shaped yellow fruit without calyx (Rev. Hort., 1878, 310, t). The last two forms are possibly hybrids. Some of the above named forms have hybridized with the Common Pear; the best known of these hybrids is the "Kieffer Pear" which has finely or nearly crenately serrulate leaves and a pear-shaped fruit with persistent calyx. 6. Pyrus serrulata, Rehder, sp. n. Arbor 7-8-metralis; ramuli hornotini leviter lanati, mox glabri, annotini purpureo-fusci, sparse lenticellati; gemmae ovatae, fuscae, perulis ovatis acutis exterioribus margine ciliato excepto glabris. Folia chartacea, ovata vel ovato-oblonga, subito vel sensim acumi- nata, basi rotundata vel late cuneata, margine serrulata dentibus adpressis et plerumque leviter incurvis acutis vel breviter acuminatis, 5.5-11 cm. longa et 3.5-6.5 lata, initio subtus tomento araneoso- lanato fugace leviter obtecta, cito glabrata, supra ab initio glabra vel fere glabra, nervis utrinsecus 7-13 arcuatis, utrinque in sicco leviter reticulata; petioli graciles, 3.5-7.5 longi, initio leviter lanati, mox REHDER. — CHINESE SPECIES OF PYRUS. 235 glabri. Inflorescentia racemoso-umbellata, 6-10-flora, rhachi circiter 1.5 cm. longa satis dense flavo-lanata; pedicelli ut receptaculum laxe lanati, 1.5-2 cm. longi; sepala triangulari-ovata, acuta vel acuminata, sparse glanduloso-denticulata, receptaculum subaequantia, circiter 3 mm. longa, extus sparse, intus dense lanata; petala late ovalia, alba, 10-12 mm. longa, subito breviter unguiculata, leviter et irregu- lariter erosa; stamina circiter 20, petalis circiter triente breviora; styli 3, rarius 4, stamina subaequantes, basi sparsissime pilosi. Poraum subglobosum vel globoso-obovoideum, 1.5-1.8 cm. longum, apice vix impresso cicatrice calycis decidui notatum, basi subito in petiolum 3-4 cm. longum contractum, fuscum, pallide lenticellatum, 3-4- loculare; semina obovoidea, 7 mm. longa et 4 mm. lata, castanea. Western Hupeh: Hsing-shan Hsien, thickets, alt. 1300-1600 m., May and December 1907, E. H. Wilson (No. 779, type); north and south of Ichang, alt. 600-1300 m., October 1907, E. H. Wilson (No. 479). This species seems to be most closely related to P. serotina Rehder which is easily distinguished by the setosely serrate, generally longer leaves, by the larger flowers with usually 5 styles and long-acuminate sepals and by the larger fruit. The Japanese P. Uyematsuana Makino1 seems to be most nearly related to P. serrulata; according to the description it differs from it in the often subcordate leaves and in the disk which is described as villose by Koidzumi; styles 3-5. Pyrus serrulata was introduced by E. H. Wilson and seeds have been distributed through the Arnold Arboretum. 7. Pyrus phaeocarpa Rehder, sp. n. Pyrus ussuriensis Lauche in Monatschr. Ver. Beford. Gartenb. Preuss. XXII. 318, t. 4 (1879), quoad fructus, non Maximowicz. Arbor mediocris; ramuli hornotini tomentosi, tarde glabrescentes, annotini glabri, purpureo-fusci, sparse lenticellati; gemmae oblongo- conicae, acutiusculae, 6-7 mm. longae, perulis castaneis vel partim griseis glabris vel fere glabris. Folia chartacea, elliptico-ovata vel oblongo-ovata, in acumen longum -sensim attenuata, basi plerumque late cuneata, serrata dentibus acuminatis apice initio plus minusve incurvis demum patentibus sinubus apertis saepe fere rectangulis, 6-10 cm. longa et 3.5-5.5 cm. lata, initio laxe araneoso-lanata, mox l Pyrus Uyematsuana Makino in Tokyo Bot. Mag., 22, 68 (1908). — Koid- zumi in Jour. Coll. Sci. Tokyo, XXXIV., art. 2, 56 (1913). Japan: Prov. Ise (ex Makino and Koidzumi). 