yields iH aati ut Abin nin t Wr 4 * i Het f Viet if Ni PT hy 4 4 Hy (i i MH iy | rbe wea DAT LL | It HT) * EED HA h | | vl 4 pe i Iie bd i | He i 1 be i Hh} Ue si aid aas ni i | Hi ni ; 4 tie a q f Hi we rt FP AA edie ty ay iy i it q i 4 | iy Nias na se Ee = ics : ign ea eels En 7 ze: = re SES 23552 = 5 = ERS ate EET > _ es: ae ES = „Ener a soe rr aa Al as nat Sg ion tia belt jij DA * oy ray Eet > Mey: es 6 : 8 laan - ern (aud ars li Sins uk ; SG: a plas! es Kad i ; Bapes Koninklijke Akademie van Wetenschappen te Amsterdam PROCEEDINGS OF THE pone oo Leen OE 8 (EEN Cee mmm en €) > 4 NEE ME BN VL: ee 16 AMSTERDAM, JOHANNES MULLER. July 1904. OE NAR ARE UD oe Kaj) ‚he Db pene AS Ba it TAO Cece van 30 Mei 1903 tot 23 April 1904. DI. XII.) Ld ERRATUM. a : ; Te “yy sa Page 644 line 36 for chloride read chlorine. eS >» 647 » 24 » 7290 » 7920 Koninklijke Akademie van Wetenschappen te Amsterdam, PROCEEDINGS OF THE Beer ob EN OK SC IEN GHS ———— 0S ae eet NT IA BT. MEL (Ist PART.) AMSTERDAM, JOHANNES MULLER. December 1903. saad a (Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Natuur u dE in i a tae tS Afdeeling van 30 Mei 1903 tot 28 November 1993. DI. XII) ‘is a Kas AX. ie we Re ce i. P pe eld ay Ere wor We vi 7 0") * ek: 2 é 3 oe heg Ut att oe ee ei ets N ede TE be ceed mal ot | Ev ad +" | 4 Sl oe OF, ale ee 4 - <4 vs CONTENTS dings of the Meeting of May 30 LOOD REE Veatch? Per aen derd A ú | June 27 RD Ene TA ee Se ¥ > > Yv —_ J er) > » » September 26 ¥ © hd October 31 » pa > Ws Oe se ON (4) November 31 oe te | 8 En an ann be yv ¥ ¥ ¥ uz bo =] eN KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday May 30, 1903. IEG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 30 Mei 1905, Dl. XII). Cia PE EN TT S. J. W. Drro: “The action of phosphorus on hydrazine”. (Communicated by Prof. C. A. Lorrv DE Bruyn), p. |. J. W. Commenry and Erxsr Conen: “The electromotive force of the Dayirii-cells”. (Com- municated by Prof. W. H. Jurius), p. 4. Jan DE Varies: “On complexes of rays in relation to a rational skew curve”, p. 12. W. A. Versiuys: “The singularities of the focal curve of a curve in space’. (Communicated by Prof. P. H. Scnovure), p. 17. P. Zerman and J. Geest: “On the double refraction in a magnetic field near the components of a quadruplet”, p. 19. ‘ J. J. van Laar: “The course of the melting-point-line of alloys (3.d communication). (Com- municated by Prof. H. W. Bakiturs hoozeBoom), p. 21, M. C. Dexuuyzen and P. Vermaar: “On the epithelium of the surface of the stomach”. (Communicated by Prof. C. A. PrEKELMARING), p. 30. E. Iek: “On the liberation of trypsin from trypsin-zymogen”. (Communicated by Prof. H. J. HAMBURGER), p. 34. A. PANNEKOEK: “Some remarks on the reversibility of molecular motions”. (Communicated by Prof. H. A. Lorenrz), p. 42. C. A. J. A. OupbEMANS and C. J. Konine: “On a Sclerotinia hitherto unknown and injurious to the cultivation of Tobacco (Sclerotinia Nicotianae Oup. et KorixG), p. 48 (with one plate). J. bk. Verscuarretr: “Contributions to the knowledze of van per Waars’ Z-surface. VII. (part 3), The equations of state and the Z-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components”. (Communicated by Prof. H. KAMERLINGIE ONNES), p. 59. The following papers were read: Chemistry. — “The action of phosphorus on hydrazine” By Mr. J. W. Drro. (Communicated by Prof. C. A. LoBrY pr BRUYN). (Communicated in the meeting of April 24, 1905.) The last number of the Berichte ') contains a research on phos- phorus by R. Scumnck. Several of his observations quite corroborate those which have been announced some time ago?) and which were made 1) Ber. 36. 979. 2) Recueil 18. 297. (1899). Proceedings Royal Acad. Amsterdam. Vol. VI. (2) in 1900—190L, but the publication of which was postponed owing to other studies which are not yet complete. In 1895') and also afterwards?) LoBrr pr Bruyn, in his studies on hydrazine, observed that yellow phosphorus in contact with aqueous hydrazine turns the solution first yellow, then dark brown and finally black. After some time brownish black amorphous flakes are deposited. As already stated, I submitted this reaction some years ago to a closer examination and studied it, both with aqueous and with anhydrous hydrazine. I. If we introduce into vacuum tubes 16 gr.(==6 at.) yellow phosphorus and 5 e.c. of a concentrated 90°/, (= 1 mol.) aqueous solution of hydrazine and allow these to be in contact for 1 or 2 months at the ordinary temperature the whole solidifies to a black amorphous mass in which a white well-crystallised substance is distributed. On opening the tubes a large quantity of hydrogen phosphide appears to be present. As preliminary experiments had shown that the white substance was soluble in absolute aleohol but not the black substances, the tubes were filled with absolute alcohol out of contact with the ai, the black substance was freed from the white crystals by repeated washing with absolute alcohol and then dried over sulphurie acid in vacuum. The crystalline product obtained on evaporating the alcohol, was particularly hygroscopic. The analysis agreed best with the assumption that it consisted of hydrazine phosphite. Found 30.4 °/, P and 12.3°/, N (this was determined in a nitrometer by means of vanadie acid) *). If however notwithstanding the necessary precautions, the substance has attracted a good deal of moisture in the course of the different manipulations, there is a possibility of its being hydrazine hypophosphite *). The black mass is insoluble in alcohol, ether and carbon disulphide and free from excess of yellow phosphorus. It has an odour of hydrogen phosphide; in contact with the air it becomes moist and the black colour changes to yellow. It contains chemically combined hydrazine which, in company with a little hydrogen phosphide, is obtained on distilling with dilute sodium hydroxide and which could be identified by means of its dibenzaldehyde-derivative which melts at 93°. 1) Recueil 14. 87. 2) Recueil 15. 183. 3) Horrmann and Kispert Ber. 31. 64. 4) SaBANEJEFF, Z. anorg. Ch. 20, 21. (1899). (3 ) The black substance is strongly attacked by dilute nitric acid and also by bromine water. On heating at 100° in a current of dry hydrogen it loses weight continuously and the black colour changes to red. On treatment with dilute acids it behaves exactly like the product _ isolated by ScuEenck from red phosphorus and ammonia‘). It is then converted into a light red amorphous powder whilst the solution appears to contain a salt of hydrazine. The red powder has the external appearance of red phosphorus but is distinguished from this by a more orange tinge and its behaviour towards alkalis. Ammonia and dilute soda or potash yield black products, which however on prolonged washing with water lose their feebly combined alkali and assume their original red color. The substance, therefore, behaves as a weak acid which forms black alkali salts which readily undergo hydrolysis. Strong alkalis act energetically on the red substance with formation of hydrogen phosphide and a salt of hypophosphorous acid. In the analysis of the black and the red substance the phosphorus was determined by means of dilute nitric acid (in sealed tubes) and with bromine water. The nitrogen determination was done volume- trically with bromine water in a current of carbon dioxide and the hydrogen by an elementary analysis. The average result was 45.9°/, P, 19.8 N and 5.5°/, H; total 71.2; the balance may be taken as representing oxygen. The red compound was free from nitrogen so that the black product appears to be the hydrazine derivative of the red substance. The product dried in a desiccator in vacuo contained 91.7 °/, P iT ee Dt id DP 2. If we place in a vacuum tube an excess of vellow phosphorus with free hydrazine N, H,, we also notice (although sooner than in the case of the aqueous solution) the formation of a black amorphous substance which in appearance quite resembles the product obtained from hydrated hydrazine. No white substance is of course formed, hardly any. pressure is noticed and also little or no formation of hydrogen phosphide takes place. This gas, like the hydrazine phos- phite, therefore owed its origin to the well-known reaction hetween phosphorus and a base. 1) That black compounds are also formed from liquefied ammonia and white phosphorus is shown by the experiments of Gore, Proc. Roy. Soc. 21. 140. (1872), FRANKLIN and Kraus, Amer. Ch. J. 20. 820. (1898), and Hveor, Ann. Chim. Phys. 21. 28. (1900). 2) This figure is almost sure to be too high owing to the nature of the process (elementary analysis). (4) The black substance was washed with carbon disulphide and alkohol and dried in a desiccator in vacuo. Apparently it has absorbed oxygen during this operation for the analysis showed a deficit of about 13 °/,. We foun@:-78:5°9/) Py 1.9 °/, Hand 60 ON. When treated with dilute acids a red substance was again formed which in appearance and properties corresponded exactly with the one already described and contained the same amount of phosphorus (found, average 92°/,|. The hydrazine has passed into the acid. 3. From the foregoing it follows that substances quite analogous to those formed by ScreNnck’s (impure) red phosphorus and ammonia are generated directly from hydrazine and vellow phosphorus. Evidently, the black compounds which are formed from aqueous and anhydrous hydrazine are of a different nature; their investigation remains however very unsatisfactory, owing to their amorphous conditions and want of tests for purity, in addition to their unstability towards washing- liquids. But it is pretty certain that the orange red product which both yield, when treated with acids, is a weak acid composed of phosphorus, hydrogen (and oxygen 5) Hydrazine is therefore capable of directly giving up hydrogen, not only to sulphur but also to phosphorus. Organic chem. Lab. University. Amsterdam, April 1903. Chemistry. — “The electromotive force of the Daxmut-cells.” By Mr. J. W. Commrrix and Prof. Ernst ConexN. (Communieated by Prof. W. H. Junius). (Communicated in the meeting of April 24, 1903). 1. In the present state of our electro-chemical knowledge an exhaustive study of the electromotive force of the Danmrr-cell would have but little importance if it related to the use of this cell as a standard-cell, as we are now in possession of standard-cells which, if properly constructed, satisfy all requirements. We have, nevertheless undertaken an exhaustive investigation of such a cell because J. Cravpmer has published in the ‘‘Comptes ‘Rendus” 5 certain views which are entirely opposed to our modern theories on the origin of the electromotive force in cells of this kind. 1) 134, 277 (1902). @ on) \ 2. CHAUDIER gives the following form to the well-known formula of Nernst for the electromotive force: » ) Py WEKT @ en log : ‘) a noe P P. JT This is evidently a mistake as the second term after the sien of equality does not belong to this formula but forms part of the well- known equation of Gipps and von HerLMHOmtz *). This mistake we may pass over. The following table contains Cuavprer’s results which have been obtained by means of Boury’s method for the measurement of electromotive forces. His cells were constructed according to the scheme: Copper sulphate solution Dilute solution of Zine Copper _ ie a oi ; | saturated at 15° C. | sulphate. Zinc. 3. The paper contains but few details of the manner in which the experiments were conducted: “Vélément Daninun est constitué par deux vases en verre, contenant Fun la solution de sulfate de zine, Vautre la solution de sulfate de cuivre; ces deux vases sont réunis par un siphon formé d'un tube de verre rempli de coton imbibe de la solution de sulfate de zine dans Pune des branches, de la solution BA BL ET. ZuSO,.7H,0 in 100 parts | Elektromot. force (15° C.) Coetficient of temperature. of water, 0 | 1.0590 Volt 0.002% 1/5 | 41138 | 0.00015 If, | 461451 | —).00013 Yo | 1.1368 0.00005 4 | 4518 0.00005 2 | 1.1263 +0 00003 4 | 4.1249 | 0 0003 6 | 1.1208 | 0.00016 10 1.4188 —().Q0003 30) 1.1054 | —0 0002 GO | 1.1003 | 0. 0002 200 (saturated) | 1.0902 — .00026 1) Cravpier wrongly calls this equation, the equation of Lord Kruvis. (6 de sulfate de euivre dans Vautre. Ce dispositif m’a paru donner des resultats plus constants que les autres.” It seems to us strange that the E.M.F. should be given to '/,, millivolt. All authors who up to the present have made a study of the Danreni-cell have pointed out how difficult it is to obtain constant values with such cells. For instance, the E.M. FE. is in a high degree dependent on the nature of the copper or zine electrode. For particulars in this direction we refer to the researches of ALDER Wricut’). In connection with the measurements under consideration the following table of FLemine’s will be found interesting: E. M. F. of a certain Danmuecell. Coprrr, perfectly pure, unoxidised 1.072 Volt PF slightly oxidised, brown spots 1.076 ” more oxidised 1.082 , IJ covered with dark brown oxide film 1.089 „ IJ cleaned, replated with fresh pinkish electro-surface 1.07247 4. In repeating CHAUDIER’s measurements it is of the greatest importance to have the determinations mutually comparable; errors caused by an unlike nature of the electrodes had to be carefully excluded. As negative electrodes we used pure zinc amalgam (1 part of zine to 9 parts of mercury) as used in the Crark standard-cell. The zine was a very pure specimen from Merck of Darmstadt in which iron was not even detectable. The mercury was first shaken with nitric acid and then distilled twice in vacuum according to Herert’s *) method. As we know, the potential difference between this amalgam and pure zine is very small. Previous experiments by one of us *) have shown that this difference is only 0.00048 volt. at O° and 0.000570 volt. at 25°. As positive electrode we used ‘at first a thick wire of pure copper. The copper sulphate solution in the different cells was prepared 1) Philosophical magazine (5), 18, 265 (1882); Freme, ibid. (5), 20, 126 (1885). St. Linpeck, Zeitschr. für Instrumentenkunde 12, 17 (1892). Comp. also CARHART, Primary Batteries (Boston 1899). Litterature up to 1893 in: Wiepemans, die Lehre von der Klektricität. (Braunschweig 1893), pag. 798. 2) Zeitschr. fur phys. Chemie 33, 611 (1900). 35) Conen, Zeitschr. für phys. Chemie 34, 619 (1900). Oe) by first making a saturated solution at 15°. Pure, Murrck’s copper sulphate (free from iron) was dissolved in water and boiled with copper hydroxide to remove traces of free acid. After filtration the liquid was cooled and after introducing a crystal of CusSO,. 5 H,O set aside to erystallise. The salt was then shaken for a long time (3 to 5 hours) with water at 15° in a thermostat, use being made of Noyrs') shaking apparatus. All the thermometers used in this investigation were tested by means of a standard thermometer from the “Physikalisch-teehnische Reichsanstalt” at Charlottenburg. To make sure that complete saturation had indeed been attained we took after 3 and 5 hours small samples from the solution in the shaking bottles and analysed these liquid by means of NnuMann’s electrolytic process *). In this way we found: (5 hours) 100 parts of water dissolve 19.22 parts of anhydrous Cu SO, (3 hours) 100 parts of water dissolve 19.28 parts of anhydrous CuSQ,. The zine sulphate solutions were prepared from a solution which was saturated at 15° in the same thermostat as the copper sulphate solutions. The different dilutions were done by weighing. The zine sulphate gave no reaction with congored; moreover the same preparation had served in the construction of CLARK-cells which appeared to be perfectly correet. By way of a check we also determined the quantity of ZnSO, which at 15° is present in the saturated solution. A weighed quantity of the solution was evaporated in a platinum dish and the residue (ZnSO, .1 H,O) was weighed *). In 100 grams of water we found 50.94 grams of ZnSO, (as anhy- dride) whereas previous determinations had given 50.88. If we accept the figure 50.94, the saturated solution then contains at 15°, 150.56 grams of ZnSO,.7H,O to LOO grams of water. We fail to see how Cuavpipr has arrived at the figure 200 (see table 1). 6. Measurements with Danirii-cells are rather difficult, for if the smallest amount of copper sulphate solution comes in contact with 1) Zeitschr. fur phys. Chemie 9, 603 (1892). 2) Neumann, Analytische Elektrolyse der Metalle, (Halle 1897), Pag. 106, We may casually remark that the figures given in the literature for the solubi- lity of copper sulphate are incorrect. Compare: Erxsr Conen, Vorträge für Aerzte über physikalische Chemie (Leipzig 1901) pag. 70. 3) See CALLENDAR en Barnes, Proé. Royal Society 62, 147 (1897); Ernst COHEN, Zeitschrift fiir phys. Chemie 34, 181 (1900). (9) the zine electrode by diffusion, the E. M. F. of the system is dimi- nished considerably. FLeming for instance states, “the smallest deposit of copper upon the zinc, due to diffusion of the coppersalt into the zine is indicated by a marked depression amounting to 2 or 3 percent”, whilst Wricnt (after prolonged diffusion) noticed depressions up to 6 percent. After a few preliminary experiments whieh convinced us of the accuracy of these remarks we constructed for the definitive measure- ments the little apparatus shown in fig. 1. po Pt (YI ) It consists of three tubes A, B, C, (Sem. high, intemal diameter 1.8 em.) which communicate by means of connecting tubes. To the tube ff, a glass tap with a very wide bore (5 or 6 m.m.) is attached. The zine amalgam is introduced into A and the platinum wire /% is then fused into it. A and B also /, are now filled with the zine sulphate solution after the bore of the tap has been plugged with fat-free cottonwool previously sucked in the same zine sulphate solution. While the tap is still closed, the saturated copper sulphate solution is poured into Cand also into /. with the india-rubber corks A, A, and A. Through A, is introduced a thin glass tube reaching just below the cork. Through this tube the copper electrode A may be introduced into the solution when the The cell is now closed measurements take place. The whole apparatus is now plunged as deep as possible in a thermostat (15°). If required the tap may be opened or closed by means of the wooden rod GH. By the introduction of the tube B the possibility of contact of the zine electrode with the copper sulphate solution is quite excluded. Even if a trace of copper sulphate has diffused into the lower part of B (if the copper solution is lighter than the zine solution, the former will float in 4 on the latter) we never find a trace of copper in the tube A. In the final experiments, the measurements lasted so short a time that as a rule no copper diffused even into ZB. 7. After preliminary experiments had shown that the cells cannot be reproduced when we make use of copper electrodes which have been cleared with nitrie acid, we afterwards followed the direction of Wricut and Fremne who electrolytically cover the copper electrode with a laver of copper immediately before the measurement. For this purpose we used the bath described by Owrrrer, *) for the copper coulometer. After being copperplated the electrode was rinsed with distilled water and dried with cottonwool. It was then at once put through the tube into the cell. We always take care that only the electrolytically copper plated part of the electrode gets into contact with the liquid. 8. The E. M. F. of the cells was determined by the compen- sation method of PoGerNporrr. As working cell we used a storage 1) Electrochemische Uebungsaufgaben (Halle 1897) pag. 5. All copper electrodes were always copperplated during 10 minutes with the same current-strength (0.15 ampère) (or density) and at the same temperature. We have also tried, but unsue- cessfully, to work with copper amalgam. As to copper amalgam, compare Prrren- KOFER, Dinater Polytechnisches Journal 109, 444 (1848) and y. Gersuem, Ibid. 147, 462 (1858). ( 10 ) cell (Deutsches Telegraphenelement), as normal cell a Werstroy-cell which was always kept in a thermostat at 25°. In this thermostat was also placed a CrarK normal cell to allow comparison between the normal elements. The rheostats used (2 rheostats of 11111.11 ohms each Hartmann and Braun) were carefully compared with a third rheostat standar- dised by the ““Physikalisch-Technische Reichsanstalt.” 9. The measurements took place as follows: after a cell had been filled with the required solutions it was (without the copper electrode) placed in the thermostat at 15°. After having reached that temperature the copper electrode was taken from the copperplating bath and after having been treated as directed it was introduced through the tube into the solution. The tap was now opened and the measurement carried out; this lasted 1 or 2 minutes. When the tap had been closed, the cell was taken from the thermostat. The solution in A was then tested for copper, but as already stated not the slightest trace of copper was found in this part of the apparatus. 10. As the measurements of ALDER Wricut, FLEMING and Lorp XAYLEIGH *), which were done with fairly concentrated solutions of zine sulphate had proved that the reproduction of these cells to less than 1 millivolt is almost impossible and as our own experiences had shown us that with more dilute zine sulphate solutions we get still greater deviations, we only give our measurements in millivolts although the method of measuring employed rendered the determina- tion of tenths of millivolts (and less) quite possible. As CHACDIER only gives one series of measurements We can say nothing as to the reproduceableness of his cells. According to our experience no importance need be attached to statements of tenths of millivolts. Whether it would be possible to attain a greater accuracy when working with solutions quite free from air is a matter which we cannot go into any further as our results are quite accurate enough to completely answer the question in dispute *). 11. Before proceeding to communicate our figures we would point out that a cell constructed according to the scheme: | copper sulphate solution | copper | saturated at 15° | Pi | | cannot practically be classed among the reversible cells. 1) Transactions of the Royal Society of London. Vol. 76, 800 (1856). 2) See Epetine, Wiep. Annalen, 30, 530 (1887) and G. Meyer, ibid, 33, 265 (1885). Zine water (:41-) We have, therefore, not repeated Cravpinr’s experiment with this cell. When we consider that cells with very dilute solutions show deviations amounting to 6 millivolt, we cannot expect much from measurements with an element of the kind described. 12. The subjoined table contains the results of our measurements. Below I and If are placed the values of the E.M. FE. which we found for the same cell in independent experiments. From these figures it may at the same time be seen in how far the said cells may be reproduced. TABLE. II: ee ——- — on — ~ - LS Grams of Zn 50,.7H,0]> Electromotive force at 15°.0 C, NPA Mee to 100 gram water. | in Volt. (ComMELIN and Conen). Bh EE, (CHAUDTER). ne I II average. ijk 1.143 1.449 1.146 1.1138 If, 4.4441 1.146 | 4,444 11151 ub 1.435 | 4,434 | 1.135 1.1368 l baat | 1.431 | 4.431 | 4.4331 2 MAD, oh eA ADA: || S495 1.1263 4 1.119 1.419 1.419 1.1249 6 AAG | 4.446 | 4.446 1.1208 10 1402 | 4.449 1119 41.1188 30 1104 1 104 1.104 1.1054 150.65 (saturated), 1.081 1.084 1.081 1.0902 (200 saturated ?) 15. From this table it will be seen at once that a maximum value of the E.M.F. at about '/, gram of ZnSO, . 7 H,O to 100 grams of water, as CHAUDIER claims to have found, does not exist. The progressive change of the values is on the contrary, quite in harmony with the equation given by Nerxst, which shows a decrease of the E.M.F. for an increase of the concentration of the zine sulphate. It would be superfluous to criticise the other conclusions of CHAUDIER as these are based on. the figures discussed. Utrecht, April 1908. ( 12) Mathematics. — “On compleres of rays u relation to a rational skew curve.’ By Prof. J. pr Vrins. (Communicated in the meeting of April 24, 1903). 1. Supposing the tangents of a rational skew curve /” of degree n to be arranged in groups of an involution /” of degree p, let us consider the complex of rays formed by the common transversals of each pair of tangents belonging to a group. So this complex contains each linear congruence the directrices of which belong to a group of Ir. If these directrices coincide to a double ray « of J? the con- ernence evidently degenerates into two systems of rays, viz. the sheaf of rays with the point of contact A of « as vertex and the field of rays in the corresponding osculating plane «. To find the degree of the complex let us consider the involution Iv of the intersections of the tangents with an arbitrary plane g. The surface of the tangents intersects g according to a curve Cm of degree m == 2 (n—1) and the complex curve of g envelopes the lines connecting the pairs PP of /’. This involution having (7—t) (p—1) pairs in common with the involution forming the intersection with an arbitrary peneil of rays, the complex is of degree (2n—8) (pl). 2. We then consider the correspondence between two points Q,Q' of Cw situated on a right line PP’. As Q lies on the lines 3) -3) (p—1’ pairs / | connecting any of (m—2) (p—1) pairs, there are (m—2) (p—l) (m points Q. The correspondence (Q, @’) has (m—2) (im in common with Zp, so the complercurve has 1 (m—2) (m—3) (p 1)? = (n—2) (2 n—5S) ple double tangents, the complexcone as many double edges. Evidently these double rays form a congruence comprised in the complex, of which order and class are equal to (n—2)(2n—S)(p—D>. The complexcurve also possesses a number of threefold tangents, each containing three points of /’ belonging to one and the same group. To find this number we make each point of intersection Sof Cm with the right line PP’ to correspond to each point P” of the group indicated by P. To each point P" belong 3 (p—1) (p—2) pairs P, P', so 4 (p—1) (p—2) (m—2) points S; each point S lies on (m—2) (p—1) connecting lines PP’, and therefore it is conjugate to (m—2) (p—1) (p—2) points P". Every time P" coimcides with S, three points P lie in a right line and each of those points is a coincidence of the correspondence (P",S); so we find 4 (m—2) (p—1) (p—2) threefold tangents. From this appears at the same time that the ( 13°) right lines of which each cuts three tangents of Rr" belonging to a same group of [P, form «a CONGPUCHCE of which order and clase ane equal to (n—2) (p—1) (p—2). ‘ 3. Let us consider more closely the group where « is a double element and a’ one of the other elements. To the just-mentioned congruence evidently belongs the pencil of rays in the plane (A,a’)— a@,, with vertex A and the pencil of rays in the osculating plane « with vertex (a@,a,)— A. So the congruence contains at the least 4 (p—1) (p—2) pencils of rays; each of the 2(p—1) singular points A is the vertex of (p—2) pencils placed in different planes; each of the 2 (pl) singular planes a bears (p—2> pencils with different vertices; on the other hand the 2 (p—1) (p—2) singular points A, and the 2(p—41) (p—2) singular planes a, each bear a pencil. The complex curve is as appears from the above of genus 4 | (2nu—8) (p—1)—1 ] [(@n—3) (p—1)—2] — (n—2) (27 5) (p—l)*- 3(n—2) (p—1) (p—2). For p=3 this becomes equal to zero which could be foreseen; for, to each point P of the curve C™ the connect- ing line P/P’ can be made to correspond, by which the tangents of the complexcurve coincide one by one with the points of a rational curve. In a plane p through a tangent a’ the complexcurve degenerates, a pencil of rays the vertex of which lies on the tangent « separating itself from the whole. In a plane a evidently (p—2) pencils of rays separate themselves. 4. We shall consider more closely the simplest case, where the complex is determined by a quadratic involution of the tangents of a skew cubic; 28, p—2. If A and B are the points of contact of the tangents a and / forming the double rays of the involution, and if @ and 8 are the corresponding osculating planes, we assume as planes of coordinates 2, =); 2, == 0,7, = 0, «2,0. successively the osculating plane a, the tangent plane (a, 4), the tangent plane (4, A), the osculating plane g. The curve F* is then represented by VORA De sale Re Bean Like Ee Ke and for its tangents we have the relation ie Dye Pra Pie Der Dey bs at. lt. The points A and B being indicated by the parameters /=0 and {= oo, the parameters t and ?¢’ of the points of contact of two conjugate tangents satisfy the relation ¢-+ (/ = 0. GE) The coordinates of a common transversal of the tangents (f) and Ct) evidently satisfy the conditions Praia tE Pra OF Pa heien 2E Pa: Pili = Ps Se BUD, = t's, Bn 20°04, ws therefore also Pia +P (Pia + 3 P33) + Ps, =O and UD ys = Pie By eliminating ¢ we find the equation of the indicated complex: Pia P aa TPs Pas (Pia 2 as) Pa Pas — U: To this cubic complee belongs the linear congruence p,, = 9, | 1),; =.0. Its direetrices / and m are represented by. == 0, z, =S and 2,=0, ©«,=0; the former connects A with the point («, 4), the latter unites B and (3, «). Each ray of the congruence rests on two pairs of tangents; the corresponding parameters are determined by the equation Psat) + (Pig + SP) + pia = U. So the complexcone has a double edge, the complexcurve a double tangent. 5. This is also evident in the following way. With given values Of Ws Yar YoY, the equation p,,—=4p,, OF .%,—Y,%,=4(Y3%1—1 Fs) represents a plane intersecting the complexcone twice according to Py, p‚,=0, and moreover according to a right line of the plane 2? (Woerd) a À (ye) ie 3 (Wara Y2t0)] oe ( %3— Ya") = U. DOP 0p =O A double edge. If the plane y,2,—y,«, =4(y,;7,—¥,#,) is to touch the complex- cone along the double edge, the three planes Us % — ¥,%, —V % YU, — ¥, %, =D, (Ay, HA) eo al (5 AY ,— AED at (v, 3 iy.) +53 (Ay, +5)", = 0 must pass through one right line, so My AY, = OY, : dAy, — À' y, = Os y,— 34y,=— ON, > Ay FY, = Oa must be satisfied. By eliminating @ or o we find Ay, Ya HAY, Y, — SY, Ys) + Is Ya — Y- The roots of this quadratic equation determine the tangent planes of the complexcone along the double edge, which becomes a euspidal edge when EN Ye Ve We = Ag Oa eae that is when ya ae or yy ee (15 ) So these quadratic skew surfaces of which the first evidently passes through /? contain the vertices of the complercones having a cuspidal ede. 6. For the points P of the Rt this cone of course degenerates into the plane connecting P with the tangent p in the conjugate point P' and a quadratic cone touching that plane. For points on the right lines / and im the complexcone must con- sist of a plane counted double and the single plane Ed ORN: For, each ray in « and 8 belongs to the complex, whilst all right lines resting on / and m are double rays of the complex. Indeed the substitution y,=0, y,=0 in the equation of the complex gives the relation «x, (y, ¢,—y, v,)* = 0.. For points on one of the tangents « and 4 the complexeone breaks up into the plane « or 8 and into a quadratie cone touching it. For a point of the intersection of @ and 8 we find a degeneration into three planes. For the complexcurves analogous considerations hold good ; e. &. the complexcurve degenerates into three pencils of rays when the plane passes through AB. 7. The complexcone degenerates into a plane and a quadratic cone if the vertex lies in @ or in 8 or on the surface of the tangents of #*. In the former case « or ? belong to it; in the latter the plane through the vertex P and the conjugate tangent p’, To investigate whether there are more points for which such a degeneration takes place, we suppose that the equation of the inter- section of the complexcone with ‚== 0, thus that YP EE Yr Ea Yad Ca zij Ys Ui as an (Ys¥s— BY 5), = + SY ,Y,U,'@,—2y,y,t,°¢,—3y,y,7,'0, + (y,y, + 3y,y,)a,c,, = 0, is deducible to the form (6, , 27+, 0,7 +0, 0,7 +26, 00,420, 2,7, +20, ,a,2,) (ot, Heat, Hoz) — 0. Then the following conditions are to be satisfied : a ee if i Deen 2 Bf at, Oy b,.¢.= IW bie PS hs) ee oh Ne eee ee age one ol: ee bies +20, ser == Yates 0, 0+ 20,50, = Has Dag, +20, se UT IIs, 5) ee eel ee ae ew va es eee: by30,+20,,¢,=3Y,Y,3 b, 3,420, 5¢; = 2Y,Y3: 553¢,+20,,c,— SU Us (bes + Dese, + bata) = His + 3y,4,- Let us in the first place put b,,=—0 and c,=y,, then 26,, is equal to —y, and 2%,, equal to ¥,. Further we find 6,, = —y, and ¢;—=—y,. After some deduction we get as only condition ( 16 ) HU Fa Oale BY Ia + Aya? ys = 9, or (Ys — Ya 3)” = Hia) (Yaa Ys) that is the verter of the compleacone belongs to the surface of tangents. If we put c,=0, we then arrive after excluding y, =O and y¥,—= 90 (for which the indicated degeneration always takes place) at the double condition yy Pes y,* and vts == 4¥.Y3, that is at the points of A. 8. Let us suppose that the tangents of /* are arranged in the triplets of a /*. To determine the degree of the complex of the common transversals of the pairs of tangents we can also set about as fol- lows. In an arbitrary pencil we consider the correspondence of two rays s and s’, which are cut by two tangents belonging to J’. To the coincidences of this correspondence (8, 8) belong the four rays resting on the double rays a, 6,¢,d of /J*; the others are united in pairs to six rays, each resting on two tangents of a triplet, so the complex is of degree 6. To find the degree of the congruence of the right lines, each resting on the three tangents of a group, let us consider the rays they have in common with the analogous congruence belonging to a second /*. If +, ”, is one of the four common pairs of the two involutions, and 7, and 7,’ successively the tangent forming with 7, and 7, a group, the common transversals of #7, 7, and 7,’ belong to the two congruences '). Evidently they can have no other rays in common than those eight, which are indicated by these; consequently the con- eruence is of order two. The complexcone of an arbitrary point has as appears from the above, fwo threefold edges; as it has to be rational, it has moreover four double edges. If P lies on the surface of tangents of A, this cone degenerates into the system of planes which connect / with the two tangents conjugate to p and a biquadratic cone with threefold edge. 9. The quadratic scrolls determined by the triplets of tangents, evidently form a system of surfaces two of which pass through any point and two of which touch any plane. This system is thus represented in point- or tangential coordinates by an equation of the form 1) This consideration leads to no result if we consider a rational skew curve of higher order. oI) Pi22Q@1vR=—0. From this ensues that all the surfaces of this system have the eight common points (tangential planes) of P=0, Q=0, R=0 in common. The degenerations of this system are four figures consisting each of two planes as locus of points and of two points as locus of tangential planes. One of those figures is formed by the planes a and a, (Aa) and the points A and A, — (ea’). The eight common points A,, B,, C,, D,, A;, B;, C‚, D, and the eight common tangential planes a,, 8,, y,, d,, «5, 2,, 5, 9, of the scrolls are singular for the congruence (2,2). The remaining singular points and planes are evidently A, b,C,D,A,,B,,C,, D, and a,8,y,0,4,,8,,7,,9,- These 16 points and 16 planes form the well known configuration of KumMEr. We can choose the notation in such a way, that A, bears the planes 8, y, d,@, and A, the planes @,,y,, d,, a, ete. Let us bear in mind that three osculating planes of Mè? intersect each other in a point of the plane of their points of contact and let us further mark the symmetry of the figure, we can then easily deduce from the preceding, that momertnerponts A.A; 4; B C.D; As Bir Case BER ij Arne Aen Br Mone EE EE Ii AA re tole ioe are situated, whilst A bears the planes a, «a, a, B, Ys %, A, I I I a, a, ds, Bs, 3 de A, " I I a, > a, a, B, Y> J, A EE, I i! a, td, ds, Pi Tin Oe It is clear that for each of these 16 points the complexcone is composed of a plane counted double and a cone of degree four. Mathematics. — “The singularities of the focal curve of a curve in space.” By Dr. W. A. Verstuys. (Communicated by Prof. P. H. Scnoute.) In paper N°. 5 of the “K. A. v. W.” at Amsterdam, Vol. XIII, I have deduced some formulae expressing the singularities of the focal developable and of the focal curve in function of the singulari- ties of a plane curve. In like manner it is possible to deduce the following formulae which express the singularities of the focal developable and of the ) Proceedings Royal Acad. Amsterdam. Vol. VI. ( 18 ) focal curve of a curve in space in function of the singularities of this curve. Let the curve be of degree u, of rank o, of class r; let its number of stationary points be z, that of its stationary tangents 7. Suppose the curve to have no real nodes or double tangents and no particular position with respect to the plane at infinity or with respect to the imaginary circle at infinity. In that case the singularities of the evolute or of the cuspidal curve of its focal developable (G. Darsoux: Classe Remarquable ete. p. 19) are the following: rank, 7 = 2 (u + ©). class, m= 2 9. number of stationary planes, a = 2 (» + 4). double osculating planes, G = 9?—9——3 (v + 0). stationary tangents, 7 = 0. nodes, H=zx=3(u—0) + 7+ 4. double tangents, w = 0. degree, n= 2(8u+r+ 6). degree nodal curve, «= 2 (u + 09)? —10u—29—3(-+ 6). number of planes through two lines which pass through a given point, y—=2 (ue)? — 4u — 49 — wt). stationary points, 8— 124—4e—6(v-+ 4). The chief singularities of the focal curve are: degree, n= 2u +4ue de —11pn—oe—3(v+ 9). rank, 7 =4uo-+ 0°—4u—4eo. number of stationary tangents, v = 0. class, m = (8u+2vr+20)(2u+o0)+3u0— 36u-4 12 0— (r+). number of stationary points, ? = 2 (Surt 6) (2u-+ 9)— 57 u+ 21 0 — 27 (» + 6). " " planes, a—= 6 (2u -v 0) (2udo) 4u — 2u0—20?— 107 n+ 47 0 —57 (r +6). When comparing these singularities with the values of the singu- larities of the evolute and of the focal curve of a plane curve, we see that they differ only in the rank of the curve in space being substituted for the class of the plane curve and in the number of stationary tangents « being replaced by (vp + @). From this follows that the singularities of the evolute and of the focal curve of a curve in space ¢ are the same as those of a plane curve d, which is the projection of ¢ on an arbitrary plane from an arbitrary point. TENT a Physics. — “On the double refraction in a magnetic field near the components of a quadruplet.” By Prof. P. Zueman and J. Gens. On a former occasion the results were communicated to the Academy, of an investigation on the magnetic rotation of the plane of polarization in sodium vapour, in the immediate neighbourhood of the absorption lines. *) In the case of very thin vapours this rotation appeared to be positive outside the components of the doublet, in which the original spectral line is resolved by the influence of the magnetic forces: between the components, however, it becomes negative and very large. In these experiments the light of course passed through the vapour in the direction of the lines of force. In the same way, if the light is transmitted through sodium vapour in a direction normal to the lines of force, we may expect from the examination of the immediate neighbourhood of the components, in which the spectral line is split up by the magnetic forces, results which are of theoretical importance. Vorer has deduced from his theory of magneto-optical phenomena the existence of a double refraction, which must be produced in isotropic media, as soon as they are placed in a magnetie field, but which should only be observable in the neighbourhood of an absorp- tion line.*) Vorer, together with Wircnrrt, has observed, that plane polarised light of a period near that of the lines D, and D,, is no longer plane polarised but has become elliptically polarised) when it has traversed the flame, there being generated a difference of phase between the components vibrating parallel and those vibrating per- pendicularly to the field. This elliptical polarisation was demonstrated by the above mentioned physicians with the aid of a BaBiNer compensator, using a flame with mech sodium and a small Rowrarp grating. The object of our investigation of the magnetic double refraction was to examine the phenomena, which show themselves, if, beginning with very small vapour densities, the quantity of sodium is gradually increased. The present communication deals only with the line D, in the case of very small densities. This line is resolved into a quadruplet by the action of the magnetic field. The grating employed for this investigation and its mounting for 1) Zeeman. Proc. Roy. Acad. Amsterdam Vol. V p. 41, 1902, cf. also Harro Dissertatie. Amsterdam, 1902, 2) Vorer. Göttinger Nachrichten. Heft 4. 1898; Wuiepemann’s Annalen. Bd. 67. p. 359, 1899. \%* - ( 20 ) / parallel light (which was necessary also now) have been described already more than once. *) The light from an arc-lamp or from the sun passed successively through a Nicols prism, whose plane of vibration was inclined at an angle of 45° to the horizon, the magnetic fieid with its lines of force normal to the beam, a second Nicol at right angles to the first. Between the Nicols the BABINET compensator was placed, the edges of the two prisms being horizontal. An image of the com- pensator was formed on the slit of the spectral apparatus; in the middle of this image the central dark interference fringe, surrounded by the coloured ones, was seen. In the spectrum a pair of dark interference fringes are observed and with the field off, only the fine absorption lines of the vapour are seen. Generally the reversed sodiumline is observed already in the spectrum of the arc-light itself and then the presence of sodium vapour between the poles makes of course no difference at all. In order to obtain the degree of sharpness of the interference fringes, necessary for this part of the investigation, we tried several compensators. Sufficient results were obtained with a Barner compensator of which the prisms had angles of about 50’, obtained from the firm Srrec & Revrer. The light passed the flame (a gas flame fed with oxygen) over a length of nearly 1*/, em. If the field had an intensity of about 23000 C.G.S. units, the quantity of sodium in the flame being very small, the image observed was very similar to that represented in Fig. 1. The latter is constructed with the aid of photographic negatives and of eye observations. The whole phenomenon is of course the magnetically broadened PD, line; moreover it depends very much on the quantity of sodium present. We did not yet succeed in getting negatives, which showed the parts which are of very unequal intensity all equally well. Already some time ago Prof. Vorer was so kind to inform one of us of the result, which according to his theory may be anticipated in the case of a quadruplet. This conclusion is easily arrived at, if the calculation be simplified by applying a certain approximation, the soundness of which cannot be judged a priori, because constants appear whose numerical value is not vet known. With this reservation the behaviour predicted 1) Zeewan Jc. and Arch. Néerl. (2) 5. 237. 1900. very delicate as it only extends to the region of dal Poon ( 21 ) ee ee by. theory is represented in Fig. 2. The dotted vertical lines are the four components of the qua- druplet. In comparing the figures 1 and 2 one must take into consideration, that in Fig. 2 is represented the shape of the fringes, which arise from a single horizontal band. In Fig. 1 in the central part of the field also occur parts, originating from fringes ose Uit lying above and under the middle. The vertical Fig. 2. medium line of Fig. 1 corresponds to the almost ever present absorption line due to the are light and is thus in no way connected with the phenomenon which occupies us. The agreement in the region between the two interior components of the quadruplet is undoubtedly of great importance. The whole form of the double curved line may certainly be regarded as a con- firmation of theory. How far the darker paris between the exterior components in the middle of Fig. 1 correspond to the U-shaped parts of Fig. 2 is at present not vet to be decided. Chemistry. — “The course of the melting-point-line of alloys.” (Third communication). By J. J. van Laar. (Communicated by Prof. H. W. Bakuuts RoozEBoom). I. I have shown in two papers (these proceedings Jan. 31 and March 28, 1903) that the expression (see the second paper): at (Ere) " 10 log (1—z) () very accurately represents the solidification temperatures of tin- amalgams. This equation may be derived from the general expressions for the molecular thermodynamic potentials of one of the two com- ponents in solid condition and in the fluid alloy. I also pointed out (in the first paper), that already the simple formula i eo Fit T, 6 ETS Nps RE nl qualitatively represents the course of the melting-point-line perfectly. This is simply done by not omitting the logarithmic function /og (1—v). Though it is a matter of course, that — log (l—r) can only be replaced by x, or at} + etc. in the case that w is very small, it ( 22 ) seems necessary to continually draw attention to this circumstance. Already in 1893 in his thesis for a doctor's degree: “De afwijkingen van de wetten voor verdunde oplossingen” Honpivus BorpiNGH used the function — log (1—w); also the correction term ex”, omitting however the denominator (1 + 77)’. Lu CHATELIER *) used the simple equation (2) in a somewhat modified form for the melting-point-curves of alloys. The way however in which he derived this equation is totally wrong *). Il. Many melting-point-curves show the same type as those of tin-amalgams; it may therefore be important to investigate, whether they also may be represented by formula (1). It must however be observed, that this formula is applicable only in the case that the solid phase does not form any mixed crystals. If the formula (1) does not hold good, this may therefore indicate the occurrence of mixed crystals in the solid phase, though it is of course also possible that other influences e.g. dissociating multiple molecules have caused the deviation. In 1897 Hrycock and NEVILLE j.a. made experiments on a great many alloys*). They found that the alloy sc/ver-/ead shows the type of tin-mercury paper). I have subjected the data relating to this point (comp. the tables of p. 37 and 39) to some numerical investigations. very accurately (comp. the figure on p. 59 of their The initial course is again nearly straight — up to about 20 atom procents of lead and this part yields for 4 the value 0,805. If we now use this value for the calculation of the quantities @ and 7 from the observations at lower temperature, we do not find constant values, as in the case of tin-mercury, but considerably different values according as we have calculated these constants at mean tem- peratures or at low temperatures. If we take the data for „0,63 and «0,80, or «2=0,63 and «—=0,96 (the eutectic point) as basis for our calculation, then we find in both cases: a=0,355 ; r=— 0,929. The following table may show how bad the agreement is, specially for the mean temperatures: 1) See ia, “Rapport etc.” (Paris, Gauthiers-Villars): La constitution des alliages métalliques par S. W. Roperrs-Ausren et A. SransrieLp. (1900), p. 24. 2) On different occasions I have pleaded already before for not omitting the function log (1—). (comp. ia. Zeitschr. für Phys. Ch. 15, p. 457 sequ. 1894). 3) Complete Freezing-Point Curves of Binary Alloys, containing Silver or Copper together with another metal (Phil. Trans. of the R. S. of Londen, Series A, Vol. 189 (1897), p. 25—69). #2 ( 23 ) SILVER-LEAD. ') 0 0.0052 0.0103 0.0154 0.0254 0.0364 0.0504 0.6733 0.1057 0.1360 0.1732 0.2156 0.2537 0.2949 0.3432 0.4038 0.4542 0.4966 0. 0.5851 *0 6312 0.6790 0.7042 0.7353 0.7692 #0. 8064 0.8333 5330 *0 9615 1) The values of « marked with al ao Via | 0 1.0000 0 1.0000 | 41.0000 | 959.4 | 959.4 0 0.00003) 4.0042 | 0 00001] 0.9966 | 41.0000! | 9540 | 9543 | — 0.3 | 0.00041) 4.0083 | 0.0000*| 0.9934 | 1.0000 | 948.9 | 949.0 | — 0.4 0.0002") 1.0125 | 0.00008) 0.9900 | 4.00009 | 9140 | 944.0 0 | 0.0006*| 1.0207 | 0.00023} 0 9835 | 1.0002 | 934.5} 9344 | + OA | 0.00139] 4.0296 | ¢.0004°| 0.9767 | 4.0005 | 924.3 | 924.4] — 0.4 | 0.00254} 1.0416 | 0.00099) 0.9675 | 1.0009 | 910.9} 910.4 | + 0.5 0.00537| 4.0613 | 0.0019} 0.9530 | 4.0020 | 890.3} 886.6 | + 3.7 0.01117] 4.0900 | 0.00397} 0 9324 | 1.0043 | 9624 | 953.4) 18.7 0.0185"| 4.4177 | 0.00657| 0.9136 | 1.0072 | 837.2 | 820.0 | 447.2 0.03000! 41.4531 | Q 01065] 0.8906 | 4.0120 | 808.4] 782.7 | 495.7 0.04648} 1.1955 | 0 01659} 0.8647 | 41.0191 | 777.2 | 74.6 | 435.6 0.0643°| 1.2356 | 0 0228°| 0.8448 | 41.0271 | 751.4] 710.0 | MA 0.08697} 1.2813 | 0.0308°| 0.8176 | 41.0378 | 725.0 | 684.1 | +40.9 0.4478 | 4.3385 | 0.04487] 0.7894 | 1.0530 | 696.3] 659.5 | +36 8 0.1631 | 1 4164 | 0.0579!| 0.7548 | 1.0767 | 663.4] 635.4 | +28.0 | 0.2063 | 4.4876 | 0.0732*| 0.7266 | 1.1007 | 638.5 | 619 3 | 4419.2 0.2466 | 1.5527 ; 0.08751; 0 7032 | 1.1244 | 619.4 | 606 2 | 412.9 0.2841 | 1.6131 | 0.1009 | 0.6836 | 4.1476 | 603.4 | 596.4 | + 7.3 0.3423 | 1.7083 | 0.4215 | 0.6558 | 41.1853 | 581.9} 580.8 | + 4.1 0.3984 | 4.8082 | 0.1444 | 0.6319 | 41.2238 | 563.4 | 563.0 | + 0.1* 0.4610 | 1.9149 | 0.1637 | 0.6073 | 1.2696 | 543.9] 548.3 | —44 0.4959 | 1.9808 | 0.1761 | 0.5946 | 1.2962 | 533.2) 536.9 | — 3.7 0.5407 | 2.0702 | 0.1920 | 0.5791 | 1.3316 | 519.5 | 523.6 | — 4.4 0.5917 | 2.4816 | 0.2101 | 0.4727 | 1.3735 | 503.0; 503.5 | — 2.5 beso) 2.3921 | 0.2309 | 0.5625 | 41.4944 | 482.5] 481.6 | + 0.9% on 9.4495 | 0.2465 | 0.5445 | 1.4635 | 465.1 | 460.6 | + 4.5 0.9245 | 3.6226 | 0.3282 | 0.5318 | 1.6943 | 303.2 | 303.3 | — 0.1* culation of the constants z and 7. asterics are those which are used for tne cal- Ki (24) Between «0,10 and «== 0,53 the agreement is decidedly bad; at. lower temperatures slightly better. It is striking that the value we find for @ is much too large, namely 0,355; for tin-mercury we found for @ only the value 0,0453. We will further investigate whether the value of @ which is calculated from the initial straight part of the melting-point-line, namely G—=0,805, is in agreement with the latent heat of solidification of pure silver. As Jo and as Person has found q, = 107,94 X 21,07 = 2274 Gr. kal., we should have for 0: 21232 Er == et 8 We have, however, found the much smaller value 0,805. This indicates the occurrence of mixed crystals already in the initial part of the melting-point curve, unless we assume, either that the value of Purson is about 1,35 times too small, or that the association of the lead, contained in the silver, is 1485: Ill. Let us discuss in the second place the melting-point curve of silver-tin. We conclude at once from the figure of Hrycock and Nevitie, that complications, mixed erystals for instance, must occur. For though the melting-point curve from 380 atom-procents tin upwards shows the normal typical course, the initial part, instead of being nearly straight, is strongly concave towards the side of silver, so that two inflection points occur, quite contrary to the course indicated by formula (4) or (2). It is accordingly impossible to determine the value of @ from the initial part of the curve. If we calculate 4, @ and 7 from three observations, for instance a = 0,48, «= 0,61 and « = 0,86, then we get with: T. = 961,5") + 273,2 = 1234,7 the following values (comp. the table of Hrycock and Nevinns, p. 40 and 41): 0 P= AD 32 a = OS =. pa — 0,277. 1) The value 959°.2 given by Heycock and Nevire has been augmented to 961°.5 on account of the accurate observations of HorBorN and Day (quoted in Z. f. Ph. Ch. 35, p. 490—491), from which appeared that pure silver, the air being excluded, so that no oxygen can be absorbed, has a higher melting point (961°.5) than silver containing oxygen (959°). We see that the value calculated for @ is considerably higher than the normal value 1,08 and that « is also again excessively high. In order to get a survey of the degree of the deviation from the theoretical course we will perform here the calculation of equation (1) with these values of 4, @ and x. (see table p. 26). This bad agreement does not improve considerably if we determine “, a and 7 from other values of, for instance from r—=0,30, +—0.61 and «0,93. For these values of x we find: Oe SIG : a — 0,474 ’ r= — 0,38, so @ has come somewhat nearer to 1,08 and « is also somewhat lower. It is true that the agreement for values of « below «#=0,30 has somewhat though not noticeably improved (A = — 70,3 for v=0,13 becomes now A= —55,7) but the agreement for values of « higher than #=0,30 is in general still worse. So we find for instance for w=0,47 for A the value =-+8,5, whilst in the above table we found A=+2,6, ete. IV. For completeness’ sake we shall draw attention to the two very short melting-point curves of lead-silver and tin-silver. We may easily calcuiate the quantities 7 from the data of the two eutectic points. As namely these lines may be considered to be straight, we find 4 immediately from We have for lead-silver : T= 327,64 273,2—600,8 ; 7—303,3-+273,2—576,5 ; «=—0,03854, therefore : 24,3 hence RT, 2X600,8 eo 1,095 Prrson found g, =5,369 X 206,9 =1111 Gr. cal. The agreement appears to be nearly perfect. From this follows that si/ver, solved in lead, occurs in it as atom, at least for small concentrations. As to the melting-point curve tin-silver we have for it: 7, = 232,14273,2—=505,3 ; 7—=221,7-+273,2—494,9 ; «—0,0885+. We find therefore : = 109% Gri cal; 10,4 0= mes 494.9X0,0385 0,546, and „5696 0 0 0 0 0.5145 0 0.5909 0 0 0.9245 ( 26 ) SILVER-TIN. 2672 4203 „5670 7019 „8808 3.0921 3.1796 3.5463 „0283 4, 4369 5.0557 5.8490 0.2858 > Sy ek (>) 1 ; [o ©) © | 0.7076 0.6884 0.6719 0.6582 0.6421 0.6255 0.6195 0.5977 0.5764 0.5824 | 0.5633 0.6269 0.5494 0.6638 | 0.5383 Sj ee ae £ a ES aa? (2 5 il =f Bl ¥ 0 0 | 4.0000} 0 | 4.0000} 4.0000 0.00459) 0.00002! 1.0068 | 0.00002) 0.9975 | 1.00002 0.01299) 0.00017, 1.0195 | 0.00012) 0.9928 | 4.0004 0.03058) 0.0009!) 1.0463 | 0.00067) 0.9831 | 4 0007 0.04842) 0 00234) 1.0739 | 0.00168) 0.9734 | 4.0017 ).08114) 0.00658) 4.1260 | 0.00473! 0.9555 | 1.0049 1394 | 0.01753] 1.2114 | 0.0125°| 0.9279 | 1.0136 A813 | 0.03957) 1.2978 | 0.02360) 0.9021 | 1.0262 9953 | 0.05075) 1.3801 | 0.0364°| 0.8791 | 4.0445 ).2633 | 0.06933) 4.4549 0.04978| 0 8595 | 4.0579 3095 | 0.0957°| 1.5514 | 0.06875] 0.8359 | 1.0898 3516 | 0.4236 | 1.6450 | 0.0887*| 0.8147 | 4.4089 3917 | 0.4534 | 1.7400 | 0.4401 | 0.7948 | 4.1385 0.4371 | 0.1914 | 1.8555 | 0.1372 | 0.7795 | 1.1776 4764 | 0.9970 | 4.9633 | 0 1680 | 0.7534 | 4.2164 5107 | 0.2608 | 2.0641 | 0.4873 | 0.7370 | 4.9544 5426 | 0.2044 | 21643 | 0 2114 | 0.7220 | 4.2998 4.3332 1.6849 1.8063 4.9412 2.0339 2.1411 2.2332 ( 27 ) 2X505,3 Gr nt = 0,546 Person found for the latent heat of solidification for tin 14,252 & 118,5 = 1689 Gr. cal. The difference is so small, that we may assume also here that the silver is present as atom also in tin. This conclusion is the more justified as Heycock and NrviLLE give for «: “somewhat smaller than 0,0385", from which follows that @ will be somewhat greater and gy Somewhat smaller, so that g, approaches still more to 1690. I draw attention to the fact, that the good agreement of the value for di found by PerSON justifies the conclusion that this value is really rather accurate, so that we must assume that the mercury (see my previous communication), solved in tin, is present in par- tially associated condition, the association amounting to about 1,5. It appeared namely that — when mercury did not occur in the solid phase, which consisted therefore exclusively of tin — the value of 0 was such, that it yielded g, = 2550. In order to make this value 1} times smaller, G must be augmented, i.e. « must be dimi- nished, and this can only be done by assuming association to the same amount. V. Let is now return to the question of the point of inflection on the melting-point curve. From: ie ax? 1 2 2 1—J@ log (1— 2) follows dT 1e 0 ax? 15 2aa ne nn ne 2 net 37 daz NSE (1474) N (1+7r2) therefore tiel A ap 0 20 an? = == -—l] i +- ie. dx? IN? (L— a)? \ NV (1+ ra)? fb Zac T, 2a(1—2re) N° 1—# (1+ 72)’ N (1-+,rz)‘ or eT ny Jk 2 0 29 ia ax? Aax(l—e) dz? oS | ( en \( + B m (1 + rin)? | os 2aN(1—2re) Fro)’ If a=0, this equation may be written: (3) ( 28 ) Emine en ae } as we have also found before (see p. 481 of my first communication), Whereas for a=O a point of inflection at z=0 (NV =1) was determined with the aid of the simple equation 20=1, or d=’/,, this condition becomes, in the case we are treating now, somewhat more intricate. If we equate namely the second number of equation (3) to zero, and further put #0, N==1, then we find: 0(20—1) + 2a=0, SO O—t01ta=0. We find therefore that a point of inflection occurs beyond z==0, always when OO TEA TD ver or a nd REN In the case of tin-mercury (see the second communication) we had J=0,396, and a=0,0453; therefore: 0,1568 — 0,1980 + 0,0453 = 0,0041. This value being positive, a point of inflection was to be expected between «=O and s=1. In fact a point of inflection was found at tdi. The equation (4) may also be derived in the following way with- out making use of equation (3). If we resolve equation (1) into a series according to 2, we get for small values of a: T=T7,(1— 6e#+ (6 —40+4+ a)x’...). The melting-point curve turns therefore at 2=O the concave side towards the ordinate «=O in the case that 0? — }0 +a<0; and as the curve approaches the ordinate «1 asymptotically, a point of inflection cannot occur. If on the other hand 6? — 30 + a> 0, then the conver side is turned towards the ordinate «=O and there- fore a point of inflection must necessarily occur between 2=0 ane vl, As @ can be +0 at the utmost, there must exist a value, which the abscissa of the point of inflection cannot exceed. This maximum value is found by equating the second member of equation (3) to zero, and 7 to © [N being equal to — @ log (1-—a)], so we find: it 2 ax? 4 ax (l—ex) leren IH) | + (La) (= log (1 — a) yi a) (1p re) | — 2alog(1—a)(1—2 rex) __ 0 (1-+-r x)‘ oe Only if a=0, this may simply be written: ( 29 ) 2 from which we find: #==0,865. If however « is not zero. then the equation — log (1-—x) = 2 transforms the above equation into the following one: —1=0, or — log (1—«) = 3, i da w(1—a)| 4 a (1 — 2nv) (eS (ltr)? fe (Vege) or INE es (lr), l—« which is only true, if if — —2 wv 1,156—2 r= == — = — 0,744. 2—w 2-—0,865 We happened to find exactly r — — 0,74 for tin-mercury, so — if O had been equal to oo — the point of inflection would have been found at 70,865. Negative values of @ (or q,) are required in order to find a point of inflection between that value of x, for which we find the point of inflection with G—=o , and v—=1. These negative values will occur very seldom, if at all. The principle result of the above investigation is therefore that the melting-point curve — the case of mixed crystals being excluded — will show a point of inflection if 6G?>—t0+a>0, : BL, Crt or, Ô being equal to —— and a to —, if Jo Jo Tok het En ——2RkT,+ a, > 0, do Eet 2RT, Yo PEN di 20, RE As fk, expressed in Gr. Cal, amounts to 2, the condition may finally be written : EE) kes rf where g, represents the latent heat (in Gr. Cal.) of the metal, which is deposited in solid condition, 7, the absolute melting temperature a, b,? — 2a,,b,b,+ a, b,? — P; N ACE m \ as 1 and a, = ug, = — Ei , also expressed in Gr. Cal. 1 ( 30 ) Cah. (Lr)? out pro molecule when an infinitely small quantity of the pure molten metal is mixed with the fluid metal mixture, the quantity a,x? will represent that same quantity of heat for «= 0. We must here notice that the accurate values of O and q, must be used, as well in equation (4) as in (5). So in the case of tin- mercury for instance @G—0,396 is accurate only if the mercury is solved into the tin as atom. If this is not the case and in the example mentioned we have every reasou to suppose that the mercury As the quantity represents in general the heat, which is given is associated to an amount of 1,5 — then @ must undergo a propor- tional increase. O was namely calculated Fom Sn If we apply the condition in the form (5), then we must substitute the erpert- mentally determined value of the latent heat for q. So in the case of tin-mercury @ will not be equal to 0,4 but in reality to 0,6, and therefore 6? — 50 + «== 0,36 — 0,30 + 0,04—0,10, from which the existence of a point of inflection appears still clearer than in the supposition @ = 0,4. If we apply condition (5), @, being equal to 0,0453>1690=77 Gr. Cal’, we have certainly 1700 oe If «, is positive, as is the general case, then the simple condition Vo cg A 1 a will include condition (5). This latter form therefore will provide us in nearly all cases with a reliable criterion whether or not a point of inflection occurs in the melting-point curve. Physiology. — “On the epithelium of the surface of the stomach.” By Dr. M. C. Drexnuyzen and Mr. P. Vermaat. Veterinary surgeon. (Communicated by Prof. C. A. PEKELHARING). We are accustomed to regard the stomach in the very first place as an organ for the digestion of food, for the preparation of the gastric juice. About its power of resorption its not so much is known. Glucose, peptones, strychnin, alcohol, dissolved in or diluted with water, are resorbed by the gastric mucous membrane. The rapidity of resorption is different in various kinds of animals. The structure of the cells which a line the mucous membrane seem to point to seeretion of mucus more particularly than to resorption. The fact is that their peripheral portion readily undergoes a radical change, whereby it swells and is expelled as a lump of gastric mucus. Unless the utmost speed presides at the fixation of the gastrie mucous membrane from any animal, the epithelium cells, which are still living but insufficiently fed, undergo intense changes when coming in contact with the by no means indifferent gastric juice. Until lately the epithelium cells of the stomach were thought by many to be open mucus cells, a kind of cylindrical goblet cells, because the above mentioned peripheral part, the so called “Lump of BrrDERMANN” ') had disappeared and only the cell-walls, which were more resistant, were left. Improved means of fixation and chiefly also the fact that histologists have gradually been brought to see the necessity ofa speedy fixation of perfectly fresh material, have been the cause that at least the open epithelium cell of the stomach has been acknowledged to be an artefact and it has been generally adopted that those cells are closed at their peripheral extremity by a smooth, convex boundary layer *). Starting from the supposition that microscopical investigation might bring to light something about the resorbing qualities, when the perfectly fresh gastric mucous membrane, is treated very rapidly with favorabie means of fixation, a few young mammals and also older ones, which received milk along with their food, were killed by a single stroke on the head and the stomach was extracted without delay, turned inside out and immediately immersed into FreMMING’s well-known mixture of °/, pCt. chromic acid, 5 pCt. acetic acid and ?/, pCt. osmiumtetroxid. White rats and mice (full grown), a rabbit of 38, one of 15 days and one rabbit of 24 days hourished with milk, were taken for the experiments. It now become evident that a comparatively small number of the epithelium-cells of the surface of the stomach contained small drops of fat: at least fine globules, which were colored black with OsO, and agreed perfectly in size and appearance with those, which were visible in great numbers in the gastric contents, which had stuck to the mucous membrane in different places of the section. The surface of such gastric cells was not smooth either, but covered with a differentiation which resembled the striated border of the fatresorbing epithelium-cells of the intestine. 1) W. BieperMann. Sitzungsberichte der Wiener Ak -d. d. Wiss. Mathem. naturw. Klasse. 71 Bd. S. 377. 1875. 2,K. W. Zimmermann. Beilriige zur Kenntniss einiger Drüsen und Epithelien. Arch. f. mikrosk. Anatomie. Bd. 52. 1898. S. 552. ( 32 ) In the rabbit and the mouse small differentiations of the mucous membrane occur between the orifices of the pyloric glands as well as between those of the fundus glands, to which no better name could be given than that of villi of the stomach: slightly prominent, blunt elevations, rich in blood-capillaries and supported by a meshwork of connective adenoid tissue, but in which nothing of a central chyle-vessel, nor of smooth muscle-fibres could be detected. They were clothed with a single layer of cylindric epithelium, of which the cells, situated on or in the neighbourhood of the upper part of such a gastric villus carried outside of the above-mentioned boundary layer of the modern histologists, an outer limb, which seemed to consist of closely packed fibrils, probably cell-processes. Each cell has its own apparatus; at the edges of the cells, where the ‘“Schlussleisten’” lie between the cells, the fibrils are wanting. Tangential sections of the upper part of those epithelium-cells of the stomach (sections of 1 u were studied) showed finely speckled pentagonal and hexagonal figures, separated by pretty wide furrows. They were stained violet with diluted Rrssert’s phosphormolybdenous hematein. The length of these bundles of cell-filaments is rather different in the various cells, but for one single cell pretty regular; they form externally gently convex lines; each cell is, as it were lined with a dome-shaped rather thick covering. There is not the least doubt that we have not to deal with adhesive gastric contents. These lie on these dome-shaped elevations and are separated from it by a small interstice, which was probably originally caused by shrinking during the process (alcohol, carbondisulphide, paraffine, etc.) The different “outer limbs” of the cells may be grouped between two extremes: on the one side the extended cell-processes are seen to diverge more or less, best to be compared to a short brush with diverging hairs; on the other side we notice the pseudopodia drawn in, settled like stiff little hairs on the cell “membrane”, and then such an outer limb resembles the well-known striated border of the resorb- ing epithelium-cells, or expressed in a more neutral expression: the surface-epithelium of the intestine. These epithelium-cells of the stomach with outer limbs now show in the preparations a peculiarity at their base which has been noticed and photographed by Cartier’), but the reality of which has been doubted amongst others, by Von EBNER in KOLLIKER’s IE. W. Caruter. On intercellular bridges in columnar epithelium. La Cellule, XI. p. 263. 1896. (33 ) handbook *). Tangential cuttings of 1 u of the basal extremities of the cells show us a picture, which agrees in high degree with the intracellular little bridges which may be seen to diverge in thin sections between the smooth musclecells (also in our preparations of the gastric wall). In other words the aspect reminds one of that of the riffeells in the rete malpighii. If it be taken for granted that all this is preformed, then the opinion of Carrier could be accepted that the epithelium-cells of the surface of the stomach are conie with their points turned towards the stroma of the cellular tissue, that they are mutually connected through fine cell-filaments, between which an extensive system of duets to convey the juices might be supposed to be present ‘Saftkanalchen”. On good grounds however histologists somewhat hesitate to accept the preformation of such structures. They might be post-mortal strinking phenomena, or perhaps contrac- tions during agony, or both. However this may be, it is a fact that we have „ot observed them in the intestinal villi of the duodenum of the same animals; the epitheliumeells there were cilindrical, they firmly closed together at their basis and had a distinct low striated border. Never could these two kinds of cells: the resorbing epitheliumeells of the stomach and those of the duodenum be mistaken for one another; but they have some resemblance. The differentiations : the outer limbs and the striated border are probably nothing else but variations of one and the same cellorgan, which we meet with to a large extent in the intestine? of invertebrate and vertebrate animals: a lining, which in the case of Ascaris megalocephala, shows the most striking resemblance to a ciliated lining, but in which we could wot notice the slightest motion, though we worked under the most favorable circumstances and had quite fresh animals, which moved about intensely. Also in man Zim- MERMANN (le. fig. 37) has represented the striated border of the cells of the colon, which bore cellprocesses strikingly resembling cilia, but not considered by him as such either. We are of opinion that the intestinal cells and at least some cells of the surface of the stomach, possess the power to send out a great number of cell-filaments, which stand closely together when the striated border is contracted and when the cellfilaments have their minimumleneth, but which can also be extended and are then enabled to diverge. The different heights of the striated border may also be seen in intestinal epithelium cells. The outer limbs of the epithelium-cells of the stomach are evidently vulnerable differentiations. In some parts of our preparations 1) A. Körumker's Handbuch der Gewebelehre des Menschen. Ge Aull. IIL. 1. S. 155. 3 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 34 ) some of them have been couverted into a homogenous hyaline mass, with distinet inward and outward boundary. Not that the external portions had become hyaline bubbles, their shape seemed little changed, but they were in a way “verquollen” as the German histologists say. We must refrain from expressing an opinion whether these outer limbs are present in all epitheliumeells or not. It is quite possible that they are much more widely spread than we suspect and that they are frequently destroyed by imperfect fixation. Manipulating correctly and applying the same methods, we were not successful in obtaining a view of them on the surface of the stomach of a small suckling eat. In studying the literature of the subject, we have found out that at the early date of 1856 a man of KOLLIkER’s importance has seen globules of fat in the epitheliumeells of fresh gastric mucous mem- branes of young cats, dogs and mice. KOLLIKER Communicated on the 28% of June 1856 to the Würzburger phystkalisch-medicinische Gesell- schaft (VIL p. 175) in a small paper entitled: “Einige Bemerkungen über die Resorption des Fettes im Darme, über das Vorkommen einer physiologischen Fettleber bei jungen Saugethieren und über die Function der Milz” that in his opinion he had seen globules of fat and also rather distinct indications of pores. With these pores he meant the openings in the “Porenmembran’, the sieve-shaped, pierced, thickened wall of the cell, which we now call ‘striated border.” As far as we know no attention has been paid to this communi- cation of KOLLIKER’s, except by OGxew (Biologischer Centralblatt XII, S. 689, 1892) who has also seen the structures of Carnumr. To our mind it is indisputable that thestomach can resorb fat from the food, although it be in small quantities and it is also probable that this excellent naturalist has been able to discern with simple means, What cannot, with the methods of the present time, be effected without difficulty : namely to point out the striated border-shaped outer limbs of the stomach cells. Physiology. — “On the liberation of trypsin from trypsin-zymogen.” By Dr. E. Hexma. (Communicated by Prof H. J. HAMBURGER). I. On the influence of acids on the liberation of trypsin from trypsinogen. As is well-known, trypsin, the proteolytic digestive ferment of the pancreas, does not appear as such in this gland, but in the form of an inactive precedent stage, which Hermrnnar, to whom we owe this discovery ') has named “zymogen”: 1) R. Hemennariy, Beiträge zur Kenntniss des Pankreas. Prrücers Archiv 1875, pag. 557. ( 35 ) As besides trypsin, other enzymes have come to our knowledge which are also secreted when in a preliminary stage, it is preferable, as is frequently done now, not to speak here of “zymogen”, but of “trypsinogen” or “protrypsin”’. From the very beginning the question arises whether the liberation of the ferment takes place in the gland or in the intestine. Accor- ding to researches made by Camus and Grrr ') and Dermzerxe *), the latter is usually the case; according to Popiiski*) always. Then the second question arises: In what way does the Miberation in the intestine take place? Until a few years ago this liberating action was solely ascribed to the acid of the gastric juice. Influenced by researches made in Pawrow’s laboratory, attention has of late been drawn to the intestinal juice *). As there appeared to be two ways that might effect the liberation of trypsin, it was important to know, what relative value could be ascribed to each of them. I have therefore made the action of acids, amongst others also of hydrochloric acid, a subject of close investigation. Tracing the communications in literature in respect to the influence of acids on the liberation of trypsin, one is always being directed to the publication of R. HurpeNHaiN, just mentioned. When we examine these writings we find that scarcely a page has been dedicated to this problem. Only the method, by means of which HuripeNHAIN has obtained the result, is shortly referred to, positive experiments are not described however. He only mentions, that, when he had arrived at the end of his investigations, he found that glycerine-eatracts from pancreassubstance operate much more effectively when the gland- substance is mined with acetic. acid, before glycerine is added ; an observation which never failed in any of the cases when he applied this method. When a man like Hemennais publishes his observations, we have to take them into account, even although the experiments are not published along with them. In different text- and handbooks and monographs, we find related that acids possess the power to effect 1) Camus and Grey; Devezenne. UC. R. Soc. de Biol. LIV. (1902). 2) L. Popterski, Ueber die Grundeigenschaften des Pankreassaftes. Gentralbl, fiir Physiol. 9 Mai 1903. 5) N. P. Scuerowatnikow, Diss. Petersburg 1899; Pawrow, Das Experiment. Wiesbaden 1900, p. 15; Warruer, Archives Ital. de Biol. 1901. H. J. Haweurcer and B, Hexma, “On intestinal juice of man.” Report Royal Academy of Sciences 1902, p. 713. ( 36 ) the transformation of trypsinogen into trypsin, resp. of promoting it *). T have been perfeetly able to confirm HumeruaiN’s iivestigations, but systematic researches have shown me, that they are only available for ylycerine-eatracts from the gland, but in no wise for watery extracts or for the pressed out juice of the pancreas. From the great number of experiments which I have made to this end, and which always led to the same results, I shall state here a single series. First a repetition of HrIDENHAIN’s experiment. The method which HipENHAIN indicates is as follows: To every gram of pancreassubstance, which has been cut into small pieces and subjected to pressure, is added 1 ¢.c. acetic acid of I"/,. The mass is again rubbed for 10 minutes, and the thus obtained compound then mixed with 10 grams of glycerine. After 3 days this compound is filtered. 1 now composed a glycerine-extract according to this prescription and, along with this, other glveerine-extracts whereby instead of Lee. acetic acid of 1°/,, I took respectively 1 ¢.c. acetic acid of 2°/, °/,, 1 ce. acetic acid of 0.5 °/, and 1. eze.” water: The hereby obtained extracts | allowed to act on white of egg without water (Col. HD) and also after addition of water (Column IIT) *). It is seen that where the glycerin-extracts of Col. I are brought to act on white of egg no digestion appears after 3 days (Col. ID). This had to be expected. Even if trypsin had been set free, it could not have worked actively in the pure glycerine; for it is well-known that trypsin is not soluble in pure glycerine. Trypsin is liberated however when the glycerine-extracts are diluted with water (Col. IL) and more so with those extracts which are composed with acetic acid (1, 2, 3) than in those where ordinary water was used 4). The acetic acid therefore furthers the liberation of the trypsin in glvcerin- mixtures with water. A proportion between the concentration of the acetic acid and the extent of its operative power, does not exist however. It could now be suggested that the trypsin from Col. 1 in Table T, which was at first inactive being in an indissoluble condition, now 1) T only mention here: Hammarsrey, Lehrbuch der physiol. Chemie, 1899. 4er Druck, pag. 295. A. Gaxere, (Deutsche Ausgabe von AsHer und Bryer), Die Physiol. Chemie der Verdauung. 1897, pag. 231. C. Oprenueimer, Die Fermente und ihre Wirkungen, 1900. p. 74 and 116. 2) For the quantitative determination of the proteolytic digestion the method of Merr was followed. The experiments were only made with pig’s pancreas. The temperature ot the incubetor varied from 37 to 39° CG. (37) TABLE I. i Il. UL — _ Millimeters of Millimeters of white of ege | white of ega | consumed after addition ot | „ee. water on 1 cc, extract, consumed, | after the first 3 days, er ern Se | 2 | After 3 days. | After the following 3 days. 4.50 + 4.70 1). Pancreas substance 1 gram | 9 Acetic acid of 19/, 1 c.c. eG: 0 4 1.70 + 4.80 Glycerin 10) e.o. 2). Pancreas substance 1 gram | A.M) +. 4.60 Acetic acid of 21/,°/)1 c.c. wes 0 18.30 4.70 + 4.60 Glycerin dee. 3). Pancreas substance 1 gram | 4.80 + 5 Acetic acid of 0,5% 1 c.c. me 0 19.70 4.90 +5 Glycerin 40% ce: 4). Pancreas substance 1 gram 2.10 + 2.80 Water BEEN LCE 0 8.50 2.20 + 2.80 Glycerin 10%-c.c. became active because of the addition of water. Table IL shows however that in the original glycerin-extract, not diluted with water, no trypsin whatever was present. In the experiments mentioned in Table II, a Na,CO, sol. of 1.2°/, has namely been added to the glycerin-extracts. If indeed trypsin had been set free, we might here have expected digestion of white of egg. The trypsin operates very effectively in presence of Na, CO, Ori .2°/. : trypsinogen into trypsin; a fact, already proved by Hriprnnai and which I have taken advantage of in all my experiments to prove, whether in certain cases I had to deal with material containing whereas the latter entirely prevents the transformation of trypsin or trypsinogen. From these figures we notice that 1 ce. acetic acid in concen- trations of resp. 1, 2'/, and 0.5°/, has not the power, just like I ce. water, to liberate trypsin from 1 gram of pancreas substance in the TABLE II. | Millimeters of white | of egg consumed. After Sdays After 6davs 1). Pancreas substance 1 gram | Acetic acid of 40/, 1 cc. an Na,CO, opl. v. 4.2%, | 0 0» Glycerin 10 ce. 2). Pancreas substance 1 gram Acetic acid of 2'/,% 1 ec. 7 3ec.4-42ce. Nas CO, opl. v.1.2%/4 | 0 0 Glycerin 40 ec. 3). Pancreas substance 1 gram Acetic acid of 0,5 9/91 ce. 3ec.4+-12cc, Na, CO, opl. v. 1.2% 0 0 Glycerin 10 ec. 4). Pancreas substance 1 gram { Water 1 ee. [7 3ce.4+12ce, Na CO, opl. v.1.2P/, 0 | 0 Glycerin 10 ce. | time (mentioned by HerpeNHAIN), during whieh these liquids had come into contact with the pancreas substance, before glycerin was added?) It is however possible, as has been proved from Table I, to liberate trypsin from the glycerin-ertracts: by means of water, after having been brought into contact with it for a lengthened period and this process is aided by acetic acid being present. But the action of acetic acid is only of indirect nature, # only seems to neutralize in some degree the unfavourable action which glycerin everts on the liberation of trypsin. Then | thought, if this be the case, the favorable action of the acetic acid must fail to be effective in watery extracts and pressed out juice of the pancreas. This proved to be true, as table TIT and IV will show. 1) It should be observed that | ee. acetic acid, resp. water and 1 gram pan- greas substance only give the relative proportions. In reality 5 ec. liquid on 5 grams pancreas substance was always taken and of course 50 ce. glycerin. ( 39 ) TABLE IIL. —_— | | | | . | sd After 18 hours. After 40 hours. | Fresh Pane. juice. eB a ‘ fe ee i ce ———————— eaction Reaction, re | ners | bat | | Millimeters of Rear teaction Millimeters of | ops. | litmus- | litmus-| white of egg | litmus- | white of ege | | |. consume ham Sere eRe a | | paper. | paper. | consumed. | paper | consumed, Rees 7 i Al Sa EN ck ae fresh P.juice Jee. acetic acid2'/,"\y acid acid 0 acid 0 | | | | 9 » +5 GC: » 4 ap » | » | () ») () | » +5 GCs » 0.5 Oy » ph 1 | ) | 0 | | | » +5 ce. > 0,4 9, » » 0 » 0 » ) GC, » 0.050 | » 0 Ran aw 1.104 )4 y) +5 Di er | weak ac. 4. Tae 29)" (0 4 | | | | » +See, water neutral neutral 0 ‘weak alk, eae 20520 { | | , = Sean DE xa iG oa | … 1.204.140) : ) 5 ce. Na,CO* sol. 0.19, | alkaline | alkaline | Sikalines \ + EN s /o | kaline aline | ) | hating 120-410) ‚60 | | | | 5 Erco | | | ») +5ce. ) 0.5 ifs N ) 0 =. 0.100. 10) 50 | | | | 0) ) | » + 5 CG. » 4| 0 0! » » | 0 » | () | | | I » + 5 ee, » 1 0/9 » » | 0) | » Q | » +5ee, » 9 wR | » | » () » () | | | » -f Bee. D) 3 gn | » ) 0 ») 0 | | » + See. Extract from the 90-44 80 oe WAO | intestinal mucosa!) neutr: al weak: alk. ri 7.30 ‘weakalk. ai MG 10 | 1 SI, 80)” LAH j) | | Table HI shows us, that when a few drops of fresh, pressed out pancreas juice, which according to fig. 9, 10, 11 and 12 contained no trypsin, are mixed with acetic acid of 2'/,, 1, 0.5 and 0.1 °/,, there is no digestion of white of egg. But when the acetic acid is used more diluted, viz. 0.05, then after a long time, formation of trypsin takes place, but not to a greater extent than when water is taken instead of acetic acid. It could now be supposed that the trypsin would, under the influence of the acetie acid be liberated, but could not operate actively in the present acid reaction. Table IV shows that this is partly the case. For when an old pancreas is taken, in which according to 9, 1) Extract from the intestinal mucosa may be used for the liberation of trypsin instead of the natural intestinal juice, In a following communication we expect to treat this subject more fully. ( 40°) TABLE IV. | Directly. After 18 hours. | After 40 hours. Juice of a pancreas which has been ex- | | | posed for 24 hours to room-temperature. Reaction Reaction Mütmeterssof Reaction millimeteren ess aes litmus- | litmus- | white of egg — litmus-' white of egg wo drops. | SE ‘ ] | paper. | paper. | consumed, | paper. | consumed. | | | 1 | old P juice +5 ec.aceticacid 21/5/, | acid | acid 0 | acid | 0 9 D) + 5 ec. » 4 9% Ly | » 0 | » { 0 3 » -+ 5 CC. D) Os A > | » 0 | » 0 | | Cad ce 11.30-41.30) - Ee 4 » +5 ce. » Ot | » » 4 yay 40) 540 | » ae 12 | | | 4 3 > 5 » + 5 ce. » O05) AF > » : ee f 40) © „80 werk ac. 3. 3013.90) 13:20 | | | ) 6 » + water | neutral ‚weakalk. ott. ie 7.90 ‘weak alk. ee $0) > | | 7 » +5 ee. Na,Co,sol.0.1"/, | alkaline | alkaline | HA 60) 6.20 | alkaline ines 90) 12.10 | | z 3 | 5 Te 999. 8 pe eee. Yes 05, | > | > iols0® » 3971389) 41.90 } j | | | | 2 j | 3) 4.3 MS 9G 6) 7 Eig bt aN ee ee, On ee Velt be 450: 302 40 | » 2 34) 10.60 | | | | 5 : 149 | 9. A D4 Div ee oa o> SO ein la ee | : oa 0.90-0.9)) | 1042 Yo, » 4 1c » 9 0 | » » € » ni 45 ce. aa, | Faa 590 | > Maolasopnn | | | & Kn Saree | 0504050). | 141.20) , - 12 | + CG: » 3 whe » | » Wao a ) ) )) AAOLI WW) 4.50 | 9 / ) ) 43 | ) + 5ee. Extract fromthe neutral weakalk. 5 dono oe 10.10 weakalk. HRE one 17.10 intestinal mucosa ) gee 10, AL and 12 free trypsin is found and according to Table HI, acetic acid has been added of 2'/,, 1 and 0.5 ,/°, there is no action whatever. The acid in these concentrations prevents the trypsin from acting. When however acetic acid of 0.1 °/, is used, then the action of the trypsin is not neutralized as is shown in Table 4, fig. 4. Therefore in fig. 4, Table IH, the Liberation of trypsin must have been prevented hy acetic acid of OA"/,. Moreover Table HI] teaches us that in no single case digestion of white of egg was obtained with fresh panereasjuice after 18 hours, except in fig. 15. Hereby is clearly shown that water and acetic acid of 0.05 °/, are far behind intestinal MUCOSA, ( 41) their influence of liberating trypsin from trypsinogen. resp. intestinal juice, with regard to Equal results as with acetic acid were obtained with Aydrochloric acid, lactic appear from the following summary. TABLE V. acid and butyric acid. For hydrochloric acid this may After having been allowed to stand for Kat AA hours in the ineu- | Millimeters of white of egg hator, so much of a | Na, CO, sol.was added Fresh pancreasjuice, two drops. consumed, to 6and 7, until the proportion of the Na, CO, amounted to if aw ie about 1 Jp. | Digest. of white egg After 17 hours. ; After 41 hours. afte ronce more 3 ec. HCI 0.02"), %o. 0 Volant ES {60 E ‘ ‘ ~ 1.70+1.60 } — 5) » +3 ee. HCL 0.05 ". 0 | 16K an, 60 {6.50 6) > + 3 cc, HCI 0.1 %o. 0 | 0 0 7) » + 3 ee. HCI 0.5%, 0 | 0 0 These figures show that hydrochloric acid extremely weak con- centrations (0.02'/, and 0.05 °/,) does not hinder the trypsin from free. The effect stronger concentrations of hydrochloric acid (O.1 °/,, favourable however. Somewhat EN 0 That no trypsin has been set free being set Is not prevent the liberation of trypsin entirely. in 6 and 7, the action of which may have been prevented by the has been proved from the fact that no digestion 2 24 hours, had been added to the liquids named hydrochloric acid, of white of egg had occurred, even after When after 41 hours a solution of Na, CO, in 6 and 7, until the proportion of Na, CO, amounted to circa 1 */, From these researches we may with certainty draw the following conclusions. 1) HerpeENHAIN's opinion, which has been current since 1875 and ( 42 ) widely accepted, as if acids could have the power of liberating trypsin from trypsinogen is not correct; on the contrary, they prevent this liberation. 2) That Hrmernnars came to this conclusion must be ascribed to the accidental occurrence, that instead of using the pressed out juice or watery extracts of the pancreas, he had taken glycerin-extracts from the gland. The favorable action caused by the presence of acetic acid in his experiments and which I have been able to confirm, is to be ascribed to the fact that acetic acid decreases the injurious action of the glycerin on the liberation. 3) As it has now been proved that the gastric juice does in no wise further the liberation of trypsin, but rather Opposes it, we may therefore draw the conclusion, that in this process of liberation all the work falls to the intestinal juice; a fact stil increasing in im- portance where the investigations of PopIELSkKI hare proved, that no Sree trypsin whatever appears m the pancreassecreta, hut that it is only there in the shape of trypsinogen. Having arrived at the end of my communication, I beg Prof. HAMBURGER to accept my warm thanks for the opportunity afforded to me to make these researches and also for the useful hints kindly given to me. Physiological laboratory of the State University at Groningen. May 1903. Physics. — “Some remarks on the reversibility of molecular motions.” sy Dr. A. PANNEKOEK. (Communicated by Prof. H. A. Lorentz). 1. The following considerations deal chiefly with the question whether a mechanical explanation of nature is possible. Mechanics treat the motion of discrete particles or of continuous masses; now the question may be raised, whether all natural phenomena can be explained by means of such a motion. In other words, it is the question, whether or no we know particular properties of these pheno- mena, which exclude the possibility of a mechanical explanation of general application. A particular property which seems to do so, is the irreversibility of the natural phenomena, the change in a definite direction. When investigating whether this is really the case, we need only consider the simplest form in which the irreversibility of natural phenomena occurs: the second law of the mechanical theory of heat. > ee ( 43 3 Poincaré says about this in his “Thermodynamique’, that it entirely excludes the possibility of a mechanical explanation of the universe. The motions of which mechanics treat, are all reversible: there occur only forces which depend on place, so relations between the Ot and the 2ed derivative according to time; if the sien of fis reversed, these equations retain their validity. It is true that in mechanics also cases are treated in which the first derivative according to / occurs in the equations (friction); we are, however, justified in calling these cases not purely mechanic, because in them heat is produced, so that in a complete explanation we must introduce considerations (thermodynamic ones), which we are just trying to solve in purely mechanic ones. It is therefore desirable to call only those cases purely mechanic which are reversible; these only are conservative. In the above-mentioned not purely mechanic cases there is dissipation of energy, so that, the law for the conservation of energy being a general law of nature, a mechanical description of them is not com- plete. The kinetic theory of gases shows us that this deseription only mentions the visible motions in the system, but not the molecular motion, which is required to make the description complete. The word mechanic, occurring in the question raised in the beginning must therefore be interpreted in such a way that we consider only ‘ases Of conservative systems as purely mechanic. The question whether the irreversibility of the natural phenomena decisively exclides a mechanical explanation, must be answered in the negative, when we succeed in giving a mechanical description of one typical and simple irreversible process, or in other words, if we can point out im a certain case that a process consisting of purely mechanic, so reversible motions, is irreversible. We must then at the same time get an insight into the question, how it is in general possible, that a process in its general character can be so different from that of the partial processes of which it consists. 2. BoitzMann has shown that we meet with such a case, though an abstract one, when we have a perfect gas, consisting of perfectly elastic spheres, between which no other forces act than those even- tuating in collisions between two particles. He proved that the fune- tion H=f flog fd, in which fd is the number of the molecules whose points of velocity lie in the volume element dw of the velocity diagram *), can only be made smaller, never greater by the collisions. l) The “velocity diagram” is obtained by representing the velocity of every molecule by a vector drawn from a fixed point. This vector ends in the “point of velocity” of this molecule. (44) As this function taken with the reversed sign, expresses at the same time the logarithm of the “probability” of a certain distribution of the velocities, BoLtTZzMANN expresses his result also under the following form: the effect of the collisions is that a gas always gets from a more improbable to a more probable condition, Here we have therefore a process, consisting of purely mechanic partial processes, which shows change in one direction only. That however BOrTZMANN’s Considerations have not yet led to a perfectly satisfactory insight, and that this contrast is felt as a contradiction, is proved by the objections and doubts, which have been adduced against these considerations without refuting them. Let us assume a fictitious system in which at the moment ¢, all the places are the same, but all the velocities exactly the opposite of those of the real system. The two systems can represent a gas in exactly the same way, there being no possibility of seeing which is the real and which the ficti- tious one. Yet the fictitious one will successively pass through all the conditions through which the natural one has passed before the time f,, in reverse order; all the collisions take place in opposite direction, and the system gets from a “more probable” to a “more improbable” condition. BOLTZMANN denies that this involves a contradiction, for the fictitious system is “moleeular-geordnet” That this remark does not solve the difficulty (Brintovurs, among others, expressed doubts as to this in a note in the French translation of BourZMANN’s Vorlesungen) must be ascribed to the fact, that the ideas “ordened’” and ““unordened” for molecular motions are difficult to define sharply. Sometimes ordened is interpreted as if it meant that in the fictitious system to every molecule its future course is accurately prescribed. This however is not satisfactory. If we know at the moment f, the places and velo- cities of the natural system, we are enabled to determine beforehand, so to prescribe, the future course for the natural and for the fictitious system and for both in exactly the same way. The fact that the motions in the fictitious system are ordened can be better pointed out by means of the following consideration. If we take two groups of molecules with the points of velocity ?, and P', which come into collision, then after the collision the points of Ee velocity Q, and Q,', B, and &,' ete, will all lie on a sphere ot which the line P,P,’ is a diameter. The places of Q, R,....on the sphere depend on the direction of the planes of coilision A, B,....; to every plane of collision belongs a definite place of the points of velocity and the latter are scattered all over the sphere, because the former have all kinds of directions. If we now take the reversed, ( 45 ) fictitious system, all these points of velocity come back in P,P,', because definite planes of collision a1,.... belong to every pair of points of velocity Q,Q,'.... The fictitious system, therefore, is sub- jected to the condition, that molecules with definite points of velocity do not collide according to arbitrarily chosen planes or to planes whose direction is determined by chance, but according to planes which are entirely determined by the position of these points of velo- city. This condition may be called an ordening of the motions. We must, however, add another remark. In the natural system we had not only points of velocity in P,/,', but also at the ends of the other diameters of the sphere P,P', PP... ete. and these too can reach the same points Q,Q,' as P,P,', if only the planes of collision have every time the required direction different from A. Of all the points of velocity and planes of collision we have just now chosen and considered separately all those which in the natural system lie before, in the fictitious system after the collisions in P, 2’. We might, however, just as well have chosen and considered separately those which in the natural system lie after, in the fictitious system before the collision in Q,Q,'; in this case we might have been inclined, to call the fictitious system unordened, and the natural system ordened. The difference between the two would of course become clear, when we paid attention to the „ember of collisions which cause the points of velocity to pass from PP, to Q,Q)', R,R,' etc. or vice versa. In reality the collisions in the natural system have a scattering effect, through which the distribution of the points of velocity over the sphere is more regular and arbitrary after impact than before. In this respect there is a real difference between the natural and the fictitious system, that in the former the distribution before the collision is more irre- gular, less accidental. The difference between being ordened and unordened in the molecular motions in the two systems appears here as a difference in the degree of the ordening. It seems to me that though we cannot bring forward conclusive objections against the denomination used by BoitzMann, yet further considerations which throw some light on these phenomena, might be of some value. 