Digitized by the Internet Archive — in 2009 with funding from University of Toronto http://www.archive.org/details/p2proceedi ngsofs15akad Ne . a e KONINKLI|KE om 7 VAN WETENSCHAPPEN — -- TE AMSTERDAM -:- N x Xr PROCEEDINGS OF THE SECTION OF SCIENCES VOLUME XV (— 2ND PART — ) my } \\ Q \\ \" im 5 ae MULLER. — AMSTERDAM 2 AUGUSMAGISe: : . a. \ \ CON TEN TS. Page Proceedings of the Meeting of December 28, 1912 and January 25, 1913 . 789 > > > > x February 22,0913. . . 2: 2 cae 95,1039 > > >» > » March 22 and April 25,1913. . . . . . 1237 7$4 KONINKLIJKE AKADEMIE VAN WETENSCILAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday December 28, 1912 and January 25, 1913. = - OC President: Prof. H. A. Lorenrz. Secretary: Prof. P. Zeeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Geers 28 December 1912 en 25 Januari 1913, Dl. XXI). CONTENTS. C. J. C. van Hoocenuvyze and J. Niruwexnvyse: “Influence of the seasons on respiratory exchange during rest and during muscular exercise.”. (Communicated by Prof. C, EykM AN}, p. 790. W. E. Ringer and H. vy. Trier: “The influence of the reaction upon the action of ptyalin,” (Communicated by Prof. C. A. PEKELHARING), p. 799. W. ve Sirrer: “On absorption of gravitation and the moon’s longitude.” part. I, p. 808 part IT, p. 824. Ernst Conen: “The equilibrium Tetragonal 'Tin ES Rhombie Tin.” (Communicated by Prof. P. van Romepuren), p. 839. C. Wixkrer: “On localised atrophy in the lateral geniculate body causing quadrantic hemi- anopsix of both the right lower fields of vision’, p. 840. (With 3 plates). L. van [varie and J. J. van Eck: “On the occurrence of metals in the liver?’ (Communi- ented by Prot. W. Eryrnoven), p. 850. F A. H. Scurememankers: “Equilibria in ternary systems”. Part II, p. 853, Part 111, p. 867. JAN DE Vriks: “On complexes which can be built ap of linear congruences’, p. 879. A. Smits, J. W. Trewern, and IL. L. pr Leruw: “On the system phozphorus.” (Communicated by Prof. A. F. Hoiieman), p. 885. Henpr. dE Vries: “On loci, congruences and focal systems deduced from a twisted eubic and a twisted biquadratic exrye” ILI, p. 890. J. D. vax per Waars: “Some remarkable relations, either accurate or approximative for different substances.” p. 903. Jan DE Vries: “On metric properties of biquadratic twisted curves.” p. 910. Jan DE Vries: “On the correspondence of the jairs of points separated harmonically by a twisted ust tic curve.” p. 9:8. Jan pr Vries: ,, On a line complex determined by two twisted cubies.” p. 922, L. H. Sierts aMrale “Determinations of the refractive indices of gases under high pressures,” (2nd Communication: On the dispersion of air and of car bon dioxide’. (Communicated by Prof. H. KamerunGnu Oxnes), p. 925. ; M. W. Breverinck: “On the composition of tyrosinase trom two enzymes.” p. 932. W. vay per Woupr: “On Sreixertan points in connexion with systems of nine ¢-fuld points of plane curves of order 32.” (Communicated by Prof. P. H. Scnovre), p. 938. H. Kamertiscu Onnes and Benxer Beckman: “On the change induced by pressure in electrical resistance at low temperature.” I Lead. p. 947. Hi. Kamertincu Onnes and C. A. Crommein: “[sotherms of monatomic substances and of their binary mixtures. XIV. Calculation of some thermal quantit.es for argon p. 952. E. Mararas, H. Kamervisen Onnes, and C. A. CrommMecix: “On the rectilinea™ diameter for argon”. (Continued), p. 960. H. KamercinGn Onnes and E. Oosrernuis: “Magnetic researches VII. On paramagnetism at low temperatures.” (Continued), p. 965. J. D. van per Waats: “Phe law of corresponding states for different substances.” p. 971. H. Kameriincu Onnes and Bexcr Beckman: “On the Hatw-effect, and on the change in resistance in a magnetic field at Jow temperaiures. VI, p. 981, id. VII, p. 988, id VILL p. 997. T. Tames: “Some correlationphenomena in hybrids.” (Communicated by Prot. J. W. Mott), 1004, c Jou. H. van Burkom: “On the connection between phyllotaxis and the distribution of the rate of growth in the stem.” * (Communicated by Prof. Went), p. 1015. Pu. Kounstamo and J. Timmer Mans: “Experimental investigations concerning oe of liquids at pressures up to 3060 atmospheres.” (Communicated by Prof. J. D. van DER Waats), p. 1021. J. P. van per Stok: “Oa the interdiural change of the air temperature”, p. 1037. Proceedings Royal Acad. Amsterdam. Vol. XV. 790 Physiology. “Injluence of the seasons on respiratory erchange during rest and during muscular exercise’. By Dr. C. J. C. vaAN HooGenuvyze and Dr. J. Nigsuwknuvyse. (Communicated by Prof. C, Ekman in the meeting of October 26, 192). The primary object of our inquiry has been to find out, whether muscular exercise increases the metabolism in man as much in the cold as in the warm season. We have taken the consumption of oxygen as the index of the metabolism. Since it is still a matter of controversy, whether the seasons in- fluence metabolism even during rest, we have thought fit to deter- mine also the absorption of oxygen during rest in the same two persons, who were subjected to the muscular test. Besides, the gas- exchange has also been examined with two other subjects only during rest. A. Respiratory Gas-exchange during rest. In 1859 E. Sarr ') presented to the Royal Society of London a series of observations upon the influence of different factors (i. a. the seasons) on the gas-exchange in man during rest. The amount of oxygen consumed was not determined, only that of carbon dioxide given off. [If we are to take the latter as a quantitative index of the metabolism, Smirn’s experiments would prove that it is more intense in the cold months and less so in the warm season. EKMAN?) made similar experiments in 1897 with improved means, and moreover measured the quantities of oxygen. As known, the latter afford a more reliable index of the intensity of the metabolism. He found no difference for the different seasons. His opinion that the metabolism is the same in warm and in cold seasons is also corroborated by his previous investigations *) made in the East-Indies, from which it appeared that the amount of meta- bolism of man in the tropies agrees with that of people in our parts. ') Philosophical Transactions of the Royal Society of London 159 p. 681. *) CG. Eikman. Over den invloed van het jaargetijde op de menschelijke stof- wisseling. Verslagen van de Koninklyjke Akademie van Wetenschappen te A’dam, 8 Dec. 1897. 5) OC. EvkMAN. Beitrag zur Kenntniss des Stoffwechsels der Tropenbewohner. Virchow’s Archiy. Band 133. 1893, p. 105. Idem. Ueber den Gaswechsel der Tropenbewohner, Pfliiger’s Archiv. Band 64, 1896, p. 57. 791 Shortly before we had brought our experiments to a close, Linp- HARD *) published an article, in which he reports the fluctuations of respiratory exchange in the different seasons, which according to him run parallel to the intensity of the sunlight. It seems to us however, that his values of the oxygen intake do not differ sufficiently and are too inconstant to warrant such a conclusion. For our determinations we used Zenrz and Grrrrrt’s*) method. The subject, whose nose is shut off by a spring-clip, breathes through a mouth-piece, corresponding by means of a T-shaped tube with two very mobile gut-valves, one of which transmits only the ar taken in, the other only the air which is exhaled. The latter passes, without encountering any resistance worth mentioning, through a slightly aspirating gasometer, a constant fraction of the expired ar being continually separated for gas-analysis by means of a special apparatus. Furthermore a supple pig's bladder had been inserted between the valves and the gasometer. This highly facilitated expi- ration, as was apparent from the working-experiments to be discussed later on. Outside air was supplied through a short and wide india-rubber tube, connected with the valves. The room which faced the North, was constantly well ventilated through the open windows. We experimented every time under similar circumstances, 1. e. the experiments were made in the morning, always at the same hour, and with the same interval after breakfast. The breakfast varied for the several subjects, but for each indivi- dually it was the same. For a quarter of an hour before and during the experiment, the subject reclined in an easy chair, resting quietly. The temperature of the room was taken, the readings of the baro- meter and the sort of weather (misty, sunny, frosty ete.) were noted down. Likewise the respiration, the number of liters of air exhaled, and the time (in seconds) were recorded on a kymographion (Fig. 1). The time the experiment took us, was also registered by a time- keeper. Furtheron the relative moisture in the room was measured too as well as the temperature and the degree of moisture under the clothes. Our subjects were four adults, all of them employed every day 1) J. LinpHarb. Seasenal periodicity in respiration. Skandinav. Archiv. f. Physiologie XXVI p. 221. °) MaGnus-Levy. Ueber die Grésze des respiratorischen Gaswechsels u. s. w. Pfltiger’s Archiv. f. die ges. Physiologie. Bd. 55. 1894, p. 9. o2* 792 at the hygienic laboratory at Utrecht. Their body-weights were widely different and did not change much with the same individual. Dt RAD Rak e Rohdhrnnhhhnhrppbhrhnh abhor \ Time (seconds) DDI AO ror Vie wav 1 } TW Respiration Liters of air exhaled. Fig. 1. The lowest temperature, at which we worked was 3°, the highest 380°. The experiments were made in May, June, July, September, October, November 1911 and in January, February, and July 1912. There was only a small difference in the summer- and the winter- attire. No overcoat was ever put on in cold weather nor was any article of attire taken off in the summer. As serious errors would originate in case the subject should shiver, this was a point of careful observation. In looking over our results, in the first place with regard to the amount of oxygen, we notice rather considerable fluctuations with the same subject under apparently similar circumstances, which is in accordance with the experience of other workers. Brenepicr '), for instance, found in experiments with the same subject under equal circumstances the following oxygen-consumption : 194—213—169, showing as great a difference as 26°/,. We also found with V. on 15—7—12, at 30°, 765,5 mm. baro- 9) the value 256,8, and on metric pressure, relative moisture of 52°/,, 16—7——12, at 30° and 765,5 mm. barometric pressure, relative moisture of 50°/,, the value 292. This yields a difference of rather more than 13°/,. It is obvious, therefore, that if we wish to demonstrate seasonal influence, an extended series of experiments is required, and further- more, that only striking differences should be attended to. If we take the average of the results at a temperature below 13° (the months of Nov. Dee. Jan. Feb.) and of those above 128° (the other months) we note 1) BENEDI( The metabolism and energy transformation of healthy man during ‘gic Institution of Washington. Publication no, 126, 1910, p. 107.) 793 below 13° above 13° with vH. (5 exp.) 281.8 ¢.¢. per min. (148 exp.) 269.2 mee 38 * 252.4 — ;, oY) ss 21 ES 256 a JE eae ZOO'S mers tse. Co el 297.4 ye Gane laa DOM peas, {|e = ae Sfat The average of 4 subjects (23 exp.) 1032.7 :4 =258.2 and (60 exp.) 1020.3 :4=255.1. In considering the results obtained with each individual separately we notice differences in one way or another, comparatively small though they may be. In connection with what has been said above we believe that no great value should be set upon these differences. Taking the averages of all the subjects, we find fairly correspond- ing values, viz. 258.2 in the cold and 255.1 in the warm season, so that we may conclude, that the season has no influence upon the metabolism in a state of repose. It appears then, that our results agree with those of EivKMAN *) who got his averages in like manner, finding 253.8 in the winter and 253.3 in the summer. Without tabulating our results at large we subjoin a somewhat more detailed report about them : 1 V. H. Body-weight 87'/g Kilos (without clothing) Height 1.84 m. Averages of results of all experiments (23): Amount of Oj-consumption and CO>-production per minute expressed in c.c. reduced to 0° and 760 mm. barometric pressure. CO, Op CO3/O2 225,2 271,1 0,830 minimum 185 min. 239,5 = 11/9 below the average. maximum 264,6 max. 322,5=19%) above , ; The average Oy-consumption in 5 experiments at 4!/,—12'/,° C. amounted to 281,8 , min. 259,9 ‘ max. 322,5 [he Oo-consumption in 18 experiments at temperatures of from 141/).—30° C. averaged ) : 269,2 / min. 239,5 max. 294,2 At the lowest temperature ( 4!/,° C.) we found 274,1, at 7!/2° C. 322,5, » » highesttemperatures (30 °C.) , , 291,7 and 294,2. Il. A. Body-weight 701), Kilos (without clothing) Height 1,80 m. | Averages of results of all experiments (29): CO, Os CO3/O2 i 230 255 0,900 min. 191,7 min. 222,2 = 13/9 below the average. max. 267 max. 292 = 149 above ,, i: 1 Cd, Ekman. Koninkl. Akademie v. Wetenschappen 8 Dec. 1897. 194 The average O,-consumption in 8 experiments at temperatures of 4—13° C. amounted to 252,4 min. 230,5 max. 285,1 The O,-consumption in 21 experiments at temperatures of 14—30°C. averaged 256 min. 222,2 max. 292 At the lowest temperatures (4 °) we found 260,7 and 285,1. . y highest 2 (30°) , , 256,8 292 and 277.7. Ill £. Body-weight 83,3 Kilos (without clothing) Height 1,82 m. Averages of results of all experiments (15) CO, Oz O2/Oo 258,6 294,7 ,801 mnin. 219,6 min. 250,8 = 15,"), below the average max. 309,7 max. 330,11 =12"/, above _,, 5 The average Op -consumption in 6 experiments at temperatures of 8—i3°C. amounted to 290,8 min. 272,6 max. 330,1 The average O -consumption in 9 experiments at temperatures of 14 —26° C, amounted to 297,4 min. 279,9 max. 328.4 lV. K. Body-weight 58 Kilos (without clothing) Height 1.75 m. Averages of results of all experiments (16) co, Oz CO,/O2 175,1 200,2 0,874 min. 152 min. 172 = 14% below the average P max. 205,9 max. 238,6 = 19"), above ,, s The average O -eonsumption in 4 experiments at temperatures of 3—121),° C. amounted to 207,7 min, 177,7 max. 228,6 The O5-consumption in 12 experiments at temperatures of 14—30° C. averaged : 197,7 min. 172,0 max. 238,6 Our endeavours to detect any influence of the seasons on the carbon-dioxide elimination, the tidal air, and the number of respi- rations per minute proved as fruitless as they had been in ascer- taining such influence on the oxygen-consumption. B. Respiratory Gas-eachange during muscular exercise. Little has been written as yet about the influence of muscular work on the respiratory exchange in the several seasons. Pal — sD edd ee Bae ‘ 945 EK. Smrru reported in his publication, of which mention has already been made, that equal muscular work has a greater influence on the respiratory exchange in winter than in summer; his experimentation, however, does not, in our opinion, vouch for this conclusion. Our experiments were made in the months of March, April, May, June, and July 1912. We proceeded as follows. The experimentation took place in the afternoon, at the same hour, shortly before dinner, in order to give scope to the presumable influence of close heat. We were sitting on a bicycle without .wheels, placed on a stand. A rotatory disk had been fixed at the place of the large chain-wheel. Round it a steel brake-band could be tightened or slackened to render the work more severe or lighter (Fig. 2). Spring-balance Wire Adjusting screw — Rotating disk -----*¥ The upper part of the band was connected with a spring-balance by means of a long wire. When the adjusting screw was tightened the friction increased and the band was taken along by the disk, while the pedalling continned, which caused the springbalance to register a higher figure. The increase, however, was not such as to alter the static moment materially. Both the bracket-spindle of the bicyele and the rim of the disk were continually being oiled during the experiment. The pedalling rate was regulated by a metronome, ticking 133 times per minute. . Before the subjects, both skilled cyclists, started pedalling, a deter- mination was made, while they were quietly seated on the bicycle; which involved only a very light static muscular activity. In the subsequent period of the experiment the subject was pedalling for a quarter of an hour, while breathing freely and after this for five minutes, while breathing through the valves. Only then the estima- tion was performed, while the subject went on pedalling; we then could reasonably presume that a condition of equilibrium between internal and external gas-exchange had been established, The breathing through the valves for the space of five minutes previous. to the estimation, served to prevent a somewhat irregular respiration that might .possibly arise in the transition from free breathing to respiring through the valves. In the interval the tempe- rature in the gasometer attained its new equilibrium. Throughout the whole experiment an assistant had to watch the springbalance, which was to point to the same mark. In case of a deviation, the band was at once slackened or tightened during the pedalling, which did not cause any disturbance. The work done was calculated by multiplying the circumference of the disk, i.e. the distance covered after one rotation, by the weight indicated on the springbalance. by the number of rotations per time- unit and by a correcting factor‘). This showed an amount of labour of 22800 K.G.M. per hour. The exertion required for the work, was not such as to exhaust the subjects. Still, at the finish of the experiment they felt tired as if they had been cycling a long distance. Our results are the following: sitting quietly (a): LO) easiness ab): Aveiages of all the experiments (12) made in March, April, May, June, July 1912, lowest temperature 12°, highest temperature 30°: CO, per min. Oo CO, Oz \ min. 299 max. 386,8 ae asa 330,4 0.850 \ 1001,5 0,8671 5:4 868, min. 781,2 max. 1448 The average of 8 experiments below 211°: CO, Os CO, Oz \ min. 299 max. 358,8 ee 323,5 0,8448 \ 863,4 0,8643 b / 746,2 min. 781,2 max. 988,5 The average of 4 experiments above 2112°: CO, Oz CO, O2 \ min. 322.1 max. 386.8 ht Piette 344,5 0,8589 \ 1277,7 0,8712 5, 13,1 min. 1052 max. 1448 Increase set in after 11—6—’12 (above 21 '/2°). ') The correcting factor is the quotient of the lever on which the wire of the springbalance is fixed and the radius of the disk. A ~J Le) ~I sitting quietly a: II. WV. pedalling b: Averages of all the experiments (14) made in the same months; lowest temperature 12°, highest 31°: €05 O» Co, ’ Oo \ min. 229 max. 314,9 a; 212,5 265,4 0,8346 \ 895,6 0,9152 b / 819,6 min. 652,1 max. 1091 The average of 8 experiments below 20!/,°: CO, Os COs Oz \ min, 229,6 max. 314,9 aes 268,8 0,7984 \ 791 0,9076 Oy 17,9 min, 652,1 max. 922,7 The average of 6 experiments above 20!),°: CO; O» EG, O2 \ min. 229 max. 288,9 a tah 260,8 0,8037 4 1034,9 0,923 5 ) 985,2 min. 977,2 max. 1091 Increase set in above 201/,°, after 13—5—’12: Also in this series of investigations the individual fluctuations were rather considerable. We see that for either subject the average oxygen-intake is higher when sitting quietly on the bicycle than when lying in a chair, viz. V. H. (lying) average Oxygen-intake 271.1 ce. (sitting) —,, 35 330.4 N. (Lying) & . 255 (sitting) —,, RD 5. We also observe that the average value of the sitting-experiments at more than 21'/,° with V. 7/. is a little higher than that of the experiments below 21'/,° viz. the first value: 344.5, the second 322.5 Again, that for N there is no such difference between the two periods. On the contrary with him rather the reverse takes place, the first value being 260.8, the second 268.8. However, this difference is too small to be taken into account. While pedalling 1”. H. shows an essential increase of oxygen- intake, when the temperature rises beyond 21°, at the beginning of June. With N the increase is not so great, but it starts a month earlier, when the temperature rises beyond 20° viz. with V.N. from average 863.4 to 1277.7, nearly 48 °/, EATING nae, - (sO a 9 a 798 The lowest value of the warm period in H’s experiments (1052) is distinetly higher than the highest of the cold period (988.5). Likewise with .V viz. the one 977.2, the other 922.7. On the days of the higher values either subject felt, as if the inuscular work required a greater physical exertion than on other days, though they were both in good health and followed their daily routine. in noting the average increase of the absorption of oxygen, result- ing from the pedalling, we find: with V. HH. below 204° §63—323.5 = 441.5 above 214° 1277—244.5 — 933.5 a difference of 491.7 (nearly 112 °/,). With NV below 213° 791 -—268.8 = 522.2 above 204° 1034.9—260.8 = 774.1, a difference of 251.9 (rather more than 48 °/,). The numbers expressing the carbon-dioxide output are running parallel to those indicating the oxygen-intake. This tallies with the approximate accordance of the respiratory quotients of the experi- ments made at a temperature higher than 20°/,° and 21'/,°, with those of the other experiments. In the case of NV the temperature under the clothes, on the cessation of the pedalling was: 35—35'/,° C., the relative moisture 65—90"/,, throughout the whole period above 204°. In the period below 205° the former varied from 30° — 34°, the latter from 30°/,—47°/,. With V. H. those values were: in the period above 214° : 34— 351/,° 90—100°/, below 214° : 30— 34, 40— 75°/, As regards the respirations per minute ant the tidal air at the end of the pedalling experiments we find: number of respir. per min. Tidal air average with I”. 7. below 214° 17.2 1009.6 above 214° 16.2 1444 with * NV. below 204° 20.1 840.7 above 205° 207 1003.5 We see, therefore, that the number of respirations per minute remains fairly constant, whereas in the warm season the tidal air is considerably augmented, viz. a 199 with UV. H/. an increase of more than 34°/, eae; ¥- ee we), We have previously remarked, that the increased respiratory exchange at a higher temperature cannot be attributed to this, seeing that the determination had not been made, until an equilibrium had presumably been established between internal and external gas- exchange. Indeed, the O,-consumption and the CO,-elimination in- creased more considerably than the tidal air. Our experimental evidence seems to show that muscular work at a high temperature is less economical than at a low temperature, and also that this difference is more marked with one subject than with another. The inerease of gas-exchange parallel to the rise of temperature was not gradual. but sudden at 21°—22°. Physiology. — “The influence of the reaction upon the action of ptyalin”. By Dr. W. E. Rinerr and H. v. Trier. (Comimunieated by Prof. G. A. Peketuartne in the meeting of November 30, 1912). One of us (v. Tr.) has for some time been studying the effect of diet on the action of the diastatic enzyme of the saliva, to which the name ptyalin has been applied. The results of other researchers into this subject are tu some extent conflicting with each other’). Nor do van Triet’s experiments positively demonstrate an influence of diet. Though, taking one with another, they seemed to point to an influence, occasionally there appeared striking deviations without our being able to fix upon the cause, so that we did not know what to make of the results. This experimentation was conducted .as follows: saliva was added to amylum solutions and after some time the reducing power of the solutions was determined. This method involves the risk of flue- tuations in the reaction of the fluids, e.g. such as are brought about by tbe flask-wall or by carbon dioxide from the air, since in approximately neutral fluids without regulatiag-mixtures the reaction may be considerably shifted by a trifling disturbance. This would account for the striking deviations mentioned just now, recent researches having shown that slight modifications of the reaction markedly affect the activity of enzymes. Now if, in proseevting our experiments, due care being taken all 1) Cf, Hammanrsren’s Lelirbuch der physiologischen Chemie. 800 the time to obviate any noxious influence of the flask-wall or of the carbon-dioxide upon the reaction, we should detect unmistakable influence of the diet, this might be: owing to various causative fac- tors. First of all the concentration of the enzyme might have been altered by the diet. In the second place the organism might effi- ciently alter the concentrations of the ions, which are so material to the action of the enzyme, especially the H- and OH-ions, as well as the Cl-ions and others. We thought proper, therefore, to cautiously watch the influence of the H- and OH-ions in order to ascertain by subsequent experi- ments, whether variations in the activity of the enzyme are to be attributed to’ changes in the concentrations of the said ions. Moreo- ver, an accurate knowledge of the influence or these ions may lead to a clearer insight into the action of the enzyme. Previous inquiries into the effect of acids and alkalis on the action of ptyalin yielded rather contradictory results"), from which it was supposed that either acids or alkalis acted favourably. As a rule we used in our investigations the methods employed by SORENSEN*) in his remarkable experiments on enzymic actions. We adopted the following course: filtered saliva, designated “enzyme” in the following tables, was made to act at 37° upon 1°/, amylum solutions. After the action of the enzyme had been arrested by heating it was estimated by the deter- mination of the reducing power of the digestion-fluid, of the rotatory power and by reaction with iodine. Various reactions were given to amylum solutions. To obtain them and to maintain them constant three buffing- or regulating-mixtures were applied, viz. 1. phosphate-mixtures, : 2. citrate-mixtures, 3. acetate-mixtures. The process of digesting lasted 20 minutes for all series of expe- riments but one. 1. Experiments with phosphate mixtures. (all the glass vessels had been exposed to steam for 15 iinutes.) Into ErtexmMever-flasks (Jena-glass), capable of holding 300 ¢.c. were placed r 10 e¢.c. of a phosphoric acid solution 1.485 n., varying amounts of sodium hydrate 0,5670 n., and water up to 50 ¢.c. To this 200 1) Cf. Hammarsten’s Lehrbuch der physiologischen Chemie. *) Comptes rendus des travaux du Laboratoire de Carlsberg. 8me Vol. Ir. Li- vraison 1909. -—.S eo” 801 c.c. of the amylum solution was added by means of a pipette. As a matter of course, all the tests of the same series were made with the same freshly prepared solution, which was obtained by mixing 25 er. of dried amylum with one liter cf water and heating it to the boiling point, while stirring the fluid and maintaining this tem- perature for about a minute. After cooling the mixture was made up to 2 liters ') and filtered through glass-wool or muslin. The flasks holding the phosphate-mixtures and the amylum, were first heated to 87° and then maintained at this temperature in the thermostat for at least 20 minutes previous to the addition of the enzyme. After the enzyme had been working on for 20 minutes, the flask was dipped into a boiling waterbath and was constantly and regularly moved, always in the same manner, till a temperature of 90° was reached, so that every time the action of the enzyme was arrested in the same way. The reducing power of the cooled fluid was determined after BerTRAND and was expressed in m. Gr. copper. per 100 ¢.c. of the fluid. The determination of the reaction was performed electrometrically. The hydrogen-electrodes were treated after HasseLBacn’s *) shaking method, and measured by means of mercury-calomel-electrodes with normal and */,, n potassium chloride. The reaction is expressed in pu: the negative logarithm of the hydrogen-ions-concentration. The following tables show the results of the most important series of experiments. rst Series of experiments. Enzyme v. T. == |_, Phos- | NaOH H,O| Amy- | En- 10 18 422 200 2 176.50 = — 6.78 Nr. puede aad lum | zyme ee ee lodine reaction Py (3 Ce oC, C.c, (GAs Gc: On * | minutes 1 | 10 13.4 26.6 200 Dye chil Gn ee —~ 5.186 Par plets.7 (26.3) 200. | 2 | te2i15 | = ae 5.69 3 | 10 14 26 | 200 2, | 212:30 | — — 5.80 ee A) 15 25 | 200 2° | 218051) = 6.22 5 | 10 | 16 (24 | 200 2 | 214.85/ — — 6.40 5 1) Oceasionally 4 liters had to be made. *) Biochemische Zeitschrift, Bd. 30, p, 317. 802 2d Series of experiments. Enzyme R diluted with 3 vol. of water. OOOO I Bae ,; NaOH H.O Amy- | En- a Rotation Nr. hrs oe lum = zyme Gr lodine reaction Py ee cc. |. Cee tics Cy Minutes , * Reduction 1 10 13 27 200 2 not +192 blue 4.53 perceptible 2 10 13.5 26.5 200 2 | 180.10) 188 blue, shade of violet 5.33 3 10 14 26 200 2 | 234.80 186 violet, shade of blue 5.86 4 10 14.5 125.5} 200 2 | 244.55 | 185 violet 6.05 5 10 15 25 200 2 235.0 186.5 violet, shade of blue 6.24 6 10 15.5 24.5 200 2 223.60 188 | violet-blue 6.30 7 10 1) 2S 200 2 179.10 191.6 blue, shade of violet 6.61 8 10 20 20 200 2 105.40 195 blue 7.01 3d Series of experiments. Enzyme D. Phos- ; : i Reduc- | “Ta Nr. Rue cece me sad ‘in zyme ole ae lodine reaction | Py ect ay nk es Pe Cu Sethe a3 1 | ee 1 10 13.2 26.8} 200 | 2 | 106.45} 194 blue 4.90 2) 10 |13.5 [26.5] 200 | 2 | 194.50 | 190.3, blue, shade ofviolet, 5.52 3 10 14 |26 | 200 | 2 | 251.25 | 190 violet-blue | 5.83 4 10 14.5 (25.5, 200 | 2 | 270.10 | 189.7 violet, shade of blue] 6.08 5 10 15 [25 | 200.| 2 | 274.20) 188 violet 6.19 6 10 15.5 Pe 200 2 265.55 | 191 violet, shade ofblue| 6.37 7 10 17 23 200 2 220.55 | 192 violet-blue | 6.61 8 10 |20 (20 | 200 2 | 156.60 195 blue \ 7.03 From these experiments it appears, that the concentration of the hydrogen-ions exerts a considerable influence upon the action of the enzyme; further that an increase of cj, consequently a decrease of pu accelerates its activity, until a certain optimum is reached, after which the action slackens again. We also observe the same beha- viour with enzymes from different sources, however with a noticeable difference in their activity. From another series of experiments we gathered that the optimal reaction lies at about the same point in much more dilute phosphate solutions; we also learnt, that all over the series the action of the enzyme was more vivid. It follows 803 then, that phosphate-mixtures are inhibitive to the action; less so in highly dilute than in the concentrated solutions. 2. Experiments with citrate-mirtures. A citrate solution was made from 275 er. of pure citric acid (pro analysi), 105 gr. of NaOH (Mrrck’s e natrio pro analysi) and water to 1 liter. 20 ¢.c. of this citrate solution diluted with water to 250 c.c. yielded py= 4.915. 4th Series of experiments. Enzyme R. Citrate NaOH H,0 Amy- En- paces Rotation Nr. solution lum zyme’ Gr lodine reaction PH Gc. CEMA CC hes Ge Gil minutes Zu 1 10 14.7 |25.3 | 200 | 2 | 247.60 | 195 bluish-violet 5.99 2 10 19.57 20.43 200 Dy 357.15 189 reddish-violet 6.49 3 | 10 19.94 20.06 200 2 380.15 189 red, shade of violet 6.526 4 | 10 20.4019.6 200 2 380.65 188 reddish-brown 6.62 5 10 21.3 |18.7 | 200 2 396.00 187 reddish-brown 6.73 6 10 22.1 |17.9' | 200 2 358.65 187 red, shade of violet 7.09 7 2 10 23 17.0 200 183.15 197 blue, shade of violet 7.425 sth Series of experiments. Enzyme R diluted with 1 vol. of water. Citrate NaOH H,0 | Amy- En- Reduc- Rotation| Nr.) solution / lum | zyme ae ; lodine reaction | PH |) ee | cc. ae Cle | GG | Cu apa 7 eat 5.0 40 | 200 2 81.35! 202.7 blue 5.80 2 5 8.20 36.8 200 2 139.70 200 blue 6.26 3 5 | 9.78 35.22 200 2 | 158.10 197 blue, shade of violet 6.55 4 | 5 110.20 34.80 PANO) |p 147.85 | 199.3 blue, shade of violet 6.74 5 | 5 I10 65 '34..35| 200 2 128.45 | 201 blue 6.85 6 | 5 10.90 34.10) 200 2 107.95 | 202.7 blue 7.046 T 5 11.05 33.95) 200 | 2 90.05 | 204 blue elit 8 5 11.30 ‘33.70 200 2 60.90 | 204.5 blue 7.41 9 5 11.60 33.40, 200, 2 eat] 205 blue 7.497 Here again an optimal reaction is educed, which, however, has slightly shifted towards the neutral point. A decrease of concentra- tion diminishes this deviation. S04 3. Experiments with acetate-mivtures. A solution of sodium acetate 170 gr. per liter) was mixed with different quantities of 1 °/, acetic acid. The following experiments were made: 6th Series of experiments. Enzyme R. diluted with 3 vol. of water Acetic Acetate acid H,O) Amy-_ En- prmece Rotation Nr. solution — solut- lum zyme 1G, lodine reaction | Py ec ion’ }eG) ec ee c * minutes ~ u c.c. 1 20 0 30 200 2 47.60 turbid blue 7.297 2 20 1 29 200 2 137.65 | 202 blue, shade of violet 6.65 3 20 2 28 200 2 182.65 199 bluish-violet 6.55 4 20 4 26 200 2 221.05 198 bluish-violet 6.21 5 20 5.6 24.4 200 2 | 222.05 195 violet-blue 6.106 6 20 1) 23 200 2 221.55 197 violet-blue 5.98 7 20 12 18 200 2 | 200.05} 199 bluish-violet 5.78 8 20 30 0 | 200 2 118.20 200 blue 5.37 Again an optimal reaction is evolved; it is equal to that of the phosphate solutions. On either side of it the action of the enzyme diminishes, first slowly, then rapidly. The optimal reaction lies in phosphate solutions at py = 6.05, as may be seen from a graphic representation of the reduction as function of the py. In acetate solutions we find jy = 6.08, whereas in citrate-experiments values vary according to the concentration. In the 5th series we found an optimal reaction py = 654. All values of py communicated thus far, were estimated at 18°. They are somewhat different at 37°, the temperature at which the experiments were made. The reactions of the fluids, that were opti- mal, have also been determined by us. We found : in the phosphate solutions py = 6.00 in the citrate solutions (10 ¢.¢. of citrate 4" series) py = 6.86 in the acetate solutions py = 6.028. The neutral point lies at 37° at py = 6.796. For purposes of comparing the action of the various regulating- mixtures we carried out the following experiment. (p. 805). It is evident from this test that, the reaction being neutral, the influence of phosphate is inhibitory; when the reaction is slightly acid (py 6.5; a neutral reaction is not easily obtained with citrate) . SOD 7th Series of experiments. Enzyme R diluted with 1 vol. of water. H2,0 | Amy- | En- eae Reaction (determined at 15°) Regulating mixture lum zyme aie p GGuhee.cs. |i cic: C H u. a none 50 200 2 318.20 electrometrical determination not practicable on account of the lack of electrolytes. Neutral behaviour to litmus, so P py £7.07 b 10c.c.phosphoricacid 19.4 | 200 2 245.05 7.07 20.6 c.c. NaOH ec 10c.c.phosphoricacia 23.75 200 2 425.15 6.50 16.25 c.c. NaOH d| 10 c.c. citrate, 20.45 200 2 221.55 6.468 19.55 e.c. NaOH & comparison between citrate and phosphate shows that inhibition is much stronger with the former than with the latter. From the removal of the optimal reaction towards the neutral point, as well as from the tests published in this paper, it is appa- rent, that citrate inhibits most strongly on the side of the minor pus, and that this impeding action weakens towards the neutral point. The optimal reactions being identical in phosphate- and acetate- mixtures, it was likely, that either of them should slacken the action of the ptyalin in the same way. The following test illustrates the fact that, if the reactions are the same, both mixtures equally affect the enzymic action. Sth Series of experiments. Enzyme R diluted with one vol. water, H,0 Amylum Enzyme Reduction Beaters Ge: C.c. cc. mGr.Cul 2H 2 | 5.886 a 10 cc. of acetate 35 200 2 489. 5 c.c. of acetic acid : bt 6 10c.c.ofphosphoric 26 200 483.5 5.886 acid 14 c.c. NaOH We now passed on to inquire how this influence of the reaction upon the action of ptyalin is to be accounted for. It may indeed be imagined, that H-ions favour the enzymic action, but how is it then that beyond the optimal cy they largely impede the activity. Is it perhaps to be attributed to an injury to the enzyme? In order to find this out we made the following experiments : 53 Proceedings Royal Acad. Amsterdam. Vol. XV. SOG Oth Series of evpe rimenis. a. 10 ©. ec. of phosphoric acid, 13 ¢. c. of sodium hydrate and ce. ¢. of waters were mixed at room-temperature with a mixture of 25 ¢. ec. of enzyme R-+ 25 ec. c. of water. We examined directly the activity of this mixture, in which the enzyme had been diluted four times. It was subsequently warmed to and maintained at 37°, while at various intervals the action was noted, every time by allowing 2 ¢. ¢. to act upon mixtures of phosphate and amylum of the optimal, reaction. Time (minutes) during Nr. which the enzyme-mixture was maintained const. at 37° Reduction Rotation Py m.Gr, Cu. minutes (jf determined). ] 0 Lai S0 194.3 6.06 2 8.75 179.10 -- = 3 16.75 179.10 193.0 6.00 4 41.75 179.10 — ~- 5 88.75 179.10 193.0 6.075 6 178.75 181.60 — _ 7 268.75 179.10 193.0 5.975 The py of the enzyme-mixture was 5.902. b. 10 e¢. c. of phosphoric acid, 12 ¢. ¢. of sodium hydrate, 28 c. «. of water. Addition: 25 c. ¢. of enzyme R- 25 c. ec. of water, amylum = solutions as in the preceding test; py of the enzyme-mix- ture 4.095. Time (minutes) during Reduction | Rotation Nr. whieh fhe SSE eS Gul) unmet ate 1 0 155.00 201.0 5.98 2 18 147.85 201.7 6.04 3 47.5 139.70 199.0 6.02 fresh enzyme-mixture made of the same Enzyme R and the same Py: 4 0 162.25 199.3 6.03 5 138 113.10 201.5 6.08 6 373 56.30 203.0 6.03 807 Our results show that the enzyme is not yet injured at py = 5.5, but is gradually injured at py = 4.095. However, in view of the relatively short duration (20 min.) of the digestion-experiments de- scribed above, the injury is, even in the case of py = 4.095 only of small account. We conclude, therefore, that the inhibitory influence of the H-ions in concentrations beyond the optimal is not attributable to injury to the enzyme. In addition we have also tried to ascertain, whether the enzymic activity is weakened in fluids made slightly alkaline. e 10 ce. of phosphoric acid, 27 c.c. of sodium hydrate, 13 ¢.c. of water. Addition: 25 ¢.c. of enzyme R-+ 15c¢.c. of water, all the umylum solutions as in the preceding test, py of the enzyme- mixture 8.718. Time (minutes) during : ‘ Nr. which the enzyme-mixture Reece Roraten Py was maintained const. at 379 © °" 7" "" =e 1 0 142.20 — a= 2 20.5 147.35 = 6.02 3 55.5 147.35 Sei = 4 103.5 147.35 ss he 5 255.0 140.70 Sy ol” ats 6 380.5 134.55 - | z Consequently no injury in two hours’ time with a faintly alkaline reaction, py = 8.718. It is obvious, therefore, that in our experiments injury to the enzyme cannot have had any influence worth mentioning; on this account we could not expect the optimal reaction to shift in a prolonged digestion-test. Researches, each lasting 100 minutes, 5 times longer than the other experiments, confirmed our supposition. Further experimentation will have to reveal the relation between the electric charge of ptyalin to its action, for which the iso-electric point has to be determined *). Summary, A . A . ‘ ‘ i For the action of ptyalin the concentration of the hydrogen-ions is highly important. In fluids in which the reaction has been deter *) Cf. MicHaE.ts Bioch. Zeitschr. Bd. 35, S. 386, Bd. 36. S. 280, 93% SOS mined by phosphate- and acetate-mixtures, we found at pu — 6.00 an optimal reaction to the action of the enzyme. On either side the action decreases, first slowly, afterwards rapidly. Even at py = 4.5 and 7.5 it is stopped almost completely. At these py’s injury to the enzyme is out of the question during the whole time of the test. The place of the optimal py does not change even when the digestion- time is five times the ordinary duration. The influence of citrate- mixtures is much more inhibitory than that of phosphate- and acetate- mixtures. The inhibition is energetic especially on the side of the minor py’s. This accounts for the fact that in citrate-mixtures the optimal reaction has shifted towards the neutral point. Astronomy. — “On absorption of yravitation and the moon's longitude.” By Prof. Dr. W. pz Srrrer. Part I. (Communicated in the meeting of November 39, 1912). By absorption of gravitation we mean the hypothesis that the mutual gravitational attraction of two bodies is diminished when a third body is traversed by the line joining the first two. If this absorption exists, it will manifest itself by diminishing the attraction of the sun upon the moon during a lunar eclipse. Therefore, in order io test the reality of our hypothesis, we must compute the pertur- bations in the longitude of the moon which are a consequence of this decrease of attraction, and compare these computed perturbations with the well known deviations of the observed longitude from that derived in accordance with the rigorous law of Newton. Nrwcoms, in the last paper from his hand (M. N. Jan. 1909) has put before ihe scientific world the great problem of these deviations or “fluctu- ations” in the moon’s longitude. They can be represented by a term of long period, for which Newcoms finds an amplitude of 12".95 and a period of 275 years (great fluctuation), upon which are superposed irregular deviations (minor fluctuations), which amount to not more than + 4" in Newcomp’s representation. Mr. IF. E. Ross, Newcomp’s assistant, has afterwards represented these minor fluctuations by two empirical terms having periods of 57 and 23 years and amplitudes of 2".9 and O'.8 respectively (M. N. Nov. 1911). The outstanding residuals are very small: after 1850 they seldom reach 5 Wes In the years before 1850 the minor fluctuations are not so well marked, probably because (owing to the smaller number and greater uncertainty of the available observations) too many years have been combined in each mean result. 809 The idea of explaining these fluctuations by an absorption of the gravitational attraction of the sun upon the moon by the earth during lunar eclipses, has for the first time been publicly worked out by Mr. Borrninerr'), the investigation having been proposed the subject of a prize essay by -the philosophical faculty of the University of Munich. | had also towards the end of 1909 com- menced a similar investigation, which was however ofa preliminary character and, as it did not lead to positive results, was discontinued and not published. The publication of Mr. Borriimcer’s dissertation led me to resume the investigation. The decrease of the attraction of the sun upon the moon can be taken into account by adding to the forces considered in the ordinary lunar theory a perturbing force acting in the direction of the line joining the sun and the moon, in the direction away from the sun. If the sun and moon are treated as material poinis, this force is m Ea ae yas Ceo) She kot Steal C8) The meaning of the letters is: m’ = mass of the sun, 2’, a’ = mean motion and mean distance of the earth, n, a =the same elements of the moon (osculating values), n,, @, —= the mean values of these elements, A,r’ = distance of sun from moon and earth, ety HT The effect on the elements of the moon’s orbit can be computed by the ordinary formulas. The perturbing forces are: radial force H cos B cos (6—$S’), transversal * H cos B sin (6—8'), orthogonal EE sig Bs where § and $' are the selenocentric longitudes of the earth and sun, and @ is the selenocentric latitude of the sun, the moon’s orbital plane being taken as fundamental plane. For the instant of central eclipse we have $—$'=0. The transversal force therefore changes its sign during the eclipse, and its total effect is very nearly zero. The effect of the orthogonal force is entirely negligible. In the expression of the radial force, we can put cos (6—S’) = 1. We have further with sufficient accuracy Bis) 6. —vo -t 1 80e ' aoe U0) a 1) K. KF. Borriincer. Die Gravitationstheorie und die Bewegung des Mondes. Inaugural-Dissertation (Miinchen). 1912. See also “The Observatory’? November 1912. S10 where s =the moon’s latitude, wo, uw’ == true longitudes of moon and sun. The radial force thus becomes H cos s. It is easily verified that the mean motion (whose perturbation must be tvice integrated to give the perturbation in longitude) is practically the only element which need be considered. We find dn Sesinv on ml Gaya Na esinv = = — — F008 8 = — ——— (1 — 2a) =| —]) cos s, (2) ps « a \2" Vi—e where v is the moon’s mean anomaly. For the excentricity e we must use the osculating value. The mean value will be denoted by e,, as for the other elements. During the eclipse we can for the coordinates and elements of the moon use their values for the epoch of central eclipse. We then find for the addition to n as the effect of one eclipse: +P any, ~dn , , l—2a fa \?a, esine % irn= | — A = — 3n,? mM? — ; ——-—- cos s] xdt, . (3) dt CNG). aes where the time is counted from the middle of the eclipse, and 7 is the half duration. Now assume the absorption of gravitation to be proportional to the mass of the absorbing body. We have then x =w.y, where y¥ is the coefficient of absorption and mw the mass of that part of the earth that is traversed by the “ray of gravitation’. This ray of gravitation, i.e. the infinitely thin cone enveloping the sun and moon, which are considered as points, by its motion during the eclipse cuts an_ infinitely thin dise out of the body of the earth. In the plane of this dise take two — coordinate axes, of which the axis of wv is parallel to the line joining sun and moon at the instant of centrality. If then o is the density and 2, and 2, are the points where the “ray” enters and leaves the earth, we have v% . fu =| odu. ry Further we have 7 d dw dy = of dt A dt or d= (CS a) Gas dw ip dt Consequently : +7 P 1 a 7 free = (eas ary 0 da dy. dw Se P - dt The double integral must be taken over the entire surface of the above considered section of the earth, and represents the mass of the infinitely thin dise. Its value therefore depends on the distribution of mass within the body of the earth. Like Borriincer | take the dis- tribution according to WincHert, i. e. a central core of density J, = 8.25 surrounded by a mantle of density d, = 3°30. The radius of the core is Rk,=0-77 R. If we call D the radius of the above considered 7) disc, we can take D=R. ait where 7’, is the half-duration of the a eclipse computed with the mean elements of the moon’s orbit, 1. e. the value which is given in Oppotzer’s Canon der Finsternisse, ex- pressed in minutes of time. The number 112 is the maximum of this half-duration. We then find easily, in the case when the section is entirely in the outer mantle mA a T,\ Jfeaea Sy Ge yi and when it also traverses the inner core (i.e. for 7’, > 71.5): aye T\2 odxdy=x Rd, {2.5 - 2 |) == ORR 7 112 Now put, in the first case Tes? df = 100 _ 112 and in the second case Je == 100. 12:5 eas 0.62 |. 112 { The function J, which is thus defined, is tabulated in Dr. Borr- LINGER’S dissertation, with the argument 7’. We have now $12 ae 1 R , -a)x Ray eT. | 5 T 100 » — dt and this value must be subtituted in the formula (3). In doing this, we can either express the coordinates and velocities in the oseulating elements, or the latter in the former, by the well known formulas 1 1 + ecosv dr _ane sin v oa 5 eae Wo Gea pasa hea dt We then find a \n an esine n= —44,(") cos $ —— we a an (lee e cos v) ; or : dx Me ayn, % ee (5) cos 8 |] —2— , Ae (8) 5) dw\? dt 3n,m* (1—a) ako, q= Y where we have put 100a,a Ee We can with sufficient accuracy *) take in the formula (5) @,’n, = a7n, and in the formula (6) 1—e? =V 1—e,?. The formulas can, however, not be used for the computations, unless they are so developed as to contain only such quantities as can be easily derived from existing tables. ') The formula (6) is derived by Borriineer from the vis viva integral. In this derivation he introduces a couple of approximations, which are unnecessary, and which are the reason why the factor Y 1—e? does not appear in his formula. On his page 12 he takes fani for sini. If we retain sind and replace it by its value 1 dr ee the square root drops out of the formula, and consequently the approximation V ds’ introduced on page 13 in the development of this same root is also unnecessary. We ; 3 6 Ohi — dp .- c then find An = ——— J— . Now we have V 1—e? = 7? —— and r = —. Bortiin- an dt dt wr 3V 1—e* dx — J, and his formula € dy (I) on page (18) then becomes identical to our formula (6). *) See however the footnote on p. 815, cer’s formula (I) on page 13 thus becomes 42 = — 813 The coordinates of the moon are developed in the lunar theory in series depending on the four arguments /, /’, / and D, where / and /’ are the mean anomalies of the moon and sun, /” the mean argument of the moon’s latitude, and / the difference of the mean longitudes of the moon and sun. For the mean opposition we have D0. The other three arguments are contained, under the names of I, Il and If, in Oppotzmr’s “Tafeln zur Berechnung der Mondfin- sternisse”’. We have 9 9 9 GS, =i, oF, = — I —87.66) 10 10 10 Denoting the mean longitudes by 4 and 2’, and the true longitudes by w, w’, we have: A AW AR DY eel SE alle where dl = 2e sin! + ; e? sin 2l — y? sin 2F represents the elliptic term G — SUL ‘), and 4A the sum of all perturbations in longitude. The perturbations in the motion of the earth can be neglected. Then, denoting the values for mean opposition by the suffix 1, we have de 180°, w,—w,' = 180° + di, + Ad, — dl; for the instant of central eclipse on the other hand we have w—w' =—180° y* sin 2F. We now put A = (w,—wv,') — (w—w’) = dl, + Aad, — dl! + ysin 2F, Then, n(1—c) and n(1—g) being the mean motions of the perigee and the node, we have, neglecting perturbations *): dw D fe = — = n(1 + 2ce cos 1 + — ce? cos 2l — 2qy? cos 2F), dt 2 i are small and of varying sign. The term containing p* is of the nature of a secular acceleration. If we denote the time expressed in centuries by 1, then p is equivalent fo D:00 7,01 dp" to 15.4 27. The individual values of dn will be given in the second part of this paper. Table | contains the values of An, Aa, A,r and 4,A for each Saros. TALBAL Es Year |Saros ‘fn Li Ly Ly) re ia 160 Newc 1703.0 +1091 628 — 3.9 5°4 I — 7.5 | 418390 | +2103 | 2756 1721.0 0 0 0 — 0.4! II — 2.3 +2180 +297 | —415 1739.1 — 647 + 6909 + 4.3 + 4.6 Ill - 2.2 | +2299 +300 296 } 1757.1 — 878 1414 8.8 9.1) IV —16.9 | +2197 —246 —3u8 r zs 4 1775.1 — 911 1954 12.2 MIS V —11.8 +2415 57 —180 bs o os 1793.1 — 972 +2084 +13.0 +12.9 VI | —8.3'| +2565 | + 74 | — 30 1811.2 — 940 +1925 +12.0 +11.7 Vil — 6.2 +2537 +152 — 58 1829.2 — 862 +1430 + 8.9 + 8.7 ; VIII | —11.1 | +2627 30 + 32 1847.2 — 542 795 5.0 4.1 IX —15.7 +2874 —202 +281 cu T - 1865.3 — 3 — 3 0 — 1.1 xX —14.8 +3200 —168 +605 1883.3 + 658 —I061 — 6.6 —- 6.1. xl —21.4 +3135 —413 +540 , 1901.3 +1086 | - 2734 —17.1 --10.2 XI | — 5.3 | +3269 | +185 | +674 1919.4 +1237 —5066 —31.7 We have A,r = — 382, 4,4 = + 2595. If we neglect the term in p®, and choose the values of 4/, and », so as to make Ap = 0 for 1721 and 1865, the perturbation in longitude given under the heading 4, results. If we add the term 4 p?4,r, at the same time altering the initial constants so that the perturbation remains zero at the same two epochs, we get the values 2, '). The reliability of these results of course depends on the reliability of the individual valnes of dn. The values of 7; in two successive eclipses differ by 155°, consequently the values of dz have opposite signs and nearly destroy each other. Therefore, to arrive at a toler- able accuracy in the final perturbation in longitude, it is necessary to compute the individual da to a much higher accuracy. The sum of the neglected terms in the series (9) will generally not exceed Yoo, OV in some cases perhaps */,,., Of the whole. The maximum value of dn is about 190, we may thus expect on this account an error of one, or in extreme cases, 2 units. The chief source of uncertainty is the function /J,. This function contains the hypothesis regarding the distribution of mass in the 1) In the original Dutch there was a mistake in the values of a, and Ag, which has here been corrected. The conclusions remain the same, 819 body of the earth. If a distrubution differing from Wrrcnert’s is adopted, the function J, is considerably altered. What is the effect of this on the final result can only be decided by actually carrying out the computation with a different hypothesis. This has been done, as will be related in the second part of this paper. Here it must suffice to state that, although there are some differences, the general character of the results is remarkably similar to those of the first computation. [It may be mentioned that also my preliminary inves- tigation of 1909, though based on a totally different and only roughly approximate formula, gave results of the same character. The hypothesis that the sun and moon can be treated as points, is also, of course, only approximate, and it is very difficult to say in how far it affects the reliability of the results. It seemed however better, at the present state ofthe question, to rest content with this approximation. The function /, however gives rise to errors in still another way. It is tabulated with the half-duration 7’ , as argument. This is taken from the Canon, where if is given in minutes of time, and can thus be a half, or in some cases perhaps even a whole minute in error. The resulting error in da may occasionally amount to 4 units. Thus, neglecting the uncertainty introduced by the hypothesis regarding the distribution of density, the purely numerical error in dn may reach an amount which can be taken to correspond to a mean error of say + 3 units. The mean error of the perturbation in 7 after p eclipses is then + 3p/p. For a Saros (80 eclipses) this gives + 16. Also the m. e. of the second sum (i.e. the perturbation in longitude, if we neglect the fact that sometimes the interval between succes- sive eclipses differs from the normal value) is found to be ze V6 p (p+) (2 p+). For the Saros this becomes + 292. It thus appears that all the values which have been found for An might very well be due to accidental accumulation of the inaccu- racies of the computations. On the other hand the circumstance that they have the same sign throughout might lead us to consider them as at least partly real; by which | mean as necessary consequences of the adopted hypotheses. The values of 4,4 also are not so large that their reality can be considered as certain, but here also the systematic change with the time may be an indication of their being not entirely due to accidental errors of computation. The only thing that can be asserted with confidence is that the values of A,» and 4), are small, and consequently that the non-periodic part of the perturbations in longitude has a smooth-running course: no other irregularities with short periods can exist in the longitude than those which are contained in the periodic part. 820 This periodic part is very nearly the same in all Saros-periods. It will be given in detail in the second part of this paper. To show its general character [ give here in Table II] the mean for the last live periods VIII—XII (1829—1919), which are the most important for the comparison with the observations. The first column contains the time ¢ counted in synodic months trom the beginning of the TASB (3B at: t 4s Foom,| +s Form. | 0 0 0];41 -521 - 523 | 88 --573 —546 |129 — 34 — 36]176+312 + 360 t | 4s | Form. t hs Form | 4s Form. 6 — 75 — 84|47 —560 —572| 94557 —491]135 + 64 + 451/182-4311, +356 12 —143 - 167/53 —578 —608]100 —545 - 426/141 +133 +120]188 +321, +337 18 —309 —359|59 —654 —631 |106 —362 —354 147 +237 +203]194 +305 +306 24-321 —331|65 —538 —640|112 —319 —273]153 +239 +247 200 +240 +262 30 —441 —406|71 —603 —635]118 —216 —190]159 +262 +-295 |206 +272) +206 36 —487 —474|77 —582 —616|124 — 117 —106}165 +316 +330 ]212-+4+174 +140 83 —577 —583 171 +314 +352|218+ 76 + 66) Saros. This periodic perturbation can be represented with unexpected accuracy by the formula: RT ie "2 at ve 2 —— 120 — UU 26 ere at (2) aoe The values computed by this formula are given in the table under the heading “Form”. The constant term, of course, is unimportant, and could be added to the arbitrary constant of integration 44,. It would almost entirely disappear, if the Saros was begun at the end of the third-group, say at about 7= 121. If the time is expressed in years, the formula becomes 2, = — 140 + 500 sin | 199.907 (t—1900) + 137.° | . 113) The course of the perturbation in longitude is remarkably similar in the different periods, the irregularities, i.e. the deviations from the sine-formula, recurring in each period at the same*valnes of ¢. The coefficient of the sine on the other hand varies from one period to another. For the first eight periods it oscillates between about 350 and 400, in the later periods it increases up to about 600 for the Saros XII (14901-—1919). oe en oe ———lO—e SC ee eee eee 821 Comparison with the observations. The excesses of the observed longitude of the moon over the longitude as computed by pure gravitational theory, which have been given by Newcoms, must still be corrected by the differences between the new lunar theory of Brown and Hansen’s theory which has been used by Nrwcoms. The corrections necessary on this account have been collected by BatrerMANN'). Out of the 43 terms given by him we need only consider the terms of long periods (14)—(22) and (48). For the discussion of the non-periodic part of the perturbation in longitude we must take account of the terms (16) to (19), which have periods between 128 and 1921 years’). I have, however, not applied these terms, the reality of the non-periodic part being too uncertain to warrant much labour to be bestowed on it. For the discussion of ‘the periodic part, we have to consider the terms (14), (15), (20), (21), (22) and (43), which can be written as follows: (14) + 0".48 sin 40°.67 (¢— 1894.3) period 8.84 years (22) +0 13 si 30 35 (¢ - 1894.6) ell a (20) + 0 .24 sin 20 .66 (¢ — 1890.7 TAS (43) + 0 .56 sin 19 35 (¢ — 1892.2) 5, dltela(0) (15) +0 13 sin 10 .34 (¢ -- 1870.4) a ae Se (21) +0 .28sin 9 .69 (¢ — 1877.6) i tiga eae The therm (43) contains the correction given by BaTTERMAN in his ‘“Zusatz”. It is very similar to the term which was already applied by Ross, viz: — 0".50 sim 2 = + 0".50 sin 19°.35 (¢ — 1894.8). These corrections must be added to the tabular longitudes, or sub- tracted from the residuals. Considering now first the non-periodic part, it is very remarkable that the values of 4, as given in Table I are between the years 1703 and about 1894 almost identical to Newcomps’s great fluctuation, if 160 of our units are taken equal to 1”. This is at once apparent from the last two columns of table I, of which the last contains the great fluctuation according to Newcoms. Therefore, if we assumed the absorption of gravitation to be the true explanation of the great fluctuation, we should have GOD Seo O2n yell y= 10r (ay Kee However, after 1894 the similarity ceases. The agreement before that date depends on the assumption of the reality of the values 1) Beobachtungs-Ergebnisse der K. Sternwarte zu Berlin, N°. 13, 1910. *) The most important of these is a correction of 0.85 to the coefficient of the well known Venus-term of 273 years period. 54 Proceedings Royal Acad. Amsterdam. Vol. XV. 822 which have been found for Sn and Aa, especially the negative value of the mean 4,v. This latter is equivalent to a secular accele- ration of which the coefficient would, with the above value of q, become — 37". This, of course, is entirely inadmissible and conse- quently it is not possible to consider the value of 4,r as real unless we take for g such a small value that the whole effect becomes entirely negligible *). The partial agreement of 4, with the empirical terms of long period can therefore not be considered as a proof for the existence of an absorption of gravitation. We now come to the comparison with the observations of the periodic part of our computed perturbation. This comparison was only carried out for the time after 1829. From 1847 to 1912 I had the advantage of being able to make use of a new and careful reduction of the Greenwich meridian cbservations which Prof. E. F. vaAN De SaNDE Bakunvyzen most kindly placed at my disposal. Prof. Baknuyzen applied to the meridian observations the correction for the difference of right ascension of the moon between the epochs of true and of tabular meridian passage, for those years in which this correction had not yet been applied at Greenwich. Then the systematic corrections, which in his former reduction (These Pro- ceedings, Jan. 1912), were taken constant over the whole interval from 1847 to 1910, were derived anew. The following are the syste- matie corrections finally adopted by Prof. Bakuuyzen for the obser- vations of the limb : 1847—48 49—57 58—68 69—78 79—98 1899—1911 0".00 —1".61 —O0".83 —O0".93 —O".62 +0".39 For the observations of the crater Mosting A the correction was derived in two different ways, which gave —0".22 and + 034 respectively. The adopted correction is 0".00. Prof. Baknuyzen then formed the means of the meridian observations of the limb, of the crater and the oceultations, the latter being taken from NrEwcoms’s paper, bat corrected by -+ 0.18, for reasons explained in his paper of Dee. 1911. The corrected results of the meridian observations and the means thus derived are given in Table VII in the second . part of this paper. From these means I then subtracted the theoretical corrections given by BarrerMann and quoted above. The resulting corrected means which are thus the excesses of the longitude of the moon over the pure gravitational value, diminished by Nuwcoms’s great fluctuation, were plotted and a smooth curve was drawn through 1) In my former investigation I was led to a similar conclusion (see “The obser- vatory” Noy. 1912 page 892). 823 them. From this curve were read off the values given below in Table Ill under the heading “Obs.” If these are compared with the computed perturbation, of which the periodic part is also given in the table under the heading As, there appears at tirst sight to be eA erase lle Obs. Obs. Obs Year Obs. 4s | 48 | Year | Obs. ds ds | Year | Obs. ds ds 500 500 500 1829 |—0"3|+ 20|—0'3] 1865 +3°8!-+ 60 +3°7] 1892 | —2"8|—340|- 2”1 35 |= 0.8|—550|-10.3) 68|42.4|/—500| 3.4| 95 |- 3.1|4300|—3.7 41 |=0.5| } 60|/—0.6| 71 | 0.0/- 630} 41.3} 98 | —2.0| +380|—2.8 47 |+1.3)+ 10 41.3 74 —1.8| —350 1.1] 1901 | +0.5) + 40'+0.4 50 |+1.1|—4401 42.0] 77 |—2.5| -230/—3.0| 04 |+1.4|—560| 42.5 53 |+1.1|—550| +2.3 80 —1.4 +330 —2.1 07 | - 2.7 —640 +4.9 | 56) 12.0) —830\-2.7| 83 |—1.4/+ 50/—1.5] 10 |+44.4|=—350| 15.1 Bam eas 0 70h eam G42) 2] —580)| 00) 12") S| 4°10'| 75.0 | | 62 |+3.8)+270/ 43.3] 89 ,—3.0|—630|—1.7 | [ad . — a certain similarity in the course of the two curves. Mr. Borriinerr. whose results on the whole agree with mine, has been led by this similarity to consider the existence of an absorption of gravitation as being established “mit guter Wahrscheinlichkeit”. In facet, from about 1840 to 1868 the observed deviations can be very satisfactorily represented by about eae smooth curve, which latter then must either be ascribed to the non-periodic part, or remain unexplained. After 1868, however, the agreement is lost. We have again a partial parallelism between 1886 and 1891, and also the increase after 1908 coincides with an increase of 2,, but it is impossible so to represent the observed values over the whole interval 1829 to 1912 by 4, multiplied by a constant coefficient, that the remaining differences form a smooth curve. Still I think we cannot consider the probability of the existence of an absorption of gravitation as established unless the residuals remaining after applying the perturbation produced by this absorption (and which then remain unexplained), are small and form a smooth curve, or at least are less irregular than the original fluctuations. The values of Obs. — &4, however, whatever value we adopt for 4, always are considerably more irregular than the observed values themselves. The sudden fall between 1568 and 1874 coincides 54* $24 with a horizontal stretch (minimum) of 4;, the quick rise from 1897 to 1906 corresponds to a decrease of 4;. The effect of absorption cannot have another period than 18.03 years, while in the observed fluctuations periods of different length are certainly present. It appears to me, therefore, that so far we have no reason to consider the existence of a sensible absorption of gravitation as proved, or even as probable. (To be continued). Astronomy. — “On Absorption of Gravitation and the moon's longitude”. By Prof. Dr. W. pr Srrrer. Part II. (Communicated in the meeting of December 28, 1912). The conclusions derived in the first part of this paper are entirely confirmed by the second computation, which was already referred to in that part, and which was based ona different hypothesis regarding the distribution of mass in the body of the earth. I now assumed a core of density d’, = 20 and radius #’,=0.55 R, surrounded by a mantle of density o', = 2.8°). In the same way as before, I put, for 7, < 93.5 ! ibe 3 Je — 84.7 ma iPS ’ 112 and for 7’, > 93.5 T 2 FUSS BA7 VA a aie 112 The multiplier 100 has been replaced by 84.7 = 100 4,'/d, in order to get the same value of qg for both computations. The result of the introduction of this new distribution of mass instead of the formerly assumed one is to increase the amount of absorption for long eclipses and to diminish it for short eclipses. The ratio J,'/J, varies from 0.51 to 1.25. It is smallest for those eclipses in which with Wiecuert’s hypothesis the core also contributes to the absorption, while in the new hypothesis the ray of gravitation is situated entirely in the mantle. For the purpose of computation this ratio J,'/.7, was tabulated with the argument 7. We have then 0 dn’ = — dn. 0 ') This hypothesis has been suggested by recent investigations by Mr. GuTENBERG, which were kindly communicated to me by Dr. VorrLincer. Mr. GUTENBERG finds that the real distribution of mass is included between the limits given by -'s = 20, 3), =2.8 and 3,'=8, 3 = 4.4. It being my intention to investigate the effect of a change in the function J), I purposely took the upper limit, which differs most from WIECHERT’s assumption. 825 With this value of dn’ the computation was then carried out in exactly the same way as with dv. Notwithstanding the considerable difference between the functions /,’ and ./, the general character of the results of the two computations is the same. The non-periodic part of the perturbation in longitude derived from the new computation is given in Table IV, which is entirely similar to Table I of Part I. We now find A,v' = — 230, A,A’ = + 2939. Neglecting the term — 4p? A,r and causing the perturbation to vanish for 1721 and 1865 by an appropriate choice of the constants of integration, we find the values given under the heading Z’,. If the term containing A,r is added, we get the vaiue 2',. The general TABLE ly. | | | | | Year |/Saros) An! PY Ey AIR a Say a Bet 1703.0 -{- 747 | — 288 We ie2 eso) —3a4e) 1912 1721.0 0 0 it | —10.4 | 42318 | —156 ) — 621 1739.1 — 490 + 315 I | —21.9 | +2346 | — 550 | — 593 1757.1 1180 | + 272 | IV | + 2.8 | +3300 | +334 | + 361 1715.1 —1322 + 403 | V | —12.3 | 43141 | —227 | + 202 1793.1 | —1361 | + 476 | VI | — 9.3 | +3380 | —115 | + 441 1811.2 —1388 | + 337 Vil | — 1.0] +3466 | +193 | + 527 1829.2 —1444 | — 64 VII | +14.9 | +3896 +751 + 957 1847.2 ee rt Te | IX | — 1.9 | 43452 | +160 | + 513 1] 1865.3 L=sesr—= 3 | X | — 9.7] +3120-| —130 | + 181 | 1883.3 4+ 699 — 336 | XI) —19.6 | +2494 | —498 | — 445 | 1901.3 2 | -+ 645 | —1655 |; XI | + 9.2 | 72630 | 4 572 | — 309 1919.4 | + 229 —3566 character of the perturbation is very similar io that of the first com- putation. But the correspondence with the “great fluctuation’, which was apparent in the first computation, does not exist here. In the periodic part the agreement between the results of the two computations is even more complete. With reference to the reliability of these results it must be remarked that the function /,’ has a wider range of variation depending on T, than J,, and consequently the possible error arising from the fact that 7, is only known to whole minutes is in the second com- putation much larger than in the first. Accordingly we find that the 826 values of Ar in the second computation are considerably larger than the corresponding values of 4,v in the first computation. Also the values of A,’ are larger than those of 4,4. We are thus led to the same conclusion as before, viz: the reality of the non-periodic part of the perturbation is not assured, and the only thing that ean be asserted with certainty is that the non-periodie part cannot have any considerable irregularities and that no other periods are possible than the Saros of 18.03. years. The following tables contain the principal quantities occurring in the computations. Table V gives for each eclipse the values of 7’, /,. 1,’ and those of dn and dn’ computed by the formula (10). The first column of the table contains the time ¢ counted in synodic months from the beginning of the Saros. The time ¢= 223 of any Saros is, of course. identical to the time ¢=O of the next Saros. The arrangement of the eclipses in groups of six is very clearly shown. The several groups begin at ‘= 0. 41, 88, 129 and 176 and end at (a {ae 118, 165 and 212. Table VI contains the purely periodic part of the perturbation A, and 7%, according to the two computations. The similarity between the different Saros-periods is very striking. In the mean motion this similarity is even more apparent than in the longitude. The mean motion is not contained in the table. but can easily be derived from the longitudes, as it is the difference of two successive values of 4, (or 2’. We see from this table that in the first computation the amplitude of the periodie part is fairly constant for the first eight periods and begins to increase after the eighth Saros. The difference between the extreme values of 4, oscillates between 700 and 830 in the periods I to VIII, and then gradually increases up to about 1200 for the Saros XII. In the second computation the difference between the extreme values of 4's is more constant and varies between about 950 and 1100. The remarkable agreement between the results of the two compu- tations justifies the expectation that. the general character of the per- turbations in longitude produced by an absorption of gravitation will be sensibly the same for any assumed distribution of density within the body of the earth. which is at all within the limits of probability. The conclusions arrived at in Part I are thus not restricted to the particular hypothesis which was there introduced, but have a much wider bearing. . 827 Deb) Bil EY: Saros I Saros Il Uw | 2) | om | ont \\ Year Te L |@,| ¢n on! | || 1703.0 | 83 22302] -4' + 58.24 34.9||1721.0| 83, 220.4| 14 + 55.5/4 33.3 6|| 035 108 18.1 [178 — 49.2\— 55.1|] 2151105) 15.2/189 — 37.0\— 37.7 12|] 04.0 |112| 173.0 1353] — 26.8— 33.5|| 22.0112)170.1| 4 — 36.1\— 45.1| 18|] 04.5 102 327.9|167 + 71.0 + 64.6) 22.5105, 325.0178 4+ 84.0 + 85.7 all 24 04.9 78 122.8 |342 — 56.3 Site .0 79 119.9 353 — 60.6 — 39.4 | | {| | | | | | | 41 || 1706.3 74 201.6 "7 4- 20.4 + 15.5|1724.4 65) 198.8 % | 2 8 41|| 06.8 84 356.6 202 4+ 7.24 4.2|| 24.8) 82 353.7/302 + 10.0 6.1| 53|| 07.3 112 151.5106 — 99.6 113.2) 25.3111 148.6 59|| 07.8 112 306.4 281 1153.0 4191.2) 25.8112 303.5 65 || 08.3 76 101.3| 95) — 55.2+- 38.6/| 26.3) 82) 98.4|106/— 73.9|— 45.1 TI || 08.7 | 72, 256.2 270 + 43.0 + 34.8 26.8 | To 253.4 281 + 54.54 38.1 : Peet) 88] 1710.1 93 395.1 45 + 43. 4+ 22.1 1728.2 92 332.2] 56 -+ 46.2-+ 24.0 o4]| 10.6| 91 130.0 220 — 84.3— 44.7. 28.6 85 127.1230 — 10.7— 41.0 100]! 11-1 111/284.9) 34 4182.6 +222.8 29.1111 282.0) 45 +186.5 4 227.5 106 |) 11.6 110 79.8 209 172.5 205.3 29.6111, 76.9 220 —174.1 —212.4 112 |} 12.1 | 58 234.7| 23/4 23.8|4+ 20.2) 30. ] 59 231.9 34 + 24.0 + 20.4 (118 || 12.5] 49) 29.6|198] 8.si— 7.5| 30. 6 03 26. 8 209 — 12.6 — 10.7 } | | bo Go 1202 159.5 + 199.3, | | 129// 1713.4. 63 313.6 158 + 20.91 + 17.8731. 5 48 310.7 169 4- 13.2) +11.2 135] 13.9 71 108.5 933 — 41.3— 34.3, 32.0 70 105.6 out — 40.6 — 34.1 14 |] 14.4 111) 263.4 |148) + 182.9 4223.1] 32.4 110 259.5 158 +177.7) + 211.5 [147|| 14.9 |112| 58.3 322] 159.6|—199.5|| 32.9112) 55.4 333 /—154.7|-193.4 153 15.4 82 213.2 127 + 44.0 + 26.8|| 33.4 90 210.3 148 4 55.2 + 29.8 159|| 15.9/ 90] 8.1 311] —11.1|- 6.0] 33.9 90) 5.2 322 — 6.8— 3.7 165 lta | | | | (176 || 1717.2 83, 87.0 86 — 78.0 — 46.8//1735.3 18, 84. 0) 97 — 61.2— 40.4| 182|) 17.7) 83] 241.9 261 + 69.4 + 41.6|| 35.8 77 230.0 272 + 51.5 4+ 34.5 188 || 18.2 [112 38.8 76| —114.8)—143.5]] 36.2112, 33.9| 86 —106.7—133.4 194 || 18.7 112) 191.7 250] + 34.94 43.6) 36.7112 188.8 261 + 24.6 + 30.8 200|) 19.2 76)346.5| 65|+ 10.5+ 7.4]) 37.2) 79 343.7| 76 + 15.1+ 9.8 | (206 | 19.7 67) 141.4 239] — 24.2 — 20.6|| 37.7, 76 138.6 250 — 40.0 — 28.0 | 212 | | } 828 TABLE V (Continued). eS ee - SS es Saros Ill Saros IV ~_=—__ ~ - = = 2 — —__——_ —-- = -~ ——| | Year Toh) ae on on |) Year| 7%) 4,42, ) on én’ | 9 1757.1 80'214°6 35 + 43.24 27. 6 103, 12.4 200| -- 27.8 — 26.4|| 57.6) 98, 9.5 211 — 17.2— 12.7] 4|| 58.1/112| 164.4 25 — 54.1\— 67.6| 4| 58.6110 319.3 200 +111.0 -+132.1, 80117.1| 4) — 64.6— 47.7|| 59.0) 80/114.3| 14|— 65.7\— 42.0] 52 196.0 130 + 6.8 + 5.8/1760.4 31 193.2 148 + 2.04 1.7 79 330.9 313 + 11.5-++ 7.5|| 60.9, 771 348.1323 + 12.9|-4 8.6. 110 145.8 128 —102 9—122.5|| 61.4110 143.0 139 —110.7)- 131.7! 2 300.7 302 }-165.3 +-206.6|| 61.9112 297.9 313 +170.5)4 213.1 | 88 95.6 117 — 93.2) — 51.3)| 62.4 94 92.8 128 —f145|— 607 80 250.5 292 + 65.7-+4+ 42.0|| 62.8 82 247.7 302) + 11.814 43.8 2.191| 329.4) 67 + 48.5\-+ 25.7/l1764.2| 88 326.5 76 + eae 25.8 7 | 76 124.3211) — 48.4 — 33.9|| 64.7) 70 121.5 |251) — 35.7\— 30.0 41.2 111 279.2) 56 +186.3 +227.3|| 65.2112 276.4 66] +-191.4| +.239.2 6/112, 74.1 |230| 175.3. -219.1]] 65.7112) 71.3 '240| —172.5|—215.6 48.1 61 228.9 45 + 24.8 + 21.1|) 66.1 64 226.2 56 + 26. 214 22.3 48.6 | 73, 23.8 220} — 15.9— 12.6]| 66.6) 80, 21.1 230 a! 90; 5 = 134 > oo own op © = ~] 1749.5 26 307.9180 + 4.74 4.0 be | 50.0 71 102.8 355 — 42.1,— 34.9//1768.0 70 100.0 5 -- 41.3 — 34.7 108 257.6 169 +168.9 }-189.2) 68.5105 254.9 179 4153.9 +157.0 5 51.0 112 52.5 344 —149.7 —187.1|| 69.0112. 49.8 354 —144. 1180. 9} 51.4 96 207.4158 + 61.3+ 38.6)} 69.5101 204.7 168 + 63. 8|+ 55.5. 51.9) 91} 2.3)333)— 2°3\— 1.2}) 70-0) 91) 359.6 343 peige (60 1753.3 73° 81.2/108' — 44.6 — 35.2'1771.3) 67) 78.5 118] — 34.4|— 29.2 53.8 72 236.1 283) +- 37.3+ 30.2) 71.8) 67 233.4 293) + 29.8)4 25.3 54.3 112, 31.0 97 98.2 —122.8} 72.3112 28.3 107 — 90.1\—112.6 54.8 112, 185.9 272 + 14.44 18.0] 72,8111) 183.2282 + 4.6) + 5.6| 55.2 84 340.2%) 87 + 22.5-+ 13.3)| 73.3) 88 338.1) 96 + 29.8 + 16.4 — 56.6— 34.5] 73.7) 88 133.0271 — 75.2 41.4) or a ~—l a IV w or io a) te 7) a 829 TABLE V (Continued). Vo ee KS Saros V Saros t — et the be | Year ‘Th Tee ii |) or n | Year| Ty). & 124 1775.1 79 211.9. 46 + 38.7 + 25.2/1793.1 75 208.9. 57 | ell 75.6 93 6.8(220/-- 9.6 — 4.9] 93.6 89 3.9 231 12|| 76.1 112 161.7 35 — 62.4 — 78.0| 94.1112 158.8 46 | 18|| 76.6 110 316.6 210 +118.3 1140.8) 94.6 112 313.7 220 24] 77.1| 82 111.4) 24|— 73.6 — 44.9] 95.1 83 108.6 35 30 || 77.6 39 266.3 199 + 11.6/-+ 9.9 i 95.6 58 263.5 210 is | | | 47||1718.9 77 345.3 934 + 15.3 + 10.31797.0 76 342.4 345 53 || 79.4 107 140.1 149 —109.8 —119.7, 97.4 104 137.3 159 59|) 79.9 112 205.0 923 +175.5 +219.4) 97.9 111 202.2 334 + | 65) 80.4 98. 89.9 138 —120.4 — 95.8 98.4102 87.1 148 11 || 80.9. 84 244.8 312 + 77.4 + 45.7) 98.9 85 242.0 323 1 | ; | 88/1 1782.2 85, 323. 7, 81+ 45.0 + 26.11800.3 80 320.9 98 | 94) 82.7 62 118.6 262 — 28.5, — 24.2] 00.8 54 115.8 273 /100 || 83.2 112 273. 5 76 +191.9 +239.9| 01.2112 270.7. 87 (106 || 83.7 112, 68.4 251 —169.3 —211.6) 01.7111 65.6 262 112 || 84.2 70 223.3| 66 + 30.2 + 25.4| 02.2 73 220.5. 76 - us| 84.7| 86 18.3 240 — 22.6 — 12.9] 02.7 91 15.4 251 129 | i 135 |] 1786.0 | 70 97.1] 15 — 41.4 — 34.8|1804.1. 69] 94.3) 26 141] 86.5 101 252.0|190 +136.7 +118.9 04.6 96) 249.2 201 147|| 87.0 112 46.9| 5 —138.7, —173.4} 05.0112) 44.1) 14 153 || 87.5 105, 201.8/179 + 62.0 + 63.2| 05.5108] 199.0 |190 159 88.0 91| 356.8 (354+ 6.1|+ 3.2] 06.0 91/353.8) 4 165 176 |] 1789.4 58, 75.6|129 — 25.4 — 21.6/1807.4 44) 72.8 139 182 || 89.8 | 62) 230.5 1303 + 24.9 + 21.2] 07.9 58| 227.7 313 |188]] 90.3 AIL) 25.4|118, — 79.5, — 97.0} 08.4110, 22.5 128 | 194]] 90.8 /110| 180.3 293, 5.2 — 6.2) 08.8110] 177.4 308 | 200 |) 91.3 91) 335.2/107| + 37.8 + 20.0) 09.3 95/332.3 118 206 || 91.8 91| 130.1 /282) — 87.8 — 46.5) 09.8 94) 127.2 202 7 | | 212| | 6 VI on n’ - 28.6-+ 20. — 3.3— 1 — 71.3— 89. +131.2)+-164 — 71.3— 46 - 26.1)+ 22 | + 16.8/+ 11 —107.7|— 105 176.1 +214 — 144.8 —131 + 78.9+ 45 + 38.44 24 — 22.7— 19 +192.2 +240 —162.6 —198 + 32.1/+ 26. — 22.5— 11 — 40.3— 34 +116.6+ 73 —132.6 —165 + 58.2+ 65 + 10.7/+ 5 — 14.7— 12 + 20.9+ 17 — 69.0 — 82. — 14.6 — 17 + 48.3-+ 28. —100.7 — 53. © © © Mm O Ry wo Oo Do oO wo o = = t or nw to ‘100 106 S wo 90 112 TABLE V (Continued). Saros VIl i 206.1 10 155.9 310.8 105.7 260.7 339.5 134.4 289.3 84.2 239.2. ty 67 241 56 230 on im l / 18.0. _s103 830 on' + 0.7] —1003 | Rig2 50.1 29.6 a 13.4 84.3) +219.7| 168.2 | + 46.9 i +- 22.4 13.1 239.6 —184.9 | + 27.6 33.2! 4+ 50.4 —I5i1-5 + 60.2 + gil 18 1.6) + 15.2 16 1829.2 20.7 30.2 30.7 31.2 31.6 1833.0 33.5 34.0 34.5 35.0 35.4 1840.1 | 40.6 41.1 416 42.1 42.6 1843.9 44.4 44.9 454 45.9 110 Saros VIII | 4, i on on' 203.3) 77) -+ 16.5| + 14.0 358.2 |252/+ 3.7/+ 25 153.1 67, — 86.1 —105.0| 308.0 241 4145.7 + 182.2 102.9 56 923 — 51.7 257.8 230 + 50.1) + 36.6 | | 336.7| 5\+ 19.8|+ 145, 131.6 180 — 88.6, — 47.0 286.5 355 +1833! +.223.6 | 81.4 169 —170.0| —195.5. 236.2 344! + 81.7| + 45.8 | 31.1158) — 48|— 4.1! 315.2119 + 228) + 19.4) 110.1293 11.9 — 10.1 264.9 108 1186.9 +228.0 59.8 283 — 151.3 —1800. 214.7| 97) + 49.1] +- 29.5 9 6 |272| — 15.5|— 10.7 | 885!47 36.9 — 31.4| 243.4 '221 + 692) + 415 383 36 —119.0 —1488| 192.2 1211) + 41.2] + 503 348.1) 25 - 20.2 + 105 143.1 200 - 187 — 15.9) 221.9 335) + 149|)+ 12.7 16.8 149 — 44.5 — 48.5 171.7|324| — 32.3] — S71 326.6 139 + 74.3) + 70.6 121.6 S13 —118.6| — 81.9 | 831 TABLE V (Continued). Saros IX Saros X t : Year liza h o\Vy on on’ || Year Tel) Geet elie tert: oll is472 | Bo! 2085 | S61 + 11.7| + 99|[1965.3| 51) 197.7] 89 + 76] + 65 | 6 || 47.7 | 72 355.4 2631+ 48 + 3.9|| 65.8) 65 3526274 + 53/+ 4.5 | 12|| 48.2 |110 1503 | 77) — 921|—1196|) 66.2 110 147.4) 88) — 99.8) - 118.8 | 18 48.7 |112 305.2 /252} 4152.4 +190.5)| 66.7 110! 302.3 263 +152.3) 4-181.2 24 49.2 | 90 100.1 | 67} —103.5|- 55.9|| 67.2| 92) 97.2) 77) 110.5) — 57.2 | | | | | | 30 49.1 | 82\ 255.0 |241| + 71.9| + 43.9]| 67.7} 88) 252.1 )252) + 90.4) + 49.7 | 47]| 1851.0 | 74 333.8 | 16] + 20.6| + 15.7||1869.1 | 74| 331.0| 26) + 22.4) + 17.0 | 53 |) 51.5 | 89 1288 |191|— 78.3) — 42.3|| 69.6 | 80) 125.9 (201) — 56.1) — 35.9 59 || 52.0 |111/ 283.7 | 5] 4-186.0| +226.9|| 70.0 |111) 280.8 | 16) 188.1 | +-220.5 65|| 52.5 |110| 786 |180] 171.2) —203.7]/ 70.5 111 _ 15.7 |191| —172.2 | —210.1 11 || 53.0 | 87) 2335 [355] + 79.6| + 44.6] 71.0) 88) Eu 5) + 79.6| + 43.8 71|| 535 | 53! 28.4 |l69|— 9.9|— 84]| 715) 65) 25.6 /180/— 13.2)— 11.2 | | 83 | | ky | gg || 1854.4 | 58 312.3 |130| + 18.1| + 15.4|l1872.4| 42| 309.5 /140/ + 98/+ 83 o4|| 548 | 30 1073 |304|— 7.0/— 60|| 729) 21) 1044314, 40/— 34 100 || 583/110, 262.2 |119 +181.7| +216.2 73.4109) 259.3 129| +176.3 | +202.7 1106 || 55.8 [110 57.1 [203] 147.4|—1754)) 73.8 109) 54.2 303 139.6 | 160.5 112) 563 | 89 2120 |l0s| + 580) + 313) 74.3 93, 200.1 119) + 61.1| + 312 '118|| 568 | 99 69 |283|— 106 |— 84) 748102, 4.1 293] 5.2|— 4.7] 129 | } 135 || 18582 | 65 85.8 58) — 34.5|— 29.3||1876.2 62] 82.9| 68| — 31.0|— 26.4 | 58.6 | 75 240.7 \232| + 45.2| + 33.0|) 76.7| 64| 237.8 |242| + 28.0| + 238 147) 59.1 111) 35.6 | 4i| 109.1] —1338|| 77.2)111) 32:7) 57 —102.2| —1247 153 || 59.6 |112/ 190.5 |22i) + 31.9| + 39.9]) 77.6 |111) 187.6231) + 208) + 254 — _ 159] 60.1 | 92/3454 | 36 + 24.4) + 12.7|| 78.1) 94] 342.5) 46] + 30.8 + 163 165 || 60.6 | 74\ 1403 |211|— 32.7|— 24.9) 78.6| 83] 137.4 |220] — 55.5 | — 333 176 mel | | | | 192 |! 1852.0 | 482192 [346] + 12.9| + 110/[1880.0| 45| 216.2|356, + 104) + 88 188 || 62.4 104 14.1 |160! — 36.5|— 35.8|| 80.5|102} 11.2|170| — 27.0| — 24.6 62.9 109| 169.0 335) — 40.6|— 467]) 81.0108 166.1 345 — 483 — 54.1 63.4 105 323.9 |149| + 84.5| + 86.2 81.4108) 321.0 159 + 99.0| +110.9| 206 63.9 98 118.7 324 —125.4|— 928)| 81.9 99| 115.9 334 —132.1 | —104.4 + — i) _ ive) c=) =) 832 TABLE V (Concluded). Year 0 || 1883.3 6|| 838 12]| 843 18 || 84.8 24] 85.2 30 85.7 4 47] 1887.1 | 53 || 87.6 | ea) i 88.1 65 |) 88.6 | 11 || 89.0 T1|| 9895 83 || 88 || 1890.4 94 |} 909 | 100 || 91.4 106 || 91.9 112 || 924 118 928 129 135 || 1894.2 141 || 94.7 | 147 95.2 153 || 95.7 159 |} 96.2 165 ||. 96.6 176 | le2 | 1898.0 188 98.5 194) 99,0 200 || 99.5 | =06 | 1900.0 212 || 00.5 218 Saros XIl Saros Xl ! To) 4 || an | an | Year|T| 4 |f| en | en’ 35| 1947 109) + 29/+ 25 a aa 58, 349.7 284) + 54) + 4.6//1901.8 54) 346.8/204 + 59/4 5.0 109 144.6. 98 —104.5 | —120.2]| 02.3 107) 141.7 |109, —106.2 | —115.8 110, 299.5 273, 4157.9, +187.9]| 02.8 110 296.6 |284) +-163.6| +1945) 96 94.4| 87] —126.2|— 79.5|| 033/99) 91.5] 98 —136.4| 107.8 92) 249.3 /262 +1035 + 53.8|] 03.8) 95| 246.5 273 4.1127 + 653 hi | 72, 3282 37/4 21.7 + 176ll1905.1 71. 325.4] 48\ + 21.6/ + 179 71) 123.1 212 — 35.2|— 292] 05.6| 59] 120.3/222 — 248|/— 214 111, 278.0 26| +1808) +231.5|) 06.1 /111| 275.2| 37 +191.0/ 4233.0 112) 72.9201] 172.8 | —216.0|| 06.6 /112) 70.1 |212' 169.3 | —211.6 | | 88 2278] 15] + 76.9| + 423]| 07.1/ 88| 225.0] 26] + 73.8|+ 40.6| | 75) 227|190| — 17.8|— 13.01] 07.6| 84| 19.9201] — 24.1|— 14.2! | | | 11! 306.7/150] ++ 0.8/4 0.7! 11)’ 101.6|325)— 1.0/— 08 107. 256.5 |139| +-165.4| 4180.3 1909.4 104 953.7 150 150.7 +1477 1109 51.4 |314] —135.1| —155.3|| 099/108] 48.6 325 —127.2|—1425 | 98) 206 3/129) + 64.7 + 47.9|| 10.4103, 2035 139 + 67.0| + 63.6) 102} 1.1/303]+ 1.9/4 1.7]] 109/103} 3584/3914 + 8.1/4 7.7] 57| 80.1| 78] — 25.7! -— 21.8|119123! 50! 77.2! 89, — 19.4|— 165! 54) 235.0 (253: + 19.8| + 168|| 12.7] 40) 232.2/264/ + 104/+ 88| 111] 29.8) 68|— 94.3| —115.0]] 13.2/110| 27.1] 78]|— 84.9] —101.0 110) 184.7|242| + 10.1) + 12.0]) 137/109) 182.0/253;+ 04/+ 05 95 339.6| 57| + 36.8/+ 21.3|| 14.2! 97) 336.9| 67| + 44.0/| + 304+ 90, 134.5 [231] 77.5 — 41.9]| 14.7) 94 131.8 242|— 92.5 — 49.0 | 44) 213.4| 6) + 9.7/4 82 1916.1 42} 210.7| 17/+ 7.9;+ 6.7 97, 8.3 /181/— 165|— 11.4]] 165) 92, 5.6/192,— 88/— 4.6 108 163.2 356 — 56.7 — 63.5|| 17.0 108 160.5, 6|— 64.2 — 19 110, 318.1 |170) 4111.1) 4+1322]] 17.5111, 312.4 /181| +1205) +147.0 100 113.0 [345 —178.4| —114.9 18.0 100 110.3 355 — 1405. ~ 116.6 15] 268.0|150|+ 1.9/4 16] 185) 45) 265.2\170| + 154 + 13.1. aa Pax | | — ie} 833 TAB L Evi Saros | Saros ll Saros III Year| 4, | Ase “Year \- 7h Year| 2, Re | 1703.0 0 0|)1721.0 o 0 1739.1 0 0| 035|+ .9|— 12|) 215 — 3|— 29] 396 — 11 — 32| 04.0} — 31|— 79]) 220;— 43] - 96]) 40.0 — 50 — 91 04.5/— 98|—179) 225 —119 —208]) 40.5 —134 —206 | 04.9; — 94|—215]) 23.0|—111;—234]) 41.0 —122 —217) | —147| —288 |—164 | 300 —175 —275 | 1706.3, —244 | —422||1724.4 | 261 | —421|'1742.4 —272 —381 06.8, —276|—479|| 24.8|—302|—476|| 42.9 —318 —433)| 07.3 —301|—532|) 25.3|—333|—525|) 43.4| - 353! —478| 07.8, —417| —688|| 25.8} 460, —693|| 43.8 --491 —646| 08.3|—380| 663) 26.3|—418|—661 |) 44.3/ —463 | - 607] 08.7| —398 |— 677|| 26.8] 450 —674|| 44.8} —528 | —619|| —373 | —656 —438 —649 | - 528 | —589]| 1710.1 | - 327| —617||1728.2| —416 | —603|/1746.2| 528. —534 10.6 | —258|—574|| 28.6 | —357! —554/| 46.7| 479 — 479! 11.1/—274|—576|} 29.1, —369 —546|] 47.2|—479 - 457 11.6 —107|—355|| 29.6] 195 —311|| 47.6; 292 —208]| 12.1|—113| - 339|) 30.1| — 195 —288|| 48.1281 —178 12.5|— 95|—303|} 30.6|—171) 245|| 48.6|—245 —127| — 86 | —274 —159 | —212 225 — 80| 17134'— 78 | —250]]1731.5| — 149| -184]]1749.5| 208; — 57] 13.9, — 48) —203] 32.0 —134) —140]) 500 —183 | — 15] 14.4|— 59|—191]| 32.4) —150| —130]/ 505 —200'— 8] 14.9| +103] + 44|| 329) + 12|+4 91|| 510 — 48] 4 189|| 15.4] +115|-+ 80] 334 + 19)+4119|| 514 — 46] -199|| 15.9| +171 | +143|] 339] + 82|+177|| 51.9/+ 17| +247]| +216 | +200 | +138 | +231 ++ 78 | +294 | 1717.2 | +299 | +304 1735.3 | +241 | +333 1753.3 4 190 +380) 17.1] +266 +314|| 358) +235) +347) 538 +206 +302) 18.2| +303 | +365|| 36.2) +281) +395|| 54.3 +260 +434) 18.7| +225| +273]] 36.7 4220/4310] 548 4216 +353) 19.2| +182) +225|| 37.2 +184) 4255') 55.2 +1835 +290/| 19.7) +149) +184]) 37.7 +163) 210) 55.7 +178 +4240 | + 92|-+123 | +102 | +137 +114 +156 | =r ees bl \— 9|+ 3 — 34 5) | i be Saros Year; 2, 1757.1 0 57.6 — 16 58.1 |— 49 58.6 — 136 59.0 —112 —154 1760.4 —231 60.9 —271 61.4 —298 61.9 — 436 62.4 —403 62.8 — 485 —495 1764.2 — 513 64.7 | —476 65.2 —475 65.7 — 282 66.1 —262 66.6 —216 —190 =e 1768.0 —152 68.5 —167 69.0 — 28 69.5 — 34 70.0 + 24 + 83 1771.3. +193 711.8 | +218 72.3 | +213 Se POST 73.3 +206 73.7 + 205 +129 IV S384 TABLE VI (Continued) Saros V Saros VI Saros VII Saros VIIl ra | | an Year| 2, 2'. || Year ee Vean tl as a Wevear| was | rie dliqs.1| 0 — olti79a. 0; oj1si12 0 © ots2—02 0] 0 6) 756) — 26 —59| 936 —40 —0/ 11.7 — 45 — 75) 207 — 54 — 91 12) 76.1|— 62 —113) 941 — 84 —142) 122 — 91 —150) 302 —104 ~ 179 18} 766|—160 255|| 946 - 139 —303|| 126 —216 - 325|| 30.7 -- 241) - 372 24| “71.1|—140 —256]) 95.1123 —300|) 13.1 —203 —327]| 31.2 —232|—383 30| 77.6|—194 —302| 95.6 —184 - 343|| 136 —278 —379|| 31.6 —315|—446 ai| |—27|—a6s|} | 248 —a82/) | —351| - 419 | - 376 —494 411718.9| —313 — 404||1797.0| —283 —403 1815.0 —391 —441 1833.0 — 409) —520. 53) 79.4| 340-430] 974/301 —412| 15.5'—412 —450|) 335 —422|—532/ 59| 799|—476 —516] 97.9 427 527) 16.0 524 — | 34.0 —524 —591 | | or oo iw) 65| 80.4|—437|—502|| 98.4|—377 —427|] 16.4!—476 —416 71|| 80.9| 527/524] 989|- 472 —459|| 169 —577 —458 | 77 | 540 | 500 || 488 —445| 504 —453 83 —583 | —477|| —504 —431| 611 — 448 g8l1782.2 —564 —459||1900.3 —517 —419|1818.3 —625 —444 o4| 82.7 532 - 409) 008 —494 —380| 188 —613 416|| 36.8 - 550 - 392 100] 83.2 —528 — 384 01.2 —494 —371|} 19.3 —616, —401|| 37.3|—551 | —372 '106| 83.7 —333 —119|| 01.7 —302 —109|} 198 —427 —147|| 37.8|—365 | —124 112] 84.2 —307|— 65|| 02.2, —272 — 48|| 20.2 —304 — 78|| 383) —330|— 56 84.7 251, + 14|| 02.7 —209 + 39]| 20.7 - 319'+ 19] 38.8|—246| + 42) = —189 | +117] 136 +177) —216 +179 | ‘191 4201 leer 155-173 1804.1 — 96 +252 1822.1 —160 +266 ||1840.1 — 53 "+288 141] 86.5 —163 +194) 04.6 — 96 +203 226 —143 +319/ 40.6 — 21 +344 147|| 87.0 — 34, +334|| 05.0 + 20 +407]) 23.1/— 33 +423] 41.1|+ 80) +441 5 [i 153| 87.5|— 44 +301]) 055 + 4 +355|] 23.6/— 49 +369]) 41.6 + 62 | +389) 159) 88.0) 4-8 +331 || 06.0 + 46 +369) 24.0, — 15)-+375] 421) + 84 ++ 388 | 165, |+ 66-364 + 98| +388 24.5|-+ 35|-+390 24) ae 171 | +124 +397 | +151 | +407 | + 76| +397] St a 176 1789.4) {-172 +425 )1807.4 4195 | +423 1825.4) +110 +403 +169 | +384 | | 182) 89.8} 2-195 | +-437)) 079 | +233 oa 25.9 | +149 +408 1843.9 | +193 | +377 | | 188, 90.3 | -253| +470 084 +202| +-455|} 26.4/-+206/ +428 || 44.4 | +232 | +383 | 194] 90.8 +231 +406 08.8 +282) +398]) 26.9) +203 | -+377|} 449 +227 +4341 1200 91.3 4-204) +336 09.3 +257|+323|| 2714/1176 +298] 45.4 | +189) +261 | 200] 91.8 +215) +286 09.8 +234 | +-276|| 27.8 | +209 | +266) 45.9 | +226 | +252 +189 +157 + 11 + 16 +-176 | +133 | +172 +144 +161 = | J+ 8 | a 6\— 6 rl -+-138 223 = 3 ae 1 Saros IX Year| 4, Ie 1847.2 0 0 AT i=" 66) 83 48,2 | —127| — 162 48,7 | —280 | — 361 49. 2| —280 | —369 49.7 | —384 | — 433 —442! 470 1851.0) —474 -- 490 51.5|—486 — 495 52.0 | —576 | —542 52.5 | —480 | — 362 53.0|- 555 —386 53.5 | —550 | —365 —555 —352 1854.4|— 559 - 341 54.8|—546 —313 55.3| —540 —291 55.8| —352 — 53 56.3|—312)-+ 5 56.8|—214 4 99 — 53-257) 1858.2| ++ 35 +343 58.6!+ 88 +398 59.1 +186 +487 59.6 +174 +443 60.1) +194 +438 60.6 +239 +446 | 261 +415 1862.0, +273 +398 62.4 +208 +393 62.9 +290 +352! 63.4 +238 + 264 63.9 +270 +262 +177 +167 + 84|-+ 72 |+ 6 7 835 TABLE VI (Concluded). Saros X | Saros XI | Saros XIl Year| Al. eae vieainy Ae | Ate | Year| 7\. pul 19653/ 0| olliesa3/ 0] o| o| o 658 — 78; - 78|| 838 — 81|— 65 1901.8 381 = 71 66.2|—151|—151|| 84.3 —157,|—125]] 023|}—170| —137 667 324 —343|| 848 —337 —295|| 028 —358 —319 67.2| 345 —354|| 95.2 —360 —287|| 033 —383| —306 67.1476 — 422) 85.7 —509 —359] 03:8 - 544 —401 551 —455 —592 | —392|| —632 | — 456 11869 1 —592 - 473]|1887.1 — 637 —410||1905.1 - 680 - 486 | 69.6, —610, —474|| 87.6 —661 —410]] 05.6 —707 — 498 70.0’ 684, —511|| 88.1| 720|—440]] 06.1! —759' —531 | 70.5|- 570/—319|| 88.6| —589 —238|| 06.6 —620 —331 71.0| — 629| —237|| 89.0’ —631 | —252|| 07.1 | —650 | —342 71.5|—608 —313|| 895 —596 —224|| 07.6 —606|—313 600 --298 ] (579 —209 586, — 298 1872.4 —593 —286||1890.4 —565 —197 ~569 — 286 72.9 — 575 —263|| 90.9|—547 —181| —549|—271 73.4 —561 —243/| 91.4 —530 —166/1909.4 —529 | —256 738 —371/— 20|| 91.9, —348) + 29]) 09.9|-359|— 93 74.3 | —321| + 42|] 924} —301'+ 69|| 10.4|—316 — 73 74.8|—210. +135|| 928)—189 -+157]| 10.9| 206 + 11 16 +298 4 20 +322 | + 10|-++180 1876.2 + 90 +387||1894.2 +134 4412|19123 +128 +272 16.7 +165'+449!] 94.7 +222 +480! 12,7 1207' 4347 712 +268 |+535|| 952 +330 +565|| 132 +336 +431 T1.6 4 269'+496|| 95.7 +344 +535|/ 13.7/+360 +414 78.1 +291|+483]] 96.2) +368 +517|| 14.2 1385 +397 78.6 +344 +486] 96.6 +429 +520|| 14.7 1454 +411 14338 4431 4308 +440. +412 4347 1880.0 +335 / 401. 1898.0 +381 +410 1916.1 +388 4312 80.5 +343 +379) 98.5/-+374 +379)) 16.5 +372) +283 81.0 +323'+333|| 99.0, +350 +337|| 17.0 +348| +250 | 814 +255 +233|| 995/+270 4231]! 17.5' +259) +145 81.9 +286 +244//1900.0 +301 +258|| 180 +201 +197 +185/-+150)} 00.5 +193 4170]| 185 +182 +122 + 84, 56| = TT) -.83 -8 + 60 | 0|— 22 \= + 1 Ea 7c tee a Finally we give in Table VII the new reduction of the meridian observations by Prof. Bakuuyzex, which was referred to above. The column M—N tabular longitude of the moon over Nrwcoms’s “great fluctuation’. , contains the excess of the observed correction to the The systematic corrections mentioned in Part I have already been applied. For the years 1905 to 1912 two results are given: the upper one is derived from the observations of the limb, the lower from the crater Mésting A. The third column contains the means of the numbers of the second column and the results from the occultations, i.e. Newcoms’s minor fluctuations. The latter were however corrected by + 0".18 for reasons stated in Prof. Baknuyzen’s paper (these Proceedings, Jan. 1912). For the years 1905.5 to 1908.5 the mean given depends on the observations of the limb and the crater alone. From these means I have subtracted the sum of the corrections for the difference between the theories of Hansen and Brown, which were given in Part I of this paper. This sum was computed by a graphical process, of which I estimate the maximum error at about + 0'.05. The thus corrected mean is given in the fourth column. The second decimal, which has no real value, has been dropped. The last column gives the residuals remaining after subtracting Ross’s empirical formula, without its constant term — 0.18, viz.: + 2".9 sin 6°.316 (¢(— 1844.5) + 0.8 sin 15°.65 (t —1880) It will be seen that these residuals, although small, are as a rule somewhat larger than those found previously by Ross himself and by Bakuvyzen. The explanation of this is as follows. The residuals 4-Ross given by Bakuvyzen in 1911 (these Proceedings Jan. 1912, p. 691) showea a marked period of nine years, which entirely disappears by the application of the perturbational corrections (14) and (22). The term (43) is nearly identical to the term which was already applied by Ross, and consequently does not affect the residuals to any appreciable extent. The terms (20), (15), and (21) however, especially (21), produce a considerable increase of the residuals, No doubt it would be possible by a small adjustment of Ross’s formula considerably to improve the representation, but it is evident that a perfect agreement with the observations can never be reached by a formula containing only two terms. If a new empirical formula were to be derived it would, of course, be necessary first to correct the term of long period, and to apply the corresponding corrections to the theory. It seems opportune to defer such an inves- tigation until the moon’s longitude for the next few years will be 2 |i = Cc 7 |8hl83 = Par Sy = fs) 48.5 --1 .22/-+1' .66) +2 515 +1 37+ .18)+1. 52.5 +1 .20\+1 15 +1. 53.5 +1 .95\+1 42 +1. 55.5 41 57/-+1 .94| 42. 56.5 +1 .40\-+1 .75 +2 57.5 12.4842 39/12. 0 4 54.5 +2.29-+1.94 +2.0 —0.1 2 0 4 58.5 |-13.71/43.70| +3 .2 3 50.5 +3 83/13 96 + 60.5 +5.17-4+4.64 +3.6 +0.1 2 61.5 14.7844 14/13. 625 +5.11.-+4.60\ +4. 63.5 +4.21/43.70 +3. 64.5 42.8342 .96 +3. 65.5 +2.04+2.42, 43. 67.5 +0 .56-+0.93 +2 :: 68.5 |--0 .30|-+0.75) +1 .8 | 69.5 +0 39/41 .10' +1. 710.5 +0 .39|+0 .64 +1. 71.5 —1.26|—1 .18| —0. 725 1.21) -1 40 - ie 73.5 1.10 —1.65 —1. 74.5 |—2.27\— 214] =2. | 76.5 —1.89—1.90 —2. 71.5 |—0.87\—1 .28 —2. 785 +0.32.—0.44 —1. 79.5 —0.23|\—0.26 —1. 80.5 —0.33 0.76 —1. 81.5 | ~0.16—0.78 —1 825 —1.39\—1.30 —1. Praceedines Roval Acad. Amsterdam. 0 7 6 6 66.5 +1 .52'4+2.26 43.6 +1 2 8 8 1 7 0 3 0 75.5 —2 .40|—2 .25| —2.5| —1 il 4 il 4 5 837 TAGs Epis 1847.5 +0"08-+0"89 +13 +08 31-1 6 49.5 +0.26+40.28 +0.8 0.0 50.5 +0.31/+0.76 -+1.0, 0.0 1|-+0.9 2|-+0,8 l ——a s a2 SS qj 1883.5, —2"41 |—2"20 —1"9 +0"1 84.5 2.30 |—2.10 - 1.7|--0.2 gai) 2146 |—2 36 —2.2|—o:2 965| —2.60 |—2.60| —2.6|—0.4 Gio) 3 at |—2.76|. 2.8)—0.6 885| —3.64 |—3.41| —3.4|—1 2 aos? 50 |= 2.90. —2 6 (08 90\5)) : =2.70 |—2 95) —2.5| * 0.0 O15) 1 =—3.65'|—3. 28|—2 -8|—0.2 925| —3.78 |-3.09| 2.8! 0.2 93,5| —3.02 |—2.76] 2.9|/—0.3 945| —2.32|-2.56| 3.3|—0.7 95.5| —1.95 |—1.98| —3 .1| —0.6 96.5! —1.55 |—1.28'-2.5, 0.2 975 —0.89 |—1.34| - 2.3)—0.3 Geet 20084) 1 07p— eal2eO.2 99.5, —0.39 |—0.80, —0.7|-+10.6 1900.5 —0.12 |-+0.04'+0.7|-+11.5 015| —0.26 |—0.08! +09) 41.1 025! 0.33 +0 .42|-11 4)-11.1 035) —0.17'|+-0.32) +1 .2|-10.4 045° 0.59 -+0.94) +1.6|-+0.3 424) 97 | 05.5 ioe 411 ,73|-+2.3|-+0.6 19 42 065) 143 4 7g} -12.4|-+0.2| 49 39 015) 9 63 49 49\-13.1|40.5 +2 64 08.5 ee +2 .65,+3.3 -+0.6 Era at 095 | 342 43.16 +3.8|+0.9 15 32 | 10.5 ae +4.84 45.1) 42.0 45.57 11.5 Be, 45.30 -+5.1)+1.9 — — — 95 839 known, or at least until we know how lone the increase, which began a few years ago, will last. The accompanying diagram shows for the years 1847 to 1912 the excess of the observed longitude of the moon over Newcoms’s great fluctuation, i. e. the number contained in the fourth column of Table VIL. Ross’s curve is also given, (including the constant term — 0".18). The broken line is the smooth curve mentioned in Part | from which the values given in Table [I] were read off. The diagram also contains the purely periodic part A, and 4’, of the perturbation in longitude produced by the absorption of gravitation on the two hypotheses regarding the distribution of density within the earth, Chemistry. — “The equilibrium Tetragonal Tin ZS Rhombic Tin.” By Prof. Erxst Conen. (Communicated by Prof. vay Rompcran), (Communicated in the meeting of November 30, 1912). It has struck me, and from several quarters my attention has been called to it, that in a communication from Mess'* Smirs and pe Lervw') “On the system Tin” there occur a number of mistakes which require rectification. 1. The relation between the existence of a transitionpoint tetra- gonal tin <> rhombic tin at 200° and the method of preparation of the so-called corn-tin or grai-tin has been first pointed out in the paper which I have published in 1904 with Dr. E. Gonpscumipr *). From the communication of Mess's Sarrs and pe Leeuw the reader might conclude that they (or ScHaum) have first noticed this connection, 2.. In the paper which | published in 1904 with Dr. E. Gorp- SCHMIDT, a conclusion was drawn, from the experiments of Wxriain, Lewkosbrr, and TAMMANN*) as to the situation of the said transition point, which proved: to be erroneous, Dr. Dgecrns has pointed this out 4) and as in my opmion he was quite right. 1 have hastened to rectify my error in the section of ABEGe’s Handbuch der anorganischen Chemie [Vol. 8, (2) 532 (4909), special p. 552 | edited by myself. Kvidently, the recent literature on this subject has not been known to Mess's Smits and pe Leeuw, for they still base their communication on my paper that appeared five years previously. ') These Proc. XV, p. 676. *) Chem. Weekblad 1, 437 (1994), special p. 446. Zeitsehr. f. physikal. Chem, 50, 225 (1904), special p. 234. 3) Drud. Ann. 10, 647 (1903). 4) Dissertation, Delft 1908, p. 35. wer or * S40 3. Mess* Sairs and pe Lesew write:') “Why in reference to these experiments Conen and GoLpscumipt give 195° for the point of transi- tion in the “Chemisch Weekhlad”, and U7Oe in the “Zeitschrift fiir physikal. Chemie” is quite unaccountable.” The difficulty disappears immediately when one refers to the said paper*); it then appears that the following sentence has escaped Mess’s Sarrs and pr Lervw’s notice: “Wir setzen hier vorliufig 170°, doch beabsichtigen wir aut die genaue Bestimmung dieser Temperatur noch spater zuriickzu- kommen. In der Figur steht irrtiumlich 195°2 » 3) I will refer again to the transition: tetragonal tin 2 rhombic tin as soon as the investigations announced in my above paper shall be concluded. Mtrecht, November 1912. vAN “tT Hore-Laboratory. Physiology. — “On localised atrophy in the lateral geniculate body causing quadrantic hemianopsia of both the right lower Jields of vision”. By Prof. C. Winker. (Communicated in the meeting of November 30, 1912). In 1904 Bervor and Contre‘) observed blindness in the upper quadrants of both the left fields of vision by an invalid, who after death proved to be the bearer of a focus in the right hemisphere, through which the surroundings of the calearine fissure, from the occipital pole to the confluence with the parieto-occipital fissure were destroyed. This observation is one of the few, in which quadrantic-hemianop- sia responded to a focus, which chietly destroyed the cortex, although the optic radiation, as shown in the drawings of Brervor and CoLsirr, here too was not spared in the least; on the contrary it was des- troyed to an important extent (especially the medio-ventral part). Bervor and Contr pointed out, that already at that time in the literature there was sufficient ground to suggest, that foci in the dorso-lateral division of the strata sagittalia of the occipital lobe can ~ cause blindness in the lower quadrants of the crossed optic fields. On the other hand foci in the ventro-medial division of these strata 1) These Proc. XV, p. 677. *) Chem. Weekblad 1, 437 (1904), special p. 449. 5) Zeitschr. ftir physikal. Chemie 50, 225 (1904), special p. 236, note 2. +) CG. E. Beevor ano James Cottier, A contribution to the study of the cortical localisation. A case of quadrantic hemianopsia with pathological examination, Brain. 1904. XXVI p. 153. 841 sagittalia can cause quadrantic hemianopsia in’ the crossed upper fields of vision (Hexscumn, F6rsteR, WILBRAND ete.) | Von Monaxkow *) proceeds still more in the here taken direction. If the dorsal division of the occipital lobe (Upper Cuneus, O,—0,) incl. the dorsal part of the optic radiation is destroyed, then exclu- sively the dorsal layer of the lateral medullary capsule of the lateral geniculate body degenerates, and of this body the fronto-medial part. On the contrary after destruction of the ventral convolution of the occipital lobe (ventral lip of the calearine fissure, the Gyrus lingualis, the Gyrus oceipito-temporalis) it gives rise to a secondary degeneration of the ventral division of the geniculo-cortical radiation and degeneration of the ventro-lateral part (cauda) of the lateral geniculate body. The projection of the retina on the cortex could no longer be interpreted as simple as Henscuen had taught us. It was not limited only to the surroundings of the calearine fissure and had to be regarded from a different point of view. It had to be borne in mind that in each lateral geniculate body there was already a first field of projection for the two homonymous retinal halves. Another projection, secondary to this, took place through the geniculo-cortical radiation, which united this body with the cortex. But in a particular way. As long as the dorsal division of the radiation and the caput of this body did not show secondary change, the vision in the lower crossed quadrants of the fields of vision was intact. (Brenvor and ConLier). As lone as the ventral division of the radiation and the cauda of the body lacked these changes, the vision in the upper crossed quadrants of the fields of vision could remain intact. The radiation from this body spreads itself however to a greater area of the cortex than to the surroundings of the calcarine fissure only. Without doubt also the upper Cuneus, O,—Q,, i.e. the whole | S. E. Henscuen. Pathologie des Gehirms. Upsala 1890-94 and 1903 Cf. Sur les centres opliques cérébranx. Rev. gén. @Ophth. Paris 1894. Revue critique de la doctrine sur Je centre cortical de la vision Congr. int. de Médecine. Paris 1900. La projection de la rétine sur la partie corticale calearine. Sem. med. 1903. Witsranpt. Hemianopische Gesichtsfeldformen, Wiesbaden. 1890. Witpranpr und Sxnaer. Neurologie des Auges. 3 Bde. 1900/1904. Férsrer. Unorientirtheit, Rindenblindheit, Andeutung von Seelenblindheit. Arch. f. Opth. 1890 and Wirsranpr, Doppelversorgung der Macula Jutea und der Férsler’sche Fall von doppelseitiger lhomonymer Hemianopsie. Beitr. zur Augenheilkunde (Festschr. fiir FGrster.) 3) Von Monakow. Gehirnpathologie. 1905. S. 757. 342 of the oecipital pole has to be taken in account as von Monxakow desires, but most probably even more. The retinal projection on the cortex, secondary to that of the lateral veniculate body is therefore without doubt much more com- plicated than Hrnscnen had figured to himself, In 1909 1 myself‘) could prove that the geniculo-cortical radiation and the geniculate body reacted differently. if by dorsally situated foci the dorso-lateral division of the strata sagittalla was cut through, than they did, if ventrally situated foci destroyed the ventro-medial divi- sion of these strata in the occipital pole. In the first case, with in- complete quadrantic hemianopsia of the lower fields of vision, the dorsal division of the radiation and the medial part of the geniculate body was greatly, but not altogether degenerated. In the second case the degeneration took place in the ventral division of the radiation and the cauda of the body. Both degenerations were incomplete. At present [ can communicate two new cases, this time of complete partial atrophy of the lateral geniculate body ‘cauda or caput), of which one with exquisite quadrantic hemianopsia, and through which [ am obliged to extend even more than Monakow -did, the areae of the cortex for the iateral geniculate body. a Nephritis. Attack of unconsciousness on Dec. 9% 1910, followed by transi- tory sensory aphasia, alecia and permanent quandrantic hemianopsiain the lower right fields of vision, which in July 1911 its tested through the oph- thalmologist. In January 1912 second insult, which causes death. Autopsic: Old haemorrhagic cyst in the Gyrus temporalis II and the Gyrus angularis, sectioning completely the dorsal optic radiations. Fresh bleeding immediately next to this in the dorsal strata sagitialia. Miss C. P. S....., 37 years, is the eldest of 9 children, of which 5 are still living. The mother of this family died 50 years old of apoplexy, the father 75 years old of nephritis. Mente! or nervous diseases did not exist in the family. No abusus alcoholicus, no syphilis. Before this present illness she had nothing to complain of. On the 9t& of December 1910, she all at once fell unconscious, remained uncons- cious for 10 days. After coming to, she spoke with much difficulty, she could not find: the words, asked for “secur” (zuur) when she meant “butter milk”’ (karnemelk), ete. Sle soon regained a certain quantity of words, although she did not understand everything allright, but even now (July 1911) she names with difficulty the objects, which she recognises well. Especially proper names and nouns she often uses in the wrong way. Moreover after the atlack she could not read, partially, as she says, because she soon grew tired, partially because she did not understand much of what she read. ') G. Winker. De achterhoofdskwab en de half-blindheid. Psych. en Neurol, Bladen, 1910 Bl. 1—16. ; — = $43 Lastly after the attack she had been paralysed on the right side, but the lame- ness had passed off completely after three weeks. . Afterwards she often had been giddy, in March, on the 4th of June and on the 15! of June; but this always happened at the beginning of the menses, which were very irregular afler the attack, She noticed that after the attack she did not see very well to the right: it seemed as if while spots were there. The electric light on the market-place seemed to hang lower than formerly to her, and now and then it was, as if brown spiders hung in front of the right eye. Since the 9h of December she sees worse through the right eye. She also often complains of headache, vomilting at the same time. Moreover the urine contains 4° , albumen and many cylinders covered with epithelium of the kidneys. On account of these complaints she was brought into my ward of the Uniyer- sity Hospital (Binnen-Gasthuis). : The patient looks very ill, is a woman of middle height. Anaemic. Much arterio- sclerosis. Somewhat enlarged heart. The second tone over the valvula aortae is Joud. Pulse 90 120 Her attitude is active, she takes interest in her surroundings, is well orientated in time and in space, sleeps calmiy, eats sufficiently. She can walk and makes every movement. Nowhere on the trunce or extremities any trouble of motility or sensibility is to be found Except a lowered abdominal reflex at the right side, all the retlexes of the extremities are within normal limits. No sign of Babinski. There ave impedi- nents in speach. She understands simple commands without an yexception and follows them out. Her abundance of words is unlimited but she often misspeaks hersell. Yost of the objects are well named; they are always well recognised. Now and then she has to think long over them and after all uses the wrong word for them. She recognises every letter of the alphabet and pronounces them correctly. Also short words. She can read loud, but she reads paraphatically and the longer words are regularly badly reproduced. She does not comprehend the reading ov only insufficiently. To comprehend the reading she repeats it several times loudly and then as a rule she does net understand it, she forgets many things. Yet slie can do light work. She manages her little affair in pottery. The smell is not affected. The pupils are equally wide, the right one does not react on light as correctly as the left. She eannol converge and the reaction of the pupils by convergence is not to be seen. The vision of the right eye is 1/4; of the left eve 1/5. There is quadrantic hemianopsia m both the iower quandrants of the right fields of vision (s. figure). Di. Surv, the ophthalmologist writes about the fundus oculi: ‘There is no ‘trace of papillitis On the right the borders of the papiila are clearly limited, but there have been bleedings and there is still some oedema of the retina (retinitis albuminurica). On the left the panilla is also clearly limited, but here too are rests of haemorrhages. There is exquisite hemianopsia in the lower quadrants of the right fields of vision. That the macula vision is lost in the right anoptic sector is probably due to the bad vision of that eye. Tke eye-movements, especially by their turning to the rght and more so of the left eye, ave limited. The left eye deviates to the temporal side. It is impossi- ble to direct both eyes to one point. S44 The hearing has not been strongly disturbed, certainly not on one side only. A licking watch can be heard on both sides at a distance of 1 Meter. re 3 ra e = be dewcleywak reeomtrwrse lam ot de hentwagroms ram com mermaa! gt cabtiretd de wstmapte tim v4 de Metwagnrer mor baw: de oriigpride reer mud bende oppranmre ant whgren vane 15 ¢M strmal ‘ ‘ Field of vision on July 6" 1911. The diagnosis was made of nephritis with retinitis albuminurica and a focus in the left Gyrus angularis, cutting through the dorsal strata sagiltalia. July the 11™ she left the hospital. On the 10 of January 1912 she was brought in unconscious and died three days later. The account of the section shows: Hypertrophia cordis with nephritis interstitia- lis chronica and a focus in the left hemisphere, in the Gyrus temporalis II and the Gyrus angularis. The brown coloured focus spreads itself out in a straight direction along the distal third of the fissura t,, and follows this along its ascend- ing branch, The dorsal bounder of the Gyrus tempovals II and the ventral Gyrus angularis are sunken in (s. fig. 1 and 2). On the section the focus proves to be a cyst with orange coloured walls, sectioning the strata sagittalia, in the neigh- bovrlood of the retro-lenticular internal capsule and sectioning them completely in more distal slides (fig 6 and 7). More distally, it soon retracts from the strata. There is however a second fresh focus im the strata sagittalia, an haemorbagy of bright colour, consisting of scarcely altered blood corpuscles (See fig. 7 in y). In resuming the clinical data, it is not to be doubted that the second fresh focus caused the letal ending insult on the 10'° of January 1912 and that the first apoplectic cyst responds to the insult of the 9" of December 1910, which brought forth the quadrantic hemianopsia as well as the secondary degenerations. The importance of this observation lies in’ the first place in the fact, that a quadrantic hemianopsia of both the right lower fields of vision, noted with all possible precaution, is caused by a foens cutting “completely” through the dorso-lateral division of the strata sagittalia. Therefore too the secondary degene- rations are of great importance. They lasted for 13 months and 845 made alterations proximally in the lateral geniculate body and dis- tally in the occipital lobe. As the reproduction of the Wetgerr—Pat preparation!) (fig. 6 and 7) and photo 1 and 2 show, the two foci are thus situated that the older cuts the dorsal division of the strata sagittalia over the whole width. This feeus the important one of the two reaches close up to the lateral geniculate body (fig 6, pointed out by the first line through fig. | and 2) and stretches, cutting through the strata sagittalia, along the dorsal boundary of the cornu inferius and posterius (fig. 7, pointed out by the first following line through fig. 1 and 2), where the fresh focus too is found. It ends about 2 im, proximally from the distal end of the cornu posterius. Nowhere the ventro-medial division of the strata is affected directly by the focus. In fig. 6 and in fig. 7, this is intact. According to the destruction by the focus, totally different fibre-systems are affected and a massive degeneration towards the occipital pole takes place. The degenerated mass of fibres has been drawn on a more distally situated section (s_ fig. 8, line 8 through fig. 1 and 2) 1 e.m. distally from the focus }). In this is visible, that the tapetum-fibres are very.soon restored after their trans- seclion, showing nearly a normal tapetum and forceps posterior round the very wide ventricle. In a less degree this is also the case with the stratum sagittale internum. It has fewer fibres than normal, and between them are spread dege- nerated fields in different spots. But the loss of fibres in the stratum sagittale externum is enermous. No normal fibres ave to be found in it. This mighty black layer in Wetcerr—Pat preparations is here replaced by a while band, as well mn the dorsolateral as in the ventro-medial division. Smaller white stripes, coming from the degenerated band round the ventricle penetrate to far into the medullary cones of the conyolutions, surrounding the calcarine fissure, also to the praecuneus and to the gyrus angularis, The gyri occi- pito-temporalis and fusiformis haye suffered least. The massive degenerated ring round the ventricle is always found distally from the ventricle-end till the occipital pole. About '/, e.m. behind this end (s. fig. 9, line 9 from fig. 1 and 2) the distal point of the restored stratum sagittale inter- num is slill touched and lies as a black island within the white degenerated mass of the stratum sagiltale externum, while nearly all the medullary cones of the convolutions are degenerated and only fibrae areuatae seem to be left. The praecuneus has suffered least. In the section, which falls about 1 ¢m. from the occipital pole (s. fig. 10, last line througli fig. 1 and 2) it is likewise. rom the massive centre degenerated stripes penetrate in every convolution. All this proves that perception in the upper fields of vision is still possible, notwithstanding the stratum sagittale externum in the occipital pole is missing. If therefore the fibres, used for visual per- ception are to be looked for in that layer, as seems probably to me, ‘) Al these figures have been drawn with the greatest care; they are enlarged 2!/) times and reduced to 7/,9 of their size at the reproduction. Photos would have shown the same things, but drawings are more instructive as combinations of several sections are possible. B46 those which are spared here, do net at all belong to the occipital pole, but they must issue from far more proximal parts of the Gyrus occipito-temporalis. This conclusion is the more valuable, if we look at the influence which the focus has had on the veniculo-cortical radiation and on the lateral geniculate body. To make this clear | have drawn in fig. 4 a normal section of the surroundings of this body and in fig. 3 a cell-preparation!) of the same, fo make comparison possible. In these figures one sees the lateral geniculate body, which shows on frontal sections the form of a shoe (s. fig. 3) and in which can be distinguished a dorso- medial part: the caput, and a jatero-ventral one: the cauda. Within its own fibre-capsule covering the whole of it, (s. fig. 4) layers of fibres — laminae medullares — are alternately followed by layers of cells. The cells in the ventral layers are large, those in the dorsal ones much smaller, although, especially in the-capital part large cells penetrate in these dorsal layers. The size of the dorsal celis differs a great deal between themselves. Many of them are very small. In the normal fibre preparation the cauda contrasts but little against the caput, because the radiation of the optic tract has already begun in this proximal section. On the dorso-lateral side the lateral geniculate body is covered by the triangular area of Wernicke through which the geniculo-cortical radiation penetrates. In the dorsal part of this area (s. fig. 4) the fibre-direction is totally different from the transverse sectioned fibres of its ventral part. A rather thick layer of very thin subependymal fibres surrounds the area of WeRNICKE against the ependym of the ventricle. As soon as the geniculo-cortical radiation has freed itself from this area, it opens its way in elegant curvings through the fronto-occipital bundle and the retro-lenticular division of the internal capsule to the stratum sagittale externum. So it seems at least, although nobody will dare to make a decided conclusion about the origin of these fibres, crossing here in all directions. If we compare the above described area of the normal brain with an identical of our quadrantic hemianopsia, it then follows, (not to mention the degenerations in the fronto-occipital bundle, in the mere proximally situated parts of the corona radiata, etc.) that the dorsal layers of the geniculo-cortical radiation, and more in particular of the area of Wervicke, are totally degenerated. The ventral division of this fibre-area on the other hand, is not much injured, neither is the neighbouring dorsal and ventral part of the proper medullary capsule of the lateral geniculate body (s. fig. 6). In the cauda of the body we find intact laminae medullares. In the caput (in its dorso medial part) the proper medullary capsule is dorsally and ventrally gone as well as the striae medullares. All the cells of this caput are (s. fig. 5) vanished, the dorsal as well as the large ventral ones. The layers in which they were situated are to be seen as thick layers of glia. The whole body ') The cell-preparations of this body have been drawn with the camera of Zeiss ; they are enlarged 20 times and reduced to 7/,, of their size by the reproduction. Idem with the retro-lenticular area. 847 is reduced to almost half its normal size '), but in its cauda the small dorsal anl the large ventral cells (s. flg. 6) ave completely intact ; there too the striae medullares as well as the proper capsule are on the whole untouched. The conclusion is readily made: the possibility of sight in’ the upper quadrants is due to the conservation of the cells and fibres in the canda of the lateral geniculate body. their projection on the cortex being preserved by the ventral layer of the area of WERNIcKE and of the geniculo-cortical radiation. But where do these cells find their projection on the cortex ¥ Not in the occipital pole which in) my opinion was totally separated by the focus from the lateral geniculate body, as is shown by the complete degeneration of the stratum sagittale externum and all the medullary cones of the occipital convolutions (only fibrae arcuatae remained). Perhaps from the gyrus occipito-temporalis, its medulla being bui partly cut through by the focus (s. fig. 7). Distally from it (s. fig. 9) the medullary cones of the temporal circouvolutions were normal, those of the occipital lobe (s. fig. 9) were degenerated. Proximally from it this convolution with normal medullary cone contributed to the forming of ihe intact ventral division of the strata sagittalia. The answer to the question where the field of projection of the lateral cells of this body was situated, was brought to me by a very remarkable right hemisphere, given to me by Professor Bok. He had found it by accident in the corpse of a woman of whose ante- cedents nothing was known. Ie This right hemisphere carries the rests of a very old pathological process, which has reduced on the transition of the basal temporal and occipital lobe all the convolutions with their medullary cones to a thin membrane. When the pia mater was removed it was torn near the cuneus. (s. fig. 11). The occipital pole is intact. On the middle of the cuneus the defect begins with a sharp edge. The proximal end of the cuneus, of the gyrus lingualis and of the gyrus fusiformis, as well as the medial part of the gyrus occipito temporalis (as far as near to the f. rhinica) ave replaced by a thin membrane (s. fig. 11, 18, 14, 15 and 16). The series of sections show the following ?). The first remarkable alteration is drawn in fig. 16 (pointed out by the line 16 on fig. 11 and comparable with fig. 9 of the first observation). Thrice the distal end of the defect has been cut. Firstly in A in the depth of the fiss. calearina. There the cortex is gone and the 1) The enlargement is similar to that of the normal figure. (s. fig. 3). *) In order to give an easy survey the seciions are reversed and drawn as if they came from a left hemisphere, 545 medulla of the cireonvolution lies uncovered. The line of Gennari ends on. both sides sharply against the defect, is not atrophied, even mightier than usual and formed by thicker fibres; secendly in B, where ventrally from the f. pariéto-occipitalis the medulla of the cuneus hes uncovered and in C. where the defect begins in the gyrus fusiformis. : In the white matter opposite the fissura calearina a triangular degenerated field is to be seen. jt is situated for the greater part ventrally, but also a bit laterally round the sectioned distal end of the strata sagitlalia In figure 15 (pointed out by line 15 of fig. 11 and comparable to fig. 8 of the lirst observation, the defect is found distally from the confluence of the fiss. cal- carina and f. pariéto-occipitalis. All the basal convolutions are missing. Cuneus, lingualis, fusiformis, as well as the medial border of the ventricle are enurely gone. The medial medullury cone of the g. occipito-temporalis lies unco vered. The degenerated field is larger, lies partly in the ventral, partly already in the Jatero-dorsal division of the stratum sagiltale internum, but also in the stratum sagittale externum, especially there where the ventral division of it passes into the lateral. For the rest the stratum sagiltale externum is seen quite distinctly here (in fig. $ totally gone), a proof that this area consists of more fibres than _the geniculo-cortical radiation only (all gone in fig. 8). In fig. 14 (pointed out by line-14 of fig. 11 and comparable to fig. 7) the splenium corporis callosi is sectioned. Except a rest of the Cornu Ammonis no conyolutions are to be found ventrally from the cornu inferius. ‘The greater part of the gyrus occipito-temporalis is gone. The intact ventral strata sagittalia, as were found in fig. 7 are missing. The dege- nerated field (due to the defect) lies laterally and dorsally from the ventricle in both the strata sagittalia. A great part of the dorsal stratum sagittale exlernum is intact. In fig. 7 exactly this large layer was totally destroyed and therefore also the geniculo-cortical radia- tion to the occipital lobe. In fig. 13 (pointed out by the lines 13 of fig. 11, comparable to fig. 6) the retro-lenticular area is sectioned !). As if this section were the negative of that reproduced in fig. 6, one hardly finds here normal fibres in fields, which were there the best preserved In the ventral part of the geniculo-cortical radiation and of the area of WERNICKE all the fibres are gone. The ventral and lateral part of the proper capsule of the lateral geniculate body scarcely consist of normal fibres, the striae medullares in the cauda are gone, and the body is reduced to half its normal size. On the other hand the dorsal part of the geniculo cortical radiation and the area of Wervxickr, the dorso-medial proper capsule and the striae medullares in the caput of the geniculate body are only relatively changed '). The same reverse is shown in the cell-preparations of the body itself. Latero- ventral, in the cauda of the body not one cell is to be found. Thick layers of neuroglia, where once the cells were alternate with less thick Jayers of neuroglia (now representing the striae), bnt all celis, the dorsal as well as the ventral, have disappeared. On the other hand, the dorso-medial part, the caput of this ganglion contains well ranged cell-layers, small dorsal ones as 1) Here, as well as before, purposely | do not point out several other degene- rations. To make things still less complicated | do not even mention the influence upon the pulvinar of both these foci. 849 well as a number of ventra! large cells, This geniculate body is in every respect the negative of fig. 5. The result of this observation is clear enough: The important defect in the occipital lobe above mentioned, was not sufficient to produce an atrophy of the dorso-medial division of the lateral geniculate body. The cauda on the other hand lost all the cells and fibres. From our first) observation we learned that the eauda remained uninjured, when the focus (s. fig. 6 and fig. 7) totally destroyed the dorsal layer of the strata sagittalia. There (according to the spot of degeneration in our secend observation in fig. 14) the geniculo- cortical radiation from the ventral occipital convolutions is already situated dorsally from the cornu inferius. Moreover on the same sections in our first observation the ventral strata sagittalia are intact, and exactly these are completely missing in the second (s. fig. 13). New was to me the exquisite total loss of all the cells and fibres, either in the lateral, either in the medial half of the geniculate body, as is found in both these observations, although | possess many other partial atrophies of it after occi- pital-lesions. Generally spoken, lesions of the medio-ventral occipital convolu- tions cause atrophy of the latero-ventral part of the geniculate body, but in my cases it has never been a total one. As long as the gyrus occipito-temporalis proximally from the cal- carine fissure is uninjured, not all the laterally situated fibres dis- appear, but cells often remain in the ventral, occasionally also in the dorsal layers.’) Only after the knowledge of such extremes as above described, I have learned to appreciate the icomplete atrophies. Wedges turning their base to the dorsal part of the geniculate body, fall out. Their localisation differs by the place of ihe focus, although they never touch the dorso-medial part of it, as long as the focus only destroys the ventro-medial occipital convolutions. In this way e.g. must be considered the ventral occipital focus with atrophy in the canda of the lateral geniculate body, described by myself in 1910. At present I complete this observation referring to the same figures in order to describe that geniculate body exactly. Ill. A basal defect in the left hemisphere (s. fig. 17, also Psych. and Neurol. Bladen 1910, p. 16 more precisely the photos on plate LV and fig 12 on plate V) elimi- ') Nearly the same can be said of dorsally situated foci (mutatis mutandis) which section the optic radiation either close to the geniculate body or further olf, L shall refer to this later on. S50 nates the Os, 3 the gyrus lingualis and fusiformis to the confluence of the calearine fissure with the parieto-occipital fissure (s. Psych. Bladen Pl. TV, fig. 6). Also a part of the gyrus occipito-temporalis, lying more proximally, is injured. Through this Jesion the ventra! division of the geniculo-cortical radiation as well as that of the area of Weraicke is degenerated, but in less degree its most ventral Jayer (cf. Ps. Bladen, Pl. V, fig. 12). The geniculate body belonging to this is drawn in fig, 18. It is smaller than normal, but not as far reduced as in both the former observations. The proper capsule is not changed dorso-mediaily and the same can be said of its cells, dorsal as well as the ventral ones, belonging to the caput of the ganglion. . The cauda is for the greater part atrophied but not the most laterally situated division of it. There, ventral and dorsal cells are to be seen within an almost nor- mal capsule. Betsween caput and cauda, not or only little changed, one finds in the middle a part, where :ll is detroyed; the dorsal and ventral cells, the striae medullares, the proper fibres and the proper capsule. In this case an example is shown of an incomp/ete atrophy of the cauda of the lateral geniculate body, inecmplete because the focus did destroy the ventral occipital convolutions, but had not touched the gyrus occipito-temporalis far enough proximally. Therefore the most ventral layers of the geniculo-cortical radiation and the most lateral parts of the cauda remained free from degenerative atrophy. Reeapitulating I come to the following conclusions : 1. Vision in the upper quadrants of the field of vision is possible, notwithstanding the total loss of all the cells and fibres in the medial (caput) division of the crossed lateral geniculate body, as long as the cells and fibres of the canda (origin of the ventral geniculo-cortical radiation) are intact. 