236 PROCEEDINGS OF THE AMERICAN ACADEMY. glaberrima, supra saturate luteo-viridia, subtus pallidiora, nervis utrinsecus 7-10 areuatis, in sicco utrinque leviter reticulata; petioli initio albido-lanati, rarius fere glabri, mox omnino glabri, graciles, 2-6 cm. longi. Inflorescentia umbellato-racemosa, 5-7-flora, albido- lanata, raro fere glabra; pedicelli 2-2.5 cm. longi, ut receptaculum initio plus minusve lanati, rarius fere glabri, mox omnino glabri; sepala triangulari-lanceolata, acuminata, glandulosa-serrata, recepta- culo paullo longiora, 4-5 mm. longa, extus sparse, intus densius lanata; petala ovalia, breviter unguiculata, 1-1.5 cm. longa et 0.8- 1.2 cm. lata, glabra, alba; stamina circiter 20, dimidia petala subae- quantia; styli glabri, 3-4, rarissime 2. Pomum pyriforme, 2-2.5 cm. longum et 1.5-2 cm. diam., graciliter pedicellatum pedicello 2-3 cm. longo, fuscum, pallide lenticellatum, 3-4-loculare, rarissime 2-loculare; semina obovoidea, compressa, circiter 7 mm. longa, fusco-castanea. Arnold Arboretum, cultivated, May 12, 1909, and October 1908 (type, raised from seed sent by Dr. E. Bretschneider from Peking in 1882). This species is most closely related to P. bctulaefolia Bunge which is easily distinguished by its much smaller 2-celled fruit, the smaller flowers, the smaller and more coarsely serrate leaves and the denser grayish tomentum persisting on the branchlets, on the inflorescence and often on the under side of the leaves particularly on the midrib until autumn. In the shape of its leaves it has some resemblance to P. Bretschncideri Rehder, but that species has setosely serrate, gen- erally larger and broader leaves and larger yellow subglobose fruit. Pyrus phaeocarpa was apparently first introduced in its pear-shaped form to the Horticultural School at Potsdam, Germany, about 1870. At the Arnold Arboretum both the pear-shaped and the apple-shaped forms were raised from seed sent by Dr. Bretschneider from Peking in 1882. Pyrus phaeocarpa f. globosa Rehder, forma n. A typo recedit fructu globoso, 1.5-2. cm. diam. et foliis paullo latiori- bus, saepius ovatis et basi rotundatis. 8. Pyrus betulaefolia Bunge in Mem. Sav. Etr. Acad. Sci. St. Petersb. II. 101 (Enum. PL Chin. Bor. 27) (1833).— Walpers, Rep. II. 53 (1843).— Decaisne, Jard. Fruit. I. t. 20 (1872).— Maximowicz in Bull Acad. Sci. St. Petersb. XIX. 172 (1873); in Mel, Biol. IX. 169 (1873).— Debeaux in Act. Soc. Linn. Cherbourg, XXXI. 156 (Fl. Tchefou, 61) (1876).— Carriere in Rev. Hort. 1879, 318, fig. 68, 69 — Hemsley in Jour. Linn, Soc. XXIII. 256 (1887).— Sargent in Card. & REHDER. CHINESE SPECIES OF PYRUS. 237 For. VII. 224, fig. 39 (1894).— Diels in Bot. Jahrb. XXIX. 387 (1900). — Schneider, III. Handb. Laubholzk. I. 665, fig. 363 o, 364 k-p (1906).- Pampanini in Nuov. Giom. Bot. Ital. n. ser. XVII. 291 (1910). Chili: near Peking, E. Bretschneider, 1881 (seeds). Shantung: Lau-shan, August 1907, F. N. Meyer (No. 308); without precise locality, September 1907, F. N. Meyer (No. 398). Shensi: Yenan Fu, 1910, W. Purdom (No. 328); Poa ting Fu plain, 1909, W. Purdom. Hupeh: without precise locality, A. Henry (No. 1654). Henry's specimen from Hupeh differs from the type in its broader and somewhat larger leaves. This species was first introduced in the sixties by G. E. Simon to the Museum at Paris unintentionally as stock of a grafted Chinese pear. In 1882 it was introduced again to the Arnold Arboretum by Dr. Bretschneider from the mountains near Peking. This pear is called by the Chinese t'ao-li (pea -pear). 9. Pyrus Calleryana Decaisne, Jard. Fruit. I. in textu ad t. 8 (1872).— Maximowicz in Bull. Acad. Sci. St. Petersb. XIX. 172- (1873); in Mel. Biol. IX. 169 (1873); in Bidl. Soc. Nat. Mosc. LIV, pt. 1, 18 (1879).— Hance in Jour. Bot. XXI. 298 (1883).— Franchet in Nouv. Arch. Mus. Paris, ser. 2, V. 272 (1883).— Schneider, ///. Handb. Laubholzk. I. 666, fig. 363 p (1906). — Koidzumi in Jour. Coll. Sci. Tokyo, XXXIV. art. 2, 55 (1913). Western Hupeh: Hsing-shan Hsien, thickets, not common, alt. 1000-13000 m. May 14, 1907, E. II. Wilson (No. 2775); Changlo Hsien, thickets, alt. 1000-1500 m., December 1907, E. H. Wilson (No. 556); Patung Hsien, alt. 1000-1700 m., December 1907, E. H. Wilson (No. 556a) ; around Ichang, common, alt. 1000-1300, March and July 1907, E. H. JJ^ilson (No. 2976) ; mountains north and south of Ichang, alt. 600-1500 m., April 1907, E. II. Wilson (No. 415a). Kiangsi: Kuling, side of streams, common, alt. 1300 m., July 29, 1907, E. H. Wilson (No. 1662). Chekiang: Ningpo, 1908, D. Macgregor. Kwangtung: without precise locality, C. Ford (No. 