3. The ordening of the motions, in which the difference between the natural and the fictitious system consists, can only be clear, when, as in the kinetic theory of gases, we examine larger masses and mean values, in which the coordinates and velocities are considered as fluently varying quantities. When we take the particles separately, in Which the coordinates and velocities are perfectly defined, the ( 46 ) difference between a natural and a fictitious system does not appear, and the process can only be taken as perfectly reversible. The result of each of the steps of which the whole process is built up (free path + collision), is determined 1st by the coordinates and velocities, 2ud by the direction of the normal to the collision plane. Im the statistical method of treatment of the kinetic theory of gases the latter is considered as an independent datum, which therefore is thought to be defined by chance; we may then give it different values, which are distributed according to chance, i.e. regularly, and in this way the scattering, regulating effect of the collisions appears, which is the cause of the irreversibility of the process. In the purely mechanic conception, in which we must take the condition of every separate particle as rigorously defined, the direction of the normal is no independent datum; in reality this direction is accurately defined by the coordinates and the velocities of the colliding particles. Here the result is therefore determined by the coordinates and the velocities only and according to this way of considering the question, the process must be considered to be reversible. The question how it is possible that a process may be considered in two ways, so totally different comes therefore to the same as the question, how quantities which in reality are rigorously determined by other quantities, may yet be considered to be independent and determined by chance. We shall find the answer to this question in the fact, that very small variations in the coordinates and velocities bring about consider- able variations in the direction of the normal. If we determine the directions by means of the points in which they cut a spherical surface described with a radius equal to the mean free path, the velocities being measured by the path covered in the mean time interval between two collisions, and if we call the ratio between the radius of a molecule and the mean free path a small quantity of the first order, then we may formulate this proposition more pre- cisely as follows: variations of a given order of smallness in the coordinates and the velocities bring about variations in the direction of the normal which are of one order lower; variations in the direction of the normal give rise to variations of the same order in the coor- dinates and the velocities after impact. If we ascribe to the coordinates and the velocities of two colliding molecules values ayy 24 Uy Yo Zo My Vy UW, Uy Vy Ww, Which are rigorously determined, then the direction of the normal Agur is also rigorously determined. If however we mean by these 12 data that these quantities ( 47) lie between x, and x, + dz, etc.... w, and w, + dw,, i.e. that the condition is ineluded in a twelve-dimensional volume element of the jirst order, then a, u and vp are left undefined. This way of proceeding is that of the kinetic theory of gases in which we are therefore justified in considering the normal to the tangent plane of two colliding molecules to be determined by chance. If we wish to know this direction accurate to the first order, then the 12 coordinates and velocities must be known to the second order. If within this volume element we determine the place by means of new coordinates .7,' y,'2,'...0,'1,', (we might call them coordinates of the 2°¢ class) which vary within that element over a finite region, e.g. from O to 1, then the direction 2 u v is a function of these coordinates of the second class, and they determine the 12 coordinates and velocities after impact also to the first order. Every collision brings about a lowering of the order of determination of the coordinates and the velocities; every collision causes a scattering by which the condition of the system becomes one order less determined. In order to know the condition (the coordinates and the velocities) after collisions (at least accurate to quantities of the first order) we must know the initial values of the coordinates and the velocities accurate to the (n + 1)" order. The longer the period is for which we want to predict the motion, the higher is the order which is required for our knowledge at this instant. The limit is here the pure mechanic conception, according to which the state is determined for ever, because the data are determined with absolute accuracy. BoLTZMANN’s observation, that a system, whose motion is reversed really proceeds from a more probable condition to a less probable one, namely to that from which the natural system started, and that afterwards conditions are reached, which show again an increasing probability, includes the assumption, that in the initial state the coordinates and the velocities were determined to the (2 + 1)™ order, so that the reverse motion brings the system after „ collisions back to the initial volume element of the first order; afterwards the direction of the normal is no longer determined, and the further process must be investigated according to the rules of the caleulus of probabilities. The condition whose validity is required for the proof of the //-theorem, is not satisfied during the whole backward course of the process; it is here therefore impossible to decide anything as to the decrease or increase of H. As soon as the initial state is again reached the direction of the normal cerses to be determined, and the required condition is satisfied. From the further course we may therefore predict with certainty, that /7 must decrease. ( 48 ) The observation may here be inserted, that we speak of chance in nature, when small variations in the initial data oceasion considerable variations in the final elements, because we cannot observe those small variations. Cyclic motions for instance will also always give rise to such cases. For the special case considered here the result we have found may be formulated as follows: when in a purely mechanic, reversible process which occurs a great many times in the same way, events occur in which small variations in the initial data occasion considerable variations in the final state, then the total process gets the properties of an irreversible process. Botany. — “On a Sclerotinia hitherto unknown and injurious to the cultivation of tobacco.” (Sclerotinia Nicotianae Ovp. et Kontne). (By Prof. C. A. J. A. Oupumans and Mr. C. J. Koning). The following communication contains five paragraphs. “ar. 1 gives an account of a visit to the tobaccofields in the Veluwe and Betuwe, in the autumn of 1902, about the time that the tobaccoleaves begin to be gathered. Par. HL contains an investigation of the disease which had attacked the plants, evidently a fungus, which had long been known as “Rot”, but the nature of which had not yet been cleared up. Par. IL gives a summary of the experiments made with the Selerotia of the fungus. Par. IV deals with the anatomy of the Sclerotia and the Se/ero- tinta produced from them. Par. V contains the result of some biochemical investigations. Par. VI gives a few hints, the application of which may prevent or reduce the damage caused by Selerotinia Nicotianae. |. A VISIT TO THE TOBACCOFIELDS. In order to study more closely the origin of the well-known patches and specks on dried tobaccoleaves, one of us repeatedly visited the tobaccofields in the Veluwe and Betuwe in September 1902. These visits repaid the trouble very well indeed, as they gave an opportunity of becoming acquainted with an evil which caused much damage, had not yet been clearly defined and so deserved a closer study. In these visits one was first of all struck by the fact that the very extensive fields under cultivation were divided into smaller square plots by beanhedges and that these hedges consisted partly of scarlet: runners (Phaseolus coccineus — Ph. multijlorus) and partly of ““curved- beak” (a variety of French beans Phaseolus vulgaris Savi). On account of their height these plants were considered effective as windsereens. Tobacco leaves namely, by their large surface as well as by their tender structure, cannot very well stand air-currents, which is proved by the fact that the scouring or rubbing of two leaves against each other by the wind, may cause discoloured spots, bruising of the tissues and even loss of substance. Though the method of protecting the tobaccoplant against wind had evidently been well chosen, yet the growers themselves had noticed that it was wrong to use two different kinds of Phaseolus, because diseased tobaccoplants are much more frequent within hedges of scarlet-runners than of French beans. Experts are certainly right in their opinion that the reason of this is that scarlet-runners retain their leaves much longer than French beans. The latter begin to lose their leaves already in September and October, when the season can already be rather damp, whereas the scarlet-runners show no sign of it yet then. Hence the soaked soil as well as the damp plants can much better be dried by the wind within the hedges of French beans than of scarlet-runners. Accordingly the “rot” is in damp years always much stronger inside the leafed than inside the leafless hedges. Another drawback of scarlet-runners is that their flower-clusters have not yet fallen off in September and October, so that, after having died, they not unfrequently drop down on the tabaccoplants and soaked through, remain hanging in the axils and in other places, where like wet sponges they foster the germination of conidia or spores. In a visit to the tabaccofields of Mr. N. van Os at Amerongen on Sept. 27, 1902, many plants were found suffering from “rot”. As such the growers considered specimens with limp, slippery leaves and with stems having discoloured stains. This was supported by the experience that such leaves and stems possess very infectious properties and that a single diseased leaf, carried to the drying-shed under a big heap on a wheelbarrow, can in one night easily infect some fifty others. Any precise idea of the agent here at work, was not found however among the experts, so that the only means of }) The tobacco-growers themselves informed us that hedges of beans, especially of scarlet-runners and “curved-beaks” as windscreens, have been in use on tobacco fields as far back as can be remembered. In accordance with this they are mentioned by the late Prof. van Hatt on page 60 and 61 of his “Landhuis- houdkundige Flora” dating from 1855. 4 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 50 ) arriving at a scientific result was to take parts of sick plants to the laboratory and to study them there. Meanwhile a continued walk through the tobaccofields had revealed that this was a case not of a bacterial disease as had originally been supposed but of a sclerotial disease, since in various places in a greater or less degree spots were found on leaves and stems consisting of a white down and besides greater or smaller black grains, embedded in or lying on that down, so that on account of other observations made elsewhere, it seemed probable that these black organisms under favourable conditions might produce an ascigerous generation, from the morphological properties of which the place of the fungus in the system and its identity or difference with other known species might be inferred. The richest crop of material for experiments was gathered in the dampest places, i.e. in the corners of hedges of scarlet-runners, while on the other hand in the vicinity of French beans often not a single grain was to be found. Where flowers or flower-clusters of scarlet- runners were held fast in the axils of tobaccoleaves, sclerotia were rarely sought in vain. It can be understood that the uninitiated — growers and working-men — imagined that the source of the evil had entirely to be sought in the blossoms of the searlet-runners. IL. INVESTIGATION OF THE DISEASE WHICH HAD ATTACKED THE PLANTS. On various days of September 1902 sick parts of stems and leaves were taken home from the tobaccofields as well as from the drying sheds. In doing so each leaf and each stem were separately put into a sterilised tube and in the laboratory placed into a sterilised glass- box over wet filtering paper. At a temperature of 22° C. a distinct change could already be observed in all the objects after 24 hours. They had developed a flimsy, transparent, much-branched mycelium. At a lower temperature the same phenomenon had occurred though less vigorously. After 324 hours small bits of the obtained net of threads were with the necessary precautions placed on malt-gelatine and kept at 22°. Already after 24 hours these bits had grown much and it was possible after another 24 hours to take away new bits from the margin of the circular cultures which had now grown to a diameter of 3,5 centimeters and to inoculate them on freshly prepared malt- gelatine. In this way a sufficient quantity of pure cultures were obtained in a relatively short time. As healthy tobacco-plants were largely at our disposal, it was 51) possible to carry the downy substance on them and to place the infected parts of leaves and stems in damp glass-boxes at 22° (, Again a beginning growth was noticeable after 24 hours. The pure cultures on the malt-gelatine plates became more and more extensive, forming circles which after three days had diameters of 8, after four days of 13 centimeters. By and by the malt-gelatine was peptonised and in a smaller or greater number of places, near the margin more than in the middle of the circles, small, white, glossy points arose, which secreted drops of a colourless, quite clear liquid, but which required no more than 12 hours to turn into black dots. These also continued the process of drop-formation for some time, when after some further increase in size they changed into shorter or longer, round or angular little bodies, which clearly belonged to the class of sclerotia. Having grown more and more independent of the hyphae which at first occluded them, these black bodies could now be removed without damaging them and they appeared to have reached a maximum length of 10 millimeters and a thickness of 5—6 millimeters. The experiments on infection with parts of living tobaccoplants were all successful on condition that the place of inoculation was kept very wet, e.g. by wrapping it up in very wet cottonwool or some woodshavings steeped in water. The attacked tissues became discoloured also here. From what precedes we may infer that the fungus cultivated on malt-gelatine does not differ from that of the tobaccofields, which was irrefutably proved later when from the sclerotia of both the same Sclerotinia was obtained. It is worth mentioning that the myceliumecultures on the malt- gelatine which had produced the sclerotium, had besides given rise in several places to dull white, granulated spots, which microscopical examination revealed to consist of 1s‘. clusters of flask- or cone-shaped conidiophores, borne by erect or ascending hyphae and 2°¢. a number of curious crystals pressed against the thread-shaped cells, partly loosely spread, partly assembled in clusters. The colourless conidiophores were high 12—16 u and broad 4 the lower end, a thinner short neck and a spherical head, which latter just slightly exceeded the neck in breadth and produced spherical colourless conidia of 2.5 u diameter, which were at first connected to short chains, but soon broke up and commenced an individual existence. The crystals and other bodies, often striated, not occluded in cells, 5m and consisted of a cylindrical body tapering a little towards ( 52 ) of varying shape and size, soluble in diluted hydrochloric acid in which they left a structureless residue, soon appeared to belong to the class of “calcospherites”: organic compounds of calcium treated by the late Professor P. Hartinc in 1872 in a quarto Treatise of the Royal Academy of Sciences, entitled: ‘Morphologie Synthetique sur la production artificielle de quelques formations calcaires organiques’’. There could be no doubt that these calcospherites stood in no relation to the fungus, but had been produced by the gelatine, while on the other hand, the presence of conidia proved that the new Sclerotinia, like other species of the same genus, could multiply by conidia as well as by ascospores. On the maltgelatine-plates which had been exposed to the air of the tobaccofields and in the drying-sheds, the same mouldy spots developed under the most favourable conditions of the laboratory, which had drawn our attention on the stems and leaves in the fields, and which had afterwards been artificially multiplied. More important still is that somewhat later the same sort of Sclerotia developed, the germination and further development of which gave origin to the formation of apothecia. There cannot be the least doubt that the conidia floating in the air, by settling on the gelatine-plates, had produced the infection and the ensuing phenomena, so that these last experiments throw a clear light on the possibility of extensive tobaccofields being ruined in a very short time, as soon as by a prevailing uncommonly damp con- dition of the atmosphere a small patch of mould has anywhere found occasion to develop threads. At the same time they show that the opinion of von TaveL (Vergl. Morph. der Pilze, 1892, p. 105): «Es (die Arten von Sclerotinia) sind parasitische Pilze, deren Sclerotien im Innern der Pflanzentheile sich bilden ganz nach Art einer Claviceps”’ cannot be admitted for Sclerotinia Nicotianae, and that here an ectogenous formation of the Sclerotium has been substituted for an endogenous one. Ill. CULTIVATION-EXPERIMENTS APPLIED TO SCLEROTIUM NICOTIANAE. The sclerotia whose development it was desired to study were buried in sand, garden-soil, forest-soil and leaf-earth respectively, placed in suitable dishes partly in daylight, partly in dark, and after having been properly watered exposed to various temperatures among which that of 22° C. Not earlier than 6 weeks later the first sign of new life was observed in the shape of numerous black-brown ( 53 ) little hills with a lighter-coloured top. The earliest appearance was in the dishes filled with forest-soil aud placed in daylight at 15° C., whereas a temperature of 22° C. seemed to have hindered develop- ment. The culture in sand always remained backward. The hills gradually assumed the shape of little rods, but took 3—4 months to reach the appearance of thin little stems or threads, bent down over the surface. These latter moved in the direction of light. The number of threads varied widely for the different grains (Fig. 2 and 5), but did not exceed 20. The progress of the growth was at first very small indeed (2 millimeters in 40 days) and was even insignificant between Nov. 1902 and Febr. 1903. But then the threads rapidly grew in length and in March measured as much as 6 centimeters. After the thickness of the sprouts had very long remained unchanged, at last (in March) a distinct swelling appeared at their top, which at first club-shaped rounded and closed, soon divided into a somewhat inflated neck (apophysis) and a broader dise-shaped terminal piece, which latter could easily be recognised as an open shallow apothecium with the edge slightly bent inward (Fig. 8). The correctness of this view appeared when the miscroscopical examination had revealed the presence of spore-bearing asci and paraphyses in the disc (Fig. 9). A single sclerotium appeared to be able to bear some six well- developed apothecia and besides some dwartish rods. Unburied Selerotia do not develop, although they remain resting on the bed of mycelium-threads which produced them. Cultures in Petri-dishes were mostly spoiled by bacteria. Bits of a fruit-stem, grown from a Sclerotium buried in humus, when: placed on malt-gelatine gave origin to the development of white pads, wiich in their turn sometimes produced new Sclerotia in a week’s time. Bits of white Sclerotial flesh behaved similarly. The fungus-generation grows very rapidly on malt-gelatine as well as on bits of tobaccoplants at 22° C., though its temperature optimum is at about 24° C. At 37° C. the growth is arrested. Between 15° and 20° C. the development is still satisfactory. IV. ANATOMICAL INVESTIGATION. The mouldy threads which in the field develop on the surface of green parts of plants and which afterwards produce the Sclevotia, grow equally in all directions and so gradually form white discs, of increasing diameter, finally reaching an average breadth of 2 centi- meters. These threads are colourless, 2 u tick, much ramified, repea- ( 54 ) iedly septate, filled with a finely granulated protoplasm and occasionally accompanied by threads five times thicker, the significance of which could not be discovered. From the thinner, creeping fibres others rise up on which either singly or in small clusters, flask- or cone-shaped organs develop, whose function is to split off conidia and which hence deserve the name of conidiophores. They are on an average 15 u high and 8.5 gw broad and consist of a thick body, tapering a little at the hottom, a short, thick neck and aspherical head, only slightly thicker than the neck. From the spherical or knob-shaped head colourless, spherical conidia of 2.5 u diameter come forth, which are very soon detached from each other, but the multiplication of which goes on for a very long time, as may be inferred from their extremely large number. The Sclerotia, externally black, internally white, diverge little from the common type as far as their structure is concerned. They consist of a pseudoparenchym the cells of which are somewhat bigger in the middle of the grains, somewhat smaller near the surface, show various, mostly distorted shapes (fig. 7), have very thick walls and are not separated by intercellular spaces. The walls of the more superficial cells are black, of the more central ones colourless. If a sclerotium rests with part of ifs surface against the glass of a tube or box, the black colour does not develop there. The spore-bearing generation (fig. 8) which under favourable conditions comes forth from not too old Selerotia and consists of a long, thread-shaped stem and a miniature apothecium, shows, in the first-mentioned part short, cylindrical or column-shaped, closely packed cells, which at the surface bend dorsally, but in doing so assume the shape of clubs or retorts and turn their broadest part outside. They have a light-brown shade and impart to the stems and cups a peculiar appearance as if they were covered with downy scales. The hymenium consists of asci and numerous loosely packed paraphyses, of which some protrude a little above the others (Fig. 10). The asci are tubular, with rounded tips, insensible to iodine, 160—180 6—7 uw and contain in their */, upper parts 8 inclined, colourless, oval spores in a single row. The paraphyses are only slightly swollen at the top and almost colourless. Germinating spores were not seen. VV. BIOCHEMICAL INVESTIGATION. In order to study the conditions of life of Sclerotinia Nicotianae, (299) the fungus was cultivated on and in different nutritive materials of known composition. It appeared in the first place that the presence of free oxygen is absolutely necessary for its growth; with anaerobic methods of cul- tivation according to BvcHNeR and Lagorivs no trace of development took place. It is not improbable that this is the reason why the mycelium only grows extremely slowly in nutrient liquids, where the quantity of oxygen below the surface is necessarily small. On the other hand the fungus appeared to grow very rapidly when inoculated on malt-gelatine, malt-agar and also on parts of leaves and stems of the tobaccoplant, sterilised at a high temperature. Then a woolly mycelium developed, in some places rising above the surface. Below the surface of liquids or filtrates, obtained from parts of stems or leaves, after inoculation with the fungus, only a meagre cloudy mycelium appeared. As soon however as part of this had reached the surface of the liquid, its growth became much more vigorous. In some cases a floating sclerotium was even produced. Next the influence of the reaction of the nutrient liquid was studied. In a solution of 0.1°/, of potassium nitrate, 0.5°/, glucose, 0.050°/, magnesiumsulphate and 0.050°/, potassiummonophosphate, containing carbon and nitrogen assimilable by the fungus, Sclerotinia Nicotianae does not easily support free acid or alkali. The acid limit lies with this solution at about 1 cubic centimetre of */,, normal sulphuric acid to 100 cubic centimetres of liquid, and the alkaline limit at 0.5 cM’ of */,, normal potassiumhydrate. Neither limit can be sharply drawn as the fungus only slowly produces acid in the solution men- tioned. With 1.5 cM’. of */,, normal sulphuric acid no growth whatever takes place any longer; with the alkaline solution the limit could not be sharply defined. Moreover an elaborate investigation was made as to which com- pounds were profitable to the fungus as carbonaceous and which as nitrogenous foods. As a carbonaceous food glycose, as a nitrogenous one saltpetre in the above-mentioned concentration, proved most satisfactory. Ammonium nitrate, a very good nitrogenous food, was not available of course in the presence of alkalies. In the further experiments the saltpetre was replaced by a similar quantity (0.1°/,) of the nitrogen compound to be studied or the elycose by the carbon compound to be studied in the same con- centration. a. Nitrogenous food. Nitrogen was offered to the fungus in the form of potassium ( 56 ) nitrate, potassium nitrite, chloride, nitrate, phosphate, sulphate, carbonate of ammonia and ammonia. Ammonium nitrate gave the best results. The other compounds showed little difference. Of ammonia which was added in very small quantities, hardly anything Was assimilated. Of amido compounds, which are generally known as good sources of nitrogen for fungi, glveocoll, asparagine, aspartic acid, alanine, tyrosine and leucine gave good results in the present case also. The nitrogen of urea, creatine, parabanie acid and urie acid has little nutritive value. From the last mentioned substance also carbon can be assimilated. . Among aromatic compounds, only the nitrogen of ammoniumsalts has any nutritive value; among the derivatives of pyridine only the nitrogen of the residue, not the carbon. To develop the fungus glycose has consequently to be added to the nutritive material. Nicotine, being a free alealoid can serve as a source neither of nitrogen nor of carbon. If assimilable carbon is present, the nitrogen is used from the ammoniumsalts of oxalic, tartaric, citric and benzoic acids, least from ammonium succinate. b. Carbonaceous food. Of fatty acids only very dilute acetie acid (0.050 °/,) has a nutritive value for carbon. The polvacid alcohols are bad sources of carbon, as was shown by an investigation with glycerine, erythrite, mannite, sorbite, adonite and dulcite. Least satisfactory was sorbite and also glycerine, a good carbon-food for many fungi, gave bad results here. Lactic acid in very small quantities, was available as a carbon-food. Very differently behaved the sugars. As was already mentioned, glycose comes first in nutritive value. Besides were studied: arabinose, xylose, saccharose, fructose, maltose, lactose, raffinose and melibiose. Of all these only xylose and arabinose had any value as sources of carbon. In all other solutions only a trace of growth was observed. Though not without difficulty the fungus was able te derive carbon from cellulose. On filtering paper wetted with the above-mentioned nutrient solution, but without glycose, a snowwhite, woolly mycelium developed. Also from inuline carbon may be obtained. ce. Nitrogenous and carbonaceous food. As mixed sources of carbon and nitrogen we must mention aspa- ragine, aspartic acid and alanine. The addition of-potassium nitrate ( 57 ) improved the growth more with aspartic acid than with asparagine, which must probably be ascribed to the two carboxylgroups, active as sources of carbon. Finally it must be mentioned that also peptone ean furnish carbon as well as nitrogen, but that the nutritive value for nitrogen is increased here by adding glycose. In accordance with the results of Krrgs, it was found that a hieh nutritive value of the liquid had influence on the formation of Selerotia with alanine, leucine, aspartic acid and glveose. These bodies appeared under the mentioned favourable conditions at the surface of the liquid in about three weeks’ time. VL HINTS ABOUT THE PREVENTION OF THE SCLEROTINIA-DISEASE (“ROT”) IN TOBACCOFIELDS. As a damp soil and a damp atmosphere are both absolutely necessary for the development of the “rot” or Sc/erotinia-disease and as this disease in wet years appears about the time when the tobacco- leaves begin to be gathered, it is absolutely necessary, for the reasons given above, to stop the cultivation of scarlet-runners (Phaseolus coccineus, also named Phas. multijlorus) on the tabaccofields and only to admit and to continue the cultivation of French beans (Phaseolus vulgaris SAVI). Besides limp leaves or stems or such as are covered with the least quantity of a white down must immediately be removed and burned. The leaves that have been carried into the drying-sheds must at once be laid asunder and hung up to be dried. Suspected leaves must be sorted out and destroyed. DIAGNOSIS LATINA. Sclerotinia Nicotianae Oud. et Koning. — Sclerotiis ad super- ficiem caulium et foliorum primo in compagine densissimo filorum mycelii niveorum absconditis, celeriter mole augentibus, mox itaque expositis, tandemque a substratu decidentibus, extus nigris, intus albis, nune subglobosis, tune iterum oblongis, 10 maxime mill. longis, 5—6 mill. maxime erassis, teretibus vel subangulosis. —- Ascomatibus plu- rimis (usque ad 20) ab uno eodumque sclerotio protrusis, longe sti- pitatis, tenerrimis; stipite filiformi, tereti, flexuoso, 4—6 centim. longo, ‘/, mill. crasso, deorsum seabro, sursum laevi, summo obesiore, sic ut ascoma satis longe apophysatum videatur, una cum ascomate ( 58 ) pallide fuscescente, floccoso-squamuloso. Ascomate proprio minimo, primo coniformi, clauso; dein p.m. expanso, perforato; tandem pa- telliformi, late aperto, 0.8 mill. in diam., 0.2 mill. alto, margine incurvato. — _ Is always positive hence 2 &Tyl Ngo is always negative; it follows that the plaitpoint on the y-sur- face is always of the first kind *). Since d,=0 when mm? + RTim,,=0, the second special case of border curve and connodal line treated by me *) agrees with the The expression 4 ¢,e, 1 The following expansion can thus be used to determine the coordinates of the critical point of contact, (cf. Keesom le. p. 342). *) The expressions for d; and e; agree with those found by Kersou (1. c. p. 341). 5) See Korrewec, Wien. Ber., p. 1158. *) Proc. Amsterdam 27 Sept. 1902 p. 329. The reference to this special case allows me to correct some mistakes in the formulae which are connected with this and the preceding special cases. In Proc. of 28 June 1902 p. 267 line 2, read : ; 7 2 Lin, ne ns 1 meten, OF on ae and in Proc. 27 Sept. p. 328, line 12: 2 2 ae inane Vaan * ns ey PPS rn | yy — = 4 2 \y — ogy). 1 x= ET Men MELO Pannen (ve a Mo, Mos RT, Further in the last Proceeding p. 329 line 9 for the coefficient of read 4 instead of bo| u (61) first double-plaitpoint case of Korrewee *). The second case for a double-plaitpoint, i. e. 4c¢,e,—d,’? =0, does not occur on the p-surface. 16. Application to a particular equation. In a communication published in the Proceedings of the Academy for 31 Jan. 1903, KorreweG has determined the plaitpoint and critical point of contact for mixtures with a small proportion of one component, but on the assumption that these mixtures satisfy VAN DER WAALS’ equation of state En Vik hy og phe u where a, = a, (le)? + 24,, e(1 -v) 4 a, 2’ and br = b, (1—«)? + 2 b,, « (1—2) + 3, 2’. The formulae found by KorreweG can be immediately deduced from my formulae, when we introduce the special forms which my coefficients will then assume. First we may note that, in this case, the critical constants for the homogeneous mixture are Se We: ee 8 Be 1 tk — and gue === 8 Diy 1) Le.p. 1166. In using the same method with Korrewee’s equation (2), as | have used to determine the critical constants, [ have found the following expression: Ac ee + d’,e,—4d,d,e, — 4e id, fe Dd en E d, ak ip and : ee rr a (He) (Ya — IH) ie 2e,(?,—4¢c,e,) where 2), %, y, and ya are the coordinates of the ends of the tangent-chord. In the special case when dz =O we get 48; 1-d, Ys = TI Pe (zv, = v,) Tig ee ee om (a, SE v,) (Ys FSi 4) 4 e‚ 9 C, D) 7 LN fal 5) Wa) = RR. (w, + 2). ast 1 By the introduction of the above values a rije coefficients, my expressions for ®, p and £ are again found. The first approximation for dz, ¢ and ez will then be certainly insufficient in the last expression. and ( 62) so that KAMERLINGH ONNES’ coefficients @, 8 and y become am) 9 paie) y= 2 bisa a, b, a, b, b, Further we find, by comparing my equation (18) with the above equation of state : eee 0°p th A, Ose _ bi: EL \òvde/rr 27 be \cas b, ate 1 a, Ms 4 =a = = = —— —. > 6\ dv? / Tr 486 b,° If these special values are substituted in my general formulae, Korrrwee’s special formulae are obtained, and in addition some which he has not given. These are not given here as they are not sufficiently simple and they can also be easily reproduced. KorreweG has already given the results obtained from these formulae. I will here only remark that the special cases 1, 2, 3 and 4 of KorreweG’s fig. 1 agree with my fig. 15 and the cases 5, 6, 7 and 8 with 14. As fig. 15 is obtained for the case that m?,, RT m,,>0 and fig. 14 when mm? + RT, m,, <0, the boundary between the two cases is determined by m?,, + RT m,, = 0, which in connection with the special equation of state can be written ibs a wee AUF : ] — ——~+2—)+4+8 a S| a, b, a, b, This is the equation of the parabolic border curve given by KoRTEWEG. (June 24, 1903). ee AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday June 27, 1903. Te (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 27 Juni 1903, Dl. XII). ROER. ay 2B IN Se SS, H. W. Baknuis Roozesoom: “The boiling-point curves of the system sulphur and chlorine”, p- 63. A. Smits and L. K. Worrr: “The velocity of transformation of carbon monoxide” (II). (Communicated by Prof. H. W. Baxuuis RoozrBoom), p. 66. J. K. A. WERTHEIM SALOMONSON: ‘tA new law concerning the relation between stimulus and effect.” (Communicated by Prof. C. W1iNKLER), p. 73. (With one plate). Extract from the Report made by the Committee of advice for the according of the Buys Barror-Medal, p. 78. C. A. J. A. OupeMANs and C. J. Konixe: “On a Sclerotinia hitherto unknown and injurious to the cultivation of Tobacco (Sclerotinia Nicotianae Oup. et Konixe). Postscript. p. 85. (With one plate). A. Gorter: “The cause of sleep.” (Communicated by Prof. C. Winkier), p. 86. C. A. Lopry pe Bruyn and C, L. Juncivs: “The condition of hydrates of nickelsulphate in methylaleoholic solution”, p. 91. C. A. Lopry pe Bruyn and C. L. Junaivs: “The conductive power of hydrates of nickel- sulphate dissolved in methylalcohol”, p. 94. : C. A. Lopry pe Bruyn: “Do the Ions carry the solvent with them in electrolysis”, p. 97, C. L. Junaivs: “The muttal transformation of the two stereo-isomerie methyl-d-glucosides.” (Communicated by Prof. C. A. Lopry pe Bruyn), p. 99. S. Tymstra Bzy.: “The electrolytic conductivity of solutions of sodium in mixtures of ethyl- or methylaleohol and water”. (Communicated by Prof. C. A. Lorry pe Bruyn), p. 104. (With one plate). W. EinrnovenN: “The string galvanometer and the human electrocardiogram”, p. 107. (With two plates). J. B. Verscuarrert: “Contributions to the knowledge of van per Waars’ ¢-surface. VII. (part 4), The equation of state and the #-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components”, (Communicated by Prof. H, KAMERLINGH ONNES), p. 115. (With one plate). J. D. vAN per Waats: “The liquid state and the equation of condition”, p. 123. J. J. vAN LAAR: “On the possible forms of the melting point-curve for binary mixtures of isomorphous substances.” (Communicated by Prof. H. W. Baxuuis Roozesoom), p. 151. (With one plate). The following papers were read: Chemistry. — “The boiling-point curves of the system sulphur and chlorine.” By Prof. H. W. Bakuuis RoozrBoom. (Communicated in the meeting of May 30, 1903). Binary systems in which the formation of complex molecules may be assumed to take place in a greater or smaller degree have been frequently investigated as regards the equilibria between a liquid > Proceedings Royal Acad. Amsterdam. Vol. VL, ( 64 ) phase and solid phases, but hardly ever with regard to the equilibria between liquid and vapour. 1, therefore, proposed to further investigate this relation in the case of vapour pressure- and boiling-point curves on a series of FP end eevee o /o 20 co L 40 59 60 7° $0 go (00 L Ste J at%S SER 2 5 examples in which the nature and the degree of the complex mole- cules varied, in order to obtain a more definite idea of the changes which these curves undergo as compared with the simple case in which the binary system consists only of two kinds of molecules. Such an example is furnished by the system sulphur-chlorine, the boiling-point curves of which are given in the accompanying figure, which is constructed from determinations made by Mr. ATEN. ( 65 ) Liquid sulphur and liquid chlorine are miscible in all proportions. If in these mixtures no compound molecules were formed, two regular boiling-point curves might be expected which would diverge very much in the centre because the boiling points of the two components lie far apart. In these mixtures, however, a fairly stable compound §,Cl, is formed. If this compound were absolutely stable, that is if a liquid and a vapour of the composition 5,Cl, consisted of nothing but molecules of this formula, then the liquid and vapour would at this point, have exactly the same composition. The system SHC would then in reality be compounded of the two systems S5-+8,Cl, and S,Cl, + Cl, which could no doubt be represented in one figure, but then the liquid- and the vapour-pressure curves would not pass con- tinuously into each other at the composition $,Cl,. As it is known that the dissociation of the vapour of $,Cl, is small it may be anticipated that, in the system S + Cl, the connec- tion at the composition SCL might become continuous, but in such a way that the vapour and liquid curves nearly coincide at this point. This state of affairs was now confirmed and is indicated in the figure by the liquid curve 1,3 and by the vapour curve 2,4. It will be seen that the curves 1 and 2 and 3 and 4 nearly meet in a point situated near the composition SCI, but in reality we have here continuity, from which it appears that $,Cl, is not absolutely stable either in the form of liquid or vapour. The difference however, is so small that this type really exhibits one of the smallest forms of deviation. In the case of binary mixtures where the compound formed is more strongly dissociated the divergence of the two curves at the point representing the compound will be much greater. The liquid curve and the vapour curve of the entire system will then more and more assume the form which in the figure belongs to both halves. The investigation however, showed a further peculiarity in the lower half. The boiling-point curves 1 and 2 for the mixtures whose composition lies between Cl and SCI only relate to mixtures, which are freshly prepared from liquid 5, Cl, and liquid chlorine. These mixtures at temperatures below 0° retain for a very long time their yellow colour and then exhibit the boiling point lines indicated at 1 and 2. At higher temperatures, and very quickly above 30°, the colour becomes darker and finally blood red, chiefly in the case of mixtures approaching the composition SCI, The boiling points then rise, sometimes very considerably, to a maximum amount of about 70° so that the line 5 is found for the 97 ( 66 ) definite boiling points of liquids which have reached their final equilibrium, which occurs after some hours at the ordinary temperature. At the same ‘time we get, in place of the vapour curve 2, the new vapour curve 6. As the velocity of reaction above 40° becomes very great, the lines 1 and 2 cannot be accurately determined above this temperature. For 1 this causes no inconvenience as its further course must be almost vertical, but the upper part of 2 becomes rather uncertain. The final boiling-point curves 5 and 6 are situated much closer together than the first named one and have moreover an exceedingly irregular shape. It cannot as yet be decided whether this is solely attributable to the formation of SCI, molecules in the mixtures, or whether other compound molecules are formed. The formation of compound molecules may be noticed not only from the change of colour, but also from a diminution of the volume and will if possible, be studied quantitatively. The important question in what manner the melting-point curve of solid SCI, is modified by the presence of more or less compound molecules in the liquid phase is still the subject of investigation. Chemistry. — “The velocity of transformation of carbon monoaide IT’. By Dr. A. Smits and L. K. Worrr. (Communicated by Prof. H. W. Bakuuis RoozeBoom). (Communicated in the meeting of May 30, 1903). In our previous paper on the above subject *) we communicated results obtained at the temperatures 256°, 310° and 340°, from which we concluded that at these temperatures the transformation of CO into CO, and C is unimolecular. Our present paper contains the results obtained at 445°. This communication appears to us to be of importance for the following reasons. Three months after our first paper a communication appeared from ScuEnck and ZIMMERMANN*) from which it appeared that they had also studied the transformation of CO into CO, and C and had arrived at the result that the reaction at temperatures from 510° and 360° was a unimolecular one, thus confirming our experiments, but that at 445° the reaction became bimolecular. On continuing our investigation we found, however, that the 1) Proc. 8 Jan. 1903. 2) Ber. 36. p. 1231. ( 67 ) reaction at 445° is also a unimolecular one and that therefore the observations of Scuenck and ZimMerMANN must be faulty as far as the temperature 445° is concerned. Experiment. In order that the reaction might not take place too rapidly the reaction vessel was now filled one third with the catalyser (pumice- nickel-carbon) *). The object of the first experiments was to determine the order of the reaction according to the method of van ’r Horr. In the first measurement the initial pressure was 770.7 m.m. He. After 5 minutes the CO tension amounted to 430.5 m.m. He from which de, — = 68,04 dt and for the average pressure of the carbonic oxide c, = 600,6 In the second measurement the initial pressure was 442.2 m.m. Hg and after 5 minutes the CO pressure amounted to 239.0 m.m. Hg. a de Here - — 40,64 and ec, = 340,6. If from this we calculate 2 according to the formula of van’? Horr de, de, log | — : — ek GR GE NZE log: (Ee 205) we obtain ju AR te 2. After having thus become convinced that the reaction at 445° is also a unimolecular one we made a series of measurements in order to calculate the reaction constant from them. The result was as follows: 1) The quantity of iron present in pumice did not appear to exert any influence as no alteration in pressure was noticed in a reaction vessel containing pumice and CO when heated to 445°. This time, however, as in ScHenck’s experiments, the iron was removed from the pumice by reduction with hydrogen and subsequen! treatment with HCI and boiling in a Soxhlet apparatus. The Ni(NO;) originally contained much iron, but was completely freed from it by leaving the solution for some time in contact with NiCO,. ?) Also after a longer time (10—15 minutes) ” was found to be practically 1, ( 68) Time | Pressure in 1 En 1 2(P,-Pi) in minutes. | m.m. He. Ie us by Pi—P, Pe t Py (2Pi—P,) ) See Se eee ee ee eee 0 769.5 4 660.4 | 0).03437 0.000129 6 | 616 6 | 1) 03666 0.000143 8 | OA 0.03707 0 000159 10 | 548.7 0.03704 0.000175 15 497.8 0.03546 0.000208 20 470.7 0 03108 0.000206 30 66.3 0.02246 0 090161 The measurement was started here half a minute after the commencement of the filling. The filling lasted */, minute. The third column contains the values of % calculated on the supposition that the reaction is unimolecular whilst the fourth column contains the values of 4’ assuming the reaction to be bimolecular, as believed by ScHeNeK and ZIMMERMANN. In concordance with what has been found above, we see that the figures in the third column are much more nearly constant than those in the fourth. During the first 15 minutes the values of / (third column) agree fairly well with each other; afterwards a slow fall takes place. That the first constant would be smaller than the next was to be expected, as during the first 4 minutes a small expansion had still to take place. Although the starting point could not be fixed with the same accuracy as before, owing to the greater velocity of the reaction, the fall of / could not be attributed to experimental errors. It therefore, made us suspect that the reaction might perhaps prove to be perceptibly reversible at 445°. It is true that Boupovarp’) had found that CO when in contact with our catalyser was completely decomposed at 445° into CO, and C, but as his method was not very accurate we felt we might doubt this result ®). In order to obtain certainty we made the following experiment. We filled the apparatus at 445° with CO, and observed whether an 1) Scuenck and ZimmeRMANN have made a mistake calculating the value of k’, 2) Ann. de Chim. et de Phys. [7] T. 24. Sept. p. 5—85 (1901). 8) SABATIER and SenpERENS noticed a complete transformation between 230° and 400°. Bull. Soc. Chim. t. 29 p. 294 (1903). ( 69 ) increase of pressure took place which would indicate that the reaction CO, + C= 2 CO was proceeding. The experiment removed all doubt as not only an increase of pressure be could very plainly demonstrated, amounting after a few hours to several ¢.m. of mercury, but after exhausting the apparatus a quantity of CO could be detected in the gaseous mixture which accounted for the observed increase of pressure. Contrary to Bovpovarn’s results we have therefore found that the reaction 2 CO = CO, + C is reversible at 445°. The reason why fairly concordant constants were obtained during the first 15 minutes although no notice had been taken in the calculation of the reversal of the reaction, is simply that the equation fe LER ALOR re MTC) dt 2 differs but very little from = a k, (A—«) . . . . . . . . (2) dt when & or x or both are very small. /, is very small at 445° and this is the reason why at first the second equation is satisfied, x being then not yet large. By means of the first equation we might be able to calculate & if we knew the equilibrium constant A = 2 2 As analysis seemed to us less accurate we have endeavoured to determine X in the following manner: The reaction vessel was filled again with CO, while the time was noted which elapsed between the filling and the first reading so as to be able to find the starting pressure by extrapolation. The heating at 445° was now continued until the pressure after the lapse of some hours did not undergo any further change. K could then be calculated from the pressure at the start and at the finish. To decide whether the final pressure corresponded with a real condition of equilibrium, the same experiment was repeated starting with CO,. If the first final condition had been a real equilibrium, the same value ought now to be found for A. Up to the present we found this by no means to be the case but we do not at all consider the research finished in this direction. We 1) It is taken for granted here that the reaction GO, 4 C= 2C0 is also a unimolecular one. (705) only mention it to explain why the values for / in our last table have not been corrected. 3. In eritieising the experiments of SCHENCK and ZIMMERMANN, it must first of all be observed that they did not reduce their NiO with CO but with H,. This is of course, wrong as during the reaction carbon is deposited and the catalytie Ni surface is changed. If, as in our experiments, we start with Ni on which previously a coating of carbon has deposited, it is evident that a further precipitation of car- bon during the experiment will be of less consequence. In our former communication it has moreover been shown that the activity of the catalyser first diminishes owing to deposition of carbon, but finally becomes practically constant. If, therefore, we start with Ni without carbon we may expect that, on account of the deposition of carbon, / will continuously decrease. The values for / found by Scnenck and ZIMMERMANN are not at all constants and show a decrease with an increase of the time. To find out what can be the cause of the bimolecular course at 445° as found by Scuenck and ZIMMERMANN we have repeated the experiment with pumice-nickel in which the NiO had been reduced with very pure hydrogen. *) Our first work was again the determination of the order of the reaction. dst measurement. Initial pressure = 756,0 m.m. Hg CO pressure after 3 min. = 528,6 y " de, tae rie En (58 wtb B 2ad measurement. Initial pressure = 275,1 m.m. He CO pressure after 2 min. = 210,9 y + de, ee Gr ads dt : : j therefore a POs): Having found that, contrary to the statement of Scuenck and ZIMMERMANN, the reaction with this catalyser is also wimolecular we made a further series of measurements in order to calculate &. The results were as follows: 1) By electrolysis of a NaOH solution, using nickel electrodes. 2) After a longer time (5—10 minutes) # was found to be practically 4. 4 dies je ¢ VAPi=P, Time Pressure in in minutes. m.m. Hg. 0 762.4 2 671.7 0 058 0 4 606.3 0.05708 6 560.5 0.05451 8 528.8 0.05143 10 508.6 0.C4753 The larger values of & and their regular change are due to the absence of a layer of carbon at the commencement of the experiment. If we compare this table with the one given by Scnenck and ZIMMERMANN for 445° | Hag Pressure in pl Po in minutes. m.m. Hg. t 2 PiP, 0 759 2 626 0.09369 4 348 0.08815 6 522 0.07090 10 510 0.04636 we notice that the very considerable change of #% cannot be fully explained by the absence of a layer of carbon but that there must have been another disturbing factor. From Scumnck and ZIMMERMANN’s description it is evident that it cannot be the absorbed hydrogen’), for this was introduced into their apparatus only in the jist series of experiments and the second series shows a still greater change. For want of further particulars as to the research of Scuenck and ZIMMERMANN we cannot make any further suggestions as to the nature of this second disturbing factor. 1) We found that H, is very strongly absorbed by finely divided Ni but gradually expelled in vacuum. According to SABATIER and Senperens [Cr. 134 p. 514—516 (1902)] CO and Hy, react with each other above 200° in contact with finely divided nickel according the equation; GO + 3H, = CH, + H,0, (73) We must say a few words about their plausible explanation of the change from a unimolecular to a bimolecular course, which they thought they had discovered. After having made the same supposition as we did for the uni- molecular course namely i CO S640 il, GO 0 == CO; they say: „Der Dissociation des Kohlenoxydes in seine Elemente würde dann ein Oxydationsvorgang folgen. Spielt sich der letztere, wie bei dem Sauerstoff im status nascens zu erwarten ist, mit sehr grosser Ge- schwindigkeit ab, welche die Dissociationsgeschwindigkeit übertrifft, so findet man eine monomolekulare Reaction. Steigt bei höherer Temperatur die Geschwindigkeit des Dissociationsvorganges verhält- nissmässig mehr an als die des Oxydationsprocesses, so fallen schliesslich die Vorgänge zeitlich zusammen, und wir erhalten den Eindruck einer bimolecularen ,gekoppelten” Reaction. Auf diese Weise lässt sich für die auffällige Erscheinung eine plausible Erklärung geben.” But what has been overlooked here is that in order that the reactions [| and II shall give the impression of a unimolecular reaction, the second must take place with immeasurabie velocity. If this is true at a low temperature it is certainly so at higher temperatures and even if the velocity of the first reaction has in- creased this will be the only one which will be observed so long as it proceeds with measurable velocity. We are, therefore, inclined to contend that it is plausible to assume that if the reaction is a unimolecular one at a low temperature it cannot be expected that the order of the reaction will increase at a higher temperature. Summary of our conclusions: 1. The transformation of CO into CO, and C is unimolecular for all the temperatures at which we have experimented: 256°, 310°, 340° and 445°. 2. Contrary to the result obtained by Bovpovarp the reaction is reversible at 445°. 3. The equilibrium constant could not be determined, as up to the present, we have found that the same condition of equilibrium is not attained starting from CO and from CO, + C. Amsterdam, Chem. Lab. University, May 1908. (73) Physiology. — “A new lauw concerning the relation between stimulus and effect” By Prof. J. K. A. Warrnnm SALOMONSON (6% Communication). (Communicated by Prof. C. WiNkKrer). (Communicated in the meeting of May 30, 1903) The numbers used for testing our law concerning the relation of stimulus and effect, were for the greater part derived from lifting-heiehts in cases of ¢sotonical muscle-contractions. During each contraction the tension of the muscle is not perceptibly altered, likewise the tension remained the same for all contractions belonging to each single series. What is the influence of any change of weight on the magnitude of the constants? It is known already that the lifting-height changes whenever the tension is changed in any manner. In the formula, expressing the law for the relation between stimulus and effect Cee ik eae ae ame the maximum lifting-height is represented by the constant A. As the lifting-height denotes at the same time the maximum quantity of external labour, we may state directly that the constant A will certainly be changed at any alteration in the magnitude of weight. As a matter of course nothing is known about the constant B, neither could I find any indication about the constant C, representing the threshold-value of the stimulus. It is thence of some importance to investigate what will happen to the constants B and C, if we alter the weight attached to the muscle. To this purpose I have recorded a series of isotonical contractions of frog-muscles at increasing stimulus. I generally used a gastroe- nemius-preparation, which was stimulated by means of the nerve. The experiments were made indifferently with muscles cut out or with muscles through which the blood circulated in the normal manner, these offering not the slightest difference between them. The stimulus employed, was the current of charge of a condensator of 0.001 microfarad. This was done by pushing down a morsekey mounted on ebonite, thus connecting the condensator with two points between which there existed a known potential difference; in so doing the current of charge of the condensator was led through the nerve of the preparation. When letting go the key the condensator was short-circuited and discharged. The variable difference of tension was obtained by means of a rheochord with platinum-iridium wire, calibrated with the utmost care, through which a constant current was sent by a large accumulator. By means of a variable steadying resistance care was taken that the P. D. at the ends of the wire, measuring one meter, ( 74 ) amounted to exactly 1 Volt. This P. D. was continually controlled by a recently calibrated precision-galvanometer of SIEMENS and Harskr. In this way every millimeter of the wire represented 0.001 Volt. By means of a vernier 0.1 millimeter could be read without diffieulty. Ever millimeter represented in this manner at the same time one millionth part of a microcoulomb. The shocks of the current followed one another with intervals of 15 seconds. I have succeeded, not without some trouble, in obtaining two complete series, one of which I have entirely calculated and inserted here. It consists of five separate series, each including from eight to ten contractions, all taken from the same gastrocnemius, but in each succeeding series the weight was increased. Series. I. Weight 10 Gr. A =A9 15 B = 0.0204 C = 356.3 R Ecaic. Emeas. P 375 6.073 6.4 ++ 0.027 400 44 297 11.0 — 0.297 425 44,435 14.4 — 0.035 450 16.318 16.6 + 0.989 475 17.450 17.2 — .250 500 18.129 18.0 — 0.129 525 18.537 18.5 — 0.037 550 18.782 19 0 + 0.218 600 19.017 19.1 + 0.083 650 19.102 19.2 + 0.098 Consequently the mean observation error of each single observation amounts to: su = 0.2102. n—d3 Series IL. Weight 30 Gr. A ANS B = 0.0213 C= 361.6 R Eat. Enea. P 375 4,521 4.4 — 0.121 400 10.173 10.2 + 0.027 425 13 491 13.5 + 0.009 450 15.439 15.4 — 0.039 500 Ab 41.2 — 0055 [550 17.883 18.3 + 0.M7] 600 18.097 18.2 — 0.103 800 18.206 18.2 — 0.006 J.K. A. WERTHEIM SALOMONSON. „A new law concerning the relation between stimulus and effect.” = il oan io OO B Cog er = ae site see H 5 HEEREN i it De, ee: H a tI He HE HoH OO EE i tt ry +t +. He HEHE En : + HEE HH EHH tE HEE HH 88 Hants et aen Proceedings Royal Acad. Amsterdam. Vol. VL v4 . wi OG es SE eed A IN ve ) gt Abed, (75) The mean observation error amounts to 0,0876, if we neglect the observation placed in parenthesis, which was not used for the calculation. Series III. Weight 60 Gr. 4 = 16.68 BEKO 0202 6. 817-0 R Ecate. Ene: s. Pp 400 6.199 6.3 + 0.101 425 10.359 10.3 — 0,059 450 12.863 13.0 +. 0.137 475 14.376 14.2 — 0.176 500 15.290 15.4 + 0.110 550 16.174 16.3 + 0.126 600 16.496 16.4 — 0.096 800 16.674 16.6 — 0.074 The mean observation error amounts to: 0.1457, Series IV. Weight 100 Gr. A == 14°52 B = 0.0209 C= sero R Pate. Emeas. p 400 2.490 2.4 — 0.00 425 7.386 7.4 + 0.014 450 10.055 10.3 + 0.245 475 12.011 11.9 — 0.111 500 13.032 13.0 — 0.032 550 13.997 13.9 — 0.097 600 14 335 14.6 + 0.264 800 14.492 14,5 + 0,008 The mean error amounts to: 0.1793. Series V. Weight 160 Gr. A UP B = 0.0198 C = 394.4 R Beate, Ema. p MO eN by 10 — 0.127 425 4.880 ed + 0.220 450 7.168 7.0 — 0.168 415 8.563 8.7 + 0.137 500 9.413 9.2 — 0.213 550 10.247 10.4 + 0.153 600 10.557 10.6 + 0.043 800 10.737 10.7 — 0.037 The mean error amounts ‘o: 0.1916. These series may teach us in the first place that no change whatever in the general course of the curve is effected by the magnitude of weight. The constants only are altered. The following table will give an easier survey of the manner in which these changes are effected. The weight is therein represented by Z, whilst A, B and C stand for the three constants of our formula; in the third column under ALV is given in gram-millimeters the amount of work done multiplied by the writing-lever. This enlargement, which in our case took place in the ratio of 5 : 1 will be denoted by V. L A ALV B C 10 19.15 191.5 0.0204 396.3 30 18.21 46.3 0.0213 361.6 60 16.68 1000.8 0.0202 377.0 100 14.52 1452. 0.0209 391.0 160 10.74 1718.4 0.0198 394.4 In this table we may observe: 1st. That at increment of weight the lifting-height diminishes, at first slowly, afterwards more rapidly, an already well-known fact. 2rd, That the work done increases at first rapidly, afterwards more slowly. As we know, the work would, if the weight were still further increased, attain at last a maximum value and finally diminish. dd, That to all practical purposes the coefficient B remains constant with increasing weight. For its mean value amounts to 0.02052, the largest deviation being at the utmost 3.8 °/,, the most probable value being: 0.02052 + 0.000395. Furthermore the devia- tions are irregular in both directions, so we may conclude that under ideal technical conditions the increment-constant would have remained, to all probability, wholly unaltered by different weights. 4th. That the constant C, i.e. the minimum threshold-value augments at increment of weight. 1 did not yet find this fact mentioned in the literature within my reach. Still it may be easily verified even without writing the record of a complete series, and it was proved beyond any doubt within the limits of the experiment. With regard to the series here communicated, we ought to make mention of the fact that still another series was written, the weight therein being 200 Gr.; this last series however showed technical faults of too much importance, than that it could be employed for the calculation of the constants. Besides the experiments on isotonical contractions with different weights, I also investigated isometrical contractions. I believe that the Cte communication of two of these series will suffice. The first was taken from the second gastrocnemius of the same frog that had supplied us with the preparation of the foregoing series. Series VI. _Isometrical. ATOS B= 0,0931 C = 384.0 R fe Ei 400 3.163 3.2 + 0.037 425 6.611 6.4 — 0.211 450 8.449 . 8.4 — 0.049 475 . 9.480 oy + 0.220 500 10.059 9.9 — 0.159 550 10.567 10.7 + 0.133 600 10.726 107 — 0.026 800 10.800 10.8 0.000 0 = 0.1675, Series VII. Isometrical. Ar 13), 2D B = 0.0096 C = 487.0 R Ecatc, Eneas. p 500 1.433 1.6 + 0.117 500 5.546 5.5 — 0.046 600 8.091 8.3 + 0.209 650 9.666 et) + 0.234 700 10.639 10.2 — 0.439 750 11.242 te — 0.141 800 11.615 11.6 — 0.015 850 11.846 Gat + 0.054 900 11.989 12.0 + 0 O1 950 42.077 12.0 — 0.077 The mean observation-error amounts to: 9 = 0.2190. Here again there is sufficient accordance to leave no room for doubt. Meanwhile it is of importance to remark that both the coefficient A and the effect / have in this series quite another signification as they did in cases of isotonical contractions. Here the maximum tension attained by a muscle during the contraction, is measured by ZL, whilst the highest tension, attainable ( 78 ) for that muscle during any single twitch is indicated by A. And in this case again it is shown that our law concerning the relation between stimulus and effect enables us to represent with sufficient accuracy the increment of effect whenever the stimulus is increased. At present we only wish to state this fact without entering into any details about its theoretical significance for our knowledge of the course of isometrical contractions. Meteorology. — At the chairman’s proposal it was resolved to insert in the Proceedings the following Extract from the Report made in the extraordinary meeting held this day by the committee for awarding the Burs-Barrvor Medal, consisting of Messrs. Junius, Haca, ZEEMAN, VAN DER STOK and Winp. In the meteorological literature of late years one definite line of development in this science has come to the front in such a degree that, in the opinion of the committee, it is obvious to award the Buys-BatLot Medal for this time to a representative of this peculiar branch of meteorological investigation. The branch referred to is one of mainly experimental investigation. In the opinion of some the material collected by the meteorologists during a long series of years grows so dangerously extensive that, for instance, Professor Scuusrer could not help in the last meeting of the British Association expressing a wish, that the meteorologists might stop their observations for some five years and during that time might unanimously try to assimilate the materials in store and to compose a reasonable programme. SCHUSTER in expressing a wish, as to stopping the observations, cannot have been in full earnest, as he will grant too that the series of observations, partly as material for climatic studies, partly as a basis and a test for future theories have a permanent value and should not be rashly interrupted. Nevertheless it is true that, in order to prevent waste of capital and labour and to avoid the loss of valuable data, it is very desirable, in continuing former series of observations, to constantly keep in view their value and not to plan others but on reasonable grounds. Yet, rather a short time ago the material referred to above, however extensive, showed an important deficit. Most obviously it did so, when considered as the foundation of a theory about the great problems of meteorology, the general circulation of the atmos- Aland (79) phere and the nature of cyclones. When leaving out of consideration the mountain-stations, whose importance for the purpose in question is rather limited, the facts observed referred on the whole to the lower layers of air. This is the reason, why opinions about the movement of the air in its higher layers, and therefore about the entire mechanism of circulation, opinions long ago defended by Dover, Maury, Ferrer, JAMES THOMSON a.o. on the ground of their more or less incomplete theories, could hold their own by the side of each other, though in some respects not in keeping with each other. For the same cause incorrect ideas about the distribution of temperature in the atmosphere, closely connected with the circulation, could remain in existence, and important inferences respecting this distribution, derived from theoretical considerations — the Committee are in the first place thinking of the interesting thermodynamic investigations of von BrzoLp — could not yet be put to the test by direct observations. As an extremely important step in the right direction, therefore, may be considered the extension of the meteorological investigations to higher layers of the atmosphere. And so much the more, with a view to the remark made in connection with Prof. ScHustTEr’s opinion, should this step be applauded, because it was taken with the utmost care and with a sharply outlined purpose. This investiga- tion, entered upon in a former decennary, has in the last ten years been systematically set about and organized in an efficient way. If there were one investigator, who could be considered as the only proper founder and promoter of this new branch of meteoro- logical investigation, the Committee would not hesitate to design him for the Bvys-Barror Medal. This, however, being not the case, but there being many explorers, who in the higher ranks have contributed to its development, it seems advisable to award the medal to him among so many, who distinguished himself most by his work. Here, again, it was not easy to choose, the conditions, under which the labour was done, showing large differences and a decisive rate of comparison being wanting. On one side the attention was inmediately drawn to A. LAWRENCE Rotcu, the energetic director of Blue-Hill Observatory, founded and maintained through private means. He was the first to make use, on a large scale and systematically, of kites, provided with registering instruments, to become acquainted with the values of meteorological elements several kilometers high in the air and to put beyond all doubt the practical usefulness and appropriateness of this method. Moreover he set the example of using steamships in the observations with kites, to overcome the difficulty of too great or too slight a force 6 Proceedings Royal Acad. Amsterdam. Vol, VI. ( 80 ) of the wind, and finally planned an expedition with a purpose of trying by experiment with kites on board a steamship to make sure about the movement of the air above the regions of the trade-winds. Another investigator, working under similar conditions with no less skill and success, is L. Trisskrenc pe Bort, the founder and proprietor of the “Observatoire de Météorologie Dynamique” at Trappes. Having been already for a long time organising ascents for meteorological purposes this excellent investigator in later years started his “ballons-sonde” in France and in foreign countries in large numbers, to record temperature and moisture of the atmosphere at a height of 10 to 15 kilometers. In the meanwhile he was inde- fatigably working at the improvement of the recording-apparatus.: Now, for nearly a year, he is — supported by the Swedish and Danish Governments — very successfully engaged in a systematic examination, by means of kites and balloons, of the atmosphere above Jutland and the Danish Isles. On the other side much respect and admiration are due to the perseverance and talent, with which H. H. HimprEpranpsson since 1873 has been trying by means of a large system of stations to make simultaneous observations of clouds and to get from these the knowledge of the movements of the upper air, necessary for a development of the theory of general circulation. He began with observations in Sweden, but knew by pointing to first results of obvious importance how to rouse gradually interest for the labour with the meteorolo- gists of nearly all nations, especially with the “International Meteoro- logical Committee.’ This led to the nomination of an international committee for the observation of clouds and in consequence to the publication of an international cloud-atlas, in which it was principally his nomenclature of the different forms of clouds that was adopted and elucidated by plain illustrations. Finally it led also to the issuing of simultaneous observations all over the civilised world during a whole year, the “cloud-year” 1896/97. Very important are the results which have been derived by HILDEBRANDSSON from the materials gathered. Some current ideas about the movements of the upper air seem to be entirely subverted. They have shown e.g. that in the (northern) temperate zone both the upper and the lower air on an average perform a whirling movement in the sense of the earth’s rotation, round the pole as a centre, but with a centripetal component in the lower, a centrifugal component in the higher layers, a movement, therefore quite different, from the southwestern lower current and the northwestern higher Be ye ; ( 81 ) current, almost generally adopted hitherto. Of the Report about the cloud-year only a first part has yet appeared. Mention must also be made of Professor H. HererseLr, the impulsive and able chairman of the International aeronautic Committee. In this quality he has contributed much to promote a systematic examination of the higher air and has taken the initiative for the simultaneous international ascents of balloons, whieh since November 1900 are being undertaken on the first Thursday of each month from some ten stations. Moreover he has by his own investigations very successfully contributed to the common task. Though it would be easy to mention some more meteorologists, to whom the new branch of investigation owes nearly equally much, it seems to be difficult, after all these men of great merits, to indicate another who should more than one of them have advanced Meteorology by his labour in the line considered. Accordingly the Committee do not intend to name one person, but wish to reeommend for the Medal two investigators — who are, however, one in their work — viz, the editors of “Die Wissenschaftlichen Luftfahrten des deutschen Vereins zur Förderung der Luftschiffahrt, in Berlin”, RICHARD AssMANN and ArTHUR Berson. The reason which has determined the Committee to hold these two explorers as more than any one else worthy of the distinction, is especially the high value of the said publication. There the editors have laid down the foundations, the course and the results of their highly important series of investigations, at the same time clearly showing their great perseverance and earnestness in their exertions, their great serupulousness and punctuality in the accomplishment of their task. This publication, in which moreover numerous new instruments and resources are described and results communicated which immediately have appeared to be of great value, is undoubtedly a work of classic importance. The balloon-expeditions, described in this work, were made from 1888 to 1899 and are divided into 6 preparatory (1888—1891), 40 principal (1893—94) and 29 supplementary expeditions; besides experiments were made with a registering captive balloon and with registering free balloons. In reality the scientific aerial voyages, made at Berlin, have not been finished herewith. Among those not described in the work we mention the rightly well-known “Hochfahrt” of Brrson and Sirinc, undertaken especially to verify the instruments of the registering free balloons by comparing their records with eye-observations made in a manned balloon started at the same time, The free balloons being meant for the greatest heights 6* ( 82 ) (twenty kilometers and more), the manned balloon, in which the parallel observations were made, had to rise as high as possible. It was planned to go as high as ten kilometers and reached even a height of nearly eleven. It is easy to see that expeditions to such a height cannot be free from danger, if we think of the atmospheric pressure of + 200 mM and of the temperature to below —40°C., which have been observed at these heights. The homage then, which the committee wish to be paid to Berson, applies partly to the courage and the intrepidity, with which this explorer has frequently risked his life in behalf of the uncommon task, which he imposed upon himself in the service of science. The whole work, published in 1899/1900, consists of three big quarto volumes. The first of these is partly devoted to an historical and critical survey of the development of scientific aerial voyages, partly also it deals with the construction of balloons and instruments and with the methods of observation and reduction. Moreover it contains the data as to the tracks covered by the balloons and the figures got by the observations. The second volume offers an ample description of the separate aerial voyages. In the third the obser- vations are sifted and discussed, being treated under different heads as: temperature of the air, moisture, formation of clouds, velocity of wind, direction of wind, radiaton, atmospheric electricity. This volume winds up with a chapter, written by von Brzorp, and entitled: “Theoretische Schlussbetrachtungen’. Here we should not omit mentioning the names of Bascuin, Born- STEIN, Gross, KREMSER, STADE and Strinc, who have all of them contributed to the composition of the great work and also personally taken part in the scientific aerial voyages. A short survey of the provisional results of a more general tenor must not be left aside here. 1st. Formerly it has sometimes been thought that the temperature in the higher layers of the atmosphere approached a limit of — 35 to —50°C.; these investigations however do not at all point to the existence of such a limit. Temperatures also, considerably lower than the above, have come to light. 2d, Tn the lower layers of the atmosphere the temperature, in rising, diminishes on the whole less rapidly than would answer to convective equilibrium. Above 4000 M, however, the rate of decrease grows larger and seems to approach that value of nearly 1° C. per 100 meters as a limit. This is in keeping with a supposition of von Brzorp based on theoretical grounds, whilst the behaviour in lower ( 83 ) layers can be accounted for by the influence of radiation, conden- sation and evaporation. The distribution of temperature found in this way, is satisfactorily in agreement with the one found by Teisserexe pe Bort, but dis- agrees considerably with that which was formerly determined by GLAISHER. ded, The diurnal variation of temperature has at a height of 2500 M. shrunk down to less than */,, of its amplitude at the surface of the earth. Of the annual variation of temperature the amplitude decreases rapidly in the lowest layer of 500 M. Higher on it is rather a retardation of the maximum and minimum of temperature than a decrease of amplitude, which is still obvious. At a height of 4000 M the highest and lowest temperatures seem to occur about the middle of September and March. The non-periodical changes of temperature in the higher layers are hardly less intensive than at the surface of the earth. 4th, Frequently low, but also sometimes higher in the atmosphere, there are layers in which the temperature increases instead of decreasing with the height. “Inversions”’ to an amount of even 16°C. have been observed. Not seldom there are also layers, in which the temperature in rising diminishes more rapidly than would answer to the convective equilibrium. It is very remarkable that these layers, which obviously tend to provoke a state of unstability in the atmosphere, are often of a great thickness, reaching even 2500 meter, for instance. 5th, In accordance with results which Hann came to in the Alps, it has appeared that above Middle-Europe, both in winter and in summer, the temperatures at equal heights in anticyclones are in general higher than in cyclones — this, at least, holding good for heights up to 8 KM. This result tends to corroborate the conviction of most meteorologists that the cyclones with their ascending and the anti-cyclones with their descending currents of air cannot as a rule simply owe their existence to differences of temperature. by still more recent investigations it has appeared that the rate of decrease of temperature above the anticyclones, though at first smaller, is at greater heights greater than the above cyclones, so that it remains possible that in the very high layers of the atmosphere the temperature above the anticyclones is lower than above the cyclones. 6th, In most of the cases several layers of a quite different nature and origin were clearly indicated in the atmosphere. 7, In rising, the moisture of the atmosphere generally decreases ( 84 ) more than Hann had derived from observations of mountain-stations and from those made by GLAIsHEr. 8. Important data have been acquired about the formation and origin of clouds, in connection with the distribution of the meteoro- logical elements. 9th, The velocity of wind increases with the height, strongly in the layers below 1000 and above 3000 M, less so between these two heights. At a height of 5000 M it was on an average 4.5 times as large as at the surface of the earth. Important data were also acquired about the difference in the direction of the wind between the lower and higher parts of the atmosphere. 10. Thermally and electrically the surface of a layer of clouds has a similar effect upon the region above it as the surface of the earth. 11th. The rate of decrease of electrical potential seems to diminish, when rising, and even to vanish entirely in the higher regions of the atmosphere. This result, arrived at from only few observations, has afterwards been corroborated. It is not only the initiative in and the organisation, guidance, partly also execntion of, this interesting investigation, which are mainly due to AssMANN. We also owe to him the construction of the aspiration-thermometer and -psychrometer, which has first rendered possible trustworthy observations as to temperature and moisture under the most different cirewmstances. It has appeared that in former balloon-expeditions (of GLAISHER e.g.) errors to the extent of even 15°, owing to radiation, must have oecurred in the indications of the thermometers. Finally we ought to mention the introduction by Assmann of the highly appropriate “Platz’-balloons made of caoutchoue, which as free registering-balloons can reach even a height of 20 to 30 kilo- meters; there they burst and, provided with a parachute, return to the earth very slowly with the instrument they convey. What is said above may be a sufficient reason for awarding the medal to AssMANN and Berson; yet the committee cannot omit referring to the excellent work which is being done in the aero- nautic observatory at Tegel near Berlin, founded by Assmann in 1899 and being directed by him. Here daily observations are made for the examination of the upper air with the aid of kites, kite- and Platz- balloons. The results are published daily and, since the beginning of this year, as graphic reviews also monthly. If an examination of the higher layers of air can furnish many important data more for our insight into the mechanism of atmos- pherie phenomena — which is hardly to be doubted — such a ee a ano ee ee ( 85 ) systematic train of working as is adopted at Tegel seems above all things to be conducive to that purpose, especially if the example given there be followed in a sufficient number of stations elsewhere. In the Tegel observatory Brrson as “ständiger Mitarbeiter” is stea- dily cooperating with its director. One of the more recent results, arrived at in the Tegel observ- atory, may still be mentioned here. In the spring of 1902 registering balloons recorded between 12 and 16 kilometers an inversion of temperature to an amount of 9°. This seems to point to an equatorial current in those parts of the atmosphere which, even higher than the region of the cirrus-clouds, could not but escape HILDEBRANDSSON’s observations. Almost simultaneoüsly an inversion was observed above France by TeisspRENC DE Bort at a height of more than 10 kilometer. The above will certainly be sufficient to give an idea of the nature and the importance of the new field and the new methods of invest- igation and to convince you that the development of these methods owes very much indeed to the two investigators, to whom we last drew attention. Concluding the Committee beg to report that in their unanimous opinion the Buys-BaLLoT Medal should be awarded to RicHarp AssMANN, Director of the Aeronautic Observatory at Tegel, and Artuur Berson, permanent collaborator to the same institution, as a homage to the great services they have rendered to the development of Meteo- rology, not only in their just mentioned qualities, but also and especially as editors of the work entitled: “Die Wissenschaftlichen Luftfahrten des deutschen Vereins zur Förderung der Luftschiffahrt’’, and as those who have had the greatest share in the investigations deseribed in this principal work. Botany. — “On a Sclerotinia hitherto unknown and injurious to the Cultivation of Tobacco” (Sclerotinia Nicotianae Ovp. et Koning). (Postscript). By Prof. C. A. J. A. OupemMans and C. J. Konine. With regard to the small dimensions of the cups (apothecia) of Selerotinia Nicotianae, as sketched in our essay (breadth 0,8, depth 0,2 millimetres) we think it worth while to point out that much stouter cups were obtained from sclerotia which on the 9" of March ult. were sown out afresh in the known manner in different ( 86 ) kinds of earth (forest-humus, garden-earth, sand, pounded autumn- leaves of Quercus and Fagus). After the experimental dishes, covered with glass, had been placed on a windowsill outside and for 8 weeks had shown no sign of life, stemmed cups were found on the selerotia in ail of them, differing from those obtained formerly in having greater dimensions. Instead of 0.8 mill. wide and 0.2 deep, the cups were now 1.4—5 mill. wide and 0.2—0.8 mill. deep; the stems on the other hand were much shorter, varying between 1.5 and 9 mill. against 4—6 cent. in March. The new numbers agree more with those of other species of Selerotinia and can only, we think, have been produced by the influence of a milder temperature and corresponding increased metabolism. The greatest number of cups, sprung from one sclerotium, was 12, as may be seen in the illustration. The special features of cups and stems, among which the swelling under the cups, resembling an apophysis, and the rough surface of the stems, were present in the newly gained specimens as in the former ones. Finally it must be stated that the selerotia with which the new experiments were made, originated from pure cultures and that between the microscopical structure of the former and the new cups and stems no difference was found. Physiology. — “The cause of sleep” By Dr. A. Gorter. (Com- municated by Prof. C. WINKLER). The different well-known theories about the origin of sleep have hitherto not furnished us with a satisfactory explanation either for the want of sleeping or for the sleeping state. By anaemia of the brain quite other symptoms are often presented than by want of sleep, and the former has been recognised as a phenomenon of repose even without sleep. The interruption of continuity in the conduction from the brain to the remaining part of the nervous system was considered already by Purkinje as the primal cause of sleep and has been treated of afterwards by Lovis Maururer in an essay on Nona. In the latter the hypothesis was put forward that the interruption of the contact occurred in those places where, in cases of Polio- encephalitis haemorrhagica, the focusses of disease were found *). This theory has more recently found a powerful supporter in Dvvar, 1) Wien. Med. Wochenschrift 1890 no 23--27, Sclerotinia hitherto unknown and injurious to the Sclerotinia Nicotianae O. et K. pn June 8 1903. f 5 mm. is not figured here. C. A. J. A. OUDEMANS and C. J. KONING. On a Sclerotinia hitherto unknown and injurious to the cultivation of Tobacco. Enlargement 10 Fructiferous sclerotium of Sclerotinia Nicotianae O. et K Collected on June 8 1903, A cup with a width of 5 mm. is not figured here Proceedings Royal Acad. Amsterdam. Vol. VI ( 87 ) who in 1895 defended the thesis that the interruption of contact is caused by retraction of the end-arborisations of the neura. This retraction of the end-arborisations however has never yet been observed, and might be, if occurring, a consequence of sleep, but the investigations of ApatHy and Berne (1894), who hold that the fibrils of different neura pass into one another, have rendered it probable that the causation of sleep is not to be found in this domain. By the third theory the origin of sleep is ascribed to the effect of so-called fatigue-substances, which are presumed to be produced by different functions during the waking state. Injections of lacteal acid, the sole known fatigue-substance, mean- while offered only a negative result, moreover this theory is not quite in accordance with the facts: 1st. Because during sleep principally such functions are disturbed as are dependent on momentaneous stimuli, i.e. the psychical func- tions, whilst other functions dependent on stimuli (nutrition ete.) received during the waking state, e.g. respiration, heart-movement, „secretion of sweat and urine, digestion ete., are influenced in a lesser degree and may be brought likewise to decreased intensity by repose without sleep. 22d. Because the want of sleep and the duration of sleep are neither of them adequate to the performed psychical and physical labour. 3rd, Because sleep may be interrupted at any time by a strong stimulus, the functions operating immediately afterwards in a perfectly normal manner. 4th. Because among psychical functions those, originating partly in preceding stimuli, still remain possible (dreams). 5th, Because in the case of a new-born babe the want of sleep and the duration of sleep both diminish with increasing functions. The insufficiency of these different theories about the origin of sleep have led the physiologist Lyonarp Hint to the conclusion: the causation of sleep must still be regarded as metaphysical 5. Meanwhile physiological psychology had taught us that the waking state is consequent on the conduction of stimuli from the surround- ings to the central nervous system, and as regards man to the psychical centra, a fact in perfect accordance with the experience that the originating of sleep is favoured by darkness, monotonous sounds and silence. The famous experiment of STRÜMPELL *), who 1) The Lancet 1890. I. p. 285. 2) Deutches Archiv. fiir Klin, Medicin, 1878 No, 22, ( 88 ) transported an almost wholly anaesthetical woman into instantaneous „sleep by shutting her one eye and her one ear still capable of seeing and hearing, and who caught from another similar patient the expression : „Wenn ich nicht sehen kann, dann bin ich gar nicht”, furnished another inducement to seek in cessation of stimuli the causation of sleep. The well-known manner in which patients are transported into hypnotical sleep, and the fact that by eliminating all external stimuli, animals may be brought to a state closely resembling sleep, both point to the same conclusion. Zienex schreibt: *) „Wahrscheinlich ist das Wesentliche bei dem Zustandekommen des Sehlafs, der Abschluss äusseren Reize und die Ermiidung der Rindenzellen.” HERMANN ®) „Die nähere Ursache welche die Grosshirnrinde ausser Thätigkeit setzt ist unbekannt. Die meisten Angaben über Verände- rungen im Gehirn sind unbewiesene und zum Theil höchst unwahr- scheinliche Vermutungen. Die oben angegeben Thatsachen zeigen dass Schlaf und Wachen im engsten Zusammenhang mit den Sinnesein- drücken stehen und man könnte sagen dass zur Erhaltung der gewöhn- lichen Thiitigkeit der Rinde d. h. des wachen Zustandes beständige Sinneseindrücke nöthig sind, womit aber das Räthsel keineswegs gelöst ist.” SpriMPELL concludes his well-known article in the Deutsches Archiv *) with these words: „Eine Reihe von Erscheinungen wie das mégliche Einschlafen trotz stiirkeren äusseren Reize, die Periodicität u. a. bedürfen zu ihrer Erkla- rung noch andere Voraussetzungen.” Sleep by intoxication (narecoties), and sleep in some cases of brain- disease, may be explained by the interrupting of the conduction of stimuli towards and within the psychical centra. The almost un- interrupted sleep of the new-born babe also may find a similar explanation in the still unfinished cortex. It becomes moreover difficult to continue searching for the causation of sleep in a peculiar state of the cortex, since dogs, whose brain had been taken away, have been found to present a relatively regular alternating of sleep and waking. Sleep therefore may be said to be caused either by disease, by intoxication, or by cessation or decrease of stimuli from the sur- roundings. 1) Tu. Zrewen. Leitfaden der Physiologischen Psychologie p. 218, 2) Hermann, Lehrbuch der Physioiogie, p. 460. 