2. It is not sufficient that the ventral oecipital convolutions are destroyed to make all the cells disappear out of the lateral (cauda) division of the geniculate body. This only occurs ‘when more proxi- mally situated parts of the gyrus occipito-temporalis are destroyed. 3. The cortical areae belonging to the lateral geniculate body are not only limited to the cortex of the occipital lobe. Chemistry. — “On the occurrence of metals in the liver”. By Prof. L. van Irani and Dr. J. J. vax Eox. (Communicated by Prof. Eryrnoyen). (Gommunicated in the meeting of November 30, 1912). In the analysis of organs as to the presence of metallic poisons, we found in the liquid obtained after destruction of 170 grams of liver, kidney and heart, in addition to traces of arsenic and copper, as much zine as corresponds with 80 mgs. of zine oxide per kilo- gram of organs. As there was no reason to suppose that a poisoning 581 with a zine salt had been attempted the literature was consulted to see whether anything was known as to the occurrence of zinc in the human body. This investigation gave a positive result: Commu- nications have been made by Leenartier and Brentamy', and by Raounrr and Brerox*) from which it appears that the human liver may contain LO--76 mgs of zine per kilogram. The quantity might be dependent on the age, the state of health and the nature of the food of the persons from which the liver is derived. As the method of investigation did not appear to us correct in every respect and as the number of livers tested was comparatively small and as, moreover, the results could not be taken as applying to Holland without further evidence, we have investigated a number of human livers of Duteh origin. We have also extended the inves- ligation to the occurrence of arsenic and copper. As regards the presence of arsenic, the results of BLOEMENDAL *) are opposed to those of the French investigators. Whereas the latter assume the presence of normally-oecurring arsenic, according to Biommenpar the liver does not normally contain the same. As to the distribution of copper in the animal and vegetable orga- '). There was nism, investigations have been carried out by LEHMANN reason to suppose that the “charring process” employed by him had ‘aused the results to be too low ; moreover, figures of Duteh origin, are also wanting here. For the destruction of the organie matter we, with a few modi- fications, made use of the process devised by Kerrsoscu in the phar- maceutical Jaboratory at Leiden. This method has the great advantage that the organic substance is completely destroyed, the only reagents used being sulphuric and nitric acids which can be obtained absolutely free from arsenic. For this purpose, a current of hydrochloric acid is passed for some hours through sulphuric acid heated at 250 —270°, whereas nitric acid can be obtained free from arsenic by distillation. In a check- experiment where 25 cc. of sulphuric acid and 250 ce. of nitric acid had been used and of which 5-6 ec. of liquid were left after distil: lation, no arsenieal mirror could be obtained in a modified Marsh- apparatus. From previous investigations, it had already appeared °) that the limit of sensitiveness may be taken as O.OOOL mg. of arsenic, ') Compt. rend. de Ac. der Sc. 84, 1877, p. 687—690, *) [dem. 85, 1877, p. 40—42. 8) Arsenicum in het dierlyjk organisme. Dissertatie Leiden 1908, 4) Arch. [. Hygiene 24, 1895. *5) BLoeMENDAL |, ¢. 852 As to the exact modus operandi of the quantitative determinations, we refer to the more detailed communication to be published elsewhere. The results of our-investigations are collected in the annexed table, angmented with the data furnished to us as to the origin of the livers. HUMAN LET VE Rs: Number of mgs. se Course per kilo of liver, Age = Occupation Residence calculated as: of death : As Cu Zn Still-born — 26.173.9 Some hours — 30.052.2 5 weeks m. Leiden 0 8.055.7 3 months m 0 Acute enteritis 0 18.955.0 3\/, years m. Rijnsburg Diphtheria trace 10.667.8 5 «etm Leiden - 0.06 2.9 — Bie f. Servant * Morbus Basedowi 0 | 5.7/36.1 PA. we f. Woudrichem§ Miliarytuberculosis 0 11.279.6 ahem’ m. Greengrocer Den Haag 0 4.8 — 2a es f. Noordwijk Pneumonia 0 14.8/56.2 See m. Navvy Friesland Septicaemia 0.03 6.050.6 Soa Fi _ Hazerswoude Carcinoma 0 | 5.07.4 SOEs f. Housewife Leiden . trace 17.760.5 Sn ae m. Roadman Den Haag 2.63!) 3.8'54.3 SOF ee) m. Gardener Voorhout Kidney tuberculosis trace 3.2 79.4 ees m. Dealer Nieuwkoop Brain bleeding trace 6.15 44.5 40-50,, m. Goldsmith Leiden Tumour in stomach trace 10.062.3 Sta $e f. Vlaardingen Tumour in kidney 0 13.864.6 1 5 f. Leiden Apoplexy 0 | 7.4/55.9 7 m. Casuallabourer 5 Hypertroph. prostat. 0.1 10.626.7 ALD 5 f. i Apoplexy 0.015 9.053.0 10; f. None in Rib fracture 0.5 9.1/86.8 So a f. Heart disease _ trace 3.835.0 SOu m. Fs Arteriosclerosis 0 8.041.1 1) Before death, the deceased had used Pilulae Blaudii c. Acido arsenicos. as a medicine. 853 In the investigation of the liver of a new-born calf were found, per kilo, 31 mgs. of copper and 81.1 mgs. of zine. From the results obtained the following conclusions may be drawn : 1. Arsenic is not a normal constituent of the human liver. 2. Copper and zine appear to occur regularly in the human liver. 3. They are already deposited in the liver during the foetal stage and, as regards copper, even in a larger quantity than in the fol- lowing period. 4. Otherwise, there seems to exist no relation between the copper and zine content of the liver and the age, sex, occupation and place of residence. 5. The figures given by Lunmann for the copper content are com- paratively low. His maximum figure of 5 mg. per kilograin of liver is, as a rule, exceeded in Holland. Pharmaceutical Laboratory University, Leiden. Chemistry. — “Equilibria in ternary systems. IT’. By Prof. SCHREINEMAKDERS. (Communicated in the meeting of November 30, 1912). In the previous communication we have observed the changes when at a constant temperature there is a change of pressure, and from this deduced the saturation lines of a solid substance /’ under their own vapour pressure. We will now briefly consider the case that, at a constant pressure, there is a change in temperature. At a constant temperature a reduction of pressure causes an expansion of the gas region and a contraction of the liquidum region; under a constant pressure the same happens on elevating the temperature. A system that exhibits at a constant temperature a maximum vapour pressure (minimum), has at a constant pressure a minimum boiling point (maximum). At a constant temperature, the influence of the pressure on the situation and form of the saturation line of / is generally small unless at temperatures close to the melting point of F; ata constant pressure the influence of the temperature is usually much greater and the movement of the line, therefore, much more rapid. Yet, as a rule, the liquidum line will move more rapidly than the saturation line unless indeed the latter is on the point of disappearing. At a constant temperature, the saturation line of /’ may disappear on inereasing or reducing the pressure; this depends on whether, on melting, an increase or a decrease of the volume takes place. Under 36 Proceedings Royal Acad. Amsterdam. Vol. XV. 854 a constant pressure it disappears at an elevation of temperature only. From all this it follows that most of the diagrams described above which occur at a constant temperature on reduction of pressure will also. as a rule, form at a constant pressure by an elevation of temperature. At a constant temperature, the liquid and the gas of the three-phase equilibrium /'+ + G each proceed along an isothermic-polybaric curve which we have called the saturation line of / under its own vapour pressure and the vapour line appertaining thereto. Under a constant pressure, the liquid and the gas of the three- phase equilibrium /'+ ZL -+4+ G each proceed along a polythermic- isobaric curve. As these solutions saturated with # can, at a given pressure, be in equilibrium with vaponr and consequently boil at that temperature we will call these lines the boiling point line of the solutions saturated with / and the vapour line appertaining thereto. The saturation. line of / under its own pressure may be circum- phased [fig. 7 (I) and 11 (1))") as well as exphased [fig. 12 (I) and 13 (I)). The same applies to the boiling point line of the solutions saturated with /, with this difference, however, that fig. 13 (1) does not occur. The saturation line of # under its own vapour pressure exhibits a pressure maximum and minimum; the boiling point line of the solutions saturated with /’ a temperature maximum and minimum. These are, however, so situated that the arrows of the figs. 7 (I), 11 (1) and 12 (1) should point in the opposite direction. We will refer later to these curves in various respects. We can also unite these boiling point lines with their correlated vapour lines for different pressures, in a same plane. We then obtain a diagram analogous to fig. 14 (I) in which the arrows, however, must point in the opposite direction. If the pressure axis is taken perpendicularly to the plane of drawing, the spaceal representation gives two planes, namely the boiling point plane of the solutions saturated with / and the correlated vapour plane. We will now consider still in another way the saturation lines under their own pressure and the boiling point lines of the liquids saturated with a solid substance. We assume that a solid substance / of the composition «, 8, and 1) The number (1) placed behind a figure signifies that a figure from the first communication is intended. 855 1—a—f is in equilibrium with a liquid ZL of the composition x, 4 and 1—«—y and with a vapour ZL of the composition «,, 7, and 1—x,—y,. We call the volumes of these phases v, I’, and J’,, their entropies 4, H, and H,, their thermodynamic potentials $, 7 and 7.. As equilibrium conditions we find : (WA 07min — (1—a) Ser ie Dag =s5 aoe v, 0Z 02, 0Z ie | . dv Oa, - oy Oy, From this we find: [(w—a) r + (v—B)s] de + [(a—a)s + (y—B)t] dy = AdP—BdT . (2) [(e,--a)r, + (vy, - B)s,] de, + [(e,—a)s, + (y,—B)t,] dy, =A, dP - B,dT(3) oV, OF wel ONE rda + sdy =r,d, 4+- s,dy, + SS — 7.) aa oE) dT (A) 1 OH, OH on ance! te OVO} sdw + tdy = s,dx, + t,dy, + & — |dP— Oy, oy If we only want a relation between dv, dy, dP. and dT’ then from the previous equations we deduce: [(@—a)r + (y ~ 8)s] de + [(y—a)s + (y—p)t]dy = AdP—BdT. (6) [(v,—a)r + (y,—y)s]dx + [(e,—x)s + (y,—y)t]dy = CdP—DadT . (7) ‘In this: =e ys SS Eile .cadamemee iC) OV * A> V—v4 (a -a) ~+(2 >, B= H—y7 +- («— a) 2+ G9 r Be av i C=V,—V+ (eae tus 5 In order to obtain the saturation line of the solid substance /’ under its Own vapour pressure we call in (6) and (7) d7’=0; we then obtain : [(« — a)r + (y — 8B) s] dv i [(« — a)s + (y—8)t]dy= AdP (8) [(@, —2) r + (y,—y) 8] da + [(w,—2) s + (y,—y)t] dy = CdP (9) The correlated vapour line is obtained by interchanging in these relations the quantities relating to vapour and liquid. In order that the pressure in a point of the saturation line under its own pressure may become maximum or minimum d/ in (8) and (9) must be = 0. Hence OH =D —Ja'l = Sal L(c— w,) a -- (y -V,) 56* Sob [(c — a)r + (y —B)s] dx + [(w-- a) s + (y—A)t]dy=0. (10) [(, —a) rv + (y,—y) s] de + [(a,—2)s + (y,—y)t]dy=0. (11) This means that in. this point the saturation line under its own vapour pressure comes into contact with the isothermic-isobaric satu- ration line of / (10) and with the liquidum line of the heterogeneous region LG@ (11). We can satisfy (10) and (11) by: ee Ph ae ee i t—a v,— et This means that the three points representing the solid substance F, the liquid and the vapour are situated on a straight line. Hence, we find that on a saturation line of a solid substance /° under its own vapour pressure, the pressure is maximum or minimum when the three phases (/', 1, and (@) are represented by points of a straight line, or in other words, when between the three phases a phase reaction is possible. If we imagine before us the equation of the correlating vapour line we notice that when the pressure in a point of the saturation line under its own vapour pressure is at its Maximum or minimum, this must also be the case in the corresponding point of the correlated vapour line. It then also follows that the correlated vapour line, the vapour saturation line of / and the vapour line of the heterogeneous region LG meet in this point. The previous remarks apply, of course, also to the boiling point line of the solutions saturated with /’; in (6) and (7) dP must then be supposed = 0. Hence we conclude: When solid matter, liquid and gas have such a composition that between them a phase reaction is possible (the three figurating points then lie on a straight line) then, on the saturation line of the satu- rated solutions under its own pressure, the pressure is atits maximum or minimum; on the boiling point line this will be the case with ihe temperature. The same applies to the vapour lines appertaining to these curves. In each of these maximum or minimum points the three curves come into contact with each other. The properties found above have been already deduced by another way in the first communication. We will now investigate the saturation line of F under its own vapour pressure in the vicinity of point / First of all, it is evident that one line may pass throngh point F. For if in (8) we call ec=a and y= @ it follows that dP?= 0; (9) is converted into: 5 ovo ‘ [(w,—a) r + (y,—8) 5] da + [(7,—e) 5 + (y,—B) t] dy = 9. (13) dy We thus find a definite value for —,; at the same time it appears Fis from (13) that in point / the saturation line under its own vapour pressure and the liquidum line of the heterogeneous region LG ineet each other. It further appears from (13) that the tangent to the saturation line in / under its own vapour pressure and the line which connects the points / with the vapour phase are conjugated diagonals of the indicatrix in point /’. (The same applies, of course to the boiling point line of the saturated solutions). If accidentally, not only the liquid but also the vapour still has the composition /’, therefore, when not only «=e and y=8, but dy : ; also v, =a and y, = 8, then — becomes indefinite. Av In this case, however a maximum or minimum vapour pressure appears in the ternary system LG‘; we will refer to this later. From (6) and (7) we deduce for «=a and y=8: (BC-AD) aT, . ae ——— Ties ates Gems (y,—P) s} dev + \(a, -a@)s 4-(y,—A)hdy (14) This relation determines the change in temperature d7 around point /; this is always differing from 0 unless one chooses dv and dy in such a manner that the second member of (14) becomes nil. According to (13) this signifies that, starting from /’, one moves over the tangent to the liquidum line of the heterogeneous region LG, We now choose dv and dy along the line which connects the point) # with the vapour phase; for this we put: de = («,—a) dA and dy=(y,—A)dA. . « . .(15) We then obtain from (14) (BC—AD) dT = (V—v) (a, —a)? r + 2 (2,—a@) (y,— 8) s + (y,— 8)? t} dA (16) In this we have replaced A by the value V—v, which A obtains for m=—=e and y= Bp. Let us investigate the sign of: R= BO — AD = (H—2) 6 = (V—») D. Now, C is the increase in volume when a quantity of vapour is generated from an indefinitely large quantity of liquid; / is the increase in entropy in this reaction. Hence so long we are not too close to temperatures at which critical phenomena occur between liquid and vapour, C is as a rule large in regard to (J’7—v); H—y and D are quantities of about the same kind. If now J” <2, then K is for certain positive; if, however, V > v, then & is, as arule, 855 also still positive on account of the small value of V — v in regard to (. We will, therefore, in future always put A’ positive; should it become negative the necessary alterations can readily be introduced. We now distinguish two cases. a. V >v, dT and di have the same sign; bh. V 0 signifies that one is moving from point / towards the vapour phase. From this we conclude: The part of a saturation line passing through the point F of the substance / under its own vapour pressure and situated in the vicinity of / moves at an increase of temperature : a. if V > v, towards the vapour phase appertaining to point F. b. als << v, away from the vapour phase appertaining to point F’. , From (6) and (7) instead of (16) we can deduce also: K dP = (H—+) \(a,—a)? r + 2 (w, —a) (vy, —8) s + (y,— 8)? Beda. (17) From this we conclude: The part of a boiling point line of the saturated solutions of F situated in the vicinity of /’ moves, on increase of pressure, always more towards the vapour phase appertaining to point F. In order to get a better knowledge of the saturation line of F under its own vapour pressure which passes through the point F and of the boiling point line of the saturated solutions of F we will also introduce in our formulae terms with dv*, de dy, and dy?. In order to simplify the calculations a little we will assume provisionally that the vapour consists of one component only. We, therefore call in our previous formulae «,=0O and y, = 0. Our equilibrium conditions (1) then are converted into: Z ad es, 18 -= ae Sten a dose tba co, ofits) OZ 0Z A —— pS ee ee Os ay We now write for (18), 7 being kept constant : 1 or Os (wr + ys) dx +- (ws--yt) dy + = ¢ + 4 e +y =) dx? +- Os a 1 : Os Ot a ae + (+445. tu 5) ae ay +5 +05 bus) dy S.A OV OV | [OS I Sa a |) ate oe en, Set Bee een, MCRL ( : dw y Oy ) sie ee From (19) follows: a Ow Os 1 Os ) -f- a ay {- B ) ) da dy } 5 (« dy | | 5) dy +t. =(—¥ eee ae Si0t0s0,c (21) : 0a Oy Let us now deduce (21) from (20) after having substituted in (20) «=e and y=~8: we find: 1 9 a 1 r.da°* + sdx dy + —tdy* +... =AdP+.... . (22) in which the coefficients of dP.de and dP. dy are nil, whereas for the sake of brevity we write the coefficient of dP in (21) —(A+C). A and C then have herein the same values as in our former equations. Then, however, we assume v= a, / = 8,2, = 0, and ¥, = 0. From (22) follows dP of the order dz? and dy’, here from (21) at first approximation : (ar +- Bs) dw + (as + Bit)dy=0 . .. . . (23) In connection with (13) it appears from this that the liquidum line passing through point / and the saturation line of /” under its own vapour pressure come into contact with each other. If we eliminate dP from (21) and (22) we obtain: or Os (ar + Bs) dx + (as + pt) dy + 3 («< -+ Ba + r+ hr ) da? +- a % Os Ot Os Ot : +{a—+ B— +s + ds }dedy +}| a— + B— +644 at} dy? = 0 (24) Ow Oa Oy Oy in which 2=—. va + For the liquidum line passing through point /’ we find: Onis OC (ar + fs) dw + (as + Bt) dy + 3 («5, -+ B + + ") dx? r CsameeaOF Os Ot : : + («5 +B ~ +- :) dudy +- 4 (« a 4 Pay _ ) Cup == Uege Ys) For the sake of brevity we write (24) and (25) as follows: aX + bY + 4 (c+ ar)X* 4+ (d 4+ ds) XY +4 (e+ at) Y7=0 . (26) Deine ek aX Ye ver? — 0). (27 Equation (26) now relates to the saturation line, under its own pressure, passing through /’, (27) on the liquidum line of the hete- rogeneous region LG passing through F’. 860 Now the curvature of (27) is given by: 2abd—ae— be 9g (a? + 6%)": a Cal] that of curve (26) by: 2abd—a*e—b? e—a(a*t + b?r —2abs) = eee (a? +- Bb)" As (28) and (29) have the same denominator we, in order to compare the curvatures of both curves, only want the numerators. For the sake of brevity we wrile: ' ahd — we = = 0s.) ee and 2 abd — ate — bc — A(a*t + b'r —2ab)=—Q—AS - (81) If, by means of the known values of a and / we calculate the value of SS we find: S= (rt — s*) (a?r 2 aBs + Bt) hence, S is always positive. In order to find the direction of the curvature we calculate the coordinates 5 and y of the centre of the curved circle and ascertain at which side of the tangent this centre is situated. Therefore, we call the origin of the coordinate system the point which in this ease represents the vapour, 0. We now find the following: the liquidum line is curved in the point /” towards O when Q< QO; it is curved i F away trom Qif Q> 0. A consideration of ( shows that this can be positive as well! as negative; hence, the liquidum line can be curved in /’, away from O as well as towards 0. In order to find the saturation line under its own vapour pressure we will consider two cases. Owing to the small value of V—v, A will generally have a large positive value. In Fig. 1, wherein for the moment we disregard the curve d’/, the liquidum line is represented by dFe; the point © is supposed to be somewhere to the left of this curve dFe so that this is curved towards 0; Q is consequently negative. ; a aaa gz Qa 24 fre e’ ~ F ? Fig. 1. Fig. 2. 861 From this it follows at once that (— AS is also negative and that the saturation line under its own vapour pressure, namely the curve ab, must possess a curvature stronger than that of the liquidum line. It further follows from our previous considerations that they must intersect also the line O/' somewhere between O and F' so that they must exhibit a form as indicated schematically in fig. 1. The change in pressure along this curve is determined in F’ by (22), from which it follows, that, starting from /’, d P is positive whether towards a or towards $. The pressure in F is, therefore a mini- mum one and increases in the direction of the arrows. The solution with maximum vapour pressure is, of Course, in this case situated on the intersecting point of this curve with the line OF. We will now disregard the liquidum line d/e of fig. 1 and sup- pose it to be replaced by d’Fe’ which is curved in another direc- tion: Q is, therefore, positive so that Q—AS ean be positive as well as negative. If the liquidum line is not curved too strongly ()—AS will be negative and the saturation line under its own vapour pressure again exhibits a form like the curve a/b} of Fig. 1. If however the liquidum line is curved very strongly and 4 is not too large, then ( —2S can also become positive, so that both curves in F are bent in the same direction. This has been assumed in Fig. 2 wherein dFe represents the liquidum line and aF% the saturation line under its own vapour pressure. As in this case, Q is larger than (2 — AS it follows, as assumed in Fig. 2, that in the vicinity of F the curve dFe must be bent more strongly than the curve aF%b. V Fig. 5. another manner. 863 In order ‘to find the saturation line, under its own pressure, of a definite temperature 7’ we take the vapour- and the liquidum surface of this temperature 7’; we then obtain fig. 5 in which the pressure axis is taken perpendicularly to the component triangle ABC. The liquidum surface is represented by the drawn, the vapour plane by the dotted lines. If the vapour contains only two of the components the vapour side reduces itself to a curve situated in one of the border planes; if it contains but one single component it reduces itself to a single point. Like in our former considerations, we further assume, provisionally, that in the liquidum side occurs neither a maximum, minimum, nor a stationary point. We further take, at the assumed temperature 7’ and an arbitrary pressure P, a saturation line of the solid substance #. If we alter the pressure, 7’ remaining constant, this saturation line changes its form. If, to the component triangle, we place perpendicularly the P-axis and if on this we place the different saturation lines we get an isothermic-polybaric saturation surface of /. This surface may lie as in fig. 6 or 7; the component triangle has been omitted from both figures, the arrows point in the direction of increasing pressure. That both cases are possible is evident from what follows : >v. At the assumed temperature 7’ the substance /’ will melt at a definite pressure. Because the substance melts with increase of volume the saturation line of / will appear on elevation of A 2 es Vis P | > P Yo Fig. 6. Fig. 7. pressure, so that we obtain a surface like in fig. 6, namely with the convex side directed downwards. Vv. We now suppose the saturation line of fig. 6 to be introduced also in fig. 5; to begin with we assime the point / of the saturation surface to be far below the liquidum side. All points of the section of both surfaces now represent liquids saturated with solid F and in equilibrium with vapour, consequently the system F+ L-+G. As the points of tne section all appertain to the same temperature, this section is therefore the previously recorded satu- ration line of the solid substance /’ under its own vapour pressure. If we project this section on the component triangle we obtain a curve surrounding point /’ like the drawn curves in fig. 7 (1) or fig. 11 (1). It is also evident that the pressure must increase in the. direction of the arrows of these figures. We now again imagine in fig. 5 the section of liquidum surface and saturation surface ; with each point of this section corresponds a definite point of the vapour surface. Qn the vapour surface is situated, therefore. a curve indicating the vapours in equilibrium with the solutions saturated with /’; this curve is the vapour line appertaining to the saturaton line under its own vapour pressure. If this curve is prciected on the component triangle we obtain a curve surrounding point / such as the dotted curve of figs. 7 (I) or 11 (I). If the temperature is increased the liquidum, gas, and saturation surfaces of /’ move upwards; as the latter surface, however, moves more rapidly than the first, there occurs a temperature where £ falls on the liquidum surface so that the solid substance / is in equilibrium with a liquid of the same composition and with a vapour. Like van peR Waats in the binary systems, we may call this tem- perature the minimum melting point of 7’. As the plane of contact /néreduced in F at the saturation surfaée is horizontal, the saturation surface must intersect the liquidum surface. We notice that this section proceeds from /° towards the direc- tion of the vapour surface. If we project this curve on the com- ponent triangle we obtain the curve a/%® of figs. 1 or 2. The curves de or de’ of these figures are the sections of the plane of contact in F at the saturation surface with the liquidum side; they are consequently the liquidum lines of the heterogeneous region LG at this minimum melting point of the substance 865 From a consideration of fig. 5 it immediately follows that the vapour lines appertaining to the curves a/% of figs. 5 and 2 are exphased and may, or may not, intersect the saturation line. If we still increase the temperature a little. the point /’ gets above the liquidum surface and the saturation line of / under its own pressure becomes exphased. We then obtain fig. 12 (1) in whieh the vapour line may. or may not, intersect the saturation curve under its Own Vapour pressure. If we increase the temperature still a little more, the saturation and the liquidum surface come into contact in a point; it is evident that on the saturation surface of /’ this point does not coincide with fF, but is shifted towards the gas surface. We now have the highest temperature at which the system “+ 1 + @ exists. In fig. 12 (1) hoth lines contract to a point; both points lie with /# on a straight line. V ..-.. & liquid’ of 67k -— solid #; aa,F ........ vapour a,+ liquid a+ solid 7; TOMB a Sipe Seiad OH oe Cis. or oe pA LOR are My GT aire we sl PET Mec Fi iy. SP OK le re sett hoe ee a ee ok On further reduction of pressure, the liquidum line apg and hs) which surrounds the liquidum region contracts still more so that on the one side the points a and g coincide at a pressure P, this ‘will be likewise the case with their conjugated points a, and g, ; the two triangles Fi,a and Fy,g then coincide along a straight line and the pressure / for the system #+ 1+ G is a minimnm pressure. The same applies when the two triangles /%0' and Fhh, coincide. After the four three-phase triangles have disappeared from fig. 2 owing to reduction of pressure, the vapour saturation line of composed in Fig. 2 of the two branches a6, and g,h, forms a closed curve which surrounds the heterogeneous region LG as well 7 57 Proceedings Royal Acad. Amsterdam. Vol. XY. STO as the saturation line of /. Hence, at these pressures only unsatu- rated vapours and those saturated with solid / can oceur in the stable condition. From a consideration of the equilibrium /’+ L-+ G it appears that the saturation curve of / under its own vapour pressure is a eurve surrounding the point /’, on which however, now occur two points with a maximum vapour pressure. The same applies to the correlated yapour curve surrounding the former curve. Each maxi- mum or minimum point of the one curve lies with the correlated maximum or minimum point of the other curve and the point F on a straight line. We have assumed above that when the liquidum and the hetero- geneous region disappear in a point within the saturation line of F two three-phase triangles, as in fig. 2. appear. We may, however, also imagine that the liquidum line of the heterogeneous region L@ in fig. 1 contracts in such a manner that it intersects the saturation line of F in two points only; only two three-phase triangles are then formed. [he saturation line of / under its own vapour pressure and the correlated liquidum line are then both ecireumphased and exhibit one point with a maximum and one with a minimum vapour pressure. When the liquidum region disappears at one temperature within and at another temperature without the saturation point of /, it will, at a definite temperature disappear in a point of the saturation line. Among all solutions saturated at this temperature with /’ and in equilibrium with vapour there will be one which is in equilibrium with a vapour of the same composition. The saturation line of 7# under its Own vapour pressure and the correlating vapour line then meet in the point with the minimum vapour pressure. We have noticed above that there exist saturation lines of /’ under their own vapour pressure which exhibit two vapour pressure maxima and two minima. Such curves must. of course, be capable of con- version into curves with one maximum and one minimum; this takes place by the coincidence ofa maximum and a minimum of the first curve causing the part of the curve situated between these two. points to disappear. The two other parts then again merge in each other. We have deduced above the saturation line under its own vapour pressure with two maxima and two minima in the assumption that the liquidum region disappears somewhere within the saturation line of /. We may also however, imagine similar cases if this disappear- ance takes place in a point outside the saturation line of /. We have only to suppose that in fig. 1 the liquidum line of the hetero- S71 geneous region LG contracts so as to disappear in a point outside the saturation line of /. After the contact of the liquidum and saturation lines two points of intersection appear; if now no further contaet takes place, these points finally coimeide in a point of contact so that the saturation line under its Own vapour pressure exhibits but one maximum or minimum. If, however, after the appearance of the first two points of inter- section a second point of contact occurs we obtain four points of intersection of which, at first two, and afterwards the other two coincide in a point of contact, so that in all four of these points are formed. The saturation line under its own vapour pressure then exhibits two maxima and two minima. By way of a transition case it might happen that the second point of contact, which appears after the formation of the two tirst points of intersection, coincided with one of these points so that a point of the second order was formed. On further change of pressure two points of intersection then again occurred, which finally coincided in a new point of contact. The saturation line under its own vapour pressure then represents the transition form between that with one maximum and one minimum and that with two maxima and two minima. After what has been stated it will surely be unnecessary to con- sider the case where, in the system liquid-vaponr, a vapour pressure maximum or a stationary point oceurs; we will refer to this and to a few peculiar boiling point lines perhaps later. We will now just consider what happens if we take the compound I? only and apply heat. If we imagine /’ placed in a vacuum at a low temperature a portion of this compound /’ will evaporate and there is formed the equilibrium: solid /’+ vapour /’. On increase of temperature the vapour pressure of / is raised; ina P,7-diagram we thus obtain a curve such as aA of fig. 8, namely the sublima- tion curve of the substance /’. At a detinite temperature 7% and a pressure ; an infinitely smal] quantity of liquid is now formed; this, of course, has uot the composition / but another composition K. As only an infinitely small amount of liquid has formed as yet, the vapour still has the composition 7. The point A’ is, therefore the terminal point of the sublimation line, called by van per Waals in his binary systems the upper sublimation point of the compound. If we increase the temperature, say, to 7”, more of the compound melts; there is then formed the three-phase equilibrium /-++ + @ in which neither Z nor G have the composition /. Z and G have a7* S72 4 such a composition that we ean form from both the solid substance /’; the three figurating points are, therefore, situated on a straight line. Besides. and G are always present in quantities equivalent to the reaction / + G—/F; L and ( are. consequently. present in such amounts that from both we can form F without any Z or G remaining. As a rule, the three-phase equilibrium /’+ 1+ G@ can exist, at the temperature 7” with a whole series of pressures. namely, with the pressures occurring on the saturation line under its own vapour pressure of the solid substance / at the temperature 7”. As in this particular case a phase reaction is possible between the three phases or in other words, as the points /, 4, and G lie ona straight line, the three-phase equilibrium exists here only at a definite pressure, namely, the maximum or minimum pressure which oceur at the temperature 7” on the saturation line of /’ under its own vapour pressure. In this particular case it is,the minimum pressure, as will appear later. At a further increase of temperature more of the substance / keeps on melting and “Z and @ alter their composition; we will regulate the volume in such a manner that there is but an infinitely small amount of vapour which, of course, does not affect the pres- sure. If we represent the pressure and temperature graphically, a curve is formed such as curve KF of fig. 3. Finally we now arrive at a temperature and correlated pressure at which all solid /” has fused; as particularly at the last moments, we have taken care that but infinitely litthe vapour is present, the liquid now has the composition /’; the vapour has quite a different composition D. On Te aie Snel. aie 873 As the solid substance /’ and the liquid now have the same com- position we have attained the melting point of /”. Ifnow we regulate the temperature and pressure in such a manner that the solid matter F’ remains in equilibrium with its melt the system proceeds along the melting point line /d of fig. 3. Here, it has been assumed that the volume v of the solid substance is much smaller than the volume V of its melt. If this isnot the case, the melting point line 7 starts from F towards lower temperatures. In binary systems, Van ber Waats has called the initial point /’ of the melting point line, the minimum melting point of the solid substance /’. Hence, we have forced the substance /’ to proceed along : @. the sublimation line aW 6. the three phase line A/’ c. the melting point line Fd we can, however, consider still other lines. In the upper sublimation point A’ we have solid /’+ vapour + infinitely little liquid. We now increase the volume until the solid substance /” has been converted totally into vapour, or else we remove the solid substance. We then have the system: vapour /’+- infinitely little liquid or we may also say, a vapour / which can be in equilibrium with a liquid. If the temperature is increased the vapour # will continue to exist; it is then, however, no longer in equilibrium with liquid. In order, to again form an infinitely small quantity of liquid, or in other words to again bring the vapour in equilibrium with a liquid, it will generally be necessary to increase the pressure. Hence, at an increase in temperature, one can always regulate the pressure in such a manner that a vapour of the composition / is in equilibrium with an infinitely small quantity of liquid which, of course, changes its composition with the temperature. If pressure and temperature are represented in fig. 2, the curve Kf of this figure is formed. In the minimum melting point / we can start from the system solid /’-+ liquid #-+ infinitely littke vapour after we have first eliminated the solid substance /’ thereof. If now, we elevate the temperature, the pressure may be always regulated in such a manner that this liquid of the composition # is in equilibrium with an infinitely small quantity of vapour which, of course, changes its composition with the temperature. The corresponding P7-line is represented in fig. 38 by the curve Fe. As, on the line ef’, a liquid of the composition /’ is in equilibrium with vapour we will call this line the evaporation line of F. On S74 the line Af a vapour of the composition # is in equilibrium with liquid ; we will, therefore, call Af the condensation line of F. The metastable prolongations of Fe and A/ are represented in the figure by Fe’ and A/’. Hence, in point / three curves coincide namely, the melting point line (Fd), the evaporation line (/’e) and the three- phase line (FA); in point A three curves also meet, namely, the sublimation line (aA), the three-phase line (A/’) and the conden- sation line (K/). The metastable prolongations of the sublimation line aA and the melting point line d/’ intersect in a point S; at this temperature Ts and pressure Ps now occurs, in a metastable condition, the equilibrium : solid #’+ liquid # + vapour /. If now the substance F behaved as a simple substance which can only yield a liquid and a vapour of the same composition, S would represent the triple point of the substance /’; owing to the occurrence of the three-phase equilibrium F-+ L-+ G this triple point is, however, metastable here. Through this metastable triple point .S now also passes, besides the sublimation and the melting point curve of 7, the evaporation line g’Sy of F. This represents the equilibrium liquid /—- vapour F occurring in the metastable condition; on this curve g‘Sg liquid and vapour, therefore, have the composition / and not, as on /’ Kf, only the vapour, and as in e’Fe only the liquid. We will call the curve g’Sg the theoretical evaporation line. In order to find what conditions of the substance F are repre esented by the points of the different regions we take this substance in a condition answering to a point of the sublimation line aA. We then have solid #’+ vapour /. From a consideration of what takes place on supply or al withdraw of heat, or on increase or decrease in volume we now deduce: to the right and below the line aX occurs the vapour region, to the left and above the line a is found the solid region of F. 7 Acting in a similar manner with the points of the other lines, we find that four regions may be distinguished, namely, a gas region indicated in the figure by an encircled G, a solid region indicated by an encircled F, a liquidum region indicated by an encircled L and a liquidum-gas region indicated by an encircled + G. Hence if the substance / is brought to a temperature and under a pressure corresponding with a point of the solid vegion, the substance /’ is solid; if brought to a temperature and under a pressure corresponding with a point of the liquidum-gas region, /” is resolved into liquid and gas ete. We will also consider fig. 3 just once more in connection with the 875 previously mentioned saturation lines of / and the liquidum and vapour lines of the heterogeneous region 4 -+ G. For this, we first choose a temperature 7’, corresponding with point A of fig. 8 and a very high pressure so that we find ourselves in the solid region. On the pressure being reduced we arrive from the solid region into the liquidum region, then into the liquidum-gas region and finally into the gas region. If we choose a temperature T';, corre- sponding with point 2 of fig. 8, the substance /” on reduction of pressure first traverses the solid region, then the liquidum-gas region and finally the gas region. Reduction of pressure at the temperature T. transfers the substance from the solid region to the gas region. We now start from the temperature 74 and a very high pressure: the corresponding diagram then consists of fig 1 (1) wherein, nowe- ver, is still wanted the gas region and the heterogeneous region L+ @ of this figure. It is now evident that the compound / can only exist in the solid condition; it can, of course, be in equilibrium with a liquid, but this liquid cannot form unless to the compound is added a little of at least one of its components. The pure com- pound /° which we have still under consideration can only occur in the solid condition. On reduction of pressure, the saturation line of / contracts so as to coincide finally with point /” of fig. 1 (1). At this pressure oceurs, therefore, the equilibrium solid /’+ liquid /, so that in fig. 38 we proceed from the solid region to a point of the melting point line Id. The heterogeneous region 1+ G of fig. 1 (1) miay, or may not, have appeared at this pressure; in any case, however, it has not yet extended to the point /” of this figure. As, on further reduction of pressure, the saturation line of / disappears from fig. 1 (1) (in order to keep in with fig. 8 we take V>v) F is now situated in the liquidum region of fig. 1 (4). Hence, in fig. 3 we must also arrive in the liquidum region. As on further reduction of pressure the gas region of fig. 1 (1) is further extended, the liquidum line ed of the heterogeneous region passes, at a definite pressure, through the point #. This means that the liquid /” can be in equilibrium with vapour. This is in agreement with tig. 3; therein we proceed from the liquidum region to the line Fe. ; On further reduction of pressure, the heterogeneous region 1 + G shifts over the point /; the compound F is now resolved into a liquid of the liquidum line and into a vapour of the vapour line which on further decrease in pressure always change their compo- sition. Hence the compound F traverses the liquidum gas region 876 which is in agreement with fig. 3. This will continue until on further reduction of pressure. the vapour line of the heterogeneous region passes through point £. This means that a vapour F can be in equilibrium with a liquid; this again is in harmony with fig. 3; therein we proceed from the liquidum gas region to the curve Af. On still further reduction of pressure the gas region of fig. 1 (1) moves over the point / so that, in harmony with fig. 3 the com- pound # can occur only im the state of vapour. Between the liquidum line de and the vapour line d,e, of the heterogeneous region + G@ of fig. 1 (1) is situated the projection of the line of intersection of the liquidum and the vapour side of the ¢surface. This line indicates a series of solutions which each can be in equilibrium with a vapour of the same composition; all these liquids and vapours, however, are metastable and break up into a liquid of the liquidum line and a vapour of the vapour line of the heterogeneous region + G. We will call this lne of intersection the theoretical liquidum-vapour line. As this theoretical line passes, at a definite pressure, through the point #, there exists at this pressure the equilibrium: liquid /° + vapour # in a metastable condition; hence, we have a point of the theoretical evaporation line Sy of fig. 8 and it is, moreover, evident that this must be situated in the liquidum-gas region of fig. 3. We now choose a temperature 7’; lower than 74; this will ‘ause the saturation line of /’ to disappear at 7's at a lower pres- sure than at 7'4. We now choose 7’, so low that, on lowering the pressure the saturation line of /’ has not yet disappeared when the liquidum line of the heterogeneous region passes through the point IF: Tp is, therefore lower than the minimum melting point of /. If we now choose a very high pressure, the corresponding diagram will then consist of fig. 1 (1) wherein, however, the gas region and the heterogeneous region 4 + G are still wanting. On reducing the pressure fig. 1 (1) is formed first, then fig. 2 (I) and further fig. 3 (I); at these pressures the compound /” still occurs in the solid condition so that it finds itself in the solid region of fig. 3. At a definite pressure the metastable part of the liquidum line dae situated between the points @ and 4 in fig. 3(1) will pass through the point F’; this means that a liquid of the composition /” may be in equili- brium with vapour; this is only possible in the metastable condition for in the stable condition F only occurs as a solid. Hence, in fig. 3 we find ourselves in the solid region on a point of the metastable curve é'F. On further reduction of pressure there is now formed from fig. 877 3/1) the figure 4 (1) or 8 (1); we first choose 7’; in such a manner that on lowering the pressure, the vapour saturation line has not yet disappeared when the vapour line of the heterogeneous region passes through the point /. So as to be in harmony with fig. 3, 7’ has been chosen lower than the minimum melting point and higher than the upper sublimation point of the compound /’”. In conse- quence of this, fig. 3 (1) is converted into fig. 4 (1) on reduction of pressure, and afterwards at a definite pressure into fig. 5 (I). At this pressure the as yet solid compound #' melts with formation of the vapour m, and the liquid m,; hence in tig. 3 we proceed from the solid region to a point of the three-phase line A /’. On further decrease of pressure /’ is resolved into liquid and gas; in fig. 38 we, therefore, proceed from the line A /’ to the liquidum gas region. On further reduction of pressure the vapour curve e, ¢, of fig. 5 (I) passes, at a definite pressure through the point /’; this means that a vapour of the composition /’ can be in equilibrium with a liquid. The compound /’ then passes, in fig. 3, from the liquidum-gas region to the line A. On further decrease of pressure is now formed fig. 6 (1), the point / lies now in the vapour region so that the compound F can only still occur in the state of vapour. In fig. 3 we, therefore, proceed from the line A/ to the gas region. Between fig. 3(1), in which we assume the metastable part ab of the liquidum line dade to pass through the point /’, and fig. 5 (1), in which we assume the vapour line d, ¢, to pass through F. there must, of course, lie another one where the theoretical liquidum vapour line passes through point /. This means that, in fig. 3, we must find, at the temperature 7’g, between the curves e'/’ and A/ a point of the curve g'Sy. If this theoretical vapour curve already passes through the point /” before fig. 5 (1) is formed through reduc- tion of pressure, the point of intersection of g'Sg with the vertical line then lies in the point 6 of fig. 8 above the three-phase line ; if, however, this theoretical line passes through the point 4’ when, through reduction of pressure, fig. 5 has formed, the above point of intersection in fig. 3 lies below the three-phase line. These results, as follows from fig. 3, are in harmony with this figure. The situation of the metastable sublimation line AVS and of the meiastable melting point line #S may be found in this manner. Here, we will just determine the situation of the triple point S. In this point there exists an equilibrium between solid /#’+ liquid F-+ vapour F. The equilibrium liquid /’+ vapour /#’ requires that the theore- 878 tical liquidum vapour line passes through point /; if this equilibrium oceurs in the stable condition, the liquidum and the vapour line of the heterogeneous region must then also pass through the point /; this is the case when, incidentally, a ternary maximum, minimum or stationary point occurs in /*. If, however, this equilibrium appears in the metastable condition, the liquidum and vapour line of the hetero- geneous region do not pass through / which is then situated between these two. As, from the equilibria solid #’+ liquid /-+4 vapour F and solid /#’+ vapour F, it follows that the saturation and the vapour saturation line of / coincide to one point in /’, the meta- stable triple point S must be situated in the liquidum gas region of fig. 3. We now choose a temperature 7 (tig. 3) lower than the upper sublimation point 7), of fig. 3; the vapour saturation line of / has, therefore, not yet disappeared when the vapour line of the hetero- geneous L-+ G passes through the point /. Starting from high pressures and then reducing the same there is first formed fig. 4 (1) wherein, at first, the gas and heterogeneous regions are still wanting, then figs. 1(1), 2(1) and 3(1) which is now converted into 8 (I); then are formed figs. 9(1) and 10(I) and finally a figure which we will call 10a and which is formed from fig. 10 when the vapour saturation line of / coincides with the point F. During this lowering of the pressure, as shown from the figures, the substance /’ only occurs solid in the stable condition; the sub- stance /’, therefore, traverses the solid region of fig. 3. Not until the pressure has been so reduced as to form fig. 10a can solid F be in equilibrium: with vapour /°. We then proceed in fig. 3 from the solid region to a point of the sublimation Jine a A. On continued reduction of pressure the vapour saturation line of [’ disappears from fig. 10a, so that /’ lies within the gas region; hence, / can occur only in the form of vapour, so that in fig. 3 we proceed to the vapour region. In the conversion of fig. 3 (1) into fig. 8 (1) the substance / passes through different metastable conditions. On reduction of pressure the metastable piece a 4 of the liquidum line passes through the point / first, then the theoretical liquidum-vapour line and then the meta- stable piece a, 6, of the vapour line of the heterogeneous region L+G. This also agrees with fig. 3; on lowering the pressure at the temperature Ze we meet in the solid region, successively, the metastableZcurves e’ J’, g’ S, and /” KX. When in a system liquid-gas a liquid and a vapour of the same composition are in equilibrium, we will call this a singular point of a “th ihe system L-+ G. The appearance of such a point has no influ- ence on fig. 8 unless this accidentally coincides with the point /’ of one of the previously examined figures. Such a singular point, that at each 7 occurs only at a definite P, proceeds in the component triangle along a curve which may happen to pass through /. If this should take place, and if this point is a statonary point, then, in the case ofthe correlated P and 7, the vapour and liquidum line of the heterogeneous region L-+ @ and the theoretical liquidum vapour line pass through /'; if this point is a maximum or mini- mum one these three lines coincide in /. From this it follows that in fig. 3 the singular point must always lie simultaneously on the lines y’ Sy, e’ Pe and /’ Wf. The coincidence of a singular point with the point /’ therefore causes the above three curves of fig. 2 to have one point in common; from other considerations it follows that they get into contact with each other. This point of contact may le in the solid as well as in the liqui- dum-gas region; in the first case, the system liquid / ++ vapour is metastable, in the second case ‘it is stable. This point of contact may — but this is not very likely — also coincide with point S of fig. 8. The system solid /” + liquid # + vapour /’ would then occur in the stable condition and the subli- mation and melting point curves would then continue up to the point JS. (To be continued). Mathematics. — “On complexes which can be built up of linear congruences”. By Prof. JAN DE Veins. (Communicated in the Meeting of December 28, 1912). -§ 1. We will suppose that the generatrices a of a scroll of order m are in (1,1)-correspondence with the generatrices 4 of a scroll of order n, and consider the complex containing all the linear congru- ences admitting any pair of corresponding generatrices a, as direc- tor lines. The two scrolls admit the same genus p; as the edges of a complex cone are in (1,1)-correspondence with the generatrices a,6 on which they rest, p is also the genus of all the complex cones‘). The rays of a pencil are arranged in a correspondence (m, n) by the generatrices of the scrolls (a), (6); so in general the complex is of order m + 7. 1) For m = n = | (two pencils) we get the éedrahedral complex. In a paper “On a group of complexes with rational cones of the complex” (Proceedings of Amsterdam, Vol. VII, p. 577) we already considered the case of a pencil in (1,1)-correspondence with the tangents of a rational plane curve. 580 The double edges of a complex cone are rays resting on two pairs a,6; they belong to a congruence contained in the complex, of which congruence both order and class are equal to the number of double edges of the cone. Evidently any point common to two corresponding generatrices a,6 is a principal point, the plane containing these lines a principal plane of the complex. If one of the scrolls is plane, the bearing plane is a principal plane too; if one of them is a cone, the vertex is a principal point’). Any point P? of a principal plane is singular, the pencil with vertex P lying in that plane forming a part of the complex cone of P. The same degeneration presents itself for any point of each of the given scrolls; so these surfaces are loci of singular points. Like- wise any plane through a generatrix a or / and any plane through a principal point is sgular. By means of one scroll only can also be obtaine complexes con- sisting of linear congruences. So we can arrange the generatrices of a scroll in groups of an involution / and consider any pair of any group as director lines of a linear congruence *). In the following lines we treat the biquadratic complex which can be derived in the manner described above from two projective regul. After that we will investigate the particular cases of plane scrolls or cones. § 2. We use the general line coordinates «,, introduced by Kiet, which are linear functions of the coordinates p of PLickrr and satisfy the identity (#2?) = = vw, = 0, while = ey. = 0 or iy) = indieates that v and y intersect each other. Then a regulus is characterized by the six relations ag = pea? + 2qe4 + Thy satisfying the conditions: (p?) = 9, (r*) = 9, (pq) = 0, (gr) = 9, 2 (g*) + (pr) = OL Likewise we represent the second regulus by ') In our paper “Swr quelques complexes rectilignes du troisiéme degré (Archives Teyler, 2nd series, vol. IX, p. 553—573) we have considered among others the case that one of the scrolls is a pencil whilst the other is formed by the tangents of a conic. 2) This has been applied to a developable in our paper “On complexes of rays in relation to a rational skew curve’ (Proceedings of Amsterdam, vol. VI, p. 12) and on a rational scroll in “A group of complexes of rays whose singular sur- faces consist of a scroll and a number of planes’. (Proceedings of Amsterdam, vol. VIII, p. 662). ” 881 be = p's A? + 2q'k A+ rh. Then we tind for the rays w of the congruente with director lines a, 6 (pa) 4? + 2 (ga) 4+ (ra) =—0, (px) a? + 2 (q'x) 2 + (r'x) = 0, which we abridge into PY+2QA+R=—0 , P#+1200+R=—0. By elimination of 4 we get the equation of the bcquadratic comple under discussion. It is (PR! — PR)? =4 (PQ — P'Q (QR — QR), or, what comes to the same, (PR' — 2QQ' + PR)? = 4 (PR — Q) (PR' — Q’). From this ensues that the complex can be generated in two different ways by fwo projective pencils of quadratic complexes. This is shown by the equations PR' — PR=2 (PQ — P'Q), u (PR! — PR) = 2 (QR' — QR) and PR — 2QQ' + PR=2u(PR— Q’), u (PR' — 2QQ' + PR) = 2 (PR — Q?”). The equation (a>) =O expressing the condition that two corre- sponding generatrices a, 6 have a point in common, gives rise to a biquadratie equation in 4 So there are four principal points and four principal planes. § 8. We now occupy ourselves with the congruence of the rays w each of which rests on two pairs of homologous generatrices (A). For such a ray w the two equations PR 4+2Q2a4+R=>0 , P#4+2Q04+R=0 must be satisfied for the same values of 4; so we have the condition PQ. Ek | PLOOR:| This equation leads to a congruence (8,3). For the quadratic complexes PQ'=P’Q and Pk'= PR have the congruence P= 0, P’=0 in common and the latter congruence does not belong to the complex QR = QR. This result is in accordance with the fact that the complex cones (and curves) must be rational and have to admit therefore thee double ——=3(): edges (and three double tangents). Both the characteristic numbers of the congruence can also be S82 found as follows. A plane through any point A, of the generatrix a, and the corresponding generatrix 4, cuts both reguli respectively in a conic «,? and a line g,. On these sections the other pairs of corre- sponding lines a, determine two projective ranges of points (A), (5). As these arrange the rays of a pencil in the plane (A,/,) in a correspondence (1,2), the lines AB envelop a rational curve of class three with @, as double tangent. Each of the three lines AB passing through A, rests on two pairs’ a,b and belongs therefore to the congruence. The curve of class three just found and the pencil with A, as vertex form together the complex curve of plane (A,),). Likewise the complex cone of A, breaks up into this peneil and a rational eubie. cone. Any point and any tangential plane of the quadratic scrolls (a), (0) is singular. Moreover the points of the principal planes and the planes through the principal points are singular. § 4. If we add the relation (p'r') = 0 to the conditions enumerated in § 2, it follows from 2(g%) + (p'r') =O that the coordinates gq‘ also determine a line, which is to cut p' and 7 on account of (p'7) =9, (qr) =0 without belonging to the regulus. So it lies either in the plane t through p' and + or on a quadratic cone with the point of intersection 7’ of p' and 7’ as vertex. In the first case each line of rt belongs to the complex and even tivice as it cuts two generatrices of the regulus (a). In other words: t is a double principal plane. In the second case an analogous reasoning shows that 7’ is a double principal point. § 5. In the two latter particular cases the complex has lost the property of corresponding dually with itself. On the contrary this property is still preserved by the complex generated by two projective reguli the first of which consists of the tangents of a conic @ (in plane @) and the second is formed by the edges of a quadratic cone p° (with. vertex /). The range of points B, on the section p,? of 8° and @ is in (4,1)- correspondence with the system (a). So the points B, are in (2,2)- correspondence with the points of intersection A, of the generatrices a and the conie g,?. So the complex admits four principal points, each of which bears a principal plane. Furthermore «@ is a double principal plane, B a double principal point. 883 The complex cone of point P has PB tor double edge; for Pb culs two generatrices a and at the same time the corresponding lines 6. So the congruence (3,3) of the general case must break up here into a (1,0), a (0,1) and a (2,2). In order to cheek this we consider the correspondence between the points A= a«a,a, and the corresponding planes 3 = 0,6,. If A describes a line, a, and a, generate an involution; as 6, and 4, do then likewise, 8 will rotate about a fixed axis. So the correspondence (A, B) is a correlation. Therefore plane @ contains a conic @,7, each point A, of which is incident with the trace 4, of the homologous plane 8,. So each point A, is the vertex of a pencil belonging to the complex and lying in plane 8,. These pencils generate a con- gruence (2,2). For their planes envelop a quadratic cone with vertex 5, two tangential planes 3, of which pass through the arbitrarily chosen point 2; so the lines connecting P? with the homologous points A, belong to the congruence in question, which evidently is dual in itself. § 6. We will now suppose that the tangents a of the conic a? in plane @ and the tangents 4 of the conic 3° in plane @ are in (1, 1)-correspondence. Then the congruence with any pair of corre- sponding tangents a, 4 as director lines generates once more a complex of order four, evidently not dual in itself. By the correspondence (a, 4) the points of the line ¢ common to « and § are arranged in a (2,2)-correspondence. The four coinci- dencies are prencipal points of the complex and the lines a, 4 con- curring in any of these points determine a principal plane So we have indicated four sheayes of rays and fonr fields of rays belonging to the complex. The planes e@ and 3? ave also fields of rays of the complex; for any line s of @ is cut on ¢ by two Jines 4 but also by the corre- sponding lines a; so s belongs twice to the complex. We account for this by saying that @ and 3 are double principal planes. The complex cone of any point ? meets ¢ in four points, i.e. in the four principal points; so we deal with a béquadratic complex. The complex cone is rational, its edges corresponding one to one to the tangents of «’; therefore it has to admit three double edges. Likewise the complex curve of any plane has to admit three double tangents. § 7. In order to investigate this more closely we consider the Ss4 relationship between any point A of @, as point common to two tangents a,,a,, and the point 4£ common to the corresponding tangents 6,, d,. If A deseribes a line /4 its polar line with respect to « will rotate about a fixed point, whilst the pair a,,a, generates an involution. Sut then ,,4, must also generate an involution, so that B describes a line /z. So the point fields (A), (B) are in projective correspond- ence (collinear. homographic). By projecting the field (A) out of any point P unto 8 we obtain in 8 two projective collocal fields, admitting three coincidencies. So the congruence of the lines 4B is of sheaf degree (order) three. Its jield degree (class) however is one; for if A describes the section of @ with any plane 77, / will arrive once in J/, i.e. JT contains only one line AB. The congruence (8,1) found here is generated, as we know, by the axes (= biplanar lines) of a twisted cubic y*, i.e. any line AB lies in two osculating planes of y°. Evidently any line AP is double edge of the complex cone of any of its points P. However the complex rays through A form the pencil A(@) counted twice and the pencils determined by the lines b,,6,; for B the analogous property holds. § 8. Evidently the three double edges of the complex cone of P are the mutual intersections of the three osculating planes of y* passing through 7. Likewise the complex curve in IT has for double tangent the axis of y® lying in that plane, the other two double tangents coinciding with the intersections of J with @ and ~. For, each of the lines 3’, b" which concur in the point c/Z determines a complex ray lying in 77, which lines coincide both with e@ 77. An osculating plane 2 of y* contains ' axes, enveloping a conic w*. Any plane 2 is singular for the congruence (AB). So the com- plex curve in @ is the conic @* counted twice. As the congruence (3,1) cannot admit singular points, no point bearing more than three planes 2, no complex cone can degenerate but those corresponding to the principal points and the points of the principal plane. We already remarked this for « and (; for any point of a single principal plane the complex cone breaks up into a pencil and a rational cubic cone. The complex cone of any point of the developable with y' as cus- pidal edge admits an edge along which two sheets touch each other (the plane section has two branches touching each other). For any 885 point of y* the cone | o:sesses an edge along which two sheets oscu- late each other (the :cction has two branches with a common point of inflexion touching each other). A cuspidal edge connects any point A, of « with the correspond- ing point », of 37. The locus of the line A,B, is a biquadratic scroll, of which « and £ contain two generatrices. Any point of this scroll admits a complex cone with a cuspidal edge. Evidently the biquadratic scroll is rational, so it has a twisted cubic as nodal curve: For any point P of this curve the complex cone has two cuspical edges. By veplacing the two conics «7, 3° (as bearers of flattened reguli) by two quadratic cones we obtain a complex evidently dually rela- ted to that treated above. If « and »’ touch the line c= « ? whilst ¢ corresponds to itself in the relationship between a and 4, the complex degenerates into the special linear complex with axis c and a cubic complex. Evi- dently the same holds for the general biquadratic complex (§ 2) if the reguli admit a common generatrix corresponding to itself. Chemistry. —- “On the system phosphorus’. By Prof. A. Smits, J. W. Trerwen, and Dr. H. lL. pr Leeuw. (Communicated by Prof. A. F. Honiemay). (Communicated in the meeting of November 30, 1912). In a previous communication on the application of the theory of allotropy to the system phosphorus*) it was pointed out that the possibility existed that the line for the internal equilibrium of molten white phosphorus is not the prolongation of the line for the internal equilibrium of molten red phosphorus, in consequence of the appearance of critical phenomena below the melting-point of the red modification. The latter could namely be the case if the system «P—pP belonged to the type ether-anthraquinone, which did not seem improbable to us. This supposition was founded on the following consideration. In the first place it follows from the determinations of the surface- tension carried out by Aston and Ramsay ’*), that the white phosphorus would possess a critical point at 422°. Hence the critical point of 1) Zeitsch f. phys. Chem. 77, 367 (1911). 2) J. Ghem. Soc. 65, 173 (1894). Cf. also ScuencK, Handb. Apraa Ill, 374. 08 Proceedings Royal Acad. Amsterdam. Vol. XY. 885 the pseudo-component «P will probably lie below 422°. The melting-point of the pseudo-component 3/ lies certainly above the melting-point of the red modification, hence above 610°, so that we arrive at the conclusion that the melting-point of the second pseudo-component is probably situated more than 200° above the critical point of the first pseudo-component. In the second place the liquid white phosphorus, which must be considered as a supersaturate solution, contains no appreciable quantity of the phosphorus insoluble in carbon disulphide even at higher temperatures from which it may be inferred that the solubility of BP, or of mixed crystals containing @/, in liquid ¢? is exceedingly slight. In these considerations we arrive accordingly at the conclusion that in the system phosphorus exactly those conditions are satisfied which a system must satisfy if there is to be a chance for the appearance of critical phenomena by the side of the solid substance. Experiment has really taught us that the pseado system of the phosphorus belongs to the type ether-anthraquinone. It is true that in a pretty extensive investigation in which pure white phosphorus in capillaries of infusible glass was suddenly immersed in a bath of high temperature, a critical phenomenon could not be observed, because the observation is very much hampered by the deposition of a red solid phase, which always precedes, but yet phenomena appeared which pointed to the existence of a critical point below the melting-point temperature of the red phosphorus. Though the observed phenomena will be more fully discussed in a following communication, we may already mention here that among others it was found that on sudden immersion of a capillary with white phosphorus in a bath of 450°, at first solid red phosphorus deposited, and that then the liquid suddenly totally disappeared, in which a shock was felt in the hand in which the iron bar was held, on which the capillary was suspended by means of a copper wire. At the moment of the shock the whole capillary filled with solid red substance, which, however did not consist of the well-known red phosphorus, for if the capillary was removed from the bath of 450°, and suddenly immersed in a bath of 510°, it appeared that already at this temperature melting took place, so 100° below the unary melting-point of the red phosphorus. The perfectly colourless liquid, however, which originated at 510°, was strongly metastable, and the velocity of crystallisation being rather great at this tem- perature, the formed liquid became soon solid again. It now appeared that this phenomenon must be explained as follows. At high temperature, i. e. at about 300°, the velocity of 887 erystallisation of the red phosphorus is so great that it begins to be deposited. This velocity of conversion, however, is not so great as is generally thought, for even at 330° the vapour tension of the rapidly heated white phosphorus, which contained pretty much red solid substance, appeared to be still the same as that of the liquid, because the liquid still present was sufficient to control the vapour tension. How long this will continue of course depends on the relative volumes occupied by the solid and the liquid phosphorus and by the vapour. In the experiment with the capillary the velocity of heating is so great that even at considerably higher temperatures liquid white phosphorus still continues to exist by the side of the solid red mass. If, however, the temperature rises above the temperature of the first eritical endpoint p of the pseudo-binary system, the liquid becomes so strongly metastable that it suddenly disappears, and then the red solid substance deposits from the fluid phase formed, through the whole of the capillary. If the capillary is immersed in a bath of 620°, a colourless liquid is obtained, which exhibits something particular when cooled exposed to the air, which was already observed by Srock and GomorKa °). They say namely: “Kiihlt man die Schmelze recht langsam ab, so faingt sie bei etwa 580° an feste, rote Teilehen auszuscheiden; der Vorgang macht den Kindruck einer Kristallisation. Bei etwa 570° iiberziehen sich dann plitzlich*) die Wande des Glasrohres auf ihrer ganzen Linge (auch oberhalb der Fliissigkeit) mit rotem Phosphor, welcher in der Hitze sehr dunkel, bei Zimmertemperatur leuchtend purpurrot aussieht. Beim Offnen des abeekiihlten Rohres merkt man, dass es auch farblosen Phosphor enthalt’. Stock and GomoLka cooled down slowly, but we found that the phenomenon became more distinct, when the capillary is cooled by exposure to the air. It is then seen that red solid substance. depo- sits in the liquid, the vapour space and also the glass wall remaining perfectly colourless there on account of the fact that the liquid which deposits from the vapour, is perfectly colourless. At a given moment a violent phenomenon is observed in the capillary, while at the same moment very clearly a shock is felt. The liquid has disap- peared, and the inner wall of the capillary is covered everywhere, also at the place where before the vapour was found, with a solid, red substance, containing rather great quantities of «P. This phenomenon is explained by means of the following consi- 1) Ber. 42, 4510 (1909). 2) The italics are ours. o8* 888 deration. The second critical end-point q of the pseudo-system lies below the melting-point of the red phosphorus: If now the tempe- rature of the capillary has fallen below this critical endpoint, the liquid has become strongly metastable, and hence at a given moment it will suddenly be converted to a fluid phase, from which solid red substance will be deposited, also there where before the colour- less vapour was found. That the solid substance formed in this way is not in internal equilibrium follows most clearly from this that on being rapidly heated it does not show the melting-point of red phosphorus, but melts at a lower temperature, e.g. at 583°. As will be shown in a following communication, this behaviour also admits of an easy interpretation, just as the phenomena observed by Stock *) on sudden cooling of phosphorus vapour heated to different temperatures. These phenomena are not strange, on the contrary, they were to be expected in virtue of these considerations, and thus afford a not inconsiderable support to the theory. An important question which remained to be answered, was this: “can it be experimentally demonstrated that in contradiction to what was assumed up to now the vapour pressure line of molten white phosphorus and that of molten red phosphorus do not belong to the same curve?’ If the system phosphorus really belongs to the type ether-anthraquinone, the vapour pressure line of molten white phos- phorus is not the prolongation of the vapour pressure line of molten red phosphorus. To find this out the vapour tension of molten white phosphorus was determined up to the temperature of 338° by means of the manometer of JAcKsoN?), as has already been described by Messrs. ScHeFFerR and TreEvs ‘*). Further by the aid of a new apparatus, which will be described later, the vapour pressure line of molten red phosphorus was determined, in which it appeared that the triple point pressure of red phosporus amounts to almost 50 atmospheres. To answer the question proposed above the vapour tension, which the liquid white phosphorus would possess at the triple point temperature of the red phosphorus (610°), was caleulated from the observations by the aid of the integrated relation: b +=logT+C. Inp = — R a RT 1) Ber. 45, 1514 (1912). 2) J. Chem. Soc. 99, 1066 (1911). 3) Verslag Kon. Akad. v. Wet. 25 Nov. 1911, 529. Zeitschr. f. phys. chem. 81, 308 (1912). 889 by putting Q—=a-+Ob7 in the formula dlnp Q Lee If we had to do with one and the same vapour pressure line, about 50 atm. would have to be found for that pressure. If on the other hand the pseudo system exhibits the type ether- anthraquinone, and the vapour pressure line of the liquid white phosphorus possesses a critical point below 610°, the prolongation of that line above this critical temperature will of course have no physical significance, but if this prolongation points to a pressure higher than 50 atmospheres at 610° the question put above will be answered by this. The result of the extrapolation was that at 610° the pressure would amount to about 350 atmospheres. This result is sO convincing that it shows the erroneousness of the earlier view with perfect certainty, so that it may be considered indisputable already now that the view about the type of the pseudo-system has been correct *). 4y Lae? 460° 6/67 1) Also the system cyanogen has been investigated and conforms entirely to that of phosphorus. In the same way as for phosphorus we have succeeded in showing by means of experiments of solidification that we have to do with diffe- rent kinds of molecules, which can be in equilibrium with each other in solid and liquid cyanogen. S90 We will conclude this communication with the schematic P7- figure of the phosphorus; the connection between the unary and the pseudo-binary system will be’ treated in a following publication. When the calculated critical temperature 422° for liquid white phosphorus is correct about 18 atmospheres follows from the vapour pressure line for the critical pressure. The critical point is indicated by &, phorus exhibits probably a peculiarity that has never been met witb as yet, viz. two critical points /, and /,, the former of which is metastable. It is of course also possible even probable that unmixing takes place in the drawing. The vapour pressure line of molten red phos- in the psendo-system between » and q, so in the metastable region. The point 4, might, therefore, lie at even lower temperature and pressure than the point 4,. Possibly the continued investigation may give an indication with regard to this too. It may finally be pointed out that when we apply Van per Waats’s : 4 A lg ™* = 7 (2 —1) p . 7 Ty logp = ee : : + (7 : 1 equation, and write 3,94 is found for the value of /. This equation does not represent the observed vapour pressure line as well as the former, the cause of this may be that J is not constant as has been found indeed with several substances. Anorg. Chem. Laboratory of the University. Amsterdam, Nov. 29, 1912. Mathematics. — “On loci, congruences and focal systems deduced from a twisted cubic and a twisted biquadratie curve’. I. sv Prof. Henprik pe Vrigs. (Communicated in the meeting of November 30, 1912). 17. If we assume that the line / itself is a ray of the complex without however belonging to the congruence deduced from 2°, then the two surfaces 2*° and 2' undergo considerable modifications, The surface 2°" has no lowering of order; instead of the regulus, namely, which is the locus of the rays s conjugated to the points of / we now have a quadratic cone (passing likewise through the cone 891 vertices) whose vertex P, is the focus of /, because the two conjugated lines of 7, which cross each other in general and exactly therefore generate a regulus, now both pass through 2? ; but /, does not le on 2°, because / is a ray of the complex, but not of the congruence. A generatrix of the cone therefore intersects 2°, as fermerly a line of the regulus, in six points, from whieh ensues that / now again is a sixfold line of the surface. And to a plane 4 through / corre- sponds as formerly a twisted cubic through the cone vertices and which now passes moreover through /), because / is a tangent of the complex conie lying in A, but which now again intersects 2’, except in the cone vertices, in fourteen points; thus in A lie 14. generatrices of the surface, so that this is indeed of order 6 + 14 = 20. The curve /'?, the section of the cone with 2°, has also 6 nodal points lying on &*, so that 2*° contains 6 nodal generatrices. The nodal curve of 2* undergoes a very considerable modification as regards the points it has in common with /. Through such a point namely must go 2 generatrices of the surface lying with / in one plane; but now / is itself a ray of the complex and three rays of the complex can then only pass through one point when the complex cone of that point breaks up into two pencils; so the only points which the nodal curve can have in common with / are the points of intersection of / with the four tetrahedron faces. These points which in § 15 we have called S; coincide with the points which were called 7;* in the same §. Let us assume the plane /7,. As now again and for the same reason as before nine of the fourteen generatrices of 2°" lying in this plane pass through 7’ (§ 18) the five remaining ones must pass through another point 7,* lying in t, and whose complex conic breaks up into 7, and the plane T,*l; now however this point coincides with S,. For the complex cone of S, likewise breaks up into two pencils, of which one lies in t,, the second in a plane through 7’,* and 7’, ; now however, to this second pencil evidently belongs our ray / and so indeed the complex cone of S, degenerates in this way into tr, and a plane through (; so S, and 7,* are identical. To S,, regarded as a focus, a ray s through 7’, is conjugated which lies at the same time on the quadratic cone, thus in other words the ray ? 7; the latter intersects 2° besides in 7, in 5 more points and the rays s conjugated to these are the 5 generatrices of 27° through S, = 7,* lying in the plane /7,; the sixth generatrix through this point conjugated to T, lies in r,, but not in the plane /7). So we see that through S, pass five generatrices of @*° lying in the same plane; so the four points S; are 4.5 .4=10-fold points 892 for the nodal curve; this curve cannot have other points in common with 1. So it cuts l in four tenfold points (i.e. the 40 points of before have changed into four tenfold ones) and so it is again of order 40 + 91 = 131. Also the surface 2* undergoes considerable modifications as the conic lying in a plane 4 must now always touch the line /. The complex cone for a point 7 of / contains the ray /; the two tangen- tial planes through / to the cone coincide therefore; from which ensues that for each point P of / the two conics passing through it, coincide. The most intuitive representation of this fact is obtained by imagining instead of the point of contact of a 4° with / two points of intersection lying at infinitesimal distance; if then on / we assume three of such like points, then through 1 and 2 passes a conic and through 2 and 3 an other differing but slightly from it, so that really through point 2 pass two conies. The loct of the conics is thus now again a 2* with nodal line 1, but this line has become a cuspidal edge, i.e. whereas formerly an arbitrary plane intersected £2* along a plane curve with a nodal point on /and only the planes through the four points S; (§ 15) furnished curves with cusps, now every arbitrary plane of intersection contains a curve with a cusp on / (and with a euspidal taugent in the plane of the conic through that cusp). Furthermore we must notice that as the points 7;* coincide with S;, the four nodal points 7’; will be found on the nodal line itself, thus forming in reality no more a tetra- hedron proper; nevertheless the property of the simultaneous cir- cumseription round about and in each other remains if one likes. 18. The curve of intersection of order eighty of 2* and 2?° is again easy to indicate; it consists of the line / counted twelve times (for a cuspidal edge remains a nodal edge), and of a curve of contact of order 34 to be counted double (§ 15) which has with a plane A through / fourteen points lying outside 7 in common and therefore twenty lying on /; these last however can be no others than the four points S;, for otherwise a generatrix of 2*° would have to touch a A° ef 2* on 7, which could only be possible (as / itself touches 4?) if a generatrix of 2?° could coincide with / which is as we know not possible. The curve of contact of £2* and {2*° passes thus five times through each of the four points S; which corresponds to the facet that five generatrices of 2*° touch in S;, the degenerated conic (viz. the pair of points ,, Z;) lying in the plane /7*. The method indicated in § 14 to determine the number of torsal lines of the first kind undergoes no moditication whatever; we can §93 however control this method here because we have to deal here with a cone instead of a regulus. The first polar surface of 2 na- mely with respect to £° is a 2° containing £* one time, and there- fore cutting 2° along &* counted twice and a residual curve of order 24, so that the circumscribed cone at the vertex P; is of order 24. Now this cone euts the quadratic cone [/)| in 48 edges, so 48 edges of [2] touch 2° and therefore £'*. The number of torsal lines of the first kind is thus indeed 48, and that this same number must now be found in general follows from the law of the permanency of the number. These numbers 6 and 48, as well as the number of points (namely 40) which the nodal curve of 7° has in common with / can be controlled with the aid of the symmetrical correspendence of order 70 existing between the planes A through / (§ 16). To the 140 double planes Jd belong, as we saw before, the planes through / and the nodal lines and those through / and the torsal lines of the first kind, together appearing there at a number of 54, but representing 60 double planes. The nodal curve of @*° has with / only the 4 points S; in common which however count. for 10 eaeh and which have the property that five of the six generatrices through each of those points lie in one plane; such a plane is thus undoubtedly a many- fold plane of the correspondence, the question is only how many single double planes it contains. Now there lie in the plane /7’, e.g. 9 generatrices through 7’ cutting / in different points; through each of the last pass five other generatrices, and so we find so far 45 planes conjugated to the plane /7%. Now we have moreover the plane through / and the 6 genera- trix through jS, (lying in +r,); however by regarding, just as we have done at the beginning of § 16, a plane 4 in the immediate vicinity of 77 and in which thus five generatrices cut each other nearly in one point of / we can easily convince ourselves that this plane counts for 5 coinciding planes conjugated to /7,. To /7’ are conjugated 45 + 5—50 planes not coinciding with /7’, and thus 20 planes coinciding with /7,; i.e. just as in the general case a plane 4 through two generatrices cutting each other on / counts for two double planes, so here each plane /7’; containing five such generatrices counts for 5><4 double planes; so the four planes /T; represent 80 double planes, and they furnish with the 60 already found the 140 double planes as they ought to. As by the transition to a ray of the complex all numbers have remained unchanged, the surface @?° contains now again 58 torsal lines of the 2"¢ kind; the 4 131 = 524 points of intersection 894 of &* with the nodal curve of 2*° lie now however a little differ- ently. The points 7. remain 36-fold for the nodal curve and they therefore furnish + >< 72 = 288 points of intersection, the 58 torsal lines of the 2°¢ kind give 58, the 6 nodal edges give 3 x 6=18 other ones; the 4 points S;—= 7;* however absorb each of them 40 points of intersection. Let us namely imagine our figure variable and in particular / continuously passing into a complex ray, we then see how the 4 points 7,* tend more and more to S;, but at the same time how the 40 points of intersection of / with the nodal curve group themselves more and more into 4 groups of 10 in such a way that each group is as it were atiracted by one of the points S;; now each of those 40 points counts for 2, each point 7;* for 20 points of those we looked for; so on the moment that 7;* as well as the 10 points of the corresponding group coincide with S; this point counts for 40, so the four together for 160 and the sum of the four numbers printed in heavy type is again 524. 19. More considerable are the modifications if finally we now assume that / becomes a ray of the congruence; nothing is to be noticed at 2*, as 7 remains a ray of the complex, but the other locus becomes a surface 2'*, for which / is only a fivefold line. The regulus of before is namely now again replaced by a cone | P.|, but the vertex itself P? now lies on 2°, because lis a ray of the congruence, thus itself a generatrix. It even appears twice as a generairix; for the cone cuts 2° according to a 4"? which has now a.o. also a nodal point in 7) and to this nodal point the line / corresponds twice. A generatrix of the cone [7] cuts 2° in Pj and in five other points; so through the corresponding focus on / pass five generatrices not coinciding with /, i.e. / ty a jivefold line. To a plane 2 through / a twisted cubic is conjugated containing the four vertices of the cones and /; and. cutting 2° in 13 points more; so in a plane 4 lie besides / 13 generatrices, i. e. ow surface is a 2° of order 18 with a fivefold line 1. d Among the generatrices of the cone [|] there are two touching k* in P; and likewise among the twisted eubies; the foci of the former are the points of intersection proper of / with two generatrices coinciding with /, the planes conjugated to the latter being the con- necting planes; thus two particular torsal planes and pinch points (see § 20). The line P, 7; is a generatrix of the cone {P| and it cuts 2* besides in these two points in four more; the corresponding four rays s pass through S;= 7;* and lie in the plane 7Z; whilst the S95 ‘ay s conjugated to 7; lies in r,, but not in / 7); so the points S; are }.4.3 = 6-fold points for the nodal curve and others this curve ean evidently not have in common with /. So it has 24 points united in 4 sixfold points in common with /, and as there are in a plane « through / }. 13.12 = 78 points not lying on / the order of the nodal curve now amounts to 24+ 78 = 102. The number of nodal points of a plane section of 2'* amounts thns now to 102 +6 +10=118, and from this ensues for the class 18.17 —2.118=70= «8; the formula eo = 2. ef — 2. eq furnishes there- fore «6 = 2.70 — 2.18 = 104 torsal lines of both kinds. The formula =) -- 9 — J now again applied to determine the number of generatrices of the cone {P| touching £* and thus of the number of torsal lines of the first kind gives the following results. The plane of the condition p euts #’* in 12 points; through each of these passes a generatrix of the cone cutting £2" besides in 7) in four points more; so the num- ber p is equal to 48, aand likewise g. The line of the condition g cuts the cone in two points and through each of these passes a genera- trix of that cone, on which lie besides / five points of 4'*; so g is = 2.20, and thus « = 2.48 — 2.20 =56. Among these however are included the six nodal lines counted twice; the number of torsal lines of the first kind amounts thus to 56 — 2 > 6 = 44. To control this we again consider the first polar surface of P, with respect to 2°, a 2* touching 2° in P; and passing through k*. The intersection with 2° consists therefore of /° counted twice and a residual curve of order 30 — 2.8 = 24 which however is projected out of 2; by a cone of order 22 only, because P; itself is a nodal point of that curve (for @° and &* touch each other in P,); this eone has with the cone |/)| 44 generatrices in common, and these touch 41°. The number of torsal lines of the 2™° kind of 2** amounts to 104 — 6 — 44 — 54. The correspondence of the planes A through / is now of order 52 with 104 double planes. For, in a plane 2 lie besides / thirteen ge- neratrices of 2'* and through each of the 13 points in which these eut / four others pass; so to each plane A 4 >< 13 = 52 others are con- jugated. The double planes are 1. the planes through the 44 torsal lines of the first kind; 2. the planes through the 6 nodal edges, each counted twice; 3. the 4 planes /7; each counted twelve times, beeause in each such like plane 4 generatrices pass through the point S; (comp. § 18); so we find 44 + 2.6 + 4.12 = 104 double planes, S96 And as regards finally the number of 4 102 = 408 points of intersection of the nodal curve with 2‘, in the four points 7; lie again 288 (comp. § 18), in the pinch points of the torsal lines of the second kind 54, in those of the six nodal edges 18 and in the four points JS;, which are sixfold for the nodal curve, 48, together 288 + 54-4 18 + 48 = 408. 20. The two particular pinch points on 7 which we have found in the preceding § were the two foci of the ray of the congruence / and the two torsal planes the two focal planes; for, in these points ¢ was cut by a ray of the congruence at infinitesimal distance. If henceforth with a slight modification in the notation the line 7 is valled s,, the focus ,, then P, lies on Q2* and it is in general an ordinary point of this surface. Let us assume the tangential plane in this point and in it an arbitrary line ¢ through P,; then this has two conjugated lines crossing each other, and if therefore a point P deseribes the line ¢, the ray s of the complex conjugated to P will generate a regulus to which also belongs our ray s,, a ray of the congruence. As however ¢ is a tangent of 2°, a second generatrix of the regulus lying at infinitesimal distance from s, will belong to the congruence, however without cutting s,. If however, we now imagine the complex cone at point ?, and if we intersect it by the tangential plane, we find two lines ¢ which are at the same time lines s, viz. rays of the complex, and whose two conju- gated lines cut each other. Now the lines s conjugated to the points P ot ¢ will deseribe two cones containing also s,, and having their vertices on s, whilst we know out of our former considerations that these vertices are nothing but the foci of the two rays ¢; and now s, will be cut in each of these foci by a ray of the congru- ence at infinitesimal distance; the two cone vertices are thus the foci of s,. So: we find the foci of a ray.s, of the congruence by determining the focus P, (lying on 2) of sy, by intersecting the com- plea cone of this point by the tangential plane in P, to 2°, and by 0 taking the foci of the two lines of intersection t. And the two focal planes are the tangential planes through s, to the complex cones of the foct. If P, is a point of the nodal curve &* of @* then s, is a double ray of the congruence (§ 12); the complex cone of P, intersects the two tangential planes of P, in twice two rays ¢, so that we now have on s, two pairs of foci and through s, two pairs of focal planes ; and as the fucal surface of the congruence is touched by each ray of the congruence in the two foci, so each double ray will touch the ee 897 focal surface four times. The four tangential planes are the focal planes, however in such a way that if one pair of foci is called F,, F, the focal plane of /, is tangential plane in F’, and reversely. Let P, be a point of &*, lying as a single curve on 2"; then s, is the tangent to /* in P, and it belongs to the congruence. The com- plex cone of /, intersects the tangential plane in this point to 2° according to s, itself and an other generatrix; so of the two foci of s, point P, is one whilst the other is the focus of the second generatrix of the complex cone of P, lying in the tangential plane; and of the two focal planes the osculation plane of &* in P, is one, because this really contains two rays of the congruence intersecting each other in P, and lying at infinitesimal distance (viz. two tangents of &£*); so it touches the focal surface in the other focus, i. e. the surface of tangents of 4A* which is of order 8 envelops the focal ‘surface, and the curve 4‘ itself lies on the focal surface. The question how the cone vertices 7; bear themselves with respect to the congruence, is already answered in § 11; 2" intersects the plane rt; according to a plane 4° and the rays s con- iugated to these form a cone of order 9 with the vertex 7; and with three nodal edges and three fourfold edges, the latter of which coincide with the three tetrahedron edges through 7%, Let us assume an arbitrary point P of &°, then to this a ray s through 7; is conjugated; now the complex cone of P degenerates into a pair of planes, of which 1; is one component, whilst the other passes through 7}, and this degenerated cone cuts the tangential plane in P to 2° along the tangent ¢ in P to &* and according to an other line ¢ through P. To that tangent the point 7; is conjugated as focus, so that for each ray of the congruence through 7; this point itself is one of the foci, the other being the focus of the line /*. In order to find the foeal plane of the considered ray s in the point Zi we should have to know according to the preceding the complex cone of 7; which is in first instance entirely indefinite ; let us however bear in mind that in the general case that complex cone is at the same time the locus of the ray s conjugated to the points of the tangent ¢; then in this case also we can have a defi- nite cone, viz. the cone which replaces the regulus if the line / passes into a complex ray s, and which contains in general the four cone vertices and which will contain here, where 7; itself is the cone vertex, the three tetrahedron edges through this point. On this cone lie the two rays s conjugated to the two points of £* lying at infinitesimal distance from each other on ¢, and the plane through these is the focal plane of our ray s in 7; but those edges of the qua- 898 dratic complex cone lying at infinitesimal distance lie of course also on the cone of order 9 (see above); so we can say more briefly that for each ray of this cone 7; is one of the foci and the tangen- tial plane to the cone is one of the focal planes. Each ray of the congruence through 7, so each generatrix of the cone of order nine with this point as vertex, must have in P; two coinciding points in common with the focal surface; so 7; is for the foeal surface a manifold point, however without the cone of order 9 being the cone of contact; for the tangential planes of this cone touch the focal surface in the foci of its generatrices not coinciding with 7; the cone of contact in 7; is enveloped by the focal planes of this last category of foci. 21. Over against the question which complex rays through 7; belong to the congruence, is the other one which complex rays out of 1; belong - to the congruence. In the preceding we have repeatedly come across these rays. Indeed, any surface £*° formed by the congruence rays which ent a line / or a complex ray s, and any surface 2** formed by the congruence rays which cut a congruence ray » contained such a ray as we proved above; we shall now show that all these rays form a pencil. To that end we imagine the tangential plane o in J; to 2° and we cut it according to the line r by 1;. We now saw in the preceding that the rays s conjugated to the points of r, form a quadratic cone with 7; as vertex and containing the three tetrahedron edges through 7; ; if the base curve of this cone lving in 7; is 4°, then reversely the points of 4° are the foci of the rays s lying in 9 and passing through 7%, for the rays s conjugated to the points of a line pass through the focus of that line and the ray s conjugated to a point of x; passes moreover through 77. If a point P describes one of the rays of the peneil [7;| lying in 9, say s,, then the rays s conjugated to the points P form the complex cone of the focus P, of sy, which point lies on 4? ; this complex cone breaks up however into a pair of planes, viz r;anda plane through /, and 7T., and the line of intersection ¢; of these two planes is the ray of the congruence conjugated to 77, in as far as this point is regarded as a point of the ray s,; so the question is how the rays ¢; bear themselves when s, describes the pencil (7;| or, what comes to the same, how the planes 74 bear them-- selves in those circumstances. We shall try to find how many of those planes through an arbitrary ray s, pass through 7Zj. In each arbitrary plane through s, the complex conie breaks up into two pencils; one has the vertex 7;, the other a point 77* lying-in 7. 899 In each plane through s, lies however one such point 7;*; but if S, is the point of intersection of ~s, with 7;, then also the complex cone of S, breaks up into a pair of planes of which one compo- nent is of course again t;, the other being a plane through S; 7; so S, is itself a point 7;*, and the consequence of this is that 7)* describes a conic 4** which passes in the first place through .S, and in the second place, as is easy to see, through the three cone vertices lying in 7,;; for if a plane through s, passes also through a second vertex, then the complex conic breaks up into the two pencils at T; and at that second cone vertex. All rays through a point 7,* of 4** cutting s, are according to the preceding rays of the complex; from this ensucs reversely that the complex cones of all points of s, in 1; have the same base curve, namely 4**. If now the degenerated complex cone of a point of 4 is to pass through s,, then that point must evidently lie also on /** and of such points there exists apart from the three cone vertices lying in t;, only one; in the pencil | 7;) there is thus only one ray for which the (degenerated) complex cone of its focus passes through an indicated ray s,, i.e. the second components of the complex cones of the foci of the rays of the pencil | 7;| form a pencil of planes, or the rays of 1; belonging to the congruence form a pencil. The axis a of the pencil of planes must of necessity cut the curve k*; for, if this were not so, then an arbitrary plane through a would cut 4? in two points, and then the complex curve in that plane would break up into three pencils (among which one at 7; is always included) instead of into two. This objection does not exist when @ cuts the eurve 4? in a point A; for then each plane through @ euts 4° besides in A in only one point 7,* more, and A itself is a point 7;* for the plane through a which touches 4°. The avis a ts simply that line which has the property that the complea cones of its points have as common base curve the conic hk? itself; for, for each plane through a the point 7; lying on 4? must lie at the same time on k*, so k* and &** coincide. For each ray of the pencil {A} lying in t; point A is evidently one focus and x the corresponding focal plane, for each ray is cut in A by an adjacent one of the pencil; the other focus is the second point of intersection 7;* with 4? and here the second focal plane passes through 7;. The focal surface must therefore touch 1; along the conic k* ; the point A itself is however a singular point, for here any plane through a is a tangential plane. For the tangent in A to 4* the two foci coincide evidently with 900 A; the focal planes, however, do not coincide, for one is 1; and the other connects the tangent to 7;. 22. Order and class of the focal surface can be immediately determined by means of two dualistically opposite equations of SCHUBERT, V1Z. &6p* = opge + Gph. — Gpe, and £6e°= Gea, + deh, — Gpe*). We conjugate to each ray g of the congruence all other rays as rays h, we then obtain a set of o* pairs of rays and we can apply to these the two equations just quoted. The symbol o indicates that the two rays of a pair must intersect each other, ¢ that they lie at infinitesimal distance and p’ that the point of intersection p must lie in two planes at a time, thus on an indicated line; so sop is evidently the order of the focal surface. The condition opge indicates the number of pairs which cut each other, whilst the point of intersection p lies in a given plane and the ray g likewise in a given plane; now there lie in a given plane 14 rays of our congru- ence, thus 14 rays g; each of these intersects the plane of the con- dition p in one point and through each of these pass 5 more rays of the congruence; pg, is therefore 14 X 5 = 70, and oph, means the same and is thus lkewise = 70. With ope we must pay more attention to the point of intersection of the two rays and to the connecting plane than to the rays them- selves; ope indicates namely the number of pairs of rays which cut each other and where the point of intersection lies on a given line and at the same time the connecting plane passes through that line; this number is evidently the third of the three characteristics of the congruence, thus the rank, however multiplied by 2 because each pair of rays of the congruence represents 2 pairs gh; so ope is = 80, so that the order of the focal surface ts equal tv 70 + 70—89 = 60. soe’ indicates the number of pairs of rays at infinitesimal distance whose connecting plane passes through 2 given points, so through a given line, i.e. the class of the focal surface. Now eg, indicates the number of pairs of rays whose connecting plane passes through a given point, whilst also the ray g passes through a given point. So there are 6 rays g and in the plane through one of those rays and the point of the condition e lie besides g still 13 others; oeg, 1) Scuupert l.c. page 62. Q)] and oeh, are thus each = 6 >< 13 = 78, and ope was 80, so the class of the focal surface = 78 -+ 78 — 80 = 76. I may be permitted to point out in passing a slight inaccuracy committed by Scuupert on page 64 of his “Kalkiil” where he gives formulae for order and class of the focal surface of a congruence taking the number ope, called by him ec, only onee into account; in Pascan-Scuepr’s well known “Repertorium” vol. II, page 407 we find indicated the exact formulae, with the rank number 7 counted twice. In a congruence of rays appear in general oc’ rays whose two foci coincide; these too are easy to trace in our congruence. For, according to §20 in order to find the foci of an arbitrary ray s, we must apply in the focus /?, the complex cone and the tangential plane to 2° and intersect these by each other; the foci of the lines of intersection are the foci of s, and the tangential planes through s, to the complex cones of the foci the foeal planes. So as soon as the complex cone of 7, touches the tangential plane 2" along a line t, the two foci of s, will coincide in the focus of ¢ and the focal planes will coincide in the tangential plane through s, to the complex cone of the only focus. The points /, whose complex cones touch 2° are to be found again with the aid of Scuupmrt’s “Kalkiil’. We conjugate the two rays s, along which the complex cone of a point P, of 2" cats the tangential plane in that point, to each other; so we obtain in that manner a set of o* pairs of rays and we apply to it the formula; &6p = Ode + Gh, 4+- Gp? — ope’); The left membet namely indicates the number of coincidences whose points of intersection lie in a given plane, that is thus evidently the order of the curve which is the locus of the points ?, to be found. og. indicates the number of pairs of rays whose component g lies in a given plane; this plane ¢uts out of 2° a plane curve /" which possesses no other singularities than three nodes and which is so of class 6.5 —2.3—= 24. and all the complex rays in this plane envelop a conic; so there lie 48 complex rays g in this plane touching £°. If we apply in one of the points of contact the tangential plane to 2", then there lies in it one ray /; so og, is 48 and likewise of course oh,. With op* we must trace the number of pairs of rays whose points of intersection lie in two given planes at the same time, thus on a given line; this line intersects £2" in six points and in the tangential ') ScHuBeERT 1. c. page 62. os) Proceedings Royal Acad. Amsterdam. Vol, XY. 902 plane lie two rays of the complex cone and thus also two pairs gh, because each of the two rays can be either g or h; so op? =12. For ope finaly the point of contact must lie in a given plane, the tangential plane must pass through a given point; so we can either apply the tangential planes in the points of a plane section of 2° and determine the class of the developable enveloped by it, or we can construct the circumscribed cone and calculate the order of the curve of contact. The latter is the simplest; for the curve of contact is the intersection of 2° with the first polar surface of the vertex of the cone and therefore of order 6.5—2.3 = 24, because the first polar surface contains the nodal curve 4* and the latter counted twice separates itself from it. But the two complex rays through the point of contact and in the tangential plane count again for two pairs and so. Gpe = 48, from which eusues sop = 45 + 48 + 12 — 48= 60: so there lies on 2° a certain curve k°° of order 60 having the property that the rays s conjugated to its points have coinciding foci and focal planes. We can ask how the curve #'° will bear itself with respect to the four cone vertices 7%, where the complex cone becomes indefinite. We now know however ont of § 21 that in the plane rt; only one ray with coinciding foci lies, viz. the tangent in A to ke; so k®° will pass once through the four cone vertices. That for that tangent in A to f? the two focal planes do not coincide, is an accidental circumstance, which is further of no more_inportance ; this result was based namely on the supposition that through an edge of the cone passes only one tangential plane of that cone; however, for the point A the complex cone breaks up into a pair of planes whose line of intersection is just the tangent in A to 4*, the tangential plane through that line to the cone is thus in first instance indefinite. The rays of the congruence with coinciding foci determine a scroll of which we will finally determine the order. To that end the scroll must be intersected by an arbitrary line and we now know that all rays of the congruence meeting a line / form a regulus 2*° and that the foci of those rays are situated on a curve /** lying on 2° and passing singly through the 4 cone vertices. It is clear that to a point of intersection of 4°? and /"° a ray corresponds with coinciding foci and cutting /, with the exception of the cone vertices; for, to 7; is conjugated as regards °° the tangent in A to 4*, on the other hand as regards /'* the connecting line of the point of intersection of /¢ and 7; with A. as we now know. Now i? is, as we know, the complete intersection of 2*" witha regulus; sv the complete number of points of intersection of /'* and £*’ amounts to 120. If we set apart _ 905 from these the four cone vertices, we then find as result that the rays of the congruence with coinciding foci form a requlus of order 116. The curve i*° intersects 1; besides in the three cone vertices lying in this plane in 57 points more, lying of course on the section h® of 2° and r,; to each of these points a ray through 77 is conjugated with coineiding foci; the 4 cone vertices are thus for the surface 2°°°" 57-fold points. Physics. — “Some remarkable relations, either accurate or approvi- mative, for different substances.’ By Prof. J. D. van per W AALs. (Communicated in the meeting of November 30, 1912). In a previous communication (June 1910 These Proc. XIX p. 113 I pointed out the perfectly accurate or approximative equality of the ratio of the limiting liquid density to the critical density, and the ‘atio of the critical density to that which would be present for 7), , rv Pea v.,-, if a should always be equal to 1. With the symbols used there 21+ y= 4s I have added the factor g, which must then be equal to 1 or must differ little from 1. The rule given there has attracted some attention. For first of all Dr. Jean Trvermans has informed me that he has found this rule entirely confirmed for six substances, for which the observations made were perfectly trustworthy. For a seventh substance there was a great difference, but he thought that for this real association might perhaps occur, as is the case for acetic acid‘). Besides this rule has also been adopted by KAMERLINGH Onnes and Kersom in their recent work for the Eneyklopadie: Die Zustandsgleichung. The rule is in- deed apt to rouse some astonishment, because it pronounces the equality between two quantities, which, at least at the first glance, have nothing in common. It is to be expected that this approximative equality will have to be explained by the way in which the quantity 4 varies with v; but it is seen at the same time that perfect equality cannot be put ‘) The numerical values have been communicated in the “Scientific Proceedings of the Royal Dublin Society”, October 1912. 59" 904 eenerally. There is. indeed, a remarkable difference for invariable molecules, i.e. for such for which the quantity 4 does not change. = : 8 Ue Uk s Phen the quantity s—=— and = —.=.3. In this case is not 3 , Vlim 9 1, bat —. If there exists a rectilinear diameter for substances with such molecules. y = 2 eae Perfect equality or almost perfect equality can therefore, only -be expected for substances for which 4 greatly varies with the volume. f Thus for substances for which s is about equal to 3.77, the value of y is about equal to 0.8 or 0.9. The following remarks are the result of my investigation to get more certainty about this question. According to the formula: rie 20 4+ y) =—=94s Vlim is by r ifs —— Y x or by pe od a 64 (7—1) lig 2 teen Gee ere or a f—-1/8 8 == = - yf }- Diim 3 9 sr 8 8 Now the thought has foreed itself upon me to put ee 1 sr and hence also by f-l btim 3 _ a) 48,58 97s, oF : Phe relation oal= [OLE aa is satisfied for substances for. 2 Ss? Cc - 9 which 4 is constant. Then 7s =, and as we saw above ¢ =e For substances with variable value of 8, 7s <8 and @ decreases, but comparatively slowly. Not before rs = 7 | would be = 1, and for substances for which rs has this value, the rule 2qa + y)=s 905 , ; id would be perfectly accurate, If rs > 7 “ib 2(1 + y) >-s, and not before 1 iS ; 2Aa+y) 4, and Blin 3 f—1 3 : : PK eee > 1; the first member of the equation, viz ——~ is then, of Ce lim course, also always greater than 1. Later on we shall set ourselves the task to inquire into the theoretical reason for this relation. But for the present we shall accept it as perfectly accurate, and see to 97 ol what conclusions it leads. If we write ; s* for f—1, we get: [ee ae Pet Dim a 64 os as 8 ; 5 b = 5 : = q The value of s can, therefore, not be smaller than —. For —- —2, o Olim goeso tor f= 7, s = = V2 = 3,77; a value which moreover already . : Sa 4 z by s follows from the equaliy —- i= put above. For ==05) 0 o7 . 0 fi =! lim . . 