68); Botanic Garden, Hongkong, Nov. 4, 1903, C. S. Sargent. Pyrus Calleryana is a widely distributed species and seems not uncommon on mountains at an altitude of from 1000 to 1500 m. It is easily recognizable by its comparatively small crenate leaves, like the inflorescence glabrous or nearly glabrous and by its small flowers with 2, rarely 3 styles. ^Yhen unfolding most specimens show a loose and thin tomentum on the under side of the leaves which usually soon disappears, but in No. 1662 from Kuling even the fully grown leaves are loosely rusty tomentose on the midrib 238 PROCEEDINGS OF THE AMERICAN ACADEMY. beneath. In No. 415a the leaves are longer, generally ovate- oblong, the pedicels very long and slender, about 3-4 cm. long and the sepals are mostly long-acuminate. The fruit of No. 556a is rather large, about 1-1.4 cm. in diameter, but a fruit examined proved to be 2-celled.2 This species was introduced by E. H. Wilson to the Arnold Arbore- tum in 1908 and the young plants seem to be hardy here. The following Japanese pear is referred by Koidzumi as a variety to P. Cattery ana. Pyrus Calleryana var. dimorphophylla Koidzumi in Jour. Coll. Sci. Tokyo, XXXIV. art. 2, 56 (1913). Pyrus Calleryana Maximowicz in Bull. Acad. Sci. St. Petersb. XIX. 172 (1873); in Mel. Biol. IX. 169 (1873), quoad plantam japonicam. Pyrus dimorphophylla Makino in Tokyo Bot. Mag. XXII. 65 (1908). Japan: Prov. Ise and prov. Shinano (ex Makino and Koidzumi).2 10. Pyrus kolupana Schneider, III. Handb. Laubholzk. I. 665 (1906); in Fedde, Rep. Nov. Spec. Ill, 120 (1807). Shensi: Ko-lu-pa, G. Giraldi (Nos. 1050, 5105, ex Schneider). This species is little known and not yet in cultivation. 11. Pyrus Koehnei, Schneider, III. Handb. Laubholzk. I. 665, fig. 363 m, 364 t-u (1906); in Fedde, Rep. Nov. Spec. III. 119 (1907).— Koidzumi in Jour. Coll. Sci. Tokyo, XXXIV. art. 2, 57 (1913). Pyrus Kawakamii Hayata in Jour. Coll. Sci. Tokyo, XXX. art. 1, 99 (1911). Chekiang: Tien-tai mountains, alt. 1000 m., E. Faber (ex (Schneider). Formosa: Nanto, T. Kawakami (ex Hayata). This species like the preceding is as yet little known and is not in cultivation. As I have seen neither a specimen from the type local- ity nor from Formosa, I do not know whether Koidzumi is right in referring P. Kaioakamii as a synonym to P. Koehnei. 12. Pyrus pashia Hamilton apud Don, Prodr. Fl. Nepal. 236 (1825).— G. Don, Gen. Syst. II. 622 (1832).— Decaisne, Jard. Fruit. 2 A closely related species, P. Fauriei Schneider (III. Handb. Laubholzk. I. 666, fig. 363 d.' 1906) occurs in Korea; it differs chiefly in its much smaller leaves and fruits. REHDER. — CHINESE SPECIES OF PYRUS. 239 I. 328, t. 7 (1872).— Wenzig in Linnaea, XXXVIII. 48 (1874).— Brandis, Forest Fl. Brit Ind. 204 (1874); Ind. Trees, 291 (1906).— Kurz, Forest Fl, Brit Burma, I. 441 (1877).— Hooker f., Fl. Brit Ind. II. 374 (1879).— Collett, Fl. Siml. 169, fig. 47 (1902).— Schneider, III. Handb. Laubholzk. I. 664, fig. 363 h, 364 e-g (1906). Pyrus variolosa Wallich, Cat. No. 680 (1828), nomen nudum. — G. Don, Gen. Syst. II. 622 (1832). Pyrus verruculosa Bertoloni in Mem. Accad. Sci. Bologna, ser. 2, IV. 312 (Piante As. II.) (1864). 3 Pyrus heterophijlla Hort. ex Decaisne, Jard. Fruit I. 328, sub t. 7 (1872), quasi synon. Pyrus nepalensis] Herb. Hamilt. et Hort. ex Hooker, Fl. Brit. Ind. II, 374 (1879), quasi synon. Western Szechuan: Ching-chi Hsien, alt. 1500 m., October 1908, E. H. Wilson (No. 1335); same locality, open country, alt. 2600 m., October 1910, E. H. Wilson (No. 4132). Yunnan: Mengtze, alt. 1400-1500 m., A. Henry (Nos. 10035, 10035 c). Himalayas: Kash- mir to Bhutan, Kashia Mountains, Ava (ex Hooker f.). This species is not mentioned by Hemsley in his Index florae sinensis, though Hooker in 1879 includes Yunnan in the distribution of the species. Wilson's No. 1335 which is in ripe fruit agrees well with typical P. pashia and the young plants raised at the Arnold Arboretum from seeds of that number show exactly the kind of finely and sharply serrate mostly deeply lobed leaves, figured by Decaisne as the form