3) D, Archiv f, klin. Medicin, No 22 p. 390, ( 89 ) Normal sleep is not caused by disease, neither, to our knowledge at least, by iitoxication, consequently it may be caused by cessation or decrease of stimuli from the surroundings, and in examining these surroundings, we observe the periodically operating cause of sleep in all nature, in The settiny of the sun with which numerous stimuli either disappear or cease to operate. The peculiar characteristic of sleep, the disturbed functions, may be satisfactorily explained by the decrease of stimuli occasioned by the setting of the sun. Many functions of the living organism depend on sunlight, and when sunlight dissappears, their intensity diminishes or they may even cease altogether. The assimilation of plants, the search for nourishment by animals, the receiving of stimuli by which psychical functions are originated, all these are dependent on sunlight. The phenomena of sleep having been once recognised as symptoms of decreased functions, all researches for the species of animals in which sleep begins, must necessarily remain fruitless, because most functions of both plants and animals in general are subject to a change, corresponding to the alternation of day and night. These stimuli which still continue, operating during sleep, partially entertain all functions, the psychical ones included, as we are made to know by experience when dreaming. The want of sleep in man is a quality inherited from the animal, and it does not appear so directly dependent on the setting of the sun as is the case in vegetal and animal kingdom, only because man continues his struggle for life with the aid of artificial light. In my opinion, the setting of the sun suffices to explain the periodicity of sleep, and going to sleep notwithstanding the excita- tion of still extant powerful stimuli, must be accounted for by heredity, and I think the solution of the enigma mentioned by HERMANN, is found here. The simplicity of this answer to the question about the causation of sleep, presenting itself as a matter of course and reminding one of the egg of Columbus, is only an apparent one, because the results of years of psychological researches have taught us to seek for this causation outside the functions, physiology having sought vainly for an explanation to be furnished by the functions themselves. The existence of night-animals may be explained in this way that ’ ATEN ‘ ol . FAT wr ( 90 ) in the struggle for life the dangers threatening them in the day-time, have led certain species of animals to shorten the day and adequately to lengthen the night, in the course of which process qualities were slowly developed, enabling them to carry on with more surety that struggle at night, whilst the want of sleep was satisfied during day-time. As regards the phenomena of winter-sleep and summer-sleep, both may be considered as a state of torpor, being no real sleep, and in all probability originated again in the struggle for life by certain animals digging themselves into the earth, after their having been driven away by stronger species to regions, either too cold or too hot. Only the strongest individuals survived, and after the lapse of a long period, their progeny may have gradually attained to the power of remaining alive, for a definite space of time, almost entirely without functions, as an hereditary quality, no longer dependent on the influences of heat and cold. As impossible as it would be for modern man to be kept from sleeping for a somewhat longer period by means of artificial light, as impossible it would be to keep a winter- or summersleeper out of its state of torpor by means of heat or cold, once the season for that state having returned. It is not known to us whether amongst animals living under- ground or in the deep of the sea, there exist any species capable of living without sleep. Until a period not so very long ago, sleep for the greater part of humanity was wholly determined by the sun. During summer man | slept little, during winter much, and even in our modern times the peasant does not consult science about the term of duration of his sleep, as his period of sleeping is determined by the sun. The stimuli | that keep him awake (issuing from his soil, his eattle and his machinery), . all cease to operate with the setting of the sun, consequently he | goes to sleep and is awakened again by the stimulus of the sunlight, | either directly or indirectly by intermediary of animals. In modern times the way in which by far the greater majority of men are living, gives rise to the question whether the want | of sleep in man may not perhaps wholly or partially disappear | in the course of the struggle for life, because we know that inherited | | qualities tend to disappear, when they are no longer of use in that struggle. Partly at least this want of sleep has already been conquered in many instances: numerous men are night-animals, sleeping only for a short period in the day-time, others continue to enjoy unimpaired (CA) health, whilst sleeping only for three or four hours out of the twenty-four. Whether in coming generations sleep may be destined to vanish altogether, cannot be predieted with any certainty, because we don’t know the exact significance of sleep in the struggle for life in its connection with the longer or shorter term of duration of human life, and because on the other hand we are not sure whether some physiological process does not perhaps continue to operate in the human organism, parallel with and dependent on the alternating of day and night. The fact may be simply stated that man is the only creature living upon the surface of the earth, capable of making himself no longer dependent on the setting of the sun, by means of artificial light, thus forcing the most intense stimuli to act without interrup- tion on his nervous system. From the point of view of modern science therefore the possibility cannot be excluded, that in some remote future a race may exist, descended from man that will have conquered the want of sleep, the term of duration for indivi- dual life, however, having become shortened. In this way the knowledge of the primal cause of sleep in nature, opens a distant prospect of the entire disappearance of sleep in man, who nevertheless, because of reasons mentioned already, will never be able to pass the first weeks of his life in a state of waking. Leiden, June 1903. Chemistry. — “The condition of hydrates of nickelsu'phate in methylalcoholic solution.’ By Prof. C. A. Lopry pe Bruyn and C. L. Junerus. 1. It is known that the old question of the relation between a dissolved substance and a solvent has been answered from two points of view. Whilst particularly of late years, some have defended the theory that the solvent is, as it were, merely a diluent which keeps the dissolved molecules apart without entering into a closer relation with them, others have upheld the view that the molecules of the dissolved substance are most decidedly more or less strongly united to those of the solvent. Owing to the development of the ionic theory, the first assumption is now the more universal one particularly for solutions of salts and their hydrates. On the other hand it must be acknowledged that no strong evidence has ever been brought forward to show the existence of hydrates of salts in an aqueous solution even though it seems natural to presume that to a certain extent ( 92 ) hydrates are already present as such in solutions from which they erystallise and which are in equilibrium with them. 2. It might be expected that the study of solutions of hydrates of salts in a solvent other than water would contribute to the eluci- dation of the problem. In view of this, one of us *) had already been engaged some ten years ago with determinations of the elevation of the boiling point caused by the introduction of hydrates of nickel- sulphate into absolute methylaleohol. The preliminary conclusion then arrived at, led to the assumption that a definite quantity of the water (about 3 mols.) remained in combination with the NiSO,. In calculating the results of the experiments no notice was taken of certain factors, the importance of which was unknown or but little appreciated in 1892, namely the occurrence of electrolytic disso- ciation, even in alcoholic solution and the influence of a dissolved volatile substance on the elevation of the boiling point. For this reason the former experiments were recalculated and partly extended. 3. In view of the last mentioned fact, we started with the deter- mination of the change in the boiling point caused by the introduction of small quantities of water into absolute methylalcohol. The fol- lowing result was obtained (Barometer constant). Evelation of Elevation GUSO HO. Boiling point for 1 pCt. 55.16 Grm. 0.5720 Grm. 0.291 0.281 } 54.89 0.6799 0.353 0.285 54.62 0.7866 0.416 0.289 | 54.35 0.8877 0.457 0.280 Average 54,08 1.0378 0.528 0.275 0.281 53.81 4.2127 0.627 0.278 53.54 1.3831 0.725 0.281 39,27 1.5565 0.819 0.280 These experiments, therefore, confirm the conclusion that water added to methylaleohol causes an elevation of the boiling point from the commencement and that no minimum boiling-point occurs here as in the case of ethylaicohol and water (containing about 96 percent of alcohol) *). 1) Lopry pe Bruyn, Handelingen 4e Natuur- en Geneeskundig Congres, Gro- ningen, 1893, p. 83. 2) W. A. Noyes and Warren. J. Amer. Ch. Soc. 23. 463 (1901). Sypney Youne and Emmy Fortey, J. Uh. Soc. 81. 717 (1902). The addition of 20 milligrs. of water to 50 grms of methylalcohol caused a perceptible elevation of the boiling-poiut. ( 93 ) 4. As regards the extent of the electrolytic dissociation we observe that although we have not succeeded in determining the amount *) the experiments have shown that it is very small. Its existence, moreover further strengthens the conclusion to which the experiments have led, namely that a certain proportion of the water remains in combination with the nickelsulphate. 5. The experiments have been made as before, in the first place with the hydrates NiSO,, 6 aq. and NiSO,, 7 aq.; a single experiment was made with NiSO,, 3 H,O 3 CH, OH. The manner in which the calculation was conducted will be seen from the following example: vz represents here the number of mols. of water abstracted from the hydrate *). 59.9 gr. CH,OH, 0.7723 er. NiSO, 6 aq. (mol. elevation of b. p. of meth. ale. 8.8. Mol. weight NiSO, 6 aq. = 262) observed elevation of boiling point == 0°.165 Calculated elevation of boiling point supposing all the water 0.7723 100 had remained in combination Me = 05.045 62 59.9 ak: elevation of b. p. caused by water delivered by the salt — 0°.122 ; ‚0,122 With this corresponds a quantity of water in solution of EE ie el The abstraction per mol. of dissolved hydrate is, therefore, 0,122 262 1 | C= 0,599 === Se =-4,9. mol. HO. (ae TTET : The results of the following experiments were : Methylale. NiSO,6aq. Elevationof b.p. z. 58.5 gr. 0.608 gr. 0°.143 5A 60.5 » 0.694 » 0.146 4.9 60.5 » Ghai > 0.125 5.3 Average from four experiments 5.4 NisO,, 7 aq. gave the following results: Meth. alc. NiSO4, 7 aq. Elevation of b. p. A 60.7 0.432 0.102 6.25 60°7 0.463 0.109 6.2 60.3 0.449 0.140 6.45 60.6 0.481 0.105 5.65 61.7 0.341 0.080 6.3 61.7 0.560 0.120 5.7 Average 6.1 1) See next communication. 2) Strictly speaking, the elevation of the boiling point caused by the same amount of water will be modified in a slight degree by dissolving the salt in methylalcohol. This influence was not taken into account; the slight amount of electrolytic dissociation (see next article) was also disregarded, @ ( 94 ) From both experiments the conclusion may be drawn that the hydrates of nickelsulphate when dissolved in methylaleohol only retain one mol. of water of crystallisation. An experiment made with NiSO, 3 H,O 3 CH,O gave as result «= + 2 and thus confirmed the above conclusion. 6. If now in a one per cent solution of the hydrates of nickel- sulphate in methylaleohol the salt still retains one mol. of water notwithstanding the extreme dilution, it may in our opinion be taken for granted that such is also the case in aqueous solutions. And _now proceeding to concentrated and saturated solutions of hydrates we arrive at the notion that the salt-molecule enters into a more or less fixed combination with the water molecules and that, there- fore, the hydrates (several simultaneously) are already present as such to a certain extent in the solutions from which they erystallise. Probably there exists in such a system a highly complicated condition of equilibrium. Some years ago PicKERING has proved by determinations of the freezing points of solutions of sulphurie acid (of different concen- trations) in glacial acetie acid that a definite amount of water remains in combination with the sulphuric acid. Amsterdam, June 1903. Organ. Chem. Lab. University. Chemistry. — “The conductive power of hydrates of nickelsulphate dissolved in methylalcohol.”’ By Prof. C. A. Losry pr Bruyn and Mr. C. L. Junatus. The determination of the conductivity of hydrates of nickelsulphate dissolved in methylalcohol is important for two reasons. Firstly, in order to ascertain whether the condition of the dissolved substance is modified after a shorter or longer period; secondly to ascertain if possible (in connection with the preceding paper) to what extent the salt is dissociated electrolytically. 1. As regards the first point we recall the phenomenon that after dissolving the sulphates (of Cu, Zn, Co, Mg, Ni) in absolute methyl- alcohol the solutions (some rapidly, others slowly) deposit ') lower hydrates or mixed alcoholhydrates ; for instance from a solution of 1) Lopry pe Bruyn, Recueil, 11, 112 (1892) and Handelingen, 4e Natuur- en Geneeskundig Congres, Groningen, 1893, p. 83. ( 95 ) NiSO, 7aq. or NiSO,6aq.a@ we obtain after some time crystals of NiSO,3H,0.38CH,O. It is however not impossible that, after dissolving, the hydrate loses water with a certain rapidity and com- bines with the methylaleohol so that a definite stationary condition is not attained immediately. If such were the case we might expect that this modification in the condition of the solution would become evident, say, by a change in the conductive power. In carrying out the experiments the conductive power was first determined as quickly as possible after preparing the solution (after about 7 minutes). A portion of the solution (which contained about 5°/, of the salt) was set aside at the ordinary temperature or boiled for 15 minutes. In the latter case the solution was made up again to its original weight. In no cases was a change of the conductivity observed. The same applies to the methylaleoholie solutions of the sulphates of copper and magnesium. The latter exhibits the peculi- arity of becoming turbid on heating to 60° and of clearing again on cooling; it was again proved that after heating at 60° for 7 minutes and subsequent cooling the conductive power remained unchanged. From these experiments we may therefore draw the conclusion that a stationary condition has very probably set in immediately after the sulphates have dissolved in the methylaleohol and that the crystallisation of lower hydrates or of aleoholhydrates, which sometimes occurs after a long time, must be looked upon as a phenomenon of retardation. 2. Secondly, the conductive power was determined of NiSO, 7 aq., NiSO, 6 aq., NiSO, 3.aq, 38 CH,O and NiSO, 1 aq. dissolved in absolute methylaleohol and at decreasing concentrations. As observed, these determinations were made with the object of studying the extent of the electrolytic dissociation of nickelsulphate in methylaleohol (in connection with the contents of the preceding article). Previous re- searches, particularly those of Carrara, had led to the result that, at least with salts composed of univalent ions, the electrolytic dissociation is very considerable, in many cases about */, to */, of that in aqueous solution. In the case of salts with a bivalent ion the conductive power in methylaleohol is considerably smaller *); that of salts composed of two bivalent atoms has, as far as we are aware, not yet been investigated in methylaleohol solution. The experiments were made at 18° according to the usual method of KonrLrAUscH—Osrwarp; the methylalcohol (sp. gr. 0.7397 at 18°) 1) Corretti1, Gazz. Chim. 33, 56. ~ Proceedings Royal Acad. Amsterdam. Vol. VI. ( 96 ) Was again fractionated after addition of some sulphuric acid; the ws have been corrected for the small remaining conductivity of the alcohol. With NiSO,6aq. pure methylaleohol was used as diluting agent in one series; in a second series an alcohol was used containing the same amount of water as that generated by the hydrate on dissolving. ‚The methylaleohol used for the experiment with NiSO, 1 aq. had, been purposely rectified over anhydrous coppersulphate. The following table contains the results of the measurements. Ni SO, 6 aq. | NiSO, 6aq. | NiS0,3 M. | Ni SO, 7 aq. | NiO, 1 aq. Anhydrous a eee isin dees Anhydrous Anhydrous CH; 0H Olo Ho O. CH3 OH CH; OH. CH; OH, V 7 Ap 7 Ap u A p ue | Au 7 Au 8 5.22 3.24 — | 3.22 -- | /— 0.66 / — 0.58 — — 0.66 === 16 2.56 2 63 2.54 2.56 — — 0.63 — 0.55 — 0.60 — 0.65 — 32 1.93 2.08 1.94 1 2.11 == 0:39 |— 0.30 — 0.32 — 0.38 — 0.32 64 1.64 1.78 1.62 153 i579 — 0.13 | — 0.06 — 013 — 0.15 — 0.09 128 1.48 ae an 1.49 1.38 1.70 + 0.02 +015 + 0.02 + 0.05 + 0.06 256 1.50 1.87.1 151 1.43 1.76 + 0.21 +0.43 +017 + 0.20 + 0.25 512 Apa Gs 2.30" | 1.68 1.63 2.01 +044 0.75 + 0.20 +0 64 | +0.55 1024 2.12 3.05 E 1.88 2.27 2.56 | + 0.52 + 1.13 +. 0.24 +0 42 + 0.80 2048 2.64 4.18 i 2.12 2.69 3.36 + 0.97 | + 2.44 — — — 4096 | 3.61 | 6.62 | — — — From the figures given it will be seen that the object of the inves- tigation, that is to say the determination of the extent of the elec- trolytic dissociation, has not been attained because we meet with the peculiar phenomenon that the conductive power at first decreases and that for v—128 a minimum for u occurs; on further dilution the conductivity again increases but a «a cannot be determined. We cannot, at present, account for this occurrence of a minimum which appears in the case of all the hydrates at the same concentration (v = 128) and is consequently a definite property of nickelsulphate. We further notice also that the conductivity of nickelsulphate in methylaleohol (also when this contains a few per cent of water) CM) is very small, many times smaller than that of salts with univalent ions, and at least 20 times smaller than in water. It is for this reason that we have thought proper to disregard the influence of the ionic dissociation on the results given in the preceding communication. Moreover, this influence would only strengthen the conclusion arrived at in that paper. Amsterdam, June 1908. Organ. Chem. Lab. University. Chemistry. — “Do the Lons carry the solvent with them in electro- lysis?” By Prof. C. A. Losry pr Bruyn. It is generally known that the behaviour of electrolytes in solu- tion has in many respects not yet been elucidated. We know, for instance, that strongly dissociated electrolytes do not conform to OstwaLp’s law of dilution. In view of this, H. JAHN ‘) some time ago developed a theory in which he attributes this “deviation” to a mutual interaction of the ions, whilst Nernst?) also assumes interac- tion between the ions and the non-dissociated molecules. A priori it did not appear to be impossible that the ions might exert an action on the molecules of the solvent which would cause them to earry the solvent with them during the electrolysis. If this were found to be the case, it wonld have to be taken into account in the study of the phenomena of electrolysis. The question whether the ions carry with them during eleetro- lysis one or more molecules of the solvent cannot as a matter of fact be studied by using purely aqueous solutions, but it can be done by means of solutions of an electrolyte, say, in mixtures of water and methylaleohol. Then if one of the ions carried with it one of the solvents, this would be found out by the difference in the pro- portion of the two solvents at the cathode and the anode both by comparing them with each other and with the original solution *). In the research an apparatus of the usual kind was employed such as is used for the determination of the transport numbers of 1) Z. ph. Ch. 36. 458, 37. 490, 38. 125. %) Ibid. 38. 487. 2) When the experiments were already in progress Prof. Apeaa told me that Prof. Nernst had already made similar experiments using water + mannitol as sol- vent. These experiments, which only appeared in the Göttinger Nachrichten [1900. 68] had not led to a definite conclusion; Prof. Nernst confirmed this statement. J. Trause (Chem. Zt. 1902, 90) also thinks it probable that each ion is in unstable combination with one molecule of the solvent. ( 98 ) ions (capacity 150 cc); a few experiments were made with a larger pattern (capacity 450 cc.) As solvent a mixture of methylalcohol and water was used of three different concentrations. As electrolyte, cuprichloride was first used; when this substance appeared to be unsuitable for the purpose (owing to formation of cuprouschloride) silvernitrate was taken. This salt was sufficiently soluble in the diluted methylaleohol and did not seem to affect it during the electrolysis. The electrodes were made of silver, the cathode was placed in the uppermost limb of the apparatus and the anode, around which the increase of concentration of the silvernitrate takes place, in the other. After placing the apparatus in the waterbath a current of 70 volts was passed for 3 to 4 hours; the strength of the current was determined by means of a milli-ampere-meter. Separate experiments had shown that the methylaleohol could be very accurately determined by distillation. The liquid to be ana- lysed (25 ce. of the cathode- and anode solutions) was mixed with 25 cc. of water and of this mixture 25 cc. were very carefully redistilled into a weighed measuring flask. The amount of silver- nitrate was found by titration and the silver deposited on the cathode was weighed. From the following particulars of the experiments, we may draw the conclusion that under the circumstances of the expe- riments there is no question of a transference of the solvent along with one of the ions. It was found previously that on dissolving AgNO, in dilute methylaleohol the volume of the liquid is scarcely affected. Methylalcohol of 25 pCt. by weight. Weight of measuring flask after distillation from solvent 36.888 36.872 , solution n. AgNO Ve I. Meth. ale. of 25 pCt. by weight. Small apparat. Curr. 0.36 amperes. Time: 3'/, hours. Silver on the cathode: 4.50 grams. Cone. Ag NO, before the experiment: normal. anode 1.30 normal sone. Ag NO, after \ Pope me NO; sey | cathode 0.54 I solution at anode 36.876 ee ine Haen eee Weight of measuring flask after the distill. | ON eathode: 56.875 Il. Meth. ale. 35pCt. by weight. Large apparatus. Current 0.32 ampere. Time: 4 hours. Silver at cathode: 4.1 grams. Te zs ( 99 ) Cone. of AgNO, before the experiment: normal. . ( anode 1.37 normal ( cathode 0.94 , original solution 36.498 solution at anode 36.508 i , cathode36.503 Iv I 7] after I I! Weight of measuring flask after the distill. mn III. Meth. ale. of 64 °/, by weight. Small apparatus. Current 0.15 ampere. Time: 3'/, hours. Silver on the cathode: 1.80 gr. Cone. of silver before the experim.: normal. ( anode: Ag NO, crystal. out I Ui y after tl Ir ie | cathode: 0.73 normal. original solution 35.100 Weight of measuring flask after the distil. | solution at anode 35.100 y at cathode 35.094 By an easy calculation we now find that if for instance, the Ag- or NO,-ion had carried with it one molecule of the solvent, for every 4 grams of silver an increase or decrease of 0,6 to 0,7 gr. of water or of about 1.2 grams of methylalcohol at the anode or cathode would have been stated. This would have been plainly detected by the analysis even though the amount had been largely diminished by diffusion *). I have to thank my assistants Messrs. C. L. Junarus and 8. Tymstra for their assistance rendered in these experiments. Chemistry. — Prof. C. A. LoBry pr Bruyn presents communication N°. 5 on Intramolecular Migrations: C. L. Juneiws. “The mutual transformation of the two stereo-isomeric methyl-d- glucosides.” 1, When in 1893 Emm. Fiscugr *) discovered the glucosides of the alcohols and proposed for these substances a formula deduced by him from the glucose-formula of ToLLENs, namely Oe ) ae he suggested that on account of the appearance of a new asymmetric 1) It is possible of course that the two ions act in the same manner and carry with them equal quantities of one of the solvents or of both. 2) Ber. 26. 2400. ( 100 ) carbon-atom two stereo-isomeric glucosides ought to be capable of existence. These two isomers would then be comparable to the two penta-acetates then known. About a year afterwards, ALBERDA VAN EKENSTEIN ') succeeded in obtaining this second isomer #-methylglucoside. He found that if the reaction between glucose and methylaleohol (with hydrochloric acid as catalyser) was stopped the moment that all the glucose as such had disappeared, the two isomers were both present, the «-form being predominant. They could be separated by fractional cystallisation. He further noticed that the 3-form passes into the «-form in presence of a solution of hydrochloric acid in methylaleohol; if, therefore, the reaction is continued for a long time, we observe that the rotation increases [the [«]p of the a-isomer is + 158°, that of the @-isomer—382°| whilst the 8-methylglucoside disappears more and more. The g-isomer therefore appeared to be the metastable and the «-isomer the stable form. The observations of ALBERDA lead to the conclusion that, as in so many analogous cases, the so-called metastable form is here the first product of the reaction and that the isomer is produced from this afterwards. It now became important to further investigate the transformation of the one isomer into the other with a view both to its velocity and to the influencing factors. The view propounded by Emin FiscHer*) that glucosedimethylacetal CH, OH- (CHOH), CH (OCH,)? may be the intermediate product in the formation of the two glucosides might be tested by an investigation of this kind. This acetal is a syrupy liquid which occurs as the first product of the action of methyl- alcoholic hydrochloric acid on glucose; it does not react with phe- nylhydrazine or Frxuine’s solution and is very readily reconverted into glucose by the aqueous acids; it was however not obtained pure and not analysed. As this substance, supposed to be the dimethyl- acetal, was converted into the two glucosides on warming with methyl- alcoholic hydrochloric acid, the transformation being however not complete and as moreover the two other substances were obtained when starting from one of the two glucosides, FiscHer concluded: „dass der Vorgang welcher vom Acetal zum Glucosid führt, umkehr- bar ist, dass ferner die Verwandlung der Glucoside in einander iiber das Acetal fiihrt and dass mithin die drei Verbindungen als Factoren 1) Recueil 13. 183. 2) Ber. 28, 1146. ( 101 ) eines Gleichgewichtzustandes resultiren”’; a-methylglucoside is then always present in the largest quantity. 2. My research has now led to the following results. If we start on the one hand from pure a- and on the other hand from pure g-methylglucoside *) the methylaleoholie solution of HCI arrives in both cases at the same condition of equilibrium in which the a-and B-compounds are both present. After removing the HCI. with PbCO, and evaporating the solvent a crystalline mass was left which was extracted with acetic ether. This on evaporation yielded an extremely small quantity of a non-crystallisable product [at most 10 milligr. from 2.5 gram of «-glucoside] which may possibly be FisHer’s dimethylacetal. Its concentration is, therefore at any rate exceedingly small in comparison with those of the two glucosides. 3. From the rotation of the solution, after equilibrium is attained, it may be found by calculation that 77 °/, of the glucoside is present in the a- and 23°/, in the 8-form. From the change in rotation with the time the velocity, with which the transformation takes place, may be calculated. It appears that the formula for a non-complete unimolecular reaction is appli- cable here; da nn Are (at 8) *) [aanda’ are the concentrations of the two glucosides at the moment the measurement begins, « is the quantity converted after the time t |. By integration this formula gives a DE x, is the total quantity converted from ¢—0O to t—= 0. k-+-k’ remained satisfactorily constant during the reaction both when the «- and when the f-glucoside was used, and led in both cases to the same figure. With a 1.34 normal solution of HCl in methylaleohol 44’ at 25° was found to be 0.0051 ; (the time expressed in hours); the transformation at that HCl-concentration therefore proceeds tolerably slowly; the equilibrium is practically attained after about 20 days. 4. The result of the velocity determinations is most simply expressed by supposing that the reciprocal transformation of the two isomers represents an intramolecular migration, in this way: «Sg. The in- 1) I have to thank Mr. ArBerpA van Exenstem for kindly supplying me with a certain quantity of these two substances. 2) This formula has been first applied by Kistrakowsky to esterification. ( 102 ) termediate occurrence of acetal is improbable; we should then have the reaction: a acetal = 3. The quantities measured being the velo- cities with which a or 8 disappears and 8 or a appears. It would satisfy the formula for the reversible unimolecular transformations only if the acetal was converted with an immeasurably great velocity into Bor a. An attempt was made to elucidate this question by means of a separate experiment. Supposing the mechanism of the transformation to be really: a-elucoside = acetal = g-glucoside we should then have two equilibrium reactions for which there would exist four velocity constants. hk, for a-gluc. acetal, 4’, for acetal — a-glue. 8 7 > ies peop " Gras Sj) U eee aay As it had, however, been ascertained that in the condition of equili- brium, acetal is practically absent, the limit for the two equilibrium reactions is situated close to the two glucosides; from this follows J MY, : 1 2 . . . oa that the ratios pt must be very large. This is only possible if 1 2 k, and k, are very small or in other words if the transformation, setting out from either of the glucosides, proceeds very slowly, or if k', and k', are very large, that is to say if the acetal is converted with extraordinary rapidity into the two glucosides. From the results of the velocity determinations already given, it follows that the first possibility does not exist; to test the second supposition, the non- erystallisable substance, which Fiscurr reservedly considered to be the possible dimethylacetal of glucose was prepared according to his directions. The syrup obtained by extraction with acetic ether was laevorotatory fit however still reduced Frnuine’s solution slightly]; it was dissolved in 2 . methyl alcoholic hydrochloric acid (about 2,5 er. in 25 e.c.m.) and the change at the ordinary temperature was observed. This took place by no means rapidly. Rotation: t—0 —1°.0 t= 19 hours +17°.5 = 42 min, + 0°.7 26.5 19 =2 hours +5°.5 43 1 22°.9 67e SED Everything considered it must be assumed to be very improbable that the syrupy substance [perhaps the acetal] occurs as an intermediate produet in the reaction B- e-glucoside. The traces of a syrup which ( 103 ) were found are then due to a secondary reaction which does not interfere with the study of the main reaction. The conclusion should therefore rather be that the two glucosides are directly converted into each other. 5. The point in question would be solved with complete certainty if the reciprocal transformation of « into B were observed in another solvent than methylalcohol. Except in water these elucosides are also slightly soluble in ethylaleohol. As aqueous hydrochloric acid causes a resolution into sugar and methylaleohol the behaviour of ethylalcoholie hydrochloric acid was investigated. In this solvent the transformation also proceeded according to the formula for reversible reactions, the same limit being reached as when methylalcohol was used as solvent *). 6. The concentration of hydrochlorie acid necessary to cause the mutual transformation of the two isomers to take place with mea- surable velocity, is tolerably large; much larger than is usually the case in catalytic reactions. The possibility is therefore not exclu- ded that HCI takes part in some unknown way in the reaction. This theory is supported by the strongly retarding influence of water on the mutual transformation. For a HCl-concentration of L.07 norm. & +4! is about 0.0040. In the presence of 1 mol. of H,O to 1 mol. of HCl. [about 2 vol. °/, water] in the solution £+2' was found to be reduced to 0.0012. If to 1 HCl, 5 H,O was added [about 10 vol. °/, of water], the transformation took place exceedingly slowly, 4 + £/ = 0.0001; in this case a little glucose was also formed. Finally, the constants which have been calculated by means of the 1 tr : formula —/——*—\ for different HCl-concentrations, point to a more rapid increase of £-+-#' with the HCl-concentration than that required by simple proportionality : er arr Concentration HCl | k+ k | ee Hel n. 1.34 (inCH,OH) | 0.0054 0.0038 »2.06( » ) 0.0094 0.0044 » 2.98 (in CH,OH) | 0.0130 0.0057 aT Games jl 0.0384 0.0082 1) The product obtained was syrupy and crystallised very slowly. Apparently, a little ethylacetal or ethylglucoside must have been formed. bid ( 104 ) 7. With a view of ascertaining whether a transformation was also possible without HCl, the 9-glucoside was kept for a long time in a fused condition. After cooling the ap appeared to be quite unchanged. Zinechloride in methylaleoholie solution is also incapable of causing the transformation. 8. In conclusion it may be mentioned that the rotatory power of a solution of methylmannoside [of which glucoside only one form is known as yet] in a solution of hydrochloric acid in methylalcohol gradually decreases without formation of mannose. It seems natural to assume that this is caused by a partial change into a g-isomer which may, perhaps, also be isolated. These investigations are being continued. Org. Chem. Lab. University. Amsterdam, June 1903. Chemistry. “The electrolytic conductivity of solutions of Sodium im mietures of ethyl- or methylalcohol and water” By Mr. S. Tustra Bz. (Communicated by Prof. C. A. Lopry DE Bruyn). In his study of the velocity of substitution of one nitro-group in o- and p-dinitrobenzene by an oxyalkyl*) Sreeer arrives at the result that the reaction constants of o-dinitrobenzene and the two alcoholates Na OC,H, and Na OCH, are not changed by dilution or by addition of a sodium salt. On the other hand, in the formation of ethers, these constants are increased by dilution, as shown by Hecut, CoNRAD and Brickner, and decreased by addition of a sodium salt as demon- strated by STEGER. Losry DE Bruyn pointed out that it would be necessary to inves- tigate the conductivity of Na OC,H, in alcoholic solution. In a further investigation of the influence of water on the substi- tution of the NO,-group in o-dinitrobenzene by an oxyalkyl*) and on the formation of ethers *) it appeared; 1st. that the velocity coefficients of these reactions remained constant when water was added up to an amount of 50 per cent by weight; 2°¢. that the addition of water decreased the velocity of reaction of Na OC,H, but increased that of Na OCH, (at least at the commencement, afterwards the velocity 1) Dissertation, Amsterdam, 1898. Receuil 18, 13. (1899). 2) Lopry pe Bruyn and Arpn. Srecer, Receuil 18, 41. 3) Lopry pe Bruyn and Atpu. Srecer, Receuil 18, 311. ( 105 ) diminishes again); 3'¢. that in mixtures of water and alcohol in which Na is dissolved, the sodium alcoholates are still present. This last conclusion seems at first sight strange. But previous observations had been made which justified the belief that Na OC,H, is present in an aqueous-alcoholic solution of sodium. HEnriqurs *) for instance showed that in the saponification of fats with aqueous-alco- holic soda the fats are not directly decomposed by the NaOH (the alcohol would then only play the part of a solvent) but that at first the ethyl esters of the fatty acids are formed. The well-known reaction of BaumMANN—ScuHorTrTen leads to a similar conclusion. Some three years after the above mentioned memoirs appeared, Lvrors *) studied the action of sodium alcoholate on chloro- (bromo- or iodo-) dinitrobenzene (1, 2, 4), and observed the influence of dilution with both absolute and dilute alcohol. It was then shown that the reaction constants are really affected by the concentration which was not the case in STEGER’s experiments; decrease of the concentration increases the constant, addition of a salt with a common ion, such as Nabr, decreases the constant both in absolute and dilute ethylalcohol. Here again the water seemed to exert an in- fluence, for in the case of ethyl alcohol a fali in the reaction constants took place whilst with methyl alcohol first a rise and then a fall was noticed. Why all this occurred could not be explained. From the above facts it was evident (and it was repeatedly pointed out in the papers in question) that it was necessary to study the conductivity of sodiumethylate and -methylate in mixtures of water and aleohol. For this reason I decided to undertake this investigation. A short review of the results is given in the following tables and the graphical representations connected therewith. A fuller description of the experiments will be given elsewhere. As starting point I always used solutions which were about tj, normal, determined their resistance and from the diluted solutions prepared therefrom, I calculated the w’s for those dilutions and deter- mined by interpolation the w’s for the dilutions of 1 molecule in 1, 2, 4, 8,.,.. 512 Litres. The experiments were all done at a temperature of 18°. In the following tables, the figures are represented graphically in Fig. I, 1, Hl and IV, where the w’s are taken as ordinates and the logarithms of the dilutions as abscissae. By using the logarithms the scale of the drawing is reduced. The alcoholic percentages are 1) Z. f. angew. Ch., 1898, 338, 697. ?) Dissertatie, Amsterdam, 1901. Recueil 20, 292, (1901). ( 106 ) by weight and have been determined by means of the specific gravity bottle. [It is to be noticed that Fig. IM is not reproduced on the same scale as Fig. I; since the methyl alcohol curves wouid intersect and the figure would therefore become confused, the scale of the abscissae has been taken four times larger]. Sodium in Bthyl Ales holt Water. Percentage of alcohol 99.44 96.54 88.8 86.50 78.83 70.40 48.18 25.44 by weight. pCt. pCt. pCt. pCt. pCt. pCt. pCt. pCt. 1 — Doe 6.866 etal 41:59 16.40 35.15 70.05 en 7.602 8:46 “44143 - 12,44 417.90 23.59 49,59, FAO pii 4030 44.99. © 4a Ay 16.87 44 99.70. 49.72". SOTO heg 12.95 14.99 18.72 20.77 96.38 3454 54.16 94.62 ge Sr 45.79 17,05, 22.04. 26,29 30.10 38.67 58.07 99.80 uso 18.92 21.4 25.27 27.66 33.48 42.19 61.34 103.4 ag 2218 24.53 28.59 - 30.86 36.60 45. 92 63.68 1072 Big 25.4 Tae 3153 33.73 39.23 47.68 64.89 109.2 P—056 28.51 30.82 34.31 36.51 44.52 49.67 65.40 4141.2 tss 31.30 33.62 37.04 38.97 43.00 50.81 64.54 4112.0 Sodium in Methylalcohol + Water. Percentage 100 95.09 87.72 S1.40 74.70 69.99 DAR of alcohol. pCt. pCt. pCt. pCt. pCt. pCt. pCt. Bl 21.49 22.77 23.89 25.72 27.85 30.21 33.48 B95 31.48 32.66 33.59 35.02 36 92 38.80 42 715 Py 4 40.38 40.97 AA .21 4A .97 A343 45.26 49.01 Hg 48.13 47 .90 47 03 47.24 48 .36 49.93 53.60 Py —16 54.78 53-63 52.07 51.41 52.37 54 04 57.33 By 39 60.77 58.65 56.15 55.03 55.73 57.30 60.47 Py —64 65.97 65.08 59.64 58.13 58.68 59.79 62.87 198 70.42 66.98 62.62 60.28 61.00 62.07 64.99 My 956 74.50 70.09 64.73 62.12 62.60 63.57 66.40 P5190 71.92 72.44 66.49 62.99 63.72 64.55 67.01 From these figures we obtain the important result that methyl- alcohol differs from ethylalcohol in its behaviour. This is seen at once from the graphical representation in Fig. IV (showing the changes of the w’s, namely of the w=1, Hr2 ete. with the amount of water). At the gas concentration (v= 22) a minimum occurs nt at hd, b f ( 7) a se “5 ‘ = U > OA ve ke S TYMSTRA: „The electrolytic conductivity of solutions of sodium in mixtures of ethyl- or methyl alcohol + water.” if Lif Na dissolved in C,H, OH and H. 0. (LN IV Na dissolved in C H, OH and 09% | H, O. nn and Ae 9.578) 99% a 747% 143 ld 09% oe 200% t — yu Li KE PACT 100 CHOW Ho Proceedings Royal Acad. Amsterdam. Vol. VI. ( 107 ) with methylalcohol. This minimum is not present in the higher concentrations but at the larger dilutions it becomes more and more evident. This minimum is found precisely in the neighbourhood of those dilutions (v= 22 and higher) at which LoBry pr Bruyn and STEGER and Lurors have worked in the experiments referred to above and the amount of water in the alcohol is also the same as that for which these investigators have found the maximum of reaction velocity, namely in 60 to 80 per cent alcohol. There is therefore parallelism between the two phenomena; for methyl alcohol + water + sodium a maximum of the reaction velocity corresponds with a minimum of conductivity. The experiments are being continued up to pure H,O and also extended to mixtures of ethyl- and methylalcohol. Amsterdam, June 1903. Org. Chem. Lab. University. | Physiology. — The string galvanometer and the human electro- cardiogram. By Professor W. Eintuoven. (Physiological labo- ratory at Leyden.) In the Bosscha-celebration volume of the “Archives Néerlandaises”’ *) the principle of a new galvanometer was mentioned and the theory of the instrument dealt with. The practical usefulness of the instrument especially for electrophysiological measurements may be judged from what follows. It may be remembered that the instrument consists principally of a silvered quartz thread which is stretched like a string in a strong magnetic field. When an electric current is passed through the thread, this latter deflects perpendicularly to the direction of the magnetic lines of force and the amount of the deflection can directly be meas- ured by means of a microscope with an eye-piece micrometer. What is the sensitiveness that can be obtained in this manner? Since the above-mentioned publication a number of material impro- vements have been made in the instrument by which it is possible, for instance, to give a very feeble tension to the string, now a quartz thread 2.4 u thick, with a resistance of 10 000 Ohms. If the tension is so regulated that a deflection takes place in from 10 to 15 seconds depending on its amount, every millimetre of the displacement of the image of the string corresponds to a current of 1O—-" Amp. when a 660-fold magnification is used. As under these circumstances a 1) W. EinrHoven. Un nouveau galvanométre. Archives Néerlandaises des sciences exactes et naturelles. Sér. Il. Tome VI. p. 625, 1901. ( 108 ) displacement of 0,1 mm. is still noticeable, as will appear from the discussion of the plates, currents of 10! Amp. can consequently be detected. As far as is known to the writer, no other galvanometer is capable of demonstrating with certainty such feeble currents. In practical work the string galvanometer must consequently be placed on a line with the most sensitive galvanometers of other construction and must be distinguished from so-called oscillographs which only react on much stronger currents. The force which deflects the string in a field of 20000 C.G. 5. with a current of 10~!? Amp. is very small and works out for a length of 12.5 em. at 2.5<10—!! grammes i.e. four times less than one ten millionth part of a milligramme. By giving the string a greater tension its movements become quicker but its deflections for equal currents less. It is easy to give the string exactly such a tension that a current of given intensity causes a predetermined deflection, as may appear from the photograms: of the two accompanying plates. These pbotograms were obtained in the same way as the formerly described capillary-electrometric curves *). The 660-fold enlarged image of the middle part of the string 1s projected on a slit, perpendicular to the image. Before the slit a cylindrical lens is placed, the axis of which is parallel to it; behind it a sensitive plate is moved in the direction of the image of the string. While the movements of the string are thus registered, at the same time a system of coordinates is projected on the sensitive plate by the excellent method of Garten *). Of these coordinates the hori- zontal lines are obtained by mounting a glass millimetre-scale close before the sensitive plate so that the sharp shadows of the scale- divisions fall on the plate, while the vertical lines owe their origin to a uniformly rotating spoked disc which intermittently intercepts the light falling on the slit. The distance of the vertical as well as of the horizontal lines has in our photograms been taken about one millimetre, every fifth line being somewhat thicker. This latter pecu- liarity can easily be introduced into the coordinate system by drawing every fifth line in the glass millimetre-scale before the sensitive plate slightly thicker and by also making every fifth spoke of the rotating dise somewhat broader. 1) See various essays in “PrLücer’s Arch. f. d. gesammte Physiol.” and in “Onderzoekingen physiol. laborat. Leyden.” 2nd series. 2) Dr. Stearriep Garten. Ueber rhythmische elektrische Vorgiinge im querge- streiften Skeletmuskel. Abhandl. der Königl. Sächs. Gesellsch. der Wissensch. zu Leipzig. Mathem. phys. Classe, Bd. 26, No. 5. S. 331. 1901. ( 109 ) The first photogram, fig. 1 plate I represents the deflections of the string when currents of 1,2 and 310-9 Amp. are successively passed through the galvanometer. In the coordinate system a length of 1 mm. of the abscissae has a-value of 0.1 second, an ordinate of 1 mm. representing 10-10 Amp. Although the image of the string has considerable breadth and has no perfectly sharp outlines — as must be expected with a magnification of 660 times — yet its displacement in the coordinate system can easily be determined with an accuracy of 0.1 mm. For if one of the margins of the image before and after the deflection is observed, observation with the unaided eye or with a magnifying-glass will show that the deflection differs from the tabulated amount by less than 0.1 mm. Hence the currents are measured in the photogram with an accuracy of 10—!! Amp. One notices that the deflections are accurately proportional to the intensity of the current, that they are dead-beat and that they are accomplished in 1 to 2 seconds according to their magnitude. The strong damping must be ascribed to the resistance of the air, for during the registering of the curves a resistance of one Megohm was put into the galvanometer circuit by which the ordinary electromag- netic damping was almost entirely suppressed. If the tension of the string is made ten times less, the galvano- meter becomes ten times more sensitive and, as stated above, currents of 10—!2 Amp. may still be observed. But with this greater sensi- tiveness the deflections are no longer proportional to the current and the movements of the string are difficult to record, as the quartz thread no longer moves exactly in a plane. Yet the instrument can still be used then for direct observation with the microscope. Figure 2 plate I shows that the deflections to the right and to the left — in the tigure corresponding to upward and downward deflections, are equal. The velocity of the sensitive plate has remained the same so that again an abscissa of one millimetre corresponds to a time of 0.1 second. But the tension of the string is 200 times stronger so that one millimetre of the ordinates repre- sents 2108 Amp. A current of 4<10—7 Amp. is alternately sent in opposite directions through the galvanometer and hence causes deviations of 20 mm. to the right and also to the left. It is easy to ascertain that these deviations are equal to each other up to 0.1 millimetre. The movement of the string is very quick so that during the deflection the string can only cast a feeble shadow on the sensitive plate. The ascending and descending nearly vertical lines which in the original negative are still visible as very thin streaks have become invisible in the reproduced photogram. ( 110 ) En] In fig. 3 plate I a movement of the string is represented when a current of 3>< 10-8 Amp. is suddenly made and broken. The sensitive plate has been moved along with a tenfold velocity and the string has ten times more tension than in fig. 1, consequently one mm. abse. — 0.01 second and one mm. ord. —10-9 Amp. The gal- vanometer circuit contains again one Megohm so that the same causes of damping exist as in fig. 1. The movement is still dead-beat, but on account of the 10 times greater force on the string it is 10 times quicker, as can easily be ascertained by comparing the great descending curve of fig. 1 with one of the curves of fig. 3 or better still by superposing diapositives of the curves of both figures. They will then be seen to cover each other exactly and since in one figure the velocity of the moving plate is ten times greater than in the other, the defleetion of the string must in one case take place ten times more quickly than in the other. At the same time the resistance of the air is proved in our case to increase proportionally to the velocity of the string itself. In recording the curves of fig. 4 and 5 of plate I the velocity of the moving plate has been increased to 250 mm. per sec. so that 1 mm. of the abscissae is 0.004 sec. The plate at first moves slowly and reaches the mentioned velocity only when it has travelled through a distance of 4 or 5 centimetres, whereas the spokes of the rotating dise always cast their shadows on the plate accurately every 0.004 second. Hence the coordinate system is in the first sixth part of the photogram compressed in the direction of the abscissae. In fig. 4 one mm. ord. = 210-SAmp., while in fig. 5 one min. ord. = 310-8 Amp. These two figures together show us the limit- value of the sensitiveness for which the movement of the string is still dead-beat. In fig.4 a current of 410 Amp., in fig. 5 a current of 610-7 Amp. has been transmitted through the galvanometer and interrupted. One sees that the deflection in fig. 4 is still dead-beat and is completed in about 0.009 see, whereas in fig. 5 the motion begins to become oscillatory and for a single oscillation takes 0.006 sec. The sensitiveness with which the motion of the string is on the border between aperiodic and oscillatory motion is consequently such that a deflection of one millimetre corresponds to a current between 2 vand "Ss 5410 Amp. In the tracing of fig. 4 and 5 only an insignificant resistance is put- into the galvanometer circuit so that here besides the viscosity of the air also the ordinary electromagnetic damping checks the motion. Now some particulars may be mentioned referring to the 5 photo- grams of plate 1 in common. (4111 ) In order to obtain the image of the string equally sharp in all parts of the visual field, the string must move in a plane perpen- dicular to the optical axis of the projecting microscope. A displace- ment of the string of 0.5 u in the direction of the optical axis suffices to cause a noticeable indistinctness of the image with the magnifica- tion used. The photograms show that such a displacement does not take place. The great constancy of the zero point and the equality of the deflections deserve notice and also — which is especially important for practical work with the instrument in electro-physiological measurements — the possibility of accurately fixing beforehand the sensitiveness of the instrument. The unaided eye can already observe in nearly all the figures of plate I that this can be done successfully with an error of less than 0.1 mm. for deflections of 30 or 40 mm., Le. with an error of less than 2.5 or 3 per thousand. Only fig. 5 shows a real deficiency of about 0.1 mm. which some greater care might have avoided. It is hardly necessary to point out that the galvanometer is not affected by variations in the surrounding magnetic field. Moreover it is not to any extent affected by tremors of the floor. It stands on the same stone pillar on which a large tin dise with spokes is rapidly rotated by an electromotor. This electromotor is only at a few centimetres’ distance from the galvanometer, while another motor, coupled with a heavy fly-wheel, for moving the sensitive plate, is clamped to the same pillar at a somewhat greater distance. Yet no trace of mechanical vibrations appears in the photograms. The first electro-physiological investigation made with the string galvanometer was one concerning the shape of the human electro- cardiogram discovered by Ava. D. Warrer *). Until now this could only be obtained by means of the capillary ,electrometer. But the curve traced by that instrument gives, when superficially observed, a quite erroneous idea of the changes of potential differences actually occurring during the registering. In order to know these they have to be calculated from the shape of the recorded curve and the pro- perties of the capillary used. This leads to the construction of a new curve, the form of which is the correct expression of the actual variations of potential. 1) Aveustus D. Watter. On the electromotive changes, connected with the beat of the mammalian heart and of the human heart in particular. Philosoph. Trans- actions of the Royal Society of London, vol. 180 (1899), B, pp. 169—194, 8 Proceedings Royal Acad, Amsterdam. Vol. VI. ( aa) An example may explain this ’). The following fig. 1 represents the curve traced for the electro- cardiogram of Mr. v. p. W. when the current was derived from byes 72! the right and left hands, whereas fig. 2 is the constructed curve. The differences are obvious. Especially the tops C and D in the registered curve should be compared with the corresponding tops R and T in the secondary curve which latter alone truly represents the ratio of the heights of the tops. We shall now try to compare the string galvanometer as a research instrument with the capillary electrometer and must first of all bear in mind that the deflections of the string galvanometer measure a current, that of the capillary electrometer an electromotive force. Jut it must be remarked that whenever variations in current or tension are measured, the mercury meniscus as well as the string moves. And during this movement the capillary must be charged or discharged by an electric current, whereas the string in the magnetic field develops an opposed electromotive force. Moreover, when there is a constant considerable resistance with negligeable self-induction, such as commonly occurs in electro-physiological investigations, the 1) See Prrücer’s Arch. Bd. 60. 1895 and “Onderzoekingen”. Physiol. Laborat. Leyden. 2nd series, vol. 2. (113) intensity of the eurrent will at any moment be proportional to the active electromotive force, so that the fundamental difference between the electrometer and the galvanometer is no obstacle to a comparison of both instruments. The string galvanometer has several advantages over the capillary electrometer. First the deflection of the string galvanometer will in many cases and especially in the case of tracing a human cardiogram be greater and quicker than the deflection of the capillary electro- meter. Then the capillary electrometer is less accurate in the constancy of its indications, their proportionality to the potential differences and their equality in opposed directions. A highly magnified image of the mercury meniscus cannot be so sharply projected as that of a fine thread and one cannot regulate the sensitiveness of the capillary electrometer to a predetermined amount. The electrical insulation of the string galvanometer is much easier than of the capillary electrometer and a phenomenon like “creeping”’ does not occur with the galvanometer. In the capillary electrometer the movement of the meniscus is damped by the friction of the mercury and sulphurie acid when streaming through a narrow tube. Invisibly small traces of impu- rities may hinder or even entirely stop the movement of the mer- cury meniscus. Many a capillary had after a relatively short time to be replaced by a new one because there was a “hitch” in the movement of the meniscus. In the string galvanometer, on the other hand, we have air-damping as well as electromagnetic damping, both of which work with perfect regularity. The electromagnetic damping can moreover be varied at will by changing the intensity of the field and the resistance in the galvanometer circuit. Plate II contains the electrocardiograms of some six persons, traced by means of the string galvanometer. In the coordinate system an abseiss of one millimetre has a value of 0.04 see., while an ordinate of one mm. represents a P.D. of 10~* Volts. By choosing these round numbers the curves satisfy generally the requirements of the inter- national committee for the unification of physiological methods. The movement of the quartz thread, as may be seen from the normal curves at the end of each photogram, was dead-beat and very quick, so that the traced electrocardiogram is a fair representation ot the oscillations in the potential difference existing between the right and left hands of the experimental person. As a rule this may be admitted for the lower tops P, Q, S and 7’ without any noticeable error. But for the high and sharp top Za correction should be applied especially in photograms 8 and 9, a correction by which 8% ( 114 ) the extremity of the top would be shifted a little to the left and upwards. The necessary correction is small however and its amount may be approximately estimated at less than 0.2 mm. for the shifting to the left and less than one mm. for the shifting upwards. Photogram 8 represents the electrocardiogram of the same person whose capillary-electrometrie curve is shown in the text. When the registered curve of fig. 8 plate Il is compared with the formerly plotted curve of fig. 2 in the text, it is evident that both curves have great similarity. The tops P, Q, R, S, and 7 are not only present in both curves, but have also the same relative height in both. In the plotted curve 1 millivolt of ordinate has been made equal to 0.1 sec. of absciss, while in the galvanometer curve 1 millivolt of ordinate corresponds to 0.4 see. of absciss. Hence the galvano- meter curve is compressed in the direction of the abscissae, as a superficial inspection will reveal. Besides the galvanometer curve, on account of the gradual transitions of one top to another, gives the impression of being in its minor details a more faithful represent- ation of nature than the plotted curve. It is obvious that of this latter curve only a limited number of points could be accurately calculated, while for the rest the calculated points had to be joined by the curve that fitted them best. But these small differences are immaterial. It may give some satisfaction that the results formerly obtained by means of the capillary electrometer and more or less laborious caleulation and plotting have been fully confirmed in a different and simple manner by means of the new instrument. For this affords us a twofold proof, first of the validity of the theory and of the practical usefulness of the formerly followed methods and secondly of the accuracy of the new instrument itself. The six electrocardiograms of plate Il were selected among a greater number and arranged after the dimensions of the downward top $ (see the figure in the text). In 6 and 7 the curve remains, at the spot where S ought to be, above the zero-line of the diastole, in 8 and 9 S is only small, in 10 and 11 great. The numbers 6 and 11 mark in this respeet the extremes which occur in our collection of electrocardiograms, whereas N°. 8, that of Mr. v.p. W. represents a sort of norm with which the other numbers may all be easily compared. The constancy of shape of the curve for a certain person is remarkable. This shape seems even to change so little in course of time, that with some practice one may recognize many an individual by his electrocardiogram. We conclude this essay with a remark on the > hIALwH Ze 1 Sec. —10 Amp 10 Abse 1mm. = 0 tee ruses eaNSa sneer Asana GeszeR ZUSEMEL SURGE CEBRA SSRSITL SUES CERSPV HA REVAT LASER RISA EREN pre eet es pee zeer 8 Amp. 0,1 Sec = 210 2. 1 mm. ” Absc. Ord ens: ATOM HUM OEE GEEN BEEREN Key: EA SEES STEN a BER CI SPR EM WE EF or tt SER EME Srna MME 2 AEASERAGLNTIUSRANALSA LSSERCKERE RITA OT Sm EUREAUR SSE RE Na TER nets ra et a SRK ee SEI BEND ES en RR ELIAS ERI EEL LAAG INC SATE OLE EVD TER CS SVARLE TM EWG LEEN DU LEUERLENE EVER RAKEN ND agereusecen 3 ’ 0 4 mm, = 4 Abse. Or OL Sec. 9 Amp. 10 d rin mG ars 0,004 See. 4. .1 mm. = Abse SS ETEN SSD Seman ee —§ 210 Amp 5. 1 mm. = 0.004 Sec. LE Absc. —3 10 Amp 3 Ord. Proceedings Royal Acad. A W. EINTHOVEN: Proceedings Royal Acad. Amsterdam. Vol. VI. “The string galvanometer and the human electrocardiogram.” Plate I. Abse 1mm. = 0,1 Sec. (Oe Lg == 10 Amp 2. Abse, 1 mm. = 0,1 Sec Ord. 1, = 10 Amp. 3. Abse. 1 mm, = 0,01 Sec. Ml, == 10" Amp. 4, Abse, 1 mm. = 0,004 Sec, Ord. 1 5. Abse, 1 mm. = 0,004 Sec, — Ord. 1 „ = 310 Amp. = » =2>X<10 Amp. dk de a | W. EINTHOVEN: “The string galvanometer and the human electrocardiogram’”’. Plate IL ‘ Abse 1 mm. = 0,04 Sec. Ordin. 1 mm —10 Volt Ad. v.d. W Kr. Proceedings Royal Acad. Amsterdam. Vol VI. ( 115 ) small irregular vibrations occurring in most electrocardiograms, where they sometimes reach a height of 0,1 to 0.5 mm. and more, but are sometimes entirely absent, as e.g. in N°. 6 of Mr. Ap. These vibrations are not caused by tremors of the floor or other irregularities which should be ascribed to an insufficient technique as is easily shown by the vibrationless normal curves at the end of almost every series of electrocardiograms. Hence they must be caused by electromotive agents in the human body itself and the question arises whether they find their origin in the action of the heart or of other organs. We may expect that an investigation undertaken with this object will give a definite answer to this question. Physics. — Dr. J. E. Verscuarreit. “Contributions to the knowledge of VAN DER WAALS’ w-surface. VIL. The equation of state and the w-surface in the immediate neighbourhood of the critical state for binary mixtures with a small proportion of one of the components.” (part 4). Supplement N°. 6 (continued) to the Communications from the Physical Laboratory at Leyden by Prof. KAMERLINGH ONNEs. (Communicated in the meeting of May 30, 1903). 17. The a, B-diagram. In the previous communications the different phenomena in the neighbourhood of the critical point in substances with small propor- tions of one component have, according to our plan set forth at the beginning, entirely been expressed by means of the @ and ò and the co-efficients that can be derived from the general empirical reduced equation of state. For shortness, and to avoid the constant repetition of the same factors (comp. §1) I have used till now, instead of the differential quotients of the general empirical reduced equation of state, the co-efficients “, where the m’s (comp. form. 19) have been expressed by means of a and 3, but henceforth, as the numerical values are more important I shall make use again of the differential quotients of the reduced equation of state itself, used in equation (1). It seemed important to me to completely determine by means of the numerical values of « and 8 the different cases which, according to the formulae found by Krrsom (Comm. N°. 75) and by me (loc. cit.), may present themselves in the relative situation of the different eritical points. To illustrate this I intend to divide an a, ?-diagram into fields in which there is a definite relative situation, by means ( 116 ) of lines, as KorreweG has done in another diagram (the x, y-diagram)'). This investigation showed that the last of the eight cases distin- guished by Kortewre of which the inconsistency was demonstrated by him for one special case only, did not exist in general, at least for all the equations of state which satisfy the law of corresponding states. Not to make the investigation too elaborate I have compared the situation of the plaitpoint only with that of the critical state of the pure substance, that is to say I have considered the fields within which Tot > OF << ol pats or pand OL wy. eae also determined in which area the retrograde condensation is of the first or the second kind; and lastly I have indicated in the diagram what had been observed experimentally. The plaitpoint temperature. According to form. (59) the plaitpoint temperature of the mixture is higher or lower than the critical temperature of the pure substance as the expression ME RT pm, , ae mn RT im, RT im, BT ken is positive or negative; and, #,, being negative, 7, — 7; has the same sign as the numerator. If for shortness we put Oy dp dp dp dp Mi aa ar An Pai Ta ne Pao = ot Ovdi Oy on and for convenience we leave out an index which refers to the critical state, because only those values are used which refer to the critical state, MP a Dice pa) C, Pieke) so that the area, where 7 > 7% is separated from that where Tnt Tr by a line of which the equation is: (B — PCP, a= 0. This line, a parabola, represented on the annexed plate ®) by 1) Proc. Royal Acad., Jan. 31, 1903. The « and y are connected in a simple linear way with « and 6 (comp. the previous communication p. 666). 2) For we have (comp. form. (19): PE py Mo, = Pk (3 Tir Por «), WU) ee ee Cts —— 2 vr? Le a ze Pao (a—3)| RAC 1 pe 1 pr Mima foes a Paor a0 = 94 ya 40” ele. ; For the definition of C, comp. KamertinGu Onnes (Arch. Néerl. (2), 5, 670, 1901; Comm. no. 66). 3) The figure is drawn by using the values of pj, pj, ete. which will be calculated in the next section. lor clearness | have represented the a’s in a 5 times larger scale than the (3’s. ( 117 bAOb’ corresponds to Korrewse’s first boundary '). Outside the parabola Pepi. des made, Tin Fy. The plaitpointpressure. From form. (60) we derive that pj: > or < peas Po (8 — Po, 0) > or KC, Pf. The equation of the boundary Por (? — Pox a)? a C, Pia B= 0 is that of a parabola represented in the figure by cOBc’. Outside the parabola px», > ps, inside < pr. The plaitpointvolume. The manner in which v,,; depends on @ and B may be derived from form. (61); it is expressed by Kersom’s formula (2c), which I borrow from him in my notations: (3- Pq CUR CMe. Hence the boundary is here: == — 9 (GP i, CP (BP) HCP (PP a)+ Cp Pubs (a- 5). This is a curve of the third degree, like Korrewra’s third boundary, with which it corresponds in this diagram. In order to investigate this curve I introduce, following the example of Korrewra, a parameter z, by putting Vrpl—=- Vk + orla) — Wro, — C,).,(8-¥ 014) —3C,p*,,@]. ijs sE ote and I find that « and 8, by means of that parameter are expressed thus: LS N neten den a Pin sol B= pl Por Par 27 + Co EP or Par — 8 Pde — Ch Pr “woh where J) ens Cent Oren ER lS Cris 2 As a and @ are single valued functions of z, all lines which are parallel to the straight line B=y,,@ (Oa of the figure) intersect the curve at one single point at a finite distance. If we put: eG a 7) jaa eee the straight line 8 = p,, a + z,, being a dotted line in the figure (CD), 1) To avoid mistakes I use here the word boundary, instead of the expression border curve used by Korrewea; for in our demonstrations the word border curve has a very special meaning, viz. that of a boundary between stable and unstable states. dy 2) As pj is also equal to the direction-cosine (a) of the tangent to the re- dt Jk duced vapour tension curve at the critical point, and as it follows from the form dp ra of that line that (=) > 1, zj must necessarily be positive. t/k ( 148 ) is an asymptote of the cubic curve. It has two branches, of which the one (JG Ed) situated above the asymptote, is given by values of 7, which are larger than 2, the other (d'OHFi'"), below the asymptote for z< Z,. a becomes equal to zero not only for z—O, but also for two other real values of z, of which the one is positive, the other negative; I shall eall the positive root z,, the negative one z,. In the same manner 8 vanishes for z—O and also for two other real values of z, of which again one (z,) is positive, the other (z,) negative. We can prove that always 2, >z,; for z, and z,, three cases are possible: both are larger than z,, and then z, >2z,, or both are equal to z,, or both are smaller than z, and then z,< z,. With the values of the derivatives, to be introduced presently, the order of the roots is: ea 0D >en and hence follows the form of the cubic curve as it is drawn in the figure *). One can easily see that v,,i >> vj above the branch z > z,, and within the branch zv7,- According to form. (41) and (26) OT > vr, When m,, and nm, + hT,m,, have the same sign; m* + RT; m,, is positive outside the parabola bAOb' and negative inside, while m,, is positive above the straight line Oa and negative below it. Hence we have vy,) >vz7, and retrograde condensation of the second kind: 1st. inside the parabola 4405 and below the straight line Oa, 2"d, outside the parabola and above the straight line; at all other points vrt < v7; and the retrograde condensation is of the first kind. Here follow the physical characteristics of the fields into which the figure is divided by the boundaries under consideration : Field 1: Ppl = Tr > Pxpl = Pk > Uxpl = Uk » UTpl SS UTr II Er 2 Pept > Tk y Papl SSPE Ol KET DELEN ED Il 3 Typl > Les Pipl Pis Val EEEN UIN SG Ons Tech 4 Tapt > Tk 1 Papl > Pk » Vapl EDE apt So ar kele Ge PT xpl pe Dg Aan Dal Pie Vapl Era A ON PE Zn I Gi Tipt

> 7, whereas the observations showed that Fi Tr; this deviation has been pointed out before. ) More- over the situation of P in field 2 points to a system of isothermals of the mixtures as represented in figs. 1 and 2 of the first paper, while in reality this system of isothermals corresponds to figs. 5 and 6, that is to say to one of the fields 7, 8 or 9. The point P lies very near the limit of field 9, and hence it is possible that a more accurate determination of « and 8 would remove the point P into field 9 where indeed it should lie according to the plaitpoint constants observed and the character of this field, if at least the law of corresponding states can be applied. The points Q and R, so far as we know with certainty, are situated in the right field. *) The straight line B= y),, @ agrees with Kortewse’s second boun- dary. It is determined by the circumstance that along the conno- Lr dal line (=) =(); we find from the formulae (37), (41) and (26) that: ) pl dir 2m, 1; ( jen Moy Soe at UT pl — UTr) = &T pl dv pl m*,, +kT)m,, : fe), RE; dijk We | da ; : so that ; becomes zero with m,,. Thus above the straight line Oa av (=) is positive, below it, negative, hence in connection with tae av 1) Comp. 2nd paper, p. 334. 2) It must be remarked that the deviation of the point Q in consequence of our insufficient knowledge of z and 3 would be much less striking than in the case of point P; e.g. whether Q ought to be placed in the neighbouring field 4 or not, could be only concluded from the sign of #4, — vk, but we do not know with certainty what this sign should be for mixtures of carbon dioxide and methylchloride. ( 1205 preceding it follows that KorrewrG’s eighth case: ryy ry de A apl< Tk 5 Vopl vk en <0 dv pl is in general not possible. A direct proof of this circumstance may easily be given. Because ml must be meegatwe, I put Sur ee 7). requires that 3 ris? G—y,, 2) == Chas. Hence we may put: «= and ADE rt ds? ; r* Ut i 2 Vepl Sh a nr) rare = PY Uk a vem Le Een ee as ore C, Pi Cai Pee so that all the terms of v,,) are positive. Hence we see that, if r r di - A oy lene Tai < Tr and (=) O, Vil Svp is an impossibility. „Jp 18. The numerical value of the reduced differential quotients. To find this numerical value I have first tried to derive it directly from the observations by means of graphical representations; but as I did not succeed in finding more or less reliable values for the higher differential quotients (»,,, Ps, 4) ete.) L was obliged to use formulae which satisfactorily represented the observations. Undoubtedly KAMERLINGH ONNES’ °) developments in series are best fitted for this purpose, although just in the neighbourhood of the critical point, where in our case they have to be applied, they deviate rather much from the observations ®). Therefore the values of the derivatives obtained in that way, especially those of the higher orders, can only be con- sidered as approximate. By means of the temperature co-efficients of reduced virial co- efficients marked by V.s.1?) derived from Amacatr’s observations, I find for those virial co-efficients (U, B, ete.) and their first deriv- atives according to the temperature (U, 3’, etc.) at the critical pomt (EU), 1) Proc. Royal Acad. 29 June 1901, Comm. N’. 71, and Arch. Néerl. (2). 6, 874, 1901, Comm. N°. 74. 2) Comp. Arch. Néerl. loc. cit. p. 887. Previously I have given parabolic for- mulae (Proc. Royal Acad., 31 March 1900, Comm. NO. 55 and Arch. Néerl. (2), 6, 650, 1901) which very well represent the observations just in the neighbourhood of the critical point. These formulae, however, do not harmonize with our consi- derations, because they do not yield finite values for higher derivatives, 3) Comm. N°. 74, p. 12. ( 124 ) Ue =e von se 105 rs + 366,25 << LO en Oe Se SIO 8 B, = + 662,387 XxX 10-3 Ge BO 10+! QS 55 855,774 pee D, = — 360,485 Xx 10! ore 7--- 789,880 x“ 102s Ge. 7 4-683,07- 3c LO @ = + 346,72 X 10-% Oe BOLE LO 5, = — 698,82 x 10-3 If further we put 2=0,00102 (calculated from 7,—304,45, pi=72,9 and 7,=0,00424, we find at the critical point: Po 0,98833, »,,=0,10305, »,,——0,16831, p,—— 5,30648, 20 Po 75579292, ,,=7,34410, p,,——9,99986, p,,— 27,76382, ete. The values of y»,,, ¥,, and »,, ought to be equal to 1, O and O respectively ; the tolerably large deviation of the two last derivatives proves that the series used do not represent the shape of the iso- thermals in the neighbourhood of the critical point so accurately as we might wish‘). Hence it follows that the values of the other derivatives calculated here cannot be very precise, and probably this uncertainty increases with the order of the derivative. I take as approximate values of the reduced differential quotients at the critical point: Pe moe y=. (Og N= (yay), —— — LO, py, = 28, while „0810. 7) According to VAN DER WAALS’ original (reduced) equation of state: St 5 tender: S01 yt” we should have oR > O Y 8 LF AS) Beers FP Por A Pai Bn SS, Ce Oe, ) and according to this modified equation : St Belt == == . tl vo Bn 9 TN 126 ah 7 Pir 12 > Pai = 36 ’ C, TE 2,7. Finally I substitute the numerical values of the derivatives obtained 1) On the cause of that inaccuracy and the possibility of improving upon it a new communication by KameriinecH ONNEs is to be expected. (Comp. Comm. no 1450 ps. 15). 2) Kersom gives (Comm. n°. 75, p. 9 and 10) Cy= 3,45, p1 =7, 9) =— 9.3. 3) It will be seen that these values agree tolerably well with the former ; it is thus not remarkable that so close a resemblance exists between the forms of the boundaries found by Korrewea and by me, which indeed is based on VAN DER Waats’ original equation. ( 4159 above in formulae (9) and (10) and compare the result with the observations. Equation (9) yields: 1 N co SU TO EET = A 30 and equation (10): 1 1 3 Drs 5 (s +»)—-1l=— re E a ale | (1 — 1) = 10,9 (1 —t). 30 Pao In order to compare these results with the parabolie formulae of Marnias *), formulae must be derived for the reduced densities of the co-existing phases; representing these reduced densities by », and ò, I find, according to a transformation employed formerly : *) 1 = Cid.) = 3.87 It a (DP) —1= (8,37 —10,9) (1-1) = 0,5 (13). In the last formula, however, the co-efficient 0,5 is somewhat uncertain. Marmas gives for the liquid branch, according to the observations of CaiLLeTeT and Maruias *), db, =1—2,47(11—)4+4,09/1—r, and for the vapour branch eames Re Be Eh a Chem eh EL Maat ae f From these formulae it would follow that the two branches of the border curve belong to different parabolae. The co-efficient of V1—t or the vapour branch perfectly agrees with the one found, and the fact that Marnras has found a greater value for the same co-efficient in the liquid branch, may clearly be aseribed to the uncertainty of the then existing data on this subject. If we neglect this difference, the formulae of MATHIAS give: Ln ova) = t+ 8) —1= 0,25 (1 — 9), a sufficient agreement with the co-efficient 0,858 later derived by him from AmaGat’s observations. The value 0,5 found above is in good harmony with this. 1) Journ. d. Phys., (3), 1, 53, 1892. Ann. d. Toulouse, Y. 2) Proc. Royal Acad., 27 June 1896; Comm. no. 28, p. 12. Mere acurately we have 3 Lil Boies Meese ager ee ES i jk 3 Uke + Pp a gp Vk ae vk ve (p ) 3) Journ. d. Phys., (3), 2, 5, 1893. Ann. d. Toulouse. VI. J. E, VERSCHAFFELT. “Contributions to the knowledge of VAN DER WAALS’ y-surface. VI. The equation of state and the J-surface in the immediate neighbourhood of the critical state for binary mixtures with a small propor- tion of one of the components.” (part 4). , 7 7 ld f / 7 7 1 1 i 7 / 7 ce t 4 ¢ 7 2) 4 daf neet a en AEEA (a) Akte a 7 F LH , 1 7 En 4 3 5 7 7 5 SPH ae EM , 2 4 5 4 3 5 349) | ik 4 J El Fe ’ & 3 3 “J a ans a 3 za za 3 3 3 sld) =d 3 3 3 te “ pa HE ! 3 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 128 ) Physics. — “The liquid state and the equation of condition.” By Prof. J. D. van DER WAALS. (Communicated in the meeting of May 30th and June 27th 1903). It has been repeatedly pointed out that if we keep the values of the quantities a and 4 of the equation of state constant, this equation indicates the course of the phenomena only qualitatively, but in many cases does not yield numerically accurate results. In par- ticular Danie. Bertuenor testing the equation of state at the expe- rimental investigations of Amacar, has shown that there occur some curves in the net of isothermals, e.g. those indicating the points for which the value of the product pv is a minimum, and other curves of the same kind, whose general course is correctly predicted by the equation of state, but whose actual shape and position as determined by the experiments of AMAGAT, shows considerable deviations from the course of those curves as it may be derived from the equation of state. In consequence of this circumstance the quantities @ and 5 have been considered as functions of the temperature and volume. Already Crausius proposed such a modification for the quantity a; for car- bonie acid he does not put @= constant, but he multiplies it with 273 rk view to the course of the saturated vapour tension. From the beginning I myself have clearly pointed out that, though a may probably be constant, this cannot be the case with the quantity 4. One of the circumstances which I was convinced that I had shown with the highest degree of certainty as well in the theoretic way as by means of the comparison of the experiments of ANDREWS, was that the quantity > must decrease when the volume decreases. So for carbonic acid I calculated for 4 in the gaseous state at 13°1 the value 0,00242 and in the liquid state a value decreasing to 0,001565. But the law of the variability of 5 not being known, I have been often obliged to proceed as if 4 were constant. In the following pages I will keep to the suppositions assumed by me from the begin- ning, namely that « is constant and that 4 varies with the volume; and I will show that if we do so, the considerable deviations dis- appear for the greater part and that it is possible to assume already now ‘a law for the variability of 4 with the volume, from which we may calculate in many cases numerically accurate data even for the liquid state at low temperatures. Such a modification seems to be required principally with a Eble To that purpose we shall begin with the discussion of the tension of the saturated vapour over liquids at low temperature. From the conditions for coexisting phases of a simple substance, that namely p, T and the thermodynamic potential are the same in both phases, follows: (pe =f, = (pv — {rt a dv a ae dv pir f = peer : v —b/, v —b}, If we put == constant i.e. 4 independent of the volume, then the latter equation assumes the well known form: a a E — —— RT log =| = E — — — RT log (—0 | v ; v 3 Properly speaking this equation is not suitable for the direct calculation of the coexistence pressure; it must be considered to give a relation between the specifie volumes and so also between the densities of the coexisting phases. At lower temperatures, however, for which the vapour phase, which we have indicated by means of the index 2, is rare and may be estimated not to deviate noticeably from the gas-laws, or the equation becomes suitable for the calculation of the pressure of the saturated vapour. In this case it assumes the following form: P RT: a pe, — — — RT log (v,—b) — RT = RT log vy We find after successive deductions which are too simple to require special discussion : a a(v,—b) a _,, pv,—) pr, — 5 Be. —{pt+ =) (v, —b) = RT log — =e p pn + = (wb) = RT log ns Piat na 1 y,— p pb — 5 — ie 5 : [RT — p (v,—b)|] = Ui ilog EEN a Pen v, v, (v,—2b) a ae Dr v,—b p + = log aed b a Pale Kd MT al ( 125 ) : . ma, OL Ee Ee Undoubtedly p may be neglected by the side of — . Even if p 2) amounts to one Atmosphere, its value is certainly still smaller than 4 v(v— 2b) 0.0001 part of —. In the same way ear v, ) may undoubtedly be negleeted by the side of > or pv, (v,—2b) by the side of a — ) a nj) and this for the same reason, for is a quantity of the same a order as —. we So the equation may be simplified to: a Pp b v,—b log — = — = en ee! ee oe eee ee ay 1 For the limiting case, when v, may be equated to h, we get: a het b og — = — ; oo RT oe If we introduce the critical data, namely : a 8 a pv ZE 57 i? and Fd a Db’ then we get the following equation for the calculation of p: p Pt el — log — = — — — log 27 Pk ona d or, as log 27 is equal to 3,3 and may therefore be nearly equated 9” to ~ we get with a high degree of approximation: og Ee ange one Pk d's This last equation is nearly equal to that derived by prof. KAMERLINGH ONNES by means of a graphical method from the equation of state with « and / constant, namely : Sheik (=) Pk T KAMERLINGH ONNES found this equation to hold in approximation up to the critical temperature, here we could only derive it for low 1) Arch. Neérl. Livre Jub, dédié à H. A. Lorentz. p. 676. ( 126 ) temperatures. If in equation (1) we do not ef introduce v, —b, we may write it as follows: a P b v,—b lo Signe” ely Se el 9 awe RT a b b? v, or a ) b v.—b v bog = Mees Db iy Capa Ln die RPI Ee 5 b? For values of v, only slightly greater than 4 we may write Did . U, al —— for log—. So we get: b pelt ) ul Tij, v,—l — log ! = : + : : == log 20 “Pk rop Le b ‚v—b The value of Dr ) varies with the temperature and starts with the value zero for 7'=0°. It may be calculated from: a . (v,—b) = RT. Ie This last equation may be written as follows: | e el rad i ) oT iy eC ) b L ID ; d A: v,—b 1 ° N ‘. Oh t = ate find for ET the value 5 and with 7 — OSE l : Yi 1 the value Tt With Piss ou Bl : 5 Oe ah varying with the temperature, the term BT does not represent the total variation of $8 with the temperature, With 5 C —b the value of 2— is equal to 0,2125. The quantity LG but the difference is small. We might calculate the value of — 7 is from the above equation, but it is simpler to calculate this quantity from the following equation : 7 Op ag de Gal Mes EL For coexisting phases this equation becomes : … dp &,—&, SS dr V,—?, or a a _, dp i? “Ue a ty aT —p= aan = a at) A OSM EN U) For low temperatures this yields: a a a(v,—b) A re Tt MR p dT Bh AE RL or a LT dp b v, Fac wierd (6 or T dp ive 2°07, v,—b Gal TAS bee For T= 7, equation (2) yields: T dp ae ae = 4. pal J; For the highest temperature, therefore, at which the pressure curve el I ) I ry. occurs, the coefficient with which k RN fs 8 : must be multiplied in order to yield ry. T dp the value of DaT’ does not differ much from that for the lowest Be temperature at which the liquid may exist without solidification. Here we have one of the striking instances, how the equation of state with constant a and 5 may represent the general course of a quantity just as it is found in reality, though the numerical value differs considerably. For the real course of the vapour tension is at least in approximation represented by the formula: Pp Erk nf log ii JN =/ ‘yy ’ Pk 1 but the value of f is not 4 or somewhat less — but for a great many substances a value is found which does not differ much from 7. Before discussing this point further, we shall calculate some other quantities whose values for the liquid state for low temperatures follow from the equation of state when we keep a and 6 constant. 9 Proceedings Royal Acad, Amsterdam. Vol. VI. ( 128 ) Let us take again p to be so small that we may write a —(v —b) = RT. ” From this we may deduce: dv v == — 2 1=(= ar) Per For — = 0,585 (Ether at 0°) = is equal to 4,7 as appears from : ER Tr, v ed am Swat (; ) — 4,7 we find: T (dv 1 PEL Jy an. 27 So we find for the coefficient of dilatation under low pressure and at this temperature which is so low that we may neglect the pressure, the value: (3) With this value vd 1 / dv 0,00567 k v \dT/p= 2,7 Comparing this value with that which the experiment has yielded and which we may put at 0,001513, we see that it may be used at least as an approximated value. B 1 dv The above equation (3) yields for — | — with v = 26 an il v dT El) ryy ¢ eee 7 infinite value and so 7 == k 5° This quite agrees with the circumstance ad 27 that the isothermal for gees touches the J’-axis and it warns us ik: Zl ev that equation (3) cannot yield any but approximated values for much lower values of 7. av For the coefficient of compressibility 8 namely =| 5 ) in that vap/T same liquid state we find dp RTv, 2a a v, af: dv, rie en Bete vt v,—b 7 iL basf — = 27 px | — —2 |. B a v,—b or (129) With the aid of the above data and putting pr=87,5 atmospheres we find : B = 0.0006 (nearly). The experiment has yielded no more than about 0,00016 for this value. So we have found it so many times too large, that for this quantity the equation of state with constant @ and 5 cannot be con- sidered to hold good even in approximation. From the well known equation: dv\ (OT) (Op __ 1 (ar), (poe) T (Ov Op \ _ r Op ee aur) si, follows and therefore With the values mentioned above and yielded by the experiment we should therefore have for ether at O°: ESO WANEN SE 07 SÀ 37,5 0,00016 Ln a i : v According to this equation v should be smaller than & which would be absurd, if 6 does not vary with the volume. Did Al . k then we find for ether Spr. / = 0,0057 circa; in reality the liquid volume appears to be smal- ler than 6. Dividing namely the molecular liquid volume by the nor- mal molecular gas volume we find about 0,0047 *). From this appears convineibly that the variability of 6 exists in reality and that there- fore an equation of state in which this variability is not taken into account, cannot possibly yield the data of the liquid state. Let us return to the equation: Pk Pit — bg = fs p 1 which holds good at least approximately, as is confirmed by the or If we calculate the value of 0 from experiments, if we take for f a value which is about twice as great as would follow from the equation of state if we keep a and 5 con- 1) Continuitiit 2nd Edition, p. 171. 2) Continuität 2nd Edition, p. 172. ( 130 ) stant. What modification must the equation of state be subjected to in order to account for this twice greater value? Cravstvs answered this question by supposing a to be a function of the temperature Er 273 e.g. by substituting a TT for it When we consider the question superficially, the difficulty seems to be solved. But it is only seemingly so. At 7’= 7; this modifica- tion really causes f to assume the value 7 — but this supposition has consequences which for lower temperatures are contrary to the experiment. If we calculate the value of d, En i AS By Ss Ye 1 di VV, a 273 as on page 4 and if we take into account that € = — 2 — zn v find a 273 lip tora WE pdT Tne GT For lower temperatures we will put v, = b and we deduce approximately : Tdp _ pe 273 pdT “tb RT? or 7} T d 27 (Ty? | oe SS ae (7 . p d1 gg fy 1 : T dp : , : For ——=— we find then for ——, a value which is not twice Pir 2 p di as great as that which follows from a constant value of a, but a value which is four times as great. The equation : E = pte | = E == pa | 1 2 yields for this value of a: p 27 (Te ty —log—- = 2K = — log | 27 1. en ida Ee ( ryt (Tk a In order to agree with / (F-1) the positive term of the right- PAT wage hire hand member of this equation should have the form A a ae and fe the negative term should not be log 2 X 27, but log 2 1) Continuität, p. 171. ( 131 } The ‘imperfect agreement between the real course of the vapour tension and that derived from the equation of state with « and 5 con- stant, has induced us to assume that a is a function of the tem- perature. It appears however that this agreement is not satisfactorily established by the modification proposed by Crausis. It will there- fore be of no use to proceed further in this way — specially be- cause this modification in itself is certainly insufficient to account for the fact that liquid volumes occur which are even smaller than 6. If we had not supposed a to increase so quickly with decreasing T TEN: ae temperature as agrees with a a if we had chosen ae ~“* for in- stance, then the greater part of the above difficulties would have vanished. We should then have found: A en IN Ir The expression (1+ = \e Tr is equal to 2 at 7 = Ty and at k T= 0 it would have increased to e= 2,728 etc.; so the increase is relatively small. But the term which should be found equal to log 27*, would also have remained far below the required value. For this reason it seems desirable to me to inquire, in how far the variability of 5 alone can account for the course of the vapour tension. | As I dared not expect that the variability of 4 could explain the course of the vapour tension as it is found experimentally, and in any case not being able to calculate this variability, I have often looked for other causes, which might increase the value of the factor f from 27 es — to about twice that value. The quantity — representing the amount Vv with which the energy of the substance in rare gaseous condition surpasses that of the same substance in liquid condition, and this Lg je C quantity seeming — from the value of ni of to be only half of what pe it should be, I have thought that the transformation of liquid into vapour ought perhaps to be regarded as to consist of two transforma- tions. These two transformations would be: that of liquid into vapour and that of complex molecules into simple gasmolecules. If this really happened then the liquid state would essentially differ from the gaseous state even for substances which we consider to be 1 ( 182 ) normal. We should then have reason to speak of “molécules liquidogenes”’ and “molécules gazogènes”. It would then, however, be required that the following equalities happened to be satisfied. In the first place the two transformations would require the same amount of energy; and in the second place the number of ‘‘molécules liquidogènes” in the liquid state *) at every temperature would have to be proportional with p(v,—-?,) the value of The following equation would then hold: a a ase eng woe, E Tdp Poe mee alen) a (‚ee pdT a p(v,—?,) v‚v,p p(os—v,) Not succeeding in deducing this course of the amount of the liquidogene molecules from the thermodynamic rules and in accoun- ting for the above mentioned accidental equalities I have relinquished this idea, the more so as this supposition is unable to explain the fact that the liquid volume ean decrease below 0. If we ask what kind of modification is required in the equation of state with constant a and 5 in order to obtain a smaller vapour tension, we may answer that question as follows. Every modification which lowers the pression with an amount which is larger according as the volume is smaller, satisfies the requirement mentioned. In the following figure the traced curve represents the isothermal for constant a and 5; the straight line AB, which has been constructed according to the well known rule indicates the coexisting phases, and the points C and D represent the phases with minimum pressure and maximum pressure. The dotted curve has been constructed in such a way that for very large volumes it coincides sensibly with the traced curve, but for smaller volumes it les lower, and the distance is the greater according as the volume is smaller. Then the point D' has shifted towards the right and the point C” towards the left. For in the point exactly below D as well as in the point d exactly below (C the value of = for the dotted curve is positive; av these points lie therefore on the unstable part of the modified iso- thermal and the limits of the unstable region are farther apart. But it is also evident — and this is of primary interest — that if for the modified isothermal we trace again the straight line of the coexisting phases according to the well know rule, this line will lie lower than the line AB. The area of the figure above AL 1) Diminished with that number in the gaseous state. (133 ) has decreased, that of the figure below AB has increased in conse- quence of the modification. The line A'S’ must therefore be traced noticeably lower in order to get again equal areas. B' will of course lie on the right of B, and we may also expect that A’ will lie on the left of A. We have, however, put the question in too general terms; for our purpose it should have been put as follows: what modification in the quantities « and 6 makes the vapour pressure at a temperature which is an equal fraction of 77, decrease below the amount which we find for it, keeping « and 5 constant and it would even be still more accurate not to speak of the absolute value of the pres- E : 5 P og : : sure, but of the fraction —. The modifications in « and 5 should > Pk then be such, — if we base our considerations on the preceding figure — that in consequence of the modifications themselves the values of 7), and p, either do not change at all or very slightly. If we make « a function of the temperature we have to compare the following two equations: RT a DSS — Î re 3 and AE aT’. ser — ob + By tek eae ee 8 a art afd Both equations yield R7; = US and py, = apie the same values for 7% and p, if a and 5 have the same values in both ( 134 ) equations. The value of p — the values of 7’ and v being the same for both curves — for the modified isothermal is smaller than that for the isothermal with constant « and 5, and the difference is greater according as the volume is smaller. According to the figure 7 ; P : 3 discussed — — the value of =. being the same for both curves — Pk Ie will therefore have a smaller value for the modified isothermal than for the unmodified one. A value of a increasing with decreasing value of v would have the same effect. But I have not discussed a modification of this kind, at least not elaborately, because I had con- cluded already before (see “Livre Jub. dédié a Lorentz” p. 407) that the value of the coefficient of compressibility in liquid state can only a be explained by assuming a molecular pressure of the form —. The Uv supposition of complex molecules in the liquid state would involve ‘ry. a modification of the kinetic pressure to sot), where @ (v, 7’) (P10, must increase with decreasing value of v. Also this supposition would lead ‘yy to a smaller value of P for the same value of —. This is namely Pk Tr 1 certainly true, if the greater complexity has disappeared in the critical state, and if therefore the values of 7). and pj, are unmodified; pro- bably it will also be the case if still some complex molecules occur even in the critical state. But whether this is so or not can only be settled by a direct closer investigation, and for this case the property of the drawn figure alone is not decisive. I have, however, already shown above, that we cannot regard this circumstance as the probable cause of the considerable difference between the real value of the vapour pressure and that calculated from the equation of state with constant a and 5. So we have no choice but to return to my original point of view of 30 years ago and to suppose b to be variable, so that the value of 4 decreases with decreasing volume. It is clear that a variability of this kind causes the kinetic to be smaller than we should find it with constant 5, pressure v— and the more so according as / is smaller. Moreover it is possible in this way to account for the fact, that liquid volumes occur smal- ler than the value which 4 has for very large volumes and which I shall henceforth denote by 6,. Or I may more accurately say that I do not return to that point of view, for properly speaking I have never left it. As the law of the variability was not known, I could (135 ) not develop the consequences of this decreasing value of 4 — but it appears already in my paper on “The equation of state and the theory of cyclic motions” and in the paper in the “Livre Jub. dédié a Lorentz” quoted above that I still regarded the question from the same point of view. My first supposition concerning the cause of the decrease of 4 with the volume was not that the smaller value of 4 corresponded to smaller volume of the molecules. 