8 . . which f=10 would belong, s would be = ae oe OD S402. > But so high a value of f or s has only seldom been found. If before in the absence of a leading idea, I assumed a still greater Sars by : ; ratio for —~, this was a mistake. A lim From : by Qs* Dlim 64 by Vk 9 (sr Clim et ss —=2(1+y) bij sii s\s : Nim Ulin 0 \S Ok Of course we find back the rule from which we have started but with a determined value for the factor ¢. As I showed before follows 906 sv <8, but for by far the majority of the closely investigated ™ D(\ bs ] 2(3 substances (sr) > 7 5: For them eee must be > 1. But the pos- sibility of ~—- <1 is not exeluded even for normal substances. Yet we should not lose sight of the fact that it has not yet been investigated in how far the existence of quasi-association has influence on the rule of the rectilinear diameter. A close investigation about the value of (rs) for different) substances, and comparison of the value of y following from this with the experimental data is, there- fore. very desirable. If from the knowledge of the value of wy we want to determine lim the value of 7, the given relations are not sufficient for an accurate by 9 (=) Biim r \8 by 9 | (f—Dr’? bisa es 27 ' 9 indeed, holds. As, however, the value of the factor of — is not accurately = determination. The relation or known, and as we only know that this factor is smaller than 1, and the bg : : . smaller as —* is greater, we can only give a value for + below lim b ; : ; = : q 2 = ; which it must remain. Thus for —--—=2 the value of 7 is below lim 3 ; } 8 8 8 es 2,12. Already with the formula — < 1, or r<-, or rq — Vy rs s 8 : ; 8 bg we arrive at the given value for. If we, namely, put s = = aoe 3 907 e ; ‘ " the part of the value calculated according to the above formula. It is, indeed, very remarkable that already with such slight varia- bility of 6 as will be the case for ua — 2, ale diminished so lim V lim bes greatly that the value changes from 8 to about 2; whereas —— only y decreases to about 0.95 or 0.96, as I calculated before. Let us now proceed to inquire whether a theoretical reason can be given for the above mentioned relations. That though they may possibly not be quite rigorously accurate, they will hold with a high degree of approximation, cannot be denied. That 4 varies with » I have had to admit immediately when | tested the equation of state given by me by the observations of ANprREWs, in which even volumes occur which are smaller than 4,. And I have long been of opinion that this diminution of 6 with smaller volume> does not mean a real diminutien of the molecule, but that this diminution of 6 would only be an apparent diminution. I have tried to subject the hypothesis of an apparent diminution to the calculation by what I have called the overlapping of the distance spheres. Then the factor 4 in the expression 4 = 4 ‘times the volume Ad ie b of the molecules diminishes. The value of — has then the form ofa My im and- I have at least ; brought the factor of the 1st power, and also that of the 2"" power in a formula, which, however, required such laborious and lengthy ealeulations for the second power that I abandoned them hopeless. Van Laar has carried out the computations, and calenlated the value of the coefficient belonging to the 2"™¢ power, and expressed the opinion that the series would consist of as many as some 20 terms. Afterwards BoutzMann has supplemented the calculations, and shown series according to ascending powers of ao that the value of would have the form of a quotient with series My b . ° 5 ~/G A - AG of terms with ascending powers of —. More and more the conviction 7 took hold of me that this apparent diminution does not exist. I have not yet obtained perfect certainty that it does not exist. But already : 5 Akias Dike before by the application of the form of — with not too great a degree j 97 of density, in which some three terms will suffice, I have repeatedly 908 found that the caleulated coefficients are much too great. To this comes that the coefficients thus calculated must be of the same value for all substances, at least if a spherical shape is assigned to all of them. Attempts to determine them when the shape deviates from the spherical form have not yet been tried by anybody, but it may be expected that they will not differ much from those that have been calculated for the spherical shape. A contribution of importance for the decision of the question whether or no apparent- diminution exists will be furnished by the experimental determination of the equation of state of a monatomic substance. If we should have to conclude to diminution of 4 with decreasing value of v also for these substances, this diminution of 4 will certainly have to be called a quasi-diminution, unless one would assign a constitution for which real diminution is possible also to an atom. A second view of the cause of the diminution of & with v would of course be obtained if one should have to ascribe compressibility to a molecule, and if one did not explain this compressibility by a diminution in size of the atoms, but by their coming closer together. If this is to be the cause, the diminution of 6 must not be found for a monatomic molecule. To decide this it would be desirable to give so considerable and judicious an extension to the investigations for such substances as those of ANDREws for carbonic acid. That a molecule consisting of atoms might be compressible in consequence of the approach of the atoms seemed a hypothesis to me worth investigating. And I carried this out in my communi- cations in 1901 published in these proceedings. I arrived at a formula there, which may be considered as the equation of state of a molecule consisting of two or three separate parts which are in thermal motion. These separate parts may be separate atoms or separate atom groups, which are in close relation at the temperature considered, and of which the component atoms are perhaps in vibration with almost vanishing amplitude and small period. This formula has the following form: a p+—~-+a (b—b,)} (b—b,) =kRT. : In this formula / is the volume of the molecules, 4, the volume of the atoms or atom groups, and the latter would be the volume of the atoms or atom groups when the molecule was compressed as much as possible. The quantity / is equal to */, for a molecule composed of two separate parts, and equal to 1 or < 1 according io the nature of the motion for a molecule consisting of three parts. = Mw er~s 2)” ihe - - 909 I have represented the attraction of the separate parts by « (b—4,), i 4 = - but I shall henceforth denote it by «& 5 ') which is hardly more y than a change of a formal nature, required to make e’ retain the a character of a pressure on the unity of surface. Just as p —+- 7: is a pressure directed inward on the unity of area, this is the case : b—b, , with and the latter represents the increase of that pressure My in consequence of the mutual attraction of the separate atoms or atom groups. It was only after a long hesitation that I dared con- clude to this value of the attraction, and when I concluded to it it was only, to quote Prof. Ricnarps, “with some conviction’. It follows from this form for the attraction that it is equal to O when the atoms touch, and becomes greater when the space allowed to the motion of the atoms, increases. Moreover [ put a’ propor- tional to the temperature. [ must acknowledge that these suppositions are not founded on a true insight in the constitution of a complex molecule. But I hoped that the study of the consequences of these hypotheses which seemed probable to me, and the comparison of these consequences with experience might contribute to the know- ledge of the properties of such a complex molecule. And so far as 1 could then compare with what was known on other grounds, the impression I obtained, was not entirely unfavovrable. And now 1 have been induced to reconsider the conclusion at which I had arrived, to see if it leads to the relations which | have drawn up in the beginning of this communication. But in this respect I have not obtained perfect certainty yet. I have repeatedly discussed some difficulties which confronted me, with my son—but these discussions have not yet led to an undoubted result. At the moment I shall confine myself to communicating the proposed relations. Later we hope to be able to derive a rule from the state of motion of the atoms in a molecule, which will perhaps lead to the form: bot ee Bi 3 when / represents the number of degrees of freedom for the motion of the parts of the molecules divided by the number of degrees of freedom for the progressive motion of the molecule as a whole, viz. 3. From this would follow / = 6,448 for 2-atomic substances, 1 -=1+ yk and f = 7 for triatomic substances, or perhaps this ought to be expressed as follows: for molecules with an axis of symmetry 910 f= 6,448. In the absence of such an axis f =7 orf > 7. But this is still entirely uncertain. If the given relations are assumed to be perfectly correct, the reduced equation of state assumes the following form : 3 by ib Bice 5 WA by oy ee p= — . v? Din Per by 3 Din b, + 7 . For 4 constant, and so also —~ = 1 and 74-*= 3 we find back Him the same form as occurs in Continuiteit p. 127. This form is found from : f— 1 ie ) ae x + yp — lie ( pv? ler by If in this equation we put 2, ry and 7’= 1, we find: a relation, which had already been found before. Mathematics. —- “On metric properties of biquadratic twisted curves” By Prof. Jax pe Vriks. (Communicated in the meeling of December 28, 1912). § 1. The quadratic surfaces #* of a pencil cut the imaginary circle y?,, common to all spheres in the groups of an involution of order four. The lines 7, joining two points of the same group enve- lop a curve of class three. Any of these lines +, is the axis of a pencil of parallel planes cutting a determinate surface ®*° of the pencil according to circles. Such a plane cuts the base 9‘ of the pencil (®*) in four conecyclic points. So we find: the planes cutting a biquadratic twisted curve of the first species in four concyclic points envelop a curve of class three lying at infinity. § 2. Let / be the axis of a pencil of planes. Any plane A cuts eo’ in four points which will be denoted by 1, 2, 8, 4, whilst J/; will indicate the centre of the circle /mn. We consider the locus of the quadruples of centres J/ and take first the particular case where 1, 2 are fixed points and line / is a bisecant of 9*. As the centres /, and M, (of the circles 124, 123) lie in the plane A normally bisecting line 1,2 the locus (1/7) consists of a curve lying in 4 and of the locus of the centres J/,, J/,. But the latter consists of two different curves, as the points /,, /, never coincide during the rotation of A about / For a coincidence of M,, .M, requires that the circles 284 and 134 coincide; as 1 and 2 are tixed points, this only happens when 1, 2, 3, 4 are coneyelic, but then the four points W/, belong to different branches of the locus. § 3. The locus of the points J/,, J/, situated in 4 passes siz times through the midpoint J/, of 1,2, for the sphere on 1,2 as diameter cuts g¢‘ elsewhere in six points. So this locus is of order vight and will be indicated by «a. The plane /, at infinity contains the centres of four circles determined by the points of 9‘ at infinity. The remaining four points common to I, and pg, originate from two nodes generated as follows. If A touches y’, infinity of .4 with respect to all the ‘“cireles” lying in that plane ; so M, and MM, coincide then in that point of contact, but belong to different branches. Through / pass three planes containing four coneyelic points ; in the centre of each of the three corresponding circles 1234 the curve mw has a node. By assigning to JV, and JW, respectively the points 4 and 3 we establish a correpondence (1,1) between the curves u* and 9‘; so these curves have the same genus. As the singular points of a curve the point of contact is the pole of the line at of genus one are equivalent to 20 nodes, the sixfold point J/, and the five nodes already obtained form the singular points of w*. So this curve is of rank sixteen; its four tangents through .J/, originate from the four tangential planes of e* through / in which planes J/, and JJ, coincide. § 4. The locus of MJ, (and likewise that of .J/,) is a twisted sextic : ‘at infinity and the a’; its points at infinity are the points of @ points of contact of y*,, with planes through ¢. Evidently it has five points in common with /; so it is rational and of rank ten. The three curves m°, «,°, w,° concur in the centres of the circles lying in the three cyclic planes through /. Furthermore each curve we has still one point in common with «a. For in the plane 1 ), Jf, (M,) is at the same time one of touching v* in 1 (or in 2), J gives 124 —— 324 and therefore W,-— M,. the points J/,, M,; for3 912 § 5. In the case of an arbitrary line / the locus of the points J is a twisted curve w". Any plane A ar a point at infinity of 94 furnishes three points of TI, lying in different directions, and on v7, the curve has feo four ‘fold sae Moreover it possesses thyee fourfolds points in the cyclic planes through /. As any plane 4 bears four points J none of which generally lies on J, w?° has with / séeteen points in common. Each of the eight tangential planes of o* furnishes a tangential plane of g?°; so this curve is of rank forty. It is of yenus one, for one can assign the point Mg, to each point k of of. So the generally known formulas r=m(m—1) — 2 (h4+ D) — 38, p= 4 (m—1) (m—2) -- (A+ D-+8), where we have r=40, m=20, D=30, p=TI, give @=0) AA); So the curve has no cusps, but 140 apparent double points (bise- cants through any point). § 6. If the points 1, 2, 3, 4 of 9* form an orthocentric group, their plane 4 cuts all the ®* according to orthogonal hyperbolas ; then all the planes parallel to 4 furnish orthocentric groups. The planes cutting a director cone of ®* in two edges normal to each» other envelop a cone of the second class. So two concentric director cones determine four planes cutting the two corresponding ® and therefore all the ®* of the pencil in orthogonal hyperbolas. From this ensues: there are four systems of parallel planes cutting ot in orthocentric groups. § 7. We consider in any plane 4 through / the orthocentres Og of the triangles /mn, which fowr points lie with the points 1, 2, 3,4 on an orthogonal hyperbola @?. Evidently w? is the section of .1 with a ®* through 9‘; now we can bring through / a second plane cutting that ®? in an orthogo- nal hyperbola (§ 6). So any point of / lies on two curves w?, i.e. / is double line of the locus of the curves w*. Therefore: the locus (O) of the orthocentra Oy lies on a surface Q2* with double pot 1. In order to determine the degree of (Y) we remark that in a plane 1 through a point at infinity of gy‘ three joints O lie at infi- nity in the same direction, which proves that P, contains four threefold points of (OQ). If A touches the circle y?,, the point of contact / is separated harmonically by 7°, from any point of the 913 tangent, i. e. of the line at infinity of 4. So all the perpendiculars of the triangles /mm coneur in / and J is a fourfold point of (QO). But then the curve is of order twenty. If two points / coincide in a plane 4 the same happens with two points Ox. So through / pass eight tangential planes of w*" and as / contains evidently scvteen points of this curve, w?" is of rank forty. It is of genus one on account of the (1,1)-correspondence between the point / of e! and Oy. Pron op), r= 40, m=20 and D=24 (as there are two fourfold and four threefold points) we find (§ 5) B=0, 4 = 146. So the curve has 146 apparent double points. § 8. If 7 joins the points 1 and 2 of 9! the locus of the points O consists of three curves. For the points O, and QO, always remain separated, if dA rotates about / But on the contrary O* and O' belong to, the same curve; for the difference between the points 3 and 4 disappears as soon as 4 is tangential plane. We now can determine the order of the curve (Q,) as follows. We lookout in the first place for triangles 234 rectangular in 2. a To that ,end, we consider the cubie curve o*, which is the projec- tion of v* out of 2 on the plane at infinity. On each line through the trace 1, of 21 we determine the points 7, separating harmo- nically the projections of 3 and 4 from the circle y*,. As 9°, cuts the polar of 1, in three points, 1, is threefold point of (//) and this curve a quintic. Its points of intersection with @*, are 1, count- ed thrice, six points on y*,. and an other sextuple forming three Pa pairs of traces of mutually rectangular lines 23, 24. So through 1,2 pass three planes for which the angle 324 is a right one; therefore 1 is a threefold point of curve (0). If line 34 is normal to 12, the point QO, lies on 1,2. So line 34 generates a hyperboloid if 4 rotates round /; so by means of a section normal to 1,2 it is immediately clear that there are two chords 34 at right angles to 12. So five points 0, lie on /; therefore (O,) is a rational curve w,* of order sie with a threefold point. The line 7 is the biseeant of w," passing through the threefold) point. Moreover we find = 10, ie — Evidently there are three positions of -/ for which 312 isa right angle; so the points 1 and 2 are threefold on the locus of the points O,,0,. From this ensues that this locus is a curve o* with two threefold points. As 34 happens to be tangent four times, @ 8 is of rank. sixteen. 914 Evidently it is of genus one (see § 3). Furthermore we have D = 8 two double points on y7,). A= 12, p=0. The surface 2* (§ 7) containing the three curves w*, w,°, w," has threefold) points in 1 and 2. For, all orthogonal hyperbolas pass through these points. Two of these hyperbolas break up into the line /=1,2 and a chord 3,4 at right angles to it. § 9. If / has only point 1 with o* in common the locus of the points ( consists of an @* containing the points (, and an w** con- taining the three other points ©; this follows immediately if we consider the points at infinity. We determine the order 14 of the latter curve independently- by means of the number of times that one of the points O lies on / The planes containing two chords at right angles in 1 envelop a cone. of class six; for the chord 12 is intersected at right angles by three chords and bears fhree planes in which the chords 13 and 14 are normal to each other (§ 8). So the triangle 1/4 is rectangular in 1 for sie positions of .f and in each of these cases a point ( coin- cides with 1. The chords of 0* intersecting / form a scroll of order sive with 1 as double director line. So there are five chords normally cutting /, each case of which furnishes a point 0 on /. So we find an w"* with sixfold point 1, through which point passes still a fivefold secant. It is of yenus one. as we can assign the point O, to the point & of of. Fron m= 14, D= 25, r= 28 (on / six tangents rest) we then derive B=0O, h= 52. The curve w" has / as fivefold secant, is therefore rational and of rank: ten (hk = 10, @= 0). Now the surface £* has a threefold point in 1. § 10. We still consider the seroll, locus-of the lines of Evrer, e. = M, Ox, lying in the planes 4. , Between the points of the curves a? and w* ence (1,1). By projecting the corresponding points Wand O out 0 exists a correspond- of an arbitrary line @ we generate a correspondence (20.20) between the planes of pencil (a). Of the 40 coincidencies 4 lie in each of the planes through @ and one of the two points /, each of these points In each of the other coin- 0 being fourfold) point of 12° and of cidencies lies a line ¢ resting on a. So the scroll (e) is of order 32. We can verify this by means of the locus of the centres of gravity G, of the triangles Jinn. It passes three times through each of the four points of g* at infinity and is therefore of order twelve. As s 915 this curve is also in (1,1)-correspondence with 2’, whilst it never happens that G;, and JA/, coincide, the reasoning given above leads here anew to the order 32 of (¢). § 11. A’ twisted biquadratic curve oe of the second species lies on one quadratic surface Y~ only. It can be considered as partial intersection of Y* with the cubie scroll +* generated by the bise- cants 4 of o* cutting a given bisecant 4,. Each point of 4, bears two bisecants 6,6’ and the plane (4,4’) passes through the single director line g of °. The pairs 6,6’ determine an involution on g. the double points of which lie in two double tangential planes of o'. Reversely the line common to any two double tangential planes of g* is single director line of a +*; for the bisecants lying in these planes are cut by one bisecant 6, only and this line is the double director line*) of >*. We now determine the number of orthogonal pairs 6, 4’. Any eglge of a director cone A* of >" is at right angles to three other edges; so the planes of the orthogonal pairs envelop a cone of class three. On A®* the pairs 6,’ determine an involution and the planes of the pairs of edges pass through an edge parallel to. From this it follows that g bears three *) orthogonal pairs /, 4’. As the lines g form a congruence, there are #* planes 2 con- taining orthogonal bisecants; so these planes envelop a surface 2? of class three. The planes intersecting ¥? in orthogonal hyperbolas are parallel to the tangential planes of a cone of the second class and envelop therefore a conic *2 at infinity. Evidently a common tangential plane of *2 and *2 cuts o* in an orthocentric group. So: the planes of the orthogonal quadrangles inscribed in @* envelop a developable of class six. § 12. We consider once more the locus of the quadruples of orthocentres in the planes / through a line /, If 4 contains a point 1) The lines g form a congruence (6,3). *) If 55 is represented by the equation (aw + by 4- cz + dja? = (ze + bly + clz + d')y? we find for any pa 0, ' the equations y = Aw, aw + by 4- cz + d= 2 (ae 4- bly 4+ ce + a). So the orthogonal position of the lines (a) and | ) requires evidently (c'a?—c)? (L—2?) 4+ (a—a's?)?— 2? (6—8'7? )? = 0. So there are three orthogonal pairs, 916 of of at infinity, the centres O,, 0,, O, lie in the same direction at infinity and give rise to a threefold point at infinity. As we have found in the case of o* (§7) 7%, contains tira fourfold points of 0). But TP, bears two points V more, originating from the two trisecants of o* meeting /. For if in a plane ./ the points 1, 2, 3 are collinear, the three perpendiculars of the flattened triangle 124 are parallel. Then the four orthocentra lie on the normal q¢ through 4 on the trisecant; so g is quadrisecant of the curve (() and the order of 0) is 22. There are six tangents of o* meeting / and therefore as many iangents of w** doing likewise; as @** has evidently 18 points in common with /, this curve is of rani 42. As it corresponds in genus io o* and its singular points are equivalent to 24 double points, we find by means of the formulas given above 3= 0, h = 186. § 18. If / contains the points 1, 2 of o*, the iocus (V) breaks up into three different curves. As in § 8 we find here through 1, 2 three planes bearing chords 23, 24 normal to each other, so 2 is threefold point of (0). But now the line 34 describes a cubie scroll (with double line /) if A rotates about /; so 42 is eut orthogonally by three chords. So we find for (Q0,) and (Q,) two rational curves of order seven. The locus of O, and Q, is once more an w* with two threefold points. The three curves are situated on a surface 2° forming the locus of the orthogonal hyperbolas 1234. For, in the three planes 4 bear- ing a chord 34 normal to (= 12, the hyperbola degenerates into these two chords and /; so / is threefold line from which ensues moreover that 1 and 2 are fourfold points. So we may conclude that for an arbitrary position of / the corre- sponding orthogonal hyperbolas form a surface of order five with / as threefold line. Let us still consider the case that / is a frisecant, containing the points J, 2, 5 of o'. Then QO, is always at infinity and each of the remaining three points ( describes its own curve. If 4 coincides with 1, (, is at infinity, which also happens if 4 contains a point of 6* at infinity and if A touches y*,. From this we conclude that each of the points (,, 0,, O, deseribes a rational curve of order seven, with threefold points in two of the points 1, 2,3. In fact each of the points 1, 2, 3 is vertex of a rectangular tri- angle for three positions of 4,.or more exactly of two suchlike tri- angles; for, if 14 is normal to the trisecant, 1 is orthocentre of 124 and of 134. Ld 917 Farthermore there are 38> 6 positions of 4 for which O coincides with 4, leading to a point common to 6! and (Q). From this we may still conclude that the planes in which the quadrangle 1234 admits one right angle envelop a surface of class 36. As to this we have to bear in mind that any plane through a trisecant of o* having the vertex of the right angle on that trise- cant must be counted twice as tangential plane. Likewise we find that the planes for which the quadrangle 1234 admits two equal adjacent sides envelop a surface of class 33, § 14. Let us finally consider the locus of the centres M/;, of the circles circumscribed to the triangles /imn in the planes 4 through J. Each ‘of the two trisecants cutting 7 furnishes again a point at infinity; each of the planes through a point of o* at infinity deter- mines three points of 1M, and each of the tangential planes of y*. through / contains a fourfold point at infinity. So we find a curve we? cutting 7 in 18 points, with the rani 42. If 7 is the drsecant 12, the points J/, and M, generate a plane with the midpoint J/, of 12 as sixfold point; for the 1th 18 curve | sphere with 12 as diameter determines on 6* the vertices of six rectangular triangles with 12 as hypothenuse. As we can once more assign J/, and J/, to the points 4 and 3, w® is like o* of yenus zero. So its singular points are equivalent to 26 double points. So it must possess besides the double points on y?,, and the sixfold point M, still fow double points more. These can only originate from concyclic groups 1, 2,3,4. So we conclude: the planes cutting 6* in four concyclic points envelop a surface of class 4. +) So the curve w? corresponding to an arbitrary line / has four fourfold points in the centres of the circles each of which -contains a quadruple of points of o*. As it cuts TP, in two fourfold points more, we get ) = 36. Byameans Of 7,=-42 and) p—0O we find p= 0, A =—174. If 7 is trisecant 128, each of the points J/,, VM a plane curve of order seven with a sixfold point. M, describes q> 1) This is in accordance with the results obtained by Mr. M. Sruyvaprt in his inaugural dissertation (Etude de quelques surfaces algébriques engendrées par des courbes du second et du troisiéme ordre, Gand, 1912; see Chap. I, Sur les plans coupant un systeme de lignes en six points d'une conique). 60 Proceedings Royal Acad, Amsterdam. Vol. XY. 918 Mathematics. - “On the correspondence of the pairs of points separated harmonically by a twisted quartic curve.” By Prof. JAN DE VRIEs. (Communicated in the meeting of November 30, 1912). § 1. We indicate by P and Q two points, lying on a chord ofa twisted quartic curve of the jirst kind, separated harmonically by this curve o*. As any point P lies generally on two chords, in the correspondence (P,Q) to any point P two points Q are conjugated. If F moves along a line /, Q describes a curve 4° of order sia. For any plane 4 through / cuts 0‘ in four points S; and contains therefore six points Q,;, where QQ, lies on a chord S;S; and is harmonically conjugated to the points 2; common to that chord and /. If 7 is an arbitrary line, Q never lies on / when 1 rotates about /. The line Q,,Q,, is separated harmonically from / by P,,S, and S,S,. By assuming a position for -/ in which S, and S, coincide with Q,, we find for Q,,@,, a tangent of 4° separated harmonically from / by P,,S, and P,,S,, whilst an other tangent of 7° takes the place of Q,,Q,,. So each of the eight tangential planes of 9 contains two tangents of 4°; sd the rand of this curve is sixteen. Moreover we find that A° has eight points in common with 9°. § 2. The line p connecting the two points Q, Q’ conjugated to P describes a regulus 4’? if P moves along /. For p is the polar line of P with respect to @', i.e. the intersection of the polar planes of P with respect to any two quadratic surfaces through 9', and these polar planes describe two projective pencils. Let us now consider one of the two lines p cutting 4 The corresponding point P? bears two chords S,S, and S,S, lying in the 109 ae Q,,,@,, lie on a line m through P harmonically separated from / by the chords SS, and WS, plane = /p. The points Q,, and Q,, lie on p, the points Q Xia ,. As A® lies on the regulus 7°, m isa line of 4. Any tangential plane of 4° contains therefore a quadri- secant of 4° and beth the reguli of 4° are arranged by A°® in a correspondence (2,4). Evidently the quadrisecants g are the polar lines of / with respect to the quadratic surfaces through g*. § 3. If we assume for / a chord of ¢*, the locus of Q breaks up into four parts, i.e. the chord / itself, the tangents 7 and 7’ in the points R, Rk’ common to / and ¢*, and a tiisted cubic Aa ihe polar line p now connects a point Q of / with the point Q’ of the second chord & passing through P. This line deseribes a regulus ee te 919 having with 4? the line / in common. So the locus of Q’ = 4/ is a curve 4* through P and FR’, as / is to have two points in common with it and FR and &’ correspond amongst other points with them- selves; the curves 4* and 9 have four more points in common. 4 § 4. If / is a unisecant of 0! in FR, the locus (Q) degenerates into the tangent r and a 4°. Any plane through / contains besides R three points Q; of these two must be combined with F, if the plane contains the tangent 7. The quadrisecants g of / become here trisecants; for 7 rests on each of the polar lines g of / (§ 2). The plane gr touches eg! in A and contains therefore two points Q united in A. In relation with the results obtained we conclude from this that by the correspondence (?.Q) to a unisecant of o* a twisted curve of order five is conjugated having a node in the point common to the unisecant and o', x So the curve is of rank ten. Through / pass six common tangential the nodal tangents lying in the plane /r. planes of 0* and 4°, § 5. The vertices 7). of the four quadratri¢ cones containing 9! are singular pots of the correspondence (7?.Q). For 7 bears ce’ chords and the corresponding points @ lie on the conie rt tothe: polar plane +, == 7,7,7, of T ‘yy - T, as vertex. , common , and the quadratic cone with To the line 7,7’, as locus of points: ? correspond in the first place the two conics t,° and r,* and moreover the line 7,7), counted tivice. For the points S; in any plane through S,S, form a complete quadrangle of which 7 and 7’, are diagonal points; in the third diagonal point @,, and Q,, coincide, whilst of the remaining four points @ two lie in +, and two in r,. So to any point of 7,7, correspond two points of 7,7’, and inversely. If 7 contains the point 7, only, the six points @ lying in a plane 2 through / consist of two points in tr, and on7,? and of four points lying on the Ime common to 4 and the polar plane of / with respect to the cone projecting 0* o* out of 7\. Then the curve (Q) breaks up into the cone r,° and a plane curve 4‘. In the two tangential planes of the cone passing through / the two points @ lying on r,* coincide with two of the remaining four in a point of intersection of 7,? and 4* where the latter is touched by the edge of contact. § 6. Let us now consider the surface of the points @Q corre- sponding to the points P of a plane J If Se are the points common to HW and o', the six lines Sy; form the intersection of JZ with the 6O* 920 locus under discussion. So it is of order siz. As it contains at the same time the lines touching g* in S,, these points are nodal points. * lying in JZ correspon! two points Q coinciding with 7%, whilst to the point of “ lying on 7,7) two To the two points of rt, points on 7, 7, correspond. From this ensues that the four points T have to be also nodes of JI. So to a plane corresponds a surface of order six with eight nodes and ten lines. § 7. Let us now consider the correspondence between two points P,Q separated harmonically by a fvisted quartic curve of the second hind 6‘. As P bears three chords of 6*, it is conjugated to three points QQ. To the points P of a line / correspond the points Q of ; for each plane through / contains six points Q. The three points Q corresponding to P lie in the polar plane of P with respect to the quadratic surface H? through o*. The plane II rotates about the polar line /’ of /, if P moves along 1. Se /’ is a trisecant of 4°. a twisted curve 4 cutting / is of order nine; so nine of these chords also intersect /’. To these nine belong the two trisecants of o' cutting / each of which represents three chords; they have to meet /’, as they lie on the hyperboloid #/* and are at the same time trisecants of A°. The remaining three chords cutting / and /’ determine the three points Q on /’. The seroll of the chords of 6 § 8. Each of the six tangential planes of o* passing through / contains a point and two tangents of 4°; so this curve is of rank twelve and rests in siz points on 6*. By S; we represent the points of o* lying in a plane drawn through /; the chord 6=S,S, is paired to the chord 6’=— S,S, and now we consider the corre- spondence between the points / and P’ in which / and 6’ intersect /. As P bears three chords we find a (8,3). If 6 and 4’ intersect / in the same point P, only the third chord through P furnishes a point ?’ not coinciding with P; from this ensues that the coinci-— dencies of the (3,8) coincide by two in a double coincidency. So through / three planes pass for which 4 and 6’ intersect in /; the line 4 separating / harmonically from 6 and 6’ then contains four out of the six points Q, the remaining two lying on 4 and 6’. So the curve A° admits three quadrisecants. § 9. Let / be a chord of o* and S, and S, the points it has in common with o'. Through any point P? of 7 pass two more chords ~~ 991 bb’ of of. So the locus of the points Q lies on a cubic seroll A* with double line /. In the plane b/ two points @ coincide in S,, two other ones in S,, whilst Q,, lies in / and Q,, in 4. If P moves along /, q=Q,,Q,, deseribes-a cubie scroll ®* with double line /; for through @,, pass two lines qq’ to the points Q,, of the chords 6,6’ concurring in the point P corresponding to Q,,- The scrolls 4*, ®* have the trisecants ¢,,¢, of of passing through S, and S, in common. For if P coincides with S,, ¢, becomes a chord 6 and, as Q,, coincides then with S,, at the same time a line 4g. As / is nodal line for both scrolls, these surfaces have still a twisted cubic 4* containing the poimts @Q,, in common. In the planes touching o* in S, and S, the point Q,, coincides with the point of contact; so S,S, is a chord of 4*. This curve intersects o* in the two points the tangents of which intersect S,S,; it has for chords the single director lines of the scrolls 4°, ®*. So by the transformation (P.Q) the chord / passes into the system consisting of 7 itself, the tangents s,,s, and a tevisted cubic. Evidently a ¢risecant ¢ is transformed into that line to be counted thrice and the tangents in the three points it has in common with o*. If 7 touches of in S,,, the scroll ®* becomes a cone with nodal edge /. In the osculating plane of 6* in S,, g lies along /; so this 34 plane is common tangential plane of 4° and *, having still in common the trisecant through S,,. The residual intersection 4* touches in S\, the tangent of o*. § 10. If 7 is unisecant of ot in S the curve 4° breaks up into the tangent s of of in S and a curve 4°. The polar line /’ of / becomes chord of 4°, s being one of the three chords cutting / and l’. The plane /’S touches H* in S and is therefore polar plane of P=S; it contains the tangent s and the trisecant of 6’ on which S lies. Of the three variable points Q@ common to 4° and a plane through /’, two coincide with S and only one lies outside S. Any plane through / contains besides S three points Q and has therefore in S two points with 4° in common. Also the plane /’S not passing through / has in S two points in common with 4°; so S is a node of 4°. The plane /s contains beside S only one point @; so it passes through the nodal tangents of the node. So to a unisecant corresponds a fivisted quintic with a node. The curve is of rank eight, through / passing tour common tangential planes of o* and «4°, 922 Mathematics. - “On a line complex determined by two twisted cubics.” By Prof. JAN DE Vrirs. (Communicated in the meeting of November 50, 1912). § 1. We will indicate the chords of the giver twisted cubies o*, 6° by eas Any plane 2 contains three chords + and three chords s, therefore nine points P=rs. In the focal system (P.) each point has in general one focal plane, each plane nine foci («= 1, B= 9). If 2 rotates about the line /, the points determined on / by two complanar chords r,s are conjugated to each other in a correspondence (3,3). As each point of coincidence furnishes a point P= vrs, / contains siz points P, the focal planes of which pass through 7; so the third characteristic number, of (2,2) is sia (y = 6). Let / represent one of the ten common chords of @* and 6*. Any ‘ focal planes. i.e. all the planes 3 through 4. point B of 4 admits a Any plane 3 admits four foci not lying on 4, whilst at the same time any point 2 of 4 is focus. So the lines / are loci of singular foci and singular focal planes. If P is assumed on e@*,s is a detinite chord of o*, whilst 7 may be any line connecting P? with an other point of 9°; then any plane through s can figure as focal plane z in which P counts for two of the nine foci. So the curves o* and 9° are singular curves for the focal system (2, 2). § 2. The polar planes of P with respect to the oo* quadratic surfaces through o* have a point R on 7 in common; P and R can be said to be separated harmonically by g*. If P deseribes any line /, the polar planes of P with respect to three quadratic surfaces of the net not belonging to the same pencil rotate about three definite lines and describe therefore three projective pencils. So the locus in four points; for on the 3 of R is a twisted cubie 4! a , Infersecting o four tangents 7, of @*, resting on /, the point conjugated to P is every time the point of contact &, °). We indicate by S the point on s harmonically separated from P by «6? and consider the relationship between F and S. To any plane ¥ as locus of S corresponds a cubie surface 1° of !) This generally known involutory cubic transformation has been investigated thoroughly by Dr. U. H. Scnovre (Nieuw Archief yoor Wiskunde, 2nd series, vol. LV. °1900, p. 90). 923 points P; as 77 intersects the twisted cubie 2* described by P when R moves along / in nine points, the correspondence (2S) is of order nine. A point of coincidence of FR and WS ean only present itself when 7 and s coincide, i.e. on a common chord 6. On any of the ten 4 the pairs (P,/) and (PS) generate two involutions, of which A, H, may represent the common pair. By assuming R in Ay, we find A; for P and Hy, tor S; so H, and //, are points of coincidence of (RS). So this correspondence admits fiventy coincideneies lying in pairs on the fen common chords 6. As a point FR, of v* corresponds to each point P of the tangent On daha tae Re 5 » corresponds to each point S of the twisted cubie 6,* into which 7, passes by the transformation (7,S) ; evidently 6,* has -3 four points in common with 6°. Consequently the curves @* and 6° are. singular curves of the correspondence (RS). If AR deseribes the tangent 7, of 9°, P remains in the point of contact of 7,; so the poimt S* conjugated to P is singular and corre- sponds to all the points of 7,. Evidently the locus of S* is the rational twisted 6’ into which «* passes by the transformation (P,S). So the correspondence (RS) admits two singular tivisted curves of order nine, o° and On 3 3 As the developable with 9* as euspidal curve cuts 6° in 12 points o* and 6° have twelve points in common; likewise 0° rests in 12 points on ¢*. § 3. We now consider the lines p= RS. If P describes the line /, p generates a scroll of order six; for we found above that the plane a —= P,, passes through / in six positions (§ 1). The line p generates a complea. We determine the number of lines p belonging to a pencil with vertex 4 and plane A. If & describes a ray / of pencil (Z,4), S generates a curve intersecting A in nine points (§ 2); we conjugate to / the nine lines /’ connecting these points with Z. In this manner we get in the pencil a correspondence (9,9) each coincidence of which furnishes a line p connecting two points & and S corresponding to each other. So : The complex (p) is of order eighteen. Evidently the 20 points H are principal points of the complex; each complex cone passes through these 20 points. § 4. Any point &, of 9° issingular, for it bears the lines p connecting it with the points S of the corresponding curve 6,° (§ 2) and so its 924 complex cone degenerates. Consequently the curves 9* and o* lie on the singular surface of the complex. The edges of the om cones projecting the curves o,* from their corresponding point A, as vertices form a congruence of which we will determine order and class. The locus of the curves o,° is the surface S'*? into which the 3 developable with @* as cuspidal curve is transformed by (P,S). The cubic¢ cones with an arbitrary point J as vertex and 0° and o as director curves, intersect in 9 edges, each of which connects a a point S of 6,° with a point R’ of 9°; if R’ coincides with the point #, to which 6,*° corresponds we have to deal with a ray of the congruence passing through J/. We will conjugate these 9 points ? to R,. The line MR’ cuts the surface S's mentioned above in “25. Soe tones correspond 12 points R. The correspondence (2,, 2’) has therefore 21 coincidencies, i.e. the order of the congruence is 21. Any plane gw contains 3 points R, and each of the corresponding 12 points S lying in general on different curves 6 curves 6,° has 3 points S with g im common; so the class is 9. So the lines S,R form a congruence (21,9) and an other congruence of the same type is formed by the lines S,2. The two congruences admit successively 0° and «* as singular curve. § 5. Any point S* of the rational 6° (§ 2) is the vertex ofa pencil of complex rays p the plane of which contains the corresponding tangent 7,. So the curves 9’ and ov" lie also on the singular surface. The x' pencils with vertices S* form a congruence which we will study more closely. In any plane gw lie 9 points S*; the tangents 7, corresponding to these points determine 9 rays p lying in g«; so the congruence is of class nine. To any point S* we make to correspond the 9 points S’ of 6° which can be projected out of the arbitrary point J/ in a point of » The line JZS’ cuts + tangents 7,, so S’ is 0? the corresponding tangent 7 conjugated to 4 points S*, As any coincidency SS’ —= S* is due to a ray of the pencil with vertex S*, Jf bears 13 lines AS*, i.e. the congruence is of order thirteen. So the complex contains eo congruences (13,9) each of which is built np of %' pencils. They admit successively 6’ and 9° as singular curve. § 6. To the complex (p) belongs the system of generatrices of the developable determined by o* and 6°. Any tangent 7, cuts four tangents s, and reversely; so the points of contact /, and SS, of the = Fi Oe Le a ae 925 tangents conjugated to each other in this way are in correspondence (4,4). By projecting the pairs of this correspondence out of a line a, the pencil of planes (/) is arranged in a correspondence (12,12). As each coincidency furnishes a line p= &,S, resting on a the developasle under discussion is of order 24; it has g* and o6* for fourfold curves. Any chord 7* of o9* meeting 6° belongs to the complex, for in the common point of 7* and o* the points 7? and S coincide. The 3 chords r of 0? cutting a line / generate a seroll of order four with o* as nodal curve; so the locus of the chords » is a seroll of order 12. On the latter surface ¢* is a sivfold curve, for through any of its points pass the common edges of the two cones projecting 0’ and o*. So the complex (py) contains two scrolls of order twelve, the generatrices of which are chords of one of the curves 0°, 6° and secants of the other. Let p* be a chord of 9* not meeting 6*; then the tangent 7, in one of the points #, common to 9° and that chord must contain the point P. If P moves along that tangent, S describes a curve o,°; 3 the cone projecting the latter curve out of #, has 6 edges in common with that of which y* is director curve. So any point of y* bears 6 rays p*. As an arbitrary chord ~ can be cut by chords p* in its points common to 9° only, so all in all by 12, the locus of the chords under discussion is of order 12. So the complex contains two scrolls of order twelve, built up out of chords of one of the curves 0%, 6°. Physics. — “Determinations of the refractive indices of gases under high pressures.” Second communication. “On the dispersion of au und of carbon dioxide.” By Prof. L. H. Simersema. (Communicated by Prof. H. KAmERLINGH ONNu«s). (Communicated in the meeting of November 30, 1912). 4. The dispersion of air. This has already been repeatedly determined both for the visible spectrum and for the ultra-red and ultra-violet rays. The results, however, diverge considerably, and, moreover, the dispersion has never been measured under high pressure. Through the kindness of Prof. KamprnincH ONNES compressed air was placed at my disposal with which dispersion determinations were made in exactly the same way as those for hydrogen described in a former paper. : 926 In the following Table are given the results of three series of observations. For the meaning of the symbols employed reference may be made to the corresponding Table for hydrogen published in the paper just mentioned. Air. a 0.546 Pressure Tem- hy (a= 0.044 1, = 0.509 1 g= 0472 = 0.496 = 0.408 in pera- a = —S = atm. ture inealy Ka re Fa Ke ey kp ky ky Ry ky 71.4 12.75°C.| 823.52 | 0.84350 | 1.07697 | 1.16423 | 1.26722 | 1.37179 71.4 12.90 $21.23 0.84346 1.07702 1.16418 1.26724 1.37176 70.6 13.19 810.84 0.84352 1.07697 1.1642) 1.26718 1.37175 66.4 13.42 759.81 0.84350 1.07697 1.16419 1.26727 1.37183 48.7 13.58 550.27 0.84352 | 1.07698 | 1.16421 1.26716 | 1.37177 31.9 13.67 359.50 0.84339 1.07701 1.16417 1.26725 1.37171 67.7 9.25 790.70 0.84345 | 1.07697 | 1.16415 | 1.26723 1.37187 67.6 10.15 787.92 0.84349 | 1.07698 | 1.16419 | 1.26735 | 1.37191 66.2 | 10.35 766.84 0.84353 1.07695 1.16414 1.26724 1.37184 49.2 | 10:75 567.32 0.84351 1.07698 1.16411 | 1.26723 | 1.37178 | 32.2 | 10.95 367.70 0.84350 1.07695 1.16414 1.26721 1.37175 OR 12275; 1170.71 0.84343 1.07698 | 1.16418 1.26729 | 1.37203 101.8 | 12.80 1168.50 0.84340 1.07699 1.16412 1.26732 1.37204 0 8 100. 13.03 1147.43 0.84338 1.07700 1.16419 1.26732 1.37204 | Mere 13.39 947.50 0.84337 1.07699 1.16415 | 1.26729 1.37207 65.5 | 13.89 745.71 | 0.84339 | 1.07704 1.16427 1.26728 1.37206 | 989.6 | 13.96 446.50 0.84328 | 1.07697 1.16415 1.26725 1.37199 | The values obtained for the various gas densities are pretty well constant, just as was found to be the case with hydrogen. The deviations are not any more one way than the other, and we can therefore conclude that the dispersion of air is constant up to pressures of about LOO atm. Saree a 927 The mean values are: hea hk. A) hk hy hy, ky, 4 hy, hy, ky, 0,84345 1,07698 116417 1,26725 1.37188 ae (lof + (),6 s= 11 (0) a= Al Ewe Hence we get for the dispersion constants inl “(vac.) —n-l 6 a 0.64403 0.99446 + 0.000020 b 0.54623 1 G 0.50873 1.00304 + 0.000006 d 0.47234 1.00669 + 0.000009 e 0.43597 1.01145 + 0.000010 if 0.40478 1.01662 + 0.000023 In order to be able to compare these with the results obtained by other observers, dispersion -constants for the wave-lengths I used have been obtained from the results given by Mascarr’), Kaysnr and Runek*), Perrwau*), Scope‘), Hermann *), Rentsco.er °), Loria‘), Kocn *), Curaprrtson *), and Gruscuke **), either by graphical inter- polation or by caleulation from dispersion formulae given by them ; these results are collected in the following Table. Correspondence between the present results and those given by Prrrvau and by Kocn is quite good both with hydrogen and with ar. Only at 4= 0,644 does Kocn find a greater dispersion for both gases. For air, the agreement with Hrrmann and with CurHprrtson is also very good. 1) K. Mascarr. Ann. de l’éc. norm. (2) 6 p. 60 (1877). ?) H. Kayser and J. Runee. Ann. d. Physik 50 p. 312 (1893). 3) W. Perreau. Ann. d. Ch. et de Ph. (7) 7 p. 325 (1896). 4) K. Scueer. Verh. d. D. phys. Ges. 9 p. 27 (1907). 5) K. Hermann. Verh. d. D. phys. Ges. 10 p. 477 (1908). 6) H. CG. Rentscuter. Astrophys. J. 28 p. 357 (1908). 7) S$. Lorm. Ann. d. Physik. (4) 29 p. 619 (1909). 8) J. Kocu. Nova acta reg. soc. Scient. Upsaliensis (4) 2 N’. 5. p. 40 (1909). *) CG. and M. Curnpertson. Proc. B.S. (A) 83 p. 153 (1909/10). I”) G. Gruscuke. Ann, d. Physik, (4) 34 p. 807 (1911). of in ) eee — ee and y= — 157) 10 al P2073 Ke so that the pressure coefficient has become eee, greater at the lower temperatures. The increase obtained between 273° K. and 90° K, changes again to a diminution. The accuracy of the measurements is still too small to allow us to attribute any significance to this diminution at the lowest temperatures. If we consider the decrease — vv in the resistance for p = 100 atm., we find that it approximates to zero at the lower temperatures. Thus we find for Pb;: 273° K. for p=100atm. —Aw=0,017 @ OD Pm ARE ae 7 — Aw= 0,008 AVES ING 55 ns 7 — Aw=| 0,001. Physics. — “J/sotherms of monatonuc substances and of ther binary miwtures. XIV. Calculation of some thermal quantities for argon”. By H. KamertinGH Onnes and C. A. CRoMMELIN. Comm. N*. J338c from the Physical Laboratory at Leiden. (Communicated in the meeting of November 30, 1912). The empirical reduced equation of state for argon, VII. A. 3, published some time ago *), enables us to calculate a number of ther- mal quantities which are essential to a knowledge of monatomic substances in general and of argon in particular. These quantities may also be obtained graphically. Calculation by means of an equa- tion which fits the experimental results over the whole region of observation allows, however, a much greater accuracy to be attained. In tl 1 (2 om n the present paper“) we give values o —}),{— | se ar ),’ \aT? J, yn (Op (dr 7 (8 ; a 22 een E ik = = . —p, (AMAGAT’S pression inte- Ov Jr 0 a 1) E. Lisert: Upsala Univ. Arsskrift 1903. 2) H. KamerRLINGH ONNes and C. A. CromMELIN, Proc. June 1912, Comm. No. 128. 3) Already indicated in Suppl N’. 23, note 492, p. 146. Preliminary values obtained by C. A. CromMetin for some of the quantities here discussed have already been published by E, H. Amacar. CG. R. 9 April, 1912. 9538 / \ rieure ')), and of ReinGanum’s a, ap = | ae »| vw, caleulated as functions of the temperature and of the density from equation Vil. A. 3%). The temperature is expressed in Krtvin degrees and is calculated from O° C.; the pressure is expressed in international atmospheres *). The importance of a knowledge of these quantities especially as functions of the temperature has already been repeatedly insisted upon‘) so that we need say nothing further here upon that point. We shall only say that according to the chief vax per WAALs equation : Op Ou ? with constant ay, Oy and Ry, - ; ) and wp should be inde- v Ov/T 2 pendent of the temperature, and consequently (sa | should vanish, so that the deviations which they all show may be taken as a measure of the degree to which argon deviates from the simple assumptions regarding molecules accepted by Vax per WAALs in deve- loping his principal equation. Agreement, at least approximate, with the chief van per Waats equation would first be expected in the monatomic substances, and therefore the investigation of these quantities for argon as well asa comparison of the results with those for substances of more complex molecular structure {s of the greatest importance, Consideration of the quantity introduced by Reincanum °), ee ‘Op Ou a= =| 755) -»|=-(5), enables us to see that, as far as the mutual actions of the molecules is concerned, the assumptions upon which van ppr Waatrs founded his chief equation with constant ay, 6, .and Ay must undergo some modification such as has recently been introduced by van Der WAALs in the various developments of the consideration of apparent association. If we retain for the moment the most immediate assumption suitable for monatomic substances such as argon, that the atoms are incompressible, then changes in a, would be wholly due to deviations of the molecular 1) KE. H. AMAGAtT, numerous papers in the C. R. collected in “Noles sur la physique et la thermodynamique™. Paris 1912. *) For the notations used in this paper see Enc. math. Wiss. V. 10. Suppl. NY. 23. 5) Ene. math. Wiss. V. 10. Einheiten. a. *) M. Remeanum, Diss. Géttingen 1899, Ann. d. Phys. (4), 18 (1905) p. 1008, Suppl. N°. 23, p. 140 sqq. *) M Reineanum. Diss. Gottingen 1899, On + 22 20 +0.0764 40 1589 60 2471 80 3409 1000 120 140 160 180 200 220) 240 260 280 300 320 340 Op Oe 0° {-0.0766 1595 2485 3431 — 20° +-0.0768 1603 2501 3457 — 40° | — 60° -+0.0770 | +0.0773 1612 1624 2521 2545 3490 3531 4517 4578 — 70° - WISE EIS I — 80° — 90° | — 100° | — 110° | — 113° | — 1160 | — 149° +0.0775 -++0.0777 | +0.0779 | +0.0781 | +0.0784 +0.0785 10.0786 -++0.0787 1630 2559 3556 4615 1638 2515 3584 4657 5790 "1646 1655 1665 1669 1672 1676 | 2593 2614 26372644 2652 2660 | 3615 3650 3690! 3703 3117 3731 4704 4159 4821 4841 4861 4883 5857 5934 6022 6051 6080 6110 T173'|' 7292 7331 7371 7411 8473 8627 8678 8730 8783 | 1.0030, 1.0098 1.0159 1.0227 1580 1662 1747 3142 3243 «.- 3348 | 4913 5041 | 6683 6839 8568 8757 | 2.0589 2.0817 2769 3044 5136 5467 | — 122° +0.0788 1680 2668 3745 4904 6141 7453 8837 1.0296 1833 3455 5172 6998 8951 2.1053 3329 5810 : . Sort isety fouor fs | | | | | | Ore £96 £6 (ee en | | | | | | 0ze ck sfokkC Gs | | ooe “ecg oro 0z9 | | | | | 08z oes aze zie | vroth iy | 092 ser Zeb Oc . | | Oz gee ecg bbe EE | | 02z ez SZC ere | | | | 002 zee 8zz 4d o1z lz | | | | 0g! zsi 6LI CLI IL col haa 4). oe ie) lost IPL Sel cel 0el 91 IL | | «| OFI 901 ZOl 001 L6 £6 zs €L £9 0z1 $L "Wel: 69 89 99 89 Ig bP 6€ ce toe | 001 St Lt oF eh et LE ce og 4 ve sI ca rat ol 08 82 LZ oz 9% 42 lie 6t LI Tt +1 Ol 6 L 9 09 el Zl Shee It i ol 6 8 9 9 € p € € OF £0000'0— €0000°0— ¢0000"0 — 0000 0 — €0000"0— 200000 — zo000"0—'¢0000°0— 10000°0—20000'0 ~ 10000°0—Z0000°0— 19000°6— 10000 °0— 0z | ocel— | ob LI— | ool l— joshi | o0II— | o001— 006 — | o008— o0L— 009 — o0h— | AC— | A ooz+ | No ; i MESO Ieee We Ie oO oN | Ou Ov + 10° OF hf) — 40° — 60° | — 70° TWIN SVE SOU — 80° —— Oe | = 00m peor — 1139 | — 116° G2 | pee 20 + 1.150! 1.198 ++ 1.254/-+ 1.314] 4. 1.381} + 1.417 + 1.454| + 1.494] + 1.583) -- 1.579) + 1.593) + 1.604) + 1.620) -+ 1.635 | 6.387, 40 60 80 100 | 120 140 160 180 200 300 320 340 4.525 9.996 17.44 4.703 10.37 18.05 4.905 10.79 18.75 | 5.134 | il 77 19.55 29.79 5.388 11.82 20.46 31.15 5.523 12.12 20.98 31.92 5.670 12.43 21.53 32.75 45.91 5.826 12.77 22.11 33.65 47.18 5.990 13.14 22.74 34.62 48.55 64.38 81.94 6.163 13.52 23.42 35.65 50.03 66.38 84.54 104.4 6.218 13.64 23.63 35.98 50.49 67.00 85.35 105.4 127.2 150.5 6.273 13.76 24.84 36.31 50.95 67.63 86.18 106.5 128.5 152.2 177.4 204.4 233.2 263.8 296.5 331.3 6.331 13.89 24.06 36.64 51.42 68.27 87.00 107.6 129.8 153.8 179.4 206.9 236.1 267.4 300.7 336.4 14.01 24.27 36.97 51.90 68.90 87.83 108.6 131.1 155.4 181.4 209.3 239.1 270.9 305.1 341.7 | | (9962 016z 998z - | | | | ove jotee Le6z S682 | | ze ‘1108 1L6z 186 | | 008 ocoe Z10¢ PL6Z | | | | 087 9608 0908 P08 092 ogie cig IS0¢ | | Fz lize LLIg PrIe Olle | | | 0zz SLZe che zlze Ogle | 002 zee 6Ig¢ Lgze coze Yaad | ogi Ise 6688 goes PEE GEE logs : | | 091 g1ce E8FE Icke SIF Lees geze | | | OFI pose =” ILE 6EcE 90¢¢ PLPE ZLes 9Lze ssie ie! fl 0z1 L6g9¢ page Igg¢ 86ee coce ZOE core SLze Z61E iats 6L6z | 001 ‘SOLE 6SLE SZLe Z698 60 poee ‘eape ‘e9ee SLZE LOIE ‘p908 862 ‘lesz |SZL2 08 S588 Lege €z8E 68L€ 9gL¢ 6P9E ‘spse ‘PSpe 998¢ esze ‘Tele ‘1662 ey iLLLZ 09 Z668 Lo6E 1Z6¢ ggse case EPLe [IP9E° gpa cape Lose ‘suze ‘9908 lara 8782 OF 880F00°0+ 0¢0F00°0+ 110b00°0+ eg6e00 ‘0+ 9F6800°0+ eeseo0'0 + cexeoo “0+ 9¢9¢00°0-+ 1¥2800°0 + esbs00"0 + ES7E00°0+ HIBIN ‘0+ 96020" 0+ exsz00-0+ Seok coll — f -oShi =) sep = | oll = | coor — | 006 — | C08 4 Sc0s— tog) | 0h — 0Z— | 0 | 00% he / 0/. =H, 0*p ) | (5: T (WI | | | | | | One myer 02 | —20? —40° | —60° 10? —80° —90° —1002 | —110° —113? —116° —119° —122° } 1 / 20 — 0.09293 —0.00273 —0.00506 —0.00233 —0.00426 —0.00203 —0.00579 —0.00366 —0. 00846 —0.00489 0.00320 —0. 00471 — 0.00462 — 0.00453, i) 879 819 1012 699 1279 1219 1543 1648 1731 1794 1761) 1885 1849 1964 a) 1759 1912 2278 2331 2983 3046 3283 3479 3635 3014 4162 4084 4160 4231, 80) 2931 3271 3796 4196 5114 5077 5793 6408 6404 7013 6884, 7226 7242 71252 100 6293 7458 7921 8496 9338 0.10039 0.10764 0.10886 0.10839 0.11094 0.11181 120 0.12165 0.13366 14193 15167 15529 15709 15717 16016 140 a? 19213 20549 «= 20812, 21207-«S «21264 «= 21304 160 ; 24925 26910 «=. 27875 = «27491 «= 27582 «=: 27498 180 34249 34579 © 35031 «= 35133-35053 200 43384 43828 43916 43514 220 ; 53470 54039 © 54304. «54090 240 65978 66567 66177 260 $0430 81051-80984 280 97396 98618 98662 | 300 1.1750 1.1942 1.2012 320 | | 1.4122 1.4407 1.4550 340 1.6950 1.7335 1.7602 950 forces from the simple initial assumptions made by van per Waats. Such changes in @p might orreinate from three causes: change in the dy, in the by or in the Ay of the chief equation, as a result of the radius of the sphere of action being but slightly greater than that of the molecule, a circumstance ') revealed in apparent association. 0° p Oy, , E ey Ove wh Ov 7 Since ‘Op } A : the question as to whether le) is independent of the temperature G 0*p and therefore | oo =0(, is most intimately connected with the ( : OY» : : : question as to whether (5 =O or not. For a long time this Ov T question remained undecided on account cf the lack of experimental data. We now know that, at least for a number of substances, Op a is in general a function of the temperature, and that therefore v v fl 7) ; — — } does not vanish. IN i If we now compare the behaviour of argon with respect to Op a 7 with that of isopentane we find correspondence in many respects. : Youn *)*) deduced from his observations upon isopentane that Op OT volumes up to ep=400c.c. it increases with falling temperature, 0 0 0 : ) decreases with falling temperature for vr < 4.6 c.c. ; at greater vo while it remains practically constant at still greater volumes. For argon, for which the volumes are expressed in terms of the normal volume as unit, if the law of corresponding states were accurately obeyed these volumes would correspond to vy = 0.00877 and vy = 0.328 or on = 265 and oy = 3.05. The argon observations embraced by VII. A. 38 lie entirely within these limits, and from Table I we see that argon agrees with isopentane within the region of observation. Over the entire region IN ae ohne : : (sr), fas with increasing temperature. At the lowest argon density 1) This circumstance causes a change in by also, cf. H. Kamertingn Onnes and W. H. Keesem, Suppl. N° 23, Nr. 47. *) M. RersGanum, Diss. Géllungen. 1899, pg. 42. 5) S. Youna, Proce. phys. soe. Londen 13 (1895), p. 602. 960 ox = 20 the diminution beeomes extremely small, pointing to con- stancy at still lower densities. Argon differs from isopentane, how- ever, in this respect that with argon at higher densities far above ox = 265, the inerease becomes still more rapid, while the behaviour of isopentane would lead one to expect a diminution in the rate of increase. From his observations upon isopentane YounG’) deduced the following oT? ‘0? p 0 mete ] Bees, OT" Jo > +n, This rule has already been coutirmed for a variety of substances, ; ; . ‘Op rule for the behaviour of : and is, as far as its second part is concerned, also obeyed by argon. For carbon dioxide, ethylene and isopentane, RrmGanum found : Bea) eo that the quantity a; = | 7 -,)—p |v? is a minimum for v about OT)» a) r, and at temperatures about 10° above ¢. If the law of corre- He | sponding states were strictly true this minimum for argon should be at ox = 380, and therefore outside the region of experiment. Nothing can be done consequently beyond trying to judge from extrapolation, if, and where, the minimum exists. If for this purpose we graph ayn as a function of ex at —122° and —116°, then extrapolation towards higher densities shows that it is probable that these curves 3 would also exhibit a minimum for argon at v= ras Physics. — “On the rectilinear diameter for-argon.” By K. Matnias, H. Kamertincn Onxes, and C. A. Crommenix. Comm. 131¢ from the physical Laboratory at Leiden. (Continued). (Communicated in the meeting of November 1912). § 5. Results. The results obtained are given in the following table *) (p. 961): The calculated values of the ordinates of the diameter given in this table have been obtained from the equation Dr = 0.20956 — 0.00 26235 ti. Ny Eafe 2) For the notations, see Suppl. No. 23. GL The diameter has been drawn through the points —175°.39 C;,, Kee and —131°.54 Gin K. deur. « \—- — = = path Ge ee Sligr Qvapr D7 (O) DO Oe: O» — 183.15 | 1.37396 0.00801 | 0.69099 | 0.69006 +. 0.00093 CH, | — 175.39 | 1.32482 0.01457 0.66970 | 0.66970 CH, | — 161.23 | 1.22414 | 0,03723 | 0.63069 | 0.63255 — 0.00186 CoH, — 150.76 1.13851 0.06785 0.60318 | 0.60508 — 0.00190 CoH; — 140.20 1.03456 0.12552 0.58004 0.57738 + 0.00266 CoHy — 135.51 0.97385 0.15994 | 0.56690 | 0.56507 + 0.00183 CoH, — 131.54 | 0.91499 | 0.19432 | 0.55466 | 0.55466 CoHy) — 125.17 0.77289 | 0.29534 | 0.53412 | 0.53794 = 0.00382 ! — — = — iQ HS ae ; aes Kz =100" § 6. Diseusswn. The slope of the diameter is given by bar = — 0.0026235. This coetlicient is very large, larger than has been found for any other substance yet investigated with the exception of xenon, for which Parrerson, Cripps and WeyrLaw-Gray *) have found —O.008055. Comparison of the values of this constant for the two monatomic substances argon and xenon again reveals the influence exerted upon it by the values of the critical temperature. With respect to the critical density the following remarks must be made. If we assume that the diameter remains rectilinear right up to the critical point, we then tind vka = 0.53078. (Op ) (F ) oT ee aus koex.k. es == OS) Using the equation the value was previously found from the argon isotherms. *) The difference between these two values is of the same order of magnitude and is in the same direction as the differences found for other substances, carbon dioxide’), methyl chloride‘), sulphur dioxide *) amongst others. The fairly large deviation from rectilinearity of the experimental diameter apparent in the neighbourhood of — 125°.17 Cink ur, agrees well with this behaviour. 3.283 was the value previously *) obtained for the critical coefti- cient on taking Kyg = Ky: we now find Kya == 3.424 which is therefore slightly greater than that for oxygen‘) (3.346) If, therefore, we leave Kyg = 3.138 for helium out of account, oxygen, and not argon, is the substance for which Kyg les nearest the theo- retical value, 2.67, deduced from van pur Waatzs’s equation. 1) Parrerson, Gries and Wuytiaw-Gray, Proc. R.S. (A.) 86 (1912), p. 579, 2) G. A. Grommenin. Proc. Dec. 1910, Comm. No. 118a, and Thesis for the doctorate, Leiden 1910. 3) W. H. Kersom. Proc. Jan. 1904. Comm. No 88; H. KAmertinen ONNES and W, H. Kresom, Proc. Febr. 1908. Comm. No, 104a ') CG. H. Brinkman, Thesis for the doctorate, Amsterdam 1904. ®) E. Garposo, Arch. se. phys. et Nat. Geneve. (4). 34. (1912) p, 127. 6) H. KaMeRLINGH OnNES and €. A. CromMe in. Proc. March 1911. Comm No. 121a. 7) E. Maturas and H. KAMeRLINGH OnNeEs. Proce. Febr. 1911. Comm. No, 117. 22 963 The density of the liquid at-—-183°.15 agrees well with the figures given by Baty and Donnan '). The difference is less than 1 "/,. Although the deviations of the diameter from rectilinearity are sufficiently small to enable one to say that argon obeys the law of the diameter, they are still too large, and especially too systematic, to be due to experimental errors. As is easily seen from the table and from the accompanying figure, the experimental diameter in the neighbourhood of the critical point exhibits a curvature concave towards the axis of temperature, while at higher temperatures it is convex towards the same axis. The same behaviour has already been observed in other substances, e. @. carbon dioxide *). In fig. 3 are given the reduced density curves and diameters for ether (Ramsay and YounG")), isopentane (YouNG *)), oxygen (MArHtAs and IKKAMERLINGH ONNuES*)), xenon (PATTERSON, Cripps and WayrLaw-Gray °)), argon and helium (KAmMpRLINGH OnNws*)), the reduction from the experimental data has been made by means of the critical density obtained from the diameter. On a previous occasion it was shown by KAmmpRLINGH ONNes and Kuusom *) how the equations of state for different substances deviate one from another, and how these differences may find expression in deviation functions. On doing thts, it appears that substances may be arranged in order so that the deviations of successive substances gradually increase, while it also appears that substances of widely divergent critical temperatures are then found to be in the order of their critical temperatures. The exemplification of this general pro- pertye afforded by the behaviour of the diameter was noticed by one of us some time ago 9) and is brought to light in fig. 8 in which the density curves are seen to enclose one another. If the law of corresponding states were strictly obeyed, then these curves ought to coincide exactly. From the diagram, however, it is seen that this is not the case. The curves enclose one another *") in yk G. G. Baty and I. G. Donnan, Journ. Chem. Soc. Trans. 81. (1912). p.911. 2) H. KAMERLINGH OnNES and W. H. Kersom. Proc. Febr. 1908, Comm. N°. 104a. J. P. Kusnen and W. G. Rosso, Phil. Mag. (6). 3. 1902. p. 624. 3) W. Ramsay and S. Youne, Phil. Trans. 178, (1887) p. 6 1) S. Young. Proc. phys soe. London 1894/1895 p. 602. a es 8) I.c. 7) H. KameruinGu Oxnes. Proc. Dec. 1911, Gomm. N’. 1240. 8) inc. Math. Wiss. V. 10. Suppl. N’. 23. ®) HE. Marutas CG. R. 139, (1904), p. 359. 1) In the diagram of N’. 36 of Enc. Math. Wiss. V. 10. Suppl. NY. 23, is clearly shown the surrounding of the boundary curve for helium by that for iso- pentane. 7. ‘e ‘3Iq such a way that a complex molecular structure and a high critical temperature (circumstances which are usually coexistent) cause diver- gence between ihe branches of the curve, while simple molecular structure and a low critical temperature appear to cause them to contract. Looked at from this point of view, it is of importance to note that the curves for xenon and oxygen so closely correspond that there appears no appreciable difference between the density curves in the diagram, and they have accordingly been represented by a single 965 curve, (The observations for xenon, however, extend only to ¢ = 0.7). The cause of this coriespondeice can well be explained on the as- sumption | ) that the contracting influence of the simpler molecule and the diverging influence of the comparatively high critical tem- perature (-++ 16°.6 C) have, at least in part, cancelled each other. Physics. — Muaynetic researches, VIL. On paramaynetism at low temperatures (continued). By H. Kamertincn OnNes and EK. QOostrrauis. Communication N'. 132e from the Physical Laboratory at Leiden. Communicated by Prof. H. Kameriincu ONNEs. (Communicated in the meeting of December 28, 1912). § 9. Crystallized manganese sulphate. The salt was procured from Merck as puriss. pro analysi. The results were * TABLE VII. Crystallized manganese sulphate MnSO,.4H.O. (I). | T z.10° | 7.7105 | Limits of H Bath PSISETIIKS |) (Cone 19140 10000—17000 | Air. 169.6 111.5 18910 8000-17000 Liquid ethylene. ee 247 19120 | 70.5 270 | 19030 | 6000—16000 Liquid nitrogen. 64.9 292 18950 20.1 914 18370 17.8 1021 18170 | 4000—16000 Liquid hydrogen. 14.4 1233 17760 Down to and at nitrogen temperatures, this substance follows pretty much the law of Curie. 1) See N”. 34 of Enc. Math. Wiss. V. 10. Suppl. No. 23. *) Prof. Weiss has kindly informed us that in the determination of standards of susceptibility in Ziivich, for this substance + = 66.77.10—6 at 14°92 G. was found. 63 Proceedings Royal Acad. Amsterdam. Vol. XY. 966 § 10. Anhydrous manganese sulphate. All the water was driven out of the salt by heating. The results are given in Table VIII. With anhydrous manganese sulphate another divergence from the law of Curie over the whole field of low temperatures was found. Down to nitrogen temperatures, however, it is only a disturbance of the first kind. At hydrogen temperatures a further disturbance shows itself which is not unlike the disturbances with solid oxygen, and at any rate belongs to a kind of disturbances that we have not yet been able to reduce to a definite type. It is remarkable that just as with crystallized ferrous sulphate the presence of molecules of water of crystallization causes a diminution of the quantity 4’ to a very small value in comparison with that of the anhydrous sub- TABLE VIII. Anhydrous manganese sulphate MnSO,, (I). A’= 249, T y.10° x4(T+0')10% Limits of H | Bath | 293°.9 K. | 87.8 27910 | 6—17 kilog. | Air. 169.6 144.2 27920 BT Liquid ethylene. 77.4 274.8 27870 5—16 Liquid nitrogen. 64.9 314.5 27960 | | 20.1 603 26590 | 17.8 627 26210 » 4—16 Liquid hydrogen. 14.4 636 24420 | | | | stance, here too 4’ becomes less by the addition of molecules of water of crystallization, and to such a degree, that, if one does not go below nitrogen temperatures 4’ appears to have become = 0, whereas with anhydrous salt 2’ = 24°. If we ecaleulate the number of magnetons for the crystallized salt with C= 77 (4’=0) and for the anhydrous with C’ =7(7+A’) and with 4’ = 24°, we find the same number of magnetons in both cases, viz. 29. This is one less than is found in the solution ‘). 1) P, Weiss. Journal de physique, 1911, p. 976. 967 § 11. Further observations upon ferrous sulphate and ferric sul- phate. After the conclusion Of the investigation treated in Comm. N°. 1294, we turned to the determination of the water contained in the preparations ferrous sulphate [and ferrous sulphate IIT. Prof. van [rain kindly investigated the preparations and found that they contained ferric as well as ferrous sulphate. They cannot therefore be taken as a reliable basis for calculations of the number of magnetons, and to make these possible the measurements will be repeated with purer preparations. The quantitative result arrived at in Comm. N°. 1294 concerning the appearance of disturbances of the first kind in Curim’s law and the possibility of finding the constant of Curim for these substances by means of a correction, still retains its value. As regards the ferric sulphate, which the measurements in § 4 of Comm. N’. 1294 referred to, the admixture of water may be put at about ‘/, in first approximation. The molecular susceptibility of ferrous sulphate is therefore * /, smaller than that of ferric sulphate, so that valency shows its influence in this iron salt also; all this in contra- diction to what was observed in § 4. We must also remark, that the sign and the order of magnitude of the corrections which would be necessary to deduce the number of magnetons for the pure materials from the measurements of the ferrous sulphate I of our Comm. N°. 1294 and those of the crystal- lized ferrous sulphate of Kampriuincu Onnes and Perrmr in Comm. N°. 122a, make it seem possible that there is a double analogy between ferrous sulphate and manganese sulphate. Just as in manganese sul- phate the number of magnetons in the crystallized and in the anhy- drous substance is equal, the same would be found for crystallized and anhydrous ferrous sulphate (viz. 26) (if for the anhydrous sub- stance Curtk’s constant is calculated with the help of the correction by A’ = 31°), and in further analogy with manganese sulphate, this number with ferrous sulphate is also one less than in the solution, if for the latter one may take the number, that has been found by WILIs *). Should the disappearance of A’ with the introduction of water wolecules be ascribable to the increase of distance between the iron atoms which is caused thereby, then it would be possible that with different contents of water of crystallization A’ decreases with the increase of the number of molecules of water of crystallization. We intend therefore, to examine a salt in this respect, that crystallizes * !) P. Weiss. Journ. de physique 1911. p. 977. *) Compare the investigation of Mlle Feytis, G. R. 153, p. 668. 1911 on the 63% 968 with a series of different numbers of molecules of water of crystal- lization, and from that to deduce a possible dependence of 4’ upon the density. § 12. Platinum. A small cylinder of pure platinum from Hrragrus was examined. ‘he susceptibility changes very little with the temperature. On account of its small value it is difficult to determine z accurately. The results are contained in Table IX. TABLE IX. Platinum I. | Limit value T 7.108 of H ‘in Kilogauss. | 200.2 K 0.973 77.4 | 1.061 | 11—17 } 20.1 | 1,080 14.4 1.087 The value at ordinary temperature lies about the middle of those of Owen, 0.80 resp. 0.89, Honpa 1.097, KorniGsberGer 1.35, FINKE 1.06 (all at 18° C.). If one wished to go so far with the application of the rule OQ’ =y (7'+ 4’) that one applied it to platinum also, then it would follow from this that A’ = 2440°, and for the number of magnetons n calculated from C” the value m= 10. § 13. Dysprosium oxide Referring to the data of § 7, we observe that, as will also appear from a further communication of KamEr- LincGH Onnes and Perrier, all the values of % which occur there must be increased in the ratio of 1: 1.065. By applying this correction also the difference from the value at ordinary temperature found by Mile Frytis which was stated upon in §2 o0fComm., N°. 122a and which was due to an error of calculation, is reduced to a divergence within the limits of accuracy; hence the dysprosium oxide appears to have been about in the same condition as the sample used by her. Our conclusions undergo no change by the ‘correction. influence of the successive molecules of water of crystallization upon y. This might be the consequence of a change in A’ with an unchanged number of magnetons, eee 969 § 14. Oxygen. The susceptibility of liquid oxygen has been deter- mined by KaAMrrLINGH Onnes ‘and Perrier by two methods. It has now also been investigated by the attraction method in about the same way as the susceptibility of.liquid hydrogen in Comm. N°. 122a. An evacuated cylindrical glass tube was hung in the magnetic field and then the repulsion measured that the tube underwent when the surrounding space was filled with liquid oxygen. The value found at 7’ — 90°. 1K. agrees well with that in Comm. N°. 116; the small difference at the other temperatures is explained by the fact that the temperatures could not be very accurately ascertained. In the following table the values found stand beside those of KAMERLINGH ONNES and Perrtmr according to their formula i PF '2.284.10-°. The question naturally arises whether the behaviour of liquid oxygen can also be represented by the formula C’ = y(7'+ JQ’). If we assume that A’ = 71° this comes out pretty well, as appears from Table XI in which the values of y are taken from KaMERIINGH TABLE X. Liquid oxygen. 7.108 | 7.106 | 3 K.O. and 0. (K.0. and P.). | 901K | 2411 | 240.6 | 79.1 | 258.1 | 256.8 70.2 | 210.7 272.6 When the atoms are assumed to be free in the molecule (C’ gives for the number of magnetons 11 per atom (calculated 11.04), TABLE XI. Representation of the susceptibility of liquid oxygen by the formula 7A(2f SE) SSO A Seige | 108 | ¥(7-+71) 106. | | Late eat | 90°.1K. | 240.6 | 38760 71.35 | 269.9 38420 | 64.9 2S 4 2h |] 38620 970) and on the hypothesis that in the liquid two gas molecules are rigidly connected it gives 11 per mclecule of two atoms. From y (7'+ 4’) = 38600 (the mean of the numbers in the table) with A’ = 71° one finds for 7=-2937 Ki %o93? K. — 106.0 « 10-8, This is very close to the value for gaseous oxygen at 20° C found by Weiss and Piccarp *), from which follows 7 magnetons for each of the oxygen atom assumed to be rigidly connected. Seeing that above 20° C. gaseous oxygen follows Curin’s law *)it seems to be by some chance that our formula with 4' = 71° gives that figure. The graphic representation of '/g as a function of 7 if our for- mula actually remained true up to 20° C. would consist of two intersecting lines that have their point of intersection just at the temperature at which the value quoted is determined, which cer- tainly would be a curious coincidence. Another possibility which Prof. Weiss suggested,in a kind private communication, is that there might be discontinuity in the region between 0° C. and — 188° C. which has not been investigated, by which it remains accidental that the continuation of the line for liquid oxygen cuts that for gaseous oxygen just at 20° C. There is much to be said for this explanation. It is quite possible that the change of density between liquid oxygen and gaseous oxygen makes 4’ into 0. This would be in accordance with what was deduced in § 10 for the influence of the water molecules upon the value of 4’ for manganese sulphate, and moreover quite in accor- dance with Wriss’s idea that the molecular field essentially depends upon the density. We can further observe, that the change of density, which takes place discontinuously with evaporation, can take place continuously by an indirect transition. In the above line of thought, if we assume that the divergence for liquid oxygen from Curir’s law may be defined by a 4’ and pay attention to the change of the number of magnetons which must be assumed in that case, the graph which represents ‘/, for oxygen of a given density as a function of the temperature would be as in magnetite a succession of straight lines perhaps connected by rounded off pieces. The magnetic equation of state which expresses the susceptibility as a function of density and 1) P. Weiss elt A. Piccarp. C. R. 155, p. 1234, 1912. *) Prof. Weiss who has particularly investigated this question, kindly tells us that the experimental results of Curte agree so well with Curte’s law within the limits of observation errors that A’ could not be more than + 8° or—8°, 971 temperature (with a view to determining which the experiments of Kameruincn Onnes and Perrier were undertaken (see Comm, N°. 116 § 1) would be given by a series of similar lines, differing for the different densities. We must not forget that it is by no means established that in the case of oxygen the divergence from Curte’s law is determined by a A’ which changes with the density, and that it obviously may be due to an association of molecules into complexes with a dimi- nution of the number of magnetons. However this may be, our attention is again drawn to the im- portant question whether the divergences from Curik’s law depend upon a peculiarity of the atom within the single molecule or from the approach of the molecules up to a very small distance. In § 38 of Comm. N°. 122a by KamertincH Onnes and Perrire, it is said that preliminary experiments with mixtures of liquid oxygen and nitrogen, which will soon be replaced by better final ones and which were based on the above mentioned association hypothesis, seemed to indicate that bringing the molecules to a greater distance by dilution in the liquid state has no influence of importance upon the divergences from Curin’s law. Here the question is raised— in this form: whether A’ is a quantity which as peculiar to the atom in the single molecule can also be found in the gaseous state or whether it can only be developed by bringing the molecules into immediate vicinity of each other. Further experiments ‘) with oxygen, already planned, must decide this. (To be continued). Physics. — “The law of corresponding states for dijferent substances.” By Prof. J. D. vAN per Waats. (Communicated in the meeting of December 28, 1912). In the following pages I shall give an account of the result of the researches which I have made of late about the properties of the equations of state for different substances. And I shall commu- nicate in them the simple conclusion at which [| have arrived for all the substances for which a chemical combination does not take place, and the molecules continue to move separately, either really isolated, or perhaps joined to groups, if this aggregation (quasi association) behaves in the same way. 1) As this communication is going to press, these experiments have advanced so far, that we may accept with great probability as the result of them, that gaseous oxygen of 9O times the normal density obeys Curie’s law down to — 130° C, When I discovered the law of corresponding states, | could state the result in two way — and in the beginning I, therefore, hesitated before making a choice between these two ways of expression: 1. if for the different substances 2 and m are equal, r= “is also Uk n equal, 2. if for the different substances 2 and mm are equal, the volume for all is the same number of times the volume of the molecules. For so far as I saw then these two expressions were both true, and it was after all immaterial whether I chose one form or the other. But the first form was more suitable for experimen: and the second form would only be of theoretical value — and so I chose the first form. In order not to get into great difficulties at once, we shall disregard quasi-association for the present, and our result will therefore, at least for the present, be valid only for higher temperatures and not great density. If we write p=ap,, RT = RTm and v=rvz, and if we put lis ’ —— =s, we derive: a‘ b 6 ae yp—— |= ms PPh rh a f—1 a = = and as we found ———=—— or = f —1, (These Proc. XIII vupeRI k s Pk vie 5 ; p. 118) we may also write: f=! Ege la yp——|)=m. 1) UE In, our latest investigations we have shown that either quite accurately, or with a high degree of approximation. Substituting this, we find : f-1 eon b 8 f—l (= +3 a p— a =e Ee 3 or J 3 ov l 3 A dg re = = = ae =) == S77 y? yA) —1 b, Ve —1 ls 3 It we put a, », m=1, we find: by. , With f= 4 and corresponding 7 = 3, we find = 1, and with My +i 7 we find: be 68 3 8 is —_ = — — = 0,978. bg rV2 Y2 i bk : 3 ; As — has been found only little smaller than 1, will also My rVYa differ but little from 1; from rs <8 follows in the case that 64 : fe —-(f — 1) is assumed as perfectly accurate, with 7s << 8: af : 8 r< = s or 8 r = SE, S 8 f—1 = a 3 r _— = ie Ys Hence 3 at r yeaa! 3 B} But it is to be expected that the value of ————— = will be : dems 3 only little greater than 1. For f=4 with r=3 we find it exactly equal to 1 and with f=7 we find a value of + little smaller than would follow from 7) 2=3, namely r= 2,1213. We accordingly determined this value at about 2,09. But then we conelude at the same time that if / should have risen to 10, the value of » would descend to below = 1,73. At all events in the equation: e f-1 ord the factor g will indeed be somewhat greater than 1, but differ only little from 1. If we confine ourselves to that part of the whole region where no quasi-association worth mentioning is to be expected, to which part the critical point also belongs, the last equation will hardly eee rn b change, if we put unity in it instead of aes And then a rule Ik follows from this holding for all normal substances, so for not really Hose : : vr associating substances, viz. for given a and m, ——~— 7 has the 7 =~ 3 same value. For substances with the same value of #—1, pr is therefore also the same and with different value of #—1 we have . r rv or according to results obtained in These Proc. p. 903. Dv v A ae 7 by ) Diim Duin : Not rigorously valid for the whole region, however. To equal reduced pressure and temperature corresponds a volume which in : an 6 reduced measure is different for the different substances, when —— lim v differs. But if we write the value — for v, and the value v f —_—_—— for vy’, we obtain: na faltin Nb r b fom hat b, ; , Al aE _ Blin, And as we have concluded to the approximate equality of 3, Dg (59 \ . : r'{——~] ete. we tind as approximate rule: At the same Dee Biim reduced temperature and pressure the same volumes are for all substanees the same number of times the molecular volume viz. by. If, therefore, we had expressed the law of corresponding states in 975 the second way, it might have been maintained unchanged for all normal substances, at least over a large part of the whole region. v r i ia ia ba ) bliin [ bhim that e.g. for the reduced volume, which in the system in which b . . q . f=4 is put equal to pv,, x, lV; must be taken in the system, lim fis b, a art : - a eth where —— = . Thus the critical volume is equal to 34,, if f= 4 e lim ; and the reduced volume is then equal to 1. But in the system in which f=7 this volume would have the value of 1/2 in critical The meaning of equation is of course this measure. That the reduced volume is found }2 times larger is due to this that we have divided by a }/2 times smaller factor. Hence the different a, m, » surfaces for substances, for which b ; : — might differ, do not cover each other, but they can be made lim to overlap for the greater part, almost entirely, if we divide the 5 by value of » by —, Dlim Then, however, the border lines, the loci of the coexisting vapour and liquid phases have not been made to cover each other. Not even by approximation, for this locus, which is determined by ve (Oe) = fe dv, vy also requires the knowledge of the properties for smaller volumes, and will, therefore, also demand the knowledge of presence or absence of quasi-association, but especially the knowledge of the wb : ; } course of —. But this will be discussed later. Iq The cause of the circumstance that the above mentioned properties only hold by approximation is clearly to be seen, if it is borne in ; id PO : ; ; mind that the quantity ; in the form found for the equation of state : om ~) o> ' by is not constant as soon as —~ > 1. If very large volumes are con- lim cerned, we may put 1 for it, and even in the critical volume, viz. ré,, the difference with 1 is still slight, and we tind from: 8 ‘WA bg bp 3 Blin —=r,f 1 ——— 5 9 1 3— T Diim b, by for —"- = 2 the value of — to be equal to 0,97 or 0,96. lim 7] We conclude from this that for the vapour volumes of the border line the rules given above hold with a high degree of approximation. Foe r : But for the liquid volumes ———-—— is smaller than would be caleu- ) 9 Diim Ss b : ad lated if we had retained — — 1, and the density of the liquid 9 greater. The limiting liquid volume is even not 6,, but dim, and so b “Ale Nae Ens — times smaller, and the limiting liquid density —* times greater. tim lim This must bring about a change in the value of the factor y. And we can calculate the value of this change. Let us put + on pL AS EL =1 +4 y(1l—m) 20 kr and for 4 constant ' ' Q gas = Oy] ae 1+ 4(1—m). =9 kr At very low temperatures the gas densities disappear. With sub- traction of the two equations we find: — Ovl tl a) 20kr* 20k For m = O we must introduce the limiting liquid density, and we get : by r—— — 3 = (2y—1) Dtin or bg ; rt = 2y+1)') lim 1) These Proc. p. 903. 977 b q . ‘ As r Ee is somewhat smaller than 3, we get: Din Hence the variability of 6 is the cause that the law of corresponding states does not hold perfectly for all volumes. If this variability was Ay by : governed by one law, and if accordingly - was the same for all Dim -; by D lim and so also of » would be the same for given a and m. If the law b, . oan ec of the variability of b, hence Va , is different, then » is indeed lim substances, it would hold perfectly. For then the value of not equal for given a and m, but the law of correspondence, as we have stated it here, holds with a high degree of approximation, at least for volumes > v,. Then for given a and m the value of v : ”) is _ ———— is almost the same or es Ee Z We bg F by > 3b, = Vk sotie r by we —- > Diim by blim As the volume decreases, the Jaw begins to fail. For v > vx it holds almost good, below this the deviation becomes greater and greater. The value of b 4);,,, however, does not seem to differ much for the different substances. It is not equal to 1 for any substance, not even for monatomic ones. So substances for which / is constant, are only fictions. When, therefore, in my continuity [ calculated the critical circumstances keeping 6 constant, this did not take place because [| thought that 4 would be invariable, but in the expee- tation that in the critical volume the quantity 6 would have chan- zed so little that the influence of the change would be inapprecia- ble. And as we have found now, the quantity is, indeed, not much smaller than 1 for a and m—=1. And even b . . q . . if we should assign to’-— a value so excessively high as would be lim the case if we put it at 3 — and substances for which this value would occur will, no doubt, have to be looked upon as fictions — 978 by. we should still find ; > 0.93. The reason, therefore, that even for ) q great densities the law of correspondence is fulfilled by approximation 4 by will be owing to this that .—- does not differ much for the different Olim substances. Moreover the region in which the deviations would become of importance, is inaccessible to experiment; e.g. for the liquid volumes which could coexist with vapour volumes at values 1 of i» < —. or for volumes under an excessively high pressure. » “ We shall add a few more remarks. . . . . r ‘al . That the coincidence of the surfaces = /(2,m) for great Vas ba Dtim values of v entirely disappears for vr very small and near vj, will e : b be clear if we pay attention to the fact that for tA ; lane ; the surface has no points below v= ae for then v’" = 6, and bo vp, — 36,. For Va equal to a value greater than 1, vj, = bi, and lim vy, = rh, or 6 : : If e.g. = = 2, we have obtained new points for the » surface, and lim ’ P 1 3 : : the surface begins at —-~-— = —. It will be obvious that in such a (=) : ; yw - bg ; circumstances with differenee of the value of —— there can be no lim question of coincidence. There is only perfect coincidence with equality b : ; oe: : ’ Tf this value differs, the surfaces almost coincide, indeed, for of lin : : » large value of vr, but for very small value of » the —— 979 4 ( ordinates will contract and approach to zero as becomes larger lim in a region, however, which is hardly accessible to experiment. Another remark. From the cireumstance that the surfaces may be considerea Iq Blin to coincide, especially for large value of », it should, however, not be concluded that the border lines coincide. The top differs already. . p . . The top lies at a2, m,and v equal to 1, and so differs ; and Ng Diim great differences are even derived for the gas-branch at low tempe- : . fs 2 ) 5 1—m ratures from the relation which holds approximatively, — fe ==; Pk m Thus we find in the region where the law of the rarefied gases would hold: ea by 8 Biim ( Ns =| 1+3— lim Hence in a region where correspondence would perfectly prevail the border lines differ exceedingly much. This is of course the con- b s ns : q sequence of the liquid volumes no longer corresponding when —— Dim differs, and the construction of the border line also requires the knowledge of these volumes. Where the gas-laws hold, =i or HV Pk vk = 1, and now we have come to the conclusion that m RT; Tr E ’ 8 by for the different substances is equal to — [7 = Then Pk Uk 3 Dim am 8 by m 3 Va or fd p 8 4 and s > 5 for monatomic sab- stances, even monatomic substances would not be perfectly hard. For all substances, with our present knowledge we may say without b : 7] , Sas - : exception, —~ > 1, and probably not very different from 2. Now lim we might account for about 2 by assuming qwas/-association. In large volume /, is the fourfold of the volume of the molecules; hence if the spherical shape is assumed and the diameter is put = 4, a a rn s "4° . . b, =4 0°. The limiting volume of the substance is present when 7 1) the pressure is infinite at temperatures 7’> 0. Then the molecules must touch, and the volume is only little smaller than 6° or 6 ;,,< 6°. Hence: 2a bg 2 5 Diim or hb, 2 2,09 Blin 5 But on the other hand we should consider that often If not the spherical shape was assumed, but as extreme case, a > ay rectangular shape, 5, would be = 40°, and dim = 0°, and —=4. ; lim This will, probably, not be expected by anybody. For ellipsoidal shape we should again find a litthke more than 2. In this way it by seems impossible to me to explain the value of ——~ < 2. But we lim shall possibly discuss this later. The original theorem of the corresponding states pronounced the equality of the a, @,9” surface. In the form given here it states the . eye . u . mn . superposition of the a, m —— ; surfaces. These two forms would Ny Bare coincide, if there was only one single law for the course of 6. In 98] the form given here the v ordinates are only "4 times smaller. But Mim the advantage of the form given here is obvious, when there are different kinds of substances from the point of view of the law of correspondence. First of all it points out the cause for the existence of these different kinds, about which cause the form given originally does not reveal anything. Secondly it appears that attempts to find perfect correspondence between these different kinds must fail, and have certainly no chance of success by variations in the a and im ordinates. And thirdly it shows that the deviation between the different kinds of substanees is a gradual one, and the coincidence in the rarefed gas-state is restored. Physics. — “On the Hati-effect, and on the change im sistance im a magnetic field at low temperatures. VI. The Hate fect for nickel, and the magnetic change in the resistance of nickel, mercury and iron at low temperatures down to the melting point of hydrogen”. By H. Wameriincu Onnes and Brener Beckman. Communication N°. 132a from the Physical Laboratory at Leiden. (Communicated by Prof. H. Kamertincu ONNEs). (Communicated in the meeting of November 30, 1912). § 17.') Magnetic change in the resistance of solid mercury. The resistance was measured of mercury contained in a glass capillary 9 ems. long, and of 0.12 mm. diameter. The capillary was U-shaped, and to either end were fused two glass leading tubes which were filled with mereury. The resistances were measured by the Kou _ravscu method of overlapping shunts, in) which the main current was J=0.006 amp. The mereury was frozen by blowing cooled hydrogen vapour into the cryostat through a glass tube whose lower extremity reached below the resistance. The resistance was found to be Cas at i — OS line 0,1014 ir oro 0,0618— Pa 1) The sections of this paper are numbered in continuation of those of Comm. N°, 130c (Oct. 26, 1912). 64 Proceedings Royal Acad. Amsterdam. Vol. XV. 982 TABLE XIx. Magnetic change in the resistance of mercury. T= 205.3 Ke Ti Nao > Ke H Lw Lw in gauss. wz X 108 H 1 wp X< 108 9760 + 1.3 10270 |} + 5.5 10270 + 1.5 10270 + 6.5 10270 + 1.6 The measurements therefore show an increase of the resistance in the magnetic field. At Aw w Pees | eae ee w == oe LOSS AH 10000 and 7 = 20°3 K were obtained as. mean values. At these temperatures the temperature coefficient of the resistance is very great, and this lessens the accuracy of the above measurements, especially at 7’= 14°.5 K. The large increase occasioned by lowering the temperature from 20° to 14° K. is very striking. § 18. The Hatiefect for, and the magnetic change in the resistance of, nickel. The material in the form of a plate of 0.053 mm. thick- AWS exe } Hatteffect for nickel Nip}. T= 2909;5)Ke T=90°K. Tp 202.ci Kenna || DP 14o aK H |RH|—Rxiol| Ho ORH|—Rxot| HW RH | —Rxtot| H RH | —Rao8 301018.8 62.4 29802.93 9.83 29701.48 4.98 | 49402.50 5.06 517031.2 60.3 49504.58 9.25 | 56402.86 5.08 | 82504.25| 5.15 726039.3 54.1 72006.31 8.65 | 72603.53 4.86 |102705.19| 5.05 9065 43.1 47.6 91107.62) 8.36 | $2504.08 4.95 | | 1027044.9 43.7 104008.29 7.98 .102704.81 4.68 983 ness was pure Scuwerre nickel. // and RH are given in C.G. 5. units. J was 0.7 to 09 amp.” The results given in Table XX are shown graphically in Figs. 1 and 2. The Hatneflect for nickel decreases as the temperature falls from ordinary room temperature; this has already been found by A. W. Smitu') to be the case down to liquid air temperatures. According to A. Kunpr?) the Hanteffect for ferro-magnetic substances is proportional to the magnetisation and not to the field. Hence, when the magnetisation attains its maximum value, the Hatreffect must also exhibit a state of saturation, that is to say, the curves giving the Hauueffect as a function of the field must show a bend. Smiru’s CG }. 50 Sa KR ab 6 le eye | v1 |. Seber 40 cau = | * t | ¥ 30 . Ss A ae (4) A000 4000 oaAv 806? W000 G Nise. —> I Fig. 1. Fig. 2. = ets] 0 200 WN GON 82 10000 Garis, => ob curves, covering a region of temperature from — 198° C. to + 546° C., show such a bend. which, as the temperature increases right up to the critical temperature for nickel, is displaced towards the weaker fields, thus corresponding to a diminution of the saturation magnetisation as the temperature rises. At 290° Kk. our present measurements show this bend clearly at about 5000 to 6GO00 gauss. At the lower temperatures there is no decided bend visible within the region of fields covered by our observations (/7 << 10400); thus if there are any bends at these temperatures, they must occur at still stronger fields. 1) A. W. Smrrx. Phys. Rev. 30, 1, 1910. ?) A Kunpr. Wied. Ann. 49, 257, 1893 64> 984 At 14°.5 kK. the Hauteffect is strictly proportional to the field, as is also the case at 20°.3 K. as far as H=9060. At 90° K. ihe Haxucoefficient is a linear function of the field, diminishing as the field increases. For the Haxucoefficient in very weak fields the relation R, = ce? holds. : R ; The Lepvc quantity Dp; = a the tangent of the angle of rotation of the equipotential lines in unit field, is here a linear function of the temperature. The following Table shows the extent to which those relations hold. TAB LES Xxx: Ro and Dr, as functions of the temperature. r Roobs, Rocatc. | teate.| PLobs. | 290° K. || 66.0x 10— | 67.5x 10-4 5.37 5.37 90 112 10.5 3.07 3.10 20.3 5.0 5.3 2.22 2230 (14.5 Beil 5.0 2.28 2.22) ss Seep eee Sar Se IS = —— For the nickel plate the magnetic change of resistance was also measured. J was 0.2 to 0.3 amp.- As the resistance of the plate is very small, and the changes were, at the most, 1.5°/,, it was not possible to evaluate them with any greater accuracy. As has also been observed by F. C. Buake’), G. Bartow *) and C. W. Heap ®*), there is an increase in the resistance of nickel in the weaker fields (H< 3000); in stronger fields the resistance diminishes, and, in the region 5600< H< 10270, it does so approximately linearly with the field. This behaviour is, to a large extent, the same throughout the region 290° K. >7' > 14°.5 K. In strong fields the diminution in the resistance is somewhat greater at low temperatures than at ordinary temperature. 1) KF, C. Brake. Ann. d. Phys. 28, 449, 1909. 2) G. BARLow. Proc. Roy. Soc. 71, 30, 1903. 3) CG. W. Heap. Phil. Mag. (6) 22, 900, 1911. eer « i = ; | | | | | | | UrOl Xe 7==! O U,-01XS7'T=M) O || Vr-O1X ENE =mM lee | lsOlXa 7 =a | = = Sf fal oe 2 al : | | | | | | | | | orl — -00F01, iN = | ai ve 2 | | | | | ; : | oe - 0LZ0 ‘Zi — | | = 2 _ | | ¢ | 0Lz01 a2 | 0116 || 6 3 t Bt BY | et 9906 6 = 0678: ees oT tes Hele a | zl — 0sz8 gg — O19 bo | 2 ; yr | | | | | | | a) eA Ae | a= OLZOI yl or9g ey | 0S6r a | | | | || Sl fA | i= —0Sz8 0 | OSLE | 4 0 | OLLE 0 SS, | | | | | BV Sif [ale Lo orgs | ose | 0zsz_ ge + ozs so + [Pay eal bP | | | | | | Laid | | le 0 OL6Z 1 + | OSLI z+ | OLZZ a0 | | | eee : Ses ; | ee i | Sota | | m | m | I} n } m Ole H || OLX H | CO, Greer H | OL eee Bice sige" || eg cig ener ea | ! mz | he aaa |eees Tee ees (cre eal ————- SEE Fae rg EE Ss ae ee 2000 YG00 6000 800010000 Gauss 4 Sig a4 = 1 Se Za oe Sen 7 S=1093 K | x = = = eee FENCES | 4 -§}— - Sais 19 l jes} Fig. 4. At 288° Kk the resistance increases in weak fields, and decreases in fields greater than 7000. This is in agreement with results obtained by L. Grunmaca and F. Werprrt’), C. W. Heap?) and others. At liquid hydrogen temperatures this behaviour is reversed, for the resistance diminishes in weaker fields and increases when //> 7000. There is a neutral zone at about #7 = 7000. 1) L. Grunmacw and F. Wetpert: Verh. d. Deutsch. Physik. Ges. 1906, 359, 2) G. W. Heap: l.c. OSs Physics. “On the Haus. effect, and on the change in resistance in a magnetic field at low temperatures. VIL. The Hau effect for gold-silver alloys at temperatures down to the melting point of hydrogen”. By Bexar Breokmax. Communication No. 132c¢ from the Physical Laboratory at Leiden. (Communicated by Prof. H. KAMERLINGH ONNEs). (Communicated in the meeting of December 28, 1912). This communication is a continuation of Comm. N°. 1300. IV. (rold-silver -alloys. § 10. Measurements at temperatures of 290° K., 20°.3K. and 14°.5 kK. of the Han effect for three Aw-Ag alloys (I, II, I) con- taining a large percentage of gold were published by KAMERLINGH Oxnes and myself in Comm. N°. 129a, § 12, and in Comm. N°. 130e, § 16. The results of my measurements made on one (1) of these alloys at 90° K. were given in § 9 of Comm. N°. 1304. I have since investigated three otber alloys containing a greater percentage of silver, and in the present paper the results of these new measure- ments on the Hari effect for Au-Ag alloys are given and are dis- cussed in connection with the former results. The observational method was the same as was formerly used, viz. the form of the compensation method developed by L&esrerr ') as used by van Everpincen 7). An iron-clad THomson galvanometer was used, with a period of about 4 secs, and a sensitivity of about 1 mm. deflection at 2.5 m. distance for 5 & 10-§ volts. In this method disturbances produced by the thermo-currents arising from the thermo-magnetic effect of von ErrincsHavseN are completely eliminated only in the case of instantaneous closing of the main current circuit. On aecount of the comparatively large period of the galvanometer this was not possible in the .present experiments; but still, these disturbances were too small in the present case to be observed, The main current was 0.5 to 1 amp. The plates were circular (11 mm. diam.) with point electrodes. The resistance of the plates was measured as well as the Hau. effect. The alloys were obtained by fusing pure gold and silver in a porcelain crneible, and then rolling them out. They were all sub- mitted to analysis. IT am greatly indebted for these analyses to ; ) Lepret, Diss. Leiden 1895. Comm. Leiden N°, 19, 1895. 2) f. vAN EverDINGEN, Gomm, Leiden. Suppl. N°. 2, Cf. also H. KAMERLINGH Osnes and B. Beckman, Comm. N° 129a, 1912. HRO Dr--C. Lic. G. Horrsema, Master of the Kart AtmstroM, Upsala. Royal Mint, Utrecht, and to Fil. In the Tables, // represents the field strength in gauss, R the Haus coefficient in ¢. @. s. temperature 7’, and 2, the resistance at Alloy ness of the plate was 0.049 mm. TABLE XVI. HALL effect for (Au—Ag). 77 } T2902 Ke H A RNa eee RH | —Rx104 222 pill MOSER aes 8250 5.25 6.36 9360 -- ~ 9750 6.25 6.41 10270 6.51 6.34 w= 8.06x 10-4 0 a te 2 S108 i) | units, wz the resistance in ohms at the absolute Ost: II contained 10.7 atomic percentages of silver. The thick- T9029" Ke RH — Rx 104 ra | 4,26 5.16 4.96 5.31 5.08 5.21 5.45 Oral w=5.43x 10-40 » —0.69 | Wo | Alloy III contained 80 atomic percentages of Ay. The plate was 0.078 mm. thick. TABLE XVII. T = 290° K. H RH | Srxin 7 8250 5.08 6.10 9065 9360 5.70 6.09 9750 10270 6018 6.02 10270 | w=9.47x 10 0 | 0 0 = 1015 Hatt. effect for (Au—Ag) 777. T= NOK RH — Rx 104 | 4.26 4.70 4.55 4.67 4.83 4.70 | Ole 102 O: = 0.825 990 Alloy IV contained 69.4 atomic percentages of Ag. The plate was 0.083 mm. thick. TeA Bal ES svi: HALL effect for (Au—Ag) IV: T=289K | T=9°K | T=20°.3K | ee AON : a ll ee SS eee RH —RXI1Ct) RH —RX104) RH |—RX104) RH |—RX104 9220 || 5.55 6.02 4.77 9.17 4.12 4.47 best 4.43 9760 5.76 5.90 a} V2 5.25 || 4.40 4.51 4.26 4.379) 10270 || 6.20| 6.04 ||5.41| 5.27 | 4.66 | 4.54 | 4.55 | 4.43 — ‘ —— — | I — — — — = i _— u w=9.8X10-40 w=8.43X10-40 w=7.92X10-40 | w=7.90X10—410 | w= 101 2 =0.815 2 — 0.82 || 2 —o0.82 Wy Wo | Wy Wy Le 1 } Alloy V contained 90.9 atomic percentages of Ag. The plate was 0,082 mm. thick. TABLE XIX. Hatt effect for (Au—Ag) V T = 290° K. | T= 90°K, T=20.°3K. | T=14.°5K, ———— — - _ | RH [Rx 104) RH —R X10! RH -— RX 104) RH _ RX 104 9065 | 6.62 7.31 5.88 6.49 / Se 22 5.76 5.16 5.69 9760 || 7.23 | 7.42 | 6.30) 6.45 5.59 5.73 | 5.66| 5.80 Lea 7.52| 7.32 | 6.58| 6.40 || 5.98| 5.82 | 5.86| 5.71 | (oes | | w= 5.291040) w= 3.8110 -44) w= 3.40X10—-4.0 w = 3.4010-4.9 | | Alloy VI contained 97.8 atomic percentages of Ag. The plate was 0.093 mm. thick. 91 TABLE XxX. HALL effect for (Au—Ag),,, | T = 290° K. T = 90° K. T = 20.°3K. T = 14.°5K. H RH —R>X104) RH —RX104) RH |—RX104) RH |— RX 104] | | | | 9220 || 7.10 7.70 6.79 esd 6.41 6.95 6.38 6.92 9500 || — — — -- _ — 6.59 6.94 9760 || 7.56 1.15 7.22 7.41 6.82 6.99 6.73 | 6.90 | 10270 || 7.95 1.74 eal 7.51 els 6.94 7.09 6.90 | | | Bers a | || = 25.2<10—5.0| w = 12.7X1040||\w = 8.7 < 10-50) |w = 8.7 & 10-50} 0 oo 99) eae = 0.525 a6 w= 0.36 | Wo Wy Wo Wo In Table XXI are collected my results for alloys of gold and silver. In it are given results for the Haut coefficient R7, and its temperature coefficient aus for the Lepvc constant Dy, = fs and for the tempe- "a00 te rature coefficient of the resistance without a magnetic field. All are expressed in ¢. g.s. units. Fig. 1 is a diagram of the electrical conductivity (@) at 77= 290° K. and at 7’=90°K. as a function of the atomic percentage of Ay. The unit in which the conduetivity is expressed is the reciprocal of the resistance in obms of a 1 em. edged cube. The conductivity was calculated from the analyses. (See a previous paper °)). At lower temperatures the characteristic curves become steeper. This is strongly marked at hydrogen temperatures as is shown by the measurements of KaMERLINGH ONNES and Cray *) on a gold-silver alloy containing about O4°/, Ag, and by Cray’s*) measurements on Au-Ag alloys with various compositions. The latter measurements have been confirmed by mine, and have been further extended to embrace cases of average and of small content of Aw. For these cases, somewhat similar results were obtained as with small content of Ag: the addition of a small quantity of gold to pure silver causes such an enormous decrease in the conductivity that, for ') Berner Beckman. Upsala Univ. Arsskrift 1911. *) H. KaAMERLINGH ONNES and J. CLAy. Comm, n’. 99. 107. §) J. Gray. Comm. n°, 107d, 1908. — - 7 ee ————— _ —_—— — TABLE XxI. es) | | l| Rogo | R | | mee ance Rogq0 | Rago | Fas) 8 14°.5 Fae | te | ae all Pt) 2002, PL) pogo | PL 72903 Au 0 || 7.2 10-4 7.6x 10-4 9.8101 9.8% 10-4) 1.05 1.36 | 0.285 0.195 | 3.2x10-7 | 12.6x10—1 133x107 ‘(Au—Ag), 2.0 | 6.8 6.6 | 6.7 16.8 | 0.97 0.98 | 0.49 | 0.30 || 2.3 4.8 | 8.03 (Au—Ag), 10.7 5.6 5.25 Be sel | 0.82 | 0.66 | 0.69 | 0.585 | 1.05 1.12 eee: |(4u—Ag) yy) 30.0 5.6 4.7 13.6 13.7 | 0.77 | 0.64 | 0.825 0.755 | 0.61 | 0.57 | 0.52 (Au—Ag),, 69.7 6.0 5.2 4.5 |4.4 | 0.87 | 0.75 || 0.875 | 0.82 || 0.64 | 0.64 0.60 (Au-Ag)y 90.9 7.35 6.45 | 5,75 \5.75 0.88 | 0.79 || 0.735 |-0.66 1.45 1.79 | 1.80 (Au—Ag)y, 97.8 |7.7 7.4 | 6.95 6.9 | 0.96 | 0.91 | 0.525/ 0.36 || 3.2 | 6.1 | 8.5 Ag 100 8.0 | 8.2 10.15 19.9 LO 2s emelercat 0.23, 0.0091 4.95 \esail 720 993 instance, an admixture of 2 atomic percentages of gold reduces the conductivity (expressed in the above measure) from 71.10 >¢ 10° to 30x10. —- 5 — : E fic | a | | iene - H | > <= ale aa eal | " Clea eS | | | | | 10 et + Og t aang 20 +0 00 a 100 mee (Tom | Ts Fig. 1. f E OT Ww, 1.35 < 10°. The curves expressing the temperature quotient — = 0, wl as a function of the atomic percentage fol!ow a similar course. The researches of KAMeERnINGH Onnes and Cray’) on various gold wires have shown that the degree of purity of a metal can be very @ 1 2 639 40 50 00 67 «680 90400 0 410 20 30 4 50 & 1 8 9 100 — ctlom 7 cla — Uoms Xs Fig. 2 and 3. 1) See note 3 p. 991. 994 accurately gauged from a determination of the temperature coefficient of its resistances at hydrogen temperatures. Figs. 2 and 3 show the Hattcoefficient Ap at temperatures of 290° K., 90° kK. and 20°.3 kK. as a function of the atomic percentage of Ay. The curves resemble those which give the electrical con- ductivity and the temperature quotient of the resistance as functions of the atomic percentage. (Cf. KamerLincu Onnes and Bene? BECKMAN, ~ Comm. N°. (30c). When silver is gradually added to pure gold, the Hanucoefficient at low temperatures diminishes, at first rapidly, and then more slowly, until, with a mixture of about equal quantities of Aw and Ag, a large change in the composition occasions only a very small change in the Hatteffect. The lower the temperature the steeper is the descent of the curve. For instance, when a 2°/, admixture of silver is added to pure gold the Hattcoefficient diminishes at = 20°sK. from "9.6 x LOS* tonGe oxel ae ate 2? \ 90% trom :.6 S10 tonb:. bodies at 2 290° Ketrom 7.210 to G8 Se 10 = Hence a small Ag impurity in gold occasions only a small varia- tion of the Haztreffect at 7 = 290° Kk. which, however, becomes more appreciable at lower temperatures. On the other hand, as is evident from the measurements of A. von Errincsnausen and W. Nernst'), E. van Avpet*) and A. W. Smitn*), the addition of a small quantity of Sr or Sé to 4i, which exhibits an unusually large Hawt-elfect, occasions even’ at ordinary room temperature a great change in the Ha1t.-effect. In Fig. 4 are shown the curves (0 of the temperature quotients 290° Rao,30 B < x A. and — as functions of the atomic Lace percentage of Ag. These curves - have the same general features as those of Figs. 1, 2. and 3. Fig. 4. In Fig 5 is shown the relation between # and 7’ for some slw-Ay alloys. The course of the curves between 20°K. and 90°K. is not quite certain, as no-observations could 0 10 20 30 40 § ) A. y. ErrinGsHausen und W. Nernst: Wied, Ann. 33, p. 474, 1888. 2) H. van AuBeL: C. R. 185, p. 786, 1902. 3) A. W. Smita: Phys. Rey. 32, p. 178, 1911. 995 be made between hydrogen and oxygen temperatures. These portions of the curves are therefore indicated by dotted lines. With Ag and el rae Eo |e = aay He Au the Haticoefficient increases. as the temperature falls. This increase takes place chiefly in the temperature region 20° << 7’< 77° K. In the hydrogen region, 207.3 > 7’ > 14°.5, R is constant within the limits of accuracy. A very small diminution of the Hat.coefti- cient is exhibited by the alloy (Aw-Ag); with 2°/, Ag at.low tem- 1 peratures. At low temperatures alloys with more than 2°/, of Ag show a distinct diminution in the Haur effect, which is greatest for alloys of medium concentrations. Thus alloy HI with 380°/, Ay gives Rago . ‘ ‘ Royo ae ; - = 0.64. With Aw and Ag the ratio —— differs but very little Ragoo R900 : from 1, while with alloys of medium concentration it differs consi- derably from 1. Of the alloys with a large percentage of Au, a distinct diminution of the Hateffect at low temperatures is already exhibited by alloy VI, with 2°/, of Aw. In fig. 6 is shown the relation between the Lrepvuc constant Dr =— and the atomie percentage of Ag at 7’= 290° K. and a T=90° K. This constant is the tangent of the angle of rotation of the equipotential lines in unit field. The curves are of the same nature as the conductivity-silver percentage diagrams; at lower tem- peratures they become steeper. When two per cent of Aw is dis- solved in Ag. Dy at T=20° 3K. sinks from 720 & 10-7 to85 x 10 It is worth noting that with alloys of medium concentration Dy, is approximately constant throughout the whole temperature region 290? > T > 14°.5; this holds for 10.7 << 90.9 that is to say, for alloys in which the percentage of neither component is less than 10. With alloys which may be regarded as dilute solutions, hence for O om: Te Fig. 6. At 7= 290° K. the Hantcoefficient for dilute solutions is pro- portional to the conductivity 6,,,° . It would undoubtedly be of the greatest importance to systema- tically extend these investigations of the Hanieffect in alloys at low temperatures, which | have, to my regret been obliged to confine to a single series of alloys, and to further investigate alloys of dif- ferent types. | hope to continue this research as soon as I can find a suitable opportunity. | gratefully acknowledge my indebtedness to Prof. Kamerinci Onnes who invited me to undertake these investigations of the Hau. effect at low temperatures. EAs Sy eer 997 Physics. “On the Warr effect, and on the change in electrical resistance in ai rynetic field at low lemperatires. VII. Zhe Harnegect in Tellurium and Bismuth at low temperatures down to the melting point of hydrogen”. By H. Kamer.incn Onnes and Brxer Beckman. Communication N°. 132d from the Physical Laboratory at Leiden. Communicated by Prof. H. KAMERLINGH ONNEs. (Communicated in the meeting of December 28, 1912). § 20'). The Haurefiect in Tellurium. The measurements were made with a short period Wirprmayn galvanometer. The primary current was /=0.2 amp. Two plates were investigated, both con- structed from the purest Merck tellurium. The first plate 7v,,; was compressed in a steel mould. and the second plate 7v,;; was cast in a steel mould. The first plate was very brittle. Both plates were circular with a diameter of 1 cm. The electrodes were platinum wires ‘/, mm. in diameter, and were fused into the plates. To these platinum wires the leads were then soldered. The specific resistance and its temperature coefficient were different for the two plates; at T= 289°K. wy, was twice as great for the first as for the second. The resistance temperature coefficient for Ze; was always negative over the whole temperature region 289° > 7’ > 20°.3 K. Te,7) cn the other hand exhibited a minimum in the resistance below 7’= 7O0°K. The thickness of the piate 7,; was 1.175 mm., its resistance at == 2907 K was 20.8 2 AA) 3} ion) and again at i—a2 0 os we): at low temperatures therefore the resistance is considerably increased; cooling, moreover, caused an increase in the resistance at ordinary temperature, which is probably due to the production of small fissures. At T= 290° the specific resistance was 1.95 x 10° ¢. ¢. s. We obtained the following results (R// and FR given in ¢. g. s. units): (see table XXV_ p. 998). At T= 290° the specific resistance of 7,77 was 1.01 10° ¢. g. s. The plate was 1.88 mm. thick. The change in the resistance with temperature is shown in Table XXVI and in fig. 5), Hence. as has already been mentioned, the resistance of the plate Tey attains a minimum at about 40° to 60° K. This behaviour is somewhat similar to that found by Dewar to be characteristic of 1) The sections of this Communication are numbered as continuations of Comm. No. 132a. 2) The diagrams are numbered as continuations of those in Comm. No. 13a. 69 Proceedings Royal Acad. Amsterdam. Vol. XY. 998 TABLE XXV. Hatteffect for Tey I H i eo T— 20083 Ks in gauss RH R RH R = Si ts eee 3750 14.65 > 104 39.1 1641-1047 |) 4351 5640 22.4 39.7 — | _ 7260 29.0 40.6 31.9 44.2 9065 35.4 39.1 |) 41.4 44.5 10270 40.2 39.1 | 46.6 45.3 bismuth containing only a slight amount of impurity, and by J. KopnigsperGer, O. Reicuennem, K. Scainuine ') for a kind of pyri- TABLE XXVI. Variation of the resistance of Tellurium, Tesip with temperature. th w 289° K 0.212 0 170.8 0.146 162.3 0.144 153.1 0.141 141.8 0.136 90 0.119 80 0.117 69.5 0.113 20.3 0.122 | ihe 0.124 14.5 0.126 O. Reicuennem. Inaug.-Diss. Freiburg 1. Br. 1906. J. Koenigspercer und K. Senmune. Ann. d. Phys. 32, p. 179, 1910. }) J. Koenicsercer. Jahrb. d. Rad. u. Elektr. 4, p. 158, 1907. 999 tes, for magnetite, mefailic titanium and metallic zirconium, a pbe- nomenon explained by J. Kounigspercer by the dissociation of elec- trons from the atoms. 3 2 ——+— SSS Se | A 04 -—— + + 4 = - 4 A “y Bre | y LE en | aaa be a | — | | | is | T a Ww h) I =| 0 50 09 150 2000 450 300 > T © Fig. 5. With this plate, too, an increase of the resistance was observed on returning to ordinary temperature 7’= 290° K after having cooled it to hydrogen temperatures. In this case, however, it was much smaller than with 7%,;, and was, at the most, 5'/,. We obtained the following results : TABLE XXVII. Hatteffect for 7e I P er || T=21°K || 7=—s99K T =20.53K T =14.°5K } in | | (gauss RH R RH R RH R RH | R 3720 | 6.90x105) 185.5 7.85x10° 210.5 7.98x105 214.5 7.85x105 211 5680 10.55 186 11.95 | 210 12.1 213 11.85 | 208.5) . - 7260 : iG. |) 187 = |\15.4 |212 |] 15.0 | 206.5 (9065 16.75 185 18.75 207 19.05 210 18.65 205.5 10270 | 18.85 | 183.5: || 21.25 | 207 21.4 | 208.5 || 21.0 | 204.5 At any definite temperature A is practically constant for various fields; at lower temperatures there is an indication that # diminishes somewhat in the stronger fields; this is most marked at hydro- 65~ 1000 gen temperatures at which FR, (R for H= 0) is about 5°/, greater than A for H = 10000. For both plates the Har.effect increases at lower temperatures, Row while the ratio ——— is the same. This is very remarkable, for the Ragok 5 plates are completely different with regard to their specific resistance, _ resistance temperature coefficient and absolute magnitude of the Hauteffect. For both plates the value of the Hatieffect is small compared with that obtained by A. v. ErrincHausen and W. Nernst’), 530, and also by H. Zann’), and the electrical conductivity is also small. According to the researches of A. Marrntrsen’), F. Exner*),W. Haken’), J. F. Kroner") and others, various modifications of telluriam occur; accord- ing to Kroner it exhibits dynamical allotropy. The two moditica- tions have very different conductivities. The specific gravity of the plate 7e,;; was 6.138; this is perhaps connected with the cireum- stance that it cooled slowly after casting, and that it was subjected to local heating when fusing in the electrodes. For a preparation very quickly cooled Kroner gives a specific gravity as low as 5.8. The modification with the lowest specific gravity seems to have the smallest electrical conductivity. § 21. The Hatuefiect in Bismuth crystals. In Table XU, Comm. N°. 1297, we gave results of measurements of the Hatteffect in bismuth crystals for the case in which the erystalline axis is per- pendicular to the field, and the main current runs in the direction of the axis. To these we are now in a position to add results for the case in which the field is parallel, and the main current perpen- dicular, to the axis. For these measurements we used one of the crystal prisms which had been used by Van Everpincen (Suppl. No. 2) in his measurements, choosing the most regular of the three (2, 3 and 5 |. ¢.) which bad been found suitable for this purpose (cf. p. 82 1. ¢.). In the following Table are given Rk, H and RH in c.g.s. At ordinary temperature and in weak fields RH is negative, as was first discovered by Van EverDINGEN and subsequently confirmed. by J. BrcQueREL’). 1) A. von ErrinaHausen und W. Nernsv. Sitz. Ber. Akad. d. Wiss. Wien. 94, p. 560, 1886. 2) H. Zann. Ann. d. Phys. 23, p. 146, 1907. 3) A. MATTHIESEN und M. von Boss. Pogg. Ann. 115, 385, 1862. 4) F. Exner. Sitz. Ber. Akad. d. Wiss. Wien. 78, 285, 1876. 5) W. Haken. Inaug. diss. Berlin 1910. 6) J. F. Kroner. Inaug. diss. Utrecht 1912. 7) J. Becqueret, C. R. 154, p. 1795. June 24, 1912. 1001 In stronger fiields R/Z becomes positive, as was also found to be the case by Van Everpincen and Becqurren. We may, however, incidentally remark that the initial negative values found by BrcQuerEL are much greater than owrs, and that with him zero is reached in much stronger fields than with us. This leads us to suspect that the initial negative values we have obtained are to be ascribed to some ‘ause which occasioned their occurrence to a much higher degree in BECQUEREL’s experiments; this would be the case, for instance, if our bismuth were purer than his, but still not yet quite free from impurity. If that were the case, then with absolutely pure bismuth we should, perhaps, at ordinary temperature, obtain nothing but increase of RH with the field, the rate of increase being slower in the initial stages. on D | o =m oo 6 Sil Ge ea : Ha sup <4 ise | 20 Pus | | fo) | x | x = | Lon TOU at ax & b ye) Te of \| Correns') pointed out this relation and called it “Faktorenkoppelung”. Some years later Batrson*) put forward a theory to explain the phenomena observed. According to Batrsox, in the formation of gametes in the case of a plant heterozygous for more than one factor, the various possible combinations of factors or genes do not arise in equal numbers. There may be two reasons for this. In the first place some factors may show a certain tendency to remain connected whilst they are however not so completely coupled as to preclude occasional separation. In the second place there can be between different factors a tendency to repulsion. Some examples of such ‘“gametic-coupling” and “repulsion” or “spurious allelomorphism’, as batrson calls these phenomena, are already known. | too made observations in the course of my in- vestigation on hybridisation that could best be explained by such a venetic correlation. Whilst however the cases known up to the present relate to characters whose presence or absence in the plants investigated is. easily determined, this is not so in my inquiry. I have studied characters whose fluctuating variability is very marked, while moreover the distinction between the parental forms for one and the same character already amounts to several genes. The characters are, as LANG*) expresses it, polymeric. On this account the phenomena become so complicated that a complete analysis is impossible or only possible by most laborious investigation. I have so far therefore taken a shorter course and.shall only show in this preliminary paper that the phenomena point to a correlation not only between two but indeed between a greater number of characters. My observations have been made on the cross already ') earlier described, between Linwan angustifolium Huds. and a variety from ‘) G. Correns, Ueber Levkoyenbastarde. Bot. Centr. Bd. 84, 1900, p. 11 of the reprint. 2) W. Bateson, Mendel’s Principles of Heredity, 1909, p. 148. 3) Axnotp L3nc, Vortgesetzte Vererbungsstudien. Zei'schr. f indukt. Abst. und Vererbungsichre, Bd. V, 1911, p. 113. 