occurring on suckers. No. 4132 differs in its much shorter and tomentose pedicels, only about 1.5 cm. long, and in the generally broader leaves mostly subcordate at the base; part of the fruits show a persistent calyx. Whether this is a variety of this species or a distinct species may be decided when the plants in cultivation flower and fruit. Pyrus -pashia was first introduced in 1825 into England from Nepal or Kumaon ; in 1908 it was reintroduced by E. H. Wilson from western China and distributed through the Arnold Arboretum. Possibly the plant introduced in 1825 represents the following variety, as it is this variety which is now found occasionally in European collections. Pyrus pashia var. kumaoni Stapf in Bot Mag. CXXXV. t. 8256 (1909). 3 In the text the references to the type specimens of this species and of P. granulosa are interchanged; "Pyrus (c)" belongs to P. granulosa and "P. variolosa Trell. [sic] var." belongs to P. verruculosa. 240 PROCEEDINGS OF THE AMERICAN ACADEMY. Pyrus Kumaoni Decaisne, Jard. Fruit. I. 328, sub t. 7 (1872). — Hooker f., Fl. Brit. Ind. II. 374 (1879).— Schneider, III. Handb. Laubholzk. I. 665 (1906). Pyrus Wilhelmii Schneider, III. Handb. Laubholzk. I. 665, fig. 363 n (1906); in Fedde, Rep. Nov. Spec. III. 120 (1907). Yunnan: Mengtze, mountain woods, alt. 1600 m., A. Henry (No. 10035a, type); same locality, alt. 1400 m., A. Henry (No. 10035b). Himalayas: Kashmir to Kumaon (ex Hooker). This variety differs from the type in its glabrous or nearly glabrous inflorescence and leaves and in the ovate, broader and often obtuse calyx-lobes. I am unable to separate P. Wilhelmii specifically from this variety; broadly ovate leaves occur also in P. pashia and the state- ment that P. Wilhelmii has only 3 styles is not borne out by the speci- men which represents Henry's No. 10035a, on which P. Wilhelmii is based, in the herbarium of the Arboretum, as the number of styles varies in that specimen from 3 to 5. Besides P. pashia there occurs in the western Himalayas another closely related species, P. Jaequemontii Decaisne (Jard. Fruit. I. t. 8. 1872). This according to Decaisne differs from P. pashia in its smooth, not verruculose, young fruits. It is so far very imperfectly known, as neither the flowers nor the mature fruits have been de- scribed. Arnold Arboretum, Harvard University. REHDER. — CHINESE SPECIES OF PYRUS. 241 INDEX. (The pages upon which the names are merely mentioned or occur as syno- nyms are indicated by italic numbers.) Pyrus betulaefolia, 227, 236. Bretschneideri, 226, 231. Calleryana, 226, 227, 237, 238. dimorphophylla, 238. chinensis, 228. communis, 227, 233. hiemalis, 233. sinensis, 233. dimorphophylla, 238. Fauriei 226, 238. heterophylla, 239. Jacquemontiana, 226, 240. japonica, 233. Kawakamii, 238. Koehnei, 226, 227, 238. kolupana, 227, 238. kumaoni, 239. Lindleyi, 226, 230. nepalensis, 239. ovoidea, 226, 228. Pyrus pashia, 226, 227, 238. kumaoni, 239. phaeocarpa, 227, 235. globosa, 236. serotina, 227, 231. culta, 233. Stapfiana, 233. serrulata, 227, 234. Sieboldii, 233, 234. Simonii, 225, 227, 228. sinensis, 225, 227, 228, 230, 233. culta, 233. silvestris, 228. ussuriensis, 228. ussuriensis, 226, 227, 235. variolosa, 238. verruculosa, 239. Wilhelmii, 239. Uyematsuana, 226, 235. Proceedings of the American Academy of Arts and Sciences. Vol. L. No. 11.— June, 1915. CERTAIN OLD CHINESE NOTES. By Andrew McFarland Davis. CERTAIN OLD CHINESE NOTES. By Andrew McFarland Davis. Presented, February 10, 1915. Received, February 19, 1915. Chinese Paper Money. The use in China, as a medium of trade, of a representative paper currency, based upon government credit dates back with reasonable certainty to the beginning of the ninth century of the Christian Era. The notes than in circulation are referred to by Chinese historians in such a way as to leave no doubt in the minds of investigators compe- tent to analyze the literature of that country, as to the authenticity of the statement that at that date a government paper money was in circulation. There are fabulous assertions by Chinese writers, as