6, being equal to four times the molecular volume, I supposed smaller values of A to be lower multiples of this volume. In this way of considering the question the decrease of 5 does not indicate a real decrease of the volume of the molecules. We will therefore call it a quasi-decrease. It can scarcely be doubted that such a quasi-decrease of the volume of the molecules exists. In his “Vorlesungen” BOLTZMANN started from the fundamental supposition that the state of equilibrium Le. the state of maximum-entropy is at the same time the “most probable state’; in doing which he was obliged to take into account the chance that two distance spheres partially coincide. And comparing the expression which he found in this way for the maximum-entropy 0e q with the expression nf 3 (i.e. the entropy in the state of equi- DE librium according to the equation of state) it was possible for him to determine the values of some of the coefficients of the expression: bte |t) +e(2) Wende . This method is indirect. I myself had tried to find these coeffi- cients by investigating directly the influence of the coincidence of the distance spheres on the value of the pressure. According to these two different methods different values for the coefficients were found. My son has afterwards pointed out (see these Proceedings 1902) that also according to the direct method a value of « equal to that calculated by Bonrzmann is found, if we form another conception of the influence on the pressure than I had formed and since then I am inclined to adopt the coefficients calculated according to the method of BoLTzMANN as accurate. But these values apply only to spherical molecules and only in the case of monatomic gases we may suppose molecules with such a shape. It is not impossible that for complex molecules these coef- ficients will be found to be much smaller. Moreover for the determina- dv ik tion of J : knowledge of all the coefficients is required — and U ( 136 ) we cannot expect that the calculations required for this purpose will soon be performed. Even the determination of 3 required an enormous amount of work — compare the calculations of van Laar. For complex molecules another reason is possible for decrease of 4 with decreasing volume. The molecules might really become smaller under high kinetic pressure i.e. in the case of high density. If the atoms move within the molecule and we can hardly doubt that they do so — they require free space. And it is highly probable, we may even say it is certain, that this space will diminish when the pressure which they exercise on one another, is increased. The mechanism of the molecules however being totally unknown it is impossible to decide apriori whether this decrease of the volume of the molecules will have a noticeable effect on the course of the isothermal. In my application of the theory of cyclic motions on the equation of state I have tried to give the formula which would represent such a real decrease of the volume of the molecules with diminishing volume. vaN Laar has tested this formula to AMAGAT’S observations on hydrogen, — and though new difficulties have arisen, the agreement is such that we may use the given formula at any rate as an approximated formula for the dependency of 5 on v. I will apply the formula, which may have a different form in different cases, in the following form: pn b—b,\? pe SD ty, eee ee v—b ba—b, The symbols 4, and 4, in this formula denote the limiting values for 5, the first for infinitely large volume, the second for the smallest volume in which the substance can be contained. For more particulars I refer to my paper on “The equation of state and the theory of cyclic motions.” Van Laar concluded from his inves- tigation that agreement is only to be obtained if 5, decreases with 7, a result which | myself had already obtained applying the formula for carbonic acid (Arch. Néerl. Serie II], Tome IV, pag. 267). If this is really the case and if it appears to be also true after we have modified the formula in some way or other compatible with the manner in which it is derived, then the following difference exists between the course of 5 with v when ascribed to a quasi-diminishing and when ascribed to a real diminishing of the volume of the molecules: in the first case 6 is independent of 7, in the second dp case however it does depend on 7. The fact that i is not per- v fectly constant seems to plead for the latter supposition. @ £8715 „For the present, however, I leave these questions and difficulties out of consideration, and I confine myself to showing that a for- mula of the form (4) can really make the considerable differences disappear which we have met with till now. The more so as this formula appears to be adapted for the derivation of general conse- quences, which follow from the decrease of 6 with v. I leave there- fore a possible dependency of 6, on 7’ out of consideration. Moreover in applying the formula I will suppose 6, = 25, I choose one — in some respect arbitrarily — from all the forms which | have found to be possible (compare also my paper in the Arch. Néerl. “Livre Jub. dédié a Bosscha). The numerous calculations required in order to investigate in how far modifications are necessary and possible in order to make the agreement with the experiments more perfect, may perhaps be performed later. A. The tension of the saturated vapour. Let us begin with the caleulation of the pressure of the saturated vapour at low temperatures and let us to that purpose write the equation expressing that the thermo-dynamic potential has the same value in coexisting phases, in the following form: a yee (v-b) (dh pv-—- RI EE EEN | AE ET ce Met PIRES ee v v—b v-b |, 2 of i a db | pe —- RT log(v-b) - aaf | = ] ta se AE an cee | v v-b |, F In my paper “De kinetische beteekenis der thermodynamische yotentiaal” I have already pointed out the signification of the term I J 5 ds , 4 a ae it represents namely the amount of work performed by v— : the kinetic pressure on the molecule when this passes in a reversible way from the condition of the first phase into that of the second phase and when its volume is therefore enlarged either fictitiously or as we now take it to be, really. We may calculate this term if we assume the chosen form for 4 and this is one of the reasons why I adhere to the idea of a real increase of the molecular volume. But though its value may depend upon the particular form which we have assumed for 6, it will certainly have a positive value for every law of variability of 5 with v which we may choose. b—l Jo db Let us for the calculation of Te 5 denote ——— by z, then we v— bb, ( 138 ) have db = (b,—b,) dz and according to the form of formula (4) chosen for 6: bob, JE 124 je wean ee, ee db ps eee : in consequence of which up Passes into dz = logz — aen Gn z Substituting into the expression for the thermodynamic potential we get: b—b 1 b—b, \’ PE EET lag BRL RT : v ä b,—b, 2 If we suppose the temperature to be low, the second phase is a rare gas phase and we have: _pv= RT, log (v—b) = — log an and = i In consequence of this we get: i I b,-b, 1 b,-b, p 1 pr, Prag (v,-b,)-RT LEN us =RT+RTlog gE or boe RTS RTlog HERT as = RT loge Pv) v, BER Ben RT or a Sates ote PU ering ee SRL CE tyr en POE eee hat vb, a Pia As yet we have not applied any approximation for the liquid condition. If in the first member we collect the terms containing p, we may write them as follows: v,7— 26,0, ; The value of v, in the liquid condition being only slightly larger than 26,, the value of this expression remains below 5, and it may certainly be neglected; if in the second member we neglect also 1 a p compared with —, then we may write the equation for the calcu- v 1 lation of the vapour pressure at low temperatures as follows: a P b, Dil bis Dinh ieee = es jm 5 ie RT's, rn tee ©) (1398) In order to draw attention to the principle circumstances, we shall assume for the present that the following equations also hold in the case that 6 is variable : 8 ys a 27 by and Werd Pk 97 bj” Equation (5) may then be written in this form : zt U REEN head FNP | FO NN v, A comparison of this equation with: T bert) Pk T shows that it is possible to satisfy the condition that the coefficient of Tr : by ae : P approaches to 7 by equating ai to 2, ie. by assuming that the 1 molecules in volumes equal to the volume of liquids at low tempe- ratures are only half as large as those in the gaseous condition. But rp : . Sale ; the agreement in the value of the coefficient of = does not suffice for establishing agreement between the calculated value and that of the formula which at low temperatures is followed by the vapour tension, though it be only in large features. For this purpose it is required that Be =O hsb v.—b ] 27 ay q 0 1 al 0 si 1 1 Ì cs 5) = i 7 dir r b, differs only slightly from 7. We must return to the equation of state in order to be able to determine the value of this expression, and we must investigate its consequences for the case that p may be neglected compared with as a So we must return to: Dv a Va pine Berden ie BE) On v ETA If we express h, and v, in the quantity z, we get: 6, =b, + 2 (6,—b,) | Ee led ~ and v,—b, = (6,—6,) ( 140 ) or yee (- + 2) Beb) A ~ Substituting these values and putting 6,= nb, we get the equation : > ~ 8 T 7 (n—1) Te Sp pele z 2 1+ En : | If t Desai 7 2 f = 0,8 we put n=Z, then we get = a Ol rn 1 7 z=— i ——0,7 5 ih? 1 Ee z= 7 ——(),65 6 Ti 1 T EEE ia 0,645) 7 Te For very small values of ¢ we may neglect z? compared to unity and we may calculate the value of z from the approximated equation: ope i 22 O71, i sae Fe i which equation yields the value of 2= cap for aa. For such we k sd —b v,—)b z v 1+2¢ small values of z we have: ——*=1, ——~=—— and S= v,—), b, l+z b, Il1+z2 We will assume that for all temperatures below 0,6 7), the vapour phase may be considered to have a sufficient degree of rarefaction for following the gaslaws; therefore we may assume z to have a Days 1) the 1 v by 1 4x16 Se: : value 4 | lig [OE == 2,56. With “this valne B. 25 value below 1 . If we choose z= aie then we find for we have: v,)/ b,—b, 2 v,—b, b It is true that this value is smaller than /og 27°, but it approaches sufficiently to that value. The fact that it is smaller than /og 27? is in perfect agreement with the circumstance that for the quantity f in P T,—T wd Pk J te bbe ah oe bei eee. k Saas ds tog Te El ae = tag 27 x 20,5 Ok the formula according to the experiments at low ( 141 ) temperatures a higher value must be chosen in order to establish agreement. For a higher value of f yields the same result as a not ry : AIEE rs : ; ; higher value of f in Ip from which a smaller quantity is subtracted. It might appear that the dependency of p on 7'is strongly increased by the difference between the values of z for different temperatures. The following relation however always holds good if 4 is indepen- dent of 7: a T dp Boe ws v, pat TRP and therefore (see p. 127) or T dp = a TO, obi p ARN BL b, b 1 which expression does not vary much with z, if z remains small. Yet we find the value of —— Pp C stances to be somewhat higher than is indicated by this formula. We should in fact have found a higher value if we had assumed b,>2b,. If therefore we had only to deal with the formula for the vapour tension, then it would be rational to investigate the conse- 1 1 quences of the suppositions: = 2 Pe 2->. Other experi- ad at low temperatures for most sub- mental quantities however follow less perfectly the formula chosen for b, if we give n these values. Therefore I will confine myself to the investigation of the consequences of the equation chosen for oy with. n — 2. I think the following theoretical observation to be of some impor- tance, even if we disregard the question whether we have established a perfect, numerically accurate agreement with the experiments, by assuming the quantity 4 only to be variable, and even this varia- bility to be independent of 7. The pressures in two coexisting phases which lie at a great distance from the critical conditions satisfy, if ( 142 ) we suppose the volume of the molecules to be invariable, the follo- wing approximated equation a Ae pe. log — = — “M rik In this formula M/ denotes the pressure of the liquid phase 1. e. a the molecular pressure, and te the heat required for the transfor- ) mation. The following approximated equation holds for molecules of variable volume: a p b, log —— = — ——— , “ Mk Pils where again De denotes the heat required for the transformation, which 1 is greater if the molecules in the liquid phase are smaller, as well in the case that this diminishing of the volume is real, as in the case that it is only fictitious. Again the molecular pressure is also higher. But the molecular pressure is now provided with the factor A. If it is a real diminishing then the signification of this factor can be sharply defined. The factor is in this case at least approximately its signification can be derived from the following ?) Lome equal to as equations, (comp. my paper: “The equation of state and the Theory of cyclic Motions”): OP. jar ue () | (bb) = RT ae eae ee Rr ob b=b, ie ae M + ori Opn be ; Db gas, pn Ge 0b Joe, OP, The quantity Ge in this equation represents the atomic forces, So we find for it: which keep the molecule intact or at least contribute to the causes which keep the molecule intact. Making use of this value of A we find : ( 143 ) iy) EEE thd EC The first member of this equation contains the logarithm of the product of two ratios, namely the ratio of the inwardly directed forces which keep the molecules — considered as separate systems — inside the vapour and the liquid phase, and the ratio of the inwardly directed forces which keep these systems in both phases intact. In the case that it is a quasi-decrease it is impossible to indicate the db signification of A in such a precise manner; but the quantity a; differing also in this case from zero, the above considerations show with certainty that the quantity A’ exists also in this case. The question whether it will be larger or smaller can only be decided by a comparison of the course of 6 with v in the supposition of a quasi decrease with that in the supposition of a real diminishing, b—b The term — EN Ml 0 has been neglected in equation (6). This equa- tion applies only for low temperatures, and for those temperatures 1 the term in question is equal to > according to the formula given ad for 6. It is remarkable that also many other suppositions concerning the nature of the forces which keep the molecules intact, different from those suppositions which have led to the form chosen for 6, yield the same equation (6), every time however only after neglection of a relatively small quantity in whose kinetic interpretation I have not yet succeeded. We obtain equation (6) when we assume, 1* that the molecule may be regarded to be a binary system consisting of two atoms or of two closely connected groups of atoms, which we shall call radicals, 2"¢ that these parts move relatively to each other, and 3'¢ that the amplitudes of these motions are of the same order as the dimensions of the atoms. If the parts are radicals, other motions take place inside those radicals, but the amplitudes of these motions are so small that they have no noticeable effect on the volume of the radicals. We have represented the forces which the atoms or radicals exercise on one another by a (/—d,), so in the gaseous state by «a (b,—,). So, as we have derived the equation: alli == 01 and as 6,—6, is constant, @ must be proportional with the temperature, — and I must acknowledge that it is difficult to image a mechanism 10 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 144 ) for the molecule in which the forces between the two parts of which it is thought to consist, satisfy the conditions, that they are propor- tional with the distance, and at the same time increase proportionally with 7. Perhaps we get a more comprehensive conception of a molecule, if we ascribe the forces which keep the atoms together in the molecule not to a mutual attraction of the atoms, but to the action of the general medium by which the atoms are surrounded. The molecules of a gas are free to move inside the space in which they are included and they are kept inside that space only by the action of the walls; in the same way it might be that the atoms of a molecule were the volume of the molecuie — free to move inside a certain space and that they are only prevented from separating by an enclosure of ether. Still assuming that 4,—é, has for all temperatures the same value, we should be again obliged to conelude that the forces which keep the molecule intact are proportional with the temperature, but this conclusion would now be much less incomprehensible. According to these suppositions it is also rational to assume that the force required to split up the molecule into two atoms is the same for all temperatures. So we should obtain the formula: b—b, pees b—b, v—b b,—b, With this equation we have: bj b, ib ee 1 bh Se = [a ee Beel — log Ein 2 —b ET EEN, Bm A PET VTE - | |. b bob, En —__—_ has now twice the value it had before, but the chief term has remained unchanged. In my further investigation, however, I will continue with the dis- cussion of equation (4), because my chief aim is only to investigate the principle consequences of the nearly certainly existing diminution of 6, independent of the question whether this diminution is real or only fictitious; and in doing so I will confine myself to a certain conception of the molecule — that which leads to equation (4) — as an instance. The term which must be subtracted from log B. The coefficient of dilatation and the coefficient of compres- sibility of liquids. Let us again assume the temperature to be so low that p may be a 5 and that we therefore have: negleeted compared with Vv ( 145 ) a — (v—b) = RT. 0) 1 / dv The value for — aT which we may calculate from this equa- v a P tion applies only to the pressure p= 0, and is therefore not the same as would be found for another constant pressure; neither is it that which corresponds to the points of the border curve. For very low temperatures the difference will probably be small. For higher temperatures the differences might be considerable; and for the temperature which is so high that the isothermal in its lowest ù \dT be absurd to suppose the two values to be mutually equal. 1 (dv point touches the v-axis, in which case — { — | =o ‚it would even Pp be ae An accurate calculation of the value of —| — yields accor- U dT p=0 ding to the relations chosen above: I~ - 1 2e ET en ME Ade ae) | eae ap an PE RE Tg ¢ (1- 2) We will put „== 1 and the following approximated relation : T (dv 22 wat) 5 Lae I With Geary (see p. 140) this yields 0,4 for the value of Ta, or D} OE aah (for ether) = 0,00146. Our assumptions therefore appear to lead to a value for the coefficient of dilatation which does not deviate much from the experimental value. YY Et If we had taken the form ae 7* for a, then the corresponding value of 7 would have been —— and we should have had: Io ’ T / do +e it fh az Amt ar which is only about *, of the true value. From this we conclude that the assumption that our relations are satisfied and that at the tate same time « has the form ae 7% leads to inaccurate results. 10% ( 146°) vdp dv 1 We might also write a value for (— ) or ri. but we will culate the coefficient only indirectly from: T ( dv dp a v\ dT P i der) ve . bans 0,413 X 6000 = 27 pe ( 2) or Vv or with approximation : A ~ I= : 122 1 which agrees with z= a The value of B calculated according to our relations may there- fore be considered to be at any rate approximately accurate. Yet it remains strange that for the liquid volume itself a calculation according to our suppositions yields a value which is much too small. According to a table in Cont. I 2ed p. 172 the liquid volume for 1 temperatures which do not differ much from — 7), is equal to 0,8 5. Even if we take into account that bo << 4, we cannot diminish the factor 0,8 to less than 0,7. We have then the equation 0;7 bg = b, A + 22) fi or 0,0 n =1-+ 2z. With n= 2, this yields z= —, which does not agree with the ul 1 value —, which we must assume for z, as we saw above. I have 7 not yet been able to investigate, what modification must be made in the relation assumed for 5; e.g. to put 2—1,8 or to suppose 4, really to be smaller at low temperatures. If we suppose 4, to be a function of the temperature, then the calculations become very intricate and difficulties of another kind arise. Therefore I prefer to regard the above considerations as conducing to point out that everything shows that / must really increase with 7. Let us investigate what consequences of general nature follow from this variability of 5. In the first place we observe that the three real values of v for given temperature and given pressure cannot be calculated any more by means of an equation of the third degree. The equation of state namely may assume a very intricate form if ( 147 ) we substitute in it the expression for 6 which we get by solving the equation which expresses the variability of 5 with v and 7’ — the possibility of a dependency of 4 on 7 being admitted. We shall represent the solution of this equation by b= g(r, T). But the general course has remained the same; e.g. the fact that for temperatures below the critical temperature a maximum and a minimum pressure occurs. The critical temperature is that for which this maximum and this minimum pressure coincide and the critical point may again be calculated from the three equations: p= Ihe), a? and me a dv? JT If therefore we could exclude all disturbing influences, if we could neglect phenomena of capillarity and adsorption, if we could neutralize gravity, if we could keep the temperature absolutely constant throughout the space occupied by the substance, if we could perform the experiments with perfectly pure substances without the slightest trace of admixtures and if we could suppose that the equi- librium is established instantaneously, then we should have coexistence of two homogeneous phases of well defined properties for all tempera- tures below the critical one, and exactly at the critical temperature only one homogeneous phase of well defined properties would exist. But the requirements enumerated here can never be fulfilled. Already below the critical temperature deviations occur. The straight line representing the evaporation parallel with the v-axis has probably never been realised as yet in connection with the circumstance that nobody has as yet experimented with a perfectly pure substance. The boiling point always varies when the distillation is continued, chiefly if we observe near the critical temperature. If in a closed vessel we heat a substance which is separated into a liquid and a vapour phase, then the properties of the liquid phase may be varied by shaking the vessel (Eversuem. Phys. Zeitschr. 15 June 1903), probably in connection with the circumstance that the liquid expanding during the heating is internally cooled in consequence of the expansion and the evaporation and reaches the surrounding temperature only very slowly by conduction; and also in connection with the always occurring impurities. If further the substance is subjected to gravity, then neither vapour phase nor liquid phase is homogeneous. To ( 148 ) every horizontal layer corresponds another density according to the formula of hydrostatics: dp = — ogdh. For temperatures far below the critical one this circumstance is of little importance; for the critical temperature itself, however, the influence of gravity is considerable. If we write namely the formula of hydrostatics in the following form: tE l dp dh —— = — g —, o do do dp dh : then we see that — — 0 or — =o at that point of the height of the do do re d do vessel where the critical phase really occurs, i. e. where — = 0. alt If therefore we construct a graphical representation of the successive densities, laying out the height as abscissa and the density as the ordinate, then we get a continually descending curve. In the beginning its concave side is turned downwards; at a certain point the tangent is vertical and the curve has a point of inflexion; farther the convex side is turned downwards. In the neighbourhood of the critical phase we find therefore a rapid change in the density. The equation of state can only account for the state of equilibrium described above as it deals only with states of equilibrium. Another question is how that equilibrium is established and whether it is established in a longer or shorter time according to the method of investigation. It has been observed several times in these latter years that the state of equilibrium of a quantity of a substance which is contained in a closed vessel slowly heated to the critical temperature, requires so long a time before it has been reached that some investigators have concluded that the liquid consists of other molecules than the vapour. Dr Hrer, Garirzing, TrAUBE and others speak therefore of “molecules liquidogenes” and “molecules gasogenes”. Some of them suppose the “molécules liquidogenes” to be more complex, others suppose them to be only smaller. This latter supposition agrees with the ideas I have expressed in my “The equation of state and the theory of cyche motions.” And for an explanation of the fact that the equi- librium is so slowly established, these investigators refer to the slow diffusion of the heterogeneous molecules. To this fact they refer however wrongly. The kinetic theory accounts satisfactorily for the slowness of the diffusion and has even enabled us to calculate the coefficient of diffusion for mixtures of ( 149 ) heterogeneous molecules which cannot pass into one another. Here however we are dealing with molecules which can pass into each other. And if in such a case the establishing of the equilibrium requires a long time, then we must account for the fact that in this ‘ase. more-atomic molecules only slowly conform their size to the varied circumstances, though in other cases they can bring their internal motions so quickly into harmony with, for instance, a variation of the temperature. I therefore think it not to be proved, that the increase of 5 being either a real or a quasi increase, requires a noticeable time to be brought about, till the real constancy of the temperature throughout the closed vessel and the perfect purity of the substance has been proved, which as yet is not the case. It must be granted that the summit of the ‘boundary curve is broadened and flattened by the variability of h and that the critical isothermal may be estimated to have a larger part which is nearly parallel with the v-axis. And this causes considerable differences of density to follow from small differences of pressure. But if no causes even for small differences of pressure can be pointed out, then the occurrence of differences of density larger than those that follow from the action of gravity cannot even be called phenomena of retardation, these latter being also a kind of phenomena of equilibrium. Another observation of general nature before 1 conclude at least for the present these considerations on the influence of the variability of 6. This variability accounts for the possibility of deviations from the law of corresponding states. If the way in which 6 varies with the volume is different for different substances 1.a. in couse- quence of a different ratio of 6, and 5, then the general course remains the same, but the isothermals become different in details. I have even begun to doubt whether the behaviour of substances acids, alcohols, water containing the radical OH in the molecule etc., which in gaseous state present no association to double molecules and which are often indicated by the name of abnormal substances — which behaviour deviates so markedly from that of other sub- stances, must really be ascribed to association of the molecules in the liquid state. In connection with equation (6) (see p. 143) the question arises : Is the OT, quantity which I have denoted by —— for these substances perhaps 0b small? Is the easy substitution of one of the components perhaps an indication of a feeble connection of the parts of the compound which involves a strong variability of the size of the molecule. The so called ( {150 ’) abnormal substances would then be those whose molecules can undergo large variations in size. More suchlike questions arise — but I will no further discuss them without a closer investigation. BOS T SUB EP TEM. When the above paper was printed I received a kind letter from Dr. Gustav TeicHner, who informs me that he has sent me one of his tubes filled with CCl, in which he has succeeded in strikingly showing tbe large differences in density at the critical temperature by means of floating glass spheres whose specifie gravity has been determined accurately. He himself however acknowledges emphatically : “dass diese Erscheinungen insofern keine Gleichgewichtszustande vor- stellen, als die Phasen in Berührung mit einander sich aüsserst lang- sam (beim Rühren sofort) zu einer homogenen Mischung vereinigen.” The equation of state deals only with states of equilibrium as I have observed already before. Discussing these anomalies as I have done in this paper, I treated questions which properly speaking lie outside my subject. I have mentioned them, because I also expected for a moment that the variability of 5 assumed by me, might account for the slowly establishing of the state of equilibrium. But this is only the case if we assume, that the molecule does not immediately assume the size which agrees with the value of 7 and v — and this seems after all to be improbable to me, though I acknowledge that molecular transformations occur which proceed slowly. The expectation of Dr. TricnNer, that the theory would lead to two really homo- geneous phases is inaccurate in consequence of the action of gravity — as has been shown already before i. a. by Govy. Not the phenomenon itself as it is seen, is anomalous, only the differences of the density are anomalously large. It is true that Dr. TricHner writes to me that he has ascertained that the temperature was constant but even a 1 difference of temperature of 100 degree yields a very considerable difference in density. For densities which are larger than the critical one we have: T dp mad T° > 5 P being comparable to unity. If therefore in a point the tempe- 7 8 i d | l I rature is AG degree too low, a diminishing of the pressure with ( 154) 1 an amount of about 100 atmosphere will keep such a phase in equi- librium, at least as far as the pressure is concerned. And a cause 1 which accounts for a difference of pressure of about 00 atmosphere accounts also for considerable differences in density as the critical isothermal runs nearly horizontally in the neighbourhood of the critical point. A return to the time when we thought to explain a thing by speaking of solubility and insolubility, seems not to be desirable to me. Chemistry. — “On the possible forms of the melting point-curve for binary mixtures of isomorphous substances.” By J. J. VAN Laar. (Communicated by Prof. H. W. Bakuuts RoozrBoom). I. The occurrence of so called “eutectic points” in meltingpoint- curves does not seem to agree with the supposition of perfect tsomor phy of the two solid components and of their mixtures. This fact has been repeatedly pointed out. It has been assumed that an inter- ruption in the curve representing the solid mixtures (as in fig. 1 of the plate) can only occur for tsodimorphous substances, and that the series of mixtures in the case of isomorphous substances was necessarily to be uninterrupted (as in fig. 2). Lately STORTENBEKER *) expressed again the same idea and this induced me to subject the question to a closer investigation. In the following paper I hope to show that an interruption in the series of the mixtures can very well occur even for perfectly isomorphous sub- stances. In order to do this we must keep in view that — especially in the solid condition — wnstable phases may occur, and that in all occurring cases it is possible to trace the meltingpoint-curve conti- nuously through the eutectic point. Only the stable conditions which generally lie above the eutectic point are liable to be realized, so the series of the mixtures is interrupted only practically. Prof. Bakuvuis RoozrBoom has expressed the idea of prolonging the meltingpoint-curve beyond the eutectic point already before; the way however in which we must think this to be performed is indicated inaccurately in the figure of an earlier paper of STORTENBEKER*). 1) Ueber Liicken in der Mischungsreihe bei isomorphen Substanzen, Zeitschrift für Ph. Ch. 43, 629 (1903). 2) Ueber die Löslichkeit von nydratierten Mischkrystallen, Z. f. Ph. Ch. 17, 645 (1895). ( 152 ) The following considerations are an abbreviated survey of a more elaborate paper which will be published elsewhere *). Il. I have shown in a previous communication’), that we may express the molecular thermodynamic potentials of the two compo- nents of a liquid mixture if we assume the equation of state of VAN DER WAALS — as follows: a,x? u, =e, — 6, A" ae (A, + Le) de log T+ ieee a RT log (1— x) 7 I 7 ry a,(1—-)? ry Uy = eC, Cs Ti (k, En R) 1 log T + l Tray aL RT log a“ The different quantities occurring in these equations have the well known signification, indicated in the paper quoted above. In order to simplify the calculation we shall always assume in : jaa b, =e ; : the following, that 7{ = — |= 0, and therefore that the equa- y | A : tions et, en ande == oa U identically satisfied, A representing yy 29). a,b —2a,, 6,6, a,b. This assumption comes to the same as the supposition that the molecular volumes of the two components differ only slightly, which supposition may be considered to be Cr a,(1—z)? and 1+rx)? (1+ rex)? influence of the two components in the mixture only approvimately. In the second place I shall assume that the above expressions also apply to the solid state, an assumption which we may expect to be satisfied in first approximation, as the case we are dealing with, namely that of mived crystals or solid solutions*), shows in many respects the greatest analogy with liquid solutions. If we also suppose 7 in the solid phase to differ little from zero, and if we indicate all quantities in that phase with accents, then we may write: For the liquid phase: “uw, me, —¢, T— (hk, + B) Tlog T+ axe? + RT log (A—z) | ( justified, as the terms represent the mutual u, =e, —c¢c, T— (k, + KR) Tlog T + a (l—a)? + RT log: For the solid phase: wise, ed, T—(&, + B) Tlog T+ a 2” + RT log (1 —2’) wee, —e, T—(k, + RT log T+ a (le!) + RT log 1) 1) In the Archives Teyler. 2) These proceedings April 24, 1903. 3) Mixed crystal will always be treated here as solid solutions, though in these latter years difficulties have sometimes arisen against this view. See La. STORTEN: BEKER, l.c, p. 633. ( 153) ~The components are in equilibrium in both phases if a ' . _ ' On Ee so that we get (the terms with 7'log 7’ cancel each other): e,—¢, T+aw2’?+RT log (le) = e,—e, T4-a! &? + RT log (1—2') Coa, Ta (l1—«a)?+ EE log U edc, T+a' (la!) JAT log a or with [ar eae ce A We , eet : Cr OF i Sg ap Cri rn Og ==: a! = qe T+ (a a?—a' x") av RT log i ! RT log = %—Y¥, T+[e(l—a)?—al(1—2')*] wv v If we pay attention to the circumstance that for =O, «'=0 the quantity 7’ must be equal to 7,, and in the same way T=T7, for w=1, w=1 (7, and 7, are the meltingtemperatures of the pure components), then we may write: pies 1 vie vB pe iis ah ’ as is =! We have therefore rm 1 le e ! 19 T | — + R log —— |= 9,+ (a #?—a' 2”) | 1 ee 4) 4 5 cine ee zel = 4, + [a(1—a)?—a'(1—a'y"] | U | or with EN Ma == Gia qi ro 2,,2 rot 1+ ie ee! ela! 2 1-+ (Ba? —p'2') : qs | Mee lee ; Ales a ee 1+ — log 1+ log — Vy le Vs a These are the two fundamental equations from which we may cal- culate the values of w' and 7’ corresponding to each given value of x, and which represent a course of the meltingpoint-curve which is perfectly continuous, at least theoretically. It is easy to see that in the case that no mixed erystals occur, 2’ is continuously equal to zero, and the equation is reduced to 1+ a hs Li E, 7 RT, 1— log (1—2#) 1 an equation which I have already deduced in a previous paper. But in the present paper we will assume that the mixing-proportion bi ( 154 ) in which one of the components occurs in the solid phase, though in the extreme case it can be exceedingly small (i. e. practically equal to zero), yet in general can never be rigorously equal to zero. In this way the continuity remains preserved, and we may give all possible values to the quantities 3 and ' as to 9 from O to oo. We shall observe here at once that the quantity which dominates | the whole phenomenon is the quantity 8’ of the solid phase. When this quantity has a high value, the solid phase will contain only a very small trace of one of the two components, and only when the value of this quantity becomes comparable with the corresponding quantity B in the liquid phase, the case of fig. 2 can occur. It is therefore of the highest importance to know the exact signification of these quantities 3 and 8', or rather of the quantities a=g, Panda’ —4q, B. From the above deductions appears namely that the quantity ar” does not represent anything else but the absorbed /atent heat required for the mixing per Gr. Mol. for the case that an infinitely small quantity of one of the components is mixed with the solution in which the mixing-proportion for this component is 1—.w. In the same way the quantity a(1—.«)’ represents the latent heat for the other component in this solution. The quantity a itself is therefore the latent heat for the first component for «= 1; ie. for the case that the first component is mixed with a solution which consists exclusively of the second component — or we may also say that a is the latent heat for the second component for «=O; i.e. for the case that this component is mixed with a solu- tion consisting exclusively of the first. The fact that these two quantities of latent heat are the same is a consequence of our supposition b,==b,, from which follows that «, S55 is equal to 1 A : Wie : nne In reality these two quantities will not always be equal. do ij That the signification we have ascribed to the quantities «av? and a (1—.r)? is the true one, may be shown from the numerators of equation (2), which being respectively multiplied with g, and q,, represent the total latent heats of liquefaction a, and w,, namely w,=q, A + Ba? — Pe”) = q, + aa? — ax” | en ee (: HEB -f (eey) =, Helle (1-2) | Jz The total latent heat required for the liquefaction is therefore equal to the pure latent heat of liquefaction, augmented with the latent heat required for the mixing of the liquid phase, diminished with that required for the mixing of the solid phase. (155°) A high value for @ (or 8) means therefore a high value of the latent heat of mixing, and when we shall presently see that a high value of 8 leads to very small values of 2 or of 1—v’, this circumstance may be interpreted as follows: If a large amount of energy is required in order to make one of the solid components enter into the solid solution (or the mixed erystal) then this solid solution will contain only a slight trace of one of these two components. HIL We now proceed to the discussion of the fundamental equa- tions (2). | : on Ua, dT Let us in the first place determine the quantities a and — by je wv totally differentiating the conditions of equilibrium — u’, + u, = 0 and —w, +u,=9 according to 7. After several transformations we get: ! 0°5 ( ! 070) Bere. a aa GAA Sos) igs , EER (l—a)w, aw, ’ de! — (Ll) w, Jew, Ö These well known equations have been deduced several times *), La. by Prof. van per Waars for the analogous equilibrium of liquid and gaseous phases. pp From (4) we may deduce the quantity (=) ‚Le. the cnitial direc- de), tion of the meltingpoint-curve. Ou, RT As — == — + 2 ars, we have Ou ie 075 1 Ou, RT — = OT — — 2a, Ow? uv Ow (1 = x) therefore, for x= 0, T= 7, a RT, we have: Gl Wed Oey) tae if we write z, for «=0. For «=O we havealso2’ = 0. The [LT denominator of aa appears therefore to be equal to (w‚), = q,, hence av en (et ) Es he au ded a. sE 2s Tn v/o 1 di vo 1) See ia. my Lehrbuch der math, Chemie, p. 118 and 123—124. (Leipzig, J. A. Bantu, 1901). ( 156 ) from which follows that — gq, being supposed to be positive — rj ! the value of (=) can only be positive if — should be greater than da ), 0 ! . . . . uv . unity. Let us therefore determine the limiting value of —. With vy T= T,; «=0,a =0 we may derive from the equationg (2): 1+2@—8) Js ee 1+ log == VE ay and we have: di, / bh (eB) 1 vy _ 4s VE 1 og = —_| — as == SOE 1 FE ih Bo : 4 Therefore the value of — remains smaller than unity, and the Lo meltingpoint-curve continues to descend, as long as we have: ME é qa, \1 2 eh In the following we will always assume 7, > 7’, or rma | 2 positive. The above condition will then the sooner be satisfied, accor- ding as 8’ in the solid phase has a higher positive value. Now probably 8 will nearly always have a very small positive value and p’ a rather large positive value. The condition will therefore probably be nearly always satisfied. If we put @=O, then we get simply : ' ! a i A a I Ge al If 8’ (or a’) is positive, i.e. if heat is absorbed in mixing the solid / B 8 ! “ : phase, then we shall always have — <1 and therefore the melting- f & 0 point curve will always descend on the side of the highest temperature. An initially ascending part and in connection with this the occurrence of a maximum-meltingtemperature is therefore almost totally ex- cluded. The possibility of a maximum exists only in the exceptional and nearly inconceivable case, that 6’ has a much smaller positive value than 2, or even a negative value. dT If we determine (=) at the side of the /owest temperature quite CS x=) in the same way, then we find, denoting 1— 2 by y: ( 157 ) Er Teale 2 (2 i ‘) du Jy = ae V3 Yo lai Yo sts V1 ip Mis i PER is Tik 2 where: ! AMR Oee : ze The quantity — is therefore always smaller than unity if Yo le Oa a ak Sk ee Ae The second member being negative, this condition can only be satisfied if 6’ has a high positive value. Two cases may therefore occur, according to 3’ being larger or smaller. In the first case the initial part of the curve near 7, descends again and a mininum will therefore occur (fig. 2). In the second case the curve ascends near 7; it will therefore descend continuously from 7’, to 7, without presenting a minimum. For the case 7, = 7, the conditions (5) and (57) pass into B ME 8 st 0, and a mimimum will always in this case occur if 8’ >8, and probably this will always be the case. dic! In the above considerations we have tacitly assumed that anoma- lous components occur in neither of the phases; formation of complex molecules or dissociation are therefore always excluded in the cases which we consider. When one or both of the components of the solid phase for instance consist totally or partially of double molecules, then the occurrence of a maximum is not excluded at all. We now proceed to the discussion of the equations (2) for different values of 8’, starting with very high values. dT The same considerations apply of course for ( 0 IV. In the following we shall always put @ =O (in the liquid phase). This simplifies the calculations in a high degree and it does not alter the results qualitatively. The equations (2) then take the following form: di, r Ql te a ie ASR 8 Ae ) Uk Reis T; (1—s d 6 pee ( Qs 4 = LG RTS) Sn ETS (°) 1+ log 1+ log — q, “1e I # Let us further assume the following values, in order to be able to execute the calculations numerically : ( 158 ) Li T200 q, — 2400 Gr. cal, Then we get (R= 2): pd, 1200 (8e 2) % 500 (1—1,28 (1—a')’) Pog ee Vg! 1 a! 1 + log — 1 + — log — “1l—e# 2 a We will begin with assuming @ to be very large, e.g. 8 = 5. As we have a =—q, B’ this means that the latent heat of mixing for the first component when «=1 (or of the second when w = 0) is five times as great as the latent heat of solidification of the first component. From the above equation: 1200 (1—52") __ 900(1—6(1—2’)’) i 9 a 1 a 1+log 1+ —log— lS Der ’ we may calculate the temperature 7’ corresponding to an arbitrarily chosen value of z, the value of «' being exceedingly small. So we get fort: zt 1200 ae 1—log(1—a)’ and for «': 1 a 25 1+ En log A = — 12 (1 —- log (le). The following table I (p. 159) gives a survey of the corresponding values of #, «' and 7. This represents the branch AA’ of the meltingpoint-curves which starts from 1200° (see fig. 3). AB' is the curve 7’ = f(a’). If we put 1—x = y and 1—2' —y then we have the equations 500 (1—6y"?) 1200 (1—5(1 —7/)’) es Ly eee | Lee epee y RE, ee —4¥ My 1 rd from which we may calculate a new series of corresponding values of w, w and 7. So we get the branch BB' starting from 500° (BA' is again the curve 7’= /(w')). The value of y' being in this case very small, 7’ may again be calculated from 500 N= - : 1—0,5log(1—y) and # from TABLE I. TABLE II. NEY. A A a” T |—>X10*| x! >< 10° y T Sr X<10° y' X 107 ON EE aa 10 0 500 | 25 0 0.4 | 4086 | 44 14 0.1 | 475 | 45 15 0.2 | 94 | 8.3 | 47 0.2 | 450| 8.6 17 Ork da ee | 4d 0.3 | 44l 4.5 14 0.4 | 794| 2.6 | 40 04 | 398| 2.0 8 0.5 | 709 | 1.2 6 0.5 | 371] 0.89 4 0.6 | 62 | 0.46 | 3 0.6 | 343 | 0.31 2 0.7 | 545 | 0.44 | 4 0.7 | 312 | 0.078 0.5 0.8 | 460 | 0.02 | 0.2 0.8 | 277 | 0.44 0.09 0.9 | 363 | 0.0014 0.04 0.9 | 232 | 0.00040 | 0.006 0.95 | 300 | 0, Oe: 0.95 | 200] 0, ey 097' 266 | 0, 0, 0.97 | 185 | 0, 0, 0.99 | U4} 0 0, 0.99 | 151 | 0, 0, Bel 0 0 0 1 0 0 0 | 1 + log x =— ik (1— 0,5 log (1—y)). Y J The values calculated in this way are found in table II (see above). The values found for y' are even smaller than those for the first branch. In both branches we clearly see the occurrence of a maximum in the curves 7’= f(a’), from which point the value 2’ (or 4) does not increase any more, but falls again to zero. The position of that maximum may be easily found from the ' dE general equation (4) for cat The tangent running vertically, the denominator (1—.r)w,-++-7w,—O0 must be zero and therefore we have, as we have assumed 8 to be equal to zero: (1—2) q, (18) + 2g, (1— 2 B (le)? = 0. Neglecting « we get: (le) 9, + 29, (- a *') = 0, 11 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 160 ) and therefore 1 gs i ok i pee q +9, (& v1) 11 VE BT Introducing our values for q, and q, and S=5, we get x,—*/,,—0,19. 1200 Le 991°. Further we have Sag RONG Ripe Um = With this value corresponds 7, a (=) = 0,00087, and therefore +”, == 0,00017, which agrees with the value found in the first table for the first branch. For the second branch we have exactly in the same way: VE vB 7 Ym — ee = Neb Wh Bh) ee See It+qle =) Gsa— 1 +78 Withop == o- this yields Wi tie ONT: 500 y! 7 18 there — 457°, |Z | = 0.000010, and therefore m 1,093 x ( Iererore y'm—0,0000017, which value again agrees with that found in the second table. If 2’, and 2’, represent the proportions in which the second com- ponent occurs in the two solid phases which coexist in the eutectic point C with the liquid phase z, then the point C may be found by solving a double set of equations (6), namely those with x’, and those with x’,. From these equations the quantities 7) x, 4”, and wz', may be solved. If 2’, and 1—.«', may be neglected, then we get simply: As Te ; ya WE == —— A Cen BT RT j= log (1—«) 1— = log a qi Je from which follows after introduction of our values for 77, ete. e=—0;809; 7452" The corresponding values of 2’ and 7! (+, and I—z’,) may be calculated as has been done above. (Compare also the tables for at 0,8). A closer consideration of the equations (6) shows (comp. fig. 3), that besides the branches mentioned above a third branch exists, which may to some extent be regarded as the connecting curve of the two former ones. This branch, however, lies wholly within the region of the negative absolute temperatures ‘and has therefore only mathematical importance for the continuity of the meltingpoint-curve. The curve 7=/ (x), namely ADB forms the connection between ( 161 ) AA' and B'B. EDF is the corresponding curve T= f(a’), which touches A'DB' in the common minimum DD, where «= 2’. The point D is therefore determined by the equations i Tape To ES ED EE) 2 or with our values: P= TA00 (1 — 52?) — 500 (1—6(1—z)*), which gives 7=.«2' = 0,494, 7 = — 264°. The point ME indicates another value of 2’, corresponding to the | ) 8 point A’ of the curve Pf (w), where v=1, but now T= — 0". This point is obviously determined by the equation (comp. (6 | Je ; — sy (Glew Oee (theretore-w, == Olten J) CEO) 12 which yields a’ = 0,592. The point / indicates a value of a’ corresponding to the point B’ of the curve T=); where «= 0, T=—0°. Now we have: LSP 0 (therefore w, = 0),..2 ai (LOB) from which foilows: a = 0,447. The curve 7’=/ (vr) has therefore obtained a continuous course through the points A’ and B’, the curve 7’—/(a') however changes abruptly at J’ from B' to H, and at A’ from A’ to #’; further its course is continuous from / through D to #. The question might be put: in what case does the point £ come in A’ and the point / in B' and has the discontinuity in the curve T = f(x’) therefore reached its highest possible value? Obviously this is the case for 8’ =o. For then w,=—O can vanish for z’=1 and w, for «=O. In this case the lines 4'D and ED coincide over their whole length with the axis «41, and the lines L'D and £D with the axis «= 0. At all temperatures above the absolute zero the values of w' and y' vanish in this case continuously; this represents therefore the case, that the solid phase contains only one component. The lines ADB and EDF lie, as we have seen, wholly in the region of negative absolute temperatures; besides this they le with their whole course in the region of the wnstable phases, as is shown by a closer examination of the relations 075 Al 0°5’ RT dw? a(l—a)’ de? (le) V. The value of @', for which the point D, where 7= 2’, is found exactly at 7 =0, may be calculated by solving the equations as Det! ¥ ( 162 ) 0=T, (LB) =T, (LRL), 12 ele e=(atve2) ete ae i.e. with our values of 9, and g,, 6’ = 3,659 and z' — 0,528. which yield : The whole curve EDF or T=f (a) of fig. 3 has here contracted to the single point D (see fig. 4), and the curve A'DB' or T = f (7) is degenerated into a straight line, all whose values coexist with that one value of a’. This line A'DS' and the point D still represent unstable phases. If for this case we calculate the maxima for # and y’ of the two principle branckes as we have done above, then we find: By, == 020 in ter = 0 PD0SS: Ym == 0,24, T= 439°, yn — 0,000062. ! The maximum value for « appears to have increased to about 5 times the value it had with == 5, and that for y' to about 36 times its former value. The maximum value for 7 now lies below the eutectic point. A simple calculation may show that in our case this already happens as soon as 8 becomes smaller than 4,55. The maximum on the other side will require a much smaller value of >’ before it descends below the eutectic point. 92 \" As soon as #' becomes smaller than (: Y=] -or ‘with sour Y. assumptions < 3,66, the curve ADB begins to turn upwards and we get the course indicated in fig. 5 for e.g. 8 = 2,5. The line A'DB' lies now wholly in the stable region for 7’= f(x), 2 — being henceforth always positive. The line EDF on the other wv hand lies wholly in the wnstable region for T= f(t), as easily orl appears from the expression for VT This latter circumstance how- wv ever is not permanently fulfilled; by continually diminishing @, a DP ad 2 point of EDI may be reached for which aa is equal to zero and this is a condition for a further change of the shape of the melting- point curve. But this will be treated in another chapter. The maximum values for a’ and y' are now the following (namely for 8 =2'255): fim => 0,315, T= 816° 5. an ='0,0044. Ym = 0357, Ans 410° ep y= 00016. a > af tier ( 163 ) ' Gradually « and 7 assume practically measurable values. We find from (9) for the maximum D: ber) = 229°; Wee linc LOE B = 0,423; de sy a Se — 0,633 (see (10) and (10%). VI. We now proceed to the description of the further develop- ment of the parts of the meltingpoint-curve lying below C. According as 8’ decreases, the curve A’ DP mounts higher and higher and finally it will touch the line BA’, e.g. in P(Comp. fig. 6). But the values of rv and 7’ of both curves 7’= f(r) coinciding in P, the values of «x also will necessarily coinci - or in other words the curves LA’ and HDF will meet at the same time, namely gr in the point Q. In this point however —— must vanish, as ? may be Our" regarded as a cusp in the continuous curve AA’ DPB. If therefore we el) trace in the figure the curv EE —0, — ie. T=a' &! (1—2') = g, Be! (1—e’), which will be a parabolic curve, whose axis of symmetry is the ordinate «='*/,, and whose summit lies lower according as ~’ decreases — then the curves BA’ and HDF meet this curve at the same time in Q. The direction of the two curves BA’ and LDF will there not be horizontal, as appears immediately from the direction of the curve 025 0’? —0 in the point Q. Therefore not only the numerators in the dE : expressions for re of those two curves must vanish u consequence Lv 2e! 9 Òz'” the two curves will meet each other at the place of their maxima for x’ and 1—2’, exactly at a point where both curves had a vertical dT tangent a moment before. So the expressions for — are undetermined Av of the factor but also the denominators (1-#)w, +-«w,. In other words: in Q and the real direction of the pieces BQ and A’Q, DQ and FQ must be determined in another way. Fig. 7 represents the position of the different lines a moment later. 8’ is here somewhat smaller than in fig. 6. It may be clearly seen that the lower branches L/P’ B’ and A’Q’F have got detached; henceforth they are isolated a0 disappear more and more downwards according as 8’ decreases. They may be regarded as rudiments of the original meltingpoint-curve. The upper parts form henceforth the proper ( 164 ) meltingpoint-eurve, namely AA’ DPB, constituting the line 7’= f (), and AB/EDQB, constituting the corresponding line 7T=/(x’). The curves 7T=/(x’) now run horizontally in Q and Q’, in consequence PR dl 2 of the relation PE for the denominator (l—e) w, + aw, no longer u? vanishes for both curves at the same time. The places in the two curves where this occurred before (we may imagine them to he between Q and Q’) have henceforth disappeared. These points Q and Q’ of the curves T= f(x’) correspond to the two cusps P and P’ of the curves 7= /(2). The process of detaching, described above, took place on the side of B — i.e. on the side of the highest temperature — but we shall see that the same process is repeated on the side of A, when 8’ still further decreases, which is represented in the figures 8 and 9. The second detaching takes place at A and S and gives rise to two new rudimentary parts of the original meltingpoint curve on the lower side. The proper meltingpoint-curve is now ARDPB for T= f(a), and ASDQB for T=/(e),. The two pomis.§ andes where the curves 7’= f(x’) run horizontally in consequence of the rl relation =( correspond with the new cusps R and fF’ in the Ou"? lines Tml: It is of course important to know at what values of 8’ the two processes of detaching described above, take place. ee In the point. Q (fig. 6) we have in the first place RE 0 or T=9, Be! (1—2'); but we have there also (1—a)w,+#w,—0, from which follows: w — Ws EE le W‚ Ws, Ww, = tls In connection with the equations (6) and taking into account the equations (8) for ew, and w,, we may deduce from these relations a set of transcendental equations from which the quantities 7, 2’ and 3’ may be solved by successive approximations. So we find for the first detaching with the values assumed by us for 7), ete.: a’ 1,545, 2! = 0,9108(Q) -, w= 0,2555(P) , T= 301,2. For the second we find as second solution: a’ = 1,1020 , «' —0,1149(S) , 2—0,9703(R) , T= 268°,9. The case of fig. 9, i.e. just after the second detaching, has been calculated by me point for point throughout its course,’ putting 8’ ( 165 ) equal: to 1,1. The following tables represent the chief branch ARDPB (T =f (2) ), corresponding with ASDQL (T= f («!)), and also the four rudimentary parts. & 7 7 x a 7 Gt) FU 0 1200 (4) 4 0 (B) 0 0.477 | 0.05 749 0.995 | 0.05 193 0.882 | 0.4 391 (R’) 0.981 | 0.104 (S')| 245 (R) 0.958 | 0.427 (S)| 292 0.995 | 0.420 193 0.929 | 0.2 335 CAN 4 0.130 (Z)| 0 0.886 | 03 384 0.846 | 04 119 0.810 | 0.5 449, 0.780 | 0.6 454 0.756 | 0.7 4583 : fe 7 (D) 0.749 | 0.749 45882 | (P) 0.748 | 0.776 (Q)| 458% 20 RM Caan Ie 0.749 0.8 | 461 gaat oe 0.9907 168 0.795 | 0.9 465 (P') ei 0.990 (Q')| 25° 0 867 0.95 476 Cae 0.970 168 0.914 0.97 484 AO 0.954 | 0 0.967 | 0.99 494 (By A 4 500 For the exact calculations, of which these tables give the results, we refer to the more elaborate paper which will appear later. Also the figures relating to them are to be found there. The maximum YD has been calculated from the equation (9), which yields «= «' = 0,7494, T—458",62. The points P and Q, ete. are calculated from (6) in connection with 025 =0, or T=¢,8'2'(1—x’). We find the following four solutions: u? I | «' = 0.7762 (Q) | « = 0.7484 (P) | T = 458°.60 HE: te! —="0:1268 (9) | » = 0.9579" (By A = 39273 Bip 06,9901. (Q) ree? KB) eee 250 IV: | a’ = 0.1035 (S’) | « = 0.9808 (B) | T = 245°.0 ( 166 ) The points / and F are again determined by (10) and (104). For, we have(@==1, 7 ='0) ia’ 0,1296 ; for Pir Ort 2 == 0.9535. Combining equation (6) for «,' and «@,', we find finally for the eutectic point C: O80 a2 == 0108893; 2,’ OMIT — Sa. / Formerly, when #/ could be neglected, we have found from (8), g = 0/809) Be 250" sfeee IV). It is remarkable that the value found for a,’ is exactly equal to 1—vz,’. It is easy to show that this is an immediate consequence of the equations (6) (compare our previous paper). In cases however in which our assumption a,’ = e,’ (which fol- lows from 6,’ = 6,’) is not satisfied, the value of x,’ for the eutectic point will also not be equal to 1 — z,’. / When the amount of heat required for the mixing of the first compo- nent for «=1 is equal to that of the second component for « — 0, then the compositions of the two solid phases at the eutectic point will be complementary. VII. We shall now discuss the question, how the two parts ending in the cusps P and F& will gradually disappear. We may follow this process step by step in the following figures. a) In fig. 10 we see that the cusp P of the line 7 = f(x), which a 2, tnt = till now was situated inside the curve -== 0, has reached that curve, OL in consequence of which the point @Q of the line 7’= f(x!) coincides with P, and also with the maximum point D, which lies between P and Q. The curves 4’ —=f(«) and T= f(a’) run therefore both horizontally in P, and henceforth the curve 7’= f(x!) will no longer touch the branch RP in D, but the branch PB (in a minimum). After the horizontal position in fig. 10 the cusp at P will be turned upwards instead of downwards. This transformation is apparently determined by the relations RR T= we Ree” Sy: de? d T — T, (i—p'x") = T, € Lay (Lo) —g, Belle) . . . (13) Ja This yields with the values assumed for 7, ete. : f= 10617 : #—0,7606 ; == AG3 So: 6. The figures 11 and 12 show a second peculiarity of the tran- ( 167 ) therefore at the temperature of the eutectic point for the first time four values of a’: a,’ and 2,’ corresponding to C, and the coinciding points «,’ and wv,’ corresponding to P. These latter two points still represent wnstable conditions. A moment later P has risen above C and the two coinciding points «,’ and «,’ have separated (fig. 12). The values x,’ and 2,’ always correspond to C, wv,’ and 2,’ to two other points of the line 7—/ (x). The phase to which «,’ relates, is unstable, that to which z,’ relates metastable. The transition of fig. 11 is determined in combination of (6) MOEI pal Soe (With | 24) sen LOT, sition. Here the cusp P lies at the same height as C; we find ’ (with w,), in connection with the relation 7’= gq, 8! x,’ (1—.2,’). By means of these relations we may determine 7) x, #,, v,', v,’, 2’, 6", if we moreover take into account (compare VI above). pes A ae c. The figures 13 and 14 represent a new and very important case of transition. Formerly the branch AR intersected the branch BP always on the left of the maximum (or minimum) D in the eutectic point C; in fig. 13 it passes evactly through the point D. From this follows, that the point «,' coincides in C with wx,’ (both = wv), which point represents a stable phase from this moment. Afterwards the minimum D lies on the left of the eutectic point C (see fig. 14) in consequence of which the realizable part of the meltingpoint curve begins to show a totally different shape, namely with a minimum (see fig. 14a). The point «,' which till now lay on the left of C, lies in future on the right of that point. On the other hand wx, has got on the left of C and it corresponds to a point of the line 7’= f(x) between B and D. It will not escape our notice that the case drawn in fig. 14a occurs to some extent in the mixtures of Ag NO, and Na NO,, inves- tigated by Mr. Hissink (see fig. 145). The difference is only that the minimum in the line 7'— f(«) in the case of fig. 145 appears beyond «1 and has therefore already disappeared. In our case we have supposed this to occur in a later stage. The case of transition of fig. 13 is calculated from the equations (6) for «’ and w,', taking into account «= 2,', and moreover me) = 1— wx’. The numerical solution of these equations yields the following values : Pi Uae lt. 3 a= .0,1940 5 a of ae EGO PE 479°.1: We may then calculate 7, and wr, from equation (6). d. Finally the figures 15 and 16 represent the most important case of transition. ( 168 ) gel Here Q and S coincide with the summit of the curve — = 0, and ave so also P and R with C. The parts with the cusps have now disappeared once for all through the eutectic point. The points w,’, v,’ and «,’ coincide with the horizontal tangent in the point of inflevion Q,S. This point QS lies apparently at’ = 4, 27 >) Ld Al . . . as the curve —-=—0 or T= q,('x' (1—x2') is perfectly symmetrical ve” on either side of the summit at 2’ = 4 according to our supposition o./ == ae.’ (in -comsequence of b,”—0,"). Not before this instant we may say that the meltingpoint curve has obtained a perfec'ly normal course, running continuously without any cusp from A to B with a minimum in D where « = x’ (fig. 16). The point of inflexion with a horizontal tangent has passed into an ordinary point of inflexion with an oblique tangent. This point of inflexion also will gradually disappear when 8/ continues to diminish, and for still smaller values the minimum also will disappear from the melting- point line which will then show a continuously ascending course from B to A. It is of course possible that the minimum has disappeared already before, of which fig. 14% gives an example. The transition of fig. 15 is determined by the equations (6) for al PE = £,'=a,') 4, in ‘connection, wils: 4 Oz’? 2 We find: LBO rr OIB EE KOOTEN == 2 1 OO eN OL i q | a io = 0,5). The points #, and wv, may further be calculated from equation (6). e). The minimum disappears apparently (see HL equation (Sbús), when 2! en Tl (14) P ET VA . . . . . e . . ER Zie | . id ~ % 2 la VA Jh aS For with 8 =O formula (5 bis) passes into —? < 7 1 or 8 > ———. This formula expresses the condition for the oceur- of i 1 rence of a minimum. Formula (14) expresses consequently that no minimum will occur. The minimum disappears therefore in our case as soon as {3 7 becomes equal to ig OF 0,5823. f. In the above considerations we have lost sight of the rudi- mentary pieces which have been detached (compare VI). J. J. VAN LAAR. “On the possible forms of the melting point curve for binary mixtures of isomorphous substances.” B XK en Te > i x Proceedings Royal Acad. Amsterdam. Vol. VI. ( 169 ) We shall now investigate when they also disappear. Apparently this is the case, when the summits P’ and Q’, R’ and S’ lie at T=0; i.e. when these points coincide with 5’ and A’. These summits are determined by the equations (6), in connection with 7=q, 8 4 (Al). Now P’ coincides with B and Q’ with A, if these equations are satis- fied by 7=0, 2=0, #’=1. It is clear that this requires p’=1. Further A’ coincides with A’ and S’ with B’, if the equations are satisfied by 40, a=1, # =O. And this can only be the = 0,8333. | ox det case when 8’ ——-, in our case 8' — q Ts er VIII. It is easy to see that the results of the above investigation would remain unchanged qualitatively, if we had not neglected the quantity 7 in the term ax?, and if we had not omitted the quantity 3 for the liquid phase by the side of the corresponding quantity 8’ (3 being nearly always very small compared with 8’). Then all the values given for p’, x, 7’ and T would be slightly changed nwmerically, but the transformations and transitions which we have discussed, would have occurred in the same order and exactly in the same way as we have deseribed above. We conclude from the above considerations, that the occurrence of a eutectic point and the apparent interruption in the series of the solid mixtures caused by it, necessarily follow from the theory represented by the equations (2) or (6), which teaches that high values of B’ (or a’), i.e. of the heat required for the mixing of the solid phase, cause the occurrence of wnstable conditions. In reality the curve is continuous, as is shown in the different figures, but in general only « part of the continuous meltingpoint-curve is lable to be realized. And only this part of course is found by means of the experiments. Finally I regard it as an agreeable duty to express my thanks to Prof. Baxknurs RoozrBoom, who has encouraged me to undertake this investigation, and who has given me many a useful hint also for my former papers on the meltingpoint-curves of amalgams and alloys. (August 27, 1903). ne - é wif i SOS mi | a 2 { j ily Titan Won el Pi ? r ’ Te rf; p A sk iat WAF LL a AEN sat MN 4] ry so) od PE ki er bledt cf) Prager / ites 4S. a ee oS ana he > wd pe KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday September 26, 1903. IE (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 26 September 1905, DI. XII). 5 ee ir ET TS A. Smirs: “The course of the solubility curve in the region of critical temperatures of binary mixtures”. (Communicated by Prof. H. W. Baxnuis RoozeBoom), p. 171, Pu. van HarreverD: “On the penetration into mercury of the roots of freely floating germi- nating seeds”. (Communicated by Prof. J. W. Morr), p. 182. (With one plate). JAN DE Vries: “The harmonic curves belonging to a given plane cubic curve’, p. 197. A. F. Horteman: “Preparation of cyclohexanol”, p. 201. Tu. Weevers and Mrs. C. J. WeEEVERS—DE GRAAFF: “Investigations of some xanthine deri- vatives in connection with the internal mutation of plants”. (Communicated by Prof. C. A. Losry DE Bruyn), p. 203. J. VAN DE GRIEND Jr.: “Rectifying curves”. (Communicated by Prof. J. CARDINAAL), p. 208. (With one plate). J. Boeke: “On the development of the myocard in Teleosts”. (Communicated by Prof. T. Prace), p. 218. (With one plate). Extract from a letter of Mr. V. Warrior to the Academy, p. 226. The following papers were read: Chemistry. — “The course of the solubility curve in the region of critical temperatures of binary mixtures” *). By Dr. A. Smits. (Communicated by Prof. H. W. Bakuuis RoozeBoom). The results of the experiments on critical temperatures of binary mixtures, which have been suggested by the theory of VAN DER WAALS, and the completion of the pressure-temperature-concentration-diagram for the equilibrium of solid phases with liquid and vapour lately given by Baknvis RoozreBoom *), made it probable that the pending 1) My first communication on this subject appeared in Zeitschr. f. Elektroch. 33, 663 (1903). 2) Proc. Royal Academy Amsterdam 1902, 276. 12 Proceedings Royal Acad. Amsterdam. Vol. VI. GEE) problem of the course of the solubility curve of a solid in the region of critical temperatures was now capable of solution. It follows namely from the combination of the two conceptions mentioned above, that the course of the solubility curve cannot show anything remarkable, unless the least volatile substance (B) occurs as a solid phase and its melting point lies higher than the critical temperature of the more volatile substance (A), which for the sake of brevity we shall call solvent. We will now consider only the case when the two substances in the liquid state are miscible in all proportions. Then there is in the pt, e-diagram a continued critical curve, connecting the critical points of the two components. Three different cases may now occur, Fig. 1. Fig. 2. A= Gas. A=Gas. P= Unsaturated solutions. B — Unsaturated solutions. Cv =Supersaturated solutions or C — Supersaturated solutions or solid 4 + vapour. solid B + vapour. Fig. 1 and 2 are p,f-projections of the representation in space, a is the critical point of A, 6 of B, while d represents the melting point of solid B. The line ab is the critical curve and cd the p, t-line for the three-phases equilibrium: solid B4solution vapour. Further ea is the vapour-tension line of liquid A, fb that of liquid B. Now the case of fig. 1 will occur when the solubility of solid B in A is comparatively great. In this case the vapour-tensions of the saturated solutions are rather small and so the curve cd lies totally below the critical curve. The line cd runs on uninterruptedly as far as the melting point of B; the series of the saturated solutions of B is not interrupted by the critical phenomena of the solution ; the solubility curve shows nothing remarkable. On the other hand the critical eurve also goes on uninterruptedly, the critical phenomena being only those of solutions which are wnsaturated of solid B, t T 23 ty ts (173° ) In the second case, fig. 2, I supposed the solubility of B in A, even at the critical temperature of A, to be still so small, that just a little above it the line cd intersects the critical curve. Then such an intersection takes place in two points p and g. Now the critical temperatures and pressures between « and p and between q and 5 refer to unsaturated solutions. At pand g, however where the p, é-line of the solutions and vapours saturated of solid B and the critical curve meet, the case occurs, when the saturated solution is found at its critical temperature; for here the vapour- tension of the saturated solution is quite equal to the critical pres- sure and so saturation temperature and critical temperature must coincide. If we were to prolong the critical curve from p to q, we should pass through the region of solutions and vapours supersaturated of solid 5. Hence eritical phenomena will be possible here only provided that the solid phase 5 does not occur. So this part of the critical curve is metastable. To prolong the three-phases-line between p and qg, on the other hand, is impossible, as will soon be evident. A third case forming a transition between fig. 1 and 2 would be the following: the curve cd would touch the inside of the critical curve in one point. The points p and g would coincide at this point. Hence the chance that such a case should occur is extremely small. A better insight than by the p, ¢-projections of the representation lil space is, however, given by the p, #-projections, especially when these are combined for different temperatures as in fig. 8 and 4, which has already been indicated by Prof. Baknuis Rooznsoom *). That is why I here add p, v-projections both for case 1 and for case 2 and in order to be able to construct from these projections the entire ¢,7-diagrams also, I have given the projections starting from the critical temperature of A up to the melting point of B. The preceding pr-diagrams 3 and 4 correspond with the p, ¢-dia- grams 1 and 2. Let us first confine ourselves to fig. 3. At the critical temperature ¢ of the substance A, ae and ac are the p,.v- curves for coexisting vapours and liquids (unsaturated solutions). The points ¢ and e indicate the saturated solution and the vapour in equilibrium with it. Further for the same temperature ge is the p,v-curve for the vapours and cf the p, v-eurve for the solutions coexisting with solid 4. According to the theory of vaN per Waars ge and cf are at bottom two portions of a continuous curve, which 1) Zeitschr. f. Elektroch. 33, 665, (1903). 127 (174 ) ésthhnk- G2 Jl B A Gas, A= Gas. B —= Unsaturated solutions. B= Unsaturated solutions. C =Supersaturated solutions or C = Supersaturated solutions or solid 2} vapour. solid B + vapour. has between c and e a part only partly to be realized with a maximum and a minimum. For a somewhat higher temperature the diagram is a little different, because now the vapour- and liquid curve continuously pass into each other with a critical point in @,, the vapour-line g,e, being shorter than at the former temperature. At rise of temperature this vapour-line continually decreases in length, until at the melting point of B in the point d it has disappeared altogether. Above the melting point a saturated solution is no longer possible and so there we get only a liquid- and a vapour-line with a critical point in a, If we draw a line through the points a, a,, a, 4, and hb, a second through the points c, c,, c, and d and a third through the points eyes e, €, e, and d, these lines indicate the said 4, z-projections; ab is the critical curve, cd the curve of the saturated solutions and ed that of the vapours saturated with 5. In accordance with fig. 1 the whole of the critical curve lies above the solubility curve; above the critical curve lies the gas-region and below the solubility curve the region of solid B + vapour or of the supersaturated solutions. After what precedes the connection between the fig. 2 and 4 is easy to see. The solubility of B in A at the temperature f, being small, the vapour and liquid-lines ae and ac are short. Above ¢, ae and ac again fluently pass into each other and have already approached nearer to each other, because the saturated solution c, and the coexisting vapour e, differ less from each other; a consequence of this is that the lines ge, and ¢, 7, have also approached to each other. At ¢,, the first critical temperature of the saturated solution, the solubility curve cc, p, the vapour-line ee, p and the eritical curve aa, p concur. This implies that at this temperature the curve Jop for the vapour coexisting with solid B is the prolongation of the curve pf, for the solution coexisting with solid B. The same occurs at a great many higher temperatures. That a continuation of the lines cp and ep is imaginary, clearly appears from this diagram, as the vapour- and the liquid-line, if both were prolonged, would change places, which is impossible. ?) Whereas from f, to ¢, saturated solutions are absolutely impossible, at ¢, the same phenomenon occurs as at /,; here also the solubility curve de,q, the vapour-line de,g and the critical curve ba, a, q con- verge and the critical phenomenon is observed with a saturated. solution. At higher temperatures a convergence of the three curves can no longer occur. and in consequence all critical temperatures between /, and f,, just as between 7, and f,, are critical temperatures of unsaturated solutions. If between p and q solution + vapour + solid B be impossible, it is conceivable, as suggested before, that we may succeed in getting supersaturated solutiors and observing their critical phenomena. In such a case the dotted critical curve - if prolonged might be realized between p and g, so this dotted line is metastable. For a thorough knowledge of the phenomenon a p, «, f-diagram is most desirable and a v, «, diagram indispensable. Both space- 1) In the first communication, Zeitschr. f. Elektr, 33, 663, this point was not sufficiently cleared up. representation I hope to communicate after some time and now I want to point out only the fact, that the point p, which is bound to a certain concentration can be reached at only one very definite volume, which holds true for g also. 3y means of the v, x, f-diagram it can also be made clear, that no line can be drawn of a definite limitation between the region for solid B + vapour and the region of unsaturated vapours. In the region for solid B + vapour we have namely a system consisting of two com- ponents in two phases, therefore a bivariant system wherein there are numberless ways in which with rise of temperature the pressure can be changed. Consequently it depends altogether on the volume what course we follow at increase of temperature. In order to test the discussed phenomena by an example I chose for the substances A and ZB ether and anthrachinon. The eritical temperature of ether is 190°, hence it is rather low, nor is the critical pressure high, namely + 36 atmospheres. It is obvious that these two circumstances make the experiment much easier. Anthra- chinon was chosen because this substance is very little soluble in ether, its melting point lies 285° above the critical temperature of ether and it is still very stable at its melting point. The experiments were carried out in thick-walled tubes of 5 e.m. length filled with weighed quantities of ether and anthrachinon. The ether was free from alcohol and water; the anthrachinon was crystallized from icevinegar. The tubes filled with ether and anthrachinon were closed by melting while in a bath of — 80° (solid CO, + alcohol) and then hanged up in an air-bath with Little mica windows. This air-bath had been supplied with an apparatus, driven by a motor, for keeping the tubes constantly swinging. ‘The temperature of the bath could be kept constant within 1°. In order to determine the solubility curve the temperature was observed at which all the anthrachinon had been dissolved. In order to determine the critical curve at very slow decrease or increase of temperature this was noted down when formation of nebula occurred, resp. the liquid phase disappeared. The average of the two tempe- ratures was noted down in the graphical representation. If possible the volume of the liquid was chosen in such a way, that on reaching the critical temperature the tube was nearly filled with liquid. Only saturation- and critical temperatures for mixtures of definite concen- tration being determined by these experiments, only a f, v-diagram ean of course be constructed from them, which is given in fig. 5. From a comparison with fig. 4 it is easy to see that the direction of the two pieces of the critical line and that of the line for the Af ae Te. ee PES 8 10 20 30 KONE SOR OOR JORE GOr GON 100 ii he Anthrachinon solutions saturated with solid B is quite conformable with the ¢, «-projection in fig. 4. The point p lies at 195°, 95°/, ether and 5°/, anthrachinon. The point g has, as regards the concentration, not yet exactly been determined; I estimate it at 70°/, ether and 30 °/, anthrachinon, the temperature lies at 241°. In order to elucidate the very remarkable phenomena we found, { shall more closely consider the case that we start from a mixture of ether and anthrachinon composed of 45°/, ether and 55°/, anthra- chinon (A fig. 5) and slowly heat this mixture. The quantity of anthrachinon being so great and the volume rather small, we always have below 195° excess of solid anthrachinon together with a saturated solution and vapour. The concentration of the saturated solution at rise of temperature moves along the line cp. At about 195° we reach the first critical temperature of the saturated solution, when more heat is added. the solution disappears and we get solid anthra- chinon + vapour. Apart from the continually increasing evaporation of anthrachinon all remains unchanged up to about 241°. At this temperature the eritical phenomenon occurs again; whereas at p the liquidphase disappeared, here it is formed again‘). On further rise of temperature more anthrachinon is continually dissolving and along 1) The points p and q can never be accurately reached in one experiment, a yery definite volume being required for every concentration, qd we go to the point A, where at 247° all anthrachinon has exactly been dissolved. If we now increase the temperature still more we come into the region of wnsaturated solutions; from A therefore, we go parallel to the Z-axis upwards to the temperature 350°, where the unsaturated solution has reached its critical tem-. perature and all passes into the gaseous state. The influence, which greatly diminishes the accuracy of the results, is the dependency of the volume; the error created by it, is small for the critical curve ap and for the solubility curve hg, because these curves have a rather slight curvature. For the critical curve bq and especially for the lower part the possivle error in the concentra- tion is rather great, so that the point g is pretty uncertain. It seemed very interesting to me to investigate, whether or not it would be possible to determine points of the metastable part of the critical curve. I indeed succeeded to get between the temperatures t, and ¢, a solution, which, as discussed before, was supersaturated. A tube filled with 6°/, anthrachinon and 94°/, ether was heated in the air-bath. The solution saturated at the first critical temperature containing only 5°/, anthrachinon, some solid anthrachinon was still left above the critical temperature of 195°. At increase of temperature always more anthrachinon passed into vapour and at last all had become gas. Now, if I made the temperature fall rather quickly, no solid anthrachinon was deposited, which would have been normal, but at 211° a nebula appeared and a supersaturated solution was formed. Then, when I made the temperature fall slowly, the solution remained over a range of temperature of 9°. At 202° suddenly a transformation appeared by which the solution passed into solid anthrachinon and vapour and the metastable phase disappeared. On subtracting more heat the formation of nebula once more appeared at +195°, the first critical temperature of the saturated solution, and for the second time a liquid was formed, but now this liquid was a stable phase. This phenomenon shows, that vapours are also possible, which are supersaturated of solid and for their transition into the stable phase choose a round-about way by another metastable phase, viz. a supersaturated solution. I repeated the same experiment with a greater anthrachinon-con- centration; now the formation of nebula appeared at 216°, it is true, but before a visible quantity of liquid had been formed, solid anthra- chinon already was deposited. These two temperatures could not serve to determine the metastable part of the critical curve, because the vapour-space in the tube happened to be too large. So the tempera- tures under observation were not critical temperatures. F 4 —_ "se =" +h (HAR The results obtained enable me to somewhat elucidate a few dark points occurring in literature. From the experiments of WarpeN and CENTNERSZWER *) on the solubility of KJ in liquid SO, up to 96°, it is obvious that after one of the two liquid layers, which are coexis- tent between 77°.3 and 88°, have disappeared, the solubility decreases and at 96° amounts to no more than 0,58 mol. °/, KJ. On account of this in their diagram they make the solubility curve below 100° terminate into the ¢-axis, as indicated in fig. 6. It is obvious, that this is not compatible with the theory given above, the prolonging of the solubility curve as far as the {-axis is certainly wrong. Most probably the same phenomenon appears with SO, and KJ as with ether and anthrachinon; the diagram may be somewhat different, the type, however, will be the same’). Hence it is not improbable, that on prolonging the solubility curve up to higher tem- peratures we should again observe an increase of the solubility, so that the direction up to the first critical temperature of the saturated solution will be somewhat like that indicated in fig. 7. Fig. 6. ¥00" 0 95 Fig. 7. go 157°. d 85 T SOs xr d ae AS 75° 4 LK | Ait nl Pe) 10 20 30 40 fo KJ Since 1880 many more experiments have been made which point to the fact, that gases above their eritical state are able to dissolve 1) Zeitschr. f. physik. Chem. 42, 456 (1903) 2) For the systems SO, + Rb J and SO, + Na J the same holds true. Zeitschr f, physik. Chem. 39, 552 (1902). ( 180 ) liquids and solids"). Vinuarp e.g. found, that when he compressed oxygen at the usual temperature (17°) to + 200 atmospheres in a tube with bromine, this evaporated in a much higher degree than corresponded with the vapour-tension at the temperature of observation. This could be observed beeanse, while the oxygen was being com- pressed, the colour of the vapour grew darker and darker and because bromine on decrease of pressure was deposited against the wall in the form of little drops. Fig 8. Prof. Baknuts RoozrBoom®) has already given an explanation of this phenomenon by means of the p-v-loop, which applies to the said system of ovygen—bromine at 17°, because this temperature lies far above the critical temperature of oxygen (— 111°) and also above the melting point of bromine (— 7,3°). According to Hartmann *) this p-v-loop has the E form, given in fig. 8. It follows from the great LE Se B rise and running back of the vapour-line HRP, that the partial pressure of the vapour of B between F& and P must be much greater than the pressure in £. Though increase of pressure alone is sufficient to increase the vapour-tension, the influence of compressed gases is much greater in consequence of the solution of the gas in the liquid. It is clear that by increase of the oxygen-tension /o/a/ evaporation ean be reached here, the region liquid + vapour having for a certain concentration of A given place to the gas-region. With the systems CH,—C,H,Cl, CH,—C8,, CH,—C,H,OH VirLarD found the same phenomenon in an even more striking way. Also with solids VirLarp could observe an increase of the partial pressure. The partial pressure of iodine was perceptibly increased by an oxygen-pressure of + 100 atmospheres, whereas with hydrogen a perceptible inerease did not occur until at 200 a 300 atmospheres At + 300 atmospheres methane dissolves very perceptible quantities of camphor and paraffine, even so much that on decrease of pressure the dissolved substances crystallize in visible quantities against the walls of the tube. At 300 atmospheres aethylene dissolves rather much J, which on 1) Hannay and Hocarru. Proc. Roy. Soc. 30, 178, (L880). Vittarp. Journ. de Phys (3) 5, 453 (1896). Woop. Phyl. Mag. 41, 423, (1896). 