4) Das Verhalten fluktuierend variierender Merckmale bei der Bastardierung. Ree, d. Trav. bot. Neéerl. Vol. 8, 1911. p. 201. LOOS Reypt of Linwn usitatissimum 1. which | have called Egyptian flax. The chief points of difference between these plants are the following : the flower, the fruit and the seed of L. angustifolium are smaller than those of Kyypttian jlax, and moreover the colour of the flower is lighter. The following mean values show. this. L. angustifolium. Lgyptian flax. Length of petal 8.08 mm 16.20 mm Breadth —,, 4.45. ,, ISO fe Length of seed 2.40 _,, 6.08 — Breadth _ ,, 14S a = De 8 By analysis of the second generation | was able to show that the difference in length of the petal of the two forms is caused by at least four factors. This holds good also for the breadth of the petal, while the difference for the length of the seed amounts to at least four and for the colour of the flower to at least three factors. The difference in breadth of the seed is also caused by several factors. *) I have attempted to trace the behaviour of the above characters on hybridisation. The first generation was wniform and intermediate in the case of all characters; in the second veneration a considerable segretation had occurred. This generation consisted for each of the reciprocal crosses of fully 100 planis. Both groups were separately investigated. Since these however gave exactly the same results, I will only deal with the crossing in which LL. angustifolium was the father. Of this I have observations of all characters in exactly 100. plants. The length and breadth of the petal were determined by taking the average values of several flowers; for the determination of the length and breadth of the seed a greater number of seeds were measured, mostly 50 to 100, and the average was taken. The colour of the flower was estimated in the manner described before *) and expressed numerically. The light colour of the flower of L. angus- 1) Since the appearance of my above mentioned paper | have succeeded in showing that the factors which cause the difference in the colour of the flower are distributed over both forms and that these forms have no common factors. The proof cf this was obtained by the appearance of white flowers. The plant was found in much larger cullure than the one previously grown. In this case the hybrid thus oversteps the limits of the characters in the parents. With respect to the factors for the other characters my investigations are not yet complete. eyelecs Dp. 200: 1006 Length Breadth | Length Breadth of seed of seed of petal of petal ae : : Y ; of petal in mm in mm in mm in mm 3.144 1.880 9.7 6.3 3 3.186 1.961 10.8 8.0 5 3.186 2.006 10.0 8.3 4 3.224 1.920 9.4 7.0 1 3.242 1.976 9.5 6.4 2 3.281 2.007 10.6 8.0 3 3.305 1.960 9.4 8.5 6 3.321 1.895 10.5 7.8 3) 3.383 2.054 11.4 9.4 6 3.387 1.916 10.1 1:5 5 3.405 1.983 9.5 ded oa 3.449 1.960 10.0 8.0 ; 2 3.450 2.006 11.0 7.0 6 3.451 2.016 10.9 8.3 6 3.458 2.095 9.6 7.0 4 3.473 2.057 11.1 9.2 8 3.482 2.023 11.0 8.3 i 3.495 1.928 11.0 8.5 7 3.501 2.104 10.8 8.9 8 3.511 2.038 19.0 8.0 6 3.529 2.022 IS : 8.0 6 3.530 2.042 9.2 1.3 4 3.552 2.067 10.6 8.0 4 3.557 2.086 11.3 15 5 3.562 2.239 | 10.5 7.0 6 85.064 50.241 259.4 195.9 124 1007 a a a Length Breadth Length Breadth Colour of seed of seed of petal of petal of petal in mm in mm in mm in mm 3.564 2.130 10.8 8.8 4) 3.570 1.993 10.3 8.5 7 3.575 2.149 10.8 726) 5 3:600 2.126 10.8 8.4 8 3.606 2.077 9.4 6.9 5 3.610 2.224 11.8 8.6 7 3.615 2.088 10.8 8.8 6 3.617 2.080 10.4 8.0 5 3.619 2.150 10.8 ees 6 3.620 2.112 10.5 7.8 5 3.624 2.437 10.7 8.6 7 3.628 2.246 11:5 9.0 7 3.629 2.333 2 1.4 4 3.629 2.157 10.6 8.4 8 3.648 2.013 10.7 8.9 2 3.650 2.145 10.5 8.4 3 3.662 2.226 12.1 8.6 3 3.670 | 2.081 10.6 7.8 6 3.671 2.050 Niboe? 7.0 5 3.672 2.036 10.0 6.3 5 3.682 2.193 10.7 6.9 9 3.716 2.267 11.4 8.2 6 3.717 2.331 12.4 9.2 8 3.723 2.183 10.3 Tats) 6 3.741 2.141 Wor 8.0 5 Length of seed in mm eS eee 3.159 3.761 3.766 Breadth of seed in mm bo ive) to bo _ tr =) = oS oo bho he) fo2) ioe) ive) ioe) or Length Breadth Colour of petal of petal ; ; of petal in mm in mm 10.8 7.0 4 11.0 8.2 5 HES} 7.6 5 eZ, 8.4 6 10.4 8.0 9 10.0 158) 4 11.2 8.5 6 10.1 8.7 10 10.2 8.2 7 11.0 9.5 7 11.8 9.6 6 NES} 8.0 8 13.0 8.6 4 10.0 7.4 1 11.0 9.2 8 ie 9.5 6 10.5 7.8 ifs 115 8.5 5 9.5 6.5 5 10,6 8.0 4 17 8.5 5 9.8 7.0 6 Li25 8.2 8 11.3 8.5 4 10.0 8.6 4 272.1 205.5 150 1009 eee SS = | Length | Breadth Length Breadth | : of seed | of seed of petal of petal | aba ; ; ' of petal in mm in mm in mm in mm 3.915 2.260 10.7 9.0 8 3.922 2.413 10.0 8.4 4 3.922 2.313 11.0 8.5 8 3.923 2.270 10.0 9.1 5 3.926 2.287 10.6 8.2 9 3,933 2.271 11.0 9.5 8 3.940 2.351 Wl 7) 9.8 8 3.948 2.361 12.0 9.2 7 3.949 2.150 11.0 8.8 9 3.968 2.298 10.5 8.0 6 3.988 2.196 10.6 9.5 8 4.016 2.218 9.5 8.2 4 4.031 2.225 eS 8.2 8 4.139 2.295 1-3 | 9.7 6 4.140 2.317 11.0 8.0 5 4.154 2.350 12.0 9.5 7 4.167 2.389 11.3 8.0 6 4.188 2.345 it 33 8.6 T 4,238 | 2.348 Iie2 9.3 9 4.244 | 2.456 11.0 9.4 5 4.274 2.446 11.8 9.8 10 4.335 2.452 13.2 10.7 8 4.350 2.311 11.2 Uae) 6 4.381 2.461 122 10.0 | 7 4.420 2.469 | 15 9.9 7 102.411 58.252 | 279.1 224.8 175 1010 tifolium was represented by T, the much darker colour of Egyptian flax by 10. I have arranged the observations according to the ascending values of the length of the seed in order to obtain a survey of the.mutual relationship of the various characters. In the preceding table the figures placed in a horizontal row refer to the various characters of the same plant, in the vertical columns those for different plants are given. The whole table is divided into four parts, each containing 25 plants. From these tables it must now be clear whether there is or is not an inter-relation between the length of the seed and the other characters. If the latter are wholly independent of the former then for each character the values in a vertical direction must follow each other without any regularity; the lowest average, and highest values for each character must be distributed equally over the four tables and the totals of the 4 successive series must be equal or nearly equal or must at least be arranged without any regularity. On the other hand should there exist an intimate relation between the length of the seed and the other characters such that they be- have as a single whole, then these other characters \ ill also be arranged in the tables according to ascending or descending values, except for small deviations due to the influence of external circum- stances. A superficial inspection already shows that for none of the cha- racters are the values in the vertical columns in a sequence; be- tween successive figures a good many irregularities occur. If how- ever the tables are compared with one another, it is seen that in general in the first lower values, in the last higher values are found, In order to make a comparison easier, I have added the values for the 25 plants of each table. Below are given the totals obtained for the different characters. ; Length | Breadth Length Breadth Colour of seed | of seed of petal of petal of petal 85.064 50.241 259.4 195.9 124 91.058 53.668 271.5 201.0 145 95.520 54.544 272.1 205.5 150 102.411 58.252 279.1 224.8 175 1011 We see the values for all four characters increase in successive series. It follows therefore that, on the whole, in the plants which have the smallest length of seed, the breadth of the seed and the leneth and breadth of the petal are smail, whilst moreover the flower shows the lighter shades, and conversely a greater length of seed is generally coupled with greater breadth and a larger, more deeply- coloured flower. In the same way as proceeding from the length of the seed, I have also determined the inter-relations of the other characters. From the above table I have arranged the values in ascending order according to the breadth of the seed and compared the others with it. The same was done starting from the other characters. It is unnecessary to give here the complete tables. Below are set out the totals obtained each time for 25 successive plants. Arranged : in ascending Length Breadth Colour order of breadth of petal | of petal of petal of seed Plant 1— 25 261.3 195.8 121 = 26-—50)|| 26920 204.5 148 ~ ot— i) 270.0 205.0 | 154 » 16—100} 282.8 221.9 171 —— rr Arranged in Arranged in = ascending Breadth Colour ascending Colour order of length order of breadth of petal of petal of petal of petal of petal Plant 1— 25 190.8 121 plant 1— 25 124 5 = "FHI Bile 148 26——50 141 > l= 9B) eile 160 e) 251-15 150 peei6—100) | 223.4 165 Pe 16—100 178 As is seen the values for successive series of 25 plants in all the above cases increase. There exists therefore a relation not only between the length of the seed and the other characters but the five characters together form a complex of which each part in_ its development depends somewhat upon all the rest. Now the nature of the inter-relation of the characters of the 1012 flower and seed which have been studied is, as the figures show, such that in general the development of all characters in one plant is in the same direction, since, for example, a long petal shows a distinct tendency to be coupled with a broad petal, with darker shade of flower and with a ereater length and breadth of the seed. From this it might be deduced that here it is only a question of ordinary consequences of slight differences in external conditions in consequence of which the best nourished plants develop more strongly and form larger deeper-coloured flowers and larger seeds, in other words that the relation observed may only be the usual correlation phenomenon of fluctuating varying characters, just as met with in homogeneous material that is in pure forms. There indeed occurs, as the observations showed, a correlation between the characters in the parent forms and also in the first gene- ration, of the same kind as the relation here described. “In F, also this correlation will play a more certain part, but only in a subsidiary way and the phenomenon is chietly due to another cause. This is already clear from my earlier investigations. Moreover | have also traced the relationships in the offspring. When the relation observed is a phenomenon of correlative variability, then the offspring of each individual of the second generation must exhibit again the same correlationfigure as the whole second generation or at least the offspring of a plant which is extreme for one or more characters must in general deviate much less from the average type than this plant itself. Now this was not the case, for it was found that the relationships as they appeared in the /-plant were in the main handed on to the offspring. Some examples having reference to the length, breadth, and colour of the petal will make this clear. The values for four different /’-plants and their offspring are given in the following table. The first /’}-plant possesses the three characters in an extreme degree, the fourth has extremely small values for them all, the two others show different combination. - vie F, Length of petal 13.2 mm = 12.1—14.8 mm Breadth 43 | 10.7 nA NO hS3— 312) a Colour - 8 7—9 Length of petal 13.0 mm 12.1—14.0) mm Breadth “ | 8.6 FA i 92 as Colour + [33 2—o 1018 Iki if, Length of petal 10.0) mm 8.5—11.2 mm Breadth . 9 if 8.3—10.1 * Colour Bs 5 5 =i Length of petal 9.5 mm $8.2—10.0 mm Breadth . OG 6.0— 7.2 Colour ne 2 (b——7) The above proves that there is. still another relation between the characters in the plants studied in addition to ordinary correlation. The whole phenomenon is only superficially like such a correlation. Just as any single character which is based on several genes, gives in the second generation a pseudo-curve which shows itself as a eurve of fluctuating variability but in which the fluctuating variability plays only a more or less subordinate role, so also here in /’, an 2 inter-relation of different characters may appear that simulates ordinary correlation, but that is in reality a completely different phenomenon which is only shghtly affected by this correlation. I point this out because it seems to me that in studying correlative variability it is of the highest importance to investigate only pure homogeneous material. Since JOHANNSEN has made known to us the “pure lines’, it has become clear that much that was formerly thought to be pure material, is a mixture of several forms perhaps also of hybrids. It is possible that the correlation found in such material is not a pure correlation between the fluctuating variability of the characters but is wholly or in part a different correlation phenomenon. This is also the case here. We must assume that here a genetic relation exists between the groups of factors for the different characters. This relation is such that in the formation of gametes in /*, definite combinations of factors occur preferentially. In general a tendency exists to make the proportion in the number of factors for the various characters such as it was in the original forms or at least to ap- proximate to these. This explains that in /’, more forms arise in which the characters all deviate in the same direction from the average than should be the case according to the laws of probability. In the crossing mentioned above the groups of factors for the various characters behave with respect to one another differently from the way in which the factors for one single character behave mutually; for my earlier investigations have shown, that for each of 66 Proceedings Royal Acad. Amsterdam. Vol. XY. 1014 the characters under discussion the genes are mutually quite independent of one another. It is most noteworthy that there exists between the factorgroups for different characters a closer relation than between the factors for the same. Further investigations must show to what extent this phenomenon occurs in other cases and whether it is always coupled with a tendency to preserve the complete image of the parent forms. In the case here described the genetic correlation is incomplete. As is clear from the tables plants are found, which for some characters more nearly approach the one parental form and for others are nearer to the second. The number in which the different combinations oceur, cannot be determined as is done by other investigators for thei crossings, also because ordinary correlation plays through it and still further obliterates the separation between the groups. If at all, the ratios could only be found by much more detailed investigation ; but it is clear from the foregoing that by this means some insight into the phenomena may be obtained. The characters mentioned all belong to flower or seed, the fruit might be added since a very close relation exists between the size of the fruit and that of the sced. I am also engaged in tracing the relation of the characters mentioned to those of the vegetative organs. I am. however, prevented by circumstances from completing this investigation in the near future. The results of the investigation may be summarised as follows: In hybrids of Limon usitatissinum and L. angustifolium an in- complete genetic correlation exists between the groups of factors or genes for length, breadth. and colour of the peial and length and breadth of the seed; whereas on the other hand the factors for the same character are completely independent of one another. The inter-relation is sneh that there exists a tendency to approxi- mate to the combination of characters as it occurs in the parent forms. The genetic correlation expresses itself apparently as a phenomenon of the ordinary correlation of fluctuatingly varying characters; the latter correlation which also oceurs, plays only through the former. Botanical Laboraiory. Groningen, 3 Oct. 1912. 1O15 Botany. Jou. H. van Burkom: “On the connection between phyl- lotavis and the distribution of the rate of growth in the stem’. (Communicated by Professor Wun). (Communicated in the meeting of November 30, 1912.) Various investigators have studied the longitudinal growth of the stem. They have for the most part paid attention to the total increase in length of the stem and only a few investigated the dis- tribution of the rate of growth in one or several internodes. Com- plete investigations, on widely different plants with regard to the distribution of the rate of growth over the whole growing region have so far not appeared. There occur indeed in the literature two important utterances which are based on preliminary observations. The first is the opinion expressed by Sacus') that the growth of stems with distinct modes differs from those with indistinct nodes. If the stem is sharply articulated then according to Sacus each internode shows its own curve of rate of growth. This rate increases from the base of the stem towards the apex, reaches a maximum and decreases again towards the upper node. If the stem has indis- tinct nodes then the whole growing region yields a single curve of rate of growth of this type. Rornert *) has further described this. He speaks of individualised internodes when each internode grows as a separate unit and passes through the great period of growth, whilst in other cases the whole stem passes through this growing-period as one internode. Notwith- standing that these two authors have clearly distinguished two methods of growth, the growth of the whole stem in one growing- period has had most attention paid to it. so that in most text books it is given chief consideration. This is the circumstance which led me in 1907 to make measure- ments on various plants in the Botanic Gardens at Utrecht. With regard to the results of this inquiry which will be shortly communicated in my Dissertation, I wish here to make a brief preliminary statement. With the aid of a little stamp made for this purpose or of a “brush and India ink, linear marks were made on the stem, so that it was divided into zones. ') Sacus Jul. 1873. Ueber Wachsthum und Geotropismus aufrechter Stengel. Flora 56 Jahrgang. Regensburg. 2) Rornert W. 1896. Ueber Heliotropismus. Conn’s Beitrage zur Biologie der Pflanzen Bd VIL. 66* 1016 Immediately on the completion of intervals of time which were as far as possible equal, the length of the zones was measured accurately to '/,; mm. [ caleulated from the increase in length the average rate of growth per m.m. during each separate space of time. In making the measurements a great difficulty was the determination of the exact boundary of the zones, because the portion of the stem on which the mark had been placed, grew at the same time. I there- fore tried to determine as far as possible the middle of the mark. In my later observations, I succeeded in avoiding the error due to this, by marking alternate zones with a lengthwise line. 1 then took the extremities of the longitudinal mark as the zone-boundary. Rapid growth also caused this boundary to become indefinite and difficult to determine. To gain an idea of the errors in my Observation, I frequently also measured in the course of my observations the zones which had already been found to have grown out. I thus obtained numerical data concerning the length of the same zone measured at different points of time. The greater number of these data were identical, only a few deviated. Calculation showed that the average error was smaller than the expected degree of accuracy. In Asparagus officinalis Lixy., Ginkgo biloba Lixy., Hedera colehica Hocn and Linwn usitatissimum Laixyx., the whole region of growth formed a single curve of rate of growth, i.e. regularly increasing growth from below upwards and then decreasing growth above this. Acer dasycarpun Enri., Acer platanoides Lixy., Deutzia scabra Tuec., Lonicera tatarica Laxy., Syringa vulgaris Laxy., and Viburnum Veitchi C. H. Wricut showed a similar curve of rate of growth with this dif- ference that the zones in which the nodes were situated showed __ less growth than ihe zones lying nearest to them. Fig. 1 shows the curve of rate of Fig. 1. Deutzia Scabra Tune. growth in Deutzia Scabra Thbg. from 13—17 Juli. 13" to: 17 July): 1) On the abscissae axis the zones have been plotted at equal distances. The thin lines give the divisionemarks between the zones, the thick lines are the nodes. As ordinates | have plotted the average rates of growth of each zone during a definite space of time. The rate of growth of the lowest zone of the stem is given in the curve on the left, and that of the uppermost zone on the right. 1OL7 In Clematis alpina Mier, Clematis recta Lins., Eucalyptus Glo- bulus Lasiwn., Dahlia variabilis Duss. Polygonum cuspidatun SB. et Zuce, Polygonum Sachalinense F. Scumipr and Sambucus niger Lins. the zones lying below the node had moreover a distinetly slower growth than the others. (See fig. 2). Fig. 2. Polygonum Sachalinense ¥. Scamipr 9—11 May. In both groups of plants in the beginning the lowest part of each internode grew fastest whilst the rate of growth near the upper end decreased till in the ‘‘node-zone” it became very. slight or zero (Polygonum). Afterward the maximal rate of growth was displaced toward the apex and diminished in magnitude. The zones in which the maximal rate of growth had lasted the longest time. during which period this maximum in the internode also reached its greatest value, increased much more than the upper- most zones in which the maximum lasted only for a shorter time and in which it was moreover mnel decreased in intensity. The difference between the first group (Acer ete.) and the second group (Clematis ete.) lies in the rate at which the maximum of erowth travels along each internode and the point of time at which it occurs. In the first group the displacement of the maximum begins in a very early stage of development and the maximum is very quickly found below the node. On the other hand this movement is slow in the plants of the second group, so that for some time, often indeed for a considerable time, the uppermost zones of an internode show less growth than the inferior zones of the same internode. Since the difference is confined to the moment of time in which and the velocity with which the maximum moves in the direction of the apex, the two groups are not sharply differentiated, and sometimes it is possible to obtain a curve of the rate of growth from plants in the one group which agrees with that from the other group. I have not yet been able to determine from my observations what factors may influence the movement of the growth maximum. When 1018 the maximum chanced to occur just under the node and was there- fore measured in the nodal zone, this zone showed the maximuin growth. The ascent of the zone of maximal growth from the basal portion of the in- ternode now continued in the lowest zone aan of the second internode up to the maxi- mum rate of growth of this internode. In this case I found in both internodes one ascent of the rate of growth without diminution in or near the nodal zone (see fig. 3). Humulus lupulus Lixx. showed two ——_ Vig. 3. Sambucus niger Livy. ilferent curves of the velocity of growth, 11—16 Mei. namely, some had a regular course (one maximum for the whole growing zone) and some with a decrease at the upper end of some internodes. These divergent results can be brought into agreement by specially noting the movement of the maximum. Its quick passage into the nodal zone, not only in the undermost growing internode but also in the second internodes, caused the curve of velocity of growth in these internodes to become a regu- larly ascending line. In the higher internodes the maximum occurred under the nodal zone. If a sufficient number of growing internodes had been marked on the same stem. I was indeed able to observe this. I think I have also observed ,that the movement of the growth maximum in an internode of Humulus takes place at about the same time as the maximum of the whole growing region is found in that internode. I regarded the growth as intercalary, if there was either in the upper or in the lower portion of an internode a short zone which maintained its growth a long time, whilst the middle of the internode was already full grown. | have observed intercalary growth in Commelina nudijlora Lixy., Equisetun limosum Lixx. and Tradescantia repens Vann. In Commelina 1 saw this stage preceded by growth throughout the whole internode with the greatest rate of growth below. The maximal rate did not, however, move towards the upper end but 1O19 remained situated in the basal portion, whilst in the upper part growth quickly diminished and wholly ceased. In order to observe well the growth of stems with individualised internodes, external conditions must be favourable. [ found that during the days on which the temperature was very low (an average of 10° ©.) the curve of rate of growth was almost a horizontal line with scarcely any maxima, and this was also the case with plants which at a higher temperature had a strongly undulating curve. All plants, which were found to have a lower rate of growth in or also under the nodal zone (to which class plants with intercalary growth also belong) possess complete nodes, that is to say, they show an external thickening round the stem at the point where a leaf is inserted. This may happen in plants with alternate leaves, but it always occurs in plants with opposite leaves. On the other hand plants in which ill-defined nodes (‘incomplete nodes”) are found, show in the growing region a single curve of growth rate and the nodal zones are not differentiated by a smaller rate. It is therefore seen from these observations that there is here a connection between phyllotaxis and the distribution of growth in the stem. With regard to the structure of the stem three theories are chiefly put forward. Next to the view that the leaves spring from the stem as independent organs (Strobilus theory) stands the phyton theory, which declares that the stem is composed of the basal parts of the leaves (Gorrne, GaAvpicHavp). CELAKOVSKY ') expressed this view in his caulome theory. A third opinion regards the interior of the stem as an axis round which there is a layer of leaflike origin. Hormeister regarded this development as ontogenetic, whilst Poronifé*) thinks that it has taken place phylogenetically. The pith is according to Poronié the primeval caulome, round which origi- nally xylem and phloem have developed from “leaf feet” (phy llopodia). CELAKOVSKY’S theory as also those of Hormuisrer and Poronié, holds that the surface of the stem is composed of parts which belong to the leaves lying above it. Detpivo *) has called these parts “leaf feet” (phyllopodia). ') Ceraxovsky L. T. 1901. Die Gliederung der Kaulome. Bot Zeitung 59er Jahrgang. 2) Poronie H. 1912. Grundlinien der Pflanzen. Morphologie im Lichte der Palae- ontologie. Jena. 3) Dexprno, Atti della reale Universita di Genova. Vol LV, Parte Il, 1883. 1020 In plants with incomplete. nodes there is found to the left and right of the point of attachment of the leaf an area. which belongs io a leaf placed above, therefore there are two different phyllopodia. When we now assume that in plants with alternate phyllotaxis incomplete nodes) the phyllopodia themselves are subject to the same growth as is also to be seen in the node of the stems» with complete nodes, then paris having a different rate of growth will be adjacent, The question now arises, how in that case will the rate of growth be distributed over the whole area of growth, when according to this supposition each piece of the stem has the average rate of growth of its Component parts. li order to trace this I have made a calculation for which the known rate of growth of the stem of Polygonum was chosen as the startingpoint, because internodes of this plant are very markedly individualised. : I assumed that each leaf only surrounded a fifth part of the circumference of the stem and that the leave were displaced along the stem to the position °/,. From the averages of the rates of growth of the five zones thus situated at the same height I obtained a regularly ascending curve with a short descending branch. lis course agreed with the curve for plants with alternate phyl- lotaxis. , Although I do not see in this any proof of the theory that the stem may be composed of leaf vases or may be covered with them, yet if is clear in either case that the observed manner of growth is not inconsistent with this. , If this theory is accepted, there is moreever agreement between the growth of plants with complete nodes and those with incom- plete ones. Finally I should like to point out that I have observed in one plant, namely, Ginkyo biloba Lixx. a difference in growth hetween- three stems, which were in the light and three which grew in the shade. Tne number of my observations is too small to warrant any cer- tain conclusion, but nevertheless I consider I have observed that the greater increase in length of the shaded stem must only be attri- buted to a slight extent to the greater rate of growth, but was more especially due io a longer region of growth, that is to say, each zone grows during a longer period of time, 1021 Physics. — “/uperimental investigations concerning the miscibility of liquids at pressures up to 3000 atinospheres”’. By Prot. Pu. Koanstamm and Dr. J. Timmermans. VAN peR WAALS fund researches N°. 4. (Communicated by Prof. van per WAats). (Communicated in the meeling of November 30, 1912). § 1. The theoretical researches of the last few years have rendered it possible to give a complete classification of the different types of unmixing which are to be expected. Whether these theoretical expectations are in conformity with reality could be ascertained up to now only for a very limited region, on account of the inaccessibility fo experiment of the whole region of pressures higher than two or three hundred atmospheres. The wellknown Caterer tubes are namely useless at higher pressures. We have, therefore, been occupied already for a considerable time in devising an apparatus intended for higher pressures, and we have finally succeeded in constructing such an apparatus, with which we have carried out measerements up to 38000 atm., and which can probably also be used up to 4000 or possibly 5000 atm. The first problem that was to be solved was, of course, to render the phenomena visible. For, to ascertain the critical phenomena of unmixing, and the phenomena of unmixing in general by means of other properties. than those which fall within the scope of direct visual observation, seems hardly possible. Our first attempts to effect this visibility by pressing a thick piece of plate glass A (fig. 1) by the aid of a nut & fitting round it, against the steel tube which would then contain the substance to be examined, or strictly speaking Fig. 1 against the packing enclosed between C and A, failed entirely. Even the thickest plate glass plates snapped off inexorably, when we tried to screw the nut tight enough to prevent leakage. Led by the figure that Amacar gives for the apparatus of his “methode des regards”, with which he has succeeded in carrying out measurements up to 1000 atm., we resolved to arrange the “windows” in such a way that neither on the front nor on the back side unequal pressures should be exerted’), but that the whole 1) The “windows” used by AmaGcar have, however, not been constructed according to this principle; they are not cones but cylindres, they bear on the end-plane directed to the observer; AMAGAT uses celluloid packing between steel and glass. We have, however, experienced that to reach the highest pressures, it should carefully be avoided to make the windows bear on their end-plane. 1022 pressure exerted by the liquid inside the tube on the “window”, should be borne by the side-walls We therefore gave the window the shape of a truncated cone, the basis turned to the side of the liquid, and the smaller plane parallel to the basis quite free and turned to the observer. The conical wall must be ground as carefully as possible into a steel cylindre with conical opening, wiich is screwed into the steel tube of observation. Fig. 2, where £6 is such a steel cylindre, and A the glass cone, ‘will probably make this sufficiently clear. If the cone A is ground with sufficient care, and then fastened in 2 with a little cement. an absolutely tight closure is obtained in this way; we have never experienced any trouble owing to leakage between glass and steel, nor has any of the glass cones ever burst in consequence of the high pressure, in such a way that the liquid could be pressed through those windows. We did meet, however, with other difficulties. First of all the difficulty of getting pieces of glass from which the required glass cones could be obtained, without too much loss of time. We Fig. 2. first tried to start from thick plates of plate glass (8 cm. thick), but it appeared impracticable to saw or cut off such small pieces (1.5 to 2 em? area) '), that they could serve for further preparation. We then applied to the “Stichtschen Glashandel” at Utrecht, which prepared octogonal rods for us, about 6 cm. long and ofa diameter of about 1:5 em. from the best plate glass. After these rods have been cut off doubly conical (two cones of 3 em. the bases resting 1!) When the conus is ready the basis turned to the liquid has a diameter of 12 m.m., the other -end-plane a diameter of 10 mm. 1023 against each other), they are cut through in the middle; the planes of section must then be ground once more and_ polished. A second circumstance which gave rise to difficulties, and some- times does so now, is the becoming opaque of the cones. If such a cone which has become opaque, is removed from the cylindre, it appears that innumerable planes of cleavage have arisen at right angles to the axis of the cone, so that it can be easily broken up with the hand into a great number of plane plates. In consequence of these cracks the at first perfectly transparent cone has become quite opaque. It appears that the cones hardly ever or never become opaque with rising pressure. It is probably the consequence of the compressibility of the steel cylindre. This extends with rising pres- sure, and so the glass cone is driven deeper and deeper into the eylindre. If then the pressure diminishes, the cone cannot return to its first position and is cracked by the immense pressure of the steel cylindre. In agreement with this is the faet that in experiments at higher temperature the cones become opaque still more frequently than at lower temperatures; the difference of the coefficient of expan- sion of glass and steel then acts in the same direction. Moreover by means of the brass model used for grinding the glass cones into the cylindre, it could be clearly demonstrated that one of the steel eylindres had widened by use. A cylindre made expressly of speci- ally hard nickel-steel yielded better results in this respect. When this was used, the cones were less liable to crack, though even then it occasionally happened. To protect the window from injury as much as possible it is also desirable to diminish the pressure as carefully as possible; a rapid increase of the pressure, on the other hand, rarely, if ever, gives rise to an accident. Though this cleaving of the cones perpendicular to the axis continues to be a drawback, because the preparation and adjustment of new cones always remains a rather lengthy work, the observations themselves are not disturbed by it, if only the experiments are made as much as possible with rising pressure, and decrease of pressure is effected with the utmost care. At present the apparatus cannot be used for temperatures much above 70°; the Cailletet cement with which the windows are fastened into the steel cylindres, melts at that temperature, or at least rapidly dissolves in the liquid which is in the pressure tube. First of all this renders the liquid turbid, but moreover it gives rise to leakages and breaking of the windows, which are now directly pressed against the steel. We are now trying to find means to apply the windows also at higher temperatures. As to the limit of pressure, we think we have to fix this for the present at about 5000 atm, 1024 § 2. A second condition which the apparatus has to fulfil, is this that the mixtures which are to be examined, can be properly stirred during the experiment. Of course there can be no question of an electromagnet stirrer inside the heavy steel vessel. The difficulty seemed the greater as during the experiment, and so also during the stirring the steel vessel, which itself is already very heavy, has to remain connected without leakage with the compression pump and the manometer. We have finally succeeded in finding a construction meeting all demands; it rests on the following consideration. The pivot of a high-pressure cock may be turned round, without giving rise to leakages; we can just as well keep this pivot still, and turn the rest of the apparatus round it. Suppose the inlet tube, which con- nects the vessel of observation with pump and manometer, at the place of this pivot, and arrange the connection in such a way that the observation vessel can turn round this inlet tube as a pivot, then it must be possible to bring about the most efficient form of stirring viz. turning upside down the whole contents of the vessel of observation. This idea is realized in the construction represented by fig. 2. C is the inlet tube of the compression pump, it has a diameter of about 15 mm.: the aperture is about 2 mm. wide. A prolongation D*) can be screwed on to the tube (©, by which a projecting cone is pressed against a conical concavity of C. In this way a steel-to-steel closure is obtained, which is quite tight even at the highest pressures. As is shown in the figure, the piece D pierces with its carefully finished and polished part through the packing /, which is enclosed between two rings, and cam be Screwed so tightly by means of the gland /° in connection with the flange G, that leaking along this packing is prevented, though the pieces G and / with this packing can still turn round DC as pivot. To prevent DC’ from being pres- sed outside through the pressure on the end-plane of D, D is kept in its place by a gland //, a ball-bearing adjusted between D and H making it possible to screw // sufficiently tight without making the friction between DY and H so considerable that it would hamper the rotation. The flange G is now again pressed against the obser- vation vessel 4 by means of the bolts A, whien pass through it, and which are screwed into the observation vessel 4, and the nuts M. In this way the same steel-to-steel closure is applied as between Cand PD. By means of the handle .V the pressure vessel 4 can, when everything is mounted and put under pressure, be rotated, ‘') This tube is only 12 mm_ externally (and has in correspondence with this also a somewhat smaller opening than (@) to make the pressure on the ball-bear- ings as small as possible. 1025 DC remaining in its fixed position. Thus the two phases in the glass tube O change places, passing through each other and becoming perfectly mixed. The handle N cannot be directly fastened to the steel observation vessel 4. This vessel must namely be surrounded by a thermostat. Quite apart from high or low temperatures, which would make: it quite impossible, it would be inconvenient even at the temperature of the room when the handle NV was /nside this thermostat. There- fore the connection of the observation vessel 4 with .V has been effected as follows. The rod ? connected with the handle (of which only part has been drawn) passes closely fitting through a stuffing box (not drawn in the figure) in the wall of the thermostat, so that P can still be moved forward and backward and rotated in the thermostat wall. The rod 7? terminates in a fork QQ. which in the position drawn in the figure encloses a pin A. which is. rigidly attached to the flange G@,, which like G, is again rigidly connected with 4 by means of bolts and nuts. So in the position represented in the figure 4 can be rotated by PN; if P is drawn hack in the stuffing box of the wall of the ther- mostat, 7, and together with it the thermostat, gets quite clear of R, Gy and L. The whole arrangement is fur- ther elucidated by fig. 3. It exhi- bits the large ScHArrrer and BupEN- BERG hydrostatic press for 6500 atmospheres, belonging to the van per Waats-fund with the mano- meter standing on it. The pump is also connected with the large Fig. 3. pressure-balance (not drawn) as a control for the manometer. One of us (K.) hopes soun to give a full description of these apparatus in connection with other experiments. The press is in connection with the tube conduit CC, Cy. from which it can be shut off if necessary, by means of the high pressure cock 7. There are two couplings S, and WS, in this tube conduit, to which we snall presently return. Inside the thermostat C rests on the bear- ing V,, which in its turn rests on the bottom of the sheet iron thermostat. This bearing at the same time fixes the tube C) so that the tube is prevented from turning round with the vessel . A second bearer J”, supports the rod 7, which is already known to us from fig. 2. Fig. 3 also displays the stuffing box in the wall of .the ther- mostat through which P passes. The thermostat is represented in 1026 section, the observation vessel is supposed in a position that the windows 4 are horizontal (hence turned through 90° compared with fig. 2). the position in which the observations are made. The qua- drangle in the figure represents a glass window in the back wall of the thermostat (not to render the figure too indistinct it has been drawn much larger than it is in reality); of course a glass window in the front wall corresponds with it. The thermostat has a capa- city of + 40 L., it is provided with a vigorous stirring-apparatus thermoregulator. and thermometer; it rests on a solid stand of LL shaped bar-iron. The coupling S, is of no importance for the experiments de- scribed here; it only serves to make it possible if required to connect the press with other conduits, and if necessary, to clean an the tubes. The coupling S,, on the other hand, is neces- 3? sary for the filling of the apparatus, as will appear when ed | the filling is described. Fig. 4 gives a section of these N4 ca | ‘i | Xe i | couplings. a | 2 J , , ’ roid. At the tops of the tubes C, and C, two cones D, and -- PD, have been serewed, which exhibit again two cones Fie. 4. fitting into each other at their ends. by means of the glands /, and /, with hexagon, J), and D, are pressed against each other, and a steel-to-steel closure is again reached tight even at the highest pressures. It is preferable to take the screws with which D, is fastened to C, and PD, to C, for such couplings with left-handed thread, that when /, and £, are tightened, D, and D, are not unserewed, but on the contrary, are screwed tighter. In connection with the method of filling another particular of the apparatus deserves being mentioned, which appears from fig. 5. This figure presents a side view of the observation vessel, a section ot which was given in fig. 2, with the parts in connection with it, 1027 on the supposition, however, that the glass windows are again horizontal (not vertical, as in fig. 2, but in the same position as if is represented on a small scale in fig. 3). So A is again the glass window; the other parts too, for so far as they are visible, are denoted by the same letters. It is clear from the figure that besides the main conduit. in which the observation tube ( lies, and the branch conduit, which connects this main conduit with DC, there is another branch conduit in the observation vessel /, at right angles to the two first mentioned. This branch conduit is used for the filling; it is then closed by a tignt stopper HW, which is again provided with a cone, and which is pressed against the vessel 1 with steel-to-steel closure by means of an oval flange G, laid over this cone, with the nuts and bolts belonging to it. This closure is further made clear by fig. 6, where the flange G', is represented seen from above, the line ZZ corre- sponding with 7/7 of fig. 2. Fig. 6 also shows “the general form of the flange plates G. Fig. 5 finally shows the octagon L,..., of the observation vessel L, which serves to fix the whole piece sufficiently firmly, when the steel cylindres £2 are screwed into it, which cylindres themselves have of course also a hexagon. The closure of 4 on L takes of course again place steel to steel by means of the raised hardened rim of 45, which fig. 2 clearly shows in section. We will avail ourselves of this opportunity to express our indeb- tedness to the instrumentmaker of the Van per Waats-fund, Mr. C. H. SrvivenperG, for his intelligent assistance in the construction of this apparatus, and particularly in the grinding of the windows. § 3. Description of the observations. When the apparatus described im the preceding paragraphs, is used, care should be taken in the first place that the composition of the examined mixture does not change, and that no impurities can appear, which might have a preponderating influence on the course of the phenomena. This result may be attained by enclosing the mixtures to be examined in a glass tube, closed at the two ends and provided on the side by a capillary (fig. 2, Q) as long as possible, which causes the pressure on the liquid inside to be the same as that on the surrounding liquid. This tube has beforehand been filled with a mixture of the required concentration, that of the critical endpoint. Then the steel tube C is disconnected at S,, being connected with the observation vessel £ at the same time. Now one of the two 1028 windows .1 with the eylindre 4 is screwed on, and the glass tube M is placed in the vessel 4. After this through the other window opening the vessel /: is filled with one of the components, till the liquid begins to flow out at S,. The tube C is then closed at JS, by means of a wooden peg, the second window is screwed on, and at last the observation vessel 4 is quite filled with liquid through the conduit terminating at JI (fig. 5). Then JV is closed. Beforehand the tube conduit @,C, has been quite filled with mereury, which has been poured in at JS,, to prevent contact of the observation vessel 4 with the oil from the press. The wooden peg is quickly removed, and the coupling at JS, is effected. The steel tube C being very narrow, only very little, if any liquid, escapes. Thus the mix- ture under examination is quite guarded against the influence of contamination, and its concentration changes but exceedingly littie on -aceount of the slight compressibility of the investigated liquids, while there can hardly be any question of diffusion through the narrow capillary in the course of the observations. Moreover a slight change in the concentration could not exert an appreciable influence on the results on account of the greatly flattened shape which the liquid-liquid plaits always seem to present. When the filling is finished, the thermostat is put in its place. An intense metal wire incandescent lamp of 3800 candles is placed behind the window in the back wall. In this way, the mixture, particularly the place of the meniscus, can be very clearly observed. We have confined ourselves in this investigation to plaitpoint obser- vations; as criterion the same phenomenon was taken as was also used by one of us (7°) in his observations in Cailletet tubes '): while the pressure is kept constant, the temperature is slowly made to oscillate round the plaitpoint temperature, the liquid being contin- uously stirred. The temperatures are recorded at which the turbi- dity resp. the transparency sets in, and the mean of all the obser- vations is taken as plaitpoint temperature. Proceeding in this way temperatures of turbidity are always obtained which diverge only some hundredths of degrees when the experiment is repeated. It may also be assumed that the temperature of the mixture follows that of the thermostat very closely, for also the mean of the tempe- ‘atures of turbidity deviates but a few hundredths of degrees from the mean of the-temperatures at which transparency sets in in general. This circumstance proves at the same time that equilibrium is pro- perly secured by the constant: stirring of the liquid. This was further confirmed when a glass ball was placed in the glass tube 1) These Proc. XIII p. 507. * 1029 QO. This would have to make the mixing still more thorough, if possible but it did not cause the slightest change of the plaitpoint temperature. The critical phenomenon preserves its characteristic peculiarities and the same intensity up to the highest pressures that we have examined, which bears further witness to the fact that the plaitpoint concentration changes only very little, so that if remains the same all over the extensive range of pressure and temperature considered heve. In this it is absolutely required to keep the pressure per- fectly constant during the measurements, as otherwise the VAN DER LrE effect *) would disturb the observations. It is fortunately, however, easy to distinguish whether the cloudiness which appears in the liquid, is the consequence of the slow cooling of the thermostat or of an abrupt cooling which takes place in the examined liquid itself owing {to an expansion by decrease of pressure. [nthe former case, namely, the cioudiness begins on the ontside. and proceeds towards the centre, whereas in the latter case it arises in the centre, and spreads from there in all directions. The sensi- tivity of the vAN per Lyn ‘effect in these circumstances shows that the equilibrium of pressure between the manometer and the liquid itself sets in almost immediately. - A last proof for the accuracy of the measurements in the new apparatus is afforded by the compa- rison of the results obtained in this way at low pressure with those obtained in Cailletet tubes. Some values will give an idea of the attainable accuracy. a. The plaitpoint temperature remains constant, also after the mixture (nitrobenzene + petroleum) under investigation has been in the apparatus for two days, under pressures up to more than 500 atm. As a mean of ten measurements 13.°95 + 0.°06 was found. 6. The plaitpoint temperature. remains constant when the experi- ment is repeated with different fillings. Water + triethylamine, critical end-point 18.°35 and 18.°36 The same system in a Cailletet tube yields 18.°33 e. The increase of the plaitpoint temperature per atmosphere is the same for different fillings, and also for determinations in a Cail- letet tube. As an example we take the system cyclohexane +- aniline. dt — between 1 and 200 k.g. per cm.’ yields + 0.0067 dp in a Cailletet tube was found. + 0.0066 1) These Proceedings, XIIL p. 517. 67 Proceedings Royal Acad. Amsterdam. Vol. XY. 1030 dt — between 1 and 1000 k.g. per cm.* yields dp for the first filling + 0.0078 for the second filling + 0.0079 The temperature determinations were made with thermometers compared with standard ones tested at the Reichsanstalt; the mano- metrical determinations were controlled with the large pressure balance ') of the vaN per Waats fund; the observations are accurate to about 10 k.g. and 0.°05. The substances used in these experiments, were identical in pre- paration and properties with those used by one of us (T.) on a for- mer occasion ?); only the decane (di-isoamyl) and the tri-ethylamine have been used here for the first time. These two substances have been purified by fractional distillation (the tri-ethylamine over sodium), they presented the following physical constants: Freezing point: Decane 52°,5 Triethylamine — 114,75; boilingpoint 160°,05 + 0.10 resp. 89°5 + 0°02; d0°/4° 0.73852 resp. 0.74585 + 7. It may finally be mentioned that all the observations have been made by one of us (T.). § 4. Results obtained : iA BSE Hexane + nitrobenzene . at Press. in kg. 3) Plaitpointtemp. | — per kg. per cm.? dp 1 | 200.81 + 0°.03 | | — 0°.0164 100 19.17 + 0. 04 — 0.0127 250 17. 27 + 0. 10 : — 0. 0083 425 15.82 + 0.05 — 0. 0051 625 14.80 + 0.05 a — 0.0031 | 825 | 14.18 + 0. 03 | For a comparison we give the results obtained with a Cailletettube: 1) See above p. 1025. *) These Proc. 1. c. 5) All the pressures and temperatures have been corrected to the standard ther- mometer and the pressure balance, 1031 tA BSE. i: Te if ‘fen aa je Press. apparat. Cailletettube Difference | 20°.81 20°.96 + 0°15 | 100 19. 17 19. 23 + 0. 06 250 Nice1 17. 29 + 0. 02 The nitrobenzene solidifies (quadruple point) at — 1°,5 under ordinary pressure at + 13°,8 under a pressure of 825 kg. per em* + 25. dt . —= + 0°,018. dp TamMANN found + 0°,022 for pure nitrobenzene. TABLE itl Decane (di-isoamyl) + Nitrobenzene | dt oF | —— NEES | | dp | | 1 28°.37 + 0°.04 | | | | — 0°.0068 | 100 27.69 + 0.05 | | — 0. 0042 250 27.06 + 0. 04 — 0. 00245 425 26.63 + 0.07 ! — 0.0010 | 625 26. 44 + 0.05 | | + 0. 0004 825 26.52 + 0.04 | + 0. 00075 1025 | 26.67 + 0.03 | +0. 0015 1225 26.97 + 0.07 | | + 0.0017 | 1425 | 27.31 + 0.05 The nitrobenzene melts: at + 1°,5 under a pressure of 1 kg. per em’, at + 28° under a pressure of 1300 kg. per cm’, ee ++ 09,020, Op 1082 TAUB LAE SIV: American petroleum !) + Nitrobenzene E vi i dt dp 1 13°.95 + 0°.06 + 0°.0018 100 14.22 + 0.07 + 0. 0017 325 14.51 + 0.09 + 0. 0030 525) | 15> 11) 2.0704 + 0. 0030 725 15.70 + 0. 03 + 0.0033 | 925 16.35 + 0.05 The nitrobenzene solidifies at 925 ke. per cm*® and 16°. AY BYE Ep ave Cyclohexane + Aniline dt De = P | dp Ist filling *) 1 30°.26 + 0°.07 | + 0. 0067 200 31. 60 + 0. 06 + 0. 0080 400 33.20 + 0.07 + 0. 0077 700 35.52 + 0. 10 + 0. 0084 1000 38. 04 + 0. 10 2nd filling 1 31°.03 + 0°.04 + 0°.0075 500 34.77 + 0.09 + 0. 00835 1000 38. 95 + 0. 08 ++ 0. 0084 1100 39. 79 0. 08 | | | | — - — For a comparison we give the following results obtained with a Cailletet tube : eritical end-point 31°,02 instead of 31°,03, !) By way of comparison with the preceding binary systems we have also carried out a few observations with this mixture. 2) With this first filling the critical concentration was not quite reached; there was a little too much aniline, and it was clearly to be seen how the cyclohexane — was dissolved in it. 10838 dt he ra H between 1 and 2007atm. 0°?.0066 instead of O°,0067. ap om The cyclohexane solidifies at 42°,5 under 1200 atm. at a | lt under 1 atm. ane + 07.036. ( (0 eA bs lve. Vi Water ++ tri-ethylamine tt p T dp First series 5 18°.36 + 0°.06 -+- 0°.0206 200 22.37 + 0. 06 : j + 0.0179 600 29.53 + 0. 06 about + 0. 0125 1000 about 34.5 See. series 5 18.35 + 0.05 + 0.0182 600 29.19 + 0.11 + 0.0127 1000 34, 26 + 0. 13 + 0.0103 1500 39.40 + 0. 20 + 0. 0080 2000 43.4) + 0.15 In neither of the series was the critical concentration perfectly reached; hence the discrepancy, which is, however, small, between the results. The critical opalescence was, however, clearly to be perceived. In both cases the experiments had to be broken off on account of the appearance of a leak in the piston of the hydro- static press. For a comparison we give the following results obtained in a Cailletet tube, which have not yet been published until now: Plaitpoint for 5 kg. per em®: 18°31 instead of 18°36 and 18°,35. lt ¢ - between 1 and 200 kg. per em?: 0°,0201 instead of 0°,0206. dp Above this pressure the plaitpoint temperature increases greatly ; at a pressure of 1100° kg. per em® the mixture remains homogeneous at every temperature, at least no turbidity sets in up to at least 85°, but a decrease of 10 atm. in the pressure suffices to bring us back to the heterogeneous region. When the temperature rises still higher, we seem to reach the maximum pressure of the plaitpoint line, where the branch which comes from the lower critical end- 1084 T ACB EE Vil: Water + methylethylketone 7 dt p dp 225 0°.7 age it . + 09.096 250) eet Seq 009 a + 0. 094 300 + 7.8 +0.2 utes 350 |-4+12.1 +0.1 + 6.079 400 + 16.05+0. 4 ; + 0. 074 450 + 19.75 +0. 15 ays 500 + 23.2 +0.1 ; + 0. 070 600 +30.2 +0.1 Ne 1502 One 70 +37.3 +0.1 | + 0. 068 S00 44.1 = 0°73 | wa 0.072 900. | +51.8 -£0:3 he | + 0. 103 1000 +61.6 +0.3 ner + 0. 1050 +66.9 +0.3 point joins that proceeding from the upper end-point. For though e.g. at 80° the mixture, homogeneous under a pressure of 1100 kg. per em®. becomes turbid when the pressure falls to 1085 kg. per em®. the pressure must be lowered to 1075 kg. at 86°.5 to reach the heterogeneous region. Moreover a mixture homegeneous at 86°5 and 1075 kg. unmixes no longer on /eating, as it did before, but on cooling; on further cooling, if the same pressure is retained, finally the homogeneous region is again reached. In the last-mentioned system the observations were less aeeurate than with the others, because the critical. opalescence is almost entirely wanting, and the indices of refraction of the two phases are nearly the same; we think, however, that we are justified in accepting the above results with certainty, at least as far as the general course is concerned, because also another filling, with a somewhat different concentration, gave analogous results. Here too the highest pressure for which there was still’ question of unmixing is about 1100 kg. per em?; the plaitpoint then was at about 80°; above this temperature the windows became opaque. § 5. Summary of the results. The preceding determinations suflicieatly prove the efficiency of 1035 the given method. The material of observation recorded in the tables gives rise to the following remarks. 1. The systems formed by nitrobenzene with a hydrocarbon sre not simple cases of retreat as we thought at first ); on the con- trary they represent cases in which the plait is split up, and belong to case II4, in reference to whieh we had to state in 1909 that we had not found an example of it for normal substances, and about whose possibility for abnormal substances we then ventured to pronounce an opinion only with the greatest reservation *). This conclusion appears with perfect certainty for the system nitrobenzene + decane; the critical end-point (meeting of three- phase line and plaitpoint line) lies here on a branch of the plaitpoint dt line with negative — ; if fhe plaitpoint line is pursued further, dp dp becomes zero, and then positive. Accordingly the plaitpoint line passes through a minimum, and this minimum is experimentally realisable: the branchplait exhibits a point where the closed portion gets detached, a homogeneous double plaitpoint, and this lies in the absolutely stabie region. The question proposed p. 409 of the Lehr- bueh der Thermodynamik *) has, therefore, been answered in the affirmative by experiment. If in this connection the closely related system nitrobenzene-hexane is considered, it appears that it is only owing to an accessory cir- cumstance that the homogeneous double plaitpoint cannot be realized. dt For here too e is negative in the critical end-point, but this negative value becomes smaller and smaller; but just before it has become zero, further investigation is prevented by the appearance of the solid phase. So the plaitpoint line becomes metastable by its meeting with the threephase line solid ++ two liquid phases; we have again a eritieal end-point,- but now the critical point of two ‘ saturated solutions”. The system petroleum + nitrobenzene — if we may compare it for a moment in this connection with a binary system — _ no more belongs to type II/, but to type Ia. In the critical end-point die an ; , : es a8 here positive, the plaitpoint line is intersected by the three-phrase ap line above the homogeneous double plaitpoint; hence the Jatter falls 1) These Proe. XIl p. 243 and table at p. 239. 2) loc. eit. p. 243. 8) Van pER WaAALS-KouNsramm, Vol. IL. Leipzig, Barth. 1912. 10386 in the metastable region inside the transverse plait, and for this reason cannot be realized experimentally. So we have now realized the suecession which we supposed possible in our first Communication *) for the systems propane ++ methylaleohol, isobutane -+- methylalconol, pentane *) + methylal- cohol, but about which we could then only pronounce a guarded opinion in the absence of further experimental material to prove the point. We now hope before long to be able to ascertain also for the system propane -+- methylaleohol whether it really belongs to ease II4, or tw case I. 2. In the second place we have been able for the first time to fully demonstrate a case of type I, with its two critical end-points / and G, and its maximum pressure /7*). The system water-methylethylketone furnishes an example of this even though we cannot quite reach the lower end-point in consequence of the appearance of the solid phase. So we have a system here for which simply by change of pressure one passes from a partially miscible system to a system with complete miscibility. So such a case, to find which many attempts have been made, appears really to occur. In how far other systems will belong to this, and if particularly the systems classed up to now in case I will appear to belong to U4, or possibly to a ease la with a plait- point line which has a line parallel to the p-axis as asymptote will have to be revealed by further experiment. In the same way further experiment will have to show whether systems may be found belonging to type Il/, in which the maximum temperature / and the maximum pressure /’ can be reached. *) Loe. cit p. 243. *) We avail ourselves of this opportunity to rectify a few inaccuracies in former tables. In the table annexed to p. 239 loc. cit, for methylalcohol + isopentane read: normal pentane. Idem in table VI, These Proc. XIU, p. 877. In the last table erro- neously a L (lower mixing-poinl) is added to the system-elthane —- methylalcohol; this should be omitted, just as it is not found in the table of our first paper. Finally the said table VI shows an L? for the system ether and water. As the note of imterrogation denotes, we thik this lower mixing-point by no means ° proved. With our new apparatus we have already carried out a few experiments with the system water + ether; they all show that on increase of pressure and decrease of temperature the two phases will approach each other more and more; they point, indeed, in the direction of a lower mixing-point, but we have not sue- ceeded as yel in definitely ascertainmg whether or no this will be realisabie on account of the appearance of the different ice modifications: We hope we shall be able to return to this subject later on. We-owe the different corrections mentioned in this note to Prof. KUENEN’s great kindness, who drew our attention to the mistakes made. 8) Big. 1 lic. 1037 Summarizing we may state: 1. That we have given an experimental method to determine plaitpoints, and other phenomena which must be made directly visible, at high pressures to an amount of more than 8000 atm. 2. That we have demonstrated that the course of the theoretically predicted ptaitpoint lines is in concordance with reality in the systems under investigation, albeit that the more intricate case of the splitting-up of a plait occurs more frequently, the less intricate case of simple retreat more rarely than was supposed. Meteorology. — “On the interdiurnal change of the air-teinperature.” By Dr. J. P. vAN DER Stok. (This communication will not be published in these Proceedings). (April 24, 1913). KONINKLUKE AKADEMIE VAN WETENSOMAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday February 22, 1913. ocr —- President: Prof. H. A. Lorenrz. Secretary: Prof. P. Zeman. (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 22 Februari 1913, Dl. XXI). COANE HENS: C. T. vax Varkensure: “On the occurrence of a monkey-slit in man.” (Communicated by Prof. C. Winkier), p. 1040. y H. J. Warrrman: “Metabolism of the nitrogen in Aspergillus niger.” (Communicated by Prof. M. W. Brwerincr), p. 1047. (With one table). Ee H. J. Warerman: “Metabolism of the fosfor in Aspergillus niger.” (Communicated by Prof. M. W. BeeERINCK), p. 1058. C. Braak: “A long range weather forecast for the Eastmonsoon in Java.” (Communicated by Dr. J. P. van DER Stok), p. 1063. (With one plate). S$. C. J. Ottvier and J. BorseKxen: “Dynamic researches concerning the reaction of FriepEL and Crarts”. (Communicated by Prof. A. F. HoLrtEMAN), p. L069. L. K. Wotre and E. H. Biicwxner: “On the behaviour of gels towards liquids and their vapours.” (Communicated by Prof. A. F. Ho_teman), p. 1078. M. W. Brrerinck : “Penetration of methyleneblue into living cells after desiccation”, p. 1086. ©. yan Wissetrxen: “On karyokinesis in Eunotia major Rabenh”. (Communicated by Prot. J. W. Mout’, p. 1088. J. K. A. Werruem Saromonson: “On a shortening-reflex”, p. 1092. L. S. Orysrerm: “On the thermodynamical functions for mixtures of reacting components”. (Communicated by Prof. H. A. Lorentz), p. 1100. F. E C. Senrrrer: “On velocities of reaction and equilibria.” (Communicated by Prof. A. F. HloLieman), p. 1109. F. E. C. Scurrrer: “On the velocity of substitutions in the benzene nucleus.” (Communicated by Prof. A. F. Hotiteman), p. 1118. R. W. Woop and P. Zeeman: “A method for obtaining narrow absorption lines of metallic vapours for investigations in strong magnetic fields.” p. i129. P. Zeeman: “The red lithiumline.” p. 1130. J. D. van per Waats: “Some remarks on the course of the variability of the quantity } of the equation of state.” p. LISL. : N. L. Sowncen: “Oxidation of petroleum, paraffin, paraffinoil and benzine by microbes.” ‘Communicated by Prof. M. W. BrtsEerten), p. 1145. ; J. P. Kuexen: “The coefficient of diffusion for gases according to O. E. Meyer. p. 1152. Jan DE Vries: “On bilinear null-systems.” p. 1156. Jan DE Vrirs: “On plane linear null-systems.” p. 1165. Miss M.S. pr Vries: “The influence of temperature on phototropism in seedlings of Avena sativa.” (Cummunicated by Prof. . A. F. C. Went). p. 1170. : J. D. van DER Waats Jr.: On the law of the partition of energy.” (Communicated by Prof. J. D. YAN DER Waats), p. 1175. P. van RomburGu: “Hexatriene 1, 3, 5.” p. i184. P. Eurenresr: “On Ersrerm’s theory of the stationary gravitation field.” (Communicated by Prof. H. A. Lorenrz). p. 1187. A. Pannekork: “The variability of the Pole-star.” (Communicated by Dr. E. F. van pe Sanpe Bakuvuyzen), p. 1192. F A. H. Scurememaxkers: “Equilibria in ternary systems”. Part LV, p. 1200, Part V, p, 1213. HW. R. Krvyr: “The dynamic Allotropy of sulphur.” (Fifth communication). (Con:municated by Prof. P. van Rompurci), p. 1228. 65 Proceedings Royal Acad. Amsterdam. Vol. XV, 1040 Anatomy. — “On the occurrence of a monkey-slit in man.” By Dr. C. T. vax VaLnensurG. (Communicated by Prof. WINKLER’. (Communicated in the meeting of December 28, 1912.) It has lone been known that under some circumstances, in case of disturbances in the development of the central nervous system of man, a slit may occur on the surface of the occipital lobe vividly reminding of the so-called monkey-slit of anthropoides. I communicated an example of this fact in a former paper.*) The slit then characterized as monkey-slit, answered to the requirement that at least part of its orcipital boundary covered convolutions at the bottom of the slit connected with the parital lobe (operculation). Eniior Smiru*) has described the brains of many Egyptians in which he very often found (70°/, of the hemispheres) a su/cus simialis sive lunatus. BRoDMANN *) corroborated this view with the brain of three Javanese. On the other hand ZuckurkaNnpL *) thinks that the exist- ence of a monkey-slit in man is by no means proved. As a proof he gives a reproduction of some hemispheres in his above- mentioned essay. On these surfaces however — of course specially selected by ZuckerkanpL — Eniior Smitn would doubtlessly diag- nosticate a monkey-slit. How are these contradictory views to be reconciled. We read in. ZecKERKANDL’s paper (l.c.): “Am = menschlichen Gehirn soll nur “dann von einer Affenspalte die Rede sein, wenn an der Hemis- “pharenoberfliche beide Rander der fraglichen Furche mit jenen der “Affenspalte am Affengehirm identisch sind. Trifft. dies nicht zu, “liegt eine Furehe vor, welche nur auf einer Seite (hinten) von einem “der Grensrinder der Affenspalte abgeslossen ist, wahrend der andere “(vordere) nicht mehr dem Gyr. angularis sondern einem Bestandteil “der Affenspaltengrube (Uebergangswindungen) angehdrt, dann hat “man es nicht mit der typischen Affenspalte zu tun.” 1) Van Varkensure, Surface and structure of the cortex of a microcephalic idiot. These Proc. XII p. 202. 2) ELuior SmirH, Studies on the morphology of the human brain. Records of the Egyptian Goverumentschool of medicine. Cairo 1904. Evuior Samira, The persistence in the human brain of certain features usually supposed to be distinctive of apes. Report of the British Assoe. for the advance. of Science 1904, p. 715. 3) BropMANN, Beitrage zur histologischen Lekalisation der Grosshirnrinde V. Journ. f. Psych. u. Neurol. Bd. VI. 5. 296. %) ZUCKERKANDL, Ueber die Affenspalle und das Opercylum occipit. des mensch- lichen Gehirns. Obersteiners Arbeiten Bd. X11, 5. 207. 104] ZUCKERKANDL strongly emphasizes a difference between monkey- slit — i.e. the slit between the operculum occipitale and the parietal convolution lying frontally to the operculated transition-convolutions -— and the monkey-slit sulcus — i.e. the sulcus lying on the bottom of the sule. lunatus. This difference must unconditionally be accepted, and to my knowledge this is done by the majority of authors (BoLK a.o.). It is however another question whether this difference is really of sneh a nature that we should be compelled by it for ever to deny the homologisation between a monkey-slit and a very similar sulcus in man. For that similarity is even readily accepted by ZUCKERKANDL, as he admits the occurrence of ‘Affenspaltresten’’ in man. ELiior Smith is of opinion that the difference is nothing but a quibble of words. Evidently the matter hinges upon the question: what is in the monkey-sht-complex the cardinal point? We have then the choice between the s//¢ — postulating the existence of bottom-convolutions and an operculum covering these — and the suleus existing on the bottom of the slit, which if there are no bottom-convolutions to be opereulated, looks like every other suleus. In lower monkeys (platyrrhines) and prosimii’) a sulcus is found that must doubtlessly be indicated as suleus lunatus whilst bottom- convolutions, operculation, a proper “monkey-slit’*) may be absent. This suleus lies in the brains uf these animals transversally — often not reaching the interhemispherical fissure — across part of the latero-dorsal surface of the lob. occipitalis. No other sulcus ends in it; it lies occipital from the sulcus parieto-occipitalis. In some platyr- rhines (ateles) the sule. interparietalis (which, as has been remarked, does not reach the sule. lunatus) forms a 7-shaped extremity, some- times already indicated in some specimens of lemuridae. I refer those interested in this problem to the report that will be given by Dr. Ariens Karpers in 1913 at the International Congress of Medicine in London: Cerebral localization and the significance of sulei. Ascending in the range of monkeys we find that the sule. inter- parietalis in katarrhines has its distal termination in the s. lunatus. At the same time we find that, at the bottom of the latter, cortical convolutions are hidden; its occipital lip has grown an operculum. The most developed katarrhines — the anthropoides — usually 1) ZreHEN, Ueber die Grosshirnfurchung der Halbaffen Arch. f. Psych. Bd 28 S. 898. 2) KiikENTHAL u. ZIBHEN, Untersuchungen tiber die Grosshirnfurchen der Primaten - Jenaische Zeitschr. fiir Naturwissensch. Bd. 29, S. 1. For further literature vide Ariens Kappers (I. ¢.). 68* 1042 show the beginning of apparent return to lower relations, because part of the transition-convolutions (the first) has become superficial. It is however still separated by the sule. interparietalis from the superficial part of the 2°¢ transition-convolution. A similar situation was to be found in the microcephalic idiot described by me in a former paper (I. ¢.). If now moreover the 2"¢ and 3" transition- convolutions become superficial i.e, if they pass from the bottom of the monkey-slit to the surface of the fob. parietalis, then of the entire s. simialis-complex there remains only the bottom-suleus which is then, with regard to its parietal lip, differently limited from what was the case with anthropoides, at least as regards the region of the 2.4 and 3 transition-convolution. This is however not always the case. Also where there is no question of great disturbances of development, as in the above-cited case of mikrocephalia, little hidden convolutions may be found (vide e. g. some drawings in ZUCKERKANDL’S paper I. ¢.). Such brains connect the monkey-slit in a more limited sense —- as it occurs in anthropoides — with the sulcus lunatus (as with Exisor Smirn we best call it) of man. About the frequency of the oceurrence of this sulcus in Europeans I cannot fix a per- centage on account of my limited material. In 22 hemispheres of idiots of the Institute for Brain-research I find it 8 times. In the brain of normal individuals it likewise “often” oceurs. EL.ior Situ fixed already the attention to the brain-photographs of- Rerzius. I could not decide with certainty whether, as it seems to be Eniior Smirn’s view, there exists any preference in this respect for the left hemisphere. Notwithstanding all these assertions it is necessary to fix as strongly as possible the diagnosis: sulcus lunatus. One cannot give a definition of it of absolute value, i.e. without imvolving in it the relation to neighbouring sulci. As conditions for accepting a sulcus lunatus I fixed in general the following relations and cireum- stances: ; 1. The suleus in question lies somewhat crescentshaped (with its concavity caudad) or more transversal, not far from the pole of the occipital lobe ; 2. In its lateral part terminates a sulcus, that is often connected with the first temporal sulcus (su/eus praelunatus) ; 3. More or less parallel to it, more towards the front, lies a 1048 suleus, into which the suleus interparietalis terminates (sule. occipitalis transversus) ; 4. The occipital extremity of the suleus calearinus falls (whether bent or not round the mantle-side) behind it, and sometimes extends between two sulci occipitales which are found there (they may be connected V-shaped). ; Fig. I represents an occipital lobe (of an idiot) seen from behind on which the above-mentioned desiderata have been most accomplished. The principal requirements are fulfilled: the situation of the sulei oceipitalis transversus (0.f.) and calearinus (¢c.a.) resp. before and behind the sulcus lunatus (Lun) is typical. At the former the suicus interparietalis (7.p.) terminates ; Bie, the suleus parieto-occipitalis (po) cuts frontally Occipital lobe of the idiot from it the medial mantle-side. An indieation D,seen from behind. The of a V-shape of the occipital sulci (0) between dotted line indicates the whieh the sule. calearinus points, is extant. direction of the section according to which fig. 4 ; 3 has been drawn; for the not immediately connected with the sule. tem- shortenings vide text. poralis primus (f,). All other hemispheres pos- sessing the suleus lunatus have a similar appearance. The greatest The suleus praelunatus (prd.) is distinet, but variation exists in the occipital sulei and the relations of the sulcus praelunatus. All our cases answer to the above-mentioned principal requirements, where a sulcus lunatus was admitted, with only one exception. In the latter case (it regards the cerebrum of an idiot, with a too little frontocaudal diameter; weight of the brain about 1000 grams) the cuneus is very narrow, because the suleus calearinus has a strongly dorsal direction. I refer to fig. 2. At the limitation of the second and posterior third part of the cuneus this sulcus splits T-shaped. The inferior branch terminates near the occipital pole, behind the sulcus lunatus, the dorsal braneh reaches the medial mantle-side immediately behind the suleus peeoto-oceiptalis ; consequently not only far ete oeeipiealeloberon the before the suleus lutanus, but even before jdiot W, seen from the me- the suleus occipitalis transversus. Vide fig. 3. dial side. po =sulc. parieto-oecipitalis ca = sulc. calcarinus C = corpus callosum (sple- ‘alearinus, and is not a cuneus-sulecus nium). I come to the conclusion that this branch must indeed be reckoned to the suleus 1044 terminating in the suleus calearinus from the fact, that its lips show as distinefly as the other part of the sulcus in question a beautiful stripe of Vicg b’Azyr. When using this argument we have introduced into our reasoning a new element of a microscopical, anatomical, and even, may be, of a physiological nature. Many ana- Fig. 3. The same occipital lobe tomists indeed regard the region over which as fig. 2,seenfrombehind; the above-mentiod stripe extends as the terminal shortenings as above. region of the centripetal, geniculo-occipital radiation, the recipient optic cortical-field (Visuosensory : CAMPBELL, Boiron, Morr a.o.). Apart from any physiological function and even from specific projection-combinations we may admit in man as irrefutable, that wheresoever the typical stria Vieq d’Azyr is found, we have to do with an area of a special character, which on account of its peculiar relations (in the greater majority of cases) to the limitations of the suleus calearinus, may be characterised as regio calcarina. Area striata (Etuior Smita) area 17 (Bropmann) and regio calearina are consequently regarded in man as synonyms. My above mentioned conclusion that in reality the cuncus-sulcus terminating in the suleus calearinus must be regarded as a final branch of that sulcus seems consequently not to be a hazardous assertion. As especially BropMann*') has taught us, the area striata (his area 17) extends in the monkey over the lateral surface of the lob occipitalis (the operculum occipitale) as far as the monkey-slit. Eniiot Smitn stated the same fact in his Egyptians, be it over a more narrow strip of the region concerned, and he uses this fact as one of the arguments for homologising his sulc. lunatus with the monkey-slit. This author conceives the connection between histolo- gically-characterised areas and brain-sulci a little schematically : very regularly he admits and represents the latter as limits of the former’). Apart from the fact that after the investigations of BropMayy, CAMPBELL a. 0. his view cannot be maintained in this form, it postulates in the case discussed here a complete homology in the relation between the sulcus lunatus and the area striata in monkey and man. As appears from the phylogenesis of the sulei there is no complete parallelism between the evolution of the sulci and the relative migrations of the special cortical zones. 1) Bropmann: Vergleichende Lokalisationslehre der Grosshirnrinde. Leipzig 1909. 2) Exntor SmiruH: A new topographical survey of the human cerebral cortex. Journ. of Anat. and Physiol, Vol. 4i. 1045 ZiwneNn') called already attention to the comparative slowness, with which in the range of development of mammals sulei change their places. In the report that he intends to give (Le.), Ariins Kapprrs comes on other grounds to the same but more developed conclusion: sulei are more conservative than the neighbouring cortical zones. Where we see in man the area striata extending as far as the suleus lunatus if the latter is extant -- we may see in if a very welcome affirmation of the similarity between sulcus lonatus and monkey-slit, ascertained by other methods (morphologically), It can however not be a point of issue for proving a homology — in the way as ELiior Smirn regarded this fact. As far as the extension of the area striata can be mapped out macroscopically (with the help of the magnifying glass) (ELLIor Switn’s investigation was made in this way) the material of the Brain-Institute does not offer uniform indications. It seems that the area striata is not always dorsolaterally limited by the sule. lunatus ; this limitation is likewise not a sharp one in this sense, that sulcus and area must join each other without any intervening space (in this respeet our material corresponds with BropMmann’s Javanese). The type of the cellamination offers the same evidence as that of the extension of Vicg v’Azyr’s stripe. Fig. 4 gives a reproduction of the latter. It has been made after a section somewhat lateral from the place where in fig. 1 a dotted line has been drawn. The preparation consequently cuts the sule. lunatus perpendicularly. The letters placed in the figure render a_ further Fig. 4. description almost superfluous. I only v=stria Vicq d’Azyr, other draw attention to the slight depth of the shortenings as above. Sagittal section through the ; occipital lobe of the idiot D. anthropoids. In man (our material) this (vide fig. 1). suleus shows a very different depth ; in this respect likewise it seems to show all the transitions between the anthropoid-like state and its total disappearance from the surface sule. lunatus, which is never found in of the brain; its extremities (medial and lateral) are most undeep. It seems as if first the hidden convolutions, afterwards their bottom is brought to the periphery; the cortex is ‘‘smoothed”. The immediate connexion between area striata and sule lunatus, 1) ZiEHEN: Ein Beitrag zur Lehre von den Beziehungen zwischen Lage und Function im Bereich der motorischen Region der Grosshirnrinde, mit specieller Riicksicht auf das Rindenfeld des Orbicularis oculi. Arch. f. Physiologie 1899, S. 173. 1046 shown by Euimor Situ in his Egyptians — also distinctly visible in fig. 4 — needs not exist in the European who possesses this sulcus. But it is even impossible — at all events in the material I had to dispose of — in cases where a sulcus lunatus is extant always to ascertain a greater extension of the area striata on the lateral surface of the brain, than in cases where no vestige of the above mentioned suleus is to be found. Of course there is no longer question of a limitation in the sense of Samira; it is an illustration of the conservatism of sulci we spoke off above, even of one that is destined to disappear. *) | have asked myself if there was any connection between ihe existence of a suleus lunatus on the lateral cortical surface and the extension of the area striata at the medial hemisphere-wall, in so far as the Jatter in general is connected with — is dependent upon — the direction and the modus of ramification of the sulcus calearinus, No regularity at all could be ascertained in this respect. A suleus lunatus can be found with all sorts of s. calear. I gave already, examples of two forms. I can add as a third, extreme, form a case where sulcus caleari- nus and suleus parietooccipitalis are nowhere connected, where a superficial cuneo-limbie transition-convolution exists at the point of the cuneus, exactly as it is found — almost always — in anthropoids. The sule. lunatus that was here very evident, showed a// the above mentioned characteristics. A more or less ‘anthropoid” condi- tion of the cuneus, caused by variations in the direction of the suleus calcarinnus does however, as it seems, not always hold con- nection with the existence of a sulcus lunatus. In general the existence of a suleus lunatus is by no means a proof of imperfect development of the brain in which it is found. In normal Europeans it is decidedly frequently met with, as EL.ior Suiru concluded already from the drawings of others. The examples shown by me were taken from idiots, because | found in a compa- ratively little material such strong variations at the medial occipital surface, each time with distinct sulcus lunatus on the lateral one. It seems probable that defective development may often be the cause of these deviations in the direction of sulci and convolutions, but with regard to the many variations in normal brains it cannot be proved. Whether and how — in a definite case — the existence of the suleus lunatus is influenced by such a “defective development” is a phenomenon that lies completely beyond the field of our observation. ') In a case of Anophtalmos there existed a beautiful monkey-slit: the area striata at the medial brain-surlace scarcely reached the occipital pole: calcarina extension normal. 1047 Microbiology. — “Jetabolism of the nitrogen in Aspergillus niger.” sy H. J. Waterman. (Communicated by Prof. M. W. Beiserinck). (Communicated in the meeting of November 30, 1912). In a previous communication ‘) I described the circulation of the earbon in Aspergillus niger. The changes which the plastic aequivalent or assimilation quotient of the carbon and the respiration- or carbonic acid aequivaient underwent in the course of time gave a clear view into the meta- bolism. In the beginning of the development a great plastic aequi- valent was constantly found, which, however, lowered quickly, whilst the carbonic acid aequivalent rose considerably in the course of time. The curve indicating the change of the two aequivalents with time could not be explained by an adsorption of nutrient substance. The existence of an adsorption, that is to say, a change of con- centration caused by molecular attraction of the components at the surface of a liquid formed by these components, gas, ete. and theo- retically foretold by W. Gispss and J. J. Tuomson, has in many cases been experimentally confirmed. For such experiments it was desirable to artificially enlarge the surface, for example by formation of scum, in order to bring the phenomenon within the reach of the relatively rough methods of observation. Animal and plant cells present a great surface in relation to their contents. So it might be possible experimentally to observe the adsorption by the disappearance of the food from the surrounding medium. The above investigation, however, has proved that this is not the case and the following experiments confirmed this. A living mould culture, some months old and washed out with distilled water, ca. 300 mers. dry and containing hardly any more glykogen, was during half an hour shaken with 50 em®* solution of 2°/, glucose, 0,15°/, ammoniumnitrate, 0,15°/, KH,PO,, and 0,06°/, magnesiumsulfate in tapwater. The mould laver, which had absorbed hardly any glucose from the solution, was then repeatedly washed out with distilled water at room temperature, boiled for ten minutes with distilled water, then filtered. The filtration did not reduce “Fehling’, consequently contained no glucose. If the concentration of the glucose in the mould were likewise 1) Folia microbiologica, Hollindische Beitriige zur gesamten Mikrobiologie. Bd. 1 p. 422. 1048 2°), at ieast 6 mers. should have been found, a quantity which can with certainty be indicated by “Fehling”. This proves that there is no question of a considerable perma- nent adsorption at the outer surface of the protoplasm, but that it behaves more like a semi-permeable wall towards the glucose. The same experiment was once more repeated, but this time with a 2°), glucose solution without anorganic substances, with shaking for two hours. Now, too, the mould proved to contain no glucose. A duplo-experiment gave only traces of glucose. Hence the adsorption in Aspergillus niger is of no significance for the accumulation of nutrient substances. Now it is a matter of course that the first stage of the aceu- mulation is an adsorption, but it evidently escapes observation. The high plastic aequivalent in the beginning pointing to an extensive fixation of carbon-containing material, relates to a further stage of assimilation. The food has then already passed into other compounds, e. g. into ely kogen. If the observations have ascertained that physiologic processes may be represented by an adsorption curve, this cannot be explai- ned by aecepting an adsorption in the first part of the process but it may be a consequence of what happens in a later stage. Such an adsorption curve does not in general represent a simple process; it is more a combination of a whole series of successive physical and chemical phenomena. In the study of the nitrogen results have been obtained corre- sponding to those found with the carbon. It has namely been observed that also the nitrogen compounds used for the nutrition, are accumulated in the organism in a way not yet explained. First I convinced myself that the plastic aequi- valent of the nitrogen at the end of the experiment is subject to only slight changes, as is shown in table I. Compare for this nrs. 1 with 2 and 8, 4 with 5, 9 with 10, 14 with 12, 13 with 14. Secondly the quantity is independent of - the nature of the source of carbon provided the weights of the mould be alike. For the levulose we tind the same numbers as for the glucose. Lowering of temperature does not (nrs. 9 and 10) influence the rate of nitrogen of the mould, nor is it changed by addition of boric acid (nrs. 11 and 12). Table II gives a view of the quantity of nitrogen fixed in the mould layer at various periods of development. After 3 days the accumulation of nitrogen is of importance. Per 1049 TABLE I. FIXATION OF NITROGEN BY ASPERGILLUS NIGER. 50 cm3, tapwater!), in which dissolved 0.15%) NH NO3*), 0.159 KH2PO4, 0.06 "/o MgSO, (free from water) with the organic food given below. Temp. 33°C. — Carbon fixed Age of the in the mould Particulars Nr. Organ. food mould (in mgrs.). 1,2,3| 2 gr. glucose 5 to 6 months PGPAR SUT) eae) (0) 45 | 2, levulose 5 to 6 A 16.5; 18.6 6 1, glucose 5 . 9.8 The culture liquid 7 No , 4to5 ‘ 9.7 contained besides 8 te F 4 2 10.1 considerable quan- 9, 10 1, es 3) | 4 Qos Sat tities of ammonia fiesta ~ 4) 5 , | 9.2; 9.2 13,14; 1 , levulose | 5to6 , 10.-; 10.6 Sree 4 ne 100 1000 mers. of assimilated glucose, i.e. per 400 mers. carbon 19, 3 = 24, 1 mers. N is fixed after that time, that is 6°/, N on the weight of mould. This value I will eall nitrogennunber. Atter 4 days the accumulation was fairly the same. The nitrogen number was decreased to 5. Nearly all the ammoniumnitrogeu (ea. 13° mers.) was taken up by the organism, for with Nussier’s test the liquid gave but an insignificant reaction. The remaining 7 mgrs. are furnished by the nitratenitrogen 1) An analysis of this water made in October last gave: solid substance 461,35 mgr. p. L. SO,” 60,5 mgr. p. L. org. a GON eae (Ve SVE ae reduction power 3,5 mgr. O, p.L. (K MnO,) NOs! traces dissolved Oy 4,54 cMS p. hi. NO,' absent free GO, PSH Meta eee NH = fixed CO, 126,8 Petree Silicie acid (Si0;) 2,0 mgr. p. L. Total GO; 127,2 Pees Al, Os 4+- Fey O; (Ged Temporary hardness (Pretrer-Warrua ): 8,07° Ca O ee, <7 Total a ( = ): 9,43° |Mg O 30,1 owe Permanent ( : ): 1,36° |! Cu and Pb absent Mg - ( ; ): 2,02° | Na,O 12005 > = oe Total im (CLARK) 7 9329° , . from rest of combu- stion 128,9 Alc he 2) With this corresponds somewhat more than 26 mers. nitrogen. 8) The temperature in these experiments was 25° C, 4) Addition of 5 mgrs. boric acid. 1050 TABLE Il. METABOLISM OF NITROGEN. 50 cm® tapwater, in which dissolved 2 pCt. glucose (free from water), 0,15 pCt. ammoniumnitrate, 0,1 pCt. potassiumchloride, 0,05 pCt. crystallised fosforic acid , 0,1 pCt. crystallised magnesiumsulfate, 0,1 pCt. calciumnitrate (free from water). Temp. 34° C. Days | Quantity of Reaction of the culture liquid - after _ nitrogen fixed Growth and with * jnocu- in the mould 3 =a : spore format 1). i i lation in mgrs. Spore arene NESSLER. Diphenylamin; sulfuricacid. 1 3 | 19.3 vigor., hardly anyspores slight strong Diss 4 4 |20.3; 20.7; 19.6; , , very few : a3 = 5 3 17.5 re et Se » rather strong . 6 a 11.8 tetas tes 45 » ” ” 13 9 9.9; 10.4 » » rather many ,, ” ” ” 9 15 8.8 » J ” ” ” » » yn” 10 18 10.6 es : ” ” ” ” ” 11 19 10 Oe 5 » ” ” ” ” Excepting nr. 1 where only 80°/, of the glucose was used, all the glucose in the other culture tubes had been assimilated. The dry weight obtained from them I have not determined in these experiments. For this my earlier investigations may be compared ’*). Notwithstanding the quantity of fixed nitrogen had decreased on the 4% day from 6 to 5°), of the assimilated carbon, the absolute quantity was not lower. On the contrary, a slight increase was observed caused by the glucose still present after 3 days. The nitro- gen excreted by the growing mould is assimilated again during the formation of new cells. When all the glucosé had been used, which was already the case on the 4" day, nitrogen only was excreted. The consequence was a considerable lessening of the quantity fixed - in the organism. After 5 days (nr. 5) only 17.5 mgrs. remained fixed. This was accompanied by a decrease of the nitrogennumber as graphically demonstrated (fig. I). (see p. 1051). After 5 days it was already decreased to 4.4, after 7 days to 3, after 9 days to 2.5. Then it undergoes but insignificant changes. 1) The use of very pure chemicals free from manganese causes the bad spore formation : 2) Folia Microbiologica, Bd. 1 p. 422 and these Proceedings XV p. 753. 1051 The metabolism of the nitrogen corresponds thus in both cases with that of the carbon, namely a considerable accumulation at first, ——_ Py - , ; fig TMi MtoL hmong logs by Kypooe tect vever , Fy ome ee >— é ¢ we 9 5 ey, - ce : 3 Joel Ceccinig crake, ora ree oppelowt 4% glaekove (watery } OOO ao honiumenCraal , 0/6, kalau So Hoe G00 aah Keg 2, < 3 ACE eens OSL ORs »Oo4% either Kelbacend Bria I TEA ome hae far, 94% acaswmy © Calnice. Kanak Perrys « Il” g Qkose ie hilakoelnl yore ae ; Sees | ee a ar a Se F eae ce Fig. I. Metabolism of the nitrogen; 50 em’ tapwater in which dissolved 2/0 glucose (free from water), 0,15°/) ammoniumnitrate, 0,1 °/) potassiumchloride, 0,05° 7 crystallised fosforie acid, 0,1 °/) magnesiumsulfate, 0,1 9/9 caleiummnitrate (free from water). Temp. 34° C. which deereases very mnch in the course of time, finally to remain nearly unchanged. Whereas carbonic acid is the form in which the carbon can leave the organism, the experiments in table II prove that the nitrogen is excreted as ammonium. The lowering of the nitrogennumber is parallel with a return of ammonium into the medium so that there is cause to consider, as before with the carbon, the course of the plastic aequivalent of the nitrogen and of the ammonium aequivalent in relation to time. The decrease of the plastic aequivalent of the nitrogen is combined with an increase of the ammonium aequivalent. This view may, however, give rise to error as to the nitrogen, the ammonium being here a product of excretion, which /iAervise is mostly the form in which the nitrogen is given to the organism. By introducing the nitrogennumber this error is avoided. When excess of ammonium- nitrate is used it is chiefly the ammonium nitrogen which is assi- milated, as proved before. In a previous paper') was shown that manganese does not change 1) These Proceedings, XV p. 753. - TABLE IIL The conditions of the cultivation were the same as in table II. Nr. | Particular. piiea en tie la | ee ee Nittogen: _ Growth and spore-forming. 1 No manganese . | After 3. days !) 19.3 | 6.0 vigorous, hardly any spores 2 0.001 mgr. MnCly 4 Aq. | Pci ear teed 823) 17:5 | 5.0 sy few spores 3, 4, 5, 6 No manganese fi cera eA fs a) 19367; 1956); 20n7s 2003 | 5.0 P very few spores i 0.001 mgr. MnClg 4 Aq. | ye 3) 18.5 4.6 » rather many spores 5 | 0.01 7 7 * my et! i 3) 17.3 4.3 - rf 7 “A 9 Oe Ba mika wear sya) 17.0 ee: wh ea 10 0.001 Zincsulphate 7 Aq. no ene we) 20.2 5.0 es very few spores a Tiel | MO eer eel instead ‘ yaa oad) | 18.6; 19.5 | 4.8 = hardly any spores S 13, 14 ‘ an (aire 7) 18.4; 17.8 4.5 - , ff 5 15, 16 * Ho Ale Eee) Lee aie, Wee 3.1 » Yather many spores 17 7 lien 7 eee) 9.-; 9.4 Pe Ae f : fs _ 18 No manganese a N)P ey, td) 10.6 2.6 ” ” ” ” 19 a areas but instead ‘ fp lMtebe Spin a)) 9.3 2.3 ” few spores 20 Vith manganese oO yee) | 8.- 2.0 “ many spores 21 . ‘ Py eed ye) 8.2 2.0 * > F Do, oR 24 OO, ‘ * en (0) 0 Beams) SrSrS.o iO.) Oem Oh 2,2 ) i i ‘) SS pCt. of the glucose is assimilated. ') No glucose is remaining in the solution. 1053 the nature of the metabolism of the carbon, but does modify its velocity and that substitution of rubidium to potassium neither changes that nature. This T have also found true for the nitrogen under the influence of the said metal, as is shown in table IIL. Nr. 2, where manganese is added, has a lower nitrogennumber than 1, which is owing to the manganese. The nifrogennumbers of 7, 8, and 9, are lower than those of 3, 4, 5, and 6, where no manganese is added. The nitrogennumber of 10 is like that of 3, 4, 5. and 6. The addition of O,OOl mgr. zinesulfate (ZnSO,.7 Aq.) changes neither the metabolism of the nitrogen nor that of the carbon. *) That the replacing of potassium by rubidium has little influence on the metabolism of the nitrogen is proved by comparing nrs. 11 and 12 with 3, 4, 5, and 6, and 19 with 18, whose nitrogennumbers are nearly equal. In the above deseribed experiments the nitrogen in the liquid was of different nature, both in the form of ammonium and of nitrate. For that reason I repeated the experiment and used ammonium- chiorid as only source of nitrogen. Various concentrations were also studied. The results are found in table TY. From these experiments we may conclude that the nature of the metabolism with ammoniumehlorid is the same as with ammonium- nitrate. The nitrogennumber, high at first (6,1), descends rapidly ; after 7 days it is already decreased to + 2,5, then to remain nearly constant. Furthermore we see that excess of nitrogen does not change the metabolism. All the nitrogen excreted is found exclusively as ammonium, the sum of the nitrogen in the mould and of that present in the solution being constant. The losses of nitrogen which may partly be ascribed to errors in the analysis, are, as seen in the table, of little import, and partly repose on the evaporation of ammonia. Thus we see that in the till now examined cases ammonia is a normal excretion product in the metabolism of Aspergillus niger. After Prof. Boérsrken’s advice I investigated if this is always the case; if also by nitrogen nutrition with KNO, ammonia is excreted. The results of these experiments are found in table V. We see from them that also with KNO, as exclusive nitrogen food the nitrogen is accumulated in the organism, albeit less quickly than NH,Cl or NH,NO,. The nitrogennumber lowers also here whilst ammonia comes into the culture liquid. There are hardly ') These Proceedings, XV p. 760. 1054 Oo oO 4 & &@ & &© BO = 2 3 re a cn : noo o8 ooo no = © © S | MerNinth, 5 >> yn = <3 Sai 900 Roe IRS os cnc mould Crome > or Soup NDZ ZR QaQs 2s no we Ne S on 2) . Rare STE ne 35 : : Nitrogennumber = 2s Oe S to tr wo eo oJ - = = x4 = 5 5 = ‘ — So ow = = ) = 3 aoe ASL = = = >. x ee = = Mgr. N. as om g =) ors Sy aie OC Sema mse eae ammonia ay Se PS OL ov 2) cy Pe Seno, oases gs ° 3 = — . : : =~. 3 3 3 in solution. = 8 > = = =. a x = w = = =] on © oa ny pS [Eo LUna Se = a2 3s & ™m S © LS = mo} a DS: tS. — | = | oo Sum = ro) ee . a . . : . =o = 4 — Oo MO oo ro Ke) Se ao < Pe er g 2 8 oS = Assimilated = wk: = S : Si oo) or ony ee ee glucose = = SS SE py. Pcie tae : = S ae 3 in pCt. é 3 =] = = . fs ae EF pi ~ a = Q = = = 2 SS OS. Te ees ce) 5 = So6¢ oe) aot Number of days 2 2. : ; S) = = = = = = = = |afterinoculation > = < n wn = = = ee ea oe SSNs oe : | ike) ess 35 £ = B & |Mgr.N. in the S is - i leis SS Tey SP ENT fe 5 mould 5 = : Nes o8 wn wo YO & on = ee —=oAogm & } : ae aes : x Nitrogennumber AMSA . 7 a peda ee) 2) to \ sua Nas | 3 3 ae maf fates 2 ay = Mgr. N. as = Fe ro) Cer ae SAT eee are Fen Es g Meo. Saas Oe ammonia EIS ARS m oo f oe St OS) : é ein as 7 =i 3 in solution. Mol se)5 Fa > = =} etna mi ae = @ = aS a Xn D a = = ca a 5: = ££ = = Se ghar Sum =< a> oOo © w a ror) wo : eo eS 2 = = 3 2 3 — — — ee ais ce nag Rul aye cea S S Assimilated £8 a3 = a > D 2 a = S438) Sie Shree ase neh glucose 6 mS at a 3 ; = Fe =} 3 3 in pCt. he 8 | = 5 = = | any losses of nitrogen, so, Aspergillus niger is able to reduce nitrate to ammonia. Furthermore it is proved that the nitrogennumber of a mature mould layer with glucose or levulose as exclusive organic food for Aspergillus niger, independent of the source of nitrogen, amounts about to 2,0. Notwithstanding a young mould culture sometimes contains 2 to 2'/, times as much nitrogen as a corresponding old one, such a young, duly washed layer, when boiled with distilled water gave no trace of the above named anorganie salts which had deen added to the medium as exclusive source of nitrogen. Here thus, too, the LOSS se 6° © te) Los) | c: -—_—_eoorororoo_—_: nh easxK—eeeee Hy a “o i: ae ‘ Z ac “ C a “a os a “a Z = fer, Zz c SOUT “ a ras) a L6 a 2 SaeGl: sd “ 0g b od Lr salods Maj A19A ‘Snot0SIA qod ur Jaquinu 9 : | gsoons “UdSOI}IN | | payepwissy | soiods Auvul ‘snoi03Ia saiods Auvul J39y}e1 ‘SNOIOSIA sa.iods AuBU Jayyet ‘SNOIOSIA saiods Aueul s9yjye1 ‘sno.10Sia Sulwtoj-a1ods Suluuiseq ‘sno103IA “SUIWAO}-o.10ds pue yjMoin skep ¢ uole[Noou! | Jaye sAep jo Jaquiny PIUIW4sajap JOU cs ore SI 6° pinbiy ayy ul PIUOLUWIP YONW Jayyer Apeoipy uo}oRaI PIUOWWE WSs Ajawasyxe AU uooeaI BIUOWWIE yes Ajawasjxa AjUO JI]SS9N YUM uoloPat OU SdAIS UOIyNJOS Ja[SSaN Y}IM uoljoR—I1 OU SdaAIs UONN[OS J3[SSON YIM Uol]e_L OU SdAIS UONIOS ‘sISW Ul ‘elu -OWWP SB UOIN[OS Ul ussosu jo Ayquen?) c'6 ol 66 Il 6 Ol ST 6 I's 8 Z Ol L 6°6 9 o Fl c SPI P Lal € FI G v's I plnow oy} ul udsO1}IU “IN Jo Ayquen?) ‘) of § = ‘dway ‘asoon]s od zg pue (pasitieyshs9) ‘OS SW 30d cI‘o {'0q “HM ‘10d cI‘o (N “48u gz) “ON 9d #'0 paaossip yoy ul Uazemdez .wo QC *‘NOILIMLON NSDOMLIN SV “ONM ‘A AIGVL anism ‘acted by the or annie nitrogen compound atti ‘oO to) y « « ANOL € “ of very quickl intermediary excess nitrogen-containing unknown, Un ¢ c into converted product. Thus, here again the is adsorption has no practical < influence on the distribution of the nutrient substanees between the medium and the mould. 69 Proceedings Royal Acad. Amsterdam. Vol. XV, 1056 These results which. as experiments have proved, hold also good for a few other examined orgamsms, show that in the literature the influence of the adsorption is often overrated ‘). In order to test the obtained views about the metabolism of the nitrogen the following experiments were made (table V1). The quantities of added ammoninmnitrogen differ very much in the tive series of experiments. In D there is just sufficient to satisfy the first wants (20.9 mers), in E was an excess of nitrogen, whilst in ©, B and A there was a deficit of nitrogen relatively to the assimilated glucose. Still in B and C the additions were sufficient to satisfy the requirements of a mature mould layer. In A this was not, however, the case and the quantity of nitrogen was even smaller than that fixed-in an old mould culture containing little glykogen and obtained at the expense of 1000 mers. glucose. To this it must be ascribed that the assimilation of glucose is slackened. After 9 days 20°/, is still unused. Fixation of nitrogen from the air could not be observed in this experiment, neither for A. nor for B or C, whilst yet these series of experiments might in particular come into consideration for an eventual fixation of atmos- pheric nitregen in relation to the mentioned deficit in the nutrient solution. In the referring literature. however, are many statements tending to prove the contrary. j We further see that also the velocity of glucose assimilation in B is diminished although the general course of the process of nitrogen fixation remained the same; a high nitrogennumber at first which for all the series decreased with the time to 2 to 3. The nitrogennumber of A. B. and C. and in slight degree also of D, «vas in the beginning bound to a certain limit determined by the added nitrogen and the mould. Series A has a deficit of nitrogen with regard to the quantity of assimilable carbon; series E is characterised by a deficiency of carbon as to the quantity of fixed nitrogen. } We should still point to the association of the plastic aequivalent of the carbon and the nitrogennumber. If the former is high this is also the case with the latter and the reverse. Summary. 1. The nitrogen fixed in the mature mould is proportional to the plastic aequivalent of the carbon independently of the nature of the carbon as well as of that of the nitrogen. 1) See also W. Retypers and D. Levy, These Proceedings, 1912, p. 482. LOST 2. The nitrogennumber, by which is meant the nitrogen per 100 parts of weight of assimilated carbon lowers with time; for a mature mould it is ca. 2 (glucose or levulose as source of carbon). 3. The metabolism of the nitrogen has much resemblance to that of the carbon. a. An accumulation of carbon is combined with a high nitrogen- number; inversely the mature mould has a low nitrogennumber. 6. The nature of the metabolism of the nitrogen does not change under the influence of many factors; neither is this the case with the carbon. c. The velocity of the metabolism is subject to great changes. d. The same factors that accelerate the metabolism of the carbon aso further that of the nitrogen. e. Substitution of rubidium for potassium is of little influence on the metabolism of the nitrogen. 4. The nature of the metabolism of the nitrogen is independent of the souree of nitrogen. At first the nitrogennumber is — high, then it decreases whilst the freed nitrogen returns into the nutrient solution as ammonia. This is proved for the cases when ammonium- nitrate, ammoniumchlorid, or potassiumnitrate is given as nitrogen- food. Aspergillus niger, thus, reduces nitrates to ammonia but not to free nitrogen, Only in the culture tubes with a deficiency of nitrogen as to the quantity of carbon, no ammonia can return into the solntion as it is directly used for the production of new cells. 6. In the cases of a deficiency of nitrogen no fixation of atmos- pheric nitrogen could be observed. Finally my hearty thanks to Professor Dr. J. Borsexen and Professor Dr. M. W. Brierinck for their valuable help in this investigation. Technical University, Organical-chemical Laboratory. Del7t, November 1912. 69% 1058 Microbiology. — Metabolism of the Sosfor in Aspergillus niger. By Dr. H. J. Warermay. (Communicated by Prof. Dr. M. W. SEIJERINCK). (Communicated in the meeting of December 28, 1912). In an earlier communication’) I have shown that the metabolism of the nitrogen in this organism is analogous to that of the carbon *). These two elements are accumulated in the organism and are later partly exereted, the carbon as carbonic acid, the nitrogen as ammonia. We find besides that an excess of these elements retards. the spore-formation. For the carbon compare tables Ila, I1é and III (p. 451, 452, and 464 Folia microbiologica); for the nitrogen see table VI (Preceding paper). I have further fonnd that the fosfor behaves in the same manner as the above elements. In the first place I ascertained that the rate of fostor of an old mature culture of Aspergillus niger is constant, independent of the way in which it is obtained. The mould layer was before the analysis washed with distilled water and -after drying destroyed by strongly concentrated nitrie acid in a closed tube. In the thus obtained solution the fosfor was determined after Finkener*) as ammonium fosfor molybdate (NH,), PO, 12 MoO,. The results are found in Table L. | For shortness’ sake I shall as for the nitrogen make use of the word “fosfornumber’, which means the fosfor fixed in the mould per 100 parts of assimilated carbon. As in the experiments of table I all the glukose (1000 mers.) had been assimilated and this quan- lity corresponds with 400 mgrs. of carbon; the number of mers. of fosfor must thus be divided by 4 to find the fosfornumber. As the table shows the fosfornumber is for an old mature mould- 1) See the preceding paper. 2) Molia microbiologica (1912) Bd |. p 442. 8) The liquid containing ammoniumnitrate and the nitric acid is heated till the first bubbles appear, then precipitated with ammoniummolybdate under continuous stirring. The precipitate is then washed out with a solution containing ammonium: nitrate and nilrie acid and dissolved in dilute ammonia. To the thus obtained clear solution is added an excess of ammoniumnitrate and a small quantily of ammo- niummolybdate, after which it is agam heated until the first bubbles appear; finally hot nitric acid is added under continuous stirring. The precipitate is dried in an air current to constant weight at 160° C. in a Goocu’s crucible. L059 T Ac Bub EY: Circumstances of cultivations: 50 cm3, very pure distilled water, in which dissolved: 2/, glucose and the anorganic substances mentioned below. Temp.: 33° C, (NH,)'PO, Fosfor in No. Anorganic substances Age | .12Mo03, mould | Seam (mgrs.) | (mgrs.) | WAbioeleta | 0,159’) ammoniumnitrate 1 0,05,, fosforic acid (crystallised) 90 dagen 33,9 0,55 0,15 1 { 0,1 » Magnesiumsulfate ( , ) bo [o. » calciumnitrate (free fr. water) | ,, = 32,9 0,55 0,15 0.1 ,, rubidiumchlorid 0,15 ,, ammoniumnitrate , potassiumchloride » magnesiumsulfate (crystall.) « 0,05,, calciumnitrate (free fr. water) 50 , 25,2 0,4 . 0,1 0,05, ammoniumfosfate 0,05 ,, fosforic acid (crystallised) | \ 0,00001 mgr.: MnCl, . 4Aq 4 As 3, but instead of 0,00001 mgr.: | ., ie 194 | 03 0,1 0.0001 mgr. MnCly . 4Aq 5 | As 4, but instead of 0,0001 mgr.: |, < 23,0 0,4 0,1 0,01 mgr. MnCl, . 4Aq { 0,4 9, potassiumnitrate 30 . 66,8 1,1 0,25 0,15 ,, KH,PO, 0,15,, magnesiumsulfate (crystall.) tapwater | ! 0,159/, KH: PO, | | | 0,06, magn.sulf. (free from water) | * 55 37,2 0,6 0,15 | tapwater and | | 0,08°/) NH4Cl 8 | \ As 7, but instead of 0,08, ee 25,2 0,4 9 || NH,Cl: 0,129, NH4Cl i i 29 0,5 SS or 10 | § As 9, but instead of 0,12'/,: 7 ; 28 0,4 0,321), NH4Cl 1060 layer rather constant so that in this respect, too, the fosfor corre- sponds quite with the carbon and nitrogen. In the second place the action of various increasing fosfate con- centrations on the metabolism of Aspergillus niger was studied. The results are found in table Il. The fosfor was added as kaliumbifos- fate to the nutrient liquid, whilst I ascertained by analysis that the rate of fosfor of this compound was indeed in accordance with the formula KH, PO,. After one day already, growth was observed in all numbers, except in Nrs. 1 and 2. After two days it had considerably increa- sed in Nrs 4—18, Nrs. 1 and 2 also showing a beginning of growth. After three days the growth of Nrs. 1 and 2 had not increased, as little in Nr. 8 where, however, more mycelium had been formed. The growth increased in the following Nrs. and was very strong in r Nr. 8. This continued also after 7 and 14 days. The retarding of the spore formation after 2 and 38 days is con- vincing in those experiments where much fosfor is added. After two days 38—6 had rather many spores. In 7 and 8 few had appeared whereas in the following Nrs. hardly any spores were seen. After 3 days 3—6 had many spores, 8 few, and the Nrs. with much fosfor very few. Only in Nrs 17 and 18 the spore-formation was considerable and about alike to that of Nr. 8. The same I have observed for the action of potassium, as before for the carbon and nitrogen, so that it seems of general significance. This may be explained thus: If an excess of the referring element, in this case fosfor, is present, the cells are continually overloaded with new food and with the therefrom arising intermediary preducts, by which the spore-formation is retarded. When the excess becomes very great it is possible that the process of the metabolism is so much acceler- ated that also the spore-formation is quickened. Probably such is the case in Nrs 17 and 18, where three days after inoculation more spores were produced than in Nrs. 9—16. After 7 days the differences in spore-formation are no more observable. However, there are elements which in feeble concentrations counter-. act the spore-formation *) and then the limits will be quite different. The quantity of mould is very small in Nrs. 1 and 2 where no fosfor was added, and amounts with increase of the fosfor; herewith the assimilation of glucose is parallel. After 4 days the solution in Nrs, 9, 10 and 11, no more contained fosfate, which after the same 1) These Proceedings, November 1912. a 10 PO! LI b'0) %oC0I ql Loc |) OT FO 001 9 L's ‘Ol cI CL'0| ~~ 96 6% or \Pl ‘St Ge él 90| “L8 0 17 II cei{0)|| > (i 0 cc'| Ol £0 =o €8 0'1 0 I‘ 6 88'0 8 696 €8 99'() L OSI cg br i) S901 + O01 “op ueueiow |2o0 | oF 0g 08) +5 | Z0°0 € %O1 + 0 ol — ee - a aa a SAPP Udd}XIS Ja}e eee UIAIS Ja}e SABp dA J0}Je sAep INO} 19]4e b= dere | ean 2 ; | [etayeur | ayrysoy se] _ "| jeisayeu | ayeysoy se : [BLayeul | ayeysoyse | = & | Fi asoonys |= q! asoon|3 | -pjnow pinbiy Je D) asoonjs | -pinow | pmby |Z 3) asoonys | -pynow pinbiy el | “IN 3 peye] jS2) poyey ul ul 30) poe | pie | ul 3 gi poze] ul ul | a qwsIom STLUISSY | eo) ICISS 7 || me on 2S! -1uissy | aE eee are S| isa : = ar | AIG ke Rattle | ‘sau ‘ur J0js04 Ball ia ‘saBut UDeIO{SOsy, |\ml eae | ‘SISW UL 10JSO4 = | — — 1 . *(19]2M Woy 3343) asoon|s 9), “og, “by *IOUW ,Sz000‘0 ‘(19}2M WO1} 99.1}) ayeaniuuunio[eo °/,S0'0 (]12JSA49) azey[Nswnisausew %/,] {9 ‘prropyounrey %/,1'0 ‘OJP WNTUOWWe %/,¢,0 : paajossip YOIYM Ul “19JBM pal[ystp aind Aye ‘euid YC MN shal teh eae 1062 time was still present in Nrs. 15 and 14. From these observations may be concluded that the mould had drawn to it all the fosfor in the three first experiments. As these quantities, especially that of Nr. 11, are considerably greater than those present in the old, mature mould layer (table 1), it was indirectly proved that also the fosfor in the metabolism is accumulated in the organism in considerable quantity at the beginning of the development. This result was then in a direct way confirmed by analysis of the mould. So it was found for Nr. 9 that all the fostor vanished from the solution was present in the organism (ca. 1 mgr.). For Nrs. 13 and 14 2.9 mgr were found in the mould, a quantity 7 tot 8 times as great as that in the old mould layer. The corresponding fosfor- number is 0.75. This number may even be higher, as is seen from an experiment which may be mentioned here for comparison. In a five days old mould layer (culture liquid: 50 em* distilled water, 0.15°/, am. nitrate, 0.1°/, KCI, 0.1°/, MgSO, (erystall), 0.05°/, Ca nitrate (free from water), 0.05°/, fosforie acid (erystall), 2°/, glucose), 3.9 mers. P was present. As all the glucose was then assimilated the fosfornumber was = 1.0. In opposition to what is found for the carbon and nitrogen this quantity of fosfor is loosely fixed in the organism. Ten minutes’ boiling with water will do to dissolve considerable quantities. Of a mature mould layer, treated in the same way, no, or hardly any fosfor is dissolved; the same is the case with lecithine or phytine. As the mould grows older the superfluous fosfor, accumulated in the organism, returns into the solution as fosforic acid. This was already indicated by the fact that the fosfornumbers of mature eul- tures were very small (table I). It was ascertained by direct analysis both of the mould and the culture liquid of N°. 15 after 7 days, and of the mould of N°. 16 after 5 days. For N°. 15 the sum of the fosfor in the mould and in the liquid present after 7 days is 8.7 + 1,6 = 10,3 mers. The totally added quantity was 10,5 mers., so that no loss of fosfor, in the form of hydrogenfosfid takes place. By this study of the metabolism of the elements we obtain a better view of their signification than was hitherto obtained. We see that the quantities of the elements present in the mature mould, do not correspond with the quantities really active during the deve- lopment. In the case of carbon the plastic aequivalent could in the course of time decrease to the half. For the nitrogen there was a threefold, for the fosfor I could point out a tenfold decrease. The quantities of the latter element required for the normal assimilation 10638 are much greater than is generally accepted, also as to the nitrogen, although in a less degree. When comparing the accumulation of the elements it thus seems, that during the metabolism this aceumula- tion is greatest for those, which form a small permanent percentage of the constituents of the organism. So we see, that in the course of an experiment the same quantity of an element may be many times active in the metabolism, one cell taking up the products excreted by another cell. Starting from this view the study of clements, such as manganese, which are already active in very dilute solutions, are interesting. Meteorology. — “A lony range weather forecast for the East- monsoon in Java.” By Dr. C. Braask. (Communicated by Dr. J. P. VAN Der StTox.) (Communicated in the meeting of November 30, 1912). In a preceding communication *) it was deduced from a study of factors of correlation that in the Indian Archipelago, with the excep- tion of the western part north of the equator, a connection is clearly perceptible between barometric pressure and rainfall. The nature of this connection appeared to depend upon the geographical position as well as upon the different seasons. In the following an attempt will be made to show that by means of this connection it is possible to make a long range weather forecast. For this purpose Java has been chosen, because a forecast is of greater value for this island than for any other part of the Archi- pelago on account of its intense cultivation. Moreover this research will be limited to the east monsoon, as the connection is less distinct in the west monsoon, and because a forecast for this season of abundant rainfall is of secondary importance. It will be necessary to prove, that the changes of the barometer- readings from year to year succeed each other according to definite rules, so that they may be determined in advance. Further we must also prove that it is possible to ascertain with sufficient accuracy how the rainfall depends upon the barometric deviations. With regard to the deviations of airpressure Java has an advan- tage over any other part of the world, because the variations of climate are determined by the variations of the barometric pressure in North Australia, which are characterised by an extraordinary regularity. No station outside North Australia can vie with it in this respect, not even Bombay of Cordova (Argentina) which stations 1) These Proceedings 1912 p. 454. 1064 were selected by Lockyer as the representatives of both types of the barometric periodical oscillation of 3.5 years') Moreover the amplitude in Australia is much greater than elsewhere. The variations of the airpressure in North Australia from the normal value are shown in curve I of the plate, by means of the six-monthly deviations of the barometric pressure at Port-Darwin, marked monthly on the piate in such a way that, for instance, the deviation in the period January-June (in relation to the normal value in the same months) is drawn on the I'st of April. Beginning with 1899 the base valne has changed, apparently because something has been altered in the barometer or its position. The curve shows some very regular series of waves, namely from 1878 till 1881, from 1885 till 1891, from 1896 till 1904. whereas in 1911 a new series seems to have begun. The maxima and minima are characteristic of fixed seasons, they develop themselves namely in the jirst and last months of the year. Minima. Maxima. 1 Dee. 1878 1 Febr. 1881 1 Oct. 1886 1 Sept. 1885 1 Febr. 1890 1 Jan. 1889 | Febr. 1898 il (Oyen, ils!) 1 Sept. 1900 1 Nov. 1896 1 1 Febr. 1900 1 Dec. 1902 1 March 1912 Febr. 1904 It is further evident, that the time which elapses from minimum fo maximum is one year, from maximum to minimum two years. The period is evactly 3 years. The curve so closely resembles this schematic interpretation, that it may be represented by the schematic broken line IV of the plate. From 1878 it has been traced backward by means of the barometric observations made at Adelaide. For simplicity’s sake the maxima and minima have been drawn on the 1st of January. These regular periods are particularly adapted to forecast the airpressure a considerable time in advance. Disturbed periods are lying between them however, in which the curve makes the impres- sion that there has been no development of the maximum for some years. The certainty with which the barometric variations may be predicted would decrease greatly, if the epochs at which these disturbed 1) Solar Physics Committee. Monthly mean values of barometric pressure. 1065 periods appear could not be predicted and one would always be uncertain whether the end of a regular series is near. Fortunately however these disturbances seem to be anything but irregular in their appearance, so that there exists a possibility of announcing them in advance. This may be seen from the comparison of the barometercurve I with the curve I, which represents Wo1r’s relative numbers of sunspots. // ts remarkable that the disturbances in the barometercurve coincide with the maxima of the sunspotcurve, whereas during the periods with small sunspot intensity the regular barometric wave is developed undisturbedly. It cannot be denied that the number of sunspot periods over which this comparison is possible, is but small, however there seems to be every reason to suppose that we have here to do with a real and not with an accidental connection. Indeed it is a matter of fact known already since long that there exists a connection between the number of sunspots and different meteorological phenomena, and the above mentioned result agrees with what has been found in earlier researches. At the close of this communication this con- nection will be still further considered. One would be inclined to go back, beginning with the year 1876 and examine still more closely the connection between sunspots and disturbed barometerperiods by means of the observations made at other stations with longer records. For this purpose i.a. the stations Batavia, Adelaide, Bombay, and Madras would be adapted. As however at these stations the oscillation itself is less regular, it is very difficult to distinguish what is disturbed by the sunspots and what is not, and the results would not be very convincing. Now the question arises how the rainfall is affected with regard to the barometer oscillations. In answering this question the disturbed periods in whieh the connection is less distinct will be left out of account and only the regular waves will be considered. In curve V the rainfall deviations in West-Java (6 monthly means, calculated in the same manner as the deviations of curve I, accordingly reduced to one month) have been represented monthly ; for the years 1875—— 1878 the curve is based on the Batavia observations only. The curve shows clearly that the connection between rainfall and airpressure is different in the West- and the Eastmonsoon, it may serve to illustrate the numbers which are given below. The investigation may be divided into three parts according to the schematic barometer curve. 1. The Eastmonsoons of the years in which the barometer is moving from maximum to minimum; these are years of transition. 