to the use of paper money many centuries before the birth of Christ. And there are specific assertions of the value assigned to white deer skins, for purposes of transfer under certain circumstances, by one of the emperors about a century and a half before Christ, which have led translators to speak of them as "Deer Skin Money." I take no consideration of this so-called money, for it was neither paper money, nor would the accounts that we have of it permit it to be defined as money at all. But the beginning of the ninth century of the Christian Era has been generally accepted by students of the subject as the period when it can be satisfactorily demonstrated that government notes were actually circulated in lieu of metallic money. There is indeed a Chinese numismatical work 1 which furnishes pictorial representations of notes emitted as early as the middle of the seventh century. The compiler of that work must have had some authority for the designs of these earlier notes which he published. If we hesi- tate to accept this date, without further knowledge as to the authori- ties upon which are based the details given about these notes, it must nevertheless be recognized as possible that the date of 650 A.D. may ultimately be accepted as that of the earliest emission of notes by the Chinese government of which we have at present any trace. The fact remains however that there is corroborative evidence from numer- i Ch'ien Pu Tung Chih, or by others Chuan Pu Tung Chih. 246 PROCEEDINGS OF THE AMERICAN ACADEMY. ous sources as to the notes emitted after 806 A.D. and that a few scat- tered specimens of some of the various emissions remain in existence, while it is said, that no other mention of those earlier notes has been met with in Chinese literature than that accredited to this particular writer. The acquisition by myself in 1910 of a Ming note emitted probably about 1375, led to correspondence and investigation on my part. Int^est in the subject was revived in the fall of 1914 by my securing possession of fourteen of these old notes, two of which dated back to the Tang Dynasty, somewhere about 850 A.D., and of course investi- gation on my part was thereby stimulated. The circumstances connected with the purchase of the first of these notes were as follows : In the latter part of the year 1910, I received a catalogue from a London book-seller which contained the following item: "Chinese Bank Note. A genuine specimen of the earliest known Bank Note, being one issued during the reign of the Emperor, Hung Wu (1368- 1398). 12| by 8^ ins. The inscription enclosed by elaborate ornamental border, the whole being printed from a wood block; mounted on limp board, with embroidered work at back; worn in places." The earliest European note was issued by the Bank of Stockholm about three centuries after the above. There is a- similar example in the British Museum, which is the only one known to me. Further correspondence revealed the fact that the description of the note, except as to the mounting was taken from labels at the British Museum. A friend in London, at my instance, took a look at the specimen which was offered for sale, and although not an expert in such matters, expressed himself as satisfied that it was genuine and I purchased it. At that time I knew nothing about Chinese paper-money. The statement that the specimen was a bank-note I rejected, as improba- ble, but the error of describing these government emissions as bank- notes is one that is frequently committed by writers on the subject, and in this particular case may perhaps be charged to the labels of the British Museum. In the spring of 1911 I wrote to one of the curators in that institu- tion asking about specimens of Chinese currency in their possession, and found that the Museum at that time had two notes precisely alike, both of the Ming Dynasty (1368, 1398) and each for one kwan. One was procured in 1890. The other in 1902. Marco Polo was in China about one hundred years before the date .':■ •;*«>■' [* ■■ if.'!™' **':fc* •I /hit* l ' *V | * >«<8««afiiiMnfiai|i