2) Die Heterogene Gleichgewichte 2, 99, 5) Journ, phys. Chem. 5 425 (1901), ea a's EB decrease of pressure is deposited in crystals. Paraffine strongly dissolves in aethylene; so much so that under a pressure of 150 atmospheres we can make it evaporate altogether. Stearine acid also easily dis- solves in aethylene, but not to such a high degree as paraffine. As yet we have not been able to explain the total evaporation of a solid by a gas above its critical state, ezthout an intermediate liquid phase; this is owing to the fact, that there was no suspicion of the behaviour shown by the system ether and anthrachinon. — If we compare the figures 3 and 4 with each other, it is obvious that if in fig. 8 we start from solid B and by compression of A at a constant temperature we follow a course parallel to the z-axis from right to left, a liquid phase will always appear first before we come into the gas-region. This phenomenon observed by VirLarp in the system camphor-aethylene will also oceur in fig. 4 between the temperatures ¢, and ¢, and between f, and ¢,, so that this be- haviour does not decide the type to which the system belongs. Investigations at different temperatures only would enable us to do so. It is, however, quite different, when the solid evaporates altogether without giving a liquid first. If this be the case we ean directly point out the type; then it belongs namely to type fig. 4, for there only it is possible when coming from the region for solid b+-vapour to pass into the gas-reqion without an intermediate liquid-phase, as long as we work between the temperatures t, and ty. Probably the systems alcohol + KI, KBr, CaCl, and Cs, + I, ot Hannay and Hocarru, ether-+Hel, of Woop and CO,-+-1, of Viniarp belong for the greater part to the type fig. 4. That, as would follow from Virrarp’s experiments, also the partial vapour tension of solids would be considerably increased by relat- ively slight pressures (LOO a 200 atmospheres) of an additional gas, seems, however, possible to me only when the vapour-line of the system solid-vapour can get a course similar to that of liquid-vapour, whieh will probably be the case only when the added gas A dissolves in the solid phase B. This point wili soon be investigated by me. Chemical laboratory of the University. Amsterdam, September 1903. ( 182 ) Botany. — ‘On the penetration into mercury of the roots of freely floating germinating seeds.” By Pu. vaN Harrevenp. (Com- municated by Prof. J. W. Morr). The first who mentioned that growing germroots can penetrate into mercury was JuLes Pinot in 1829. He placed various seeds in a thin layer of water on mercury and observed that on germination a number of roots pushed themselves into the mercury. His experiments were important in two respects. Firstly from a physiological point of view: the penetration of the germroots into a liquid of so high a specific gravity as mercury proved that during growth considerable forces are developed. And secondly from a physical point of view: the seeds lay loose and yet the germroots were not lifted out of ihe mereury by the upward pressure. These two results of Prixor’s experiments must be clearly distin- guished. On the first much work has later been done; Sacus and other investigators used mercury repeatedly in order to give a great and uniform resistance to a downward growing root. On the second point, the physical paradox of the root which penetrates into mereury without a hold, no publication has appeared after that of Wicaxp in 1854. Pixor himself was only struck by the second result of his experiment, the penetration of loose lying seeds. As this phenomenon could not be explained by physical laws, he called in the aid of vital force, as was still very common in his days. The vitalistic doctrine however had found a fierce opponent in Durrocuet'). The latter declared the experiments to be untrust- worthy. Several investigators, on the other hand, confirmed Pixor’s observation. Thereupon Dvuranp and Dvrrocurr gave, in 1845, an explanation of the curious fact which was generally accepted. Although Wicaxn in 1854 assured once more that Pixor’s observation was correct and still awaited an explanation, no further attention was paid to it. Pior was often quoted for his first result ; for the phenomena of freely floating seeds at best reference was made to the refutation by Duranp and DerrocHer. Reading the astonishment of Wicanp, when he was obliged to state the correctness of Prnot’s observations, I repeated the experi- ments. I found that Pinot was right indeed. The explanation of the seeming physical paradox can nowadays be easily given; a “vital force’ is not needed for it. In the older literature on geotropie phenomena one meets with such contradictory opinions about the penetration of freely floating 1) J, Sacus, Geschichte der Botanik 1875. pag. 900. . % ( 183 ) seeds, that it may be useful to give a short synopsis of the literature on the subject. I shall afterwards compare the various opinions with the true explanation. Historical synopsis. On February 23, 1829, Jurms Pryor sent to the Paris Academy of Sciences a paper on the penetration of germroots into mercury. The Academy appointed a committee of three members to examine this paper. Pinot repeated his experiments in the „jardin du Roi” in the presence of two of the members of this committee. He also showed one member a new experiment, in order to guard his conclusions against possible objections. In a letter to the Academy, dated July 27, 1829, he gave a description of it. Neither the paper nor the letter seem to have been printed. But Pinot published a short account of his first paper, together with an extract of his letter. about the new experiment, in the Revue Bibliographique of July 1829 *). According to this account he arranged his experiments in the fol- lowing manner: a little trough, 18 mm. deep and 10 mm. broad was filled with mercury and a thin layer of water poured out on the mercury. The trough stood in a small dish with water over which a little bell-jar was placed. Seeds of Lathyrus odoratus, soaked in water, were placed on the mercury with the hilum turned towards the mercury surface. The layer of water was sufficient to maintain germination, but was on the other hand, as thin as possible in order not to favour rotting of the seeds. Now on germination the roots of the freely floating Lathyrus seeds penetrated to a fairly considerable depth into the mercury without lifting the seed. Also with other seeds the experiment was successful ; the penetration sometimes exceeded 8 or 10 mm. When however the growing little stem was killed by a drop of sulphuric acid, the root came to the surface. 1) Revue Bibliographique pour servir de complément aux Annales des sciences naturelles; par M. M. Audouin, Ad. Brongniart et Dumas. Année 1829 page 94—96. This Revue Bibliographique only appeared in the years 1829, 1830 and 1831. With many specimens each of the three yearly volumes is bound with one of the three volumes which appeared annually of the Annales des sciences naturelles. As they have a separate pagination however, it is not sufficient to quote the number of the page and the volume of the Ann. d. sc. nat., as Hormersrer (1860), Crestenkt (1872) and others do. A. P. De Ganpotte in his Physiologie végétale Il. p. 828, note (1) calls this Revue Bibl. wrongly: Ann. sc. nat., Bull. which may cause confusion with the “Bulletin des sciences naturelles et de géologie”, which appeared from 1824 (T. 1) till 1831 (T. XXVII). ( 184 ) In order to discover to what extent the weight of the seed and its adhesion to the moist mercury-surface could be the cause of this penetration, Pivot devised the following experiment, described in the extract of his letter. A silver needle rested in the middle very movably on an axis. On one end a germinating Lathyrus seed was stuck, on the other end a movable pellet of wax, just balancing the seed. The seed hung about two millimetres above a moist mercury-surface ; a bell-jar again kept the air moist. The germination now proceeded somewhat more slowly, but the root still reached the mercury-surface; next it forced itself into the mercury, as in the case of the unsup- ported seeds, without pushing the balance-arm upwards. For this experiment Lathyrus was chosen because with it the cotyledons remain within the coats of the seed. Neither could the weight cause the penetration as it was balanced by the wax-pellet and also adhesion between the cotyledons and the mercury was excluded as they did not touch each other. Pinot gave the facts as he observed them but he did not venture an explanation. That he would not have been averse to using the vital force for it, however, appears from the mention he makes of the sulphuric acid: as soon as he kiiled the germinating plant by it, the root came to the surface of the mercury. Pinot also communicated his discovery to the “Société de Phar- macie de Paris”, which gave an extract of his letter in the Bulletin of the transactions of its meeting of August 15, 1829.*) The same article is found in Flora of that year*), in the Edinburgh New Philos. Journal ®) and in the Annalen der Gewächskunde *). These publications drew general attention, firstly because it appeared from them that roots grow downwards with great force and secondly because it remained unexplained how the seeds found a point of resistance against the upward pressure of the mercury. This latter point occupied more particularly Pixor’s countrymen, whereas some foreign workers were especially struck by the former. Among these Craas Murper of Franeker repeated the experiments and gave a translation of Prior’s article in the Revue Bibliographique together with the description of his own experiments in the autumn of 1829. *) 1) Journal de Pharmacie et des sciences accessoires, T. XV 1829 pag. 490—491. 2) Flora oder Botanische Zeitung, XlIIter Jahrgang Zweiter Band 1829 pag. 687—688. 3) The Edinburgh New Philosophical Journal, July—October 1829 pag. 376—377. 4) Annalen der Gewiichskunde, Bd. IV pag. 407—408. 5) Bijdragen tot de natuurkundige Wetenschappen, verzameld door H. G, van Hatt, W. Vrouk en G. J. Murper. Vierde deel 1829 pag. 428—437, ( 185 ) He took “small beer-glasses” of a little more than 5 em. diameter (Murper speaks of N. inches, i.e. new inches or centimetres) and filled them with mereury 4 em. deep, on which lay a layer of water with pigeon-beans (Vicia faba minima) and buckwheat. The roots of buckwheat did not penetrate into the mercury and went on creeping over the surface for a month. When the beans had grown stems of two centimetres, five of them had their roots in the mereury: the rest lay on the surface but had evidently been submerged. In order to prevent capsizing, a few of the seedlings of Vicia were picked out which had straight roots and these were stuck through holes in a thin slice of cork, floating on the water above the mercury. Especially between the wall of the glass and the mereury he now observed the penetration of the secondary roots. His conclusion is that these experiments afford a new proof that the innate tendency of the root to grow downwards, must be con- sidered as a vital action dependent upon internal force which external circumstances can hinder, modify and even render almost irrecog- nisable, but by no means destroy. *) Murper thinks only of the force with which the roots grow downwards. The physical paradox escapes his attention, although it was exactly this which was emphasised by Pinor’s experiment with the silver needle. By bis using big seeds, seedlings in an advanced stage and cork, his experiments differ materially from those of Pivot. A short account of Murper's experiments by C. MORREN appeared in the Revue Bibliographique *); also in Linnaea there is an extract of his article. *) . H. R. Gorprerr at Breslau repeated Pinor’s experiments as MeLper did, when he read an account of them in Froriepr’s Notizen für Natur- und Heilkunde Nr. 530, Aug. 1829, page 154. He described his experiments in an article, entitled: “Ueber das Keimen der Samen auf Quecksilber”. *) Gorprert used peas and oats ; only the primary roots of the peas made a small depression in the mercury, the other roots crept over the surface. Better than with Prvov’s silver balance he thought to eliminate the weight of the seeds by putting them into the holes of a wooden cross which above the mercury was held fast in a conically shaped glass No more than Murper he noticed Pinot’s physical paradox, for the friction of the seed in the ') Le. pag. 436. 2) Revue Bibliographique. Dec. 1830, pag. 129—130. 3) Linnaea Bd. 5, pag. 191 of the ,Literatur-Bericht”. 4) Verhandlungen des Vereins zur Beförderung des Gartenbaues, VIfter Band 1831, pag. 204--206, ( 186 ) holes of the wooden cross now counteracted the upward pressure of the mercury. GorePerT worked even with the bulb of a hyacinth! It has been remarked above that in France it was exactly the unsup- ported condition of the seeds which drew attention because it seemed to plead for “vital force”. Durrocurr had commenced the great fight against this latter and consequently he was prompt to stave off the danger. He repeated Pinov’s experiments and obtained a negative result. Thereupon, on Noy. 16, 1829, he made the following communication to the Académie des sciences, of which he was a corresponding member.) “Par les journaux et particulierement par les Annales d’expériences présentées a Académie” *) he had learnt that the roots of plants would penetrate into mercury to a greater depth than corresponded to their weight, consequently by a physiological action. He had repeated these experiments carefully but had by no means obtained the result of the author. The root never went deeper than it ought to by its weight and when after a few days it turned black and died, it did not come to the surface either. The author must be entirely mistaken; there was nothing that could be ascribed to physiological or vital action. In this meeting of the Academie MirBer communicated that the committee of enquiry had also repeated the experiments, but had obtained the same result as Derrocner *). This statement is contrary to what Pinor had said of the committee in his letter to the Academie of July 27, 1829. The committee has given no written report ’). Durrocuet evidently was no unprejudiced observer when he repeated Prnot’s experiments. They were troublesome to the new conceptions of which he was a champion. A considerable part of Durrocuet’s observations on various subjects 1) Revue Bibliographique. Dec. 1829, pag. 146—147. 2) A periodical of this name is not known to me. Only in 1835 the Académie began to publish a printed account of its meetings viz. the: Comptes Rendus hebdomadaires des séances de Académie des Sciences. Of its transactions, entitled: “Mémoires de |’Académie des Sciences de I’Institut de France’, the new series was commenced as early as 1818, but not all the Mémoires that came in, are found in it. It contains an account of the proceedings of the Académie of some years; vol. XI 1832, has the account of 1828, vol. XVI 1838, that of 1830 and 1831, but exactly an account of 1829 is wanting in the intermediate volumes. Yet one reads in the “Analyse des travaux de l'Académie pendant l'année 1851” in Tome XVI 1838, page CCI: “Dans l'analyse des travaux de 1829, on a déjà donné une description...”, from which would follow that the account for 1829 had been published. 3) Revue Bibl. Dec. 1829 p. 147. ‘) Comtes rendus T. XX 1845 p. 1258. 7 per, Re oe lis. has later been proved to be false. And in spite of all the praise which Sacus justly bestows on him, he adds that Durrocuer “sich oft durch seine eigenen Vorurtheile beirren liesz” *). Meanwhile the question remained unsettled, for Durrocuer gave only a negation and no explanation. On Dec. 9, 1829, he also read his article to the Société de Pharmacie de Paris *). In 1832 appeared the Physiologie végétale by A. P. pr CANDOLLE who gave a short description of the experiments of Pinot and Murper *). He wrongly was of opinion that Pinot fixed the seeds, for his silver needle was a movable balance. From Murper's experiments he drew the conclusion that the roots penetrated into the mercury on account of their ‘‘stiffness’’; the tender roots of the buekwheat were not stiff enough then to force themselves in. To the penetration of freely floating seeds he opposed Durrocuer’s negation. Several handbooks of those days, as those of Biscnorr, LINDLEY, Treviranus and Mryren, make no mention of the experiments with mercury. Durrocurr himself omits them entirely from his “Mémoires pour servir a [histoire anatomique et physiologique des végétaux et des animaux’, 1837. On May 27,1844, however, Parrr sent a paper to the Académie, entitled “Mémoire sur la tendence des racines a s’enfoncer dans la terre et sur leur force de pénétration.” In this paper he described his experiments which seemed to confirm Pixot’s observations. The paper itself does not seem to have been printed; an extract of it however was given by Payer in the Comptes Rendus *), while an elaborate report of it occurs in the Comptes Rendus of 1845 °). Payer devised an apparatus in order to determine the depth to which a germroot could penetrate into the mercury. For this purpose he used layers of mercury of varying thickness, keing at the bottom in contact with a layer of water. In a glass trough namely, one or 1) Sacus, Geschichte der Botanik 1875 p. 555. 2?) Journai de Pharmacie Tome XVI 1830 p. 28. 3) A.P. pe Canpotte, Physiologie végétale Tome II 1832 p. 827—828. *) Comptes rendus Tome XVIII. 1844 pag. 993—995. HormetsreR gives p. 933 instead of p. 993; this mistake is found in the following papers: Hormeister, Ber. der kön. Siichs. Ges. d. Wiss. zu Leipzig XIL 1860 p. 203. Hormerster, Pringsh. Jahrb. HI 1863 p. 105. Hormetster, Die Lehre von der Pflanzenzelle 1867 p. 284. A. B. Frank, Beiträge zur Pflanzenphysiologie, 1868 p. 22. Tu. Chesteukr, in Gohn’s Beiträge zur Biologie der Pflanzen I, 2 1872 p. 11. A. Scnoser, Die Anschauungen über den Geotropismus der Pflanzen seit Knight, 1899 pag. 9. 5) Comptes rendus Tome XX 1845 p. 1257—126s. 13 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 188 ) more pieces of platinum gauze were fixed horizontally, on which a patch of muslin or cotton was placed. The trough was filled with water as high as the patch, in some experiments it contained oil or only air; then the mercury was poured on the patch. The tension of the lower mercury-surface was great enough to prevent the mercury from being foreed through the meshes. Now Payer made various seeds germinate in the layer of water on the mercury. It will be presently seen that he fixed the seeds to some extent. Of some he saw the roots penetrate through a layer of mercury of as much as two centimetres and appear in the water under it. Of other seeds the roots remained creeping on the mercury, of others still they only penetrated a few millimetres. Hence Payrr concludes that the roots have a different penetrative power, not depending on differences of weight, stiffness or size. Weight alone cannot be the cause, for if the roots are taken from the mercury they do not sink in it again. They remain floating and only the growing part can penetrate again. Differences in stiffness cannot cause the varying behaviour, any more than differences in size. For roots of garden-cress (Lepidium sativum) do penetrate, those of buckwheat do not, although the latter are bigger, stiffer and heavier than the former. Of the committee which had to report on this paper by Parrer, Durrocuer (since 1831 an ordinary member of the Académie) was the reporter. The report was late in appearing and meanwhile on March 24,1845, Duranp sent a paper to the Académie in which he thought to be able to reconcile the conflicting opinions. Duranp says in the extract of his “Mémoire sur un fait singulier de la physiologie des racines” *) about the experiments of Pivot, Merper and Payer: “J’avais toujours vu là, au contraire, une de ces expériences trop légèrement faites et illégitimement imposées a la science, dont elles faussent ou paralysent les inductions: un fait a rayer des catalogues physiologiques.” Therefore he wants to repeat these experi- ments and to give their normal explanation. He makes a clear distinction between loose and fixed seeds. He gives the following synopsis of the cases which can occur. 1. The seed is fixed above the mercury ; the root then penetrates into the mereury perpendicularly to a depth of more than 4 centimetres. 2. The seed is loose. Here we have two cases : A. It reaches the margin of the mercury-surface. Then the root 1) Comptes rendus Tome XX 1845 pag. 861—862, ( 189 ) forces itself between glass and mereury and is held fast by the lateral pressure of the mercury. B. It stays in the middle. Here again two cases: a. The mercurial surface remains pure. Then the root does not sink deeper than it should do on account of its weight. b. A resistent, flexible layer is formed on the mercury, consisting of soluble matter of the seed which on evaporation of the water remains on the mercury. The root can then penetrate as this layer sticks the seed to the surface. Case a occurred in Durrocurt’s experiments and in those of the committee for Pinot’s paper; case hb is that of Pixor and Mourper. With Murper buckwheat did not penetrate because it gave off little or no soluble matter to the water. So Duranp reduces all the cases of a penetration, greater than the weight, to the first-mentioned case, fixation of the seeds. It appears from Durrocuet’s report that Duranp also speaks of ‘une adhérence capillaire entre la graine et la surface du mercure”, *) which gives the seed some support for the penetration of the germroot when the layer of water has almost evaporated. It is not clear whether he means the evaporating layer of water or the resistent layer which he later uses for the explanation of the case under 5. On April 28, 1845, i.e. a month later, a combined report appeared on the papers by Payer and Duranp. DutrocHEet was the reporter. ®) In the meantime it had become clear that Payer had not distinetly felt the difference between experiments on germination upon mercury with loose and with partly fixed seeds. He had not mentioned namely in his Mémoire that his germroots were put through holes in a slice of cork or lay in cottonwool; not till later, on April 15, 1845, he had declared this to the committee. Payer moreover declared that he had used the word “penetrative power only in a superficial meaning, not involving a special vital force. So Payer’s experiments were no longer alarming, especially now that Durand had given an explanation of those of Prior. For in these latter the seedling was stated to have stuck to the surface of the mercury, because on evaporation of the water a sticking-plaster was formed of soluble substances of the seed with mercury. In his report Durrocuer says”): “La couche dont il est ici question est une mixtion avec le mercure des substances organiques qui ont été dissoutes dans l'eau.” “Telle est selon M. Duranp, la cause de la 1) Comptes rendus Tome XX 1845 p. 1263. ?) Comptes rendus Tome XX 1845 p. 1257—1268. 3) Idem p. 1264, 13% (190 ) pénétration de la radicule dans le mercure lorsque la graine est déposée sur la surface de ce métal couvert d'un peu d'eau; il faut que la graine soit agglutinée a la surface de ce métal par le moyen dun enduit qui sy forme pour que cette pénétration ait lieu. Lorsque le mereure conserve son poli, les radicules ne s’y enfoncent jamais au delà de ce qui est déterminé par la pesanteur des graines.” So the paradox had been subjeeted to known physical laws. The matter seemed to be settled for good and all, when in 1854 once more an investigator confirmed Pinor’s observations. Atpert Wicanp at Marburg wrote in his “Botanische Untersu- chungen” a chapter, entitled “Versuche über das Richtungsgesetz der Pflanze beim Keimen”*). He mentioned in it the experiments of Pivot, Murper and Dvrrocner, without quoting the literature on the subject. He said that Pryor and Mcnper fixed the seeds but that Derrocuer let them free and hence obtained a negative result. *) Evidently he derived this erroneous idea about Pixor from Ro6psr’s translation of Dy Canporze’s Physiologie végétale. Wicanp dared scarcely confess that he also had made seeds germinate when they floated on the mercury, so firmly was he convinced of the impossibility of success in this case. *). - | But the result was undeniable, and so he nevertheless described his experiments. The seedlings grew in a very thin layer of water on the mercury or on dry mercury in an atmosphere saturated with water-vapour. Some roots penetrated perpendicularly into the mercury as far as 4 “Zoll”.*) Others grew in a slanting direction into the mercury or at first perpendicularly and then more horizontally or the apex came out of the mercury again or it grew horizontally at first and then perpendicularly downwards. A great number of roots remained creeping over the surface. Seedlings that had been taken out of the mercury could be replaced to the same depth. Along the glass wall many roots penetrated. For seeds of smaller size than beans, weight was hardly a factor for the penetration; a seed of garden-cress made scarcely any de- pression in the mercury and yet the root penetrated fairly deep. Nor could the reason be found in a greater adhesion of seeds and mercury by the secretion of certain substances. For often mercury 1) Botanische Untersuchungen von Dr. ArBert Wieaxp, Braunschweig 1854 pp. 131—166. 2) Idem p. 136. 3) Idem p. 137. : 4) 12 Linien = | Zoll = 27,075 mm. ere A ea a eT ee, ee 2 POLST AN ATEN BN C KORN stuck to the radicles, to be sure, but only to old, dying, not to fresh and growing roots. WiGAND gave no explanation. ‘To him it seemed to be “ein bis jetzt ungelöstes mechanisches Paradoxon, nicht minder als Miinchhausen, der sich und sein Pferd an seinem eigenen Zopfe aus dem Sumpfe zieht” +), But he entirely confused the force with which the root penetrated and the cause which prevents the seedling from capsizing in the mercury. For he thought the penetration of germroots in a solid soil quite as mysterious, although here there was no question of upward pressure. | No attention has later been paid to these observations; not even by those who quoted various other points from this chapter of WiGAnp. It was considered sufficient to refer to the refutation by Dvranp and Durrocner in 1845. So Hormeister wrote in 18602): “Pixor und Payer sind bereits 1845 durch Derarp und Derroener so gründlieh widerlegt, die Ursachen der Täuschungen jener sind so vollständig aufgedeckt worden, dass die ausfiihrliche Mittheilung von mir selbst über diesen Gegen- stand angestellter Beobachtungen kaum noch nöthig ist” *). Hormrisrer obtained the same result as Dtranp and Derroener : penetration by weight or because the seedling stuck to the mereury by dissolved matter. SACHS wrote in 1865: “Die an sich schon unglaublieh klingenden Angaben Pinot’s und Parer’s über das tiefe Eindringen der Wurzeln in Quecksilber, wurden schon von Duranp und Dutrocunt widerlegt” *). In 1867 Hormrisrer wrote that the penetration of growing roots into mercury was caused by stretching of the hypocotyl, “wie bereits Duranp und Durrocuet erschöpfend gezeigt haben” *). Experiments on germination upon mercury now became very frequent in the following years in order to combat Hormrtstrr’s theory of positive geotropism. This latter namely, like KoNicur’s theory, was based on the supposition that the apex of the root was of a plastic nature and therefore the penetration of the roots into 1) ERG pytAo: 2) W. Hormeister, Ueber die durch die Schwerkraft bestimmten Richtungen von Pflanzentheilen, in Berichte über die Verhandlungen der kön. Sächs. Ges. der Wiss. zu Leipzig, Mathematisch-Physische Classe, XIlter Band 1860, pag. 175—213. The same article in Prinesuem’s Jahrbücher fiir wiss. Botanik [IL 1863 pag. 77—114. 8) 1. c. p. 203 resp. p. 105. *) J, Sacus. Handbuch der Experimental-Physiologie der Pflanzen, 1865, pag. 104. 5) W. Hormetsrer. Die Lehre von der Pflanzenzelle, 1867, pag. 283 Anm. 4, ( 192 5 mercury was no welcome fact to these theories. In this way arose the fierce controversy between Hormeisrer and FRrAxK *), concerning which we also mention the papers by N. J. C. Mürrer ®), N. SPESCHNEEFF *), Tu. Cresmeiki‘), Sacus*), SAPOSHNIKOW °), and WacuTEL’). FRANK, like WicGanpb, derived from Dr CanpouiE ®) the erroneous idea that Pivot fixed his seeds *), and for the rest entirely embraced the views of Duranp and Dvtrocuet*’). To the loose lying seeds none of them paid attention nor is anything found about them in later text- or handbooks. In 1899 Dr. A. ScHoBer gave a historical synopsis of the various hypotheses on geotropism in which he also deals with the experi- ments on germination upon mercury "'). He does not deal with loose seeds in it however. Explanation of the phenomenon. The penetration of the roots of entirely freely floating seeds into mercury has been stated by few investigators only. From the preceding historical synopsis it would appear that this was done only by Pinor and Wicanp. Murper, Gorppert and Payer gave support to the seed, by putting the roots through holes in a slice of cork (Mvrprer and Payer), in a wooden cross (GOEPPERT), or by placing the seeds in or on a plug of cottonwool (Payer). Hereby the frictional resistance against upward movements was increased and also the circumstances at the surface of mercury and water were modified, so that the seeds were less easily lifted out by upward pressure. So I repeated the experiments as Pinor and Wiaanp had made them. Although Wicanp gives no dimensions, yet one can see from his description that he did not use such small troughs of mercury 1) Bot. Ztg. 1868 and 1869. 2) Bot. Ztg. 1869, 1870 and 1871. 3) Bot. Ztg. 1870. 4) Coun’s Beiträge zur Biologie der Pflanzen I, 2 1872. 5) Arb. des bot. Inst. in Würzburg I, 3 1875. 6) Report in Bot. Jahresbericht XV, 1 1887; less extensive in Bot. Centralblatt Band 33, 1888. 7) Bot. Centra'blatt Band 63, 1895. 8) Physiologie végétale II, 1832, pag. 82. 9) Beiträge zur Pflanzenphysiologie, Leipzig 1868, pag. 5. 1) Idem pag. 22. 11) Die Anschauungen über den Geotropismus der Pilanzen seit Kxieir. Ham- burg 1899. pp. 9 and 18. ’ ( 193 ) as Prxor who used them only about one centimetre broad. So I took first rectangular glass troughs of 4 em. breadth and erystallising dishes of 10 em. diameter which were filled with mercury about two centimetres deep. On the dry mercury I had to pour a fairly large quantity of water before this would spread over the whole surface; by means of a pipette so much was drawn off that only a very thin layer remained. In this water the soaked or dry seeds were put. The seeds had to emerge for a great part above the layer of water; if this latter was too thick they rotted and grew mouldy, especially if the temperature was somewhat high, as in a hothouse. The dishes were covered with glass or placed under a bell-jar in order to prevent strong evaporation. Distilled water was used by preference. The seeds used were: pea (Pisum sativum), garden-cress (Lepidium sativum), wheat (Triticum vulgare), buckwheat (Polygonum Fago- pyrum) and Lathyrus odoratus. The garden-cress grew quickest, so that I could make a number of experiments in succession in a short time with it. Most roots crept over the surface of the mercury or only pene- trated into it with their extreme tip. Sometimes however a radicle had advanced to a fairly considerable depth. Thus on February 19, 1900, the radicle of a seed of garden-cress of two days was 7 mm. long, of which 3 mm. were in the mercury. On March 17, 1900, several radicles of garden-cress had, after three days, advanced 4 to 6 mm. perpendicularly into the mercury, of a pea the radicle was 5 mm. in the mercury. On March 23, 1900, after three days, again a few radicles of garden-cress were 5 mm. in the mercury. The radicles that had found their way into it had for the greater part had a downward direction immediately at their germination, so that only a short piece protruded above the mercury. Sometimes however roots of garden-eress, after having grown laterally about one centi- metre, had still pierced the mercury 4 mm. with their apex. With wheat the three secondary roots crept over the mercury, an apex seldom penetrated any length. Radicles of buckwheat I did not see penetrating. Lathyrus sometimes 5 to 7 mm. On further growth the plantlets that had pierced the mercury were upset and were lifted out of the liquid as was the case with the great majority of seedlings at the very beginning. Hence the experiments were soon finished. So the circumstance that the roots turned black and died later and that the seeds rotted and grew mouldy, gave little trouble. The mercury however had to be per- fectly pure, since otherwise the radicles stopped growing too soon ( 194) and turned brown. The purification took place with dilute nitric acid. In these experiments some roots had so far grown down that weight alone could not explain this. My radicles did not go down so deep as those of Wicanpd however. Now it soon became clear in what respect the plantlets that had grown into the mercury were distinguished from those which had not. They were not quite free, namely, but lay against another seed; round and between both seeds the water had risen through capillarity and gave some support to the seed by the tension of its concave surface. The molecular forces of the water thus opposed the upward pressure of the mercury. Durand calculated the force with which the mercury forces seedlings of Lathyrus odoratus upwards. For a cylindrical radicle of */, mm. Qa\2 . . > vo 5 diameter this foree amounted per mm. length to a (=) Sa, milligrammes; for a length of 20 mm. this is 120 milligrammes. The volume of the radicles can be approximately determined from the length and the thickness in various places; or by weighing the cut off radicles. (The specific gravity is about one). The tapering of the roots towards the top makes the determination of the volume from measurements of thicknesses rather inaccurate. For approximate values the two methods supplement each other sufficiently, however. For radicles of Lathyrus of 5 to 7 mm. length I found volumes of 5 to 8 mm’; the upward pressure of the mercury is then 68 to 109 mg. The Lathyrus plantlets weighed about 200 mg. Roots of garden-cress of 5 to 9 mm. had volumes of 1 to 2 mm’; the upward pressure is then 14 to 27 mg. The cress plantlets weighed, before the seedcoat had fallen off, about 17 mg., after the falling Ol SE). The weights of the plantlets are considerably diminished, however, by their lying in the water with parts that are much more voluminous than the radicle. When the upward pressure of the layer of water has been subtracted, the weight that must be compared to the upward pressure of the mercury remains. In the case of Lathyrus this weight will still be in excess, but with garden-cress there is a greater or smaller deficiency. For the greater depths of Pivot and WrI1GAND this deficiency becomes greater still, but its amount remains small and can easily be compensated by the molecular forces of the water. If the seedling be raised through a very small distance, the surface of the water that has been raised against the seed by capillarity, 1) The cast off seedcoat alone weighs about 16 mg., evidently because it is filled with water, relained by capillarity. 5) (195 ) must be extended along the whole margin. The capillary constant of water is 8,8, hence for each mm. of the circumference of the raised water a force of 8,8 mg. is necessary. This circumference measures with the swollen seed of garden-cress 14 mm., with Lathyrus about 29 mm., so that a force of more than 100 mg. is available for compensating differences of upward pres- sure and weight. Therefore it is necessary however that the seed or plantlet cannot capsize too easily. The capsizing is a rotation round a horizontal axis by which the water-surface need not be increased. The vertical component of the surface-tension is consequently of no effect to prevent the plantlet from being upset and hence being lifted out. This rotation is rendered more difficult by water, rising by capillarity between two seedlings that lie close together, or between the glass and the seedling, because this water has a greater horizontal surface which must be increased during the capsizing. Hence it is against the glass wall that the roots penetrate most frequently, in which case also the friction between wall and root facilitates the penetration by the unilateral horizontal pressure of the mercury. The thinner the layer of water, the closer the centres of surface- tension and upward pressure le together and the shorter is also the lever-arm with which a lateral component of the hydrostatic pressure acts on a somewhat slanting radicle in order to upset the plantlet. With a seed in an entirely free position, penetration will be possible but in the most favourable case only an unstable equilibrium will exist. The penetration of freely placed seeds will consequently be generally absent, not because the upward pressure soon exceeds the weight of the little plant, but because the plant is overturned by rotation. Pixor immediately obtained such a good result because his mereury- troughs were so small, only one centimetre broad. So I also repeated the experiments in this way. Of a glass tube of one em. diameter bits were cut off and closed at the bottom with a cork. These troughs were filled with mercury and in each a soaked seed of Lathyrus or garden-cress was put with as little water as possible. The water that was raised by capillarity now stuck the seed against the glass wall and the root penetrated more easily because it was less easily upset. When I placed the seeds with the radicle turned towards the centre of the trough, it grew down into the mercury itself, not between the glass wall and the mercury. Pryor used still another and effective means to prevent capsizing and at the same time to eliminate the weight of the seed, viz. by the experiment with the silver needle, deseribed above. I repeated ( 196 ) this experiment in the following manner, see fig. 1. Of thin sheet- aluminium a flat balance-Leam was made, 6'/, em. long, resting with a brass cap on a steel point. On one end a Lathyrus seed was stuck, to the other a small bit of paraffin was melted, balancing the seed. Exactly under the seed a small trough of mercury was placed with very little water on the mercury. By another small vessel, filled with water, and by a little bell-jar over the whole arrangement, the air was kept moist. The root after a few days grew down 7 mm. into the mercury, without the balance being lifted. By adding to it and by melting away from it, the small bit of paraffin was occasionally brought into equilibrium with the growing seedling, after the latter had been dried with filtering paper. The upward pressure of the mercury which amounted to more than 100 mg., was now balanced by the surface-tension of the water, raised by capillarity. It might even have been a great deal more, for on the other arm of the balance I could still place about 100 mg. in addition to the bit of paraffin before the plantlet was lifted out of the mercury. We can now explain why various investigators could give such totally contradictory reports. In the first place we may trust Pivor’s results (1829). The description of his experiments gives the impression that he observed accurately. Durrocner (1829) did not repeat the experiments with the perse- verance which is necessary to obtain a good result. The experiments of Murper (1829) were too coarse and valueless for Prxot’s problem. Of Gorprrert (1831) the same may be said. Parer (1844) used a slice of cork or a plug of cottonwool on a thick layer of water, so that later writers wrongly always mention Pixor and Payer together. His experiment, described above, with a layer of mercury above a layer of water, is ingenious. I repeated it, using lacquered iron-gauze instead of platinum-gauze. The roots of seeds of Lathyrus and Phaseolus, stuck on pins in corks, grew very finely through the mereury into the water; see fig. 2. The mercury is indistinct in the figure because of the patch of muslin which lies on the gauze. It was namely pushed downwards in the glass trough in order to show the seeds stuck on the pins. Payer stated that the roots did not penetrate again into the mer- cury once they had been taken out of it. Pinor and Wieanp asserted the contrary. This can easily be explained. The latter left the seeds free indeed and the surface-tension acted as before when the plant was replaced in the mercury in its former position. Parer’s seedlings, on the other hand, were fixed; they penetrated into the mercury | | ee enn Cm te PPT vere eS en oe on Pi on eS ss ee ee eee et Pu. van HARREVELD. „On the penetration into mercury of the roots of freely floating germinating seeds.” Proceedings Royal Acad. Amsterdam. Vol NA. : Ù Ld } wt! » oe j r j { ' . . : ; Pa i a k 10 9 { ‘ . 1 : ‘ iy ad? ia en | | JA ( 197 ) to a far greater depth and when they had been taken out of it, they did not so easily regain their former support. Dovranp (1845) gave the explanation which a large, old seedling on mercury suggested to him. It had stayed so long on it, that an adhesive layer had been formed on the mereury of sufficient thickness to fasten the plant to some extent. That therefore all seedlings whose roots penetrate into mercury, should stick to it by such a layer is not true. The penetration takes places after a short time when the mercury is still bright. Durrocner (1845) accepted Duranp’s explanation and made expe- riments on the formation of the sticky layer. But he did not put to himself the question whether in all the observed cases such a “plaster” had been present. Wicanp (1854) has undoubtedly obtained Pinov’s results. In his discussion however he confused and complicated the question as Murper had done. For this reason later investigators did not bestow much attention to the paradox which he had so clearly pronounced. Where he speaks of penetration into dry mercury, this must cer- tainly not be taken literally; the soaked seeds retain a layer of water. Hormmisrer (1860) studied the penetration of roots in relation with his theory of the plastic apex. He did not obtain the result of Pivot and Wicanp and accepted Duranp’s explanation which also Durrocner had aecepted. Later investigators all followed Hormrister’s opinion. Mathematics. — “The harmonic curves belonging to a given plane cubic curve.” By Prof. JAN De VRIES. 1. The “harmonic” curve of a given point P with respect to a given plane cubic curve #’ is the locus of the point /7 separated harmonically from P? by two of the points of intersection 4,,A,, A, of k® and PH). We shall determine the equation of the harmonie curve h® when 4 is indicated by the equation a’, —b*,=(a, «, + a, a, + a, x) = 0, and P by the coordinates (4, Y,, 4»). 1) This curve appears in Sretner’s treatise: “Ueber solche algebraische Curven, welche einen Mittelpunkt haben,..... ” (J. of Crelle, XLVI), and is there more generally specified as a curve of order ”. Stereometrically it has been determined by Dr. H. pe Vries in his dissertation: “Over de restdoorsnede van twee volgens eene vlakke kromme perspectivische kegels, en over satellietkrommen”, Amsterdam 1901, p. 6 and 83. = (198 ) To the points of intersection of %* and 4° belong the points of contact of the six tangents from / to 4”. If A, is one of the remaining three points of intersection, then A, and A, are harmonically separated by A, and P, that is P lies on the polar conic of A,; from this follows however that A, lies on the polar line of P. So the curve h® passes through the points of intersection of 4° with both the polar conic p? and the polar line p' of P. Its equation is therefore of the form wa*®,4a,a?,b?,b,=9. If point X belongs to the harmonic curve of point Y, it is evident that } lies on the harmonic curve of Y; so our equation must be symmetric with regard to the variables a; and y;; that is, it has the form a>, b°, + Lary dy be b*y = Ons aM EN To determine 2 we suppose P to be lying on a,=0 and we then consider the points of 4? which are lying on z,=0. If we represent the linear factors of the binary form a*,—*,—(a,¢,+a,«,)® by Px Je and 7,, then the points H, H,, H, are indicated by the equation Ws = (Px Qy + Py Qe) (Pe ry + Py 72) (qe ry + Fy 72) = 0, or by Mn = Rete ay pclae Be Based tate Oo: ae eens We now have 3 ay Gy = Px Je Py + Px Vy Px H Py Ve Vrs 3 by by = Pe Qy Py + Py Ve Vy + Py Vy Pa and as we moreover have Py Vy Py =O we find out of (2) == Sa dy by b°, a by == 0a ae ee This equation also represents the harmonic curve, if we but again regard «?, as the symbol for (ae, + 4,7, + 4,%,)). 2. The polar conic of P with regard to the curve 4°; repre- sented by (1) has as equation 3 aa, bey + 2 (2 ay ay by by 4- ey 6°) — 0, or, if we put Oy ty = 1K and dy a’, — L, we find (3 ADELINE See ee It is evident from this that the polar conies of P with respect to the curves of the pencil determined by # and 4” touch each other ; 3 ( 199 ) in their points of intersection with the polar line p', therefore the polar line of P with respect to all the curves 4°) of this pencil. For the curve 4% passing tbrough Z ensues from this that it must have a node in P. Evidently the equation of this curve is a, b*y — ay ay byb?,=0, . . eet Oren whilst its polar conic is indicated by dr dy b°, — dx ay b, b° sl) or by KL =0, from which is evident that it is composed of the tangents through P to the polar conic P with respect to 4°. ‚For 4—=—=3 we find a 4? with the polar conic L?=0. So it possesses three inflectional tangents meeting in P. 3. The satellite conic of P with respect to 4° (that is the conic through the points where f° is intersected by the tangents drawn out of 7) has for equation *) AN Arp dr de bbp ON Ne Le ee) or Ee RN A TE Le To determine the satellite conic for the curve 4°, we put Pea? bey + A az dy by by. Then we find 3 Py ly = (A +- 3) a, ay boy + 22 ay a’, by b*y 5 6 1, Py = 2 (A + 38) ay a’, DP, + 22 (a*y by b*y + ar a’, by), or bl, = (A + laa’, by Py = (A+ 1) a’, by. So according to (6) the equation of the satellite of 4% is A[(A+-3) a*zayb*y + 22 az07 ybyb* y| (a+ 1) c*,d*, — 9(4+ 1)? aa? yb? yo,c7 yd’ y = 0, or as a, 6, c and d are equivalent symbols, (4 À + 12) a? ay b°, — (A + 9) ar a’, br b?y = 0, or BDE (ee Opel a. M8) From this ensues that the satellite conies and the polar conics of P with respect to the curves 4% belong to the same pencil. If we represent this by the equation 1) The deduction of this equation is found in Saumon “Higher plane curves” A stereometrical treatment of the satellite curves is found in the above-mentioned dissertation of Dr, H. pe Vries, p. 18, 19 etc. ie - on En Nd ( 200 ) BK pd Deen So oe ee then u = 24:(4-+ 3) furnishes the polar conic, wi = — (24+ 9): (444 12) the satellite conic of 4°). Between the parameters gp and w’ exists the bilinear relation p—4y'—3. So for »=—1 and p—o we find two curves &*, for which polar conic and satellite coincide. In the first case we have 2=—J1; so we have the curve 4% possessing in P a node. In the second case we find 2=— 8, so a curve for which the polar conic is a double right line. For 2= — 9 the satellite is indicated by A —O. We then have the harmonic curve for which the satellite coincides with the polar conic of 4°; this well-known property indeed, ensues immediately from the definition of 1’. 4. Let us now consider the svstem of the satellite conics of a given point 2 with respect to the cubic curves of any pencil A+aB—0. By means of a selfevident notation the just mentioned system is represented by the equation A (A, A 2B) (Ba AEN (La 2 LN = 6: So through each point of the plane pass two satellites; the index u is here tivo. The satellite consists of two right lines when / is situated on the HessraN. Now the Hessians of the pencil evidently form a system with index three; the number of pairs of lines d is therefore three. A double line is found only when P lies on the cubic curve; consequently for our system 1 is equal to 1. Between the characteristic numbers of a system of conics exist the wellknown relations 2u=v ty and 2y—p-t J. We find from the first r= 3, u being equal to 2 and 4 to 1. The second then gives d=4. From this ensues that the just men- tioned satellite formed of two coinciding right lines must at the saine time be regarded as a pair of lines, thus as a figure in which the centres of the two pencils of tangents have coincided. From the equation 9 (Ka-+a Ki) (La-++4 Li) (AHA B,) (AHA BO ( 201 ) it is evident that the harmonic curves of P with respect to the curves of the cubic pencil also form a system with index two. For #° passing through P the curve 4° breaks up into the system of the polar conic and the polar line of P with respect to that curve which touch each other in 2. As k* and 4? have in common the tangents out of P, being thus of the same class, the harmonic curve has only then a node when this is the case with the original curve. 5. If with respect to a given 4° we determine on each right line through P the points b,, B, LB, in such a way that B; is harmonically separated by A; from A; and Aj, we get as locus of the points B a curve of order ser, h°, with a threefold point in P. For, if B, coincides with P, then A, is one of the points of inter- section of 4° with the polar line of P and the reverse (see § 1). As the points 6 correspond one by one to the points A, the curve h® is of the same genus as 4°, so it has still 6 double points or cusps. This last is excluded because in that case nota single tangent could be drawn from P to h°, whilst it is clear that the tangents out of P to 4° also touch A’. From the definition of 2° follows immediately that this curve can meet the curve 4? only in the points of contact R of the above mentioned six tangents: so in each point / they have three points in common. The right line PR having in R&R two points in common with 4°, but three points with 4’, R must be one of the six nodes of h° and PR one of the tangents in that node. Chemistry. — “Preparation of cyclohexanol.’ By Prof. A. F. HOLLEMAN. The preparation of ketohexamethylene in somewhat large quantities is one of the most lengthy operations, whatever known process may be used. Since, by means of the addition of hydrogen to benzene, by the process of SABATIER and SENDERENS, hexa-hydrobenzene has become a readily accessible substance, it was thought advisable to use this as a starting point for the preparation of tlie said ketone by first converting it into monochlorohexamethylene, converting this in the usual manner into the corresponding alcohol and then oxidising this to ketone by the process indicated by Barver. Mr. van DER LAAN has tried, in my laboratory to realise this, ( 202 ) The method, however, appeared impracticable as the chlorocyclo- hexane was not readily converted into the alcohol. Markownikorr has tried to attain this by using alcoholic potash; we have tried it by shaking the said chloro-compound for several days and at different temperatures with silver oxide and water + alcohol, but a trans- formation worthy of the name was not controlled. The chlorination of cyclohexane in quantities of 80—100 grams to the monochlorocompound was moreover a disagreeable and slow operation. The most satisfactory results were obtained by MarKowNikorr’s first method (A. 801, 184) by pouring the hydrocarbon on to water in a Drechsel flask and then passing chlorine into the water at 30-—40°. The influence of light is very pronounced in this case. Direct sunlight causes explosion. If chlorine is passed through the hydrocarbon exposed to faint light it dissolves with a yellow colour. If now this solution is exposed to sunlight a violent evolution of hydrogen chloride takes place; in strong light this is accompanied by luminous phenomena. Mr. van DER Laan, however, succeeded in readily preparing ketohexamethylene by another process. It appeared that phenol and hydrogen combine to hexahydrophenol by the method of SABATIER and SENDERENS and that the cyclohexanol obtained could then be oxidised to the corresponding ketone: C,H,OH + 3H,=C,H,,OH ; C,H,OH + 0=06,H,,0+H,0. For the preparation of cyclohexanol C,H,,OH a combustion tube was quite filled with nickeloxide which was then reduced by means of pure hydrogen. By means of an asbestos stopper, one end of the tube was connected with a wash-bottle containing phenol; this was placed in an airbath heated to 160—170°. The tube was placed in a combustion furnace in an iron eutter lined with asbestos. The bulbs of two thermometers were also placed in the gutter and the flames were so regulated that they showed 140—160°. By means of another asbestos stopper, the other end of the tube was connected with an adapter leading into a flask closed with a doubly-perforated cork. Through the second hole was passed a gas exit tube by means of which the absorption could be controlled. The current of pure and dry hydrogen which was passed into the wash-bottle containing the phenol charged itself with vapour which in the presence of an excess of hydrogen was exposed to the catalytic action of the nickel. In the receiver a liquid consisting of two layers collected, the bottom layer being water. The top layer was submitted to distillation. From 85°—110° a liquid ty ( 203 ) distilled, which separated into two layers one of which consisted of water whilst the other had a bitter peppermint-like odour. From 110° the temperature rapidly rose to 160° and from 160—180° a consi- derable fraction passed over. What distilled above 180° was mainly unchanged phenol,. which was again subjected to treatment with hydrogen. To remove any phenol, the fraction 160—180° was washed a few times with dilute soda-lye, the alkaline washings were shaken with ether to recover any dissolved cyclohexanol, the ether was evaporated and the residue united with the main liquid. After a few more distillations a liquid was obtained, perfectly clear and of a thick consistency, boiling at 160—161°, the b.p. of cyclohexanol being recorded as 160°.3. A combustion gave the following result. 0.1740 erm. gave 0.4610 erm. CO, and 0.201 7erm. H,O; found: | C 72.2 H12.8 calculated for C,H,,0: C 72.0 H 12.0 By oxidation with Brckmann’s chromic acid mixture (1 mol. K,Cr,O, + 2'/, mol H,SO, in 300 germs. of water) of which 185 grams were used for 10 grams of hexanol and operating at a low temperature, hexanol gives a fair yield of ketohexamethylene. Mr. VAN DER Laan has not determined the exact amount of cyclo- hexanol obtainable from phenol but this is certain that the yield is quite satisfactory. If four tubes with nickelpowder are heated at the same time 1 kilo of hexanol may be easily prepared within 7 or 10 days. As a result of this investigation some substances which were only accessible with the greatest difficultly, have now become easy of preparation. First of all cyclohexanol and ketohexamethylene. The latter may be nearly quantitatively oxidised to adipie acid and as its calcium salt gives a fair yield of ketopentamethylene when sub- mitted to dry distillation, these two latter substances are no longer to be regarded as chemical curiosities. Groningen, Lab. Univs. September 1903. Vegetable Physiology. — “Jnvestiyations of some xanthine derwa- twes im connection with the internal mutation of plants’. By Dr. To. Wervers and Mrs. C. J. Wrrvers —DE GRAAFF. (Com- municated by Prof. C. A. LoBry pr Bruin). The investigations of CrAUTRIAU *) and of Suzukr®) as to the function of caffeine have shown that this substance must probably be regarded as a decomposition (“Abbau”’) product of albumenoids. Meee ES Craurriav. Nature et Signification des Alcaloides végétaux, Bruxelles 1900. 2) Suzuki. Bull. Coll. Agric. Tokyo Imp. Univ. Vol. 4. 1901. pag. 289. 14 Proceedings Royal Acad. Amsterdam, Vol. VI. ( 204 ) These investigations, however, did not clearly show that the caffeine when once formed again took part in the internal mutation processes ; they rather pointed to a preservation of this substance as such and in such cases where it was shown that the quantity of caffeine had decreased, this might have, possibly, been due to migration. We, therefore thought it desirable to subject plants containing xanthine derivatives to a renewed investigation, to examine as many species as possible and particularly to study the question whether these xanthine derivatives are an intermediary or a final product of the internal mutation. Coffea and Thea species were the only plants investigated up to the present so we also included in our research Kola acuminata Horsf. et Benn. and Theobroma Cacao both of which contain caffeine as well as theobromine. A stay at the Botanical Gardens at Buitenzorg (Java) afforded us ample opportunity *). At Buitenzorg many physiological experiments were made and material collected for quantitative determinations, the results of which wili be published later on; qualitative and microchemical tests were also made and of these a short description will be given below. First of all a few words as to the methods employed for the detection of the xanthine derivatives in the various parts. Brnrens’s method was used for plants containing caffeine only. The parts were triturated in a mortar with quick lime and extracted with 96°/, alcohol. A few drops of the alcoholic solution were then evaporated to dryness and the residue sublimed. The sublimate after breathing on it then showed erystals of hydrated caffeine. In the case of plants containing both caffeine and theobromine the parts were boiled with water slightly acidified with acetic acid. The aqueous extract was filtered and precipitated with lead acetate ; the filtrate after being neutralised with sodium carbonate was then evaporated to dryness. Up to this stage the method proposed by Benrens had been again used but the dry mass was not now heated in order to sublime the xanthine derivatives but was extracted with a little chloroform. Both xanthine derivatives passed into this solvent and on evaporating the same they were left behind as well defined crystals; sometimes the residue had to be first sublimed. Both methods are very delicate; traces of either caffeine or theobromine may be detected. The investigation extended over the following plants: Coffea arabica L., C. liberica Bull., C. stenophylla G. Don., Thea assamica 1) Paullinia sorbilis Mart. and Ilex paraguariensis St. Hilaire could not be investigated but we hope to do so on some future occasion. ( 205 ) Griff., T. sinensis Sims., Kola acuminata Horsf. et Benn. and Theobroma Cacao L. 5. a. Roots: In Thea sp.) Coffea sp. and Theobroma neither the roots of the full grown plants, nor those of the seedlings showed traces of caffeine or theobromine. In Kola acuminata the roots of the full grown specimens did not show any either; those of the seedlings, however, contained theobromine but no caffeine. b. Stems: 1. Extending young shoots contained : caffeine in Thea sp. and Coffea sp. caffeine and theobromine in Kola acuminata. ‚theobromine no caffeine in Theobroma Cacao. 2. One year old branches contained: caffeine in T. assamica, T. sinensis, Coffea liberica, C. arabica ; no caffeine or theobromine in Coffea stenophylla, Theobroma Cacao, Kola acuminata. 3. Two years old branches contained: caffeine in T. assamica, T. sinensis, Coffea arabica, none in any of the others *). In branches, these xanthine derivatives are always found in the bark and not in the wood, at least if the branches are old enough to render possible a neat separation of the two. G: Leaves ; 1. young leaves of Thea sp. and Coffea sp. contained caffeine, those of Theobroma Cacao and Kola acuminata theobromine and caffeine. 2. Full grown leaves of Thea sp., Coffea arabica and Coffea liberica contained caffeine; those of Theobroma Cacao traces of theobromine. Those of Coffea stenophylla contained no caffeine, those of Kola acuminata neitaer theobromine nor caffeine. d. Flowers: Thea assamica: caffeme in all parts of the flowers, calyx, petals, stamens and pistil. Coffea liberica: caffeine in the pistil only. Theobroma Cacao: theobromine (no caffeine) in the pistil only. 1) Coffea bengalensis Roxb. Camellea japonica L., C. Sasangua Thb. and C. minahassae Koorders were also tested bul in neither of them any caffeine was found. *) These species are only those mentioned above and not those in note 1. 5) The bark of very thick old branches of Thea assamica contains caffeine; none is found in that of Thea sinensis. 14%* ( 206 ) Kola acuminata: caffeine and theobromine both in the petals and stamens of the & and in the corolla and pistil of the ? flowers *). a. Pris: Thea sp.: both young and ripe seeds (in husk) contained caffeine (but only in very small quantities). Coffea sp.: much caffeine in the cotyllae and also in the testa and husk. Theobroma Cacao: When the fruit is ripening, theobromine first makes its appearance in the external fruit wall; afterwards a xanthine derivative (caffeine) occurs in the fruit pulp; finally the seeds them- selves show the presence of theobromine and caffeine while the theobromine is disappearing from the external fruit wall. Kola acuminata: The fruit wall, fruit pulp and also the seeds contain both xanthine derivatives during the maturation process. On looking at these facts we first of all observe that the said xanthine derivatives are present in all the young parts of these plants which grow above ground even when they spring from old parts utterly devoid of these substances. For instance, the flowers of Coffea liberica sometimes result from old branches, the bark of which is devoid of caffeine and still they contain this substance. In the case of Theobroma Cacao the flower branches (and sometimes the young shoots) always spring from old branches utterly devoid of theobro- mine and with Kola acuminata this is still more pronounced ; the flowers and young shoots always result from branches in which no theobromine or caffeine can be detected either before or after the budding. From this it is evident that during the period of development and growth of the young parts of the said plants, caffeine or theobromine is always formed and remains localized in those parts for a longer or shorter period. This fact may be very well reconciled with the theory that these substances may be decomposition products of albumenoids *) although, perhaps another explanation may be possible. At the same time, however, it appears from the above that these xanthine derivatives very often diminish in quantity during the growth of the young parts and that they disappear from the full grown ones. They are found to disappear from the leaves of Coffea stenophylla, Theobroma Cacao and Kola acuminata, from the branches of these species and from those of Thea sinensis, Coffea liberica and C. ara- ') Flowers of T. sinensis and Coffea arabica were not at our disposal. 2?) How the facts observed with roots may be reconciled with this theory remains as yet unexplained. im 7 ( 207 ) bica; one would, therefore, be inclined to think that caffeine and theobromine may again take part in the internal mutation. Let us, therefore, take the case of a fairly young non-blossoming specimen of Kola acuminata. During the unfolding of the young buds the plant is very rich in caffeine and theobromine; the young leaves and branches, however, retain these substances for a short time only, so that after two months they have completely disappeared. There is then not a single part, young or old which contains any caffeine or theobromine and as no parts have become detached, this fact can only be explained by assuming that these xanthine derivatives have again entered into the internal mutation. With the Thea species the matter appears quite different ; the young leaves and also the full grown ones are rich in caffeine and the quantity found in the bark is a mere nothing as compared with that contained in the leaves. Here it would appear as if, with the falling of the leaves, the caffeine as such would be lost; this view, however, is not correct. On testing tea leaves which had turned yellow and would fall at the merest touch, it appeared that they were quite caffeine-free both in the case of Thea assamica and T. sinensis. The same was noticed with Coffea liberica and Theobroma Cacao (also in regard to theobromine) that is to say in the case of all species whose full grown leaves still contained xanthine derivatives, with the exception of Coffea arabica. During our stay at Buitenzorg it was, however, not possible to obtain leaves which had fallen after having turned yellow in the normal manner. All the leaves had been attacked by Hemileia vastatrie which causes a premature turning yellow and falling. It is probably due to this fact that no caffeine-free yellow leaves were met with. We, therefore, see that these xanthine derivatives disappear from the leaves shortly before they fall, whilst the bark of the older branches bearing these leaves is either free from these substances (and remains so as in the case of Theobroma Cacao and Coffea liberica) or contains such a trifling quantity thereof that it is as nothing compared with the quantity disappeared. from the leaves, as in the ease of Thea sp. If we now take into consideration that the leaves of the branches which are quite devoid of young shoots or flowers also show the same behaviour, we can state with certainty that the xanthine deri- vatives again enter into the internal mutation and are, therefore, at least in this case, an ilermediary and not a final product. This * ( 208 ) conclusion may be supported by quantitative determinations, but these are not necessary in order to prove its correctness. The shrubs of Thea assamica of the Agricultural Garden at Tjikeumeuh bear a number of variegated leaves often so discoloured that one side of the midrib is yellow whilst the other side is green. These two sections which are of course, equally old and exactly similar and which differ only by the absence or presence of chorophy Il, were compared as to their amount of caffeme. The operation was conducted in the manner previously described!) for catechol. Of a small number of leaves a yellow and an equally large green piece was taken, both were triturated separately with quick lime, extracted with the same amount of alcohol and the deposits obtained by sublimation were then compared. Each time the sublimates obtained from the yellow part of the leaves were found to be much denser; the part free from chlorophyll consequently contains decidedly more caffeine than the one containing chlorophyll; a very significant fact which may enable us to get a better insight into the chemical processes of this plant. At the end of this preliminary communication we desire to thank Prof. van RomBvren acting director of the Botanical Gardens at Buitenzorg, for his kind assistance. Mathematics. — ‘“Rectifying curves.” By Mr. J. VAN DE GRIEND Jr. communicated by Prof. J. CARDINAAL. It is known that every motion of an invariable piane system can be regarded as the rolling of a definite curve of the moving system (the “movable polar curve’) over another definite curve of the immovable plane (the “fixed polar curve’). In the following paper the special case will be treated of this general motion, where the movable polar curve is a right line and the motion therefore consists in the rolling of one of the tangents of the fixed polar curve over that curve. Here, however, the constant polar curve itself will not be given; according to a stated law (see N°. 1) this will have to be deduced from another curve given in the moving plane (its rectifying curve) which takes its place and determines it by means of the rectilinear movable polar curve. The replacement of the fixed polar curve by its rectifying curve will give rise to the advantage that in some cases the rectifying curve will be a much simpler one than the rectified 1) Investigations of glucosides in connection with the imternal mutation of plants, September 1902, ( 209 ) polar. curve itself, which will cause its properties to be easily studied and calculations of surface and length of are to be executed in an easier way. And it will be possible to trace in what way the consi- dered fixed polar curve can be described by other curves, the recti- fying ones of which are likewise given (N°. 3,4). Moreover the investigation of these rectifying curves in a certain case (N°. 12) leads back to two kinds of spirals, found already by Putseux in consequence of their tautochronism for forces proportional to the distance (Journal de Liouville, T. IX), but of which by this theory more could be found about their geometrical properties. Summing up in the following the chief points of my investigations very concisely I intend, if possible, to revert to them more in detail. § 1. Notion of the rectifying curve; simplest case. 1. Given in a movable plane an invariable system (=) consisting of a right line AB (the axis fig. 1a) and a curve (/’). The system moves with the axis AB as movable polar curve. Let point Q of this axis be the momentary pole, Q’ the following, QP and Q’P’ 1 AL. Let the elementary rotation de round Q’ be taken of such a dimension that the right line QZ” coincides after the rotation with Q’P regarded as a right line of the immovable plane; let then the rotation around Q’’ be taken in sucha way that Q’’P”’ coincides with Q’’P’ ete. Then point Q describes a curve (/)(fig. 14) the locus of the poles in the immovable plane, so the fixed polar curve or the envelope of the axis AZ in the immovable plane. We call (/) the rectifying curve of (f); then (/) itself is the rectified curve with respect to (/’). The lines QP and Q’?P’ being two successive normals of the curve (f) cutting each other in ZP, the point P is the centre of curvature of (/). If we assume in the system (2) the axis AB as a-axis and a right line OY perpendicular to it as y-axis, we then immediately see on account of the nature of the generation of the curve: a. that the abscissae « of (/) are the lengths of are and the ordinates y are the radii of curvature of (/), so that the rectifying curve is at the same time the curve representing the radius of curvature 9 as a function of the arc s; 6. that the elementary x rotation of the system (XE) or the angle ; ne ee de of contingency of (f) is de = —; y c. that the trajectory of point P moving along (/’) in the immo- (AN) vable plane is the evolute of (f) of which the length of are is found on the ordinate of (4%); d. that the trajectory of an arbitrary fixed point C of AB is one of the evolvents of (f) starting from that point of (/), which becomes the pole in the immovable plane when Q is in C; e. that the area of the figure, comprised between the rectified curve {f), its evolute (P) and two of its radii of curvature, is half of the area of the figure between (/’), the axis AB and the corre- sponding ordinates. 2. Right line as rectifying curve. Let the rectifying curve be the right line AB (tig. 2) and let the motion have advanced as far as the pole Q, centre of curvature of (f) P. The following motion is an elementary rotation de= / P’Q’P or /QPQ round Q’. If we let fall out of Q and Q’ perpendiculars QV and Q’V’ on AB, then at the limit the points V and Q’ lie on the circle, deseribed on PQ as a diameter. So / QVQ’=/ QP, consequently also ZVV =/PQP', the elementary rotation. Farthermore / Q’ V’A being a right angle the system rotation round Q’ causes point PV’ to arrive in V represented as a point of the immovable plane. The same holds good for the following rotations. So the (variable) pro- jection V of Q on AB in the immovable plane is a fixed point. As moreover the angle VQA (angle of the tangent of the rectified curve with the radius vector out of WV) remains constant, the rectified curve is a logarithmic spiral with V for pole. The trajectory of the pole of the logarithmic spiral in the movable system is the right line AZ. So when a logarithmic spiral rolls over one of its tangents, its pole describes a right line. The place of the pole in the movable system is found for every moment by projecting the corresponding momentary centre Q of the motion on the right line (£). The part QA of the z-axis corresponds to the are of the logarithmic spiral, which approaching the pole, winds round it in an infinite number of revolutions ; the point A of the x-axis is unattainable by this are; QA is the limit of the length of are of Q measured towards the pole. The shape of the logarithmic spiral depends exclusively upon one datum: the angle of the right line (/) with the a-axis. As a special case there is the right line parallel to the x-axis as rectifying curve: the rectified one becomes a circle (logarithmic spiral where the angle between radius vector and tangent is aright one; the pole of the spiral becomes the centre of the circle.) at The — ( 214 ) § 2. Movable and variable rectifying curves. 3. If two curves (f) and (/") osculate each other in a point Q and if the evolute (p') of the latter is allowed to roll over the evolute (p) of the former, the curve (f) which does not move, will be the envelope of the moving curve (/") described osculatingly by it in all points; the point of contact Q displacing itself along the moving curve (/”’) describes the fixed curve (f). Let us take of (f) and (/’) the rectifying curves (/’) and (/”) (Fig. 3), then for the first condition (osculating each other in Q) the w-axes of these rectifying curves must coincide and the two rectifying curves must intersect each other in P perpendicularly over Q. The following ordinate (radius of curvature of (/’)) PQ’, of 4”) is equal to the ordinate (radius of curvature of (7)) P,Q, of (’). To make these rays of curvature coincide a displacement of the system of the rectifying curves (/’”) is necessary over a distance Q’,Q, So the above-mentioned osculating description of a curve (f) by another curve (/’) corresponds to the description of its rectifying curve (f) by the rectifying curve (£%) by means of a parallel displa- cement of (/’) parallel to the x-axis; the variable point of intersection P on (#”) describes the curve (/’). The amount of the elementary displacement Q’,Q, =de — de’ is determined by the difference of the abscis-elements dv and dv’ which correspond in both curves to the increase of the coinciding ordinate y to the following ordinate y + dy. 4. When the rectifying curve (/”) does not intersect the rectifying curve (/’) but touches it, the rectified curve (/’) has the following radius of curvature in common with (/) which it touches by a contact of the third order (four consecutive points in common). If we allow (/’) to be described envelopingly by the rectifying curve A”) which then not only changes its position but also its shape according to a definite law, then this corresponds to the description in fourpoint contact of the rectified curve (7) by the variable and moving rectified curve (/’). The evolute of (f) is deseribed osculatingly by the variable and moving evolute of (/’); the evolute of the evolute of (/) is enveloped by that of (/’\ in twopoint contact. 5. In particular an arbitrary rectifying curve can be deseribed intersectingly by a right line of constant direction or tangentially by a right line of variable direction; this is (2) every curve in threepoint contact by a constant logarithmic spiral or in fourpoint contact (5135 by a variable logarithmic spiral. If the right line of the constant direction is parallel to the x-axis, then the osculating spiral becomes circle of curvature (however not remaining of constant size during the motion). So the osculating deseription of a curve (f) by a variable circle of which the centre generates its evolute, becomes a special case of the oseulating description by a constant logarithmic spiral, of which the pole JV (determined according to 2) generates a definite eurve to be called an oh ique evolute of (7) (because it is formed by the intersection of the successive right lines forming with the suceessive tangents of (7) a constant oblique angle). By changing the oblique angle we obtain for one and the same curve (/) an infinite number of these oblique evolutes. In contrast to this there.is only one single trajectory of the pole of the variable logarithmic spiral in four- point contact; the pole V of this spiral is found in every position of the system by projecting the describing point Qof(/) on the tangent of the rectifying curve in P. We wish to determine the tangent and the radius of curvature (7, 8) of the oblique evolutes or trajectories of the poles of the logarithmic spirals in threepoint contact and of that of the spiral in fourpoint contact. Some investigations must however precede concerning the motion of the line connecting Q and V (6). 6. To determine the point of contact *) of the right line Q V (fig. 4) we notice that the motion of this right line as invariable system is determined by the motion of the point Q following the deseribing point of (/) and having thus a displacement equal to dv along SQ, and the condition QV 1 SP, must remain tangent to (/). For the latter it is necessary that the rotation of QV is equal to that of SP; so we have first to determine the motion of SP (inva- riable system determined by the motion of / as the deseribing point of the evolute of (f) (lc)) and the contact of (/’)). The motion of SP results from two rotations: the system rotation de Sn round 1 Q and the rotation de of the radius of curvature M/P round the centre of curvature J/ of the rectifying curve (/’), which gives the tangent SP its following position. So the momentary centre of the resulting motion of SP lies on J/Q; moreover P having in conse- quence of this resulting motion to cover the element of are of the evolute of (/), that is having to undergo a displacement dy 1 AQ, the momentary centre must also lie on P/ i PQ and is thus the 1) Point of intersection of the right line QV with its following position. ( 213 ) point of intersection U of MQ with PI. The rotation of SP round 4 QUE (his point is times the rotation round Q, that is Pane This same rotation must be performed by the invariable system QV round its unknown momentary centre A, whilst Q is displaced along AQ covering a distance = dv = y de. From the latter ensues that the unknown momentary centre A must lie on QP, where QM N ; : MOS HT: X de =yde. From this we find XQ UM PM y QM DM Therefore the point of contact 2 of QV is found by drawing NRV and as also PV 1 QV, the above mentioned equation becomes RQ PM VQ DM’ So this is the equation which determines the position of the point of contact Ron QV. 7. Trajectory (V) of the pole of the logarithmic spiral in four- point contact. a). Tangent. Let us describe a circle (MN) through P, V and Q (fig. 4), we can then regard this circle as a similar varying system of which point P has a motion dy 1 SQ and point Q a motion dr alone SQ. The centre of the velocities of this motion is WV, because eer MOO hande VP VO = dy: dx. This centre, ot-the velg: cities being situated on circle (N) itself, it is at the same time one of the points of contact of circle (NV). Point V has in general dis- placed itself along the circle in its second position; the tangents of the two positions in JV differ infinitesimally, so the tangent to the trajectory (V) is the tangent VV’ to the circle (WV) in JV. D). Radius of curvature. To find the centre of curvature of the trajectory (V) let us search for the point of intersection of two consecutive normals WJ) of this trajectory. For that purpose we shall consider A VNQ. The vertex Q is displaced in the direction QQ’, the vertex V according to the tangent VV’, the vertex N, as a point of the similar system (N), in the direction NN', if LZVNN'=7VQQ’. We can easily convince ourselves that these three directions coneur in one point. So the triangle moves perspec- tively; so the points of contact of the sides lie in one right line. The point of contact of NQ (normal of the curve (/)) is P (centre of curvature of (/')); the point of contact of QV is FR (6). We then (A4) find the point of VN, in other words the required centre of curva- ture M, of (V) as the point of intersection of NV with PR. 8. Trajectory (W) of the pole of the constant logarithmic spiral in threepoint contact. | a). Tangent. Let the rectifying curve of the logarithmic spiral be Sw P (fig. 5), pole W. Angle PS, Q remaining constant the triangle PIVQ forms during the whole motion a similar varying system. Of this system V, the pole of the spiral in fourpoint contact (7), is the centre of the velocities, because “7 VPP’ = 4 VQQ' and VP: VQ= dy: de. So the vertex W of A PWQ moves in such a way that (-VWW' = / VPP. As P, W, V, Q are concyclic it is easy to see that JV JV’ lies in the production of QW. So QIV is the tangent to the trajectory (IV). b). Radius of curvature. To find the centre of curvature of the trajectory (IV) we must find the point of contact of the normal PW of this trajectory, that is that point of PW of which the motion is directed according to PIV itself, if we regard this right _ line again as a right line of the similar varying system QWP. This point is found by letting down VM, out of the centre of velo- cities V in such a way that / VM,So= 7 VPP’, or 7 VM, P= supplement of ~VPP’ = / VIP. So I, M,, V, P lie on a circle and //VP being a right angle “JM, P is a right one too. So the desired centre of curvature J/, is found by producing QV 1 S,P till it intersects P/ in J and by letting down a perpendicular /M, out of J on to SP. § 8. Comes on thew axes as rectifying curves. 9. As a means for the treatment of the conies as rectifying curves let us first regard the right line PN (fig. 6), where P in the system motion of (2) describes the evolute of (f) whilst N is a fixed point of the z-axis and let us then determine its point of contact. The right line PN of which the motion is determined by the motion of P and N (describes the evolute, NV one of the evolvents of (7) (4)), can be regarded as a similar system ; point P has a motion = dy 4 AN; point .V, as a consequence of the system rotation — de about Q, a motion = QN X de likewise 4 AN. So the point of contact 7 in question lies on /°V in such a way that LP dy ( 215 ) ; du gt y dy dy Now de is equal Lo a (1), 50 IN — QN En V dr QV 1 tangent SP as far as the intersection Z with PJ // x-axis. So DR SEE =P, if we produce That is: the point of contact 7 in question is the point where PN is intersected by QV. 10. Ellipse on one of us axes as rectifying curve. If we take for the constant point MN of the «z-axis (9) the centre O of the ellipse (fig. 7), then the displacements of ( and Pare respectively — du é —wrdxu . Q Os de ade = x and dy; the quotient ——— is according to y y dy . A . a” “NY Be 2 the central equation of the ellipse constant = De So the point of ) contact of the right line OP remains during the whole mot on a fixed point; this point of contact is the point & where OP is inter- sected by QV (9); so this point of intersection remains a fixed point during the whole of the motion. The quotient of the displacements atu and. isthe he, so RO: hPa: In order to find the nature of the rectified curve, making use of this fixed point Rk, we determine *) of PQ, considered as similar system, the points moving perpendicularly on their radius vector out of R; these points 7 prove to be real for the ellipse and lie in 7 b such a way that —-—= + —; their distance to #& remains constant LQ a during the whole of the motion; they describe a circle with centre 2. If we produce A7 till it intersects the v-axis in U and the y-axis in Y, then PU and UY also remain constant during the entire motion. From all this ensues that the rectified curve is an epi- or hypocycloid with R as centre; 7’ describes the circle of the basis. 11. To find the length of the radii R7Z’and 5 7'U (fig. 7) expressed in the half axes « and 5 of the ellipse, we presuppose the figure in such a position where 7? has arrived in the production of the small axis ; NN On Po) ame we make use here of the above given relations — = — and —— = -. RO a TQ a Without any difficulty we find for the radius of the rolling circle “x, ab r= tT U0 =—— 2 (a + b) 1) We give here for shortness’sake the results only. ( 216 ) and for the radius of the tixed one ab? ab? fs — DE Cc Moreover R b R b == en = = 2r a—b R+2r a For a=—b (circle)- & becomes equal to oo, the rectified curve equal to a cycloid. 12. Hyperbola on one of its axes as rectifying curve. Let us first take the real axis as the axis of the ares (fig. 8). As in 10 it is evident, that the point of intersection R of OP and QV is a : ‘ E RO a fixed point during the whole of the motion, where — —=— — RP b (2a and 2) real and imaginary axis of the hyperbola). The point 7 (10) is imaginary here; instead of this we consider the constant three- point logarithmic spiral whose rectifying curve WP is parallel to one of the asymptotes of the hyperbola. Let us project both & and JV (pole of the logarithmic spiral) on PQ, it then follows from the equation PR: RO= 0? : a’, that Fie b° the quotient of the projections of PR and RO is equal to —, and a” from the rectangular triangle PWQ, where PW: WQ =b:a, that the quotient of the projections of PW and WQ is likewise equal to 6? :a°. So the projections of & and W coincide in L. So the tangent IQ of the trajectory (JV) (8) forms a constant angle W’WR= 7 WQO with the radius vector AW; so the trajectory (W) is a logarithmic spiral of the same shape as the constant describing logarithmic spiral (IP), that is the curve (/) is described by a constant logarithmic spiral which moves in threepoint contact with itself in such a way that its pole describes the same logarithmic spiral with opposite curvature. Allowing for the modification of the figure we find that these considerations are literally the same for the hyperbola on the imaginary axis as the axis of the ares. Of the additional geometric considerations to which the two kinds of spirals whose rectifying curves are hyperbolae give rise, we shall mention only that the two kinds of spirals are each other’s evolutes and that both of them approach asymptotically logarithmic spirals of a definite position, with which they have a fourfold contact at infinity (the rectifying curves being the asymptotes of the hyperbola). J. VAN DE GRIEND Jr Proceedings Royal Ac: | J. VAN DE GRIEND Jr. „Rectifying curves.” en: aga y Fig. 3 2 to) ne N Proceedings Royal Acad. Amsterdam. Vol. VL 18. Parabola on the avis as rectifying curve. For the parabola (fig. 9) the centre O is at infinity; the considerations about the point fF based on this centre do not hold good here. If we determine the radius of curvature of the evolute as a special case of a polar trajectory of a threepoint logarithmic spiral (8) by drawing QV L tangent PV, it is evident according to the properties of the parabola that this radius of curvature remains constant, equal to p, parameter of the parabola, because P/ represents the length of the subnormal. So the evolute is a circle and the rectified curve (/) an evolvent of the circle. Point Zè (point of contact of QV) coincides here with /, because I is a fixed point of WV. So it is situated here too on the right line (PD) connecting / with the centre of the parabola. 14. Tautochronism. The condition that a motion along a given curve be tautochronous is: the tangential component of the force must be proportional to the length of the are between the moving point to a point of the curve; in that case the motion takes place as a single oscillatory motion. For the curves whose rectifying curves are central conics (10, 12) where the force is supposed to act from the fixed point Zi, LL (fig. 7, 8) is proportional to QO as b? to c° (10). In order that the motion along those curves be tautochronous with O as centre, the tangential component of the force must be proportional to RL, so the force itself (directed along LQ) proportional to RQ, that is to the distance. So for a force acting from the centre R in pro- portion to the distance both curves are tautochronous. But the centre of tautochronism © is to be reached along the curve only in the cases of circle, ellipse or hyperbola (v-axis imaginary) as rectifying curves, so only cycloid, epi- and hypocycloid and the spiral of the second kind (rectifying curve a hyperbola on the imaginary axis) are in reality tautochrone; for the spiral of the first kind the centre of tautochronism does not lie on the curve, for the evolvent of the circle it lies at infinite distance. For the epicycloid the force must repel; for the hypocycloid and the spiral of the second kind it must attract. For the cycloid point £ lies at infinite distance; the force becomes constant and is directed according to the tangent in a cusp. ( 218 ) Physiology. — “On the development of the myocard in Teleosts.” By Dr. J. Boerke. (Communicated by Prof. T. Pracu.) During the last few years much attention has been given to the structure of the heart muscle, and several investigators have stated the opinion, that the heart muscle of the vertebrate heart is not composed of definite cells, separated by clearly defined limits, but that the heart muscle forms a syncytium, in which no cell bound- aries can be recognised. For the embryonic heart this is shown most completely by GopuewskKr, independently from GopLewsKi, but less fully by Hoyer and Hemennary, confirmed and worked out by Marceau. For the adult heart (homo, mammalia) it has been M. Hrmennatin’), who has done most in this direction, and who has most strongly urged the conception of the heart muscle as asyneytium. According to him the septa, the “Treppen”’, the delicate lines standing at right angles to the course of the myofibrillae, which are regarded by other investigators as cell-limits, have nothing to do with real intercellular structures (except perhaps from a phylogenetic point of view); they are “Schaltstücke”, portions of the musclefibre which remained as it were in an indifferent state, and play a part in the process of longi- tudinal growth of the fibres. For the still growing heart Hrermrnnain draws the following conclusion: “dass die Schaltstücke ihrem ursprüng- lichen Verhalten nach wachsende Teile sind, Teile, welche das Längenwachstum besorgen und nach beiden Segmentenden hin das Material für die Angliederung neuer Muskelfacher liefern” (I. c. 1901 Pag. 69). Hocur *) on the other hand takes these “Schaltstücke”, for real cellular limits, though incomplete. He maintains that the Schaltstiicke, the cement substance between the cells of the heart muscle, which according to EBERrTH*®) are homogeneous and after Browicz*) are in some cases homogeneous, in other cases composed of small rods arranged parallel to each other, separate the cells of the myocard, but only in the course of the myofibrillae. Between these ‘“batonnets” “le sarcoplasme qui remplit les interstices des fibrilles se continue sans interruption apparente d'une cellule dans l'autre.” ‘The small rods are lying just between the ends of the myofibrillae of the 1) Anat. Anzeiger Bd. XVI 1899. Anat. Anzeiger Bd. XX 1901. ?) Bibliogr. Anatomique 1897. 3) Arch. für path. Anat. und Physiologie, Bd. 37. 4) Virchow’s Archiv. Bd. 139, 2 adhd Ei i a la di N ZE DVI TRS NN EET CHG adjoining cells, which they bring in connection with each other. “Cette zone des batonnets constituerait done....une réelle limite intercellulaire, mais une limite incomplete.” Von Epner') regards the cementlines, the “Schaltstiicke’, as broken- off perimysiummembranes, “abgerissene Perimysiumhäutchen’”. SZYMONOWICZ reproduces in his textbook of histology, which appeared two years ago, a drawing of a section through the heart muscle of a hydropie cor, in which the myofibrillae of one cell are seen clearly to be in connection each with a fibrilla of the adjoining cell. For the embryonic heart the disappearance of the cell boundaries has been described by several authors in different animals. HEIDENHAIN *) reproduces a section through the heart of a duck embryo three days old, in which no traces of cellular limits are to be seen and the myofibrillae may be followed with great distinctness without interruption over a great area and the same fibrilla passing different nuclei. According to Hoyer *) in the cells of Purkinje the fibrillae (found only in the peripheral region of the cell body) may be followed without break through many cells. In young larvae of Triton Horer found a complete absence of cell boundaries. According to this author the heart muscle is originally composed of isolated cells, but these cells fuse during the later stages of development, and the result is a syneytium. That this is really the case is shown by Gopruwskr. A preliminary communication *) appeared simultaneously with the paper by Hoyer. In the elaborate study *) which appeared somewhat later, this process of fusion of the cells of the heart muscle in young rabbit and cavia embryos is described very fully. Here the cells of the myocard form at first a network composed of loosely arranged cells. By division and growth these cells get nearer to each other, and the intercellular protoplasmic bridges thicken, the intercellular spaces narrow; “dadurch verschmelzen die Zellen allmählig in eine einheit- liche Masse, in welcher die Kerne zerstreut gelegen sind... Schliess- lich stellt die Anlage des Herzmuskels eine vollkommen einheitliche Protoplasmamasse dar.” In the protoplasm of this syneytium there appear small granules, staining deeply with iron-haematoxylin ; during the next stages of development these granules arrange themselves in 1) Sitzungsber. Wiener Akademie. Math. naturw. Classe. Bd. 109 1900. Abth. II. 2) l.c. 1899 en 1901. 3) Bull. internat. de I’Acad. des Sciences de Cracovie 1899 Nov., 190L Mars. 4) Bull. internat. de l’Ac. des Se. de Cracovie Mars 1901. 5) Arch. f. mikrosk. Anat. Bd. 60, 1902. Proceedings Royal Acad. Amsterdam. Vol. VI. ( 220 ) rows (the same process was described by GoprewsKt for the striped muscle fibres of the body muscles) and in this manner the delicate primitive histological myofibrillae are formed. In these originally homogeneous fibrillae during the course of development two elements appear, staining differently with iron-haematoxylin and eosin, the first sign of cross-striation, of the anisotropous and isotropous dises. The later stages of development and the appearance of the “Schalt- stiicke’” were not studied by GODLEWSKI. An essentially similar view has since been advocated by Marcrat *) (1902). In a series of brief papers this author described the continuity of the heart muscle fibres in mammals, birds and lower vertebrates, and accepted in the main HeIDENHAIN's suggestion of the function of the “Schaltstiicke” in the adult and the still growing heart. In teleosts — I refer especially to the eggs of the Muraenoïdae, which provided me chiefly with the materials for the study of the processes I am about to describe here — the heart muscle cells are derived from the cells of the median portion of the walls of the pericardial cavity, which, as is the case in all anamnia, grow from either side underneath the entodermal tube and fuse with each other in the median line, so that a tube is formed between them, which opens at one end into the yolk-sac, at the other end into the arterial vessels, formed at the same time (ostium venosum and ostium arteriosum). Inside of this tube the endothelium of the heart is formed out of cells of the “masses intermediaires” of the mesoderm of the head and partly out of cells which migrate from the region of the tail-knob towards the heart, and lay themselves against the myocard there where the heart tube opens into the volk-sac. In fig. 1 is reproduced a longitudinal section through the region of the heart of an embryo of Muraena N°. 