At HE EE be KN rat 4 valle Hitt ii Ihahirvities dy, wren HI if rik : Hip ri AN ne At ie st i a KA Hi, dn! rit es ty a) Phy init Ni itt PANTS) Hed SRE: ini ATR nik : Alt Obra i {it lk Hd EN Ee ‘ales cca BORE EEE i | en Ha ete iy (Ny a5 nl i ee i i 4 HL i Lita ao KAN En He sh EENES ai ees i ot Bi a Kn AN et iH ie ite ma KI ii Abas bed a dk isa a ra Ee A a ae EK Ee it Ke bes ‘ at a Geeta = ") i VP detent as bh a hi a Hi si pi nite te ti Kit i BELADEN ge Hi VK Lh a= = sae pe a : ee 7 5 ae ee at 6 oS oe i ; Mies ' ' i bede TY ) i il Hate) ee tataci aM mata Beh, { Hi Alisa U SEA a eS EAP RE EOE it 4 i At Bi Abia FSI f i } sey HM Ee aR 4 ie ny ty i : ae HD Dt a ik ne RD ne SS os os $a a Neti Ses tere Jeri) : Hi lat verre at uae dike ¢ ry t Y hi | nt Kion KEO en anu | 4 wl Ke ‘i ich Hi ii a Mn u ie ‘ i ae 4 ny iene wit iN Hat Hf HOHE RH MAU c= “ane AE ¥. iW ik Ma | oy) # fi iti nui Aut Py hi HEEE hate see MASIS it a iy We hi bent it iy ily ih His Ki = DE EN Ht i “Se ih jer in f 1, 4 a end ae as ei i it a. He t ih Herent fy Hi at jt 4 eat if nits na tity sr’ 4 wnt } J vat AEC HE ? a lee AE AKOROEE DE NEP i 3 Ae k js Wijhe 1 Ais is 4 ay Ì Ha, ¥ i uhh in i ii 7 sat KIN ER on GIRL ERS B minnie tant bekt na it Hi ( ‘ j vi (a By ii Hat it HAN qi } na te dede } ' Li a B: ia Et taal Hie Ha dis ivi fiat t AUDIO HEH He © Esen iy i ae oS Hy iH ae a ie ith , a HE 45 {Ke i fh rant a | ee Hite yor a = $ = sarc aie a if ae a thy Ltr A ARL SA dt ae ee LT Ap As Te ae ava 1 ees le ans AL Cee VACANTE i y ati f KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN -- TE AMSTERDAM -:- PROCEEDINGS OF THE PEG BION -OF -SCIENCES VOLUME XI JOHANNES MULLER :—: AMSTERDAM JULY 1909 me ¥ p | di au A, 7 SKOENG ( as Kt of (Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natu Afdeeling van 30 Mei 1908 tot 23 April 1909. Di. XVII.) KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN -- TE AMSTERDAM -:- PROCEEDINGS OF THE *°<¢¢’? SECTION OF SCIENCES VOLUME XI ( — IST PART — ) JOHANNES MULLER :—: AMSTERDAM ° ; : DECEMBER 1908 : dk ce EIT el S| UREUNO RO TRE NG” TOE AT ANU AVE TO © EEEN ENDS SET DN LAD TEAN AAR ATA il 7 7 ; § 4 | (Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Nana Afdeeling van 30 Mei 1908 tot 28 November 1908. DI XVII.) Ah | | og. Mejy. Aoecrny ERE aA BN EE NETS. oe em Proceedings of the Meeting of May 30 and June 27 1908 . . ... . 1 » » » » » September 26 » eA Oil te EO » » » | » » October 31 » Ne eens a ER » > » » » November 28 > EEn tn 0 Le KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETINGS of Saturday May 30 and June 27, 1908. en (Translated from: Verslag van de gewone vergaderingen der Wis- en Natuurkundige Afdeeling van Zaterdag 30 Mei en Zaterdag 27 Juni 1908, Dl. XVII). Saw: EE EN PS. A. P. H. Trivertr: “A contribution to our knowledge of the solarization phenomenon and of some other properties of the latent image”. (Communicated by Prof. S. Hoocrwerrr), p. 2. (With one plate). H. KAMERLINGH Onnes and C. Braak: “Isotherms of diatomic gases and their binary mixtures. VIII. The breaking stress of glass and the use of glass tubes in measurements under high pressure at ordinary and low temperatures”, p. 30. (With one plate). G. C. J. Vosmaer: “Poterion a Boring-Sponge”, p. 37. J. J. BrANKSMA: “Reduction of aromatic nitro-compounds by sodium-disulphide’’. (Communi- cated by Prof. A. F. HOLLEMAN), p 42. A. K. M. Noyons: “About the determination of hardness in muscles”. (Communicated by Prof. H. ZWAARDEMAKER), p. 43. (With one plate). J. Borke: “On the structure of the ganglion-cells in the central nervous system of Bran- chiostoma lanc.”. (Second Communication). (Communicated by Prof. G. C. J. Vosmarr), p. 53. (With one plate). L. E. J. Brouwer: “About difference quotients and differential quotients”. (Communicated by Prof. D. J. Korrmwee), p 59. M. W. Brwerinck: “Fixation of free atmospheric nitrogen by Azotobacter in pure culture. Distribution of this bacterium”, p. 67. H. C. Prinsen Geeruics: “Rapid change in composition of some tropical fruits during their ripening”, p. 74. JAN DE VRIES: “Congruences of twisted curves in connection with a cubic transformation”, p 84. C. SANDERS: “Contributions to the determination of geographical positions on the West coast of Africa” III. (Communicated by Dr. E. F. van DE SANDE BAKHUYZEN), p. 88. C. SANDERS: “Contributions to the determination of geographical positions on the West coast of Africa” ILL, Appendix. (Communicated by Dr. E. F. van pr SANDE BAKHUYZEN), p. 107. C. SANDERS: “Observations of the transit of Mercury on November 14, 1907 at Chiloango in Portuguese West-Africa”. (Communicated by Dr. E. F. van pe SANDE BAKHUYZEN), p. 108. P. P. C. Hork: “Some results of the investigation of the Cirripeds collected during the cruise of the Dutch man-of-war “Siboga” in the Malay Archipelago”, p. 110. L. S. Ornstern: “Calculation of the pressure of a mixture of two gases by means of Girss’ statistical mechanics”. (Communicated by Prof. H. A. Lorenrz), p. 116. Tu. Vareron: “Lindeniopsis. A new subgenus of the Rubiaceae”, p. 123. S. H. Koorpers: “Contribution NO, 1 to the knowledge of the flora of Java”. (Third Con- tinuation), p. 129. J. D. vaN DER Waats Jr.: “On the law of molecular attraction for electrical double points”. (Communicated by Prof. J. D. vaN DER Waa ts), p. 132, F. A. H. SCHREINEMAKERS: “Equilibria in quaternary systems”, p. 158. J. Wreeper: “The investigation of the weights in equations according to the principle of the least squares”. (Communicated by Prof. H. G. vAN DE SANDE BAKHUYZEN), p. 142. J. D. vaN DER Waats: “Contribution to the theory uf binary mixtures”. VII, p. 146. S. H. Koorprrs: “Contribution NO, 1 to the knowledge of the flora of Java. (Fourth Con- tinuation), p. 158. A. Smits and J. P. Wisaur: “The dynamic conception of a reversible chemical reaction”. (Communicated by Prof. A. F. HOLLEMAN), p. 162. A. Suits: “The P.7.X spacial figure for a system of two components which are miscible in the solid or. liquid crystalline state in all proportions”. (Communicated by Prof J. D. vaN DER Waats), p. 165. (With one plate). H. KAMmerLINGH Onnes: “The liquefaction of helium” p. 168. (With 3 plates). K. Martin: “The age of the layers of Sondé and Trinil on Java”, p. 185. EN i Proceedings Royal Acad. Amsterdam. Vol. XI. (9 Physics. — “A contribution to our knowledge of the solarization phenomenon and of some other properties of the latent image”. By A.P. H. Triverur. (Communicated by Prof. 5. Hoocrwerer). (Communicated in the Meeting of March 28, 1908). I. The image. In order to enquire into the density gradation a photographic plate may be exposed in two ways: a. with constant light intensity and varying time of exposure; b. by equal exposures, with different light intensities. In order to eliminate the possibility of other circumstances being different, particularly those under which development is carried out, the first method has been adopted, a plate being divided into strips, and each succeeding strip receiving a longer exposure than the preceding one. This is combining several trial plates into one. In my opinion an “image” cannot be said to appear in this case; it only appears if the second method is adopted. The results obtained by equal exposures with different light inten- sities I will call copies. A copy always shows an image, which may be positive or negative. By a normal or non-polarized copy I understand copying positive- negative-positive- etc, which may be represented by tE > FE By a polarized copy I understand copying positive-positive-ete. or negative-negative- etc., which may be represented by de According to the investigations of WARNERKE"), W. ABNzy *), K. Scraum and V. BerracH ®), R. Nevwaus*), and W. SCHEFFER *), the differences in density which appear in a photographic plate after exposure and development, may be ascribed to differences in the depth of the reduced silver haloid. So the image must have a 1) Phot. Archiv. 1881; S. 85 u. 119. Phot. Mitt. Bd. 18; S. 65, 98 u. 235. J. M. Eper, Handb. d. Phot. 1902; Bd. I[I; S. 106 u. 108. 2) J. M. Eper, Hand. d. Phot. 1902; Bd. Ill; S. 102. 8) Phys. Zeitsch. 1902; Bd. IV; 8. 4. J. M. Eper, Handb. d. Phot. 1903; Bd. III; S. 819. 4) Wied. Annal. d. Phys. u. Chem. 1898; Bd. 65; S. 164. 5) Phot. Chronik. 1904; S. 366. Phot. Rundschau. 1904; S. 121. (3) plastic shape similar to that formed by the pigment-gelatine printing process, the insoluble part being a normal copy, the soluble part a polarized one (monochrome pinatypy). It is characteristic of the normal copy, if exposed and developed normally that the portions where the density is greatest show a duller surface when seen by light reflected at an angle than the clearest portions. This is to be attributed to the presence of reduced silver-haloid grains immediately under the free surface. If the image lies against the free surface, it may be called a surface image, in opposition to a “depth” image, with which this is not the case. The cause of the appearance of the surface image has been ascribed by P. H. Eyxman and myself’) to the surface tension of the wet gelatine. So a silver-haloid gelatine layer may be looked upon as consisting of a series of layers, of which the top one, i.e. the one at the free surface, is the most sensitive, while every succeeding one lying under it, is less sensitive. The exposure required to render a beginning of reduction by the developer visible, the liminal value (“Schwellenwert””) consequently seems to increase in proportion to the depth; that of the topmost layer is equal to the liminal value of the plate itself. We will call this the “absolute”, that of the succeeding layers the “relative” liminal value. Leaving aside, for clearnes’s sake, the mutual differences in sensitiveness of silver-haloid grains in one single layer, to which J. M. Ener?) and J. PLener*) have drawn attention, the differences in size and shape and the topographic situation of the grains, the normal copy may be represented as is shown in cross section and graphically in fig. 1. | The shape of the image of a polarized copy might be represented as indicated in fig. 2. I have found that this explanation cannot be applied to a single photographic image, but it is applicable to chemi- graphic processes, catatypy and the silver-pigmentgum process. In the case of some polarized copies, as the counter-positive and -negative, a normal copy is developed first, the reduced silver haloid of which is dissolved and, after a diffused exposure, redeveloped. Now a depth image originates (fig. 3). Owing to the diffused exposure the base of it, leaving aside slight differences in light absorption, will everywhere be about equally distant from the free surface. 1) Drude. Annal. d. Phys. 1907; Bd. 22; S. 119. 2) J. M. Eper, Handb. d. Phot. 1902; Bd. III; S. 64. Phot. News. 1883; p. 81. 3) Phot. Korresp. 1882; S. 306. 1* ( tf) According to the investigations of E. Enarisn *) and J. M. Eper”) there are two images in the case of solarization. This question has not yet been satisfactorily cleared up, and a certain amount of con- fusion prevails as to the distribution of the normal and the polarized copy. If the time of exposure, resp. the light intensity is increased, the reducibleness of the silver haloid increases in depth, finally to such a degree that provided the time of development be sufficient, the reduction extends to the glass, as is shown by the excellent micros- copic preparations of W. Screrrer ®). If solarization sets in, it will first occur in the apparently most sensitive layers, i. e. those at the free surface ; consequently the reducibleness decreases from there, and on the time of exposure, resp. the intensity of the light being increased, it constantly extends further down. Thus an image is obtained as is graphically shown by fig. 4, from which it is at once apparent that the solarized image is a normal copy and a surface image. Under this image there is a polarized copy of greater density with AB for its base and from there to the glass there is a strip of fog, the den- sity of which depends on the thickness of the emulsion. That after all, in the case of solarization, the copy appears polar- ized, is therefore owing to the normal copy being of less density than the polarized one. It will, however, more or less reduce the contrasts and the wealth of detail. Zé is consequently contrary to fact to understand polarization by solarization, as is always done. (In the figure the section of the solarized image is indicated by finer granulation, which is meant to show that the density has been reduced in that portion). This at once accounts for the phenomenon occurring in the case of solarization of silver iodide gelatine discovered by Lürro-CRAMER *) 1) Phys. Zeitschr. 1900; Bd. 2; S. 62. J. M. Eper, Jahrb. f. Phot. u. Repr. 1902; S. 79. Archiv. f. wiss. Phot. 1900; Bd. Il; S. 260. 2) Zeitschr. f. wiss. Phot. 1905; Bd. II; S. 340. J. M. Eper, Handb. d. Phoi. 1906; Bd. 1; T. 2; S. 287. Sitzungsber. d. Kaiserl. Akad. d. Wiss. za Wien. Mathem-Naturw. Klasse; Bd. CXIV; Abt. Ha; Juli 1905. 8) J. M. Eper, Jahrb. f. Phot. u. Repr. 1907; 5. 31. 4) I cannot omit quoting this experiment, which so clearly confirms the above : “Eine auffallende Erscheinung beobachtete ich endlich noch bei einem Solarisie- “yungsversuch mit Jodsilbergelatine. Unter einem Negativ ergaben die Platten in “drei Sekunden bei diffusem Tageslicht ein ausexponiertes Bild. Eine sechs Stunden “lang unter demselben Negativ belichtete Platte schien sich in Amidolpottasche, “in welcher sie neben der drei Sekunden belichteten Platte entwickelt wurde, zuerst (5) and which points to the very rapid decrease in reducibleness of silver iodide when solarized. Il. A few phenomena occurring with solarization accounted for by considering the form of the image. From the form of the image in fig. 4 it appears how impregnation of the silver-haloid gelatine plate with bichromate before exposure may influence the result obtained, which was pointed out by Bouas *). J. M. Eper and G. Pizziguniii’) attributed the result exclusively to hardening of the gelatine, by which development in the normal image is disturbed, and in which solarization acts hardly any part. It is evident that this image in tbe hardened gelatine more or less coalesced with the solarized image, in proportion to the strength of the bichromate solution employed, by which the development of the latter is suppressed to a greater extent and the polarized copy appears richer in contrast and detail. The fog, however, is not done away with. While in the case of normal copies the latter may be removed with FarmeEr’s reducer *), this treatment does not succeed in, the case of polarization. The slight diffusion of this reducer discovered by W. Scuerrer*), by whien the action slowly progresses downwards from layer to layer, at once accounts for this phenomenon. Of more significance to our knowledge of the latent image is the so-called neutralization of solarization by retarded development. That the said phenomenon is regarded as such is only attributable to the ideas of solarization and of polarization being confounded. Development is retarded either by decreasing the amount of alkali “gar nicht zu reduzieren, während das kurz exponierte schon in allen Einzelheiten “erschienen war. Nach einiger Zeit merkt man indes, dass auch auf der tiberbe- “lichteten Platte ein Bild vorhanden ist; dasselbe sitzt nur in den tieferen Schichten “allerdings als normales Diapositiv, d. h. noch nicht solarisiert während in der “Aufsicht erst nach längerer Entwicklung etwas zu sehen ist. Beim Fixieren merkt “man deutlich, dass in der obersten Schicht der lange belichteten Platte kein Bild “vorhanden ist, inlem nach kurzem Fixieren das Bild auch in der Aufsicht kräf- “tiger wird, offenbar weil das unreduzierte Jodsilber der obersten Schicht wegge- “nommen wird’. (J. M. Eper, Jahrb. f. Phot. u. Repr. 1903; S. 46. Zeitschr. f. wiss. Phot. 1908; Bd. I; S. 17). 1) J. M. Eper. Handb. d, Phot. 1902; Bd. III; S. 115. Phot. News. 1880; Vol. 24; p. 304. 2) J. M. Eper. Handb. d. Phot. 1902. Bd. III; S. 115. 3) J. M. Eper. Handb. d. Phot. 1902 Bd. III; S. 555. 4) Brit. Journ, of Phot. 1906; p. 964. J. M. Eper. Jahrb. f, Phot. u. Repr. 1907; S. 26. (6 ) in the developer or by the addition of potassium bromide. That only the rapidity of reaction of the developer is reduced, [ was able to ascertain by the so-called neutralisation of solarization with a de- veloper (rodinal 1 in 10) at a lower temperature, First a normal copy is developed, which when development is continued, turns into a polarized one. However, the normal copy obtained in this way, differs very much from an ordinary one. When viewed by light reflected at an angle, it is just in the densest portions that the surface is found to have the highest gloss; consequently here the grains do not lie against the surface. After the copy has changed into a polarized one, in which the polarized depth image predominates, the surface remains unchanged, and now shows the highest gloss in the clear portions. Consequently the surface image has not undergone a rever- sion of density proportions, from which it follows that the normal copy obtained by retarded development must be the solarized image’). This cannot be ascribed to a change of the solarization, i.e. to a change in the substance of the solarized latent image. Consequently in the surface glass we have a means of ascertaining in the case of solarization, whether an agent reacts upon the sub- stance of the latent image or upon the development. Thus I could ascertain inter alia, that chromic acid mentioned by J. M. Eper *) and ammonium persulphate referred to by K.Scuaum and W. Braum, which both exercise a hardening influence upon the gelatine, at the same time also react upon the substance of the latent image in the case of solarization, by which it is reduced to the substance of the ordinary latent image. UI. Sapatier’s polarization. If during the development of a plate light is admitted, three different phenomena may occur: 1. If a very slight amount of light is admitted, the plate in the developer shows an increase of reducibleness. 1) It stands to reason that during the appearance of the normal copy in the developer, consequently before polarization sets in, development of the non-solarized silver haloid in the lower layers may take place. Consequently it is better to say that the solarized image is only formed within a certain definite time of development. 2) Phot. Korresp. 1902; S. 647. J. M. Eper. Jahrb. f. Phot. u. Repr. 1903; S. 28. J. M. Eper. u. E. Vatenta. Beiträge zur Photochemie. 1904; II; S. 168. J. M. Eper. Handb. d. Phot. 1903. Bd. Ill; S. 828. 3) Phot. Mitt. 1902; S. 224. ——-—-- Cr) 2. If more light is admitted the image partly disappears, and a more or less fogged plate is obtained with partly a normal and partly a polarized copy, which shows great resistance to further development. 3. If still more light is admitted, the copy is polarized. This last phenomenon I call SABATIER’s polarization. J. M. Eper*) credits SaBATIER with first observing it, and says that Srrty gave the following explanation of it: The beginning of the development takes place at the surface; by the secondary expo- sure this developing image is copied upon the silver haloid under- neath it, and as this exposure is more powerful than the first, the second image also develops more strongly, and total polarization results. From the experiments carried out by me it appeared that the secondary exposure stopped the development of the surface image, for by reflected light it was seen that it did not increase in density any more, while total development of the whole surface might be expected. In order to ascertain to what extent the copying action of the developing surface image is operative in polarization, I effected the secondary exposure, at the advice of P. H. Hykman, on the glass side of the plate. The exposed plate was developed for a short lime, and just after the appearance of the image it was, while still in the developer, covered with a piece of opaque, black paper, which was everywhere pressed tightly against the emulsion to prevent the formation of air- bells, from which uneven development might arise, and then the glass side was exposed to direct daylight. As the quantity of developer soaked up by the paper was small and the temperature was below the normal one, the plate, to save time, was put in the developer again in the dark room, great care being taken to prevent light from reaching the front of the plate. After fixation a polarized copy appeared. This shows that the copying of the developing image at most acts a very secondary part in the appearance of polarization. The latter can only be ascribed to the further development of the surface image being stopped, and to the reducibleness of the silver haloid underneath it being increased. Consequently here again two images are formed, one under the other: at the top a normal copy of little density, and under it a polarized one of greater density, corresponding to that of the polarized copy in fig. 3 in the case of solarization. 1) J. M. Eper Handb d. Fhot. 1898; Bd. Il; S. 82. (8 ) The similarity between Sapatrier’s polarization and solarization is so great, that R. Lyrr') attributed the phenomenon mentioned sub 2 to the first zero condition of JANssny’s periodicities of solarization being reached*). In one of my experiments it appeared to me that this similarity only existed in so far as no image was to be observed. The first zero condition is characterised by the maximum of density obtainable, whilst the plate in question remained very thin. Conse- quently the cause of the disappearance of the image cannot lie in this. By transmitted light, too, the plate does not show polarization in the portions exposed most intensively by the primary exposure, but in the portions that received the smallest amount of light. (Therefore SABATIER’s polarization cannot be ascribed to solarization). It is easy to understand that the relative liminal value of a lower layer is first reached in those portions where the absorption of the surface image is the least, and where this layer, at the same time, is situated nearest to the free surface. So in this case the copying quality of the surface image exercises its influence. LV. Herschel’s effect. By Herscuet’s effect I understand polarization by double exposure. It differs from polarization by solarization in that much smaller amounts of light-energy are sufficient to produce it, and in the reducibleness of the primarily exposed silver haloid Gocteacme at once on a secondary exposure. The duration of the primary exposure must always exceed the liminal value of the plate. After the secondary exposure has exceeded a certain maximum (the critical exposure), the plate shows a normal copy again. The value of the critical exposure depends entirely on the primary exposure. This has led to the so-called Crarpen’s effect *) (black lightning) being looked upon as a new phenomenon of the photographic plate. The first observation dates from 1839, and was made by J. Herscuzt, who stated that the red and the yellow rays of the spectrum could 1) Phot. Centralbl. 1902; S. 146. 2) Compt. rend. 1880: T. 90; p. 1447, T. 91; p. 199. Moniteur de la Phot. 1880; p. 114. Beibl. z. d. Annal. d. Phys. u. Chem. 1880; S. 615. J. M. Eper, Handb. d. Fhot. 1906; Bd. 1; T. 2; S. 806. 1898; Bd. II; S. 78. J. M. Eper, Jahrb. f. Phot. u. Repr. 1894; S. 378. 8) J. M. Eper. Jahrb. f. Phot. u. Repr. 1901; S. 610. Camera Obscura. 1901; bldz. 513. J. M. Eper. Handb. d. Phot. 1906; Bd. I; T. 2; S. 312. 1903; Bd. III; S. 834, 7 n ” n (9) destroy the latent image of the blue and violet ones. At the same time a change in the degree of colour sensitiveness was ascertained. This was confirmed by Crauper*), H. W. Voeren ®), W. Apnmy ®), P. Virarp*) and R. W. Woop‘). E. Eneriscn®), H. W. Voce and W. Asner, however, considered this phenomenon to be solarization. An experiment published by P. Virrarp clearly shows that in the case of very advanced exposures the critical exposure does not appear any more, and the whole phenomenon coalesces with solarization. The highest sensitiveness of the plate is manifested towards red, the lowest to green. WARNERKE ’) observed Hurscunt’s effect in images obtained by print- ing, and P. Varzarp, R. W. Woop, R. Lurner and W. A. UscHKorFr *) with Röntgen rays in the case of primary exposure. At the same time they demonstrated that the phenomenon did not appear if these exposures were reversed. J. Srerry *) communicated another variety, viz. that certain kinds of chemical fog can be neutralized by weak light. Some time ago one of my friends showed me a few camera exposures on Eastman films *®), which I recognized as the phenomenon observed by J. Srerry. They had been exposed once, but had been in the camera for about 3 years without any precautions having been taken except that light had been prevented from reaching them. Consequently in this case the diffused exposure had been replaced by a chemical process of analysis, which had acted similarly, and had been exercised upon the silver bromide by the vapours given off by the celluloid, which had been diffused in the silver bromide gelatine. Fig. 5 is an outdoor subject; it had a short exposure and shows various abnormalities. Nearly the whole copy is polarized, with the exception of the sky near a, where the critical exposure had been exceeded. The dogs in the foreground, reflecting the greatest amount of light there, show the beginning of the formation of a normal copy, ie 1) Annal. d. Chimie et de Phys. 1848; 3e série; T. XXII. 2) H. W. Voaeu. Handb. d Phot. 1890!; Bd. 1; S. 221. 3) Phot. Archiv. 1881; S. 120. 4) Soc. d’encourag. pour l'Industrie nation. Extr. d. Bulletin; Nov. 1899. 5) Astrophys. Journ. 1903; Vol. XVII; p. 361. 6) J. M. Eper. Jahrb. f. Phot. u. Repr. 1902; S. 73. 7) Phot. Arch. 1881; S. 120. 8) Phys. Zeitschr. 1903; S. 866. 9) This paper I only know from a resumé in J. M. Eper. Jahrb. f. Phot. u. Repr. 1903; S. 425. 10) The lens of the camera was a slow aplanat, and was used with full opening for the interior; for the outdoor exposure it was stopped down. (10) and so do the shoulders of the female figure to the right, owing to which especially the left shoulder shows a false relief. Consequently the critical exposure is reached after the greatest transparency of the image has been obtained. Between these beginnings of a normal copy and the polarized copy there is a clear strip, which is narrower where the exposure has been stronger. The dog to the left shows greater density of the normal copy than the one to the right, where the bright strip is broader. This strip occurs in the brighter parts in a manner that is the exact opposite of the way it oceurs round the outlines of the leaves of the “tree and of the bare trunk in the background; a few shoots are even quite white. Here the strips are found in tbe darkest parts, and decrease in width towards the right of the tree top, round which a smaller light intensity has been active. The wall was more strongly lighted to the left than to the right, and appears slightly darker there, but still it remains polarized, which is easier to see in the original film than in the reproduction. The left side of the tree top shows more halation than the right, while no halation whatever is to be seen in the part of the sky near a, which was subject to the action of light with greater contrasts. Here, however, one would have expected that halation would have acted in the opposite direction, viz. not decreasing in density in the darkest portions, but increasing in the lighter ones. The comparatively slight density of the sky near a is striking, and so is the low colour sensitiveness to green (grass and foliage), while the dark blond and dark brown hair of the two female figures show a stronger action of the light, which can be seen better in the original copy. The wall in the background is white, so that here the colour sensitiveness to the red of the bricks cannot be ascertained Fig. 6 renders the critical exposure still more strikingly. It repre- sents an interior; the film was exposed a few seconds, and shows every object in the room polarized, even a large portion of the halation owing to the light from the left window. What is seen outside through the windows has been copied normally ; here, consequently the critical exposure has been exceeded. The halation has partly made the lead setting of the coloured glass appear normal again, while to another portion it has given greater density owing to the action of the light being stronger. A large part of the right half and a smaller part of the left bottom section show differences in density, which must be ascribed to uneven action of the chemical reactions during the time the film was kept. Fig. 5 also shows this, but in a slighter degree ; here, however, it is less noticeable on account of the wealth eet") of detail of the image. The action being slighter to the right, the images are seen to be thinner accordingly. The same thing is to be observed in a Röntgenogram placed at my disposal by P. H. Eykman. The plate was exposed to Röntgen rays with a so-called intensification screen (calcium wolframate screen), and laid aside some time before development. Calcium wolframate postluminesces *) owing to which a plate is consequently further exposed. The objects photographed with Réntgen rays were a piece of bone, a piece of thin and a piece of thicker, insulated copper wire. Fig. 7 gives a reproduction of the negative. The places of the thin copper wire show development of the silver bromide which is nearly as strong as in the field, where the Röntgen rays and the luminescence together have acted most strongly. A narrow strip along the edge indicates how far the sereen covered the plate ; con- sequently there only the R. rays have acted. The place of the thin copper wire does not show a trace of development there; conse- quently the exposure remained below the liminal value. The development of this place cannot be put down to irradiation through the screen; in that case the same thing would have to be observed in the case of the thick copper wire and the edge of the screen. Consequently the R rays must really have acted in such a way in that place, that the sereen luminesced and this acted upon the silver bromide, while the exposure to R. rays remained below the liminal value. P. H. EYkMAN also showed me a negative in the case of which the screen after irradiation had only been brought into eontact-with an unexposed plate’). It showed a very thin image, from which it follows that the strongest action of the screen takes place immediately after the transformation of the absorbed Röntgen energy. Consequently if in the case of a röntgenogram with a calcium wolframate screen the action of the R. rays could be prevented, much shorter exposures would be sufficient to produce a good image. Hitherto this has proved to be impossible. Another fact important for our knowledge of the latent image may be gathered from fig 6. The right bottom corner shows that the thinner the fog of diffused exposure becomes, the thinner also the polarized copy is. From this it follows that in the case of secon- dary exposure the liminal value is lower than in the case of pri- mary exposure, de. the amount of light necessary to effect the begin- 1) Fortschr. a. d. Geb. d. R-Str. 1901; Bd. IV; S. 180. 2) The calcium wolframate screen was exposed to the R rays at the same time as the negative of Fig. 7. (12) ning of a decrease in reducibleness is smaller than is necessary for a beginning of an increase of this power with the original condition of the silver bromide. V. The theory of the latent image. In the case of the theory of the latent image two facts have to be observed, which are directly connected with each other: 1. The action of the light upon the silver haloids ; 2. The physical or the physical and chemical changes in the silver haloid resulting from this action. The theory proper of the latent image is only restricted to the latter, consequently comprises only secondary phenomena. Of all the theories enunciated, only the subhaloid theory of Croiset and Rate’) has maintained itself, especially owing to the subsequent investigations of M. Carey Lea’), H. Wuiss*), J. M. Eper‘), and others. While J. M. Eper*) looks upon silver subhaloid as a molecular compound, M. Carey Lea‘), B. Bauer’), L. GUNTHER *), and Lürro-CrAMER ®), consider it an absorption compound of colloidal silver and silver haloid, thus practically maintaining AraGo’s old silver-germ theory in a new shape. However, it is impossible yet to point out a single fact in photography from which it appears which of these two theories is to be preferred; all chemical reactions on the latent image might be accounted for by either theory and 1) Compt. rend. 1843: T. 16; Nr. 25. ” sh oe EMT De K J. M. Eper. Handb. d. Phot. 1898; Bd. Il; S. 111. 2) Americ. Journ. of Science. 1887; Vol. 33; p. 349. Phot. Korresp. 1887; S. 287, 344 u. 371. 8) Zeitschr. f. phys. Chemie 1905; Bd. 54; S. 305. Chem. Centralbl. 1906; Bd. I; S. 807. J. M. Eper. Jahrb. f. Phot. u. Repr. 1906; S. 473. 4) Sitzungsber. d_ kaiserl. Akad. d Wiss. zu Wien. Mathem.-naturw. Klasse. Bd. CXIV; Abt. Ila; Juli 1905. Zeitschr. f. wiss. Phot. 1905; Bd. Ill; S. 329. J. M. Eper. Handb. d. Phot. 1906; Bd. I; T. 2; S. 277. Phot. Korresp. 1905; S. 425 u. 476. 1906; S. 81, 134, 181 u. 231. 1907; S. 79. ) ” 5) See note 4. 6) See note 2. 7) Zeitschr. f. phys, Chemie. Bd. 45; S. 618. 8) Abhand. d. naturk. Ges. Nürnberg. 1904; Bd. 15; S. 26. 9) Phot. Korresp. 1906 u. 1907. Lippo CRAMER. Photogr. Probleme. 1907; S. 193. -_— En aa ( 13 ) neither of them has hitherto afforded a definite explanation of the various photographic phenomena. As the photo-chemical process of analysis upon the silver haloid is only characterized by a continuous reduction process, it is quite natural to assume this also in the cases of the solarized latent image Still there are a few phenomena which seem to contradict this. Thus W. Aprey ') assumed the formation of an oxybromide, and founded this assumption on the fact observed that potassium bichro- mate and potassium permanganate, perhydrol and a few anorganic acids promote solarization. The anti-solarizing action, also pointed out by him, of reducing agents, like pyrogallol, ferrous sulphate, ferrocyanide of potasium, nitrites, and sulphites, has only been judged from the appearance or non-appearance of polarization, and may be entirely reduced to retarded development. Lippo-CraMeR’*) considers the oxidation theory of solarization absurd. He points to the solarization of the plate even if no oxygen is admitted, and to the circumstance that all the agents that prevent solarization, are halogen-absorbing substances. As a characteristic example he mentions silver nitrate, the anti-solarizing action of which is, according to him, to be ascribed to halogen-absorption, not to oxidation, and considers this action analogous to that of nitrites, sulphites and hydroquinone. This view is at variance with his criticism of the oxidation theory, in which he also points to the continuous loss of halogen in the case of continued exposure of the silver haloid, and to his obser- vation that a bromide solution counteracts solarization, and may even entirely neutralize the latent image’). Consequently halogen-absorption must promote solarization. The promotion of solarization mentioned by W. Asnry, and referred to above is not to be ascribed to oxida- tion, but to halogen absorption. That oxidation of the substance of the latent image neutralizes solarization, has been ascertained by J. M. Eper *) with his chromic acid reaction, and by K. Scuaum and W. BrAUN®) with their ammo- nium persulphate reaction. That in this case we really have not the 1) Proc. Roy. Soc. 1873; Vol, 27; p. 291 a. 451. 2) Lippo-Cramer. Phot. Probleme. 1907; S. 138. 8) J. M. Eper, Jahrb. f. Phot. u. Repr. 1902; S. 481. 4) Phot. Korresp. 1902: S. 647. J. M. Eper, Jahrb. f. Phot. u. Repr. 1903; S. 23. J. M. Eper, u. E. VareNra, Beiträge zur Photochemie. 1904; Il; S. 618, J. M. Eper, Handb. d. Phot. 1903; Bd. III; S. 828. 5) Phot, Mitt. 1902; S. 224. (247) phenomenon of retarded development I could observe through the formation of a dull surface image. Further Liippo-Cramer') proved that the silver subhaloid of Porrrvin’s photochromies undergoes regression to silver haloid by oxidation. J. M. Ener?) described the same thing in his investigations of the latent image with the nitric acid reaction. Quite a different view of the progressive photochemical analysis of silver haloids, was given by H. Lueein*). He stated that in the case of more intensive exposure, also a proportionately greater amount of formed silver haloid, under the influence of the increasing halogen pressure takes from the silver haloid the power of afiording germ-points for the deposit of metal, and that consequently halogen- absorbents (chemical sensitizers) would be the best means of keeping the halogen pressure as low as possible, and so of preventing solari- zation. Consequently he considers solarization as a phenomenon con- sisting in the prevention of germ-formation. His statement: “The beginning of solarization may often be obviated by selecting smaller stops and increasing the exposure accordingly,” is confirmed in the case of silver iodide gelatine *). Still this proposition that halogen absorption prevents solarization is at variance with what goes before. I have therefore investigated this matter more closely. Silver haloid is decomposed by the action of light, but a polished silver bar exposed in the light to halogen vapours, at once combines with it to form halogen silver. Consequently in the presence of an excess of halogen the silver haloid is not decomposed. A highly sensitive silver bromide gelatine plate, which was partly coated with collodion, was exposed to direct daylight. It was observed that the photo-chemical decomposition under the collodion remained considerably behind that of the free surface, and had not even increased appreciably after an exposure of several weeks. The violet brown discolouration appeared only at the free surface, and could be removed by the plate being rubbed carefully. A plate, exposed at the same time on the glass side, also showed retardation as to the photo- chemical decomposition process, and against the glass the silver bromide seemingly remained unaltered. Consequently the fact that halogen prevents diffusion counteracts decomposition. In the case of 1) Phot. Korresp. 1907; S. 439. 2) See note 4, p. 3) J. M. Eper, Jahrb. f. Phot. u. Repr. 1898; S. 162. 4) J. M. Eper, Handb. d. Phot. 1906. Bd. I; T. 2; S. 309. Lijppo-CramMeR, Phot. Probleme. 1907; S. 152. (15) an excess of liberated halogen the opposite reaction takes place, which is quite in accordance with the regression of the latent image by a bromide solution in the case of silver bromide, as found by LürPo-CRAMER. The diffusion of liberated halogen will always take place in a smaller degree in the series chlorine, bromine, iodine, on account of the atomie weight rising. H. Lueein’s rule must, therefore, be modified to the effect that in the case of a certain definite light intensity the progressive and regressive reduction get into a condition of equilibrium, which is only got over by a loss of halogen (absorption by the chemical sensitizer and diffusion). The same thing was said in other words before now by J. Precur *), but on the ground of the appearance of solarization. With this modified proposition of H. Lueain the deviations’) from R. Bunsen’s and H. Roscoe’s reciprocity rule’) can be accounted for, to which also belong the phenomena in the case of silver iodide gelatine just mentioned. The knowledge of the latent image is arrived at by development. While the exposure causes decomposition of the silver haloid accom- panied by a quantitative increase in silver subhaloid, a decrease of reducibleness appears during development after a certain maximum of exposure. The solarization phenomenon is, therefore, a development phenomenon in the sense that development, owing to the modified properties of the latent image, shows a change. Consequently in order to account for solarization a knowledge of the nature of development is requisite. Without it solarization remains an unsolvable problem. Two methods of development are distinguished: The physical and the chemical method *). Physica) development is characterized by a deposit of a reduced silver compound from the developer on the exposed silver haloid; chemical development by reduction of the exposed silver halogen itself. 1) Zeitschr. f. wiss. Phot. 1905. Bd. III; S. 75. 2) J. M. Eper, Handb. d. Phot. 1906; Bd. [; T. 2; S. 48 u. 49. : 5. -s « va. L902; Bdy IKE, -S..238. eek. He tyes. 5 {5 OD DLs Se Ms oe Phot. Mitt. 1890; S. 261, Proc. Roy. Soc. 1893; Vol. 54; p. 143. 3) PoGGENDORF Annal. d. Phys. 1862; Bd. 117; S. 538. 4) J. M. Eper, Handb. d. Phot. 1898; Bd. II; S. 29. = 7 Es » 1906 B, LRZ B. 250. ( 16 ) By W. Osrwarp'), K. Scuaum and W. Braun?) it was supposed that the reduction of the silver bromide with chemical development was in the first instance brought about by a minimum amount of silver bromide dissolving as positive silver- and negative haloid-ion, after which the reduced substance was precipitated upon the germs. Lippo-Cramer*) succeeded in sbowing that a number of developing processes which were formerly looked upon as being purely chemical in their nature, not only in reality proceed physically, but that every chemical development is also partly of a physical character. W. Scuerrer*) was the first to show by a microscopical investigation that the entire chemical development is physical in its nature, i.e. it is brought about by molecular attraction between the photo- chemically reduced silver haloid, the germ, and the reduced feeding- substance. This, consequently, accounts for the altered structure of - the exposed silver bromide gelatine plate before and after development ®). Still the development of the photographic plate by the so-called chemical method really shows a difference from the physical method. Lippo-CraMer’) succeeded in demonstrating that the substance of the image in the case of a negative developed by the so-called chemical method, still contained bromine by tbe side of ordinary silver, which bromine he supposed to be a constant solution of silver in silver bromide. From this he infers that during the development, beside the silver another intermediate product must originate. It is only natural to assume, on the analogy of the reduction process of the silver haloid to silver through subhaloid, that also in the case of so-called chemical development the reduction takes place in the same way. Thus it appears that between chemical and physical develop- ment there is only this difference that the former keeps the subhaloid in solution with more difficulty than the latter, owing to which perfect reduction cannot take place. This at the same time accounts 1) W. OsrwaLp. Lehrb. d. allgem. Chemie. 1893; Bd. 2; S. 1078 2) J. M. Eper. Jahrb. f. Fhot. u. Repr. 1902; S. 476. Phot. Mitt. 1902; S. 229. 8) Lippo-CramMeER. Phot. Probleme 1907. S. 159. 4) Phot. Rundschau 1907; S. 142. Phot. Korresp. 1907; S. 384. 