1066 2. The Eastmonsoons following the barometri¢ minimum. The pressure remains below normal during the whole year. 3. The Eastmonsoons preceding the barometric maximum. The pressure is above normal during the whole year. The first case is apparent in the years 1878, 1886, 1889, 1897, 1900, 1908, and 1912. The departures of the rainfall from its normal condition from June till November (the latter included) '), were in these years, averaged monthly, in millimeters. 1878 1886 1889 1897 1900 1903 1912 West-Java East-Java —24 (Batavia) Not observed. + 1 +20 +67 +50 29 -30 +34 +43 +24 ills) + 2 (June-September) —21 (June-September). The second case is apparent in the years 1876, 1879, 1887, 1890, 1898, 1901, and 1904. The rainfall departures are in the same months as above averaged monthly : 1876 1879 1887 1890 1898 1901 1904 West-Java Kast-Java + 4 (Batavia) Not observed. 69 +79 29 i 52 44 8 18 15 1s Sl 17 In the last case are the Eastmonsoons of 1877, 1880, 1885, 1888, 1891, 1896, 1899, 1902, and 1911. The rainfall departures in the months June-November are : 1877 1880, 1885 1885 1891 1896 1899 1902 1911 West-Java . East-Java — 74 (Batavia) Not observed. + 62 23 == fsts! —53 — 86 + 2 — 99 —=6() —102 —51 — 12 —4d1 —104 —57 ices ag ey 1) These are the months which have negative correlation between airpressuré and rainfall as appears trom the preceding communication. L067 In the years of transition mentioned sub 1°, evidently the rainfall is also in a state of transition; the signs of the departures are changing and have no fixed character. On the contrary all Eastmonsoons mentioned sub 2° without exception have been too wet in West- as well as in East-Java, whereas of the Eastmonsoons mentioned sub 3°, out of 9 cases 8 have heen too dry in West-Java and out of 8 cases 6 too dry in Kast-Java. Tt cannot be denied that among the favourable cases there are some in which the departure is but small. but on the other hand it is a matter of fact that with 2 of the 3 unfavourable cases the departure also remains small. In these years the character of the monsoon has been indefinitely developed, or has been different in different parts of Java or, as occurred in 1911, the character was different during the different months. Certainly 1911 must be reckoned among the dry years, even though the heavy rainfall in June caused a positive departure in East-Java. It must be remarked that to the numbers given for 1876— 1878, as taken from the observations of only one station, but little value can be attached. It is however a well known fact that 1877 was a dry year over the whole of Java and that therefore the strong negative departure observed in Batavia has a general validity. Above has been given a scheme of barometric changes and cor: responding fluctuations of rainfall which may be applied to 23 years out of the 37 of the period 1876—1912. If we exclude the year 1876 for the above mentioned reason, this scheme gives for 15 years (mentioned sub 2 and 3) a definite answer to the question what was the sign of the rainfall departure in the Eastmonsoon in Java. With one exception in West-Java and two exceptions in East- Java this sign corresponds with reality. ; On the principle upor which the scheme has been based it also would have been possible to forecast for these 15 years the sign of the rainfall departure in West-Java 14 times, in East-Java 13 times, if we had considered that the term should be taken somewhat shorter at the beginning and at the end of a regular wave series eg. half a year, whereas it might be taken longer between them, even 1 or 2 years. What may be coneluded from the scheme for the near future about the rainfall in Java?’ The circumstances for a forecast may presently be called really favourable, because a new regular series of barometer waves has already made its appearance during the present sunspot minimum. We have already passed the barometer maximum and the pressure 1068 is changing exactly in the direction indicated by the scheme, so that there is every reason to believe that the next minimum will appear at the expected time (namely about the 1st of January 1913), while there is no indication in the course of the sunspot number that points to an early disturbance. Therefore also the appearance of the next barometric maximum about the 1 of January 1915 is rather certain. From this already now may be concluded, with certain reservations that must be admitted with every forecast, that most probably the Kastmonsoon in Java of 1913 will deviate in the wet, and that of 1914 probably in the dry direction. Finally a remark may be made abont the barometercurve itself. In the preceding communication the question was raised as to whether the barometerperiod of 3.5 years has a terrestrial or an extraterrestrial cause; as for the Port Darwin curve, (and to this one a considerable weight should be attached, because it is not only the most regular one, but it has also the greatest amplitude), I should like to call attention to the fact. that the epoch of the marima and minima seems to be entirely controlled by the terrestrial seasons. This seems to me a new proof for its terrestrial origin. The cosmical influences instead of causing the barometric oscillations, seem to disturb them (namely during the sunspot maximum). If the variations of climate (departures of airpressure, tempera- ture and rainfall) of short period (Brickxrr’s period and the longer ones excepted) are described as a combination of waves of terrestrial origin with a period of about 3 years, and a cosmical disturb- ance, which is acting during the sunspot maximum, it seems to me that a satisfactory explanation may be given of the influence, that (as a result of different researches) is attributed to the sunspots. By a combination such as deseribed above the fact may be especially explained, that although in many cases a connection is found, it manifests itself at different epochs in a different way, as e.g. KOpPeN has established for the temperature in the tropics. The idea here given about the origin of barometric variation of 3 years is contrary, it is true, to the opinion of Lockyrr and Bicr- Low, whose ideas are that it is controlled by the number of prominences. However the data on which this opinion is based are by no means convincing as a comparison between curves I and II may teach. In curve III we have put down the observations made at Rome and Catania about the number of prominences, which data have also been used by the two above mentioned in- vestigators. Again the 6 monthly means of departure have been represented monthly in such a manner however that, following the 1069 example of BiceLow, for the elimination of the 11 year period the departures from the nearest 60 months (5 years) have been ealen- lated and not those from the normal of the whole period. Comparison teaches that in the beginning till 1891 the baro- metercurve shows indeed much conformity with ‘he prominence curve; afferwards however every similarity has vanished and in the later years in which the prominences hardly show any variation, the barometeroseillation goes on with the same regularity as before. Therefore very likely the connection during the first years has been only aecidental. Weltevreden, 10 October 1912. Chemistry. “Dynamic researches concerning the reaction of FriepkL and Crarts.” By S. C. J. Ontvirr and Prof. J. Borspken. (Communicated by Prof. A. F. Honiemay). (Communicated in the meeting of December 28, 1912). Dynamic researches have already been carried out with AICI, or analogous substances as catalyst. The first are those of A. Staror’), who investigated the action of ehlorine on benzene in the presence of SnCl, and FeCl,. The absorption of the halogen dissolved in an excess of benzene was measured, and it) was found that this proceeded according to the reaction scheme of the first order the constant being proportional to the amount of the catalyst. We may conclude therefrom that the catalyst is constantly active ; that its action is not sensibly altered by any of the reaction products. Further we mention the research of Bb. D. Srmrnn*), whe has studied the ketone synthesis and the formation of phenyltolylmethane under the influence of AICI, and FCI, where the progressive change of the reaction was determined from the amount of hydrogen chloride evolved. 1) Proc. 19, 135 (1903); Journ. Chem. Soc. 83, 729 (1903); Zeils. phys. Ch. 45, 513 (1903). L. Bruner had carried out measurements as lo the bromination of benzene, but as a catalyst iodine was used which is not directly comparable with AICI; moreover it was not sufficiently taken into consideration that the bromine unites with the catalyst (see Dissertation S. CG. J. Ontvrer). Stator has also used iodine as catalyst. Although this research is very interesting as regards the benzene substitution, this part may be passed over for the reason stated. 2) Journ. Chem. Soc. 83, 1470 (1903). LO70 Although, in our opinion, this modus operandi (see Dissertation C.S. J. Ontvier) cannot be expected to give accurate results it was rendered probable by him that, when in the ketone synthesis the proportion AICI,:C,H,COCI is smaller than (or at most only equal to) unity, the reaction was of the first order. With an excess of AIC], a reaction of the second order would have ,to be assumed where the AICI], would combine with the acid chloride as well as with the toluene. The latter course of reaction would always have to be assumed with FeCl, as catalyst. The figures found by him for the synthesis of phenyltolylmethane differ so much that they do not admit of a safe conclusion. Much more regular are the figures obtained by H. GoLpscamipr and H. Larsen‘) in their research on the chlorination of nitrobenzene and the benzylation of anisole in the presence of substances such as SnCl, and AICI,. They obtained the result that the reaction was ‘of the first order and that the constant was directly proportional with the concentration of the catalyst. As in the chlorination of benzene, the action of the catalyst appears not to be disturbed by the reaction products. If we consider that AICI, unites with the nitrobenzene as well as with the anisole to molecular compounds, and that these substances were always present in large excess, this result is not a matter of great surprise. The catalyst is then greatly paralysed, which condition cannot be modified to any extent by the formation of chloronitrobenzene (benzylanisole, respectively) in small quantities in regard to the nitro- benzene (anisole, respectively). That in the benzylation of anisole AIC], is not very active is shown by the fact that this reaction could still be measured at 25° in a V/,, solution of AICI, although as a rule the hydrogen atoms of anisole are much more readily substituted than those of benzene. The exceedingly slow chlorination of nitrobenzene at 50° may be. due to the paralytie condition of the calalyst as well as to the lesser activity of the benzene hydrogen atoms. From this survey as to what has been carried out in this direction it follows that a systematic research under various conditions was very much to be desired. The only somewhat trustworthy results were obtained in the 1) Zeitschr. phys. Ch. 48, 424 (1904). 1071 chlorination of benzene with SnCl, (Siavor) and in the just mentioned research of GoLpscumip?T and Larsen in which, however, neither the progressive change of the reaction nor the rdle of the catalyst has been much elucidated. For this reason we have more closely studied the reaction between p-bromophenylsulphonchloride and benzene. It was first our intention to carry this out in a neutral solvent for which carbon disuphide was chosen; it appeared, however, ‘) so that we were compelled to choose the hydrocarbon itself as the solvent. that the reaction then took quite another course The p-bromosulphonchloride was prepared from bromobenzene by sulphonating this with fuming sulphuric acid, neutralising the mixture with lime and converting the calcium salt by means of sodium car- bonate into the sodium salt; the sodium p-bromosulphonate thus obtained was converted by PCI, into the chloride. This was freed from POC], with cold water and recrystallised from ether. We had chosen the sulphonchloride as starting point because this is not decomposed by cold water, whereas it is rapidly decom- posed on warming with aqueous silver nitrate, so that the unat- tacked sulphonchloride could be freed, by means of cold water, from the AIC], and the HCl formed and afterwards be titrated with silver nitrate solution of known strength. The benzene hydrocarbons were dried carefully over AICI, and kept in stock with exclusion of moisture. The measurements were carried out by making (with exclusion of light and moisture) a solution of definite quantities of sulphon- chloride, aluminium chloride, and hydrocarbon; from time to time a definite volume of this solution was withdrawn and analysed. For details we refer to the dissertation of Mr. Oxivier which will appear shortly. We reprint therefrom a few series of analyses. The benzene required for this was treated before the reaction with AICI, and distilled; a thiophene-free benzene which had not thus been dried and distilled exhibited a small initial value and a strong course of the constant. From table I we see that the reaction between 1 mol. of AICI, and 1 mol. of acid chloride is one of the first order; when, however, 80°/, of the original quantity has been converted a serious retarda- 1) It then proceeded according to the scheme: Br C,H,SO,Cl + AICI; + C,H, = Br CyHySO, AlCl, + C,H; Cl + HCl. ‘ 70 Proceedings Royal Acad, Amsterdam. Vol. XV, 1072 TWN Shei ss E Action of BrC,H4SO,Cl (1 mol.) + AIClz (1 mol.) on excess of benzene. Concentration acid chloride = 0.1 n.; T = 30°. (a—x) = concentration acid chloride in grammols. after the time ¢ in minutes K = constant monomolecular reaction. K = > bi > » t | a—x)j103 K 7 | K Il E -_ : Soe x 0 86.1 _ _ 120 | Tesh = 0.00111 0.0139 240 | 66.4 0.00108 0.0144 360 | 59.2 | 0.00104 | 0.0146 480 © 50.6 0.00111 0.0170 720 39.2 0.00109 0.0193 1500 | 21.5 [0.00093] = 4320 | 19.3 [0.00035] = TAB WE WW Action and concentration as above. Benzene not again dried. t | (a—x)103 | Ki = = = Meileee eo atte wee 6 | 787 0.000698 210 | 71.8 | 0.000636 1320 | 50.6 | 0.000367 {ion is noticed. We attribute this: 1st to the absorption of moisture during the manipulations, which exerts an influence particularly when the amount of the active catalyst has become small; 24 {o a slight paralysis caused by the reaction itself. Injluence of the temperature. 1073 TABLE If As in table I, temperature = 40° (a—x)10° Ki 0 = = 30 61.6 — er; 523° | = -e00278 165 | 43.1 0.00251 a . Kk; -+- 10 eh. PE 7 The proportion = = + 2,5, is therefore normal. \¢ Injluence of the concentration. TABLE IV. As in table I. Concentration of AICIz;°as well as of BrCgHyS9.Cl =0.2 n (The expression !/,(a—2)103 indicates the percentages of the acid chloride originally present. | | 1/(a—x)103 K) 0 36.6 és 120 | 281 | 0.00220 300 | 19.6 | 0.00208 540 | 14.7 | 0.00169 The much more rapid progress of the reaction compared with that of the N/10 concentration was shown by the fact that after scarcely a quarter of an hour, which is the time required to obtain a homo- geneous solution, more than 65 °/, of the original quantity had already been converted. The constant for the /5 concentration is twice that of the N/10 concentration. We should conclude from this, that the entire course of the reac- tion can be represented by the reaction: dx a =kC ich, (a—«) that is to say, of a monomolecular reaction influenced catalytically, 70* 1074 in which the velocity of the reaction is proportional to the amount of chloride present and to the quantity of the catalyst. In that case, at a given concentration of the catalyst, a change of the initial concentration of the acid chloride should not cause any modification in the value of the constant. If, however, we take an excess of acid chloride we obtain the following : ABLE OV. Concentration AICl3 = 0.1 n.; acid chloride = 0.15 n.; t= 30>. t 2/3 X (a—x)108 Ky) | Ky ie | = = 0 | 90.8 = — 120 83.9 0.000656 0.00106 240 3 TS 0.000662 0.00110 369 72.5 0.000617 | 0.00105 TABLE VI. Concentration AlCl; = 0.1 n.; acid chloride = 0.2 n.; f= 30°. t | Wy (a—x)103 Ky | Ky 0 89.7 — - 185 82.0 0.00487 0.00117 370 76.6 0.00427 | ~~ 0,00108 585 70.9 0.00402 0.00110 Herein K, has been calculated as if all the acid chloride present is concerned in the reaction, hence in accordance with the above schema, whereas A’, has been caleulated as if only the acid chloride which has formed a molecular compound with the AICI,, enters into reaction. It is easy to see that, only on the latter supposition, we obtain a constant without course and which agrees with the constant obtained with equimolecular quantities of acidchloride-AlCl, (concentration W/,,). The exeess of acidchloride is therefore quite inactive; only that acidehloride which is combined with the aluminiumehloride is active. Hence in connection with the preceding, applies the relation: LO75 dx oe KX Caich X CBr€,H,S0.CLAIC & In solution of one of the active molecules, the velocity of reaction is therefore proportional to the quantity of the other molecule, in so far as this has united with the catalyst, as well as with the total quantity of the catalyst. The part thereof which during the reaction passes to the sulphon: AICI,BrC,H,SO,Cl + C,H, = HCI + BrC,H,SO,C,H, AICI, although not capable of rendering the acid chloride active must retain its catalystic activity in other respects. We may explain this by assuming that AICI, renders active the benzene, with which it forms xo compound, never mind whether the catalyst is united to the sulphonchloride or to the sulphon*). If the above relation is correct, the addition of an equivalent amount of sulphon to the catalyst before or during the reaction must either prevent or stop the same, because one of the necessary mole- cules cannot, or no longer, be rendered active. From Table VIla and b this appears really to be the case. TABLE Vlla and 6. — — 1 a ~ ——— ~-——— — = — —_—_—= — 1] b | As ia a; the sulphon 0.1 n has been added after all had become homogeneous. a | AICl3 = 0.1 n.; sutphonchloride=0.1 n. | sulphon = 0.1 n. t Sel t (a—x)103 es 0 | 99,2 0 83.6 180 | 99.3 | 155 83.9 500 | 99.8 435 83.6 | } 1200 85.5 [f on the other hand our explanation is correct, an excess of AICI,, which cannot then be paralysed either by the sulphonchloride or by the sulphon, must exert a perceptibly stronger action. For we have assumed that the catalyst renders active the benzene also and it will do this undoubtedly better still when it is in looser combination ; this is also confirmed by the experiment. (Table VIII). 1) It is possible and even probable that the action of the AICl,; does undergo a slight change; the course of the constant (see table I) might be partly attributed to this. 1076 TABLE VIII. AICl3 = 0.2 n; sulphonchloride = 0.1 n. t (a—2) 103 | RK nae 1 sax Se hives. hee The AICI; | remained ie | a ee undissolved hae hres 0.0120 | '° Srable 240 =| 3.4 | 0.0120 extent. When compared with table I, the reaction constant has become 10 times greater; also it is constant till the end. The lesser value at the commencement will, probably, have been caused by the fact that the benzene was not yet saturated with the catalyst which is but slightly soluble therein. Hence, it must be observed that the relation given above only applies to partly paralysed AICI,; the free aluminiumehloride has a much more powerful action. We can now go a step further. The above reaction may be ima- vined to take place in two phases: loan | 1 BrC,H,SO,Cl. AICI, + C,H, = BrC,H,SO,CIAICI,C,H, Il BrC,H,S0,C1AICI,C,H, = BrC,H,SO,C,H, AICI, -+ HCl The first (1) represents the real catalytic reaction which shows us the formation of a ternary compound, called by one of us the dislocation. |This dislocation applies here to the benzene because that of the other molecule in the formation of BrC,H,SO,Cl. AICI, has already taken place before the starting of the reaction. The arrows indicate that the benzene is rendered active by all the AICI,]. The second (If) is the elimination of the hydrogen chloride. If now we supposed that I would proceed with infinite velocity in regard to If we should measure the reaction of decomposition of the ternary compound and the constant thereof could not be depen- dent on the concentration of the aluminium chloride. Only by assu- ming that I proceeds slowly in regard to Il we obtain the course of the reaction as found by us’). 1) Nol the existence of a similar ternary compound is, therefore, essential because the course of the reaction shows that it breaks up, but the act of its formation called by one of us dislocation. (Also compare Dissertation H. J. Privs Delft 1912 p. 12 and 54). 1077 The research which is being continued in different directions in order to confirm the result obtained has elucidated the catalytic action of AICI, thus far that it does no¢ exert its action because it unites with one of the molecules, for the free AICI, was much more active than the combined portion. The view already expressed many times by one of us that the catalytic action of aluminium chloride is based on an influence (called by him dislocation) which makes itself. felt before the real compound is formed, has, therefore, been confirmed by this research. In harmony therewith it appeared that there was measured an additive reaction of the acid chloride with benzene, the first rendered active only in so far as it is united to AICl,, the second rendered active by the total aluminium chloride present. We have also carried out some measurements with henzene deri- vatives in order to get some knowledge as to the influence of the substituting group on the reaction velocity ; there it was shown that the reaction with toluene using N/,, acid chloride AlCl, at 30° proceeded so rapidly that the conversion had already practically taken place after the mass had become homogeneous; a constant could only be approximated. We give here also the reaction constants for benzene, chlorobenzene, bromobenzene and nitrobenzene at 30 and for a N/, concentration of the acidchloride-AICl, . toluene for 0.1 n. | > 0.0064 benzene ,, Orn 0.0021 bromobenzene ,, 0.00102 chlorobenzene. ,, | 0.00080 nitrobenzene _,, | 0.00000 From this little survey we notice that in the reaction of FRIEDEL and Crarrs, another succession of the velocity influences is observed than in the nitration where, according to the researches of HoLLEMAN and his students, it is exactly opposed to this in the ease of the methyl group and the chlorine atom. It may, however, be pointed out that our succession is based on measurements whereas the succession of the nitration is deduced from a comparison of the dirigent power of the groups on the entering nitro-group which, perhaps, has no direct connection with the velocity of nitration. When carrying out the reaction of Frieper and Crarrs it is desirable, according to this research, to have the catalyst in small excess when it forms an additional compound with one of the reacting molecules. Delft— Wageningen, December 1912. 1078 Chemistry. — “On the behaviour of gels towards liquids and their vapours’. By Dr. L. K. Wore and Dr. E. H. Bicnyer. ‘Communicated by Prof. A. F. HoLiemay) ’). (Communicated in the meeting of December 28, 1912), A paper by Mr. Bancrort’), which came to our notice only a short time ago, induces us to publish the following account of an investigation, which we do not yet consider completed. It concerns a phenomenon, discovered by von ScnrorpEr,*) who found that gelatine, swelling in water vapour, behaved differently from gelatine, swelling in liquid water: in the first case it absorbs much less water than in the second. This phenomenon seems to contradict the second law of thermodynamics, which immediately leads to the principle, that, if a certain number of phases are in equilibrium, the equilibrium will not be disturbed, if one of the phases (in our case, the water) is taken away. Being convinced of the validity of the second law, and not satisfied by the given explanations; we started this research. We can at once refute a seemingly obvious remark. It might be supposed, that the absorption of water vapour finally takes place so slowly, that the equilibrium would only be reached after a very long time, 7. e. that we have a false equilibriam. The erroneousness of this suggestion is immediately proved by the fact, that gelatine, swollen in water, loses water, when brought into a space saturated with water vapour. Von Scurogper found, that agar-agar showed the same phenomenon, though not so markedly, but he observed the reverse in the case of filter paper. As far as we know, no other experimental investigation of the subject has been published after von ScHRoEDER’s paper, though theoretical considerations have been given by FreunpiicH and Ban- crort, which we will treat of Jater on. We first repeated von ScuroxpEr’s experiments, concerning gelatine and agar; and we obtained the same results. Both substances, when used in the proper concentration, can be quite easily dried with filter paper, which is an essential point, as it was suggested that mechanical adhering of water to the surface of the gelatine might serve as a means of explaining the phenomenon. When the plates grew mouldy or the growth of bacteria was noticed, 1) Although much work has been done, since the original paper was written (Dec. 1912), we prefer only to present the translation of the Dutch communication and to postpone the publication of our new results. 2) J. physic. chemistry 16, p. 395. 58) Z. physik, Chemie 45, p. 76. 1079 the experiments were rejected. We used very pure gelatine (NeLson), the same as VON ScHROEDER used. The agar too was very pure and freed as far as possible from foreign substances by continuously treating it with water. The substances were placed in desiceators in a room, which was as much as possible kept at temperature. The data of an experiment on gelatine will be found in the following table; a solution of about 2°/, gelatine was solidified into a plate. ? Weight of the fresh plate Vi97 Gr. f after 8 days in water vapour 0.056 , 8 more days in vapour 0.056 > » 93 days in liquid OSUAIS, op es ee pOur 0039" =, _ ae eA se, -gy liquid Oxjocuman Fe Seo) ss | 5 vapour OO4Si G35. =; liquid 0.800 Whereas gelatine in water vapour absorbs not yet half its weight, we see that it takes up more than twenty-five times its own weight in liquid water. The experiment was repeated with other plates and always with the same result. A similar proportion is found with agar-agar. Weight of the freshly prepared plate 2.111 Gr. # after 8 days in vapour 010327 a » 8 more days in vapour 0.037 ,, f , 3% days in liquid O42 Fe oy WL soy SOON OSS ee i ee esas liquid ORS Fi HuLGe 7 hx vapour 0.040 ,, os auPGm.,48 5, liquid OR9ar aes 35.1%). Vapour OBS 4 It will be observed that in our experiments agar shows the phe- nomenon much more distinctly than in von ScHRoEDER’s. This author also tried the experiment with filter paper; we however did not, because we found it impossible to free this material from the water adhering to the surface. Then we investigated, whether other substances show the same phenomenon, and we found a very striking example in nitrocel- lulose. Celloidin Scurrinc was used, which is known to be very 1080 pure. This substance swells strongly at room temperature in 98 °/, ethylaleohol, without being solved to any considerable degree ; placed in saturated alcohol vapour at the same temperature, it loses a great part of the absorbed alechol. Celloidin in ethylaleohol. 1. Il. Weight of dry substance 0.774 Gr. Weight of dry substance 0.561 Gr. In liquid In vapour after 2 days 4.591 Gr. after 2 days 0.806 Gr. Sepa) Weare me EU ee 5) lot, Ooo 3 Stal. aeo 4000s, Se ese UL Composition of the gel 14.3 °/, cell. So ee HeOie Then in vapour spllel — LORY after 2 days 5.139 Gr. Composition: 52.9 °/, celloidin Sd a eee PAO 5 ye Then in liquid Gn, Ssto0uss after 2 days 3.270 Gr. 9. oe 4-098; 37 Obs) -oroeone AD SASS LORe, So Sooo lees 16, 4.316~ 5 Composition: 16.5 °/, cell. AR a pe ESATO Be. This quantity, now once more ee a1 eg ss ea placed in saturated vapour, ede Ye Sale. lost weight as in exper. I. Weight in equilibrium, caleulated from experiment II, 1.601 Gr. It was noticed, that, when the swollen celloidin, taken from the liquid and well dried off, was placed in the vapour, a few drops of aleohol were found after some days on the bottom of the weighing- bottle; these were removed before weighing. Celloidin also shows the phenomenon in methylaleohol; the absorp- tion in liquid, as well as the loss in vapour are nearly equal to those in ethylaleohol. It was also found with rubber (“gummi elas- ticam” Ph. Ned. IV) in xylene and in chloroform. In these systems a difficulty presented itself viz. that the swollen rubber almost became liquid; we sueceeded in separating it from the xylene or chloroform by centrifuging. Rubber is more soluble in these liquids than the other substances investigated are in water or alcohol, but that does not decrease the results of our experiments. Laminaria and cornea of the ox show the phenomenon quite clearly in water; from the latter, though well dried after being taken out of the liquid, big drops were found on the bottom of the LOSI dish. The structure of these two substances, however, is so compli- cated, that we must allow for the possibility, that their behaviour may be explained in quite a different way. Until now we have only treated colloids; we thought it quite worth while to examine, if the phenomenon could also be found in erystalline bodies. A paper of Fiscnrr and Bopertac') drew our attention to myricyl alcohol’), together with chloroform and amylaleohol. We are inclined to conclude, that this substance really shows the phenomenon, but the differences, which we found, are much smaller, and absolute certainty about the fact has not yet been obtained. The principal error in these experiments lies in the liquid adhering to the surface, and its influence will grow, according to the decrease of the total difference. Besides this substance we in- vestigated stearic acid with acetic acid and anthracene with ethyl- alcohol; the differences in these systems are still smaller and the uncertainty therefore is still greater. *) All the above mentioned substances show the phenomenon more or less; a few others do not do so or at least they show differences, not exceeding the experimental errors; viz. silica jelly, (as could be seen from VAN BEMMELEN’s investigations), coagulated albumen (serum- albumen, Merck) and amongst the crystalline bodies stilbite ; the latter absorbs only 3°/, water in toto. We did not investigate the hydroxydes of the heavy metals, because we did not think it possible, to free them from the surface water. Therefore we do not wish to oppose ourselves to the researches made by Foorr ‘) and Rakowski’). A word must be said, however, concerning a remark- able observation of Foorr, to which Mr. Rakowskt drew our attention. Foote found, that a crucible, containing pure water, placed in a well closed’ weighing bottle, on the bottom of which was some water, and which was pending in a thermostat, lost some weight. Now theoretically the water on the highest level must evaporate wholly, but, if we do not consider this fact, we notice, at all events, 1) Jahresber. d. Schles. Ges. f. Vaterl. Kultur 86, 36. *) This substance was prepared for us of carnauba wax in Prof. Honpws Bot- piNGH’S laboratory; a crystallographic examination by Dr. B. G. Escuer proved that it was wholly crystalline. We wish to express our hearty thanks to these gentlemen for their kindness. 8) Whether the phenomenon also appears in two normal, non miscible liquids, is a question, directly connected with the above. Experiments about this problem have been commenced. 4) J. Amer. Chem. Soc. 30, 1388. ») Zeitschr. fiir Chem und Industrie der Kolloide. 11, 22. 1082 that the difference, which Foorr speaks of (7 m.G.), is out of pro- portion to the differences, found by us (a hundred and more m.G.). We now wish to proceed to consider the given explanations. In doing this the first question that suggests itself is, whether the examined substances are composed of one or of two phases. Since vAN BemMeLen and Harpy’s investigations it is pretty generally assumed, that gels are systems of two phases. As to bodies like silica, we do not oppose this statement; but for gelatine, celloidin and rubber, it does not seem to be at all certain. Let us examine the grounds, on which it is based : 1. the well-known “Umschlagpunkt” and the behaviour of silica jellies (vAN BrmMeLen); agar, gelatine, celloidin, and rubber do not show a similar behaviour. 2. the pressing experiments; these do not prove anything. In the same way, one can expel the water from a salt solution, by exposing it to a pressure that exceeds the osmotic one, in a pot with semipermeable walls. Under these cireumstances some water is pressed out; but nobody will maintain this solution to be a system of two phases. In the case of agar the canvas, between whieh the agar is pressed, acts as a semipermeable membrane. 3. the analogy to mixtures of water, alcohol and gelatine, in which Harpy ') succeeded in observing the separation of small drops. Leaving the question, whether the drops appear just at the point of solidification, out of discussion, we are not allowed to apply results, obtained in a ternary system, to a binary one *). 4+. the behaviour of gelatine and agar, which are soluble in water, when liquid, but insoluble, when solidified, whilst the solution generally solidifies as a whole. If one takes the hysteresis into account it does not seem impossible to explain this behaviour also in a system of only one phase. 5. the structures found by Biscuit. These however do not seem to be of much value, since they are on the limit of the power of the microscope and since they have to be called into existence by all sorts of artificial means. Moreover Zsigmonpy and BacuMann*) have lately shown, by using the ultramicroscope, that both silica gel and gelatine are built up of much finer elements. It is doubtful though, if in this case we can speak of “phases”. We too think it very likely, that molecular aggregates are formed in solutions of gelatine; but these are also to be observed (by means of the ultramicroscope) 1) Z. phys. Chem. 33, 326. 2) Bacumann, Z. Anorg. Chem. 73, 125 expresses the same opinion. 8) Z. anorg. Chem, ‘71, 356; 73, 125. 1083 in greatly diluted, non-solidifying solutions’), which, then, ought also to be considered as systems of two phases; a view, which to us seems to be without any foundation whatsoever. 6. the forming of a membrane in gels by opposite diffusion of salts that give a precipitate*). It is not clear to us, why these preci- pitates should only arise in the cavities of the gel. Let us first of all examine Bancrort’s explanation, which is identical with the one, originally put forth by us, but which we have rejected for the reasons, we shall presently discuss. It assumes two pha- ses in the gel — one with much, the other with litthe water — which are separated by curved surfaces. The equilibrium in the vapour decides the composition of the second phase; the water, which is taken by the gelatine up in the liquid, forms the first. According to our observations, the concentrated phase of agar would contain 50°/, agar, whilst 3 to 5°/, would follow from Harpy’s pressing experiments. So this does not agree exactly! If we try to obtain — as is necessary a more detailed conception of the strue- ture of the gel, we have to choose between an open and a closed cell structure. Assuming the former, one could only accept Bancror?’s hypothesis, if the surface tension of the diluted phase with regard to the concentrated one is as that of mercury with regard to glass. We have investigated, whether this is the case by covering glass capillaries on the inner surface with a thin layer of gelatine, agar, celloidin or rubber. We found a behaviour as that of water-glass ; only in the ease of vapour-swollen or dry gelatine we observed a convex meniscus; gelatine, swollen in liquid, behaved as the other bodies. An open cell structure is, therefore, not consistent with Bancrort’s explanation. Another fact may be mentioned. which also speaks against this assumption; a plate of gelatine, dipped half way and vertically in water, only swells for the lower part, while the part above the water surface presents exactly as gelatine in equilibrium with vapour. For if there were an open cell structure, the canals should fill them-- selves by capillary action. Whether an open or a closed structure is obtained, will depend on the question, which phase separates first. If this is the most concentrated and consequently the most viscous one, an open structure will arise and the water will have a concave surface ; if, on the contrary, the latter appears first, it will cf course show a convex meniscus. If, therefore, we accept Bancrort’s explanation, we are abliged to suppose that the phase with much water separates first in all the systems that show the phenomenon ; of course, this 1) See especially Bacumann, loc. cit. *) Becunotp, Z. phys. Ghem. 52, 185, 1084 is not impossible. In the case of silica and alumina jellies, where the concentrated phase separates, an open structure is to be expected. Since the surface tension will probably be similar to that of water- glass — the gel is completely moistened by water —, the gel will not show von ScHrogDER’s phenomenon. In fact, we did not find it (nor did van BEMMELEN), in opposition to Bancrort’s declaration, that gelatine and aluminium gel are theoretically equivalent. It is, therefore, possible to explain in this manner, why gelatine, swollen in water, loses water, when in a space saturated with vapour ; we should even be able to calculate the size of the drops by the difference of the vapour pressures of the gelatine swollen in vapour and in water. Von ScHRoEDER has tried to measure this difference by allowing gelatine to swell in salt solutions and by determining the concentration of the solu- tion, in which the phenomenon no more appeared. He found this to be the case in a solution of sodium sulphate of a normality between 10-5 and 10-®. This would give a difference in vapour pressure of + 3.10-° mm. of water, out of which the radius of the drops in the gel can be calculated’ to + 9 mm.'), evidently an impossible result. In fact, we have, in repeating voN SCHROEDER’s experiments, obtained different results: celloidin, swollen in a solution of 3°/, sublimate in absolute alcohol, does show the phenomenon. We intend to try to determine the difference of the vapour pressures by a direct method. If, on the other hand, we suppose the diameter of the drops in gelatine to be 5 yu’), we calculate, that the vapour pressures must differ + 100 mm. of water, which to us seems a rather high amount. There is, however, a serious objection to be raised against this explanation. The gel, swollen in liquid, loses water in the vapour; in consequence of which either cavities, filled with air and vapour, are formed, or the gel shrinks, according to its losing water. Silica jelly shows the first alternative, as is proved by its opaqueness, appearing at a certain point; gelatine, agar, celloidin and rubber, however, remain quite clear, but their volume is diminished. Now, if there are no cavities, we do not see, why they should be formed anew, when the gel is replaced in the liquid. This objection, we think, entirely pulls down Bancrort’s theory. As to von Scurogper’s remarks, we must observe, that they do not give an explanation in. the proper sense of the word. Von ScnroeDER only wants to put an end to the controversy against the second law, by remarking, that the gel is taken from the liquid and 2 1) According to the formula: Ap = FH (see Chwolson, Lehrb. d. Phys. IL, 744), and assuming that the drops are bulbs. *) 5 wp is the diameter of the capillary canals in silica jelly, as put by Zsigmondy, LO85 placed in the vapour very quickly and that the velocity of this process influences the work done. As Banororr says, this alleged explanation is not likely to satisfy anybody; moreover it can be refuted by arranging VON SCHROEDER’s imaginary experiment in a slightly different manner. Pour upon the gelatine (in equilibrium with vapour) as much water, as can be totally absorbed, and place the whole in saturated vapour; it will now lose weight, till the vapour equi- librium is reached again. In this way the excess work, ii von SCHROEDER’S Opinion necessary for taking the gelatine quickly out of the liquid, is eliminated. ; FREUNDLICH ') introduces special attracting forees of the surrounding liquid on the gel. As long as one does not enter into detail as to the nature of which these forees are, nor why they have so much influence especially with the gels, this explanation does not seem to be more than a circumscription of the facts, and we agree with Bancrort, who declares it to be ‘neither very clear, nor very convineing”. _ We must acknowledge, however, that we ourselves are not able to give a better one. When looking for the directions, in which the solution might be sought, we find hysteresis, gravity, and capillary action. Hysteresis, of course, would do away with the possibility of a perpetuum mobile of the second kind; we should then have to assume, that every time slight changes are left in the gel, and that it would consequently be impossible to detect ad infinitum differences in water content, when the process of transferring the gel from liquid to vapour, and vice versa, is repeated. No fact, pointing in this direction, has however been found, neither by von ScurorpER nor by us; but it may be, that the process has not been repeated often enough; of course, this is not a more fundamental explanation either. ~ Concerning the influence of gravity, we wish to remark, that it might possibly explain the loss in the vapour, but never the gain in the liquid. Moreover, von ScurorpER made some experiments with regard to the influence of gravity, but with negative results. This would not, however, be a sufficient ground to deny the effect of gravity, since, as Bancrort justly remarks, the effect might be too small for observation. When, at last, we try to ascribe the phenomenon to the action of capillary forces, we do not make more progress than Freunpricn, though in this direction perhaps success will be most probable. Path. Anat. and Inorg. Chem. Laboratories University of Amsterdam, 1) Kapillarchemie, p. 494—497. 1086 Microbiology. — ‘Penetration of methyleneblue into living cells after desiccation”. By Prof. Dr. M. W. Bewerrinex. (Communicated in the meeting of December 28, 1912). It is generally known that methyleneblue does not enter living yeasteells, when these are first soaked with water or swimming in a fermenting liquid, whilst it colours the dead cells intensely. It is even possible several days to cultivate yeast in wort, coloured dark blue with this pigment, without the cells being coloured in the least. On wortagar plates with methyleneblue, colourless colonies will develop. On these facts a method is based to ascertain in living yeast the number of dead cells, which gives very good results. Meanwhile there is an exception to the rule that the cells, colouring blue are dead, and this exception will be more closely considered here. At the examination of dried yeast, most cells of which take a dark blue colour with methyleneblue, whilst only a very small per- centage remain colourless, the fermenting power often proves so great, that no other explanation can be given, but that the blue-colouring cells have for the greater part preserved that power. This is not unexpected, for it is well known that the alcoholic function is more permanent in dieing cells than the power of growth. Meanwhile, counting-experiments, whereby on one hand the number of cells colour- ing with methyleneblue was microscopically determined, on the other hand by plate culture, that of the cells growing out to colonies, showed that from certain dry yeast samples a much greater percentage of colonies developed, than the percentage of cells not colouring with methyleneblue. This fact was indeed unexpected and induced to a more minute observation. First of all it was proved that the number of cells, colouring in a dilute solution of methyleneblue, depends on the way in which the solution is brought into contact with the cells. If this is done by introducing dry yeast into the solution, all the cells colour dark- blue and cannot be distinguished from the dead ones. In plate cul- tures, however, a greater or smaller number of colonies may be obtained from these cells, although all seem perfectly alike in their dark blue colour, and should be considered as dead by anyone ignorant of their origin. In favourable circumstances the number of colonies mounts even to 100°/,, which is to say, that all the cells may colour blue and still grow out to colonies. This is in particular obvious when the cells are beforehand coloured with methyleneblue, and the coloured material is used for — 1087 sowing; it is easy then to recognise the blue cells on the plate and watch their germination under the microscope. The blue colour is then commonly seen to disappear before the formation of buds begins. But many of the later germinating cells remain blue and produce colourless daughter-cells. I never saw young cells taking the least trace of blue from the mother-cell. But if the dried cells are beforehand allowed to swell up in wort or in water and if the soaked material is laid in the methyleneblue solution, which is the usual way to effect the colour reaction, the result is quite different. Then only part of the cells assume the colour and this part is the smaller as the cells have longer remained in the uncoloured solution. A certain percentage, however, continue to take up the colour without having lost their reproductive power, and it seems to be very difficult to soak these cells with water. The simplest way to effect these experiments is by using dry yeast, quite free, or nearly so from dead cells. I obtained it by centrifugation of the small-celled variety of pressed yeast from strong fermentations, these being in their most active state. To this end it was cultivated at 28° C. in nearly neutral wort, after 6 to’ 8 hours brought into the centrifuge, and then quickly transferred to tilterpaper in a thin layer for desiccation. The large-celled variety of pressed yeast is less resistant to drying, To compare the two varieties, of which the smallcelled is richer in protoplasm than the other, the yeast must very cautiously be dried, first at low temperature, e.g. 25° C., then ata higher one, e.g. 50° C, This precaution is not, however, necessary to render the blue- colouring of the dry living cells visible; to this end drying of com- mon yeast at room temperature will do. I have, however, also met with commercial dry yeast satisfying the requirement of containing hardly any dead cells at all, namely the “Konservierte Getreide Brennerei Hefe” of the yeast works of Herbina in Hamburg, which was sent directly from the manufactory. This preparation is delivered in solidly closed tins, but after some time it loses its power of growth and fermentation; its quality thus evidently depends on the length of time past since its fabrication. It seems that this loss corresponds to that of the germinative power of seeds, which depends on their state of humidity. I possess some more preparations from the same factory, that have hardly any fermen- tative power and contain no cells fit for reproduction, but they have not been directly got from the manufactory and are already some years old. When using seed of Brassica rapa, soaked in solutions of 1 per 71 Proceedings Royal Acad. Ainsterdam. Vol. XIV. 1088 1000. or less of methyleneblue, the pigment penetrates through the seed coat into the germ, which partly colours blue. The germroot iakes up the colour the earliest; then follows a triangular field on the outer of the two seedlobes, which lie folded up in the seed. The base of the triangle, which colours first and most intensely, lies at that margin of the cotyledo, which is turned towards the germroot. Obviotsly the pigment has very quickly- penetrated through the micropyle of the seed, and only later through the seed coat. With stronger methyleneblue solutions the experiments do not succeed much better, because then the pigment accumulates so much in the seed coat, that even water can only enter with difficulty. After 24 hours such seeds are but imperfectly swollen but, somewhat later, the germination takes place as well. The coloured germs swell at 30°C. so vigorously, that many soon burst out of the seed coat. When the partly blue germs, freed from the seed coat, germinate on filterpaper, they yield part of their pigment to it, but especially in the meristem of the germroot it continues to show for several days and disappears only at length, by the dilution which accompanies the growth. It is then easy to see how the part near the rootmeristem grows the most rapidly whilst the region of the roothairs grows no more at all. That the pigment, without killing the cells, has penetrated into the inner part of the tissues, is not only shown by the germroots, but also by the coloured spots of the seedlobes, whose phloembundles even have taken up the colour. Botany. — “On Karyokinesis in Eunotia major Rabenh.”. By Prof. C. van WissrnincH. (Communicated by Prof. Mott). (Communicated in the meeting of November 50, 1912). LavrErBorn’s ‘) detailed investigation on Diatomaceae suddenly brought about in 1896 a complete change in our knowledge of the karyokinesis of these organisms. This investigator studied the process’ in Surirella calearata, Nitzschia sigmoidea, Pleurosigma attenuatum, Pinnularia oblonga, and Pinnularia viridis. He came to the conclusion that the nuclei always divide karyokinetically. The karyokinesis here is not less complex than in higher plants. It shows an important deviation. For Lavrersorn found that in all cases during karyoki- 1) R. Laurerporn, Untersuchungen tiber Bau; Kernteilang und Bewegung der Diatomeen, 1896. . LO89 nesis a body appears, which plays an important part, namely the central spindle (Zentralspindel), a body which does not occur in higher plants, but is specially found in Diatomaceae. During karyo- kinesis the nucleolus and the nuclear membrane disappear. The net- work forms a skein (Kniiuel) and by segmentation the chromosomes arise out of it. They are long and well-formed. In Nitzschia 16 appear and more in Surirella. In the middle the chromosomes form a ring round the central spindle. By division of this ring there arise two rings which separate from each other along the central spindle. Kach of these rings consists of the halves of the chromosomes. The daughter nuclei develop from the rings. Shortly after Lavurerporn a paper was published by K1LeBaHN') on karyokinesis in Rhopalodia gibba (Ehrenb.) O. Miller. He describes the diaster stage and mentions the central spindle and the chromo- somes which to the number of 5 or 6 are placed in a cirele and are granular in shape. Some years later Karsten *) described in detail the karyokinesis of Surirella saxonica. In general his results agree with those of LautEr- BORN ; in one point however they disagree greatly, for Karsten found the chromosomes in Surirella calearata and other Diatomaceae short and of irregular shape in complete contrast with the observations of LavTERBORN. In October 1903 I found an Eunotia in a ditch near Steenwijk. After fnrther examination and consultation of the descriptions and drawings of the various species"), I assumed that the specimen found was Eunotia major Rabenh. In the healthy, although not plentiful, material I saw numerous stages of karyokinesis, and since this pheno- menon had not yet been described in Eunotia, I determined to utilise this opportunity of studying it. The living object was first investigated, and then material which had been fixed with FrLemMine’s mixture. In order to study the karyokinetic figures better I treated the fixed material with a solution of chromic acid of 20°/,. Various constituents of the cell-contents successively dissolve in it and finally there remains inside the siliceous skeleton of the cell-wall, when the cells contain no fatty oil, only the nuclear network, or what results from it. The prepa- 1) H. Kuesaun, Beitrige zur Kenntnis der Auxosporenbildung, I. Rhopalodia gibba (Ehrenb.) O. Miiller, Pringsheim’s Jahrb. f. wiss. Bot. Bd. 29, 1896, p. 595. 2) G. Karsrry, Die Auxosporenbildung der Gattungen Cocconeis, Surirella und Cymatopleura, Flora, 1900, Bd. 87. p. 253. 3) L. Dipper, Diatomeen der Rhein-Mainebene, 1905, p. 125. Van Heurcx, Traité des Diatomées, p. 298. ; : 1090 rations can easily be washed with water and stained, for example, with Brillantblau extra griinlich. The nuclear network, the nuclear plate or its halves whieh all fall over during the action of chromic acid are then stained a fine blue whilst the siliceous skeleton is not stained. I will not enlarge on the method followed. I have already earlier stated the advantages which it possesses and which must be borne in mind in ifs application *). Like other Diatomaceae Ennotia major has but one nucleus, situated in the centre and surrounded by cytoplasm, which sends out strands in various directions. As seen from the side of the belt it shows an oval shape and seen laterally it is round. It is provided with a membrane and consequently shows a sharp outline. The nuclear network consists of grains which are united by threads of protoplasm. In the centre of the nucleus is the nucleolus. The latter dissolves in chromie acid more readily than the network. Special filamentous organs, such as occur in the nucleolus of Spirogyra, I have not been able to distinguish and to separate by the use of chromie acid in the case of Eunotia. The nucleolus agrees with that of the higher plants. The cells in which karyokinesis is about to occur are broader than the others and possess four large flap-shaped chromatophores. When the cells are viewed from the side of the belt, the nucleus is seen in the midst of the four chromatophores, two of which lie in the epitheca and two in the hypotheca. When a cell has divided, two chromatophores lie in each daughter-cell. These change their shape and position. They become twice as long and place themselves opposite each other in the epitheca and the hypotheca. A constriction then oceurs in the middle and (finally each chromatophore has divided into two. This process, the division of the two chromatophores, there- fore precedes the division of nucleus and cell. The first phenomena of karyokinesis show agreement with those observed in other plants. The nuclear network becomes more and more roughly granular in appearance. In a number of places it comglomerates and forms lumps, which unite into larger masses which more or less resemble short threads. I have not been able to determine the number of these thicker parts in the network. They always remain united to each other by slender connections. 1) Ueber den Nukleolus yon Spirogyra. (Bot. Zeitung. Jahrg. 56. 1898. Abt. I. p. 199). — Ueber das Kerngeriist. (Bot. Zeitung. Jahrg. 57. 1899. Abt. 1 p. 155). — Ueber die Karyokinese bei Oedogonium. (Beih. z. Bot. Centralbl. Bd. XXIII. 1908. Abt. Lp. 138 ff). — Ueber die Kernstructur und Kernteilung bei Closterium. (Beih. z. Bot. Centalbl. Bd. XXVIII 1912. Abt. I. p. 414). ee ee 1091 The thicker parts are comparable to chromosomes. Well-formed chromosomes, such as are met with elsewhere in the vegetable kingdom, do not occur in Eunotia. The nuclear wall dissolves and conse- quently the nucleus loses its sharp outline; the nucleolus also gradually disappears. To this point karyokinesis in Eunotia presents nothing peculiar, but the further course of the process is wholly different from that in higher planis. In the centre of the mass of protoplasm in which the nucleus is found, the central spindle can soon be distinguished. It is a strand of protoplasm of which the outer ends are turned towards the two shelis. At first I could distinguish the central spindle as a short rod embedded in the protoplasm, but in later stages of karyokinesis I observed it extending right across the whole mass of protoplasm ; the two ends were seen to be club shaped and thie- kened. ( was unable to study the origin of the central spindle, since the amount of material at my disposal was insufficient. The nuclear network contracts around the central spindle, and in this way the ring shaped nuclear plate is formed in Eunotia. The latter divides into two halves which are likewise annular and separate from each other along the central spindle, until they are finally quite at the spindle ends. Together with this, there ocenis division of the mass of protoplasm in which the nuclear plate lies. It divides into two parts, which send ont strands of pretoplasm in different directions just as did the whole mass and at first they are also connected with one another by strands of protoplasm. The whole figure very much resembles the diaster stage in higher plants, although I have never been able to distinguish a nuclear spindle. Meanwhile the primary division-wall has developed; it broadens out more and more and approaches the nuclear figure ; the proto- plasmic links between the halves of the nuclear plate and the central spindle are divided into two. The central spindle disappears. The daughter-nuclei are now very close against the division-wall, then separate again from each other, move into the neighbourhood of the epitheca and hypotheca and finally take up a position in the middle of the daughter-cells. With the development of the annular halves of the nuclear plate into daughter-nuclei the same phenomena appear as in the formation of the nuclear plate from the resting nucleus, but in reverse order. The rings divide into lumps or short thread-shaped pieces which remain connected with each other by fine threads of protoplasm ; the division proceeds to a point at which the nuclear network agrees again with that of the resting nucleus. In fully-developed 1092 nuclei I always saw one nucleolus and in less-developed ones often there were two. Probably also in Eunotia the nucleoli which appear in the daughter-nuclei gradually coalesce. The primary division-wall, of which mention has been made, is a lamella easily soluble in dilute chromic acid. The siliceous shells are formed later. I have not found a centrosome in Eunotia. Conclusions. In Eunotia major Rabenh. the nucleus divides karyokinetizally just as in other Diatomaceae, a fact established by LauTErBorn and Karsten. In Eunotia major a central spindle (Zentralspindel) also ocenrs, a body which plays an important part in karyokinesis, as the above authors have also shown in other Diatomaceae. Well- developed chromosomes are not found in Eunotia major. The nuclear network forms short bodies of indefinite shape, which crowd round the central spindle and form an annular nuclear plate, which divides into two annular halves; these separate from each other along the central spindle and develop into daughter-cells. With regard to the chromosomes, I may say that my results agree with those of K1impann and Karsten, but not with those of Lavrersorn. He found in Surirella calearata and other Diatomaceae, in the mother-nucleus as well as in the daughter-nuclei, well deve- loped long chromosomes, whose number could be ascertained (16 or more). KLEBAHN has not been able to see such chromosomes in Rhopa- lodia gibba nor Karsten in Surirella saxonica, but as I did in Eunotia major they found only a few short thick bodies of various shapes which could not be accurately described, and whose number was indeterminate. It must be remembered that the results which differ were obtained with different species. Physiology. — “On a_ shortening-reflex’. By Prof. J. K. A. WERTHEIM SALOMONSON. (Communicated in the meeting of December 28, 1912). By the expression shortening reflex I propose to indicate the con- traction of a muscle, the ends of which are passively brought nearer together. I shall try to prove this contraction to be a real reflex, though the primary shortening of the muscle may not be the direct cause. We shall first consider what happens when any part of an extre- 1093 mity is moved passively, in which case one set of muscles is stretched, another group being shortened. A living animal’s muscles at rest are generally not entirely relaxed. A slight degree of elastic tension, called fonzzs, persists. Tonus is for the greater part caused and restrained by regulating impulses, originating from peripheral sensory and higher motor neurones. Also the cortex and the gangliongroups of the cerebrum, the laby- rinth, the cerebellum control and influence the muscular tonus. Tonus varies under different circumstances, but it adapts itself auto- matically to the rate of stretching of the muscle. If the muscle be slowly stretched by a passive movement of the limb, its form changes. The muscle grows longer and thinner. But its tension does not change at the same rate. Only if the stretching be carried very far or happens within a very short space of time its elastic tension grows appreciably. With a passive shortening of the muscle something analogous occurs. The length diminishes, the diameter increases but the tension adapts itself automatically to the new condition, and the muscle does not become slackened so far as to show folds or furrows. This adaptibility only persists as long as the muscle remains in contact with the intact nervous system. As soon as the muscle is freed from its nerve, its reflex-tonus disappears and it seems to behave simply as an elastic string, in which a definite tension corresponds to a definite length. The action of the nervous system seems to equalise the tension for different lengths and causes the resting-length of an innervated muscle to be a varying quantity. If the passive shortening of a muscle is effected within a very short time we sometimes observe a genuine contraction of the muscle followed by the thickening caused by the reflextonus. This pheno- menon I have called the shortening reflex. If the foot be passively and somewhat forcibly extended (= dorsal flexion) we are sometimes able to see and feel a very short con- traction of the m. tibialis anticus. After this contraction the tonus- thickening becomes visible. The contraction cannot be elicited in every healthy individual, and even where it is to be found, it is often rather difficult to obtain. We get it most easily in the tibialis anticus by extending the foot. In some cases I have also found it in other muscles, as in the flexors of the arm, the flexors of the leg after flexing the arm or the leg. I have recorded the phenomenon with a special apparatus, con- structed some 9 years ago for recording the foot-clonus. The difficulty was to rigidly attach a pair of Margy’s tambours to the bony parts of the leg, so as not to become displaced by the violent movements 1094 of the leg during the clonns. This difficulty was overcome by attaching a clamp to the upper part of the tibia and another to both malleoli, and connecting them by a very light hollow rod. To this rod the tambours were screwed with a pair of collars. With this arrangement which proved to be entirely satisfactory, I was able to record the thickening curve of any desired muscle of the lez and also the displacement of the foot with respect to the leg. Fig. 1. Shortening reflex in the tibialis anticus of a healthy man. Upper curve: displacement of the foot. Middle curve: thickening curve af tibialis anticus. Lower curve: time marks of 0.1 second. I reproduce a few records (tig. 1 and fig. 2) which were taken in this way. The upper line shows the movement -of the foot ; rising of the curve indicates dorsal flexion. The middle curve is a record of the thickening of the tibialis anticus. The time curve gives marks of O,1 of a second. Fig. 1 shows the tibialis contraction occurring with a short dorsal flexion of the foot. Fig. 2 gives the record of tibialis contraction caused by a rapid dorsal flexion of the foot, the foot being kept in dorsal flexion for nearly two seconds. In tlis last record we clearly see the initial tibialis twitch followed by the reflextonus-thickening. From the records we soon gather the fact, that the tibialis re- sponse immediately follows the foot inovement. By comparing a great many records we also find that the interval between the commence- ment of the foot-movement and the beginning of the tibialis-muscele- twitch is of a very short and yet extremely constant duration. If as | L095 the beginning of the footmovement be taken a point where the curve has risen about 1 millimetre, and a_ similar point on the ») Fig. 2. ee EATS eA eSoft ttf fe fe fir Si fi i fr fe tin | Shortening reflex in the tibialis anticus of a healthy man. Upper curve: displacement of the foot. Middle curve: thickening curve of tibialis anticus. Lower curve: time marks of 0.1 second. tibialiseurve as the commencement of the musele-twitch, the interval comes out as something between 0.028—0.032 second. This fact points in the direction of a reflexphenomenon. If we had to deal with a voluntary contraction, the latent period would have been a great deal less constant. It is also a facet, that the interval between an external stimulus and the commencement of a voluntary movement is of the order of 0.12—0.15 second with a fairly expe- rienced subject. Constancy of this latent period is only to be expected with the most experienced subjects or after a special training. The latency of sensory reflexes is much more constant, but it depends in most eases chiefly on the intensity of the stimulus. The highest con- stancy is shown only in the deep reflexes, in which the intensity of the stimulus does not seem to possess any influence on the latency. The latent period of the superficial reflexes is generally of the order of 0.07—0.09 of a second, whereas the deep reflexes show a latency of the order of 0.035 second. With these figures we have to take into account that the latency is measured from the commencement of the stimulus until the commencement of the muscular response as indicated by the mechanical record. If we had recorded the current of action we should have found lower figures. In my experiments I was not able to get more exact or smaller 1096 figures for the latency. This was not due to the fact that I used a mechanically recording instrument, but only to the difficulty in deter- mining the exact moment of the stimulus. The stimulus is applied during the passive movement of the foot. But we cannot tell the exact moment at which the stimulus is produced. Must the foot move with a certain velocity or must it travel over a certain distance ? Perhaps both conditions are necessary. At least with a very slow movement of the foot we only obtain the tonus-thickening and with a very rapid movement over a short distance only, we sometimes fail and sometimes succeed in getting it. Therefore it is impossible io indicate the exact point in the record of the foot-movement which is to be considered as the beginning of the stimulus. If I take the first point in which both curves begin to rise from the zero-line, I find a lateney from 0.038—0.045 of a second, with an average of 0.041 second. If we take a rise of 1 millimetre in both curves as the beginning of the stimulus and the response, we get an average of 0.029 second. Though the exact figure is doubtful, it is yet of interest to note that it agrees closely with the ,average latency found in the deep reflexes. The duration of the museular response has also to be considered. From direct observation and also from most of the records we come to the conclusion that we have before us a simple muscle-twitch, the duration of which is something between 0.2—0.5 second. Only in cases where the foot has been moved with great force, or has been kept in prolonged dorsal flexion, a muscular response of longer duration may be found. But in these cases the contraction shows a peculiarity, clearly visible in fig. 3, viz. a second contraction appear- ing before the first is finished. We shall consider this point later on. As from our observations we see that: 1'Y the latent period is constant, 2“ that the latency agrees with the latency observed in deep reflex, 3%'y that the contraction is generally a simple muscle- twitch, we may conclude that the phenomenon itself is a real reflex. This being established we may ask where the reflexcentrum is situated, which is the reflexogene mechanism and which is the signi- ficance of the reflex. i: We may conclude from the latency that the reflexcentrum cannot be situated very high up in the central nervous system. I believe that another supposition as a medullary seat for the centrum need not be considered. The reflex has a close similarity to the deep reflexes and may probably be regarded as a third group of this kind, the other groups being formed by the tendonreflexes and the periost- reflexes, L097 It is somewhat more difficult to understand the reflex-mechanism. We only know that the reflex is elicited by passive dorsal flexion of the foot. But then two things happen simultaneously : the extension- muscles of the foot are shortened and the triceps surae is stretched. Which of the two causes the reflex? I fail to see the possibility of choosing between the two on clinical grounds only. In the accident of a torn or cut Achillestendon, which is unlikely to occur in a healthy man, only a positive result would have any significance, as the reflex cannot invariably be elicited in healthy individuals. Some pathological arguments might perhaps be brought forward in support of the hypothesis, that the reflex is primarely caused not by the shortening of the muscle itself, but by the stretching of the antagonist. As regards the significance of the reflex we may assume that it is the same as that of more elementary reflexes, viz, a means of protecting the organism against exogene stimuli. The obvious fact is that the contraction assists the automatic tonus-mechanism in attaining as soon as possible the necessary muscular tension corresponding to the changed attitude. Hence we conclude that the reflex is a protect- ing mechanism against a total want of control over the position of the foot, if the foot is passively moved. I have already mentioned that in a few records a second con- traction of the tibialis anticus appeared immediately after the first (fig. 3). This may be caused either by a voluntary or by an invo- Fig. 3. Shortening reflex of the healthy leg of a hemiplegic patient. luntary impulse. In my experiments I have tried to exclude as much as possible any voluntary movements by impressing upon the subjects 1098 to keep their muscles relaxed, and to try not to make any movement. Judging from the curves, this request has been attended to, as the duration and form of the second contraction seem to exclude the possibility of a voluntary origin. I think I may assume that the second contraction was not caused by any intended or conscious impulse. But then we have two possibilities. Either the second con- traction was also a reflex-response, but from a higher nervous level, or it might be the first from a strongly damped clonus. I am inclined to think, that in most cases the second contraction was caused by a reflex from -a higher level, though I cannot prove it. But on the other hand I must also accept the other explanation. Amongst a series of curves taken from the ‘normal’ leg of a hemiplegic patient, which often show the form of fig. 3. I found one single record Fig. 4, Curve from the same patient from whom fig. 3 was taken. reproduced in fig. 4. Here we see that the tibialis contraction as soon as it is started, degenerates into a series of rhythmic, gradually ceasing clonic oscillations. In another patient suffering from a medullary disease, I obtained the record, shown in fig. 5. This reeord differs from the fig. 1—4 in as much as the upper curve does: not represent the movement of the foot, but the thickening of the triceps surae. We immediately see, that the dorsal flexion of the foot starts the reflex and at the same time a series of clonie con- tractions in both the tibialis anticus and the triceps surae. These last contractions prove at least the possibility of the second tibialis contraction being the first of a strongly damped clonus. As yet I have not considered the literature. There is some reason for this, as I have not been able to find in it any reference to a LO99 reflex sueh as has been deseribed as appearing in healthy subjeets. I have only found the well-known paradoxical contraction of Shortening reflex in a case of arteriosclerotic medullary disease ; clonic contractions in triceps (upper curve) and tibialis anticus (middle curve). Westrans (1880), which is a fonic contraction of the tibialis anticus appearing at dorsal flexion of the foot in some patients. It is of rather lone duration, Wrstrann observing a contraction of 27 minutes, ERLENMEWER Of 45 minutes’ duration. CHArcor has seen the same contraction, also after massage of the calves and has taken graphic records, one of which, taken from his article in Brain (VIII p. 268 I reproduce here (fig. 6). From this curve and the explanatory text, also reproduced, we immediately see, that this contraction is not at all the same thing as the shortening reflex. But there seems to be no doubt, that a relationship exists between Fig. 6. Same patient (April 12th). Tracing of contraction of th tibialis anticus obtained by massage of the muscles of the calf. — A, B, C, beginnings of three consecutive experi- ments. (In this and the last figure—muen reduced in size—the length of XX represents one whole turn of the cylinder, viz. thirty minules.) 1100 the shortening reflex and the paradoxal contraction. I am inclined fo suppose that the latter is the pathological form of the first. The curves I have given as physiological were those taken in a patient with a severe trigeminus-neuralgia caused by periostitis alveo- laris, who is now cured. His reflexes were not altered in the least. The curves 3 and 4+ were taken from the healthy side of a hemi- plegie patient and are perhaps not to be considered as purely physio- logical. There is some reason to suppose, that hemiplegia may cause a heightening of the shortening reflex of the healthy extremity. Amongst the pathological forms of the reflex we might perhaps include some forms of hysterical contraciure and also some cases of crampi. But I intended to consider only the physiological aspects of the reflex. ° Physics. — “On the thermodynamical functions for mixtures of reacting components.” By Dr. li. S. Ornstern. (Communicated by Prof. H. A. Lorenz). (Communicated in the meeting of November 30, 1912). In his dissertation Dr. P. J. H. Hornen has developed a theory of the thermodynamical functions for mixtures of reacting components *). Considerations closely connected to those of this dissertation are obtained if the statistical method of Gripns is applied to the study of the equilibrium in chemical systems. I will show this in the following communication, and will restrict myself to the case that only one kind of reactions is possible in the mixture, the extension to other cases being possible without any difficulty. In the following considerations I shall use a canonical ensemble R 3 of the modulus @ (=5 r) (R is the constant of Avogrado for the vrammolecule, V the number of molecules present in this quantity of matter. We might as well use the micro-canonical ensembles; but for the calculations then being somewhat more complicated. The molecules participating in the reaction are indicated by py .- ty... fuk Then the reaction will be characterised by the stoechiometrical formula k > ee oe to G5 Y(t) 1 the numbers v, indicating the smallest numbers of molecules that 1) Dissertation Leiden 1912, comp. also these proceedings XV p. 614. 1101 can take part in the reaction. The v’s are necessarily whole numbers, some of them must be negative. We will imagine the molecules to be built up of atoms @,...d5...a, in such a way that the chemical formula for the z#"* molecule is (x = Yui, +--+ YerOr +... Uap ss WA. one (2) the numbers y,< being positive whole numbers or zero. We will first treat the case that the system has so great a volume that the mutual action of the molecules may be neglected in the expression of the energy. The state of the system can be characterised by the coordinates of the centres of gravity of the molecules and the corresponding moments of momentum and by a certain number of internal coor- dinates and moments of momentum. The expression giving the energy of each molecule consists in the kinetical energy of the centrum of inertia, a quadratic expression in the moments of momentum of this centrum, the coordinates of the centrum of inertia not playing a part. Further in the energy corresponding to the internal coordinates, which I shall represent by «, An element of the extension in phase corresponding to the internal coordinates of the #* molecules will be represented by dz,. Be the mass of the molecules m,. Be the total number of systems of the ensemble A, the statistical free energy W. We now want to know the number of systems (2") in this en- semble; for which n,...7,...n, molecules of the different kinds are present in the volume V. That is to say those molecules produ- ced by a completely specified combination of atoms, for which the internal coordinates and moments are situated in completely determined elements dd,...da,...day. As for the situation of the molecules within the volume J’, and the moments of momentum of the centres of gravity, we will aot apply any restricting conditions’). We find for 2" aH & =k nN, — — Ny = @f é oO a Zu Ne (22m,0) e di, See Ricarpea 4 62) 1 The number of systems in which no restrictions are applied not even for the internal coordinates and moments is obtained by inte- grating Over the dA,’s with respect to all possible values. We now put bo| oo 1) Comp. for the case that one should want to specify for these quantities also, my diss. p. 39, where the case of non-reacting molecules is treated. . 6 (22m,@) v fe hy = 1s: 2, 4, ee in which the integration must be extended over the above mentioned space. Now the number of the systems considered 2’ may be repre- sented by ate Ce | n 2’ = Ne I] e&. whe 4 eee 1 Now we have to determine the number of systems in which the atoms ave combined so as to give 7, molecules of the #'" kind, ete. We must bear in mind that the total number of atoms of each kind is fixed; so that when 2, is the number of atoms of the at kind, we have p equations of the form ipa i Pee Seeger Te PG A TA es (LO! Now, in order to get the number of combinations possible, we must in the first place consider that x, atoms are to be combined into groups of 7,7,.... particles in az! (MY x)! -. = (Mex)! 2 (nikx)! (7) different. ways. Further, that the number of different ways, in which 7,¥,x particles are to be combined into x, groups of y,; particles, is given by (”, Yiz) / (8) (yya)m 2 (Yre—1)! In order finally to obtain the total number of cases possible, we still ought to consider in how many ways the n, groups of y,,-.Y:5-- Yip particles may be combined into molecules @,y,, + ..42y,;<-.+ aq, Suppose p, of the quantities 7,. to differ from zero, then the wanted number of the combinations in question will be CA et homme cS ((S)) For the total number of combinations we find, bearing in mind that (n,/)% ete. occurs in the denominator my! oe Mel oe MeL (Yyy oe Yar oe Yap) one (YI -+ Yer Yh "& (Y., —1)! .. (Yip—1)! By uniting into a constant C the quantities not depending on n,, we get for the total number of systems, in which n,.... molecules * are present (2) 1108 k n Oaks ; nyt (7 et Yureee Yn, "2 ; » (in which only those y,.’s are to be taken into account that differ from- zero). I will represent the factor (y,, .. yx. Yor) DY S,. Now in order to examine which of all systems is the most fre- quently occurring in the ensemble, which therefore is the system in equilibrium, we have to consider for which values of the 7, z or log z, i.e. k = nz (log I,—logn, + I—logs,) . . . . . (12) 1 is a maximum, (n/ being developed here according to the formula of StiruinG). The variations to which the numbers 7, are submitted are @r;, in which @ is a positive or negative whole number. The condition of equilibrium that is reached in this way is k SS Dy (log 1,—log n,—log == 0) 3 F A j 3 (12') l Introducing 3 I, = (22m, @)2 Vy for /,. we get hk k I: Sy 3° San — rh, ky R\3/_» i UMM hile hes, Cy : SAMA far s,s, 2 | iz ==" 1 [ V a sae (LS) 1 / s xy contains still terms that depend on 7’, this formula cannot yet be compared to that of Dr. Hornun; however, in many regards Wed R it is already analogous to it. Now, applying the theorem that = log w, an which w is the probability of a state) is identical with the entropy, we find the entropy 4 of an arbitrarily chosen state to be given by 2 i: v y= — J 0, jlog L.—logn, + 1—logsi} . . . . (14) 1 This quantity therefore must agree with the entropy of a non- equilibrium state as defined by Dr. Hownex. As appears from what is mentioned above, it possesses the quality of being a maximum in the state of equilibrium. Now I will first use the result we obtained to caleulate Y and through means of it the equation of state. Developing z with respect to @ and summing sp, we find for Proceedings Royal Acad. Amsterdam. Vol. XV. y 5 —— i e 9=C' 1Ae = sea 1 ner sos Yep \"*e n (” is obtained, from C, by dividing the total number of systems; n, denotes the value in the state of equilibrium. Applying the relation Ow p= — — ; OV we find for the pressure Oo & "k re o——— Sn, + + OD (log L, — log n, — log «)! ae) : J 1 1 dV where 7, relates to the state of equilibrium of the volume V, 7‘, to that of the volume V + dV. These numbers always differ ey,, and so, taking into account the condition of equilibrium, we find > & : P=ap2* we AS Ae ee In order to calculate the average energy we can apply the relation a Ow 00 : whieb gives, when the condition of equilibrium is taken into account 2m a ga : Now, in many cases ‘y, inasmuch as it depends on @, may be represented by @”q, (q independent of @) or in other cases by a complicate function of @. So, in the first case, — R k 3 oe PE m(5 + v) ae 2 Putting the energy that is supplied when: the numbers x, change with vr, — = P;, 6 +r), then we find that the condition of equilibrium (13) changes for this case into k k N k hype ease p = RR lal n, "=V 1 nl Ti 1 i When we represent the energy of the molecules «, by @ constant a, plus a function of the internal coordinates, then in the formula (132) the factor 2am, R\*l2 v, - ee lee 88 1105 bs a,v, N no Ate @ still must be added. The formula obtained in this way agrees with that of p. 12 and 13 of the cited dissertation. Just as in this dissertation p. 16, we can by comparing d(Q—=de +pdv and dy show that Hise Ne eer hs coo ve! ok nL) 1 if we have to do with the changing into a state of non-equilibrium, I will now consider what will become of our condition of equili- brium in the case we apply the theory of energy-quanta. Let us suppose we have the case of the molecules possessing 3 degrees of freedom of rotation, and /, vibratory degrees of freedom of the frequency t ». The value of 7, can be given then. On account of the 3 rotations it contains a factor 62, further the integral is equal to a product of 1 integrals of the form Etiz re: | e Diz relating to each of the vibrations. This integral has the value cs Introducing for each molecule the energy «, for the zero state and a constant originating from the integration with respect to the angu- Jar coordinates of the rotations, then the condition of equilibrium takes the form k k .. k Si 5 Syke eee l red ac at aa = v Ee Des iy ht, \ VA i ea 7 e S24 is aes (18) 1 1 1 ht, \ ae in which all constants relating to the molecules x are contained in S,. If the theory of quanta must be applied to some of the rotatory energies, then the exponent of 7’ will be smaller. As appears from the calculations of Dr. Scuerrer*) the experi- 1) The complications arising when equal frequencies occur are easily lo be overcome Comp. these proceedings 8 March 1912 p. 1103 and 1117. *) These proceedings XIV. p. 743. 72* 1106 ments can more sufficiently be represented by applying the formula not of Erxsreiy, but of Nernst-Linpemann for the specifie beat; the equation (18) leads for the specific heat to the formula of Ernstew. For solid matter Born and VAN Karman have given a theory leading toa formula which seems to represent the experiments on s. h. as well as the formula of Nerxst-Linpeman. They start from the conception that there cannot be attributed one definite frequency to the atoms of solid matter, but that, because of the coupling a great number of frequencies occur, which accumulate infinitely at one or more definite frequencies. The fact that the formula of Nernst is the more appropriate also for gases, makes it acceptable that also in eases, through the mutual influence of molecules, there cannot be spoken of a finite number of definite frequencies. 1 may still observe, that for the given consideration the way in which the system at length comes into the most frequently occurring state, is of no importance. That it will get into it, may be regarded to be sure, as well from the point of view of statistical mechanics as from that of the theory of energy-quanta. I will still consider now in what way we can, in liquid states, come to the condition of equilibrium. We must for a moment return to equation (3), then. There we could divide into parts relating to each of the molecules, the general integral which, according to the definition of Grtsps, denotes the number of systems of given state. However, in the case now considered we cannot proceed likewise, because of the mutual influence of the molecules. The number of systems of specified state is in general given by W—s Ne de. Ain, M, AG. .- My ditny GA where 2,,---,, represent the coordinates of the centres of gravity, n,, the velocities, and where da relates to the internal coordinates and moments of all molecules. Now considering a system with n, molecules x, built up of specified atoms, and allowing all values for the coordinates of the centres of gravity, the total number of- systems obtained in this way 2 may be represented by k ! 3 Re é k aL =n, == nv[ [ez m,@)°" 1 [ e Ods,...da. vv 1 The value of the integral can always be represented by k = Ny Ue V T(V mn, re. - . NM O) LLO7 For a gas the function / takes the form of the funetion considered above. We will not consider the form more closely now. This being observed, it will be easy to point out the changes which (11), the formula that gives the number of systems, will undergo. We find . 3 E (2 w O m,)2 vt Vv" Cres (Crip (MG iin on of aoe oUt 0) | | - - (19) i n 4 nz! (s,) Asking again which is the most frequently occurring state, we find for the condition of equilibrium ‘ 3 0 log if apy (- log Ny +- =) log (22 © m,) + log V —log 4 5 — ) bee (240) Ny For the statistical free energy we find k k ye = 5 A! rn, 3 En; 7) CTV, --.ne--0m, O) Vi» aay a e ee 3 ee ” n ——9)' Ze—-te ot Fc} TN Caters 3) My $71. . S, the numbers 7,..7, relating here to the maximal system. Caleulating the pressure from Y we find RT Ls RT 0 log f — ay Ny, ON Var N ov where the terms again are zero on account of the condition of equilibrium. Like Prof. H. A. Lorentz in his “Abhandlungen” also Dr. Hornen uses the equation of state Ihe GP LE —— > i ( Re Ne Sar (1 put it in molecular form), the term g then denotes the deviation from the gas-laws, the q there used therefore agrees with our RT 0 log f ae N ov log f may be given the form al aa cig, f= — sep f 14 + 4 i where # is a function of temperature depending on the 7, also. Introducing this into (20) then D k 3 Oo N. & ¢ 0g - = v,loyn,= Lv, | —log (221@m,)+ log V—logs,+ - | — = { r,dv. 1 : l gees : : On Lind fay ) On, x P] 1108 Now if g is a function of the numbers 7, the variation of q, if « varies with de, is because of dn, then being v,d«, : 0 So that this sum may be represented by 5, da. a The condition of equilibrium thus changes into I: k (/3 e = v,logn,= = IG log 22Om, | + logV— lvgs,+ 1 1 u ma 0d N 0g cd) Gr maiiatta) ope OF On, RI) 0a = Putting the zero-energy «, and introducing 3 vibrational freedoms then, when the remaining part of % is represented by ¢, we get Sy, | 18 get Sata ee ange | at, (09 h, = = vo lOC i — 5 a NG 85 == ry, = ogn g L + log RI 04 aa N Og — — | — dv RT) 0a ihe constant s, containing all quantities that do not depend on Vand 7. The k quantity Sv, og s, may also be substituted by a single constant. 1 F R Also in the case considered the quantity = log w can be defined L X for each state as entropy, and likewise we have for the supply of dQ : eae heat a < dy for states of non-equilibrium and = dy for states of equilibrium. It may be regarded as an advantage of the statistical method, that it contains at the same time the thermodynamical consideration of Dr. Hornen, and the kinetic result -— the law of GuLpBErG and Waacre — that he is bound to introduce besides his thermodynamic considerations. Groningen, November 1912. 1109 Chemistry. — “On velocities of reaction and equilibria.” By Dr. F. kK. C. Scuerrer. (Communicated by Prof. A. F. HoLnmnman). (Communicated in the meeting of January 25, 1913.) 1. In a previous paper in conjunction with Prof. Kounstamm °). I discussed the relation between the velocity of reaction and_ the thermodynamic potentials of the substances participating in the reaction. It then appeared that the velocity of a reversible reaction may be given by the expression : dou RL RT ee (/ @ —e ) be . 4 (1) dt in which «, represents the sum of the molecular thermodynamic potentials of the substances of the first member, u,, the sum of the potentials of the substances of the second member of the reaction equation. The constant C accounts for the choice of the unities of concentration and time, and has therefore the same value for all reactions when the same unities are used. We have shown that the function / possesses the same value for both partial velocities, that it is independent of time and volume, and that it is equally in relation with both systems before and after the reaction. As further, quantities of energy and entropy must occur in the quantity /’, we have tried to make clear that in general in case of chemical reac- tions “intermediate states” mnst be assumed, and we have pronounced the possibility that the energy and entropy of these transitional states are the only quantities dependent on the nature of the substances, which occur in the function /. By entropy we mean here the entropy “free from concentration”; we have namely shown in our cited paper that /’ is independent of the concentrations in case of gas reactions and reactions in dilute solutions; hence it can contain no terms originating from GipBs’s paradox. The value of the two partial velocities would therefore be determined according to this by the difference in energy and entropy (free from concentration) of the reacting substances and the transitional state. This in my opinion obvious assumption comes to this that both the difference of energy and the difference of entropy between the first and the second system must be split up into two parts; the first part then gives the differences of energy and entropy of the first system with 1) These Proc. Jan. 1911. p. 789. 1110 the transitional state, the other the differences of the second system with this transitional state. As far as the values of energy are concerned such a solution was already proposed by van “? Horr in the Etudes de dynamique chimique and recently also Travrz has tried an analogous splitting up of the values of energy, as we already mentioned in our previous paper. Though in his earlier papers on reaction velocities Travtz considered a universally holding resolution possible, against which we thought we had to protest in the cited paper, Trautz has introduced as pos- sible ways different from reaction to reaction in his later papers, and with them different ways of splitting up, so that as far as the values of energy are concerned the difference between our considera- tions and those of Travurz has partly disappeared. Yet also in this respect a difference continues to exist in our views, for TRaw?Tz exe- cutes the splitting up of the energy at the absolute zero, and it seems more plausible to me to attribute the course of the reaction to the difference of energy at the reaction temperature. For the present it will certainly not be possible to obtain a definite decision of this question, as for the greater part the quantities occurring in the expressions for the velocity of reaction, have not yet been measured with sufficient accuracy, or sometimes are not even liable to direct measurement. With regard to the splitting up ot the entropy the difference | between the mentioned views is still greater. Whereas Travutz does not execute a splitting up of the entropy and introduces the absolute value of the entropy of the reacting system into the equation of velocity making use of the integration constants of the vapour pressure, an analogous splitting up seems necessary to us also for the entropy, especially when we adopt the views which BortzMann has expressed on chemical actions in his Gastheory. In the cited paper we have illustrated by the example of the chlorine-hydrogen equilibrium, how we think we have to imagine the transition states occurring there. If we adopt the standpoint of 30LTZMANN’S theory, we must assume that the two hydrogen atoms in the hydrogen molecule are bound, in consequence of the fact that the “kritisehe Raiume” of the two hydrogen atoms cover each other entirely or partially, and also those of the two chlorine atoms in the chlorine molecule. If we now inquire into the reaction between a chlorine and a hydrogen molecule, we must imagine that the two molecules get so close together that the four “kritische Raume” of the four atoms will entirely or partially coincide, so that the four atoms are in each others’ sphere of action. After this transitional 1114 state a separation fakes place of the “kritische Réume’ of the hydrogen atoms and the chlorine ators inter se, the dissimilar atoms remaining bound. Hence the energy quantity /“must be the energy which prevails, when the four “kritische Raume” coincide, while the value of the entropy must take account of the volume of the coinciding Réiume. When we consider that the difference of energy between the reacting substances and the transitional state is no more to be eal- culated aprioristically than any other chemical change of energy, and that as yet we have no means at our disposal either, to predict the volumes of the “kritiseche Raume” by the aid of the properties of the substances, it is clear that we cannot test the above conside- ‘ations except by examining whether we can assign plausible values of the energy and the entropy to the transitional states to get into harmony with the known material of facts. It is true that Nernst’s theorem of heat, in the form as it is conceived by PLanck, fixes the values of the entropy of solid substances at the absolute zero, so that the entropy constants of the gases are brought in relation with the integration constants of the vapour pressure, but even if one is convinced of the validity of the theorem of heat, yet the imperfect knowledge of the specific heats presents too great a diffi- culty up to now to calculate entropies a priori. With regard to the transitional states such a calculation is a fortiori impossible, as the facts known to us indicate that these transitional states greatly vary for different reactions, and are e. g. greatly influenced by catalysers. When we now inquire into what the material of facts can teach us with regard to the transitional states, we will examine in the first place whether the energy in the transitional state is greater or smaller than in the initial or in the final state, or whether it perhaps lies between these two latter values. To answer this question I will (to keep the considerations as simple as possible), consider a reac- tion in a rarefied gas. mixture that completely takes place in one direction. In this cas® the second partial velocity has a negligibly small value compared with the first. The velocity of the reaction is then represented by : Ee IN Oy If we now insert the value of uy, for the dilute gas-mixture, which according to oar preceding paper may be represented by : 3 3 ‘Cy i — = P/E 5, — Tv, +4 Sn, feo,dT—T>m, | 7 aT + | (3) + RV Dv lng + RLZv, 1112 into equation 2, in which we write «&— 7’: for F, where & and 7, represent the above values of energy and entropy of the transitio- nal states, and in which we separate the functions of concentration as separate factor, we get: de + Cy : ae of. agp sl Lag pr Ty Srje, 1 Erie ¢ Vy fe, ATT v, [EAT ERTS eye T a ae RYT are, (4) In this equation 2c, represents the recurring product of the con- centrations of the reacting substances. The factor of ac, is the so- called constant of velocity and is generally represented by the letter i. If we now determine the value of /nk and differentiate it with respect to 7’we find : * Sve, + Lr, fo dT dlink _ ki ae if eg w3¢ 1 (da-_ 7 dn 5 rape RT? rr oRT\ar at) © If now «& and » have the signification of energy and entropy (ree from concentration) of the transitional state, the last term of the second member of equation 5 is zero; this is clear when we consider that /=e,— 7, can contain no functions of volume. Hence equation 5 reduces to dink = &—& ae © Re in which ¢, represents the energy of the first system ‘at the tempe- (6) rature of reaction. If we now return to the reversible (gas)-reaction, the relations dink, 87] ate dink, b SEEM Gib Ee dT Ie he will exist for the two partial velocities. Hence the splitting up of the energy difference « — *, into two pieces &—& and &,— Fy, is very prominent. If we now con- sider that in general the velocity of- chemical reactions increases with the temperature, it is clear that & will be greater than €7 and e;. The energy of the transitional states is therefore greater than the energies of the systems before and after the reaction. Accordingly this result necessarily leads us to the following concep- tion: On coincidence of the “‘kritische Réume” of the reacting molecules gain of energy takes place, in other words there is work (7) 1118 done against repulsive forces; the transitional state possesses there- fore a mavimwm of potential energy. As is known when molecules draw near to each other attraction takes place; this led us to expect in our previous paper that the transitional state would possess a minimum potential energy. As appears from the above consideration at such a distance that the “Kkritische Ranme’” invade each other, the repulsive forces out- balance the attractive forces and oppose therefore the invasion of the sphere of action. A similar conelusion concerning the energy of the transitional states occurs already in Travtz’s first papers. He imagined that the transitional state consists of free atoms. It is then clear that this state contains more energy ttiian the initial and the final state, since heat will be required for dissociation into atoms. That Travurz makes this resolution take place at the absolute zero does not involve an essential modification. For this question is in close relation to the question whether it is allowed with regard to these transitional states to speak of specific heats, or what is the same thing of a mean value of energy at a certain temperature. And so far as is known the difference of temperature between the reaction temperature and the absolute zero generally causes no reversal of the sign of chemical heat-effects. - 2. Before entering into a discussion of the energy and entropy values of the transitional states, I shall insert here some considera- tions on the energy and entropy differences between the systems before and after the reaction, referring to a paper on gas-equilibria that has appeared earlier in these Proceedings '). The algebraic sum of the entropies of the substances participating in a gas-reaction was represented in the cited paper by : s > (Oy Se = Sn pt >n| p at—KSninc.-. . : (8) il; 1 If we join the first two terms of the second member of equation 8, and represent it by 2nH.—. (the entropy free from concentration) this equation passes into : Si — hee ULG ee (9) According to the cited paper the equilibrium condition for the gas mixture is: 1) These Proc. Dec. 1911. p. 748. 1114 Sn = SnE—TlnH + SnkT = 0. If in this we introduce the entropy free from concentration, this equation may be written as follows : Sn —TSn = + RTZ_nlne -- =nRT —0. If we now express Sn/nc by InK,, in which therefore AK, repre- septs the so-called equilibrium constant (in concentrations), then : RTinK, = — SnE 4+ TEnH=1—=nRT . . . (10) Differentiating this equation with respect to 7’ after division by RT, we easily tind the well-known equation of Van ’r Horr : dinK, 2nE oT = Er: Me oe od be | ( If we now imagine YnZ to be a very weak temperature function, which may be put practically constant over a limited temperature- range, equation 11 yields on integration : =nE ink; == == LY phic Se nK, Sqedee (12) On comparison of equation 12 with 10, it appears that on this supposition also the entropy free from concentration may be put independent of the temperature. This conclusion is moreover also clear when we consider that both the change of 2n/ and that of YnH,—, with the temperature is exclusively determined by the value of Yne,. If therefore really the value of Svc. in a certain range of temperature is negligibly small, the observations in this range may be represented by equation 12, in which two constants occur: =nE ; a ‘ y Se the change of energy divided by the gas constant, and C, which contains the change of entropy and the gas constant. And inversely when it appears that the constant of equilibrium as function of the temperature may be represented in an equation with two constants like 12, a measure will be found in the value of these constants for the change of energy and entropy during the reaction. If therefore in one graphical representation R/nk. is repre- : 1 : : : sented as function of 7 and in another 7/nA. as function of 7" and if the observations in the first graphical representation give a straight line, this is also the case in the second. The inclination of the line in the first representation yields the energy value, that in_ the second the value of C in equation 12, so the entropy value, at least if the fact is taken into account that according to equation 10 C€ also contains the gas constant and Yn. If we now assume that the observations have been made with great accuracy, in gene- 1115 ral the curve in the first graphical representation will deviate from a straight line. If we now connect two points from this graphical representation, the slope of this straight line will indi- cate the value of energy which belones to a temperature which lies between those of the two connected points. It will then be clear that if we wish to determine the energy value in a similar way, the found value will differ the less from that which corre- sponds to the two observation temperatures as Svc, is smaller. Hence the energy value will also be found with the treater relative accu- racy as the energy value itself is greater, ie. the energy found graphically will then proportionally differ only little from the energy values at the observation temperatures. If we now fill in the graphi- cally found value in equation 12 and if we apply equation 12 to the two observation temperatures, a too great value for the energy difference will have been chosen for the one temperature, a toc small value for the other. For a temperature between the two temperatures of observation the energy value is then chosen exactly right; hence the correct entropy value has therefore been yielded by equation 12 for this temperature. Therefore when equation 12 is used the found values of entropy will deviate somewhat from the real ones at the two temperatures of observation. If we denote the two temperatures of observation by 7, and 7, and the temperature for which the graphically found value of the energy holds, by 7’, and if we imagine the value of energy found at 7’, and the corresponding entropy substituted in equation 10, we may question what deviation equation 10 gives us for the values of K, at the temperatures 7’, and 7’. The error made in the energy . T; : nis P= Ie ; when we apply equation 10 as 7’, amounts to | a dT, that in ¢ T r, Olah the entropy-term amounts. to re -—— dT. If we now consider x a 1 that the energy and the entropy occur with opposite sign in the second member of equation 10 and _ that d nk dn, —| | ene we see that these two errors cancel each other for the greater part rs ; in the second member of equation 10, and that therefore in spite of these approximations a pretty accurate value of A. can be found. This fact explains why notwithstanding an appreciable value of the J116 specific heats many gas equilibria can be accounted for by means of two constants, not only over a small temperature range, but sometimes even over a very large one, at least if the observations are not particularly accurate. The dissociation constant of the nitrogen tetroxide can e. g. be expressed by an equation of the form 12 ‘Scureser’s equation), and also the dissociation equilibrium of car- bonic acid, the errors of observation being comparatively large here, can be accounted for by equation 12 over a temperature range of hundreds of degrees. These considerations teach us accordingly that observations of equilibrium constants with comparatively large energy and entropy values enable us to caleulate them pretty accurately, but that gene- rally no conclusion can be drawn about the influence of the tempe- rature on energy and entropy, the errors of observation being generally too great for this. Thus the above formula of SCHREBER enables us to find a mean value for the heat of dissociation of the nitrogen tetroxide and for the ‘“kritische Raum” of the NO,-mole- cule’), but the influence of the temperature on either is not to be derived from the measurements of the equilibrium. 3. If we now return to the reaction velocities, we can also apply the considerations mentioned in the preceding paragraph here mutatis mutandis. Equation 6, which indicates the dependence of the velocity constant with the temperature, presents great analogy with VAN °T Horr’s equation of equilibrium (equation 11). If &;—», isa very weak temperature function, equation 6 yields on integration: fee EEE 2a bt heh ne in which as appears from equation 4+ £ does not contain any constants depending on the nature of the substances, except the difference of entropy. So in this case too the difference of entropy between initial and transitional state is practically independent of the temperature. Here too we can therefore graphically represent r 1 = 3 Rink as function of a and determine the differences of energy between initial and transitional state. It seems therefore natural to examine whether the material of facts referring to the reaction velo- cities can be represented by equations of the form 13, where ¢;—«, and 4 are considered as constants. In his Etudes de dynamique chimique van “rt Horr for the first time gave an expression for the dependence of the velocity con- 1) Boutzmaxn. Gastheorie IT. § 66. 1117 stant on the temperature. Led by his relation ef equilibrium (equa- tion 11) he pronounced the supposition that for the velocity constant an equation would hold of the shape : dink A av This equation has been repeatedly put to the test in later times, BS GC idee OER ee eC) generally, however, for reactions in dilute solutions. First of all the question suggests itself whether the considerations which have led us to equation 6, may also be applied to dilute solutions. Though the velocity of 6 for dilute solutions cannot be rigorously proved, an application also for these reactions does not seem open to serious objections. We have, namely, tested our original equation, by reae- tions in dilute solutions in the cited paper; it proved to be able to account for the course of reaction, and the reasons which led us to the assumption of transitional states, hold unchanged also for reae- tions in solution. Accordingly the shape of equation 6 leads us to expect that this will be generally valid. Van ’r Horr’s equation (equation 11), moreover, holds also for equilibria in dilute solution, and it is therefore certainly natural to assume, that the splitting up of the value of energy will be essentially the same for all reactions. Van ’t Horr’s equation is generally not applied in the form as it is given by 14, but in the form which arises when either A or B is put zero in 14. The expression which arises by the introduction of zero for 6 has been later defended by Arruenius, and has appea- red to be compatible with a great part of the material of facts. If, however, one puts £ equal to zero in 14, really equation 13 is obtained by integration, and all the reaction-velocities which satisfy ARRHENIUS’ expression, can therefore be represented with the aid of the two constants ¢;—e«, and 6 of equation 13. Reversely equation 13 furnishes us also with the possibility of pretty accurately caleu- lating the differences of energy, at least if they are not too small; the absolute value of the difference of entropy, however. remains unknown, because 4 among others cuntains the unknown constant, which accounts for the unity of concentration and time. The above considerations, however, suggest that besides the difference of entropy £6 will not contain any constants dependent on the nature of the substances. In perfect analogy with the conclusion of § 2 we conclude also here that measurement of reaction velocities, at least if they have not been very accurately executed cannot decide whether the difference of enerzy and of entropy depends on the temperature. I will apply the above considerations in my next paper to a series of experimental data from organic chemistry. 1118 Chemistry. — “On the velocity of substitutions in the benzene nucleus.” By Dr. PF. E. C. Scnerrer. (Communicated by Prof. A. F. Hor.emay). (Communicated in the meeting of Jan. 25, 1913). 1. In the preceding paper the dependence of the velocity con- stant on the temperature was represented by the equations ; Unk Fi \ ie ee and 5 Sher VN — ee ee . en (2) and it was shown that the greater part of the experimental data allows the substitution of a constant value for «— «,. According to the considerations of the preceding paper this value furnishes a pretty accurate measure for the energy difference between the react- ing substances and the intermediate state during the reaction, at least if the velocities have been measured with sufficient accuracy, and the value of the energy difference is not too small. In order to arrive at an opinion about the efficiency of these con- siderations and the equations 1 and 2 derived from them, I have tried to apply the latter to the experimental data. I have for this purpose tried to find those examples where we may expect the sim- plest behaviour, and in my opinion they are to be found in the department of organic chemistry. If we imagine a reaction which is indicated by the equation of reaction A+ 5=... and if we determine the reaction velocities at different temperatures, the above mentioned energy value can be ‘alculated. If we then replace the molecule A by another A’, we can find the required quantity of energy also for the reaction of this molecule A’ with 4, and in this way obtain an insight into what influence a substitution of A’ for A exercises on the differences of energy with the intermediate state. Let us e. g. suppese that the molecule benzene is nitrated ; we might then calculate from measurements of the nitration velocity at different temperatures what quantity of energy is required to force the nitrie acid molecule into the sphere of action of one of the hy- drogen atoms in the benzene nucleus. If we then replace the mole- cule benzene e. g. by chloric benzene, we can calculate the quantity of energy required for this reaction also by measurement of the ni- LIL9 tration velocity, and obtain an insight in this way into what in- fluence the chlorine atom in the benzene has on the required quan- tity of energy for the substitution. In this way a value ean then be found which can quantitatively be expressed for that which is generally expressed by the intensity of the binding of the atoms which are liable to substitution. Such calculations, however, cannot be carried out in the absence of the required material of facts. Determinations of velocity of sub- stitutions as mentioned above have been hardly carried out as yet; though Prof. Hon_eman and his pupils have collected a considerable number of data on the relative velocity of the substitution of the different hydrogen atoms in the same aromatic molecule. All these measurements refer to simultaneous reactions, and it is just for this kind of reactions that the application of the above mentioned equations is very simple. When we expose the molecule toluene to the action of nitric acid, three substitutions appear simultaneously. In the toluene three diffe- rent kinds of hydrogen atoms liable to substitution occur, two on the ortho-, two on the meta, and one on the para-place with respect to the chlorine atom. So we have here three reactions proceeding simultaneously, each with a definite velocity constant. If we now want to apply the above equations we must first of all bear in mind that the velocity constant is determined by the energy and entropy difference required for the substitution, and that accordingly if these quantities were equal for the ortho-, meta-, and para-substitution, there would yet be formed twice as many ortho- and metadisubsti- tution products as paraproducts, because in a definite quantity of toluene there are twice as many ortho- and metahydrogen atoms liable to substitution, as para-hydrogen atoms. If therefore the ve- locity constants for ortho-, meta-, and para-substitution are repre- sented. by £,,4,, and &,, the substitution velocities v,, v,, and vy) are represented by the equations: yA , = 9 “CsH;Cl CHINO, ? (2a) i entere Cano, - = - «++. + (2b) and w= keowceano, © * * - + +e (2e) The ratio of the Guantities ortho, meta-, and para-produets, which are formed in the unity of time, therefore, amounts to 24, : 2é:, : ka; hence it is independent of the time. If therefore the reaction is allowed to proceed regularly to its close, or if it is stopped at an arbitrary moment, the ratio of the obiained substitution products is 73 Proceedings Royal Acad, Amsterdam, Vol, AY, 1120 at the same time the required ratio of the velocity constants’). Not the velocity constants themselves, therefore, only their mutual ratio is to be derived from the measurements collected by Prof. HOLLEMAN. If we now apply equations 1 and 2 to these examples, it appears. that the application becomes so very simple in this case in consequence of the equality of the energy ¢ of the reacting substances for all the three reactions that take place simultaneously, and that therefore the difference in velocity of substitution at an ortho- and metaplace e.g. is different only in consequence of this that the quantity of energy (and entropy) to replace the ortho-hydrogen differs from the energy required to cause the substitution at the meta-place. The objection that these reactions do not take place in dilute solution cannot be advanced against the application of the two equations, for in these substitutions a great exces: (molecular) of the substituting substance is generally present. In nitrations e.g. the substance that is to be nitrated is added in drops toa large quantity of nitric acid, and the nitration is practically completed before the following drop is added. Moreover I pointed out already in the preceding paper that the objection of higher concentrations cannot be serious, since it is self- evident that the splitting up of the energy values must always be carried out in essentially the same manner. It has, moreover, repeatedly appeared in these substitutions that different ratio of the reacting substances has no appreciable influence on the mutual ratio of the reaction products. If we now represent the energy of the intermediate states for the three substitutions by & . &,, and Et then equation 1 gives: k, ne & — & dT Rei (Pa) inthe eas Ey OR et pee en ST 17 Toe | kit a as se pete Jee ee dT VTS Here the third equation is of course dependent on the two others. 1) Hotteman, Die direkte Einfiibrung von Substituenten in den Benzolkern, p. 72. We also vefer io this work for the experimental dala occurring in this paper. 1121 These equations enable us to calenlate the differences of the required substitution energies from measurements of the velocity, at least for so far as they have been performed at different temperatures. If we now also apply equation 2, we get: y ky = a, aaa EB SB ty he eas (4a) Kn vie ‘ ln ur — “ty Ea +4 18; Ja. alee cd, dh atte ee (4b) kp RT ras ie kim = ft, Ps Sli 4 B B } ; E A ° . (4c) ky RT oe With respect to the constants 4 from the equation 4 we know that each of them consists of the required entropy difference and of constants which do not depend on the nature of the reacting sub- stances. These latter disappear therefore in equation 4+, where always differences between two #-values occur, so that the value B,,—B, of equation 4a can be replaced by 4 —y;, and just so for the other equations. So we see that the difference of the substitution energies and entropies can be directly calculated for these reactions from the experimental determinations. The accuracy with which these caleu- Jations can be carried out, is of course determined by the value of the errors of observation. When I applied equations 4 to the data, it soon appeared that the values for 4, —, ete. in general possess small amounts, and sometimes differ very little from zero. | have therefore examined whether it is possible to account for the observations on/y by a difference of energy, lence by assuming that the difference in sub- stitution-entropy would be zero for the different hydrogen atoms. Mathematically this comes to this that every substitution might be represented by the aid of one constant, which would then have the meaning of the difference in substitution-energy. On this hypothesis the equations 4 are transformed into: ‘ fe Er In =a (5a) In z — pacts Gd OS es Baer . (5d) ae wonete Us : ln me = Giacinto ~ (de) 73* 1122 To show that the material of facts really admits of such a hypo- thesis. | subjoin the values which must be assigned to the differences of energy of the equation 5, expressed in calories. Nitration of chlorobenzene. Nitration of brombenzene. Oa ‘tp == 825 #4 — ‘tp = 647 Z— 0 t= — 30 | i—a) t=— 30 = is! | | found cal. found cal. found cal. found} cal. | ortho 30.1 30.4 26.9 26.6 ortho 37.7 | 37.7 | 34.4 | 34.3 | para 69.9 69.6 | 73.1 73.4 - para 62.3 | 62.3 65.6 | 65.7 Bromation of toluene. a ty 058, | t=25 t=50 | £—=T15 | fre las) an a ea ee found calc. found calc. eee calc. © { | ortho | 35.5 | 35.5 | 23.5 | 23.5 | 6.2 | 6.0 | |ortho} 14.4 | 15.9 | 18.5 a 2223: | 2001, meta | 85.0 | 83.5 | 80.2 | 80.31 76.5 | 78.1 para | BBC) BIL) |Psysesy || SPs || seb. |) “earl Nitration of benzoic acid. “ty = el | t= — 30 | (0) t—s0) | | | l Nl | found calc. found calc. found, calc. | Nitration of ethyl-benszoate. a Ta = 500 t=-— 40 E10 is Il 3 | : found calc. found, cale. found cale. | ortho 25.5 25.0 28.3 | 27.5 | 27.7 | 28.5 73.2 | 73.7 | 68.4 | 69.2 | 66.4 | 65.6 | meta ues Nitration of toluene. @ a = 135 Z ——s 4 tm fo f£=30 t= 60 found cale. found cale. found calc. found calc. para | 39.3 | 38.7 | 38.1 37.6 | 26.8 ortho | 57.2 58.6 | 58.0 58.6 58.8 meta Seo 207 3.9 36.6 | 35.3 | 35.7 58.5 | 59.6 | 58.2 3.8) 4.4) 4.9 |. 5.1 6.1 If we extend the investigation to the introduction of a third sub- Stituent in the twice substituted benzene, we eet: Nitration Of m-chlor-benszoic acid. ') b> —iq= 1290 t=— 30 0 found calc. found calc. @ (13; 6)" 393" | 935") S291 91-5 Pay 32)\(" 7 | 6.54] -8 | 8.5 Nitration of m-brom-benszoic acid. po a= 1020 found calc. found = calc. @ (1;,3;6)| 89 | 89.2) 987 5173.2) (Aly b10-8-| 13 86.8 13.2 _ Nitration of m-dichlor-bensene. eRe sg: = 1400 f=— 30 Z—0 found calc. found calc. a (1, 3,6) | 97.4 | 97.3 | 96.2 95.4 Gi a2 )iee2s60" Que |) Sst 3.6 yy In these tables the place of carboxyle is indicated by 1 1124 Nitration of o-dichlor-benzene. found | cale. | | | @ (1, 2,4)| 94.8 | Krase Sea be 6 (1, 2, 3) | 5.2 5.2) 2) 70 Nitration of o-chlor-bengotc acid. found calc. i all | t= — 30 — ce | | ‘found | calc. found] calc. a (1,2,5)| 86 | 86.4 b (1,2,3)| 14 | 1 16 | 16.2 | Nitration of o-brom-bengotc acid. | ie es) — | = t= — 30 t=0 | | | : | found} cale. found. calc. | a (1, 2,5)| 82.9 | 82.9 | 80.3 | 80.3 Bl, 233))| 174 | V7eL | 19: Tete 197 | When we now pass in review the results of the above tables, it appears that the harmony between the found and the ecaleulated values is very satisfactory in general. In the majority of the examples the deviations very certainly remain within the errors of observation. Only in the nitration of benzoic acid an appreciable deviation between the found values and the calculated ones cccurs. This nitration, however, is according to Pref HoLLEMAN one of the first carried out examples, in which the “method of extraction” was applied, which was later replaced by more accurate analysis methods. 