1 with 38 pairs of muscle segments, which illustrates these features clearly. On the left side of the drawing the rostral end of the chorda is seen, and beneath the chorda the entoderm, which shows the widening of the oesophagus corresponding with the preopercular apertures, the primary — gill-clefts. Between the entoderm and the periblast the heart is seen, and at the venous end of the heart tube lies a cluster of loose separate cells, which by their peculiar form and by the protoplasmic processes with which they (the greater part in the following sections), unite with the endothelium of the heart, appear as cells which aid to build up the endocard. The history of the genesis of the endocard however we will drop for the present, the repro- 1) G. R. de la Soc. de Biologie, T. 54, pag. 714—716, 981—984, 1485—1487; 1902. eye duced drawing serving only to show the topographic relations. It is only the myocard that interests us here. The cells of those parts of the walls of the pericardial cavity that form the myocard, are di- stinctly separated at this stage of development, are of a cubical or cylindrical shape and very regular, as is shown in the figure. They possess a rather large round nucleus and have a granular looking protoplasm which shows no definite structure organisation. At both ends of the heart tube they gradually diminish in height until the flat shape of the cells of the other parts of the pericardial plates is reached. The cell boundaries between the heart muscle cells are every where sharply defined; in preparations stained with iron-haematoxylin, at both sides of the heart tube (that turned towards the endocard and that turned towards the pericardial cavity) a delicate black line, following the cellular limits, is to be seen — the “Schlussleiste”. The first signs of differentiation, which showed themselves in the heart muscle cells, tend already to give rise to a fibrillar structure. A granular stage, as described by GopLuwskt, during which the proto- plasm of the cells is full of deeply staining granules, which arrange themselves in rows and fuse to give rise to the myofibrillae, I have not been able to find. On the stage of the granular looking mesh- work with small meshes, the usual appearance of protoplasm, there followed in my preparations immediately a stage, in which at the basal end of the cell (viz. that turned towards the endocard), extremely delicate fibriliae are to be made out, which in most cases run at right angles to the longitudinal axis of the heart tube. These fibrillae, as far as could be made out, are homogeneous from the beginning, and do not give the impression of being composed of or derived from granules arranged in rows. However, this need not lead us to doubt the formation of the fibrillae in this way even here; the beautiful figures and clear descriptions of GoODLEWSKI are too convincing on this point. Perhaps this stage lasts only a short time and is not represented in my preparations which are stained with iron-haematoxylin. Be this as it may, we only find the extre- mely delicate fibrillae *), which thicken and become more distinct during the following stage. To this stage belong the sections drawn in fig. 2 and fig. 3 (longitudinal sections) and fig. 4 (cross section through the heart tube). In order to understand these drawings rightly, the following may be of use. The heart is during this stage still lying as a straight 1) A regular network consisting of large protoplasmic dises as described by Mc Cattum, | have never been able to find. 15% (240) cylindrical tube in the direction of the embryonic axis, but always the heart tube deviates in its course somewhat to the right (or to the left). In longitudinal sections through the embryo the heart therefore . is cut obliquely, and in the same section of 4+ or 5 u we are able to study the external half of the heart muscle cells (that is to say the side of the cells turned towards the pericardial cavity) at the venous end of the tube, the basal half of the adjoining cells, and then the endocardium and the median cross section of the heart muscle cells at both sides of the heart. In fig. 3 are shown the two parts of the heart muscle cells as seen in one and the same section. The two parts of the figure are in the section continuous, but are lying in different optical planes. It was not possible however to reproduce the two parts in the same drawing, because in the section (thickness 4 u) different optical planes presented a different aspect of the same point. So I separated the two halves by a line, to indicate the point, where the drawing is made after a different optical section. On the right side the cells of the myocard are seen from the side turned towards the pericardial cavity. They appear to be separated by distinct boundaries, are very regular, and show between the cells the black lines and meshes of the “Schlussleiste”. On the left side of the figure the basal side of the heart muscle cells is to be seen. Beeause of the curved surface of the heart tube, at both sides the cells are seen in cross section, in the median part of the figure the basal part of the cells comes into view. In this part of the heart muscle cells the cell membranes have completely disappeared. There is only a mass of protoplasm to be seen, which has taken a faint stain with eosin; imbedded in it lie thin fibrillae stained black with iron-haematoxylin; these fibrillae run for the greater part at right angles to the heart axis round the heart-tube; some of them run more or less obliquely (fig. 3). The same fibrilla may be followed through more than one cell. At both sides the fibrillae curve round and run at right angles to the surface of the section. They present there a small point of a darker colour. The fibrillae are entirely homogeneous. That these fibrillae are lying in reality only at the basal end of the cell is shown in fig. 2, in which a part of the myocardium is drawn as it appears in a median longitudinal section through the heart tube; as the fibrillae are running here at right angles to the optical plane, they appear as dots and where their course is more or less oblique, as short lines. In the corners of the cells we see (at the side of the cells turned towards the pericardial cavity) the black ere f “te a ie dots of the “Schlussleisten”. The cell boundaries cannot be followed now from one side of the wall to the other; at the basal side of the cells, there where the fibrillae are formed, the cell membranes have disappeared and the protoplasm of the cells is continuous. It seemed to me that the disappearance of the cell limits preceded the differen- tiation of the myofibrillae, on the other hand the question arises, whether the differentiation of the fibrillae does not give the impulse for the disappearance of the cell membranes. For in studying these cells closer, we sometimes find in cells, where only at the basal side of the cell the cellular membranes have disappeared, fibrillae lying there where the cells are still distinctly separated. These fibrillae do not pass from one cell to another, but end close to the cell-membrane with a small thickened point (fig. 3), and sometimes in two adjoining cells a pair of such fibrillae are seen just opposite to each other. In following stages of development in this part of the cells a greater number of fibrillae is to be found; these fibrillae then are seen to pass through different cells and the membranes of the cells have disappeared here too. These facts remind us of the appearance of the fibrillae on the boundaries of the myotomes (in longitudinal sections), and this being the beginning of the fusion of the fibrillae of the adjoining myotomes, the question arises, whether a similar process is going on in the heart muscle cells. Be this as it may, the fact remains, that only at that side of the cell in which the myofibrillae are formed, the membranes disappear and the protoplasma fuses. We may call attention here to the fact, that the black meshes and lines of the “Schlussleiste’” have disappeared at the basal side of the cells, there where the cell limits ceased to exist; at the other side of the cells, there where the cells are still sharply separated, they remain as clear and distinct as before. In fig. 4 one half of a cross section through the heart tube is drawn, to demonstrate once more the course of the fibrillae and the structure of the myocard cells. In the figure we see the endocardium (end.) composed of flattened cells, and around it the myocard *). The fibrillae are here cut length- wise, and may be followed without break through different cells. The cellular limits, seen in the outer half of the cell-body and absent in the inner half, we need not describe at length any more. In preparations in which the centrosomes are stained in the other embryonic cells, in some cells of the myocard too they were visible 1) A pericardial membrane as a covering of the myocard, as it shows itself in salmons during the later stages of development, is not yet developed here. The heart lies entirely free inside the pericardial cavity. as minute black granules (diplosomes) in the centre of an ovalshaped “heller Hof”. They were lying on the side of the nucleus in a rather indifferent position now on this side of the cell, than on that. In the course of development the cells of the myoeardium flatten more and more. The cell membranes disappear from between the cell bodies throughout the entire thickness of the myocard. In this stage the fibrillae are not so exclusively confined to the basal side of the cells, but are found more or less scattered throughout the cells. The greater part of the fibrillae, however, is still visible in the basal half of the heart muscle syncytium. In fig. 5 a surface view (of the atrium) of such a myocard is drawn. Beneath the fibrillae we see three nuclei, no trace whatever of cell boundaries is visible. The course of the fibrillae is not so regular as it was before. They seem to be running now in different directions, although there is still one predominant course. This fact is due to the rate of growth of the heart tube being not the same in different directions. The heart has no more the shape of a simple cylindrical tube, but is differentiated already in sinus venosus, atrium and ventricle. With the growth of the different parts of the heart tube the displacing of the bundles of fibrillae goes hand in hand. As shown in the figure, the myofibrillae of the heart now present a beautiful cross striation. But it must be noticed that the commen- cement of the functions of the heart muscle, of rhythmical peristaltic contractions coincides with the differentiation of the homogeneous fibrillae mentioned above. The differentiation of the fibrillae in isotropous and anisotropous dises takes place after the heart having contracted quite regularly for a long time already, and has nothing to do with the contractility of the fibrillae. In this stage of development (the last stage which can be studied here, the muraenoid larvae invariably dying after having reached the eritical period) the wall of the heart is still a simple membrane, The bundles of muscle fibres so characteristic for the adult vertebrate heart are not yet developed. For this reason I have reproduced in fig. 6 a part of a longitudinal section of the myoeard of a larva of Salmo fario of 22 m.M., where the sponge-like structure of the myocard was established already. The myofibrillae, for the greater part arranged in bundles, may be followed over a great area past different nuclei of the myocard-syncytium. There is no trace of cellular limits, nor of “Schaltstücke” te be found. So we must draw the conclusion, that in the case of teleosts too the myocard forms a syneytium, as maintained by GODLEWSKL, of the myocard in Teleosts.” “On the development J. BOEKE. a tee, han FI tae Proceedings Royal Acad. Amsterdam. Vol VI. Heenan, Hoyer and Marceau ; that the myocard originally is formed of distinct cells, but that during the differentiation of the myofibrillae the cell limits of the myocard cells get lost, the cell bodies fuse and in this manner a syneytium is formed; that this disappearance of the cell membranes can be stated at first only there where the myofibrillae are formed, and that chronologically the formation of the fibrillae and the disappearance of the membranes coincide. Where now the formation of this syneytium by a fusion of originally separated cells can be demonstrated in lower vertebrates and in the higher vertebrates, and the continuity of the fibrillae over a great area can be stated, there the hypothesis of HeEIDENHAIN, that in the adult mammalian heart the ““Schaltstücke” (cement lines) of the myocard which are not to be found in lower vertebrates and which appear in mammals in a relatively late stage of development, have nothing to do with cell limits, seems to have some truth in it. That this is of great importance for the physiology of the heart muscle, for the problem of the conduction of the impulse by the heart muscle fibres, I need only mention here. As to the functions of the ‘“Schaltstiicke” we are, I think, still entirely in the dark, but for the hypothesis of Hemennain. This must be tested by further study. The study of the later stages of development of the mammalian heart with the use of the modern histological methods will throw more light upon this, as was pointed out already by Gopnewskr. Perhaps the study of the structure of the museular bridges, connecting the different parts of the mammalian myocard, too will throw some light upon this question. DESCRIPTION OF THE FIGURES ON THE PLATE. Fig. 1. Longitudinal section through the heart of an embryo of Mur. N°. 1 with 38 pairs of muscle segments. ph = pericardial cavity, m = myocard, e = endo- card, per = periblast, ent = entoderm, ch = chorda, oes = oesophagus. Enl. = 240. Fig. 2. Two cells of the myocard of an embryo of the same species of Mur. N°. 1 with 44 muscle segments. Longitudinal section, sublim.-formol, iron-haema- toxylin and eosin. Enlarg. = 800. Fig. 3. The same, cut tangentially. Enlarg = 800. Fig. 4. Cross section through the heart of a slightly older embryo. Fig. 5. Surface section of the wall of the atrium of a larva of Mur. N° 1, five days old. Fig. 6. Section through the wall of the ventricle of a larva of salmo fario of 22 mM. Enlarg. = 800. ( 226 ) Mathematics. Extract of a letter of Mr. V. Wior, to the Academy. In his splendid work entitled: “Théorie, propriétés, formules de transformation et méthodes d’évaluation des intégrales définies” Mr. Brerens pe Haan takes as basis to determine the general formulae (143, 144, 145, 146) of page 134 a definite discontinuous integral the value of which has been established farther on in the work (Partie TH, Méthode 9, N°. 16) at page 333 as rt , Sr D for pe) cos (qu ern for Pl et put vien (1) 0 0 forp ? so that in the continuation of his deduction we find that the term @ / Kd Ae Jt J sin re cos ge = ei et corresponding to g—=7 amounts to double the value of the real value and that the general formulae of page 154 are to be rectified in this way as well as the applications. Particularly on page 639 formula 1900 we find oo a 797 A ¢ ynai—l sin & COS Cat NK @ xp é: de = — > pr» = - D 1—2 pceosa+p? @ 2p « 2 lp 0 whilst the exact value of this integral. is x | pe! It l+p ; + pt A pl 4+ pir? ke | ET ik 9 2 And really writing after multiplication by p: an p sin @ COS AX / Wa ltp ; Ca SS == P 4 zis 1—2pcse+tp*? « A 1—p 0 it is sufficient to develop the first factor of the function of which the integral is to be found p sin © on — == = pk sin ka 1-2peset p* k= to refind by means of the integral (1) the development of the Sea term of the equation: CIN > epen zl. pe eS pe il SS l—p 212 i + perl + pet? +... | ’ It was in looking for a way to place in a form of a definite integral the general term of the series of Lambert modified by CLAUSEN: lar , A (sin a cos (n+1) @ de Lan a J 1—2u" cos aan a 0 that I found this error. It is easily seen that the rectification has to be extended to the whole N°. 12 of the method 41 of which the above mentioned integral forms a part and to any other application of the general formulae of page 134. This paper was given to Dr. J.C. Kruyver, who made the follow- ing communication about it: The remarks of Mr. Wirror are on the whole correct. In the “Exposé de la Théorie etc.” of Brerens pr Haan we really find on page 639 wo sin © COS Ak fa d pel am oe 1—2p cos «+p? x 2 l—p 0 and this is incorrect whether « is an entire number or not. Mr. WILLIoT now gives as an answer 4 1-+-p p nd | + and that will do for @ as an entire number. In the meanwhile he might have observed that this result neither holds good for « (not an entire number) and that we find for any fp" possible positive a: 9 [a] Jp latò] wee : EE En 1 a ps4] -f. pla] EO pea aa” (Here [a] means the greatest entire number smaller than «). (October 27, 1903). KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday October 31, 1903. INE (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 31 October 1903, DI. XII). GO RE B MES J. D. var per Waars: “The equilibrium between a solid body and a fluid phase, especially in the neighbourhood of the critical state”, p. 230. J. J. van Laar: “The possible forms of the meltingpoint-curve for binary mixtures of isomorphous substances.” (2nd Communication). (Communicated by Prof. H. W. Bakuuis Roozenoom), p- 244. (With one plate). H. W. Bakuuvis RoozrBoom: “The phenomena of solidification and transformation in the systems NH4NO3, AgNO; and KNO3, AgNO;”, p. 259. A. F. HorreMaN and J. Porrer van Loon: “The transformation of benzidine.” p. 262. H. Raxen: “The transformation of diphenylnitrosamine into p-nitrosodiphenylamine and its velocity.” (Communicated by Prof. C. A. Losry pr Bruyn), p. 267. W. H. Juus: “The periodicity of solar phenemena and the corresponding periodicity in the variations of meteorological and earthmagnetic elements, explained by the dispersion of light”, p. 270. Hars Srranr: “The process of involution of the mucous membrane of the uterus of Tarsius spectrum after parturition.” (Communicated by Prof. A. A. W. Husrecur), p. 302. J. C. Kruyver: “Series derived from the series ue Hq jo a G. Gruxs: “The Ascusform of Aspergillus fumigatus Fresenius.” (Communicated by Prof. FE. A. F. C. Wert), p. 312. W. van BEMMELEN: “The daily field of magnetic disturbance.” (Communicated by Dr. J. P. VAN DER STOK), p. 313. J. IL. Bonnema: “A piece of Lime-stone of the Ceratopyge-zone from the Dutch Diluvium.” (Communicated by Prof. K. Marry), p. 319. S. Hoocewrerrr and W. A. van Dore: “On the compounds of unsaturated ketones and acids”, p. 325. Tu. H. Benrens: “The conduct of vegetal and animal fibers towards coal-tar-colours”, p. 325. The following papers were read: DoD 16 Proceedings Royal Acad, Amsterdam. Vol, VI, ( 230 ) Physics. — “The equilibrium between a solid body and a fluid phase, especially in the neighbourhood of the critical state.” By Prof. J. D. -vaAN DER WAALS. After the publication of the experiments of Dr. A. Sirs in the proceedings of the September meeting, communicated by Prof. BaKnuis RoozrBoom, I had a discussion with the latter chiefly on the question if and in what way the liquid equilibriums and the gas equilibriums which may exist by the side of a solid phase, must be thought to be connected by a theoretic curve at given temperature, in conse- quence of the continuity between liquid and gas. It is in agreement with the wish of Prof. BaKnvis RoozeBoom, that I communicate the following observations. Let us imagine the w-surface of a binary mixture, anthraquinone and ether, in which we will call ether the second substance, at a temperature slightly above 7% for ether. Then there is a liquid- vapour plait, closed on the side for ether. Let us add the y-curve or the w-surface for the solid state, the w-curve when the solid state has an invariable concentration. If only pure anthraquinone should be possible in the solid state, this y-curve would lie in the surface for which «=O. For the sake of perspicuity we shall start from this hypothesis in our first deserip- tion. Then we find the phases which coexist with the solid anthra- quinone, by rolling a plane over the y-surface and the conjugate w-curve. On account of the slight compressibility of the solid body, we can describe a cone, unless the pressure be excessively high. This surface enables us to find the coexisting phases; its vertex lies viz. in the point «=O, r=v, and wt, if v‚ represents the molecular volume of the solid anthrayquinone and y, the value of the free energy, both at the temperature considered. The curve of contact of this cone and the y-surface represents then the coexisting phases. For shortness’ sake we will use for it the name of contact-curve, though it is properly speaking also a connodal curve on the w-surface of the binary mixture having its second or conjugate branch on the w-surface of the solid state. Now we can have three cases for the course of this contact-curve. dst. It may remain wholly outside the liquid-vapour-plait, and will form then a perfectly continuous curve. 2"¢. It may pass through that plait, in which case one part of this curve will represent gas phases and another liquid phases, which two parts will be connected by a third part lying between the two branches of the connodal ( 231 ) curve and representing metastable and unstable phases. 3". It may touch as intermediate case the connodal curve of the transverse plait in a point which will be the plaitpoimt, as will appear presently. As to the course of the liquid part of the contact-curve we may at once conclude, though this will be shown afterwards in a more striking way, that two cases may occur. From the point on the connodal curve where it enters the liquid part of the y-surface with increasing pressure, the curve will namely move more and more towards decreasing values of «, and finally terminate at «=O — or it can move towards increasing values of w. If we trace the y-curve for «=O, and add a portion of the q = fig. 1 (a) y-curve for the solid body to the figure, then if this portion has position (a), so if the volume of the solid body is smaller than that of the liquid, only one bi-tangent can be drawn, and this will represent a coexisting gas phase. If on the other hand the added portion of the y-curve for the solid phase has position (4), (6) fig. 1 (b) so if the volume of the solid phase is larger than that of the liquid, two bi-tangents may be drawn. At low pressure, a coexisting gas phase will exist, and at high pressure a coexisting liquid. In the latter case the liquid part of the contact-curve will move towards points for which « decreases when the pressure increases. ta ( 232 ) For a econtact-curve which passes through the plait of the y-sur- face, the property holds of course good that the pressure is the same for the two points, in which it meets the connodal curve of the transverse plait. If namely a bi-tangent plane is made to roll simultaneously over the y-curve (or the surface) of the solid substance, and over the gas part of the y-surface of the binary mixture, then if this tangent plane meets a point of the binodal curve of the transverse plait, this tangent plane will also touch the w-surface in a point of the other branch of the binodal curve, and this point will represent a liquid phase. Three phases are then in equilibrium. The pressure that then prevails, is therefore the three-phase-pressure at given temperature. If the temperature should be such that the contact-curve no longer passes through the plait, then no three- phase pressure exists any longer for that value of 7. For the intermediate case the solid body is in equilibrium with two phases, which have become equal and the two points of the connodal curve which the contact-curve has in common with it, have coincided in the plaitpoint. Particulars as to the course of the contact curve are found from the differential equation of p, when « and 7’ varies. If we represent the concentration and the molecular volume of the solid body by av, and rv, and that of the coexisting phase, whether it be a gas phase or a liquid phase, by ‚and vy, this equation may be brought under the following form, which is perfectly analogous to that which holds for the coexisting phases of a binary mixture : | ns Wate Uxf dp = (sf) bs def + —~ dl Coley ps For the signification of vr. and IV, 1 refer to Cont. II, p. 107 ete. If 7 is kept constant, we have for the course of p the differential equation : As long as the contact-curve does not pass through the plait, d°8 dau* is always positive. If in the solid state only the pure first substance (in the case under consideration anthraquinone) should occur, then, = 0. But the same differential equation holds also, if «2, shouid be variable. For the case of anthraquinone and ether the value of « in the gas phase is higher than that of the liquid phase for coexisting liquid and gas phases, or ez, > ,. It is therefore to be expected, ( 233 ) that the value of w, in the solid state will a fortiori be smaller than that of the phase coexisting with it, whether the latter is a gas or a liquid phase. We do not wish to state positively that there are no exceptions to this rule. But for the case ether and anthraquinone we may safely assume that #,— wf is negative. Now it remains only to know the sign of vy, to be able to derive the sign of a av f The expression v,¢ stands in the place of wv) (tf) i ‘ . . day PT and represents the deerease of volume per molecular quantity when an infinitely small quantity of the solid phase passes into the coexist- ing phase at constant pressure and constant temperature. If this coexisting phase should be a vapour phase, this decrease of volume is undoubtedly negative. But this quantity may also be positive, and if we make the series of pressures include all kinds of values, so if we make the pressure ascend from very low values up to very high ones, there is undoubtedly at least once reversal of sign, and for the case that the contact-curve under high pressure moves towards increasing values of w there is even twice reversal of sign. To demonstrate this, we inquire first into the geometrical meaning of vs. Let the point P be the representation of the solid phase, with », and wv, as coordinates —- and the point Q the representation of the coexisting fluid phase with vy and wy as coordinates. Let us draw through Q@ the isobar and let us determine the point P’, in which the tangent to this isobar of Q cuts the line which has been drawn through P parallel to the volume-axis, then —vy~=PP’. If the point /” lies on the positive side of P, then vy is negative. For the special case that the tangent to the isobar of Q passes through P, vs = O. In the same way v.¢ would be positive, if P’ should le on the negative side of P. In order to know the sign of vy, the course of the curves of equal pressure must therefore be known. In my ‘Ternary systems’ I (These proceedings Febr. 22:d 1902, p. 453) I have represented for the analogous case of a binary system, for which the second component has the lowest 7%, the course of the isobars by the line BED EB’ in Fig. 2. 1 have added another isobar to the repro- duction of this figure — and I have represented the solid phase by the point P,. The added isobar passes through the plaitpoint. This isobar has an inflection point somewhat to the right of the plaitpoint. Bach of these lines of equal pressure having an inflection point, there is a locus for these points, which I have left out in the (234 ) fig. 2 — figure. It extends all over the width of the figure. Always when Z, lies on the side of the small volumes of an isobar, two tangents may be drawn to such a line from ZP. These tangents touch the isobar at points, lying on either side of the inflection point; and for these points of contact y= 0. Another isobar will furnish two other points of contact, if we leave the point P, unchanged. We have therefore for every point P, a locus, consisting of two branches, for which cv. =O. If the point Ps lay at greater volume, 1. e, on (- 235 ) the other side of the isobars, it would no longer be possible to draw two tangents, and the locus for which, with regard to s, the value of r‚p is O, would have but one branch. Now, however, the point P, is variable, first because the volume of the solid body depends on the pressure, and secondly when the concentration should change. This enhances of course the difficulty, if we wished to determine this locus. But this will not detract from the thesis that for the contact-curve, when it ascends from low pressure to high pressure, twice vj is 0, when the solid body has a smaller volume than it would have in fluid form at the same temperature and under the same pressure — and that only once vsp is O in the opposite case. When Z, is variable, the locus for which vs¢ = 0, is construed by drawing from every special position of P; the tangents to the isobar of the pressure of 7s, and by joining the points of contact obtained in this way. If the contact-curve does not pass through the plait, the value of ver iS negative for the points outside the two branches of the locus ry — 0, and positive for the points inside. If however the contact-curve passes through the plait, the value of vsp is more complicated. In the figure the two tangents have been drawn to the isobar BEDD'L’L’, P, being supposed to be in the position that corresponds to the pressure of this line. In this case too the value of vsy is negative for the points lying outside the two points of contact. For the points between the points of contact we cannot assume v,¢ to be positive, however. This holds only till the points D and D’ are reached. Between D and D’, vy is again negative, and the transition from positive to negative takes place in the points D and D’ through infinitely great. sy dar” In the same way the value or ( ) is complicated for the pa points of a contact-curve, passing through the plait. [have stated this already in ‘Ternary systems” I, Proceedings February 22nd 1902 footnote p. 456. For the points between the connodal and the spinodal curve this quantity is still positive; for the points between the Op spinodal and the curve for which — is 0, it is negative ; whereas Ov? for the points inside this last curve it is again positive. This last transition from negative to positive takes place through infini- tely great. : NE. ate dps: Let us write the equation for the determination of — in the fol- ef lowing form: p/ dy dp dw og sf nn (v,— v,) NE pe Uf dry Ore day? or dy dp dw dw / a2 = = = Usf nn, (asf) pe ES é fama (da, * def” wpdvy) | In this way we simplify the discussion. The factor of «,— x, never becomes infinitely great in this case. This factor is then positive outside the spinodal curve and negative inside it. On the spinodal curve itself it is zero. As «,— ry is always negative in the case of anthraquinone and ether, the second member of the last equation is negative outside the spinodal curve and positive inside it. From this last equation follows: 1st that if we follow the contact-curve throughout its course, there exists a maximum and a minimum value for the pressure for the points Iving inside the plait, that is when the spinodal dp curve is passed. 2°¢ that when r‚/ = 0, the value of — is either ( ar = = . e = dp twice or only once infinitely great. In the points where |; dvp* dp ‚(òp B — has the value of ( , as follows from the equation given if day Ot)» F O° ur ; we put there SPN —0, but which also follows directly from : Ory” 7 ] Op ] Op ] AP =— WERT => ass t Ory Ovy Ley OP pate. =S: Ove For contact-curves which pass through the plait not far from the plaitpoint, it appears clearly from the figure, that the points for : 2) ern Rie ae? : : . ‚dp which —— is infinitely great, lie outside those for which de: ak def That is to say, that the locus for which v.¢ = 0, lies outside the spinodal curve. In the neighbourhood of the top of the plait they lie even outside the connodal curve. Also for the isobar LE DD! LE’ B’ I have drawn them in the figure given in such a way that the = 0) points of contact of tangents from Z, lie outside the spinodal curve. I have not yet been able to decide whether there are any exceptions. In the following figure (8) I have represented the relation between p and wy for a contact-curve, assuming that the points of contact lie as I have drawn them in fig. 2, and as they are sure to lie, when we are in the neighbourhood of the plaitpoint. The gas phases which are in equilibrium with the solid body lie below £. The liquid equilibriums lie above C. The position of the line BC indicates the three-phase-pressure. The curve LCP denotes the liquid-vapour equilibriums, of which the part lying below CL may only be realized by retardation of the appearance of the solid state. Let us now examine what happens at higher temperature as well to the curve of the liquid-vapour equilibriums as to that of the equilibriums between the solid state and the fluid state. From the theory of the binary mixtures (Cont. IL, p. 107 ete.) we know, that the first mentioned curve LCPBE contracts and moves upwards. If we assume (7 to be infinitely small, all the points of this curve will be subjected to an infinitely small displacement, with the exception of one point, i.e. that for which JV,, = 0. This point can lie on the right or on the left of the plaitpoint 7, according as the plait- point curve descends or ascends. Also the curve of the solid and fluid equilibriums is transformed and displaced. The modification which this curve undergoes with increase of temperature has been denoted by the dotted curve in fig. 4 and fig. 5. We shall presently explain this further. Now two cases may take place, which both occur for mixtures of anthraquinone and ether. Either the three- phase-pressure rises with 7, or it fails. But in both cases such a temperature may occur that the straight line, which joins the two fluid phases coexisting with the solid body, has contracted to a point. To the former of these two cases applies fig. 4. In this case the curve APB moves towards smaller values of . with increasing tem- perature. Not indefinitely, however. Near the highest value of 7’, ( 238 ) Fig. 4 the branches AA’ and BR’ have value for the value of wy. met, and so there is a minimum To the second case applies fig. 5. Then the curve AB will move to the right with decreasing temperature. With decreasing value of laa : n . T the branches A’A and BR’ will approach each other; and this Pp T+aT: 7 ep" ( 239 ) leads to the conclusion that there will be a maximum value of rg. In fig. 6 the value of « for the two fluid phases of the three-phase- pressure as function of 7’ is graphically represented. The highest temperature (the triple point of anthraquinone) applies to.« == 0. The lowest point of the part of the «, 7’ figure lying on the left is one plaitpoint and the highest point of the part of the «, 7’ figure lying on the right is the second plaitpoint. If we represented the relation between p and. for the fluid phases of the three-phase-equilibrium, we should also get two separate parts. It is easy to see that for smaller values of « an ascending closed branch is obtained, not unlike the closed p,v curve for a binary mixture at constant temperature and that for higher values of a similar but descending curve is found. The p,7 projection for the three-pbase-pressure, so of the curve according to which the two p,.w, 7’ surfaces intersect, consists of two separate curves, that for the higher temperatures being a JS . ® . ‘yy . . . 2 descending curve, terminating in the p and 7’ of the triple point of anthraquinone. The part for the lower temperatures is an ascending curve, beginning in the triple point of ether, if namely, we assume ( 240°) perfect mixture also for the solid state. The two p,.« 7’ surfaces meant in the preceding statement, are that for the coexistence of the two fluid phases with each other and that for the solid state and the fluid phases. I shall proceed to give a few mathematical observations, which may serve to gain a better understanding of the whole phenomenon, and which are also required for the proof of some properties, which have been given above. First the assumed deformation in the shape of the p, # curve (solid and fluid phase) for inerease of temperature. From the equation: a Lee Vr dp = (as—ay) dep + —~ dl a A def pT 7 follows that for constant zy the equation holds: ow er En „(ep Wy ove …* dT Er en) dy V ; ò ve 4 Wp being negative, the numerator of this expression is negative oe Ob Rf: outside the curve for which an and positive inside this curve. ” The numerator is the same quantity as has been discussed before (p. 235). From this follows that for constant a, the curve p,7’ has a tangent normal to the Z-axis in two points, and between them two points, in which a maximum and a minimum value of p occurs — just as was the case with the p,. curve at constant temperature. One curve might be substituted for the other, but still, there is a difference. The p,.« curve has its maximum and minimum coinciding in the plaitpoint. The p, 7’ curve has it, when it runs through the Oy point for which DE has two coinciding values equal to zero; so in the point which would be the critical point, when the binary mixture behaved as a simple substance. *) The consequence of this is, that if we trace the two p, 7’ curves, (that for liquid and vapour and that for solid and fluid), these two curves intersect in the plaitpoint for the value of « of a plaitpoint, and that they do not touch as is the case with the p,v curves. Only for another value of z (the maximum 1) It has appeared to me that the course of the p,7’ curve requires further elucidation. | intend therefore to soon add some remarks on this subject to this communication. ( 241 ) and minimum discussed above) the two p, 7 curves touch. This point of contact yields of course an element for the three-phase-pressure. The differential equation for the section of the two p, 7, » surfaces, is found from the two relations which hold both at the same time : 0°s We ryy va dp = (w,—2,) (=) de, + er i | ; 1 and 075 Ws he el rr vs, dp = (ws) | —— | da — dT. dp (oe) (55) den +5 We find then: 07g ar du, a dp Ces? pr sl (ws) —(@,—4,)Ws, Osj Va sy (si) (we —w,)v5, We shall shortly mention some obvious consequences. (1) If arg : xe (; — | = 0, the p, w and the 7, x figure show a minimum or a vy jw maximum. So they exist for a plaitpoint. (2). For a maximum or . w . . . u S1 minimum of 7, must be — . Poy Voy Now: de, Wir PO a Pee eae Ca aon dr On, J pT and : de, Ws, SS Psi LE Es Ei (Us) Aes (See Cont. II p. 110). From this we derive : : dps, dps, dos ; s leads Ee ee OL rords, the direc- This leads to (4: ,) (3 g 7p > OF in words, the direc tion of the (p,7), curve for liquid and vapour, and that of the (p,Z). curve for solid and fluid state are the same in the point of maximum and minimum value of « and the same as that of the pT curve for the three-phase-pressure. The p,7’ curve of the three- phase-pressure descending with the temperature in the case of minimum wv and vice versa, we conclude concerning the point of contact that in the first case it lies between critical point of contact and maximum pressure of the liquid vapour curve, in the second case on the vapour branch of the curve, ( 242 ) If we suppose that the two critical phases with which the solid body can coexist, and which differ considerably in concentration for anthraquinone and ether, approach each other, the two separate parts of the 7’,« figure and also that of the p,« figure and that of the p, 7'figure will approach each other. At the point of contact the two parts of the 7’, figure, and that of the p,.v figure will intersect at an acute angle. If we continue this modification further, the two upper branches of these figures have joined, forming one con- tinuous curve; in the same way the two lower branches. Then the p, Teurve shows a maximum. The existence of this maximum three- phase-pressure has already been demonstrated and discussed by me on the occasion of former investigations by prof. Bakuurs ROozeBOOM *). We find again the result obtained before, now under the following form: Pee) Ee ee Wes v,)+&s—é, af (Gig) ees 4 b] Ld 1 Ws which means, that if we write for that special point of the three- yhase-pressure : | err deet 1 s 2 ‚dp Lw dT Av’ the value of Law would be 0. If we now examine the course of the ,7’ curve for the three- r phase-pressure more closely, making use of the formula on p. 241, or what comes to the same thing according to the formula of Verslag 1897, Deel 5, p. 491, it appears, that other complications may oceur; and that it is not perfectly accurate to say that the p.T curve on the side of the anthraquinone is an ascending curve, till the triple point of this substance has been reached. Then we can also account for the asymmetric behaviour of the p, 7’ curve. It ascends from the triple point of ether and descends on the other side. In this consideration we shall denote by vg, a and ws the concen- tration of the vapour, of the liquid and of the solid body. In the same way we shall use €g, et and e,; then we get for a very small quantity of the admixture : 1 za ea + ped l mj ed per 7 dp lr 1 ws & + pus as A(va— #5) — (er —®s)(r +4) 3 dT l wa va (ras) (vi —vs) — (a1 —a's) (vds) late oo) LBs D5 1) Verslag Kon. Akad. Amsterdam, 1885, 3e reeks, Deel I, pag. 380. 2) The more accurate value of the numerator of the last fraction is: (wa —%,) jaa (lr) + Apes — (eres) ra (1 — wa) + vB od In this we have, however, disregarded the heat of rarefaction. ( 243 ) We denote then the latent heat of liquefaction by 4 and the heat of evaporation by r. Let the principal component be anthraquinone at its triple point. If we add a very small quantity of ether, 7, and a; and wx, will be small but wg > aj > at. We may even assume by approximation for this case, that no ether passes into the solid phase; hardly any will be found in the liquid, but most of it in the vapour. So Liye - J Sse 5 m0 and “is very great. For the limiting case which may be wv supposed, in which 2, would be zero, we have: dp À He 1 eS CES ap a The initial direction of the p,Z7’ curve is that of the melting curve, and when > vs, this curve begins as an ascending curve with increasing temperature. But as soon as after further addition of UL ds Uns — has become equal to ———, in which still a Ud—dls Ud Ta Us ics ether the value of very small value of x; is supposed, the numerator of the expression dp dT numerator is reversed and the p,Z7 curve is no longer ascending, but descending with increase of 7”. Now let ether be the principal component. In this case we have to distinguish two different cases. 1st. Ether and anthraquinone are in solid state miscible in all proportions; then the solid substance which we must think present, is solid ether and we start from the triple point of ether. 2"¢. For all equilibriums anthraquinone remains unmixed with ether. Then the temperature must be thought slightly above tbe triple point of ether. In the first case, if at the triple point of ether a little of the so much less volatile substance, anthraquinone is added, it is to for 7 is infinitely large and on further addition the sign of the be expected neither in the vapour, nor in the solid body, but only in the liquid; then we find: aT ys. So an increase of p with 7’, as occurs in the case of equilibrium between vapour and solid, in concordance with the rule, that if two phases of a mixture in which more phases are present, are of the same concentration, the equilibrium conforms to these two phases. In the second ease, in which we think ether present in liquid and vapour state at slightly higher temperature than that of the ( 244 ) triple point, added anthraquinone in solid condition will not pass into the vapour state. Then «,—= 1 and «y= 0. We get: Tr dp re (r + 4) dT vg vi wilva—s) The quantity 4 is now the latent heat of liquefaction of anthra- quinone. For vanishing value of «,; we find increase of p with 7’, as is found in case of equilibrium between liquid and vapour. In neither of these cases the numerator can become equal to zero when a small quantity of the second substance is added to the principal substance. But I shall not enter into more particulars, nor discuss the treat- ment of special circumstances. If they are brought to light by the experiment, they can necessarily be derived from the above formulae. Nor shall I discuss the 7,., 7’ curves, which would lead to greater digressions. For this discussion we should have to make use of two equations, of which that for the coexistence of liquid and vapour occurs in Cont. IL, p. 104. For the v,v projection of the three- phase-equilibrium we get for anthraquinone and ether two separate branches, lying outside the limits of the maximum and the minimum value of « mentioned above. When these two values of coincide, these branches meet, intersecting at an acute angle; at further modification the two rr curves, viz. those for liquid and vapour, will yield a highest and a lowest value for the volume; at any case the v‚r curve for the vapour phase. As appeared in an oral communication, Dr. Sirs had already arrived at this result. I shall conclude with pointing out, that cases of retrograde solidification must repeatedly occur, both when the temperature is kept constant with change of pressure and when the pressure is kept constant with change of temperature. Chemistry. — “The possible forms of the melting poit-curve for binary mietures of isomorphous substances.” By J. J. VAN LAAR. (294 communication). (Communicated by Prof. H. W. BAKHUIS RoozEBooM). 1. My investigations concerning the possible forms of the melting- point-curve for binary mixtures of isomorphous substances, commu- nicated in the Proceedings of the meeting of the 27" of June 1908, have, apart from the different theoretical considerations, led to the following practical results, ( 245 ) a. When the latent heat of mixing in the solid. phase a’ = q, 9’ is great, the solid phase contains but very little of the second com- ponent. The portion of the meltingpoint-curve which may be realized, has a course as in fig. 1 (see the plate). The curves 7’ = f(z’), viz. Aa and Bh show maxima at m and n, which maxima descend gradually for smaller values of #' till they are below « and +, the maximum at 7 sooner than that at m. (fig. 2). [We leave for the moment out of consideration what happens below the horizontal line through the point C, the eutectic point: for this see my preceding communication |. hb. For smaller values of 8’ we get the case of fig. 3, where the branch BC shows a minimum, no longer below the temperature of C, but exactly at C. Immediately after (i.e. when 8’ is still somewhat smaller), the meltingpoint-curve assumes a shape as in fig. 4. C remains the: eutectic point, where the two branches of the melting- point-eurve meet with a break. As appears from the figure, we have now got parts of the meltingpoint-curve, which may be realized, also below the point C (see also fig. 14 and 14a. of the communi- cation referred to). It is however very well possible, that in the meantime the minimum at D has already disappeared, and then we get a course as is represented in fig. 5 (observed i. a. by Hissink for mixtures of AgNO, and NaNO,,. (see also fig. 146 lc). c. For still smaller values of #' the curve 7 —= f(x’) becomes continuously realizable. The points 6 and a coincide in a point of inflection 6, a with horizontal tangent (fig. 6), which point of inflection soon passes into one with an oblique tangent L (fig. 7), while in most cases it disappears afterwards altogether for still smaller values of Ben. he. 8), The break at C has disappeared in the case of fig. 6 and from this moment there is no longer question of a eutectic point, and the meltingpoint-curve assumes the perfectly continuous shape of fig. 7 and 8. d. As has already been observed in 5, also the minimum at D will sooner or later disappear. For very small values of 8’ we get then always a course as in fig. 9. | Observation. As has been elaborately demonstrated in the preceding paper, a maximum at a 7 si) (ee) 2) 5 a EN we must also retain the terms of lower order, as those of higher De order disappear. We have further : tha : ag’ heey ‚[eas'—ar PURE bee aa rf DRE SS (7 2) a an oA | dc —ar w, me ek ME eee oe ee ; The term mentioned becomes mA a : Ee ‘ : ia a = (ra!) (a —«)(1—A) — (1—20)) = (ee) (c— A). ES Hence we get: 4 ban fa Ca eh : dT dT 2 (dT . a 8 © wy, Ge JA it LAN des, Ian A (w—w)T, sand Wis 7 a or introducing the value of A, and of i dk mee a t 0 4 ; st : ie ET a dT ES iat aa ee Wy Jeen -w, 400 ut UE oy NOES) I, x «| (w-e)T, 3S se . dT’ AT, Bs wa ara «| Sh > 1— — |—2 —-— 4- —-— —- ——-4 le |= dz }, op 5 x ce a ave)? vie EC aT ay LE gts alae ey {5 7a hae af Fre el | dx ), T, 1 fe w, (#—2)T, #3 | Now (wv,), =@. + a— a, (w‚), = 41, SO that we finally get: N ta Dy ey: dT 1 (dT Nas eT —47 — AT, —2(g, dad) — EDO) erts ca a (=) —a il nl . . . . . . . . . . . . . (9) En 8 1 av 3 <> Sean ae a 4 Lv 0 é ' he wv = ~ where (1) has the value given in (8). 0 dd sae B ( 953 ) VEA Al {2 This expression for (=) is still very complicated, even after the aXe” great simplifications, which attend the introductign of «= 2’ = 0. 12 ey! Besides by a direct calculation, the corresponding value for (=) € 0 may also be found by changing letters and signs as mentioned per and the latter method is even the easier. Then we get: a ea de ) E (1 ze art) a—o 2) TR: v& | q,—4T ,—2(q, +a—a') — (9a) EAR | We FT In the diseussion of the two quantities and | —= |, two 0 0 da? da"? limiting cases are chiefly worthy of consideration, viz. a’ =o and a’ —0. Let us further always put « (latent heat required for the mixing of the liquid phase) = 0. a a. For e' =o — becomes exponentially == 0, hence En & . & . . > Lim. (« 5) will. be 0. The two expressions are then trausformed 0 Gio) = 2 (ae) ane PA) BOL O40) ts OF THO: der ay Oee h into: (i= er ea (10) den da!” == de' These expressions teach us, that in case the solid phase contains dT very little or nothing of the seeond component, (5 : a 4 becomes 0, 0 when g, = 4 7,. In this case therefore the point of inflection appears in the curve 7, f(x) exactly at «= 0. dT : den ; ad being negative, « ‚) will also be negative if q,>4T. Aah atv The meltingpoint curve will then turn its concave side to the z-axis at A, and no point of inflection will occur. This is in perfect agree- ment with what we found in our former paper. *) de always be negatively large. For great a’ the concave side of the curve T'—= f(z’), running almost vertically downward, is turned towards the z-axis, but the curve 7’= f(a’) finally touching the ordinate «=O asymptotically at 7'==0, a point of inflection must at any rate be present beyond the maximum of the curve 7 —= f (4!) (see fig. 1; at L). This point of inflection Z will occur immediately after the maxi- mum at m for large values of a’, and these two points gradually approach the point A, where 7 —= 7, 2 =0. As to the maximum m, this is of course represented by dT eine dT As to {—-]. we see that this expression, just as i will 0 Ts w (Al—r)w,Jaew,=0 (see (6)) or z = eae Now w,=q,—a'«?*=q,, and 1 2 w, = q,—e« (1— 2x)? =— a’, when a’ is large and 2’ very small; henee the maximum occurs at ( 1 B h = tu voli gta a p If therefore 8’ approaches to oo, then #7, (so also z’;,) approaches to 0. As to the point of inflection at Z, the following remarks hold good for it. da’ From the expression for es (see (a) follows, when «a =O and AL a’ is large: Od, dT e(l-e) Ww, dT) go dT salle de dx «'(1-«')w,ta(w,-w,) de & qa dx & 1e At small 2’ we get: (b) — re Ve i ~ log (le) V1 hence : LT (yee Hen al An 1 dir © a NP ae gq, (l-a)(1 + 2 62)’ as N? = (1—@ log 1—a))? = (A HOrt.) = 1+ 2 42). 1) These proceedings, Febr. 25th 1902, p. 427; June 24th 1903, p. 29—30, es 4 We have therefore : dT BO 1 SO ae REE GB (1+ 26x)(1—p'z) ier) Tjen a’ 1— ge’ when 8' is great with respect to 6, and hence: «' (1— Ba) aoe (1-2 a— pla! a) os RT? da! da? = 7 a, PE (1 Be) = nfs Consequently this is 0, when t de de x (1—p'x) a 1—8, ar — ae der da = a x da Now we may write for da (see (0) ): Lv der uv (lr) 1 den a 1 — Be eke so that ——— 0, when da’? 8'r (la Sa) (rr pu eS or lx br == l=f'efel wae = 4s ae (1+ 5.) or Ee es Hel : ) fre ( TBE ( Ween From this we find: so finally : BR ey og Sia Mice nadeel) ne bide a PE being the value of we, at which for large values of 8’ the point of ; ' 1 inflection will be situated after the maximum at sa (see (11)). So this value of x too approaches to 0, when 3’ approaches to oo. It is now evident that according to (10) for large values of 8' the 2 ad quantity ed approaches to — oo. For already in the immediate AL 0 neighbourhood of A the direction of the curve 7’= 7 (x!), which was initially a/most vertical, changes into a perfectly vertical direction at the maximum. ( 256 ) 6) The other limiting case is a’ = 0. The expressions (9) and (9a) take then the form Gr) =i Loe) Jeter || | de Lad aie ale Je +47,+(5) | aA dv? ag ‘ 7 or de | (a i 5 lar (E) | Ge AT )-2(g,- | (c=0),(73) vig dT Gls eG JE Hm (5) Jt ary 240-19} || where according to (8) the limit of the proportion (5) is represented by 7 PL 0 Gat whist (5) as, ae Sial a oben A EN 0 We see from these expressions, that even with 3’ = 0 a point of inflection at «=O (and so also before it) is possible for the two curves T—=f(e) and T— f(t’). For this it is required for the eurve 7’= f(a), that oe a n—47, es 1 U Jo (q,—47 hee (q, ae gyi. c 1111 ; or at iem. 5 3 5 : : Ee “amr 8 not large, we may write for it by approximation : Bs ee STO AT Ag: Daris Rn The condition may now be written as follows: ee pv) aoe T AT, Pe : We see that in any case must be positive. or hence Lt ge Ds de Ed ea ye te (LB) AT, fi ei hes ME Mate ON) EE D= IOO == A00 "7 1980, the “hrst Lay 10/ 5 7 /9 /9 mm member is 1/,, the second member jn np STONE: DTe nf A | he term VREES dd JOEL 440 —- under the /og-sign is here —— == !/, |. g,—4T, | he 2200 k Even with 8'=—=0 a point of inflection can very well occur somewhere in the curve 7’= f(x). The corresponding condition for the occurrence of a point of inflection at «=O in the curve PS f @\ becomes: (5) een nt+47, Te i ALY a 7 q HAT —g, —g.) 12 Yi Is aA, VE was ! = — log tee le : EN. 1e ; g, +47, for which we may write for small values of , — 49, : or VE gal ry Wi Ye TE (Em ID) a a 4 Ë : ea ad 2 vit ante This is only possible when 9, >> g,. Again we may write: Tis zn (HTI) 2) (1 at Vy ) (Gr pf 1), Is Zod be ae AT, fe 0 di, or dn (G-1 a f ENZ, da Ee Te ae ED 7 a A 1) Vene — Ì die If e.g. T ole Ne SN NE 2200, di 1650, the first Pee, 37) member is again */,, and also the second member is ay 3 ied En Din a 1100 1 The term 2 ————— is now —— = — |. n+, 6600 6 Also in the curve 7 = f(a’) a point of inflection may occur even wating == 0. And now we have given a complete answer to the question ( 258 ) raised in the beginning of $ 3. The point of inflection at L (fig. 7) need not have disappeared in either of the two meltingpoint-curves, when 8’ has reached the extreme value 0. In a following paper we shall give a fuller discussion of the important limiting case 8 = 0. 4. Finally we wish to discuss more at length an important property of the eutectic point C, which was only shortly mentioned in the preceding communication. (le, p. 166). A rule was namely given there of very general application, 1. e. : When al, =a, (i.e. latent heat required for the mixing of the first component with «= 1 is equal to that of the second component with — 0) the compositions of the two solid phases will be complementary. We shall proceed to give the proof of this thesis. Evidently the system of equations holds for the eutectic point (the compositions «,/ and wv,’ of the solid phase are there in equilibrium with that of the liquid ~) : my ' 13 n(” p ry) rm ! iz T= ds (ie vy S| A. Ja bs Be Tl -pe, ) “rid Ate eh op iene Sr eS ENE EE 1+ log ~ 1] + log . ZA 1 Js a“ I, : Bela F dn 3 (le) ) Ja = Nt tk pel oe ae es ry ee) | Sid. Ie 1 aa log la i bay If we solve from this log ek: and loge, we get: Wee ie tage tion ! Ja qq; ! 1 \2 loge = loge, 4 R bee = — RT 8 (le) log (l—e) = log (1—a’,) une log (1— B log (1— a Ki — (a 5 ; aes i= 8 As log x = log «’, +2 ale RT 8 (le) from which follows by eee SPL Big pee Spay? Eee log 1—z,! EF RT B (w, vy )s og A at [( We ( je alg which is evidently satisfied by Er Nal ae aia eee a eee (17) qed: J. J. VAN LAAR. “On possible forms of the meltiugpoint-curve for binary mixtures of isomorphous substances.” (2nd communication). Bien: Fig. 6. Fiel: Fig 8, Proceedings Royal Acad. Amsterdam. Vol. VI. ( 259 ) The two above equations pass now into one : 1—2,' q log - pve ee BL 2x ') Et va! He Ue ce ee 18 ee 1 i ba ( ; ii In this complementary composition we have a distinct criterion, whether or no it is allowed to put «, =a’, (i.e. r==0). Further the equation (18) furnishes a simple means, when 7 may really be put = 0, for calculating the quantity B from the composition «,' of the solid phase at the eutectic point. If we find e.g. #', = 0,1, we may find by means of 7, — 500, g, = 2400: BOD wy a n= 1000 Brox OLS. hence : ee ej IE log 9 = Ean: If x had been 0,01, we should have found with the same values of Te and g,°: La log 99 = — B X 0,98, 5 hence: 125 B' = — log 99. = 1,95. 294 ° It is seen, that a slight increase of 8’ is able to depress the composition 2,’ of the solid phase at the eutectic point very strongly. This is of course in connection which the enormously strong decrease ! > . d . . . . . » of the relation — with increasing 3’. This relation was e.g. for T=T, ¥ TL ! DUA Al x ke 1 *)\ . and great p’ represented by (7) =, (see § 3), which con- K 0 verges very quickly to 0. Chemistry. — “The phenomena of solidification and transformation in the systems NH, NO,, AgNO, and KNO,, AgNO,.” By Professor H. W. Baknuis RoozrBoom. (Communicated in the meeting of September 26, 1903.) Of the nitrates of univalent metals, those of Li, Na, Ag, NH,, K, TI have been studied more in detail as to their mutual relations. It has already been shown that the nitrates of the first three are very prone to yield mixed crystals and the same takes place with the last three. LiNO, and also NaNO, do not seem to form with the ( 260 ) nitrates of the last group any mixed crystals at all or else only to a small extent and in any case they do not enter into chemical combination. As regards the relation of AgNO, to the nitrates of the second group, the only system examined up to the present (by van Erk) was that consisting of AgNO, + TINO, in which a compound in the proportion 1:41, was formed. To complete our knowledge in this direction, the systems NH, NO, + AgNO, and KNO, + AgNO, have been investigated by Zawtpzki and Ussow and the results are com- prised in the Figures 1 and 2. Lov iy Ag 2 /8o} 7 ri 0 ig eae 4 1x [Be she APN. A zn ENE ot PCR WE OR fou > Go Bs § OF AITO DEPOT ADA OO ae Oe oe ae Ain Nos fig NM 0s aide Fig. 1 and 2. The first system is interesting on account of the fact that with NH, NO, four and with AgNO, two solid phases succeed each other which, starting from the melting-point, we will designate by Am 1—4 and Ag 1—2. It now appears that in the case of mixtures of the two salts the > a” ( 261 ) transition point of AgNO, and the first transition point of NH, NO, falls in the region where these mixtures are still partially liquid; the two lower transition points of NH, NO,, however, are situated in the region where everything has already become solidified. Owing to this, the deposition of AgNO, from melted mixtures rich in silver takes place according to two lines which meet each other at 160°; the solidification of NH, NO, from mixtures rich in this salt, also takes place along two lines which meet each other at 125°. Neither transition point is modified by the mixing process, from which we may conclude that the salts are deposited in a pure con- dition and do not yield mixed crystals. From the intermediate concentrations, however, a compound D = NH, NO, AgNO, is deposited with a pure melting point at 109.6°. Its melting-point-line extends towards the Ag-side only up to 52 Mol. °/,, .towards the NH,-side up to 30°/, Ag. Consequently, all mixtures of 50—100°/, Ag solidify at 109°.6 to conglomerates of D + Ag, and all mixtures of 0—50°/, Ag at 101°.5 to conglomerates of Am, + D. The latter, on further cooling, undergo a new transformation at 85° and 35° owing to the reversion of Am, into Am, and then into Am,. As both take place in the different mixtures at the same tem- perature at which reversion of the pure AmNO, takes place, this proves that no mixed crystals occur between this salt and the double salt. If now we express the liquid mixtures by L we have in Fig. 1 the following regions. 1 Am, L 7 Am, + D 3 L-+ Ag, 2 Am, + L 8 Am, D 4 L + Ag, 5 D +L 9 Am,+D 6 D-+ Ag, The system AgNO, + KNO, is simpler in so far that KNO, has only got one transition temperature at 126°. The transition point of AgNO, again falls within the partially liquid region and the solidification of the mixtures rich in Ag therefore, again takes place according to two lines which meet each other at 160°. Under normal conditions, the transition point of KNO, falls within the solid region, consequently there is only one melting point line for the first form of the KNO,:K,; in the figure this line is represented only from 210° to lower temperatures; it must be imagined to extend to the KNO, axis at its melting point of 338°. From the intermediate concentrations there is also deposited a double salt D—KNO, . AgNO, but its melting-point-line only extends from 18 Proceedings Royal Acad, Amsterdam. Vol. VI. i) ( 62 ) 131° and 38°/, KNO, to 184°.5 and 45°/, KNO, Consequently, there exists no pure melting point but D is trans- formed on heating to 134°.5 into KNO, solid + solution of 45 °/). All mixtures of 0—50 KNO, solidify at 131° to Ag, + D, all mixtures of 50—100 KNO, at 134°.5 to conglomerates of D + K,. The first named remain unchanged on further cooling. The last named ought to change at 126° into D + k, but this takes place with great difficulty. The double salt is also not readily formed. If it does not make its appearance, the melting-point-line for A, runs through to 126°, and below this K, is converted into K, much more readily than in the solid conglomerates. The melting-line of K, runs through to 120° at 42°/, KNO, where it meets the prolongation of the melting line of Ag,. If D does not appear, all liquid mixtures solidify at 120° to a conglomerate of Ag, + K,. The following zones comprised between the full lines represent stable conditions 1 Apres, ds DEK Do eee bp ND, BD EK, TND EER All metastable boundaries are indicated by dotted lines. The regions concerned may be easily deduced from the figure. From the above it follows that at the ordinary temperature, only the simple salts in the forms which are stable at that temperature and also the double salts 1:1 can occur as stable conditions; this agrees with what Rercers has previously found for the products of crystallisation from aqueous solutions at 15°. Chemistry. — “The transformation of benzdine’. By Prof. A. F. HOLLEMAN and J. Porter van Loon. (Communicated in the meeting of September 26, 1903). In the report of the meeting of this section of Nov. 29, ’02 there will be found a preliminary communication as to the experiments conducted in my laboratory by Dr. J. Porter van Loon, who has since brought his research to a close. His results are briefly described below. The method by which he succeeded in obtaining benzidine and hydrazobenzene in a perfectly pure condition has already been given in the preliminary communication. In connection with this it may be mentioned that hydrazobenzene was separated as a snow-white hh tt en ee _— ( 268 substance, but after a few days exposure to the air it again turns faint yellow. An improvement was also desirable in the quantitative determina- tion of benzidine. At first vaN Loon collected the precipitated benzi- dine sulphate on a weighed filter, which was then dried at 100° in a steam oven and reweighed. Here we met with the unpleasant fact that the filter often turned blackish probably owing to a decom- position of the sulphate, which may unfavourably affect the deter- minations. The improved process now consisted in removing the washed sulphate from the filter and boiling it with excess of standard alkali. If now the excess of alkali is titrated at the boiling heat with standard acid, the benzidine sulphate behaves like free sulphuric acid when litmus is used as indicator. In this way the determination becomes more rapid and accurate. The usual correction for the solubility of benzidine sulphate had, of course, to be made. The determinations made by Dr. van Loon of the ratio between the quantities of benzidine and diphenyline formed during the transformation of hydrazobenzene by acids have demonstrated the influence of various circumstances on that relation and may be best represented in a tabular and graphical form. I. INFLUENCE OF THE CONCENTRATION OF THE ACID (HYDROCHLORIC ACID). a) Solvent: Water. Temp. 18°—25°. Weight of dipheny- line on 100 Amount of Concentration Mer. mol. acid in %/) benzidine. hydrazobenzol. mer. mol, of the acid. | parts of benzidine. 250, = 7.8 n. rie ed 84.5 18.3 250% = 7.8 n. hats 2.011 80 0 25 3.90 n. TS gd 90.0 14 Len. 50 oe 90.5—89.5 10.5—12.4 b) Solvent: Alcohol of 50°/,1). Amount of Concentration | acid in mer. mol. of the acid. | Mer. mol. hydrazobenzol. Temp. 25°. Weight of dipheny- line on 100 parts of benzidine. oot Dl, 77.8 2.— 80.0 25 1, n. 50. — 2.— 84.8 47.9 0.6 n. 30 — 1.440 83.6 49.6 Ot | 5.— 2.— 83.0 20S 1) Always percents of weight are meant, ( 264 ) II. INFLUENCE OF THE SOLVENT. Temp. 18°—25°. HYDROCHLORIC ACID. Nature of the Concentr. Ue Mer. mol OO Weight of diphenpe acid in line on 100 solvent. of the acid ; hydrazo. | benzidine. re mer. mol parts of benzidine. Alcohol of 97%, | 042 n. 12 1.535 80.5 24.2 | » D: 1500/71" 204 sn: 10 and5 |1.6304and2)84.1and83.1 18.9—20.3 » » 50% 1, n. 50 2 84.8 dF » » 15% OR èn. 5D 2 | 87.5 14.3 | | Water I, n. 50 1.6504and2 | 90.5and&9,0 10.5—12.4 Methyl alcohol Ot n. ) 2 | EO | 301 Aleohol and methyl aleohol alter the relation of the transformation to the disadvantage of the benzidine and the effect becomes greater when the amount of water becomes less. This may be caused by the circumstance that in another medium the reaction may take a different course (for instance, the velocity of the formation of diphe- nyline may increase) but it is also possible that the deviation must simply be attributed to the increased solvent action which dilute alcohol exerts on hydrazobenzene or an intermediary product of the reaction. It is „of due to an increased solubility of benzidine sulphate in dilute alcohol as has been proved by a purposely made direct experiment. II. INFLUENCE OF THE KIND OF ACID. oh Ten 100°. Water. Acid. [cms Concentration. ee fens 0/, benzidine. 0.05 n. 4 1.6304 66.4—70.6 HNO, 0.05 n. 6.4 1.6304 67.3—71.7 H,SO, | 0.03 n. | 4A 1.6304 63.4 HBr 0.03 n. 4 1.6304 65.8 As at 100° a small quantity of azobenzene or aniline may be formed (the formation of the latter has not been investigated for the weak hydrochloric acid concentration) the figures for the forma- tion of diphenyline would be valueless and they have, therefore, been omitted in table III. Those for benzidine are probably a little too low as the formation of azobenzene could not be entirely avoided. ( 265 ) b), Temp. 25°. 50 %, Alcohol. Columns as under I and I. HCL. Vn. 50 2 84.8 17.9 HNO,. 1, n. 50 2 82.2 21.7 HSO, In. 50 2 89,8 114 CHCly.COOH. in. 50 9 83.5 19.8 Except for sulphurie acid which yields a higher value, the relation of the transformation does not differ much in the case of the other acids. IV. INFLUENCE OF THE TEMPERATURE. a) Alcohol of 500. Hydrochloric acid. Amount of Weight of dipheny- Cone. Mgr. mol. Temp. acid in 0/, benzidine. line on 100 of the acid. hydrazo. mgr. mol. parts of benzidine. mmm A E> 0° Orden: 5 1 87.8 13.9 25° In. 50 2 84.8 17.9 50° In. 50 2 79.0 26.6 75° In. 50 2 67.4 48 4 4) Water. Hydrochloric acid. 18° aan 50 1.6304 00.5 105 Jo 1, n. 50 9 89.0 19 4 50e 1, n. 50 2 86.6 15.5 ge In. 50 2 80.8 23.8 OOS Oe Ueno | 50 ME 74.9 33.51 100° | 0.03 n. | A 1.6304 66.4—70.6 | D0.6—41.6 The figures given in the tables are in most cases the average of several fairly concordant determinations. The influence of the temperature as shown by this table is again the same for both solvents and is shown by a fall in the ratio of the transformation with a rise in the temperature. The following observation should be made as to the last column contained in these tables; the substance which was not precipitated as benzidine sulphate is supposed to have been converted into diphenyline. This, however, has only been once isolated as such, so that it is not impossible that other bases besides diphenyline may have been formed, the sulphates of which are soluble in water. As other investigators have already taken up this subject, Dr. van Loon has not extended his research in that direction. The graphie repesentations, following here, are those of the above mentioned tables, ( 266 ) Fig. I. Influence of the concentration of the acid on the ratio of transformation. Temp. 25°. rr) r=) oS w o a oO SN oe © u oO 100 Formed benzidine in procents. Figuur II. Influence of the amount of alcohol on the ratio of transformaticn. 0.1 n. hydrochloric acid, ¢ = 25%, 55 50 u) Q u) o w co oO XN KR To] 100 9 90 60 Formed benzidine in procents. a oo c 80 60 40 20 Figuur IIIf. Influence of the temperature on the ratio of transformation. 1.— n. hydrochloric acid o u) 3 Ee R re) 100 95 90 85 8 60 55 50 Foymed benzidine in procents, 208 40° 60° 80° 100° o° Standard of the hydrochloric acid. ents in weight of ethylalcohol. a + Prac Temperature. ( 967 ) Dr. van Loon: has also been engaged in determining the velocity of the transformation. An excess of finely powdered hydrazobenzene was introduced into dilute alcohol, to which had been added acid of a definite coneentration, the mixture being vigorously stirred. At stated times certain quantities of liquid were withdrawn from the mixture and the amount of benzidine was quantitatively determined. If CC), is ealled the concentration of the benzidine formed, Ciyei that of the hydrochloric acid at any moment, the equation ale dt was found to represent the transformation; in this ¢ is the time (in minutes) and A the reaction constant. No special figure is given for the concentration of the hydrazobenzene as this may be taken as constant in the modus operandi followed. The transformation is due to the hydrogen ions of the acid, for on comparing the action of hydrochloric acid and dichloroacetic acid the reaction constant was shown to be proportional to the degree of ionisation of the acids employed. This caused Dr. van Loon to sug- gest that during the transformation two H-ions are first linked to hydrazobenzene forming GERNE: NE © EL H+ | H+ and that then the repulsion of the two positive charges causes the molecule to break up between the two nitrogen atoms, whereupon the two portions again unite in such a manner that the positive charges are at a greater distance from each other. This representation accounts for the presence of C*gc im the equation of velocity, as according to this equation one mol. of hydrazobenzene reacts with two H-ions. == Ki GE HOI Chem. Lab. Univ. Groningen, July 1903. Chemistry. — “The transformation of diphenylnitrosamine into p.- nitroso-diphenylamine and its velocity.” By H. Raken. (Com- municated by Prof. C. A. LoBry pr Bruyn as communication N°’. 6 on intramolecular rearrangements). (Communicated in the meeting of September 26, 1903). In 1886 Orro Fiscumr discovered the interesting fact that under the influence of alcoholic hydrochloric acid the nitrogen-combined nitrosogroup of methylphenylnitrosamine changes place with the para-hydrogen atom of the benzene nucleus and is thus converted into the isomeric nitrosobase. ( 268 ) Mea ee Fiscuer and Ep. Hepp have made a closer study of this reaction and found it to be a general one’); it also takes place with diphenylnitrosamine. It was deemed of importance to study the exact conditions under which this transformation takes place and particularly to learn its order by means of a determination of the reaction velocity. A method which permitted the quantitative estimation of the two isomers in presence of each other with sufficient accuracy, was not at hand. The chemical behaviour of the two isomers does not differ greatly and the nitrosobase (at least in this case) is far too weak to be titrated. It was therefore attempted to utilise the difference in colour of the two isomers; diphenylnitrosamine has a faint yellow colour, which in dilute solutions may be neglected. The nitrosobase however, in combination with hydrochloric acid forms a brown powder whose dilute alcoholic solution is deep yellow, whilst more concentrated solutions are dark brown or red. It was therefore decided to carry out the measurements by means of a colorimetric process using the polarisation-colorimeter of Kriss. An unexpected difficulty arose, however, owing to the fact that different preparations of the hydrochloride gave greatly different results when examined in the colorimeter, although they had been prepared in exactly the same manner. As it was, of course, necessary to prepare the standard liquids with the perfectly pure salt, I have taken a great deal of trouble to obtain this. It appeared that a solution of this salt is slightly decomposed and darkened by the oxygen of the air and by prolonged contact with excess of hydro- chlorie acid; the salt was therefore prepared in an atmosphere of carbonic acid and under specified conditions. The compound was taken as pure when different preparations gave the same result in the colorimeter; an analysis was of no service. And after it had been found that the free base (which in the solid state forms steel- blue needles) exhibits the same colour as the hydrochloride in dilute alcoholic solutions, the basis of the measurements was obtained. From the colorimetric identity of the free base and the hydro- chloride it follows that the latter, in very dilute solutions, must be ‘completely aleoholytically dissociated and also that only solutions of a certain degree of dilution are comparable with each other. 1) Ber. 19. 2991. 20. 1247. 2471. 21. 861. Ann. 255. 144. (1886—1889) etc. ( 269 ) The concordant and very definite results obtained during the measurements may in turn be taken as a proof that the standard- comparison solutions were trustworthy. Experiments were made in alcoholic solution with hydrochloric acid as catalyzer. The results are briefly as follows: 1. The reaction is one of the first order. 2. The reaction constant is proportional to the concentration of the hydrochloric acid causing the transformation. In absolute ethy] alcohol at 35° (time in hours) was found for 1 mol. ECI 2 mols. HCI 3 mols. HCl k = 0.0081 0.018 0.026 3. Addition of water causes a serious fall in the reaction con- stant; for instance, for {== 35° and 3 mols. HCl in abs. alcohol: Tk = 0,026; mnve.92.5:?/; alcohol 4 —= 0.0026: The water apparently withdraws a portion of the hydrochloric acid or renders it less active. 4. The temperature coefficient is very great; about 5 for each 10°. We may therefore draw the general conclusion that the trans- formation of the nitrosamines into the nitrosobases is a real intra- molecular displacement of atoms. This is all the more likely if we consider that in this case the velocity with which the transformation product was formed, was measured. This result remains the same if we suppose that at first (with unmeasurably large velocity) an intermediate additive product was formed from the nitrosamine and the hydrochloric acid acting as catalyzer. We then have, practically, measured the transformation of the latter into the isomer; that trans- formation however requires also an intramolecular rearrangement. We shail later on return to the possibility of the occurrence of an intermediate product. Further particulars will then be communi- cated as to the action of other catalyzers and on the influence of other solvents on the migration; experiments in this direction are already in progress. * Physics. — “The periodicity of solar phenomena and the corre- sponding periodicity in the variations of meteorological and earth-magnetic elements, explained by the dispersion of light” By Prof. W. H. Juurvs. (Communicated in the meeting of September 26, 1905). Table of contents. Introduction. I. The path of the projection of the Earth on the Sun. The probable origin of the 11-year period, Il. The variability of the solar radiation. Ill. The periodical variations in the appearance of the Sun. 1. Sun-spots and faculae. 2. Prominences. IV. The periodicity in the variations of meteorological and earth-magnetic elements. 1. Do these phenomena require the hypothesis that the Sun exhibits a varying activity ? 2. Effects of the movement of the Earth through the irregular field of the Sun’s radiation. A. The semi-annual and annual periods in the position of the Earth in the irregular field of radiation. B. The periodicity of the fluctuations of illumination which coincides with the periodicity of solar phenomena. 3. Polar lights. 4. The annual variation in the diurnal inequality of terrestrial magnetism. 5. Magnetic disturbances. 6. The annual variation in the daily oscillations of atmospheric pressure. 7. ‘he annual and secular variations of atmospheric pressure. 8. Cosmic influence on other terrestrial phenomena. Summary of results. INTRODUCTION. The whole science of astrophysics rests on the hypothesis that the same laws, which we have recognized by observation and experimental research, hold good for other celestial bodies as well as for the Earth, and that we are justified in applying to the Sun and the comets, to nebulae and double stars, the results of thermo- dynamics, of spectrum-analysis, of the theory of electrons. It would therefore be illogical to make an exception with regard to our knowledge of the refraction and dispersion of light in masses of variable optical density; and by adhering to the supposition, that in the Sun and its nearest vicinity the light travels in straight lines, we should take an untenable standpoint. ‘J The results of some recent investigations ') all tend to confirm the hypothesis that the causation of anomalous dispersion is a general property of matter. Thence, even highly rarefied gases, whose density is unequally distributed, cause some kinds of rays to be considerably deflected. All the conclusions arrived at by Youre, Lockyrr and others, as to the thickness of the various concentric layers in the solar atmosphere, the velocities of the prominences, the displacement of matter in the sun-spots, the dissociation of elements in the Sun ete, must be sacrificed in so far as they are based on the erroneous notion that the objects are situated in the exact direction where they are seen by us. A. Scumipt?) has gone so far as to demonstrate that the sharply defined circular outline of the Sun’s dise is no proof of the Sun being a spherical body. Owing to the curvilinear propagation of the rays, a gradually fading luminous mass of gas might appear to us as a sharply outlined disc. We may therefore be allowed to consider the Sun an unconfined gaseous mass. By taking also into account the laws of the anomalous dispersion of light, we succeeded in finding explanations for almost all the phenomena observed on the surface of the Sun and on its edge *). We felt justified in starting from the simple supposition that in the gaseous, unlimited body of the Sun, the several elements are not locally separated but intrinsically mixed. Perhaps future investigations may lead us to admit that in the solar body some elements are locally separated, but I think that the present state of our knowledge regarding the properties of sun-spots, faculae and prominences does not warrant such an assumption. Our new conception of the Sun leaving no longer any room for the hypothesis of a periodical activity manifesting itself in violent eruptions, we are naturally led to inquire whether all the phenomena attributed to this cause, may equally well — perhaps better — be explained as effects of the dispersion of light. The following data may assist in the elucidation of this question. 1) O. Lemmer und E. Prinesnem, Zur anomalen Dispersion der Gase, Physik. Zeitschr. 4, S, 430—431. 1903. H. Egerr, Die anomale Dispersion der Metalldiimpfe. Phys. Zeitschr. 4, 5. 473—476. H. Egerr, Die anomale Dispersion und die Sonnenphiinomene, Astr. Nachr. 162, S. 194—195. 2) A. Scummt, Die Strahlenbrechung auf der Sonne. Stuttgart, 189". 3) W. H. Jvuvs, Proc. Roy. Acad. Amst. Il, p. 575—588; III, p. 195—203; IV, p. 162—171; 589—602; 662—666. I. THE PATH OF THE EARTHS PROJECTION ON THE SUN. THE PROBABLE ORIGIN OF THE 11-YEAR PERIOD. If it be true that sun-spots, faculae and prominences are effects of ray-curving, it stands to reason that their form and situation will depend in a far greater measure on the position occupied by the observer, than would be the case, if they were themselves light-emitting bodies. A correct idea of the movement of the Earth with respect to the revolving body of the Sun must therefore be the basis of our invest- igations. Unfortunately it is impossible to give an absolutely exact idea of this relative motion, for not only are we in ignorance of the exact period of the Sun’s rotation, but it is extremely difficult to define the meaning of that term, because we take the Sun to be a mobile gaseous mass. On the other hand it is quite evident that we ave dealing with a periodical phenomenon ; the only question therefore is, whether we shall sueceed in selecting from the various values on record, the one which has the greatest significance from our point of view on Earth. As a matter of course we select a synodical period of revolution. It is a known fact that different values for the period are obtained from the movement of spots and faculae, varying from 26 to 30 days according to their heliographie latitude. By the application of Doppimr’s principle, Dunér found that near the equator, the period of rotation of the photosphere was 25,46 days and at 75° latitude up to 38,55 days. In 1871 Hornstem observed in the deviations of the magnetic declination at Prague a period of about 26 days, which other invest- igators have found also in various meteorological phenomena. The results obtained led to the conclusion, that the rotation of the equa- torial regions of the Sun exercises a greater influence on the Earth than that of the other zones. From the following table it will appear how indefinite as yet is our knowledge of the period of the Sun’s rotation : STRATONOFF (faculae near the equator) 26,06 *) CARRINGTON (sun-spots near the equator) 26,82 5) DerÉr (photosphere near the equator) 2540 HoRNsTEIN (magnetic observations at Prague) 4650 zn Ap. Scumipt (most probable value deduced from the mag- 1), Arruentus, Lehrb. d. kosmischen Physik, p. 148. 2) This value is communicated by Dunér as being the sider eal period of rotation, and appears to have been generally accepted as such. Prof. J.C. Kapreyn, however, kindly informed me that in Dunér’s interpretation an error has slipped, and that he result must be taken as the synodical period. (278) netic observations of Broun, HoRrNsTEIN, MULLER and LizNAm, until 1886) 25,92 9 Ap. Scumipt (magnetic observations at Batavia) 25,87 3) VAN DER STOK (barometrical observations at Batavia and St. Petersburg and magnetic observations at Prague and St. Petersburg) 25,80 *) von Brzorp (thunderstorms in S. Germany) 25,84 *) Exnotm and Arruentus (polar lights) 29,929") BieeLow (meteorological and magnetic observations in the United States of America) 26,68 *) The justification of the choice we make between these different numbers must for the greater part be found in the value of the con- sequences we derive from it. However, there are some good reasons why we should prefer a priori the value obtained from investigations on the frequency of polar lights by EKHorm and Arruentus. For although the results of others (especially those of Ap. Script and of VAN DER STOK), from a point of view of careful and critical reaso- ning, are of no less value than those of Exnonm and ARRHENIUS, the variations of the barometer and the oscillations of terrestrial magnetism are phenomena of a more complicated nature than polar lights. They are influenced by local conditions, the distribution of land and water, ete.; because they partly depend on the circulation in the lower layers of the atmosphere. On the other hand it would appear that the polar lights take their origin principally in the higher layers and thus, by revealing to us more directly the action of the Sun’s radiation, they will propably lead to a sharper determination of the period. Whilst the periods of rotation necessarily differ in the various parts of the Sun’s mass, there must be somewhere in the plane of the equator a series of points, where the synodical period of rotation is 25,929 days. Through these points we imagine a sphere B, the centre of which is laid in the centre of the Sun, and we make the sphere rotate around the Sun’s axis with a constant angular velocity, so as to bring its synodical period of rotation at circa 25,929 days. This sphere represents to us “the rotating Sun”, but we must keep in mind that with respect to 5 the various parts of the gaseous mass may alter their position. 1) Ap. Scumipr, Sitz. Ber. Kais. Akad. d. W. Wien, Bd. 96, p. 990 and 1005. 2) Van per Srox, Verh. Kon. Akad. v. W. Amsterdam, 1890. 3) Arruentus, Lehrb. d. kosmischen Physik, p. 148. t) Bieevow, Un. States Weather Bureau Bulletin No. 21, Washington, 1898. See also Scuuster’s criticism, Terrestrial Magnetism III, p. 179. The line AZ, which connects the centre A of the Earth with the centre Z of the Sun, intersects B at the point ?. We call this point “the projection of the Earth on the Sun” and will determine its track on DB. The inclination of the Sun’s equator on the ecliptic is 715’. About the 4% of June and the 6 of December the Earth passes through the nodal line. Fig. 1 represents part of the sphere B; EL is the intersection with the ecliptic, QQ that with the Sun’s equator. On the 4 of June the Earth's projection is in P,. Through this point we draw the first meridian J/. In the space of about 25,929 days J/ has made a synodical revolution and is intersected for the second time by the line AZ (not marked in the diagram) but this time at the point P,, a little to the north of the equator. In the interval P has been describing one convolution P?, PP" P, of it helical course. The next points of intersection P, and P, of the path of P with the first meridian again le somewhat more to the north, but about the 4% of September the path has reached its utmost latitude 7°15! and then gradually descends towards the equator, which on the 6" of December it intersects a little beyond ZP. All the points of intersection for one year are marked on the meridian J/ in its first position. P, to P,, lie in the southern hemisphere. P,, is reached after 14 > 25,929 = 363,006 days; the sideral year has 365,256 days, consequently P,, does not coincide with P,; the track of P intersects the Sun’s equator 2,25 days later. During the second year, /, in its helical course, passes through entirely different points of our spherical surface than in the first year, and so do the successive annual spirals; they each time skip an angle ( 275 ) a. The spirals of the twelfth and thirteenth year come again very close to that of the first year and lie on each side of it. It is therefore reasonable to expect that after a period of a little more than 11 years a very similar succession of incidents will take place. *) It now remains for us to consider which conditions and phenomena may be governed by the position of P? on the sphere. The Sun is an immense mass of matter, and considering its age we may take it for granted, that within the memory of man it has remained in an almost stationary condition. We know that the violent eruptions which have been thought to take place on its sur- face, have led to a quite different conception, but at present we can realise ®) that relatively small local variations in density, such as necessarily must occur in vortices along the surfaces of discontinuity between stationarily streaming layers of gas, are quite sufficient to produce strongly marked variable optical effects, such as promi- nences etc. The large currents of the general solar circulation must be cyclic movements, which do not perceptibly alter the configuration of the entire mass, only causing along the surfaces of discontinuity a somewhat varying distribution of matter, due to undulations and whirling. We admit that on account of the Sun not being perfectly symmetrical around its axis, the movability of the parts involves a gradual change of form, but this change we will leave for the present out of consideration. The rays emanating from the intensily bright core of the Sun reach us, whatever be the position of the Earth, through a space in which matter is unequally distributed. P therefore determines the principal characteristics of what might be called the ‘‘optical system” through which we see the Sun. When P shifts its position, this system changes with it; when P for the second time traverses the same path on the rotating sphere, to the eye of the observer on Earth all the phenomena which are produced by the refraction of light in the gases of the Sun, will repeat themselves in the same order. 1) Had we for the Hornstein period taken 25,924 days, instead of 25,929, 95,924 2,32 then the mean value of the spot period would have been = 11.17 years. If therefore we wished to supplement the table on p. 272—273 with a value derived by theoretical considerations from the Ll-year period, the number 25,924 would commend itself. *) W. H. Junius, Proc. Roy. Acad. Amst. IV, p. 162—171, Il. THE VARIABILITY OF THE SOLAR RADIATION. It is well known that the composition as well as the intensity of the Sun’s radiation is incoustant. As to the variation of the total intensity, this could not be ascertained by actinometrical measure- ment, owing to the capricious disturbances caused by the clouds; it has therefore been determined in an indirect way, from the values of the mean temperature all over the Earth. But the variability in the composition of the light has been revealed by a careful study of the FRAUNHOFER lines which has shown that several lines are at one time more enhanced than at others (JeweLi') Hain’), LANGLRY®)). In the spectrum of sun-spots also, in which several lines are com- paratively very wide, N. Lockyrr‘*) noticed that the mean type of the spot-spectrum undergoes a periodical modification, the period of which coieides with that of sun-spot frequency. As yet we have no certain indications that this periodicity also exists in the varying aspects of the FRrRAUNHOFER lines of the average photosphere spectrum. The abnormal spectrum photographed by Harn’) in 1894 (ie. at a sun-spot maximum) presented, as has been shown elsewhere °), this peculiarity that the lines, which in the chromo- sphere spectrum are generally strongly marked (principally belonging to Fe, H, Ca, Sr, Al, 72), were very faint, whilst the strong lines (belonging to Zr, Mn, Y, V and some of unknown origin) did not correspond to any of the chromospheric lines. The periodical variability observed by Lockysr in the spot spectrum consisted herein, that when: at spot maximum the most enhanced lines were selected, they proved for the greater part to be “unknown lines” i.e. lines which in the normal solar spectrum are extremely weak, and that the strong lines of Me, Nz, 7%, which during minima of spot periods often appear very wide, were then searcely visible. 1) Jewett, Astroph. Journ. 3, 89—113, 1896; 11, 234—240, 1900. 2) Hare, Astroph. Journ. 3, 156—161, 1896; 16, 220—233, 1902. 3) Lancrey, Annals of the Astroph. Observatory of the Smiths. Instit., Vol. I, 1900. On p. 208, 209 and 216 mention is made of irregular changes in the heat spectrum (especially in ®, # and ©), which do not seem to be occasioned by absorption in our atmosphere and are therefore the effect of cosmic influences. Lanetey’s excellent method of investigation may prove of the utmost value in the study of the variability of the Sun’s radiation, as il gives directly comparable values for the energy of the various kinds of rays in this important part of the spectrum. 4) Lockyer, Proc. Roy. Soc. 40, p. 347; 42, p. 37; 46, p. 385; 57, p. 199; 67, p. 409, (1886—1900). 6) Hare, Astroph. Journ. 16, 220—233. 