5). S, E. Saepparp and C. E. K. Mers. (Zeitsch. f. wiss. Phot. 1905; Bd. III; S. 355) consider V. BrLuacu’s observation that the size of the grain of the developed image decreases during the drying of the emulsion, to be in accordance with G. QuincKE’s foam-structure theory of the silver haloid grains which, according to him, contain gelatine. The ron-coalescence of the exposed with the developed grain shows the incorrectness of this view. 6) Phot. Korresp. 1905 S 319 (27) for the fact that the image developed with certain developers loses density in the fixing bath; this loss of density is analogous to what is observed in the case of P. O. P. papers with silver chloride. This further explains another apparent contradiction. While with silver chloride a lower and with silver bromide a higher degree of sensitiveness to light is observed, in other words, while quantitatively the same photochemic decomposition of silver bromide takes place with less absorption of light energy than in the case of silver chloride the exact opposite is seen to take place with the increase in density during development, which has been pointed out by H. and R. E. LiksEGANG '), Konic’) and Lijprpo-Cramrr’*). Considering that silver chloride possesses a higher solubility, resp. has the power of bringing a greater number of ions into solution than silver bromide, it is easy to understand that quantitatively reduction can take place ina larger measure per unit of time, notwithstanding silver chloride is a more constant compound than silver bromide. With silver iodide the same thing is observed still better. The reducibleness, resp. solubility is still less in this case, which has often occasioned the unjustified conclusion, that silver iodide is less sensitive to light than silver bromide, while the exact opposite is observed in the case of daguerreotypy and the wet collodion process, since here the feeding substance for development is introduced from without. Accordingly LürrPo-CrAMER could use with silver iodide developers like amidol potassium carbonate, triamidophenol, diamidoresorcin, and triamidoresorcin, which show a far too great rapidity of reaction for silver bromide plates. The higher sensitiveness of silver iodide-bromide plates as compared with silver bromide plates, owing to which more detail can be obtained in the darkest parts of the image, may therefore be ascribed to the more rapid formation of germs in the case of silver iodide, while the silver bromide serves as feeding substance for the developer. This further appears from the optical sensitizing of silver iodide-bromide plates. While silver bromide can easily be made colour sensitive, this is not the case with silver iodide, which has been pointed out by J. M. Eper *), Lippo-Cramer ‘), and others. Still both may be dyed 1) Phot. Mitt. 1901; S. 362. Phot. Wochenbl. 1901; S. 405. J. M. Eper. Jahrb. f. Phot. u. Repr. 1902; S. 572. 2) Phot. Korresp. 1903; S. 14. 3) J. M. Eper. Jahrb. f. Phot. u. Repr. 1903; S. 401. 4) J. M. Eper. Handb. d. Phot, 1906; Bd. I; T.2; S. 269. 5) J. M. Eper. Jahrb. f. Phot. u. Repr. 1903; S. 46. ” ” ” ” ” ” 1904; 5: 390. Zeitschr. f. wiss. Phot. 1903; Bd. I; S. 17. Proceedings Royal Acad, Amsterdam, Vol. XI. (18 ) by optical sensitizers, but in this case the silver iodide-bromide plate behaves more like a silver iodide plate. At the 79'k German Physical and Medical Congress held in Dresden in 1907 W. ScHerrer*) communicated a solarization theory founded upon his microscopic investigations ®), which explains solarization in quite a simple way. When the exposed silver bromide gelatine plate is being developed certain grains (“Ausgangskörner”) send ont germs, upon which the reduced substance is deposited, because other grains (“Nahrkörner”, formerly called “Lösungskörner”) are dissolved in the developer and cause the growth of the germs. In an overexposed emulsion too many germ-producing grains “explode”, and an insufficient number of “feeding” grains remain, so that no image of sufficient density can be formed. Consequently this theory is founded upon the transition of “feeding” grains into germ-producing ones by exposure, or rather of silver haloid into silver subhaloid. This theory cannot be reconciled to the fact found by J. Srerry’), J. M. Eprr*) and Lippo-Cramer ®), that solarization can also appear with primary fixation, for in this case the feeding substance is sup- plied from without. The same holds good with regard to daguer- reotypy. B. Homorka’s solarization theory °): “In the decrease of the amount of silver bromide I recognize the primary cause of solarization’, is irreconcilable to the above, not to mention the circumstance that these two theories cannot explain the second reversion of solarization, and cannot account for the fact that even with the strongest over- exposures an excess of silver haloid, i.e. of feeding substance, can be proved to be still present in the emulsion. From the solarization with primary fixation it therefore appears, that the silver haloid germ loses this germinating property on further exposure, i.e. through the continued photochemical decomposition it has passed into another subhaloid containing less halogen, which possesses no germinative property. O. Wiener’) proved the possibility of the existence of more subhaloids. Let us call the first the «-silver subhaloid and the second the g-silver subhaloid. 1) Phot. Korresp. 1907; S. 487. 2) Phot. Rundschau. 1907; S. 65 u. 142. Phot. Korresp. 1907. S. 233 u. 384. 3). J. M. Eper. Jahrb. f. Phot. u. Repr. 1899; S. 289. 4) J. M. Eper. Handb. d. Phot. 1906; Bd. I; T. 2; S. 312. . 5) LüpPo-CRAMER. Phot. Probleme, 1907; S. 150. 6) Phot. Korresp, 1907; S. 168. 7) J. M. Eper. Jahrb. f. Phot. u. Repr. 1896; S. 55. (19) The reappearance of reducibleness in the case of continued exposure, the so-called second reversion of solarization might then again be attributed to a newly formed y-silver subhaloid, or, as the third reversion has not been observed, to a metallic silver germ or what is also possible, to both. It must be emphasized at the very outset, that it is by no means impossible that before the a-silver subhaloid one or more other sub- haloids, richer in halogen, are formed, which possess no germinative property, for a primary exposure below the liminal value of the plate points to photochemical decompositions taking place through the occurrence of auto-sensitizing'), so that the liminal value cannot be considered identical with the photochemical induction. Nor must it be inferred from the above that the «- or the 8-silver subhaloid does not consist of more than one silver subhaloid. Consequently it appears from all this that sensitiveness to light and reducibleness must on no account be identified, as is generally done. The untenableness of the existing theories of Hrrscnur’s effect by Crauper, P. VirzarD, R. W. Woop and WARNERKE is accounted for by this faulty identification of reducibleness with sensitiveness. For the appearance of Herscunun’s effect it is necessary that the primary exposure should exceed the liminal value of the plate. Con- sequently a-silver subhaloid must have been formed. That by the secondary exposure a regressive reaction occurs between the a-silver subhaloid and halogen, cannot be assumed, because in the case of prolonged exposures HmrscuE’s effect coalesces with solarization, in connection with which the formation of the B-silver subhaloid without germinative property has already been stated. The experiments of W. ABNey mentioned above, also prove that halogen absorption promotes the phenomenon. Consequently the secondary exposure acts in such a way that the a-silver sub- haloid formed photochemically by the first exposure is reduced to B-silver subhaloid more rapidly than it has been possible for an equal quantity of a-silver subhaloid to be formed afresh. (In this case it may happen that the silver subhaloid has already entirely been photochemically dissolved, before the silver haloid has been able to supply it). This appears from the discussion of fig. 6. The photochemical induction of the q@-silver subhaloid is, therefore, lower 1) Vide: J. M. Eprr. System der Sensitometrie phot. Platten. Sitzungsber. d. kais. Akad. d. Wiss. in Wien 1899; Ila; Bd. 108; S. 1407. J. M. Eper u. E VALENTA, Beiträge z. Photochemie. 1904; Bd. Il; S. 48, 2% ( 20 ) than the liminal value of the silver haloid. Consequently the a-silver subhaloid is a substance of greater sensitiveness to light than the silver haloid. If with the secondary exposure the amount of a silver subhaloid originally present is exceeded, a normal copy is obtained again. The critical exposure, therefore, is that secondary exposure by which the same amount of @ silver subhaloid is formed as was present after the primary exposure. So the best gradation of the polarized copy in the case of Herscreur’s effect is obtained, if lower light intensities are employed, as is shown by experiments. The amended proposition of H. Lueain states that with a certain definite light intensity the progressive and the regressive reaction in the silver haloid arrive at a state of equilibrium, if the liberated halogen is not removed. This removal of halogen, either by diffusion or by chemical sensitizers, is therefore of paramount influence upon the origination of Hurscuern’s effect. Consequently the most successful experiment is obtained with an emulsion which immediately absorbs the liberated halogen, or what is better even, if between the primary and the secondary exposure the plate is put aside for a considerable time, by which the liberated halogen is diffused out of the emulsion. It is still suapler to treat the plate after the primary exposure with a halogen absorbent, as was done by W. ABNeY, and we therefore regard judson blue, mentioned by H. W. VoeceL*) as a substance probably behaving analogously. Therefore the direct decomposition of the silver haloid by reducers as in the case of J. Serry’s experiments and fig. 5 and 6, in which the liberated halogen enters into combination, acts so favourably upon HerscHEL’s effect. This makes P. Virrarp's statement clear that not all emulsions are equally suitable for experiment, as in the various emulsions there are different chemical sensitizers (both in quality and in quantity). At the same time the nature of the phenomena in the case of intermittent exposure becomes clearer now. That the effect of development upon silver bromide gelatine (but not necessarily the photochemical decomposition) is always slightly less than with a continuous exposure of the same duration was observed by W. Asner’), K. ScHWARZSCHID®), and others. Many 1) H. W. Vocer. Handb. d. Phot. 1890; Bd. I; S. 221. 2) Photography 1893; p. 682. Phot. Archiv. 1893- S. 339. J. M. Eper. Jahrb. f. Phot. u. Repr. 1894; S. 373. 5) Phot. Korresp. 1899; S. 171. ( 21) beginners in photography have observed the same thing when having made two exposures of different objects on the same plate. In this case it is easy to observe that not the sum of the two images is obtained, but that in one place one object dominates, in another place the other object. According to K. ScHwarzscHiLD the result in the case of the exposure being intermittent depends, iter alia, upon the relation between the interval and the duration of the separate exposures; the longer the interval the better opportunity the halogen has of escaping by diffusion, or of being absorbed by a chemical sensitizer, and the more readily the next exposure will photochemically decompose the « silver subhaloid germ, which is more sensitive to light than the silver haloid, into 2 silver subhaloid and halogen, owing to which the result of development, apart from the photo- chemical induction which is to be exceeded again, will remain below the sum of the components. The difference in sensitiveness to light between silver haloid and the a silver subhaloid appears, according to the above experiments, to depend largely upon the kind of light with the seconday exposure. The less sensitive the silver haloid and the more sensitive the « silver subhaloid is to a given colour, the more pronounced Herschel’s effect will be. The smaller this difference, the more rapidly the silver haloid will produce fresh a silver subhaloid germs; it is true, in this case polarization is observable, but the minimum reducibleness is soon reached. Further this is, of course, also dependent upon the amount of « silver subhaloid, i.e. upon the duration of the primary exposure. Perfect neutralization of reducibleness need not occur then. Consequently . the colour sensitiveness occurring in the case of Hrrsoumr’s effect is to be ascribed to the colour sensitiveness of the a silver subhaloid. Not one of the theories of the latent image enunciated hitherto can account for the phenomenon in such a simple way as the subhaloid theory. The subhaloids are dyes of quite different colours from silver haloid, and consequently with quite different spectra, owing to which the possibility exists of quite different colour sensitiveness, as in fact actually appears from the experiments of O. WIpNER ’). P. VirrarD proved spectroscopically that the greatest difference between the liminal value of the silver haloid and the photochemical induction of the a-silver subhaloid is situated in the red 1) Probably these photochemical decompositions proceed according to an expo- nential formula. 2) J. M. Eper. Jahrb. f. Phot. u. Repr. 1896; S. 55, ( 22 ) and consequently that the a-silver subhaloid is a substance sensitive to red. If @ silver bromide gelatine plate is exposed to the action of a continuous spectrum, the reducibleness in the case of increasing exposure will proceed from blue to red. While after development it is observed that with increased exposure the density of the plate increases about and in the spectral blue, the yellow, the orange, and especially the red obtain only very slight densities. Consequently it is evident that the cause why the density of the image in the red, yellow, and orange portions cannot increase above a maximum, which is very low, lies in the a silver subhaloid possessing a far greater sensitiveness to red than the silver haloid, so that very soon a state of equilibrium has been reached, in which in a progressive process as much a-silver subbaloid is formed as destroyed. The substance of the developable latent image is considered identical with M. Carey Lxa’s photohaloid. Now how does this behave in red light? M. Carey Lea’) exposed his pink photohaloid to the action of a spectrum ; while under all colours the photohaloid changed, it remained unchanged in the red. From this it appears that the subhaloid germ of the latent image must be another substance than M. Carey LrA’s photohaloid. The behaviour of Röntgen rays differs from that of other kinds of light. According to P. Vrrrarp, R. W. Woop, R. Luruer, and W. A. Uscnkxorr they show no Herscuet’s effect in the case of secondary exposure. This cannot be ascribed to total non-sensitiveness of the a silver subhaloid to Röntgen rays. It is true, F. HAUSMANN *) and others stated that Réntgen rays produced no solarization, and consequently that there was no formation of 2 silver subhaloid, but P. H. Eyxman’*), and subsequently K. ScHaum and W. BRAUN ‘) could show that they do. So the silver subhaloid is also sensitive to Röntgen rays, and the non-appearance of Hrrscrer’s effect must be put down to the cause that for Röntgen rays the silver haloid has a liminal value as great as, or greater than the photochemical induction of the « silver subhaloid. It is therefore assumed that in the case of réntgenography the intermittent exposure, apart from the photographic induction to be exceeded each time, does not produce a photographic effect that remains below that of a continuous irradiation. ; 1) Americ. Journ. of Science 1887; Vol. 33; p. 363. 2) Fortsckritte a. d. Geb. d. R.-Str. 1901; Bd. V; S. 89. 8) Fortschr. a. d. Geb. d. R-Str. 1902, Bd. V, Heft 4. 4) Zeilschr. f. wiss. Phot. 1904; Bd. 1; 5. 382. (23 ) From H. Lveer’s modified proposition it appears clearly, how the chemical sensitizers promote the photoehemical decomposition process of the silver haloids by halogen absorption. They consequently pre- vent regression. Lürpo-CrAMER *) describes the following experiment, which confirms this. Precipitated silver chloride shows neither with silver nitrate, nor with ammonia, both chloride absorbents, any increased sensi- tiveness to light when photochemically decomposed ; in an emulsion where the rapid escape of the liberated halogen is prevented, the action of the chemical sensitizer is therefore observed. From this it follows that the chemical sensitizer does not react upon the silver haloid itself at all. Even from the considerable deviations from the reciprocity rule in a silver bromide gelatine plate with very low light intensities it follows that gelatine is not a chemical sensitizer, which has also been proved in another way, experimentally, by Lippo-Cramer.’) While the chemical sensitizers act very favourably in the printing- out process, they have no, or even a detrimental influence in the ease of silver haloid emulsions intended for development, as has been pointed out by LüpPo-CraMER*). If it is borne in mind that the a silver subhaloid germ itself is a substance very sensitive to light, which with loss of halogen, passes into the 8 zilver subhaloid without germinative property, it is clear that a too active chemical sensitizer does not promote reducibleness. A number of chemical sensitizers, however, are oxidizers at the same time. From what has been said above it has appeared that oxidation transforms the 8 silver subhaloid into « silver subhaloid (neutralization of solarization), which may be thus represented : B silver subhaloid + oxygen = silver oxide (Ag,O?) + a silver subhaloid. This reaction seems to proceed very slowly in the case of sub- bromides. Owing to this complications may arise, so that the chemical sen- sitizer, while on one hand promoting the photochemical reduction, on the other hand again partly oxidizes the silver subhaloid that has been formed. Here the action of the chemical sensitizer is favourable for the process of development, as in the case of the 1) Phot. Korresp. 1901; S. 224. Lürppo-CRAMER. Wissensch. Arbeiten 1902; S. 87. J. M. Eper. Jahrb. f. Phot. u. Repr. 1906; S. 648. 2) Liippo-Gramer. Phot. Probleme. 1907; S. 33. 3) Phot. Korresp. 1903; S. 25. (24) silver iodide collodion plate with silver nitrate, which in the pre- sence of light is a powerful oxidizer’), and the question is whether the so-called neutralization of solarization by silver nitrate is not to be ascribed to this as well, and consequently is real neutralization. If silver haloids are allowed to be photo-chemically decomposed, the great influence of the size of the grain at once becomes evident. While fine grain silver chloride or bromide is decomposed rapidly, the latter even more rapidly than the former, the directly visible decomposition in the case of course-grain silver haloids is slower. This can at once be accounted for by H. LuaaiN’s modified rule. At the surface of the silver haloid grain the liberated halogen can escape more easily, or enter into composition; inside the grain it acts regressively, so that the progression will decrease from the surface to the centre. H. LuveeiN®), too, refers to the same thing in the case of silver iodide. But even if it is in a very finely divided condition, the directly visible photo-chemical decomposition does not take place rapidly. Owing to its greater atomic weight the liberated iodine not only diffuses more slowly, but moreover it is a solid substance. By absorption of this iodine, e.g. by silver nitrate, the directly visible photo-chemical decomposition at once becomes more rapid, so that it is clear why a silver haloid which is more sensitive may all the same yield a less advanced photo-chemical decomposition. The surface decomposition of the silver haloid grain at the same time points to the fact that here, too, the seat of the latent image is to be looked for. This is also to be inferred from further data. Thus the deposits of reduced silver haloids discovered by W. Scuer- FER ®) always start from the surface of the silver haloid grain, which appears from a microphotograph published by him. Further Lippo- CRAMER *) pointed to the dependence of the quantity of dye in the case of optical sensitization upon the surface to be coloured (i. e. upon the size of the grain) with silver chloride and silver bromide. When it has been pointed out that in the appearance of solarization by primary fixation and secondary development the existence of a 1 M. Carey Lea (Phot, Korresp. 1887; S. 346) and Liippo-CRAMER (Phot. Korresp. 1907; S. 538) showed that silver subiodide is a substance which is extremely easily oxidized. 2) Zeitschr. f. phys. Chemie. 1897; Bd. 23; S. 611. 8) Phot. Rundschau. 1907; Heft 6. 4) J. M. Eper. Jahrb. f. Phot. u. Repr. 1902; S. 58. - sa Se ee aoe ( 25 ) silver subhaloid can be proved, this is not enough to account for the solarization phenomenon. In order to illustrate this let us assume a photo-chemical decom- position with direct recomposition of the liberated halogen. If the exposure of a photographic plate is prolonged, the silver haloid will keep forming a silver subhaloid, which is the germ for development. From Hurscuet’s effect, however, it appears that this a silver subhaloid in itself is a highly light-sensitive compound, so that it is not to be assumed that a continual accumulation of germs is taking place. Consequently the « silver subhaloid rapidly decom- poses into 2 silver subhaloid and halogen. At the surface of the silver haloid grains a condition therefore arises in which the number of germs present depends upon formation and destruction. If the quantity of the remaining grain surface silver subhaloid decreases, the quantitative formation of « silver subhaloid will also decrease, and as the latter itself is highly sensitive to light, the consequence of this will also be a quantitative decrease of the number of remaining germs, in other words, the reducibleness will decrease, i.e. solarization will set in. This phenomenon is, therefore, entirely dependent upon the avail- able surface of the grain (size of the grain). In his experimental researches LürPpo-CRAMER *) repeatedly pointed to this fact. In reality this, of course, does not take place so rapidly. The various makes of plates have chemical sensitizers which differ from each other (qualitatively and quantitatively). This, together with the prevention of diffusion, is the reason why the different commercial plates begin to get solarized after mutually different exposures. The thiosulphate reaction shows peculiarities which can be accounted for now. The subhaloids are decomposed by the action of thiosul- phate into silver and halogen silver, which after being converted into silver thiosulphate, dissolves as a double salt. The place of the a silver subhaloid germ and the 2 silver subhaloid is consequently taken by silver, which also possesses the property of germination, as appears from the development of primarily fixed plates. Strong solarization, however, still produces solarization during development after primary fixation, so that the reaction between 9 silver subhaloid and the thiosulphate in the binding material is a slow one, as is the oxidation process already referred to. So if a highly sensitive course 1) Phot. Korresp. 1901; S. 350. Lürppo-CGRAMER. Wissensch. Arbeiten. 1902; S. 41. LürpPo-CRAMEB. Phot. Probleme 1907; S. 146, ( 26 ) grain plate, i.e. one with a small grain surface, in other words, with a small quantity of 2 silver subhaioid, which has been exposed till solarization has set in, is treated, the reaction in the gelatine will be complete sooner than with a greater quantity of @ silver subhaloid in the same gelatine plate, as is the case with fine grain emulsions. The reducibleness will consequently show an increase (not to be confounded with acceleration), so that in proportion to the strength of the thiosulphate solution employed, and the duration of the action, the solarization will be removed, either to a smaller or to a greater extent, or totally. This phenomenon was observed experimentally by KoOGELMAN *), Vipar?) and E. EnerrscuH *), while Liprpo Cramer‘) could not demon- strate solarization at all with primarily fixed, highly sensitive, coarse- grain plates, which fix more slowly than fine-grain ones. Sulphocyanides act analogously in reducing solarization. In the case of SABATIER’s polarization the strong decrease (dis- appearance ?) of development of the image after it has appeared is not to be ascribed to the decrease of the number of germs, as they have already fulfilled their function *). So the decrease of develop- ment can only be a reduction of the speed of development, which is to be accounted for by a strong decrease in the supply of feeding substance. From the theory given above of the so-called chemical method of development it has appeared that the silver subhaloid proves to be less soluble in the developer than the silver haloid. Therefore the more soluble silver haloid can, after reduction, be precipitated upon the germ, which still remains unchanged in its place. Consequently if the secondary exposure is of an intense nature, the feeding substance will be enveloped by subhaloid, by which development is retarded. This will take place in the developer all the more readily, because it is an absorbent of halogen. In conclusion reference may be made to a possible explanation of the variations in the optical sensitizing of the photographic plate which is characterized by a considerable decrease in reducibleness being noticeable in the places where the power of absorption is spec- 1) J. M. Eper. Jahrb. f. Phot. u. Repr. 1895; S. 419. 2) Bull. Soc. frang. Phot. 1898; p. 583. 3) J. M. Eper. Jahrb, f. Phot. u. Repr. 1901; S. 608. 19023-5479: r nn BS Seg OE 4) Liippo-CramerR. Phot. Probleme. 1907; S. 150. 5) So far there is not a single reason for assuming that this reduced substance consists exclusively of « silver subhaloid germs, which pass into silver subhaloid by. the secondary exposure, by which further development would be checked. ” ” ” ” n ” ( 27 ) trally highest. From M. ANDRrsEN’s experiments ') it appears that the photo-chemical decomposition products remain in contact withthe dyestuff, so that the a silver subhaloid obtains a different colour sen- sitiveness. In this case complications may occur, if the dye is at the same time an absorbent of halogen (a chemical sensitizer), by which it changes or loses its absorption spectrum, and a consequent promo- tion of the photo-chemical decomposition action sets in. VI. Conclusions. From what has been said a few conclusions ay be drawn, which may be of importance in practice. Both « silver subbromide and iodide are substances of a much greater sensitiveness to light than the corresponding silver haloid. Consequently if it was possible to compose emulsions in which these substances were present side by side with the silver haloid which as feeding substance is indispensable for development, plates would be obtained not only of a higher sensitiveness than the present ones, but in them a chemical sensitizer would be practically desirable in every respect to prevent regression. Such plates would entirely comply with the reciprocity rule, and would render the light grada- tions of the objects to be photographed much more correctly, which may be of great value to astronomical photography, e.g. for the determination of the light intensity of stars by the photo-chemical method (Photometry). The « silver subhaloid can be optically sensitized, so that its ap- plication might obtain a great extension. The exact colour sensiti- veness of the « silver subhaloid separately is not yet known exactly. (That in the case of secondary exposure the highest sensitiveness is situated in the red, the lowest in the green, points with great pro- bability to the « silver subhaloid being a green substance). The experiments mentioned indicate everywhere only the difference in light sensitiveness between silver haloid and the a silver subhaloid. The greater this difference, the more favourable the result obtained. Consequently the best expectations might be entertained with respect to silver chloride plates with a silver subiodide, and it is an open question whether the latter may not be allowed to ripen too. The B-silver subhaloid seems to possess, photo-chemically, an extremely low sensitiveness, which can only be advantageous in practice. This process yields directly polarized copies (positives through the 6) Phot. Korresp. 1898; S. 504, ( 28 ) camera). On one hand this seems an objection, as all printing methods are based upon the production of normal copies (the negative process). But it should be borne in mind that hitherto very few researches have been made in this domain. For direct colour photography *) with colour elements lying side by side under the emulsion, according to L. Ducos pu Hauron’s system (which especially lately has given promise of a great future), which requires directly polarized copies, and which so far has only succeeded in obtaining them in an indirect way, this method would also be practically valuable. In this direction little experimenting has hitherto been done from a photo-chemical point of view, and even in what has been done it has been impossible to account for the phenomena that occurred, so that for the present there is no need for us to take too pessimistic a standpoint with reference to this. VII. The shape of the image in the case of Herschel’s effect. As to the shape of the image in the case of Hrrscrer’s effect fig. 8 may be referred to. It is clear that after the critical exposure the normal copy is again a surface image. If a considerable portion of the surface silver haloid present has already been decomposed into a silver subhaloid and halogen, the secondary exposure will not be able again to form as much « silver subhaloid as would have been the case if the primary exposure had not taken place. A negative is obtained then the density of which is less than that of a plate not previously exposed. This case presents itself in the sky a in fig. 5. Advanced primary exposure may result in solarization, in which case the surface silver haloid can no longer supply the same quantity of germs as was present before: Hrrscumr’s effect then coalesces with solarisation, and the critical exposure can no longer be ascertained. The greater light sensitiveness of the « silver subhaloid as compared 1) I expressly call this method “direct”, because I cannot agree to the judgment of a number of others, who want to classify it among the indirect methods. They say that it is not direct colour photography, but three-colour photography, ignoring the fact that the bleaching method which is reckoned to belong to the direct methods, is also three-colour photography. Nor can I agree to A. v. Hüpr's classification (Phot. Rundschau, 1908, p. 2), by which the bleaching process would be assigned to the indirect methods. The fact of the matter is that the difference is only a question of method, i.e. whether the colours are obtained directly after exposure (with development), or only through subsequent addition. roperties of the latent image.” A.P. H. TRIVELLI, ‘A contribution to our knowledge of the solarization phenomenon and of some other properties of the latent image.” Ss | P 7Z ; d wp Fig. 1. Fig. 2 Hil oI Fig. 6 =e Fig. 3. a JE Fig. 4. Proceedings Royal Acad. Amsterdam. Vol. X. Fig. 8. Fig. 7. (29) with that of silver haloid is also shown in the amount of halation. In fig. 5 the foliage of the tree is affected by it, while the houses round the sky near a do not show any; there the halation was too slight to exceed the liminal value of the silver haloid. In fig. 6 the dark lead frame of the window also shows the destruction of the germ owing to halation; on the other hand on the right side it was able to form fresh germs through a more powerful action. That the difference in light sensitiveness between the germ and the silver haloid is- great, appears from the backs of the dogs, and from the shoulders of the female figure to the right in fig. 5. The narrow white strip indicates that after the germs had been totally destroyed at the free surface, for some time longer the silver haloid again began to supply germs, first in the most strongly exposed portions, and then gradually also in those which received less expo- sure. Consequently if the action of the light increases, these strips must become narrower, which is also shown by the figure, as the dog to the left was more glossy than the one to the right. The white strips along the edges of the black objects in the back- ground are of quite a different nature. These are to be ascribed entirely to irradiation, for in the case of stronger light intensities occurring side by side they are broader than where the intensity is less great. If observed very closely by light reflected at an angle, these bright strips are seen to possess a greater gloss than the portions immediately adjoining them. To the left of the tree top this is easier to see than to the right. The light from the wall has acted more intensely to the left than to the right, and notwithstanding the polarization a copy of greater density is shown there. That the critical exposure should have been surpassed, is out of the question here. This phenomenon, too, can be accounted for according to the theory given, for in this theory it has been stated, that the critical exposure is not surpassed till the secondary exposure has formed a greater amount of a silver subhaloid than is present in consequence of the primary exposure. Consequently after the liminal value of the silver haloid has been surpassed, a new surface image can originate, the density can increase afresh, and still at the same time the copy will remain polarized. All the abnormalities in the figures 5 and 6 have thus been accounted for. In conclusion I wish to express my best thanks to Mr. P. H. Eykman for finding materials and placing them at my disposal, and for his constant interest in my work. ( 30 ) Physics. — “Jsotherms of diatomic gases and their binary mixtures. VIII. The breaking stress of glass and the use of glass tubes in measurements under high pressure at ordinary and low temperatures’. By Dr. H. KAMERLINGH ONNEs and Dr. C. BRAAK. (Communication n°. 106 from the Physical Laboratory at Leiden by Dr. H. KAMERLINGH ONNEs). (Communicated in the meeting of April 24, 1908). _$ 1. Introduction. With former determinations of isotherms (Comms. n°, 78 April 1902, 97¢ March 1907, 997 Sept. 1907, 1007 and 1005 Dec. 1907, 1024 Dec. 1907 and 102% Febr. 1908) we could not raise the pressure above 60 atm. For in order to reach the required accuracy of about '/,,,, we want a manometer which is reliable to the same degree. And till now we could only reach this degree of accuracy by means of a calibration with the open manometer de- scribed in Comm. n°. 44 (Nov. 1898) which reads to 60 atm. only. Already long ago we intended to include the higher pressures in our investigation. As a first step in that direction we have raised the upper limit of the pressure to 120 atmospheres. For while keeping the same arrangement we could easily complete the existing open manometer to one of the same accuracy reading to 120 atmospheres by merely adding a number of new manometer tubes of greater resisting power than those we had. The new manometer and also the other apparatus intended for pressures to 120 atmospheres are nearly completed and will soon enable us to determine the isotherms to 120 atm. Afterwards we hope that these will be followed by measurements at still higher pressures. It seems even possible to reach 500 atmospheres with almost the same accuracy. For all these investigations it is a great advantage when the piezometer- and barometer tubes can be made of glass. Therefore we have investigated in how far this would be possible with regard to the breaking stress of glass. The breaking stress of glass has been investigated most at ordinary temperature, because it is in the first place desirable that the reservoirs of the manometer tubes of the open manometer and the divided stems of the piezometer tubes should be made of glass. To these measurements we have added a series of determinations at lower temperatures in order to judge to what extent glass piezo- meter reservoirs could be used for the higher pressures at these temperatures. (31) Investigations on the maximum strain of glass have been made by GarrrziN*) and by WiINKELMANN and Scnort *®). The former has determined the inner pressure which cylindrical glass tubes. can resist, the latter two have determined the maximum strain of glass rods. Gawirzin’s determinations, however, were made only at relatively small pressures, those of WINKELMANN and ScnorrT only at ordinary temperature. In our investigation we partly follow the method of Gatrrzin. From the theory of elasticity we can derive in connection with the dimensions of the apparatus the maximum tension in the glass from the maximum pressure which the glass tube resists. The results obtained in this way were compared with the direct data obtained in a second series of measurements, where the maximum strain of glass rods was determined. If we take into consideration the material investigated, it is not astonishing that the results of the two series show irregular differences. These differences however are of no influence upon some general conclusions that may be drawn from the measurements. § 2. Determinations at ordinary temperature. Survey of the observations and arrangement of the measuring apparatus. 1. Deterirination of the maximum inner pressure. The experiments were made with ordinary Thiiringer glass. A cylindrical reservoir of the glass to be investigated was fused on to a thick walled glass capillary. The capillary was provided at its end with a steel nut with a hexagonal part by means of which it could be screwed on to a steel capillary which is connected to a pressure pump with a metal manometer. For measurements to 200 atms. it was fixed on the glass by means of sealing wax, for higher pressures it was soldered to the glass (comp. Comm. N°. 99a § 15, October 1907). If carefully made this connection proved able to resist the highest pressures (1200 atms.) The tubes were previously annealed carefully. According to their dimensions they can be divided into three kinds: a. thick-walled tubes with large inner bore. b. thick-walled capillaries. _c. thin-walled tubes with large inner bore. It will appear that these three kinds of tubes give results different for each group. 1) Bull. de l’Acad. Imp. des Sciences de St. Pétersbourg, Ve Serie, B. XVI N°. 1. *) Wied. Ann. 51. (32) The accuracy of the manometer is about 2 °/,, which is quite suf- ficient for our purpose. 2. Direct measurement of the maximum strain T„ by the deter- mination of the breaking stress. In order to prevent as much as possible unequal strain during the suspension we have used here glass threads of at the most 0.6 mm. thickness *). In order to reduce the tensions to minimum the glassrod was bent to a hook at either end. It was then suspended by the upper hook and the rod was drawn out in the middle to a thread by applying a certain force to the lower hook in about the same way as in the actual experiment. The weight used was a beaker into which water flowed. § 3. Results. 1. Determinations with cylindrical tubes and internal pressure. In order to facilitate a comparison with GaLirzin’s results we take the same value 5 for the coefficient of contraction. Let P,, be the maximum internal pressure, 2/A the external diameter, 2R’ the inner diameter (this is further on expressed in mm), and letn = R then we can represent the maximum tension 7, in the glass, (in this case that of the internal portions of the glass in a direction perpendicular to the axis of the cylinder) by: Pml oP + di — ) n—l | If, as is the case in the following tables, P„ is expressed in atmospheres, we find 7’, expressed in KG/mm* (as it is given in the following tables) by multiplying the value found above by 0.01033. For the three series mentioned in §2 sub a, 6 and c the results have been combined in the table below. The meaning of the columns will be clear after what has just been said. Where several results are given under one number we have after the tube had partly burst (for instance so that only the end had broken off, or the tube had broken near the steel piece) used the same tube again for the following experiment. The results for 7;, are lowest for series a and highest for series 5. In the last series this is especially the case for the tubes with a very 1 tn 1) In the experiments of WinkELmann and Scuort where thicker rods of 10—20 mM?. section were used this required great care. | TABLE I. ( 33 ) Maximum internal pressure and tension of cylindrical glass tubes. No. | 2R | 2R’ | n | Pm | Tm Series a 4 9.3 Sob 9.66 340 5.38 me 8.8 4.0 2.20 980 4.94 3 Sey 4.2 2.07 930 4,9 4 9.4 On 2.94 970 4.10 5 9.2 3.0 Sy 380 Dai) 6 9.7 4.2 2.31 370 6.30 7 10.4 4.0 2.60 240 3.83 8 12.8 5.8 | 260 4.54 9 17.6 5.0 3.52 290 4.19 Series b 10 7.4 4.00 7.40 510 6.74 41 6.8 1.00 6.80 420 5.57 19 7.5 0.27 27.78 460 5.93 Als 6.5 0.35 18.57 500 6.46 540 6.97 14 67 0.24 97.92 800 10.33 1100 14.21 15 6.7 1.08 6.20 530 7.08 16 5.9 0.70 8.43 680 5.9 Ali 5.8 0.46 12.61 1200 15.61 | 18 5.9 0.62 9.52 820 10.74 19 5.3 0.46 11.52 920 11.99 20 5.5 0.46 11.96 1060 13.80 21 6.6 1.00 6.60 660 8.78 22 7.2 4.40 5.14 520 7:07 23 6.4 4.35 | 4.74 520 J.de Series c 24 3.8 2.42 a, 283 7.42 95 5.6 4.00 1.40 193 6.09 26 6.4 4.78 1.34 221 7.84 27 6.9 3.1 1.76 329 7.06 28 7,4 5.11 1.45 479 5.24 29 7.9 5.46 4.45 157 4.57 30 a5 oie es 4.54 261 6.78 31 6.8 5.13 EE 203 7.52 a 7.4 5.49 4.43 201 6.04 33 6.8 5.78 1.18 66 3.83 34 3.8 2.42 4557 ats 9.49 35 Soe 2.50 4.52 271 7.36 36 6.0 4.37 ior 179 5.96 ae 6.8 5.47 4.31 159 6.02 38 6.8 4.85 1.40 169 5.33 39 18 5.62 1.30 109 4.292 Proceedings Royal Acad. Amsterdam. Vol. XI. ( 34 ) small inner bore if we except nos. 12 and 13 where the soldering was ineffective. Helped by the experience made we have treated the following tubes more carefully. With the tubes which have burst under a too low pressure the existence of irregular tensions appears clearly from the way of bursting, where the break has a transverse or irregular direction and not, as theory requires, parallel to the axis. 2. Maximum strain of glass threads. The diameter of the threads lies between 0.1 and 0.6 mm. The results are combined in the two following tables. The bore was determined by a measurement of the diameter in two directions at right angles. The mean of these two measurements is given in the tables. The first table contains the results obtained with glass threads which have undergone only the operation mentioned sub § 2. To investigate the influence of irregularities which thus may remain in the structure of the glass we have made a series of measurements by means of threads which had beforehand been heated to incan- descence and then cooled very slowly. The results of this series are combined in table III. | TABLE II. Maximum strain of uncooled glass threads, Dal - nn Stress | Diameter | Tn Stress | Diameter Tm in grams | in mm ie KG/mm* || in grams | in mm. in KG/mm? 257.6 0.119 23.1 2615 0.424 18.4 496.5 0.192 17.5 2785 0.446 47.8 457.8 04159 22.9 1425 0.351 44.7 2325 0 384 19.8 1635 0.370 ES 1175 0.257 22.7 | 1325 0.325 16.0 1475 0.325 1756 1555 0.298 22.4 1695 0.311 22.4 2335 0.370 Pan) 4A05 0.487 22.4 Except the thread for which 7 is lowest viz. 14.7 all the threads of table IL show where broken a sharply ridged structure while we find at the edge a small semicircular smooth spot as was found by WINKELMANN and ScHOTT.”). 