1125 Probably the deviation remains within the errors of observation also here. This supposition seems not too hazardous when the results are considered which were obtained in the nitration of the methyl! ester of benzoic acid, where very probably in the nitration an error oceurs at O°, which is greater than the above deviations. Prof. Houtn- MAN informed me that he too considered the agreement in the tables as very satisfactory. The above test, therefore, really leads to the conclusion that the substitutions in the benzene nucleus can be satisfactorily accounted for up to now by one single constant, the difference of energy for substitution at the different places in the nucleus. If there were only one example known where the errors of observation were undoubt- edly smaller than the deviation from the theoretically caleulated value, the originally proposed hypothesis would have to be rejected ; so it will have to appear from the continued investigation whether really all the examples without exception conform to the rule, for which no exceptions have been found as yet. Equations 8 and 5 accordingly, account for the facts which are known up to now. If we now compare the two equations, we come to the following conclusion: The second members of the two equations bave always opposed signs; if therefore in equation 5a hk, Ck, i.e. if on substitution more meta- than orthoderivative is formed, then & —s, is negative. k dlIn— It then follows from equation 387 that the value of 7 See posi- ¢ tive. We can express this generally as follows : The quantity of the product which is formed to a sinaller degree, increases relatively on rise of temperature. In this we should bear in mind that to decide whether a product is formed in a smaller quantity, it is necessary to divide the quan- tities formed by the value that indieates the number of equivalent places in the nucleus. Thus the nitration of toluene furnishes seemingly an exception, as seemingly the quantity of ortho is greater than the quantity of para-nitrotoluene. If however, it is borne in mind that in this substitution there are two ortho-places. available to one para-place, and that therefore para and not ortho is the product that is formed in greater quantity, the stated rule appears to be valid also here. As far as I am aware there are no exceptions to this rule either. Only the nitration of iodo-benzene does not follow it, as here the 1126 quantity of ortho-compound does not increase on rise of temperature, but decrease; this nitration is repeated in Prof. Honiemay’s labora- tory, because the presence of dinitro-compounds may possibly give rise in this case to comparatively great errors in the analyses. In the case of another example that departs from the rule, the quantity of para-product in the nitration of benzoic acid and its methyl! ester, the changes at varying temperature are so slight that the errors of observation may even have changed the qualitative conduct. Moreover the above consideration establishes the already known practical rule that in general it is desirable for the preparation of pure substitution products to work at low temperature ; for according to the stated rule Ligher temperature always promotes the formation of by-products. When we examine what influence the above result exercises on our theoretical considerations, we arrive at the following conclusion : When a hydrogen atom in the benzene nucleus is replaced by an atom or a group of atoms, an intermediate state makes its appearance, which is caused by exactly the same atoms for the substitutions at all available places in the benzene-nucleus. For instance in the case of a nitration the intermediate state is caused by the coincidence of the “kritische Réume” of the carbon atom of the nucleus at which the substitution takes place, of the hydrogen atom, and of the OH and NO, group of the nitric acid molecule, at least when in an analogous way as Bo.rzMann ascribes a “kritische Raum” to the NO, molecule, we do so tor the groups in question. Then the above conclusion would involve that the volumes of the Raume which eover each other, do not differ, or only very little for the substitutions at the different places, but that the different velocity of substitution is caused by the fact that the more distant atoms influence in a different way the energy required for the different places. 2. An entirely different question, which, however, can be brought in connection with what precedes, is the following: Is it possible when the quantity of the products, which are formed when a second substituent is introduced, is known, to calculate that of the substances which are formed when a third substituent is introduced> In other words is it possible to draw a conclusion from the energies required for the introduction of a second substituent, about the energy required for the introduction of a third? Tf e.g. we suppose that toluene is nitrated on one side, chlor benzene on the other, we know the relative quantity of the nitroproducts formed ; if we now nitrate chlor toluene, it is the question whether the quantity 1127 of the nitroproducts formed in the latter case is to be caleulated from the former case. In the first place we should bear in mind that the energy of the substances we start from is different, and now it is true that this energy is cancelled in the determination of the relative quantities, yet the energy of the intermediate states may depend on this energy. To obtain an answer to the given questions we should therefore have to introduce a hypothesis concerning the energy quantities. These hypotheses must necessarily be very arbitrary, as analogies with other phenomena are not yet known for them. One of the most plausible hypotheses would in my opinion be the following: Let us denote the energy required for the substitution of the NO,- group for the hydrogen atoms in the benzene molecule by ¢,. Then the energy for substitution of the hydrogen atoms in toluene and chlor benzene resp. may be represented by &,+ ¢,,, & + &,,,& +), resp. &, + &,, &, + &,, and & +48,,. If we now think a substitution carried out in the molecule ortho- chlortoluene, we might assume that the energies required for every substituable place must be added CH, av Nol (v - For substitution at the place @, which is in an ortho-position with respect to chlorine and in metaposition with respeet to CH,, an energy quantity «, + &,, + «, would then be reqnired. Reasoning in an analogous way &, + &,, + &,, would be required for the place 4. Applying equation 5, we get: In ky fee (&, + &m + &eo)—(E, + En + Ema) Es ka RT RT ail (&n,—&), )—(Em,— €, ) RT When we now consider that the introduction of the seeond sub- stituent requires: k Lae k, 2 E m (pL SSS ee See ken, RT long RT we find easily by combination of the three equations: 1128 In ——t 17 Kin —In Foy a my Cis or ky iy ing | ae ay ae This is the so-called rule of multiplication, which Prof. HoLLeman tried to apply for such calculations already before. This rnle appeared to be in pretty close agreemeit with the observations fur the nitra- tion of the ortho-chlor and ortho-brom benzoic acids; in other cases, however, great deviations from the calculations are found. Afterwards HvtsinGa proposed a “rule of summation’, but this too presents satisfactory agreement only in some cases. If we examine what relation would have to exist between the energy quantities required for substitution to arrive at a rule of summation, this relation appears to assume such an intricate form that it cannot be accounted for in my opinion from a theoretical point of view. A general rule for the calewation of substitution energies at the intro- duction of a third substituent from the values of energy which are required for the introduction of a second, seems to me impossible to find. It may, however, be possible to find a relation between analogous substitutions, and this relation might possibly be discovered by means of the energy values calculated above. Up to now I have however not made an attempt to do so, because the energy values on which the above tables are founded, can certainly still be modified in the units, and sometimes even in the tens; the extent of these modifications, namely, is in the closest relation with the errors of observation which may be allowed in the determinations. Moreover I will finally point out that in this paper I only intend to show that the material of facts admits the assumption that the substitution entropies are identical for the different places in the nucleus. That this is really perfectly true has of course not been proved by the test; we can certainly also account for the data by means of equations with two constants (equation 4), in which the second constant in general possesses a small value. It appears in. any case that in general the course of this type of reactions is chiefly determined by difference of energy. and the difference of entropy plays only a secondary part. As I showed at the end of § 1 our theoretical considerations about the mechanism of the chemical re- actions may be brought into harmony with these results. In conclusion | gladly express my cordial thanks to Prof. HoLtemax for supplying me with the information which I required for the foregoing investigation and for his interest in this work. Physics. — “A method for obtaining narrow absorption lines of metallic vapours for investigations in strong magnetic fields.” By R. W. Woop and P. Zeeman. (Communicated by Prof. P. Zeeman). (Communicated in the meeting of January 25, 1913) In the summer of 1911 we intended to make together some observations concerning magnetic double refraction of metallic vapours. The magnetic double refraction of some vapours was first discovered (and predicted) by Voier, afterwards commented upon by Zeeman and GEST. In the paper of the last named authors the interesting region between the components of the magnetically divided sodium lines was investigated and the results represented by drawings. It seemed desirable to extend this investigation using very narrow lines, which can be maintained constant during a long time and to fix the result by photograms. Our investigation never passed the preliminary stage and has become now superfluous by the paper of Voier and WaGner which has since appeared. During our preliminary observations we tested a great number of methods of obtaining narrow and constant absorption lines. It seems to present some interest to record one of our results. ‘The absorption lines of sodium were obtained beautifully narrow by using small glass tubes charged with a little metalli¢ sodium, then sealed to the vacuum pump and evacuated. A tube some centimeters in length was placed vertically between the poles, the magnetic field being horizontal. It is quite possible to use tubes of an external width of some millimeters. Of course much of the light of an are lamp is reflected and diffused by the tube, but enough remains to observe the inverse magnetic effect with a large Rowuanp grating. The magnetic resolution of the narrow lines can be splendidly seen and photographed in a reasonable time. The heating of the tube can be done by a flame, but preferently electrically. Of course tubes with other volatile metals can be prepared in the same way'). 1) The method has been since applied with success in an investigation by Mr. Wo xrtver in the Amsterdam laboratory; the results will be given separately. 1130 Physics. “The red lithium line”. By Prof. P. Zruman. Only those spectrum lines, which belong to pair series or to threefold series, are resolved by magnetic fields into complicated types, i.e. not into triplets. The canse of the complicated resolution is intimately connected with the presence in the spectrum of natural eroups of two or three lines (series-doublet or series-triplet). It has nothing to do with the distribution of lines in series, for there exist connected series of lines, which are resolved into Bees by mag- netic fields ‘). a Recently *) Pascuen and Back discovered that lines belonging toa very close seriés-triplet or series-doublet, influence each other in a very peculiar manner, Under the action of a sufficiently strong mag- netic field we might expect to observe a superposition of the types of separation of the compounds, but contrary to expectation a normal triplet is seen. Among the lines investigated by Pascnen and Back are also the lithium lines. Many physicists by analogy with the other alkali metals and their series expect that the lithium lines ‘are very close pairs. Sometimes the opinion has been expressed that the laws for the other alkali metals do not apply to lithium. This then might explain the result obtained by Votsr*) that the red lithiam line (6708) contrary to Presron’s rule is resolved by a magnetic field into a triplet, which is at least nearly normal. The measurements of Back ') for four lithium lines prove that within the limits of the errors of observation the separation’ has the normal value. It is therefore very interesting to know whether the lithium lines are really very narrow pairs or not. In the tirst case Pascnen and Back are right placing the lithium lines in parallel with the other doublets they investigate, but they also indicate 6708 Li as a ‘theo- retische Doppellinie’, because it has never been resolved. I have been able to do this, using the method given in the foregoing Communication. As glass is strongly attacked by heated lithium it is necessary to place a small iron or copper vessel inside the giass tube; the life of the tube is then at least increased. 1) LonMANN, Physik. Zeitschr. 9 p. 145, 1908; PascHen, Ann. d. Phys. 30, 746, 1909, 35, 860, 1911, Royps 380, 1024, 1909. 2) PascHen u. Back, Normale u. anomale ZeeMAN-effekte, Ann. d. Phys 39, 897, 1912. 3) Vorar, Physik. Zeitschr. 6, 217, 1912. 4) Anhang Back. |. ¢. 1151 The observations were made in the second order spectrum of a large RowWLANp grating. The red of the second order is superposed on the blue of the third order so that the line 6708 is seen in the absorption spectrum as a blue line. With small vapour density the line resolved into two components; this proves that the conelusion drawn from the analogy of the spectrum series of the alkali metals is true. That component of the double line which has the smaller wavelength seemed to be the most intense. The distance between the components could only be measured in a roundabout manner by means of a divided scale in the eye piece of the spectroscope. This measurement gave for the cistance between the components about one fourth of an Angstrém unit. From the empirical rule that in the case of the elements of the same family the frequency differences of the pairs are nearly proportional to the square of the atomic weights, it would < : ae ore : ae ; follow that for lithium this distance ought to be 6 & — = 06 Angstrom units. The observed. distance is much smaller. Physics. — “Some remarks on the course of the variability of the quantity b of the equation of state.” By Prof. J. D. vay per Waals. (Communicated in the meeting of January 25, 1913). In my preceding communications I came to the conclusion that the differences which occur in the normal, not really associating, substances are to be ascribed to the different value of the quantity by Dim a en and s = z a i The deviation exhibited by the law 3 Diim 3 Biim : of corresponding states, is also a consequence of the different course of the quantity 4. Thus it becomes more and more clear that every- thing that can contribute to elucidate the cause of the difference in As this quantity is greater, both / and s are greater, viz. this course must be considered of the highest importance. If the course of 6 is traced as funetion of v, a line is obtained which runs almost parallel to the v-axis with great value of v, and approaches asymptotically to a line parallel to the v-axis at a distance b, from the latter. Not before v= 2, does an appreciable difference begin to appear, and has the value of 4 descended to e.g. about 1132 0,96 /,. On further decrease of the volume / descends more rapidly — and when also a line has been drawn which starts from the origin, so from v0 at an angle of 45° to the v-axis, the conti- nually descending 4 curve will meet this line at 6 =dj,. If 6, and hj, ave given, this curve is determined. If 4, should have the same value, and if 4,,, should be smaller, the curve lies lower throughout its course, and reversely if dj, is greater, the whole 6 curve lies higher. Of course if there did not exist a similar cause for the variability of 6, we might imagine a more irregular course in the different 6 curves. But if such a cause is assumed, nobody will doubt of the truth of the above remarks. | have even thought I might suppose that there is a certain kind of correspondence possible in the course of the different 6 curves. The points of these curves which are of importance for the equation of state, run from v= djim to v=o. At a value of v= nb, (and » can have all values between 1 and o), b, — 6 is smaller as by — bjin is smaller. Now I deemed it probable that there would be proportionality between these two latter quantities, and that therefore the following character of these curves can be put, viz. b, —b au | | by — Bien Vlin » and that this function of — is the same, entirely or almost entirely. Viim When I considered the question what the meaning of this equation might be, the following thonght occurred to me. Could possibly the quasi-association be the cause of this variability of 6 with the volume ? I treated this quasi-association in an address to the Academy in 1906, and later on in some communications in 1910, and I came then to the conclusion that it must be derived from the increase of tension of the saturate vapour in the neighbourhood of the critical temperature that at every temperature and in every volume a so-called homo- geneous phase is not really homogeneous; but that dependent on the. size of the volume and also on the temperature there are always aggregations of a comparatively large number of molecules which spread uniformly. In very large volume the number of these aggre- gations is vanishingly small and with small volume, and especially at low temperature this number increases greatly; so that at the limiting volume the number of free molecules has become vanishing small. If in each of these aggregations the value of 6 does not differ much from 4,;,, or perhaps coincides with it, the following value of 1133 b might be derived. For that part of the substance that is in the state of free molecules the value of / is equal to 4,. If the fraction of the quantity of substance that is in the state of ageregation is put’ equal to w, and the fraction which is in the state of single molecules equal to 1— z, then 6 = (1 -— 2) Og + Otin or b b, — brim ———=, bs And if we compare this result with the equation the significance of which we tried to find, we see that nee) is the function which Vlim determines the value of 2 in every volume, but we must at once add at any temperature. That 4 might also depend on 7’ T have never denied; I have only denied that putting 6= /(7') would enable us to account for the course of the equation of state, but that chiefly the dependence of v is indispensable. So we should now have arrived at the relation: b,—b k v M —— == GF —— f (| —— <2"). by aa Dias Viin But I must not be detained too long by these considerations, tor on further consideration [ have had to reject the thought that quasi- association has influence in this way. For various reasons. First of all becanse at so great contraction of the volume the name of quasi-— association would have to change into real association. Secondly because the generated heat would then have to be much more con- siderable — and further the course of association would also have to be different for almost complete association, to which I may possibly have oceasion later on to draw the attention. This, however, —b — dependent on 7, and we Ay— Flim obviates the necessity of making return to the simpler equation : by =i) * v - = = || == fle b,— tim Vlim And though I am not yet able to give the theoretical form of this funetion, and though I cannot indicate a priori the constants occurring in it, | can apply a correction in the value of vim , which I gave in my least communication; and this has greatly weakened if not removed the objections I had to the assumption that the decrease of 6 with the volume is only an apparent explanation. I have arrived at the value of vj, = On by following the same train of reasoning as when I drew up the equation of state. For 4 113: the only new thought about the influence of the dimensions of the molecule (Chapter VI) was this that the volume inside which the motion of the molecules takes place, must be considered as in reality smaller than it seems at first sight. If in case the molecules should be material points, the consequence RT of the collisions is that they resist an external pressure +4- ——, the : i consequence of their own dimensions is that they resist a pressure v - . . . . —— times as great. And we cannot dispense with this consideration. a We may introduce this thought immediately; and without having to speak of repulsive forces, write directly: p - — = 5 OF if it is preferred first continue the course of the calculation with the aid of the theorem of the vira/ further than I have done. But finally to arrive at the true formula it is again necessary to follow the course taken by me. I showed this long ago. When I wanted to determine the value of this new quantity 4, however, I soon per- ceived that this would be attended with great difficulties. It was not so difficult to determine the value of 4,, and I could at once conelude that 4, is equal to 4 times the volume of the molecules. And it was also easy to see that / would have to decrease with the volume. Already the consideration that for infinitely large pressure the volume would have to be smaller than 4 times the volume of the molecules, and would have to depend on the grouping in that smallest volume, and that therefore 4,;,, would have to be < by, was sufficient for this. In reference to this I say what follows in Chapter VI (p. 52), after I had reduced the way to determine the quantity 4 to the abbreviation of the mean length of path, and had therefore put: “but this formula cannot be applied up to the extreme limit of con- densation of the substance’, ete. as far as the word “verwachten”. It appears from the cited passage that I felt already then that the quantity 4 in a definite volume would have to be determined by - the determination of the distance, at which during the impact the centre of the colliding molecule must remain from the central plane at right angles to the direction of motion, in consequence of the dimension of the two colliding molecules. This appears among others ewhen L say that when ¢ < 44, not only the double-central shocks, aii il 1185 but also the double tangent ones will not take place, and the factor 4 will not diminish so rapidly as might have been expected without taking this in consideration. To make clear what I mean, imagine a molecule in motion to strike against another. On the supposition of spherical molecules draw a sphere which has its centre in the second molecule with a radius = 27 (if » is the radius of a molecule). Then at the moment of the impact the centre of the colliding molecule must lie on that sphere with a radius twice as long as its own. Now imagine also through the second molecule a central plane at right angles to the direction of the relative motion, in which ease the second molecule may be taken as stationary, then the mean abbreviation of the free length of path is the length of the mean distance at which the centre of the moving molecule lies from the said central plane. In very large volume the chance that the centre of the moving molecule strikes against a certain area of the sphere with 27 as radius is proportional to the extension of the projection of this area on the said central plane. It follows from this that the mean abbreviation of the free length of path is the mean ordinate of a haif sphere . 4) : pe with 427° as basis, and so equal to —. It is true that this is the 3 abbreviation of the length of path for 2 molecules, but this is com- pensated by the fact that an abbreviation of the same value exists also at the beginning of the free length of path for the moving molecule. If also in a small volume the chance to a collision with the sphere with 2r as radius could be determined, the way had been found to determine the value of 6 in every volume. For v <4+ the double central impacts must be eliminated, but also the double tangent ones. And strictly speaking in every volume, however great, if not infinitely great, the chance to double central and double tangent impacts must have lessened. Here a course seems indicated to me which might possibly lead to the determination of the value of } for arbitrary volume. I do not know yet whether this will succeed, but at any rate it has appeared to me that this may serve to calculate 6; and not only for spherical molecules. The latter is certainly not devoid of importance, as the case of really spherical molecules will only seldom occur. Let me first demonstrate this for spherical molecules. In the extreme case when they are stationary, they lie piled up, as is the case with heaps of cannon balls, each resting on three others. Let us think the centres of these three molecules as forming the tops of the ground 74 Proceedings Royal Acad. Amsterdam. Vol. XV. 1136 plane of a regular tetrahedron. For a volume infinitely little greater than the limiting volume the limiting direction of the motion of the 4%) molecule is that which is directed at right angles to the ground plane, and in case of collision the three molecules of the ground plane are struck at the same time. The sides of the tetrahedron have a length equal to 27, and the perpendicular from the top dropped 2 on the ground-plane is equal to 27 Vas The abbreviation of the length of path in consequence of the 9) dimensions of the molecules is equal to half 27 |= if one wants to make this comparable with the above found one of a because this value referred to the abbreviation at a collision of two molecules, whereas the now found abbreviation holds for a collision of ; ee 2 4 molecules. The number of times that ers greater than 7 45 4 : by b is the value of + (Ore lin lim 4 3 8 : — ——— es IE 3 2 3 : Vice ; For spherical molecules, therefore, [aes or f almost is equal to equal to 5,9 and s = —11,633 or about 3,3. And then it would € oa) follow that these values /=5,9 and s=3,3 must be considered as the smallest possible values. But I do not lay claim to perfect accuracy for these values. Doubts and objections may be raised against these results, which I cannot entirely remove. Hence the above is only proposed as an attempt to calculate Oy. for spherical molecules. The first objection is this — and at first sight this objection seems conclusive. The value of 4g, must be equal to vj. Is the thus ealeulated value of bi, then the smallest volume in which stationary molecules can be contained? This is certainly not the ease. The volume of n* stationary spheres placed together as closely as possible is equal to 4n*ry/2 if n is very great, and accordingly 2 times smaller than if they should be placed so that every molecule would require a cube as volume with 27 as side. If this value must be the value represented by djin, 4 — zer* by 3 a2rY2 7 2 ; ; — = ——_—— =—,—- and so in connection with the law given Dtin 4/2 3 : by me /—1 and s* would become much greater than the value given for them by experiment. But the thus caleulated value for stationary molecules is not what I have represented by jim; 1 should prefer to represent it by 6, . At the point where the 4-curve meets the line which divides the angle between the c-axis and the 4-axis into two equal parts, need not and cannot be the point in which 4 is equal to 4,. The 4-curve does not cease to exist in this point; if passes on to smaller volume, or possibly follows the line v = 6. On closer consideration the /-curve appears to touch the line v= 6 and at smaller volumes than that of the point of contact the value of v appears to be again larger than 6. In the same way as kinetical considerations were required for the determination of the value of 6, to show that 4, is equal to . 4 four times the volume of the molecules, and so equal to far, é bijim Cannot be found without the aid of kinetical considerations. And the attempt which I make to calculate the value of dj, follows the same train of reasoning as has been efficient for the determination of 6,. This train of reasoning is as follows. If the mean length of ) See and if the iL cate path for molecules without dimension is equal to v v abbreviation amounts to #7, then = = ——, or b= 427°. v—b v—Nd4ar Br 3 For b, is P=Te and if the above given calculation is correct, 2 the value of 3= Va for bj. So that, if we also introduce a Vlim 5 A =b,, — amounts to=—1,814. If we assume a regular » value v 0 0 arrangement of the molecules in v, and v;,,, the distances of the centres are not equal to 27 in vy», but equal to 2r 81,814 — 1,22 times 2r. But for moving molecules such a regular arrangement is pertectly improbable. For them no other rule is valid but this that within a certain small space of time in equal parts of the volume, if not in contact with the walls, the mean number of molecules is the same. But their arrangement in such an equal part of the volume is 74* 1138 entirely arbitrary and always varying. A regular arrangement as would be the case for cubic distribution, when in every molecule, 3 directions could be pointed out at right angles to each other according to which they would be surrounded by 6 neighbouring molecules placed at equal distances, while in all the molecules these three directions and distances would be the same, is altogether inconceivable. This is a fortiori the case with the other mentioned regular arrangements, according to which it would be possible in every molecule to point out several directions inclosing angles of 60°, according to which they are surrounded by other molecules. This would only not be absurd for stationary molecules, and then v, is not equal to 4,, but v,>6,. Now it might appear that the by, introduced by me would really have to be 4. I introduced the biim When I discussed the ratio of the greatest liquid density to the critical density. and made use for this purpose of the rule of the rectilinear diameter. This greatest liquid density occurs for 7’ = 0, and would therefore seem to hold for stationary molecules. This, however, is only seemingly in my opinion. Below 7’ equal e.g. to E or = 7), this rule cannot be verified, but apart from its appro- ximative character this rule is extrapolated. It is then taken for granted that what we have observed over a wide range of tempe- rature, will also hold outside these limits. And I too have assumed this in the determination of vy, All this refers to a volume in ‘ ; vr Uk P which moving molecules occur. And so, if we put —~ = 2(1 + y), Vlim sews, BOE é : the value };;, in the relation of —- =2(1 + y)=r is also that Vlim dlim which holds fer moving molecules. If observations could also be made at 7’—0O, the volumes which are smaller than that in which the curve touches the line v = 4, could be realized. And I do not doubt at all that in the immediate neighbourhood of 7’= O the rule of the rectilinear diameter would entirely fail. Let us summarize the foregoing. There is only one point in which the 6-curve has a point in which v=. This takes place ata value of 4 which we have ealled 6,;,,, and in which, because » = 4, the Re ae db : value of the pressure is infinitely great. In this point aa Then in; dv dp 2a db hae dv ; a v—b , a Ele 1139 dp -) aoe because p and —— — infinite, also av dp dv 0 20 Dp i n- And the determination of v,;,, and 4), takes place as follows. In the formula yielded by kinetical considerations, viz. v—b v—4ar*Br v v Vim must be =4ar7r*?Br. And for the determination of v;;,, the smallest value for 8 will have to be found. For collisions with 1 4 inolecule at a time, 8 = = For collisions with 2 molecules at the 0 same time, so that at the impact 3 molecules are in contact, — V3. For collisions with 3 molecules at the same time, the oo | bo 2 value of 8 is equal to Y= as we saw above. And collisions with a greater number which are in contact at the same time, are by 4 3 8 | excluded. So that now the value of __ =e >= = tor lim - v spherical molecules has been found back, but now on better grounds than above. But this does not terminate the investigation into the value of Dim. I have put the chance that in w;,, collisions with a single molecule or with 2 molecules might take place equal absolutely to 0. By putting vj, = 427? pr I have assumed the possibility that there is also a chance of collision for points the projection of which on the central plane at right angles to the direction of motion lies at the edge of this central plane, also still at this great density. A more complete investigation would probably yield a still somewhat lower value of ~. My principal aim was to draw attention to the difference in the value of 6, and by. Thad been astonished myself at the comparatively b b ‘ small value of —~, whereas a has such a large ratio. For spherical lim 0 4a bg molecules the latter amounts to See almost 3, whereas —— may = Ofim possibly come near to half 3. The relations at which I had arrived, eta 8 by . viz. —— = —— ands= — —— would be altogether incorrect, if 3 iim 3 Duin 1140 one should confuse 4; and 4,. It is, however, very easy to see that the pressure equal to infinitely great can occur when v = 4, but that this is not the case for / = 4,. Then tor spherical molecules v 3V2 : : . ee Sees And so the final point of the /-curve does not lie in the line which divides the angle between the » and the 4 axes into two equal parts, but in the line which makes a much smaller angle 1 with the v-axis, the tangent of which is about equal Oa or about 0,74. I have questioned myself whether [ can account for the result at which I have arrived. Especially the existence of },;,, and the relation of this quantity to the existence of groups of molecutes which simul- taneously, four at a time, collide, or at any rate are so close together that the space between them may be considered as zero. And though there are still numerous questions to which the answer cannot yet be given, and there is therefore reason to hesitate before publishing the foregoing, yet the considerations which result from this question have given me the courage which might else have failed me. How large is the space allowed to the motion for molecules with dimension? The external volume must be diminished 1 by a volume at the wall. The centres of the molecules cannot reach the wall, but must remain at a distance =r. Hence if O is the area of the wall, a volume = Or must be subtracted from the motion. 2. the centres cannot reach the surface of the molecules, but must remain at a distance =r. Then a volume = O’7 would have to be deducted, if O’ is the area of the joint molecules, and so it would be the same thing if the molecules bad a radius = 2r. But then if the molecule A collides with the molecule 4, we have counted the space that is to be deducted, twice, both for A and for 4. Of course the space to be deducted mentioned under 2 greatly preponderates on account of the great number of molecules. But the occurrence of collisions is a reason for b, to be diminished. If a molecule strikes against the wall or if a molecule approaches the wall so closely that there is no room for another to pass, two parts of the space inaccessible to the motion overlap, and hence the extent of the inaccessible space diminishes. This is also applicable for the collisions of the molecules inter se. If two molecules are so close together that a third cannot pass between, part of the space which is inaecessible to the 3'¢ molecule overlaps, and 6 is diminished. The greater the number of collisions, so the smaller the volume, the more & is diminished. Whether also the temperature has influence L141 on this diminution of 6 has not yet been decided. In case of greater velocity there are indeed, more collisions, but we may also assume that they are of shorter duration. At the moment, however, I shall leave this point undecided. What I have said here about the cause of the diminution of 6 with smaller v is’ practically what I had assumed as cause already before when I assumed the so-called overlapping of the distance spheres as cause. D The formula then derived for 6 = 6, — a 2s + 8 (=) etc. was not a satisfactory, and gave a far too rapid decrease with the calculated coefficients @ and p. And the cause of this at least I think I shali have to attribute to the quasi association. If for a moment I disregard the motion, and think all the molecules to be distributed in pairs, every pair being in contact, the ditmination in the value of 6 is 4 N-times the overlapping of the space at the collision between these molecules. But if in the motion I again admit the arbitrary pretty regular distribution and if I assume the originat space, the diminution in 6 would of course be much less, and would only hold for those that collide. So for every kind of collision either of 2 or 3 or 4 or perhaps of a greater number. the chance that such a collision occurs in the given volume must be calculated, and this fraction must be multiplied by the parts of the spaces which overlap at every kind of collision. g— by, bg \*. bg In the formula oi ae + 6B (=) ete. a represents the chance that 2 molecules come near enough to each other to bring about overlapping of the distance spheres; in the same way | the chance that 3 distance spheres overlap ete. And multiplied by a certain coefficient this would also be the case in complete absence of any cause of association, so if there are no special reasons for the molecules to aggregate. The quantities «, 8, are the pieces of the distance spheres that overlap. For 6, all the molecules without exception are counted, whether they are separate or whether they are part of an aggregation — and for the factor of e@ all the groups of 2 molecules, whether or no they appertain to a larger aggregation. But I have not yet calculated all this. That with diminution of the volume the decrease of ) will take place more and more rapidly may already be inferred from this that the number of every kind of collision or rather sufficient approach to each other, increases in a heightened degree, and at last if only the volume has become small enough, it may be assumed 1142 that overlapping of the distance spheres takes permanently place. For an arbitrary direction of motion we shall probably not have to go any higher than to a sufficient approach of 4 molecules, and this would justify the above given caleuftion of vg, = dim. We should have calculated this point when with decrease of v, the decrease of 4 is equal to it. Then a =1. With values of v << 7%, all the molecules are not yet in contact; then there are still motions possible in this space, e.g. flowing of the substance or vibratory motions. But the motion which we call heat, has become impossible. Not until , is reached does every motion become impossible. The points of the J-curve, which IT have continued as far as in 6, above, have of course, no physical significance. The portion of the d-curve between Aim =, is then only to be considered as a parasitical branch. In the formula for the calculation of 4 this branch is probably also included. Accordingly I have entirely returned to the idea that the diminution of 6 is an apparent diminution of the volume of the molecules. In these remarks T have touched upon several points which are of importance for the theoretical treatment of exceedingly condensed substances — without being able as yet to bring the investiga- tion to a close. That 1 mention them already now is because I hope it may stimulate others to give their attention to it, and that they may try their strength to bring the investigation to a close. The determination of vy., seems to me of special importance. Summary of the results obtained in this and previous communi- cations. If it was rigorously valid the law of the corresponding states would have taught that all substances belonged to the same genus. This has proved not to be eatirely complete. Experience teaches that from this point of view, there are differences. All the substances, indeed, belong to the same genus, but there are different species. If the quantities characteristic of a substance are called the quantities Jf, s, and 7, they appear to differ. But these differences need not be considered as differences in 8 characteristic quantities, but they may be reduced to a single quantity. If this single quantity is called h, P— ] 8 then — =a = Vh and 2 is at least approximately equal to i: When we try to find the significance of this characteristic U quantity, it will be found, as was a priori to be expected in what was left out of account in the derivation of the law of corresponding 1143 states, viz. the variability of 4. This variability of 4 differs for different substances, and depends on the form of the molecules or on the quasi-association, which indirectly influences the course of 6. If we put 6, for the greatest value of 4 and 4,;, for the smallest value which is of importance for the equation of state, the ratio 2. is different. This ratio however, oscillates comparatively little lim round the value 2. 0 Ales Y-axls (|x) axis of the association. Ax —. = Viton. c («-x) Vv. Ving, —, V-atts Fig. 2. b This ratio h =—— determines, if I continue to speak of species, lim the species to which the substance belongs. 1144 The value of fy, is that value of 4, for which v has the same value as 4, and the pressure is therefore infinitely high. This value of Vim Pin is the smallest volume in which the substance can still be in thermal motion, but it is still appreciably greater than the joint volume, in which the molecules, when they were stationary, could be contained. The reduced equation of state which has the form F(x, v, m} = 0, if / should be put constant, assumes the form : D ; \> ves m Dey ; | Diim ! when the variability of 4 is taken into account, with gradually increasing deviation, however, as the density approaches the limiting density. The form of this latter funetion is: b, \ tim | | v 8 b | x+3 3- OTe | »? | | [4 by rs by : A Btim The deviation gradually increasing -with the density is caused by b the variable term © The influence of this deviation may be ne- 8 glected for large values of v. At the critical density the different differ only a few percentages. At the limiting YD values of —— bg Din : 1 density the value of this latter quantity is equal to foi Now that / oscillates round 7, this greatest difference is after all perhaps less great than might be feared, “but yet not negligible, and manifests itself in the different directions of the rectilinear diameter *). 1) For more accurate and more definite views arrived at later I must refer to my ‘Weiteres zur Zustandsgleichung’” Akademische Verlagsgesellschaft Leipzig, which will shortly appear. 1145 Microbiology. — “QOwidation of petroleum, paraffin, paraffinoil and benzine by microbes.” By Dr. N. L. S6unceN. (Communi- cated by Prof. M. W. Buterinck). (Communicated in the meeting of January 25 1913). In the following it is shown that the hydrocarbons ') of the paraffin series, which chemically are so difficult to decompose, are easily oxidised to carbonic acid and water under the action of microbie life. Most of the fat-splitting moulds do not grow or only very poorly on paraffin. Raun’*) has deseribed a white Penicillium which ean use paraffin as source of carbon whilst, according to this experimenter, bacteria cannot grow on hydrocarbons. But the latter statement is incorrect. Most of the bacteria which oxidise the hydrocarbons cannot decompose the fatty acids, which in their chemical composition differ little from the paraffins, but some species are also able to split fats by secretion of lipase. Henee, the paraffin-oxidising bacteria can be classified in two groups: fat-splitting and non-fat-splitting. To the former belong: b. jluorescens liquefaciens, B. pyocyaneus, B. punctatus, B. fluorescens non liquefaciens, B. Stutzeri, B. lipoly- . ticum a, p, y and d, and the Micrococcus paraffinae, described below. To the second group belong some species of the genus Mycobacterium.) Oxidation in crude cultures. The oxidability of petroleum, paraffin, vaselin and benzine was ascertained as follows. To 100 em* of a culture liquid consisting of: tapwater 100, ammoniumehlorid 0.05, bikaliumfosfate 0,05, in Ernenmrysr flasks ') For these experiments were used: paraffin (Griipter), paraffinoil (Merck), vaseline, petroleum (American and Russian), and benzine Beside the common commercial petroleum I ofterz used a more purified product obtained as follows. American petroleum was shaken with sulfurie acid D. 1,84, with repeated refreshing of the acid, then with polash solution; after this again treated with acid and once more with potash; it was then dried on sodium and distilled. The fraction 150°— 250° (free from nitrogen) served after removing of a small quantity of sulfuric acid by potash solution as food for the microbes. *) Rawn, Em Paraffin zersetzender Schimmelpilz. Centralblatt fiir Bakt. 2 Abt. S. 382, 1906. 8) A. Weper, Ueber die Tuberkelbazillen abnlichen Stabchen und die Bazillen des Smegma’s. Arbeiten aus dem kaiserlichen Gesundheitsamte 1903. Bd. 19. S. 251. Neumann und Lesmann, Grundrisz der Bakteriologie. 5e Auflage 1912. S. 619. 1146 of + 450 em* capacity, was added about 1°/, of one of the paraffins ; this medium was inoculated with about a gram of garden soil and placed at 20°, 28° and 37° C. Commonly after two days already growth of microbes is observed in the tubes at 28° and 37°; after about 7 days in those at 20°. The acceleration of the development is then very marked, so that the liquid becomes cloudy in consequence of the great number of microbes growing at the expense of the hydrocarbons. The growth in the cultures, transferred to a similar medium, is also very strong and the droplets of the hydrocarbons are enveloped by a thick slimy layer of microbes. In a short time the hydrocarbons, disappear entirely from the medium. From the foregoing follows that petroleum, paraffin, paraffinoil, vaselin and benzine are oxidised by bacteria. This explains the disappearance of the petroleum, daily brought at the surface of canals by motor boats and in other ways, and from the sewage water of the petroleum refineries. Isolation of the bacteria. The paraffin-oxidising bacteria were isolated by streaking the above described crude cultures on plates consisting of: washed agar 2 (or gelatin 10), bipotassiumfosfate 0,05, ammoniumehlorid 0,05, magne- siumsulfate 0,05, distilled water LOO. To this medium was added as source of carbon, petroleum in the form of vapour, from a small dish placed on the cover of the inverted culture box. Fig. 1. Culture method on agar a with salts and petroleum as vapour from the dish p. In this way only those bacteria which can oxidise petroleum vapour develop on the agar to colonies and are very easily isolated. The growth of the microbes is vigorous, the bacteria assimilating, beside the vapour directly taken up, the petroleum 1147 condensed around the colonies and forming an iridescent ‘layer on the agar. On comparison of the velocity of growth of the various species, much difference beiween them is observed. By direct sprinkling of soil, canal water, or other material on the plates, several species which do not accumulate in the deseribed culture liquids, can be isolated. Moreover it is possible in this way to determine the number of paraftin-oxidising microbes in any ma- terial. So, in one gram of garden soil at Delft + 50,000, in one em*. canalwater + 8000 paraffin-oxidising microbes were found, which shows that they are very conumon. It is clear that this method is also applicable to other volatile compounds. For a nearer examination the cultures were sown, beside on the above plates, on broth gelatin and broth agar, and on media of other composition. Accumulation of parafjin-oaidising species at various temperatures. When the above media, consisting of tapwater, anorganic salts, and one of the hydro-carbons, are placed at temperatures between 15° and 25° C. and the transfers are also cultivated at these tem- peratures, B. fluorescens liquefaciens, B. punctatus, and other lique- fying species are particularly obvious, but there likewise occur some fat splitting, non-liquefying bacteria and micrococei, which can all be distinguished on broth gelatin. In the tubes placed at 26°—80° C. the number of liquefying bacteria is still very great, yet, non-liquefying species are more com- mon than at lower temperatures. At the same time the non-fat- splitting group of the paraffin-oxidising species, the mycobacteria, begin to develop, but especially at 30°-—37° C. they find their optimum. They are very striking by their morphological properties and pigment formation. By this method white, brown, red, and red-brown species were isolated. At 387° C., with paraffin as carbon source, a fat-splitting micrococcus developed in almost pure state, which oxidised parattiins vigorously ; it was called Micrococcus parafyinae and is in its properties, except in shape, similar to 5. hpolyticum’). If instead of garden soil, sewage water is used for the infection, the growth of fluorescents and of B. pyocyaneus may become so intense, 1) These Proceedings, 1911. 1148 that the above mentioned species do not wel develop and often quite disappear. At infection with pasteurised soil (5 minutes at 80° C.) no growth takes place, which shows that to the spore-forming bacteria no parattin-oxidising species belong. Under anaerobic conditions paraflins are not broken off by bacteria. Description of the parafyjin-oxidising mycobacteria. These bacteria are immotile; in young cultures (8 hours on broth agar at 30° C.) they are rod-shaped, length 4—10, width 0.5 9y—1.5 9, after division it often occurs that the two individuals are still jomed in one point. Very characteristic is the appearance of ramifications in these microbes, which remind of bacteroids such as are found in . radicicola. After some days’ culture en broth agar or broth gelatin, these rod-shaped bacteria pass into Streptococcus-like organisms, the cells of this form having a diameter equal to the width of the rod form. The Streptococcus-form produces, on a new medium, first the rod form, which then again passes into that of the Streptococcus. Spore formation does not occur; heating during 5 minutes at 65° is not resisted. All species secrete some slime. The growth of the mycobacteria, which after their pigment-forming power on potatoes or on broth gelatin are distinguished in Mycobacterium phlei Leamann and Neumann, MM. lacticola L. and N., M. album, and M. rubrum, varies very much on different media as is shown in the table below, where some of the results on growth and pigment formation are given, On potato these microbes form most pigment’) and grow very well; likewise on broth-, malt-, und glucose gelatin. A very good medium is also broth gelatin or broth agar with 3°/, glucose. Besides on the above substances the fat-sphtting bacteria and the Mycobacteria grow on humus compounds without these being deco- loured. The best source of carbon is peptone, then follows aspara- vin, ammonium chlorid, and potassiumnitrate. Nitrate is reduced to. nitrite ; denitrification does not take place. In broth, with 3°/, pep- tone, indol is not formed. In broth with 3°/, glucose, no fermentation is observed. Tyrosin is not changed into melanin. ; ') The pigment of Mycobacterium rubrum is probably carotine; it resists hydrochlorid (38 °/,), potash solution, and ammonia, dissolves in chloroform and ether and is coloured dark blue by sulfuric acid of density 1,86. 1149 | YJMo1s | | | | 3nat | poe ou | — pa | pol ‘Dal — - — poi-yiep — Pat-yJep | pat-y4ep | pai-ysep | wniqns yyMol3 | yymoi3 | (pioB) yyMo1s i a MO|I9 ay MO][9 _ MO]JaA | saqySys | mMopyad| moyjad | Moyock = _ -y1ep MO][aA Molad “ysep} Mofad |) B[091\9e] MOIaA ynq ‘yas | | yymois | uMOIg | | MOTTAA | MoT[aA peq (pior) UMOIq |UMOIq |uUMOIG — -pal|) ajzeyeu | -98ueio | -aSubIO| ‘aSuviO | — — a3ueilo — pal -pat “pad soryd yyMoi3 3 | ‘oyBd se | ywsys | ; | | | | Adana | (pio) _ ayy | 9yyM| ayy ayy | UYyM | opyyM| dzlym PSO1OPYM ASOso}1Y AM | ayuM | wngye ene gh Uo er Ae Pedi le eee Ses Li oe = | _ 7398 ‘yas as yas | ek) aI ES || oar 3 738 “a8 yas noe 3 ajoiusof , ajpjaan | aypadyng | ayojpu ue tA wl \eeelé ike ite spsns el 0jDJ0q | pitted Ep ie aa | sunaqo') | wintaq07 | MEV) ajiuubpy | asojjoy | asojav7 | asoanjy aun) J]DW | youg wnhliajzIeBqoodAW — aa ee ss — —— = —— = = = = ~~~ ee = VIGAW SNOINVA NO WAIHYFLIYAOIAW AG NOILVWAOA LNAWDId GNV HLMOYD 1150 Aesculin and indican are not decomposed. Urea is only splitted by Mycobacterium album. In feebly acid media the growth is inhibited ; it is best in neutral or feebly alkaline solutions. At the oxidation of paraffins, organic acids, probably fatty acids are formed as intermediary products; they are, however, only present in slight quantities and evidently are oxidised almost as quickly as produced. Acid formation from paraflin could, however, be shown with the help of washed agar plates to which a litthe congo red had been added, or in which some caleiumfosfate was precipitated. In the former case blue fields appeared under the inoculation streaks, in the latter clear ones. Velocity of the petroleum and parafyjin oxidation. The velocity with which Mycobacteriwn album, M. rubrum, Micrococcus paraffinae, and Bb. fluorescens liquefaciens oxidise petroleum, was ascertained by weighing the quantity of carbonic acid formed in a certain time. The diminution of the petroleum could not be directly stated as it always evaporates. The quantity of the produced carbonic acid was ascertained as follows. As culture vessel was used a one liter ErLenmerer flask provided with a ground glass stopper, bearing a vertical glass tube, reaching to near the bottom, and a side tube. It was filled with + 200 em‘ of a sterile culture liquid, consisting of distilled water, anorganie salts, and 2 em*. sterile petroleum. The vertical glass tube was connected with a large U-tube filled with soda lime; the side tube was joined to an apparatus succes- sively formed by U-tubes, tilled with sulfuric acid, beads and paraf- finoil (to keep back the petroleum vapour), caleciumehlorid, potash solution to weigh the carbonic acid, and ealciumehlorid for control, with a K6Ortinc pump at the end. When the cock of the pump is opened a current of air, freed from carbonic acid, passes through the fluid and yields the dried carbonic acid, formed in the culture, to the potash tube. During 24 hours are formed in the culture, if infected and placed at 28° C., Milligrs. carbonic acid by : Mycobacterium album 55 Mycobactertum rubrum 41 M. parafyjinae 34 B. fluorescens liquefaciéns 27 Crude culture 93 L151 About a third part of the weight of the carbonic acid corresponds to the oxidised petroleum, The velocity with which paraffin is oxidised by these bacteria was estimated by stating the diminution in weight, by the bacterial action, of two grams of paraffin, very minutely mixed with distilled water and anorgani¢ salts, after a month’s culture at 28° C. The rest of the originally added paraffin was dissolved in petro- leum-ether ; of this solution a certain quantity was evaporated and the remaining quantity of the paraffin was weighed. So it was found that during a month’s culture was oxidised in mers. by : Mycobacterium album 300 - rubrum 330 Micrococcus paras jinae 180 B. fluorescens liquefaciéns 180 Crude culture 540 Summary. 1. Pavaffins (petroleum, paraffin, benzine) can be used by certain species of microbes as source of carbon and energy, and are oxidised to carbonic acid and water. As intermediary products acid could be indicated. The bacteria were obtained by means of the accumulation method, with the said substances as source of carbon. 2. The microbes active in this process belong to two groups. a. Fat-splitting bacteria, very common in nature, as B. fluorescens hiquefaciens, B. pyocyaneus, B. punctatus, B. Stutzeri, B. lipolyticum, M. parafjinae. 6. Non-fat-splitting bacteria belonging to the genus Mycobacterium likewise widely spread, of which the following were distinguished : Mycobacterium album, M. phlei, M. lacticola, and M. rubrum. 3. The paraffin-oxidising species decompose, on an average, 15 mG. petroleum and 8 mm. paraffin in 24 hours at 28° C. per 2 cm’. surface of culture liquid. Microbiological Laboratory of the Technical University, Del/t. 75 Proceedings Reyal Acad. Amsterdam. Vol. XV. 1152 Physics. — “The coefficient of diffusion for gases according to O. E. Mrrer.” By Prof. J. P. Kugnen. (Communicated in the meeting of January 25, 1913). Among the various methods of deriving an expression for the coeflicient of diffusion from the kinetic theory on the assumption that the molecules behave like elastic spheres there is one — that of O. E. Mryrer*), — which leads to a result differing largely from the others and from observation, although the fundamental assump- tions are essentially the same. The deduction of Meyer's formula is shortly as follows*): a plane of unit area is considered at right angles to the gradient of concen- tration and therefore to the diffusion stream, and the numbers of molecules of each kind are caleulated which cross the plane per second. It is assumed that the molecules have on the average had. their last collision at a distance / (mean free path) from the point where they cross the plane and that their number in each direction is proportional to their density at the point where the last collision has taken place. The numbers in question of both kinds of molecules are found to be a and iS = =, = ; Soda where uw is the mean molecular velocity, 2 the number of molecules in unit volume and a the direction of the diffusion stream ; obviously dn, dn, — for /, and /,, the mean free paths of the two kinds of mole- ay nd dx dx cules in the mixture, we have = : m,+m 1s |VEn 02 tm c0| ZA : "| é ™m /5 2 9 m,--m Voi acess trae | se m 1 and =: where s is the diameter of the molecule and 6 = } (s, + s,). Owing to this double stream of moleenles a total number a, + a, pass through the plane: this would in general represent a motion of the gas. As the gas considered as a whole is supposed to be at rest, the stream a, + a, will produce a pressure gradient by which a stream of the gas as a whole of the same amount in the opposite 1) O. E Meyer, Die kin. Theorie der Gase p, 252 seq. 1899, 2) e, g. L. Bourzmann, Kin. Theorie. I. p. 89 seq. 1896. eee Il (ee L15: direction is generated. When this stream is superposed on the first, - ny n, the numbers of molecules become a, — (a, + a,)anda,— * (a, + a,) n and the coefficient of diffusion D 1 10) a (n,u,l, + n,u,/,). According to this formula, D would vary strongly with the com- position of the mixture, when m show this we put successively 7 limiting values of D: , and m, differ much. In order to ,=O0 and n, =0 and find for the are m D (rn, = 0) = — —s ees 3 n76* m,-+-m, ‘ ue m, D (n, = 0) = — —-~ — — 3 00" m,-+m, Using the relation w,’*m, = wu,.?m, = ae where / is the constant Th in Maxwenr’s law of distribution, we can also write Dae eae ea D (a, = 0) = ——_ — ass & 3ano? V ah m, m, +m, as | ela Dit 0) — A : 3ano?V ah m,m,-+-m, The two values of D are to each other as m,:m, e. g. for car- bon dioxide and hydrogen as 2: 44. The experimental evidence ') is in favour of a coefficient which varies with n, and 7,, but only to a very small extent, s0 that a variation as given by Meryer’s formula is out of the question. The coefficient of diffusion according to STEFAN °*) is: p= 3 l [ae 16no? V xh mm, therefore independent of the composition of the mixture, which agrees approximately with experiment. The same expression follows from Maxwetr’s second theory when applied to elastic molecules ; this was proved by Laneevin*). The only simplifying supposition which 1) Compare A. Lonius, Ann. d. Ph. (4) 29 p. 664. 1909 2) J. Sreran, Wien, Sitz.ber. 65 p. 323. 1872 3) P. Langevin, Ann. chim. phys. (8) 5 p. 245. 1905. Maxwett himself had used the same method (Nature 8. p. 293. 1573): his result given without proof differs by the factor */, from that of Langevin. (3* 1154 he had to make in order to carry out the required integrations was, that in ordinary slow diffusion Maxwew’s law of distribution may be taken as fulfilled. The want of rigour which this implies may perhaps account for the small difference between the formula and observation mentioned. The question arises, what causes the great difference between Mryrr’s result and the others. Gross') criticised the superposition of the gas current on the diffusion current: he tried to improve the theory by leaving out the former and by taking $(a@,-++a,) as the real diffusion stream; but this is certainly illegitimate, as the definition of D presupposes the gas to be at rest or the plane through which the diffusion stream is calculated to move with the gas. LaNGEVIN*) pointed out, that the dynamical action between the two kinds of molecules is lost sight of altogether in MryeEr’s method, but he failed to indicate, how to modify or supplement it in order to take this action into account. Neither does BoLrzmMann explain the striking contradiction between the two methods. It is possible to remove this contradiction for the greater part by making use of the notion of persistence of molecular velocity which Jeans*) introduces into the kinetic theory and which also plays an important part in the theory of the Brownian movement. This quantity depends on the principles that, when a molecule collides with other molecules, it will after a collision on the average have retained a component of velocity in the original direction. Jeans has calculated what fraction of the original velocity this component is on oor average: he calls this fraction the persistence 0 and finds = =F tgp yd +V2 = 0.406. oo shows that the usual caleulations in the kinetic theory of the various transport-phenomena of which diffusion is an example have to be corrected for this persistence. For the sake of simplicity it is assumed that a molecule describes the same distance / between successive collisions. Owing to persistence a molecule will on the — average after describing a path / travel on in the same direction over distances successively of /%, /9* ete., therefore altogether describe a distance //(1—®) before its motion in the given direction is exhausted and similarly a moleenle which reaches a plane from a distance / will not on the average have had a component O in the given ) G. Gross. Wied. Ann. 40 p, 424 1890. 4) l.c. 3) J, H. Jeans. The dynamical theory of gases p. 236 sqq. 1904, 1155 direction at that distance before it collided there, but at a distance (1—). We can also say, that the molecules which have had a collision at a distance //(1—®%) succeed on the average in getting to the plane before their velocity in the given direction is reduced to 0. In the calculation of the numbers that cross the plane it was assumed that the velocities were evenly distributed in all directions at a distance 7: as it now appears that this condition does not hold for a distance / but for the distance //(1—9), the correct result is obtained by replacing / by //4—®) in the final formula. ' In this manner Jans corrects Mryer’s formula’), but it is clear that by this means no improvement is effected, as J is multiplied by a constant factor and the anomalous dependence on n, and 7, remains. An important point has however been overlooked by Jeans viz. that the persistence obtains a different value when one deals with a mixture of two kinds of molecules of different mass. When the calculation of % is carried out for a molecule m, amongst molecules m, one finds 1 1 m,-+-m, | — 2 ay log 1+y 2) m, — 0.188 m, = == — Mm, + Mm, m, m, For m,—m, this expression reduces to the one given by Jwans. As a molecule , collides not only with molecules m, but also with molecules of its own kind, the correct expression for the persistence is obtained by multiplying the average number of collisions of the latter kind by 0.406 and that of the former by the above fraction. In this manner the factor 1/(1—®) becomes = : it m,+m,. m,—0.188m, Ina, V21,0.406—n, nat] : Ly eae ar = ; : z m, m,-+-m, a: for the molecules m, and ' = Fi m,tm,. m,—Q0.188 f,=1: |} 1—n,ms,? V2.1, x 0.406 —n, 20? pee rms ———— ee | m, m,+ mM, for the molecules m,. Repeating Muygr’s argument we find for D iL iD = Sn (nul, 7, B= nyu,l, f,). If we now put n= 0, we obtain 1) Jeans I.e. p. 273. Comp. M. v. Smotucnowsk!, Bull. de l’Ac. d. Se. de Gracovie 1906, p. 202. u, m, 1 D (rn, = 0) = —— — — on 36" m, + m, m, — 0.188 m, u, Pee: m, 1 2 1 1 [AS = ——— ——— —_ = — - 555 - : 3n 16" 1.188 3220? 1.188 V ah m, m,m, The symmetry of this expression shows that exactly the same value holds for n,=0O. The form of D also agrees with STeran’s expression: the coefficients are in the relation of 1: 1.05; therefore, considering the approximate character of the deduction, there is practically complete agreement. For intermediate compositions the difference between the two expressions for D becomes material only when m, and m, are very different. This is probably due to the method of calculation which compels us to work with averages from the beginning. Moreoyer Jeans’s method of calculating the persistence is not rigorous: it might perhaps be found possible by applying more rigorous methods to reduce the remaining difference between Meryer’s corrected formula and the other one. As a matter of fact the object of this paper was not so much to deduce a correct formula, considering that the near accuracy of Lancrvin's method cannot well be doubted, as to remove the strong contradiction between the two results. In conclusion it may be added, that the method which is indicated in this paper can immediately be used to deduce rational formulae for the viscosity and the conduction of heat for gas mixtures. > Mathematics. — “On bilinear null-systems. Prof. Jan DE Vries. Communicated by (Communicated in the meeting of January 25, 1913). § 1. In a bilinear null-system any point admits one null-plane, any plane one nul/-point. The lines incident with a point and its null-plane are called nud/-rays. If these lines form a linear complex, we have the generally known null-system, which is a special case of the correlation of two collocal spaces (null-system of Mésius). The null-rays of any other null-system (1,1) fill the entire space of rays; with R. Sturm we denote by y the number indicating how many times any line is null-ray. In the first we suppose y= 1 and we examine the null-systems which may be called ¢rilinea and which can be represented by (4;1,1). tate § 2. If a plane ¢ rotates around the line / its null-point / de- scribes a conic (/)*; for on account of y—=41 there is one position of ~ for which F lies on /. The null-points of the planes gy passing through any point 7 lie on a quadratic surface (P)’; evidently it contains /? and on account of y= 1 one point more on any line through 7. Evidently the null-plane of P touches (P)* in P and cuts it according to two lines g,g’. Any point & of one of these lines is null-point of a plane g passing through / and also through P. Therefore these lines are null-rays of o' pencils (/,7), i.e. singular. So the singular lines of a (1,1,1) form a congruence (2,2). All the other lines of (/?)’ are characterized by the fact that the null-planes of their points concur in P?; otherwise: P is the vertex of the quadratic cone enveloped by these planes. § 3. Two surfaces (P,)? and (P,)? have in common the conic (J)? corresponding to the line /—=P,P,. As any other common point S bears two and therefore @' null-planes, it is seagulir. The locus of this point S is a conic 6° meeting (/)* in two points. The surfaces (P\? corresponding to the points P of / form a pencil; the surface passing through any point / is indicated by the point of intersection of / and the null-plane of /. The null-planes of any point S evidently form a pencil, the axis of which may be repre- sented by s*. As o? contains two points of (/)’, the line / bears two null-planes the null-points of which lie on 6’; therefore the locus of the axes s* is a quadratic scroll or regulus. According to the laws of duality there is a quadratic cone >, any tangent plane of which is singular, as it contains o' null-points lying on a line s,; these lines generate a second regulus. § 4. We now consider three surfaces (P)’?. As any pencil of planes (s*) admits a plane passing through a point P,, the surface (P,)? also contains 6’. Amongst the points common to (/,)? and the conic (/,,)” we find in the first place the points of intersection of (d,,)? and o?. One of the two remaining points common to (/,)? and (,,)? is the null-point of the plane P,P,P,, the other which may be denoted by 7’ lies in three null-planes which do not pass through a line, on account of the arbitrary position of the points P; so T bears w? null-points, i.e. 7’ is principal point. Evidently all the surfaces (?)* form a complex with the singular conic 6* and the principal point T as common elements. This com- 1155 plex is Jinear, for through any triplet of points /’, passes the sur- face corresponding to the point of intersection of the null-planes Pir Pa Po The verter of the singular cone SY, bears w' singular null-planes 6 not passing through a line; from this ensues that it coincides with the principal point T. In an analogous way the plane tr of the singular conic o? is prin- cipal plane of the nuil-system. Let us consider the plane through 7’ and one of the axes s*; it has for null-point the singular point S lying on s* but at the same time the principal point 7’; so it is singular and its null-points lie on the line sy= 7S. So the regulus s, is a cone and consists of the edges of the cone projecting the singular conie 6? out of 7. Likewise the axes s* form the system of tangents of a conic lying in the principal plane t. § 5. The conies (/)* form a system oo‘ admitting a representation on the lines of space. For through any two points /\, /, one (/) passes, which is completely determined by the line 7 common to the null-planes ¢,,7.- The cones {/], each of which is-the envelope of the null-planes of the points of a line / also form a system o*; any of these cones can be determined by means of two planes v,. gy, the null-points of which indicate then the line /. If 7 lies in a singular null-plane o, the conie (/)* breaks up into the line s, bearing the null-points of 6 and a second line / which is bound to cut s,; so the principal point 7’ which also can figure as null-point of o cannot lie outside sy. So we find once more that the regulus (s,) is a cone. If 7 passes through the vertex of +, and bears therefore two sin- gular planes, (/)? degenerates into two intersecting lines, the point of intersection coinciding evidently with the vertex of S,; for the null-point of any other plane through / must coincide with that vertex. § 6. A special trilinear null-system is determined by the tangential planes of a pencil of quadratic surfaces #° touching each other along a conic o*, where the point of contact forms the null-point. *) 1) In the case of a general pencil with a twisted quartic as base we get a null-system (1, 3,2), treated at some length by Dr. J. Worrr (“Ueber ein Null- system quadratischer Fliichen”, Nieuw Archief voor Wiskunde 1911, vol. LX, page 85), EOE EE 1159 If the pencil is represented by wv? + @,? + 4,° 4+ 4a =0') the tangential plane in (y) has the equation ; Yt, + Yet, + Ye, + Ay,7, = 0, 2 being determined by Ge eaten te Aye —— 0.6. soo oh ON So for its coordinates (7) we find fin oe Ee = Th eh eng Tee (2) or M1 = Ys = Ma Yas = Ms 2 Yas = Mi — (Yr? +? + ys") - (3) From (1) and (2) we deduce P ad ep Us alld ays harp Uy Yr? MMs = Yo? MMs = Ys? M31, = Y.? — CL? + 0.7 + 05") - (4) So (4) shows that any plane has only one null-point. If the null-plane (jj) passes through the fixed point (2%) we have > 2; 7 =O, so the equation of (P,? is YY s 1 2YoYs 1 2sYsYs— 24. + ye.’ + ys") - - + (5) The intersection of this surface with the surface belonging in the same way to the point Q(v,) breaks up into the singular conic ya — 9, Yo ys + Ys = and a second conic lying in the plane (2,4, — 2,,) y, + (2.0, — 2,0,) y, + (2,0, — 2,,) y; = 0. The latter contains the null-points of the planes passing through PQ. From this ensues that y is equal to one. ?) All the surfaces (P)* pass through the principal point y,=y,=y,=—0. As could be expected, this point is the vertex of the quadratic cone touching all the surfaces of the pencil (®*) along o?. The null-planes (¥) of the points (y) of the plane § envelope the quadratic surface 51MM, + Saas + S3%s%4 = $4 (M,? + 4,7 + 9,7). All these surfaces forming a system o* touching the plane 4, = 4, = y,; = 0 (ev, =0) and the quadratic cone with the equation 4, = 0, 1) Coefficients which might present themselves have been comprised into the definition of the coordinates. *) This ean also be found by considering the involution determined on PQ by the pencil (#7); one of the coincidencies lies in the plane of the conic ;2, the other is point of contact with one of the quadratic surfaces. 1160 7, + 7,7 + 9,7 = 0, also represented by 2,7 + 2,* + 27,7 = 0. So we find once more that the plane of 6? is the principal plane and that the common enveloping cone of the surfaces ®* touches all the sin- gular null-planes. By replacing o° by the imaginary circle common to all the spheres, we find the metric null-system in which any plane has for null- point the foot of the normal out of the fixed point 7” We also find a trilinear null-system in the following way. Let o* be any conic and 7’ any point. We then consider as null-plane of any variable point Y the polar plane of 7’Y with respect to the cone with Y as vertex and 9° as directrix. By assuming O, in 7’ and representing 6? by Ee te (05 20) we find for the null-plane of X the equation Ya (Yrey + Yatta + Yats) = (1? + Ys” + Ys’) te So the coordinates 7 of this plane satisfy My = Ysa = Na 2 Ys g = Ms Ysa = Me? — Yi" 1 Ya” + Ys’) As these relations are identical to those of (3) this null-system is equal to the former. § 7. We now pass to Ailinear null-systems where y = 2. Then the locus of the null-points of the planes of a pencil with axis / is a twisted cubic curve (1) cutting / twice. Analogously the null-planes of the points of a line / envelope a developable with index 3 (torse of the third class), i.e. they osculate a twisted cubic. f The locus of the null-points of the planes passing through a point P is a cubic surface (P)?. Two surfaces (?)* and (Q)* have the curve (/)' determined by the line 7= PQ in common. In general they admit as completing inter- section a twisted sextic o°, eutting (/)° in eight points and forming the locus of the singular null-points, each of which bears a pencil of null-planes. (If these planes were to envelope a cone o° has to- be manifold curve on (/)* and this is impossible if we surmise that the intersection of (P,*° and (Q)* breaks up into two parts only). The axes s* of the pencils of null-planes through the points S of 6° form a scroll of order eight; for the points of intersection of 0° and (/)* determine eight null-planes through 7, each of which has a point S as null-point and contains therefore an axis s*. The surfaces (P)*, (Q)* and (R)* have the singular curve o° in common and moreover one point only, the null-point of the plane 1161 PQR. For (R)* meets the curve (/)* belonging to 7—= PQ in eight points on 6° and therefore in one point outside o°. Evidently o° is base curve of the linear complex of surfaces (/)’ § 8 A special null-system (1,1, 2) can be obtained in the following manner. We start from two pairs of non intersecting lines a,a’ and 6, 6’. We assign to any point / the plane @ of the two transversals ¢ and w through /' over a,a’ and bh, bh’. The hyperboloids (/aa’) and (/bb’) admit a curve (/)* of which / is a chord as completing intersection. So we have indeed y = 2. Also a, a’, 6, 6’ are chords of (/)°. Here the singular curve 6° is represented by the lines a, a’, b, b’ and their quadrisecants q,q’. So the figure of singularity has eight points in common with (/)’. For any point S of @ the transversal w is determined while we can assume for ¢ any ray of the pencil (Sw’). So the null-planes of S form a pencil with axis w. So the scroll (s*) breaks up here into the four reguli with the director lines (a, 6, 6'), (a', 6, 6’), (b, a, a’), (6, a, a’). For any point of g the transversals / and w coincide and the same happens for any plane through q'. So the lines q,q are not only loci of singular points but also envelopes of singular planes. As this is also the case with the lines a, a’, b, 6’ the two dually related figures of singularity are united. § 9. For a line / intersecting a in A the locus (/)' breaks up into a conic (/)? and a line w containing the null-points of the sin- gular plane (/a); the conic lies in the plane (Aq’) and passes through A, this point being the null-point of the plane connecting / with the transversal wv, through A. If / meets g, the curve (/)’ degenerates in q and an (/)*. The lines / determining conics (/)* form therefore si special linear complexes ; so there are o* conies (/)’. If 7 meets both lines g and q' the hyperboloids (/aa') and (/bd’) intersect in /,q,q' and a fourth line / meeting g,q' as / does. So the relation between / and / is involutory ; each of them contains the null-points of the planes passing through the other, the planes containing either q or q’ discarded. If / meets a and 4, the curve (/)* breaks up into a line w in the plane (al), a line ¢ in the plane (4/) and a line /' cutting ¢ and w containing the null-points of the other planes through /. If we assume for / a transversal ¢, the curve (/)*° is represented by the lines w and w’ of the planes (al), (al) and by ¢ itself. This 1162 line evidently contains the null-points of the remaining planes through t; therefore it is singular. We derive from this that the surface (P)* contains the transversals ¢ and w passing through P; so the null-plane of P is a threefold tangential plane. The third line of (P)° lying in that plane admits the property that the null-planes of its points envelop a cubie cone with P as vertex. If a,a', 6, 6' form a skew quadrilateral each null-plane touches one of the quadratic surfaces of the pencil with those four lines as base. Then the surfaces (P)* have four nodes in common, the vertices of the tetrahedron with a, a’, b, b',q,q' as edges. § 10. We still examine an other null-system (1,1,2) the singular curve of which degenerates. ; Let us assume the conic 6? in the plane z and a pair of non intersecting lines. Through / we draw the transversal ¢ over a,a’; then the polar plane of ¢ with respect to the cone /(o*) may fignre as null-plane of F. Reversely, if the plane t is cut by g according to the line d and. D is the pole of d with respect to o’, the transversal through D determines in ¢ the null-point F. If g rotates around /, the line d describes a pencil around the trace FR of 7 as vertex and JD describes a line of rv. But then ¢ describes a vegulus with a,a’,7 as director lines, in projective corre- spondence with the pencil of planes (y). Consequently the null-point F then describes a twisted cubic (/* with / as chord. The two.points common to (/) and (/)' lie on the regulus. Each point A of the line a is singular. The transversal ¢ describes a pencil in the plane (Aa’), its trace D with the plane rt describes a line e bearing the trace A’, of a’. So the polar line d rotates round a point / (pole of e); the null-plane of A describes therefore a pencil with axis AL. If A describes the line a, the line e keeps passing through A’, and therefore E describes the polar line of A’,. So the axes of the pencils of null-planes corresponding to the singular points A forma regulus. A second regulus contains the axes of the pencils corresponding to the singular points A’ of a’. The conic 6° too is singular. Any point S of it admits as null- planes all the planes touching o in S. All the surfaces (?)* have in common the singular curve o*, the singular lines a,a’ and also the line s through the traces A, and A,’ of a and a’ with 1, containing two points S,, S, of 0°. 1168 For any point of s the cone projecting 6? degenerates into the plane +t counted twice; so its null-plane is indetinite and this explains why s must lie on each surface (/?)’. Indeed the plane x is principal plane; for the null-plane of any point of t lying neither on 6? nor on »s coincides with + as polar plane of a line ¢ not situated in r. In connection with this result the cubic torse of the null-planes of the points lying on / always contains the plane rt, i.e. t is common tangential plane of all the surfaces of class three enveloped by the null-planes of the points of a plane. The trace d of a singular plane must be incident with the pole D, i.e. it must touch o?. In this case ¢ is transversal of a, a’, 6? and each of its points may figure as null-point. The locus of these trans- / versals is a quartic scroll |t\* with a and a’ as double director lines and the line s mentioned above as double generatrix. The polar surface of any point P with respect to [¢}‘ intersects o in six points; the planes touching [¢|* in these points are singular null-planes. So these planes envelope a forse of class six. § 11. In the null-system considered in the preceding article the transversals ¢ form a bilinear congruence. If we replace it by a congruence (1,7) we get a null-system (1,1,2- 1)'). If the plane gy rotates once more around the line /, in which ease its trace d describes a pencil in t and the pole Da line 7, then the ray ¢ resting on 7 describes a scroll of order n+ 1. So the null-point of y lies (n + 1) times on 7 (y =n +1) and deseribes a twisted curve (jr. Let the congruence (1,7) be determined by the director curve « and the director line a, which is to have (n—1) points in common with a”. Hach point of « is s¢ngular and bears a pencil of null-planes (see § 10). From a point of a the curve @” is projected by a cone of order n with an (n—1)-fold edge a. To the trace of this cone, considered as locus of ) corresponds a curve of class 7, the envelope of the trace d of the null-plane y. So each point A of a bears c' null-planes enveloping a cone of class rn. So a is an n-fold line on the surface (P)"+?. Here also any point of the singular conic c* bears a pencil of null-planes, the axis of which touches o. The intersection of two surfaces (?)"+® breaks up into a curve ()7+*, the curves e” and oe’, the line a (to be counted n?-times) and 1) For n=O we get the null-system of § 6, for »=1 that of § 10, Lib4 the n rays of the congruence lying in r. As in § 10 the line s these n rays partake of the property that the null-plane of any of their points is indefinite. The singular null-planes touch in the points of o? the scroll [¢}2"+2 with o*, a", a@ as director lines and n double generatrices in +. The polar plane of P cuts o* in 2(2n-+1) points each of which bears a singular null-plane; so the singular null-planes envelope a torse of class (4n + 2). Evidently t is once more principal plane. The bisecants of a twisted cubic «* determine in an analogous way a null-system (1,1, 4). Here each point S of the singular curve «’ is vertex of a quadratic cone enveloped by the null-planes of S. Now two surfaces (P)’ have in common the singular curve a’, to be counted four times, thé singular conic 6’, a curve (/)* and finally the three chords of @* lying in t. § 12. By the considerations of § 11 we have shown that bilinear null-systems with y > 2 do exist. Now we will prove that ~the locus of the singular points of a null-system (1,1, 7), with the condition y > 2, cannot be a single curve. Evidently the curve (/7+' containing the null-points of the planes through / is rational, 7 being a y-fold secant. The null-points of the planes through P lie on a surface (P)/+! touched in P by the null-plane of P. The surfaces (P)+! and (Q)7+' have a curve (/)+! in common. Now let us suppose that the completing intersection is a curve 6 of order y (y+ 1). In order to determine the number of points common to (/) and we first determine the number // of transversals passing through any given point O and resting on (/) and o.- For this number the known relation m(u— 1) (»—1)=2hk4+ A holds, where u,v are the orders cf both the surfaces, whilst m is the order of the first curve and / the number of its apparent double points. Here we have p=v=m=y+1, 2h=y(y— 1), as (J is ratio- nal. So we get H=y(y?-+ 1). The transversals under consideration are common edges of the cones projecting (/) and o out of OU; the remaining common edges pass through the points of intersection of both the curves. J165 For the number of these points we find therefore y (y+ 1)* — Hy + 1) = 27". Now the surface (R)/+! has in common with (/) besides the 2y? points lying on 6 and the null-points of the plane PQR still y (2—y) more points and this is only possible for either y= 1 or y= 2. So we may conclude that for y > 2 the singular points must be arranged at least on fvo curves. Mathematics. — “On plane linear null-systems’. By Prof. Jan de Vrigs. (Communicated in the meeting of January 25, 1913). § 1. By a plane nuill-system (a, 8) we understand a correlation between the points and lines of the plane in which to any point F correspond « null-rays / passing through it and to any ray / correspond 8 null-points situated on it. We restrict ourselves to the case «=1 in which any point F bears only one null-ray (linear null-system) and represent by & the second characteristic number. If the ray / rotates around a point P, its & null-points describe a curve of order 4-1 passing through P and touching in P the null-ray of P; we denote that curve by (P)+. The curves (P)*t' and (Q)‘t! have the & null-points of PQ in common; any of the remaining (4 + 1)? —£ points of intersection bears a ray through P and another ray through Q, therefore a pencil of null-rays; so these points are singular. Therefore a nudl-system (1, k) admits 4° + 4+ 1 singular points. The curves P+! form together a net with 4? -+ 4+ 1 base points; through any pair of arbitrarily chosen points , JY’ passes one curve determined by the point common to the two null-rays 2, y. A pencil of curves g” with * base points determines a linear null-system, in which to any point /’ corresponds the tangent / in F to the curve passing through F. This pencil intersects an arbi- trary line f in the groups of an involution of order n, admitting 2(n—1) double points, therefore 4 = 2(n—1). This null-system admits (4n7—6n -+ 3) singular points. To these belong the »? base points, lying on o' tangents; the remaining ones must be nodes of curves gy". So we fall back on the known property of the pencil (p.) to contain 302—1)* curves possessing a node, 1166 § 2. The bilinear null-system (1,1) has three singular points A, B, C. The line AB admits A and BF as null-points and bears therefore x’ null-points. So the sides a, 6, c of triangle A B C are singular lines. If / describes any line /, the null-ray / envelops a conic touching a, b,c and 7 (the latter in its null-point). The conic (P)? degenerates if P lies on a singular line. If we assume P on a the null-points of the other lines through P lie on the line PA. Let /f be a line cutting a,b,c in A’, B’, C’ and F its null-point. If f rotates around A’ the point / describes a line through A, and the cross ratio (A’ B’ C’ F) remains constant = d-1f / rotates around B’, the point F describes a line through B and (A’b’C’F) is once more = Jd. So this cross ratio has the same value for all the rays and is characteristic of the null-system. Now, according to a known theorem, we have also F (A BC/S)=4d. So any null-system (1,1) consists of the pairs (FP, f) connected with each other with respect to the singular triangle ABC by the relation F(A BC f) = const. In his “Lehre von den geometrischen Verwandischaften” (vol 1V, p. 461) M. R. Srurm proves that this construction furnishes a (1,1) but probably it has escaped him that we can get avy (1,1) in this way. A pencil of conics touching each other in two points A, B deter- mine a (1,1) by its tangents. Then the singular points are A, band the point C common to the common tangents in A and B. If in any collineation with the coincidencies A, 6, C the point 2” corresponds to /, the line f= FF’ admits / as null-point in a bilineair null-system *). § 3. From a given linear null-system (/’, 7) we derive a new one (F, f*), if we replace f by the line 7* normal to it in F. In this construction # and /* are harmonically related with respect to the absolute pair of points. By a /armonic transformation we will understand the transformation of a null-system in which f and /* are harmonically separated by the tangents from F to a given curve g? of class two. ' For any point F of ’, the null-ray / passes into the tangent f* of g?® in F; if f touches ¢* in /, we may assume for /* any line through F#, and F, is a singular point of the new null-system 1) From y, = C, 5 pad x, =0, TERY E =O we deduce pf) = (Cg—C3) %%, ete, ie o&\%, = Cg—Cz, ete. 1167 (1, 4%), As any singular point of (1,4) remains singular, 4* must surpass /\. In order to determine A* we bear in mind that all the rays /, which pass into a detinite ray /* by means of the transformation considered, must pass through the pole P?* of /* with respect to y?. So the null-points of 7* lie on the curve (P*)F+! corresponding to F* in the null-system (1, 4). So a (1,4) passes into a (A, k + 1) by the harmonic transformation. From these facets we can derive that 2 (/+-1) singular points of (1, 4+-1) must lie on gy’. We can confirm this result as follows. Let G * with a ray / admitting a null-point / on g?. Then the curve (G)ét+! cats gy? in G and in 2k +1 points /’ more. In any of the 2 (4+41) coincidencies of the correspondence (/’, ), the ray / touches gy* and /* can be taken arbitrarily through /’; then /’ is singular. By repeating the transformation (/’, 7*) must pass reversely into _the original null-system (1, 4). The null-points of 7 lie on the curve (P)' corresponding to the pole P of / in the null-system (1, 4-+1). On this curve we also find the points of contact of g* with the tangents passing through P; these points are null-points of / in the special null-system (0,2) of the pencils the centres of which lie on gy*. So the null-system (1, 4-+1) is transformed into the combination of (1,4) and a (0, 2) admitting exclusively singular points (the points of ¢’). If a is a singular ray of a null-system (1, 4), harmonic transfor- mation with respect to a pair of points lying on a@ generates once more a (1,4). For in this case) the pole P* of a ray J* lies on a, which implies that the locus (?*)*+! breaks up into a and a curve eutting #* in & null-points #’*. be the second point of intersection of ¢ § 4. In the case of the null-system (1, 2) the curves (P)* forma net with 7 base points. Any net of cubic curves with 7 base points determines a null-system (1,2), in which any line / admits as null- points two base points of a pencil belonging to the net. For the curves of the net generate on / a cubic involution of the second rank, the neutral pair of which belongs to o* triples, i. e. consists of two base points of a pencil. The figure of singularity has no special characteristic, as we can choose the base points of the net arbitrarily. As soon as three singular 1) So the null-system (1, 1) of the tangents of a pencil of conics in double con- tact passes by transformation with respect to the absolute pair of points into the ° null-system of the normals. 76 Proceedings Royal Acad. Amsterdam, Vol. XV, 1168 points are collinear, the line bearing them is singular, as it contains three and therefore o' null-points. Though we can determine any (1,2) by a net of cubic curves we do not judge it superfluous to point out some null-systems (1, 2) which can be obtained otherwise. If the points # and £” correspond to each other in an involutory quadratic transformation (quadratic involution) they may be considered as null-points of the connecting line /. Then any line is cut by the conic into which it is transformed in its null-points. Then the figure of singularity contains the four points of coincidence and the three fundamentai points and consists therefore in the vertices and the co-vertices of a complete quadrangle, the .siv sides of which are singular lines. The same figure of singularity is found in the case of the null- system, where any line has for null-points its points of contact with two conics of a pencil. Another null-system (1,2) is determined by a pencil of cubic curves admitting thre® collinear points of inilexion B,, B,, B, with common tangents 6,,6,,6,. The cubic involution determined by the curves of this pencil on any line / has a threefold point on the threefold line 6,— 6,6,b,; so / is touched by two cubic curves only. We generate a (1, 2) by considering their points of contact as the null-points of 7. Three of the singular points coincide with the vertices of the triangle 6,4,6,, whilst B,, B,, B, are three others; the seventh is node of a non degenerating cubic curve. Evidently there are four singular lines. By applying the harmonic transformation to a null-system (1, 1) with ABC= abe as singular triangle in such a way that the conie y* touches a,b,c respectively in A’, b’, C’ we get a null-system (1,2) of which A, B,C, A’, B’,C’ are singular points whilst the seventh can be found by a linear construction. Here a,b,c are singular lines. ; § 5. For any null-system (J, 4) the curves P*+! form a net with the singular points as base points. Here any line / bears an involution of order &£-+-1 and the second rank admitting a neutral group formed by the & null-points /’. But for &>>2 the net is not morea general one; for this would cut any line in an involution with 4h (k—1) neutral pairs. Indeed a general net of curves g*+' admits at most $4 (/--5) base points, whilst the curves (?)4+! pass through (A?+-A4-+-1) fixed points and the latter number surpasses the former by 4 (&—1) (k—2). 1169 Evidently a null-system (1,4) can be determined by the equations §,2, + §¢, + §,7,—0, §,a4 + §, bk -f- §,ck —— (1): The null-points of the line (§) are its points of intersection with the curve indicated by the second equation, For the curve (P)*+' corresponding to the point P(y) we find, by means of the relation on <= ae rn ~ oc J aL on o S we = the equation ak pk ok Yo x x So the singular points are determined by v, &, @, ak bk ek —a | z= wo | By harmonic transformation with respect to the conic «2 —0O we € : rut find a null-system (1, 4+), in which the line (jj) indicated by aa,=0 corresponds to the point (7). If we put for short wck—a bk — ARTI, xuk—a.ck — BEY, x, bk§— oak = Ck, x zx w zx =x a" x zz t then we find SerGenG, == Abr. BEL: Cet, x < Oy 1G: (@,,A+4,,B+a,,C)n, + (4,,4+4,,B +4,,C)n,+(a,,4+a4,,B+a,,C)y,=9, and this equation determines with uy, + 2,4; + 2,7, — 0 the new null-system. That it is impossible to deduce any arbitrary (J,4-+ 1) by har- moni¢ transformation from null-systems (1,4) can be shown already by remarking that the 2(/-+ 1) new singular points furnished by this transformation lie on a conic, which does not happen generally for k > 2. 1170 Botany. — “The injluence of temperature on phototropism in seed- lings of Avena sativa.” By Miss M. S. pe Vries. (Communi- cated by Prof. F. A. F. C. Went). (Communicated in the meeting of Jan. 25, 1913). In connection with Reverrs’') investigation on the influence of temperature on the geotropic presentation-time in Avena sativa seed- lings, | have undertaken experiments to find out how far temperature influences phototropism. I had originally no intention of making a preliminary statement at this stage because some of the experiments are not yet complete, but after the publication of Torsten NyBerGu’s*) work on the same subject in which results wholly opposed to mine are given, it became desirable to make a communication now. Torsten Nyperch comes to the conclusion that temperature has no influence on the process of phototropical stimulation. According to him therefore the influence of temperature on phototropism may be represented graphically by a straight line. The results I have ob- tained at various temperatures can however be represented by a defi- nite optimum-curve. Before I consider the results, I should like to say a few words about the method. Seedlings of Avena sativa having a length of about 2.5 em. were used. The boxes of seedlings were warmed for at least an hour. beforehand in the thermostat used by Rourcaers at the temperature to be investigated; they were then exposed to light in the thermo- stat and then taken out of the apparatus. The seedlings always exe- cuted their curvature at 20° C. While the seedlings were in the thermostat, fresh air was drawn through it, moreover the dark room in which all the experiments took place was ventilated as much as possible. The warming of the thermostat was done by electrie lamps ; gas was not burnt in the dark room, so that the atmosphere was as pure as possible. The source of illumination was incandescent vas light, placed outside the room; the light entered through a frosted glassplate, when the diaphragm was open. 1) A. A. L. Rurgers: The influence of temperature in geotropism. Proceedings Royal Acad. Amsterdam. Vol XIII, p. 476, 1910. A. A. L. Rureers The influence of temperature on the geotropic presentation. time. Recueil des Trav. Botan. Néerlendais. Vol. IX, 1912. 2) Torsten Nysered. Studien tiber die Einwirkung der Temperatar auf die tro- pistische Reizbarkeit etiolierter Avena-Keimlinge. Berichte der deutschen Botan. Gesellschaft. Band 30, 1912. ity The quantity of light-energy which at various temperatures was necessary {to cause a definite degree of curvature was determined. As a standard a curvature of 2 mm. was always taken, that is to say, the apex of the coleoptile was bent 2 mm. out of the vertical. To begin with, experiments were made at 20°U., since a quantity of light energy of 20 M. C. S. (metre-candle seconds) gave a cur- vature of 2 m.m. In order to find the quantity necessary for a curvature of 2 mm. a few boxes of seedlings were stimulated fora varying number of seconds, and it was ascertained after about 1°/, of the seedlings showed a curvature of 2 mm. served as a standard. The product of duration of stimulus and intensity of light then gave the 1 ’ required quantity of luminar energy in M. C. 58. hours how many seedling bad curved. Boxes in which 50°/ The experiments were performed at temperatures ranging from 0° to 40° C. No experiments were made above 40° C.; after one hour’s preliminary warming at 40°, so prolonged an illumination was necessary and the curvatures which finally occurred, were so indis- tinct, that there was no question of determination after more pro- longed warming. At 48° the seedlings died. From 0° to 25° the observations were made at intervals of 5°; above 25° more frequent determinations were found to be necessary. At each of the temperatures to be investigated there was first a warming of one hour’s duration, afterwards of 2 hours, 4 hours, 6 hours ete:, in order to see whether increased duration’ of preliminary warming had any effect. The results of the experiments are collected in the table given below, in which in successive columns is given in M. C. S. the luminar energy necessary for a curvature of 2 mm., after 1 hour, 2 hours’, 4 hours’ warming, etc., corresponding to the temperature given in the first column. It is clear from the table that the phototropic stimulaticnprocess is dependent on temperature and that at higher temperatures the time- factor is of a great influence. From 0° to 25° the length of preliminary warming has no influence on the quantity of luminar energy. At 27.5° and 80° longer preli- minary warming has a favourable influence; that is to say after a longer exposure to a higher temperature a smaller quantity of lumi- nar energy causes the same curvature as a greater quantity after a shorter preliminary warming. The harmful influence of longer preliminary warming is first observable at 32.5° and this is the case also at 35°, 37° and at higher temperatures, in always increasing amount. 1172 Temp. | 1 hour 2s, brs Oe 12 hrs. | 18 hrs. | 24 hrs. | 48 hrs. | ss xxx =| — 2 |) 2 20h | | | Lp 160 | 160 | 160 “160 | | | | Bini hed vO 70: /\\ p70" PRO | “30° 4? Sasi} "Sp.5) Sets! 52.5| | | 15 | 24.5 | 24.5) 24.5 24.5 5 24.5 | 20 20) | 20 |20' 9) 20 20 | 25 9.5 | 9.5) 9.5, 9.5 9.5 | bo) Fores 9.201 7a) “sie ene eA 4 4 | 30 8 6 eee ks 2 hal eae | 2 eae EN ae TEI me oy | 32.5| 9.2 | 12 | 13.6 14.4 14.4 | | fedaee 10 5 | 20 |ae | a5 | 8g % | 26 37> ly, yao 64 80 88 92 ie 37.5| 48 72 | 104 ae 176 «184 184 | SST) ewe 84 | 128 | 160 272 320 | 30° Yap 976 2/240 le 400 | 40 |+ 16001) | | ai / / | A YY | (a) al _—) a NI ea iN = is a j=] FO20/ UE eS Ss ' t, A B t/. Y = \ | Ny JX a || a B LI Fig. 1. i) For the absolute correctness of this figure I cannot vouch on account of the difficulty mentioned on a previous page. The favourable influence of longer preliminary warming at 27.57 and 30°, also the unfavourable influence of a longer exposure at 32.5° and 35° is represented graphically in figure 1 in which the abscissae show the duration of preliminary warming, and the ordinates the energy in M. ©. S. It is further clear from the figure that there is a transition point between the favourable and unfavourable influence; the amount of M. C. 5. is here constant. Figure 2 represents graphically the energy in M. C. S. which causes a curvature of 2 m.m., as a function of temperature. The abscissae represent temperature, and the ordinates luminar energy in M. C. S. As the drawing is much reduced the lines representing longer preliminary warming are omitted for the sake of clearness ; only the line for one hour’s warming has been drawn. 200 | ee: leat r =F 160} _ | IL = + 2 r2o|_| | (a eee Fig. 2. Evidently we are here concerned with an optimum-curve. The optimum is at 30°. Finally there is the question whether van ’r Horr’s rule applies to phototropism. The energy in M. C. S. decreases to the optimum because perception takes place more rapidly. To determine the temperature-coeflicients, the ratios of the quantities of luminar energy must not be taken, but the ratios of their reciprocal values, as was : E K done by Rurerrs') for geotropism. For this reason —° ete. is taken, 30 bal and not —* ete. 10 The following temperature-coefficients are then found: 1) A. A. L. Rutgers. Proceedings Royal Acad. Amsterdam, Vol. XIII. 1174 a= 3 z= 2.6 K, == 218: se 2.5 TS. i — 2.6 z — 0.95 The quotients appear to remain constant up to 30° and after that decrease markedly, in agreement with what is observed in other vital. processes. T refer to the paper of Conen Stuart’) for this point. Does the observed influence of temperature only affect perception or is the time of curvature (reaction-time) also influenced by tem- perature? The reaction took place at 20° C in all the experiments. Of course it is conceivable that there is an after-effect of the preliminary warming at the temperature investigated. The times of curvature (reaction-times) amounted to: At O°C. 120 minutes a Dare 90 Fs Sere UD gees 90 . et loss 90 cS Pie UAS 90 3 me 2 85 m 20° ,, 85 y; aoc 90 _ afier 1 to 12 hours’ previous warming after longer warming 120/ oii 90 Fe after long warming 120’ 9 OOnG wats LOO . after long warming 120’ Seo es. oan + 40° ,, ‘/, to 3 hours. By time of curvature (reaction-time) there is here meant the time which elapses till 50°/, of the plants are curved. The reaction-time is therefore fairly constant except at O° and at the high temperatures. It seems clear from the tables, that, if there is any influence of the temperature at which the plant was warmed beforehand, on the reaction, this is found exclusively at 0°, 39° and 40° and, when — the previous warming is of very great duration also at 35°, 37° and 38°. If may therefore be considered probable that the influence of temperature specially acted on perception. I hope later to give further theoretical considerations and a review of the literature in a fuller communication. Utrecht, January 1913. University Botinical Laboratory. 1) CG. P. Gonen Srvarr. “A study of temperature-coefficients and van ‘t Horr’s rule’. Proceedings Royal Acad. Amsterdam: Vol. XIV, p. 1159, 1912. 1175 Physics. — “On the lav of the partition of enerqy.” | J. D. van per Waats Jr. (Communicated by Prof. J. D. van pER WAALS). (Communicated in the meeting of January 25, 1913). § 1. Introduction. The law of equipartition of energy must hold for the kinetic energy of all systems whose equations of motion ‘) can be represented in the form of the equations of Hamiroy. This is shown in statistical mechanics. Experiment shows that this law is not fulfilled. This has first clearly appeared from the fact, that the kinetic energy of monatomic and diatomic gases, as it may be derived from the value of ¢,, accounts for only 3 and 5 degrees of freedom respectively, whereas the molecules of these gases have undoubtedly more degrees of freedom, which appears ia. from the light which they can emit. Later the observations of Nernst and his disciples have shown, that the c, of solids decreases indefinitely when we approach to the temperature 7’—O (absolute) which is also in contradiction with the equipartition law. Finally we usually deduce from the equipartition law that the partition of the energy over the different wavelengths in the normal spectrum must be as it is indicated by the spectral formula of Rayietcn. In this case also experiment shows that the conse- quences of the equipartition law are not fulfilled in nature. It appears from the above considerations that we are obliged to assume, that the equations of motion of the real systems cannot have the form of the equations of Hamiutox. The following conside- rations are to be considered as an attempt to find a way, which may lead to the dedvetion of the form of the equations of motion of the real systems occurring in nature. In this attempt I will assume that the partition of energy in the normal spectrum is accu- rately represented by the spectral equation of PLanck; so I will try to indicate a way which may lead to the drawing up of equations of motion from which the equation of PLanck can be derived. In consequence of the mathematical difficulties, however, I have not succeeded in finding those equations of motion themselves. 1) With ‘equations of motion” I mean the equations which are required to reduce the time derivatives of the independent variables by which the condition of a system is determined from the values which fhese variables have at a given ime, independent whether or no these changes refer to motions in the strict sense. 1176 It seems natural to assume, that these equations when they shall have been found, will be able to account for the different above- mentioned deviations from the law of equipartition of energy. In fact these deviations are closely connected with one another. If e.g. the energy of visible lightvibrations at 100° is imperceptibly small compared with that of infra-red rays, we cannot wonder that the vibrations of electrons which are in equilibrium with those light vibrations have an energy very small compared with that of vibra- tions of greater period. The thermal motion of the molecules may here probably be considered as a vibration of rather large period, although it is not a simple harmonic vibration. At a higher tempe- rature the small wavelengths become more predominant in the spectrum. It is therefore to be expected that also the vibrations of the electrons of short period, which at a low temperature are devoid of energy, at a higher temperature will obtain a measurable amount of energy, so that the specific heat with constant volume will increase with the temperature. The physicists occupied with these problems have noticed this connection between the normal spectrum and the specific heats from the beginning. Jeans’) e.g. has applied his theory, which originally was meant to be an explanation of the c, of gases, to explain the properties of the normal spectrum; and it is not astonishing that vice versa the theory of PLanck for the normal spectrum was soon used for the explanation of the specific heats. The method in which we start from a theory for the normal spectrum and deduce from it the value of c, seems to have advan- tages over the opposite way. For we have in the spectral formula of PLanck a relation which agrees well with the observations and which moreover is independent of the special nature of the walls. I will therefore follow this method. § 2. The centra of radiation. We may make the following two assumptions concerning the way in which the partition of energy of the normal spectrum is brought about. ist. We may assume that every vibrator considered separately has the property to transform radiation of an arbitrary partition of energy into the partition of energy of the normal spectrum. 2nd| We may assume that this property only belongs to groups 1) J. H Jeans, Proc. Royal. Soc. of London 67, p. 236, anno 1900. Phil. Mag. (6) 2, p. 421 and 638, anno 190). Proce. Phys. Soc. of London 17, p. 754, anno 1901, ete. Ly lings of vibrators, when their vibration is influenced by their interaction (collisions). [ shall start from the first supposition. In the first place because it is simpler. But it seems to me also to be more plausible. For we cannot doubt that the equations of motion are not linear. A vibrator therefore, when set into vibration by a perfectly homogeneous ray of light, will not exeeute perfectly harmonic vibrations. The radia- tion, emitted by it will therefore contain vibrations of other period than the incident ray. If therefore it is inclosed in a space with perfectly reflecting walls it will change the partition of energy of radiation which is also inclosed in that space. If now the spectrum which originates in this manner was not the normal spectrum (be- cause this latter was only brought about by a great many inter- acting vibrators) it wonld be astonishing, that even the most rarified gases, in which relatively only a few collisions occur, always give rise to the normal spectrum, and not to a spectrum whose partition of energy lies between the normal spectrum and that of one vibrator. I will therefore imagine one single vibrator. If its motion was determined by the equation: ae a, Ba ped : m— -— fe —¢g—-— =e. - > G ae dt? : ae (1) in which the coefficients m,/7,g,e were constants, then it would necessarily give rise to a partition of energy agreeing with the spectral formula of Ray.eien *). Therefore we shall assume from the outset that the equation (1) is not satisfied. The vibrator will then not be able to execute per- fectly harmonic vibrations, but its vibrations, when analysed in a series of Fourimr, will consist of several, in general of an infinite number of harmonic vibrations. This seems not to agree with the fact, that undisturbed vibrating vibrators as they occur in gases, emit very sharp spectral lines. We must, however, bear in mind, apart from the fact that no element exists whose spectrum consists in one single line, — that according to the electron-theory the mass is not perfectly constant and the light of a vibrator therefore not perfectly monochromatic. It is true that light of a period 7, differing from the fundamental period 7’, of a vibrator, often occurs only to an imperceptibly small amount in its radiation. But it cannot be totally wanting. Now it is well known that the intensity of radiation of a certain period in the normal spectrum does not depend upon the emission alone, but upon the ratio between emis- 1) Comp. H. A. Lorentz, Nuovo Cimento V, 16. Anno 1908. 1178 sion and absorption, so that a certain wavelength may be represented in the spectrum to its normal amount, even if the emissive power of the walls be imperceptibly small for that wavelength, provided the absorption have a corresponding, small value. The small value of the emissive power has no influence on the final partition. It only occasions that radiation of other energy-partition will only very slowly be transformed into the normal partition. So we shall assume that the centra of radiation are vibrators whose equations of motion are for the present unknown. These equations cannot have rigorously the form (1), but they need differ only very little from it. § 3. The independent variables. The ensemble. We will imagine an ensemble each system of which consists ofa parallelopipedic space inclosed in’ perfectly reflecting walls and containing one vibrator, whose centre has a fixed position in that space. We will assume that the motion of that vibrator is determined by one coordinate. The choice of the independent variables requires a certain circum- spection. The aether namely represents an infinite number of degrees of freedom, each of which can therefore possess an infinitely small amount of energy. The vibrator on the other hand possesses a finite amount of energy. It seems, however, difficult to deal with an ensemble in which one variable possesses on an average infinite times as much energy as the other variables. Therefore I will choose the variables as follows: If a monochromatic ray of light passes a vibrator the latter will be set into vibration. After a certain time this vibration will have become stationary. Now I will determine by one coordinate the amplitude of the ray and the stationary vibration of the vibrator caused by it. Besides this I will assume that the vibrator has a “proper” coor- dinate. Now if this proper coordinate, and also its time derivative are zero, this does not mean that the vibrator stands still in its position of equilibrium. It does mean that the motion of the vibrator consists exclusively of the stationary vibration, which it assumes through the influence of the radiation to which it is subjected. If the proper coordinate is not zero, then the vibrator has a motion which does not agree with the absorbed vibration. So it is possible to assume, that in a radiation field which is in equilibrium (i.e. in which the energy partition is that of the normal spectrum) the proper coordinate of the vibrator has always an infinitely small amount of energy (in the same way as the separate coordinates which determine - 1179 the condition of the aether), and that yet the vibrator vibrates with a finite energy the amount of which agrees with that calculated tor it by PLANck '). We can divide the Facianaonctic field into two parts: 1s* The electrostatic field which agrees with the momentary position of the electron, 2°¢ A field consisting of the really existing electric and magnetic forces diminished by those static forces. In agreement with the above we assume, that the position of the electron and therefore also the 2° field is determined by the first. As for this latter field we have Div E = 0 and Din f= 0; we can represent it as follows, if for simplicity’s sake we assume, that the space in which it is inclosed is a cube with a side equal to unity : E, = DV (qa + qa’) cos 2 ux sin 2x vy sin 22 we E, = = (98 + q'8') sin 2% ux cos 2m vy sin 20 wz S. = Zl (¢y + q'7’) sin 27 ua sin 2x vy cos 2H wz (2) Dy = = (p'a + pa’) sin 2m wx cos 2a vy cos 2a wz om wb P=, D, = = (p'B 4- pS') cos 2a ux sin 2m vy cos 2% wz DN, = > (p'y + py’) cos 2a ux cos 2x vy sin Aw wz In the summation we must take for 2u, 2v, and 2w all positive integers; Vu? + 07-4 w? represents the number of waves in 1 em. and 2acVu? + v? + w* =p the number of vibrations in 27 seconds. The quantities «, 3, y and a’, 6’, y' are the direction coefficients of two directions which are mutually perpendicular, and also perpendicular to u v w the direction determined by — == -,—= ——, uty saa "VY wet tw? Vu? tv? w? The quantities g,q’ and p, p’ are the independent variables. One of these variables corresponding to a certain set of values u,v, 2 will be represented by qu. OF Pu-w- It can be proved that the variables 1) Comp. i.a. Max Pranck. Acht Vorlesungen iiber theorelische Physik. p. 84. In fact our suppositions quite agree with what Pranck does, when he treats his vibrators as resonators and assumes that their energy is perfectly determined by the radiation field, to which they are subjected. In that case it is however -not allowed to equate the entropy of the system to the sum of the amount of entropy of the radiating energy, and that of the vibrator. For the motion of the vibration is perfectly determined by the radiation; the vibrations of the vibrator and of the radiation are therefore coherent and their united entropy is no more equal to the sum of their separate amounts of entropy as this is the case with the entropy of two coherent rays of radiation. (Comp. M. Lave, Ann. d. Phys. 20 p. 365. 1906; 23 p. 1 and p.-795. 1907 eic.). 1180 p may be considered to be the momenta corresponding to the coor- dinates g. As however we must assume that the equations of HamiTon do not apply, this observation is of no consequence for the equations of motion of the system. Now if no vibrator occurred in the space, every partition of energy would remain unchanged, and there would be no occasion to speak of an equilibrium partition. If a vibrator occurred which had the property to be able to transform radiation of every wavelength into every other wavelength and whose motion was determined by the equations of Hamiton, then the energy partition would approach to that indicated by the formula of Rayieica. In this case we might represent the condition of the system by means of an ensemble for which the probability of phase would be represented by ’) : gee 1 p— 7, 29 — 75? P=e 6 ere ee 1 1 where yw and 6 are constants and i6 =q a6 = p* is the energy of the system, the summation being extended over all quantities g and p, also over those provided with accents. Properly speaking this expression for the energy is incomplete. In the first place the energy of the proper coordinate of the vibrator has been neglected, but moreover we have neglected the energy of the vibrator, which it has in consequence of its forced vibrations. If we imagine the volume sufficiently large these approximations will meet with no serious objections. More risky is another simpli- fication which I will introduce; I will namely represent an element of extension-in-phase*) by IZdpdq and here also I will neglect the proper coordinate (or coordinates if the electron has more degrees of freedom). I think I may suppose that this simplification also will not affect our conclusions greatly. Perhaps it is even perfectly justified. It is namely possible that we must assume, that the motion of the vibrator is entirely determined by the electromagnetic field, and that therefore there is no reason to introduce a “proper” coordinate. As the spectral formula of RayLricn is not satisfied by the expe- riments, the formula (3) cannot give the right expression for the probability of phase. I shall therefore put: 1) Comp. Gress. Elementary principles in statistical mechanics p. 16, *) Comp. Gipss, l.c. p. 6. = Gi Cia 7) See ee roe (4) If it is possible to find sueh a form for the function gy (which represents a function of all variables gq and p) that the following formula is satisfied : eas a yp? eee tae. 46" | ee es, . “ee hy J 56? P(q---p) Ddgdp a eae l i Cer sO fb (>) Uh NH, —_— =p" = a € fe 6 gf (q---p) Hdgdp then the average energy in the ensemble for every degree of freedom has the value which is indicated for it by the spectral formula of Puanck. The function of g must of course have such a form that an equation of the form (5) is satisfied for every variable, not only for the q’s, but also for the p’s. The function y may moreover contain the frequencies », but it must be independent of 7, for else the equations of motion of the system would depend on 4, whereas the conception “equation of motion” involves, that they are perfectly determined by the condition of tie system at a given instant (the qs and p’s and constants), and that they do not contain a quantity as @, which is not characteristic of the individual system, but of the ensemble. If the condition that g must be independent of 6 did not exist, then it would be easy to find several solutions for the integral equations (5). With this condition it seems to offer rather ereat difficulties *). 1) The integral equation can in general be brought into the following form : 2 vh e a Gf (q-+Pp) een ee Idgdp = 0. 