6) W. H. Junius, Proc. Roy. Acad. Amst., IV, 589— 602, (ITT The analogy between these abnormal appearances and those of the spectrum of Hare is obvious. Unfortunately the part of the spectrum investigated by Lockyrr (extending from 24863 to 25893) lies entirely outside the part photographed by Ha um (4 38812—a 4132) which renders direct comparison impossible, but the parallelism to which we pointed, makes us anticipate that also in the aspect of the average photosphere spectrum, as well as in the spot spectrum, the 11-year period will be found. Lockyer holds that in years of spot maximum the Sun’s activity is greatly increased; that the more violent eruptions then cause a considerable rise in its temperature. To this fact he ascribes the appearance of “unknown lines” and the weakening of the known lines, on the same principle as that which governs the variations produced in the emission spectra when passing from the are to the induction spark *). On the other hand Cu. NORDMANN *) has published the results of an exhaustive inquiry into the variations of the temperature all over the Earth, between the vears 1870 and 1900. From his statements it appears that the mean temperature undergoes indeed a periodical variation coinciding with the sun-spot period, but in this manner, that the maxima of the curve of spot frequency correspond to the minima of the temperature curve. This result seems to us a serious objection to the views of LOCKYER. We will now see if by applying our theory, based on the disper- sion of light, if is possible to find a consistent explanation for the results both of Lockypr and NORDMANN. To us the peculiarities of Lockyrr’s spot spectrum are phenomena of the same nature as those observed in the abnormal spectrum deseribed by Hair. We have found an explanation for the latter by supposing that just at the time when the photograph was taken, a long corona streamer was directed to the Earth, so that the line of sight almost coincided with the tangent af a surface of discon- tinuity. The visible structure of the corona with its long, almost straight lines, is to us an indication that the light of the Sun, accor- ding to the position occupied by the Earth, must at one time reach us along sharply defined surfaces of discontinuity and at others not. Provisionally neglecting possible variations in the distribution of matter which might take place in the Sun itself, the condition for each successive moment will be accurately defined by the place 1) LockyErR, Proc. Roy. Soc. 67, p. 411—4J6, (1900). *) Cu, NoRpMANN, G. R. 136, p. 1047—1050, (1903). 19 Proceedings Royal Acad. Amsterdam. Vol. VI, occupied by P in its helical course on the sphere, and we need only admit that at sun-spot maximum the separate rays of the total beam of light reaching the Earth, and from which PA is the central line, more often pass for a considerable distance closely along surfaces of discontinuity, than in times of minimum. If we admit this view, then our explanation of the spectral peculiarities reads thus: A monochromatic beam of light, passing on its way closely along a surface of discontinuity, will undergo a marked change of diver- gency, When, for those particular waves, the medium has a great (positive or negative) refraction constant. We may rather expect an increase than a decrease of the divergency, because the medium becomes more rarefied with the increasing distance from the Sun’s centre. As a rule such a beam will reach the Earth with a lesser intensity than the beams of rays which undergo less refraction. The consequence is that, through the scattering of neighbouring rays, all FRAUNHOFER lines which cause anomalous dispersion will have a somewhat darkened background. With some lines this background is broad (//, A, the lines of hydrogen, iron, in a word, all the well known widened lines of the solar spectrum); with others it is narrow; it depends on the proportion of these elements contained in the solar atmosphere and on the shape of the dispersion curve; but at all events, the mean intensity over the entire spectrum must have become less, by the light passing along the surfaces of discon- tinuity. In years of sun-spot maxima this happens more often than at minima, and this gives us the explanation of the results obtained by NORDMANN. *) It now remains for us to prove that the same cause, which in the period of spot maximum makes weak lines in the spot spectrum to appear strengthened, makes also strong lines to appear weakened. We again refer to our explanation of the abnormal spectrum of Harn. At that time we supposed the structure of the corona to be “tubular”. Later considerations have induced us to define the structure of the exterior parts of the Sun as rather “lamellar”, a correction 1) The kinds of rays which by dispersion have disappeared from the sunlight visible to us, travel to other parts of the universe, far from the orbits of the planets, where they would be seen as faculae, chromosphere light and corona light. If it were possible, by means of the spectroscope there to study the mean radiation, we should find in the continuous spectrum some bright lines, lying on both sides of the real absorption lines and in close proximity to them. Some stars present this phenomenon. It may, therefore, be explained by the assumption that they are bodies resembling the Sun, but that our line of sight forms a rather large angle with their equator. ( 279 ) which does not affect the arguments of our former conclusions. When the light travels through this stucture almost parallel to the surfaces of discontinuity, the most strongly refracted rays follow undulating paths (vide Proc. Roy. Acad. Amst. IV, p. 596—597). They are kept together, are so to speak guided along the lamellar structure, and their intensity when reaching the Earth is greater than that of rays which undergo a lesser refraction. Consequently in the FRrACNHOFER lines which show a broad background (being produced by elements which are rather strongly represented in the coronal gases and which therefore, even during the minima of spot periods, give rise to marked anomalous dispersion) the parts nearest to the true absorption line will at periods of spot maxima appear brighter. In fact, the greater ray-curving, which marks these periods, enhances the shadowy background, but at the same time it restores the light to the central parts of the band. Thence the impression that the absorption line has been weakened. On the other hand, lines with a faint, narrow background will at times of maxima appear considerably strengthened, because their brighter central parts, if present, are too narrow to be visible. The explanations here given are supported by the results of an experimental investigation. a detailed account of which will appear elsewhere. Our object was to ascertain the action of a system of artificial surfaces of discontinuity on the absorption spectrum of sodium vapour. In principle the apparatus is similar to that deseribed in my paper: “On maxima and minima of intensity sometimes observed within the shading of strongly widened spectral lines *).” A beam of electric light, which had first been passed through a long sodium flame was directed on the slit of a big grating spectroscope. But a great improvement had been since made in the burner. The aperture is 75 e.M. long and 0.15 ¢.M. wide; the supply of an adjustable mixture of gas and air is so regulated that the flame burns evenly over its whole length. A special contrivance within the burner allows of the feeding of the flame with sodium vapour during the experiment and regulating the quantity as required. By means of this instrument we tested the effect on the absorp- tion spectrum of the variations in the angle of inclination between the planes of discontinuity and the beam of light; of modifica- tions in the quantity of sodium vapour; of diaphragms on the path of the rays, ete. All the phenomena observed may be explained 1) W. H. Juurus, Proc. Roy. Acad. Amst. V, p. 665. 19% ( 280 ) from the different measure in which the anomalously dispersed rays are curved; and the varying peculiarities of the sun-spot spectrum are easily reproduced in this experiment. We make particular mention of the fact that, when the flame is parallel to the beam of light, a small quantity of sodium vapour produced very dark enhanced D lines, e. g. 0.5 or 1 Angstr. units wide; by adding more of this vapour the lines extended into very wide bands in which the central portions became gradually brighter, leaving only a narrow, well- defined central absorption line. EEE: THE PERIODICAL VARIATIONS IN THE APPEARANCE OF THE SUN. Sunspots and faculae. In a communication dated Febr. 19007) 1 started the hypothesis that sun-spots are the results of refraction, more especially of ano- malous dispersion. Since then Esrrt*) has published an experiment in which, through the dispersion of the light of an are lamp in a flame of burning sodium, effects were produced, closely resembling the phenomena observed in sun-spots, such as their spectral peculiar- ities, reversals, displacements, ramification of the lines, ete. I have recently repeated this experiment, but instead of using pieces of burning sodium, I employed the long flame, which afforded greater facility for controlling the operation and noting the phenomena. They were substantially the same as those observed by Eprrr. Moreover, the use of the long flame enabled us to make some observations with respect to the optical effects of almost flat surfaces of discontinuity. Similar surfaces being important factors in our theory, a short description of our experiment may be found useful. The light of an are lamp was concentrated on a diaphragm 15 m.M. in diameter, which was placed almost in the focus of a second lens. The emergent rays were slightly divergent; within this beam, at a distance of 20 M., a telescope was placed and focussed on the lens. By pushing out the eye-piece an enlarged image of the lens was projected on a screen; this represented the Sun. Between the lens and telescope, but close to the former, was placed the long flame. When the mouth of the burner was so adjusted as to lie exactly parallel to the axis of the beam, so that the prolongations of the surfaces of discontinuity intersected the objective of the telescope, 1) Proc. Roy. Acad. Amst. II, p. 585—587. 2) H. Eperr, Die anomale Dispersion glühender Metalldämpfe und ihr Einfluss auf Phiinomene der Sonnenoberfläche. Astron. Nachr, 155, 5, 179—182. ( 36%) there appeared on the screen a system of two very dark spots, corresponding to the two sheets of the tlame, in which the combustion principally takes place. Even a slight change in the position of the burner had a marked effect on the form of the spots. By turning it a few degrees round a vertical axis the distinct spots rapidly disappeared ; but then, of course, over a larger space of the illu- minated surface quivering shadows of varying intensity remained visible. Let us now more fully consider, what, in the present state of our knowledge, we may take the structure of the gaseous Sun to be. We find there the surfaces of revolution, first deseribed by EmpEN '), surfaces of discontinuity, where according to v. HermHorrz undulation and formation of whirls take place. It is not unreasonable to suppose that the striped appearance of the corona presents to us, in some way, the generatrices of these surfaces, although at present we cannot enter into the question of how this takes place. As a rule it will be found that the density varies most rapidly in the direction perpendicular to the planes of discontinuity ; and wherever the whirling process is going on, the density will be least in the axes of the whirls. In broad terms, therefore, the structure of the Sun may be called lamellar and at the places where whirls are formed, we would rather call it tabular. The position of the whirls in the surfaces of discontinuity is varying, but the average direction of the axes of the whirls coincides with the generatrices of the surfaces of revolution. The prolongations of some of the surfaces of discontinuity intersect the Earth; whenever this happens, our line of sight, when directed on the Sun, very nearly touches a sheet of such a surface. These sheets are projected on the Sun’s dise in the form of bands of greater or lesser width, stretching parallel to its equator. The narrower these bands are, the nearer our line of sight really touches the surfaces of discontinuity and the greater will therefore be the effect of refraction, i.e. the dispersion especially of the anomalously refracted light. The width of these projections on the various parts of the Sun’s dise will of course vary with the position oeeupied by P on the sphere /. If the axis of a whirl falls exactly in the line of sight, we see a dark speck. In parts where the whirling process is very active, the separate axes of the vortices need not be parallel to each other, but it is essential that they should all lie in the surfaces of discon- tinuity. This explains why a spot, i.e. an accumulation of a great ‘) R. Eupen, Beiträge zur Sonnentheorie. Ann. d. Phys. [4], 7, p. 176—197, ( 282 ) many whirls, notwithstanding the Sun’s rotation, may remain visible for a long time, although continually changing its form, for we really look along a succession of other axes of whirls. The experiment deseribed above, may serve to illustrate the fact that whirls, situated in surfaces of discontinuity which are not projected in very narrow bands, will not be seen as distinct spots. This is e.g. the case with whirls, formed at more than 30° heliographic latitude. Near the equator also spots are rarely seen; but this follows, according to Empry’s theory, from the circumstance that in those regions there is less cause for the formation of whirls. To resume, spots will be seen in those parts where the distri- bution of matter is such as to cause an abnormal merease in the divergency of the beams of light on their way to the Earth. As a matter of course, there must also be parts where the distribution of density causes a decrease in divergeney and these are the places where fuculae are seen. On a smaller scale we find the same con- trast in the so-called ‘pores and granulations” of the photosphere. All these solar phenonema are subject to rapid changes, because the complicated optical system through which the rays of light reach us, continually alters its position with respect to the Earth. The periodicity of the sun-spots. We will now endeavour to prove that in order to explain the 1l-vear period in the frequency, the total spotted area and the mean heliographic latitude of the sun-spots, we need not admit the hypothesis of a periodical change in the Sun’s activity”. Let us for a moment suppose that all actual changes in the form of the Sun suddenly came to a stand-still, but that its rotation con- tinued; even fen an v-vear period would be observable in the Sun's appearance, the position of spots and faculae etc, because each time, after .« years have elapsed, the point ? follows again nearly the same path. However, the real configuration of the Sun is „ot perfectly con- stant (although probably its change is very slow and gradual) and so we may consider the 11-year period to be the result of the joint action of a continuous (perhaps somewhat irregular but not necessarily periodical) change in the Sun's surfaces of discontinuity, together with the periodical variation in the position of the Earth with respect to the “average rotating sun). We define the meaning of this latter expression by our sphere J, whose synodical period of revolution coincides with the period of circa 26 days, which has been noted in terrestrial phenomena. ( 283 ) It seems expedient here to enter somewhat further into the question as to how the periodical change of position of our point of view may cause the number of spots seen in the course of a year era- dually to decrease for a period of 6 or 7 years, then to go on increasing, till after 11 years the maximum is reached again. With that object we again refer to our spiral and start from the 14 convolutions of the year of spot maximum. The second year’s spiral is slightly shifted with respect to that of the first, but it runs still very close to it and therefore its position with regard to the system of surfaces of discontinuity will resemble that of the first, which was the most favourable for the observation of spots; thence we may conclude that the difference between the number of spots seen in the first and second year will be but small. The spiral of the third year diverges again from that of the second and is consequently somewhat farther removed from the spiral, which traversed the series of optical combinations most favourable to the observation of spots, and so on. We must not lose sight of the fact that the track of P has but a slight inclination with respect to the surfaces of discontinuity, so that at one time the Earth may remain for a rather long while under the influence of such surfaces, at other times, during much longer periods still, may pass between them. There is no reason to expect that the decrease in the number of spots seen will proceed in a perfectly regular manner, but at all events there must be a vear-spiral in which the circumstances are most unfavourable for their observation ; for in proportion as the twelfth spiral is approached, which nearly coimcides with the first, the con- ditions must necessarily again improve. The length of the spot period is irregular and the height of the maxima varying. This would already be the case, were the Sun totally stationary, for the twelfth spiral of ? does not exactly coincide with the first; besides it is evident that modifications in the distri- bution of matter may cause even greater irregularities in the suecessive fluctuations. 2. Prominences. On a former occasion ') we have already given an explanation of the appearance of prominences and their spectral peculiarities, based on our hypothesis that they are due to the anomalous dispersion of the photosphere light in the whirling parts of the surfaces of discon- 1) Proc. Roy. Acad. Amst. IV, p. 162. ( 284 ) tinuitv, which are seen projected on the edge of the Sun's dise. It will now be easy to determine in how far they are connected with spots and faculae and to understand, that, like the spots and for the same reasons, they may be expected to show a certain periodicity in their frequency and place of appearance. The so-called) metallie or eruptive prominences are only seen in the vicinity, at least in the zones, of the sun-spots, never in the polar regions. Nebulous prominences, on the contrary, are found in all latitudes. In accordance with our theory this fact may be thus explained. The anomalous dispersion of the kinds of light found in the spectrum of the metallic prominences near the lines of Na, My, Ba, Fe, Ti, Cr, Mn, is less intense than that of the light close to the lines of A, He, Ca; and therefore greater differences in density will be necessary to produce eruptive than nebulous prominences (in which asa rule only the lines of H, He and Ca are seen). The results of EMDEN’s inves- tigation in fact prove, that a more active formation of vortices may be expected in medial latitudes than in the equatorial or polar regions. The zones where prominences appear must extend farther than those where spots are seen; for as soon as we have gained a clear conception of the direction of the surfaces of discontinuity and of the axes of the whirls in them, it becomes plain that to see spots, the position of the Earth with respeet to the structural elements of the Sun is subordinate to preciser conditions than in the case of promi- nences. For prominences are visible as soon as the line of sight, directed on the apparent edge of the Sun, passes closely along a series of whirls; more particularly so, when the line of sight touches the surface of discontinuity near the whirling area. In order to see spots it is not only essential for the line of sight to touch the surface of discontinuity in the area of the whirls, it must at the same time coincide with the direction of their axes. The periodicity of prominences. The parts of the Sun’s edge where at a given moment the prominences appear, will not only be determined by the condition of the Sun itself, but at the same time by the position of P. Consequently the periodicity in the frequency and position of the prominences must agree with the periodicity of the motion of i A eraphie survey of the periodicity of spots and prominences in eonnexion with their heliographie latitude has been given by Sir N. Lockyer and W. J. Lockyrr') in a paper on “Solar prominences and spot circulation from 1872—1901.” In some of their former communications?) the same observers had already alluded to the fact l) Sir N. Lockyer and W. J. S. Lockyer, Nature 6 2) The same authors, Nature 66, p. 249; 67, p, 37 7, p. 569—571, (1903). ip ( 285 ) “that the epochs of maximum prominence disturbance in the higher latitudes are widely different from those near the equator. The latter are closely associated with the epochs of maxima spotted area, the former occur both N. and S. at intervening times.” Now it follows from our theory, that prominences are seen in places where the line of sight touches whirling parts of surfaces of discontinuity near the Sun’s edge; so it is evident that at spot maxima this will happen most often in the spot zones, and that the most favourable occasions for seeing them in other latitudes fal! at other times. Therefore, although in the curve of prominence frequency the 11- year spot period is easily recognized, yet in several points it deviates from the spot curve. Smaller maxima and minima of frequency are superposed upon the head curve and point to a three-year period. We find a rational explanation for these minor fluctuations too in the successive positions assumed by the Sun with respect to the Earth. IV. THE PERIODICITY IN THE VARIATIONS OF METEOROLOGICAL AND EARTH-MAGNETIC ELEMENTS. 1. Do these phenomena require the hypathesis that the Sun exhibits a varying activity? In the preceding pages we ascribed the inconstancy of the solar phenomena principaliy to the continuous change of the point of sight from which we look at the Sun. We supposed the modifications, produced in the general condition of the body of the Sun itself by radiation and by the relative motion of the gaseous layers, to be comparatively slight and regular. Our theory had no need of the interference of violent eruptions, commotions, periods of increased or decreased solar “activity”; it allowed us to consider the quantity of energy emitted by the Sun in a unit of time, to be almost constant. For this reason it would now at first sight seem more difficult yet to account for the periodical variations of several terrestrial phenomena which closely follow in their course the frequency of spots and prominences. But even with the hypothesis of a variable solar output as a starting point, as far as I know, nota single theory has been advanced in explanation of the connexion between sun-spots and terrestrial phenomena, so convincing, that it would be a pity to abandon it. Let us briefly consider what has been attempted in that direction. Periods of maximum spot frequency are marked by certain commo- tions on Earth and by inereased circulation; the rainfall is greater, ( 286 ) cyclones, polar lights, magnetic deflections are more frequent. But because at those times the mean temperature over the entire Earth is somewhat lower than in the minima periods') we come to the conclusion that the total energy which reaches the Earth in maxima of spot cycles must actually be less. This is our first objection to any explanation based on a periodical variation in the total output of the Sun’s energy. Now it might happen that, although im years of spot maxima the average output of solar energy be lessened, the emission exhibits at those times a greater variability than at minima. Various and numerous observations have been undertaken with the object of ascertaining whether the appearance of spots and faculae, or their crossing the central meridian of the Sun, was generally accompanied by excessive manifestations of terrestrial phenomena, and the results proved that this was of invariably the case. An exhaustive inquiry into this question has been recently made by A. L. Cortin®*). The investigations of Farner SIDGREAVES, extending over the years 1881—1896, had already clearly shown that periods of increased solar activity were indeed marked by violent magnetic storms, but that many spots were not accompanied by magnetic disturbances and that such disturbances often took place when the Sun was spot-free. “These results’, says Corvin, “are adverse to any theory which would place the cause of magnetic storms, and by the cause we mean the efficient cause, any where on or in the vicinity of the Sun.” He himself for three years (1899— 1901) studied the appearances of the Sun’s face in connexion with the magnetic curves registered at Stonyhurst. He found that the annual means of spotted area and of the variations in declination fairly agreed; but his table on p. 207 shows that this is not the case when the average results for each single solar rotation are studied; and the immediate comparison of the daily solar observations with the diurnal magnetic curves shows more clearly still, that spots and disturbances do not necessarily always go together. For example, during a great magnetic storm on Febr. 12 1899, the Sun was almost entirely free from spots, and the very large spot observed in May 1901, which persisted during two solar rotations, was not accompanied by any unusual magnetic disturbance. CorTin comes to the conclusion that sun-spots and magnetic storms probably are correlated as “two connected, though sometimes independent effects of one common cause.” 1) Cu. NoRDMANN, CG. R. 136, p. 1047—1050, 1903. 2) A. L. Cortiz, S. J., Astrophysical Journal 16, p. 203—210, 1902. If, therefore, spots and faculae are not in themselves the factors Which by their peculiar radiation of light and heat cause the supposed fluctuations in the output of solar energy, it might be expected that entirely different agencies play the most conspicuous part in the production of the phenomena under consideration. In this sense ARRHENIUS') has started an hypothesis in which the latest discoveries in connexion with the kathodic rays, the ionisation of gases, the properties of ions and electrons and the pressure of radiation have been introduced. He attributes the said periodical phenomena on Earth to solar matter, charged with negative electricity and being propelled from the Sun’s surface by certain centres of activity there present (thus accounting for the period of 25,929 days). The amount of electricity thus generated varies with the Sun’s activity, it being greatest at maxima of spot frequency. This solar matter is scattered through space by the pressure of radiation and causes the higher layers of the terrestrial atmosphere to be charged with negative electricity. By the discharges kathodic rays and polar lights are produced; the electrified particles, carried along by the wind, form electrical currents which disturb the magnetism of the Earth. Several points of this theory have been criticised by Cu. NORDMANN ®), who offers an entirely different explanation for the variable influence of the Sun on meteorological phenomena. He ascribes it to long electrical waves, sent out by the Sun, more particularly in the regions of spots and faculae, and at times of maximum spot frequency. Whenever these Hertzian waves penetrate into the higher layers of the atmosphere, they increase their conductivity and render them luminous. In this manner he accounts for the fact that during spot maxima stronger electrical currents are present in the atmosphere, magnetic variations are more marked and polar lights more frequent and intense. But we have seen before that neither important magnetic disturbances nor intense polar lights invariably accompany very conspicuous solar phenomena. NORDMANN’s theory therefore requires the admission of the existence on the solar surface of separate emission centres of long electric waves, independent of spots and faculae. This hypothesis does not simplify our conception of the constitution of the Sun. Bierrow*®) ascribes the influence of the Sun on the magnetism of 1) Arruentus, Rev. gén. d. Sc. 13, p. 65—76; Lehrb. d. kosm. Physik, S. 149—155. 2) Cu. NoRDMANN, Rev. gén. d. Sc. p. 379—388. *) Bicerow, Solar and Terrestrial Magnetism, U. S. Weath. Bur. Bulletin No. 21, 1898; Eclipse Meteorology and Allied Problems. Washington 1902. p. 104. ( 288 ) the Earth for the main part to direct magnetic action of the Sun; he supposes the magnetic condition of the Sun to be very variable. Jut as Lord Kenvin') has demonstrated that the solar magnetism and its variability ought to be enormous to produce, by direct induction, these disturbances of the terrestrial magnetism, BierLow also admits a variable generation of electricity in the higher layers of the at- mosphere, through the ionising action of the Sun’s inconstant radiation. These views of BignLtow have been analysed and criticised by ScuusTER?). All these theories fail in one important point. Indeed, the meteoro- logical and earth-magnetic disturbances generally manifest themselves in such a manner that they cannot be considered simply an increase or decrease of normal activity. For instance in the case of magnetic storms, the disturbance-vector is entirely out of keeping with the normal daily variations. The capricious origination and course of the barometric depressions, which play so prominent a part in deter- mining the weather conditions in many parts of the globe, cannot be explained as merely resulting from increased ordinary atmospheric circulation; and many more examples might be added to these. We must therefore consider the nature of the cosmic influence to be such, that, although emanating from the Sun and striking the Earth within cones whose opening is only 17,6" wide, it notwith- standing acts very differently in the various regions of the globe. Moreover, this influence distinctly shows a semi-annual periodicity. As yet no theory, based on the conception of a variable solar output, has been found to account for these striking characteristics of the cosmic influence. If then, in order to explain the periodicity of solar phenomena, it has not been necessary to admit a varying activity of the Sun, we need not be deterred from accepting this conclusion by the consideration that it implies the abandoning of all prevailing ideas as to the influence of the Sun’s activity on meteorological disturbances. 2. Lyects of the movement of the Earth through the irregular field of the Sun's radiation. When the rays of the Sun fall through a piece of ordinary window- glass on a distant screen, we notice an irregular distribution of light. In the same manner we imagine the rays proceeding from the inner parts of the Sun, after traversing the outer and thinner layers, 1) Lorp Kervin, Nature 47, p. 107—110. (1892). 2) Scnuster, Terrestrial Magnetism 3, p. 179—183, (1898). ( 289 ) to spread with unequal intensity through space. Consequently the Earth moves through an irregular field of radiation. And although we know the refractive power of the coronal gases to be but small, still we may assume that those kinds of rays, which undergo anomal- ous dispersion, will be lable to a rather strong incurvation and their beams to variation in divergency, especially in those places where they travel closely along the surfaces of discontinuity. On this principle we base our explanation of the periodically varying influence, which an almost unchanging Sun exercises on terrestrial phenomena. A. The semi-annual and annual periods in the position of the Earth in the irregular field of radiation. At great distances from the centre of the Sun the surfaces ot discontinuity become nearly flat. Those which are near the plane of the equator will be almost parallel to it. This assumption is in har- mony with the appearance of the structural lines of the outer corona as well as with theoretical considerations. If now we suppose the surfaces of discontinuity to be (geometric- ally) prolonged to the orbit of the Earth, it is evident that they will intersect ifs surface in a series of parallel circles, but the position of these circles with regard to the parallels of the Earth, will change with the position of the Earth in its orbit. Let us consider some particular positions. Fig. 2, a represents the position of the Earth on the 21st of March, as seen from the Sun, In the spring the Sun’s south pole is ( 290 ) turned towards the Earth; on the 5" of March the Earth moves through that point of its orbit which lies farthest from the plane of the Sun’s equator. In our diagram the latter might therefore be represented by a line running almost parallel to the ecliptic /, ata little over 7° heliographie latitude to the north of it. (The radius of the Earth is only 8",8). The prolongations of the planes of disconti- nuity at 7° south of the Sun’s equator being still almost parallel to it, their position may be indicated by the dotted lines ¢ which, on the 21st of March, are only slightly inclined to /. In Fig. 2, 6 we see the illuminated hemisphere of the Earth on the 21st of June. A short time before, on the 4% of June, the Earth passed through the nodal line of the Sun’s equator and the ecliptic, so that, on the 21st of June, the planes of discontinuity ¢ may still be represented by lines with an inclination of about 7° to the ecliptic. Fig. 2, ¢ shows the position on the 22¢ of September; at that date the Sun’s equator lies south of the Earth. Fig. 2, d represents the position of the Earth on the 21s* of December. From these diagrams it is plain that about the time of the equi- noxes any point on the strongly illuminated parts of the Earth (we except those places where the Sun stands low) in its diurnal rotation always moves in the same sense with regard to the planes of dis- continuity, making with them rather large angles (about 23°). But soon after the solstices, in the beginning of July and January, at midday the said point will move about parallel to the planes of discontinuity; in the morning and in the afternoon its movement with regard to these planes is in contrary directions. Now, as in the system of the surfaces of discontinuity the most rapid changes of density occur in a direction perpendicular to the surfaces, it follows that any point on the Earth, in its diurnal move- ment, will pass through a greater variety of conditions in spring and autumn than in winter and summer. Besides it is evident that the variations in the said conditions will be less marked in the winter than in the summer solstice, because in the former season the days are so much shorter. We may therefore expect an annual variation in the amplitude of certain daily inequalities showing the following periodicity : maximum end of March minimum beginning of July maximum end of September minimum beginning of January ( 291 ) whilst, especially in the temperate zones, the winter minimum will be lower than that of the summer. Let us here once more eall to mind the optical significance of the surfaces of discontinuity. As a rule they impart a greater divergence to the beams of light which travel closely along them; consequently at their intersection with the surface of the Earth they determine zones where the illumination will be weakened, whilst in the intermediate regions it will be strengthened. This does not apply in the same measure to every kind of light in the spectrum, but especially to the waves which undergo anomalous dispersion. All terrestrial phenomena which are governed by the conditions of illumination will therefore, to a greater or lesser extent, be sub- ordinate to the above-mentioned periodical variations. There is probably still another reason for the greater variability of the effects of radiation in spring and autumn than in summer and winter. It is namely not improbable that in regions 6° or 7° distant from the Sun’s equator greater differences of density will be found along the surfaces of discontinuity, than in the equatorial zones. B. The perwdicity of the fluctuations of illumination which comcides with the periodicity of solar phenomena. In the course of a certain number of years the Earth deseribes through the system of the surfaces of discontinuity a somewhat complicated path, which we have represented by the track of P on the sphere B. The Earth therefore continually comes under the influence of another portion of the system; and the phenomena appearing on the Sun inform us whether, in a certain space of time, the light on its way to the Earth passes more or less often closely along surfaces of discontinuity. For this circumstance is intimately connected with the frequency of prominences and sun-spots and with the aspect of many of the FrAUNHOPER lines (especially in the spot spectrum). A so-called “maximum of solar activity’? means, that the Earth during that period has been many times intersected by the prolongations of sharply defined surfaces of discontinuity, and all the terrestrial phenomena resulting from the variations of illumination will then also be at a maximum. As to the nature of the connection between sun-spots and promi- nences on the one hand and the values of meteorological and mag- netic variations on the other, it has been universally conceded that no other definition was possible but this: “that they were the effects of one and the same common cause.” We believe to have found this common cause in the varying ( 292 ) position of the Earth with respect to the surfaces of discontinuity and in the fluctuations inthe conditions of illumination resulting from it. Not only the fluctuations in the total intensity of illumination, but the changes in the composition of the solar light also, will have their significance in this respect. 3. Polar lights. Polar lights belong to that class of phenomena which seem but little influenced by the local conditions on the surface of the Earth. The altitude at which they originate has been variously estimated ; it is generally supposed to be very high, several kilometers. No one doubts but that this phenomenon is closely connected with the solar radiation, an opinion supported by the existence of a daily period with its maximum at 2'40™ p.m. and its minimum at 7'40™ a. m. (CARLHEIM-GYLLENSKIOLD). Most probably polar lights owe their origin to the discharges of electricity generated during the day in the higher layers of the atmosphere through the ionising action of the Sun’s irradiation. If this be so, local differences in the Sun’s irradiation must favour the appearance of polar lights and consequently we may expect in their frequeney the semi-annual and annual periods described under A as well as the less regular variations spoken of under J. The following table, taken from the Lehrbuch der kosmischen Physik by Arruenius, p. 913, gives a survey of the frequency of polar lights from the enumerations made by EkKnorm and ARRHENIUS for various parts of the globe. Sweden. Norway. Iceland and U.States of Southern Greenland. N. America. Polar lights. 1883—1896. 1861—1895. 1872—1892. 1871—1893. 1856—1894. January 1056 251 804 1005 56 February 1173 331 734 1455 126 March 1312 335 613 1396 183 April 568 90 128 1724 148 May 170 6 1 1270 D4 June 10 0 0 1061 40 July D4 0 0 1223 30 August 191 18 4O 1210 75 September 1055 209 455 1735 120 October 1114 355 716 1630 192 November 1077 326 811 1240 112 December 940 260 863 942 81 ( 293 ) The last two columns distinctly show the expected periodicity : maxima in March or April and in September or October, minima in June or July and December or January, whilst in each case the Winter minimum is lowest, although the lone winter nights favour the observation of polar lights. In the other three columns, dealing with higher latitudes, the summer maximum, as ARRHENIUS observes, is only apparently so low, because in these regions no time is left for the observation of polar lights owing to the length of the days. The data collected by Frirz and Arruenivs (Lehrb. d. kosm. Phys. p. 915), moreover afford sufficient evidence that the sun-spot period too is reflected in the freyuency of polar lights. 4. The annual variation in the diurnal inequality of terrestrial magnetism. It is an acknowledged fact that the magnetism of the Earth is under the influence of the Sun’s irradiation. In recent years this view has been strengthened by the appearance of magnetic disturbances within the belt of totality during total eclipses of the Sun. Let us suppose the mean magnetic force at every point of the Earth to be represented by a vector. If we now represent the daily varia- tion by an additional, variable vector, the whole of all these additional vectors will form the ‘‘variation field”. Scuustmr and v. Brzorp have computed and constructed this field and shown that by its move- ment from east to west with a velocity of 15° an hour, a fairly accurate idea may be obtained of the diurnal deflections of the mag- netic needle on all parts of the Earth. This “variation field”, according to Scuusrer, is formed for about */, parts by electrical currents in the atmosphere and for */, part by Earth currents. By the electrical current in the atmosphere we under- stand a convection current formed by electrified particles, which are carried along by the cyclonic and anticyclonic movements of the general circulation. This theory of Scuuster and v. Brzorp therefore implies that the diurnal magnetic variations will increase both with the intensity of the general circulation and with the amount of ionisation in the higher layers of the atmosphere. If one or both of these processes are in a great measure influenced by the variability of solar irradia- tion (which is not improbable, vide Arrupnius, Lehrbuch p. 886, 888, 890, 898), then all the periods which according to our theory occur in the variability of the Sun’s irradiation must find their counter- part in the diurnal inequality of the elements of terrestrial magnetism, 20 Proceedings Royal Acad, Amsterdam, Vol, VI, ( 294 ) A clear and concise exposition of the variations of terrestrial magnetism has been recently published by Curren?) The “mean monthly range” of a magnetic quantity is according to his definition: “the difference between the greatest and least of the twenty-four hourly values in the mean diurnal inequality for the month in question, based on the five quiet days selected for the month by the Astronomer Royal”. If this range be represented by f and if S means the number by which Worrer expresses the sun-spot frequency, we have, according to Curer, the following relation : R=a+by. His investigation extends over the 1l-vear period 1890—1900. He divides the twelve months into three seasons: November to February : winter; March, April, September and October: spring and autumn; May to August: summer, and finds the following values for « and 6. Declination. Inclination. Horiz. int. Vert. int. a hb a b a b a b Winter | 3.23 0.0323 0.63 0.0105 105 0.461 7.0 0.032 Spring and | 739 90478 | 12 0.047 | 235 0.921 | 172 0.096 autumn) | Summer | 891 0048 | 41.61 0.0137 | 30.6 0.190 | 99.7 0.055 | : | | Mean 6.49 0.0410 1.17 0.0130 DAR 0.191 15.6 0.031 | | | a marks the variability according to the seasons, irrespective of the spot-period. b shows in how far the influence of the spot-period depends on the seasons. S in the period under consideration oscillated between 0,3 and 129,2, its mean value being 41,7. From the point of view of our theory these figures prove that : a in each element shows a minimum in winter and a maximum in summer; this we explain by the greater intensity of the Sun’s irradi- ation in summer increasing both the general circulation and the generation of electricity. But the table shows also that the values of a in spring and autumn are invariably greater than the mean value for the whole year; this points to superposed macima during the equinowes, and this we ascribe to the way in which the variability of illumination is dependent on the position of the Earth’s axis with respect to the surfaces of discontinuity, (periodicity A p. 289). 1) Curee, Preliminary Note on the Relationships between Sun-spots and Ter- restrial Magnetism. Proc. Roy. Soc. 71, p. 221—224, 1903. ( 295 ) In the values of 4 the periodicity A plays a far greater part than in those of a. That stands to reason; for the term 4S less concerns the amount of the general atmospheric circulation, than it does the peculiarities of the surfaces of discontinuity in respect to the Earth. In the values of the vertical intensity, 4, as compared to a, has a far lesser significance than in those of the other three elements. Curr makes the mean value of 4 over a whole year LOO and then arrives at the following values of 6 for the seasons. Declination Inclination Horiz. int. Winter 79 81 85 Spring and autumn 117 118 116 Summer 104 106 QQ Thus it appears that the amplitude of the diurnal inequality, taken absolutely, depends in a far greater measure on sun-spot frequency at the times of the equinoxes than at other times. The reason of this we find in the fact that the greater variety of sharply defined planes of discontinuity which at spot maxima intersect the Earth, causes greater diversity in its illumination when the projection of the diurnal motion on the normals to the planes is large, than when it is small. (Compare Fig. 2 p. 289). Now, if we consider the influence of the spot frequency not abso- lutely, but in comparison with the influence of the annual variation taken for average spot frequency, a relative value which Cure for ) expresses by the quotient ‚ then we obtain : a Declination Inclination Horiz. int. Winter 0:42 0.69 0.60 Spring and autumn 0.27 0.49 0.39 Summer 0.20 0.35 0.26 which shows that the influence of the spot frequency on the ampli- tude of the daily inequality is comparatively strongest in winter. This must be attributed to the fact that during a winter day the changes of position of a point on the globe with respect to the Sun and to the surfaces of discontinuity are proportionally small, and consequently the variations in illumination are then principally caused by irregular- ities, occurring in the system of the planes of discontinuity itself. The investigations of Curr were confined to the observations at Kew. A synopsis of the annual variations in the daily inequality of 2 ys the horizontal intensity, collected from the various readings in different parts of the globe between 1841 and 1899, will be found in Prof. Frank BigeLow’s “Studies on the Statics and Kinematics of the atmos- agi DIS phere in ‘the U. 5. of America”, p. o6 The figures tally in every respect with the above results. 5. Magnetic disturbances. If now we apply the preceding arguments to the irregular disturb- ances or magnetic storms, their explanation will offer no difficulties. We attribute these phenomena to extraordinary differences in density, which may at times be found on each side of the planes of discontinuity in the line connecting the Earth with the Sun. The system of the surfaces of discontinuity moves so rapidly with respect to the Earth, that almost all parts of the illuminated hemisphere are influenced simultaneously by the extraordinary local condition of the radiation field; whereas it is evident that the abnormal illumination at the same time may be more intense in some regions of the Earth than in others!). Consequently magnetic storms will be noticed everywhere almost simultaneously, and their effects will be almost identical in places lying rather close together, whilst, in regions farther distant from each other, they may be entirely different, perhaps quite opposite. Eris has made a study of the annual variation in the frequency of magnetic disturbances and classed them into certain groups. “Strong disturbances”, (over 1° in declination and 300 units of the fifth decimal in horizontal force) have two maxima, one in April and one in September; “weak disturbances” (10 and 50 units) show a maximum in summer and a minimum in winter. The characteristics of periodicity A (p. 289) at once strike us here, and it seems to us also to afford a satisfactory explanation in this case. Besides we find especially in the curve of the disturbance frequency an argument in favour of the opinion expressed on p. 291 viz. that along planes of discontinuity at 6° or 7° from the Sun’s equator, greater irregularities in the distribution of density will be met with than in the equatorial zones. And in the diurnal period of the disturbances, which in the tropics shows a maximum at midday, we see another argument in support of this assumption. After the explanations given under 2, it will cause no surprise to recognize in the magnetic disturbances the periodicity of solar phenomena. There is but an indirect connexion between magnetic 1) The rapid changes noticed in Hate’s abnormal spectra support this view. 7 storms and sun-spots, faculae, prominences. Both kinds of pheno- mena depend on the presence of sharply defined surfaces of discon- tinuity, but the appearance of the solar phenomena is more particularly determined by the direction and divergency of the rays of light in the vicinity of the ‚Su, whereas the terrestrial disturbances rather depend upon the divergency of these rays nearer the Zath. Therefore it may often happen that magnetic storms coincide with the appearance of large sun-spots, or faculae, or prominences, but this is not an indispensable condition. According to Lockyrr “great” magnetic storms are synchronous with maxima of prominence frequency near the poles of the Sun, whilst the curve for the mean variability of terrestrial magnetism is almost an exact reproduction of the curve for the prominence frequency in equatorial regions '). This fact may be explained as follows. The appearance of promin- ences near the poles is the result of the optical effects of parts of surfaces of discontinuity which are strongly inclined on the plane of the equator. We may assume that similar parts will also produce irregularities in the radiation field, at the site where the Earth is situated, and that the structure of these irregularities will not be parallel to the principal structure, i. e. to the solar equator. In moving along the Earth they must give rise to stronger and more evanescent distur- bances in the terrestrial magnetism than the irregularities corre- sponding to the normal lamellar structure, which makes but very small angles with the ecliptic. 6. The annual variation in the daily oscillations of atmospheric pressure. The polar lights and the variations of terrestrial magnetism are principally governed by conditions in the higher layers of the atmos- phere and but little by those on the surface of the Earth. The barometric pressure, the temperature, the rainfall, the direction of the wind and all meteorological phenomena which accompany them, are to a considerable extent influenced by the distribution of land and water. Among local influences, cosmic action therefore, will not be prominent in these latter phenomena. In the higher layers of the atmosphere the matter becomes much simpler, A short time ago BicuLow *) has called attention to the fact that 1) Lockyer, C. R. 135, p. 361—365, (1902); Proc. Roy. Soc. 71, (1903). *) BiceLow, Studies on the Meteorological Effects in the Un. States of the Solar and Terrestrial Physical Processes, Wheather Bureau No. 290, Washington 1903, ( oe) the well-known semi-diurnal period in the pressure, the atmospheric electricity, the vapour tension and the absolute humidity, disappears in proportion as higher layers of the air are examined and resolves itself into a simple diurnal period, having its minimum about 3" a. m. and its maximum at 3" p. m. However it is only in recent years that a systematic investigation of the higher layers of the atmosphere has been undertaken, prin- cipally in N. America and in Germany, and the results published until now are insufficient to deduce from them the cosmic periods. Anyhow, the same annual variation as that which marks the polar lights and the terrestrial magnetism has been observed in the diurnal oscillation of barometric pressure near the surface, notwithstanding the complexity of the influences there at work. The table here subjoined, taken from the handbook of ARRHENIUS p. 603, gives the mean amplitude of the semi-diurnal oscillations of the barometer, expressed in m.im., for the following places: 1) Upsala 59°52’ n. lat, 2) Leipzig 51°20’ n. lat, 8) Munich 48°9’ n. lat., 4) Klagenfurt 46°37’ n. lat, 5) Milan 45 28’ n. lat, 6) Rome 44°62’ Aat <7) 22 8075. Tats BLOEI ‚Jan. ‘Febr. Mreh | Apr. | May.| June.'July. | Aug. |Sept.| Oct. | Nov. | Dec. | Year 1) 0.43'0.14/0.15)0.16)0.44) 0.13 | 0.13)0.44) 0.17, 0.15 )0.11 0,16 [0,43 PANES Wee a) 0.90) 0.94) 0.27) 0,92 | 0.20 | 0.21 0.23 | 0.27 OPO VOLT KO MG KOTS | | | | | 3) | 0.24 | 0.931 0.28| 0.29} 0.28 | 0.96 | 0.25 | 0.26} 0.28! 0.97 | 0.21 | 0.5 bo a, 5 > Ot | A) } 0.930 89] 0.85) 0.96 | 0.26 | 0.25 | 0.24) 0.27 | 0.27 | 0.24) 0.21 | 0.24 | 0.97 5) 0-304:0:35.10 38 | 0.36! 0.30/ 0.29] 0.290 311.32 /@.33] 0.31 | 0.29) 0.32 3310.35) 0.32 | 9.29] 0.26 | 0.26] 0 30] 0.35 | 0.36) 0.33 | 0.991 0.31 0.66) 0 72/0 72/0 69 0.66 | 0.67 8) |0.79 | 0.801 0.83/0.82/0.73| v.65 | 0.65 | 0.69 |.0.75/ 0.78 | 0.82/ 0.79 | 0.76 | | | | | It will be seen that the maxima again coincide with the equinoxes; that the winter minimum for places above 45° lat. is lower than the summer minimum, thus agreeing in every respect with the perio- dieitv deseribed under A. It is indeed easy to understand that the amplitude of the fluctuations in the atmospheric pressure will increase or decrease according as the variability of the illumination increases or decreases. The circumstance that in lesser latitudes, north as well as south of the equator, the July minimum seems lowest, is ascribed by Arruenicvs to the fact that the Earth is at that time farther away from the Sun than in January. (AR) i. The annual and secular variations of atinospheric pressure. When we compare the system of isobars obtained for each separate month, it becomes at once apparent that the annual variation of the barometric pressure is very different in the various regions of the farth. In the tropies the fluctuations are generally insignificant; in the central parts of the continents of the temperate zones the atmospheric pressure is low in summer and high in winter; in mid-oeean this is the reverse; beyond 45° lat. south the pressure is uniformly low ; on the other parts of the globe the greatest diversity exists in its annual course. Nevertheless most of the annual curves (especially those of the temperate zones) display, next to local peculiarities, a common charac- teristic. They exhibit, more or less distinctly, two minima at the times of the equinoxes and maxima in winter and summer. The regions near the North Pole seem to make an exception to this rule (perhaps also those at the South Pole); there the maxima occur in spring and autumn and the minima in winter and summer. Some important statistics in connexion with the atmospheric pres- sure in N. America have been published in the Report of the Chief of the Weather Bureau 1900—1901. Vol. II. Chapter X treats of the annual and secular variations; there we find the monthly deviations from the mean barometric pressure over a certain number of years (1875—1899) arranged by Prof. Bicknow into 10 groups, according to the geographical position of the observation stations, and the mean annual course of these deviations charted for each group. The ten curves thus obtained show great differences, due to the more continental or more maritime character of the region to which they refer, but all reveal a cosmie influence in showing minima at the times of the equinoxes and maxima during the solstices. From our point of view this cosmic influence may be thus defined. The greater variability in the Sun’s irradiation during the spring and autumn increases the atmospheric circulation, and this augments the average horizontal velocity component of the air as well as the evaporation, and both processes cause the atmospheric pressure to decrease. In the polar regions the solar radiation exercises a lesser influence; in those parts compensation can take place and conse- quently the maxima occur in spring and autumn. Biertow has also tabulated the same data in another manner. He has caleulated for each station the successive yearly means and subtracted from them the check mean of the whole period (1873 ( 300 ) 1899) thus obtaining 27 residuals. The stations were then again gathered into the same groups, this time only eight in number (because the observations for the West Indies were considered too meomplete) and for each group the 27 mean values of the residuals were computed. The curves representing these mean residuals show for each of the eight districts the secular variations of atmospheric pressure in that region. The eight curves certainly exhibit many differences when compared to each other; nevertheless in the number of their maxima and minima we observe such an unmistakable similarity, that it is evident they are acted upon by a common influence, the cosmic nature of which is not doubtful. Similar charts have been framed by LoekverR and by BreeLOw for other parts of the globe and compared with the curve of prominence frequency. They resulted in the conclusion that an undeniable relation exists between these phenomena. However, to find this relation is not such a simple matter. In some regions of the Earth the maxima of prominence frequency coincide with the maxima of atmospheric pressure (Bombay, Batavia, Perth, Adelaide, Sidney), in others on the contrary with the minima (Cordoba, Mobile, Jacksonville, Pensacola, San Diego), whilst else- where again the maxima are shifted, although the general character of the curves persists. As yet the barometrical observations undertaken in elueidation of this question are confined to too small a number of places to allow of general conclusions being drawn from the data collected. It is therefore under reservation that we emit the following hypo- thesis as a guide for further investigation. At periods of maximum prominence frequency the atmospheric circulation is intensified owing to the irregularities of the solar radration field, This causes a decrease of the mean barometric pressure at all those places, where the enhanced circulation causes an excess of humidity, whilst at places where this is not the case, the mean atmospheric pressure will be above the normal. 8. Cosmic influence on other terrestrial phenomena. If the Earth moved through a perfectly regular radiation. field, there would be a certain normal atmospheric circulation, and in connexion with this circulation there would be at each place a fixed ( 301 ) and regular state of the weather, varying of course with its geograph- ical position and the actual seasons, but otherwise recurring from year to year with only small accidental variations. As things are, meteorological conditions are the reverse from reliable. We attribute their variability to the irregularity of the radiation field. The peculiarities of the surfaces of discontinuity add their quota in determining the localities, where minima of atmospheric pressure will occur; they influence the depth and movement of the depressions, the course of the cyclones, the direction of the wind, the formation of clouds and the rainfall. Menprum found that between the equator and 25° southern latitude, eyelones are more violent and more frequent at spot maxima than at minima. Pony established the same fact for the cyclones in the Antilles; and to this again it is attributed that in years of spot maxima during the spring, south winds are predominant in Western Europe ; that less frosty days occur at that season, the ice melts at an earlier date than usual, the water-mark stands higher for the great rivers, plants are more forward, ete. (ArrHENIUS Lehrbuch d. kosm. Phys. p. 141—146). Neither does it seem out of place to attribute the periodical alter- nations of years with much rain and years of drought in British India *), which react in so conspicuous a manner on the economical condition of that country, to the periodicity in the varying position of the Earth with respect to the surfaces of discontinuity. An excess of rainfall seems there a regular occurrence within a three year period around the maximum and a three year period around the minimum of sun-spots. The intervening years are marked by drought, the cause of famine. The regular course of these meteorological phenomena was interrupted in 1899, when great drought and excessive famine coincided with a spot minimum; but at the same time the widened lines of the spot spectrum presented an abnormal appearance. Here again we find a circumstance in support of our assumption, that the irregularities of the mean atmospheric circulation are caused by the surfaces of discontinuity. However, similar local meteorological phenomena depend on so many conditions, that we dare not look forward to a speedy solution of the problems they present. SUMMARY OF RESULTS, Overlooking the results of this investigation we see that the prin- 1) Sir N, Lockier and W. J. S, Lockyer, “On Solar Changes of Temperature and Variations in Rainfall in the Region surrounding the Indian Ocean”, Proc. Roy. Soc, London 67, p. 409—431 (1901). ( 302 ) ciple of anomalous dispersion opens a way to account for the con- nection between solar phenomena and terrestrial disturbances. There is a striking feature in the manifestations of solar influence on meteorological and :earth-magnetic elements, which it is especially difficult to explain by other principles, namely the circumstance that this cosmical influence does not affect the illuminated hemisphere uniformly, but often appears to act variously on different regions of the Earth, although the solar parallax is only 8.8" This peculiarity of the solar influence, as well as the divers perio- dicities observed in the variations of meteorological and magnetic elements, may be readily explained as consequences of the irregulari- ties of the solar radiation field, which in their turn are caused by surfaces of discontinuity. Our aim has been also to show, that even when supposing the solar output to be constant, periodical alterations in the frequency of spots, faculae and prominences and in the appearance of widened spectral lines must result from the mere change of the Earth’s position relative to our rotating luminary. The 11-year period, especially, seems to follow as a natural consequence from these considerations. It may be that we have touched here the only efficient cause of the periodicities noticed and that there really remains no ground for the admission of a variable solar activity. This latter inference we have, however, not proved, but for the sake of argument taken for granted. Zoology. — “The process of involution of the mucous membrane of the uterus of Tarsius spectrum after parturition.” By Prof. Hans SrRAHL of Giessen. (Communicated by Prof. J. D. van DER Waats, on behalf of Prof. A. A. W. Huprecut). I am indebted to Professor Husrecut for some exceedingly interesting specimens of uteri of Tarsius spectrum, which enable me to throw some further light on the different phases of the process of involution gone through by the uterus during this animal’s puerperal period. This material was especially valuable as I had an opportunity, on previous oceasions, of examining the same process in a series of other mammalia, and I am now enabled to determine how far Tarsius agrees with the forms hitherto under observation, and where it differs from them. I had a considerable number of uteri at my disposal, some from the ( 303 ) latest period of pregnancy; a great many dating shortly after delivery, others again of later date, and some showing the condition of the uteri in a non-puerperal or non-pregnant state. Before summing up briefly, in this paper, the results of my expe- riments, | must at once point out that the involution process in the case of Tarsius, throughout its development, takes its own peculiar course and is unlike any of the other forms of mammals that have had the uterus carefully examined up to now. As far as we know up to the present, we can divide the mam- malia with so-called full-placenta, (all classified under the heading of deciduata in the old-fashioned terminology), into three groups according to the process of involution. In the species of the first group, to which man and the monkeys belong, the placenta is spread out flatly on the inside of the uterus while in the mucous membrane, which has turned into decidua vera, the epithelium is entirely absent. In the second group the placenta is also spread out over the entire inside of the uterus, but in addition to this the womb is covered throughout with uterus epithelium. Such uteri are found in carnivores. In the rodents we often meet with the third form; here, towards the end of gestation, not only is the womb covered with cell-tissue, but this epithelium also runs from the fimbriae right underneath the placenta, undermining it till it is finally only adhering to the walls of the uterus by a slender cord, carrying the vessels. It is evident that, — taken as a whole class, — the uteri of the 3'¢ group will resume relatively quickly their non-puerperal appearance, while those of the first-named have to go through a complicated process of involution. We may add at once that Tarsins belongs to the third group. The lumen of the uterus gravidus just before parturition was found to be entirely covered with epithelium which ran underneath the rm of the placenta towards the centre of it, up to the connecting tissue-string, carrying the vessels of the placenta. As already deseribed by Huprecut in his excellent work on the placenta of Tarsius, we find in this placenta-cord conglomerations of uterus-glands, the cell-tissue of which present every possible phase of involution, while others are covered with well-preserved cells. These remains of glands in the placenta play a prominent part in the puerperal involution. In two of the puerperal uteri I find the placenta still existent ; | think if possible that here it is so far a question of physiological and not of pathological. circumstances, as perhaps the placenta, ( 304 ) instead of being at once thrust out after the parturition, has remained for a litthe while in the mother’s genital ducts. Once the placenta gone, the seat of the placenta in the mucous membrane of the uterus can be traced microscopically or by means of a magnifying glass for some considerable time. It is found to protrude above the surrounding mucous membrane like a round or oval-shaped body which I will call the placenta-bed. This bed, as we learn from the microscopic preparations, is limited by the accumulation of the remains of the glands lying along the vessels situated in the placenta-cord, which I will give the name of “paravascular epithelial tubes’ and in the centre of which the remains of the vessels of the placenta in a state of thrombosis, form a “placenta-plug”’. By the side of the placenta-bed the mucous membrane forms little folds which often protude into the lumen of the uterus in the shape of vesicle-shaped cavities. Among the changes that now set in during the process of invo- lution we have to distinguish between those which take place inde- pendently, in the material at our disposal, and those which are noticeable from a topographical point of view. As regards the first, even during pregnancy so much material has been accumulated for the formation of the new mucous mem- brane — the changes in which will only be described here — that it has now really become a question of elimination of the super- fluous. It is especially epithileum which is got rid of, as far as dispensable, by its being shed. Topographieally two things are happening. At what used to be the seat of the placenta we find as paravascular epithelial tubes remains of uterus-glands, in considerable number, while in the other sections of the womb there is a small number only of these uterus- glands. In both the uterus-horns of the non-puerperal uterus the glands which in this condition of the womb are of a narrow and elongated shape, run close together and are equally distributed, but this condition can only be arrived at by means of two simultaneous events: At the recent seat of the placenta the material of the large and wide paravascular vessels is almost entirely got rid of by its dying off. A little of it survives, to form the nucleus of fresh uterus glands. In the other parts of the womb a large number of new glands ure developing at the surface of the epithelium in the same way as the glands are growing during the time of pregnancy, namely ( 305 ) through the forming of small epithelium plugs, growing downwards from the surface. And while the whole uterus is trying to regain its normal shape by means of contraction of all its muscles throughout, the mucous membrane must of course shrink considerably; this process follows new lines, different from those which I have so far met with in any of the puerperal uteri of mammalia, hitherto examined. How this involution process progresses will be described in details by Dr. W. Kurz in an exhaustive work, freely enriched with illu- strations, and in which due attention is paid to the works of reference written on the subject. 2 u 7 = Ld a = ulo) be) » . Mathematics. — “Series derived from the series & ——.” By Prof. rn Ja KrLorvuR: By u(n) we denote an arithmetical function of the integer im which equals O if mm be divisible by a square, and otherwise equals +14 or —1, according as m is a product of an even or of an odd number of prime numbers. The series >) NZL tlm) 1 1 il 1 L 1 1 >. == if sa 9 = oe Be -- 3 = . . . . . =f 5 = ET C c ns 5 PN) 2 3 5 6 A0 “29 30) m1 was considered by Eurer, who concluded that it converged towards 0, a theorem only recently proved by von Marcorpr (1897) and by Lanpavu (1899). In this paper it will be shewn that in innumerable ways we may select from Ev Ler’s series infinite groups of terms, each of these groups again constituting a convergent series. In fact we may assume a linear congruence aa | aan ener Dj and from Eurer’s series retain only those terms the denominators of which are solutions of the congruence. From N= eg (171) Tije Bee sm) ml we get thus the new series Le v (nb +h) foe Mb Jh m0 Li ( 306 ) and it will be found that this series has a definite sum, whatever may be the integers 6 and h (4<)). Firstly consider the case 4 =O and suppose 4 to be prime. As it is necessary to start with finite series we write, g being any positive number, mb ee h 1,0 b,0 hl or (Oo ee { b 4 ge TT T TE jj . . . . . . Us b,0 b 1,0 i Lh 1,0 ( 1) and in the same way q eu q pe? iia De pig? b,0 hb 1,0 h b.0” nL 1 g q ry v2 > D8 Leoni fl ——— 1 a En E 5 5,0 ; 1,0 h bo Supposing g to lie between 6% and AFL we infer from these equations Pan Nn ea b,0 wt DK 1,0 Ee ill Now it follows from the identity m ; 4 jn el Po pos: apes , and in that case we have = u (bd) = (6). a dsm Hence we may write n—D ~ ge(mb) 2b NS gelo ) — u (h) re zb, mm | cd == Ds: po oe pie ) “ (a relation still holding for any 4 having square factors). Integrating from the above equations we deduce N= A (7m) b=: log (lm) = — 2, et 9 ; m=l MZ (ml) at bee N log (A— 2") =— u(b) N = fot) wet nb ml Aj Ape B and subtracting h=hl m= ; a(mb +h) zb :, = as ‘ () EA : log (1— gmbh ) Ze at u(b) NE CA ml mm mbh Sm nb =| m=0 Ay 9 Ay pve Ap. Denoting by / a number less than 4 and prime to / I substitute Jk Qe is ; hl and afterwards make z tend to unity. The righthand side ultimately takes the value of where g (/) indicates the number of integers less than 4 and prime to h and the equation itself may be written A=b—1 ae pear u (/ ) oF DT wh EF Fn St log \ 1 e : = eae ==: 5 eee (C) = . gb) ==) It implies # prime to 4, but for other integers / less than 4 and not prime to 4 a similar equation can be established. ( 309 ) Suppose fk k ERE where 4’ and 6’ are now prime to each other, then we have I=) WI k! iia Dri 5 ari a(d!) \ Ty vw X log \1 —e el ae oat 140 N= But denoting by / all integers less than 5 that satisfy the con- gruence | h=h'...(mod. b') we have evidently “om ry N (UN Si EN AE a0 Lye WS beet ee (D) cara h and also ak | „hk Wk N 271 — ET dt Tin X log \1 —e °/= Ty X log \1 —e h hence in case / is not prime to 4 we are led to the equation IS Be oni u(b') ie ee ig th Se ea EE PN 2 ae Paar ae) = = if only we omit at the lefthand side the terms corresponding to those integers / that are. multiples of 6’. With this limitation the equation (£) applies to all values of &, for if & be prime to b, from it we get back the equation (C). In this way we obtain by putting successively 4 —1,2,...b6—1 a set of —1 equations, from which we find in the shape of deter- minants finite values for the 5 — 1 quantities Tr. Actually we have got more equations than were wanted, for we may separate real and imaginary parts. We put xz — [el — a ze), 9 ad so that P(x) stands for the fractional part of the number «© minus md >: Now we have generally ad log (1 — e?rir) = PE log 4 sin aa Hia P(«), hence instead of (£/) we get the two equations 21 Proceedings Royal Acad. Amsterdam. Vol. VI. ( 310 ) h=b—-1 EEN f hk l NTL Dd en reen 2 cos 2 T— ot 2 mat age) (de ill and h=b—1 hk Werd k . Tan Oe = AR in te SG x b hl Again the equation (/°) supposes that if we have k ke An. no multiples of 6’ should be substituted for 5 in the summation at the lefthand side. As for the equation (G) this limitation is super- fluous since the discontinuous function P(r) vanishes for integer values of w. As the solutions of the equation (/’) and (G) seem in general to present neither regularity nor symmetry, we will proceed to consider some particular cases. In the case 6 = 2, we have at once 1 1 1 1 19,0 i” Se | ee SEOs Boe hoe TA Lye ae La ey care. a es NG RER Putting 4 =—=8 and substituting #=1 in (G) we find 1 1 V3 —-—— T —T359= — 5 Wonk was 2x and since T31 + 13,2 =0, we have A De ENE a 3/8 Pen — : Go Oks yas elt 2a ber Dee 33 T39= —-—- TTS dies ; 2 Hy) 1: Reape bt an In the case ) = 6 we may apply (D). Thus we obtain relations Ig Al 7 Id Al ry. Id Al os Ter + 165 = foe Bes tso ler ed ok Id Al Ld Al Bi 46, Beast Tea to Os, Taat las haer Joining to these the equation resulting by substituting bb =a AG) ( 311 ) 2 1 For Ta) P(G ya (Poa — To (=) = — — sin 6 n there follows Bed V3 En a | Pe NH ES pr en ah Pris. 10731 A 2126738 BA Miers 1 V3 1 fel Tet = = = SSS EE 6, Bie 11723 x oh tor starts: If we take 6 = 4, we have by applying (D) Pas), Tarifs ba); and by the substitution b—=4, k=1 in (G) 3 1 nrs ) + ts Kak jm 4 n hence we find re 1 En Dis Ea AL x eee mabe otc By, Whine Ck TEL A5 7 And by subtraction we obtain a u(Am+1) w(d4m+3)]_ 4 pe 4Am+1 by Amen m0 a result which may be compared with LerBrirz’s theorem n= ES 1 1 es ocean 4m-+1 4m+38 re dp m=—0 Lastly the series 75, can kk ae (i) and b=», k= ts hk in (GE ie 2a J (Lin +Ts,4) log 4 sin? — + (15,2 HT'5,3) log 4 sin? REE Adf 2 cos ús J J 1 2 1 2 (15,1 —T5,4) (=) + (152 — T5,3) P (=) — sin? —, bid | BS Ox (P- Pl moreover we have Psi + 159+ 153+ 154 == — 150 —= 0. Solving the four equations, the result is as follows 1 1 ) + (Tso — nar) = — —' sin? a= J Jt 21% be evaluated if we substitute b—5, Thus we obtain 1 ( 312 ) T5;= 14+—-— 4. 8 +. — (8 sin 72° + sin 36° == ie TE ADD VER ee ) 1 + 4 cos 72° EE 1:12 8 log 2 sin 18° Ke Tin 1 1 1 1 1 Ein os a eld RET wenende — 3 sin 36°) + 1 + 4 cos 72° =! — = — 0,710 8 log 2 sin 18 de 1 VRS ie hae | WEEDE Rd EN lee sin 12° + 3 sin 36°) + 1 + 4 cos 72° 6 ie 8 log 2 sin ig? 7 thee yi cele 1 at: Bee ij. Ea hk: 54 Pane Tal ag kak teas eas — 3 sin 72° — sin 36°) — 1 + 4 cos 72° apse — + 0.034. 8 log 2 sin 18° . . 100 As a numerical test I have directly calculated 75), . The results were respectively: -+-1.128, —0.685, —0.449, +-0.036. From these few particular cases it will be evident that the equations (F) and (G) always permit to evaluate 7%, and the fact that such a series has in all eases a finite sum may with more or less justice be interpreted thus: Among the integers without quadratic factors less than a given large number g, that are solutions of a given congruence Sh. ~~ Wo. 5) | the integers made up by an odd number of prime factors are sensibly equal in number to the integers made up by an even number of prime factors. Botany. — “The Ascus-form of Aspergillus fumigatus Fresenius”. By Dr. G. Gruns. (Communicated by Prof. F. A. F. C. Went.) While during the last course I was occupied with determining fungi in the botanical laboratory under the superintendence of Prof. WENT, I noticed that in a pure culture of Aspergillus fumigatus, a couple of months old, sporefruits had formed; on imoculation from this culture these same bodies were always produced in the new cultures. As nutrient substance I used Konrne’s malt-canesugar-agar-agar. The ascus-form of Aspergillus fumigatus has not yet been described, for the statements of Benrens and SIRBENMANN are justly doubted by Wenner, nor do they agree with my result. — ee ( olan) The conidiophores agree so well with Wrrer’s deseription') and with his picture, also with regard to dimensions, that the diagnosis need not. be doubted. The fruit-bodies appear as small globules having the colour of fresh hazelnuts; their size is only about */, mm. With feeble mag- nification they appear to be enclosed by an envelope of small, round, highly refractive, greenish globules, enclosing a dark body. The globules on stronger magnification turn out to be mycelium cells with a greatly thickened wall, which remain joined by a few thin threads. The body within is little transparent, deep red and irregularly egg-shaped. It has a thin fragile wall, consisting of two layers of flat cells in which a red pigment is found. ; The space within is filled up with a dense web of colourless hyphae, the contents of which are homogeneous and between which the asci are found. These are egg-shaped and have a very thin wall, which in mature asci is difficult to observe, but which can easily be recognised in immature ones still containing colourless spores. The mature spores, of which eight are found in each aseus, have a deep red colour, which is turned blue by alkali (ammonia). They have the shape of convex lenses, the thickness of which differs only little from the diameter. Round the aequator a hyaline seam is found, showing fine radial striae or folds. The perithecia consequently resemble those of Aspergillus nidulans which differs, however, by wanting the ramified sterigmata. Also the ascospores with their radially striated seam are different from those of nidulans which show a groove. Terrestrial magnetism. — “The daily field of magnetic disturbance.” By W. van BEMMELEN. (Communicated by Dr. J. P. van DER STOK). In 1895 I published *) the results of a research on the change in magnetic foree on days following large magnetic disturbances. By comparing the mean daily force on a day directly following a disturbance with the force some days after, a differential vector was obtained directed chiefly South with a deflection to West or East of rather constant azimuth for each station. '!) C. Wenner. Die Pilzgattung Aspergillus, Genève 1901. p. 71, 2) Meteorologische Zeitschr. 1895, pg. 321, ( 314 ) Later considerations’) brought me to the result that the regular part of the disturbance phenomenon might be ascribed to the existence of a circular system of electric currents chiefly in the higher layers of the atmosphere, compassing the earth, and parallel to the lines of equal frequency of aurora borealis. Considering with Scumipt *) magnetic disturbances to be caused by movement of smaller current-rings over the surface of the earth, the whole exhibits a strong analogy to the great cyclonic movement of atmospheric air around the poles and the wandering depressions within it, so as it has recently been described by H. HitpEBranpsson. It seemed evident that such a system of circular currents must undergo a daily fluctuation caused by the rotation of the earth and I tried to separate this influence by taking the difference of corresponding hourly values on days following a magnetic disturbance. Though the results pointed to an influence indeed, they were too vague to lead to definite conclusions; the minuteness of this daily fluctuation as compared with the irregular changes accompanying magnetic disturbance being no doubt the cause of it. Now in 1899 Dr. Lüperixe *) showed that sharp results were to be obtained, when comparing the hourly values of the horizontal com- ponents on quiet days (Normaltage) with those for all days. In his interesting paper he gives the hourly values of the horizontal com- ponents (vs and y¥,) of disturbing force for the arctic stations for the months June and July 1883. The vectordiagrams drawn by him show the remarkable fact that the vector for all stations moves anticlockwise, with the only excep- ton of that for the station Kingua Fjord where the vector moves decidedly in a clockwise direction. Also at Godthaab during part of the day the same occurs. In order to study these diagrams for other parts of the earth I computed them for Greenwich, Washington, Tiflis, Zi-Ka-Wei, Batavia, South Georgia and Cape Hoorn for the same months (June, July); also deriving on the same principles the vertical component for these latter stations and the arctic ones, I found this component to exhibit chiefly a single daily fluctuation of an amount of the same order as that found for the horizontal component. It was easy to classify the stations in the following groups: 1) Terrestrial Magnetism V, pg. 123. *) Meteorologische Zeitschrift 1899, pg. 385. 5) Terrestrial Magnetism IV, pg. 245. ( 315 )j Station Hor. vector moves in diagram : Vertical component shows: Max. Min. Kingua Fjord — clockwise Evening Mornin 5 J S Godthaab anticloekwise, but clockwise in the evening. Cape Thordsen \ Evening Morning Jan Mayen At Ssagastyr 2 unthrusty. Ssagastyr At Nova Zembla two maxima and Bort Kas anticlock- two minima, 2; tends to disappear. Poi B wise, At Point Barrow and Bossekop the omt Barrow fluctuation is the contrary and shows Nova Zembla a max. in the morning and a Bossekop / min. in the evening. Sodankylä anticlockwise, but clockwise in the morning. TheE/W Evening Morning compon. tends to disappear. BO | clockwise Greenwich \ Morning Evening Tiflis clockwise, but Washington anticlockwise in Morning Evening. the evening. Zi-Ka-Wei No change Morning Evening in direction, which stays WSW-ENE. Batavia anticlockwise, but Noon Morning clockwise in the evening South Georgia / ene clockwise Cape Hoorn } je Morning Evening The change in the sense of rotation of the horizontal vector and in the times of occurrence of maximum and minimum of the vertical component proceeds quite regularly, when classifying the stations, as has been done here, by their distance from a pole, which may be called pole of aurora borealis and is located in + 80°.5 N and a2) 802.W. Now it is remarkable that in my paper on the “Erdmagnetische Nachstörung”’, quoted above, L came to the result, that the disturbing force acts in planes, which cut the surface of the earth along curves converging into this pole. In order to study the behaviour of the horizontal component the ( 316 ) simultaneous horizontal vectors for the arctie stations (after the data given by Litprime) have been plotted in a series of 12 maps cor- responding to the hours of 0%, 2%, 4%... 22" mean Göttingen time. These maps revealed the fact that one part of these vectors pointed to one focus and the rest emanated from another. The successive places of these foci have been determined as unbiased as possible. Rectangular coördinates have been made use of with the origin in the north pole and taking for # and y axis the meridians 180° and 90° E from Greenwich. The unity for the values of the coordinates as given underneath is 2 47 0°.5; accordingly the value of Va dy* represents nearly the polar distance in degrees, because the maps have been drawn in stereographic projection. The focus to which the vectors point has been called a positive focus, that from which they emanate a negative focus. Mean Göttingen Positive foeus Negative focus hour Jin UE Hi yy. Qh 74 —22.2 — 8.2 1.6 2 9.6 —17.0 —13.2 — 54 4 11.2 —11.0 —13.2 — 88 6 11.2 — 6.2 —16.0 —11.6 8 8.8 2.2 —12.6 —21.2 10 0.0 2.2 — 8.8 -—28.0 Noon — 4.4 2.2 2.2 —23.6 14 — 88 — 0.6 8.8 —23.6 16 —11.8 — 6.6 13.8 —10.4 18 —14.0 15.4 9.4 — 6.0 20 —13.2 —26.2 2.8 8.2 22 — 88 —830.2 — 6.2 6.2 Mean — 11 —10.7 — 34 —10.2 Harmonie formulae calculated for these four series: feng WS EEF 185 sin (€ 115") $21 sin BOE + 19) es Ly = 10.7 4 148 sin (£ + 14°—90°) + 2.4'sin 2 (2°) feng (OBA + LBG sin (t + 24° 4 180°) + 3.2 sin 2 (15%) OS by = —10.2 + 15.7 sin (f+ 24+ 90°) 4 3.0 sin 2 (t—50°) From the constants of these formulae it follows evidently, that both foci move in nearly the same circular path with almost constant velocity and with a mutual distance of 180°. | This being granted and calling «, the mean of the a’s for positive —1.1—3.4 and negative focus: a, = St 2.8, andi y, the mean — A ge — 10.7 —10.2 We She for the y’s for the foci: y, = 2 - == —10.5, the values of ad (rt) —(@yoh—®y)s (Ygh—Yo) and (—y,,a—y,) and so on, must represent the same quantity, from which we may compute a set of 12 means. The harmonic formulae representing this set is : cr == —2.3 + 14.5 sin (w + 22°) + 1.3 sin 2 (w + 28°). The term of the second order, already small in comparison with that of the first order, having been still more diminished by this operation, it may be safely neglected. So we may adopt (for Greenwich time): ee ee 14.5 sin (w + 12°) Ue Ree —10.5 + 14.5 sin (a + 12°—90°). The centre of the circular path, which is best called “pole of dis- turbance” lies accordingly in ta) Ne and: 78. WW? For the pole of aurora borealis I accepted 80°.5 N. and 80° W. and according to Scumipt the magnetic axis for 1885 cuts the surface in 78°.5 N. and 687.5 W. So we have arrived at the remarkable result, that the daily move- ment of the arctic foet of disturbing force takes place in a circular path of 14°.5 radius around a pole practically coinciding with the pole of aurora borealis and lying very near to the north end of the magnetic avis. When now supposing this fluetuation of disturbing force to be caused by a field, which slides around the earth from East to West (as has already been remarked by LüprrinG in his paper quoted above) and this in analogy with our actual views regarding the field of the ordinary daily variation, we are obliged to assume the field of disturbance to revolve around the axis just found, viz. Lo De coe ton ie eS. 101° B. In order to represent the daily field, we have to study the vector- diagrams themselves. Of course the vector-diagrams of one group show mutual differences caused partly by insufficient material (for the arctic stations 2 or 3 months only) and partly by local influences, as has already been indicated by Scumipr (Met. Z. 1899). In order to avoid irregularities bringing confusion in the result, which may prevent interpretation of this phenomenon (this being of (818) course the principal aim), I have chosen as representative for each group one station with an obviously regular diagram. They are: Kingua Fjord, Jan Mayen, Sodankylä, Greenwich, Tiflis, Zi-Ka-Wei, Batavia, Cape Hoorn, (Godthaab has been left out, it being rather superfluous for the horizontal component, and the vertical component not being available). The values of the components have been graphically smoothed. Now to obtain a representation of the daily field the method at present common of distributing the successive hourly values for each station along the parallel of that station, has been applied, and thus I have constructed a map in Mercaror’s projection but according to the axis of disturbance with the lines of equal vertical component and horizontal vectors on it. The lines of equal vertical component compass chiefly eight foci of maximum and minimum vertical foree (of which two are double), tabulated hereafter. (It should be kept in mind, that latitudes and longitudes are according to the axis of disturbance). The longitude of the sun for its position on June 21st has been taken zero. Latitude Longitude Amount Latitude Longitude Amount ety shar ee Ne ee 6K es il re a AT y 171° SIE eee \ 52 156 W a= | 5 sE i 5g BLW 4 7 Ne —10 41 W + 3 23 129E — 15 South of —60 2 W — ? South of —60 ? E + ? The horizontal vectors drawn in the same map are pointing almost without exception towards the positive foet and away from the negative ones. Supposing the disturbing force to originate from existing electric currents, the fact that these currents must follow nearly the course of the lines of equal vertical force conducts to the hypothesis of systems of circular currents with eight foei revolving daily around the axis of disturbance. The horizontal vector being directed to the point where the vertical component is upwards, the application of Amprrn’s rule teaches that these currents must flow for the greater part above the surface of the earth. Remarkable is the rapid diminution of the force with the polar distance, almost parallel to the equally rapid diminution in the occurrence of auroral display. I must emphasize an important divergence between the fields of ordinary daily variation and that ( 319.) of disturbance: viz. the former has its foci near the meridians of noon and midnight, the latter near the line of separation of day and night. The axis around which the field of disturbance revolves is so nearly coincident with the magnetic axis of the earth, that it seems the field is caused by any emanation from the sun, deflected by the earth-magnet acting as a whole, and not by the surface distribution of terrestrial magnetic force. Full account on this research will be soon given in the Natuur- kundig Tijdschrift voor Nederlandsch-Indië. Geology. — “A piece of Lime-stone of the ceratopyge-zone from the Dutch Diluvium.’ By J. H. BoNNmmaA (Communicated by Prof. Martin). In a few papers which a short time ago appeared in these reports, I communicated some particulars of the Cambrian erratic blocks from the loam-pit near Hemelum; this time I intend to treat of the Under-silurian ones. First of all, however, I wish to add something to my information concerning the way in which Under-cambrian sandstone with Disci- nella Holsti Moprre is spread. I then’) said that I had not been able to find anything certain, in German literature, about erratic- blocks of this stone. This was a consequence of my sources of information on sedimentary erratic-bloeks being incomplete. After my paper had appeared, Prof. Srorrer®) was so kind as to send me an essay that had seen the light already a few years before, in which the occurrence of this kind of erratic-bloeks in the German diluvium is made mention of. No more did I find, here in the Hemelum loam-pit, the opinion confirmed expressed i. a. by STARING ®), MARTIN *) and ScHROEDER VAN DER Kork ®, that Under-silurian erratic-blocks were almost entirely 1) Bonnema, Some new Under-cambrian erratic-bloeks from the Dutch Diluvium. Proc. Royal Acad. Amsterdam. Vol. V (1903) p. 561. 2) Srottey, Einige neue Sedimentärgeschiebe ans Schleswig-Holstein und benach- barten Gebieten. Schriften des Naturwissenschaftlichen Vereins für Schleswig- Holstein. 1898. Bd. XL. p. 133. 5) SrariNG, De bodem van Nederland. 1860. IL. p. 99. 1) Martin, Niederländische und Nordwestdeutsche Sedimentiirgeschiebe. 1878. p. 14. 5) ScHROEDER VAN DER Kork, Bijdrage tot de kennis der verspreiding onzer kristallijne zwervelingen. Dissertatie, 1891. p. 51. Stelling VIL. ( 320 ) absent in our diluvium. With regard to Groningen this was already told us by Van Canker’). Afterwards I pointed out the same thing for Kloosterholt *), and it will appear, too, that boulder-clay of Hemelum contains as many Under-silurian erratic-blocks as the loam of the places mentioned. That the above-named writers are of different opinions may be easily explained by the way in which stones used to be gathered. Formerly the hammer was hardly ever used and there is no doubt that only those stones were gathered whose outward appearance drew the attention. Now, this very rarely happens with Under- silurian erratics. The polyparia of syringophyllum organum L., which are probably without any exception Under-silurian, are con- spicuous for their form, and we really see that old collections contain these fossils in large numbers. The Upper-silurian erratics, however, on the outside of which it is sometimes already visible that they are rich in fossils (which is i.a. the case with limestones with chonetes striatella Dalm), much sooner draw the attention. This is especially the case with petrified corals, which mostly bave an Upper-silurian age. They form, indeed, the greater part of the old collections. Even if one uses a hammer while gathering stones, one is sure to find, in proportion, more Upper-Silurian erratics with determinable fossils than Under-Silurian ones, because as a rule the former are much richer in fossils than the latter. Moreover, in Upper-Silurian erratics Leperditia-valves are frequently found. As, in consequence of their comparatively small size and their smooth surface, these valves are easily exposed to view and the different kinds of Leperditia are easily distinguished and are charac- teristic of different strata, one may, by means of these remains, deter- mine the age of many Upper-Silurian erratics. A great part of our Under-Silurian erratics, however, consist of pieces of tough, greyish lime-stone, which does not possess many petrifactions, so that these pieces seldom give a determinable fossil. Very often an Asaphus, an Ilaenus or an Endoceras, found in them, proves their Under-Silurian age, whereas these remains are too incomplete to allow of their being ranged under a definite division of Under-Silurian erratics. This is even more the case with that kind of limestone of frequent 1) Van Carker, Ueber das Vorkommen cambrischer und untersilurischer Geschiebe bei Groningen. Zeitschr. d. deutsch. geol. Gesellschaft. Bd. XLII. pag. 792. 