1) p. 718 loc. cit. ( 35 ) | TABLE III. Maximum strain of cooled glass threads. | | | | Stress Diameter Tn Stress Diameter Tm in grams in m.m. in KG./mm*|| in grams in mm. |in KG./mm* er | 9920 0.438 19.4 1940 0.325 23.4 3930 0.597 12.6 1760 0.322 21.6 2120 0.532 a | 9850 0.445 18.3 | With regard to the series of table III we may remark the following. In order to prevent changes of form of the threads suspended in the furnace and softened by the heat under the influence of gravitation, which afterwards during the measurements might give rise to irre- gular tensions, we have shaped the extremities (cf. $ 2) not into hooks as in the former series but to closed rings in such a way that the whole becomes as symmetrical as possible with regard to a plane through the longitudinal axis. A comparison of the tables II and III shows that the two methods lead to the same results. Of the glass thread with the lowest 75, (cf. table III) the section was little ridged but smooth, to the next value of 7m (= 12.6) belonged a relatively large smooth semicircular spot, while for the highest Tn (= 23.4) no spot was to be seen, but the whole section showed a very sharply ridged structure. All these facts agree with what has been found by WINKELMANN and Scuort *). On the plate we show the structure of the sections of a couple of threads at the place where the thread has broken. They both clearly show the smooth parts and the structure radiating thence. The smallest diameter of the sections is 0.530 and 0.555 mm. respectively. § 4. Conclusions. Table I shows that as to the series a and ec our results agree tolerably well with those of Gatirzin *). Those of the series 6, however, show that the result derived by him for the maximum internal pressure, viz. 623 atms. is too low, because the highest pressure observed by us is 1200 atms. For the tubes of the series 5 7’, appears to lie higher than would be expected from the observations in the two other series. Probably this must be explained as follows. From a comparison between the 3 series _}) loe. cit. 2) Table I p. 12 and 18, loc. cit, 3* ( 36 ) it appears that series a gives the lowest results for 7, series 5 the highest. The fact that the values for a are lower than for c, must probably be ascribed to the circumstance that with almost equal in- ternal bores the wall is thickest for the first series and hence the chance of abnormal stresses is greater. For series 6 the wall is thicker than for c, but the inner bore is much smaller, and hence the existence of inequalities and scratches on the surface which unfavourably influence the breaking stress') are reduced to a minimum. For the tubes for which 2R’ = 1mm. it seems that the two factors neutralize each other, for those with the smaller inner bore the favourable influence of the surface being smaller preponderates. In order to investigate in detail in how far the above mentioned two unfavourable factors influence 7, we have applied the direct determination with thin glass threads of which the surface is as smooth as possible and where owing to the small bore abnormal ten- sions are necessarily small. The results which are much higher than those of WINKELMANN and Scuort, agree with those found by means of the first method and seem to justify the supposition made above about the unfavourable influence of a not perfectly smooth surface and inner abnormal stresses. They point to an upper limit for En == 1700 aims, § 5. Determinations at low temperatures. The determinations in liquid air were made in the same way as those at ordinary temperature. The lower hook of the glass thread was fastened to a wooden bearer, placed beside the thread in a vacuum glass with liquid air. The first determinations gave results which differed much from the later ones. Their mutual agreement is very bad and they are characterized by very high values for the maximum strain, which vary from 44 to 73 KG. per mm.” while for the ordinary temperature the highest strain was 23 KG. per mm.?. Also the structure of the section was totally different, being scarcely ridged but smooth. The smooth spot on the section was as a rule missing. In these measurements the threads were pulled asunder almost immediately after they had been placed in liquid air. Before the following measurements they were left at least 20 mi- nutes in the bath of low temperatures. The latter gave lower results with a better mutual agreement. The structure of the section is similar to that at ordinary temperature, generally a little less distinct. The results are combined in the following table. 1) Cf. WinKELMANN and Scuort, loc. cit. Dr. H. KAMERLINGH ONNES and Dr. C. BRAAK. Isotherms of diatomic gases and their binary mixtures. VIII. The breaking stress of glass and the use of glass tubes in measurements under high pressure at ordinary and low temperatures.” Fig. 1. Fig. 2. Proceedings Royal Acad. Amsterdam. Vol. X. ( 37 ) TABLE IV. Maximum strain of glass threads at the temperature of liquid air. Stress Diameter Tm Stress Diameter Tn in grams. in mm. in KG/mm? | in grams. in mm. in KG/mm’ 1993 0.280 32.4 | 2498 0.297 35.9 2653 0.372 24.3 2055 0.286 31.9 2523 0.290 38.2 3550 0.359 35.1 1293 OF 256 2975 3865 0.396 31.3 The results are still much higher than for the ordinary tempera- ture, a very favourable result for measurements at low temperature. Lastly a single determination in liquid hydrogen was made. Fifteen minutes after the thread had adopted the temperature of the bath it was pulled asunder. The total weight was 3013 grams, the diameter 0.271 m.m., hence the maximum strain in KG /m: == 52.1 again much higher than at the temperature of liquid air. The structure of the section was striated, unridged and no smooth part occurred. Zoology. — “Poterion a Boring Sponge.” By Prof. G. C. J. Vosmarr. (Communicated in the meeting of May 30, 1908). In 1822 Harpwicke published *) a short notice on a remarkable “Zoophyte, commonly found about the Coasts of Singapore Island.” The author stated that it belonged to the Sponges, and called it Spongia patera. Evidently not acquainted with this publication SCHLEGEL 1858 7%) proposed the name Poterion neptuni for a sponge, which universally is considered to be identical with Harpwickr’s sponge. According to the rules of nomenclature the object has, conse- quently, to be called Poterion patera (Harpw.), as first pointed out by Soumas *). Both Harpwickr and ScHLEGEL state that the sponge is fairly common. No wonder that this object, which presents itself as a gigantic cup, with a height of more than 1 M. and an aperture of 30 cm. or more, drew the attention of sailors. It is also found in many museums, especially in Holland. The Leyden Museum of Natural History, the Museum of the Utrecht University and the Museum of the Amsterdam Zoological Gardens (“Artis”) possess beautiful specimens, together more than 30. This rich material induced Hartine 1) Asiatic Researches XIV, p. 180. 2) Handleid. Dierkunde II, p. 542. 3) Anr. en Mag. Nat. Hist. (5) VI, p. 441 (1880). (38 ) to study the sponge, as far as the dry specimens allowed it. HARTING published in 1870 his well-known “Mémoire sur le Genre Potérion’’,’) the result of an examination of 27 specimens. Since that time the sponge has hardly been mentioned. It seems indeed strange that since SCHLEGEL’s publication — half a century ago — these gigantic specimens which obviously were far from rare were never or hardly ever sent to any of our museums, and that none of the numerous expeditions of later times brought home even a single specimen of Foterion. As far as I can judge even the Siboga- expedition is no exception. My request to several people in our colonies in the Malay Archipelago remained unanswered, till last year, when I received a letter from Dr. P. N. van KAMPEN, assistant Zool. Mus. Buitenzorg, mentioning, that in his presence three spe- cimens of Poterion were dredged off Bantam at a depth of about 25 M. Thus the sponge was found again at last. Dr. VAN KAMPEN was kind enough to send me fragments, well preserved in 96°/, alcohol; he also told me from time to time when new specimens were collected all from the West part of the Java-sea. We learn from this, that the sponge is not rare. Since nothing was known about the anatomy of the “soft parts” of Poterion, I was rather anxious to study microscopical sections of well-preserved specimens. It struck me at once that the structure of this Poterion closely resembles that of the so-called Osculina polystomella O. S. of which I prepared a deseription and drawings many years ago”). Now this Osculina is nothing but the “free form” of a boring sponge, as first pointed out by Carter’); LENDENFELD afterwards (1895) *) proclaimed O. polystomella as the free form of Vioa viridis O.S. Independently of LENDENFELD I arrived at about the same result. It was, therefore, but a logical conclusion to suppose that Poterion patera was likewise the free stage of a boring sponge, and I begged Dr. van KAMPEN to look whether in the localities where Poterton was dredged, shells, corals, limestone or similar substances occurred which were attacked by Clionidae. Meanwhile I reexamined the specimens of Poterion in the Leyden Museum. The director of the Museum, Dr. F. A. Jentink was so kind as to allow me to cut 1) Natuurk. Verhandel. Prov. Utr. Gen. 2) MS. for Fauna and Flora of the Bay of Naples. By unforeseen events the publication had to be postponed more than once. I am indeed very glad to be able to say that the bulk of the MS. is ready and I hope that no serious inter- ruptions will prevent me from going to press soon. 3) Ann. d. Mag. Nat. Hist. (4) V. 4} Zool. Anzeig. p. 150, ( 39 ) one specimen across for further examination. This I did with a specimen to which I gave the number 338. At the base of the sponge, which is somewhat broadened, I found between the “roots” much sand, rather large pebbles and a number of shells. One of these is a Voluta scapha Gmel. of about 10 cm. x 5 em.; it shows on its surface numerous holes of a boring sponge, which has pierced the shell a good deal and which has already destroyed a portion of the surface. Microscopical examination of the dried sponge-substance in the interior of the Voluta proved that the spiculation closely resembles that of the Poterion 338. The sponge substance on the surface of the shell is continuous with that of the Poterien. My supposition that Poterton represents the free stage of a boring sponge is hereby proved. I am not yet prepared to say whether it is identical with one of the numerous known species. I hope to be able to settle this later on and to give a full account (with illustrations) of the subject. I shall then discuss why only a small portion of Voluta is destroyed and the possible mode of growth. As to the anatomy of the spirit-specimens now at my disposal, a brief account may follow here. A longitudinal section through the wall of the cup, somewhat nearer its basis than its border, where the wall has a thickness of about 25 mm., shows that the cortex has on both sides about the same thickness, viz. 1—5 mm. The parenchyma shows large incurrent and excurrent canals, both surrounded by a transparent tissue. The main incurrent canals have a diameter of 0.5 mm., the main ex- current canals of 0.5—1 mm.; with the transparent tissue the former are, on an average, 3mm. the latter 5 mm. Both enter deeply into the parenchyma; the former 15—20 mm., the latter 10—15 mm. In their course through the parenchyma the incurrent canals show several round apertures — the beginnings of secondary canals. The mass between these main canals and the surrounding tissue is composed of a crumb-of-bread like substance, and the trabecular network of the skeleton. At this part of the cup the incurrent apertures, stomions, are situated on the outside. They are congregated into pore-areas of indistinct outline; these areas are nevertheless clearly visible as dark brownish spots on a buff-coloured background. The areas have a diameter of a little more than a millimeter, and are situated at about the same distance from each other. In some places the areas are somewhat sunken; in dry specimens this shrinkage goes a good deal farther. I have not been able to detect the stomions on the surface; but sections clearly show that they are placed more or less in rows which start from a common centre. They are the apertures ( 40 ) of narrow and short canals which open just under the dermis into wider canals of which generally 5—6 unite in a common centre. These canals cause the star-like figures, already described by Harting. Tan- gential sections show this plainly; it becomes then obvious that these cortical canals sometimes ramify; but the final result is always that on an average five unite into a common wider canal, at right angles to the surface which runs through the rest of the cortex. It is evi- dent that this latter canal corresponds to the incurrent chone *) of Tetraxonia, as sections at right angles to the surface prove. The incurrent chones lead into the main incurrent canals; some of these, as stated above, run more or less straight on for about 15—20 mm. at right angles to the sponge surface; they then bend and run in a direction almost parallel to the sponge-surface. In their course they give off branches, which ramify and terminate between a group of the mastichorions. These are ellipsoidal in shape and open with wide apopyle into the excurrent canals, the system being eurypylous. A certain number of excurrent canals flow together and finally open into the main canals, mentioned above; they traverse the cortex with excurrent chones, which open by procts on the inner surface of the cup. The soft tissue, surrounding the main canals, excurrent as well as incurrent, is very remarkable. I found the same sort of tissue in many sponges, but especially well developed in the so-called Osculina polystomella. LENDENFELD has seen this tissue, and in his description of “Papillella suberea” says*): “Das hyaline Gewebe, welches die Hauptkanäle umgiebt . . . . besteht aus einer glashellen Grund- substanz, in welcher zahlreiche multipolare und auch bipolare Zellen liegen, deren lange und schlanke, verzweigte Ausläufer überall mit 1) Of course I use here the term chone in the sense of Sorras, and not in the sense of LENDENFELD. This latter author is entirely wrong in using chone as a synonym for sphincter. Sottas wrote in 1880 (Ann. & Mag. Nat. Hist. (5) v. p. 135): “The cortex is traversed by the intermaginal cavities of Bowerbank, or, as I shall term them, the ‘‘cortical funnels” or “‘chonae”. They consist essentially of a tube divided by a sphincter into a shorter proximal and a longer distal part, the “ectochone”’ and “endochone” respectively”. Apart from the evident lapsus that in this sentence the words ecto- and endochone stand in the wrong place Sottas’s meaning is plain enough and this definition is generally accepted. However LENDENFELD has another opinion. Thus, for instance, he writes in 1897 (Die Clavulina der Adria, p. 102—103): “In halber Höhe der Rinde..... vereinigen sich diese Sam- melkanäle zu vertikalen Stammkaniilen..... ” And further: “Oben ganz dünn, verdickt sich diese schlauchförmige Kinfassung des Stammkanales..... nach unten hin sehr beträchtlich und bildet proximal, in der Umgebung der erwähnten Verengung, mächtig verdickt einen starken Sphincter, der als eine Chone aufzufassen ist”. I do not wish to discuss the matter here at length. The quoted passages leave no room for misunderstanding. 2) Clavulina der Adria p. 104—105. mmm lee eee (41) einander anostomosiren, so dass hier ein engmasschiges, spongidses Netz zu Stande kommt. In einigen der Knotenpunkte dieses Fadennetzes liegen die Zellleiber mit ihrem kugligen Kern, in anderen trifft man nur unbedeutende Plasmaanhäufungen an.” In my MS. description of this tissue in Clionidae I differ somewhat from. LENDENFELD’s interpretation; in Poterion I find the same sort of tissue, only still more pronounced. The fact is that the reticulum is by no means simply formed by a network of “Ausläufer” of cells, as it becomes clear by careful focussing that a number of the supposed thread- like processus are really membranes. In Poterion these membranes are sometimes of enormous size, even larger than in Cliona (Osculina). The tissue has a close resemblance to the so-called lymphoid or reticular tissue, as RANVIER and PEKELHARING conceive it. As to the skeleton of Poterion, this is formed by a trabecular very firm network of bundles of closely packed tylostyles. I found in Osculina that in some portions of the skeleton the spicula were united by a little spongin. The same holds true for Poterion. This is, however, only the case in the centre of the pillars or trabeculae; there is a mantle of spicules at the periphery which is devoid of spongin. The spicula of Poterion are tylostyles; the spicule for which I proposed?) the name spinispira I did not find in the specimens of Poterion 1 examined. We know, however, that in the genus Cliona itself spinispirae are often very rare or absent, especially in the so-called free stage. I am of opinion that Papillina suberea O.S. is identical not only with Osculina polystomella O.S., but also with Papillina nigricans O.S. and Vioa viridis OS. They are all nothing but modifications of the very variable Cliona celata, as I hope to prove in my “Sponges of Naples”. LENDENFELD (1897 Le. p. 99) considers Papillina suberea O.S. as a species different from Papillina nigricans OS. This is especially on account of the absence of spinispirae in the former, in a type-specimen of which LENDENFELD failed to find tbem. I found, however, in the collection of the Zoological Station at Naples a sponge labelled by Scumipt P. suberea ; in this specimen I did find spinispirae. I found them likewise in some of the specimens I collected near Trieste. For these reasons I cannot distinguish nigricans from suberea. Consequently there is in the absence of spinispirae in Poterion no ground for not placing this sponge in the same group as Cliona, since in every respect the anatomical structure of Poterion resembles that of Osculina. Leyden, May 14, 1908. 1) On the shape of some Siliceous Spicules of Sponges. (Kon, Akad. v. Wetensch. Amsterdam, 1902. Proceedings p. 104—114). (4) Chemistry. — “Reduction of aromatic nitro-compounds by sodium disulphide.” By Dr. J J. Buanksma, (Communicated by Prof. A. F. HoLLEMAN). (Communicated in the meeting of May 30, 1908). I have pointed out previously *) that sodium disulphide may act on aromatic nitro-eompounds in two different ways, namely by sub- stitution or by reduction. 1. Substitution occurs when halogen atoms or nitro-groups are present which under the influence of ortho- or para-placed nitro- groups have become moveable. These on being treated with sodium disulphide are readily replaced by 5S, and the disulphides thus formed may be converted by oxidation into sulphonic acids. A fairly large number of these cases have been communicated previously *). 2. Reduction takes place when the nitro-compounds do not contain any moveable halogen atoms or nitro-groups; a nitro-group is then reduced to an amido-group, whilst generally a small quantity of azo-oxycompound is also produced according to the equations: RNO, + Na, S, + H,O = RNH, + Na, S, O, 2 RNO, + Na, 5, = RN — NR + Na, S, O, ee Ö A preliminary investigation had shown me previously that alcoholic solutions of nitrobenzene and o-nitrotoluene are readily converted by Na, S, into aniline and o-toluidine, the Na,5, being oxidised to Na, S, O;,. m-Dinitrobenzene and p-dinitrobenzene when treated with Na, S, yielded, respectively, m-dinitroazo-oxy benzene and p-dinitroazo- benzene. It was then’) our intention to further investigate the reducing action of Na, S,. Meanwhile, however, a patent has been granted to Kunz *) for the reduction of aromatic nitro-derivatives to amido-derivatives by means of sodium disulphide in aqueous solution and afterwards sodium disulphide has been used by BRAND“) as a partial reducing agent. I have now studied the reduction of aromatic nitro-compounds by Na,S, in alcoholic solution in a number of cases. The reduction is carried out as follows: Six grams of nitrobenzene are added to a boiling solution of 12 grams of crystallised sodium sulphide and 1.6 gram of sulphur in 1) Dissertation. Amsterdam 1900; Rec. 21, 121, 141. 2) These Proc. 1900, (Oct.) 8) Chem. Centr. 1903 II 818. 4) Journ. f. pract Chem. 1906. (2) 74, 499. ( 43) 300 ce. of 96°/, alcohol. After boiling for 6 hours, the alcohol is recovered by distillation and the aniline which still contains a little nitrobenzene is distilled in a current of steam. It is then converted into the hydrochloride to separate it from the admixed nitrobenzene ; about 5 grams of aniline hydrochloride are obtained. In the same manner were treated o-m- and p-nitroanisol, m-chloro- and bromo- nitrobenzene and dichloro- and dibromonitrobenzene 1. 3. 5. from which were readily obtained the corresponding amido-derivatives to the extent of about 70 °/, of the theoretical quantity. In the case of ortho- and para-chloronitrobenzene where the halogen atom is replaced by S, a simultaneous reduction takes place to a slight extent with formation of o- and p-chloroaniline. Ortho- and m-nitrotoluene readily yield ortho-and meta-toluidine ; with para-nitrotoluene a secondary reaction occurs, p-amidobenzal- dehyde being formed as well as p-toluidine *). Besides the above mentioned mononitro-compounds a few dinitro- compounds were subjected to a partial reduction. From sym-dinitro- toluene we readily obtain by means of alcoholic Na,S, 3-nitro-5- amidotoluene ; sym-dinitroanisol yields 3-nitro-5-amidoanisol; from 2-4-dinitroanisol (or phenetol) is obtained 2-amido-4-nitroanisol (or phenetol) whilst sym. trinitrobenzene yields 3-5-dinitraniline. A small quantity of the azo-oxycompounds is generally formed in addition to the amido-derivatives. I will also point out that in the reducion with Na,S, the formation of chlorinated byproducts, which are often generated in the reduction of aromatic nitro-compound with Sn and HCl, is avoided. The fact that sodium disulphide may be weighed also gives it an advantage over ammonium sulphide as a reducing agent. From the above facts it is obvious that an alcoholic solution of Na,S, may be used as a convenient reducing agent. Physiology. — “About the determination of hardness in muscles.” By A. K. M. Noyons, Assistant in the Physiological Laboratory at Utrecht. (Communicated by Prof. H. ZwAARDEMAKER.) (Communicated in the meeting of May 30, 1908). At an inquiry into the causes and qualities of the autotonus it struck me how a muscle seemed to become harder, as its autotonus increased. Hitherto the hardness of a muscle was always estimatively determined by digital touching. The above mentioned fact caused 1) Chem. Centr. 1900. I. 1084. I hope to communicate more analogous cases of intramolecular oxidation later on. ( 44 ) me to look for means of expressing such changes in hardness more accurately in measure and number, as an approximate determination would not do here. A communication by J. von UrxKürL *) on the 18 of April last “Die Verdichtung der Muskeln”, led me to a separate description of my investigations about the determination of hardness in muscles. In this communication he says: “wir besitzen zwar kein geeignetes Instrument, um das Hartwerden der Muskeln zu messen”, while he winds up as follows: “Ich habe geglaubt, auf diese wichtige, aber allzusehr vernachlässigte Eigenschaft der Muskeln hinzuweisen, in der Hoffnung, dass sich jemand findet der einen brauchbaren Apparat konstruiert, um die Muskelverdichtung unabhängig von der Muskel- verdickung zu registrieren.” For many decades together mineralogists have made determination of the hardness of materials, in which a number of methods were employed, whieh, however, in that form could not be applied to living objects. The literature only gathers for what is called hardness in general, data, for which I refer to some authors *) in behalf of those who wish to become more thoroughly acquainted with the subject. Hardness is a collective idea, including and typifying an amount of qualities: cohesion, elasticity, plasticity, gliding, splitting and fracture. It is on the value which in a concrete case is assigned more especially to one of the qualities mentioned, that depends the general definition which shall be given of hardness. For living objects gliding, splitting and fracture need not be taken into account. I desist from a more detailed separate description of the three remaining qualities: cohesion, elasticity and plasticity. But if these three qualities are paid attention to, AUERBACH’s *) definition of hardness will no doubt be agreed to: ‘Harte ist eine Art von Festigkeit, nämlich der Widerstand gegen die Bildung von Unstetigkeiten oder dauernden Deformationen beim Drucke zweier sphärischer Oberflächen gegen einander, und kann Hindringungsfestigkeit genannt werden... Sie ist quantitativ durch den Grenzeinheitsdruck im Mittelpunkte der Druckfläche bestimmt.” 1) J. v. Uexküm. Die Verdichtung der Muskeln. Originalmitteilung. Zentralblatt für Physiologie. Bd. XXII NO. 2. 2) H. Rosensuscn und E. A. Witrine. Physiographie Allgemeiner Teil. Stuttgart 1904. G. Tscuermax. Lehrbuch der Mineralogie. Wien 1905. Econ Miter. Ueber Hirtebestimmung Inaug. Dissert. Jena 1906. 3) F. Aversacu. Kanon der Physik pag. 119, Leipzig 1899. ( 45 ) The determination of hardness may give absolute and relative values. Among the methods of relative determination that of Tuouzer *) appeared to be useful also to determine the relative hardness of living objects. Trourer examined the elasticity of rocks and found points of comparison for this in the number of reflections and in the angle of reflection of a swinging ball suspended in the air. Indeed, if we drop a hard, elastic object upon an other, it will among others depend on the hardness of the surface that is hit, how often and how far the reflection will take place. Now, if this principle is put into practice with a much weaker object like a muscle, these reflec- tions will, though in a smaller degree, yet take place in the same manner, which is corroborated by experience. The angle of reflection of a falling globule resp. the number of its perceptible taps or reflections depends: 1. on the cohesion, elasticity and plasticity of the falling globule. 2. on the cohesion, elasticity and plasticity of the object hit, in this case the muscle. Now as in case of comparing determinations sub 1 remains constant, sub 2 must be the only changeable, determinative factor. The investigation takes place as follows with an apparatus that I call physiological sclerometer. Physiological Sclerometer. Schematic drawing. Pi FE, 1) M, J. Trovrer. Recherches sur Pélasticité des mineraux et des roches. Comptes rendues de l'Academie des sciences. Paris. Tome 96. 1883. ( 46 ) A small pendulum with a fixed turning-point, of which the short beam points upwards to a height of 6 cM., bears on the head of that short arm a handled glass-tear, whilst the other longest arm, 15 cM. long, is provided with a small, movable weight, in consequence of which the moment of that lever-beam is variable. By this way the force with which the head of the glass-tear hits the object, can be made variable. In order to enlarge the living force of the falling object, the pendulum may be given different initial amplitudes. On a scale along which the longest lever moves, this height of falling is expressed in degrees. The muscle to be examined is by means of its two tendons attached to a somewhat rough surface, here a hard cork-plate, to prevent removal of the muscle by the falling, tapping object. It is advisable in this way to determine the hardness of a muscle under isometric conditions, for, when the muscle is examined under isotonic conditions, the data are getting far less trustworthy, as: 1. in shortening the muscle, the point that is to be touched, by not shor- tening changes its place and can only be found back by marking it beforehand with colouring matter; 2. the weight necessary for the stretching seems to make the differences in hardness smaller. The number of times that the glass-tear is reflected by the muscle before it is at rest, is determined either acoustically or by means of photography. The photographic registration has this advantage that at the same time the width of the reflections can be followed. The photographic registration takes place as follows: the light of an arc-lamp of 220 volt and 10 ampere is by a condenser more or less pressed together into a cone of rays having its focus in a dia- phragm. This focus in its turn serves as a source of light and pro- cures by means of a biconvex lens the parallel bundle of rays emitted. This bundle reaches the removable slit of a small box which in its opposite side is provided with a cylinder-lens of GARTEN. The light that has entered through the slit, is by the cylinder- lens, which is graduated, nipped together to an horizontal line of light, which falls through another slit into a second larger box on a drum that is in rotatory motion and to which sensitive bromide- paper of Dr. ScnÄrrELEN is fixed. The box containing the drum is impenetrable to light by means of light-free axes. This drum is moved on by a clock, as it is used in the telegraphic Morse-apparatus. Between cylinder-lens and the larger box is placed the long beam of the lever of the sclerometer which during its movements removes a silhouette on the sensitive silver-paper. The following experiment was made: M. sartorius of Rana temporaria is alternately passed through by an electric current, arising ( 47 ) by a potential difference of 1.4 volt. For this purpose two brass plates serving as electrodes for the current, had been sunk in the cork sub-stratum of the muscle, whilst by means of a commutator the direction of the current can be changed. At the beginning of the experiment the anode is found at the distal tendon; afterwards the current is turned and ends in its original direction. In the subjoined table occur the widths of the first 4 reflections in mM. é Anode at the Kathode at the Anode at the Reflection distal tendon distal tendon distal tendon I 52.5mM. 52mM.l54mM. 53) mM.) 54mM.)53mM.)|/50 mM.}50 mM. II 29.5 99 31 30 31 a4 29.5 29 Ill 21 21 93 OD 29, 22) 2075 21 IV 16 16 18 a “7 17 16 45.5 The following table gives the difference between the M. sartorius of Rana temporaria through which a galvanic current has passed and another through which it has not passed. Reflection Muscle through which no Muscle through which a current is | current is passing passing Anode at the distal tendon I 40 mM.| 40.5mM. | 40.5mM.|| 45 mM. 43 mM./43 mM.| 43 mM, II 24.5 25 25 28 26.5 26 27 Ill 16.5 17 17 18 47,5 17 11.5 IV 11 a4 11 12 41.5 115 12 That abundant moistening of a muscle with mutually equimolecular salt-solutions, the effect of which on the autotonus is antagonistic, can alter the hardness, appears from what follows, also holding good for the M. sartorius of Rana temporaria. Moistening Moistening | Moistening with kaliumchloride with kaliumchloride | with natriumchloride mM. mM. mM. mM.|| mM. mM. mM. mM. mM.|| mM.| mM.| mM.| mM. I 48 49.5 | 41 40.5 || 40 37 33 38 38 38 38 38 39 u |(33 |95.5/95.5/26.5|/25.5/24.5/22.5/24 |23.5//93 |92 |92 |23 We |{24 |47 |46.5|47 |[46.5/47.5/46.5/46 |45 [45 |44 44.5] 44.5 Iv |]47.5]44 [40.5/44.5]]42 |42.5/42 [40 [10 |] 95/9 | 9 | 95 Peis says | 8-0 don kiss oka ls 1-8.) 8 Mi hoh aes 7.5 15) gps Gf ek EN ( 48 ) For a plain muscle whose fibres are parallel as in the M. sartorius of Rana, the above method is a rather fit one, though not in all respects. For the shortening of the muscle is accompanied by a thickening, in consequence of which the distance between muscle and glass-tear is somewhat altered. This is not of much importance for the thin M. sartorius, but if the experiment is made with muscles like M. gastrocnemius, this difference becomes more considerable, so that it ought to be taken into account. Besides the peculiar rounding of the surface of the muscle may somewhat alter the place of tapping, and in the end the glass-tear sometimes slightly sticks to the muscle, when we are tapping with a small load on the longer beam of the lever. To meet these and similar drawbacks the following alterations were made. Between muscle and tapping glass-tear is inserted a thin glass plate, which intercepts the taps and transfers them to the muscle. In these circumstances the angle of reflection resp. the number of collisions depends on: 1. the cohesion, elasticity, plasticity of the tapping glass-tear ; 2. the cohesion, elasticity, plasticity of the inserted glass plate ; 3. the cohesion, elasticity, plasticity of the object to be examined. Sub 1 and 2 remaining constant, only sub 3 is variable. In order to come to a determination, the following technical precautions ought to be taken into consideration. The glass plate, a covering glass, is hanging, slightly movable, on a couple of rather stiff horse-hairs. Now the muscle presses this glass plate against an immovable metal fork, so that the glass plate can only make move- ments in one direction, viz. in the direction of the muscle, as soon as the glass plate is hit by the tapping glass-tear. At every touch of the covering glass the glass globule produces a clearly audible tap. The number of taps is easy to count and isa pretty accurate measure for the number of real movements of the glass, without agreeing with it in number. In proportion as the covering glass is pressed more against the fork by a harder mass of muscles, the oscillations of the little lever will retain a longer and wider amplitude and will also occur more frequently. The height of falling is of great importance for the effect that is to be reached, in the first place with respect to the number and amplitude of the oscillations. When at different heights of falling the number of feta audible taps is counted for the same muscle, the latter may be represented by a curve, in which the ordinate renders the number of audible taps and the abscis the height of falling in degrees. The curve thus got shows a peculiar course, NO. of 4 the experiment e Observations and culture time | i 1 4 gr. 24 Febr.--10 April 0,05 K cM3, t 2 2 gr.of | 26 Febr.—4 April K2HP | | | 3 2gro 13 March—4 April K2 H tapwa 4 12gr.o 26 March—29 April K2H tapwa 5 4 gr.of Microscop visible o April—23 April K?HP infection tapwa | 6 4 gr.of | Microscop. visible 4 April—29 April K2HP | infection tapwal 7 4 gr.of No microsc. visible 1 April—2 May (K2H F infection tapwal Zgr.of Microcosp. and bac- 8 13 May—29 May (K2 K teriologically pure tap wal 9 4gr.of| | 6 April— 23 April (005 K | cM3, t | of cha 10 {grof} | 16 March—29 April 0,05 | cMs3, t 11 1 gr. of 16 March—8 May nate, ( 1100 cl NO. of the experiment and culture time Components of culture medium in grams. | Inoculation- Produced calcium- Volatile acid in Totally disappeared| carbonate in grams material grams | limesalt in grams | milligrams Nitrogen found Nitrogen fixed per, after Ksetpan in! gram of decom- | posed calciumsalt Observations | eee 1 24 Febr.—10 April 0,05 K2 H PO4, 200 of crude culture in 2 26 Febr.—4 April 3 13 March—4 April 4 26 March—29 April 5 o April—23 April 6 4 April—29 April 7 7 April—2 May 8 13 May—29 May 9 6 April- 23 April 10 16 March—29 April 1 16 March -8 May | 4 gr. of Calc. Mal. cM3, tapwater. | 2 gr.of Cale.Mal.0,05 K2H PO4, 200 cM3,/ tapwater. 2 gr of Calc.Mal.0,05 |K2H POS, 100 cM. tapwater. l2gr.ofCalc.Mal.0,05, K2H PO4, 200 cM3, tapwater. 4 gr.of Calc.Mal 0,05) K2H PO4, 100 cM3. tapwater, 4 gr.of Calc.Mal.0,05 Ke H POS, 100 cM3, tapwater. 4 gr.of Calc. Mal.0,05 IK2H POS, 100 cMô. ‘tapwater 2gr.of Calc, Mal.0.'5 K2 K PO4, 100 cM3 tapwater. 4gr. of Calc, Lactate 0,05 K2 H PO4, 100 cMS, tapwater, | gr. of chalk. |! gr.of Calc. Acetate,| 0,05 K2 H PO4, 100, \cM3, tapwater, 1 gr. of Calc.Propio- \nate, 005 K2HPO4, 100 cM3 tapwater. Ist re-inoculation | canalwater in same liquid | | 24 transferring of the preceding. | | 3d transferring of the preceding | 4'h transferring of the preceding. Pure culture of Azotobacter | Pure culture of | Asotobacter | Pure culture of Azotobacter Pure culture of Asotobacter Crude culture from 1. Crude culture from 1. Crude culture, 157 0.872 0.552 0.494 08103 0.576 0.494 0,632 0.112 0,042 0.036 0.101 3.3 10.7 2.2 0.89 1.39 8.1 1.6 5.9 2.8 47 2.5 2.6 28 4.7 Microscop visible infection Microscop. visible infection No microsc, visible infection Microcosp. and bac- teriologically pure ( 49 ) The above experiment was made with a dead muscle, to avoid as much as possible all variable factors of the living object. These come into operation, as appeared from experiments, in which first a curve was produced by observations of a living muscle, and the next day a second curve could be formed from observations of the now dead muscle, which under a glass cover with saturated vapour of water and thymol-vapour was preserved resp. from desiccating and rotting. The values denoted by the curve are averages got from at least five observations each time, which did not materially differ from each other. Fig. 2. Hardness with regard to different heights of falling by a muscle in its dead and living situation. —— = living muscle. ------ = dead muscle. The ordinate gives the number of audible taps and the abscis the initial height of falling in degrees. In different ways the hardness of a muscle can be made to undergo changes, which are either permanent, or which exist long enough for the determining investigation : 1. by making a galvanic current pass through a muscle; 2. by abundant moistening with equimolecular salt-solutions ; 3. by faradaic excitement, either direct or indirect, so that the muscle is in tetanus; 4. by heating, resp. cooling. An example of the two first mentioned manners was given before; one of the two other manners is as follows: a muscle is by indirect excitement with a faradaic current alternately brought to tetanus. At corresponding moments the determinations of hardness take place. 4 Proceedings Royal Acad. Amsterdam, Vol. XI. ( 50 ) The subjoined table contains the width of the first 8 reflections which were reproduced photographically; at the same time the duration of these 8 reflections was calculated. M. gastrocnemius of Rana temporaria. Normal | Excited to | Not Excited to Not Excited | muscle | tetanus | excited tetanus excited | after rest 1 26 mM. | 61 mM. | 56 mM. | 57 mM. 56 mM. | 59 mM. H | 38 | 4 | 39 43 40 4h 5 Il | 29 | 38 | 99 | 33 31 33 IV 22 | 98 | 22.5 26 23.5 26 V 17 29.5 | 47.5 21 18 21.5 vi | 43 | 48.5 13 16.5 14 17 VII u 45.5 1.5 13.5 12 12.5 VIII 9.5 12.5 10 1.5 10 11.5 Duration of the first eight reflections. 4.4 sec. 4 sec. | 4.3 sec. | 4 sec. | 4.3 sec. 4 sec. From this it appears that in comparing the first 8 reflections not only the amplitude changes, but that also the time in which these oscillations take place, varies with the greater or smaller degree of hardness of the muscle. As the experiment progresses, it may be observed in the table that the heights of the reflections are getting larger also at the moments when the muscle is not excited. This must be connected with the changes in the constant state of con- traction (autotonus), which arise in every fatigued muscle. That the muscle becomes really tired, is proved by the fact: 1. that the muscle visibly contracts less, 2. that changes in duration and height of the reflections diminish after repeated excitement, 3. that after the rest the effect of excitement agrees again with what was observed in the beginning of the experiment. We add a tabulated statement of an experiment in which the muscle at the end of the experiment had become entirely inexcitable, as appeared from the absence of visible contractions, both for indirect and direct faradaic excitement, though stiil slight alterations in hardness appeared to be perceptible. ( 51 ) M. gastrocnemius of Rana temporaria becoming inexcitable according to every-day parlance. a es Excited a d | Excited | Pee d Excited I 53 mM. | CO mM. 48 mM. | 52 mM. 48 mM. | 50 mM. Il 40 50 35 38 35 36 Ill 28 36 24.5 26 24,5 26.5 IV 21 27 | ie 18 17.5 19 Vv 15 1.5 13 | 14 13 15 VI 13.5 17 12 12,5 12 12,5 VII 10.5 13.5 u 44 11 44.5 VIII 10 11.5 10 10 10 10 Total duration of the first 8 reflections. 5.4 sec. 5.9 sec. ya) SEC. | 5 sec. 4.4 sec. 4.8 sec. M. gastrocnemius of Rana temporaria. Temperature in temperator 12,59 Celsius | 56° Celsius [ 49 mM. 49 mM. 50 mM. 50 mM. II 38 39 MA 4A lll 27 15 31 30.5 IV 19.5 20 25 24.5 V 16 16 21 21 VI 13:5 14 18 18 VIII 12 seh 14.5 14.5 Audible taps EN eae eae Total duration of the first 8 reflections in abscis-length VII 13 13 16 16 3.6 cM. | 3.8 cM. | 3.2 cM. | 3 cM. | ( 52 ) If a striated muscle is heated, it shortens: this is accompanied, as appears from the experiments, by changes of hardness. In order to trace this, the muscle in the sclerometer, instead of to a corkplate, was fixed to the thin copper bottom of a temperator, now serving as resting-surface. Through this temperator, as THUNBERG pointed out for the examination of the cold- and heat-points of the skin, alter- nately cold and hot water could be made to circulate. The copper bottom communicates the heat to the muscle; the temperature in the temperator and that which the muscle gets, will not soon be the same, but still is always in close connection with it. As a demonstration I give here a couple of photographic repro- ductions of the oscillations of the beam of the sclerometer, as they were made, and from which among others the above table was partly derived. Fig. 3 gives the sclerometric reproduction of hardness of a muscle at a temperature of 12.5° C. in the temperator, whilst fig. 4 shows the reproduction when the same muscle 1s heated to 56° C. (See figs 3 and 4). If a muscle is heated to not too high a temperature, a decrease of hardness manifests itself again after cooling, even though the muscle does not quite reach its original degree of hardness. The subjoined table makes this clear. M. gastrocnemius of Rana temporaria. Temperature in temperator 13° Celsius | 61° Celsius | 11° Celsius ] | 49 mM. | 49 mM. || 50 mM. | 50 mM. | 50 mM. || 49 mM. | 49 mM. I | 37 38 49 A MA 38 39 II || 28 30 34 33 33 30 30 V || 24 24.5 29 28 28 25 25 V 20 20 25 25 24 24155 22 VI 47 175 22 22 21.5 18,5 19 VII || 14 15 20 19,5 19 46.5 17 VIII |] 12.5 12.5 18 | 47.5 47.5 14.5 15 Audible taps A. K. M. NOYONS. „About the determination of hardness in muscles.” Figs3: Fig 4. Sclerometric reproduction of hardness: at 12,5° Celsius. at 56° Celsius. Proceedings Royal Acad. Amsterdam. Vol. XI. ( 53 ) Such warming and cooling can be repeated a couple of times, whilst in proportion to this the number of reflections continues varying, provided the muscle be not for too long a time exposed to too high a temperature, as in this case a clearly perceptible perma- nent hardness will show itself. Physiology. — “On the structure of the ganglion-cells in the central nervous system of Branchiostoma lance.” (Second communic.) By Dr. J. Boerke. (Communicated by Prof. G. C. J. VosMarr). (Communicated in the Meeting of May 31, 1908). a. The infundibular organ. The cells of the differentiated part of the ventral cerebral wall of Branchiostoma, which I described some years ago in these Pro- ceedings*), and which was then called the infundibular organ on account of its place and the homology that could be drawn from that, are quite different in their structure from the other cells, of which I gave a description in my former paper’). Among the authors, who in recent years have published researches on the central nervous system of amphioxus, Kuprrer*) gives the same description of the cells as I gave in my paper in 1902, and only mentions the organ as consisting of long cylindrical cells with eurved cilia and a clear hyaline protoplasm. Kuprrur homologises the differentiated epithelium with the tuberculum posterius of the craniote embryos. JosEpH*) only mentions the organ without adding anything to the description. EpiNGeR®) who examined preparations stained after the method of Brerscnowsky, calls it “das aus grossen Flimmer- und Sinneszellen bestehende Infundibularorgan’’, without mentioning on what is founded the opinion, that there are two kinds of cells to be found. In the drawings reproduced in his paper nothing is to be seen but a faint striation of the ventral wall of the brain at the place of the infundibular organ. According to Worrr °) there is a striking resemblance between the differentiated epithelium of the infundibular organ and the gelatinous tissue that we find in the 1) Proc. Roy. Acad. of Sc. of Amsterdam, Math. Phys. Ci. Meeting of April '07 p. 86. 