8 rh | peg eae It is possible that ; may be split up into a product of functions f(g, +) each of Which contains only one variable and the number of vibrations belonging to it. In this case the equation for the determination of f(g, v) may be written; 1182 Yet 1 have thought it useful to draw attention to this equation as its solution would be an important step on the way which leads to the drawing up of a system of dynamics from which not the spectral formula of Rayieicu, but that of PLanck would follow. ln this system of dynamies the equations of motion can of course not be brought into the form of Hamiiron. Instead of the law of conservation of density in phase, which follows from this form of the equations of motion, another relation can be derived, which is found as follows. In order that the state is stationary, it is of course required that the probability of phase for a point with constant coordinates is constant. If we indicate the time derivative for such 0 : a point with re then we have in the case of equilibrium: ~ Of fe tty a Ot 0g Op dy, op 2. DPS 2 pe) Ss F oe iG i 3 )= _ G ae Op >) It follows from the form of P that we may also write: 0g dp —S — ak. ~ 1 (i= oe) When the function g is aan by solution of the equation (5), then (6) is a relation which the equations of motion must satisfy. It has for the modified mechanics the same significance as the thesis of LiouvitLe has for classical mechanics. or § 4. The equations of motion of the electrons. Though the vibrator does not figure explicitly in equation (6), the values of q and p occurring in it are determined by the properties of the vibrator. For the motion of the electron we can deduce the following equations. We start from the expression for the electrical force of which the Y-component can be represented by : Se In the original Dutch paper there is an error in these two formulae and in equation (51, which | have corrected in the English translation. 1183 €, = > (qa + 7) cos 220 we sin 2a vy sin 20 we 4- m m denoting the electrical moment of the vibrator. From this expression follows : dE, (- BS) a =< ey E, ie , = r)\| — 00; == —= (qa +. q a) COS S2MUUSIN aT VY sin 2 we Oy Oz, < : a dm Azr* dt and in connectiun with (2) and with equations of the form va’ = c(vy — wp): {q+ rp) a 4 (9! +arp') a} cos 2a ux sin 220 vy sin 20 we = a dm a eer me dcese gigs The divergence of the vector in the lefthand member of this equation is zero, and so also that of the vector in the righthand member. We can therefore represent it by : = (Ga + oa’) cos 2a we sin 2 vy sin 2a we. Equation (7) being satisfied identically in 2, y and z, we have qm =o q + rp'=o' Sate rn ee 1G) Differentiating these equations respectively with regard to g and Qeawe eli: 09 eo 0g’ pee ‘ [=5 Tei oS 7S) If we treat the expressions for the components of /) in the equa- tions (2) in the same way, we find: p = 1) = 10) p' — rq’ ==): . : : . . (8a) and - Op Op! EY ae. Ls, we >, (98) Op Op and therefore : dg Oop\ 1 dp- dg- do — 5) || = 4b S| JS = —— oy = aoe! f late?) ae) When g is known, we can substitute in (10) the values for q and p from (8) and (8a) and so we get a relation which the coefficients 6 as functions of g and p must satisfy. The value of the os on the other hand depends upon the value of 9 as a function ae dm | : a ; of w, y, and z and upon the velocities («. a in equation (7) ) which ¢ i Proceedings Royal Acad. Amsterdam. Vol. XV, 1184 ihe electron assumes under influence of the field determined by q and p. § 5. Conclusions. In the above considerations I have tried to show that it is possible to account for the partition of energy in the normal spectrum with the aid of differential equations, which admit of a continuous emission and absorption of energy, and that it is therefore not necessary for the explanation of the normal spectrum to have recourse to the supposition of quanta, either of energy or of “aetion’’. For this explanation it is necessary to draw up a system of mechanics, in which a relation of the form (6) takes the place of the equation of Liovvinte in “elassical”’ mechanics. In order to determine this equation further knowledge of the function gy would be required, which function can be found by solution of the integral equation (5). I have however not succeeded in this solution. If such an explanation with the aid of continuous equations is possible for the partition of energy in the spectrum, then this will also be the case for the variation of the specific heat with the temperature, which follows from this energy partition. Chemistry. — ‘Hevatriene 1, 3, 5.” By Prof. P. van Rompureu. (Communicated in the Meeting of February 22, 1913). In previous communications, published in this Proceedings '), an account was given of the results of an investigation carried out jointly with Mr. van Dorssen and which had led to the prepa- ration of the above hydrocarbon. Owing to the departure of Mr. vAN Dorssen the continuation of the study of hexatriene has expe- rienced considerable delay. Since then, however, a fairly considerable quantity of this substance has been prepared and kept in sealed bottles. As hexatriene as might be expected from its analogy with other unsaturated compounds (and what also proved to be the case)-ex- hibited a tendency towards polymerisation particularly on warming, 1 have submitted the contents of the bottles which had been kept for five years, to investigation. On distillation fully 50°/, passed over below 80°; the residue in the flask was then distilled in vacuo. At + 100° about 30 °,, passed over whilst in the flask was left behind a colourless, very viscous mass which dissolves in benzene. From this solution it is again pre- cipitated by acetone or alcohol. [f the residue is heated more strongly, 1) Nov. and Dec. 1905; June 1906. 1185 there remains a colourless, transparent, gelatinous product which swells in contact with benzene, but does not dissolve therein. The liqnid boiling at about LOO’ in vacuo, when distilled at the ordinary pressure passes over at + 215° with formation, however, of produets with a higher boiling point. Afier fractional distillation in vacuo the bulk was obtained as a perfectly colourless liquid which is more viscous than hexatriene (b.p. 99°.5 at 16 mm. pressure). The elementary analysis (found: C 89.438, H 10.1; calculated C 89.91, H 10.09) and the vapour density determination (according to HOrMANN: found 5.5; calculated 5.5) led to the formula C,, H,,, so that the sub- stance is to be considered as a dimer of hexatriene. D.11 = 0,880 nil = 1.51951 MR = 55.2 Calculated for C,, H,, |F 53.54") matt} The density is considerably higher than that of hexatriene (0.7498 at 13°) whereas the exaltation of the molecular refraction is mueh smaller. This is particularly striking when we compare the spec. exaltations. For hexatriene ES), = 3.125 For the dimer E =), = 1.037 The dimer of hexatriene readily forms an additive compound with one mol. of bromine; on further addition much hydrogen bromide is eliminated. It is rapidly oxidised by a solution of potassium permanganate. The investigation thereof is being continued. The method by which hexatriene was formerly obtained (inter- action of formic acid on s. divinylglycol) did not exclude the possi- bility that it might be contaminated with hydrogenated derivatives thereof and hence it was thought desirable to try other means and get it in a pure condition by regeneration from crystalline deri- vatives. Mr. Mutter who for a considerable time has been engaged on the study of hexatriene has succeeded in regenerating the hy- drocarbon from the beautifully crystallised dibromo additive com- pound. By treating hexatriene with sulphur dioxide he has also obtained a solid product, the investigation of which is not yet con- cluded and from which the hydrocarbon may be prepared also. It was further to be expected that hexatriene would also be for- med by dehydration of the hexadiene 1.5-ol 4, which alcohol might be obtained by reduction of the divinylethylene oxide recently deseri- ') Here it has been assumed that with elimination of two double bonds, a ring has been formed, as suggested by the high density. ox ~ C Or Ce; 1186 ° bed by Mr. tx Hevx'). The yield of the alcohol from the oxide, already so difficult to prepare, was, however, so small that the ap- plication of this method was out of the question. Jointly with Mr. van Dorssex, I endeavoured some time ago to prepare this alcohol according to the method applied by Ferro. Tiemann and R. Scumipt*) in the preparation of homolinalool where they allowed a mixture of allyl iodide and methylheptenone to act on granulated zinc. With acraldehyde and allyl iodide we did not get a successful reaction. Nor did we succeed in obtaining the desired aleohol by the interaction of these substances in ethereal solution oy “activated” zine (Griepsronk and Trise), whilst in an experiment with 70 grams of zine filings, 60 grams of allyl iodide and 60 grams of acraldehyde only a slight action took place, so that we refrained from further experiments. Mr. te Hevx has tried, in vain however, to obtain the desired alcohol by means of allyl bromide, acraldehyde and magnesium. The favourable result obtained by Dr. C. J. ENKLAaR *) when ap- plying the method of Fouryrer *) to crotonaldehyde for the prepara- tion of the heptadiene 2.6-ol +4. induced Mr. Le Hevx to allow (according to Fourniger’s directions) allyl bromide, zine turnings and absolute ether to act on acraldelyde with the object of obtaining the alcohol in larger quantities. With a yield of 30°/, of the theoretical quantity, the hexadiene 1.5-ol 4 was now obtained as a liquid boiling at 132°.2 — 132°.4 under 769 m.m. pressure. The elementary analysis and the vapour density determination confirmed the for- mula C,H,,0. a1, = ().8698 nit? = 1.45231 MR = 30.44 calculated 30.498 The odour of the alcohol reminds of that of allyl alcohol but it does not produce the irritating after effect, however. With acetic anhydride and a drop of sulphurie acid the acetate is formed as a liquid boiling at 151°.2 — 152°.7. Phosphorous tribromide yields the bromide (bp. 59°-—63° at 35 mm. pressure) which very readily absorbs 1 mol. of bromine; a further addition of bromine acts but very slowly without, however, yielding hydrogen bromide. From this alcohol Mr. Mvnier has obtained a hydrocarbon, by the 1) Proe. April 1912. *) B. 29, 691 (1896). 8) Chem. Weekbl. 10, 60 (1912). 4) Bull. Soc. Ch. [8] 11, 124 (1894), 1157 action of potassium hydrogen sulphate as well as of phthalic anhy- dride, which, judging from provisional experiments consists of hexatriene. In consequence of the fact noticed by Dr. C. J. ENk1AAR (loc. cit.) that the homologue of hexatriene which he prepared can be obtained in a crystalline condition by strong cooling, Mr. Munien has cooled a freshly prepared and carefully fractioned specimen of hexatriene in a mixture of solid carbon dioxide and alcohol and obtained it also in the crystalline form"), so that this fact may be utilised for the purification of this hydrocarbon. Finally it may be mentioned here that Mr. Le Hnvux, by reduction of the chloroacetine of s. divinylglyeol with a copper-zine couple in ethereal solution with addition of hydrochloric acid, obtained a liquid boiling at 77°—81° which on strong cooling beeame crystalline and consists very probably of hexatriene 1, 3, 5. At any rate it yields with bromine a dibromide identical with the dibromide from the said hydrocarbon. Utrecht. Org. Chem. Lab. Univ. Physics. — “On Linstein’s theory of the stationary gravitation field By Prof. P. Enrenrest. (Communicated by Prof. H. A. Lorentz). (Communicated in the meeting of Febr. 22, 1913). § 1. Let a “laboratory” “ with the observers in it have some accelerated motion with regard to a system of coordinates a, y, 2, which is not accelerated. Let it e.g. move parallel to the z-axis with some positive acceleration or other. Then the observers will find that all the inert masses which are at rest with regard to the laboratory, exert a pressure on the bodies which are in contact with their bottom side. There are two ways for these observers to explain this pressure : a. “Our laboratory has an acceleration upwards, hence all inert masses press on the bodies under them.” J. “Our laboratory is at rest. A field of force acts in it, which pulls the masses down.” Observations on the course of the rays of light seem to make it possible to decide experimentally between the suppositions a and J: with regard to the system of coordinates x,y,z the light travels rectilinearly. Hence with regard to an accelerated laboratory cwrvi- linearly. By means of this curvilinear propagation of the rays of light the observers might therefore ascertain that their laboratory has an accelerated motion. ') Preparations which have been kept for some time and then contain polyme- rides do not solidify even at this low temperature. 1188 The possibility of snech an experimental decision disappears imme- diately when also in a stationary laboratory, in which there is a field of force, the rays of light are admitted to have a corresponding curvature. The “hypothesis of equivalence” on which Ester bases his attempt at a theory of gravitation *), really requires such a curvature of the rays of light in a field of attraction. The hypothesis of equivalence, namely, demands that a laboratory L’, which rests in a jield of attraction, is equivalent with respect to all physical phenomena with a laboratory L without gravitation, but accelerated.” It is therefore required that the observers which are in ZL, cannot ascertain in any way by experiments, whether their laboratory has an accelerated motion, or whether it is at rest (in a corresponding field of attraction). So we are here concerned in the first place with an attempt to extend the theory of relativity of the case of uniform motion of a laboratory to that of non-wrzform motion. The physical significance of E:sterin’s hypothesis of equivalence would, however, chiefly lie in this that it requires acertain functional relation between the field of attraction and other physical quantities (e.g. the velocity of light). When working out the hypothesis somew hale more closely, ErNstErn is confronted by certain difficulties. These led him to pronounce the supposition *) that the theory of equivalence would possibly only be valid for infinitely small regions of space and time, and not for finite ones. Erysters confined himself here to a mere supposition, as the said difficulties only presented themselves in the consideration of the dynamic phenomena in the laboratory L’, and he had to do there with derivations from so great a number of suppositions, that it becomes difficult to see, where the difficulties arise from: the hypo- thesis of equivalence, or one of the other more special suppositions (as e.g. concerning the dynamie actions of rigid kinematie connections). The following considerations try to throw light on this question. They show that similar difficulties already occur in those phenomena which are the most elementary in Ernstery’s theory: in the propa- gation of rays of light in a statical field of attraction. The principal result is: AJl/ the statical fields of attraction with the exception of a very particular class, are in contradiction with Einstein's hypothesis of equivalence. Already the statical field of 1) Ann.*d. Phys. Bd. 35 (1211) p. 898; Bd. 38 (1912) p. 355 and 443. 2) Ann. d. Phys. Bd. 38 (1912) p. 452—456. 1189 attraction brought about by several centres of attraction which are stationary with respect to each other, is not compatible with the hy po- thesis of equivalence. § 2. Let, therefore a laboratory Z' be given, in which there is a statical field of attraction. With Einstein we suppose that the rays of light propagate in it curvilinearly in some way or other, but so that the following conditions are satisfied : When once a ray of light may have passed through the points A, B,...F, G of the laboratory L'*), then [A] this way A, b,...#, G must ahvays be possible for the light (“Constancy of the ways of light’), [B] the reversed way G, F,...B, A must also be always possible (“reversibility of the ways of light’). The hypothesis of equivalence now compares this laboratory L’ resting in the field of attraction with a laboratory 4 which is free from gravitation, but bas a corresponding acceleration instead. //ow must the points of this laboratory in which there is ro gravitation move, so that the observers in it shall observe constancy and reversi- bility of the ways of light in the sense of the hypothesis of equivalence ? § 3. For the sake of simplicity we confine ourselves to a two- dimensional laboratory “L. As fundamental system of coordinates, with respect to which 4 moves in an accelerated way may serve the system of coordinates w, y, which has no acceleration, and the time ¢ measured in it. With respect to this system which is without gravitation, the rays of light move in straight lines and with constant velocity 1. In the corresponding wx, y, +world-space of Minkowski every optical signal travelling in this way is represented by a straight line forming an angle of 45° with the ¢axis. Such a line in the x, y, t-space is called: “a line of light’. The motion of the different points A, b,...#.G of the moving laboratory / is represented by the same number of (curved) world lines a,b... /, 4. When the observers in the laboratory JZ state that they have succeeded in making an optical signal S, pass through the points A, b,... 4, @ of their laboratory this means that the corresponding line of light s, intersects the world lines a,6,.../,g of these points of the laboratory. According to condition [A] of § 2 the observers in the laboratory Z must in this case be able to send light signals .S,, .S,... through 1) These points may be imagined e.g. as apertures in the walls of the laboratory. 11S0 the points A, B,... FG of the laboratory at other moments as many times as they like. Geometrical representation in the 2, y, /space : The world-lines a,6,.:.f,g are intersected by all the oo! lines of light s,,s,...; they all lie on the ruled surface formed by the oc’ light lines.- In agreement with condition [B] of § 2 the observers of the laboratory Z must then moreover as often as they like ‘be able to send optical signals S’,, S’,... in opposite direction G, F,...B, A. In the 2, y,¢space again oo' light lines s’,,s’,,... correspond with ‘his, which all intersect the world lines a, 6,...7,g. Hence the world lines a,6,...g,/ all lie on a surface covered by two systems each of o* light lines. If we then bear in mind that the light lines all make an angle of 45° C. with the Gaxis, it is easy to see that such a surface must necessarily be an equilateral hyperboloid of revolution with the axis of revolution // to the ¢axis; i.e. the equation of this surface has the form: A(v?+-y? —#) -+ Be + Cy+ Dt+H=0... . (il) In particular the case may also present itself that A= 0, ice. that the hyperboloid degenerates into a plane. Such hyperboloids will be briefly called ‘“light-hyperboloids”’. Ac- cordingly the world lines a,/,.../,g of the points A, b,...F,G of the laboratory Z lie on a common “light hyperboloid” Hy. Now the observers. might just as well have sent a light signal instead of from A to 2B, from A to any other point 45’ of the laboratory. In exactly the same way we see then that also the two world lines a and 4’ must lie on a common light hyperboloid H,,. Let the equation of this be: Ale? +y?—t) + Be+Cy+Dt+E'=0.... Q) So the world line a les at the same time on two different light- hyperboloids H,, and H.; it is the section of both, and this is necessarily a plane section. (Multiply equation (1) by A’ and equa- tion (2) by A, and subtract). If we now bear in mind that the point A of the laboratory must never have a greater velocity than that of light, of all the plane sections of a light-hyperboloid only two types deserve consideration: hyperbolas the two branches of which run from ¢= —o to t=-++ o, and as limiting case the light lines of the hyperboloid. (In other words the sections with planes which 1 cut the gorge circle of the hyperboloid, and 2 make an angle of < 45° with the Gaxis. As besides, the case may occur that the light hyperboloids which pass through the world line a, degenerate to planes, the world line » may also be a straight line, making an angle with the ¢axis, which is smaller than 45°, 1191 A, however, was an arbitrary point of the laboratory L. So we have proved the following : “If the observers in a moving laboratory Z, which is without gravitation are to observe constancy and reversibility of the ways of light, it is necessary that the “world-lines” of the points of the laboratory are a system of o* branches of lhyperbolas, or else straight lines in the 2, y, -space.” Without a new supposition, only in consequence of the cireum- stanee that through every pair of these world-lines eg. p and q — can always be brought a light hyperboloid //,, ‘), it ean further be proved: that the «* world line hyperbolas lie in x! sarfaces, which pass fanlike through a straight line I of the x, y, space; they cut I in two real or conjugated imaginary points 2; and 2,, (which may also coincide). In this way dependent on the situation of the points 2, and 2,, ow" fields of world lines originate, which are of a very particular nature. *) § 4. The frequency of the static fields of attraction caused by n centres which are stationary with respect to each other, is already greater than o° for n23. But the “hypothesis of equivalence’, cannot be satisfied in any other case than in that of the very special fields of attraction, which correspond to the ow" fields of acceleration of the preceding §. REMARK. Up to now we have only used the constancy of the form of the rays of light. Moreover in every point of the laboratory L’ the velocity of the light must also be independent of the time. In order to introduce this condition, the measurement of time in L’ would have to be taken into account in the considerations, which renders them more intricate. Possibly the class of fields for which the hypothesis of equivalence is admissible, might then be still further limited. The field of hyperbolas which in the w, y, ¢+space represents Born’s “motion of hyperbolas” of a two-dimensional laboratory, is contained in the oo° fields of hyperbolas of § 4 as a special case. Moreover it satisfies (with suitable measurement of time in L’) the condition that the velocity of the light is independent of time. 1) Formed by the lines of light of the signals, which may be sent from P to Q, and from Q to P. *) A proof for these theses and a classification of the above mentioned c® fields of world lines is found in a paper by Mr. Cu. H. van Os, which will shortly appear. 1192 Astronomy. — “The variability of the Pole-star.” By Dr. A. PANne- KoEK. (Communicated by Prof. E. F. vay pe Sanpr BakauyzeEn). (Communicated in the meeting of January 25, 1913). A slight variability of @ Ursae minoris has already several times been suspected by different observers (SkmDEL, Scumipt). When in 1889 and 1890 I executed a great number of observations (estimates with the naked- eye after ARGELANDER’s method) for the determination of the brightness of the stars of the 2°¢ and 3¢ magnitudes, such great differences showed in some of these stars, that they were being observed as regularly and as often as possible in the following years with a view to probable variability. Among these stars was also the Pole-star'). In 1890 I found that the period was about 4 days; each time 2 days after a great intensity came a faint one and the reverse. I did not succeed, however, in finding an accurate value for the period. From the observations in December 1890 I found two maxima or Dec. 7.0 and Dec. 29.8 (in reality they occurred on Dec. 6.6 and Dee. 30.4), which yielded a probable period of 3.8 days; this however did not agree with the observations of that winter. After all it must mdeed have been hopeless to derive the elements of the variation from these observations only. As the mean error of an estimate amounted to 0.7 of the whole amplitude, as appeared later on, it might even happen that a maximum and a minimum seemed to have changed places owing to errors of observations. Moreover the remembrance of the results of previous days may spoil an observation. If on one particular day the star has, perhaps wrongly, been estimated very faint, one expects to see it very bright two days afterwards, and this may influence the estimate. On the other hand the small number of observations in a given interval of time, say a month, owing to bad weather, did not allow to counteract the uncertainty of the separate estimates, by uniting a great number into a normal place. | have long continued the observatious of this star, up to 1899, in order to have material for a closer investigation, in case the variability should be proved and the period should be accurately known. In 1898 Camppett discovered that the radial velocity of this star is variable and hence that it is a spectrocopic double star with a 1) The other stars in which I consider variability to be probable, although L cannot prove it with certainty owing to the smallness of the amplitude, are ¢ Tauri (period of a few days), 40 Lyncis (26 days) and x Herculis (14 months); the latter two are of a red colour. 1193 period of 3.968 days. Lack of time, because of my work at the observatory, prevented me from immediately reducing my observations by means of this value for the period and so testing the variability. The probability that @ Ursae minoris was indeed a short-period- variable of the type of fd Cephei grew stronger, when I found in 1906 ') that it showed the same peculiarity in its spectrum as those stars (c-character after Miss Maury) and has, as all stars of short period of this type, an extraordinary slight density. In a footnote attention was already drawn to these moments of probability. Starting from the consideration, that for all these short-period- variables the photographic amplitude is much larger than the visual one, Herrzsprunc at Potsdam has thereupon (in 1910 and L911) taken a great number of photographs (418 plates in 50 nights) of Polaris, and from this settled with absolute certainty a variability with an amplitude of 0.17 magnitude *). For the epoch of maximum light he found J. D. 2418985.86 + 0.08 Greenwich M. T. Subsequently J. STEBBINS has executed a number of photometric measurements with lis exceedingly sensitive selenium-method in 1911—12; these also clearly show a variability with a visual amplitude of 0.07 magnitude *). The epoch of greatest brighness as found by him, viz. J. D. 2418985.94 Gr. M. T. agrees very well with Hertzsprune’s result. I have also reduced my observations of 1890—1900 with the aid of the periodic time 34.9681, as spectrographically found. In the second half of each year | used for comparison the stars of Perseus and Andromeda, in the first half those of Ursa major. Thus the observations form two mutually independent series, partially over- lapping in wintertime. For the 1s* series @ Persei = 6.3, 8 Andromedae = 3.8, 7 Andromedae = 3.1, and exceptionally @ Arietis = 5.4 and « Andromedae = 2.3 were used as a scale of comparison-stars ; for the 2°¢ series served ¢ Ursae maj. = 2.4, 7, Ursae maj. = 0.0, and, exceptionally, « Ursae maj. = 4.0. The observations were not corrected for atmospheric extinction, since this influence disappears in the mean of many observations and at the most can make the mean error seem too great. Taking all together, from 1890 up to 1899 259 comparisons with the Perseus-Andromeda-stars were available and 251 comparisons with those of Ursa major. With the aid of the periodic time 3.968 all epochs of observation were reduced to ') See A. Pannekorx. The luminosity of stars of different type of spectrum. Proceedings Acad. Amsterdam 9, 1906, p. 134. *) Astronomische Nachrichten 4518 (Bd. 189, 89). 5) Astronomische Nachrichten 4596 (Bd. 192, S. 189). 4194 one single period, viz. Aug. 8—7 1894, and subsequently united into normal places. These normal places are the following: First series Obs.—Cale. Second series Obs.—Cale. Aug. 3.12 3.72 (18) + 0.03 Aug. 3.21. 0.59 (18) —0.03 3.42 3.94 (16) + 11 3.18. 0.68 (16) — 08 373 411 (21) + 08 3.65 0.59 (18) — 28 396 3.91 (17) —— 29 3.92 113 48 + O07 199° 3.94 (20) — 42 4.25 1.39 (20) + 10 4.54 468 (17) + 18 4.46 1.40 (22) 00 4.76 4.86 (16) + 33 4.65 1.69 (24) + 22 4.94 4.76 (16) + 24 4.94 1.55 (14) + 05 rea os b bulge eee 592 4.20 (17) — 22 5.52 4.45 (14) + 19 5.46 4.97 (18) — 308 5.76 441 (20) + 02 5.792.102 (20) 9-2 ne 5.94 3.67 (18) — 29 6.22 0.74 (19) — 04 623° -3:67)(46) = 14 6.48 0.86 (16) + 22 66.9078 (1) E20 6.86 0.67 (16) =a 6.738 3.7949) + 16 Both series show, as does the graphic representation, with un- mistakable certainty a periodical variation of the brightness to an amount of about one scale-unit with a maximum on 4.8 August. The calculation of a sine-formula resulted in (zero epoch 3.0 August): 1st series 4.08 + 0.45 sin (p — 72°0) Maximum 4.79 Aug. + 04.13 2d series 1.03 + 0.47 sin (y —78°9) Maximum 4.86 Aug. + 01.09 3 ia ed bo Ze 8.0 BPAaNSHuUP ATTEN Fig. 1. 4.5 hice 1195 The remaining deviations Obs.—Cale. have been placed in the last column. They yield for the mean error of a normal place do qo $0 60 yo 8.0 vO Fig. 2. according to the mean of the two series, 0.21 (if we adopt this same value for both series, then each maximum has a mean error of 09.11), from which we find 0.84 as mean error of one obser- vation, while 0.7 had been found from the differences between the separate results and the adopted normal places. The deviations of the normal places from the sinusoid, it is true, show a systematic character, in the sense that the maximum is very sharp, the mini- mum very flat, hence that a term with 2 is indicated, the positive maximum of which falls together with the maximum of the principal term. Since, however, nothing of this kind is to be observed in the light-curves of HwerrzsprunG and Sreppsins, no further attention has been paid to this phenomenon. Thus my observations yield as epoch of the maximum, after reduction to Greenwich-time : 1894 Aug. 4.81 Gr. M.T. = J.D. 2413045.81 + 04.08. The interval between my normal-epoch and that of Hertzsprunc J. D. 2418985.86 is 5940.05 days = 1497 periods of 3.9680 days. In order to reduce the brightness of maximum and minimum to the same photometric scale, the catalogues of Potsdam and Harvard were used. For the reduction of the magnitudes given there to the homogeneous scale that has been derived and adopted in my dissertation "Untersuchungen iiber den Lichtwechsel Algols’” (p. 146—158) first a correction was added to the values of Harvard 44, in order to reduce them to Harvard 14. This was derived from the differences between the {wo catalogues, caleulated by Ménimre and Kemper and communicated in their ’Generalkatalog der photometrischen Dareh- 1186 musterung” '), Einleitung S. XXII. For our purpose they were given the following form: H. 44 — H. 14 = — 0.01 + a (c- 4.0) in which ¢ is the colour-number according to Ostsorr and a a function of the magnitude, varying linearly with the difference between the apparent brightness of the star in the two photometers, calculated in the manner as has been indicated on p. XXIV of the same inwwoduction (for magnitude 1.0, 2.0,3.0 we havea = + 0.062, + 0.054, + 0.042). Subsequently to these magnitudes, reduced to H.14 and to the magnitudes of H.14 itself, the correction for colour was added, which has been found in my dissertation p. 158. There is also to be found the correction varying with the magni- tude which has to be added to the results with Photometer C II, in order to reduce them to the same system *). All stars used by me have been observed in Potsdam also with Photometer C III. As they have no excessive apparent brightness in this instrument and hence no variation with the brightness is to be expected in this case, a constant correction —0™.23 was added to the results with C ILL. For the employed comparison-stars, supplemented with a few other stars, continuing the scale further to the fainter side, we give suc- cessively : the colour according to OstHorr, (derived in the manner as indicated in my dissertation p. 168), next the magnitudes of Har- vard 14, Harvard 44, Potsdam C II and C III, all corrected in the way already mentioned, subsequently the adopted simple mean valne from these four and then the brightness in the employed scale of comparison-stars. “1) Publicationen Potsdam 17. : 2) Miter and Kemer have not corrected the results obtained with CII, because they could not discover a systematic difference between CI and CIl (Kinleitung S. XIV). Since, however, for the comparison of these instruments they could only avail themselves of stars belween magnitudes 3.5 and 5.5, this does not clash with my result that a correction is needed for the brighter stars up to the 224 magnitude, which of course can only be found by comparison with another cata- logue. While the comparisons employed by Mitten and Kempr can teach nothing about the absence of systematic errors for these bright stars, the fact that increas- ing negative corrections are needed for CI above magnitude 4.8, and for photo- meter D above magnitude 61 (Einleitung S. XII), renders it exceedingly probable that similar corrections are needed for CIl above magnitude 3.5, such as I deri- ved in my dissertation. The final values of the Potsdam “General Catalog” are there- fore likely to be systematically erroneous above the 3° magnitude. For this reason [ have not been able to use simply the Potsdam system for the magnitudes of the comparison-stars, as would have been a matter of course for fainter stars, By using the Potsdam system 1 should have found the amplitude too small. Star Colour, H 14 | H 44 |P.CIl end IIl Mean Scale | Calc. | | x Persei 3.4 1.94 } 1.88 | 1.87 | 1.95 | 1.91 6.3 | 1.92 x Arietis 5.4 2.03 | 2.10 1.96 | 2.03 5.4 | 2.02 to => <>) _ ~ = Andromedae 6.2 2.20 | 2.05 2°11 1 2e10 3.8 | 2.14 , Andromedae 5.2 2.13 |} 2.19 | 2.09 | 2.14 | 2.14 SeliezskO « Andromedae 1.8 2ROGNE 2.22) | 2eeti| 2a |e Ze Ad 2d) |e 2alo to ~ ioe) to SS) w ol to , Cassiopeiae -24 | 2.23 | 2.28 0.8 | 2.25 tO © bo _ eo bt fol oO to we oa to 8 Cassiopeiae .33 | 2.41 | —1.7 | 2.43 | « Ursae maj. 4.9 | 1.96 | 1.88 | 1.79 | 1.77 | 1.85 4.0 | 1.86 = Ursae maj. 1.8 | 1.86 | 1.89 | 1.98 | 1.847] 1.89 2.4 | 1.89 , Ursae maj. 1.4 | 2.03 | 2.03 | 1.98 | 2.05 | 2.02 0.0 | 2.03 © Ursae maj. 2 Ge) De2O) We Deter || os | 2.20 3.6 | 2.25 « Coronae | 1.8 | 2.39 | 2.38 | 2.32 | 2.39 | 2.37 —4.8 | 2.32 = Bootis | 4.8 | 2.55 | 2.57 | Zo | 2.52 | 2.50 | —5.7 | 2.43 8 Ursae maj. 1.7 | 2.63 | 2.71 | 2.41 | 2.42 | 2.54 | —8.9 | 2.56 7 Ursae maj. | 1.8 | 2.59 | 2.66 | 2.54 | 2.39 | 2.55 | —9.7 | 2.61 The relations between the seale-values m and the magnitudes m are represented by the following formulae (3.7 is the colour-number of « Ursae minoris) : 1st series m= 2.335 — 0.065 n + 0.020 (c—3.7). 29d series m= 2.07 — 0.059 n + 0.020 (e—3.7), The magnitudes of the stars calculated after these formulae are viven in the last column of the preceding table. With the aid of the same relations the sine-formulae for the brightness of «@ Ursae minoris, become expressed in magnitudes : 1st series 2™07 — 07029 sin (y—72°O 26d series 2"™01 — 0™028 sin (g—78°9). So the amplitude of the variation of light amounts to O™057, while we find as mean error of an observation based on the deviations of the separate observations 0.043 and on the deviations of the normal places from the formulae O.051. 1198 bis Among the older material that may serve for the examination ot the variability of Polaris, we must in the first place consider the observations executed by G. MU Lier in 1878—81 at Potsdam for the determination of the atmospheric extinction and published in Vol. Ill of the Potsdam ”Publicationen”. As these observations consist in measurements of the differences in brightness between Polaris and 5 other stars observed in very different zenithdistances, they yield abundant material for the determination of the variability of Polaris For this purpose | have examined the deviations of these differen- ces from their mean value, remaining after correction for mean extinction, which are to be found in Miz.gr’s Table IV, last column but one (p. 261—265). Excluded were all observations in which the zenithdistance exceeded 60° and all those indicated as uncertain by the observer. The others) were arranged according to the phase, counted from 1879 December 12.0 + n 32968. The unit of these deviations is that of the third decimal place of the logarithm of the proportion star: Polaris, i.e. 0.0025 magnitude. In order to give the positive sign to the maximum light, the signs must be reversed. In the following table are given the normal places formed from these deviations reversed in sign and reduced to magnitudes; the number of observations on which each normal deviation depends has been added in brackets. Epoch — Deviation O—C Epoch — Deviation O—C Dee. 12.02 +07022 (25) -+07001 Dec. 14.11 — 0028 (24) — 07012 12.34 + 030 (8) 000 14.50 — 009 (20)-+ O15 12.64 4+ O47 (23)+ 014 14.81— 009(23)4+ 013 12.92 + 008 (20)— 021 15.05 021(25)— 004 13.21 + 028 (48)+ 008 15.20— 048(19)— 036 13.63 + 006 (20)+ 008 1534+ 017@4)+ 023 13.84 — 010 (17)— ~ 004 15.69 + 008 (29)— 001 Here also the variability of Polaris appears with unmistakable clear- ness and it may be expressed by the following sine-formula: Deviation = + 07004 + 07028 sin (gy + 35°) Maximum Dee. 12.61 =1879 Dec. 12.57 + 0.14 M. T. Greenwich The last column of the table contains the differences Obs.—Cale. The mean error of a mean value from about 22 observations is 07016, hence the mean error of one observation O™077. The immense number of photometric meastrements made at the Harvard Observatory, in which Polaris has been used as comparison- 1199 star, have already been condensed into normal values by Prckerine ‘). Calculating the time of maximum light also from the mean devia- tions given by him, by means of a sine-formula, we obtain: Deviation = + 0702 + 0039 sin ‘g + 254°) Phase Deviation O.—C.- | Phase ~- Deviation O.—C O42 +001 (120) +0047 242 + 003 (123) -- 0011 0.6 06 (197) O31 | 2.6 + 03 (179) - O02 a) == OR) sfalisy) O12 30) OO (168) 012 Led Oh GPX 025 3.4 03 (169) 015 1.8 + 09 (126) + 056 Bret 02 (450) + 011 The last column again contains the differences Obs.—Cale. The mean error of a nermal deviation is 0"033. As a positive sign here means a greater brightness of Polaris, the maximum-light oceurs at the phase 24.16 + 07.24. The zero epoch of the phase is at J. D. 2400000 + 3.9683 2; for / = 2078 this becomes J.D. 2408226.29, so that the normal epoch of maximum becomes J.D. 2408228.45 + 0.24. ILI. Putting together the hitherto obtained results for the light-variation ef « Ursae minoris and comparing them with the formula for the maxima given by Herrzsprunc : J. D. 241 8985.86 + 3.9681 F we find the following table: Year Ei. Observed O—C Amplitude Observer 24 1879 — 2845 07696.57 + 0.14 —0"05 07056 vis. MULLER 1881 — 2711 0822845 + 0.24 + 0.11 0.078 vis. Harvarp 1894 — 1497 13045.81 + 0.08 +.0.20 0.057 vis. PANNEKOEK 1910 0 18985.86 + 0.08 0.00 0.171 ph. Herrzsprune 1911. (+100) 18985.94 + 0.09 + 0.08 0.078 sel. Srrepins Attempting to correct with these data Hrrrzsprune’s formula, we find (adopting as weights 2, 1, 4, 4, 4) as correction : + 09.07 (+ 024.06) — 0.00001 (+ 0.00004) Thus for the length of the period the exact value adopted by HerrzsprunG is found. The most probable formula for the maximum- epoch of «@ Ursae minoris now becomes : J. D. 241 8985.93 (+ 0.06) + 3.96809 (+ 0.00004) £. 1) Harvard Circular Nr. 174, Astronomische Nachrichten 4597 (Bd. 192. S. 219), 78 Proceedings Royal Acad. Amsterdam. Vol. XV 1200 Chemistry. — ‘“Lquilibria in ternary systems’ IV. By Prof. F. A. H. SCHREINEMARERS, (Communicated in the meeting of January 25, 1918). We consider a liquid Z, saturated with the solid substance and in equilibrium with the vapour G. We allow this tiquid to proceed along & straight line which passes through the point 7. If we call dn the quantity of solid substance /’ that dissolves in the unit of quantity of the liquid, we get: dx = (a—x) dn dy = (B—y) dn If we substitute these values in (6) (II) and (7) (IT)") we have: — dis AAP Bak os 5 oe fe ee Nisin == Cd P— DED. vr eos - neeone) where for the sake of brevity : , M = (a—a)?r + 2(7—a) (y—B)s + (y—B)*t : N = (x,—a)(a—a)r + (a—a)(y,—y) + (@,—a)\y — is + — Mu — 8) From this follows: DM—BN DM—BN dex dP = ———— . dn = ————_ ,——_ .. .. .. ... (8) (RES AD) BG AV pee CM—AN ae CM—AN dx 4 We BC-AD. BOLD dP DM—BN ; ai GM=aN > a ee As in the previous communication, we assume the very probable case that BC—AD is positive. M If now we call z=« and y= 8 then M=0, N=0 and —_=0, Cue, N : y—Pp but —— does not become 0 as a rule. If -we call tg =—— we a— xz C—€ get: apes Bl(w, —a)r + (y, —8)s ats — as + (9, — BG 9g] dv . (6) BC—AD and for d7’ a same form with this difference that in the numerator B has been replaced by A. To perceive the significance of this we take fig. 1 in which the closed curves indicate the boiling point lines of the solutions saturated with /°. The exphased ones, as has been stated previously, have )) The figures (I, (Il), and (IL) refer to the former communications, 1201 shifted to that side of /’ where the vapour region is situated. On increase of pressure, the boiling point line disappears finally in the point J/, the correlated vapour line in the point J/,. The point PD indicates the vapour which can be in equilibrium with the solid substance / and the liquid /’, therefore the vapour which forms at the minimum melting point of the compound /. The line XF'Y is the tangent in / at the boiling point line passing through /. We have already noticed previously that the lines D/’/ and NY are conjugated diagonals of the indicatrix in /’ at the liquidum side of the $-plane. We now lay down through /' an arbitrary line 7/7, and let a liquid proceed along this line; as according to (6) dP and d7’ have a definite value differing from né/ it follows that in this point neither the pressure nor the temperature is at a maximum or a minimum. If, however, we choose the line in such a manner that * (w,—a)r + (y,—8)s + (ez, —@)s + (y,—BH tap =O . . (7) then dP as well as d7' is nil. From (13) (1) it follows that (7) is satisfied when the line drawn through # comes into contact in # with the boiling point line passing through this point, therefore when the liquid proceeds along the straight line X/'Y. If now we introduce a line element dg positive in the direction away from /’ and negative in the direction towards /, and if we let y change from O° to 360° we have dze=cos gy .do so that (6) is converted into: pe ers WE ae Pose Ee Ga Dae) Fg) BC— AD ‘ The factor (@,—a)r + (¥,—B)s} cos p + (7, —a)s + (¥,—B)H sing (9) in the point # is nil towards X as well as towards }’; in all other directions it differs from nil. If to gy is given such a value that the line passes through the point ) we notice that the factor (9) is positive. Hence, in the point /” the value of (9) is positive in the direction towards D and negative in the direction towards /. We may now easily deduce that (9) is positive if, starting from F’, we move towards that side of the line X/’'Y where the point D is situated; and that (9) is negative when we move from / towards the other side of the line X/’)’. These positive or negative values are, however, very small if the direction almost coincides with FN or /Y so that at some distance a reversal of the sign may perhaps take place. 5 = H— being positive it follows from (8) that the pressure when starting from / increases towards that (at 1202 side of the line V/’Y where the point D is situated and decreases when starting from / towards the other side of the line VF Y. Hence, if a liquid proceeds along the line PD or FM, or FZ the vapour pressure increases starting from F’; if it proceeds along the line FZ, or FG or FE the vapour pressure decreases from /’. Only in the direction of F towards \ or towards ¥ the vapour pressure remains at first unchanged. It will be easily perceived that these considerations are in harmony with tig. 1. For the closed curves drawn in fig. 1 are the boiling point lines of the solutions saturated with /’; each curve, therefore, applies to a definite constant pressure. As the pressure becomes higher, these curves draw nearer to J/ to tinally disappear in this point. Of course, it may happen also that on increase of pressure a curve moves away entirely or partially from J/ to again draw nearer to JM at a further increase of pressure. In the point / this, however, is not the case; we have already demonstrated that the part of the boiling point line passing through /’ situated in the vicinity of / moves on increase of pressure towards J/, and on reduction of pressure away from J/. Fig. 1. Fig. 3. In fig. 2 the line ZZ, represents the same line of fig. 1; the part /’Z lies, therefore, at the same side of \/’Y" where the point D is situated; the part /’Z, lies, therefore, at the other side. Perpen- dicularly on the line ZZ, we place the pressure axis, hence the vapour pressures of the liquids saturated with /’of the line Z/'Z,. As 1208 according to our previous considerations the pressure increases from F towards Z and decreases towards 4, the vapour pressure curve in #” must have a direction like curve af’). As the line /'Z comes info contact with one of the exphased boiling point lines, the pressure in this point is a maximum; on the curve aF”/ of fig. 2 a maximum vapour pressure must, therefore, occur somewhere between a and /”. If, however, the line Z7/Z, of fig. 1 is turned in such a manner that it keeps on passing continually through /’, the curve af’ of fig. 2 will change its form although it will of course, also keep on passing through #”’. From our previous considerations it follows at once that the direction of the tangent in /” and the position of the point with maximum vapour pressure changes. If ZZ, coincides with \/FY we obtain in fig. 2 a curve c/’d with a horizontal tangent in 1” We have assumed in fig. 1 that the boiling point line passing through /’ is curved in the point / in the direction towards D; in our previous communication (11) we have noticed, however, that, in the vicinity of /° it may be curved in some other direction also. It may then present a form such as curve aF% of fig. 2 (II) in Which, however, we must imagine the arrows to point in the opposite direction. We have deduced this form while assuming that the vapour contains one of the three components onty. Although- in this case, the appearance of such a form is not very likely, the possibility thereof is greater when the vapour contains the three components and when, for instance, in the system LG a maximum femperature occurs. We now imagine through point /’ of tig. 1 and also at somewhat higher and lower pressures, boiling point lines of this form. Lines proceeding from /” towards that side of VF Y where the point J is situated will then each again come into contact with a boiling point line, so that a pressure maximum must occur. Lines which proceed from / towards the other side of V/’Y either do not come into contact with a boiling point line at all, or else they meet two of these, so that there oecurs one point with a maximum and one with a minimum vapour pressure. The latter ease will occur on lines in the vicinity of “NX and FY”. On turning the line ZZ, of tig. 1 we will, therefore, have vapour pressure curves like af’) of fig. 2, further like a/”) of fig. 3, and if ZZ, coincides with NF Y of fig. 1, a vapour pressure curve cF'd of fig. 3. In order to investigate the change in temperature in the point F’ on the lines passing through this point we take the formula corresponding ,with (8): | 1204 | AL @,—@) rE(y, —B) 8} 208 + f(@,—a) s +(y, 8) 0} sin g a - - — do. (10) BC—AD rf in which A=V — v therefore positive or negative. From this it follows that d7’ will be ni/ when (9) is ni/, therefore when the line drawn through /’ coincides with the tangent Y/Y in F at the boiling point line passing throngh this point, or what amounts to the same thing, at the saturation line under its own vapour pressure. We now distinguish fwo cases. \”>v. The saturation lines under their own vapour pressure are now situated as in fig. 14(1); we now imagine, in this figure, the tangent drawn on to the saturation line under its own pressure, passing through /. As in fig. 1 we will call this Y/Y. The point corresponding with the point D of fig. 1 is, of course, situated in tig 14(1) on the vapour line correlated to the saturation line under its own vapour pressure which passes through the point /. Hence it is situated, as in fig. 1 to the left of the line VFN. If now we move in tig. 14(1) from /’ towards that side of the line NE)’ where the point YD is situated, then, as follows from (10), ihe temperature increases starting from /’; when moving towards the other side of the line Y/Y the temperature decreases from F’. After the previous considerations in regard to Fig. 1 it is evident that this agrees with fig. 14 (1). If in this figure we imagine a line drawn from / towards that side of V/')” where the point D is situated this will come into contact with one of the exphased satu- ration lines under their own vapour pressure. As each of these curves belongs to a definite constant temperature differing, of course, from curve to curve, the temperature in this point of contact is a maximum one. If now in fig. 2 we imagine the pressure axis to be replaced by the temperature axis we again obtain a curve like a/”) with a maximum temperature between a and /”. If in fig. 14 (1) we turn the line passing through / until it coincides with V/')’, the curve al’h of fig. 2 is transformed to curve cF’d of this figure. Should the case oceur that in / the saturation line under its own vapour pressure becomes curved away from PD, we obtain curves as in fig. 3 in which we must again imagine the pressure axis to be replaced by the temperature axis, Vv. In the P7-diagram of fig. 4 aA represents the sublimation, 1206 AF the three-phase and Fi the melting point curve of the compound F’; these three curves are therefore the same as the homogeneous curves of fig. 3 (LI). The direction of the melting *point curve /d fig. 4) is determined by: dP Hy erie From (12) it follows that, in point F of fig. 4, the P7*curve ZIZ, must come into contact with the melting point line Fd. The further course of this P7-curve in the vicinity of the point # may be traced in the following manner : We proceed in fig. 1 from /towards Z,, PR thus becoming negative. a) From (J1) it now follows that remains positive so that the curve 7 must be situated like curve FZ, of fig. 4. If. in fig. 4 we move from F towards 7, R becomes positive. A being small, the denominator of (11) will soon become n// so that curve FZ of fig. 4 must have a vertical tangent in the vicinity of the point /. If in fig. 1 we move further from / towards 7, then 5 J e from (11) will become negative first, and n/ afterwards, so that t } dP curve FZ of fig. 4 must have a horizontal tangent. As a after- wards becomes positive, curve /Z is bound to fall at a decreasing temperature. Proceeding from point 7 we find on curve Z/Z, first a pressure- and then a temperature maximum, further a point of contact with the melting point line /d of the compound / at the minimum melting point of the compound and finally a receding branch /Z,. All this reminds of the P, 7-curves deduced by Van per Waars for solid + liquid + gas in binary systems, To some differences, for instance that the P?, 7-curves mentioned here do not meet the sublimation line of / in the maximum subli- mation point, I will refer later. In fig. 4 it has been assumed that curve ZZ, exhibits a double point 4, namely a point of intersection of the branches #Zand FZ. In order to perceive the possibility of a similar double point we take a cireumphased boiling point line (fig. 1). On this occurs a point with a maximum and another with a minimum temperature. These points divide the boiling point line into two branches and in sueh a man- ner that to each point of the one branch appertains a definite point of the other branch, namely in that sense that both points indicate 1207 solutions of the same temperature and the same vapour pressure, and saturated with 2. Of all straight lines which unite two such correlated points of the two branches one is sure to pass through the point / If now, we allow the line Z/’Z, of fig. 1 to coincide with the above men- tioned connecting line, we then find two solutions situated at different sides of #, which have the same temperature and the same vapour pressure. The branches /'Z and FZ, of fig. 4 then must intersect each other at that temperature and pressure. Vwhat has been said previously, we will still consider a few of these points in another manner. On warming the solid compound /’, this, as mentioned previously, proceeds along the sublimation curve a A of fig. 4 until the upper sublimation point A’ is attained ; then the equilibrium: solid #7 + liquid +- vapour is formed which proceeds along the three-phase line AF of fig. 4 until the melting point line /d has been obtained. We have already noticed previously that the liquid and vapour continually alter their composition therewith and we may now ask what curves they proceed along in fig. 1. 1210 At the temperature 7’x of fig. 4, therefore at the upper sublimation point of the compound F/ the vapour has the composition / and the liquid which can be in equilibrium with that vapour the com- position A’ of fig. 1. At the temperature 7 of fig. 4, therefore at the minimum melting point, the vapour has the composition D and the liquid the composition / of fig. 1. Whereas the compound F proceeds in the P,7-diagram of fig. 4 along the three-phase line FK the liquid in fig. 1 proceeds along a curve from A’ towards F and the vapour along a curve from /’ towards D; we will call these curves the curves AF and FD. We now imagine drawn in fig. 1 some more boiling point lines of the solutions saturated with # among which also those passing through the point A’; on each of these a maximum and aiminimum temperature occurs. The curve AF’ now intersects each of the boiling point lines situated between A’ and /° in the point with the maximum temperature, or in other words the curve A’ is the geometrical place of the points with a maximum temperature on the boiling point lines situated between A and F. The liquid and vapour of the three-phase line A/’ of fig. 4 being formed from the solid substance /, the three points /, Z, and Gin fig. 1 must always lie on a straight line. This means that the temperature along the boiling point line of such a liquid is a maximum or a minimum one. From a consideration of fig. 1 it follows that here the temperature in this case is a maximum, from which follows at once what has been’ said above as to the course of the curve AL’. In the same manner we find that the curve /D also intersects each of the vapour lines conjugated with the boiling point lines in the point with the maximum temperature. F In fig. 1 we might also have drawn instead of the boiling point lines the saturation lines of / under their*own vapour pressure. We then should’ have found that the curve AF’ intersects each of these lines in the point with the minimum vapour pressure. We now turn the line Z/Z, of fig. 1 until it intersects the curve AF of this tigure; the corresponding ?,7-curve in fig. 4 must then meet the three-phase curve /’A in a point. For in the point of intersection of the line ZZ, and the curve A¥ in tig. 1 the pressure and tem- perature for both curves is namely the same; as, however, the curve KF’ passes through the points with maximum temperature of the boiling point lines in fig. 1 and as this is not the case with the line Z/'Z, a higher temperature (the pressure being equal) is found on curve AF’ than on the line Z/Z,. The P,.7-curve of the line 1211 ZFZ, therefore comes into contact with the three-phase line AT’ of fig. 4 and is situate further above and to the left of this three- phase line. In order to deduce something more from the P?,7-curves, we take a temperature 7; lower than the minimum melting point of the compound /. The saturation line of / under its own vapour pressure has at this temperature 7’z a form as in fig. 7 (1) or 11 (1); the minimum vapour pressure in the point in of this saturation line under its own pressure we call 7P,,, the maximum pressure /y;. Of all the equilibria of # + liquid + gas appearing at the temperature Tz, the highest vapour pressure is, therefore, 4, and the lowest P,. If, in fig. 4, we represent both pressures by the points M/ and m, one P.7-curve passes through the point Jf and one through the point m, whereas ail the others must intersect the perpendicular line placed in 4 between Jf and m. One obtains the P, 7-curve passing at Ty, through the point J/ when the moving line Z/'Z, of fig. 1 coincides with the line 437, and the one passing through the point m when the line Z/’Z, coincides with the® line 2),.0f sigs 7 (nor 11 (1). In fig. 4 two P,7-curves must pass through each point between J and m. For if we choose a pressure P? between /?y, and P, we notice from fig. 7 (I) and 11 (I) that at the temperature T, two different systems: solid /’ + liquid + gas have a vapour pressure P, from which it follows at once, that in fig. 4 two P,7- curves must pass through each point between J/ and iv. If on the curve Mam of fig. 7 (1) or 11 (1) we imagine two points of equal pressure connected by a straight line, we notice that there must be a definite pressure 7, at which this conjugation liie passes through the point 7” If now, the straight line 7/’Z of fig. 4 passes through this conjugation line, the corresponding 7, 7-curve at the temperature 7’; and the pressure P; must exhibit a double point. This curve is represented in fig. 4 by Z0/%Z,. All the other P,7-curves as a rule intersect the line J/m in two points of which one is situated above and the other below the point /. If the temperature 7’; is changed, then in fig. 7 (I) or 11 (I) the saturation line under its Own vapour pressure changes its position and form, while Py. P,, and P, also change. The points M, m and / in fig. 4 then proceed along a curve; the curve through which the points Jf and m go, is represented by 1/)/,1/,M/,/m,Km; we will call this curve the boundary curve of the system: solid F + liquid + gas. The equilibrium between solid 7, liquid, and gas is determined by (6) Il and 7 (IL). To the point J/ and m also applies the relation; From this follows for the boundary curve: dP __(w,—2)B—(x--a)D iP (2, 2). A—(a—a)C so that this boundary curve must come into contact with the subli- mation line of the compound in the maximum sublimation point and with the melting line in the minimum melting point /. Further it is evident that the three-phase line AF’ of the compound F is a part of the boundary curve. Hence. all the P.7-curves in fig. 4 are situated in the region encompassed by the boundary curve; through each point of this region pass two P, T-curves and through each point of the boundary line passes a P,7-curve which meets this boundary line in that point. The boundary curve itself is, therefore. no P,7-curve in that sense that it corresponds with a straight line passing through /’; this, however, is the case if only one of the three components of F oceurs in the vapour. The double point / passes in fig. 4 through a curve terminating in the point /. When the saturation curves under their own vapour pressure possess, in the vicinity of the minimum melting point 7’p, a form as in fig. 12 (1) no double point of a P.7-curve appears above Ty. The double point curve in fig. 4 then proceeds from F towards lower temperatures. If, however, the saturation line at 7 under its own vapour pressure has a form such as the curve a/b in fig. 2 (II) the double points are still possible above 7p and at each temperature more “than one may appear. From (11a) it appears that 2 can become nil only for «= e@ and y =, therefore, in the point #. Rk, however, may become infinitely great and change its sign in other points of the component triangle. This will be the case when the denominator becomes O, hence: { (x,—a) r + (y,—y) 8 cos -+ { (a,-- x) s + (y,—y)t} sin p = 0 .« (16) Let us call the solution for which this is the case, the solution g; (16) then means that the line /g comes into contact in q with the liquidum line passing through the point g, of the heterogeneous region L + G. We may express this also as follows: becomes infinitely great when the conjugation lines liquid-solid and liquid-gas are conjugated diagonals of the indicatrix in the liquidum point, As R=a, (11) is converted into: 1213 dP D ILE in which D and C' have another value than in (14). peli) Equation (16) is, of course, also satisfied «=.2, and y=y, hence by a singular point of the system liquid + gas. In this ease, dP D and C and consequently Til obtain the same value as in (14). ( We now imagine also the ?,7-curve of the singular point drawn in dP fig. 4; we may then easily demonstrate that a is determined for this curve by (14). If now, on one of the straight lines ZZ, of fig. 1 a singular point occurs, so that in the equilibrium of solid /’ + liquid + vapour the two latter ones have the same composition, its ?,7-curve must meet the ?,7-curve of the singular point in fig. 4. Such a case occurs when at a definite P and 7’ a singular point appears or disappears on the saturation line of /, so that the satu- ration line and the correlated vapour line meet each other in that point. With the aid of the previous formulae we might be able to inves- tigate more accurately the course of the ?,7-lines if we expressed the quantities 7, s, ¢ etc. by means of the equation of state of Van per Waatrs, in which a and / must then be considered as funetions of v and y. (To he continued). Chemistry. — “Lqwilibria in ternary systems.” V. By Prof. F. A. H. SCHREINEMAKERS. (Communicated in the meeting of February 22, 1913), In the previous communication we have disregarded the case when the straight line Z/Z, of tig. | (IV) coincides with the line NXI’Y of this figure. If a liquid moves from the point /’ of this figure towards NX or towards ) then, as follows from (112) (IV) both the numerator and denominator of R are = 0. 7] C = ° ayia The value of a from (11) (IV) then becomes indefinite so that we will consider this case separately. In order to simplify the eal- culations we again limit ourselves to the case when the vapour contains one component only so that we may put «, and y, = 0. Our conditions of equilibrium are given in this case by (18) (11 (19) (11). We now write these: (1) 7 0Z Fis tise Aa (a—a) 52 + (y—§8) ae Z+6=0 If we develop these with regard to w, y, P and 7’ and call va and y=— we find, if we keep to the same notation as in communication (11): adu +- bdy +- hedx*? -+ ddady + hedy? + .... 22 CaP 4 ates.) ON lee a eee a brda* + sdady + ttdy? + ...= AdP—BdT +... . . (3) In equation (3) are wanting the terms de dP, dydP, de dT and dy dT. A, B,C. and D have herein the same signilicance as in communication Il; therein, however we must now call «=e, y=9, = Gand sa —0. We now allow the liquid, saturated with / and in equilibrium with vapour, to proceed along the line Z/'Z, in fig. 1 (IV). For this we call dy=tgq .dv; from (2) and (3) now follows: (a + btgg) de + ke + 2dta gp + eta’? g)de? 4+.... =its CAPEL DaTiae kk ioe web See ee L(r + 2stqgy + tig’ gp) dx? 4-...= AdP—BdT 4+ .... . (5) We now allow the straight line Z/’Z, in fig. 1 (LV) to coincide with the line V/’)" of this figure. As X/’)’ is the tangent in the point / at the liquidum line of the heterogeneous region passing through /. this is determined by : (ar + fis)da + (as + By)dy = ada 4- bdy = 0. Hence, if in fig. 1 (1V) the line ZZ, coincides with the line ANFY, a+b tg ¢ = 0. If we substitute this value of ty y in (4) and (5) we get: 1 gp Q de +... =—CdP+ DUT +... . « « (6) , : ppd det. = AdP—BaT Eo In this Q and S have the same value as in communication (1D, namely : ; Q = 2abd—ate-—b?e S= at + b?r—2abs = (rt—s") (a’r + 2afs + Bt) At first, we may limit ourselves to terms recorded in (6). and (7); from this we find: (8) in which gw and A have the same significance as in communication U1), namely C — A and uy = = and further: 2 oF. a pei. Ghe” ~ ath Se i Sat =—dG: se (9) PA (BCC A= AID) 267 BE—AD wherein, as in the previous occasion, we take BC — AD > 0. Let us first take a /, x-diagram such as in fig. 2 (1V) and 3 (IV). As B= H--y is always positive, dP has the same sign as Q—w/S. In communication (Il) we have seen that Q—ysS is negative when the boiling point line, of the solutions saturated with /’ passing throngh /° is curved in the point / towards O. The point O here represents the component occurring in the vapour. The boiling point line then has a form like the curve a/’) in fig. 1 (ID. dP now being negative, the P,2-curve must have a form like c/’d in fig. 2 (IV). If the boiling point line of the solutions saturated with /’ is curved in the point / away from the point © so that it presents a form like curve a/*/ in fig. 2 (ID, Q@—wsS will be positive. From the value of dP from (9) it now follows that the P, «curve must have a form like curve c/’d of fig. 3 (IV). In order to tind the 7,v-curve in the vicinity of the point / we must distinguish two cases. V>v or A> 0. If Q—4S is negative, the saturation curve of /’ under its Own vapour pressure is curved in the vicinity of /’ towards O and, therefore, has a form like curve a/’é in fig. 1 (I); dT is now negative and the Za-curve has a form like curve c/’d in fig. 2 (IV). If Q—AS is positive the saturation line of / under its own vapour pressure will have a form like a/’) in fig. 2 (11); d7’ from (9) is now positive and the 7z-curve has a form like c/’d in fig. 3 (LV). V henee “A> 0: and 40>; Q—238<0 »: Q—nS0 follows namely 2—w>0). If in fig. 1 the line d, Fd represents the tangent at the point /” of the not drawn melting point line, the P,7-eurve X/’)" will, in its turning point /°, have a tangent like the dotted line in fig. 1 passing through /. From (18) and (19) and also from (9) it follows that ¢@P and d7'are negative, so that the curve N/’)” in fig. 1 must proceed from /’ towards lower temperatures a and pressures. The latter may be found also by other means. For this we take the minimum melting point of the compound I’, therefore the temperature Tr of fig. 1; as Q—iaS< 0, the saturation line of / under its Own vapour pressure has at this temperature a form like LT curyevaronin fig. 1 (IJ) in which Fig. 1. we must also imagine the tangent XFY to be drawn. As this tangent has only one point in common with the saturation curve, namely the point of contact /, a vertical line passing in fig. 1 through the point / may intersect the curve AX/'Y in tlie point / only. We now take a temperature Z” somewhat lower than 7'p; if 79* 1218 ow in fig. 1 (11) we also imagine to be drawn the saturation line under its Own vapour pressure of this temperature 7”, we notice that this intersects the line X/’Y in two points. In fig. 1, therefore, a vertical line corresponding with the temperature 7” must intersect the curve \/’Y’ in two points. If we take a temperature 7’” somewhat higher than 7’, we find that the vertical line corresponding with this temperature does not intersect the curve X/’)” in fig. 1. We now take the boiling point line of the compound /’ of the pressure Py, that of a somewhat lower pressure ?’ and that of a somewhat higher pressure ?". As Q—weS< 0 it follows that that of the pressure Py has a form like curve a/b of fig. 1 (ID) in which, however, we must imagine the arrows to point in the opposite direction. From a consideration of these boiling point lines it follows that in fig. 1 curve \/’) is intersected by a horizontal line corre- sponding with the pressure Py in / only, and in two points by a horizontal line corresponding with the somewhat lower pressure P’. V>v therefore A >0 and 2>0; Q—’S< 0; Q—wS> 0. a) t From (8) it follows that a is negative, from (9) and also from € (18) and (19) that /7’ is negative and dP positive. In tig. 2 d, Fd again represents the tangent at the point /° of the not drawn melting point line; the dotted line passing through the point /’is the tangent in the cusp /° of curve X/'Y; The fact that the curve X/')’ proceeds from F towards lower temperatures and higher pressures may be deduced also in the following manner. From a consideration of the saturation lines under their own j vapour pressure of the temperature Ty, the somewhat lower tempe- @ rature 7”, and the somewhat higher temperature 7"", it follows that curve NXI’Y in fig. 2 is intersected by the vertical line corresponding with the temperature 7’, in / only and in two points by the vertical line corresponding with the somewhat Fig. 2. lower temperature 7”. As Q——wS > 0, the boiling point line of the solutions saturated with /’ has, at the pressure Py a form like curve a/b of fig. 2 (11) Be Xy Zz By in which, however, the arrows must be imagined to point in the opposite direction. If we imagine in this figure the tangent Y/Y, 1219 we notice that the latter, besides the point of contact /’, has another two points of intersection in common with curve a/b, which both appertain to a lower temperature than 7’. The horizontal line in fig. 2 corresponding with the pressure Py must therefore intersect the curve NF'Y, besides in F, also in two other points to the left of point F; the one point of intersection must lie on the branch N/’, the other on the branch J'/. If now we take the boiling point line of a somewhat lower pres- sure 7”, this will be intersected in fig. 2 (Il) in two points by the line NF’). Hence, the horizontal line in fig. 2 corresponding with this pressure ?” must intersect curve Y/’)" in two points. The boiling point line of a somewhat higher pressure /?” is inter- sected by- the line NV/')’ in four points, of which two lie on the part .V/’ and two on the part )’/' of this line. The horizontal line corresponding with this pressure /?" in fig. 2 intersects therefore each of the branches Y/' and V/" in two points. If in fig. 2 (ID we take a straight line ZZ, whose direction differs but little from the tangent V/’)" this wiil intersect the boiling point line of the pressure Py not only in /’ but also in three other points namely two on #Z, and another on FZ. The horizontal line in fig. 2 corresponding with the pressure Py, therefore, intersects the curve ZFZ, in F and further the branch ZF in one and the branch ZF in two points. Hence, on branch 7,/ must occur a point with a maximum and another with a minimum vapour pressure V > v therefore A >0 and 2>0; Q-AS>0; Q-uS> 0. > dP | From (20) follows : ai positive and greater than c from (9) and v, also from (18) and (19) follows dP and d7' positive. The curve VF Y must therefore have a form as drawn in fig. 3 wherein d,/d again represents the tangent in the point / at the omitted melting point line ; the dotted line passing through /’ represents the tangent in the cusp / at curve XFY. The fact that curve Y#F'Y in fig. 3 must proceed from / towards higher temperatures and pressures is again evident from a considera- tion of the saturation line of the tem- perature 7’ under its own vapour pressure, and of the boiling point line of the solutions saturated with F of the pressure Py. For both curves have in this case a form 1220 like in fig. 2 (Il) so that the tangent XFY besides meeting the curve ah in the point /, also intersects this in two other points. In har- mony with fig. 38 we find that the vertical line corresponding with the temperature 7'p must intersect the curve Y)’F' in two points above /’, and the horizontal line corresponding with the pressure Py must intersect this curve in two points at the left of /. From a consideration of the straight lines whose direction differs but little from the tangent Y/')" it follows that their ?, 7-curves in tig. 3 must exhibit on the one branch proceeding from /’, a point with a maximum temperature and one with a maximum pressure, and on the other branch, besides two similar points, also one with a minimum temperature and a minimum pressure. The deduction and further consideration of the other cases 1 must leave to the reader. We can also determine the course of the saturation lines under their own vapour pressure and of the boiling point lines of the solutions saturated with solid matter, which has been discussed in the previous communications, in a different manner. For the stability requires that if we convert a system, at a constant temperature, into another having a smaller volume the pressure must increase; if converted into one with a greater volume the pressure must decrease. We may also perceive this in the following manner. At the pressure P exists the system S which is converted at the pressure P+ dP into the system JS’. We represent the § of the system S, at the pressures P and P+ dP by Sp and Spy.p, that of the system .S’ by Up and ’ pLap.- As at the pressure P the system S is the stable one, it follows that Sp < o’p. As at the pressure P+ dP S’ is the stable one it follows that prop < Spzip. If we represent the volumes of S and S’ at the pressure P by V and JV” the latter condition can also be expressed by : lp + VidP V if dP is negative. The volume V" of the system \S’, is, at the pressure P+ dP, iV" ave : like VW’ + ae dP, in whieh aie negative ; from this now follows : V'V if dP is negative, 1221 Hence, if we compare two systems SS and WS’ which are converted into each other, at a constant temperature, by a small alteration in pressure, it follows from the foregoing that : If S exists at a higher pressure than /S’, the volume of S is smaller, if S exists at a lower pressure than S’, the volume of S is greater than that of S’. And reversally : if SS has a smaller volume than JS’ it exists at a higher, if it has a greater volume than JS’ it exists at a lower pressure than 4S’, We may express this also a follows : a system JS is corverted by increase in pressure into a system with a smaller and on reduction in pressure into a system with a greater volume. And reversally : if a system S is converted into another with a smaller volume, the pressure must increase, and if converted into one with a greater volume the pressure must decrease. We may then compare the volu- mina of the two systems either both under their own pressure or both under the pressure of the system S, or both under the pressure of the system |S’. It is evident that a similar consideration applies to two systems S and S’ which, at a constant pressure, are converted into each other by a small change in temperature. For the case in question, the equilibrium : solid ++ liquid + gas we may also deduce the above rules in a different manner. For this, we take at the temperature 7’ and the pressure P a complex consisting of quantities /’ + 1 quantities £,-+ q quantities G. We now allow a reaction to take place between these phases at a constant 7’ and P wherein : (n + dn) quantity / + (m+ dim) quantity L' + (q+ dq) quantity G’ is formed and in which “’ and G’ differ but infinitesimally from Z and G. The increase in volume A in this reaction is then determined by : i . OV OV ON OV, vdn + Vdm + V,dq + m a du + m i dy +- q a dx, + 4 a dy,. ue yl 1 Wel As the total quantity of each of the three components remains unchanged in this reaction we have: adn + xdm + w,dq 4+ mda + gdec, = 0 Bdn + ydm + y,dq + mdy + qdy, = 0 dn + dm + dq—0. After elimination of dn, dm, and dq we find: m ‘(y,—B) A + (8 y) (A+ Oj da —m {(a,—@) A + (ua )(A 4+ Ody -q(y—s) A,+ (@—y) (A,+ C,)} da q(@ —a) A 4- (a—2,) (A, +C))} dy, =(v,—a) (y —B) — («—a) (y,—8)} A which for the sake of brevity we write : mAydx — mA,dy — gA,,dx, + qAz,dy, = E.A 1222 We wil! choose the new system #’+ ZL’ + G’ in such a manner that it is in equlibrium at the temperature 7’ and the pressure P+dP. Then, as follows from our previous communications, dv, dy, de, and dy, are determined by: [(2 — a) r + (y—B)s] de 4+ [(e — a) s + (y — p) t] dy = AdP [(«,—a) r + (y,— 3) s] dw + [(w.—a) s + (y, —p) t] dy = (A+C) dP and two corresponding equations which determine dz, and dy,. From this we find: E (rt —s*) dz = — (sAz+tA,) dP E (rt—s’*) dy = oe dP E (r,t, —8,7) dz, = (8, Az, +t, Ay,)@P E(r,t,—s,”) dy,= — (r, Ax, +3,A,, dP. After substitution we find: yA%, + 23AzAy +: tA, -. 7,A%, 4 28 Ax, Ay, + A%y aw m — = - ; — == — £7? = rt — s° Tq rt, —s,? dP so that 4 and dP must have the opposite sign. In the above relation 4 represents the change in volume if both— systems are compared at the same pressure 7; if, when the new system is taken at the pressure P+ dP, the change in volume is represented by A’, we get: w= a+ .dP in which V+ represents the total ect of the new system at the pressure P. From this follows that 4' and 4 have always the same sign and A’ and dP always the opposite one. Let us now consider the system /’-+ 1+ G at a constant tem- perature, namely the saturation line of / under its own vapour pressure and its conjugated vapour line. These are respresented in fig. 7 (1), 11 (1), 12 (1) and 13 (I) by the curves Mamb and M,a,m,b,. We now take the system S—=/+ 1+ G which is stable at the pressure P and the system S’ = + L’ + G’ which is stable at the pressure P’. If now the volume of S’ is smaller than that of S, P’ will be greater than P; if the volume of S’ is greater than that of S, P’ will be smaller. Reversally, if 2’ is greater than P the volume of S' is smaller than that of S; if P’ is smaller than P the volume of S’ will be greater. All this applies, as we have noticed previously, if S and S’ ean be converted into each other and when P and P’ differ but little. We now omit from the system S the vapour so ‘that we retain F+L only. We now can distinguish two chief cases, depending on whether a phase reaction is possible, or impossible, between the three phases of the system /’-+ L-+ G. al. No phase reaction is possible. The three phases form the apexes of a three phase triangle such as, for instance, /’aa,, in fig. 4 (I). We may further distinguish three other cases, namely 1. + L is converted by a change of pressure in the one direction into # + L’ + G’ and by a change of pressure in the other diree- tion, into /’-+ ZL". Hence on change of pressure in the one direction vapour is formed, but not when in the other direction. 2. # + L is converted by a change of pressure in the one diree- tion into # + L’+ G@’, and by a change of pressure in the other direction into /-+ L" + G". Hence, vapour is formed on increase as well as on decrease of pressure. 3. /’+ L is converted by a change of pressure in the one diree- tion into /’-+ LZ’ and by a change in the other direction into + L". Hence, no vapour is formed either on increase or on reduction of pressure. The case cited in 1 is the one generally occurring; those mentioned in 2 and 3 only occur exceptionally. ZL. A phase reaction is possible. The three phases are now repre- sented by three points situated on a straight line. The system /’+ can then be converted by a change in volume unaccompanied by a change of pressure, into the system /’-+ 1 -+ G. So long as these three phases are adjacent, neither the pressure nor the composition of liquid or vapour is altered by a change in volume; all that hap- pens is a reaction between the three phases. As regards this reaction, we can now distinguish three cases: fee eG. In the graphic representation, the point /” is situated between the points L and G. On a change in volume in the one direction solid matter is deposited; when in the other direction this disappears. 2. F+ L2G. In the graphic representation the point G is now situated between the points # and ZL. On change in volume in the one direction, gas is formed; when a change takes place in the other direction the gas disappears. cee Gah. : In the graphie representation the point Z is now situated between the points # and G. On change in volume in the one direction, liquid is formed, when in the other direction this disappears. If, in one of the veactions sub A and 4 vapour is formed, the volume will as a rule become larger and if vapour disappears it will become smaller. The reverse, however, may also occur as will be perceived in the following manner. In order to convert #-+ ZL into + L’+6" we first of all form from Z a little of the vapour G’; the liquid 1 1224 is hereby converted into a somewhat different liquid ". Now, so as to convert L” into L’ either solid / must dissolve in Z” or erystallise from the same. If now this solution or crystallisation of / is accom- panied by a great decrease in volume, this may exceed the increase of volume occurring in the generation of the vapour; the system + L is then converied with decrease in volume into #+ L'+ G’'. Such a conversion may be particularly expected in points of the saturation line under its own vapour pressure which are adjacent to the point #. The liquid then differs but little in composition from the solid substance / so that in order to slightly alter the compo- sition of the liquid large quantities of solid substance must either dissolve or else crystallise out. Moreover, if in this case the solid substance /# melts with increase in volume, the latter will increase on addition of / and decrease on the separation of the same. If F melts with decrease in volume, the volume will decrease on addi- tion of # and increase when this substance is deposited. Hence, in the case of points of the saturation line of F under its own vapour pressure situated in the vicinity of /, the system /+ L can be converted with decrease in volume into /+ L'+ G': |. if in that conversion solid matter separates and if this melts with increase of volume (V >»). 2. if in that conversion solid matter dissolves and if this melts with decrease of volume ( 7 < 2). We may now apply the above considerations in different ways. If. for instance, we take the change in volume along the saturation line under its own vapour pressure as known, we may determine the change in pressure; if the value of the latter is known we may determine the change in volume. We now merely wish to demon- strate that these views support our previous considerations. We first take the case when all the points of the saturation line under its own vapour pressure are removed camparatively far from the point J, so that the two-phase complex /’-+ ZL is converted with increase in volume into the three-phase equilibrium /’-+ ZL’ + G’. We represent the eae r+L+G by the three-phase triangle Jaa, of fig. 3 (1) or + (1); the two-phase complex #-+ L is then tepresentel by a point a the line Fa. As, according to our assumption the system /’-+ L which exists at the pressure P, is converted with increase in volume into the three-phase equilibrium /’+ L’-+ G” existing at the pressure P’, the new pressure ? must be smaller than 1. From a consideration of fig. 3 (1) or 4(1) it follows at once that the new liquid ZL’ must be situated in such a way that the new 1225 conjugation line /’/’ is situated at the other side of a than the point a,. From all this it follows that, on reduction in pressure, the conjugation line solid-liquid turns away from the vapour point, and that on increase in pressure it turns towards the same. We notice at once that this is in conformity with the change in pressure along the saturation line under its Own Vapour pressure in fie. 7 (1) and 11 (1). For if we allow the conjugation line solid-liquid to torn away from m towards M or along mad or along mbJ/, it always turns towards the vapour point while the pressure increases. We now take the case when the saturation line of / under its own vapour pressure is situated, in part, adjacent to the point /. We now distinguish two cases depending on whether the substance /’ melts with increase or decrease in volume. V>v. The substance melts with increase in volume. For these points of the saturation line under its own vapow" pressure which are removed far from the point /’, /-+-L will be converted into P+ L/+ G’ with increase of volume; for points in the vicinity of /, #+ L may pass into /}+ 4’ + G’ with decrease in volume, provided that. as stated above, much solid matter is deposited in this conversion. We have already seen above in what direction the conjugation line solid-liquid turns when /’+ ZL is converted with increase in volume into /+ L’ + G’; we may now readily deduce that this conjugation line will turn in the opposite direction if that conversion takes place with decrease in volume. Hence, we find the following: we take from the three-phase equilibrium /’-+ 1+ G the two-phase complex F+L; if M+ L is converted into “+ L’ + G’ with increase of volume the conjugation line solid-liquid on veduction of pressure turns away from the vapour point; at an increased pressure it turns towards the vapour point. If / + LZ is converted into /’+ L’ + G’ with decrease in volume the conjugation line solid-liquid turns in the opposite direction. Let us now consider the saturation line of fig. 12 (I) under its own vapour pressure of which a part is adjacent to the point /’ and which, as we have seen before, applies to the case when the substance /’ expands on melting (V > v). We draw through /’ two tangents at this curve Mm; we will call these points of contact R and R’. As seen from the figure. the conjugation line solid-liquid now moves, On increase in pressure, on the branch RAZR’ towards the vapour point; on the branch Rm’, however, it moves away from the vapour point. In connection with the above, it now follows that the conversion of /’+ ZL into + L’ + G’ is accompanied 1226 on the branch RAZR’ with an inerease and on branch Rm’ with a decrease in volume. In the points of contact themselves where both branches amalga- mate, the case sub A 3 now occurs. Let us take the two-phase com- plex /’+ liquid . We now see that, on increase as well as on reduction in pressure, the conjugation line /-liquid R gets out- side the new three-phase triangle so that no vapour can be formed. Let us now see what happens in a similar point of contact FR if the pressure changes but infinitesimally. At this infinitesimal change of pressure, the liquid then moves at an infinitesimal rate along the tangent /'R either towards or away from /*. The only thing what happens is that in the liquid a little / is dissolved, or else crystallised from the same, without any vapour being formed. If now a substance / melts with inerease in volume and, there- fore, in this case also dissolves with increase in volume, it will crystallise out on increase in pressure and get dissolved on reduction of the same. This also is in harmony with the change in pressure along the saturation line under its own vapour pressure in the point R of fig. 12 (1): on elevation of the pressure the liquid moves, starting from Fk, from the point /’; this signifies that solid matter is being deposited. On reduction of pressure the liquid moves from / towards the point /; this means that solid matter is being dissolved. The fact that in a point of contact A no vapour takes part in the reaction may be also demonstrated in the following manner. We again take at the pressure P? a system S consisting of: n quantities /’+ m quantities L + q quantities @ ; at the pressure P+ dP is formed thereof the system S’ consisting of: (n-+-dn) quantities /’+-(m-+-dm) quantities L’+(qg-+dq) quantities G’ From the three relations already employed for this and which indicate that the quantity of each of the three components remains the same in this conversion we can deduce: Ein = — m{(y,—y)de — (#,—2)dy} — ¢ (yx—y)de, — (@, —a)dyy Edg = = m({(8—y)da — (a~a)dy} + q\(8—y)dx, — (a—2)dy,} Edm=—— m\(y, —8) de — (@,— a) dy} + ¢ (y, —B)dx, — (w,—a)dy,} in which all the letters have again the same meaning as before. If now we proceed at the pressure P from the system /’-+ L we must call g = 0; we then obtain: Edn = — m\(y,—y)da — (w,—2)dy} Edqg = = m\(3—y)dx — (a—«)dy} Edm=— m{(y, —B)de — (w,—a)dy}. 1227 Hence, as a rule dn, dm and dq are not 0; if, however, we eat draw through the point «,y of the saturation curve under its own vapour pressure a tangent passing through the point /° we find: dy = p—y da a—w hence dqg=0, whereas dn and dm differ from nz/. It means that no vapour takes part in the reaction so that the system /’+/ jis converted into another system /°-+ L’ devoid of vapour. We have noticed previously that the saturation line of the sub- stance /’ under its own vapour pressure which passes through the point #’ can have a form like the curve ‘ab of fig. 2(I1). At a somewhat lower temperature this curve still pgssesses about this form but it becomes circumphased. In fig. 4 a part of this curve has been drawn. So long as the point / is situated sufficiently close to this curve we can draw through /’ four tangents at this curve with the points of contact R, Rk’, NX and \’. Let us now imagine in fig. + the saturation line under its own vapour pressure to be shifted further towards the left and also its correlated vapour line to be drawn. We now allow a conjugation line solid-liquid to turn from m in such a direction that the pressure -increases. Let us now proceed from im towards a. On Fig. 4. the branch mf, the conjugation line /“liquid turns towards the vapour point, from PR to /’ away from the vapour point and from #&’ to @ and further on it again turns towards the vapour point. The same applies to the branch mA’) on whieh, in the points VY and \’, the direction of the rotation of the conjugation line gets reversed. The conversion of /’+ ZL into /’-+ L’ + G then takes place on branch mA and i X (andi X) with increase in volume, on branch RR’ (and VX’) with decrease in volume and on branch R’a (and X’)) again with increase in volume. In the point of contact I now appears the case sub 42 and in the point of contact /’ the case cited sub 43. Let us take for instance the two-phase complex /’+ liquid Rk. We now notice that on increase as well as on decrease in pressure the conjugation line / liquid / gets situated within the new three-phase triangle so that /’-+ liquid /? is converted into + L’ + G4’. On an infinitesimal change in pressure, nothing takes place in the points Rand PR’ but a solution, or a crystallisation of solid matter. As: / melts with inerease in volume and in this case also dissolve 1228 with increase in volume, crystallisation will occur at an inereased and solution at a reduced pressure. This is, moreover, in conformity with the change in pressure in the points R and &’ along the saturation line under its Own vapour pressure. The same considerations as the above-cited may be also applied io the case when the substance / melts with decrease in volume. (To be continued). Chemistry. — “The dynamic Allotropy of sulphur.” (Fifth commu- nication.) ') By Dr. H. R. Kroyr. (Communicated by Prof. P. van RompurGa.) (Communicated in the meeting of January 25, 1913). As point 5 of the résume of my third paper on the above subject I wrote in 1909: “Es wurden neue Untersuchungen iiber den Einfluss des S$, auf den Umwandlungspunt S,, 22 Smon in Aussicht gestellt’. In connection therewith I wrote *) in July 1911: “Dr. van Kioostrr of Groningen has this year started that investi- gation and although the provisional result is only of a qualitative character as yet it may be taken for granted Nevertheless. Messrs. Smits and pr Leeuw published, in’ these Proceedings (XIV, p. 461), an investigation concerning this question. In the Zeitschr. f. Electrochemie*) | communicated, in connection with some other questions regarding sulphur, that the above investi- gation bad been continued and brought to a close, also to what conclusions it had led and that a detailed communication would soon appear; recently it appeared as the fourth communication in this series. Meanwhile, Dr. pe Lesuw (Proc. XV p. 584) has contradicted the above cited conclusions and condemned the still unpublished investi- gations in advance. : Although I should have every reason not to take any notice of that paper, two reasons in particular have induced me to repeat and extend 1) For the previous communications see Zeitschr. f. physik. Chem. viz. 1: 64, 513 (1908); Il: 65, 486 (1909); IIL: 67, 821 (1909) and IV; 81, 726 (1913), 2) Chem. Weekbl. 8, 643 (1911). 8) Z. f. Elektrochemie 18, 581 (1912), 1229 the investigations of Dr. pe Leruw and to communicate here the results. First of all, the criticism did not concern my work only, but also that of Messrs. vAN KLooster and Srv who carried this out at my request and whose work [ wish to defend and in the second place, owing to a paper by Messrs. KonnsramM and OrnstKin '), the question as to the change of the transition point of sulphur has been intro- duced into the discussion of the heat theorem of Neryst. Looking at the eminent importance of the problem whether the facts confirm, or do not confirm the conclusions from the heat theorem, each ex- perimental fact supporting the theorem must be as much as possible elucidated. Therefore, I will discuss the said treatise of pu Leeuw, but only in so far as required by the considerations just mentioned. I have first of all verified whether the result of pe Lrxuw’s ex- periment is correct namely, that a dilatometer, which contains a sulphur mixture rich in S,, after it has been placed for some hours in a thermostat at 70’—80° C., exhibits. a rise of the liquid in the capillary which is followed by a fall. This indeed proved to be the ease. This verification appeared to me necessary because the state- ments in bE Leguw’s table only contain observations of changes which sometimes amount to only 1'/, mm. and seldom more than 2 mm. For no one who has experience with the dilatometer these observations will have any definite value. And although the fact first investigated proved correct, the conclusions arrived at by pr Leeuw are not procf against a more elaborate investigation. The rise observed is attributed in all the treatises cited to the change in volume in the conversion 5, Sion, because the con- versions Smon Sy, 5.2 S,n and S,—Snon take place with con- traction of volume. Owing to the reaction S,—S, taking place meanwhile, the S, concentration is altained at which the conversion Sri > Sinon at the temperature of experiment ceases; hence the rise in the capillary ceases also and a fall is exhibited there as a con- sequence of the still proceeding reaction S,—S,;. On elevation of the temperature the phenomenon ought to repeat itself each time. Such are the views of Dr. pr Lenuw. In fig. 1 the thin line with the arrows indicates the changes of condition which the sulphur in the dilatometer ought to pass through. ' In my experiments, however, it appeared that the behaviour of the dilatometer is absolutely contrary to the expectations raised by this diagram. ') These Proceedings XIV p, S02. 1230 Owing to the peculiar method followed by Dr. pe Luegvuw to observe for a few minutes only whether the dilatometer exhibits a rise or a fall, one gets from his communication the impression as if each time, with the different (rising) experiment-tem- peratures, a similar phenomenon repeats itself. Now, such is by no means the case. Only once or twice, the said maximum occurs. I have observed repeatedly that it then returned no more. The slight increase, or decrease observed by him at the subsequent temperatures have no significance, moreover, such trifling values never have a definite meaning; the dilatometer is not an instrument of precision not even when the best acting thermostat is used. In order to obtain really trustworthy results the experiments should be so arranged that the reaction studied exhibits a suitable rise or fall; this should then surely exceed a few m.m. Below are given some of my investigations. : As, for these experiments, glacial acetic acid is a much more appropriate liquid than turpentine-carbon disulphide (see communi- cation IV), these experiments have been carried out with that liquid. The thermostat has been described in communication (III). The sulphur was treated exactly as directed by Dr. pe Lenuw. Table I contains the result of a series of experiments represented graphically in’ fig. 2. We notice that, when we wish to attribute the great rises at 76°.2 and 83°.0 to conversions according to the scheme of fig. 1 it becomes inexplicable why at the temperatures 86°.7 and 91°,9 the pheromenon does not appear, but returns at 97°.8. Moreover, the conversion at the latter temperature exhibits the plain character of a conversion above the transition temperature. From this series I already gained the impression that the maximum occurring at 76°.2 and 83°.0 has nothing to do with the conversion — Fig. 1. Sri mon « One might imagine that, during the time corresponding with the falling branches in A and B fig. 2, so much S$; has been. regene- rated that at the subsequent rises of the temperature one does not arrive any longer above the line AC in fig. 1. True, that difliculty TAS Bi Beal A. Temperature 76°.2. C. Temperature 86°.7. Day Hour Dilatometer | Day Hour Dilatometer M. 9.55 a.m. placed Th. 10.00 a.m. attained 12.03 p.m. 533 11.00 482 1.00 560 12.04 p.m. 477 2.18 583 mince 467 4.07 607 E: 9.25 a.m. 439 7.24: 645 D. Temperature 91°.9. 9.14 635 E =a —_ Tu. 9,29 a.m, 585 Day Hour Dilatometer 1.52 p.m: 580 owes. a EF: 10.25 a.m. attained B. Temperature 83°.0. 11.00 483 a a “ 12.00 480 Day Hour Dilatometer 3.00 p.m. 482 27 pie) ae : 5.05 481 Tu. 2.15 p.m. attained 5 Sat. 9.48 a.m. 474 Sc8il/ 517 4.53 558 E. Temperature 97°8. 10.20 694 ; Day Hour Dilatometer 10.50 701 - W. 9.25 a.m. 741 Sat. 10.25 a.m. attained 12.12 p.m. 731 11.25 438 4.28 727 12.15 p.m. | 548 | Th. 9.44 a.m. 677 3.40 | > 1000 then applies a fortiori to pr Lervw’s experiments where the dilatometer liquid does not obstruct that conversion which certainly was the case in our experiment. In order to avoid this objection anyhow, I proceeded, in a subsequent experiment, to the higher temperature so soon as the maximum had been attained. The teaches other things as well (Table II). result is shown in a series which in addition Proceedings Royal Acad Amsterdam. Vol XV 659 pee E. 97°.8 609 800 700 B. 83.°0 700 609 600 50 Cc. 86°.7 500 | fe) 1 ie} = 400 }10 i! 4 D. 91°.9 sre Fig. 2. This table gives us two minor results and two highly important ones. The first is that in Table II A a previous fall in the dilatometer occurs. Hence, the total behaviour on introduction is: a rise and a fall — a rise and a fall. This first rise and fall finds its explanation in the Reenautr effect and bas been predicted and discussed in my fourth communication p. 736. The negative catalysis of the acetic acid WYN sh JES Ne A. Temperature 75°.3. E. Temperature 95°.2. Day | Hour Dilatometer | Day Hour Dilatometer M. 11.05 a.m. p aced W. 3.10 p.m. attained 11.33 476 3.22 510 12.02 p.m. 465 3.45 510 | 12.14 458 4.18 511 T22 465 6.21 510 ee ShO7 525 Pye) 625 reer ack | eee | pee F. Been during the night 8.45 628 z ; 9.04 624 at 95°.9. No change. G. Temperature 97°.2. B. Temperature 84°.8. Sere — Day Hour Dilatometer Day | Hour Dilatometer Th. 9.30 a.m. attained = ; 10.06 629 leaves stent 11.17 631 - | ‘ea ae sg 1.50 p.m. 630 | 10.30 439 —_—_— Tu. 9.31 a.m. 406 H. Temperature 98°.6. Day Hour Dilatometer C. Temperature 93°.0. = Th. 2.05 p.m. attained eer j | Peis) 692 Day Hour Dilatometer 245 603 —— = : 3.22 767 : 3.48 870 Tu. 10.04 a.m. attained 10.2 745 Daa p.m. 745 J. Temperature 96°.4. 5.05 748 ' 10.10 748 Day Hour Dilatometer W. 9.34 a.m. 740 Th. 5.00 pm. 757 D. Temperature 949.2. Ee) ee eae oes fat als) 778 D Dilat t al Hour igeaisy a ae K. Temperature 95.8. Ww 10.37 am | pitesned Day Hour Dilatometer Me s7s 464 12.14 p.m.) 464 F. | 11.45 a.m. 753 ) 2.14 460 12.04 p.m. 752 3.00 458 1.10 753 1 After the position had been regulated with a sweeping capillary, 1254 causes the rising branch to maintain itself here so much longer than in the experiment described previously. We may, meanwhile, conclude that notwithstanding the acetic acid present, 5, present in large con- centration, rapidly reverts to 5,, a conclusion that bad already been drawn in my fourth communication; for the explanation of the experiments it is not to be neglected because it is thus shown that the S, concentration has already considerably receded at the moment that the rise observed by pe Lesuw commenced. Secondly, the rise in this experiment appeared to occur only once, and not to repeat itself either at 84°.8 or at 93°.0. Much more important are the following conclusions: The rise has no connection with the conversion SzZSmon. If at the lower temperatures, monoclinic sulphur had formed it would have been impossible to realise a retardation of the said conversion above the highest transition temperature. The tables Il G and H, however, clearly prove the possibility thereof. Even at 98°.6, 40 minutes after this temperature had been attained, the conversion had yet to start; onee started it was, of course, very evident, also still at a tempera- ture of 96°.4 (Table II J) whereas when unintroduced it had not appeared at 96°.2 (Table II G). The fourth conclusion is derived from Table II K, namely, that at 95°.8, the reaction S,,27Smon stops in the presence of some percent of S,, just as was shown by the investigations communi- cated in my fourth paper, again in conflict with the communications criticised here. If one should opine that the phenomena are fundamentally different owing to the use of acetic acid as dilatometer liquid, it may be communicated here that I have also carried out the experiments with turpentine-carbon disulphide. There it appeared, as might have been expected, that the first maximum appears in a less pronounced manner and also that, on using that liyuid, subsequent risings at higher temperatures do not take place; in fact no fundamental dif- ference occurs. The above investigations had therefore demonstrated that the explanation of the dilatometer behaviour at temperatures of 70°—80° by the conversion S$, 1240 leucite basalt of East-Borneo, discovered by Prof. MoLencraarr ‘). This last-mentioned biotite is not resorbed, and is often deposited in the rock of the Ringgit round the older resorbed crystals, however with different optical orientation of the optical groundmass. These little brownish-red erystals which also occur dispersed through the rock, and as a rule do not show any definite shape, enclose particles of the groundmass. The groundmass consists of leucite, augite and ore. Sometimes the leucite attains somewhat larger dimensions than the majority of the crystals of the groundmass, without forming real phenocrysts, the augites are column-shaped and colourless or light-green, the ore is plentiful in the rock. Macroscopically one sees already locally in little cavities neogenic minerals of very sinall dimensions, many of which show the shapes of crystals of leucite or sodalite, or also of feldspar. Under the microscope one sees in these little cavities isotropic crystals, together with neogenic feldspar and sometimes some biotite, whilst the dark background against which the prisms of augite set off be- tween crossed nicols, is often interrupted by anisotropic portions, which for some distance have the same optical orientation, and poi- clitically surround the particles of the groundmass. These anisotro- pic portions sometimes consist of kalifeldspar, twinned according to the Carlsbad-law ; polysynthethic twins have not been observed, but the zonal structure which is often distinguishable, points also to the presence of plagioclases. These minerals have been formed after the crystallisation of the groundmass of the rock and point to pneu- matolytic elements in the magma, which have been set free after the final crystallisation; consequently they are no normal constituents but products of the autopneumatolysis in the rock. Locally they may occur in considerable quantities. The enclosures of this leucite are coloured light-red or brownish, and contain little phenocrysts of plagioclase where they have not been altered into a hypo- or cryptocrystalline groundmass. In some of the enclosures examined the plagioclases show micros- copically a well developed zonal structure, in others they are only slightly so, or sometimes not at all. Major twins according to the Carlsbad-law of the polysynthetically twinned feldspars occur. The basicity of the feldspars sometimes decreases regularly from the centre to the margin, in which case transitions were observed from labrador or bytownite to oligoclase or andesine, but alternations of 1) H. A. Brouwer. On micaleucite basalt from Eastern-Borneo. These Proceedings, June 26, 1909 p. 148. 1241 more basic and more acid lamellae are very frequent, and sometimes are found repeated several times in one and the same crystal. Phenocrysts of the dark minerals are not met with as such, but sometimes we find specks consisting of opaque secondary minerals proving by their shape that such phenocrysts may originally have been present. The grcoundmass is likewise strongly weathered and contains laths of plagioclase, flakes of chlorite and opaque products of disintegration of the ore which is not found in large quantity ; moreover often an isotropic substance is found in large quantities, which is considered as glass; in this case the rock must be called an andesite. Metamorphosis. The metamorphosis of the enclosures examined encludes in the first place the alterations caused by the magma itself, appearing only at the immediate contact, and consisting, at the utmost, of remelting and recrystallisation after chemical exchange; in the second place the alterations caused by imbibition of volatile substances which penetrate well into the interior of the enclosures. From this the intermediary place becomes apparent, which this contactmetamorphosis occupies between that of the basaltic and that of the trachytic rocks. Especially the intensity of the pneumatolytic influences varies greatly in the different enclosures ; sometimes the chemical exchanges in the contactzone can be explained without pneumatolysis. In the examined rocks it is most frequently the case that in part of the enclosures a porous structure has been developed even to a great distance from the contact, whilst in the cavities neogenic minerals have been formed showing great analogy to the autopneumatolytic minerals of the enclosing leucitite, whilst in the contact zone the combined effect of remelting and pneumatolysis can be observed. The formation of a gold-yellow aegirine-augite is characteristic. As an example may serve an enclosure of a few centimeters in diameter in which to a great distance from the contact a neogenic yellow pyroxene is formed in very small columns, sometimes accu- mulating locally and then accompanied by an isotropic mineral with low index of refraction and by neogenic feldspar. The angles of extinction of this yellow pyroxene point to aegirine-angites of varying composition. The ore is strongly disintegrated, here and there a reddish substance has been formed pointing to an oxydation to hae- matite. A small quantity of the yellow pyroxene is also found in the phenocrysts of plagioclase. The transition-zone with the leucitites 1242 is characterised by the occurrence of a very great number of little columns of gold-coloured aegirine-augite and of a few larger crystals with yellow margin which are mixed with feldspar, consisting partly of kalifeldspar, partly of plagioclase. In this transition-zone we find only a very little quantity of ore, whereas the larger augite crystals with yellow margin have after all originated from phenocrysts of the leucitite. Very near to the contact we find the original plagioclases of the enclosure as an opaque central portion in the neogenic feldspars; whereas at a short distance the original plagioclases have been conserved as such, and the neogenic minerals have been crystallized in small cavities of the rock. The appearance of the ore points to chemical interchanging of elements between the lava and enclosures; the gold colour and the modified optical properties of the augite and likewise the crystallization of neogenic minerals to a great distance from the contactzone of the enclosure which has become partly porous, indicate the influence of pneumatolytic gases. Leucite-tephrites of the Somma metamorphosed by fumaroles show very similar modifications. That in the contact-zone really melting has taken place is in such- like enclosures often proved by the fact, that the transition-zone penetrates tongue-shaped into the magma which has been crystallized as leucitite. Macroscopically the line of demarcation be’vveen the transition-zone which is only a few millimeters wide, and the leucitite can often easily be followed by the rapidly decreasing of the percentage of ore, and by the colour which for this reason becomes lighter. Among the smaller enclosures there are numerous ones, which have entirely been altered into a very porous rock, have obtained a yellowish colour, and contain besides the colourless neogenic minerals and the yellow pyroxene also a few crystals of haematite which macroscopically are perceptible as little black specks. In a larger enclosure with a diameter ‘of about 20 centimeters the transition-zone was hardly brighter in colour than the leucitite, and this fact appeared to be accompanied by a much more gradual diminution of the percentage of ore. Moreover the augite shows no change of colour, and neither do we tind the gold-yellow augite in the enclosure at some distance from the contact, notwithstanding the porous structure and the crystallization of pneumatolytic minerals. In the transition-zone little, but likewise much larger crystals of neogenie kalifeldspar and zonular plagioclase can be observed, enclosing the ore and the little columns and larger crystals of unmodified augite. In this contact-zone again borders of neogenic feldspar appear around the opaque plagioclases of the enclosure. 1243 The metamorphoses described above, which are connected by all sorts of transitions show great resemblance to those found in blocks of leucite-tephrite of the Fosso di Caucherone (Vesuvius)') which have been altered by the action of fumaroles. The microlithes and phenocrysts of augite have become yellow, and the extinction-angles agree with those of an aegirine-augite, sometimes with those of aegirine. Haematite is abundant with the exclusion of magnetite. The biotite and amphibole show modifications of colour. In the ‘“‘sperone” of Latium, likewise a metamorphic rock which by transitions is connected with a normal black leucitite, the normal green augite has been altered into a gold-coloured one, whose angle e:¢ varies between 65° and 85° whilst likewise the original magnetite has more or less completely disappeared. Moreover there is often formed a yellow melanite ’). Finally a green-yellow aegirine-augite occurs in varieties of the shonkinite of the Katzenbuckel (Odenwald) which has been modified by pneumatolytic processes*). The tron-ore has here been altered into pseudobrookite, the feldspars are more or less zeolitised. Analyses made by LaTreRMANN indicate that in the rock modified by pneuma- tolysis, the percentage of Fe,O, had increased from 5,86°/, to 8,51°/,, whilst in the variety with yellow augite the FeO of 3,23°/, which had been found in the original rock, had entirely disappeared. Like- wise in the analyses of sperone the Fe,O,') dominates strongly over the FeO; evidently the metamorphosing agencies had an oxydizing influence. The modification of the optical properties of the gold- coloured pyroxene tends to prove that the Na,O percentage has also been increased, which could not be concluded from the different analyses. In connection with what has been said a second locality of rocks with gold-coloured pyroxene may be mentioned (II of the annexed map) situated directly South of the road from Panarukan to Besuki at mile-post 18. At the northern foot of a bare hill a porous light-grey rock that microscopically proves to be rich in gold-coloured pyroxene, appears between rocks of dark-grey biotite-leucite-tephrite. 1) A. Lacrorx. Etude minéralogique des produits silicatés de l’éruption du Vésuve (avril 1906). Nouv. Archives du Muséum. 4e Série. Tome IX, 1907, pp. 73, 94. 2) A. Lacroix, |. c. p. 95. 3) W. FreupenserG. Geologie und Petrographie des Katzenbuckels. Mitt. Groszh. Badische Geol. Landesanstalt V. I. Teil, 1906, p. 81. 4) V. Sapatint. I Vulcani dell’ Italia centrale. I. Vulcano laziale. Mem. Carta geol, d'ltalia, X, 1900, pp. 150, 163. 1244 In the dark-grey leucite-tephrite one sees, macroscopically, phenocrysts of plagioclase and dark minerals few millimeters in diameter, the former contrasting litthe against the groundmass. Under the micro- scope it appears that the plagioclases have a well marked zonal structure, the augite crystals are light-green and often include numerous specks of ore. The little phenocrysts of biotite are sometimes strongly resorbed; the angle of the optical axes is very small, the pleochroism is strong from brown-black to light-yellow. The groundmass is composed of plagioclase with zonal structure, leucite (and some nepheline), green augite, a little biotite and much iron-ore. The latter mineral often obtains somewhat larger dimensions, without forming real phenocrysts. The leucite has likewise somewhat larger dimensions than the majority of the crystals in the groundmass. The porous light-grey rocks with gold-coloured pyroxene show numerous phenocrysts of white plagioclase (some as long as 0.75 e.m., but usually smaller) and smaller phenocrysts of the dark minerals ina groundmass which is either dense or micro-crystalline; in the cavities neogenic minerals have been formed. Under the microscope we see porphyric crystals of strongly zonal plagioclase and gold-coloured or partly still green pyroxene, in agroundmass of strongly zonal plagioclase, gold-coloured pyroxene iron-ore, an isotropic, sometimes light-brownish substance, and a few little columns of apatite. Further a few rather large broad prisms hexagonal in cross section of an optically negative mineral with one optical axis, with a high refraction index, have been observed, which are slightly pleochroitical with « > 0; they are almost colourless or tinged very lightly brownish, and include sometimes particles of a black or vermilion-red substance. A cleavage parallel with the axis of the prisms is indistinctly developed. in case originally some leucite has been present in this rock, the mineral is now altered into pseudomorphoses, on account of its feeble resistance against pneumatolytic agents. Without entering into details about the metamorphosic and preneo- genie minerals found in these rocks, it can be mentioned that the aegirine-augites belong to different chemical combinations ; we observed e.g. in sections parallel to (010) made across columns twinned accord- ing to (100), symmetrical extinctions of 14°, whilst several lath- shaped sections extinguish with angles of 20° to 30°; very small angles of extinction were equally observed. Black iron-ore, blue-black in reflected light, is found in great abundance in the rock, sometimes it surrounds as a border the aegirine-augites, which likewise can include the ore in great quantity. Moreover one sees elongated sections consisting entirely of black 1245 ore, around which a mixture of ore and prisms of gold-coloured aegirine-augite columns is formed. The metamorphoses described above by which gold-coloured pyroxe- nes with the optical properties of aegirine-augites are formed, appear to be connected with pneumatolytic processes in magmas rich in alkali. Finally it may be mentioned here, that to the South of the road Panarukan Besuki, quite near to mile-post 13, a loose piece of a leucitite was found with phenocrysts of leucites as large as 4 m.m., which certainly had come down from the northern slope of the Ringgit and consequently may be expected there in greater quantities; hitherto such types of rocks were not recorded from the Ringgit-mountain. Mathematics. — ‘“Hupansion of a function in series of ABEL'S functions (a). By Prof. W. Kaprryy. (Communicated in the meeting of February 22, 1913). 1. In the Oeuvres completes of ABEL') may be found the follow- ing expansion where n n & Prlw) = 1—Cye + Co Sie +(—1) - «: n: C}, representing the binomial coefficients. These polynomia form the object of the dissertation of Dr. A. A, Nuianp (Utrecht 1896) and have been treated afterwards by E. Le Roy in his memoir “Sur les séries divergentes” (Annales de Toulouse 1899). In this paper I wish to examine when a given function of a real variable may be expanded in a series of this form FG) =a, aip.(2) +t aye) o-.. 9: os 2. In this article we collect those properties of the polynomia ~,(v) Which we want for our investigation and which we take from NiLANb’s dissertation. In the first place we have the important relations ') Oeuvres Completes II p. 284. 1246 fos m(x)pr(x)da = 0 (m =\= n) os ee ERB) ferences —— 0 In the second place ¢,(z) satisfies the differential equation Lpr' (v) + A—a)yn (x) + nep,(z) = 0 which also may be written d ae (we—2ep;,(2)]| += ne=2—;(2) 0. 3 ls) Lv In the third place we have the following properties, which may be easily obtained : Gx(z) = Gn(*)—GP'npi(t). - - « « - . (4) & 5 (== (ENC (a 9 6 59 a 6 ((D) (n-£1) gn 4i(z)—(2n +1 —2)pa(a) + mpnale) = 0. . . (6) [eran («)de =(—1)" Crniims Deca e ((() — —10) (m>n) 3. If the expansion (1) is possible, the coefficients a, may be expressed by means of the equations (2) ay = [rs orpstayte 0 With these values the second member of (1) reduces to wo S= SF gnlo) e “f(a)palda.. 2. i SeeaiR) In order to determine this sum we introduce ¢,(v) in the form of a definite integral. This definite integral, which has been given - by Ly Roy, may be found in the following way. Denoting by ./,:¢) the Besselian function of order zero, MACLAURIN’s expansion gives easily ad, (247 aa) = pe (@) se oO 0 mI! e—*a' da , . Te: and integrating Hence, multiplying both members by between the limits 0 and a 1247 @ ot 1 «am s 7 = fe —4enJ (2 ax)da = > — fe 2a"Pm, (a)da Us _ ni nl om: 0 where the second member may be reduced by means of (7) to bs n an > (—!)" Cn = —— (i) 0 ! Therefore we have ‘ vs) ec ea Pn (v) = = fe SCA VA GEE CG) a. Ag ae { (1K) 0 and 7 g— & Pile) ee Man eal PP (a mB) dB Sa SO [re de fF J, 2 VaR) a 0 0 Now, from the equation (9) we obtain ao pn n\e ss J, (2 V px) G ni thus S = [ro tu fJ, (2 Va) J, (2 V Be) ap, 0 0 or, putting 6? instead of B S == 2 [7 (a) def J, (28 Ye) J, (28 y AAC 5 “5 (ila)! 0 0 3. This double integral may be determined by a theorem of Hanker. (Math. Ann. Bd. 8 p. 481), who proved that sf yp (y) dy /f. J, (8y) J, (8S) Fas = (5) 0 0 where § represents a positive value and (és) a function which satisfies the conditions of Diricaier for all values between 0 and o. Putting y= 2Va, §—2V2, yp (2V«) =f (2) this theorem gives immediately S=2 Fa)de f1, C8) J, 28 (x) BdpB=f(z) . . (12) 0 0 1245 Thus we have established the result, that every function / (2) which satisfies the conditions of DiricuLer for all values between 0 and o may be expanded in-a series of the form ft («) =a, + 4 @, (*) + a, p, (#7) +... OS eto) where a, =r fn (a) da 0 It is to be remarked that the values f(¢-++-0) and f(c—-0) being different, the second member reduces to }[ /(¢ + 0) + f(¢ +0)]. 4. We now proceed to give two interesting examples of this expansion and to show the value of this expansion for the problem of the momenta. : : ] As a first example suppose it is required to express f(x) = ise & in a series of ABEL’s functions @» (2). Evidently this function satisfies the conditions of DiricuLer from 30 to «lo, thus 1 ges ee P, (&) + 4, P, (@) + FOE where 2 “e—* Py (a) da | i lta 0 Now the following relation holds between successive functions ¢: (n + 1) gag (a) = (2n + 1— 0) gn (@)— Guile). . (6) is nn — Multiplying this by da, and integrating between 0 and a l+a we obtain 1 or a en (a) d = n —{s nN Np —| = Pa te " (n +- 1) a4 n+ l)ja NAn—| shee a 0 But, as a 1 = il l+ea l-ta we have liar Gn (a) da= |e-* pn (a) da — ay 0 u 1249 where the latter integral, which may be written ao fe * yp, (a) gn (a) da 0 vanishes according to (2) if x > 0. Therefore three successive coefficients of this expansion are related in the following way (n + 1) ay41 = 2 (n + 1) a, —nay_i (rn > 0) so that all the coefficients may be expressed in a, and a, . Now g, (a) =1l—a *e-4 (1—a) ca [2—(leae\ie a, = {- da = | — —— da = 2a,—1 l+e lta 0 0 which proves that all the coefficients are dependent on the first = "da ail a Sl - BIL ) (OOS 4tace ae a e These coefficients may also be obtained in another way. From ABEL’s expansion hence 1 ! =F, = = as == > Py (2) vo 1—v 0 which holds where mod v<1 we see, by putting i that oe ey, (o) + — 9, (0) + iw ae a a+9:% 7 if d : 1 mo: a Multiplying this equation by et dt and integrating between the limits O and «, we obtain 1 ee =a, + a, g, (c) + a, 9, (&) + -. where 1250 a yn et a ay =|. (por CE ee oy eee CLS) 0 Comparing this result, with the former, we obtain the interesting formula J tn At y(t) ot = dhe ee Je ets We! fe (lot ak es ee it) 0 which is evident if we put n= 0. From (13) we see also that ¥ @ 1 : 1 a @ van =e (75) dt = fe Gh =I - 0 1+t » \l+t 0 0 which shows, that the expansion 1 « ees — a an Yn (@) holds for a= 0. 5. As a second example we will expand a discontinuous function. Supposing f(z) =1 from z=0 to e=1 and f(e)=0 fore >] we have J (x)= a, + 4, g, (@) + 4, , (2) + «. 1 Qn =e (a) da. 0 This coefficient may be determined in the following way. From the differential equation where d , Ane e— @,' {#)| + neg, (z) == 0. . . 