2) Bonnema, De sedimentaire zwerf blokken van Kroosrernozt. Versl, y. d. Koninkl, Akad. v. Wetenschappen. 1898. pag. 448. a ( 321 ) occurrence, which petrographically resembles the lithographical one and probably is of the same age as the Wesenbergen stratum. In this stone a petrifaction is hardly ever found. Consequently it takes a long time to gather a collection in which the different divisions of Under-Silurian stone are clearly represented. I did not succeed in composing such a collection from the Hemelum loam-pit. This is partly owing to the fact that this opportunity to gather erratics existed only a short time. The boulder clay proving unfit for use in brick-works, digging has been left off. The principal cause is, however, that boulder clay used to be dug there in the beginning of winter, and that in the latter part of that season the erratics found were broken to pieces for macadamizing roads, whilst in this very part of the year neither my occupations nor the weather allow of my making excursions. The erratic: I am going to treat of, was found by me in the Hemelum loampit a few years ago; it may undoubtedly be ranged under the Ceratopyge-zone, the eldest of the Under-Silurian kinds. It contained a kernel of compact, splintery limestone, of a light- grey, more or less greenish colour. This kernel was surrounded by a yellow-brown, softer crust, caused by corrosion, which was coloured greyish at the surface. Occasionally I distinguished small glauconite- and pyrite-grains. When I broke it to pieces, the kernel naturally did not give me any fossils; I sueceeded, however, in exposing to view, from the corrosion-crust, the following fossils : 1. Ceratopyge forficula Sars"). Of this species I found a head- midshell, a free cheek and three fragments of pygidium. These remains come from the variety acicularis Sars et Boeck, the axis of the pygidium consisting of 6 segments. The head-midshell, too, bears more resemblance to fig. 15 than to fig. 17. 2. Symphysurus angustatus Sars et Boeck ?). One glabella and three small pygidia were found. In the latter it becomes quite clear that as a rule the axis may be clearly distinguished only in stone-kernels. 3. Holometopus (?) elatifrons Ang*). Numerous more or less unin- jured head-midshells presented themselves. Only in one specimen, one side of which is still in the stone, the prick in which the glabella ends towards the back is visible. 1) Bröceer, Die silurischen Etagen 2 und 3. p. 123. Tab. [IL fig. 15—22. 2) Bröaeer loc. cit. p. 60. Tab. Ill. fig. 9, 10, 11. 3) Bröceer loc. cit. p. 128. Tab. IIL. fig. 13, ( 322 ) 4. Kuloma ornatum Ang). A piece of a head-midshell and of a pygidium were exposed to view. 5. Agnostus Sidenbladht Linrs.*). This species is represented by a head-shell. 6. Shumardia pusilla Sars*)? I am inclined to range under this head a very small pygidium, which doubtless comes from a Shu- mardia-species. That I am not quite certain here, is owing to the fact that it shows a lateral compression and consequently is not so broad as the pygidium pictured by Mosrre *). The latter, which has been produced from slate, may be somewhat flattened, whereas the pygidium out of my erratic-bloek has probably retained its original shape. It is also possible, however, that it comes from a new Shu- mardia-species. According to Hennig *) such a new species is met with in the Ceratopyge-zone of Fgels’ng. Unfortunately the essay in which this species was to be described — which essay was shortly to be published, according to that writer —, still keeps us waiting. 7. Orthis Christianiae Kjerulf®. Several valves of this little srachiopode were found. The three first species of Trilobites are, according to TULLBERG *) also met with in the lowest strata of Oeland Orthocere-lime, but as this does not appear to be the case with the other fossils, I do not hesitate to call this erratic-bloek a piece of Ceratopyge-lime. Erratic-blocks from the Ceratopyge-zone with remains of Trilobites seem to be very rare in the German and the Dutch diluvium. As far as I can see, only two have been made mention of by Reme.s *) and one by Srorrey®), as most certainly belonging to this zone. 1) Bröaeer loc. cit. p. 97. Tab. Ill. fig. 5, 6. 2) Linnarsson, Om Vesiergotlands cambriska och siluriska aflagringa. Svenska Vetenskaps-Akademiens handlingar. 1869 Bd. 8 No. 2. p. 74. Tab, II. fig 33, 34. 3) Broacer, loc. cit. p. 125. Tab. XII. fig. 9. *) Mopere, Om en afdelning inom Oelands Dictyonema-skiffer s°som motsvarighet till Ceratopygeskiffern i Norge. Sveriges geologiska undersökning. Ser. C. No. 109. p. 4. 5) Hennie, Geologischer Führer durch Schonen. 1900. p. 33. 6) Gacet, Die Brachiopoden der Cambrischen und Silurischen Geschiebe im Diluvium der Provinzen Ost- und Westpreussen. Beiträge zur Naturkunde Preussens, heraus- gegeben von der Physikalisch-Oeconomischen Gesellschaft zu Königsberg. No. 6. 1890. p. 34. Taf. Il. fig. 22. 7) Tutteere, Förelöpande redogörelse för geologiska resor pt Oeland. Geologiska Föreningens i Stockholm Förhandlingar. 1882. Bd. VI. p. 231. 5) Remert, Ueber das Vorkommen des Schwedischen Ceratopyge-kalks unter den Norddeutschen Diluvialgeschieben. Zeitschr. d. deutschen geol. Gesellschaft 1881. Bd. 33. p. 696. ®) Srorzey, loc. cit. p. 135. ( 323 } They are, however, not like the Hemelum piece, those of Rumuru being many-coloured and that of Sroniny being a piece of yellow iron-ochre, which according to him probably originates, through the influence of corrosion, from a clayish kind of stone, which is rich in iron. Formerly RemeLé*) declared that the erratic-bloek found near Neustrelitz, from which Bryricn deseribed his Harpides rugosus, most probably was Ceratopyge-lime. He came to this conclusion especially beeause in the Swedish and Norwegian Ceratopyge-zones is found the species that is the nearest relation to Harpides rugosus Sars et Boeck, and that at the time no specimen of this species had been found in higher strata. Now that Tunipere’) has informed us, however, that in the lowest, grey Orthoceratite-lime of Oeland a new species of Harpides is found, this erratic-block is much less likely to be Ceratopyge-lime. The less so, as according to RemeLé this erratic greatly resembles glauconite Vaginaten-lime (= lowest grey Orthoceratite-lime). If attention is paid only to the petrographical nature and the presence of Orthis Christiniae, most probably more erratics of the same kind have been found in the German diluvium. GorrscHe *} at least makes mention of a light-grey, splintery lime-stone, green- and yellow-tinted, which LuNDGREN took for Ceratopyge-lime. He also tells us, however, that this stone perfectly resembles pieces of Ceratopyge-lime that were gathered by Dames near Aeleklinta, whereas Horm *) informs us that this Under-silurian zone is entirely absent there. It is possible, too, that to this kind belongs the Ceratopyge-lime which SrrussLorr ®) under 6 deseribed as light-grey lime with a greenish tint and a little Orthis. Corresponding erratics seem also to have been found by Sroniey *). 1) Remeré, loc. cit. p. 500, 695. 2) TuttBere, loc. cit. p. 232. 3) Gorrscue, Die Sedimentär-Geschiebe der Provinz Schleswig-Holstein. 1883. p. 14. 4) Horm, Om de vigtigaste resultaten {rin en sommaren 1882 utförd geologisk- palaeontologisk resa pi Oeland. Oefversigt of Kongl. Vetenskaps Akademiens Förhandlingar. 1883. p. 67. 5) SreussLorr, Sedimentiirgeschiebe von Neubrandenburg. Archiv des Vereins der Freunde der Naturgeschichte in Mecklenburg. 1892. p. 163. 6) Srottey, Die cambrischen und silurischen Geschiebe Schleswig-Holsteins und ihre Brachiopodenfauna. Archiv fiir Anthropologie und Geologie Schleswig-Holsteins und der benachbarten Gebiete. 1895. Bd. L. p. 43. ( 324 ) Only those pieces are considered which, as he says, are so compact as to resemble serpentine. An erratic-block of the same kind has perhaps also been found in the eastern part of the German diluvium. GaGEL’) at least speaks of a greenish, hard piece of limestone, with yellow spots here and there in consequence of corrosion, in which little glauconite-grains occur rather scattered. He does not tell us whether it is compact. Though in all these pieces, except that of SrevssLorr, Orthis Christianiae is declared to be present, and though petrographically they seem more or less to resemble my erratic-block, — I dare not take it for granted that they are closely related to it. It must further be traced where corresponding limestone is still found as firm rock. This is certainly the case at Ottenby on the western coast of the southernmost part of Oeland. Last summer I could convince myself of this. Ceratopyge-lime is there not only of the same petrographical nature (in most cases at least), but is also rich in fossils. Horm informs us that towards the midst of the island this stratum is less developed; its colour is more reddish here, and it is less rich in fossils, so that as a rule only Orthis Christianiae is met with. In the northern part of Oeland it is altogether absent, according to Hora. In Schonen, Ceratopyge-lime has been found only near Figelsing, as far as one knows for certain. This kind, however, is more bluish- coloured, which I can observe in a piece I received from Prof. Moere. Corresponding limestone may also occur in West-Gotland, on Kinne- kulle and Hunneberg. According to Linnarsson *) the Kinnekulle-stone is a hard, light-grey, mostly bluish and greenish limestone, often with numerous small, blackish-green glauconite-grains. He says that the Hunneberg limestone is little or not at all bituminous, now com- pact, now crystalline, either black or grey, and frequently containing pyrite. So there is a possibility, to be sure, that such-like limestone is found there; but without any material for comparison nothing can be said with certainty. - Ceratopyge-lime, which, as is generally known, is not met with in the Russian Baltic-seaprovinces, moreover still occurs as firm rock in the south of Norway and in the environs of Christiania and Mjösen. Horm *) declares it to be occasionally so much like that of Ottenby in Oeland, that he is unable to distinguish one kind from 1) Gace, loc. cit. p. 9. 10. 2) LinNArsson, loc. cit. p. 30, 56. 3) Hora, loc. cit. ( 325 ) the other. BRrÖGGER*), however, tells us again and again that it is blue-coloured, so that I suppose that in colour it more resembles that of Fagelsing. A piece of Ceratopyge-lime which I saw at the Groningen Geological Institute, seems to confirm this opinion. Finally it remains to be examined where we must look for the origin of this erratic-block. I suppose it to come from a place not far from Ottenby. The in every respect perfect resemblance between our erratic and Ceratopyge-lime that is found there, may first of all be said to speak in favour of this opinion. The circumstance, secondly, that in the Hemelum loampit I found many kinds of erratic-blocks that are also found in Oeland, makes this highly probable. I need only remind of those pieces which I formerly described, pieces of Scolithus-sandstone, sandstone with intersecting layers and Discinella Holsti-sandstone; whilst there are many more, as I hope I shall point out within a short time. This resemblance in erratic-blocks makes it more probable, first that the ice came down to us via those regions, and at the same time that a piece of Ceratopyge-lime was brought from there to here. Chemistry. — In the meeting of Saturday May 30, 1903 Prof. S. Hoocrwrrrr and Dr. W. A. van Dore communicated a paper: “On the compounds of unsaturated ketones with acids” and in the meeting of Saturday September 26, 1903 Prof. Tu. H. Benrens com- municated a paper: “The conduct of vegetal and animal fibers towards coal-tar-colours’’. (Both communications will not be published in these Proceedings). 1) Bréaeer, loc. cit. p. 14. (November 25, 1903). ; i de na PIN , ; cae Rn We ” PF i ye a): ee ree Bi nig ae ge x AAE hk N ol we toet ver OEE dijk PIKE 5 SNE Ke G v a el mer 5 ANO +3 Ye at, Ros Ek | Pia Pe ME are ae tie Bis tee , wit gin Rae a ee sae . ; et, * ‘ 8 + ie , ee 0E- el ian ME a | a ha? a er) 2% «24 } Shale , Be Boi ‘ . i J ; 5 i hb, a s Pa Pro vi ; é ; As! = vi ib igs “ait? aif 42. hs Pte) ar Jes ASE rn d f ch ea ee eee 4 + ha \. ¥ * . ® ‘ ksk Fr 4 ve HR “ 1 de i : . ol s r iss u ELIES LE ‘ EN eo Th pe 4 redde > 9 {She J ke 4 je . K = ‘ F. i U 4 % ‘ “ r . ” 5 i nd _ - : i kh , = Ed ’ , ¥ . a a / ' - ak ' i 4 ’ = ‘ KONINKLIJKE AKADEMEE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday November 28, 1903. ae OC — (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 28 November 1903, DI. XID). CO) Neste ate SE Sy A. F. Hotiemsn and J. W. Beekman: “Benzene fluoride and some of its derivations”, p. 327. Il. W. Bakuvis Roozenoom: “The system Bromine + Iodine”, p, 331. R. O. Herzoe : “On the action of emulsin”. (Communicated by Prof.C. A. PEKELHARING), p. 832. Eve. Dveois: “Deep boulder-clay beds of a latter glacial period in North-Holland”. (Com- municated by Prof. K. Marri), p. 340. G. van Rigxperk: “On the fact of sensible skin-areas dving away in a centripetal direction”: (Communicated by Prof. C. WiNkreER), p. 346. C. WINKLER and G. vaN RiJNBeErK: “Structure and function of the trunk-dermatoma’, LV, p. 347. J. D. var per Waars: “On the equilibrium between a solid body and a fluid phase, especially in the neighbourhood of the critical state”, (II part), p. 357. P. H. Scnovure: “Centric decomposition of polytopes” p. 366. J. M. van BEMMELEN: “Absorption-compounds which may change into chemical compounds or solutions”, p. 368. The following papers were read: Chemistry. — “Benzene fluoride and some of its derivations.” By Prof. A. F. HorLEMAN and Dr. J. W. Berkman. (Communicated in the meeting of September 26, 1903). Benzene fluoride has, up to the present, been a not at all readily accessible substance. The best known method of preparation is that of Warract and Hrvusurre (A. 245, 255) which consists in first preparing benzenediazopiperidide and decomposing this with De, Proceedings Royal Acad. Amsterdam, Vol. VI. ( 328 ) hydrogen fluoride. These chemisis are even of opinion that benzene fluoride may thus be readily prepared by the kilo. As regards the course of the reaction our experiences are quite in harmony with those of Warracu and Hruster, but we differ in the appreciation of the convenience of the method. Apart from the fact that in our numerous experiments we have never succeeded in obtaining the yield of 50°/, (on an average we only got 30°/, from the aniline employed) which they claim to obtain, the recovery of the piperidine proved to be very tedious. Notwithstanding its price is considerably lower than it used to be, as if is now prepared by electrolytic reduction of pyridine, it is still such that this recovery could not be avoided. The base must be again isolated in a state of perfect purity, beeause the yield of diazopiperidide becomes very small if the smallest impurity should be present. The method is also very tedious as not more than 10 grams of diazopiperidide at a time should be treated with hydrofluoric acid, otherwise the reaction becoming too violent. After having prepared about 150 grams of benzene fluoride in this way we, therefore, decided to abandon this method and to endea- vour to obtain benzene fluoride by the direct diazotation of aniline. For this purpose VALENTINER and Scnwartz have taken out a patent (Centralblatt 1898 I, 1224) consisting in heating a solution of benzenediazomium chloride with hydrogen fluoride. We may surmise that the product will be a benzene fluoride contaminated with benzene chloride; on following their directions this proved to be the case to such an extent that after repeated fractionation of the product 100 grams of aniline yielded only two grams of fairly pure benzene fluoride. This showed that in the diazotation of aniline, intended for the preparation of benzene fluoride hydrochloric acid should be avoided. I do not wish to enter into particulars as to the various ways in which we have tried to prepare benzene fluoride directly from aniline. Dr. Beekman has stated something about this in his dissertation. It will be sufficient to mention here that the yield of the desired product increased with the amount of hydrofluoric acid employed. This is the method which we finally adoptes : 98 erams of aniline are dissolved in sulphuric acid and diazotated in the usual manner, care being taken that the volume of liquid does not exceed 1.25 litre. The ice-cold solution is then poured slowly with vigorous stirring into a copper vessel containing 500 ee. of 55°/, hydrofluoric acid heated nearly to the boiling point and kept at that temperature. The benzene fluoride distills over and is condensed ina leaden worm-condenser surrounded by ice and salt. The distillate consists of a colorless liquid, which is freed from traces of phenol ( 329 9 by washing with a little alkali. After drying over calcium chloride it at once distilled over at a constant temperature of 85°. From 93 grams of aniline 37 grams of benzene fluoride are thus obtained in a per- fectly pure condition, that is to say 40°/, of that required by theory. The deficiency in the yield is caused by the formation of phenol. Probably this may be reduced to a minimum if instead of hydro- fluoric acid a mixture of sulphuric acid and calcium fluoride is used in such a manner that the concentration of the hydrogen fluoride remains about constant. As this plan involves vigorous stirring and as our mechanical appliances were inadequate to stir the resulting paste of gypsum, we have not been able to practically confirm this obvious conclusion. In quite an analogous manner the para- and metanitrobenzene fluoride may be prepared from the corresponding nitranilines and the three toluene fluorides from the toluidenes. Anthranilic acid, however, only yielded small quantities of o-fluorobenzoic acid and was nearly all converted into salicylic acid. It was very interesting to notice that, when treated by this process, orthonitraniline did not yield a trace of ortho-nitrobenzene fluoride but only resinous masses. Warracn has also been unable to prepare this substance by his own method as he did not succeed in purifying the piperidide required, We have made two further attempts to prepare this substance. Firstly by isolating it from the nitration product of benzene fluoride, but as this contains but little of it we did not sueceed either by freezing or by fractional distillation. Secondly from parafluoronitro- benzene; the p-aniline fluoride obtained by its reduction yields when nitrated in sulphuric acid solution Gre EP LNELONO: (1:45 2) so that by eliminating the amido-group, o-nitrobenzene fluoride must be formed. But only resinous masses were again produced here. The determination of carbon, hydrogen and nitrogen in the fluorine compounds could be done in the usual manner. For that of the fluorine we used a platinum tube 85 em. in length and 1.8 em. in diameter in which the substance was introduced mixed with CaO. After heating the mass contains the fluorine as calcium fluoride, which is then freed from the excess of lime by treatment with dilute acetic acid, collected on a filter and weighed. As we never found lime to be perfectly soluble in dilute acetic acid, it was purified by dissolving it in dilute acetic acid, precipitating with ammonium carbonate and igniting the carbonate so obtained. The physical constants of some of the compounds prepared by us, were accurately determined and the following values were found: 29% hl ed m. p. b. p. sp. gr. at 84°.48 m-nitrobenzene fluoride 17, 205 12582 p= 95 4 % 26.5 205° 1,2583 p-aniline fluoride ee 187° = nitraniline fluoride(1: 2:4) 98° es _ benzene. fluoride eee i ay SDP 1.0236 (at 20°/4) It is a well known fact that the halogen in the halogen benzenes is very inert but that on further substitution in the benzene nucleus its displacement may be much facilitated. In how far this is the case with benzene fluoride and its derivatives has received but insufficient notice up to the present. Wannacn and Heustur (A. 248, 242) state that sodium acting at a gentle heat on an ethereal solution of benzene fluoride abstracts all the fluorine with formation of diphenyl. We repeated this experiment, but noticed but Little formation of diphenyl although considerable quantities of resin were formed. Moreover, the sodium was but little attacked. Another process for studying the decomposition of halogen benzenes is that of LÖWENHERZ consisting in dissolving the compound in a large excess of alcohol and then adding sodium. If we call (Va) the number of gram-atoms of sodium which is present at a given moment in a kilo of solvent, « the original halogen compound and wv the portion then converted we have according to him the relation da: ACN) = K (a — x) in which A is a constant which he gives the name of “useful effect” (Nutzeffect). We repeated one of LÖWENHERZ's experimental series with benzene chloride and found the useful effect to be 0.261 whereas he had found 0.254 and 0.268. On applying the process to benzene fluoride it was found that sodium when acting on its alcoholic solution does not abstract a trace of fluorine, so that the useful effect = 0. This result is sur- prising, because according to the investigations of LÖWENHERZ the useful effect is about equally great for the other halogen benzenes. It shows that the fluorine in the nucleus is more firmly combined than the other halogens; some data of WanLacn and HerUSLER agree with this view, for instance, that by the action of sodium on an ethereal solution of p-benzene fluorobromide for 8 days a large amount of sodium bromide had separated but not a trace of Na FI. On the other hand we notice the great facility with which the fluorine of the benzene nitrofluorides reacts with sodium methylate ; the m- and p-compounds, when heated for a short time with this reagent in a methyl alcoholic solution, are quantitatively converted into the corresponding nitro-anisols. In the ease of benzene dinitro- fluoride (FL. NO, : NO, = 1:2: 4) the progressive action of the sodium methylate was studied by the method employed by Lerors for the corresponding Cl-compound and it appeared that the reaction was quite completed within a few minutes. Owing to this ereat celerity, accurate quantitative measurements were very difficult ; but it was found that the reaction constant in round numbers is 600 times larger than with the chlorine compound. Gronmgen, Sept. 1903. Chem. Lab. University. Chemistry. — “The system Bromine + Iodine.” Pye Brot Hawi, Baknuis RoozeBoom. (Communicated in the meeting of September 26, 1903.) The elements chlorine and iodine yield two chemical com- pounds which have been accu- rately investigated by Srorrmy- BEKER. Up to the present the relations of the other halogens remained in obscurity. The system Bromine and Todine investigated by Mr. Mrrrum Tur- WoGT gave, provisionally, the results represented in our tem- perature-concentration figure, Kirst of all the two boiling lines ADB and ACB, which were both determined at 1 Atm. pressure. The first line represents the boiling points of the series of liquid mixtures from LOO°/, Br. to 100°/, 1; the second line represents the vapours yielded by these mixtures. The correspond- ing points are situated on hori- zontal joining’ lines, y The figure shows that these Bx curves are continuous, but OO. \ 52 ) approach each other between 50 and 60°/, I. This case, therefore, 1s similar to the behaviour of the mixtures of Cl and S studied some time ago’), with this difference that for the composition 5,CL, the lines nearly came into contact, whilst in this case the distance remains much greater. The peculiar form of the boiling lines points, however, to the existence of combined molecules of the two elements. Whether these answer to the formula Br I cannot be decided from the form of this line, but perhaps better from the p,x-lines which will be studied afterwards. Below the line ADB the region of the liquids is situated. These on further cooling deposit solid phases. These phenomena are represented by the two lines EFG and EHG. The second line shows the initial and the first line the final solidifying points. They form two continuous lines which however come into contact at 50 atom percent I. A similar type of solidification points as a rule to mixed crystals. The equality of the composition of liquid and solid at the con- centration Brl — without this point being a maximum or a mini- mum — could, however, only be explained by assuming that Br I is a chemical compound. Possibly this is the case, which has never as vet been satisfactorily proved, where a compound is mixable with both its components. We will endeavour to elucidate this matter by a determination of the density ete. Chemistry. — “On the action of emulsin.” By Dr. R. O. Hurzoe. (Communicated by Prof. C. A. PEKELHARING). (Communicated in the meeting of October 31, 1903). lL. If we mix a solution of canesugar with invertin and determine the quantity inverted in definite times at a constant temperature, it appears that the inversion does not proceed as a reaction of the first ‘ it a order G — —/.—— }, the ‘‘constants” calculated from this equation t a—w#v increasing continuously during the period of the inversion. This might be explained by the increasing activity of the enzyme or by the influence exerted by the invert sugar formed. V. Henri?) has shown in an exhaustive paper that the latter is the cause and that the reaction proceeds according to the law 1) These Proc. June 1903. *) Zeitschr. für physikalische Chemie 39, 194 (1901). regulating the unimolecular reaction where the products of reaction act (positively) autocataly tically, For a similar case, OstwaLp ') has given the equation of reaction: du = (hk, + k, Cd ORE are ee EL) dt If we integrate this equation and take «== 0, t=O we find: ] ; aka dk.) lett he H-k,a klar) In this equation @ is the concentration at the beginning, « the amount of sugar inverted at the period ¢, # and #, are the velocity constants. Tf we call SS bo —_— an Je — we obtain the expression if ader (1 He) a which is more convenient for purposes of calculation. bne tue particular ease _s =de! therefore for mt kk, Equation (4) now becomes: 1 ate Ctr be Pe hr WS RY hd CE bn vet 2. If we measure the velocity of the emulsin action it appears that the “constants” of the logarithmic expression keep on decreasing as has already been stated by TAMMANN ’). As it appears from Hrnris experiments *) that the enzyme suffers no change, at least when the time of reaction is a short one, it was evident that the cause of the phenomenon was to be sought in a negative autocatalysis namely, am the retardating influence of the products of inverston. In a similar case the equation of the reaction assumes, according to Osrwarp *) this form: der i roa (he, hee) (ESR pas) CON Mee ones OF After integration and calling «=O f=—=0, we find: 1) Lehrbuch der allgemeinen Chemie. Il, 2. 1 Teil. S. 264, 265. 2) Zeitschr. fiir physikalische Chemie 18. p. 426 (1895). 3) Thèses P. 106. 107. (Paris 1903). alen 2455 . 334. ) 1 uk (hk, — hye De A0 bn aL (7) kak, k,(ak,—k,@) If again we take : ak, d Se : k, (8) we find: 1 a—ér 7 == : {) LS ee () or ‘ea a ig ee aie ee (10) aw in which « is the concentration at the beginning, 7 the amount of sugar inverted in the period 4, 4, the velocity constant of the reac- tion if taking place without autocatalysis and #, the constant of the autocatalvsis. 3. This formula was investigated in a number of cases and it appeared that the reaction may indeed, be represented by that expression. As in the case of invertin it has appeared that the quantity €, which, according to the assumption made, need only remain constant during the same series of experiments, as a rule suffers but little change (from 0.6 to 0.8). Probably, the value of ¢ depends on the previous history of the enzyme, but it should be remembered that emulsin is much more sensitive than invertin. In the following tables a stands for the concentration at the start wv the quantity inverted, therefore a = the relative quantity inverted ¢ the corresponding time in minutes. The third column contains the value of 4, (1—s) caleulated accor- ding to (10). : 1 a In the fourth column we find 9 = — = ( 335. ) öxperiments by V. Henxri') on October 30, 1902 |. OPEN Saliem solution == 056, 7 be) [(1—=) £, | 10° | 224105 2) 0.132 | 5 [6 | JAG 0.209 55 SO 185 0.306 87 Sl 182 0.534 214 78 | 157 | 0.603 | 24 | 76 | 448 0.686 | 375 | 73 135 0.950 | 1825 | 1D 100 II 0.07 N, Salicin? solution -= 0.6, Wee WS oe ide em ba. K t [(4—2) #,j 40! | 2105 a | OPEL Zet 24 15 345 0:351 54 16 BAS 0.450 86 14 302 0.691 210 | 13 DAB Pact tay 27) 14 240 0.847 ok 14 1 220) Experiments by V. Henri on October 8, 1902. i, IT. 0.144 N. Salicin solutfon :-—0., 0.07 N. Salicin solution -=0.6. wv , Pr ke 2 t (1—=) #,} 10 * t ((1— =) 4,] 10! 0 110 of [GS | 0,476 122 1} 0.305 193 n3 0.651 200 12 0.447 214 DR 0.691 275 10 0.516 276 56 0.767 342 LI 0.523 343 56 !) Thèses P, 108 —109. *) Calculated by Henri Le, p. 103, IIT. 0 035 N. Salicin solution e=—(0=6. = t | [dk 104 0.182 28 13 0.564 5 a 15 0 685 208 | 15 0.818 275 | 16 0.879 341 | 17 Experiments by V. L 0.44 N. Salicin solution = =0.8&. 4 t {—<) k,]10° : (A5) 4) 0.179 GO | 0.371 177 927 OFS IO4 IS 0.550 355 97 0 579 IAS 25 [bk 0.075 N. Saliem solution + 0.0385 N. (Saligenin + glucose) > —=() &, t | [ 1- =) 4} 10° Otay 57 IN 0.400 Bj 32 0.539 291 31 0.507 JD Oe Henrt on October 10. 1902. Bl 0.105 N. Salicin solution -=0O.8, i } : a a { ((1—=) #,] 10° 0.216 6) 39 0.462 176 37 0.606 293 40 0.636 357 36 ne 0.105 N. Salicin solution + 0,035 N, (Caligenin + glucose) == 0 8. L re pe t [UL --2) 4,] 10° 0.128 50 22 0.344 176 25 O5 293 23 07525 357 24 V, VI. 0.07 N. Salicin solution + 0.07 N, (Saligenin + glucose :=0.8.) 0.7 N. Salicin solution := 0.8. OER e & On ag ie £ | Ri Tree a Anken one | ee OA%6 15 By 25 0.921 SR | ‘ul OBA ie ATI A 23 0.524 172 50 0376 | 292 | (17) 0.688 | 291 55 | | | 0.536 | 335 | 25 0.712"); 355 49 VAT: VIL. 0.035 N. Salicin solution + 0.095 N. (Saligenin + glucose) = 0.8. 0.035 N. Salicin solution :—0.8, ¢ € we mer ke eee “2 wv = = | ze | | ((4—=) 1 40° En | | a ENA 5 a | t | [(1—z) 4] 10 5 | t. | [Ae 4] 10 0.194 D7 36 0 394 D6 95 0.469 170 | 42 0.695 | 470. | 92 0.618 289 | 12 0.880 | 988 | 436 Experiment communicated by TAMMANN. Zeitschr. fiir physikalische Chemie. 18. 486. 3.007 gram Salicin in 180 cc. water :=0.6. © ; . Ee 4 ay ER | (2) | (d=) 4] 103 | 2>< 10% 3) 0.15 | DA 61 EE: | 25 7 | 0.58 D | [38] [75] 0 65 & | ov DS 0,76 12 | 29 O2 { 0.91 26 | 27 40 | | 0 9S | 50 | YS xD By way of comparison L cite an experiment with amyedalin which I have made in the course of another investigation. 1) In the original paper it says 0.612, but this is probably a mistake. 2) In hours. 5) Calculated by Tammany, ( Soo 9 The hvdroevanie acid was titrated by Linpic’s method; in the first period of the reaction, values are found corresponding with those of the sugar determination *). | 0.4 N. Amygdalin solution. wv | en oe | irae 0507 |} ~ 60 | 2 0.619 | 80 | 26 0.732 | 199 97 4. These tables show that the immutability of the expression in the third column is satisfactory. In Heyes experiments those values differ but little more than those of the invertin action. ‘To some extent the experimental errors may certainly be attributed to the sensitiveness of the emulsin and partly also to the method followed. The table with TAMMANN’s experiments proves this. The constants vary within rather large limits but agree reasonably with an average valne. 5. If we now accept the hypothesis of the negative *) autocata- lysis, and after what has been stated this seems to me quite per- missible, there will be found to exist an evident parallelism between the action of emulsin *) and invertin. The ferment-reactions which up to the present have been accurately studied proceed therefore according to the scheme : Ek (BE) oO Sa ee in which 4, may also be zero *). This, however, only means that / is constant for the same series of experiments or fora definite concentration of material *) and enzyme. We may say that there exists a function of the form: ONIN tare MON aes 6 in whieh « is the concentration of the inve:tat.le matter and 4 that of the ferment. 1) Compare Tammany, Zeitschr. für physikalische Chemie. 3, 27 (1589). 2) This may,be one of the causes that the synthetical experiments with emulsin (Tammany, Exwernine) have given a negative result 3) This is probably also the case with other ferment-reactions. \) It is not inconceivable that cases may occur where if ¢ is small, © would at first act positively and afterwards negatively. 5) Up to the present it is only haemase for which Sexter (Zeitschr. fiir physi- kalische Chemie 44. p. 257, (1903)). has obtained different resulis within a small concentration limit. In any case we may conclude that the differential equation (11) is incomplete and that it would be better to give it the form for a reaction of a higher order’). cla Ae OO ME Le re een lo dt which corresponds within certain limits with experience *). Generally this relation is expressed by the equation: b, n hk, = NEN ey ee el AE 14 (5) rs oe From TAMMANN’s*) experiments with emulsin if appears that in any case . eae (COMO re tetra al eee ai he cc eh > AEN It is also important to observe that /, is apparently only changeable within the limits of the experimental errors, whether we start from the concentration @, of the substances to be inverted or whether we choose as the starting point the concentration «, +, in which a, << a, and 2 corresponds with an amount of inverted product corresponding with @,—a,; Henri has already pointed this out for invertin. ak, : From —* = constant we obtain the somewhat unexpected result: hy hy a h, ct st V2 in which « and « represent the concentrations of the substances undergoing inversion, #4, and 4, y, and y, the corresponding velocity constants. | hope shortly to revert to this matter. The matter communicated here has no connection with the later formulation of Henri') which I cannot vet accept as conclusive, Utrecht, Lab. gen. and inorg. Chemistry University. da k ') The formula Rn (4, k,w)(a — «&) = kh, (3 — r) (a ~- wr) represents cht indeed an expression for a bimolecular reaction. 2) Compare, Zeitschr. für physiologische Chemie. 37, 159. (1902). There is an evident connection with Horrsema’s experiments (Zeitschr. für physi- kalische Chemie) 17, 1 (1895) but it seems to me that we must not think with Hoser (Physikalische Chemie der Zellen und Gewebe, 1902 p. 312), ef any diss >- ciation of the ferment, but rather of that of the substances dissolved therein. Like Hoéser however, | attach no particular importance to an explanation of this kind based on analogy. 5) Zeitschr. für physikalische Chemie. 18. 426, (1895). 4) Lois générales, p. 107. ; ( 340 ) Geology. — “Deep boulder-clay beds of a latter glacial period im North-Holland’. By Prof. Eve. Depots. (Communicated by Prof. Marri in the meeting of May 30, 19053). In the dunes near Castricum, borings have been done lately, a provincial Iunatie asylum being planned on the spot. With the kind permission of Mr. J. ScHoiren, chief-engineer of the “Provinciale Waterstaat” in North-Holland, | was allowed to make some hydro- logical observations and to inspect the specimens of the sediments met with in the borings. When examining them a remarkable peculiarity came to light, which I subsequently learned to have been found also in a former boring at Uitgeest. While, namely, in the dunes at Castricum, down to the lowest depth of the borings, no geological facts were observed not known to me from elsewhere, in two boring-holes, at a distance of about half a kilometer from each other, from north to south, at a depth of 325 > A.P., a very tough clay was: found which -possesses all the qualities of boulder-clay. Immediately on it rests a bed, about 12 M. thick, of coarse-grained sand and gravel, which, near to its basis, together with Rhinish pebbles, contains also Scandinavian ones. Very probable —_ several circumstances point in that direction — many, at least of the latter, had been imbedded in the clay. As already said, the clay was very tough, mixed however with very angular, finer and coarser grit. Washed, it proves to consist for a large proportion of real clay (hydrous aluminous silicate). Dried it is hard as bricks. In short it is a real, glacial boulder-elay. The colour is bluish-grey ; yellow or reddish clay could indeed not be expected at such a depth. The pebbles from the gravel-bed, and partly no doubt from the clay, are remarkable for their petrographical character. Besides quartzite of different colours and fine-grained sandstone largely intermixed with mica, white quartz, lydite, flint, there are granite and some other stones of eruptive rock species; amongst others also alndite, altogether 80 pebbles, all of them evidently of Scandinavian origin, but | also picked up from the gravel, overlying the clay-bed, (part of it apparently had got washed out from the clay-bed by the boring process) some thirty pebbles of Silurian limestone, mostly beyrichian-limestone, of the same kind as those, ( 341 ) well known to me, from the bottom-moraine of the Mirdum Klif in Gaasterland, which fact places their origin beyond any doubt. The biggest of those limestone pebbles, consisting of coral-lime- stone, is of 32, the smallest of 8 mM., maximal dimension. A dark slate stone of -38 mM. greatest dimension, shows a polished surface as by ice-action. The fact that we meet here with a formation of the same kind as the one found on the south coast of Friesland, grew perfeetlv clear when examining specimens of deposits from borings, done by Mr. A. J. Srorr, near the station of Uitgeest, at 5 or 6 K. M. south- east of those near Castricum. Mr. Storn who made also the borings in the dunes near Castricum, had not only kept the specimens of those at Uitgeest, but of many others done by him, which speci- mens he allowed me to study. Also at Uitgeest, at a depth equal to that at Castrieum, i.e. from 31 M. down to 38 M.~+A.P., a large number of stones have been found imbedded in clay, mixed with grit of rocks, perfeetly similar in their petrographical character to those at Castricum; those stones were even of considerable dimensions and for more than the half undoubtedly of Scandinavian origin. Under the clay again gravelly sand, to a depth of 43 M., where it rests on a bed of rather stiff clay, According to communications from Mr. Srorr, the stones, for the greater part, come from the clay-bed, 7 M. thick. Indeed some of the stones show some still adhering clay. Amongst the rocks are prominent, besides quartzite — of which the biggest stone is 85 m.M., maximal dimension —, white quartz, an odd lydite and sandstone, some pieces of crystalline arkose, from the Bunter on the Rhine, of the size of a walnut, further different eruptive rocks of Scandinavian origin, namely granite, Compact porphyry, lestivarite, ornöite, especially flint nodules, some of these being 60 mM. But also here, the Silurian limestone-pebbles are the most important; 5 of them have been kept, consisting mostly of beyrichian-limestone, strikingly resembling those which occur in the boulder-clay of the Mirdum Klif. Those pebbles are of the following dimensions. k3I 33° wedde mM: UE 44-35. LS em Ms UI. 33 X 25 X 25 BY) ok as SDN, SOS ars, IT and IL show unmistakable signs of having been polished and characteristically striated by glacial action, whereas the three others, although not very hard stones, have at least the angular appea- rance of glacial pebbles, ( 342 ) We may further mention that here, as in the till of the Mirdum Klif, flints and Silurian lime-stones, occur most frequently. Lately Mr. Srorn gave me a number of Scandinavian stones from a boring at Koog near Zaandam. Amongst these, met with at about 40 M. — A.P., are an alnöite of 120 m.M. largest dimension, a eranite, not much smaller, different Silurian limestones, one of which is 65 m.M. The facts stated prove, that in the mentioned part of North- Holland, beneath 81 > A.P. there is a bed of boulder-clay, a real bottom-moraine. On it rests at Uitgeest and at Castricum, coarse-grained sand and gravel from the lowest part of which, no doubt, some of the described erratica come and which contains shells, marking it to belong to the so called Eem-bed, the equi- valent of the Flandiien of Rutot. Of importance, for the comparison of the geological structure with other localities in our North-Sea provinces, is the fact that boulder- clay was lacking at a corresponding depth in two other borings, [about mid-way between the two described] in the dunes at Castri- cum, one of which went as deep as 45 M.— A.P. There, at 40 M.— A.P., was a thin layer of 0.30 to 0.40 M., and between 30 to 35 M. — A.P. coarse-grained sand and- gravel, containing similar small pebbles of beyrichian-limestone. On account of the absence, in the two last mentioned borings, of distinetly marked houlder-clay, the existence of a bottom-moraine, immediately under the Eem-bed, would have been presumed as little here as in most other cases elsewhere. Still proofs of its existence, also in other. spots in -and near the dunes of the North-Holland mainland are not wanting. For instance, at borings done, some years ago, in behalf of the Harlem waterworks, at 3 K.M. west of Santpoort and 12.5 K.M. South-west of the boring-hole at Uitgeest, at a depth from 38.75 to 43.75 — A.P., a bank of sandy clay or rather till was found, 5 M. thick, towards its base changing into sand mixed with clay, which now appeared being only another part of the same bottom- moraine as the one at Castricum and at Uitgeest. Shells of the Eem-bed occur in it, down to 35 — A.P., although the clay or the till seems to be rather pure, washing shows it for quite '/, to consist of angular grains of sand, containing some small stones of a peculiar nature. From about 100 cM*. of that clay 9 angular pebbles, of beyrichian-limestone were obtained, of which the biggest is 10 mM., and 12 fragments of eruptive rocks of different kinds, of Which two are of felsite-porphyry. An about equal quantity of sharp sand, mixed with clay, taken at the basis, 43.55 M. > A. P. deep, produced ten pebbles of the same Scandinavian limestone species, the biggest having 12 mM. maximal dimension, besides 15 pieces of various eruptive rocks, amongst which two of compact porphyry. For the rest the specimens contain only a few red and grey quart- zites and an odd flint-nodule; the typical Rhinish rocks are at any rate by far in the minority. No doubt this clay of the northern extremity of the prise d'eau of the Harlem waterworks is a boulder- clay of Seandinavian origin, the bottom-moraine of an ice-sheet preceding the deposition of Eem-bed, which is considered to be the youngest stratum of the Diluvium in our country ; so the basis of the mentioned bed with sea-shells, indeed corresponds with the end of the last advance of the northern ice. In a recent, much larger boring, in close proximity of the just mentioned one, the uppermost occurrence of Scandinavian stones, measuring 4 ¢.M. ad marin, side by side with a large majority of stones of Rhinish origin, is found to be at 32 M.--A.P.. The boring did not go deep enough to reach the boulder-clay bed, but at 33.5 > A.P. it met with a thin layer of black loam, containing some remains of freshwater-plants. The basis of the Pleistocene shell-bed clearly is at 32 M.— A.P. At Harlem Lori found that basis at 35.6 M. — A.P. and | found it at a similar depth myself, in a number of borings done at Harlem, of which Mr. Srorr had kept the specimens. At Velsen, shells characteristic for the Eem-bed are found down to a6 oM: A.F sat Castricum to 31:5. M:, at Uitgeest. fo 31 M. at Purmerend to 32 M.; at Alkmaar to 34 M.; (a similar figure is given by Lomm), at Vogelenzang (according to Lori) to 36.6 M.; in the dunes between Katwijk and Scheveningen, in borings for the Leyden and the Hague waterworks, the shells were found, down to 28 M. — A.P: and at Monster, in borings for the Delft waterworks, down to at least OU DE. ALP. A little higher, at about 30 M. — A. P. average depth, or a few meters less deep, lies in the western chief part of North- and South- Holland, the upper side of a zone of coarse-grained, often gravelly sand, even of real fine gravel, which often contains bigger or smaller stones. It corresponds with a last increase of the geological transport in the Pleistocene, which was connected with a last period of glaciation. Fourteen vears ago, its existence was thought not altogether impossible by Dr. Lori, though, (considering the knowledge we then had of the Duteh soil), he did not venture to draw a 23 Proceedings Royal Acad. Amsterdam. Vol. VI. ( $44 ) more definite conclusion’); the fact that in the Mlandrien Seandi- navian erratic stones occur, was stated by Rutor?) in 1899. That here indeed we have before us evidence of a glacial period is proved not only by the above stated facts, but also by the other fact that, in the mentioned zone of coarse-grained sand and eravel, often big stones occur, in the very midst of less coarse material, which stones in some cases are of Scandinavian origin. So in the mentioned deep-borings for the Harlem waterworks, at 36 > A. P., a very big pebble of calcareous sandstone was found of which a frag- ment LL eM. long has been preserved, and in other deep-borings near the Harlem water-tower, at 338.5— A. P., a flint of 12 and a quartzite of 7 ¢M. largest dimension. At Hillegom, where the oravel on the whole is. rather coarse, I saw fragments of a reddish sandstone (from the German Bunter), found there at a depth of 32 M.— A.P., which must have been bigger than a fist, and from Heemstede a violet (Bunter) quartzite stone, of 9 cM., largest dimension, raised from a depth of 25.5-> A. P., among small oravel, with many shells. Mr. D. E. L. van DER AREND, showed me from borings, done at Adolfshoeve in the Harlemmermeer polder, a number of pebbles, raised among coarse-grained sand and fine gravel, amonest which was a erey quartzite of 10 eM. In borings done in behalf of the Leyden waterworks, in the Katwijk dunes, where, just as at Hillegom, the gravel is coarser-grained than mostly elsewhere, at a corresponding depth, pebbles of the size of a walnut, up to that of an ege, were repeatedly met with. Nearly all these stones are of Rhinish origin, giving evidence of transport by floating ice. Mr. J. LANKeLMA of Purmerend, told me, that in the many borings he yearly does, he had generally found in North-Holland, at about 30 M. > A.P., stones, sometimes in such a large number and of such a considerable size, that they considerably hindered the borings: even to such an extent, in the Oostschermer polder (Polder Kk), on the Blokker road and at 1 K.M. south of the church, that they had to throw up the work, any further progress being rendered impossible by the bore striking on an impenetrable stone-bed, immediately under the shell-bed. At Enkhuizen, Mr. LANKELMA found, at an equal depth polished and = scratched Scandinavian stones, which he had frequently come aeross (according to his opinion: granites). From borings done at Alkmaar, Mr. Srorr, gave me a fragment almost as 1) Bulletin de la Société belge de Geologie, de Paléontologie et d’ Hydrologie, Tome 3, (1889), Mémoires, p. 449. | 2) Ibid. Tome 4, (1899), Procés-Verbaux, p. 321, ( 345 ) big as a fist, of a smooth, but angular stone, consisting of felsite- porphyry, raised from a depth of 46 M.-— A. P.’) Those instances may suffice to show the very frequent occurrence, in North- and South-Holland, of evidence of an increased transporting power, in the latter part of the Pleistocene or Diluvium Period, not only of the water, but also of an other means of transport, i.e. by the ice. The facts known at present, no longer leave any doubt as to the real existence of a younger ‘gravel-diluvium”’, here and there alter- nating with boulder-clay. This younger formation is less powerful than the older “graveldiluvium”, for it rarely considerably exceeds ten meters, but it has an equal right as the already long known older and more powerful one to be considered as partially produced by an advance of the Scandinavian land-ice, partially by an increased and modificated transporting power of the Rhine, which river then carried much floating ice. Before concluding I may be permitted to add a thing observed, a year ago, in the boulder-clay of the Mirdum Klif. Amongst other beautifully scratched, glaciated stones, | collected there four, of which three consist of beyrichian-limestone, which are not less typically faceted as those described from the elacial Permian in the Salt Range of the Punjab, from which circumstance it is evident that there is no necessity to suppose for the Palaeozoic glacial period, circumstances entirely different from those of the Pleistocene Ice Age. 1) Towards the east of the Harlemmermeer polder stones occur at a much higher level. This was frequently stated in borings done on the grounds of the military waterworks near Sloten; amongst more other pebbles, | saw a fragment of greenish grey sand-stone, 14 ¢.M., largest dimension, which fragment had been raised near the Ringvaart of the Harlemmermeer polder, from a depth not greater than 16,5 M. > A.P. A similar fact is known from Aalsmeer. The undisturbed horizontality of the deep peat-layers in this region (the one, more continuous, having its base at 11 or 13 M. > A.P, the other, fragmentary, at about 18 M. — A.P. and nearly continuous to the north and north west, from Purmerend to Hoorn and Enkhuizen and from Wormerveer, Velsen and Beverwijk to LJmuiden, its base being, indifferently, at 17 to 20 M. > A.P.) shows that we have not before us at Sloten and Aalsmeer, the result of a general sloping of the strata, but only a locally higher situation of the upper part of the Diluvium, the coarse sediments having here been locally upheaped. 23% ( \ AG 5 OF Physiology. — “On the fact of sensible skin-areas dying away ina centripetal direction.” By Dr. G. vaN RINBERK. (Com- municated by Prof. C. WINKLER) . / (Communicated in the meeting of October 31, 1905.) The manner in which, in our experiments on dogs, ') the isolated root-area of the skin (dermatoma), dies away, if the root to which it corresponds, is killed by compression, gives rise to the supposition that this peculiar series of gradually narrowing and shrinking areas, proceeding from ventral to dorsal part, from the lateral parts towards the centrum, may be caused by very simple reasons. This point was demonstrated in our last Communication. In the case of a root being slowly destroyed, its sensibility in the sensible skin-area dies away first in its most peripherical part, continually diminishing further in a centripetal direction. In order to test this conclusion still in another way, L have chosen the old experiment of compressing the nervus ulnaris in the human body. Having taken the necessary precautions’ for securing a precise loca- lisation of the trauma, L tried this experiment twice on myself. The results, as far as I can judge, were in perfect accordance with the rule, established in our former essays. They may be described as follows: shortly after the compression has begun. (by means of a pencil put into the fossa ulnaris), paraesthesia’s are observed, princi- pally in the tops of the fourth and fifth finger, descending slowly from thence to extend over the whole of the ulnar side of the hand, and finally ending in perfeet insensibility. If the skin of the ulnaris-area is pricked with a sharp pin in the first period of the paraesthesias, it is experienced beyond any doubt that the pain- sensation is much less acute in the little finger than in the lateral part of the hand. Somewhat later a new symptom may be observed : the sensation is becoming distinctly dissociated. At every renewed pricking, at first only a slight touch is felt, and only a little after- wards a sensation of pain sets in, continuing for a rather long period. This symptom of dissociation too has its beginning in the little finger. After some lapse of time it also reaches the lateral side of the hand, whilst in the little finger it has already undergone a change, the interval between the sensation of touch and that of pain having become longer, and this latter sensation greatly diminished. 1) Prof. CG. Winkrer and Dr. G. van RujnBeRK. On function and structure of the trunkdermatoma I, Il, Ill, Royal Acad, of Sciences, Amsterdam 1901—’02 and IV ibid. 1903. At last the sensation of pain is wholly lost, and only that of touch remains, till finally the latter too has disappeared, and first the little finger, afterwards also the external lateral part of the hand have become absolutely insensible. As I said before, these results appear to me to be in perfect accordance — for the paimestimuli at least with the rule we have tried to establish: putting to work nearly equal causes, (i.e. both slowly destroying the conduction in a nervepath) the consequences, as well for the sensible ulnaris-area as for the dermatoma, will be equal too. In both skin-areas the pain-sensibility begins dying away in that part, situated at the greatest distance from the centrum, the most peripherical part therefore, this process continuing slowly in a centripetal direction. As to the dissociation, our experiments on dogs have taught us likewise that it may not so very rarely be observed, how the reaction on the pain-sensation, when pinching the sensible area, is retarded. Principally in cases where this area was a small one, or only the remnant of the central area after a very considerable reduction of it. In such cases moreover the pain-reaction was generally very protracted. The results of the experiments taken on dogs and of those tried on myself, are there- fore in perfect accordance with one another. As to the sensation of touch, the experiments on dogs could not teach us anything about this, because it was impossible to make use of any other but pain-sensations for our definitions. The ulnaris- experiment however has shown us, that paralysis of the sense of touch does begin in a later stadium than that of the pain-sensation: Whilst its dying away in a centripetal direction cannot be demon- strated with the same evidence as for this latter sensation. At any rate the first fact is very significant, the more so, if considered in connexion with SHERRINGTON’S communication ') on dissoviative anaesthesia, as has been explained more fully in our fourth com- munication *) on funetion and structure of the trunk-dermatoma. Physiology. — “Structure and function of the trunk-dermatoma” IV. By Prof. C. Winker and Dr. G. van RIJNBERK. (Communicated in the meeting of October 31, 1903). In the course of three preceding communications *), a few observations coneerning the structure and the functions of the trunkdermatomata, have been treated of. 1!) Journal of Physiology. Vol. 27. 1901—02. 2) Royal Acad. of Sciences, Amsterdam, Oct. 31, 1903. 5) See: Proc. of the Royal Academy Noy. 30, Dee 28th 1901, Febr. 22th 1902, 848 ) At present, guided by some new experiments in this matter, we intend to make an endeavour towards constructing our former results provisorily into a whole, in order to bring the facts, found by means of physiological researches, into accordance with the anatomical records of the peripherical skin-innervation of the trunk. We know but little with certainty about the topography and the exact form of the different trunkdermatomata in man. Our knowledge of both, such as it is, is due for the greater part to a more just evaluation of the skin-innervation of the nervi intercostales *). It is evident however, that in the physiological experiment the anatomical proportions will have to find their expression on the periphery, and to all probability our dermatomata, determined by physiologie methods, will be proved to be wholly identical with the extension-areas of the skinbranches of the nervi intercostales. According to our belief, on dogs this supposition has been even proved already by our experiments. For by means of a careful examination of a series of central areas, it has been made clear that the differences in shape, manifesting themselves by shortenings or interruptions, may all be retraced to anatomical proportions. The division of the interrupted central area into a dorsal and a ventral part, follows almost directly from the anatomy of the intercostal nerve, whose skinbranehes consist in a posterior and an anterior, respectively a dorsal and a latero-ventral branch. The place where the central area generally suffers interruption, or where in favorable cases on the contrary it is found to be broadest (the lateral part therefore of our trunk-dermatoma) corresponds to the skin-area of the rami cutanei laterales of this nerve. In this way, for the physiologist too, the central area is divided into three individually different parts, form and function of each of which ought to be treated separately. For a knowledge of both is necessary in order to understand the significance of the dermatomata on the extremities. The dorsal part of the central area is shaped like a truncated triangle, whose basis is situated against the mid-dorsal line. Its apex approaches the lateral line. Between the latter and the mid-dorsal line a line may be traced from the dorsal border of the axilla to the fossa inguinalis. It has become evident already from our former communications that in favorable cases the dorsal central area towards the mid-dorsal line possesses almost the same breadth as the whole dermatoma. 1) Bork. Ken en ander over segmentaal-anatomie etc. N. T. v. Geneeskunde 1897, Vol IL eNo 0; 349) In less favorable cases it is narrowed, in very unfavorable ones if has shrunken away to the sensible area situated at a small distance from the mid-dorsal line (fig. 1, 2, 3, +, «). It is there (see fig. 1 a) that is situated a maximum of the dorsal part of the central area, at the same time the ultimum moriens of the whole dermatoma. t / / 2 3 4 | ehh. 1 / Ni Fie. 4. The different parts of the dermatoma. d — mid-dorsal line. » == mid-ventral line. L =lateral line. Id = dorso-lateral limitline (from dorsal border of axilla to fossa inguinalis). ip — ventro-lateral limitline (from ventral border of axilla to fossa inguinalis). 1 = Boundaries of the theoretical dermatoma. 2 = Boundaries of the dermatoma (central area) as it may be observed in very favorable cases. 3 = Boundaries of the central area in less favorable cases. 4 = Boundaries of the dorsal part of the central area and 6 = Boundaries of the ventral part of the central area as they are observed in very unfavorable cases with interrupted central areas. 5 == Boundaries of the lateral part of the central area. Gy) a= dorsal, QD b= lateral, c= ventral maximum, ( 350 ) The lateral part of the central area, more difficult to be rendered because of its great variability of form, may be represented, in cases very favorable to isolation, by a nearly hexagonal figure (see fig. 1, 5). In very unfavorable cases it cannot be shown at all. In such cases the central area appears to be interrupted. Between both extremes other cases may be observed, in which the lateral central area has been only partly preserved. An instance may be forwarded by the following observation: I. On a strong male dog the 16th dermatoma is isolated in the usual manner. The day after the operation a central area is determined, the extension of which is represented in fig. 2, Possessing a broad basis at the mid-dorsal line, it ends in a point towards the mid-ventral line. Fig. 2. A continuous central area, extending itself from the mid. 1: to the mv. 1. , After two days, this area has fallen asunder into three parts, viz. a triangular area towards the mid-dorsal line, a rhomboidal area towards the mid-ventral line (see fig. 7), and a circular area situated between the former two (see fig. 3). Fig. 3. After two days, this area has fallen asunder into three parts. a en 851%) Evidently in this case the three separate parts, into which the originally continuous central area of the dermatoma has divided itself as it were under our very eyes, may be considered as the three unities which we believed ourselves justified in distinguishing in the dermatoma '), their considerable shrinking having made it possible to demonstrate each of them individually. For these same reasons the small circular arca between the dorsal and ventral parts, signifies here a maximum (see fig. 1 4) in the lateral part of the central area, similar to the one shown already in the dorsal part. Though it may not be found very often, the foregoing observation stands in no wise alone. In the experiment also, from which the annexed fig. 4 was taken, the central area, having fallen asunder into three pieces, might be observed for more than a week. The proportional rarity of this last maximum may be easily accounted for. In the first place it is relatively a feeble maximum. If therefore the traumatic lesion of the central area is too important, the maximum is destroyed, together with the whole lateral part. If on the contrary it is not important enough, in such a manner that, all- though there has been an interruption of the central area, still a larger part of the lateral piece remains unimpaired, the sensible remnant of the lateral piece will confound itself with the ventral piece. In order therefore to demonstrate an isolated maximum, we need a certain degree of exhaustion of the lateral piece, not strictly definable, not strong enough to render this part quite insensible, vet sufficiently strong to destroy its eventual connexion with the ventral piece. *) Finally the ventral part of the central area. This may be represented as an oblongly stretched oval along the mid-ventral line (see fig. 1,6.). Very rarely this may be observed as an isolated whole, because it easily unites itself with a part of the lateral piece of the central area, situated roundabout the lateral maximum. Still the case does present itself sometimes, whether or no the maximum of the lateral part has been preserved. Fig. 5 and 6 offer instances of this case, whilst in fig. 7 the same dog, represented already by fig. 2 and fig. 3, is designed in another attitude, in order to show the ventral part. 1) See the Proc. of the Royal Acad. of Sciences, mentioned before. 2) See: Proc. of the Royal Acad. Nov. 30: 1901, fig. 4 and also : CG. WinkLeER, Ueber die Rumpfdermatome. Monatschrift fiir Psychiatric und Neurologie. Bd. NHL Heft 3. Bk “wore [eaguoo ayy Jo syaed ooaqyg ay} Buraous ‘Sop 1oygouy 4 ‘oly Fig. 6. Fig. 5 and 6, Dorsal and ventral central area, defined two days after the operation, Fie. 7. The same dog from Fig. 2 and 3, photographed in another attitude in order to show the whole of the ventral piece of the central area, The ventral part of the central area too possesses its maximum, still to be demonstrated in cases, where the maximum of the lateral central area (see fig. 6) has already descended under the threshold of sensibility, and is therefore lost. It is of a somewhat rhomboidal form (see fig. | €). in resuming the total of our observations, we obtain for the trunkdermatomata the following results: Ist. The central area is composed of three parts of distinet signifi- cance, their individual difference showing itself already in the manner in which they overlap one another. *) ged, They may be demonstrated independently of one another. 3rd. Each of them suffers in a different way the reducing influence of the operative trauma. 4th) Each of them individually possesses a maximum, centre or ultimum moriens: in this manner that the ultimum moriens of the dorsal piece must be understood at the same time to be that of the whole dermatoma. 5%. Each of them corresponds to the extension-area of a different branch of the intercostal nerve. Starting from these facts, an endeavour may be made to explain the singular reduction of the sensible area, because of which it becomes only possible to demonstrate that part of the dermatoma we have called its central area. Though its cause certainly ought to be songht in the operative trauma, yet this accounts in no wise for the different manner, in which the reduction may be observed in the dorsal, lateral and ventral parts of this central area. The pointed narrowing of the cental area towards the ventral side, hitherto has been accounted for by the greater stretching of the ventral part of the trunkskin as compared with its dorsal part. It was supposed that an originally equal number of nerve-arborisa- tions existed on the dorsal as on the ventral side. This number being extended over a larger surface — as is the case for the ventral side — the result will be a higher threshold of sensibility on this side. In our nomenclature this was called: enlarging of the marginal area at the expense of the central area. Partly too, the perhaps still larger extension, caused by the erowth of the extremities, may be called in aid to explain the fact, that the lateral piece is at once the broadest as well as the feeblest part of the dermatoma. But yet there must needs be found another collaborating factor, if we intend clearing the apparent contradic- 1) See: Proc. of the Royal Acad. Febr. 12th 1902. ( 355 ) tion, that it has been proved impossible to isolate a ventral piece, the breadth of which is in any way comparable to that of the dorsal, much less to that of the lateral part. For though the streteh- ing of the lateral piece caused by the growth of the cone of the extremities, must be very considerable, yet it does not become sufficiently clear at first sight why it should be precisely the ventral parts of the dermatomata that remain the narrowest portions of the central area, even in the most favorable cases. We believe it is in the peripherical relations of the skin-inner- vation, that the factor will be found, accounting for the fact that, in favorable cases, the lateral part of the dermatomata has been observed to be so much broader than the ventral part. Experience has taught us that each simgle part of the central area is slowly becoming insensible from its periphery towards its maximum or centrum, and that the central area as a whole does the same from ventral towards dorsal side, and as these maxima or centra correspond with tolerable accuracy to the entrance-place of the peripherical sensible nerves, some explanation is already afforded. The maxima thence would be those places situated nearest to the centrum (ganglion or medulla). If now by means of a trauma hitting the nerve-root, the free conduction of stimuli is hindered, the stimuli, retaining their activity longest, will be those that are enabled to reach the centrum along the shortest path from the root-region. This rule prevails for the whole dermatoma as well as for each single part of the central area. In the case of dogs, where the medulla is situated very close to the back, the distance from ventral skin to medulla is at least twice as large as the distance from back to medulla. For this reason alone already, the ventral part, indepen- dently of its greater extension, will be the first to be reduced, and the ulfimtun moriens of the whole dermatoma will be found opposite the entrance-place of the dorsal skin-branch into the dorsal piece of the central area. The lateral piece of the central area, being put by its tension into unfavorable conditions, probably even more unfavorable than those of the ventral piece, still remains less ill- conditioned than the ventral piece of the central area, because of the shorter path followed by the stimuli in order to reach the medulla. In cases favorable to isolation, it is to this latter factor that we have to look for discovering the final cause, why the lateral piece remains very broad, and why the ventral piece, its nerve- path being so much ionger, becomes narrowed. In cases unfavorable fo isolation on the contrary, it is the other factor that prevails, and ( 356 ) the greater tension causes the lateral part to become insensible earlier than the ventral part. This opinion is supported by the facts which we may observe, when compressing a peripherical nerve, e. g. the nervus ulnaris. Im that case too, the sensibility for pain-stimuli slowly dies away from the periphery of the innervation-area on the skin towards its centrum, i.e. the entrance place of this nerve into the innervation-area. The recent communications Of SHERRINGTON *) too, apparently point to this same fact: the central areas dying away slowly in a centripetal direction. His third conclusion especially may be said to be of importance in this matter: “In the skin of macacus the ‘pain-field” and the “heat-field’” of a single sensory spinal root, at least in the case of certain spinal nerves, are each less extensive than is the “touch-field” of the same root.” As in our experiments the stimuli employed were exclusively maximum pain-stimult, a doubt may arise, whether our central-areas ought not to be considered simply as those areas of the dermatoma that are sensible to pain. The peculiar way, in which the intensity of the operative trauma exerts its influence on the form of the central area, renders this supposition highly improbable. Much more probable it is, that the before-mentioned conclusion Of SHERRINGTON expresses in a different manner that the pain-sensibility in sensible skin-areas is dying away in a centripetal direction. The sensibility for pain however — and the ulnaris-experiment also points this way — is lost much sooner than the sense of touch. Experiments made by one of us on sharks, that will be communicated afterwards, are in accordance with this observation, Both the peculiar proportions of the peripherical skin-innervation (entrance-places, extension-areas of the skin-branches in the root-area), and the general rules for the nerve-conduction, are therefore of equal importance for determining experimentally the form of the dermatomata. 3ecause three afferent nerves of different significance innerve three pieces of the trunkdermatoma, possessing each of them a different degree of extension, the sensibility for pain, decreasing (in cases of progressive lesions) in a centripetal direction, will be the cause of the apparently capriciously-shaped central areas, described in the course of our observations. 1) SHeRRINGTON, On dissociative anaesthesia (Journal of Physiology. vol. 27, 1901 —'02). rar) add Physics. — “On the equilibrium between a solid body and a fluid phase, especially in the neighbourhood of the critical state. (il part). By Prof: J. D. van DER Waats. In my former communication the curve of the three-phase-equili- briums was considered as the section of two (p, 7,2) surfaces, viz. that of the two fluid equilibriums, and that of the equilibriums between solid and fluid phases. For anthraquinone and ether this section consists of two separate parts, one on the side of the ether, and the other on the side of the anthraquinone. For values of wv ranging between two definite values, the two mentioned surfaces do not intersect. These values of . are nearer to each other than those of the critical phases coexisting with the solid body. I have indicated them in my preceding communication as a maximum value or a minimum value of vw. We might also distinguish them by writing Te and x, for them. Then 2, is the smallest value of « for which the two (p, 7, r) surfaces have still a point in common on the side of the ether. In the same way 2, is the largest value of «x for the corresponding point on the side of the anthraquinone. In order to examine closer the particularities which take place in the points in which the two (p, Tw) surfaces separate, it is useful, to draw besides the pp, sections of the preceding communication, also the sections of the two (p, 7e) surfaces for constant value of wv. As the particularities in the points, at which the two surfaces separate, differ on the side of the ether from those on the side of the anthraquinone, I have drawn the two following figures, fig. 7 representing the particularities on the ether side, and fig. 8 those on the other side. In fig. 7 we see first traced the well-known loop for the fluid equilibriums, (Cont. II, p. 138). It is taken for the value of « of the critical phase on the side of the ether, which coexists with the solid body. Let P? represent that critical phase and so be the plaitpoint. This plaitpoint has been chosen left of the maximum pressure, in accordance with the circumstance that the plaitpoint pressure will most likely inerease with the temperature. In this point the two (p, 7.) surfaces would have a common tangent, which would be normal to the plane of the figure, and so does not appear in the figure given. This common tangent is of course a tangent to the section of the two surfaces, which section is projected on the plane of the figure as the (p, 7’) curve for the three-phase- equilibriums. As in this (p, 7’) curve the value of p increases with T, it may be traced in two ways; either as has been done in the i , ' i we F 6 ie Bl iB / ‘ P AE ‘ - aw ; y ak ae 1 be * va EEE ij LA Li Hy iy / : / / Aw / PDN ‘ ° ‘ RESON 7 vid ¢ rd Fig. 7. f) figure, passing through a point af of the upper branch, or through a point which has not been indicated and which would le on the lower branch. This projection of the three-phase-pressure is denoted by a curve, which consists of alternate dots and dashes. So besides P, also the point A is a point of the section of the two (p, 7) x) surfaces for the value of . chosen; the point 1, however, at lower temperature. The two curves A and PCD indicate further points of the section for constant value of . of the solidfluid surface, in so far as this section does not He within the region, in which one fluid phase splits up into two fluid phases (liquid and vapour). Instead of the theoretical course of the section between the point A and P, we get the three-phase-pressure. one circumstance, which decides whether the course of is as it has been traced, so There is the curve of the three-phase-pressure running to a point d of the liquid sheet, or whether it ought to run to a point of the vapour sheet. For a value of « lying nearer S we! 1 Fig. 8. to the side of anthraquinone, the theoretical part, in whose stead we get the three-phase-curve, must become smaller, and it will finally contract to a point of contact lying somewhere on the curve AP. Vf therefore for a certain smaller value of, the above mentioned curves are drawn as has been done by the dotted curves, the defor- mation and displacement of the other curves must be such, that a point of contact can occur on the line AP. So the question is, to what modification must the (p, 7) curve of the fluid equilibriums be subjected, when it is traced for smaller value of «#. The answer to this question is given by the sign of (2) . Both for the equili- wv Ih. briums between two fluid phases and for those between a fluid and a solid phase, this quantity is positive as a rule. Only in a limited region reversal of sign may take place. But this does not prevent us from seeing immediately, that in fig. 7 for smaller values of the main position of the liquid-vapour curve will have to be lower and in order to be able to touch the curve AP the position of this latter curve must be as it is drawn. If it had the other 24 Proceedings Royal Acad, Amsterdam, Vol, VI, (eas) position which has been stated as possible, the contact could only be brought about by drawing the dotted lines higher. In the first place this proves that the last point which the two (p, 7,7) surfaces have in common, lies on the upper sheet of the equilibriums between the fluid phases and secondly, that the section of the surface of the equilibriums of the solid phase for the value of « of the point of contact must have besides two vertical tangents, also two horizontal tangents. This is in so far in concordance with what has been observed on p. 240 of the preceding communication, that a similar course for such a curve has been given there. But in so far different, that on account of an incomplete investigation the opinion was expressed there, that the two horizontal tangents are Ory subjected to the condition - = 0. For, if they were subjected to 2 this condition, they would exist theoretically, but they could not be realized. I shall continue and complete the investigation of p. 240 presently, when it will appear, that the shape derived in fig. 7 for a section can occur at constant « and that it can really show a maximum and a minimum in the realizable part. But let us now proceed to examine fig. 8. There the particulari- ties of the contact of the curves are drawn in the neighbourhood of the « of the second critical phase which can coexist with the solid body, viz. that which is richer in anthraquinone. Again for the « of the critical phase the (p,7’) curve has been drawn of the equilibriums between the fluid phases, and the plaitpoint ? on this curve has been chosen left of the maximum pressure. If the course of this dp plaitpoint curve should be such that oF is negative for this plaitpoint, ( we ought to have chosen it right of the maximum pressure. But for our purpose the place where P is chosen, whether right or left of the maximum pressure, is of no account. Only P must not be chosen on the lower sheet, as would be the case for Zò. CL HL. Also the projection of the three-phase-pressure has been drawn this time, in concordance with the fact, that p decreases with increasing value of 7. Now that P is chosen on the left, the three-phase-pressure need not deerease so rapidly, as would be the case, when P? was chosen on the right. The points ? and Q of this figure are now two points of the section of the two (p, 7,.) surfaces for the value of x, which we may denote by (v;)a. For the point of contact of the two surfaces we must know the circumstances at #, which value is larger than (v;),. Now we shall be able to bring about the contact, which is assumed to take place in the figure in point 72, by raising ( 361 ) the curve of the equilibriums between the fluid phases, which is necessarily attended by contraction. In this position the (p, 7’) curve of the equilibriums between solid and fluid phases need not show the maximum and the minimum of p, and only the necessity of the two vertical tangents remains. For still larger values of « and so for « > vq, the two curves, which are dotted in fig. 8 and touch in F, and which also touch the curve of the three-phase-equilibriums in the same point, are separated, and the (p, 7) curve of the equili- briums between solid and fluid phases surrounds the equilibriums between the fluid phases altogether, so that the latter could only appear im consequence of retardation of the appearance of the solid phase. What precedes fully explains in a graphical manner the way in which the two (p, 7,.) surfaces get detached, and it remains only ; ‘ : / ‚ap B to complete the discussion of p. 240 on the course of (5) ‚which ( . a has not been fully carried out there. For the determination of this quantity we have the equation: The course of the denominator in the second member, viz. Vr, has been discussed p. 233. It has been proved there that a locus exists in the (V,.) diagram, generally consisting of two branches, outside which this quantity is negative. These two branches are further apart than the points D and D’ (fig. 2 of the preceding com- munication), and at least in the neighbourhood of the plaitpoint, also further apart than the points of the spinodal curve and even the connodal curve. It is possible and even probable that the two branches of this locus meet. If namely the direction of the tangent in the inflection point of an isobar points just to the point 1, of the figure 2, the two branches coincide. And whereas in the point A’ the direction of the tangent is parallel to the v-axis in the inflection point, in inflection points more to the right of the igobars the tangent mentioned assumes more and more a position, directed to P;. This locus, for which v, = 0, is therefore a curve closed on the right, just as is the case with the connodal curve and the spinodal curve and the curve of the points D, for which Op | Alay . aes 0. Outside this region vy <0, and inside ry > O — only in that part of the region, however, that lies outside the locus of the ( 362 ) 2A and v. we need Ow? not make a difference for the points inside v,¢ = 0, and we may points J. If however we take the product of assume that outside the locus, for which v. = 0, this product is negative and inside it, positive. | need hardly mention, that just as 2 Ov modified and displaced according to the temperature, also the curve vg =O depends on the value of 7. On the whole it will contract and move towards the side of the anthraquinone with increase of temperature, and so follow the same course as the other loci mentioned. the connodal curve, the spinodal curve and the curve — Obare The course of the value of the denominator, viz. of IW. has not yet been discussed. In the preceding communication I had thought that I could leave out this discussion, first because I did not think t necessary at all, but also because I thought that the result of this discussion could not be brought under a simple form, and finally, because I did not wish to add another to the number of loci. The particularity in the course of the (p, 7’) curve, for the equilibrium between solid and fluid, however, to which we have had to conelude in fig. 7, has proved, that the discussion is not to be evaded, at least if we wish to explain fully by theoretical means, the way in which the two (p, 7,.x) surfaces get detached. And the result of the discussion of the quantity IW, has proved to be very simple — and almost exactly the same as the result of the discussion concerning the quantity Vp Just as there is a locus for which V,¢=0, so there is one for which Ws 0. Just as the curve for which V.7 = 0 consists of two branches further from each other than the points D and D’ of fig. 2, which two branches meet outside the top of the plait, in the same way the curve W‚p==0 consists of two branches, further from each other than the points D and D’, and these two branches meet also, either outside the top of the plait, or inside it. And finally the locus, for which Ws 0, lies entirely within that for which Vf = 0. The resemblance goes further. Outside V‚f=—=0 this quantity is negative, and outside W.~—0 the value of Wp is negative. Inside Vs; 0 the quantity V‚f is positive and increases to infinite when we reach the points D and DL’, being again negative inside these limits. The same applies to the quantity Wor. Inside the curve for which yy = 0, this quantity is positive. In the curve of the points D and D’ the value has increased to infinite, being again negative inside the points D and D’, If we ( 363 ) Op examine the product In Wp we see that this product is negative Ov" ; ; outside IW. —=0, and positive inside it. There is therefore only a small region, in which the quantities Wy and Vp have different signs, namely that region inclosed between the loci, for which these quantities are zero. In this case dp d en Brine : ; } ar) is negative. In fig. 7 this is the case for some points on the ; vp curve B’A’RC” on the left of A’, so for the points lying between the point for which the tangent is vertical, and the point A’, for which the tangent is horizontal. In the same way for some points on the right of the maximum, up to the point where the tangent is vertical. In order to arrive at this result as to the course of the quantity Wer, I had first brought this quantity under the form which has been given Cont. IL, p. 110, for the analogous case of the equilibrium between two fluid phases, viz: at 5 der Wap = DV sp Fles Ef — (#s — a7) ( f) der) We may write then (I refer to the page cited of Cont. II and the following page for the signification of the notation): ryy dp é (Es lp fi = mis = 5 dl wp Vs If we represent in a figure the value of ef for a curve of equal pressure, passing through the unstable region, eg. BEDD' Lh’ B’ of fig. 2, we obtain a curve as is represented in fig. 9. The points of this curve, for which ef is small, represent the energy of the liquid states corresponding to this pressure. The points lying between the two vertical tangents represent the value of er for the unstable phases, and the remaining points represent the energy for what we may call gas states. The absolute height of the curve is not deter- mined by anything, as it represents energy. Only if we also represent the energy of the solid body, the latter energy, being smaller than that of the liquid phase of the same concentration and of the same pressure and temperature, will be indicated by a point lying below the curve traced. I have represented it by €. Whenever the tangent s P to this curve cuts the axis above &),, (exp)p is negative and vice versa. Ss The same circumstances which occur for the sign of Vr, are also found here. hed. Dt. But though I have concluded to the course of this value of ee above mentioned from considerations derived from this figure, | have understood afterwards, that we may acquire a survey of this course — in a simpler way. We may give JV, ne a somewhat different shape, which occurs on p. 1 Cont. II, viz. ae de; Ws, == E + a ae 7 Ver a (E5/)o About the quantity (&/)s we know, that it is negative, save for the exceptional case of water below 4°.') Of Vy we know, thats inside the locus for which this quantity is equal to zero, it is positiv and increases rapidly, till it is infinitely large on the curve of the — points D and D'. And as the factor of Wp is necessarily positive, i it follows, that Wp is equal to zero on a curve, which lies between that for which V‚f is equal to zero, in which case Wir (&f)b and ; ; | negative, and the curve, on which Wp is positive and has risen to =e infinitely large. The latter curve is that of the points D and Dean ae We have come to the conclusion that the curve Vp Dd in the G Nea 1) See for the value of (&)» also “Ternary systems HI.” These Proc, IV p. 632. 3 had ( 365 ) neighbourhood of its tops passes round the top of the plait in a fairly wide circle, so that it also encompasses the plaitpoint. We know about the curve of the points D and D', or the points for which Ory Ov? W.¢=90, which lies between them, we do not know a priori how its top is situated with regard to the top of the plait. We may only expect, that when there is a great distance between the tops of the plait and those of the points Wp 0, there is a greater chance that also the locus W‚p==0 will pass round the plait. For the plaitpoint of fig. 7 the latter case has then be realized. For the plaitpoint of fig. 8 probably the opposite case. QO, that its top lies inside the plait. As to the new locus For the points, for which V,-=0, we get: dp def ef (5). : : i (5) Le fi dp | dT He we OT U, L je EA We might immediately have come to this conclusion. For from : es Op zi Op ie Op ke di DT 4 J Se 5 dr an oe Os Op follows the above relation, keeping « constant, and — or ae being zero. (, U dp ih el dT “Op (Es/)p I, ls al pe or If we write: and now take into consideration that (&/), is negative, we derive: dp 4 Op Kea ze fs eS Ji gi when Wp is negative and vice versa. dp dT the immediate neighbourhood of a plaitpoint, with the value of If we compare the value of 7’ for the three-phase-pressure in dT point, it may be demonstrated in several ways, that these quantities ER) Ros eae r( ) for the equilibrium of solid and fluid phases in the next GG have the same value. In fig. 7 it has been really represented like this, but in fig. 8 we see in the neigbourhood of P a sudden break in the direction of the pressure, which does not exist in reality. ( 366 ) The curve extending upwards from # should therefore be bent in such a way, that its initial direction was the same as that of the curve of the three-phase-pressure. The tangent plane to the (p, 7, #/) surface being normal to the plane of the figure, because it contains a line which in P is normal to the figure, every curve on that surface, passing through P, will have its projection in the section of the tangent plane with the plane of the figure; and so both the curves extending upwards from P and those extending downwards, will have their projections in this same section. This follows also from the values of p. 241 (preceding communication). We have for the three-phase-pressure: Ws, W,, ‚dp ne ER en aT Orie Vs dst, td, ; : 4 ’ eon er ta 21 Vai In the immediate neighbourhood of a plaitpoint — and — a A EY v ee 2 1 2 1 dT oT One more remark to conclude with. Now that we have concluded to the existence of the tops of the curves V‚p=—=0 and W,-=—0O, i . : dp Op is equal to zero, (Cont. II, p. 125); and we find = : we shall also have to accept the conclusion, that the complications in the course of the (p,.) and the (p, 7’) sections of the surface of fluid phases coexisting with solid ones, remain restricted to the neighbourhood of the critical phases. It is therefore uncertain, whether in a section for given w, if the latter is e.g. chosen halfway between ve and %, the two vertical tangents still oceur. As soon as they have coincided, the section has no longer any special point, and so the retrograde solidification has also disappeared. Mathematics. — “Centre decomposition of polytopes.” By Prof. PH. ScHours. In the following lines it will be shown how a regular polytope can be decomposed according to its vertices or to its limiting spaces of the greatest number of dimensions into a system of congruent regular polytopes with a common centre. For this pe shall re- present a regular polytope, limited by m spaces $,: in S,, with a length 7 of the edges; and moreover we shall omit as much as possible the number # of the dimensions and always each of the predicates “regular”, “congruent”? and “concentric”. ( 367 ) In our space the theorems hold good: ae : : i Ly le. “The eight vertices of a cube Z% can be arranged into two quadruples of vertices not connected by edges, or of non-adjacent : : : (V2) vertices, the vertices of two tetraeders 7 ree ok d 5 r 1) 1’. “The eight faces of an octaeder Z% can be arranged into two quadruples of planes of which no two planes pass through one and the same edee, i.e. of quadruples of non-adjacent planes, the (2) faces of two tetraeders ZP, ae : ; GIJ Iie. “The twenty vertices of a Pio form taken twice the vertices [KI4-Y5)] of five DP and taken once in two different wavs the vertices [(4Y5) V2, DE) Dhstive J? Id Al . hd (1) . Ls . Il’. “The twenty faces of a Mo form taken twice the faces of HH 5D five 15 and taken once in two ways the faces of five | ay ( 3 /5 ) “9 pe +175) 4 4 The length of the edges indicated for the components follows immediately from the observation that for the decomposition according fo the vertices the radius of the circumscribed sphere, for the decomposition according to the faces the radius of the inscribed sphere remains unchanged. For Sy we have the following theorems : 1) ; Ill. “The sixteen vertices of a Ps can be arranged into two octuples of non-adjacent vertices, the vertices of two sixteen-cells (2) | Ce: Pig - In like wav Pig gives according to the limiting spaces two (11/2) pes, S . vs ry . . . 1) . IV. “The twenty-four vertices of a Po4 form the three oetuples /2 of vertices of three Pig . In like way Poy gives according to the ee We), limiting spaces three /?s y , . . I . bd . V. «The one hundred and twenty vertices of a Zoo form in five : EHS different ways the vertices of five /s4 ‚In like way Pio gives ; ri 8 : ; RE, T4-30/5, 0/2] according to the limiting spaces in five ways five /4 2 : É ee en : a. VI. “The six hundred vertices of a Pioo form in two different — 20445172) “Cis ea a ways the vertices of five ig . In like way Zoo gives in two a aE: was D/s ways the limiting spaces of five Pao ft With the aid of these theorems it is easy B arrive at the remaining possible centric decompositions of the four-dimensional polytopes. Ar 4 bie : In spaces with a greater number of dimensions it is known bee 3c but three regular polytopes are to be found, i.e. in S, the simplex Po, the polytope of measure Ps, and the polytope Fin reciprocally a rt : related to the preceding. With respect to these there is an extensio nae for theorem I and theorem IIT only, namely [ for n= A and — Ill for = 2". These extensions run as follows: (1) =x a eee, form ne Ug ze EE kes SEN In like way « gives — 5 Pl : Vil. “In space Si», the 2 vertices of a / P ‚tp vertices of 2 £ simplexes ies math EN zn UE ee according to the limiting spaces of 2’ —2 dimensions 2°” pV). ol | Pp ee Vilhelm space: 15. „hers vertices of a PV ae from the vertices _ 9! 7 hs Me Pi Ca MER al . . ) limiting spaces of 2/—1 dimensions 2 ae - a! ven Aiel St de Jen ote ee pre ] In like way a P|, gives according to the 33 In the meeting of June 27, 1903 Prof. J. M. van BemMnnen com- municated a paper: “Ou “ington pane which may change — ER into chemical compounds or solution.” AN Ë 4 -— ae (This paper will not be published in these Proceedings.) (December 23, 1903). KWT RN far Ht REE A ad vas) ra cre PROCEEDINGS 1 „OF THE 1 EM OE URE BAE: (Ist PART.) _ AMSTERDAM, JOHANNES MÜLLER. December 1903. t- ry (Translated from: Verslagen van de Gewone Vergaderingen der Wis- en Na Afdeeling van 30 Mei 1903 tot 28 November 1903. DI. XII). AK : | De ¥