2) Proc. Roy. Acad. of Sc. of Amsterdam, Math Phys. Cl. Meeting of April ’02 p. 695. 8) Handbuch der Entwickelingslehre (Hertwia), Vol. 2, 3d part. 4) Verhandl. d. Anat. Gesellsch. 18. Vers. 1904. 5) Anat. Anzeiger, Bd. 28, 1906. 6) Biol. Centralblatt. Bd. 27, 1907. ( 54 ) central nervous system of the higher vertebrate animals, but evidently he has not seen much of the real structure of the tissue. Besides these statements nothing more is to be found about this part of the brain of amphioxus, and so we seem to be justified in giving an exact description of it here. To do this it is necessary to study first of all very thin carefully orientated median sections, as well as frontal and cross sections; the statements by Epincer made it necessary to examine a great many BreLscHowsky-preparations to form a correct opinion in this matter; hence we took so long for our research. From the very early period at which the infundibular organ is regularly found and the constancy with which it appears, always in exactly the same form and structure, it is evident that it must play a distinct and important part in the animal’s life. Already in larvae with only three primary gillclefts the differentiated epithelium is very obvious. Just where the narrow central canal opens into the wider part of the brain-ventricle, we see the ventral limit of the central canal rise slightly and sink again to the former niveau immediately after. This elevation is caused by the cells in the ventral wall growing out into long cylindrical elements, each cell bearing a long hair or cilium curving backwards, the cells lying regularly one beside the other. It is an important feature in the development of the infundibular organ that the elongation of the cells first shows itself not in the median line but at the left side of the median plane; afterwards the cylindrical cells are also found at the right side. It is only at a much later stage that the long cells fuse in the median line and become one single mass. This and peculiarities in the course of the nerve-fibres springing from the cells in the full-grown organ, point to a bilateral origin of it. The cylindrical elongation of the cells is the only change we find. There is no indentation at all of the wall of the brain in front of the organ to be found. Already in very young animals we see in well-preserved and well- stained preparations that the cilia of the long cells point backward with a slight curve, the cilia of all the surrounding cells pointing forward, to the anterior neuroporus. In older specimens we find the same state of things, but the cells get still more elongated, and the nucleus, now being small and sphe- rical, is lying near the basis of the cell. All cells are directed backwards, that is to say, their free surface being turned craniad. (fig. 8). For the topographical relations of the differentiated epithelium to EE nd (55 ) the other parts of the brain I refer to my former paper (1909). I can only state here in reference to the contradictory statement of Epincer, that even in more developed and in full-grown specimens I never found another kind of cells in the organ nor an indentation of the brainwall in front of the infundibular organ (Kuprrer). In fig. 1 is drawn a median section of the full-grown organ, and here we see that the cells are not slanting any more, but are directed perpendicularly to the longitudinal axis of the body. In slightly younger animals one often finds the greater part of the cell still curved backward, while the upper part of the cell has assumed the perpendicular direction already (fig. 4a). The cause of this change must be sought in the different rate of growth of the surrounding tissue, the whole cerebrum becoming shorter, and changing from an oblong into a more rounded form. As I mentioned before, the cells of the infundibular organ have all a backwards curved cilium; these cilia form a plume reaching to the narrow part of the central canal. In young animals being examined alive under the microscope the transparent tissue all round the brain ventricle allows the course of these cilia to be very clearly visible, and then the cilia of all the surrounding cells, pointing forward to the anterior neuroporus, appear as straight hairs forming a compact bundle which runs towards the neuropore, into which the hairs can be traced as long as it is open. The back end of this bundle of cilia is crossed by the cilia of the infundibular-cells; The form of the cells in the full-grown animal is shown in fig. 45. The neurofibrillar differentiation in the protoplasm of the cell described it already in my former paper, the neurofibrillar network round the nucleus and the way, in which the neurofibrilla leaves the cell is in Fig. 3 clearly to be seen. The course of the nerve- fibres after they left the cell-body I could not trace much farther with a sufficient amount of certainty. They all seem to curve back- wards (caudal), and from the study of frontal sections it was possible to draw the conclusion that the nerve-fibres Springing from the cells form two bundles, each at one side of the median plane, r backwards, but getting lost to view between the other fibres medulla very soon after. I never succeeded in finding an indentation of the ventral cerebral wall in front of the infundibular organ, as described by Kuprrrr, although a large number of serial sections were examined. It is true, that, as I mentioned before, often the nuclei in the ventral] wall in front of and behind the differentiated epithelium lie closer together than in the other regions and in a few eases the arrangement of sas] unning of the (56) these nuclei made the impression of a solid indentation. But upon closer examination I always found that this was only an apparent and no real indentation (infundibulum). Here one must be very careful not to draw any conclusions from a few series of sections. In a median section through the infundibular organ from one of my longitudinal series of a 47 mm. long Branchiostoma one would be inclined to draw the conclusion that there exists a groove-shaped indentation of the brainwall behind the organ, no trace of any indentation being found in front of it. So I think it dangerous to found a homology on this indentation, as Kuprrer did, and I adhere to the denomination “infundibular organ’, as its structure and develop- ment have more resemblance with the epithelium in the saccus vasculosus of the ichthyopsidae, to which I gave the same name, than with the tuberculum posterius, which is still somewhat pro- blematical. b. Shape and development of the brain-ventricle. I will here only mention those facts that are important for the comparison between the Branchiostoma cerebrum and that of the craniotes, and for the question whether the differentiated epithelium mentioned above may be homologised with the infundibular epithe- lium, or with the tuberculum posterius. The second homology might be concluded from the drawing pu- blished by Kuprrer in 1894 and 1903, representing a median section through the cerebrum of a 2 c.m. long amphioxus. But this drawing seems to me not to represent the real state of things. Neither exactly orientated median sections (fig. 8) nor the median sections recon- structed from series of cross-sections (fig. 7) ever gave me anything like this drawing. And yet it is in this case that the recoustruction-method must give an absolutely certain result. By this method we are able to correct entirely the deviations of the cerebral axis from the longi- tudinal axis of the body as they are found in almost every specimen. And as the cerebral vesicle has such a simple uncomplicated form this method gives us in every case an exact reproduction of the median section (which is certainly of the high value for the com- parison of the brain Kuprrer ascribes to it), and at the same time allows us to get a sure knowledge of the width of the cerebral cavity. I give here three drawings of the median sections recon- structed from the cross-sections, one of a very young larva of 3.4 mm. (fig. 5), one of a young amphioxus of 10 m.m. (fig. 6) and another of a specimen 21 m.m. long (fig. 7). All these are (57) reconstructed from cross-sections of 5, magnified 800 to 1600 times, and afterwards reduced by means of photography. To fig. 5 I added the cross-sections lying on the spots indicated with a, 6, c, d, to show the width and form of the cavity at the different spots. In fig. 8 I give the reproduction of a real median section through the brain of a specimen of about the same age as the one the recon- struction of which is given in fig. 7, to show how much they are like each other. The reconstruction of fig. 5 shows, that even in very young larvae, (larvae of 1.5 to 2 m.m. give about the same picture), in which the brain is still larger in diametre than the spinal cord, there exists a dorsal dilatation of the cerebral cavity, which may be compared with the fourth ventricle of craniote embryos (fig. 5, 6, VQ). It represents a dorsal dilatation of the central canal (fig. 5c) and is connected with the anterior vesicle by a narrow part (tig. 55). In all my specimens this connection of the ventriculus quartus with the anterior vesicle could be stated with absolute certainty, contrary to the well-known observations by Hartscurx. Even in very young larvae the connection was very conspicuous. In the caudal part of the dorsal dilatation (fig. 5d) the midpart of the narrow fissure-like central canal is obliterated, so that this part of the fourth ventricle is separated from the ventral central canal which remains open. In older animals this obliteration proceeds craniad. The dorsal wall of the fourth ventricle is very thin consisting of one layer of flattened cells, but it is always visible even in very young larvae, if only the specimens are well-preserved. In much older individuals, which passed through the meta- morphosis long ago (fig. 6), the fourth ventricle is still very con- spicuous and connected with the anterior vesicle by a narrow dorsal canal. The dorsal wall is still thin and membranous. The large dorsal ganglion-cells (vide my former paper) that are now developed to a certain extent, are still only visible at both sides of the median plane and do therefore not appear in the median section through the brain. Afterwards this peculiar group of cells is developed to such an extent (fig. 7, fig. 8), that they occupy the entire dorsal part of this region of the central nervous system, and so appear also in the median section. It is only then that the distinct fourth ventricle becomes indistinct, irregular, flattened, alters its shape and even disappears here and there. Then we find the peculiar irregular dilatations of the central cavity, described by Kuprrer as ‘‘quere Schenkel” and “blasenförmige Erweiterungen”’. They are not seg- mental, are only of secondary importance, and are not to be com- ( 58 ) pared with special parts and stages of development of the brain of craniote embryos. After these statements I will add a few words concerning the cranial or rostral part of the cerebrum and the adjacent organs. In his paper of 1906 Epincer describes a new organ, the “frontal organ”, lying in front of the brain and being innervated by a special nerve. I regret to say that I (no more than Worrr in his paper of 1907) could find no trace of a frontal organ. Even after a most careful study of a number of individuals I can only find in the rostrum the often queerly shaped irregular mucous canals (Schleim- canäle) lying ventrally and dorsally of the chorda. They are never connected with the epidermis, but all receive very thin nerve-fibres from the first cerebral nerve. ; Although the existence of a distinct nerve connecting the olfactory groove of KOLLIKER with the brain, is denied by Epincer, I could find it in my preparations as a bundle of fine nerve-fibres, connecting the sensory cells of the groove with the dorsal part of the brain. In all respects I could affirm the exact observations of Docier (1903) *) both concerning the sensory cells in the olfactory groove and the nervous connection of them with the brain. In the dorsal part of the cerebral wall I find a distinct commis- sural system, wherefrom bundles of nerve-fibres curve backwards (much like the fasciculus retroflexus of the commissura posterior of the craniotes) and a few fibres curve round forward. There are more systems of fibres to be found in the wall of the cerebral vesicle, but they are rudimentary and composed of only a few fibres. This is not the place to enter into details about these things. But when we take all this into account I think it is not permissible to consider the amphioxus-cerebrum as an “archencephalon” (KuPrreR), that has remained on a very low stage of development, but we must regard it as a degenerated cerebral system, which has become rudimentary in many of its parts, a brain which has many of the features of the brain of the ichthyopsides, but there are entirely lacking the organs of the side-line system (lens of the eye, ear, side-line) and because of that and of the fact, that the head has not developed as in the higher vertebrates, it is degenerated and rudimentary. In connection with this and with the elongation of the chorda the foldings of the cerebral vesicle do not appear. Even a plica ventralis does not exist. The infundibular organ remains in the niveau of the ventral cere- bral wall. Leiden. Histological part of the Anat. Kabinet. 1) Anatomische Hefte 21. Bd. 1903. > mn Pag? G4. f heer ate 909% o Je M J. BOEKE. chs os D> Proceedin J. BOEKE. “On the structure of the ganglion-cells in the central nervous system of Branchiostoma lanc.” EEE Tj, Ree ° @ Int Fig. 3. Fig. 4. Fig. 8 J. Boeke del. Proceedings Royal Acad. Amsterdam. Vol. XI. ( 59 ) DESCRIPTION OF FIGURES. Fig. 1. Median longitudinal section of the infundibular organ of a Branchiostoma of 52 m.M. in length, 600: 1, Fig. 2. Cross-section through the same of a Branchiostoma of 54 m.M. in length, 600: 1. Fig. 3. The same as Fig. 1. Neurofibrillae stained with chloride of gold. Fig 4. Cells of the infundibular organ, a of a Branchiostoma of 22 m.M. in length, 6 of 50 m.M. in length, c cross-section of the upper ends of the cells. Fig. 5. Median section of the brain of a Branchiostoma larva of 3,4 m.M., recon- structed from cross-sections. Fig. 6. The same of a specimen of 10 m.M. long. Fig. 7. The same of a specimen of 21 m.M. long. Fig. 8. Median section through the brain of a Branchiostoma of 28 m.M. in length. Mathematics. — “About difference quotients and differential quo- tents”. By Dr. L. B. J. Brouwer (Communicated by Prof. D. J. KORTEWEG). (Communicated in the meeting of May 30, 1908). Different investigations have been made which are very completely summed up in the work of Dini: “Grundlagen für eine Theorie der Functionen einer veränderlichen reellen Grösse” Chapt. XI and XII, on the connection between difference quotients and differential quotients, particularly on the necessary and satisfactory properties which the difference quotients must possess in order that there be a differential quotient. One however always regards in the first place these different difference quotients in one and the same point a, together, forming as a function of the increase of x the derivatory function in x,. The existence of a differential quotient means then, that that derivatory function has a single limiting point in 2, i.o.w. that in x, the right-as well as the left derivatory oscillation is equal to zero. Other conditions for the existence of a differential quotient are found when in the first place the difference quotient for constant z-increase A is regarded as a function of zv and then the set of these functions for varying A is investigated. Let f(x) be the given function which we suppose to be finite and continuous and let ga (x) be the difference quotient for a constant z-increase A. The different functions pa (©) form an infinite set of functions, in which each function is continuous. We shall occupy ourselves with the ( 60 ) case that the set is uniformly continuous, i.e. that for any quantity s, however small it may be, a quantity o can be pointed out so that in any interval of the size of 5 not one of the functions of the set has oscillations larger than ¢. Concerning infinite uniformly con- tinuous sets of functions there is a theorem that if they are limited (ie, if a maximum value and a minimum value can be given between which all functions move) they possess at least one continuous limiting curve, to which uniform convergence takes place’). We shall prove, that for the set of functions of the difference quotients of a finite continuous function, if it be uniformly continuous, follows in the first place the limitedness and furtheron for indefinite decrease of the z-increase the existence of only one limiting curve, so that holds : Theorem 1. If a finite continuous function f(w) has a uniformly continuous set of difference quotients, then it possesses a finite con- tinuous differential quotient’). To prove this we call ,e, (z) the size of the region of oscillation between 2 and «+ A of the difference quotient for an z-increase d. If we allow Jd to assume successively all positive values, then it follows from the supposed uniform continuity, that A can always be chosen so small as to keep all values ‚e (7) below a certain amount as small as one cares to make it. If we thus call ga (v) the maximum of the values ,¢,(«) for definite wand A, then e, (z) tends with A uniformly to 0. - in ee We have fartheron if — is a proper fraction: n 1 1 1 1 nl Pp (#7) = PA en (« ate a) eat en Pe (+= a) (1) 1 i 1 1 pat pp, (@)=— va (a) + — gaf e+ 2 a) palet a) (2) in P ni Pp x n P ae n If we break up each of the n terms of the second member of (1) into p equal parts and each of the p terms of the second member of (2) into n equal parts, then the difference of those two second members can he divided into pn terms, each remaining in absolute | value smaller than — .&, (w), SO that the difference of p‚ (a) and yp 4 (a) pr = n remains smaller than «, (#) in absolute value. 1) Compare Arzeu\, “Sulle funzioni di linee’’, Memorie della Accademia di Bologna, serie 5, V, page 225. 2) We suppose the function to be given in a certain interval of values of the independent variable x. ( 61 ) So if we regard for any definite w all difference quotients the x-increases of which are equal to proper fractions of A, then the amount t, (©) of their region of oscillation is smaller than 2e, (7). The same holds for the region of oscillation of all difference quotients for definite z with z-increases smaller than A, because these can be approximated by the preceding on account of the continuity of f. So if we allow A to decrease indefinitely, then also r, (7) decreases indefinitely ; as furthermore when A becomes smaller, each following region of oscillation is a part of the preceding, the limit of the region of oscillation is for each a a single definite value, to which uniform convergence takes place, which is the limit of the difference quotients, the differential quotient. That this (forward) differential quotient cannot show any disconti- nuities, is evident as follows: If there were a discontinuity, then there would be a quantity o which could be overstepped there for any interval by the oscillations of the differential quotient; but if the value of the differential quotient differs in two points more than o, then there is also a difference quotient the values of which in those two points differ more than 5; so there would be for each interval, which contains the indicated discontinuity, a difference quotient with a region of oscillation larger than o, i. o. w. the functional set of the difference quotients would not be uniformly continuous. Out of the continuity of the forward differential quotient follows at the same time that the forward and the backward differential quotient are equal. Analogously it is evident that also a point at infinity in the differential quotient would disturb the uniform continuity of the difference quotients; in this is at the same time included the limitedness of the difference quotients, for they would otherwise on account of the finiteness of f be able to tend to infinity only for indefinitely decreasing z-increase, but that ould furnish an infinity point in the differential quotient. Theorem 2. Of a function with finite continuous differential quotient the difference quotients are uniformly continuous. Let namely e be a definite quantity, to be taken as small as one likes. Now we may have each « included by an interval 7 in such a way, that the oscillations of the differential quotient within each of those intervals remain smaller than */,e. On account of the uniform convergence, evident from the formula p‚(z) = f'(@ + 94), a A’ can be pointed out in such a way that all pa for which A << A' differ from the differential quotient less than */,¢ for any w, thus ( 62 ) have their oscillations below « in the intervals mentioned. On account of the uniform continuity of f we may furthermore have each z included by an interval 7’ chosen in such a way that for all A > A' the corresponding gs have within those intervals oscillations below é only; to that end we have but to choose 2’ in such a way that the oscillations of ‚f remain within the intervals below */,¢ A. If thus 2” is the smaller of the two quantities 7 and z', each 2 can be included by an interval 2" in such a way, that the oscillations of all difference quotients within it remain below «, with which we have proved the uniform continuity of the difference quotients. Theorem 3. If there is among the difference quotients of a finite continuous function a uniform continuous fundamental series with indefinitely decreasing z-increases, there exists a finite continuous differential quotient. Let namely ga’(z), par(x), . . . . be the fundamental series of func- tions under consideration, then for any quantity e we can point out a quantity o in such a way that fo) (@ + 2) — Gy (2) Ze for any a, any he. If we now approximate A° by a series a,4',a,A",..., where the a’s represent integers, in such a way that ap APA (ap HIA®, then also gxo(e +h) — puole) is approxim- ated by PAP) (e +h) — PaP (z), which last expression always remains << however large p may become, so that p‚o(w +k) — 9,°(@) cannot be D>e, so the set of all difference quotients is uniformly continuous, and there is a finite continuous differential quotient. Theorem 1 is applied when building up the theory of continuous groups out of the theory of sets, (where one remains independent of Liz’s postulates), in a certain region finite and continuous functions of one or more variables occurring there, whose difference quotients are in a certain system of coordinates linear functions of the original functions. *) As on account of the finiteness of the original functions there cannot be a region within which any quantity could be over- stepped everywhere by one and the same difference quotient, the 1) Comp. L.E.J. Brouwer, “Die Theorie der endlichen continuierlichen Gruppen unabhängig von den Axiomen von Liz”, Atti del 1V° Congresso Internazionale dei Matematici. It is the differentiability in one and the same system of coordinates of all the functions, which express the different infinitesimal transformations of a group, which is proved in this way. ( 63 ) coefficients of the above mentioned linear functions remain within finite limits, the system of the difference quotients is uniformly con- tinuous, and the differential quotients exist. Theorem 4. If the conditions of theorem 1 are satisfied and if the system of all second difference quotients (of which each is determined by two independent z-increases) forms a uniformly con- tinuous system, then there exists a finite continuous “second differential quotient” which at the same time is the only limit of the above set of functions when both z-increases decrease indefinitely, and the differential quotient of the (first) differential quotient. To prove this we call ex (z) the maximum size of the regions of oscillation of the different second difference quotients between z and «-+ A; then again ea (x) tends with A uniformly to zero. If we represent the difference quotient of pa (w) for an z-increase A, by waa, («) and if Pi and Ps are proper fractions then we have: n, n, Lo Ali A A Pd dy (©) = = 5 onale th +h), Re N,N, ky=0 kg=0 tn n, Ns eri" El A A ‘ Oe = a A ee ee ee Reece tS hoe If we break up each of the n,n, terms of the second member of (1) into p,p, equal parts and each of the p, p, terms of the second member of (2) into n,n, equal parts, then the difference of those two members breaks up into p, p, 7,7, terms, each of which 1 remaining in absolute value smaller than —— Ea, HA, (2), so that PiPs 3 the difference of pas, (z) and Pprdr pads (v) remains in absolute value ny Ng smaller than €'a a, (2). So if we consider for any definite « all difference quotients whose z-increases are equal to proper fractions of A, and A,, then the size taa,(z) of their region of oscillation is smaller than 2e's,+4,(2), from which we deduce as above in the proof of theorem 1 the existence of one single limit, to which the convergence is uniform and which is finite and continuous. If we now regard the difference quotient with z-increase 4,, on one hand for all g,’s, whose A is smaller than A,, and on the other hand for the (first) differential quotient, then the former all differ less than Ea, ta, (v) from the limiting function just deduced, so also the latter, which can be approximated by them. This holds independently of A, ; ( 64 ) the difference for z-increase A, of the (first) differential quotient can therefore not differ more than € „, (7) from the just deduced limiting function which is thus differential quotient of the (first) differential quotient i.e. second differential quotient. Theorem 5. If a function possesses a finite continuous second differential quotient, then the system of the first and second difference quotients is uniformly continuous. To find namely an interval size 2” which keeps the oscillations of all second difference quotients everywhere «. Let us now approximate A,° by means of a series @,A,',a,4,",.... and A,° by means of a series B,A,',8,4,",..., where the a’s and 9’s represent integers, in such a way that ay? ZAL < (a + DAP and BAP TAL SB + A”, 1) The uniform convergence of all difference quotients is evident from that of the difference quotients, for which A, = A, (out of these the other can be approxi- mated in the manner indicated in the proof of theorem 6); the latter is evident by developing the terms of f(x +2 A) —2f (e+ A) + f(x) according to Tavtor’s series, in which we make the second differential quotient form the restterm; the terms preceding this restterm then destroy each other. ( 65 ) thenalsog.c , (rz + h)—gp‚o ,0 (x) is approximated by Sp Lae ea) he et Pa), a a(?) (2 + h)—g, a), a(p) (2) » v p 2 pi p 2 which last expression remains >e,; so the set of all second diffe- rence quotients is uniformly continuous and there is a finite conti- nuous second differential quotient. Theorem 7. If there is among the second difference quotients of a finite continuous function a uniformly continuous fundamental series, in which both wz-increases decrease indefinitely, the function possesses finite and continuous first and second differential quotients. For, according to the above given proof of theorem 6 the whole „system of the second difference quotients proves to be uniformly continuous, and out of the above given proof of theorem 4 this system proves to possess for indefinite decrease of the two z-increases one single finite continuous limiting function /"(«) to which they converge uniformly. Let t' be the maximum deviation from this limiting function of the second difference quotients, whose w-increases are smaller than A’, and A’,, and let us regard the system § of all ~, (x) whose A ) 3) 9? So that the fruits gave off 2.3 grammes or 0.44 °/, of carbonic acid in four days. The chemical changes taking place during the after-ripening process were now studied. Each day a banana was broken off from a green unripe bunch of the fruit and when doing this care was taken to select the specimen from the same row of the bunch from which the previous one had been taken and thus to obtain samples of the same initial ripeness. The fruit was first peeled and rubbed to pulp in a mortar. I determined the amount of moisture by drying 10 grammes to a constant weight. Next 100 grammes of the pulp were extracted with alcohol and the residue dried and weighed. I evapo- rated the alcoholic solution after addition of a little calcium carbonate with the object of neutralising the acids. The residue was dissolved in water, additioned with a little solution of neutral lead acetate and made up with water to 100 cM’ in order to get the sugars in the solution in the same concentration as that in which they originally were present in the pulp. I determined polarisation and reducing sugar in this solution both before and after inversion and calculated from the figures obtained the amount of sucrose, glucose and fructose ( 76 ) after having stated that no other sugars were present in the liquid. I pulverised the dried residue left behind after the alcoholic extraction of the pulp and extracted part of it with cold water. This extract was evaporated to a small volume and precipitated with alcohol. The precipitate was collected on a weighed, ashless filter washed with alcohol, dried, weighed, incinerated and the loss of weight occasioned by the combustion of organic matter was recorded as dextrin after I had convinced myself by the red coloration which iodine solution produced in the solution of such a precipitate that it really was dextrin. A second portion of the residue was hydrolysed with hydrochloric acid under pressure and the amount of glucose thus obtained calcu- lated as starch. Finally, I determined the percentage of nitrogen and calculated from this figure the amount of albuminoids by multiplica- tion with the factor 6,25. The figures for the different analyses follow here: bs jen | | | : | 47th {9th | Q(th 22de | 93d 24th | | | Date of the analysis | April | April | April | April | April | April | | GEEN Unripe | ae | the skin) Unripe | Begins, ee IE ao Degree of maturity adheres the skin, to ripe _ Ripe ripe oo ‘loosens | ripen 0 Skin 45 Ad 43 | 39 | 37.8] 36.2 0/) Fleshy matter 55 56 Bi 61 | 62.2 | 638 Composition of the pulp | Moisture 58.94 | 59 21 | 59 48 | 59.86 | 60.88 | 61.12 Dry substance | 41.76 | 40.79 | 40 52 | 40.1% 39.02 | 38 88 Insoluble in alcohol 39 41 | 3406 | 29 58 | 20 98 | 15-30 | 13 00 Soluble in alcohol 935 6.73 | 10 94 | 19.16 | 23.12 | 25.88 Sucrose | 0.86 4.43 6.58 | (0550 | 43°68) | 10236 Glucose at | = 0 306 | 1080 348 ECN! Fructose | ate 0.90 | 1.53] 2.70 | 3.61] 48 Dextrin trace | 0.52 | 0.59 | 0.69 | 0.65 | 0.63 Starch 30.98 | 94.98 | 20 52 | 13.83 959 | 7.68 Albuminoids 265 | 260| 260] 2:58] 2.58] 2.55 Ash 0.94 | 0.96 | 0.97 V0 1.60 | 1.01 The skin. contains much rubber, fibre and also a small amount of CHR soluble carbohydrate and its composition calculated in 100 parts of dry substance does not vary considerably in the green and in the ripe state. The water content, however, diminished greatly during ripening so that the shrinkage of the skin is chiefly due to loss of water. . The analysis of the pulp shows large differences during the after- ripening because of the starch being rather suddenly transformed on a large scale into sucrose. That the sugar present in the ripe fruit was really sucrose was proved by evaporating to a small volume the clarified alcoholic extract from fully ripe bananas and allowing it to erystallise. After some time it deposited crystals which were recognised to be sucrose by numerous chemical and physical tests. In the ripe fruits this sucrose becomes partly inverted or consumed by the aspiration either as such or as products of its inversion. The latter possibility is the more pro- bable one, as, first of all, much carbonic acid is formed during the after-ripening and secondly because the fructose is in every case present in a smaller proportion than the glucose. It is evident, therefore that these two constituents are not consumed together as sucrose, but separately after the splitting up of that body and then the fructose more readily so than the glucose. During the saccharification process a little dextrin is formed too. 6. Mango (Manaifera). The mango fruit, as a rule, is picked when still unripe; in this state the fruits are internally white, hard, acid and flavourless, but within a few days they undergo an after-ripening process which renders them tender, full-flavoured, and yellow or orange-coloured. This period is, as in the former case, soon followed by over-ripeness and decay. A few mango fruits, of a variety which bears very sweet and well-flavoured fruits when ripe, were picked green, placed on a cool spot at a temperature of 28° C. and weighed every day with this result No | 29th Sept. | 1st October | 2d October | 4th October I 247 Gr. 243 Gr. 241 Gr. 240 Gr. I] 229 226 224 223 Ill 227 223 222 219.5 IV | 249 247 246 244 (78) Five green mangos were weighed and placed under a glass bell jar, through which a current of air free from carbonic acid was conducted which afterwards was made to pass through a Liebig potash bulb. This latter was weighed daily and the 5 fruits only after the end of the experiment. The 5 fruits weighed originally 1139.3 grammes After 3 days Wi Bed ee and therefore lost in 3 days 18.0 grammes The potash bulb increased during the first day by 1.712 grammes the second day by 1.276 of the third day by 1.570 ee Or in three days 4.558 grammes The fruits gave off 4.558 grammes or 0.40°/, of carbonic acid in three days. Just as in the case of bananas a mango fruit from a parcel having practically the same initial maturity was daily analysed; and this time the analysis extended with a determination of free and total citric acid. I had previously stated that the acid in the mango really was citric acid and that no other organic acid could be found in it. I determined the free citric acid by titration with 1/10 normal potash in the boiled fruit whilst the amount of total citric acid was determined by extracting tbe boiled fruit with alcohol and precipitating the citric acid in the alcoholic liquid by means of barium acetate. The precipitate was filtered off, washed, incinerated and finally, I deter- mined the carbonic acid in the ash which was of course equivalent to the total citrate in the precipitate. The figures obtained follow here. The yellow colouring matter, which is produced during the ripen- ing process, shows the same reactions as the carotine from carrots, the same spectroscopic appearance and in fact resembles it in every respect. During the after-ripening the starch is transformed into sucrose, which later on becomes hydrolysed and splits up into glucose and fructose. In the beginning of the process the fruit liberates water but this constituent increases afterwards owing to the combustion of the carbohydrates. The citric acid is vigorously attacked and the decrease in the acid taste during the after-ripening is not due to an increase (79) Date of the analysis 29th Sept. | 1st October | 2d October | 4th October | Degree of maturity Unripe | Almost ripe | Ripe | Over ripe Moisture 83.24 82 95 81.95 | 83.20 Dry substance 16.66 | 417.05 18.05 | 16.80 Soluble in alcohol 6.36 15.18 15.54 14.70 Insoluble in alcohol | 10.30 1,87 |. ah PVM Sucrose ray | 10.50") "| 12 | 9.31 Glucose 0 60 4.58 | 1.30 | 2.40 Fructose 1.90 210 | 2.01 | 2 60 Starch 8.53 0.55 | 0 | 0 Free citric acid | 1.36 0.34 | 0.25 | 0.10 Total citric acid 1.31 0.37 | 0.4 0.10 Ash 0.42 0.44 | of | 0.48 Albuminoids 0.80 | 0.80 | 0.75 | 0.73 in the sugar content, nor to a neutralisation of the acid but solely to combustion and thus destruction of the organic acid itself. C. Tamarind (Tamarindus). The tamarind fruits remain on the tree untill they are fully ripe and thus do not undergo any after-ripening process after being plucked or shaken off. In the unripe state the flesh is white and hard and fills.the whole pod so that the woody skin is firmly attached to it. Later on, when the fruit ripens, the flesh becomes tender and brown and owing to evaporation, shrinks in such a way that a large empty space exists between the dry pulp and the hard skin. The composition of the pulp of tamarind fruits in several stages of ripeness is given here. (see p. 80). In this case too the starch has become transformed into sugar, during the ripening but this time not into sucrose, but into a mixture of glucose and fructose. At the same time a great deal of water was evaporated, causing the fruit to shrink in its envelope and finally much acid was consumed by respiration, since the amount of total tartaric acid in the dessicated fruit was smaller than that in the so much more juicy one of a month before. The increase of the percentage sugar after the period of maturity is due to the (80 ) Date of the analysis 11th May 27th May 20th June 15th July | | Degree of maturity Green Almost ripe Ripe | Dessicated Dry substance 15.86 38 46 40 92 76.20 Moisture 84.14 61.54 50. 08 33.80 Glucose 0.40 10.10 20.4 25.10 Fructose 0.33 5.10 11.6 10.6 Fibre and pectin 3-91 8.10 7.90 14 57 Starch 3.33 | 1:25 | 0 0 Free tartaric acid 3 25 |’ 458 14.6 os Total tartaric acid Ben eS AE 16 4 14.4 Potassium bitartrate. 4.00 5.76 4.50 — strong concentration by evaporation, because no fresh formation of sugar can possibly have taken place in so dry a fruit. d. Sapodilla (Achras sapota) The fruits are plucked tree-ripe; in which state they are green and hard, and contain tannin and gutta-percha dissolved in the sap, which render the fruit unfit for eating. After they have been preserved in bran, the gutta-percha as well as the tannin, become insoluble and the fruit itself gets tender, full-flavoured and palatable. On examining sections of the fruit one sees the coagulated gutta- percha as a series of white strings, while the tannin is deposited as insoluble matter in some cells. The analyses of such fruit in a tree-ripe and full-ripe condition are given here. Tree-ripe Full ripe Moisture 74.76 75.20 ; Dry substance 25.24 24.80 Sucrose 7.80 7.02 Glucose 2.85 3.7 Fructose 2.70 3.4 Starch Absent Absent Pectine 3.34 4.00 Albuminoids | 0.45 0.40 Ash © 1.50 1.50 ( 81 ) Unlike the after-ripening of the former three fruits, this one is not due to saccharification of starch. The amount of sugar before and after the full ripening is the same, but in this case the fruit has become palatable by the softening of the hard pectin and by the deposit of tannin and gutta-percha from the juice as insoluble bodies. I have to mention here that I did not find lactose in this fruit which has been stated by Boucnarpat as being one of its constituents. They, however, contain much pectin and owing to the presence of this body the juice yielded a fair amount of mucic acid on oxidation with nitric acid; this renders the supposition probable that this acid, considered by BoucHarDaT as an evidence of the presence of lactose, has simply come from the pectin. II. Agents of the saccharification during after-ripening. When studying the fruits which come first into account in the research under consideration, viz. the banana and the mango fruit, we found in a certain stage of the development a rather sudden transformation of starch into sucrose, followed in a later stage by inversion and partial transpiration of the products of inversion. From experiments on the determination of the carbonic acid in the atmosphere in which this sudden transformation took place, I came to the con- clusion that just the period of the rapid saccharification coincided with a strong development of carbonic acid, or with a powerful oxidation and degradation. At the same time the moisture on the inside of the glass bell jar in which the fruits ripened showed that a copious evaporation had accompanied the oxidation. The figures for the carbonic acid from the bananas showed on the second day a strong development which decreased very soon, whilst those for the mangos remained somewhat stationary for the three days under observation. These data correspond very well with the more rapid after-ripening of the former fruits during this experiment in which they turned from green into yellow even on the second day. The transformation is therefore accompanied by oxidation and I tried to check it by excluding the fruits from the free access of oxygen. To this end I covered a few green mango and banana fruits with collodion and kept them together with a few similar fruits not covered with an impermeable layer. The fruits covered with collodion did not ripen well, and were converted into decayed masses, while locally the wrinkles occasioned by the dying off of the fruit caused the collodion layer to burst and thus made the experi- 6 Proceedings Royal Acad. Amsterdam. Vol. XI. (82) ment unreliable. Moreover it might well be that the decay was not only to be aseribed to the exclusion of oxygen but to the hindered evaporation which would be injurious to the fruit. In order to elucidate this point, a few bananas were placed in a tube, through which a current of nitrogen passed, while at the same time some other bananas from the same part of the bunch were kept in the ordinary atmosphere. When the latter had become yellow, tender and ripe, those in the nitrogen tube had still retained their green appearance. The analyses of the peeled fruits of the two parcels yielded these figures. In nitrogen In air. Moisture 70.54 68.36 Insoluble in alcohol. 25.90 11.06 Soluble in alcohol. 3.57 20.58 Sucrose 0.31 13.66 Reducing sugars 0.94 4.80 It followed then, that the after-ripening in the air had gone on uninterruptedly whilst the fruits kept in the nitrogen atmosphere had remained unchanged and had preserved their starch content; so that free access of oxygen is an indispensable condition for the saccharification of starch in the fruit. The following experiments were undertaken with a view to ascer- taining whether this saccharification was brought about by a vital process or by the action of some diastatic ferment present in the fruit. A jelly consisting of isinglas and agar agar of such a compo- sition that it was solid at the ordinary temperature was mixed with 1°/, of starch, poured into a series of Petri dishes and sterilised. Slices of green mango and banana fruit or pieces of half ripe tamarind fruit were placed on the stiff jelly in some dishes and on that of others figures and letters were traced with a pencil dipped in mango- juice. After two, or sometimes more, days the particles of fruit were removed and the jelly covered with a very dilute solution of iodine in potassium iodide which after having remained there for a minute was washed off. In every case not only the spot where the fruit had been placed or where the pencil strokes had been applied, remained white, but all round a white stain spread out, lined with a red border which gradually faded into the surrounding blue coloration of the still unattacked starch. The longer the dishes had been allowed to stand, the larger was the white stain. In every one of these cases, (83 ) therefore, a diastatic ferment had diffused from the fruits and from the juice, which had transformed all the starch, it could get hold of through the state of dextrin into sugar. When the iodine solution was allowed to act too long on the jelly, the iodine penetrated through the surface layer and reached the lower one, where the starch was still unattacked, thus colouring the whole dish blue. Finally pieces of banana and tamarind fruit were placed on slices of sterilised potato ; the result was that the sacchari- fication of the starch caused more or less deep cavities to appear in the places where the fruits had been applied. All this however is not yet a direct proof that the saccharification has been occasioned by a ferment; and in order to make this clear I immersed slices of banana into alcohol, left them there during a couple of days, then took them out, expelled the alcohol by means of a current of sterilised air and placed them again in Petri dishes on a layer of starch emulsion stiffened with isinglass and agar agar. Though not so rapid as in the case of the much more juicy fresh fruit, yet also here the ferment diffused through and after the application of the iodine solution the white stains with the red borders became visible. A quantity of mango juice was added to a boiled and re-cooled solution of 3°/, starch at 50° C. and kept at that temperature for some time. The liquid, which, at the outset, had given a deep blue reaction with iodine solution only became red when at the end of the experiment this test was repeated; this coloration did not undergo any change even if the mixture was kept for some time longer or if a fresh quantity of mango juice was added. The total amount of sugar, contained in the liquid (for the mango juice itself had also contained sugar) was higher after the reaction than before, which showed that the mango juice had contained a diastatie body with power to transform starch into dextrin and into sugar. Now the question still remained which sugar is formed in the laboratory outside of the living organism. The ripening fruits and their juices already contain so much sugar, which mixes with the small amount of sugar formed by the sacchari- fication of the starch that the proper identification of that latter portion is extremely difficult if not impossible. In order to eliminate the influence of the already existing sugar, ripening banana fruits were peeled and repeatedly triturated with alcohol and the extracted pulp, which contained as little sugar as possible was pressed and brought into glycerin. After a few days the amount of sugar and its nature was ascertained in the glycerin by 6* ( 843 polarimetric and copper tests both before and after inversion. Next 100 grammes of this glycerin were mixed with a 3°/, starch solution, warmed to 40° C. and kept at that temperature for a couple of hours. After that the dissolved starch and dextrin was precipitated with alcohol, filtered, a pinch of calcium carbonate was added to the filtrate to prevent inversion by the slightly acid reaction of the filtrate, and the aleohol was evaporated off. The syrupy residue was dissolved in water, diluted to the volume of 100 eM.? and used for the determination of the sugars by the polarimeter and Fehlings solution before and after inversion. The original glycerin solution had contained 0.17°/, of glucose both before and after inversion, while after the treatment with starch 100 grammes of the solution contained 0.60 grammes of reducing sugars before inversion and 0.67 after that operation, which shows that 0.43 grammes of glucose and 0.07 grammes of sucrose (?) have been formed from the starch by the ferment. The polarisation of the solution was + 0.9 before and — 0.4 after inversion, giving evidence, that notwithstanding the precipitation with alcohol, a small amount of starch or dextrin has still remained dissolved. At any rate from the fact that the exclusion of oxygen prevents the saccharification of the starch in the fruit and from the negative results of the experiments on formation of sucrose by means of fresh juice and of the precipitated and re-dissolved ferments, it follows that the rapid transformation of starch into sucrose during the after-ripening of some fruits is a vital process and not a consequence of the action of some ferment contained in the fruit which, just as diastase forms maltose from starch, could be isolated to form large quantities of sucrose from any kind of starch in the laboratory. Mathematics. — “Congruences of twisted curves in connection with a cubic transformation.” By Prof. JAN pe Vries. (Communicated in the meeting of May 30, 1908). § 1. If z,,z,, #3, 2, are the coordinates of a point X with respect to a tetrahedron having O,, O,, O,, 0, as vertices, then ' wad 1 3 determines a cubic transformation which transforms the right line mn = dar + wb; into a twisted curve w?, represented by | 1 den Zar + ubI The congruence F of the curves w° through the five points ! ! ! — UU, = UV, Ue, ( 85 ) Ork =1,2,3,4,5) is now transformed into a sheaf of rays having as vertex the point 0’, conjugate to O,. To the bisecant 6’ through O’, of the curve o’* brought arbitrarily through O,, O,, O,, O, corresponds a 8? through O,, O,, O,, O,, O,; having the right line s as chord. The following will show that the indicated transformation enables us to deduce by a simple method a number of well-known properties of systems of curves ow’. § 2. Let us consider the curves w* of the congruence I cutting the right lines / and m. They are transformed into the right lines through 0’, resting on two curves 2° and w’*. Now the cubic cones, projecting these curves out of O’, have besides the right lines O’, Oj (k = 1, 2,3, 4) five edges more in common, which are the images of as many twisted curves belonging to I. From this is evident that the curves of I cutting a given right line / form a surface A’ of order five. The image of 4° is a cubic cone, projecting 2’* out of O’, and having the bisecant 6’ out of O’, as nodal edge. Therefore the curve B® of T having / as bisecant is a nodal curve of A’. If we bring the right line m through O, its image is a right line m’ passing likewise through O, and having therefore with the above mentioned projecting cone of 2 besides (, two points in common. From this we conclude that 4° has five threefold points Oy. So the section of A’ with O,O;O, consists of the right lines O,01, Or On, OnOz and a conic through Ox, O1, On cutting 0,0, and forming with this right line a cubic curve of I. Consequently eleven right lines and ten conics lie on A’. 13 $ 3. The curves 9’ of I touching a given plane g, are trans- formed by the correspondence into tangents € through O', of a cubic surface &* having conic points in O, (4: =1,2,3,4). The polar surface of O passes through the four double points O, so it has as image a quadratic surface through those points. The section of the latter with gq is the image of the locus of the points, in which #" is touched by the right lines ¢. This conic contains therefove the points in which @ is touched by the curves 9°. Through 0’, pass six principal tangents of ©’, the congruence I contains therefore six curves, osculating gp. The enveloping cone g'° out of O', to ®* has four nodal edges O',O;; for a plane through O',O; cuts ®'* according to a cubic curve ( 86 ) pe with node Ox, sending but four tangents through O',, so that in that plane O',O, replaces two edges of the cone. So yg” has with an arbitrary cubic curve through the four points O7 ten points in common lying outside O,. By applying our trans- formation we find from this that the curves of T' touching p form a surface ® of order ten. A right line through O, cuts g* in four more points; on its image therefore rest four curves 9’ touching gp. From this ensues that °° has five siafold points Oy. The right lines 9,0, lie therefore on ®'°; it can as follows become evident that they are nodal rightlines. A right line resting on O,O, and 0,0, has six points in common with g’*. So its image must have on O,O, and 0,0, four points in common with &. The section of ® with O,O,0, consists of the right lines O,O,, O,O,, 0,0, to be counted double and a curve of order four, having nodes in O,, O,, 0, and in the point of intersection of the nodal line O,0,; thus it consists of two conics. These conics form evidently with OQ, 0, two cubic curves of I, touching g. Consequently there le on #' ten nodal lines and twenty conics. When we regard the tangential cones out of O', to two quadri- nodal cubic surfaces ®* it follows readily that I” contains twenty curves touching two given planes. § 4. To determine how many curves g° can be brought through four points QU; having the right line 5 as bisecant and resting on the right lines c and d, we have but to find the number of right lines 7” which cut B* two times and 7? and d®* one time, when these three curves have four points Oz in common. Now the chords of 6” resting on a right line / form a biquadratie scroll on which p® is nodal curve, having thus with y’* besides the four points O four more points in common. From this follows immediately that the right lines cutting 6° twice and y* once also form a biqua- dratie scroll &'*. The cones which project these curves out of a point of 6" having two edges in common, not containing one of the points OV, the curve 6% is also nodal curve on =. With d” this scroll has besides O, four points in common; so on y* and d* rest four chords of p’*, and by applying the transformation we find that the curves g° which cut 6 twice and ce once form a surface =* of order four. If we bring d through O,, then its image d' has with =" two more points in common; consequently d cuts the surface >* in two points lying outside O,, so that O, is a node. Therefore the surface =* has four double points Oy. ( 87 ) Evidently 4 is nodal right line of S*; for, 6 is the image of the nodal curve 8" lying on ". Through a point S of 5 pass two curves 9°; their two points of intersection S’ and S’’ with 5 are the points which 5 has still in common with the surface 4° determined by c, S and the points O. As the pairs of points S and S’ form a (2,2) correspondence, four curves e@*° can be brought through four points, which touch a right line and intersect an other right line. The section of +* with the plane O,O,O, has nodes in O,, O,, O; and in the intersection with 4; so it consists of two conics. One of these conics contains also the intersection of c; it is completed to a degenerated g° by the right line out of O, resting upon it and upon 6. The second conic contains the intersection of the transversal drawn out of O, to 6 and ce and forms with this right line a 9’. On the surface =‘ lie therefore eight conics, nine simple right lines and a nodal line. $ 5. The number of curves e° through O; (4 = 1, 2, 3, 4) resting on the right lines a,b, c,d is evidently as large as the number of transversals of four cubic curves a’,p’,y’,d* brought through O;. The scroll (a, 8,1), having «’, 3° and a right line / as directrices, is of order 14, / being fivefold and each plane through / containing nine right lines. If /, passes through OU, a plane through /, contains but four right lines, so that the order of the scroll (a, 8, /,) amounts but to 9. From this ensues that (a, 8, /) possesses four twofold points Ox. With ° the scroll (a, 8,/) has 22 points in common outside 0; ; so (a, B, y) is of order 22. On the scroll (a, 8,/,) we tind that O, is fivefold, because a right line through O, cuts four generatrices; on the other hand O,, O, and OU, are threefold points, for a right line through QO, cutting the fivefold right line /,, meets but one generatrix more. With y* the seroll (a, B, /,) has still 9& 3 — 5—3X3=18 points in common besides the multiple points. In connection with the above follows from this that O, is a ninefold point on (a, @, 7). Of the points of intersection of (a, 8, y) with d* 36 lie in Ox; consequently a’, 8°, 7°, d° have thirty common transversals. Therefore we can bring through four points thirty cubic curves resting on four given right lines. 6. Let us now consider the surface w°° formed by the curves J o* resting on a, b and c. Through a point A of a and the points O ( 88 ) pass five @° cutting 6 and c. From this is evident that a, b and c are fivefold right lines. With a right line m through QO, the seroll (a, 8, y) has thirteen points lying in QO, in common, so its image m’ (right line through 0) cuts w*® likewise in 13 points lying outside O,. We conclude from this that the four points O are seventeenfold on w°’. So the right lines 0,0, lie on this surface; that they are fourfold right lines ean be shown in this manner. As Oy and O, are ninefold on (a, 8,7) the right line 0,0, is cut outside those points by 22—18—4 transversals of the curves a, 8, y; the images of these right lines are conics through O;, and (resting on OnOn, 6, c and d and forming with OO, a 9° of the system. The section of w°° with O, O, O, can consist outside the three fourfold right lines only of, conics; these are easy to indicate. In the first place we can bring through O,,0,,0, a conic cutting & and c; it is completed to a @° by each of the two right lines out of O, resting on the conic and on d. Then the sections of d and of the transversal with O, to 5 and c with O,,0,,0, determine a conic forming with the indicated transversal a g°. So we have in O,,0,,0, three double and three simple conics; with the three fourfold right lines they form a section of order 30. On w°° lie therefore + seventeenfold points, 3 fivefold, 6 fourfold and 36 simple right lines, 12 double conics and 36 simple conics. Astronomy. — “Contributions to the determination of geographical positions on the West coast of Africa. II” By C. SANDERS. (Communicated by E. F. vaN DE SANDE BAKHUYZEN). (Communicated in the meeting of May 30, 1908). I. Introduction. After a stay in Europe during the winter 1902—1903 I returned to Portuguese West Africa and remained there until the autumn 1906 when I again went to Europe for some time. During this period 1903—1906 I have once more tried to contri- bute to the determination of geographical positions in these parts as much as time and circumstances allowed. Circumstances, however, were often unfavourable to my observations, and hence the results obtained are less than I had desired and expected at first. The results obtained may be ranged under three heads. 1. New determinations at Chiloango. In November and December (89 ) 1903 I made here a new series of determinations of latitude by means of zenith distances in the meridian. But I did not succeed in securing new data with which to correct the determination of the longitude, and at last I have entirely given up this plan, untill should possess a telescope of the required dimensions for the obser- vation of occultations of stars‘), because the observations of the latter will certainly lead to a greater accuracy in the determination of the longitude than can be attained by means of lunar altitudes with my relatively small instrument. 2. Determinations of astronomical coordinates at different stations in the Chiloango district. On two journeys, one to N’Kutu on the upper course of the Chiloangoriver from 22 to 31 December 1903 and a longer journey through Mayombe’) in June 1904, I was able to make determinations of latitude and longitude. The reason why these could not be made oftener lies chiefly in the peculiar difficulties attached to the transportation of the instruments especially of the chronometers. The best way of transporting them is by water by means of a canoe, and even then one must constantly pay attention to avoid shocks caused by trees floating down the river. When the chronometers had to be transported by land, I used a hammock suspended from a long stick carried by two negroes ; while mounting hills they tried to keep the stick as much horizontal as possible. Another circumstance which makes it difficult to obtain accurate results is that these excursions can be undertaken only during the dry season, when the nightly sky is as a rule overcast, so that one must take recourse to observations of the sun, and lastly in many parts one meets with great difficulties in finding a proper dwelling place, because prosperous negro villages, which formerly existed, are almost entirely depopulated and turned into desert in consequence of the trypanosomosis, which has raged there. On my journey in December 1903 the instruments were entirely transported by water, first by steamer to Mayili then by canoe to N’Kutu. At this latter station I secured determinations of latitude and longitude. ; The journey through Mayombe in June 1904 also began by steaming up the Chiloango- (or Loango-) river to Mayili. We there arrived on June 2 and I made a time determination in order to control the longitude determined previously. We then travelled by land to 1) I received for some time past (1907) a telescope of Zeiss of 80 mm. aperture and 120 cm. focal length, with which I have already made some experiments. 2) The name of a part of the Chiloango district. (90 ) Chimbete (June 3) and then per canoe up the river to N’Kutu. The first transport by land, when the carriers were not yet accustomed to their uncommon task, unfortunately caused a perturbation in at least one of the two chronometers, which appeared from the com- parisons between them. Also at N’Kutu I made a time determination on June 5, in order to obtain another result for the longitude of that place. On June 6 we continued our journey by land often along very difficult roads through woods and over hills and some times across small streams. We first went to the north east as far as N’Vyellele, a village 28,5 kilometers north east of N’Kutu (June 7), and then we travelled to the west during three days until June 10, when we reached Buku- Zan, a village on the Luali, a tributary river of the Loango. On June 13 and 14 we made an excursion from Buku-Zan to the north to M’Pene Kakata, but the rest of the time until June 16 I stayed in the former place and availed myself of this opportunity to determine its longitude and latitude. On June 16 we returned from Buku-Zan to N’Kutu. This time we went directly to the south east, and after we had covered a distance of 38 kilometers we arrived at N’Kutu on June 17. Thence we returned by the way we had come via Chimbete and Mayili to Chiloango (18—23 June). In the mean time I secured determinations of latitude and longitude at Chimbete. 3. Connection of a great number of secondary points with the astronomically determined stations, by means of compass directions and distances. It was my intention to form by means of my astronomical determinations a net of primary points with which I might connect a great number of intermediate points whose relative positions I had determined on many journeys by means of compass directions and distances, in order thus to reach also for the latter a satisfactory accuracy. In this I have partly succeeded, but for the southern part of the district it is still necessary to make the astronomical deter- mination of one and if possible 2 stations on the Lukula river, Chipondi and perhaps Pouro, the more so as the preliminary result of my secondary determination of the station Lemba on this river differs much from that which Mr. CaBRA had obtained some years ago, when he determined the demarcation between the Freestate and Portuguese Congo. 1 shali try to fill up this gap. But the difficulties are especially great in these parts, as the trypanosomosis has badly raged here of late. At any rate it will be desirable to put off till later the communication of my secondary determinations. (A) CORRECTIONS AND RATES OF THE CHRONOMETERS. ag | ee (Temp. ER kaden hs ab Chron. Hohwü on | ‘ | Corr. | D. Rate | 90? a Corr. D. Rate h m s ms 1903 May 15 | 8 12 447 59 03 446 55 03 „20 | 8.15 | 24.5 58.38 | —0 13 | —1 25 56.38 | +0 27 , 2% | 8.46 | 240 57.24 | —0.23 | —1.93 57.24 | 10.47 fe ons 4a | 92.0 |) .- 38.43 | —0.74 | A 24 48.13 | —0.35 , 2% | 8.40 | 19.6 31.41 | —0.96 | —0.86 | 45.44 | —0.39 July 3 | 8.32 | 19.6 26 06 | —0.g9 | —0.79 40.06 | —0.89 dee 404/48. 96 49.7 48 71 | —1.05 | —0.97 32.71 | —1.05 „ 417 | 8.40 | 20.4 44.47 | —1 08 | —1 10 27.57 | —0.73 „ 2% | 8.50 | 19.1 1 98 | —1.45 | —0.93 20.48 | —0.89 Aug. 4 | 8.45 | 9.7 | 446 51.06 | —4.09 | —1.01 15.06 | —0.54 „ 4 | 8.92 | 21.0 44.03 | —0.50 | —0.52 8.53 | —0.33 Oct. 12 | 8.45 | 24.4 41.88 | 40.02 | —4.08 | 13.38 | +0.10 , 49 | 8.10 | 25.6 44 45 | 40.37 | —1.03 17.95 | 40.65 Nov. 5 | 7.93 | 25.5 54.35 | 40:58 | —0.80 | 1 85 | 40.23 , 46 | 8.53 | 26.0 | 447 2.31 | 40.72 | —0.78 22.81 | 40.09 „ 20 | 7.98 | 95.6 4.32 | 40.50 | —0.90 | 23.92 | 10.98 Dec. 20 | 8.05 | 25.3 | 17.97 | -£0.46 | —0.86 | 48.97 | 10.83 1904 Jan. 3 | 8.04 98.08 | +0.72 52.08 | +0.22 66.48) 05.8 98.70 | +0.91 | A.M 53.20 | 40.37 oh eae 0 aaa 35.56 | +0.62 | —0.80 | +47 0.56 | +0.67 , 22 | 8.20 | 5.4 37.35 | 40.36 | —0.99 | 5.35 | 40.96 , 29 | 844 | 52 40.79 | +0.49 | - 0.81 | 10 79 | +0.78 Febr. 9 | 8.40 | 25.3 45.93 | 40.47 | —0.85 | 19.43 | +0.78 „ 20 | 8.05 | 25.8 55.41 | +0.86 | 9.59 | 44 | +0.18 March 4 | 8 93 | 25.8 | +48 8.69 | 44.02 | —0.43 30.69 | +0.74 ER ee) 95.7 38.47 | $1.40 | —0.32 43.47 | 40.47 May 12 | 8.08 | 25.5 | +49 13.51 | +0.83 | —0.85 | +48 8.01 | +0.58 „ 23 | 7.80 | 24.5 14.83 | 10.42 | —1.00 48.33 | +0.94 „ 30 | 8.37 | 94.4 15.66 | 40.44 | —0.99 26.66 | +4.48 June 24 | 7.70 22.83 | +0.29 47.33 | +0.83 Aug. 1 | 8.30 | 20.9 17.42 | ~0.44 | - 0.36 | 449 8.92 | +0.57 Sept. 30 | 7.90 | 4.9 | 48 58.86 | _o.31 | —0.61 | 20.86 | +0.20 Oct. 14 | 8% | 93.8 | 449 1.48 +0.19 | —0.79 | 95.98. | +0.37 (93) ds ie ~ en. etic En: Hewitt | p Chron. Hohwü Ae a | C. | Corr. | D. Rate | Eee Corr. D. Rate he Wl | ns Bl Ss Ss m s Ss 1904 Oct. 24 | 8 30 | 4.3 | +49 5 35 | +039 | —0 69 | +49 33 85 | -+L0 79 Nov. 5 | 8.25 | 24.6 10.03 | +0.39 | —0.76 42.03 | +0.68 , 40 | 8.95 | 25.4] 44.93 | 40.38 | —0.90 44.93 | 0.58 , 48 | 8.07 | 25.4 15.25 | 10.42 | —0.86 51.75 | +0.85 , 29 | 7.99 | 5.5 19.97 | +0.43 | —0.95 | +50 3.97 | 44.14 Dec. 9 | 8.10 | 25.4 96.46 | +0.65 | —0.63 11.96 | +0.80 , 49 | 8.32 | 25.0 28.54 | 0.21 | A 03 99.04 | 44.14 1905 Jan. 2 | 8.42 | 24.6 31.26 | +0.19 | —0.96 34.26 | 40.87 nk MEN BAO || 2527 | 36.40 | +043 | —1.04 | 46.40 | 1.01 „ U | 9.24 | 25.6 38.64 | 40.32 | —1.08 52.14 | +0.82 Febr. 12 | 8.43 | 25.9 | 49 17 | 10.48 | —0.99 | +51 2.47 | +0.46 „ 25 | 8.54 | 26.2 | 57.37 | +-0.63 | —0.91 | 7:87 | 0 March 5 | 8.03 | 26.4 | +50 2.93 | +0.61 | —1.00 | 6.73 | —0.14 , 95 | 7.94 | 26.6 | 16.72 | 40.72 | —0.92 10.72 | 40.20 Apr. 21 | 8.22 | 26.6 36.74 | +0.74 | —0.90 1.24 | —0.35 June 27 | 8.20 | 24.4 50.70 | +0.21 | —0.82 | +50 57.70 | —0.05 Sept. 4 | 8.66 | 21.0 99.38 | —0.32 | —0.57 29.38 | —0.43 vs 8.644] 22,6 29.36 | —0.01 | —0.65 28.86 | —0.26 BV APT) 335 1'129;6 98.35 | —0.25 | —0.90 24.35 | —1.13 Oct. 19 | 8.05 | 24.0 33.86 | 10.13 | —0.86 1.86 | —0.54 , 31 | 7.99 | 25.2 37.20 | 40.28 | —1.03 | +49 53.70 | —0.68 Nov. 4 | 8.32 | 25.1 40.33 | 40.78 | —0.50 52.53 | —0.29 „ 22 | 8.39 | 6.1 51.46 | +0.62 | —0.91 39.96 | —0.70 Dec. 6 | 8.18 | 26.3 | 451 2.09 | +0.76 | —0.82 31.09 | —0.63 , 46 | 8.20 | 25.6 9.58 | 10.75 | —0.65 23.58 | —0.75 1906 Jan. 8 | 8.24 | 26.2 96.52 | 40.74 | —0.81 9.02 | —0.63 Febr. % | 8.45 | 26.3 | +52 8.84 |-+0.90 | —0.68 | +48 11.34 | —4.93 March 11 | 8.37 | 97.3 26.09 | 14.15 | —0.67 | +47 58.09 | —0.88 „ AU | 8AL | 26.7 33.93 | 10.78 | —0.90 48.43 | —0.97 Apr. 3 | 7.90 | 26.6 43.32 | 10.72 | —0.92 35.62 | —0.99 May 6 | 8.45 | 25.8 58.36 | 10.46 | —1.00 0.96 | —1.05 Hine fleas ee | 24 | 52.20 | —0.24 | —1.98 | 146 20.84 | —1.21 , 48 | 8.09 | 22.7 39.07 | —0.77 | —1.43 1.57 | —1.66 July 49 | 8.52 | 20.8 | 8.52 | —0.98 | —1.22 | +45 9.59 | —1.68 (93 ) H. Yime determinations at Chiloango. Corrections and rates of the chronometers. In 1903 before I left for Africa I added to my chronometer of Hewitt another of Honwi. During my stay at Chiloango from May 1903 to July 1906 I have regularly controlled both by making at proper intervals time determinations in the same way as before by altitudes determined with my altazimuth. Moreover I have daily intercompared the two chronometers. With regard to the time determinations themselves I need only add to what has been said before : 1. that new determinations of the value of a level-part yielded 5.4, exactly as before; 2. that the flexure and the division errors of the instrument were regularly taken into account according to the formulae in ‘“(Contri- butions I’. Here follow the results for the corrections and rates of the chrono- meters. The rates, and also the temperatures added to them, refer to the interval between the date on one line above and that on the line itself. The temperatures for the periods of the two journeys are wanting. To the “Rates Hrewirr 20° C.” I shall refer later. I have first investigated the rates of the chronometers with regard to the temperature and to this end I have formed mean rates for periods of about 2 months, in each summer and winter. an Period | eg | Chron. Hewitt. § Chron. Hohwii. 1903 June 20—Aug. 4 | 19.63 | — 1 05 | — 073 Nov. 5—March 31") | 25.58 | + 0-71 | a 050 1904 June 24—Sept. 30 | 21.03 | — 0.24 | + 0.34 1905 Febr. 12—April 21! 26.42 + 0.70 | — 0.01 June 27—Sept. 1 | 20.95 | — 0.32 | = 0.8 1906 Jan. 8—April 3 | 26.83 + 0.90 | — 1.10 June 18---July 19 | 20.82 | — 0.98 — 1.68 For the chronometer of Hewirr I found a very distinct influence of the temperature and, in so far as I could find then, no variation with time. 1) I have excluded the period of my journey from Dec. 20 to Jan. 3. (94 ) For the simple means of the 4 winter and the 3 summer rates and of the temperatures belonging to them I find: 26°.28 + 08.77 20 .61 — 0.65 hence : Variation per degree + 05.25 *) By means of this coefficient of temperature I have reduced all the rates to 20°; these reduced rates are given in the table above in the column: D. Rate 20°C. The simple mean value of these reduced rates is — 05.87, from which the real mean reduced rate — 05.83 differs only little. By forming the differences between the reduced rates and their mean I found for the mean error of a daily rate, disregarding the different lengths of the intervals between the time determinations: M.E. + 05.225 a very satisfactory result, especially in consideration of the fact that for the whole period of more than 3 years we have adopted a constant rate depending on the temperature only. For the chronometer of Honwü the results are somewhat less favourable. One sees at a glance a distinct variation with time which from 1904 seems to continue in the same sense. In order to derive the coefficient of temperature I have compared each summer rate with the mean of the two neighbouring winter rates and thus found: Rate summer— winter + 05.78 + 0.08 — 0.05 A regular influence of the temperature does not appear from these data and the greater value of the first difference must be ascribed to an irregular variation in the beginning. Therefore I have accepted for the coefficient of temperature 05.00 and, in order to investigate the variation which is independent of the temperature I have formed mean rates for periods of about three months. They follow here together with the corresponding values for the chronometer of Hewirr reduced to 20°. 1) It was impossible to determine also a quadratic term on account of the small differences of temperature. For the years 1901—’02 the temperature coefficient was found to be + 0518. (95) DAILY RATES FROM PERIODS OF THREE MONTHS. eeh | D. Rate Hohwü S ge oe 1903 May 15—Aug. 4 — 1.08 — 0.49 Aug. 4—Nov. 5 — 0.90 + 0.07 Nov. 5—Jan. 29 — 0.86 + 0.65 1904 Jan. 29—May 12 — 0.51 + 0.55 May 12—Aug. 1 — 0.56 + 0.72 Aug. 1—Nov. 5 — 0.66 + 0.34 Nov. 5—Jan. 21 — 0.93 | + 0.91 905 Jan. 2i—Apr. 21 SOG NE +. 0.10 Apr. 21—June 27 — 0.82 — 0.95 June 27—Nov. 4 — 0.72 — 0.50 Nov. 4—Febr. 24 — 0.76 | — 0.90 1906 Febr. 24—May 6 | — 0.90 | — 0.99 May 6—July 19 | — 1.29 | — 1.51 The values of this table also show the greater regularity of the chronometer of Hrwirr for which only the last rate shows a greater deviation. The rate of that of Honwü seems tolerably constant during the period 1903 Nov. 5—1905 Jan. 21 for which the mean rate amounts to + Os.61. From the differences between the single rates in this period and their mean we find, again disregarding the lengths of the intervals: M.E. Daily rate Honwü + 05,30 still greater than for Hewrrr. But on the other hand the large coefficient of temperature of the latter is a disadvantage for periods for which the temperature is not accurately known. ITT. New determination of the latitude of Chiloango. ‘ In the months of November and December 1903 I made a new determination of the latitude of Chiloango, again by altitudes observed with my universal instrument, with the only difference that « much greater number of stars was observed, but with only one pointing for each of them at the moment of transit over the meridian. The observations were arranged so that 2 northern and 2 southern stars ( 96 ) 1903 DECEMBER 7 Adopted runcorrection for 10' —0'.66 ”) zenith point 239°59'47"'.32 Temperature and barometer for Ist star 25.3 759.4 4th | 24.9 759.5 6th | 24.6 759.6 12th | 240 759.8 | Readings aoe oe | Star £ nee | Zenithdist. Retr... cat | Micr. A Micr. B | | | | | | | | eal Seca eels one « Sculptoris | R | 964040! 15” | 39'51" | — 3789 | 24040197112 | 25"37| 6801 | 15 51 | we | # Phoenicis | L | 19758 49 |58%% |— 2.97 | 42 114.53 | 49.73 69.94 | 48 23 | | # Andromedae R 280148 7 | 17 42 0.00 | 4018 8.93 | 46.82 64.95 | 7 47 | | | s Cassiopeiae |L |175 5 24 | 5 5 |H 2.59 | 64 54 31.00 157.41) 65.87 ‚Phoenicis |R | 278 35 57 | 3533 |+1.08| 38 35 58.96 | 44.13] 67.91 58 33 | « Eridani (L | 187 29 33 |29 15 | — 2.43 | 52 30 26.79 1 12.04} 66.67 | 34 u | ¢ Persei R | 995 93 16 | 9257 |— 3.78 | 55 93 14.98 |4 20.03| 66.71 12 56 | « Cassiopeiae |L | 171 38 9 | 37 56 | + 0.54 | 68 21 44.73 (2 18.50, 62.93 9| 55 | « Hydri R | 296 49 0 | 4839 |+0.81 | 5649 1.24 1 24.44] 65.02 | 48 58 35 | 7 Andromedae) L 499.56 47 | 56 23 [ree See aes | 59.55, 62.48 | 45 29 | x Arietis |R | 26842 3 | 4438 |—41.62| 98419 2.97] 99.75) 59.02 fas 5 38 f e Eridani L | 193 15 4 | 1455 |+ 2.70 | 46 44 35.38 | 58.91) 64.91 22 56 | Date | Star 1903 November 28 Zenithp. 180° December 2 Zenithp. 210° December 6 Zenithp. 210° December 7 Zenithp. 240° Proceedings Royal Acad. Amsterdam. Vol. XI. | ¢ Toucani « Phoenicis « Cassiop. 7 Cassiop. « Sculptoris £ Phoenicis 8 Androm. v Piscium 3 Cassiop. Mean 7 Cassiop. « Sculptoris 2 Androm. Mean « Sculptoris _ B Phoenicis 2 Androm. ò Cassiop. 7 Phoenicis « Eridani Mean « Sculptoris 2 Phoenicis 8 Androm. d Cassiop. 7 Phoenicis « Eridani y Persei e Cassiop. De seer.» OE er © RP =| ES 7 Cae U A oO R L R LE R E R L (97 ) Zenith dist. 60° ze oF i 2 a ae to OC) ee RCC er} or ziee (Oh (Up) te I Ep NG, wo Jo) 68 Latitude NR INE sr | se | | — 5011! 5742 5821 66743 71/99 49.73 59.27 65.53 71.42 67.73 66.56 | 71.70 | 53.58 | 58.74 67.85 57.cA 67.85 | 67.85 | 67.85 | $7.91 60.98 64.35 69.94 69.59 63.53 59.45 69.94 69.59 62.26 61.90 68.01 69.94 64.95 65.87 67.91 66.67 66.74 62 93 | Zenith | Latitude Date = | _ Star en | neat er ED — 5° 11! Dec. 7 cont. x Hydri R STB 65!'02 7 Androm. L N 47 6."48 « Arietis R N 28 | 59/02 y Eridani Ë S 4] 6491 Mean 63.56 | 63.76 | 66.98 | 67.17 December 10 6 Cassiop. ie N 65 63.41 Zenithp. 270° | 7 Phoenicis | R S39 68 08 « Eridani if S 53 69.66 y Persei R N 55.1 filers e Cassiop. i: N 68 64.79 « Hydri R Sd 68 58 2 Trianguli R N 40 | 62.54 y Eridani E Sar 71.22 Mean 61.86 | 63.95 | 68.33 | 70.44 December 14 | 7 Phoenicis | R 5 ied 62.22 Zenithp. 300 « Eridani Lil 2S dao | 62.88 f Arietis R N 26 | 58.44 a Hydri Rie 2 | 65.99 | vAndrom. | L | N 47 59.56 | 2 Trianguli R N 40 | 64.07 ¢ Eridani iB S 47 61.99 ò Hydri R S 64 64.13 Mean 61.24 | 59.56 | 64.11 | 62.44 December 15 | 2 Cassiop. | L | N 65| 68.96 Zenithp. 330 | 7 Phoenicis | R | S 39 64.05 « Eridani E > 00 59.03 y Persei R N God. 2 aa ae = Cassiop. if N 68 68.16 « Hydri R 5 7 57,46 7 Androm. R N47) 67.46 £ Trianguli I N 40 68.18 ¢ Eridani iE S 47 59.67 Mean 69.82 | 68.43 | 60.76 | 59.35 ( 99 ) were observed alternately, and of each of these pairs the one in the position circle to the right, the other in the position circle to the left. The readings were always made with each of the two micros- copes both on the preceding and on the following division. The corrections for run and for the level reading were applied exactly as before (comp. Contrib. I. p. 280), the refraction was derived from the tables of Bresser and the declinations of the stars were taken as before from the Nautical Almanac, i. e. from the catalogue of Nrwcoms. Only now and then I have also observed stars from the Berliner Jahrbuch, namely v Piscium, d Cassiopeiae and g Persei. To reduce them to Nuwcoms I have applied to them the following corrections: —0"1, —0".8 and + 0".7, according to data communicated to me by Dr. E. F. v. p. SANDE BAKHUYZEN. The reading for the zenith was assumed to be constant for each night and determined so as to make all the stars agree inter se as well as possible. By the regular alternation of the positions of the instrument an error in the adopted zenith point was eliminated almost entirely. The observations were made in 6 positions of the circle, each differing from the next by 30°. As an example I will first give the observations of one night in full. I now proceed to give for all the observations the resulting values for the latitude in 4 columns: for the north stars circle right and left and for the south stars circle right and left. To these I add the approximate zenith distances of the stars. The observations at zenith point 210° are distributed over two nights, Dec. 2 and Dec. 6. Because it is not permissible to consider the zenith point for the two as exactly equal, it seemed better to exclude from the observations of Dec. 2 the only southern star obtained. For the rest no observations are excluded, not even the few which deviated rather much. For each position of the circle I have combined the results for the two positions of the instrument, but I kept apart those from the northern and from the southern stars and so I obtained: (see p. 100) To the results from the northern and the southern stars I have added their differences and their means. In so far as we may assume that the north and the south stars had in the mean the same zenith distance, the former represent the corrections to the measured arcs of 22 for errors of division + double the correction to the measured z for flexure (comp. Contrib. 1 p. 285), while on the 7 ( 100 ) Zenithpoint North stars | South stars | N—S abu — 5° 11! — 5°12! 180° 69'43 56'16 — 1297 2"64 210 68.81 “62.08 — 6.73 5.44 240 63.66 67.08 + 3.42 Dot 270 62.90 69.38 + 6.48 6.14 300 60.49 63.28 + 2.88 1.84 330 69.12 60.06 — 9.06 4.59 Mean 65.67 63.01 — 2.66 4.34 same supposition the means from the north and the south stars are free from these two errors. : To derive the errors of division and of flexure we obtain, the mean zenith distance amounting to 49°, with the same notations as before : a’ = Za sin 98° = — 1016 b= — 2b am 98° = +, 0.83 c= 2c sin 49°— — 2.66 whence, if « stands again for the circle reading: Correction for division errors to the circle reading —5."13 sin 2a—0."41 cos 2a = +5."15 sin (2a—175.°4) Correction for jlerure to the zenith distance —1."76 sin z. The mean of the values in the last column is: gy = — 5°12'4".34. The formula for the correction for division errors agrees very well with that derived from the observations of 1900—0O1, which is of importance for the correction of my other observations of zenith distances. For the coefficient of the flexure I had formerly found —()."60; the difference may still be ascribed to accidental causes. Finally I give here the 12 separate results for thé latitude, each corrected for division errors and flexure. (see p. 101). Their mean value must of course be equal to that of the uncor- rected results. From the comparison of the former with their mean we derive for the mean error of the final result + 0."57. Hence this is: y = — 5°12'4".34 + 0.57. (101 ) North stars | South stars — 5040 1809 | 2172 | PAS 210 5.30 5.59 240 5.23 5.51 270 6.65 5.63 300 1 5. 2.43 330 4.89 4,29 This result may be combined with that of 1900—01. For the latter I adopt the first value of Contrib. I p. (284), but I estimate its mean error to be not less than that which I have now found. Thus: Latitude of the pier of observation. 1900—01 — 5°12'4".01 + 0".6 1903 4 34 + 0.6 Together — 5°12'4"2 +04 I think that the agreement is quite satisfactory. IV. Determinations of the longitude and the latitude of N’ Kutu, Mayili, Buku-Zan and Chimbete. 1. Journey of 1903 December 22—31. Observations at N’ Kutu. During this journey the chronometers were transported all the way by water, hence extraordinary perturbations are not to be feared. But the temperature was certainly higher than at the same time at Chiloango; it amounted at least to 26° and may have been between 26° and 30°. A comparison of the rate of Hewrrr from Dee. 20 to Jan. 3 with the mean reduced rate for those months would yield a temperature of 26°.4, which is of course an uncertain estimation. Although there is no reason to expect any difference in temperature between the journey to N’Kutu and the journey back, yet the uncer- tainty about this affords a disadvantage for Hewrrr and therefore, for the determination of the longitude, I have finally given equal weights to the two chronometers. The computation of the time and the latitude at a place of which the geographical position is unknown had of course to be made in successive approximations. Here I shall give only the final results. ( 102 ) The observations were made in the factory of the firm Harron and COoKSON. Determination of the longitude. A time determination of 26 Dec. by means of 4 observations of 8 Orionis in both positions of the instru- ment, each time over 7 horizontal threads, yielded the following corrections of the chronometers to the mean time of N’Kutu. Together with these I give the corrections to the mean time of Chiloango derived by simple interpolation — the best thing to be done — between the time determinations of Dec. 20 and Jan. 3, and finally the resulting difference of longitude. December 26.296 (M. T. Chiloango). Hohwii Hewitt Correction to M. T. N’Kutu + 48™48*.85 + 49™228.35 8 ere: Chiloango 46 50 .29 47 2227 Difference of longitude — 1 58.56 — 1 60 .08 Adopting the simple mean of the two results, we find for the longitude of N’Kutu reiatively to Chiloango — 1m 595.32. Determination of the latitude. On December 29 I secured a deter- mination of the latitude by 3 pairs of observed zenith distances, i.e. three observations in each position of the instrument, of 3 Andromedae (¢ — 40° North) and by 2 pairs of « Eridani (2 = 53° South). The results were : 8 Andromedae 1st pair — 4°57’ 9".90 24 pe 11.06 3d te 11.24 Mean 10.73 Corrected — 4°57' 5".74 a Eridani dst pair — 4°56'57".69 dak ae 59.81 Mean 58.75 Corrected — 4°57' 3".72 Hence the mean result for the latitude is: PR 57 Ay (103 ) 2. Journey of 1904 June 2—23. Corrections of the chronometers. As this journey was made almost entirely by land the circum- stances were much less favourable for the regularity of the chrono- meters, in spite of all precautions taken. The intercomparisons, which were made at least once every day, clearly show small irregularities now and then and once on June 3, when the earriers were not yet accustomed to their task, as I have said before, a serious perturbation occurred. The instruments were almost always carried in the shadow of the woods and only a few times they can have been exposed to the sun- beams. We must assume, however, that they were subject to the general fall of temperature which occurs in these parts in June, and thence follows that we may not accept a constant rate for the chrono- meter of Hrwirv. From my regular thermometer readings in 1903 and 1905 I derive for the mean fall of temperature during June 2°.18, i. e. on an average per day 0°.073; this would cause a variation of rate for Hewitt of — 0s.018 per day. On this supposition and starting from the time determinations at Chiloango of May 30 and June 24, the daily rate would have been at the beginning (May 30—31) + 05.50 and at the end (June 23—24) + 05.08. As the temperature coefficient of Honwti may be considered zero, we may gather some evidence on this point from the relative rates during the journey. Beginning after the perturbation on June 3, I find the following differences between the two chronometers, each being the mean result from at least three comparisons, and derive from them the relative rates subjoined. Hohwii — Hewitt June 5 + 49.500 10 NS 15 FAT eM oe 20 en 24 EE a As the mean rate of Honwi was about + 0.59, these values agree fairly well with the assumed variable rate for Hewitt, which I there- fore adopt as the most probable. For the middle of the period, June 42, the chronometer correction derived by means of the latter rates differs from that which would follow from the constant rate + 0.529 by 1.836. A great difficulty is caused by the perturbation on June 3, when the difference between the chronometers seems to have varied abruptly ( 104 ) 3 secs. It was probable that this must be attributed to the chrono- meter Honwt, which supposition seems confirmed by the time deter- mination at N’Kutu of June 5 if we reduce it to Chiloango with the difference of longitude determined in Dec. 1903, but it is undoubtable that we have here a source of uncertainty for the following deter- minations of longitude. I already remark here that I have finally accepted no jump in Hewirr and one of 2 seconds in Honwt. For the daily rate of the latter we then must accept -+ 05.91 instead of + 0s.83. In addition I remark that also for the determinations in 1904 I have assigned equal weights to the two chronometers. 3. Determinations of longitude in 1904. Mayili. On June 2 I here secured a time determination by means of Sirius west, and of « Bootis east of the meridian. The results obtained from the two, corrected for division errors and flexure, differ inter se by 05.37. Here follow the mean results, to which I have added the correc- tions to the mean time of Chiloango derived by means of the adopted rates (+ 08.91 for Honwi and a variable rate for Hewrrr) and the difference of longitude derived thence. June 2 655 M.T. Chiloango Hohwü Hewitt Correction to M.T. Mayili -++ 49™50s.89 + 50™36s.39 » » Chiloango + 48 29 .33 + 49 17 .08 Difference of longitude — 1 21.56 +=) di A9 aon Mean — 1™20:.44 In 1902 I had found — 122153. If we had derived the correction of Honwit with a rate of +-0°.83, the difference of longitude according to this chronometer would have been —1™218.80, while Hrwirr with an assumed constant rate would have yielded — 1™195,89. N’ Kutu. Here I was obliged to have recourse to the sun for determination of time and on June 5 I obtained the following results from 4 observations of the two limbs in the two positions of the instrument. I now begin by deriving the correction of Honwi to the M. T. of Chiloango, without accepting a jump, and therefore with the rate + 08.83. ( 105 ) June 5 311 MT. Honwü Hewitt Correction to M.T. N’Kutu + 50™285.54 + 51™175.54 as » », Chiloango + 48 31.45 + 49 18.30 Difference of longitude — 1 57.09 — 1 59.24 while the result of Dec. 1903 was — 1™59s.32. From this it would appear that on June 3 a perturbation occurred in Houwü and not in Hewirr and that the jump in the former amounts to about 2 sees., which agrees sufficiently with the observed abrupt variation in the difference between the two. For a more accurate investigation of the perturbation I have tried to avail myself of the time determination of June 2 at Mayili, after having reduced it to Chiloango by means of the difference of longitude determined in 1902, but this has not thrown more light on the subject. Everything considered I have finally accepted as the effect of the perturbation: a jump of 2 seconds in Honwü. As to the longitude of N’Kutu itself, it will be best to use for it only the determination of Dec. 1903, although the new determination by Hewirr perfectly agrees with it. Buku-Zan. My observations were made in the factory of the firm Hatton and Cookson. For a time determination I could obtain only 3 pointings at the sun’s limbs on June 14. To their results I have added the corrections to M. T. Chiloango according to the adopted computation (i.e. with a jump in Houwié and a variable rate of Hewitt) and also the difference of longitude derived from them. June 14 450 M.T. Honwü Hewitt Correction to M.T. Buku-Zan + 50™13543 + 50™57593 A » », Chiloango + 48 38.12 + 49 21.22 Difference of longitude — 1 35.31 — 1 36.71 Mean — 1™36°01 Computed with constant rates and without an assumed jump the results would have been — 1™84°51 and — 1738502, hence in less good harmony. Chimbete. Also here (factory of Harron and Cookson) I could observe only the sun for a time determination, but I secured at least a complete set of 4 observations of both limbs in both positions ; the two pairs computed separately differ by 0.883. The results were the following; to these I have added the cor- rections to M. T. Chiloango according to the adopted computations, and the difference of longitude derived by means of them. (106 ) June 21 3'6 M. T: Honwü Hewitt Correction to M. T. Chimbete + 5013773 + 51™15s73 » », Chiloango + 48 44.46 + 49 22.52 Difference of longitude Snes ace ee | Mean — 1™ 53524 whereas if computed with constant rates without an assumed jump I would have got — 153903 and — 1™53*81. Thus the results following from the two computations differ much less than for the other places. 4, Determinations of latitude in 1904. Buku-Zan. For a determination of the latitude I could observe only on June 15 one star in the south, 3 Centauri. Of this star I obtained 8 pointings distributed equally over the two positions. The results were: 1st pair p=— 4° 46’ 4"46 nd 52. TAR 8.54 Elfers Biot Mean 6.26 and after correction for division error and flexure p= — 446 111. Chimbete. 1 only succeeded on June 20 in securing 10 pointings on « Crucis, distributed equally over the two positions, with the following results. dst pair g = — 5° 1' 18.40 adi, 18 .65 Oe ne 21285 PR 20:53 GEE 11952 Mean 190 and after correction for division error and flexure p= — 51245 5. Final results. I finally accept the following values as the most probable results of my determinations of the longitude and the latitude of the four stations in the interior. For the longitude of Mayili I take the mean of the two determinations and for that of N’Kutu I use only that of 1903. Difference of longitude Fishin with Chiloango Mayili — 5° 4' 40" —1™ 205.9 N’Kutu —4 57 5 —1 59 3 Buku Zan — 4 46 11 —1 36.0 Chimbete ab AD = eee (107 ) Astronomy. — “Contributions to the determination of geographical positions on the West-coast of Africa. III. Appendix.” By C. Sanpers. (Communicated by E. F. van Dr SANDE BAKHUYZEN). 6. Modified computation of the determinations of longitude in 1904. For the computation of the corrections of my chronometers to the M. T. of Chiloango during my journey of June 1904 I have supposed that the chronometer of Hewirr had not been influenced by the perturbation on June 3 and that the one of Honwii had advanced 2 secs. I had adopted the value of 2 secs. chiefly in order not to exaggerate. But the result of the time determination on June 5 at N'Kutu, taking into account the modification of the rate involved in the supposition of a jump of a given amount, as well as the com- parisons on June 3 render it more probable that Honwi advanced 3 secs. I shall therefore give here the results which we obtain on the latter supposition, assuming a daily rate for Honwü of + 05.95. [ shall also show to what results we should arrive if we adopted the extreme supposition in the opposite sense, namely that Honwü was not perturbed and that Hewirr had omitted 6 beats = 8 secs, and if we again assumed daily rates of both in accordance with the last supposition. This supposition is not very probable but neither quite impossible, and in this way we may at least form some idea of the still remaining uncertainty. For the rest [ still hold the supposition that the rate of Hewirr has varied during the journey owing to the fall of temperature. Here follow the values obtained for the difference of longitude between the + stations and Chiloango : a on the previous supposition ; 6 adopting for Honwt a jump of 3 sees. ; c adopting a jump of 3 secs. in the opposite sense for Hewirt. Houwü Hewirr MEAN Mayili a —1m21556 19:31 — 1m 20544 b 21.45 - 19.31 20.38 c 21.80 19.66 20.73 N’Kutu a —1™58962 5924 — 1m58s93 b 59.39 59.24 59.32 c 57.09 56.94 57.02 Buku Zan a —1™35831 36571 — 1m: 36501 b 35.73 36.71 36.22 c 34.51 35.49 35.00 ( 108 ) Honwü Hewirr MEAN Chimbete a — 1753527 53821 — 1m 5324 b 53.41 53.21 53.31 c D3.03- 53.65 53.93 We find in the first place that the longitude of N’Kutu on supposition 6 agrees exactly: with the result of December 1903 which was 59s.32, and on supposition c differs strongly from it, whence appears clearly that the latter is less probable. It further appears that, with regard to the three other stations, the results on the two extreme suppositions 6 and ec differ 18.2 for Buku Zan and only 0s.4 for Mayili and Chimbete, while the results on suppositions a and 6 differ for Buku Zan 05.2 and for Mayili and Chimbete less than 0.1. The results from the two chronometers separately accord fairly well inter se, Mayili excepted. As we reject the result of 1904 for N’Kutu and replace it by that of 1903 and as for Mayili we can take the mean of the results of 1902 and 1904, we find that the uncertainty caused in the final results by the perturbation is less than was to be feared. Lastly I give here the final results obtained in this way, assuming thereby the most probable supposition 6: Difference of longitude with Chiloango Mayili — 1™205.8 N'Kutu — 1 59.3 Buku Zan — 1 36.2 Chimbete — 1 53.3 The differences with the values adopted before are at the utmost 05.2. Astronomy. — “Observation of the transit of Mercury on November 14, 1907 at Chiloango in Portuguese West-Africa’. By C. SANDERS. (Communicated by Dr. E. F. van DE SANDE BAKHUYZEN). (Communicated in the meeting of May 30, 1908). For a short time I have possessed a telescope of Zwiss of 80 mm. aperture and 120 cm. focal length. With this telescope I intend to observe in the first place occultations of stars in order to determine the longitude of my observing station with greater precision than hitherto has been possible. For the present the telescope has an azimuthal mounting, which however soon will be replaced by an equatorial mounting with slow motions and small divided circles. In the mean time ( 109 ) I have been able to use the telescope for observing, at least partly, the transit of Mercury on November 14 1907, and I venture to publish my results here. To give my telescope a firm basis I had a pier built of beton surrounded by an isolated floor and provided with a movable roof open at the sides, which roof can be entirely moved aside. For the transit of Mercury, however, I kept the roof over the instrument in order to protect myself from the burning sunbeams and especially to keep out the light from outside as much as possible. For the observations I had constructed a projection apparatus, a kind of camera having the shape of a truncated pyramid, of which one side is open and the three others are coated with black paper. The base on which the image was to be formed was at a distance of about 14 cm. from the eye piece. The camera was adjustable in distance and in inclination, to secure the proper position of the plane of the image. With the highest power of the telescope, 133, the diameter of the projected image of Mercury was nearly 1 mm. The fine solar spots that were present could be sharply observed and those in the neighbourhood of the western limb could be seen surrounded by very distinct faculae. Unfortunately the beginning of the transit was hidden from my view by clouds. Towards 1 o’clock mean time of Chiloango it began to clear up and, after Mercury had been visible on the sun as a well defined disc, its egress could be observed very well. I found: third contact at 2'35™38s M.T. Chiloango last a le de The moment of the 4‘ contact, that at which the last impression on the limb seemed to disappear, was difficult to estimate within some seconds chiefly owing to the unsteadiness of the images, but I hold that but for this unsteadiness the observation of the Ìast internal contact could have been made with great precision. The corrections of my chronometers were derived from time determinations before and after the transit. The times computed from the Nautical Almanac for the 3rd and the 4'” contact at Chiloango were 2'35™47s and 2'38™24s. Thence follow for the differences observation — computation: — 98 and — 175.) 9 1) (Note added by E. F. v. p. Sanne BAKHUYZEN). According to the mean of the observations made at Leiden, these differences were —6* and —21s, Hence the results of Mr. Sanpers agree very well with these..The greater difference for the 4th contact must probably be ascribed to the circumstance that all the observers have observed this phenomenon too early. {1104 Zoology. — “Some results of the investigation of the Cirripeds col- lected during the cruise of the Dutch man-of-war ‘“Siboga” in the Malay Archipelago.” By Dr. P. P. C. Hoek. Having explained the position the Cirripeds occupy in the Class Crustacea the author emphasized first of all the great advantage or possessing Darwin’s well-known Monograph’) when studying the animals of this group. This book may still be considered as a model for similar monographs, not only in treating the Sub-Class from a general point of view, but also for the description of the different species. As might be expected the study of the material collected with the “Siboga’”’ has considerably increased our knowledge concerning the biology, the mutual relations and the anatomy of these animals: a few interesting cases have already been communicated to the Academy’) and a more detailed treatment is given in the Report on the group published in the Results of the Expeditions edited by Prof. Max Weger. The first part of this Report on the Cirripeds was published in September 1907, a great deal of the second part and the deter- mination of nearly the whole material has been achieved by this time. To have an idea of the importance of the material collected by the “Siboga”’ it is worth while to compare it with that obtained during the English expedition with the “Challenger”. The English man-of-war the “Challenger” made a cruise round the world, which lasted about three years and a half, and brought home collections from nearly all the oceans and seas of the earth’s surface; the Cirripeds collected during that cruise were also worked up by the present author, the report on the group was published in 1888. From the accompanying table it may now be seen that the material collected by the -‘Siboga”’ in the course of one year, and, comparat- ively speaking, in an area of limited extension, is not inferior to that of the “Challenger”; the latter, however, collected the greater part of its spoil from the bottom of the great oceans of the world where as a rule the depth was very important. The “Siboga” on the other hand, had better opportunity to investigate coasts, reefs etc. Hence it is easily understood that whereas the “Challenger” from depths to over 5000 m. obtained a richer collection of true deepsea-animals, the “Siboga” succeeded in collecting along with an 1) Darwin, Cu., Monograph of the Subclass Cirripedia (in 2 Volumes). Vol. I. The Lepadidae or Pedunculated Cirripedes, 1851; Vol. II. The Balanidae (or Sessile Cirripedes); The Verrucidae etc. 1854. London: Printed for the Ray Society. 2, Proceedings of the Academy of Sc. of June 25th, 1904 and January 27th, 1906, use, COMPARISON OF THE CIRRIPEDS COLLECTED BY THE “SIBOGA”, WITH THOSE OBTAINED BY THE “CHALLENGER”. Siboga: Malay Archipelago Challenger: Voyage round the world ale fen g CREE |g. g Sane) a = HO RS =| Genera SE EG Se dE eee KE — o a. TD & aD u = bot ro) Q, | Mo) de (>) en En 88 | g& |o8 3/48 | 28 | of 22,2) SZ En | So [2851] §7) Ea Eu Ses l) Ey ER SS |\Saao| ¥4 | SY |S SSA Zo a Sea iS a alOs © 10 n | u Lepas 2 — — 6 = = Poecilasma i 3 3 — 3 2 em! 2) Dichelaspis 5 4 — 1 1) 1 1 = 1 6) Conchoderma — == — == 2 = os Ee. Megalasma 2 4 1 — 1 4 en = Alepas 5 5 1 22) 1 1 | — 1 7) Microlepas n. gen. 1 1 — — — = = as bla 2 1 Te ES Eg cn aw pbs Scalpellum 38 32 8 22 43 43 7 36 Pollicipes y| — — — — SEND Ie — Lithotrya 4 1 — — — |— = Balanus +20*) | +10*) 3 4 3) 10 5 2 de Acasta 2 1 — — 1 = = en Tetraclita 3 — — — 2 ne zi pan Pyrgoma 3 2 1 x! — ae = 15 Creusia 1 — = == = == en = Coronula — — == = 4 = aoe on Chthamalus 2 — — — 2 | = = Hexelasma n. gen. 1 eld dl lan i} — = nn. ah Verruca 7 6 — 6 6 6 = 6 Total 106 68 x | 33 78 60 9 47 *) Provisional determination. 50 deepsea-spec. 1) Dichelaspis Weberi from a depth of 560 m. *) Alepas morula from 538 m. and Alepas ovalis from 984 m. 5) Balanus alatus from 564 m. 1) Hexelasma arafurae from 560 m. 5) Poecilasma carinatum from 750 m. and P. gracile from 740 m. 6) Dichelaspis sessilis from 1800 m. 1) Alepas pedunculata from 740 m. 8) Balanus hirsutus from 900 m. 56 deepsea-spec. (a important deepsea-material, a greater number of shallow-water forms: a richer collection altogether, as many species of Cirripeds belong to tbe coastal fauna. However, this table was not compiled especially to show the greater number of species collected by the Dutch expedition. Its main object is to point out that the deepsea-material of all the oceans and seas of the world together, as far as Cirripeds are concerned, has after all no other composition than that which was collected in a relatively small area, the Malay Archipelago. For both collections that composition comes to this, that after all only two genera Scalpellum and Verruca, in deeper water, are represented by numerous species and that the other genera which do occur in that deeper water are represented there by very few forms only. It is true that the genera Scalpellum and Verruca, in shallow water, are also represented by several species: we now know 125 species of Scalpellum, which are so-called “good” species and which in any case, almost without exception, can easily be distinguished from one another; of these 90 live at depths of over 500 m. to ca. 5000 m. and 35 in shallower water. The number of known species of Verruca now amounts to 36; of these 5 were observed in shallow water and 31 at depths from 500 to ca. 3400 m. In deep water, however, only these two genera found circumstances specially favourable for the formation of new species, whereas the same for other genera holds good in more shallow water. As an instance of the latter the genus Balanus may be pointed out: of this genus by this time over 60 species are known and, therefore, it can safely be considered as one rich in species. However, only 5 of these have been observed in water of a depth of 200—500 m. and of the latter only 2 at a depth down to 564 m. On the other hand 55 species of this genus are known, which inhabit the coast or relatively shallow water only. The author thinks that at the present moment our knowledge is by far too incomplete to permit of an explanation of phenomena of this kind; in such cases all we can do is to try to state and to control the facts as accurately as possible and we must then confine ourselves to considering it as a peculiarity of a few genera that their numerous species divide themselves over so strongly divergent depths, whereas it is characteristic of other genera that none, or a single, or a few species only have been able to adapt themselves to somewhat more considerable depths. It is remarkable at the same time, and this holds good for the genus Scalpellum especially, but for most of the known species of Verruca also, that such richness in species is accompanied by so great ( 113 ) an isolation of the different forms. Of course, we cannot express our opinion on this matter with absolute certainty, as dredging, especially in deeper water, always remains an insecure method of testing the greater or lesser commonness of a species at the place where it occurs. Yet it is very striking, that in the collections made the species of Cirripeds from deeper water nearly without an excep- tion are represented by one or by a very few specimens only. Especially when taking into consideration that the pelagic Cirripeds and those living near the coast or in shallow water, are nearly all of them characterised by numerous specimens living in the neighbourhood of one another, we are brought to admit, that where the depth is more considerable, relatively large distances separate the places, where the animals of a certain species occur, from one another, or, that specimens of such a species are never numerous and not to be found at all at very many places. This is also proved by the circumstance, that the “Siboga’” found again specimens of two species of Scalpellum only out of the ten which were collected by the “Challenger” in the Malay Archipelago. That the “Siboga” found again the only species of Verruco which the “Challenger” brought home from deeper water in that area, would not be in accordance herewith — in both cases, however, that species was also represented by very few specimens only. Finally, it seems astonishing in this connection that in several cases representatives of two and three species of the genus Scolpellum, sometimes moreover accompanied by a single specimen of a species of Verruca, were obtained with the same haul of the dredge, from the very same locality in consequence. Such stations seem to be very favourable for the occurrence of these animals: however, for these found there the same holds good, viz., that they were collected in very few specimens only *). For some deepsea-species of Scalpellum it was possible to make out, that they produced only a few but relatively large eggs, and that their metamorphosis was an abbreviated one. There is good reason to suppose that these peculiarities are of importance for the question of their scarcity — we cannot say, however, that the one is explained by the other. Nevertheless, so far as our knowledge 1) It is obvious to admit, that the condition of the bottom in such eases is all- important. Without denying it. we must point out, however, that to judge from the information regarding the condition of the bottom as given in the list of the stations, its importance for the distribution of the Cirripedia is by no means so apparent as might be expected. So we can well say that many species of Scalpel- lum were found at places where the bottom was muddy, but several other species were obtained from a bottom of hard sand, of coarse sand or of coral sand ete. ete. é, 8 Proceedings Royal Acad. Amsterdam Vol. XI. (114) now goes, we must consider the deepsea-species of Scalpellum and Verruca as hermits; as the number of species of these genera especially is very large, most probably they furnish precious evidence for the ideas, about the influence of isolation on the origin of new species, which were brought forward originally by Moritz WAGNER *) and were criticised and adopted in a much modified form only by WEISMANN *). For the geographical distribution of the Cirripeds the study of those collected by the “Siboga’’ has also been very instructive. With the exception of the pelagic forms, which are found attached to floating objects: pieces of wood, vessels, animals swimming at the surface : Cetaceans and others, ete. ete. and many of which are found in various parts of the world, these Crustaceans live attached to stones, shells of molluses, corals ete. ; the latter have good oppor- tunity for active locomotion only in larval condition. But even in that condition, in consequence of their nearly microscopic size, their activity is only very limited; Nauplius- and Zoéa-larvae have limbs which enable them to move about, but more important is no doubt the distribution they are subjected to in a passive way, i.e. by means of the currents. However, even the latter distribution as a rule seems to be a very limited one: we only know very few non- pelagie Cirripeds which have a world-wide range or which occur in several of the eight provinces which were proposed by the present author in his Report on the “Challenger” Cirripeds for the animals of this group. The East-Indian or Malay Archipelago combined with the Philippines, Malacca, New-Guinea and the East coast of (British) India is one of these provinces; the investigation of the “Siboga’- material has shown again that this province indeed possesses its own Cirripeds, with the exception only of those species, which so to say spread themselves over its boundaries into other provinces, per- haps also of a few species which are at home in an adjacent pro- vince and came over its frontiers into the Malay Archipelago. Of the deepsea-Cirripeds we only know one single species, which can be said to occur at widely distant places of the earth’s surface : Scalpellum acutum. The “Challenger” collected this species in the Atlantic Ocean (near the Azores) and in the Pacific (near the Kermadec- Islands) at a depth of 940-1800 m.; the “Talisman” also in the 1) Wacner, Morirz, Die Darwin’sche Theorie und das Migrationsgesetz der Organismen. Leipzig, 1868. 2) Weismann, Aueust, Ueber den Einfiuss der Isolirung auf die Artbildung. Leipzig, 1872, (115 ) Atlantic (not very far from the coast of Portugal) at a depth of 1925 m.; the ‘“Siboga’, finally, at three different places in the Malay Archipelago and at depths varying from 825 to 1265 m. But this does not change the rule, which still can be accepted as general, viz. that whereas several genera of Cirripedia, and those of the deepsea in the first place, are spread over the whole surface of the earth, the species of Cirripeds and especially the deepsea-species have been found to possess a very local distribution only. To close this article a few words on the relation of the deepsea- forins to the extinet Cirripeds of which fossil remains have been preserved. The material collected with the “Siboga” in this regard also fully confirmed the conclusions arrived at by the working up of the material from the ‘Challenger’. The species of the genus Scalpellum, which in the deepsea are so largely represented, have their representatives already in relatively old layers of the earth-crust, in secondary as well as in tertiary formations. We can even say, that a great majority of the species of the deepsea, with regard to an important anatomical characteristic (shape and structure of the so-called carina), show the greatest affinity to the oldest fossil forms (all those found in secondary formations); for this genus, therefore, we can safely admit that the deepsea-species, at least to a certain extent, show an archaic character. Side by side with the fossil Sca/pellum’s, in the same formations and even in the same rocks or stones, numerous species of the genus Pollicipes were found. To this genus of which Darwin alone enumerated 22 different fossil species belong the oldest known fossil Cirripeds and under the living it is still represented by half a dozen species. The “Challenger”, however, did not succeed in collecting one single species of this genus even from slightly deeper water, which, when the author worked up the material of the “Challenger”, gave rise to the remark, that the possibility of future investigations of the deepsea bringing to light species of the genus Pollieipes, could not be denied. Well then, the “Siboga” investigating the deepsea very carefully in one of the areas, where one of the living species of Pollicipes (P. mitella) is very generally distributed, did not obtain from deeper water one single specimen of a species of this genus either. So the exactness of the opinion pronounced in 1883, that, as far as the genus Pollicipes is concerned, the littoral or shallow water forms have preserved a more archaic character, has been completely confirmed by the results obtained with the “Siboga’’-expedition. Of the genus Verruca a few species have also been found in older formations: one of these (V. strémia) is still 8* ( 116 ) living and a well-known shallow water form and was also observed in glacial deposits and in Red and Coralline Crag in England as well; a second species is found according to Darwin in tertiary formations in Patagonia; a third (Verruca prisca) in the chalk of England and Belgium. As far as we know the last-named species, a certain affinity of this extinct species with several of the deepsea- species of Verruca cannot be denied. But for V. strémia, the genus Verruca, therefore, in this regard also would show a greater analogy with Scalpellum than with Pollicipes. Physics. -— “Calculation of the pressure of a miature of two gases by means of GiBBs’s statistical mechanics.” By Dr. L. S. ORNSTEIN. (Communicated by Prof. H. A. Lorentz). By the method of statistical mechanics I have calculated in my dissertation’) the pressure of a mixture of two gases, neglecting terms of an order higher than the first with respect to 6,*, 0,° and o*. The quantities 6, and 9, are the diameters of the mole- cules of the gases composing the mixture, and o has been put te zie In a recent paper’) H. Harper has determined the pressure of a mixture by means of a method due to L. BoLTzMaANN, retaining terms of higher order with respect to the above quantities. As the method of statistical mechanics seems to me more exact than the one used by Harper, I have been led to apply it to the problem which he has treated. J. W. Gisss has shown *) that the pressure of a gas is given by the equation for RM ke where V is the volume, and Y what may be called the statistical free energy. We have therefore to determine this quantity W. Let us suppose that the volume V contains n, molecules of the first kind with the diameter 5, and the mass m,, and x, molecules of the second kind with the diameter ¢, and the mass mm, 1) Toepassing der statistische mechanica van GiBBs op molekulair-theoretische vraagstukken. Leiden 1908. 2?) H. Harper. Zur Kinetik und Thermodynamik der Gemische. Ann. der Phys. 1908 Bd. 26 p. 95. 5) J. W. Gisps. Elementary principles in statistical Mechanics. New-York 1902. (117) We suppose that the molecules are perfectly rigid and elastic and that they attract each other with forces acting at distances so great that we may consider the sphere of action as uniformly filled with matter. . For this case the value of Wis given by the equation eae ae te dite fae —(2 0.0 m.)* (20m)? jk 0 de,,..deon,. -« (2) I shall represent the coordinates of the molecule .£ of the first kind by wir, Yik and zip, and those of the molecule / of the second kind by x21, Yot and Za). _ The integration has to be extended to a 3 (nm, + n,)-dimensional space, the notion of which is obtained if we take the 3 (nm, + 7,) coordinates of the centres of the molecules as cartesian coordinates of a single point, and give all possible positions to the molecules of the gas. We must exclude from the space all those points at which a con- dition of one of the forms (ere — eu)? + (ye — yi)? + ae — eu? < a (ik — #21)? + (Yin — you)? + (eik — 221)? ZO (ar — war)? + (yor — you)? + (ear — 221)? ZO, is fulfilled. ; I have proved *) in my dissertation that the large majority of the systems of a canonical ensemble may be considered as identical in all properties that are accessible to our means of observation. For all these equivalent or identical systems the value of the potential energy of the attractive forces is equal. The sphere of action being uniformly filled, this quantity (e,,) can be represented by (3) a,n,* + 2an,n, + an,’ SE Ril Sie a aN a a As to the potential energy of the repulsive forces, we need not speak of it when we take into account the conditions (3). We shall obtain a good approximation, if, in the equation (2), we write €, instead of €, (which differs from ¢,, only in a small part of the systems). By this, the exponential factor becomes a constant and we may put it before the sign of integration. | The quantity W is thus expressed by the equation le. p. 14 (118 ) ee 5 is Zoo e @=(2276m,)? ' (22 6™m,)? ve dildo fa ia . (5) and its determination is reduced to the calculation of the integral on the right-hand side. Let the function x (n, , 2,) represent this integral. In my dissertation I have determined this function to the degree of exactitude indicated above. Before proceeding to the determination of the terms of higher order I shall repeat the former calculation which now only wants further extension. The 3(n, + n,)-dimensional space of integration can be decomposed into n, + n, threedimensional spaces, each corresponding to one of the molecules. We shall divide these spaces into elements which are small in comparison with the volume of a molecule. In order to determine the integral defining the function x (, , ,) we decompose it into a sum of products of n, + 2, elements chosen in the spaces in question, each space being represented in the product by one and only one element. In order clearly to see the way in which the products are formed with the restrictions imposed by (3), we proceed as follows : We number the spaces corresponding to the molecules of the first kind from 1 to n,, those corresponding to the molecules of the second kind from n, +1 to n,-+n,, and we choose the elements in the order indicated by these numbers. We bave to consider that, if we have chosen for the centre of the kth molecule (k << m,) an element lying at a point zik, Yir, Zik, we must exclude from the & +1 up to the n,'" space those elements which are situated in spheres described with the radius 6, around the points of these spaces whose coordinates are equal to zin, Yi and zij. Similarly we must exclude those elements from the spaces from 2, +1 up to n,‚ +u,, which lie within the spheres of radius o described around the points of the spaces having for coordinates Di, Ye and zin. If, further, in the space n,+-v, an element has been chosen at a point with the coordinates #45» Yana Zam we must exclude in all following spaces the elements of spheres with radius «, described around the points of those spaces having their coordinates equal to zn, Yantyo> Zam toa: The elements in the spaces 1 to n, + n,— 1 having been chosen, there remains in the last space »,‚ + n, a region Gn, for the choice of the (n, + 7,)'* element. In determining the sum we can first take together all those cases in which the elements of the spaces 1 to n, +, —1 are the same. Considering that 2, and n, are very great numbers, and that the (119) elements have been chosen quite arbitrarily, we easily see that the quantity gn4tn, must be the same for the greater majority of the possible ways of choosing the elements in the spaces up to the (nm, +m, — 1)", and that we may therefore write Ay n= Grate heren er OD nn, being now a quite definite quantity, which it remains to determine. It is very easy to find a first approximation to its value. For this purpose we have only to neglect the fact that the above mentioned spheres in the (n, + 7,)"* space intersect. Doing so, we find 4 4 Inin, = V—n, as 0°— (n,—1) is: GP ress a) From (6) and (7) we deduce by successive reductions = 4 4 U mjs) Xn) | | G mg TO —(v,—1) 520). ap) . ‘ where we have affixed to the sign of the product the highest value that we have to give to the number denoted by the corresponding Greek letter. A similar notation will be used in later formulae. It is easily seen that, with the degree of exactitude to which we have now confined ourselves, the value of x (n,) is given by xm)= [](v—» 5 20) ere AK eee In order to push our approximation further, we have to deter- mine gJy,+n, more accurately. We must take into account that the spheres mentioned above intersect, and that we have therefore sub- tracted too much from the total volume. Now three cases are to be distinguished. 1. Intersection between the spheres of radius o described around the points corresponding to the centres of the molecules of the first kind. The distance z of the centres cannot be less than o, and must be less than 2 o. 2. Intersection between the spheres of radius o, described around the points corresponding to the molecules of the second kind. The distance of the centres must lie between 5, and 2 ,. 3. Intersection between the spheres of radius o and o, described around the points corresponding to the centres of molecules of the first and second kinds respectively. The distance 2 of the centres must lie between 6 and o, + o. I shall determine the parts corresponding to these three kinds of ( 120 ) intersections, which have been subtracted too much from V. These parts are equal for by far the majority of the possible combinations of elements in the spaces from the first up to the (n, + n, — 1). We may suppose that the distribution of the points corresponding to the centres of molecules from 1 tot n, + n, —1 is uniform in the (n‚ + n,)'" space. 1. The number of pairs of points (corresponding to molecules of the first kind) with mutual distance lying between z and «+ dz amounts to 27," dd (10) KN Tp EEN u The common part of two spheres of radius o having a central distance w is given by 4 a a(5e—oet etal Ee sib key bee kee Hence, the total part subtracted too much on account of these intersections is equal to 25 22°n,? 8 1 5. = AG ox? 0 +— B= ae peer dhs Bon mn (12) o 2. The number of pairs of points (corresponding to the centres of molecules of the second kind) with a mutual distance between zand «+ dz is ede earl) 27 (z, OH 1) (n, TE 2) The common part of the spheres is found for this case, if in (11) we replace o by o,, so that we find for the part subtracted too much from V 2c ECN RE ae i ont! 5 JIS 6,°4?-6,20* + — ) dz @, — El a) (14) 716 3. The number of pairs of points such that one point corresponds to the centre of a molecule of the first kind and one to that of a molecule of the second kind, the mutual distance lying between x and «+ dr, amounts to vida 5 (15) Ann, (n, — 1) ( 121 ) The common part of the spheres is now given by 2 Bo sene Le 6,2) | 0, oe — , a | Bi 3 2a 2a T (e+ oF En oy (a? A ie 6,7) 24 2° 24 x? Di and the total part subtracted too much from V by 4 umd [2 3 3) m2 1 2 2 3 nO [| ertoe — eta — 1 2 3\ 3 | Pd 2% (n, —1) I 6 4 nt ree tO 0) et] Eem à nn + 6, o*) (17) The value of g,41, is found by adding (12), (14) and (47) to (7) and substituting the obtained value in (8). By successive reductions we get + (16) tind = need] Ir ae zo — (v, ~1)5 zo ai 1g? It is easily seen that to the degree of approximation now required, x(n,’ is represented by a 17 — 1) (rv, — x=] (Ve gro’ + 3 8 2 2)! 0) (19) Substituting these values in (5), taking the logarithm of the result, de De eaf 1 a SSS oO le 6 J- le * ) (18) , 1 and developing this logarithm in ascending powers of One find en a,n,?-- 2an,n,+a,n,’ TR on eee v,—l14 v,—1) (v,--2) 15 wr 7 fae = gore | + = n, 4 (v,—1)4 (vy, — 1) (v,— 2) 15 . eagle yg oe ee ps | KE. De 36” % ZENE ann ee ar Br Ee eg pt Os 16.2, (el) mel) 1m, (4-1) edn a ig xy na, al (1223 C being the part which is independent of V. Since m, and n, are very large numbers, we easily see that the expression (20) can be transformed to y a,n,?+ 2an,n,+a,n,’ B 5 B en Sn nn a > 1 (thn) lag V — ee a Mee ies VY 16 ye — 2n, n, Sn, ?n FN ae Ln sn 2 5 ws hpi ace tn 2 6 RAN Te nn 8 n, n,” 2g 443 a In, n,' 2 50° 1 bbe) ny” 2 6 (21) ge 6 ee es EE foes BiG? sl ops cae ee: BG Wa se 2 2 2 where 8, has been put for a m0 8. for 5 x 6,’ and B for — me Finally, differentiating ¥Y with respect to V, we find the following equation for the pressure P La n +n, kk nb, i 5 uele i n, Bs 3 5 n° By 2n,n, 8 6 V V3 ye V3 8 Vv? Vy? Rt B 9 8-0 1 B, 4 B, 0, "i g(—4g 4225) woe KE 2 2 an’? +2an,n, + an, rat ob oe The quantity @ is proportional to the absolute temperature. The expression for p is of course symmetrical in the quantities relating to the two kinds of molecules, and it would have been possible to find the same result by arranging the spaces in a different order. Our result agrees with that of Harper, the only difference being in the notations. (123) Botany. — “Lindeniopsis. A new subgenus of the Rubiaceae’. By Dr. Tu. Vareron (Buitenzorg). During an official journey through the island of Billiton in March 1907 Mr. Ham, Inspector of Forests in the Dutch East Indies, gathered a small, but not unimportant herbarium collection, which he gave over to me for study. The importance of this collection mainly depends on the fact, that it was formed on lands, which are extremely rare in the Indian Archipelago, and are as yet florally almost unknown. These are the socalled ‘‘padang’” lands (compare VerBeeK in Jaarboek Mijnwezen 1897, p. 60 and 61). The soil of these lands consists of young, loose sediments of recent origin, namely quartz sand and clay, both often containing iron and manganese; the soil, however, owes its peculiar character to the presence of a mineral, which the Chinese call fo sau kak and which consists of quartz sand, which has been moulded together by organic acids into a pretty firm, dark brown sand-stone. “These padang lands are characterized by a sparse and peculiar vegetation, in consequence of the small permeability to water of the “fo sau kak’, so that level padang-lands are frequently inundated after heavy rains, and the roots of the plants, which can only pene- trate with difficulty into the hard “fo sau kak’, rot and die off.” (VERBEEK l.c). Besides in Billiton, these padang soils are also found in Banka between Doeren and Boekit (VerBeeK le). In other parts of the Archipelago they do not appear to be known. The most important of these lands are found in the north and north-east of the island, between Boeding and Manggar, and were studied botanically by ‚Mr. Ham. From verbal information and from the journal of the voyage, which Mr. Ham kindly lent me for perusal, I obtained the following data : The appearance of the padang soils is not everywhere the same. Mr. Ham distinguishes: 1 grass padang, often rich in flint, where grasses and sedge-grasses predominate, 2 fern padang where ferns (Pteris aquilina L., Nephrolepis acuta Prrsr.), form almost the whole vegetation, being only mixed with Ayris microcephala Hassx., Fim- bristylis spec., Melastoma spee, Calophyllum pulcherrimum War, Psychotria viridiflora Bu. and 3 sand padang, where the soil con- sists of blinding white quartz sand. The white layer varies in thick- ness from '/,—5 centimetres; under this the soil is grey, obviously through humus, and sometimes it is grey immediately below the ( 190) surface, when fine, black humus or mosses occur at the bottom. The vegetation nowhere forms a compact mass or sod. Groups of low and high shrubs, generally with higher shrubs or small trees in the middle, alternate with a lower vegetation, which is also always limited to separate spots or clumps, so that the white sand can everywhere be seen through it, and in many places even has the upper hand. Of the plants which were collected here, the following are mentioned as characteristic : Drosera Burmanni Vanr. in the dampest parts, forming dark-red areas, when seen from a distance, often placed on small columns of sand; Fimbristylis spec, Rhynchospora spec., Xyris microcephala Hassk. and Xyris bancana Mig; more rarely Salomonia oblongifolia D.C., Lindernia stemodioides Miq., Thuarea sarmentosa Pers. Of the shrubs the following are prominent: Baeckea frutescens L., which in low-lying padangs forms more than half of the vegetation, and reminds one very much of the Calluna of European heaths, Jambosa buzifolia Mig., Leptospermum flavescens Sm., Leucopogon malayanus Jack., Vaccinium malaccense Wicut, Cratoxylon glaucum Kortu., Calophyllum pulcherrimum Warm, Timonius spec., Garcinia bancana Mig., Syzygium varifolium Mig., the last three arborescent. On the lowest lying padangs south of Manggar and near Boeding, where Baeckea frutescens and Limbristyis spec. formed the chief vegetation, Zschaemum spec, Archytaea Vahl Cnorsy, Wormia suffruticosa Grier., Melaleuca minor SM. and a non-determinable species of Eugenia were also noticed; in addition mosses and lichens. Further there were collected in these localities Ahodomyrtus tomentosa Wieut, Nepenthes spec, Tristamia obovata R. Br., Dischidia spec. Bromheadia palustris Linpu. [Orchideal, /sachne australis R. Br. Burmannia bancana Mig., a species of Lucinaea, which is probably new, and finally a new Rubiacea, about which I wish to make a communication here. The above-described formation has in consequence of the predo- minant occurrence of the Calluna-like Baeckea frutescens a super- ficial resemblance to the sandy and boggy heaths of Northern Europe. Already JuncHuHN, in his description of the Battak countries I, p. 158, refers to an Erica, which above the forest zone characterizes the alpine flora in company of other woody Myrtaceae, and he doubtless means Baeckea frutescens. From Southern China and the Philippines to New-Guinea, where Berccart found the plant at Goldfinck Bay (altitude?) and Wicumann on the G. Siép at about 800 Meters, the area of distribution of this species extends; it is wanting in Java and its nearest allies (numerous Baeckea-species) inhabit Australia. ( 125 ) Everywhere it is characteristic of physiologically dry plateaus and rarely descends to the low-lying plains, as in the present case. Drosera and the Cyperaceae also tend to emphasize the resemblance to heaths. | Through the other vegetation, of which the sclerophyllous and sclerocarpous Myrtaceae form an important constituent, this formation, however, approximates much more to that which was called by ScuimPer (Pflanzengeogr. p. 538) “Hartlaub formation” and of which he describes a number of regions, occurring round the Mediterranean, in California, in Chili, in South-Africa and in South-Australia. These regions are all characterized by dry and hot summers, alternating with moist winters. Hence climatologically there is little resemblance between these and the padang-formation of Banka and Biliton, where it rains almost the whole year. As regards the condition of the soil, there is, on the other hand, a resemblance with the South-Australian “scrublands’”’, described by ScHomBurekK in his Flora of South-Austratia 1875. (See Scuimprr |. ec. p. 559). The dominant influence of the soil on the character of the forma- tion cannot here be doubted; this influence, which according to ScuiMPER is relatively rare in the Tropics, has been but little in- vestigated. (See Scuimprr |.c. p. 405. Edaphische Wirkungen in den Tropen). The padang-formation does not correspond even roughly with any of the vegetation-pictures and formations, mentioned in that chapter. As has been mentioned, it can only, to some extent, be compared with tropical alpine floras and with the “Hartlaub formation”. The plants, collected by Mr. Ham, probably do not represent a complete, but nevertheless give a very typical picture of this rather poor flora. As regards the distribution of these plants, it is at once noticeable, that not a single one of these occurs in Java, with the exception of two wide-spread grasses, which have crept in from the beach, namely Thuwarea sarmentosa and Lsachne australis, and with the exception of the two pantropic ferns and of Psychotria viridi- flora, which plants were, moreover, not found in the typical sand padang. A wide distribution from Malacca to Australia through the northern part of the Archipelago, but excluding Java (probably up to and including Timor), is observed in the case of baeckea frutescens, and also of Leptospermum flavescens, Rhodomyrtus tomentosa, Melaleuca minor, Drosera Burmanni, Salomonia oblongifolia and Bromheadia palustris. From Malacca and Borneo are known: Calophyllum pulcherrimum, Garcinia bancana, Vaccinium malaccense, Leucopogon malayanus, Archytaea Vahlii, Wormia suffruticosa. From Banka ( 126 ) and Billiton only the following are known: Jambosa buaifolia, Syzygium varifolium, Tristania obovata, Schima bancana, Xyris bancana and Lindernia (Vandellia) stemodioides; Cratoxylum glaucum and a Lucinaea spec. nova were only known from Borneo. The as yet undetermined Lugenia, Nepenthes, Dischidia and Ischaemum, and a few others, are doubtful in this respect. Endemic, as far as our present knowledge extends, is only the new species, now to be described. Unfortunately data are wanting about the dimensions and habit of this plant, but it belongs to the suffructicose inhabitants of the low sand-padangs, referred to above; it is among the species, poor in individuals, and it reaches a height of */,—2 metres. The rod-like erect branches which are often 60 centimetres long, and bear at their tops the crowded inflorescences with grey hairs, the small stiff, aciculate, erect leaves, all these characters indicate a strongly xerophytic nature. At the first examination this species seemed to me to constitute a completely new genus. It belongs to the tribe Cinchoneae of the sub-order Cinchonoideae (K. ScHuMANN), and to the sub-tribe Hillieae. On applying the analytical key, prepared by K. Scuumann (Natiirl. Pflanz. Fam. IV 4 p. 42) one does not arrive at any genus in parti- cular, but in the immediate neighbourhood either of Cosmibuena Ruiz and Pavon, or of Coptosapelta Korru., according as to whether one takes the style to be little or very much longer than the corolla- tube. A closer comparison with the genus Cosmibuena, to which a small number of Central- and South-American, epiphytic shrubs belong, at once, however, reveals considerable differences in the structure of the calyx, stamens, stigma and in the dehiscence of the fruit, so that there can be no question of a union with this genus, although in habit and in the shape of the flowers the agreement is closer than with Coptosapelta. As regards the latter genus, it is said in the above-mentioned key: “style quadrangular and hairy”, so that, if one were to adhere strictly to this, one would be forced to set up a new genus for our species, in which the style is cylin- drical and glabrous. On further comparison with the characters given in the generic diagnosis for Coptosapelta, the following differences are also found: Calyx, small, saucer-shaped, five-toothed in Copto- sapelta ; in the new species much longer than the calyx-tube, divided to its base into five lanceolate, pointed, erect divisions. — Corolla- tube very short, as long as or shorter than the Jobes of the limb, and hairy at the tube-mouth, in Coptosapelta; in the new species 4—6 centimetres long, thin and straight, much longer than the lobes of the limb, and glabrous at its mouth. — Anthers almost as long as the lobes of the limb and hirsute on their dorsal side, with deeply cleft base, in Coptosapelta; here much longer than the lobes of the limb, glabrous, and with a two-lobed base. Seeds with a regularly fringed wing in Coptosapelta; here surrounded by an entire wing. Finally as regards the habit, the two known species of Coptosapelta are high-climbing shrubs with fairly large leaves and many-flowered pendulous panicles of small flowers, whereas the new species is a small erect shrub with erect cymes of few, prominent flowers. . Superficially there seems therefore abundant reason for setting up a new genus for this new species, and on account of the great resemblance in habit, leaves, inflorescence, calyx and corolla, to the American genus Lindenia, which belongs to the tribe of the Ronde- letieae, | gave it the name Lindeniopsis. A closer comparison with Coptosapelta flavescens Kortn, which occurs in Java, induced me, however, to withdraw this genus and to bring the new species under Coptosapelta. Some of the points of difference, deduced from the literature, proved to be the result of errors in the existing descriptions. For instance, the style in C. flavescens is not quadrangular and hairy as described by Scaumann, but, except at the top, cylindrical and glabrous, as in the new species; the calyx is not saucer-shaped, but deeply divided into five divisions, and resembles, except in size, that of the new species, and the mouth of the tube is not hairy, but quite glabrous. In this way a number of the enumerated points of difference already disappear. There is further perfect similarity in the structure of the ovary and fruit of the two plants. The very peculiar stigma, which in contradistinction to the neighbouring genera, is not two-lobed, but quite entire, and receives pollen on the stigmatic papillae which cover the whole of its hairy surface. The anthers are identical in structure and in their mode of attachment. Finally, what is very important, the pollen of the new species has, like that of C. flavescens, an exine with net-shaped thickenings of wide mesh, and, as would appear from the figures in the Flora brasiliensis, the plant herein differs completely from the other genera of the Millivae. Having regard to all these similarities, there can be no doubt, that our new species must be included in the genus Coptosapelta, but forms in it a special, monotypic sub-genus. As a morphological peculiarity, which confirms the relationship to C. flavescens, | here draw attention to the glands, which alternate with the calyx divisions, and have, as far as I know, not yet been ( 128 ) described in any other of the Rubiaceae (with the possible exception of Dichilanthe Hook.). They have the same structure as the colleters, resembling intestinal glands, which in this genus, as in most Rubiaceae, are placed at the inside of the base of the stipules’) and are also found on the leaf base in Apocynaceae and in Loganiaceae. They are found in the new species, as in C. flavescens, alternating with the calyx divisions singly or two together; in the latter species they are however, only '/, mm. long and have hitherto been overlooked by investigators ; in the new species they are well over 1 to 1.5 m.m. in length. Perhaps, on closer examination, they will also be found to exist in other Rubiaceae. Obviously they must be interpreted as rudimentary stipules of the sepals. Coptosapelta Kortn. Descriptio nova: Calycis tubus ellipsoideus, limbus eo nunc brevior nune duplo longior, persistens, dentatus vel ad basin usque 5-partitus, segmentis erectis imbricatis cum glandulis parvis stipularibus erectis teretibus singulis vel binis alternantibus. Corolla coriacea tomentosa, hypocraterimorpha, tubo brevi vel longo, gracili, tereti, intus glabro vel fauce hirta, limbi Jobi obovato-lineares aestivatione contorti. Stamina 5 ori corollae inserta, filamentis brevibus subulatis; antherae oblongae vel lineares apice apiculatae, basi sub- bilobae vel bipartitae glabrae vel dorso hirsutissimae, dorso prope basin affixae, patentes demum saepe tortae. Pollinis granula subglo- bosa, poris 3°, insigniter reticulata. Discus carnosus cupularis. Ova- rium biloeulare. Stylus teres glaber elongatus corollae tubum aequans apice exsertus. Stigma magnum integrum, fusiforme velclavatum, in alabastro per longitudinem striatum, puberulum; ovula in loeulis numerosa, placentis magnis septo affixis peltatis linearibus apice et basi liberis dense imbricatim affixa, peltata, marginata, ascendentia. Capsula obovoidea lateraliter compressa obsolete costata calyce longius persistente coronata, glabrescens ad medium versus loculicide bivalvis, vel demum saepe quadrivalvis. Semina placentae cylindricae, sub- carnosae, loculum implenti extus affixa, peltata, imbricata, erecta, testa membranacea in alam hyalinam nunc insigniter fimbriatam nune subintegram crenulatam radiatim striulatam expansa, albumine carnoso; embryo rectus parvus radicula tereti infera. Frutices nunc alte scandentes nunc parvi erecti, canescenti -sericeo- villosi, ramulis tetragonis foliis coriaceis, subtus + villosulis. Stipulae interpetiolares parvae ovato-trigonae. 1) Vide Sorereper, Anat. Charakt. der Rubiaceae 18938, p, 179. ( 129 ) Cymae terminales et in axillis superioribus trichotomae nunc den- siflorae et ample paniculatae pendentes, nune pauciflorae erectae. Flores brevissime pediceliati, bracteolis (prophyllis) 2, pedicello in- sertis calyce appressis eoque brevioribus instructi, nunc parvi nunc conspicui. Subgenus I Hucoptosapelta Var. Calycis limbus ovario brevior. Corollae tubus brevis, limbi lobos aequans vel illo brevior, faucis orificium glabrum vel hirsutum. Antherae lineares, basi bifidae, dorso dense villosae, demum tortae. Stigma elongato-fusiforme vel quadran- gulare. Seminum ala fimbriata. Frutices alte scandentes ramulis subteretibus. Foliis majusculis patentibus subtus ad nervos villosis. Paniculae terminales foliatae multiflorae, densiflorae, pendentes. 1. C. flavescens Kortu., (Stylocoryne racemosa haud CAVANILLrs, Mig.; St. tomentosa Bu): Corollae tubus limbi lobos circiter aequans, faux glabra. Calycis tubus brevis. Habitat: Malaccä, Burma, Borneo, Java. 2. C. Griffithit Hoox.: Corollae tubus limbi lobis multo brevior. Faux dense hirsuta. Calycis tubus elongatus. Habitat: Malacca, Singapore. Subgenus IL. Lindeniopsis Var. Calycis limbus ovario plus duplo longior, ad basin usque partitus segmentis erectis lanceolatis acutis. Corollae tubus gracilis lobos pluries superans, faucis orificio glabro. Antherae oblongae basi bilobae, glabrae. Stigma magnum, clavatum. Seminum ala subintegra. Frutices parvi erecti, ramulis acute tetragonis erectis elongatis, foliis parvis erectis rigide-coriaceis, spinuloso-apiculatis subtus appresse villosis. Cymae terminales et in axillis superioribus trichotomae, pauciflorae, erectae. 3. C. Hammii Var. Characteres subgeneris. Habitat: Biliton. Botany. — “Contribution N°. 1 to the knowledge of the Flora of Java.” (Third Continuation)'). By Dr. S. H. Koorprrs. § 6. Further data concerning Oreiostachys Pullei Gamble. §§ 1. Additionsandcorrectionsto p. 674—686 ofthe “Proceedings”. The proof-corrections, which Mr. GAMBLE sent me from England last April, were, nevertheless, much to my regret, received by the printers too late for incorporation in the number of the Proceedings 1) Continued from p. 773 of the Proceedings of the Royal Academy of Sciences, Amsterdam, ordinary meeting of the Math. and phys. section April 9:2 1908. 9 Proceedings Royal Acad. Amsterdam. Vol. X. ( 130 ) of the Royal Academy of Sciences, which appeared in April 24™ 1908. I now append these proof-corrections, which date from last April and are due to Mr. J. S. GamBLe, to whom I tender my thanks: p. 683 line 11 from bottom: after Kurz, insert: Munro in Trans. Linn. Soc. London. XXVI. 146. p. 683 line 4 from bottom : before (GAMBLE msc.) insert: and possibly. so establishing a connection between it and the Schizostachyum, the description of which by Hasskart and Kurz are somewhat imperfect”. p. 683 line 4 from bottom: after additional msert: material. p. 684 line 16 from bottom : before conspecific insert: very probably. $$ 2. On the fruits of Oreiostachys GAMBLE, which have been discovered by Mr. K. A. R. BosscHa. On p. 684 of the English edition of the Proceedings of the Royal Academy of Sciences, Amsterdam, meeting of February 28th 1908, it was pointed out by me, that it might be possible to trace this species locally by means of the constant native name, 1. a. in order to obtain the fruits, as yet unknown. I am now privileged to announce the collection of these fruits, as yet unrecorded in the literature, and to communicate certain further details, taken from a letter of Dr. Ta. VALrTON, dated Buitenzorg May 12% 1908 and from the enclosures to his letter, for which [ here wish to thank him. “Enclosed I am sending you three fruits of Oreiostachys GAMBLE, of which ten were sent me in November 1903 by Mr. K. A. R. Bosscua, after I bad received in May flowers from the same station. I propose that you should send these to Mr. GAMBLE, in order that he may complete his generic description, which has been published by you. I am also sending you some notes about observations, made in the locality by Mr. Bosscua, and further some references to the literature, which already exists about this species.” (Dr. VALBTON mse. May 12t 1908). I quote below the paragraphs in the letter referring to the obser- vations of Mr. Bosscna. “Mr, Bosscua drew my attention to the fact, that the plant bears flowers in two ways, namely at the end of small branches’) with 1) Mr. Gampre and I have not, as yet, had at our disposal these thick-leaved branches, flowering at their ends, but only the sterile leafy branches of Junanuyy and the almost leafless flowering twigs, without fruits, of Pure described by Mr GAMBLE. > ( 121 ) thick foliage and also close to the stem on quite leafless lateral branches.” “Mr. Bosscna also told me, that when he arrived in Malabar in 1896, old natives, who were thoroughly familiar with the forests of the district in which the plant occurs, were ignorant of the fact, that this bamboo had ever flowered. In 1902 the flowering began, and it recurred fairly regularly until 1906. Since then the species has died off in most places, and is now decidedly scarce. This year it has again, however, been found in flower in Taloen (a plantation on the Malabar) in May 1908.” “Now, however, young plants are beginning to appear every where, obviously self-sown.”’ “This phenomenon partly agrees therefore with what has been observed in the case of other bamboo-species in British India, although the flowering period has been especially long in this case’. (Dr. VALETON msc. May 12 1908). While I here refer with special appreciation to the fact that Dr. Tr. Vateton placed the three fruits and the above-mentioned data at my disposal, I need scarcely say, that I at once complied with his request, and sent the fruifs, received by me on June17" to Mr. GAMBLE. Although the examination of the fruits is not yet complete, and will be referred to later, as soon as the supplementary diagnosis by Mr. GAMBLE shall have been received, I nevertheless consider the discovery, by Mr. K. A. R. Bosscua, of the fruits of this bamboo- species of sufficient importance to call for attention here. It is evident from Dr. VareroN’s letter quoted above that the receipt by him at Buitenzorg from Mr. Bosscua of the fruits of Oreiostachys Gamsre with the flowers (the fruits having remained unknown in the literature until now) was prior to Mr. GamBre’s discovery of the type of a new genus in the flowers collected by Dr. Puur. It may further be mentioned, that the fruits discovered by Mr. Bosscua, and the flowers collected by Dr. PunLe on the Wajang- Windoe in 1906, are from the same district, namely the locality mentioned on p. 686 of these Proceedings. In an enclosure to his letter to me of May 12t» Dr. VaLrron gives certain specific names, which he regards as synonyms (Bambusa elegantissima Hassk., etc.) and also the other literature references relating to this subject. Since these names, and the literature references, with the exception of “Munro” (see above, §§1), have already been published by Mr. Gamsre and myself in the Proceedings of April 24th, it seems to me unnecessary to repeat them. Although I have not had at my disposal the terminally flowering gx (132) branches with thick foliage collected by Mr. K. A. R. BosscHa, on which Dr. Va.rton’s addition to GamBin’s diagnosis is based, I can now conform this amplification of Gamprix’s diagnosis, sent me on May 12% by Dr. Vaeron, thanks to supplementary material received to-day (June 27 1908) from Dr. A. Putte (Utrecht) and at once forwarded to Mr. Gamsie. In order to complete the diagnosis of Oreiostachys, and to settle the question of the further probable synonymy of this interesting species, a question raised by Mr. GAMBLE and myself in the Proceedings of April 24" there now only remain as desiderata the collection of stem-sheaths and the examination of the authentic specimens of Bambusa elegantissima Hassx. and Schizostachyum elegantissimum (Hassk.) Kurz, which so far have not been found, either by Dr. Va.eron at Buitenzorg, or by myself at Leiden or Utrecht. Leiden, June 27% 1908. Physics. — “On the law of molecular attraction for electrical double points”. By Prof. J. D. van per Waars Jr. (Commu- nicated by Prof. Dr. J. D. vaN DER Waars). Several physicists have already urged the supposition that the molecular attraction results from the electrie forces exercised by electrically charged particles which are contained in the molecule. One of the simplest suppositions we can make in trying to explain the molecular action from an electrical origin is that the ‘molecules will behave as electrical double points. This has, in fact, been assumed by Mr. REINGANUM') and by Mr. SuTHERLAND’). As the formula for the action between two electrical double points, which is the same as that for the action between two magnetic 1 ; : molecules *), contains — as a factor, — r representing the distance i between the two double points, — these physicists concluded that the molecules would attract one another with a force proportional 1 Pe A to —. The opinion that the electron-theory supports the supposition Up 1 of a molecular attraction proportional to — has accordingly been often li advanced. 1) M. Remeanum, Phys. Zeitschr. 2, 241 (1901); Drupes Ann. 10, 334 (1903). 2) W. SurHertanp, Phil. mag. (6) 4, 625 (1902). 3) Cf. J. C. Maxweu, A treatise on electr. and magn. Art. 387. (43de + On closer inspection, however, this opinion proves to be unfounded. If the double points have not yet yielded to the directing couples which they exercise on one another, and if therefore the axes may be directed in any direction, the mutual action will as often be a repulsion as an attraction, i. e. the mean attraction will be zero. If on the other hand we might assume that they had perfectly yielded to the directing couples, they would attract each other with forces i proportional to —. It is, however, evident that the molecules will i only partially have yielded to the couples, and that they will be more perfectly directed according as they have approached each other more closely and therefore lie in a stronger field of forces. The consequence will be that the resulting molecular action will be an attraction which with increasing r varies more rapidly than 1 ee —. This circumstance has not escaped the attention of ReINGANUM a and of . SUTBERLAND. They, however, thought that the law of 1 attraction would only slightly deviate from — and assumed this law f. to be, at least approximately, accurate. In 1900 the present writer expressed the supposition that the 1 resulting attracting forces would vary more rapidly than nh It is true that he founded his calculation on a somewhat different sup- position as to the nature of the molecules, namely that they would act not as constant but as periodical double points, but this difference is probably not essential, as the law of attraction for vibrating double points will not improbably agree in a high degree with the law for constant double points, at least when the mutual distance of the molecules is small compared with the wave-length, which con- dition is satisfied in the case of gas-molecules at pressures of the order of one atmosphere. At present it is my intention to investigate more accurately what will be the law of the resulting attraction for constant double points. We shall see that the attraction in this case really varies more 1 rapidly than proportional to—. To render a rigorous treatment of yr! this problem possible, we shall assume the following condition to be satisfied : 1) J. D. van per Waats Jr., Dissertation, Amsterdam, p. 85. ( 134 ) ist. The molecules are electrical double points with a constant moment m. 2"d, The mean distance of the molecule is so great that we may neglect the cases in which more than two molecules interact. 3d, The velocities and the accelerations of the molecules have a value relatively so small, that we may assume that their field of force does not differ appreciably from the electrostatic field of the double points. A consequence of this supposition is that the energy of the system may be represented by : Li, YmEcspt C where L represents the kinetic energy of the system, € the electric force, g the angle between the axis of a molecule and the electric force at that place, and Ca constant which does not depend on the velocity and the mutual position of the molecules. | If this last condition is satisfied the statistical mechanical conside- rations of BOLTZMANN and of Gips are directly applicable to our problem. If on the other hand it is not satisfied these considerations cease to be applicable and then it is impossible to solve the problem before a statistical treatment of a continuum as the electromagnetic field has been worked out, which is analogous to GuBBs’s treatment of systems with a finite number of degrees of freedom ; this however is not the case as yet. A rigorous discussion of the case that the molecules are vibrators is therefore as yet impossible and so we shall have to confine ourselves to the supposition of constant double points. Let us imagine a molecule A and at a distance r another mole- cule 5. The angle between the axis of A and the radius vector will be called &, then the electric force exerted by A at the point where the molecule 6 is found, will be: (pe VE VY 3 cos? 9 + 1. or sr? If again p is the angle between © and the axis of B then the potential energy of B is: m? ea gas od -+ 1,cos p According to the well-known theory of BOLTZMANN and Gras the probability that the angle p will fall between the limits p and pd dp and the angle & between the limits # and 9 + d®& is: m2 V8 cos? SH 1. cos ¢ 3röt /, sngpdp.snddd.e ( 135 ) where ¢ represents twice the mean kinetic energy for one degree of 2 freedom or a of the mean kinetic energy of the motion of the centre of gravity of a molecule. So we find for the mean value of the potential energy of a molecule at a distance r from another molecule: nWV3 cos? S n2V'3 costs + I. cos 9 ; 1 M= ffe ‚W3 cos* 9 1 cosp.e ee DEN or *) mW/8 cos? S +1.cos¢ E t bor x 3 rit = ae sin dd | cos p.de 0 0 2 m = Let us put menen and W3 cos? 9 + 1 ==, then we find by par- a tial integration : t 7” 1 E= — a sin & dd jer Jet — — (eT— ECE) 4 CT 0 If we take into account that : wa UG clea LF (9) +f (x—9)} da, then we see instead of cts the above integral between the md x limits O and + we may take twice this integral between 0 and DN Now we may introduce 2 as new variable, writing : F eee 1 xda cos 9 = v3 V«?—1, and therefore — sin ddd = V3V al making use of the following series : cia? 2c*x* 3c'x® | 1 eer x = = (ez ss e—cr) —4 Cx BR uee ev A we find : 2t Eila Cea? des Sere’ NEN ME EN ENT 7 ed 1 t + dy Ory Bory? Sot Fi ee he eg ETE, ed 1 1) | am indebted for the reduction of this integral to Prof. Dr. W. KapreyN from Utrecht, to whom I gladly express my thanks for his kind assistance, If again we substitute Wy—1 —z then the different terms assume the following form: 4 ykd V3 nt (1+ zede = 1 0 a 3 k(k—1) 3° k(k—1) (k—2) 3? | So we find for W a series É the ee form : ie’ V3 aoe rare at Pit i + I the coefficients p having a B values : p == 3.2 27.6 E=-—- 47,29 B . 602 5.7.9 70 0 Jee Pe eee . V3 ooo In order to Ee whether this series converges or not, we ze ea PE props en notice that in the factor Wy—1 is always positive between l e the limits 1 es 4. So the oe of the integral lies between the values : nj vy =j andy’ Sv == where 7/ represents the mini- mum aid and 7" the maximum value of y between the given limits. Here we have y —=1 and y'=4. The value of the term of order / of the series for / lies therefore between the terms of order & of the two series : Cage Gs ae it = oF start | and 3 (2c)? 2.(2c)' 8. (2c)! Bra — 2 | + af st ee and as the ratio between two consecutive terms of these series verges for terms of high degree to zero. the series for # will also converge. ( 187 ) Having determined the value of Z, we find the law of attraction by changing the sign and differentiating with respect tor. Of course we must first replace c by = The value which we find for the or force is negative; this indicates that the force represents an attraction, as we knew beforehand that we should find. The lowest degree of 1/r which occurs in the series is the seventh degree, therefore the ; 1 force will vary more rapidly than proportional to ES In connection with this result I wish to make the following remarks. 1** The law for the attraction which we should find on the sup- position of vibrating double points whose distance is small compared with the wave length, will probably not differ very much from the law established here, though this question cannot as yet be answered with certainty. 2nd If we assume that m, without being periodical can yet increase or decrease under the influence of &, then we find a still more rapid variation with 7. Also if we assume that the molecules are nat simple double points but more complex configurations, quadruple or octuple points for instance, we find a more rapid variation with 7. The double points assumed here seem to yield the slowest variation with 7 that we can find when we interpret the molecular forces by means of equal positive and negative electrical charges in the molecules. Much sooner, therefore, than to assert that the electron-theory supports the supposition of a ; 1 molecular attraction proportional to — we are justified in declaring a that this supposition is excluded by the electron-theory. 3d, If we assume m to be independent of the temperature 7, then the attraction which we find, does, indeed, depend upon the temperature and that in such a way that at increasing temperature 1 it decreases more rapidly than a We have, however, no reason for supposing m to be independent of 7’; moreover it makes here an enormous difference whether we are dealing with constant or with vibrating double points. It is therefore impossible to say whether the electric explanation of the molecular forces justifies us in assuming the attraction to increase or to decrease with 7. 4%. We may wish to determine the shape of the equation of state which follows from the here assumed suppositions as to the action of the molecular forces. If we then follow the virial-method (138) the virial of the resulting mean molecular attraction need only be taken into account. It is true that the molecules exercise on each other still other forces besides this mean attraction, but these forces yield a virial zero. The forces normal to the radius vector, namely form together a couple, and the virial of a couple is zero. For the same reason the directing couples working on the molecules need not be taken into account. And from the forces working in the direction of the radius vector we need only take into account the average value, for attracting and repulsing forces which equally often occur between different pairs of molecules, cancel each other. In calculating the virial, the influence of the molecular attraction on the distribution in space of the molecules must of course still be taken into account. Chemistry. — “Lquilibria in quaternary systems.” By Prof. Dr. F. A. H. SCHREINEMAKERS. In the system: Copper sulphate, ammonium sulphate, lithium sul- phate and water two more solid compounds oceur at 30° in addition to the three sulphates namely, Cu SO, (NH,), SO,, 6 H,O and Li, SO, (NH,), SO, We will again represent the equilibria in the wellknown manner with the aid of a tetrahedron but now choose quite a different pro- jection than that used in the previous communication; we will in fact project all saturation lines and surfaces perpendicularly on one of the side planes of the tetrahedron. A projection of this kind is represented in the figure; the points ( 139 ) Cu, Li, NH, and W indicate the four components Cu SO,, Li, SO,, (NH,),5O, and water; the triangle Cu Li NH, is the side plane on which all is projected. The dotted lines Cu W, LiW and NH, W are the projections of the rising sides of the tetrahedron and it is obvious that the point W must lie in the centre of the triangle. The question is now what connection exists between the position of a point in the tetrahedron and its projection on the triangle Cu Li NH,. Let us take a phase with the composition: Cu proportions of Cu SO,, Li proportions of Li,SO,, N proportions of (NH,), SO, and W proportions of water. The projection of this point on the triangle CuLiNH, may then be taken as indicating a phase which only contains the three components Cu SO,, Li, SO, and (NH,), SO, Let us call these proportions Cu’, Li’ and N’. It is now easily demonstrated that Gu = Cn + Li=Li+— W=oN+— so that if the composition of a phase is known its projection may be readily represented in a drawing. The double salt Li, SO, (NH), SO, is represented in the figure by Dri; it is obvious that it must be situated on the line Li NH, as it consists merely of the components Li, SO, and (NH,), SO. The double salt CuSO,. (NH), SO,.6 H, O which contains three compo- nents must lie on the side plane W Cu NH, and is represented by Dou. Both copper and lithium sulphate occur as hydrates, namely Cu SO,. 5H, O and Li, SO,.H, O; they are represented in the figure by Cu, and Li,; of course Cu, must lie on the side Cu W and Li on Li W. Let us first consider the three ternary equilibria. 1. Copper sulphate—ammonium sulphate—water. The equilibria occurring in this system at 30° have been determined by Miss W. C. pr Baar; the results of this investigation are represented by the saturation lines ah, hpg, and gc; ah indicates the solutions saturated with CuSO, 5H,O; ge is the saturation line of solid (NH,), SO, and hpg represents the solutions saturated with Cu SO, (NH), 50,. 6H, O. As the line W Do, intersects the saturation line hpg, the double salt is soluble in water without decomposition; its solubility is represented by p. 2. Lithium sulphate—ammonium sulphate—water. The equilibria occurring in this system at 30° are represented by the saturation lines be,eqf and fc; the first is the saturation line of Li, SO,. H, O; ( 140 ) the second that of the double salt Li, SO, (NH), SO,, the last that of (NH), SO,. As the line W Di: intersects the saturation line of the double salt it is soluble in water without decomposition. As regards the branch be I stated that this indicates solutions which are in equilibrium with Li, SO,. H,O; this is not quite correct for lithium sulphate, although only to the extent of a few */5 gives mixed crystals with ammonium sulphate. 3. Lithium sulphate—copper sulphate—water. Whereas in the two previous ternary systems a double salt occurs, this is not the case in this system at 30°; the isotherm therefore only consists of two branches; ad is the saturation line of CuSO, 5H,O and Bd that of A Piri 0 ED. These two branches have been determined by Mr. Koopat. The quaternary equilibria at 30° are represented by surfaces, lines and points. The surface ahkd is the saturation surface of Cu SO,, 5 H,O; it there- fore indicates the quaternary solutions which are saturated with CusO,.5 H,O. The surface dkleb is the saturation surface of Li, SO, . H,O. The surface c/mg is the saturation surface of (NH,), SO, The three surfaces observed are the saturation surfaces of the com- ponents or of their hydrates; in addition we also have the saturation surfaces of the double salts; that of Li, SO, . (NH), SO, is represented by elmfq; that of Cu SO,.(NH), SO,.6 H,O by hklmgph. The saturation lines are formed by the intersection of the saturation surfaces taken two by two; they consequently represent solutions saturated with two solid substances. We now see at once that solutions represented by the points of the lines: hk are saturated with CuSO,.5H,O and Do. dE if se Cu SO, BO and lave oo BIN 23 3. SOR HD and le » » a bil SO, : Ee) and Dy; brit ae bj ns Eman DAE ote MU 155 2 » Dg and (NH), SO, MIS. af » Doa and (NH) SO, The quaternary saturation lines may be distinguished into external lines and middle lines; the external lines such as kh, kd, le, mf and mg each terminate in a point of a side plane, therefore in a ternary solution; the middle lines such as 4/ and /m are situated quite within the tetrahedron. | ( 144°} In each of the saturation points three saturation surfaces and there- fore also three saturation lines meet each other; such a point there- fore represents a solution saturated with three solid substances. From this it follows that the solution represented : by & is saturated with CuSO,.5H,O, Li, SO,.H,O and Deu aoa tty gee a » Drs, Li, SO,.H,O and Dou A ae 4 et Dis (NE SOy and. Weg. This shows that each of these solutions is saturated with Cu SO, . (NH,), SO, . 6 H,O. With the aid of this figure we may readily draw some conclusions. Let us therefore observe the external lines, for instance dk. The point d represents a ternary solution saturated at 30° with CuSO, . 5H,O and Li,SO,.H,O. To this solution we add (NH), SO, ; the solution will now alter its composition until at last a third solid phase appears. What is this phase? (NH), SO, forms a double salt with copper as well as with lithium sulphate and the question now arises which of these two will appear first. The experiment shows that CuSO,.(NH,),SO.6H,O is formed. If we start from the ternary solution A which is saturated at 30° with CuSO,.5H,O and CuSO,.(NH,),50,.6H,O and if Li,SO,.H,O is added the solution undergoes the changes represented by points of the line Ak until finally the third solid phase occurs in & in this case Li, SO, . H,O. If we start from the ternary solution / saturated at 30° with (NH,),50O, and Li, SO,.(NH,),SO, and if we add CuSO,.5H,O and represent the solution by m CuSO,.(NH,),SO,.6H,O is formed as the third solid phase; if we start from the ternary solution g which is saturated with (NH,), SO, and Cu SO,. (NH), SO, . 6 H‚,O and add Li, SO,.H,O, Li, SO,.(NH,),SO, will form in m as the third phase. If we start from the ternary solution e which is saturated with Li,SO,.H,O and Li,SQ,.(NH,),SO, and add CuSO,.5H,O the solution traverses the branch e/; in / however a new solid phase is formed, namely, Cu SO, . (NH), SO, . 6 H,O. Suppose a plane is passed through the points W, Cn and Di: of the tetrahedron; the points of this plane represent solutions with a constant proportion of the components Li, SO, and (NH), SO, ; this ratio is the same as that in which they occur in the double salt. This plane intersects the saturation surface leg fm of this double salt, so that this is not only soluble without decomposition in water but also in solutions of copper sulphate of a definite concentration. ( 142 ) In order to find the composition of the solid phases which can be in equilibrium with definite solutions I have acted in the same manner as I did previously with ternary systems; I have applied the “residue-method”. If the solution is in equilibrium with one solid substance the conjugation line solution-residue must pass through the point indicating this solid substance; if it is in equilibrium with two solid substances the conjugation line solution-residue intersects the communication line of the two solid substances and if it is in equilibrium with three solid substances it intersects the triangle which has those three solid substances as its angular points. These constructions are much facilitated by taking a rectangular tetrahedron instead of an equilateral one and projecting the whole on two of the side planes. Astronomy. — “The investigation of the weights in equations accord- mg to the principle of the least squares’. By J. Weeper. (Communicated by Prof. H. G. van pe SANDE BAKHUYZEN). When results of measurement deduced from different modes of measuring or originating from different observers are equated mutually, it is generally advisable to test the weights assigned to these results, before equating, with the apparent errors produced by the equation in order to be able to judge whether it is necessary to correct them and to distinguish in what direction correction is obtained. Let the material of observation break up according to its origin into groups and let out of the apparent errors of each group separately the mean error of the unity of weight be deduced, then it is a necessity for the differences of those values to be small, at least they may not overstep the limits which can be fixed taking into account the num- bers of apparent errors in each group. Already at the outset of such investigations the problem thus appears how the mean error of the unity of weight can be calculated, if one wishes to use but a part of the apparent errors. When equating determinations of errors of division of the Leyden meridian circle I have applied the following formula: Here n= the mean error of unity of weight, g =the weight of a result of observation, ( 143 ) J =the apparent error calculated for this result, n = the number of errors out of the group, k=a number depending on the weights of the results of measure- ment and on the coefficients the unknown quantities, determined by the equating, are associated with in the equations expressing the connection between these unknown quantities and the results of measurement of the group. In what way 4 is dependent on the above-mentioned quantities will become clear by an example for which I choose the case that 3 unknown quantities z, 7, 2 are determined by MN equations of the form av + by + cz =/, whilst to the quantities 7 appearing in this equation and obtained by measurement the weights g are due. In this case k= Zg (a? Qax + 2ab Qry + 5? Qyy + Zac Qrz + 2be Qyz + 0? Qz2) where the summations in the formulae for £ and gu include expres- sions relating to the same results of measuring. In the above for- mula the quantities Q, the well-known numbers of weight, can be calculated by means of the coefficients of the normalequations. For the deduction of this formula we have the same considerations which lead to the mean error of the unity of weight out af all observations. If the real errors are indicated by 4 then nu? = > gh’; this sum is expressed in the apparent errors that can be calculated, and in the errors Az, Ay and Az of the quantities z, y and z, calculated out of the normal equations, by means of the relation h=f +aAr + bAy + cAz, so that nw = 2 of? + 2(Ax = gfa + Ay Z gfb + Az =S gfe) + + (Az)? > ga? + 2 (Ax) (Ay) 2" gab + (Ay)? &" gb? + + 2 (Az) (Az) & gac + 2 (Ay) (Az) & gbe + (Az)? & ge? If we were to use the whole material of errors, then the first three of the unknown terms would fall out on account of [gyfa] = 0, [9/6] =0 and [gfc| = 0. (Here and for the future I make use of [ ] as sign of a summation extending over all observations). To take as well as possible the unknown terms in the above into account we replace them by their mean values in the supposition that the same complex of observations repeats itself manifold times so that all calculable quantities return unmodified in each repetition. In that supposition Ar, Ay and Az have zero as mean values and the mean values of their squares and products are in the above order: Gre? © Gey? » Qyy Bw? » Crew? , Qyzu® and Q.. u? If we connect these mean values having u? as factor with the term (144) nu? in the above equation, if we put = 9 (a Qerz + 2abQry + b°Qyy + 2acQuz + 2heQyz + C° Q2z), equal to k and if we solve u out of the equation, we obtain ob gee p= zie the formula of which I made use to determine nN — the mean error of the unity of weight out of a particular group of apparent errors. I arrived at about the same result by another consideration putting to myself the problem to determine the mean value M of a definite apparent error /;, In the relation : fiiz=t—aq«—b y—¢G z I substituted for 2, y, z respectively [a/],[@l],[,7] to obtain f in the form of a linear expression of the results of measuring / which are supposed to be quite independent of each other. Then : My; = j51—2 (a; a: + 5; B He yi Erle a db; B + e; we]. It would now be the only way of reduction of this equation to make use of the well-known relations existing between the coefficients a, B, y and a, b, ce and the numbers of weight Q, namely : a= g(a Qra + b Qey + ¢ Qaz), B= g(a Qey + b Qyy + ¢ Qyz), Y= 9 (a Qrz + b Qyz + ¢ Qzz), in order to prove that er en B 1 E a+b; Be ¥)’ =| g Ji I propose however to deduce this equation directly from the minimum condition : [g (J — ax — by — cz)*| = minimum. If here too z, y, z are replaced by [al], [8/7] and [y/], then after calculation and combination of the equal powers and products of the quantities / an expression appears of the form = = C,/,1l, having for the right set of coefficients «, 8, y a minimum value. I observe here that the coefficients «, 8, 7 have to satisfy the minimum condi- tion independently of the particular values which the measurements furnished for the quantities 7. Out of this observation ensues that the partial derivatives of C, with respect to each of the coefficients a, 8, y furnish zero by substitution of the right values of these coefficients. ( 145 ) By calculation and arrangement of the terms of the minimum condition we arrive at C2, = 2 [9 (aay + BBu + cy) (ae + bir + eys)] — — 2 gu (apa, + bu B, + cn yr) — 2 qr (as ap + bv Bu + Co Yu) The expression [g(aas + 68,.+c¢y,)(aa +68, +cy,)] being put equal to F, the conditions for the minimum furnish the following equations : cis nant ee Aes ETR = Jy Oy, = Jy Cx OF OF OF ae, =a ary = dove = GJ p.pe Such an expression FF which, as far as the coefficients a, B, y appear in it, contains only products of one of the a, Bu ya with one of the a, 8,y, can be written as linear expression in each of those sets of 3 coefficients in the following way: pn tage + Bae fs OF EON EL OF eee ay Om. OB aoe So that by ey We the Rn resulting from the minimum we arrive at the following relations: F=glaran + by Bu + ov yu) = Ju (an ds + bu By + ou Ys): In words this relation runs: with equal weights an error in J, has equal influence on the apparent error f, as an equally large error in 7, has on the apparent error f,. If the weights of the two results of measuring are unequal, errors in these which are in inverse ratio with their weights will cause each other’s apparent errors to deviate to the same amount from the true ones. Let us put in the condition [gl — a [al] — BLU] — e [y!] }?] = minimum i; =1 and all other quantities /= 0, then from this arises gi (1 — 2aja; — bi, — 2eiy;) + [g (aai + 68; + ey; | = min. from which we deduce putting [9 (aai + 08; + ecyi)?] = G: GEE 0G 0G a and from this ensues again: 0G pe Gee 0G, G= 33g, We 5 Bian, + a tay, = gi (aja; + bii + e;y i) With the aid:of the above deduced theorem each term of the summation in the expression [g(aa;+ 68; + cyi)?] can be replaced | 10 Proceedings Royal Acad. Amsterdam. Vol. X. (146 ) by a corresponding one in which the constant index is given to the coefficients a,b,c, so we have: — e=|% (aja + bi B+ ¢; » |= gi (ai ai + bi Bi + ei yi) from which results after division by gi* the relation I was to prove. Using this relation I find: Mi = (1 — aj a; — bi Bi — ci ¥i) ze Jt If we call aa +58 Hey =x, then ier can be calculated de out of each apparent error and the mean value of this system of errors is equal to u, as that of the system of unknown errors is hV q. It therefore seems to me not only permissible, but for a test of the weights even useful, to make use of that system of errors which allows the mean error of the unity of weight to be deduced out of each definite part of these errors. The connection between the quantities x and the number # of the above formula applied by me can be indicated by the relation 2 x = hk. Physics. - “Contribution to the theory of binary mixtures’. VII. By Prof. J. D. van DER Waats. ON THE RELATION BETWEEN THE QUANTITIES @,, AND @, AND @,, WHICH OCCUR IN THE THEORY OF A BINARY MIXTURE. I have already frequently traced the course of the thermodynamic curves for the case that for a binary system minimum plaitpoint : ay Bree temperature occurs, and so also the quantity bas a minimum value zt for certain value of z. Both the course of the isobars and the course of the lines & 2) = 0 and En )=0 may be assumed as known for that case. And experiment has shown that the shape of these lines predicted by theory it at least qualitatively accurate. I purpose to demonstrate in these pages that in the case mentioned the course of these lines (see among others tig. 1 page 626 Vol. IX of these Proceedings 1907) is not compatible with the supposition emi, ( 147 ) d, 1 begin with pointing out that the line (2) =ohasan asymptote v ag which asymptote da either exists or must be supposed to exist for a value of # which is negative, and that this curve approaches the line v= 5 asympto- tically for continually increasing values of 2 — at least if a, +a,—2a,, is positive. I shall presently come back to this supposition, but on da page 626 I have explicitly stated this supposition in the form Zet positive. With increase of 7’ this line proceeds to higher value of x and v. db for such a value of z for which MRI = & d, At lower temperatures the line (2) = 0 consists of two separate WU) dp dv a d*p dv? de ' dx dv branches. From = 0 follows that the liquid branch has d ue Maximum volume on the line 5 = = 0 and the vapour branch mini- tav mum volume on the same curve, which curve has an analogous d, course to (2) = 0. It has the same asymptotes, but is always con- wv fined to greater volume. For 7’= minimum critical temperature the se eee dp dp two branches coincide in a point for which both — and —— dv* da dv @} is equal to 0, so in such a point of the line 2 dz dv = 0, for which dp d*p Ee i : Be = 0 and also ae = 0. Hence in the critical point of the mixture its, v Ax hs ; - taken as homogenous, for which z, has minimum value. At still higher x d value of 7’ the curve eo =0 has split up into a lefthand branch dv Jz and a righthand branch, both which branches possess tangents parallel aes ; dp dp to the v-axis, in points for which also a = Oand = 0. Among U/ zr v the special values of this constantly increasing value of 7 we must mention in the first place that for which the last mentioned point d has got on the line (Z)=o the point P of fig. 31. This is the de) 5 10% ( 148 ) remarkable point for which plaztpoint and critical point of the mixture taken as homogeneous coincide. So at this temperature the two curves d d 5 — 0 and (3) = 0 still inter- dz v dv x sect in two points. The other point of intersection lies, of course, at greater volume. With further rise of temperature the two curves contract d. further. The line (2) =o moves to LI) d Fig. 31. the right and the line al = 0G OO the left. At a certain temperature these two curves touch, and at still higher temperature they have got quite detached. This point of contact of the two curves lies, of course, on the vapour branch of d A (F)=° and so has a greater volume than the critical volume. WH We can calculate the volume in ease of contact. The condition of di contact of eee and (Z)=0 is given by equal value of a/v U/ |= 25S ser eeen ( 149 ) MRT db dal (v—b)? da dev’ @) and MRT 2a mm = TT . . . . . . . . . 3 (vb) v 6) If now we make use of (2) and (3) for the elimination of MRT db v é and of ie get a simple form for ee Kij d'a da \* Vv ae L DN ER We may also get a quadratic equation in = , but then it appears iat gue: ef the values of a — 1, and that at 7=O the linev =b may be considered as coinciding with the branch of the volumes of dp hd oP — |= 0, and also with | — |= 0. In the same way the line v = oo. dv x dz v ; ; da’? d'a ‘ If we now write for the ratio of fn and a — the quantity m, v dx? da \? =) so that m == then (4) becomes: des? v _3—2m b 1l—m v And drawing 5 2 ordinate when m is laid out along the axis of the abscissae, we get fig. 32. For m=O we have = = 3 and for Vv Vv m==1 we have = For m>1 = is at first negative, but for v Vv mf as 0, and for greater values of m zi positive and stead- 3 Vv ily increasing. The limiting value is eo 2. For negative value of Vv . es . v Mh >, 16 always positive, descending from a 3 to == 2: The v b ( 150 ) traced curve is an equilateral hyperbola. So a value of - larger than 3 is possible only when v lies between O and 1. Thus Led requires a value of m= ‘/,. Accordingly it is impossible to account for a minimum plaitpoint temperature of substances for which m does not lie between 0 and 1. Now I have already repeatedly called attention to the equation : d'a da \? : a de + 4 (a,a,—a,,’), which follows from the supposition that a is a quadratic form of z, and already in my Molecular Theory for a binary mixture I pointed out, realizing the desirability of a relation being found between a,, and a, and a,, that the equation of the spinodal line for a binary mixture might be very much simplified if we were justified in assuming a,,2—a,a,. I also pointed out other relations between these quantities; but I have carefully refrained from even giving so much as tbe slightest indication of the greater probability of one relation. I have only repeatedly, then and later, assumed as relation for mixtures with minimum plaitpoint temperature a, + a, > 2a,,, and reversely, when also mixtures with maximum plaitpoint tempera- ture might occur: a,-+a,< 2a,,. And I have repeatedly pointed out that there is no reason whatever for putting e.g. a,,° = a,a,. And to this the following considerations have chiefly led me. In the equation of state for a simple substance the two constants b and a have not been introduced on equally sufficient grounds and with the same certainty. To the existence of the quantity 6 we conclude with perfect certainty if we believe that to occupy space is an essential property of matter Even Maxwe 1, who would not attribute a volume of their own to the molecules, but wanted to consider them as so-called material points, understanding that colli- sions could not take place between material points, could not but attribute to them at least an apparent volume. By assuming a repulsive force he had to account for their never meeting, and for their behaviour as particles possessing impermeability on approaching each other with reversal of motion. A hypothesis whose improbability is not to be denied. The force would be a repulsive one, and pro- bably in inverse ratio to the fifth power of the distance. How and why the attraction at somewhat larger distance is converted into such a repulsive force is a question that was probably never put by him, (151) and at all events was not answered by him. So the introduction of the quantity 6 into the equation of state is perfectly natural — and for everybody who assumes the existence of matter as real, indis- pensable. But this is not, at least not in the same degree, the case with the quantity a. Why should molecular attraction be a necessary attribute of matter? From the idea: “matter is something that neces- sarily occupies space” does not follow that matter will also have to possess attraction. Perhaps we shall sooner or later learn to form a conception on the nature of a molecule which involves that they necessarily attract each other and learn to compute the value of this attraction. Of late attempts have therefore been made to get a better insight into the nature of molecules, and they are supposed to be either vibrating or permanent electrical double points’). But even if this supposition appeared to account satisfactorily for the molecular attraction, yet it does not necessarily follow that attraction exists. Then the question has changed in so far that it runs: are there electrical double points in the molecule or not? It is true that in my Thesis for the Doctorate (1873) p. 92, when the question occurred whether hydrogen possesses a critical temperature I answered in the sense of a high degree of probability, but only on a ground which leaves some room for doubt, viz. that “It may be presumed that matter will always have attraction”. It is not to be denied that everything that we accept as matter is subjected to gravity; but to derive from this that the existence of the NEWTONrAN attraction involves the possession of molecular attraction is more than hazardous. All this is not intended to raise doubt about the existence of a e.g. for helium, for now that all other substances possess a value for a we may repeat what I said before for hydrogen, but to draw attention to the fact that the value of a does not only depend on the molecular . . a a . . . weight. If this was the case, — — —, a relation which is cer- m, Ms A he . a a a tainly not fulfilled. Then also —-=—~=—, and a,,?=a,a, m,* Ms mms which very probably will never be fulfilled either. I was convinced from the outset that we should not be able to explain a number of phenomena occurring for binary mixtures by means of such an unfounded supposition. Already a long time ago Kortrwre showed in his paper “La surface wp dans le cas de symétrie” in how high a degree the phenomena exhibited by a binary mixture, depend on the value ascribed to a,,. For values of a,, between 1) See these Proc. p. 132. (152) certain limits not only three phase equilibrium but even four phase equilibrium would be possible, then of course always at a single value of 7. So the supposition a,,* =a,d, is not one without far- reaching consequences. Yet we see repeatedly that this supposition is made. And I have undertaken this investigation to show that such a supposition would also render the existence of minimum plaitpoint temperature impossible. At the same time I wanted to point out how the course of the isobars which I have given in fig. 1 of these contributions would be entirely modified on other suppositions about a,, than those I have started from. If we put in equation : 2 d'a (da : oe aa (=) ae 4 (a,a, — gs ) da? d'a for (> the value ma — in which, if there is minimum plaitpoint da dx? temperature the value of m lies between O and 1 for the point of d d contact of & = 0 and (2 = 0, we find: sy dv) 2 1 da i 4 ; (Ste on ta (2 — a, = 4 (a,a, — a,,”) da Now Fir a Te As at the same time we cannot have a,a,=a,," and a, 4a,—=20,,, unless in ihe case a == an this equation cannot be fulfilled but by putting a,a, >a,,’. The supposition a,a,=a,,’? gives for m the value 2, but then v, dp dp also for — in the point of contact of | — }=0O and | — ]=0O, the b daz v dv Nd value 1 (see fig. 32). — Only when we put a, 4, 2, and do we find for the point of contact of the curve v mentioned, values of a which are larger than J, and which can there- fore exist, but then this value can rise to 2 at the utmost. In such d, d cases there is contact of (?)= O with the liquid branch of (Z)= 0. Vv Ls y x And this means for fig. 1 of these contributions that then again the oie dp dp liquid branch of a =0O may approach to En = 0 on the right ONE z side, but then to that part of this curve that lies beyond the minimum Ls bas 3 Ca = a 5 Mas | Fig. 32. volume, and where it proceeds again to greater volumes. On the supposition that a,,° might rise above a, a,, fig. 1 would not repre- sent all possible cases of the course of the isobars with respect to d 5 4) = 0. But I observed already on page 630 in what way fig. 1 would v/v have to be extended if other suppositions on a,+a,—2a,, are admitted e.g. a, + a, — 2a,,=0 or a, +a, — 2a,, negative, and the supposition a, a, < a’,, lies in this direction. If we continue increasing a,,, not only above Va,a,, but even da a, +a, dz] . , We, above —— then 73 = - is negative, and-— lies between 2 2 d'a b da* dp dp and 3 for the point of contact of [| — }=0 and | — |=0, and so da), dv Jz d this point of contact always lies on the liquid branch of ee U)/x We might also have arrived at the above results by another course, which would give us an opportunity of making some new remarks. For if we think the quantity v eliminated from the two equations ( 154 ) d d € = 0 and 5) = 0, we obtain a relation between x and 7. In daz O Je general we find two values of x for the same value of 7. The value of 7, at which these values of z coincide, or in other words, the maximum value of 7, then gives us the value of x for the point of contact of the two curves. From MRT 2a (ob)? v and MRT db a 1 dv (v—b)? dev? da db da de de | we find ——==— for a point of intersection. . (6) AR a As for values of v which will be realisable, v >>b and v must be positive, a point of intersection of the two curves can only occur if da db Lis positive, and if aa | This latter condition may be written ax a a Ge b? Tait 0. So the two curves can never intersect in a region of in- av creasing critical pressure. Let us therefore confine ourselves to decreasing critical pressure. The locus (6) has as differential equation: db d'a dae Dn np vn de dv he dx? 5 == eer ie v? dx a” (“) da? a dv . : ’ ‘ So when m= —= at © a 8 negative. Only in a region where 2 i da lv m has become = 1, — will be positive. And if we should assume ak a,a,—a,,", so if we put m= 2, the locus of the points of inter- section of the two curves would move to greater volume with increasing 2; so perfectly different from what happens for mixtures with minimum plaitpoint temperature. If we substitute the value of v which follows from (6), in: v we get: 1 da dat a a de 2a da MRT = — - ne Rd EN 1 b -1 db 1 db b da b de pe ee Sd eed °9 5a For values of z for which — = 0 and — —=— — or =e dx b dz a dx dz the value of 7 =O. Thus the same value of 7’ always belongs to a couple of values of z which approach each other. And at the maximum value of 7 the two values of x have coincided. By differen- tiating (7) we get an equation which may be written in the form: da da\? i 2adb 4 dz? de ) da bde da da\? dx as dx from which, taking (6) into consideration, we obtain again (4). It appears from the foregoing that putting a,,*°—=a,a, comes to the same thing as putting m— 2. For mixtures with minimum plait- point the value of m differs much from this value, as it is then smaller than 1, and so a,,’ will have to differ pretty much from a,a,. If we put a,,? = (a, a,, in which ? <1, we find from: d'a da n dn ii + 4(1—l)a,a, 2 da (2—m) a— = 4(1—l’) a, a, da? or m (: — =) (a, + a, — 2a,,)a=(1—P)a,a, It may be derived from this equation that m may lie near 2, even when / differs comparatively much from 1. The value of a varying with 2, also the ratio of 1 — >and 1—? will vary with wz. If we make a increase with z, which probably _ will be in general the case, then a, is the smallest value of a and (156 ) 1 a, the greatest value, whereas the value of a for Dr will be a, Ja, +2a,, TC UT en en 4 m 1 ee 2 1 So the ratio hes is. for ¢ =O, caer and. ¢ == 1: m a, je ae 2 Te a, = : Pe a a (\Y2 x 1) + (ld ve a, a, en 4 aard 4a, a, be: a, Ll re Mac gee & a 1) id (ey a, a, m Ln 2 alge are ate Ea, EES pe ie oe If we choose the second of these equations, from which it is easiest to draw conclusions with regard to the value of m at given value of ?, we write it first in the following form: 4 (1- Pe “Ey If we always take the same value of 1— /?, but different values bo a of —, we find very great differences in the value of m. For instance a, in @ = 9 We have =e : but with + = gen eS ie En jn Ce ith 7 we have = ( );. (OF van 148 (Lr) u a 2 ith ~—1 al t = ——_—_—_—_. With? = 1 wi = 1, m is found equal to m ET ith / we find of course in both cases m= 3. But for smaller values of l the values of m differ considerably. For {== 0 these values are 2 2 — and 2 KS) 1,44 ( 157 ) If we had discussed the third of the equations, the values of m would have been found still. higher. According to the first of the equations of course smaller. d Let us finally examine the course of the line (2) el im (the Hi v ; d, cases that there can be no contact with the line (2). or only on UY) x the side of the liquid volumes. We saw already above, that then the locus of the points of intersection of the two curves mentioned (cf. 7) runs to greater volumes, if 2 is made to increase. Then at given 7, d, only that part of the line (3) = 0 exists, for which this line runs to greater volume. The lefthand part, for which this curve may reach infinitely large volume lies in the common case ata value of z db MRT — v dz a da da and the first part of this equation is then equal to the unity, because db d to be calculated from MRT — = es . Then daz dz ee Bate b v b should be =O. This can only occur, when extrapolating we also admit negative values of 2, and moreover choose for 6 such a func- tion of z that it can become equal to O for negative value of z. This is the case for a linear function, but putting 6=6, (1 —) + bx is only an approximation. Whether this can also be the case with a more exact shape of 6 = f(z), must be left undecided. Moreover it is necessary, if we choose always greater negative value of z, that can also be eqnal to 1 in another case, viz.: if d, we first find 5 — 0, before finding En =— 0. But then the shape of a the p-lines must also be modified. I shall however not enter into a discussion of this, for one reason because Dr. Konnstamm informed me, that he had already been engaged in the study of the modified course of the isobars, and that he had also come to the conclusion that the relative situation of the values of x, for which 6=O and da Et 4 a is decisive. Moreover I leave undecided for the present a whether also on other suppositions than 0< «<1 there can be question of minimum plaitpoint temperature, which is to be distin- . . hd e . a guished from minimum value of i & ( 158 ) Botany. — “Contribution N°. 1 to the knowledge of the Flora of Java.” (Fourth continuation).’) By Dr. S. H. Koorpens. § 7. Plantae Junghuhnianae ineditae. I. Notes on some javanese species of an as yet unpublished collection of Junghuhn’s plants, in ’s Rijks Her- barium at Leiden. A few months ago, while searching in ’s Rijks Herbarium at Leiden for some herbariumspecimens of JUNGHUHN’s Javanese alpine plants, which were required by me, one of the officials of that institution found among the separately preserved collections of “Indeterminata” a fairly extensive collection made by JuNGHUmN. This collection had already undergone preliminary determination by me, in 1896 (during a short stay at Leiden), at the request of Dr. J. VALCKENIER SURINGAR, but for the rest remained wholly un- determined. As I noticed in this collection a number of Javanese alpine plants, and as it seemed worth while to study the collection as a whole, I resolved to complete the determination, begun in 1896, and to publish the results. The latter, as far as an enumeration of the Javanese specimens is concerned, are ready for the press, but will be published separately; here I only append a few remarks on this collection of Junghuhn. The whole collection consisted of fifteen large packets and fully 560 collecting numbers. As is the case of very many old herbariumcollections, the labelling of a large number of these specimens left much to be desired. On the other hand some specimens were provided with detailed col- lecting labels, written by Juncuunn himself. With a few exceptions, all the specimens were quite undetermined (without determination of the genus and order). Most of the specimens were also without a collecting number on the label. In consultation with Dr. J. C. GORTHART, Keeper of ’s Rijks Herbarium, it was accordingly decided to give running numbers to this whole collection of “Plantae Junghuhnianae tneditae”’, these numbers being independent of the old numbers, extant in some cases, but not explained by any list or publication. Printed labels have also been added, running partly as follows: “Plantae Junghuhnianae ineditae. In insula Java legit Dr. Fr. JUNGHUAN anno 1838—1863 sub n....” Except for the substitution of the word “Sumatra” for ‘Java’, the specimens from Sumatra in this collection have received a similar label. 1) Continued from these Proceedings p. 132. (159) I have not been able to ascertain, why this extensive collection of JUNGHUHN’s plants has not been worked at during so many decades, and apparently was ‘never in the hands of Mique. I surmise, in the first place, that it was not received from JUNGHUHN either until the period 1855—1864, or until after his death, de. after 1864; the receipt of the collection is noted on the outside in an unknown handwriting as “from Bandong’’. In the second place I surmise that this unpublished collection was accidentally mislaid among the mass of material in ’s Rijks Herbarium at Leiden, and was consequently not found again, when MiqverL was Director of that Institution (1862—1871). For had this collection been in the hands of one, with so good a knowledge of the East Indian flora as that possessed by Miqver, there can, in my opinion, be no doubt, that he would at once have discovered the 9 species mentioned below, which at the time were new to the flora of Java and were found by me undetermined in 1896. Nor would these 9 species have been omitted from the Javanese flora in the publication *} “Plantae Junghuhnianae” of 1854 or in the other publications of Mrqver (e.g. Flora Ind. Bat., Ann. Mus. bot. Lugd. Bat., etc.). | As such I mention the following species: Pl. Jungh. inedit. n. 368, 380, 381, 385 and 394 — Tur pinia parva Koorp. et VaLeTon (first published in 1903) Pl. Jungh. ined. n. 545 = Ilex Hookeri Kine (has not yet been mentioned in the literature as occurring in Java), [tea macrophylla Wall. var. minor K.et V. (at the time not recorded in Java); Pl. Jungh. ined. n. 207 = Aglaia heptandra Koorp. et Varrron (first published in 1896); 1) The title of this publication is: Plantae Junghuhnianae. Enumeratio plantarum quas in insulis Java et Sumatra detexit Fr. Junauuny, Leiden, 1854. In the Index Kewensis it is often quoted as Mroums Pl. Jungh., although Miguet's name does not appear in the title. Most of the phanerogams in this publication were treated of by Miquen himself, some other families by others i-a. by Bertram (Leguminosae), Moukensorr (Loranthaceae), W. H. pe Vriese (Pri- mulaceae, Dipterocarpaceae, etc), HasskarL (Commelynaceae, Amaranthaceae), Büse (Graminae), Bureerspuk (Violaceae), and A. J. pe Bruyn (Polygonaceae). In the catalogue of the University library at Leiden, this publication Plantae Jungh. Enumeratio plant. etc. (1854) is stated to have appeared in 1851—1855. In the only copy in ’s Rijks Herbarium I found the year 1854 given as the date of publication. This bound copy ends with p. 552, where as the copy of the Royal Academy of Sciences at Amsterdam is slightly more complete, ending with p. 570. The publication seems to have been stopped prematurely, the less incom- plete copy of the Royal Academy of Sciences ends on p. 570 wm the middle ofa word and is therefore, evidently no more rounded off than the copy 1 found at Leiden. The date of publication is given on the title page of the latter copy as 1853. ( 160 ) Pl. Jungh. ined. n. 91 et 103 = Mallotus campanulatus J. J. Suita (first published in 1907 in Icones Bogoriensis); Pl. Jungh. ined. n. 113 = Ostodes macrophylla Bextu. et Hook (not recorded for Java even at the present time); Pl. Jungh. ined. n. 462 = Hlaeocarpus Griffithii A. Gray (not kuown for Java at that time); Pl. Jghn. ined. n. 488 = Saurauja dasyantha Dr Vriese (even now not mentioned for Java in the literature); Pl. Jghn. ined. n. 256 = Eugenia cuprea Koorp. et Vareron published in 1900); Pl. Jghn. ined. n. 426 = Symplocos Junghuhnii (published for the first time below). The specific description is as follows: Symplocos Junghuhnit Koorp., nova spec. — Arbor ramulis gla- bris. Folia tenuiter coriacea, supra glaberrima, subtus praeter costam laxe appresse pilosam glabra; 12—15 cm. longa et 4—5 cm. lata, subintegra v. valde indistincte serrulata, basi angustata, apice sensim vel abrupte acute acuminata; nervis secundariis plerumque impressis, petiolo 1—1'/, em. longo. Racemi simplices axillares et terminales villosi petiolo 4—5-plo longiores; bracteae ovato-acutae extus basi puberulae calycem aequantes; pedicelli calyce paullo breviores, calycis tubus extus villosus, lobi rotundati glabri marginibus ciliatis, corolla calyce duplo longior utrinque glabra stamina ultra 100 satis distincte pentadelpha; filamenta filiformia glaberrima; ovarium 3-loculare gla- brum, stylus glaber; fructus ignotus. West-Java (Preanger). — Pl. Jungh. ined. n. 426 in Herb. I. B. The foliage of this species greatly resembles that of Sympl. Hen- schelii Brand [in Engler Monogr. Symploe. Pflanzenw. IV. 242. (1901) 89], but the floral structure is different, as is evident from the above diagnosis. In the system of the Symplocacae of Branp Le. this species will have to be placed in the subgenus Hopea (L. f.) CLARKE, and in the section Bobua (DC.) Branp., and probably in the subsection Palura (Buch.-Hamilt.) Barr, et Hoox., immediately near to Symplocos ribes Juncn. et De Vriese [in De Vriese, Pl. nov. Ind. bat. (1845), AAE Branp lc. 39.] Through the extra-ordinarily large number (100) of stamens Symplocos Junghuhnii seems to me to differ from S. rides, and from the other more or less closely related Javanese species, S. aluminosa Buume BRAND l.c., S. odoratissima (Bu.) Cxoisy and S. sessilifolia (Bu.) GÜrke. S. polyandra, Branp. |. ce. 36 of the Philippines, which is also related and also has about 100 stamens, is distinguished from the Javanese plant since it has panicles instead of simple racemes. ( 161 ) In 1856 Miquet evidently resolved to bring out a second part of the publication, which appeared in 1854 (Plantae Jungh. Enum. pl.). This follows for instance from his quoting in the Flora Ind. Bat. IT (1856) p. 1053: “Pl. Jungh. I. p. 84”. My publication on the Pl. Jungh. ined. might therefore perhaps have been called “PI. Jungh. II”. Since, however the only part, which appeared in 1854, was not specially designated as part N°. I, I have now, for the sake of clearness, not called my present publication also “Plantae Jungh.”, but “Plantae Junghuhnianae ineditae”. I found this latter designation for the first time in Miqver Fl. Ind. Bat. I. 2. (1859) p. 356. An authentic herbariumspecimen of Flueggea serrata Miq., collected by Jurenvan in the higher mountain regions of Java, and found by me in the University Herbarium at Utrecht, is published there for the first time and is quoted by Miqurr Le. as Pl. Jungh. inedit. The authentie herbarium-labels, preserved at Leiden, which refer to the species treated of in the above-mentioned publication (Pi. Jungh. Enum. pl., 1854) bear numbers, which correspond with that publi- cation of 1854 and are sometimes also quoted in the later publications as Pl Jungh. n. 1, 2, 3, ete. In order to avoid any possible con- fusion with these numbers, I have quoted below the specimens in the collection now described by me, as follows: Pl. Jungh. ined. n.°1, 2, etc. The number of exclusively alpine Javanese species met with in the above collection, is not large. Nevertheless I found several more or less characteristic Javanese alpine species represented, sometimes by a profusion of specimens. As such the following may be mentioned among others: Urtica grandidenta Mig., Thalictrum javanicum Br, Myrica javamca Br, Euphorbia Rothiana Serene, Viola serpens War, Leptospermum javanicum Br, Clethra canescens RriNw., Leucopogon javanicus (JUNGH.) DE Vriese, Lysimachia ramosa WALL. var. typica Knutu., Primula imperialis Junen., Buddleia asiatica Lour., Vaccimum Teysmanni Mig., Vaccinium varingaefolium Miq., Rhododendron retusum Brnn., Lonicera oxylepis Mig., etc. With some specimens of the collection, now described by me, I found labels, on which, presumably about half a century ago, was written in the hand-writing of the late Professor W. H. pr Vrinse: “legit Junghuhn, herb. de Vriese”. It seems therefore, that before ’s Rijks Herbarium at Leiden acquired this collection of Junghuhn whether by purchase or by donation, it belonged wholly or partly to that herbarium. The determination of the above-mentioned JuNenunn’s collection, En Proceedings Royal Acad. Amsterdam. Vol. X. ( 162 ) was chiefly carried out by me at Leiden, with the aid of the mate- rial for comparison in ’s Rijks Herbarium, and for a few rare species with the help of the collections of the University Herbarium at Utrecht. Leiden, Juni 23% 1908. Chemistry. — “The dynam conception of a reversible chemical reaction.”’ By Prof. A. Sirs and J. P. Wisaur. (Communi- cated by Prof. A. F. HOLLEMAN.) It is generally known that our kinetic views lead to the assump- tion, that with every reversible reaction we meet with two reactions, which proceed in opposite directions. The following consideration, however, seemed to show that a direct proof for this dynamic conception could not be given. Our power of observation only enables us to observe differences; so if we observe something of a conversion, this is the consequence of this that the velocity of one reaction is greater than that of another, and we get an impression as if only one reaction takes place, which proceeds with a velocity equal to the difference of the velocities of the two reactions. As we shall see, this reasoning, which is perfectly correct for conversions in homogeneous systems, does, however, not hold good in all respects in a single case for a conversion in a heterogeneous system in consequence of particular circumstances. The above arguments, however, seemed so convincing that up to now the following indirect proof has been considered the only one possible. The already indicated conception of a reversible reaction leads to a simple relation between the constants of equilibrium and the two k constants of reaction, which runs: K=~. This relation, now, sup- 2 plied a means to test the kinetic conception of a reversible conver- sion, and it is known that experiment has shown for the few cases which have as yet been investigated, that this relation is really satisfied. Yet it seemed very desirable to prove the correctness of our dynamie conception of a reversible reaction by a direct way. The conversion by means of which we have reached our purpose is this 200 = CO.-+ 0. ( 163 ) That the choice fell on this reaction was due to this that it has appeared from the investigations of BoupovarD') and others that when CO is converted into CO, and C, the carbon is deposited in the form of graphite, so that it was to be expected that when we start from the righthand system, and lead CO, over diamond at constantly increasing temperature, graphite, which will be immediately visible even in exceedingly small quantities will deposit on the diamond, the reaction proceeding simultaneously from left to right. [It is hardly necessary to observe here that we discuss the reaction in the gas phase, in which the gaseous carbon is one of the reading components. The circumstance that the system is heterogeneous, and according to the molecular theoretical views by the side of the homogeneous reaction two more heterogeneous transformations take place, viz. : diamond — Cyayour and Cyapour — graphite, between which the homogeneous reaction forms the link, made us suppose, we had found in this example a means to test our dynamic conception con- cerning a chemical reaction | ’*). It is self-evident that if the experiment is to prove anything, care must be taken that the temperature never falls, because in this case the depositing of graphite might be ascribed to a shifting of the equilibrium from left to right. To be sure that this was out of the question it was desirable to make the temperature constantly increase during the experiment. Before proceeding to the experiment we gladly avail ourselves of this opportunity to mention that the diamond powder with which the above mentioned investigation was made, had been kindly sup- plied to us by Messrs. AsscHer, to whom we here express our great indebtedness. As it was important for our investigation to start from white diamond powder, the diamond received by us, which had a grey colour in consequence of impurities, was heated in an open china mug, by means of which a perfectly white powder was obtained. Before now proceeding to the decisive experiment, it was necessary to investigate first of all whether at the temperature at which we intended to perform our investigation, diamond is already converted to graphite. For this purpose the white diamond powder was heated for an 1) Ann. Chim. Phys. (7) 24, 5—85 (1901). 2) The passage between [ ] is added in the English translation. ak ( 164 ) hour to 900° in an atmosphere of pure nitrogen by means of an electrical furnace, on which it appeared that under these circum- stances nothing was to be detected of a conversion of diamond into graphite. When this favourable result had been obtained, a china dish filled with diamond powder was placed in a china tube which was slowly heated in an electrical furnace, a current of pure CO, passing through the china tube. : The escaping gas was led through a very sensitive solution of PdCl,, so that the presence of CO in it was at once to be detected. The experiment showed that under these circumstances the reduc- tion of CO, by diamond begins to be noticeable only at about 750°, and proceeds rapidly at 850°. So after the conversion CO, + C—>2C0 had been shown in this way, we had to ascertain whether the reverse reaction 2C0= CO, + C had taken place in the course of this process. For this purpose the CO, stream was suddenly broken while the temperature was still increasing, and the gas-mixture in the china tube was expelled rapidly and completely by means of pure nitrogen. Only then the temperature was lowered, and the furnace cooled down to the temperature of the room. The contents of the boat showed in an unmistakable way that the latter reaction had really taken place, for the colour had become grayish, in consequence of the depositing of graphite, which had taken place throughout the mass. On repetition of the experiment the same result was obtained, so that we think that we have given in this way for the first time a direct proof of the correctness of the dynamic conception of a reversible reaction. Anorg. chem. Laboratorium Amsterdam, June 1908. opie nmmoraiae (465 ) Physics. — “The P-T-X-spacial figure for a system of two com- ponents which are miscible in the solid or liquid crystalline state in all proportions.” By Prof. A. Smits. (Communicated by Prof. J. D. van peR WAALS). When we project the spacial figure mentioned in the title above it appears that its most remarkable feature is this that three two sheet surfaces must intersect viz. the vapour-liquid sheet, the vapour- mixed-crystal sheet, and the liquid-mixed-crystal sheet, of which we know that for the simplest case, i.e. for the case that these sheets possess neither maximum nor minimum, they show great resemblance in form. To examine how this intersection takes place we consider first of all a p-x-figure for a temperature below the triplepoint temperature of the two components. If we call as is usual, the component with the highest vapour tension (and the lowest triple-point temperature) A, this p-a-diagram has a sbape as indicated in fig. 1. On line acd we find the mixed-crystal phases, which coexist with the vapour phases, which lie on the line ad 6. Between these two curves lies the region for vapour + mixed- erystal, GJ F, and above the line ach the region for the mixed- erystals J, and under a db the region of the vapour G. If now we choose a temperature above the triple-point temperature of A, but below that of B, and if we assume for a moment that at the temperature considered A is found in a solid, so supersolidified state, we get a p-a-figure as indicated by afbga in fig. 2, which is quite analogous to that represented in fig. 1. Solid A, however, being metastable at this temperature, part of this p-z-figure will be metastable on the A-side, and now the question rises what stable equilibria will take the place of these metastable equilibria. This is immediately seen when we imagine the case, that the two components are liquid at the temperature considered, and so B occurs in superliquefied state. In this case we should find a p-z-figure as indicated by cldge, where we notice that d lies below 6, and c above a, b and c denoting the vapour tension of metastable states of A and Z. The line cld indicates here the liquid phases coexisting with vapour phases on cgq. The p-a-figure afbga being metastable on the side of A and eldge being metastable on the side of B, it is at once evident thay ( 166 ) the stable p-r-figure will contain the lefthand part of the former and the righthand part of the latter p-z-figure, which parts will meet where a vapour phase coexists at the same time with a liquid phase and with a mixed-erystal phase. As follows from the diagram the vapour branches of the two p-x-figures intersect in g, so that g is a vapour which does not only coexist with the liquid /, but also with the mixed-crystal phase f. So the three-phase-equilibrium G + 2+ F, which is non-variant at constant temperature constitutes the transition between the series of mixed-erystal phases af, and the series of liquid phases /d, which can coexist at a series of pressures with vapour phases of different concentration. We find the region of the liquid Z above the line d/ and the region of the mixed crystals / above the line af. The two regions are separated by a region of liquid + mixed crystals lying between the lines lg and fg. If we now draw some p-r-figures corresponding with different temperatures in the same graphical representation beginning with the triple point temperature of A, and ending with the triple-point tem- perature of B, we get what is represented in fig. 3. Figure ab corresponds to the triple point temperature of A and a,b, to that of B, the p-z-figures a,b, and a,b, referring to intermediate temperatures. From this collection of p-a-figures we see that when we join the corresponding points of the different three-phase-pressure lines g//, a three-phase-region is formed composed of two two-phase-regions, first of the two-phase-region for the equilibria between vapour and liquid, and secondly of a two-phase-region for the coexistence of liquid and mixed crystals. If we think the p-a-diagrams corresponding with the different temperatures placed in succession, the vapour-lines form a vapour- sheet, the liquid-lines a liquid-sheet, and the mixed-erystal-lines a mixed-erystal-sheet. The line dgg,a, indicates the intersection of the vapour-sheet of the mixed-crystals *) with the vapour-sheet of the liquid phases, the line bli,a, that of the liquid sheet of the mixed-crystals with the liquid sheet of the vapour phases, and }/f/,a, the line along which the mixed- crystal sheet of the liquid phases intersects the mixed-crystal sheet of the vapour phases. 1) By the vapour sheet of the mixed crystals we must understand here the vapour sheet coexisting with the mixed-crystal sheet. Five. i. A. SMITS. “The P-T-X-spacial figure for a system of two components which are miscible in the solid or liquid erystalline state in all proportions ” Tix C | a a G x B Fig, 1. A : B ie Ei 2 Fig. 3. Fig 4. Proceedings Royal Acad, Amsterdam. Vol. XL ( 167 ) All this becomes perfectly clear when we consider the spacial representation, fig. 4, to the right of the plane v,v,v, v‚. Sa is the triplepoint of the component A Sp 2 0» ” a) 99 ” L ceS4 is the vapour-pressure-line of solid A ee. © ER ml „ liquid A terminating in the critical point A4. aSpg is the vapour-pressure-line of solid B and ay 9 rt iM „ liquid B terminating in the critical point Az. S4S'4 is the melting-point-line of A and SpS'g the melting-point- line of B. Sag Sp fSa is the three-phase-region discussed before, and the p‚x-section drawn between the triple-points Sy and Sp shows that Sag Sp is the vapour line, S4/Sp the liquid line, and S4/Sp the mixed-crystal line. On the two-phase-region S4qSg/S,4 lie the vapour and liquid phases which are in equilibrium with the mixed-erystals, and on the two-phase-region S4/S,/fS,4 are found the liquid and the mixed- erystal phases which can coexist with the vapour. The two-sheet surface for mixed-crystal and liquid rests on this latter two-phase-region, which surface will in general be very steep. It has been assumed in the spacial figure that as is actually the case as a rule, = of the melting-point lines of the components is at first positive, which causes the two-sheet surface mentioned to run to higher temperatures with increasing pressure, which is here represented in an exaggerated manner. A consequence of this situation is this that, as has been indicated in the section, at a temperature lying between the triple-point tem- peratures of A and J, the region for liquid and mixed crystal ceases to exist above a certain pressure, 7, so that the three regions of two-phase equilibria, mixed-crystal-vapour, liquid-vapour, and mixed- erystal-liquid are limited on all sides. dp. N It is evident that when ee is negative for both melting-point lines, C point » will not lie on the melting-point line of the component