2 SR) it appears that r xv e—* op, (x) + nfo gn (x) de = 0 0 therefore, putting «= 1, we have 1 an = — — thn (I) (n > 0) ne or, according to (5) 1 Dive ee [Pn—1 (1) — Yn (1)] (n > 9) 1251 The two first coefficients may be obtained directly, for l é 1 a= fe @ de == 1 — « 0 and 1 1 (i, = [y, (1) — g, 1) = =e The remaining coefficients are dependent on these. For putting v=1 in the recurrent velation (m + 1) Prqi (w) — (2n + 1 — 2) pn (@) + rGngi(e)=9 ~. (6) we get (wm + 1) Gti (1) — 2n Gr (1) + 2 Gr—i (1) = 0 and, changing n into n+ 1 (nm + 2) gng1 (1) — 22+ Dori (I) + + DG) =. thus, subtracting the former from the latter equation (n + 2) ante — (2n +1) an4i + na, = 0. 6. The expansion holding for the value «=O, we must have @ 0 er 0 and remarking that «= 1 is a point of discontinuity o, DS i Cie (WS tc 0 To prove these equations directly we may remark that n Il £2 1 2 4) = a Ue) me Pe ee Pn (1)) so a Pell, a ee = a, =— — — Limy, (1). l e @ n= Now, the number n being very large, we have ite eee ef), (Vn) Pn (a) = 1 — ne + 2B) and nee Tae, =F x Lim Gn (x) = LimJ, (Vnv) = Lim —— cos (Ve — =) =(/ na N00 n=o aV new 4 therefore z 1 ry ap == and finally 1252 1 1 a,+ 2a =1——+4+-—-S1. 1 e e The second equation may be obtained as follows. From the differential equation d a [we-= g,' (2)] + peg, (@)=0 . .. = . () we may conclude 1 1 id 1 | e— ¢p,” («) dz = — =| () d [xze-= gp,’ («)] = 0 0 1 1 1 = — = [xe—* yy (0) g'p (@)] + — fj wet y,!* (@) dx P g P so ] : x 1 ‘| ez |v (x) — e gs ) i} == — = Py (1) Pp. (1) = Ay Py (1). 0 Now, the equations (4) and (5) give Ly? (#) = Pp (2) Gy! (@) — ¢'p 1 (I ; Go. (2) = Pp (v) Ly, (x) — Py (7)] hence a py (%) — i wv (®) = Pp (#) Pp! (@) — Gy (@) pH (@) and n = |W QS B gy" | = Po (%) Py (®) — Pn (@) 4'n4r (2)- This shows that 1 [0 = 106) Pr] de = ¥ ayy) 10) where 1 1 1 Je Po (a) 4! (a) dw = — fe-* de = —1 + — e 0 0 To obtain the second integral, the value of n being very large, we observe that according to equation Pn (#) = Gn' (et) — P'ngi(w). . . . « « « (4) the functions 1253 Pu (v) and Pr+1 (7) tend to the same limit. If, therefore n is very large, the second integral, tends to 1 I feva n(@)(p'n+1(«)da = fou n(&) pn (@) = 0 0 =|" “Dn ey 1 fon «) dz = — } 4 wo 1 2 ti ay aire ate bs and we obtain Thus, adding to this equation 1 a, p, (1) =1— om we get finally the required relation i = ; — = Gp Pp (1) = t- 7. In this article we wish to give a second verification of the former expansion because this leads to a very interesting integral coniaining Bessri’s functions. This verification is obtained by direct summation of a, + apy (@) + agg, (a) +. where 1 eh ER and an = 4 [gn—1 (1) — gn (1)]. It appears from the equation (10) that 2) r=) = fe SO lle (2V.a) da 0 e S, Pn (1) = S fe a J, (Va) da n 0 therefore gn-1 (1) — na (1) = = J J, (2V a) d (e~ 2a) or, after partial integration Proceedings Royal Acad. Amsterdam. Vol. XV. 1254 m ee, ur (1) = gn (I) = fear J, Va) o 0 If n=O, the first member has no meaning, as g@_—) (1) has not been determined. The second member however reduces to c fem Je (2a) ae le J, (2a) dea = Va 0 v cred = 2 va4(5) rej == ale [| Nrersen, Handbuch der Theorie der Cylinderfunctionen p. 185 (7) |. By applying again the equation (10), we have ye x Sahih - a= [yn a(1) — ga) pale) = — frvene 7 fewer V/Be)dg. (n!) ‘ Via and by summation from n=O to n=, as wo apn me . == Soy = Liv) Ca ~ r = ihn? — = Sagoo fen “J ,(2V a) fe PI, (21V a3) J, (2V Be) dp. 0 Va 0 0 Putting 8* instead of 6 in the latter integral, this reduces to no 2 dee J, (28 a) J,(2BV x) Bag = e—2 +2 J, 2 az) 0 (Nietsen p. 184); thus Ea o — ae Hy (A) == 2Vaxr) J, (2Va) Sonne) eee 0a) 2 or, changing @ into a Sagn (z) = | (apa) J, (a) de. : 0 The second member of this equation has different values according to the value of wz, for — bo Ge oO % YO wet ay (ax) J, (a da) = | 4 oo 0 1 0 «> 0 (Nietsen p. 200), and for «=O fv (aV/ 2) J, (a) da Se (a)da=1. 0 0 8. Now we will apply our expansion to the problem of the momenta. In this problem the question is to determine the function f(y) from the integral equation a, = a F (y) yn dy. 0 Where a, is a function which is given for all positive integral values of 7. Putting f(y=e Fy) (n= a e—Y yn @ (y) dy. 0 Supposing @(y) to be a function which satisfies the conditions ot DiricHLeT, we have Gy=h +4.9,%¢/ +59.) +... we obtain SO ao ty = J by fev y” pe (y) dy. 0 0 Now, this integral has the value zero, when p>n, therefore a) en = = by few Yy" Pp (y) dy 0 . Moreover, according to the equation (7) Gp =n! = (—1) b, C," ) so, with (10) i) 2 ee ee a O(a) le uw I, (2 Vary) de. 0 0 : 0 82* 1256 If now we expand the function xP g (x) =P z bp s = e—t X in a power series, we have, differentiating m times, and putting d D=— da g” (2) = D" (e X) =e 7z#(D+4+ 1) X —e-2 5 (—1p C* Do») X 0 where G 7 2 xP DO X= 3 dty which, for the value «=O, gives Do) X = bs. Introducing this value, we obtain n ai n -. Gy g) (0) = & (—1)p bay Cp = (—1)" = (— 1)" & Cp =(—1)" — 0 0 nS @o (he g(x) = (—1)” =a 0 nm: and _ finally nD oe fly) = [1,2V-2x) = (1) — onde ; (x!) ne 0 This solution agrees with that of Lr Roy. In his memoir the discussion of this formula for different values of @, may be found. Mathematics. — “Some remarks on the coherence type 4.” By Prof. L. E. J. Brouwrr. In order to introduce the notion of a “coherence type’ we shall say that a set M is normally connected, if to some sequences / of elements of M are adjoined certain elements of J/ as their “limiting ~ elements’, the following conditions being satisfied : 1st. each limiting element of / is at the same time a limiting element of each end segment of /. 2d. for each limiting element of / a partial sequence of f can be found of which it is the on/y limiting element. 3. each limiting element of a partial sequence of / is at the same time a limiting element of //. 4". if m is the only limiting element of the sequence {m,} and m, for « constant the only limiting element of the sequence {77,,{, then each of the latter sequences contains such an end segment }17,;{, that an arbitrary sequence of elements m,, for which j continually increases, possesses m as its only limiting element. The sets of points of an n-dimensional space form a special case of normally connected sets. Another special case we get in the following way: In an n-ply ordered set*) we understand by an iterval the partial set formed by the elements w satisfying for e < 8—2 x 6—-10 = 10 points are arranged in associated pairs. So, the pairs of poimts of the involution I* lie on the rays of a complex of order five. Any point G of g is associated to two points of y, the points common to g and to the curve ((7)* corresponding to G. So g is a singular line of the /*; the pairs of points lying on it generate an involutory (2,2). 1D) Oo Proceedings Royal Acad. Amsterdam. Vol. XV. 1270 Also the 27 common bisecants of a’, #*, y* taken two by two are singular lines of the /'. A common chord of «*, 6° bears o' pairs of points determined on it by the pencil (c’*). § 11. We now consider the locus 4 of the points P’ associated to the points P of a line /. To the points common to 7 and each of the surfaces A‘’,G'* correspond respectively 16 points of @* and 12 points of g. Any surface a* contains these 28 points P and moreover the two triplets corresponding to the points common to a? and J. So the locus A is a curve of order 17. As / contains eight coincidencies P= TP’ it is an eightfold secant of the curve 2'7; so any plane ¢ through 7 contains 9 points P’ associated to points of 2. So, the pairs of associated points lying in a plane generate a curve of order nine. The curve (G)’ corresponding to the trace G of g meets ~ in four points; so G is a fourfold point of the curve gy’. In an analo- gous way the nine traces A,, By, Cy of the base curves are double points of ¢. The intersection d® of g and the surface of coincidencies has a fivefold point in G. So g’ and d* intersect each other in 9 x 8 — —-4<5—9 x 2= 34 points differing from the traces of the bases. To these points belong the points of contact of the curves, corre- sponding to coincidencies of the /* the bearing lines of which are contained in ¢. In order to determine their number we consider the three pencils of conics common to y and (a*), (6°), (c*). The polar curves of these pencils with respect to a point P describing a line 7 generate three projective pencils (*), (4°), (c*). The first and the second generate a curve c® with G as node and passing through the three base points A; of «@ and the double points of the three pairs of lines. The curve 6’ generated by the pencils (a*) and (c*) also contains these points. So 6° and c® admit 25 —4—3—3=15 points of contact of three corresponding conics forming therefore coincidencies of the /* with _ a bearing line lying in ¢. So g*® and & have four coincidencies in common the bearing lines of which intersect the plane ¢. 1271 Physics. — “The diffraction of [lectromagnetic waves by a crystal.” By Dr. L.8. Ornstew. (Communicated by Prof, H. A. Loran). (Communicated in the meeting of Febr. 22, 1913). In the “Sitzungsberichte der Kénigl. Bayerischen Akademie der Wissenschaften” ') M. Lave has published a theory —- and together with Messrs. Frieperich and Kwyippinc experiments also — about this highly remarkable phenomenon. W. L. Brace, in a paper entitled “The diffraction of short electromagnetic waves by a_ crystal” *) doubts of the explication of this experiments given by Lave being satisfactory. He proposes an elementary theory, in which he points out that we can describe the phenomenon of Lave by regarding all as if the R6nreun rays were reflected on the sets of planes that can be brought through the molecules of the crystal. In the following lines | will develop the theory proposed by Brage, and at the same time I will give a provisory discussion of some experiments made in the Physieal Laboratory of the University of Groningen which Prof. Haga has been so kind as to put at my disposal, for which I may cordially thank him here. I will confine myself to a regular crystal, the extension to crystals with other Bravats or SOHNKE point-systems being possible without any difficulty. 1. Let us suppose a plane beam of ROn?TGEN rays (direction of ray: z-axis) to strike a regular crystal, of which one of the cubical axes of the point system is set parallel to the incident beam. The origin of coordinates is chosen in a molecule lying within the crystal in the middle of the part through which the rays are propagated. The y and 2-axes are oriented parallel to the other cubic axis. Be the length of the side of the cubes a. The coordinates of a molecule of the crystal then are eka te Pies e f:hdie-eeectuh (ils) in which /,, £, and /, are positive or negative whole numbers. We shall examine the influence of the rays in a point with coordinates §, 4, $, at a distance 7 from the origin. Now whatever may be the constitution of primary R6nrGEN rays, we can always imagine the disturbance of equilibrium being dissolved, according to the theorem of Fourter, into periodical movements. In 1) Loe.cit. June 8 & July 6 1912. Interferenzerscheinun yen bei Réntgenstrahlen. 2, Proce. Cambridge Phil. Soc. Vol. XVII, Part 1. The diffraction of short electro- magnetic w by a crystal. 83 4272 the same way, the movement and radiation of molecules can be described. Thus knowing the effect of the radiation from the mole- cules when a periodical radiation strikes them, we can from this cal- culate for each case the influence of a crystal on ROnTeEN rays. I will therefore consider the problem of a radiation of the wavelength 2 striking the erystal. Under the influence of this radiation the molecules will emit spherical waves. I will indicate the vector of radiation for the radiation emitted by a molecule situated at the origin, by A 9 t r 2 Son 28 | = es Oe ; r Yee ) this formula representing the vector of radiation in the point §76§, while A depends on the direction. The radiation of a point (4) in the point §2$ is now represented by where @ denotes the distance of $75 from (1). This distance is given by g=r— = Gin, H+ Sh tht th) + sale bite 74) A F ? TANG: r a Substituting in the amplitudo @ by r (which is allowed since k,a is smal! compared with 7 etc.) then we get for the vector of light considered a § es (See ge ais ( 2rd And in order to find the total vector of radiation we have to sum up the expression (38) over all molecules struck (or rather put into vibration) by the primary radiation. In doing so we obtain the formula given by Lave and with that, his cones of maximal intensity. However, we can show that there are ofher maxima still, besides the cones of Laur. I will suppose r to be so great that we can neglect the fourth term. The maxima that do not appear in Lavr’s theory can be made to appear by first taking into account the interference of the points for which t, (1-2) —74,— 24, =0 rT bf Tr +7k, +24) (3) x Tr 1273 Further I wil substitute */, by a, */, by 8, °/, by y, then a + 6? + y?=1, thus in this notation we have to fix our attention upon the interference of the radiation from those points for which the numbers /& satisfy the equation k, (4—a) — Bk,—y k, = 0. Now if this equation determines a great number of points, the pulses originating from the molecules will interfere without differ- ence of phase. This will be the case when the plane w (1—a) — y 8 passes through the molecules of the crystal. Now, a plane through molecules may in general be represented by hier tebytetee aN GP key, h, fed) where ac are whole numbers, that we constantly suppose to be reduced to their smallest values possible. The values of «fy, where maximal intensity is thus to be found on account of the cooperation of the points of a plane, we can find by putting eee Feary, ay =O a ra b oe c while «+ 8?-+ y? must be 1. From this we find B=0, y= 0, a=1 (i.e. the light transmitted directly, a point of interference that is not observable) and __ +c —al 3 OS tn Cao Sh (5) ara pea bs bd - —2ac 1=5 a? Eb? -b 2 Now we can easily show the direction thus found to agree with the direction in which the R6nreen-beam would be reflected if the chosen plane rich in molecules should be a mirror. For the angle of the normal of (4) forms with the z-axis an angle of which the cosine is ————_————, the plane of incidence has for equation: ane ae ty—bz=0, the direction cosines of the reflected ray are a'p' y'. Thus we have (a + 1)a4 BO y'c=0 | Bc—yv'b =0 | Sy esas 6) at + php y2=1 1274 The set of valnes (5) satisfies (6). In this way we .have shown the maximum to lie really in the direction of reflection. We can see this without calculation, and I principally gave-the above calculation to show the connection between ].ave’s considerations and mine. For if P the origin of rays, and Z the point of observation, both are situated at a distance from the molecules of a plane which is infinite with respect to the dimensions of the plane of which A and B are arbitrary molecules, then the way PAL = PBL, and there is interference of the light emitted by the molecules, if the angles of PA and AZ with the normal of the plane are equal. Thus there is interference in Z, if the point lies in the direction of the ray reflected in the plane. For the rest the disturbance of equilibrium, if N is the number of particles of the plane, will be \ times as great as the disturbance caused by one particle, and therefore the intensity will be \’ times as great. The intensity of the maximum is of the order of the number of molecules in a plane, i.e therefore, of the order of the “two-cone” maxima of Laus. As we may now presume, all pulses will interfere in the same direction which originate from planes in the erystal parallel to the one considered. The equation of similar planes is aa + by - tz == 2 sa where I must be a whole number, zyz being whole multiples of the side a, the coefficients 4, , and ¢ also being whole numbers. Expressed in «@y the equation takes the form z (1 —«)—yB—2y =d. We therefore have a h c sa = = ==) 1 Sar pon y @ which gives for «py the same values as in the preceding formula, whereas we have SSS a? + b? -+ ¢? or Qs aa. a? + b? + c® It is easy to introduce into this formula the smallest distance of a thy (1 —«) aes B—Kk, i — . a . the planes under consideration. It amounts to ———— . For if Va? Ie are ? 1275 ar + by +¢z=d is a plane, we pass to another plane of the same kind by putting: ae + by + cz =d + (a,a + BO + y,c)a where @, 8,7, are whole numbers. Now the distance of the two planes considered is = (4,0 + 3,6 + y¥,c) Var + §% -+ ¢? which, a6c being given, must be a minimum. This minimum is reached if «,,,,7,, are such that a0 + p,6 + y,c =1. a, 6 and ¢ being given, this equation can always be satisfied in a? ways. The minimum distance of tke planes I will represent by /,,. We may still observe that in applying the above results we have the means of easily comparing the number of molecules lying in the different planes. The number of molecules that each plane contains will be greater, the greater the distance of the planes of a given kind is. If the number of molecules pro unit of volume is yr, then a plane with parameters abe, contains Lo eae molecules pro unit of surface. Veit+o+ec The plane of the kind considered, denoted by the parameter s, contains V, molecules. The contribution to the vector of radiation, originating from this plane, thus amounts to NsA (; r 281 Ln ) cos 22 | — — ———— Us 7 Xd We + 2 Je c° Taking the sum with respect to s over all possible values, then we obtain the total vector of radiation originating from the emission of molecules. Generally, however, the contributions to the vector of radiation here considered and originating from parallel planes, are 4 5 4 a Uy incoherent, unless, which may exceptionally occur, and ——— Via? + 6? + ¢? are mutually measurable. If we have to do with several wave- lengths, this will certainly cause incoherence. Now, the intensity of the maxima observed ean easily be found if for a moment we imagine an equal number of points getting into vibration in all planes considered. Then, if 2 is the number of planes considered, the intensity is nN, where nN? is therefore substituted for ENS 1276 Taking into consideration that nN represents the total number of the molecules struck by radiation N, then we see that the intensity of the maxima is proportional to RN so that the spots are the more intense according as they are caused by planes in which the number of molecules pro unit of plane is greater.') We can even to some degree extend what was observed above, so as to come to a conclusion which perhaps can be controlled by experiments. Take an z-axis in the direction of the normal of the planes, then « will pass through the values +1, + Ql, + kl, ete., in which the same positive and negative value ought to be taken for y, when the origin is chosen in the centre of the plate. For each value of x the part cut off from the plane by the incident beam can be calculated. Be this part S,, the number of molecules pro unit of plane is r/,, the contribution to the intensity of the plane S,, therefore y? eve ise and the total intensity is therefore »* /,? 2,7, for which we may approximately write y? In {8* dx. By applying this formula in different cases, we may come to a further trial of the theory ; however, we do not yet possess the necessary photometrical experimental measurements. The intensity of the maxima now under consideration is greater than that of the “two-cone” maxima of Laur (of the order 10’ times as great), it is, however, of the order 10’ times as small as that of the 3 cone maxima of Laur. However, the experiment forces us to such a degree to accept the explication by reflection, that probably in no other way than in the one described above the photograms may be explained, as I will show below. : We may still observe, that in the consideration as given above, the molecules are assumed to contain only one electron. We can, however, easily get rid of this supposition by multiplying V and v by s, where s is the number of electrons pro molecule. Perhaps, by taking this into account, we may derive an estimation of the proportion of the numbers of electrons pro molecule in different erys- tallised matter. 1) We may here observe, that by this we have the means of comparing the numbers NV, in matter with given density, for planes that are struck by equal radiation under similar circumstances, an We may also observe, that in the direction of the propagation of the primary radiation too an interference can be noticed between the secondary pulses emitted and the primary radiation. At this interference a difference of phase shows itself, which to such a degree diminishes the primary radiation as is necessary to deliver the energy of secondary pulses emitted in the directions of reflection. We can still somewhat nearer consider the influence of a single plane. Be the reflecting plane chosen as yz-plane, be the «y-plane the plane of incidence, and « the angle of incidence. Let us now consider the vector of radiation in a point ®=rcos a, y=rsina + 9, ae The vector of radiation is given by ils Aka t r kia kia — > = cos 2x -—-— + —y+ Gal: vig . which, when summed up with respect to £, and 4#,, will give aga a,A t = ay Gee ane, EL: :os N— arcos N —: N +1)— asin(N : cove ( 7” cos N a CEA ax sin(N } Da xx sin(N +1) a anx , aba 2A 22 For 7 =0 ¢=0 we obtain the maximum found above (diffraction maximum of the order zero) with the intensity there given. A second maximum (first maximum of diffraction) could appear if ya af ; 22 2a F — =—1, or —=1, or thus if 77 =— or [=—. Now r is about 4 2d 2A a a in the experiments, and a is of the order 10-8; should 4 be much smaller than a, then this second maximum would be observable. In the photograms we do not find diffraction-rings of this kind. Thus if the wavelength is very small with respect to 10-8 then such images do not oceur, but if 4 is of the order of @ or not much smaller, then we can neither observe such images, the latest estimation giving for 4 a quantity of the order 10~-°. This might well thought to be consistent with the result that circular fringes do not appear on the plates. BraGG has explained the form of the spots, — ellipses whose long axis has the direction of the line perpendicular to the plane of inci- dence which belongs to the plane observed — by observing that the different layers are struck by waves not wholly parallel. However, he does not take into account that in each point the radiation of molecules of all the planes interferes. The form might rather be explained by observing that the intensity in the said direction 1278 approaches less rapidly to zero than that in the direction perpendicular to it, whereas we have also to take into account that the distance between the source of radiation and the point of observation is not infinitely great with respect to the dimensions of the plane struck by radiation. Trying to explain the form of the spots by assuming a rectilinear propagation we do not come to the right result. E. g., if we have to do with a reflecting plane lying cblique to the beam, then the photographic plate would cut the reflected cylindre just in an ellipse, whose longest axis is perpendicular to the direction in the plane already considered, whereas on the photograms we observe just the contrary. In the pencil the beams are not wholly parallel. What is the influence of this on the diffraction image ? If the beams forming a small angle will have to give the same reflected beam then the reflecting planes must form a small angle too, and otherwise. Now if e+ + by-+cz=0 is the plane rich in molecules, then a plane very little differing from it as to its direction will be if 1 ts (Bo (o bye (or tan 1g q J where p, g, 7 are large whole numbers ; or, gr (pa + 1) + (69 + D2 + Co + I pg=0. This plane however will be very poor since /, here becomes ] Vgr(ps+1) +... is thus exclusively ruled by the planes very rich in molecules. Of course, each of the pencils in the incident beam gives a reflected pencil to a plane rich in molecules, but since the incident beams differ but a little, the reflected ones will not do so either. Always, when among the planes considered one is rich in molecuies the spot will be formed by the influence of one of the pencils. When we want to consider directly very thin pulses, we come to a problem which agrees in some way with the one treated by Prof. Lormntz '). However, we can now directly consider the pulses. reflected by the molecules, which were dealt with in this treatise, to be combined to pulses formed by the planes rich in molecules, since in this case each of such planes gives only one pulse. This fact hinders the coinciding of the pulses considered in the publication mentio- ned. Take e.g. pulses originating from a definite set of planes, be the , which is very small. The forming of the patterns l dimension in the direction of the normal /, then we have 7, Dulses, m 1) Verslagen Kon.Akad.y.Wet. XX11912/13p.911. ,Overden aard der Réntgenstralen”. 1279 of pulse thickness A, together having a thickness // = 4 or l! m nme Which is a small quantity so long as 4 is small with respect nm to /,, as is generally the case. When the pulses do coincide, which again will be the case when we take into account the primary dis- turbances of equilibrium emitted successively by the anticathode, then the considerations developed by Prof. Lorentz must be applied. Thus also when operating with the hypothesis that the Roénreun rays exist in pulses, the incoherence of the pulses originating from the different parallel planes is a matter of fact, and therefore also on this assumption the intensity of the spots in the photogram will be proportional to the number of molecules pro unity of sur- face of the corresponding plane. We may suppose that in this direction also the solution is to be found of the question why the effect of the motion of heat which causes the molecules to vibrate around the corners of the net, is so small. Now we may still with a single word discuss the photograms which were at our disposal. The way in which they were taken agrees in many points with that of Laur, only it has been somewhat less complicated. In order to shorten the time of exposition, a fluorescent screen was used. The spots occurring on the plates may be arranged very conveniently into ellipses, hyperbolas, straight lines and sometimes parabolas; as Brage has already explained, points of such a conical section originate from the reflection on planes rich in molecules, which have a line rich in molecules in common. The conic section then will be the inter-section of the photographie plate and a cone, produced by letting the incident beam turn about the said line rich in molecules. The photograms at my disposal were: 1. Rock-salt. The direction of incidence was lying along a cubical axis. The diagram produced agrees with the one for zinc-blende. The distance of the crystal from the photographic plate was 4 em., while 3.56 in Lavr’s experiment. By magnifying Lavn’s pattern in the corresponding proportion I got one perfectly congruent with that of Prof. Haca. Only a few ellipses were missing or were re- presented less intense, which may be attributed to the fact that with NaCl the net is centric cubical, whereas ZaS shows cubes with centrie cube faces. This agrees with the erystallographically deducted cleavability, which lies in the direction of the plane richest in molecules. The fact that the patterns for matters of totally different kinds are identical, is a strong proof for the above developed theory. 1280 2. CaF* transmitting the radiation along a triangular axis, gave a pattern identical with ZnS. 3. Topaz, transmitting radiation in the direction of the bisectrix of the acute angle of the optical axes, gave a pattern which can be explained by assuming the net of the molecules to be built up from parallellograms with equal sides in the plane perpendicular to ihe bisectrix, and by points perpendicularly placed above the net points obtained in this way. From the photogram I calculated the angle of the pg. It amounts to 66°10’. A trying of this angle with the angles of the planes of the prism, known from erystallographic data, gives a suitable agreement. [ hope to have an opportunity to calculate the proportion of sides ete. for more types of Bravais nets. We may suppose that in this way we shall obtain the possibility of deciding between the different structure theories, and of coming to a rational description of crystals. 4. The experiment of reflecting RONTGEN rays on the cleavage plane published by Brace in “Nature” of 23 of Dec., was repeated with mica. Because of the plate being longer exposed this time, there appeared on the plate, besides the reflected spot upon the planes parallel to the cleavage plane already found by Bragg, also a number of other points of which by far the greater part were lying upon an ellipse rather changed into a circle. For plane of incidence the principal cross-section had been chosen, the photographic plate was placed perpendicular to the plane of incidence. The circle was lying asymmetrically, although the plane of incidence had been chosen in a principal cross-section. Supposing the monoclinic net for mica to exist in a rectangle (in the cleavage-plane) and a side inclining with respect to this rectangle, lying in a plane perpendicular to the cleavage plane, then in order to explain the patterns we must take for the proportion of the sides of the rectangle and the inclining side 8:13: 100, and besides we must suppose the angle of the cleavage plane and the inclining side to amount to 85°. The pattern obtained can still better be explained by using the second net of the monoclinic system. The basis then is a pg with very long and almost equal sides, and an angle of about 85° between the short diagonal and one of the sides. The third side is perpendicular to the pg considered, the rectangle through the short diagonal of the basis is centric. The cleavage plane then is // to this rectangle. This structure shows for mica an approach to the hexagonal type. The same results were shown by the pattern obtained when 1281 mica was crossed by a radiation in a direction perpendicular to the cleavage plane. The photogram so obtained was much weaker, although the time of exposition was taken equally long, and although the intensity of the primary radiation was the same. This may be explained by observing that in the reflection the cleavage plane rich in molecules gives a spot, which does not appear with the transmitted radiation. But the other images are to be taken with respect to corresponding planes. The explication therefore must run otherwise. In both cases a cylindrical pencil with cross-section of about 1 mm. strikes the plate. Consequently the part struck by radiation of the plane richest in molecules, the reflection taking place under an angle @ near 90°, is a good deal greater, namely in the proportion —, the number of working layers being COS the same. In the most unfavourable case of the vector of radiation lying in the plane of incidence, the working vector of radiation, if a = 90 —és where @ is a small angle, is — Ssin 28. The intensity of the image reflected thus will be proportional to I? sin? 28 (ow)? sin’? B of particles pro unit of surface). For the case of the vector of radiation lying in the plane of incidence, sin 23 in the numerator is to be substituted by the unity; then the intensity will be great. As the incident pencil is not polarised, we have to expect a stronger effect with the reflection than with the light being directly transmitted. (where o is the diameter of the pencil, w the number 5. The reflection on rock-salt (perpendicular to a cubical axis) again gave a set of spots very clearly observable, situated on conical sections through the central spot. The spots were lying close together on the plate; as may be supposed they are partly to be assigned to different not wholly parallel layers in the erystal. Anatomy. — “Nerve-regeneration after the joining of a motor nerve to a receptive nerve.” By Prof. J. Bonkn. (Communicated in the meeting of February 22, 1913). After the primary discoveries of Fontana, Monro, CrviksHank, at the end of the 18 century, no phenomenon of life has been more closely studied than the process of nerve-regeneration. Attention was drawn to the primary degeneration of the peripheral portion of a cut nerve deprived of its trophic centre, the ganglion cells (WALLER), and the’ manner after which a new nervous union was established 1282 by the growing out of the fibers of the central end into the old path of the peripheral nerve-portion became better and better known. It was seen how the new nerve-fibers growing out from the cut-end may extend to the organs normally supplied by the nerve in question, form new end-organs and how thus even a functional regeneration may take place. It was seen how regenerating nerve-fibers may even grow into a nerve-path belonging to another (cut) nerve, and how motor fibers from the cut-end of the nervus accessorius for example may grow into the peripheral degenerated portion of a cut facialis nerve and thus in the end provide with motor nerve-endings the atrophying muscle-fibers of the mimic muscles. This phenomenon leads naturally up to the question, whether it would be possible, after a nerve containing motor and receptive fibers has been severed in its course, that motor nerve-fibers from the cut-end grow into degenerated receptive fibers of the peripheral portion of the nerve, and vice-versa. This question, which was studied for the first time by Bipper in 1849 and more closely by Pamapravx and VuLpian in 1863 and 1873, and by different authors in the course of the years, has been answered almost universally in a negative sense. Even Laneiry and AnprrsoN, who studied the question as late as 1904, denied the functional and trophic regenerative union of motor and receptive fibers, and Beran, who studied the question for (as far as I could gather) the last time in 1907‘), gives as the results of his investi- gations the following statement: “dass auch unter den fiir die Ver- einiging giinstigeren Bedingungen (nach Durehschneidung dev moto- rischen Waurzeln) eine functionelle oder auch nur trophische Ver- wachsung zwischen rezeptorischen und motorischen Fasern_ nicht eintritt.” (I. ¢. page 481). And yet, notwithstanding these statements, the question must be answered in a positive sense. To study the question, the same course was taken as that followed by Puitipravx and VuLpiaAn making their classic experiments in 1863 and 1873 (Verpian). The nervus lingualis and the nervus hypoglossus of the same side were both eut through. Only I did not join the central end of the lingualis to the peripheral portion of the nervus hypoglossus *), as was done by the investigators mentioned above, but followed the example given by Berne in 1903, and joined the 1) Prtuseas Aieniv, 1i6 Bd. 1307. *) In a second note | hope to describe the results of this line of expériments. 1283 central end of the n. hypoglossus to the peripheral portion of the nervus lingualis. The two other nerve-ends were both exstirpated as far as they could be reached. The entire cycle of experiments was the following : a. In a number of fullgrown hedge-hogs (14 in all) the right nervus hypoglossus was cut through, and the ends joined together. After a lapse of several days, weeks or months the animals were killed, the bloodvessels were rinsed by means of the fluid of Rineer-Lockr, and the tissues were preserved by means of an injection of a very slightly alealine solution of formalin into the aorta; afterwards the nerves and the nerve-endings inside the tongue were stained by tbe Bintscnowsky-method, and cross-sections or sagittal sections of the tongue examined under the microscope. The phenomena of regeneration of the motor fibers after the reunion of the severed ends of the n. hypoglossus I will not diseuss here. In this connection it only interests us to know, that in preparations made of the tongue of animals killed 5 to 10 days after they were operated upon, all the fibers of the n. hypoglossus of the right half of the tongue were entirely degenerated, the fibers of the nervus lingualis having of course remained entirely intact. In this way I obtained a very accurate insight into the topographical relations, the course and distribution of both nerves throughout the tongue. These relations are very systematic, so that when we only take care to compare analogous cross-sections of different tongues with each other we are able to tell immediately in a given cross-section the places where the nerve-fibers of the n. lingualis and those of the n. hypo- glossus (at least the larger rami) are to be found. For a safe and accurate judgment of the results of the following group of experi- ments (6) these preliminary experiments are absolutely necessary. b. In another series of full-grown hedge-hogs at the right side of the neck the nervus lingualis and the nervus hypoglossus were cut through, great care being taken to make as small a wound as was possible and to injure no other elements. After this the central cut- end of the n. hypoglossus was joined with the peripheral portion of the n. lingnalis, the two other ends were exstirpated as far as possible, and the wound closed. After a lapse of some weeks or months the animals were killed, and stained sections through the tongue examined after the manner described above. To prevent ulcerative processes to occur in the lamed and anaesthetic half of the tongue, before the operation all the teeth of the right side of the mouth were stripped of their crowns. After that ulcerative processes in the tongue did not occur any more. 1284 Examination of the place of section of the nerves showed in the first place that in the greater half of the cases, viz. in 11 of the 20 aminals of group 4 which were operated upon, a complete union of the heterogeneous nerves had taken place. The central cut-end of the hypoglossus adhered firmly to the peripheral portion of the lingualis, and after one or two months the peripheral portion of the joined nerve had turned white again, viz. had become myelinised. After a due lapse of time even the place of union of the nerves, the cicatrice itself, was white. I however got the impression, that the process of union of the cut-ends has a somewhat longer duration than after the dissection and joining of homogeneous nerve-portions. The experiments of group a showed, that already after the lapse of one month regenerating nerve-fibers were visible in the tongue, and after one and a half month regenerating motor endplates were visible on the muscle-fibers even at the tip of the tongue. In the experiments of group / it was only after 2 or 3 months, that I was able to detect the regenerating fibers inside the tongue. These results were confirmed in all points by the microscopie examination. The regenerating nerve-fibers of the hypoglossus had grown through the cicatrice, had reached the peripheral portion of the lingualis and had grown into it just as in the regenerative union of homogeneous nerve-ends. Sections through the place of union tend io show the same intertwisting of the neurofibrillar bundles, the regenerating axons, in the cicatrice, the slow forward movement, and at the end the same picture of the regenerating axons penetrating into the channel of the degenerated peripheral portion, in casu the n. lingnalis. Nearly all the regenerating fibers of the hypoglossus penetrate into the peripheral nerve-end, in casu the n. lingualis. A few fibers only pass alongside and are seen growing out into the surrounding tissue, the perineural connective tissue. The examination of the microscopic sections gave me however the same impression as the macroscopic inspection, viz. that the process of regeneration, especially of the penetrating of the regenerating axons into the peripheral nerve-end (lingualis) has a somewhat longer duration and slower movement than in the union of homogeneous nerve-ends. The intertwisting of the axons is more dense, and a greater number of the so-called spirals of Prrroncrro are formed. As however the nervus hypoglossus possesses a far greater number of nerve-fibers than the nervus lingualis, finally the peripheral nerve- end (lingualis) becomes entirely filled-up with the regenerating axons of the hypoglossus nerve. The examination of the cross-sections through the tongue gives 1285 corresponding results. When we examine such a cross-section in a successful experiment (and only those are considered), we find all the sections of the branches of the n. lineualis filled with regenerating nerve-fibers, whilst those of the n. hypoglossus are entirely (or nearly so) devoid of them, showing only the so-called bands of Binenrr of the degenerated nerve-tubes. This is — and that gives us the answer to the question mentioned above, why no physiological regeneration is to be found not only the case with the larger branches, but also the smaller and smallest branches present the same aspect. When the larger branches of the hypoglossus are devoid of regenerating axons, no trace of these is to be found even in the smallest branches of the hypoglossus, whilst even the smallest branches of the lingualis are full of regenerating axons, and a dense plexus of regenerated nerve-fibers is present in the mucous membrane of the tongue, in the connective tissue of the submucosa, but not a single motor nerve-plate is to be found on any of the musele-fibers, in sharp contrast to what we find after the regeneration of the nerve-fibers of the hypoglossus into the peripheral end of the hypoglossus itself (group a), where we find everywhere the regenerating end-plates on the muscle-fibers. When regenerating nerve-fibers have penetrated into the old channel of a peripheral degenerated nerve, it clearly is impossible for them to get out of if and they are compelled to travel it to the end. Nowhere is this rule demonstrated so clearly as it is done here. The branches of the lingualis nerve wind their way towards the final station, the mucous membrane, between the bundles of musele- fibers, and often seem to come into close contact with them, as is clearly shown by the examination of the sections in the experiments of group a And yet not a single nerve-fiber of the regenerating hypoglossus nerve leaves the channel of the lingualis in group to form an endorgan on the muscle fibers as it is to be seen every- where in the experiments of group a’). Now the question might be asked, whether these regenerating nerve fibres growing into the peripheral end of the nervus lingualis are in reality hypoglossus fibres, and whether it is not more probable that the ingrowing fibres are after all lingualis fibres, which grew out from the central end of the lingualis and have found their way into the old nerve channel. To exclude this source of errors, in a number of animals, in which 38 and 4 months ago the central end of the n. hypoglossus bad been joined to the peripheral end of the 1) J. Borkr, Ueber De- und Regeneration motoriseher Endplatten, ete in Verhandl. der Anat. Gesellsch. Versamml. in Miinchen. April 1912. S. 152 84 Proceedings Royal Acad. Amsterdam Vol. XV, 1286 n. lingualis (group 4), the cicatrice was opened again, and after it had been ascertained, that the nerve-ends had grown together and that the peripheral portion was myelinised already, the eentral ecut-end of the nervus lingualis was prepared again, and cut out with a part of the surrounding connective tissue as far as it was possible to reach it, the connective tissue being exstirpated because it might be possible that some nerve fibres from the central end of the Jingualis had grown into the connective tissue and from there had reached the point of joining of the two nerve-ends. Ten days were allowed to the eventually cut nerve fibres to degenerate, and after that time the animals were killed and prepared after the manner described above. Ten days may be supposed to be entirely sufficient for the degeneration of all the nerve fibres eventually supplied by the central portion of the lingualis nerve. One of these experiments, which looked entirely successful, was studied as accurately as possible, and gave the following results: from the central portion of the lingualis nerve not a single nerve fibre entered the peripheral lingualis, nor had any other nerve (a small muscle nerve for example) regenerated into the peripheral lingualis, except the nervus hypoglossus. From the central cut-end of the hypoglossus, which was in full process of regeneration, a large number of regenerating nerve fibres had grown out and had all penetrated into the peripheral end of the nervus lingualis. Only a very few tibres had grown into the perineural connective tissue around the lingualis nerve. Inside the tongue all the lingualis branches were full of regenerating fibres, the hypoglossus branches were entirely devoid of them. The regenerating fibres, which here could have no other source than the hypoglossus, had followed the course of the lingualis nerve down to the smallest branches of the nerve plexus in the mucous membrane of the tongue. Of so-called autogenic regeneration (A. BerHe) no trace was found (only full-grown animals were used for experiments). The fibres of the hypoglossus nerve, having arrived at the end of the terminal branches of the lingualis, begin to form nerve-endings of - different patterns. It is here not the right place to deseribe elaborately the differences in form and in extension of the nerve-endings. I hope to do that in extenso elsewhere. Here I will only mention two or three points. It is certainly an interesting fact that the hypoglossus fibres after having penetrated into and arrived at the end of the lingualis tract, begin to form terminal branchings and different end-bulbs. But net only that they form nerve-endings in the connective tissue, but 128% they even penetrate into the epithelium. In most eases the terminal fibrillae do not penetrate far into the epithelium, but remain Fig. 1. Nerve endings of hypoglossus fibres in the epithe- lium and the connective tissue of the mucous membrane of the tongue. a, b, ¢. Ascending fibres, not penetrating into the epithe- lium, but turning round and descending again towards the connective tissue. é = fibres penetrating into the epithelium. in the basal layers, where they form small endnets around different epithelial cells, but sometimes they penetraie into the upper layers of the epithelium (fig. 1 e). It seems however that the epithelium offers a certain resistance against the ingrowing fibrillae, that makes it difficult for them to penetrate into the epithelial membrane. In the normal half of the tongue at all points of the epithelium the neurofibrillae may be seen 84* 1288 io penetrate far into the epithelium, sometimes as far as the super- ficial layers of cells. In the other half of the tongue, where the fibres of the hypoglossus nerve are regenerating along the nerve paths of the lingualis, one sees often strikingly how the nervous fibrillae grow right up against the basal side of the epithelium, but then do not penetrate it, but turn round and descend again, ending inside the connective tissue with an endknob or endnet, or run for a shorter or longer distance along the basal side of the epithelium es if seeking entranee, and then turn round and end between the elements of the connective tissue as described above (fig. 1 a, 4, ©). In the second place it is an interesting fact, that the terminal branches of the hypoglossus nerve fibres often show a striking resemblance to the endplates formed on the muscle fibres during regeneration after simple cutting of the hypoglossus nerve (group of experiments). An example is given in the figs. 2 and 3. In fig. 2 is drawn a set of terminal branches formed by a hypoglossus nerve fibre against the basal membrane of the epithelium, in fig. 3 is drawn a regenerated motor end-plate on a muscle fibre of the tongue after x 1 \ Fig. 2. Terminal branches of a hypo- Fig. 3. Regenerated motor end- glossus nervefibre in the connective plate on a muscle fibre of the tissue of the mucous membrane of the longue (hedgehog group a). tongue (group 0). ——— 1289 the cutting of the hypoglossus nerve. It is ceitainly interesting, that even in such atypic surroundings the hypoglossus nerve fibres try to build up their proper typical endformations. In the third place the following point may be mentioned. In the course of the branches of the lingualis nerve are distributed groups of ganglion cells of sympathetic nature, probably belonging to the chorda-tympani part of the lingualis nerve. The fibres of the lingualis (chorda tympani?) form a_ beautifully impregnated network with meshes and interwoven fibrillae on the surface of these cells. After the cutting of the lingualis nerve this network of fibrillae disappears entirely, the cells themselves undergoing apparently no alteration. The fibers of the hypoglossus nerve appear to be unable to regenerate this network of neurofibrillae, at least in all my preparations, even there where the nerve plexus in the mucosa and the submucosa was very well regenerated, and all the branches of the lingualis nerve were full of regenerating fibres, no trace of the above mentioned network could be found. To conclude, it appears from these facts that fusion of heterogenic nerve-ends is not only possible, but may lead to distinct regenera- live processes which do not differ much from these following on the fusion of homogenic nerve-ends. A functional (physiological) regeneration however does not take place, because the regenerating fibres are not able to reach their proper destination, and no contact with the muscle fibres is acquired. And yet a certain amount of functional regeneration may be obtained after all. Firstly some fibres of ihe hypoglossus nerve will erow out, not into the neural tubes of the lingualis, but in the connective tissue of the perimeural sheath. These fibres after a time will reach their destination, the tongue, and these fibres will have no difficulty in coming into contact with the adjoining muscle fibres and will form new motor end-plates on them. Secondly here and there in the preparations a fibre was found, which in forming terminal branches in the connective tissue of the mucous membrane of the tongue, had come in contact with the end ofa muscle fibre, and was seen to run alongside it for a distance (towards the centre of the tongue) and then to form a small end plate on the surface of the muscle fibre. This last mode of functional regeneration | met with however only in a few cases. Leiden, 18 February 1813. 1290 Physiology. — “Vhe efject of fatty acids and soaps on phagocytosis”.*) By Prof. Hampurcer and J. pe Haan. (Communicated in the meeting of February 22, 1913.) In our former paper *) we drew the attention to the particularly noxious effect of fatty acids on phagocytosis. Already at a concentration of 1: 1000,000 the pernicious influence of propionic acid became manifest. The law of division-coeflic:ents, obeyed by all the other fat-dissolving substances,.examined by us, did not lead us to expect such a poisonous effect of propionic acid. How could this abnormal action of propionic acid, and likewise of butyric acid, which was also examined by us, be explained ? Is it caused by a noxious effect of ions of H, or perhaps also by a specifically injurious effict of the anion of fatty acid? At that time we failed to supply an answer to this question. In order to determine to what extent the ions of H are respon- sible for the noxious effect of the fatty acids we exposed the TABLE I. Comparison of sulphuric acid- and propionic acid solutions with equal percen- tages of ions of H. The solutions act upon the leucocytes during 5), hours; the leucocytes are brought into contact with carbon during 25 minutes NaCl-solution in which ,; Number of | Number of leuco- Percentage leucocytes cytes having of has been dissolved: examined taken up carbon phagocytosis nothing | 349 | 101 29 hee "100-000 208 0 Yeas 1 Proprionic acid 1-5)199.000, 301 0 0° > : ees? 1500-000 194 i 6.7> Proprionic acid '5/500.000 180 0 OF | | Hie "500-000 148 33 | 22.2> 3 Propionic ac. !5/590.000 215 | 52 24.22 | | 1) A more detailed account will be published in the Archiv. f. (Anat. u.) Physiologie. 2) The effect of substances which dissolve in fat on the mobility of Phagoeytes and other cells. These Proceedings Vol. XIV p. 314. 129] leucocytes to the action of fatty acid and of sulphuric acid-solutions containing the same percentage of ions of H, and determined subse- quently its phagoeytarian power. The table on p. 1290 will need no further explanation. It follows from this series of experiments that the noxious effect of aqueous sulphuric acid- and propionic acid-solutions manifests itself at the same concentration of ions of /7. This renders it in a high degree probable that the noxious effect of a strongly diluted solution of propionic-acid must be attributed to the action of ions of H. If this view was the correct one, if it was not the anion of pro- pionic acid, but the ion of H which had to be reckoned with, it might be expeeted that the propionate of sodium, in the correspond- ing dilution, would have no bad _ effect. This was indeed not the case, as appears from the following table. TABLE II. Effect of Na-propionate on phagocytosis. The propionate acts upon the leucocytes during half an hour. The leucocytes are brought into contact with carbon during half an hour at 37-. NaCl-sol. 0.9% in which Number of | Number of leuco- Perc. leucocytes cytes having of has been dissolved : examined | taken up carbon phagocytosis | | 768 373 | 48.5% nothing | 323) | 163 | 50.4» | | | Na-propionate 1:100 ) | (i.e. 1 gr. propionate dis-} | 923 535 He i Ors solved in 100 ccm, NaCl) ) | Na-propionate 1 : 250 549 332 60.4 » ae 1000 ih) Fat 460 58.6 > 412 247 59.9 » > 1: 5000 344 83 24.1»? | > 1 : 25000 891 437 49 >» > 1: 100.000 633 321 | 50.7> 1292 A hurtful effect of anions of #7, even in much greater concen- trations than those in which ‘he anion was used in the propionic acid experiments, is evidently out of the question. The propionate 1: 25000 and 1: 100000 leave the phagocytarian power intact ; propionic acid in this concentration destroys all the leucocytes. But what is much more remarkable than this result is the favour- able effect of still higher concentrations of propionate 1: 100; 1: 250; 1: 1000) on phagocytosis. By dissolving for instance 1 gramme of propionate in 250 cem. of NaCl 0.9°/, the phagocytosis is found to increase by 100 °/,. This increase, which was also caused by the Na-salts of butyric acid and formic acid, was all the more remarkable, as the fluid was made strongly hyperisotonic by the addition of these soaps, and as was shown hyperisotony has nearly always a highly injurious effect upon phagocytosis. This is clearly confirmed by the following experiment in which isosmotic NaCl-solutions, with and without propionate, are compared with each other. The comparison relates to the following isosmotic solutions: NaCl 0,9°/, and NaCl 0,9°/, NaCl 1, °/, ,, NaCl 0,9°/, + Na-Propionate 0,165°/, Nah iiys Se eiNaClOioyees, 2 eee. 0,23 °/, NaCl aoe. a aNaClOeye it] a. ee 0,5 °/, NaChk1,3°/, 4 .Na@l.0,99/. 1 5 abe: 0,66 °/, These fluids acted for half an hour upon fresh leucocytes ; then TABLE III. Effect of isosmotic NaCl and NaCl-Propionate-solutions. NaCl-solution 0.9% Percentage of Percentage of Solution | leucocytes having leucocytes having | taken up carbon + taken up carbon : Nacl0.9/, | 132 s¢ 100 = 28.20) nothing | 88 x 100 = 25.50) Oe | ae 266 ag » 1 » | 135¢10024.7> |Na-Propionate 0.1650),| 22 >< 100 == 12.9 457 ‘ +ieay esos é 62 113 » 11> ogre tatbe > 0.33 < 316 < 100 = 35.9» } 69 193 ey aye | ag 26 100 = 13.1 > > 0.5 » 643 >< 100 = 30 » 6 | 116 a > 1-3) | 979 % 100 = 2.2> > 0.66 > 40g 100= 27.12 1293 /, hour the suspensions were brought into contact with coal for at 37°, and the preparations were made. This result is indeed interesting, for we find that when by the application of a strongly byperisotonie NaCl-sol. (1.1°/,) the phago- cytosis has been reduced by 50°/, (from 28°/, to 15,5 °/,) a NaCl- solution, isosmotic with the former, in which, however, part of the NaCl has been replaced by propionate, promotes phagocytosis to a considerable extent (to 35.7 °/,). A similar result was obtained with lenecoeytes which had been left in serum containing citrate of Na during one night, and which had consequently lost part of their phagocytarian power. After the results obtained with the propionate it might be expected that also the butyrate and the formate would give the same results. This was indeed the case. We subjoin a table, showing the results obtained with butyrate. This table shows that Na-butyrate in a dilution of 1:1000 has TABLE IV. Effect of butyrate of Na on phagocytosis. The NaCl-solutions containing butyrate have acted upon the leucocytes for half an hour at room-temperature; then they were brought into contact with carbon for half an hour. NaCl-solution 0.9%) | Percentage of | leucocytes having + | taken up carbon ax 100 = 29.39), nothing Na butyrate 1: 100 | 448“ 100 — 29 138 2 1:250 | 75 X100=28.8, 1: 1000 321. 100 = 38.1 v 841 7 Y 306 5 1 :5000 nog 6 100 = 37.8, 1:25000 | 200° 100 =39.7 » os 55478 =i i ” 1294 increased phagocytosis (from 28°/, to 38°/,), and that this increase is still mere obvious in a dilution of 1: 25000. As regards the formiate, here too a dilution of 1: 1000 caused an important increase, which continued at 1; 2000, and which was still clearly visible at 1 : 10000. An attempt at an explanation of the facts observed. How must the favourable effect of propionate and of other soaps on phagocytosis be explained ? Is the cause the same as that which we adduced to explain the effect of lipoid-dissolving substances such as iodoform, chloroform, chloral, ete. ? Also in the case of these soaps we might think that propionate — for convenience sake we shall only mention propionate when we should also name the other two soaps which were experimented upon — dissolves in the lipoid surface of the phagocytes, softens them and facilitates in this way the amoeboid motion. Numerous experiments, however, showed that propvonate is absolutely insoluble in olive-oil. We have then tried to find another explanation, and it occurred to us that soaps have in a high degree the property of lessening the surface tension of oil. The reader knows Gap’s experiment: if oil is brought into contact with a soap solution, an extremely fine emulsion is formed. As far as we know these experiments have only been carried out with soaps of higher fatty acids (sapo medicatus or olive-oil containing some fatty acid). Therefore we have repeated them with soaps containing a smaller number of C' atoms in their molecules. It appeared indeed that the propionate, butyrate and formiate of Na have an emulgent effect on olive-oil’ The formiate of Na was more active than the two others. We may conceive that the soaps lay themselves against the surface. of the phagocytes, reduce the surface-tension, and in this way facilitate the amoeboid motion. The following observations point in the same direction. By way of an illustration we beg the reader to glance at Table II. In this series of experiments the leucocyte suspensions, after having been in contact with carbon for */, hours at 37°, were suddenly cooled down by water at 13°. Then the phagocytes were fixed by means of a drop of an osmium-solution. 1295 Microscopical examination showed that in the NaCl-solution of 1,1°/,, 1,2°/,, and 1,3°/,, all the leucocytes had regained their round shape, while in the isosmotic NaCl-propionate solution nearly all the cells still had pseudopodia. Even in the NaCl-solution 0,9°/, relatively few leucocytes with pseudopodia were found, and yet the phagocytosis had reached about the same stage as in the latter fluid, which contained much propionate (12,7°/, and 15°/, respectively). It follows from this that propionate has the property of influencing the amoeboid motion of the leucocytes in a favourable sense; one might be inclined to say that they are made more resistant. For what was observed to take place ? In the NaCl-solution 0,9°/, the leucocytes drew back their protru- sions owing to the lower temperature, but in the propionate-sol. with the saine degree of phagocytosis they remained, notwithstanding this low temperature. Similar results were arrived at in the experiments of Table II: in NaCl 0,9°/, no pseudopodia, in NaCl combined with propionate 1:100, 1: 250 and 1: 1000 many pseudopodia, in propionate 1 : 5000 fewer, and in 1: 25000 and 1L000.000. none. Now it would be incorrect to look upon the promotion of phago- cytosis and the capacity of resistance of the pseudopodia as being identical. First there are a number of leucocytes which protrude pseudo- podia, but whieh show no phagocytosis, and secondly it appeared from another series of experiments with propionate and CaCl, where both substances equally promoted phagovy tosis, that after being cooled down and fixed, the microscopic pictures were entirely different. In the CaCl,-solution namely the lower temperature had caused the psendopodia to disappear almost entirely, in the propionate-solution on the other hand, this was not the case. But since the formation of pseudopodia is one of the conditions for phagocytosis, it may be concluded from the observation with propionate that propionate by influencing the formation of pseudo- podia in a favourable sense has contributed to the promotion of phagocy tosis. That the effect of propionate is due to a surface-action and not to a dircet action on the contents of the cells appears trom volwme- trical determinations, The volumes of two equal amounts of blood corpuscles, exposed to the action of isosmotic solutions, are equal, as we know, but only on condition that the substances do not penetiate into the blood cor pus- 1296 cles and that therefore the pheno.nenon remains restricted to an inter- change of water between the cells and the surrounding fluid.’) Conversely it may be concluded that if two isosmotic solutions give the same volume to the blood-corpuseles, the latter are imper- meable to these substances *). Therefore we have investigated to what extent a certain amount of blood-corpuscles in a solution of NaCl 1,2 °/, bad the same volume as a solution, isosmotic with the former and which contained 0,9 °/, NaCl] and 0.5 propionate of Na. If the volumes were equal then it might be concluded that pro- pionate did not penetrate or hardly into the cells. The experiments showed that only traces of propionate could have penetrated into the blood-corpuscles. Consequently Na-propionate acted upon the red blood corpuscles like for instance NaBr and other anorganic Na-salts. Now it might be objected that the permeability of the red and the white blood-corpuscles need not be alike. As regards this we may observe that none of the many researches carried out in this direction, have established any difference. The agreement goes even so far that the same hyperisotonic salt solution causes the same relative decrease in volume in the red and_ in the white blood corpuscles*). And this also applies to the hypisotonie one. The analogy also appears from the way in which anisotonic salt- solutions act upon phagocytosis ‘*). We arrive, therefore at the conclusion that until now we have discovered three causes which may increase phagocytosis. 1. Traces of a calcium-salt; there can be hardly any doubt but here we have to do with an action of Ca on the cell-protoplasm. It has not been verified as yet whether the Ca also acts upon the surface. 2. Kat-dissolving substances such as iodoform, chloroform, chloral, turpentine, ete. When applied in homoiopathie quantities (e.g. Chlo- ‘) Perfectly equal when the isosmotic solutions are isotonic. Hedin, Priicer’s Archiv 60, 198, p. 300 2) Only urea, aS appears from investigations by Griuxs and myself, makes an exception. 8) Hampurcer. Archiv, f. (Anat u.j Physiol. 1898 S. 317; Osmot. Druck u. lonenlehre L S$. 337, 4) Hampurcer and Hexma. Biochem. Zeitschr. 7, 1907, 102. Further Hampurcer, Physik. Chem. Unters. tiber Phagocyten u. s. w. Wiesbaden, J. F. Benamann. 1912. 1297 roform 1:500000, Propionic acid 1:10000000) they restriet their action {o the lipoid surface, which they weaken thus facilitating the amoeboid motion. When applied in somewhat greater quantities a second factor becomes of importance viz. the noxious effect of these substances on the protoplasm. All these substances indeed penetrate easily into the cells, thus causing paralysis. 3. Soaps, such as propionate, butyrate and formiate. These sub- stances, unlike the fat dissolving substances, do not enter into the phagocytes. Their action upon the phagocytes is therefore entirely different from that of the fat-dissolving substances, for even when applied in high concentrations (1:250), in concentrations in which the fat dissolving substances would inevitably kill the cells, they have a very favourable effect upon phagocytosis. When applied in still greater quantities their action is a perni- cious one, but this may be due to the solution being too hyperiso- tonic. Further it is a remarkable fact — and in this respect the soaps are distinguished from calcium as well as from the fat dissolving substances — that within rather wide limits, the degree to which phagocytosis is promoted is independent of the amount of soap, found in the solution. (Cf. Tables If and IV.) The researches, described above, have given rise to different questions, which, owing to the present cirenmstances we cannot enter into now. Physivlogical Laboratory. Groningen, January, 1913 Astronomy. — “A proof of the constancy of the velocity of light’. By Prof. W. pe Sirter. ‘Communicated in the meeting of February 22, 1913). In the theory of Ritz light emitted by a source moving with velocity w is propagated through space in the direction of the motion of the seurce with the velocity c+ wu, ¢ being the velocity of light emitted by a motionless source. In other theories (LORENTZ, EINSTEIN) the velocity of light in always c, independent of the motion of the source. Now it is easily seen that the hypothesis of Ritz leads to results which are absolutely inadmissible. Consider one of the components of a double star, and an observer situated at a great distance A. Let at the time ¢, the projection of 1295 ihe star’s velocity in the direction towards the observer be uw. Then from the law of motion of the star we can derive an equation : “= 7 (1). re eee The light emitted by the star at the time ¢ reaches the observer at the time r=?f-+ 4/,—-au. In Ritz’s theory we have, neglecting the second and higher powers of “'., a= 4/2. In other theories we have a= 0. If now we put r, =f, 7 4/- , we have u= f(t—7, + au) or ue Piers ee ey The funetion gy will differ from 7, unless eu be immeasurably small. Therefore if one of the two equations (1) and (2) is in agree- ment with the laws of mechanics, the other is not. Now @ is far from small. In the case of spectroscopic doubles w also is not small, and consequently @z can reach considerable amounts. Taking e.g. u= 100 = and assuming a parallax of O”.1, from which 4/e= 33 years, we find approximately « w= 4 days, 1. e. entirely of the order of magnitude of the periodic time of the best known spectroscopie doubles. . Now the observed. velocities of spectroscopic doubles, i. e. the equation (2), are as a matter of fact satisfactorily represented by a Keplerian .motion. Moreover in many cases the orbit derived from the radial velocities is confirmed by visual observations (as for JS Equulei, § Herculis, ete.) or by eclipse-observations (as in Algol- variables). We can thus not avoid the conclusion « = 0, i.e. the velocity of light is independent of the motion of the source. Rurz’s theory would force us to assume that the motion of the double stars is governed not by Nrwron’s law, but by a much more complicated law, depending on the star’s distance from the earth, which is evidently absurd. Chemistry. — “hyuilibria in ternary systems’. VI. By Prof. F. A. H.» ScuREINEMAKERS. In a manner similar to that in which, in the previous communi- cations, we considered the saturation line under its own vapour pressure we can also consider the conjugated vapour line. Instead of the two-phase complex /’"-+ / we now, however, take, the complex F+G and if in the three-phase equilibrium /-++ L-+ G no phase reaction occurs, we must in the conversion of /’-+ G again — distinguish three cases. }299 Let us now take the case generally occurring in which, on a change in pressure in the one direction /’-++ G is converted into F+ 1’ +G’, and into F+G" on a change in pressure in the other direction. Hence, on a change of pressure in the one direction liquid is formed, but not when in the other direction. In the previous communication we have deduced: if /’--+ L is converted into /-+ L’ + G’ with increase in volume, the conjuga- tion line’ solid-liquid will, on lowering the pressure turn towards the vapour point. If /’+ ZL is converted into /’ + L’/ + G’ with contraction of volume, the conjugation line solid-liquid turns in the opposite direction. In a similar manner we may now deduce: if / + G is converted into #F+ L’+G" with inerease in volume, the conjugation line solid-vapour, on lowering the pressure, turns away from the liqui- dum point, and on increasing the pressure it turns towards the same. If # + G is converted into #+L’+G" with contraction of volume the conjugation line solid-vapour will turn in the opposite direction. The conversion of “+ LZ into /'+- L’ + G’, or as we may also eall it the formation of vapour from / + ZL generally takes place with increase in volume and only on certain conditions with a decrease in the same. The conversion of /+G into #-+-L’-+-G", or in other words the formation of vapour from /’-+- G takes place as a rule with decrease in volume and only in definite conditions with an increase of the same. In the previous communication (V) we have demonstrated that the rule for the rotation of the conjugation line solid-liquid is in con- formity with the saturation lines under their own vapour pressure as deduced in communication (1): in the same manner we may now also show that this is the case with the movement of the conjuga- tion line solid-vapour. Let us imagine in fig. 7 (I) a tangent to be drawn through F on the vapour saturation curve of /’ under its own vapour pressure, therefore, on curve J/, a, m, 6,. As on a change in pressure in either direction the new conjugation line solid-vapour falls outside the first three-phase triangle, the system /’-+ G, in this particular case, is converted on a change in pressure in the one direction into /’ + G’ and by a change in the other direction into /’+- G". Hence, no liquid is formed either on an increase or a decrease in pressure. At an infinitesimal change in pressure nothing happens but evapo- ration of a little solid substance /’ in, or else a slight deposit of solid F from the vapour @. On evaporation of /, the volume will as a rule increase; as the 1300 gas then draws nearer to the point /’, the pressure along the vapour saturation curve, starting from the point of contact, will decrease towards /’ and increase in the other direction. This is in agreement with tig. 7 (1) and 12 (1) but not so with fig. 13 (1); from the deduction of this last figure; however, it is more to be expected that the curve 1/7, m, is either cireumphased or exphased, but is then situated at the other side of F like curve Min. Let us now consider the case when the vapour saturation curve of # under its own vapour pressure possesses a form like curve amb in fig. 4(V); the saturation line should then be supposed to lie more towards the right. We may then draw through / tangents to the vapour saturation line with the points of contact R, Rk’, X and .X’. In the point &’ CX’) now also takes place the above considered conversion of M+ G into #+ G6’ and + G". In the point R, however, the system /’+ G is converted, on change in pressure, in the one direction, into /’+ L’ + G’, and by a change in the other direction into /’-- L" + G'". Hence, liquid is formed on increase as well as on decrease in pressure. At an infinitesimal change in pressure, only a little solid substance /’ evaporates into, or else a little of this is deposited from the vapour; hence, when starting from the point of contact, the pressure along the vapour-saturation curve will decrease towards /’, but increase in the other direction. We have noticed above that the rotation-direction of the conjuga- gation line solid-liquid depends on the change in volume when vapour is formed from / + “, whereas that of the conjugation line solid-vapour depends on the change in volume when liquid is formed from /--G, In the three-phase equilibrium /#’+ 4+ G we may now suppose four cases to occur. 1. The formation of vapour from # + LZ takes place with increase, the formation of liquid from /#’-+ G with decrease in volume. 2. The formation of vapour from F + ZL takes place with decrease, the formation of liquid from /’-++ G with increase in volume. 3. The formation of vapour from #-+ Z/ and that of liquid from FAG both take place with increase in volume. 4. The formation of vapour from /'+ Z and that of liquid from F+ @ both take place with decrease in volume. Let us first take the case mentioned sub 1 which is also the one usually occurring; from what has already been communicated it follows that, on inerease in pressure, the conjugation line solid-liquid turns towards the vapour point and that the conjugation line solid- vapour tums away from that point. 1301 Hence, on increase of the pressure, the three-phase triangle turns in such a manner that the conjugation line solid-vapour gets in front; on diminution of the pressure the three-phase triangle turns in the opposite direction, but in such a manner that the conjugation line solid-liquid precedes. On inerease in pressure the two three-phase triangles cf fig. 8 (I) with their conjugation line solid-vapour in front, will therefore move towards each other; on diminution in pressure they move away from each other, with the conjugation line solid-liquid in front, to be converted, for instance, into fig. 8 (I). If in fig. 11 (I) we sup- pose each liquid to be united with its correlated vapour and the solid substance /’ we notice that the three-phase triangle moves in conformity with the above mentioned rule. It is evident that we must not look upon this rotation of the three-phase triangle as if this turns in its entirety without a change in form; during this rotation not only the length of the conjugation lines solid-liquid and solid-vapour is changed, but also the angle formed by the two lines. In the ease mentioned sub 2 the changes in the volumes have the opposite sign to that mentioned in the case sub 1; the three- phase triangle then of course will turn in the opposite direction namely in such a manner that on increase in pressure the conjugation line solid-vapour gets in front. A similar case we meet in fig. J2 (I), if in this we take two three-phase triangles, one at each side, and adjacent to the straight line Fin m,; the two triangles turn the conjugation line solid-vapour towards eacli other. On lowering the pressure the two triangles must move towards each other and on increasing the pressure they must part from each other, which is in conformity with fig. 12 (1). In the case mentioned sub 3, the two conjugation lines, solid- liquid and solid-vapour, of the three-phase triangle will, on increase in pressure, move towards each other, and on decrease in pressure part from each other; in the case mentioned sub 4+ they move in opposite directions. Let us suppose that the exphased vapour saturation line of /, in fig. 13 (1) is situated at the other side of #. We now take a liquid close to the point m so that its conjugated vapour is adjacent to the point m,. The three-phase triangle then forms in /’ an angle of nearly 180°. As here occurs the case mentioned sub. 3, the two con- jugation lines solid-liquid and solid-vapour must draw nearer each other on increase in pressure. And this is in agreement with fig. 138 (1). If we take a liquid close to the point J/ and hence a vapour 85 Proceedings Royal Acad, Amsterdam. Vol. XV. 1302 adjacent to the point 17/,, the case mentioned sub 4 occurs and the movement of the conjugation lines is in conformity with the rule deduced above. The cases mentioned sub 3 and sub 4 also occur in other figures, for instance also in fig. 12 (I). In the above considered conversion of / + LZ we ean distinguish three special cases. 1. The case, mentioned above sub A 2 and A 3, which has already been discussed in detail, when no vapour is formed at an infini- tesimal change in pressure or in volume. 2. At an infinitesimal change in volume the quantity of the liquid does not alter (its composition, of course, changes). 3. At an infinitesimal change in volume the quantity of solid matter does not change. In each of these cases one of the sides of the three-phase triangle will occupy a special position. We have already noticed previously that in the case mentioned sub 1 the conjugation line solid-liquid meets the saturation line under its Own vapour pressure. In the case mentioned sub 2, dm in the formula given in the previous communication V (p. 1213) must be taken =O: from that it follows that the tangent drawn in the liquidum point to the saturation line under its Own vapour pressure is parallel to the con- jugation line solid-vapour. In the case mentioned sub 3 dn in the said formula must be taken =O; this signifies that the conjugation line liquid-vapour touches in the liquidum point the saturation line under its own vapour pressure. In the saturation curves deduced previously diverse examples of these cases are to be found. It is evident that in the system /’-+ G, three corresponding cases may be distinguished; these then relate to the direction of the tangent in the vapour point of a vapour saturation line under its own vapour pressure. We will now consider the case already mentioned in the previous - communication sub B, when a phase reaction between the three phases takes place. The three phases are then represented by three points of a straight line and the pressure for the system #’-+ L + @ is then a maximum or a minimum, Let us first take the case mentioned sub B41. when the reaction F2L+G occurs; the point /’ then falls between the points Z and G as, for instance, in fig. 4(1), if in these tigures we suppose a, to bave coincided with 6, and a with 4. We then obtain fig. 5 (1) 1308 in which the points m,, /’, and m correspond with the homonymous points in fig. 7 (1). If now we suppose first that the reaction “=z L + G@ proceeds from the left to the right with increase in volume, the system L-+-G will then appear at lower pressures and the systems /’+ JZ and + G at higher ones. Hence, on lowering the pressure, fig. 5 (1) will be converted into fig. 6(1) and on inereasing the same into fig. 4 (1), which is in agreement with our previous considerations. As, on increase of pressure, fig. 5 (1) is converted into fig. 4 (1) the pressure for the system /'+ LZ -+ G@ in fig. 5 (1) is consequently a minimum. If we had assumed that the conversion “= L + G took place from the left to the right with decrease in volume, the pressure would be a maximum. Such a change in volume can only occur when the liquid differs but little in composition from /’, and when Ff melts with contraction of volume. If we imagine in fig. 13 (1) the curve M,m, to have shifted so far to the other side of /' that M, gets situated at the other side of /, this case will occur in the system /’ + liquid V+ vapour J,. Let us now take the case mentioned sub B2, namely when the reaction “+ L2G takes place, so that the point G lies between the points / and L. This is, for instance the case in fig. 9 (I). Let us now assume first that the reacuon takes place from the left to the right with increase in volume. The system #'+ Z will then appear at a higher, the systems “+ G and L+G at a lower pressure. In agreement with our previous considerations fig. 9 (1) will be converted, on increase in pressure, into fig. 8 (I) and on lowering of the pressure into fig. 10 (I). As on increase of pressure fig. 9 (I) is converted into fig. 8(l) the pressure for the system F4+L-+G in fig. 9(1) is a minimum. This is also in harmony with the situation of the points m, m, and F’in figs. 11 (1) and 18 (1). Let us now just take a system #’+ L,-+ G, in which JZ, differs but little from L, and G’, but little from G; this system will then be repre- sented by a triangle situated in the vicinity of the line /’mm,. As the reaction /’+ L2G takes place with increase in volume, the conver- sion of /’ + L, into / + L’, + G’ inthe infinitesimally differing system f+ L,-+ G, will take place with increase in volume and the conversion of /+ G, into # + L’, + G’, with decrease in the same. We have noticed previously that, in this case the three-phase triangle must turn in such a manner that, on increase in pressure, the con- jugation line solid-vanonr gets in front and that on reduction of pressure the conjugation line solid-liquid precedes. This also is in 85* 1304 agreement with tigs. 8(1) and 9(I). On lowering the pressure, the first figure is converted into the second and we notice that in this conversion both three-phase triangles turn in such a manner that the conjugation line solid-liquid gets in front. In the case now considered when the reaction “+ LZ G takes place from the left to the right with increase in volume, the pressure can also be a maximum; I will elucidate this with a single example. We take a saturation line of the solid substance Fat the pressure P; this is represented in fig. 1 by the curve fyi; within this satu- ration line is situated a vapour region encompassed by a heterogeneous region, of which the liquidum line is drawn and the vapour line dotted. On lowering the pressure the vapour region expands and at a certain pressure ?), the saturation line of /’ and the liquidum line of the heterogeneous region meet each other in J/. There is now formed ~ the three-phase equilibrium solid ++ liquid ./-++ vapour M, represented by three points of a straight line, whereas the vapour phase J, lies between the points /’ and WM. Hence, the reaction is / + LSG@ namely from the left to the right with increase of volume, whilst the pressure Py, is a maximum. At a pressure somewhat lower than Pj, is now formed a diagram as in fig. 2 in which, however, we must imagine the only partially drawn saturation line af and dg of F to be closed. The vapour 1°05 » the liquidum line ad and the vapour line saturation line «, ¢, > a,d,b, have been drawn only to the extent where they represent stable conditions. We have noticed previously that from the system “+ L -+ G, which exists at the pressure /4;, are formed, on increase in pressure, the systems # + G and £+ G; we find this confirmed here also in figs. 1 and 2. We also notice, in agreement with the rule given above that the two three-phase triangles Maa, and /’bb, turn, on reduction in pressure, in such a manner that the conjugation line solid-liquid gets in front; on increase of pressure the conjugation line solid-gas precedes. I must leave the consideration of the other cases to the reader. In our previous considerations we have compared the course of the saturation- and vapour-saturation lines under their own vapour pressure with the change in volume that takes place in the con- version of # + ZL and of (+ @ into /+ L’ + G’. In the same manner we might compare the course of the boiling point-line and the vapour-boiling point line with changes in entropy occurring in these reactions. Instead of increasing, or decreasing the volume of the systems /’-++ 7 and #+G we must either supply, or withdraw, a little heat to, or from the same. If we distill a ternary liquid at a constant temperature, then, as is well known, the pressure continuously decreases during the distil- lation. The liquid and the at each moment distilling vapour proceed along a curve which we distinguish as the distillation curve of the liquid and of the vapour. We obtain, as is well known, clusters of these distillation curves which emanate from one or more definite points (the distillation points) and meet in one or more definite points. If now at the temperature of distillation a solid substance / also occurs, this can modify the course of the distillation lines; of course, not the theoretical but the experimental course. According to whether the initial and terminal points of the distil- lation curves are situated within or without the saturation line of F’ under its own vapour pressure, we may now distinguish several cases, of which we will only take a single one. Let us choose a temperature below the minimum melting point of the solid substance /’, so that its saturation line under its own vapour pressure is circumphased. In fig. 3 has been drawn a part of this saturation line with the point of maximum pressure J/ and of minimum pressure im; the dotted curve M,s,a,), is a part of the correlated vapour line. f M 7 Fig. 3 From the situation of the points J/ and m it is now evident that the arrows do not, as in the previous. figures, indicate here the direction of the increasing pressure, but that of the decreasiny one. Let us now imagine in fig. 3 to be drawn the distillation curve of a liquid and its conjugated vapour curve. It is now evident that if the first does not intersect the saturation line under its own vapour pressure, the second will also not intersect the vapour saturation line and reversedly. We further perceive at once that in this case the distillation curve will suffer no change owing to the appearance of the solid substance. When, however, the distillation curve, such as the curve rstuv in fig. 38, intersects the saturation line under its own vapour pres- sure, matters are different; the arrows on this curve rstwv indicate the direction of decreasing pressure, hence also the direction in which the liquid moves during the distiltation. It is now evident that with a point of intersection s of the distillation enrve of the liquid and the saturation line of / under its own vapour pressure must correspond a point of intersection s, of the distillation curve of the vapour and the vapour saturation curve of /’ under its own vapour pressure. As s, represents the vapour which can be in equilibrium with the liquid s, the distillation curve of the liquid must meet the line ss, in s. If no solid F occurred, the liquid 7+ would, on distillation, proceed along the curve rstwv; now however, when it has arrived in s something else takes place. For if we withdraw from the liqnid s a small quantity of vapour s, the new liquid will be represented by a point of the line a/’; we must then suppose the point a to be situated adjacent to s. The new liquid will now resolve into solid F and the solution a of the saturation line under its own vapour pressure. The liquid, therefore, does not proceed along the distillation curve sfu, but moves, with separation of /, along the saturation line under its Own vapour pressure from s towards a. If now we again generate a little vapour which can be in equilibrium with the liquid a, therefore the vapour q@,, the liquid @ moves, with separation of /, along the saturation line under its own vapour pressure in the direction of 0. If, as assumed for the point 4 in fig. 8, the conjugation line liquid-vapour (the line 4, 6) meets the saturation line under: its own vapour pressure in the liquidum point 4, then, as we have seen previously, the system /’-+ Z is converted, at an infinitesimal change in pressure, into /’-++ L’ + G’ without any solid substance either dissolving or crystallising. If, however, we withdraw a little more vapour, so that the liquid 4 is converted into d, / is dissolved and d is converted into liquid e. Hence, on distillation the liquid s will traverse a part of the saturation curve of # under its own vapour pressure, first with separation of solid /’ and afterwards with solution of the same. The point / in which all solid substance has again disap- peared will, as a rule, not coincide with the point w of the distillation curve ¢séuv. Starting from the point /, the liquid, on continued distillation, proceeds along a distillation curve fy. If no solid substance /’ did occur the liquid » would, on distil- lation, traverse the distillation curve rstuwv; as now, however, solid matter /’ appears, it first proceeds along curve rs, then along curve s/f and finally along curve fy. From the foregoing consider- ations it follows: if a distillation curve meets the saturation line under its own vapour pressure it proceeds starting from this point of intersection, along a part of the saturation line under its own vapour pressure and abandons it in another point along a distillation line which, with regard to the first one, has shifted. We may also express this as follows: If during the distillation of a liquid a solid substance /’ separates, the liquid leaves the distil- lation curve in order to proceed along a part of the saturation line of # under its own vapour pressure. As soon as, on continued distillation, the solid substance /” again disappears, the liquid again proceeds along a distillation curve which, however, does not coincide with the prolongation of the first. The occurrence of the solid substance has, therefore transferred the liquid to another distillation curve. Although, as stated above, the appearance of a solid substance generally causes the shifting of a distillation line, yet in some eases no shifting can take place so that the liquid after the disappearance of the solid matter traverses the prolongation of the original distil- lation curve. This will be the case when the vapour contains only 1308 one of the three components; the distillation curves of the liquid then become straight lines, those of vapour and distillate are reduced to a single point. When a distillation curve of a liquid meets the saturation line of F wnder its own vapour pressure in the point 4, it will not penetrate within the heterogeneous region, but meet this saturation curve in 6; its vapour distillation curve will then also meet the vapour satu- ration curve. Among all distillation curves intersecting the saturation line of under its own vapour pressure there is one that behaves in a parti- cular manner: it is the one that intersects the saturation line in the point Jf and, therefore, meets the line MA/, in J/. If we with- draw from the liquid J/ a little of the vapour J/,, M/ will not change its composition, but the reaction: liquid J/—solid /+-vapour M, will appear. If now the vapour is continuously distilled off, the liquid iW will disappear without change in pressure and only the solid substance /’ will remain. The distillation curve arriving in J, therefore, terminates in this. point without proceeding any further along the saturation curve of /. What follows next is dependent on the temperature; this, as we have presupposed has been chosen lower than the minimum melting point of F. We now can distinguish two cases. 1. The distillation temperature is higher than the maximum subli- mation point of /. The saturation curve and the vapour saturation curve of F under their own vapour pressure then possess a form like in fig. 7 (1), the isothermic-isobaric diagrams are as shown in figs. 1 (1)—6 (1). After, on distillation, the liquid J/ has disappeared and only the solid substance /’ remains, the pressure conforming with fig. 2 (I) will fall to the pressure to which fig. 5 (I) applies. At this pressure, the reaction solid /’°= liquid m-— vapour m, now oceurs. If now the vapour is continually Criven off, the solid substance / will dis- appear and the liquid m will remain, without any change in pressure. On further distillation. the liquid transverses the distillation curve, starting from point m in fig. 3. The liquid, therefore, proceeds first along a distillation curve terminating, at the pressure Pj, in the point M, and then along another one starting from m at the pressure P,,; at the transfer of the liquid from the one to the other distillation curve, hence, between the pressures Py and P,,, it is converted into the solid substance J. 2. The distillation temperature is lower than the maximum sublimation L309 point of /. The saturation- and the vapour-saturation curve of / under their own vapour pressure then have a form as in fig. 1 1(1), the isothermic- 9(1) and 10/1). As soon, as on distillation, the liquid JW has disappeared and, isobaric diagrams as in figs. 1(l), 2(1), 3 (1), 41), 8(D, consequently, only the solid substance /’ remains, the pressure con- forming with fig. 2 (1) will fall. [f now, however, the pressure P,, , which now conforms with fig. 3(1) has been attained, the solid matter #” will not be capable of splitting, as in the previous case. On further lowering of the pressure, fig. 10 is formed; hence, the substance /” will only appear in the solid condition. On further decrease in pressure the vapour saturation curve of fig. 10 (1) under- goes contraction and finally, at a definite pressure, coincides with the point /*, The solid substance /’ can now be in equilibrium with vapour of the composition /’, or in other words: the substance F sublimes. Hence, the liquid first traverses, at a pressure Py;, a distillation curve terminating in the point J/, where it is converted into the solid substance /’, which at a further lowering of the pressure sublimes at a definite pressure. The distillation of the liquid is, therefore, finally changed into a sublimation of the solid substance F’. We will now investigate what happens when we distill a liquid saturated with a solid substance /. We take a liquid s (fig. 3) and the solid substance /’ in such proportion that the complex is repre- sented by point A of the line s/. We now withdraw from this complex A’ a little vapour s,, which can be in equilibrium with this complex; the complex now arrives in / and hence, is resolved into liquid a + solid #. The little straight line AZ is now an element of the curve which the complex A’ will traverse on distillation; we will call this curve the complex distillation curve. From the deduction of this curve it now follows at once that the tangent drawn in the point A at the complex distillation curve which passes through this point, passes through the point s,. Further, it is evident that this applies to all complexes situated on the line /’s. From this follows: in order to find the direction of the tangent to a complex distillation curve in a point (4) we should take the three-phase triangle, whose conjugation line solid-liquid (s/’) passes through this point A. The line which connects this point (A) with the vapour point (s,) of the three-phase triangle is the looked for tangent. We may express this also as follows: in the point of intersection of a complex distillation curve with a conjugation line solid-liquid the tangent to this curve passes through the vapour point correlated to that conjugation line, 1310 From this follows: if we intersect a cluster of complex distillation curves by a conjugation line solid-liquid, the tangents in these points of intersection form a cluster of straight lines which all pass through the vapour point appertaining to that conjugation line. Further, it is evident that the vapour distillation curve representing the vapour distilling over at each moment is the vapour saturation line of 7 under its Own vapour pressure. We can now demonstrate that a complex distillation curve turns in each point its convex side towards the correlated vapour point and that a definite point will be a point of inflexion if the tangent which passes through this point meets the vapour saturation line of F under its own vapour pressure and if this latter point of contact is not itself a point of inflexion. If we intersect a cluster of complex distillation curves by a conjugation line solid-liquid, then as we have seen previously, the tangents in these points of intersection all pass through the vapour point correlated to this conjugation line. If now, in the proximity of this vapour point the vapour saturation curve under its own vapour pressure is situated outside the three-phase triangle none of the above mentioned points of intersection will be a point of inflexion. We can imagine a curve transmitted through the points of inflexion of the complex distillation curve, which we will call the point of inflexion curve; this curve may be fuund in the following manner, We draw to the point NX of the vapour saturation line under its own vapour pressure a tangent; the point of intersection of this tangent with the conjugation line solid-liquid appertaining to the point Y we will cail S. If now the point XV traverses the saturation curve under its own vapour pressure the point S will traverse the looked for point of inflexion enrve. This point of inflexion curve always passes through the points M, and m, of the vapour saturation curve |Fig. 7 (I), 11 (1, 12 (D] and if we can draw through / a tangent to this vapour saturation curve also through the point /. For our purpose, only the part of the point of inflexion curve which is situated within the heterogeneous region has any significance, that is in so far as it intersects the conjugation line solid-liquid between the points indicating the solid substance and the liquid. In the points of intersection of the saturation curve under its own pressure with the point of inflexion curve, the conjugation line liquid- vapour meets the vapour saturation curve. In the proximity of a maximum or a minimum point of the three- phase equilibrium /’-- + G the three-phase triangle is very narrow and as noticed previously, we can distinguish many cases. From a consideration of these cases appears the following. We represent, as before, the liquid with the maximum pressure by JZ2 the correlated vapour by J, the liquid with the minimum pressure by mm and the correlated vapour by m,. The complex distillation curves have, in the vicinity of the line /M (im) a direction about parallel to this line from / towards W/(m) or reversedly so. If, however, the vapour point JZ, (m,) is situated between /’ and M(m) they proceed from / and AM (m) towards the point JM’ (m,) or reversedly so, and in the vicinity of this point they inflect in definite direction away from the line /'/(/'m) or towards that line. Let us take the case of a distillation temperature lower than the maximum sublimation point of the solid substance /’; the saturation line of # under its own vapour pressure and the correlated vapour line then possess a form as in fig. 11 (1). In fig. 4 a part MWdbm of this saturation line has been drawn but the correlated vapour line has been omitted. From a consideration of the three-phase triangles we can readily deduce the course of the complex saturation curves ; the arrows indicate the direction in which the complex moves on distillation. If these complex distillation curves are intersected by a straight line passing through the point /’ the tangents and curva- tures in these points of intersection must then satisfy the conditions deduced therefor. mM ya Fig. 4. If in the vicinity of the line /m,m we imagine a three-phase triangle so that the vapour point is adjacent to m, and the liquidum point adjacent to m, we notice that a part of the complex distilla- tion curves must proceed towards the point / and another part towards the point m, whilst there is one that, without bending 1312 towards /° or m, draws near to the point m,. This is represented by dm,. The point 4 of fig. 4 corresponds with the homonymous one of fig. 3; it is, therefore, that point of the saturation line under its Own vapour pressure in which the side liquid-gas of the three- phase triangle meets this saturation line. The points d and 4 divide the branch Wdbm of the saturation line under its own vapour pressure into three parts. On distilling the liquid d a complex /’+ ZL is formed which tra- verses the complex distillation curve dm, ; the pressure therefore falls from Pa to the minimum pressure P,, and the liquid itself tra- verses the curve dbm. As the pressure gets nearer P,,, the liquid and the solid substance /’ will be left behind more and more in that proportion in which the vapour m, can be formed from them; at the last moments of the distillation we notice the solid matter and the liquid to disappear simultaneously. Let us now take a liquid ¢ of the branch J/d. On distillation of this liquid, a complex /#’-+ ZL is formed which traverses the complex distillation curve proceeding from c towards /. The pressure, there- fore, falls from P,. to the minimum pressure P and the liquid itself traverses the branch chm. The nearer the pressure gets to P,, the less liquid will be retained in the complex which finally will practi- cally consist of the solid substance /’ only. Let us now take a liquid s of the branch dé; this on distillation forms a complex /’+ ZL which traverses the complex distillation curve sf. Hence, the pressure falls from P; to Py and the liquid itself proceeds along the curve sh/; the liquid s is, therefore, con- verted into the liquid / at first with separation of solid matter which is then again redissolved. We notice from this that the point d is a point of demarcation and insuch a manner that all the liquidum distillation curves which meet the saturation line under its own vapour pressure between d and M do not leave the heterogeneotis region, whereas those meeting this curve between d@ and / abandon that region. If we take a distillation temperature higher than the maximum | sublimation point but lower than the minimum melting point of the substance /’ the saturation- and vapour-saturation curve under their own vapour pressure will have a form as in fig. 7 (1). All liquidum distillation curves which meet this saturation curve abandon the heterogeneous region. [| must leave the consideration of the other cases to the reader. (To be continued). 1313 Chemistry. — ‘“Kquilibria in Ternary Systems’ VII. By Prof. F. A. H. ScHREINEMAKERS. Up to now we have only considered the occurrence of a single solid substance /’; we will now take the case when a second solid substance /” also appears. Tet us first investigate what happens if a mixture of both substances /’ and /” is brought together. If, at a low temperature, we introduce a mixture of the substances F and /” in an evacuated space, a vapour (@ is formed causing the equilibrium /’-+- /” + G to appear. The vapour G' is of course represented by a point of the line /’/”. According to the composition of the vapour G or in other words according to the position of the three points in regard to each other, the following reactions can occur at a supply or with- drawal of heat or at a change in volume, P and 7’ being constant. 1. If the point G is situated between / and /” the reaction F+ lh’ 2G oceurs. Hence, if / and F’ are placed in an evacuated space a part of each of the solid substances evaporates. We will call this a congruent sublimation. 2. If the point /” is situated between /’ and G the reaction f’2rF+G takes place. Hence, if both substances are placed in an evacuated space only a part of #” will evaporate while solid / is being deposited. The formation of vapour is, therefore, accom- panied by a transformation of /” into /#. We will call this an incongruent or transformation sublimation. 3. If the point /’ is situated between /” and G the reaction F2I’+G@ occurs. This case is quite analogous to that mentioned sub 2. so we call this also an incongruent or transformation sublimation. 4. As a transition case between 1 and 2 or 3 the point G can also coincide incidentally with #” or with FP. At an elevation of temperature, the vapour pressure of the system F+ F’ + @ inereases when (, of course, alters its composition; hence, in a P,7-diagram we obtain a curve such as aD of fig. 1 which we will call the sublimation curve of /’+ +”. If, between the three phases occurs the reaction mentioned sub I we. call a'D a congruent, if the reaction mentioned sub 2 or 3 takes place we call a’ D an incongruent or transformation sublimation curve. It is evident that the one part of a curve may be a congruent and the other part a transformation sublimation curve. On further heating the system /’+ /” + G@ a temperature 7'p 13t4 and its correlated pressure Pp is attained at which an infinitesimal quantity of liquid Z is formed. The sublimation curve, therefore, terminates in a point D of fig. 1 representing the temperature 7’p and the pressure ?p which we will call the maximum sublimation point of #+ #’. The liquid 1 which forms in the point D will as a rule not be represented in an z,y-representation, by a point of the line FF’. As, however, the quantity of this liquid Z is as yet but infinitely small, the vapour corresponding with the point D will still be represented by a point of the line FF’. If the temperature is increased still further, still more liquid is formed and the four-phase equilibrium # + #’ + LZ + G appears. As, however, a finite quantity of liquid is now present, Z and @ must be in opposition in regard to the line / F”; only incidentally, ZL and G may fall both on this line. At a constant Pand 7 one of the following reactions takes place’ between the four phases on increase or withdrawal of heat or on a change in volume. 1. PS STAG! 9 ER Sr ae ohn eee We will call the reaction 1 a congruent reaction, the reactions 2 and 3 incongruent ones. Which of these reactions takes place depends on the situation of the four points in regard to each other. As the system + #”+L+G has formed from + F” it is evident that in this four-phase equilibrium / and G are always present in such proportions that both disappear simultaneously in the above reactions. Hence by warming the system + F’ + G we have arrived on the four-phase line # + /” + L+.G. As on this line the three components are present in four phases, this system is a monovari- ant one, so that to each temperature appertains a definite vapour pressure. Hence, the four-phase line in a P, 7-diagram will be represented by a curve; a part of this curve is represented in fig. 1 by DS; we shall see later that it continues in the points D and S. This — curve, as we shall see meets the sublimation curve of / + F’ in its terminal point D. We now take a TZ’ and P at which is formed from /’'+ F” a liquid without vapour, hence the system /-+ /’ + L. The liquid will then, of course, be represented by a point of the line FF’. According to the situation of Z in regard to the points /and F’, - the following reactions may oceur at a constant P and 7’ on a supply, or withdrawal of heat, or on a change in volume. 1. If the point L lies between / and #” the reaction f+ PSL (lo) by takes place. The liquid is, therefore, formed by the fusion of a part of each of the solid substances. We will call this a congruent or mutual fusion of #-+ 1”. 2. If the point /” is situated between /’ and ZF the reaction F=2F-+ L oceurs. Hence, the liquid is formed because a part of F’ melts with separation of /. The formation of liquid is thus accompanied with a conversion of /" into #. We will call that an incongruent or transformation fusion. 3. If the point / lies between /” and L the reaction ’= k” + L occurs. This case is quite analogous to the previous one. If we change the temperature we must, of course, also change the pressure in order to keep together the three phases /°, /’, and L. The liquid Z then also changes its composition. In a P, 7-diagram we thus obtain a curve like d’S in fig. 1, which we will call the melting point line of # + 4”. If between the three phases occurs the reaction mentioned sub 1 we call d’’S a congruent or mutual melting point ne of /’+ PF’; if the reaction sub 2 or sub 3 occurs we call d"S an incongruent melting point line or the transformation melting point line of /’+ LF”. We now allow the system /’-+ /” + LZ to traverse the melting point line d'S in such a direction that the pressure diminishes; at a definite pressure Py and its correlated temperature 7'p an infinitely small quantity of vapour will form so that the four-phase equili- brium + #” + L + G again appears. The complex therefore passes from the melting point line on to the four-phase line DS. The melting point line therefore terminates in the point S and, as we shall see presently, comes into contact with the four-phase line in this point. We will call S the minimum melting point, or the melting point of the complex / + /” under its own vapour pressure. The vapour G forming in the point S will as a rule, not be repre- sented by a point of the line /F#’, but the liquid ZL will, of course, still be represented by such a point. The sublimation line a’D and the melting point line Sd" of the complex # + #”’ are therefore connected with each other by the part DS of the four-phase curve. The fact that the points D and S will not, as a rule coincide may be perceived in the following manner. In the maximum sublimation point the points /, /’, and G, in the minimum melting pomt /’, /’, and ZL are situated ona straight line. Hence, both points will coincide only then when incidentally the four phases of the system /°+ 7” + 1+ @ lie on a straight line. The course of the sublimation curve, of the four-phase curve and of the melting point line is, as we will see presently, determined 1316 by the relation: GP. “Wi aE AG p (1) “LW is the quantity of heat which must be supplied, 4 V the change in volume occurring when, between the phases in equilibrium at a constant 7’and P, a reaction takes place in the one or in the other direction. Let us first consider the sablimation curve a” D). For each of the reactions meationed sub 1-—8 taken in such a direction that vapour is formed, AW and AV are positive. From (1) it thus follows, as drawn in fig. 1, that, at an elevation of temperature, the sublimation curve must proceed towards higher pressures. The point J lies as well on the sublimation- as on the four-phase curve. As, however, in this point J, the quantity of liquid of the four-phase equilibrium is still but infinitesimal, 4 17 and AV are the same for both systems so that the two curves must meet in D. Let us now consider the melting point line Sd’. We take each of the reactions mentioned sub 1—8 in such a direction that liquid is formed so that SIV is positive. At the congruent and incongruent fusion of /+ /” SV may, however, be positive as well as negative. The melting point line can therefore, proceed from S towards the right as well as to the left; in fig. 1 the first case has been drawn. The fact that the melting point line and the four- phase line meet each other in S follows in the same manner as that given above for the meeting of the two curves in D. In order to deduce formula (1) for the sublimation or the melting point curve, we consider the equilibrium /-+- 4” + G@ or #+ #’ +L. We represent the composition of / by «, 8, that of /” by a’, B’, that of L or G by «x, y. We call the volumina of these phases v, v and JV, the entropies 7, 1 and #/, the thermodynamic poten- tials & 6 and Z. As F and /” are in equilibrium with ZL (G) we have: OZ OZ Z —(e—a) — —(y—8) — =S .... . (2) Ow Oy OZ 0Z Ne at ead Dae re <0 hs) “agli From the condition that the three points /’, #” and ZL (G) are situated on a straight line, follows: («—a) (y—6') = («—a') (y—B) - ... « . « (4) 1317 From these relations between the four variables w, y, P and 7’ follows : \(e—a) r -+ (y—Bf) s} da +- \(@—a)s + (y—B)# dy = AdP — BdT’ (5) \(a—a')s + (y—B' edu + {(e—a’)s + (y—f') dy = A'dP — B'dT (6) (B—Bi)idai==(a—a)idy 3 « = 2 « « = (0) If from this we wish to deduce the relation between dP and dT’ we may divide (5) by (6). In consequence of (4) we get: r—a Ad P— BdT } co peas or after reduction : dP (a —a)H + (x —a’) 9 + («@—a) 1] dT (a'—a) V 4- (c—a’) v + (e—a) v' © (9) which corresponds with formula (1). Henee, as we have seen above, if we choose the exact conditions, we can compel the complex /'+ /” to traverse the sublimation curve a" D, the four-phase curve D S and the melting point curve Sd'. We will now investigate which conditions of the complex F'+ F” are represented by points situated outside these curves. We distinguish therein different cases. 1. The complex /-+ /” has a congruent sublimation line, four- phase line and melting point line. Let us first introduce the complex /'-+ /” in a point of the sublimation curve so that /"+ #” + G@ is formed. From a conside- ration of what happens on supplying or withdrawing heat or on a change in volume we deduce: at the right of and below the line a'D are situated the regions + G and #’ + G, at the left of and above curve a’D is situated the region / + F”. Acting in a similar manner with points of the other curves we find: at the left of and above a"DSd" is situated the region + F’. at the left of and below a" Dare situated the regions / + G and /” + G AS oo 2/o ier » 9» » +04Gand f’+04+G4 eh ee 2 ae 55 f Ways F+ Land F'+ L. Let us enter the region /+L-++G from a point of the fourphase curve in a horizontal direction. We then, at a constant pressure, raise the temperature of the system #-+ + G. The liquid and the vapour of this system then traverse a part of the boiling point and vapour boiling point curve of the substance /’. If we enter the region /-+4+ 2+ G@ from a point of the four- phase curve in a vertical direction we then, at a constant tempera- 86 Proceedings Royal Acad. Amsterdam. Vol. XV. 1318 ture, lower the pressure of the system / + Z-+-G; the liquid and the vapour of this system then traverse a part of the saturation- and vapour saturation curve of the substance / under its own vapour pressure. The same applies if we enter the region /” + 1+ G from a point of the four-phase curve. In order to find the limitation of the different regions we draw in fig. 1 the sublimation curve a XK, the three-phase curve AF and the melting point curve Fd of the compound F and the same curves a’K’, K’F” and F’ d’ of the compound /”. We will assume that / and F” also melt with increase in volume. The curves Fe and Af have the same significance as the homony- mous curves in fig. 3 (III); the same applies to the curves /”’e’ and K’7’. The question now arises: where are these curves situated in regard to the corresponding curves of the complex /’+ L”. Fig. 1. Let us first take a pressure so high that # and F” as well as their complex /’-+ /” have a melting point. Now, as is well known, the mutual melting point of /’+ F”’ is situated lower than than of each of the components individually. A horizontal line intersecting the three melting point lines must therefore intersect the melting point line of /’-+ £” at lower temperature than the two other melting pointylines. 1319 In the same manner we find that a horizontal line which intersects the three sublimation curves must cut those of /’+- 4” at a lower temperature than in the ease of the two other ones. Curve a’ DSa" must, therefore, be situated in regard to the curves akFd-and aK’ F’d’ as in Fie. 1. The regions /’-++ L and I’ -++ L+ @ are separated from each other by means ofa curve, where /’-++ ZL appears in the proximity of an infi- nitesimal amount of vapour. We call this system "+ 14+ G° ; signifies here that the other phases can be in equilibrium with a vapour of the composition G but that only an infinitesimal amount of that vapour is present. If, owing to solution of large quantities of / in a small quantity of L, the system /’-+ L + G®° approaches to solid / + liquid # + G° the system /’-++ 1+ G° then approaches the minimum melting point of the substance /’. If from /-+ L+ G° the solid substance /” is separated, so that the system /’+ /” + 1+ G° is formed, we find ourselves. in the minimum melting point of complex /’-+ F”. Hence, the P, 7-curve of the system “+ L + G®° proceeds in fig. 1 from S towards Ff. In the previous communication IV we have already extensively considered this system + 1-+4+G°. The liquid Z of this system traverses at an elevation of temperature a straight line passing, in the 7, y-representation, through the point F’, for instance the line ZE ov ZF in fig. 1 (IV). The P,7 curve corresponding with this line is represented in fig. 4 (IV) by curve ZF or ZF’. The curve S/' must, therefore as a rule come into contact with the melting point line Fd in the point F. In fig. 1 it has been assumed that curve SP’ corresponds with branch ZF of fig. 4 (IV). The regions #”-+ ZL and F’ + 1+ G are separated from each other by a curve /” + 2+ G®; in a similar manner as above we tind that this is represented by a curve S /”. In fig. 1 we have drawn the two curves S/¥ and S#” in agreement with branch ZF of fig. 4 (IV); we might have drawn both or one of them also in agreement with branch 7,/ of this figure. The boundary curve of the regions ##+L-+G and #+G@ is formed by the system r+ 1°+ G; that of the regions 7” + L+ G and F’ + G by the system /” + 1°-+ G. L° signifies here that the other phases may be in equilibrium with a liquid 4, but that only infinitely little of that liquid is present. In an analogous manner as above we find that the P, 7-curves of these systems are represented in fig. 1 by the curves SA and SK’. These curves meet in A and XK’ the curves 86* 1320 ad and a'd. On both curves a point with a maximum pressure and one with a minimum temperature is supposed to occur. Besides the regions whose limitations we know now we find at the right of curve a'd' also the regions 1+ G, ZL and G which, however, are not drawn in the figure. In order to survey the connection of these regions we might draw a representation in space; for this we imagine the composition of the complex #-+ F” to be placed perpendicularly to fig. 1. Instead of the spacial representation itself we will here consider its sections with planes. If we place a plane perpendicularly to the concentration-axis we get a P,7-diagram which applies to a definite complex, if we placea plane perpendicularly to the Z-axis we get a pressure-concertration diagram which applies to a definite temperature, and if we piace a plane perpendicularly to the P-axis we get a temperature-con- centration diagram which applies to a definite pressure. Let us place first a plane, which intersects the three sublimation curves, perpendicularly to the Z-axis; we then obtain a section as in fig. 2 in which F/ and F” represent the two compounds and F”. Perpendicularly to this line #'¥” is placed the P-axis. In order to be able to indicate readily the different regions occurring in this and the following diagrams we will represent : The liquidum region by JZ, the vapour region by G, the solid region by + F’, the region + G by 1, #”+G by 2, F+L by 3, F’+-L by 4, L+G by 5, F+L+G by 6 and #”+-L+G by 7. If in fig. 1 we suppose a straight line, which intersects the three sublimation curves, to be drawn parallel to the P-axis, we notice that in fig. 2 the regions #4 FF’, 1=F+4G, 2=/’+ G and the region G must appear. The points s, s' and s” represent the sublimation pressures of the solid substances / and £” and of their complex /’-+- /”; the complex, therefore, has a higher sublimation pressure than each of its components by itself. The curve ss" represents the vapours which ean be in equilibrium with solid /, curve ss" those which can be in equilibrium with solid /#”; these curves have in s and s' a horizontal tangent. We now take a complex /-+ F” of the composition c, so that the complex itself is represented by a point of the line cc’. As this line intersects the regions /’+ #4”, 2 and G, then according to the pressure chosen, there 1321 is formed either /’-+ F” or /’+G or G. If the complex has such a composition that the line cc’ intersects the regions /’-+ #”, 1 and ( either /-+ #” or F+ G@ or G is formed. Let us now take a pressure concentration diagram for a temperature higher than the maximum sublimation point, but lower than the minimum melting point of the complex /’+ /”. If in fig. 1 we draw a vertical line which intersects curve DS we notice that this diagram may be represented by fig. 3. Besides the regions G, /’-+ #”, L and 2 which appear already in fig. 2 we also find here the regions : Be Jb JL e 6=F4+L+4G6 and 7=F'+L4 4G. If from /’+ F” is formed one of the systems G', / + G or /” + G, the vapour G always has a composition that can be represented by a point of fig. 3; the same applies to the liquid Z if from 4+ F” is formed one of the systems L, “+ LZ or /” 4+ L. If, however, LZ -+ G is formed as in the systems 1 + G, F4+ L+G and /” + L-+ G, such, as we have seen previously, is no longer the case and neither 4 nor G can be represented by a point of the diagram. Let us take for example a complex A (not drawn in the figure); this complex is resolved into a liquid LZ and a gas G, both situated outside the plane of fig. 3. If Z is situated above this plane, ( lies below the same and reversedly so and in such a manner that their conjugation line intersects the region 5 in the point A. If we take a complex A’ within the region 6(7), we then suppose this to be resolved first into /’(#”) and a complex A of 14+ G; the complex is, of course, represented by a point of fig. 3. To this complex now applies the same as to the complex A’ within the region 9. Hence, if from /-+ F” is formed a system in which Z + G appears, the com- plex L + G@ is certainly represented by a point of fig. 3 but Z and G separately are not; one of these phases lies in front of, the other behind the plane of fig. 3. By way of distinction from the other regions, the regions 5, 6, and 7 are dotted; we may imagine that these points represent the points of intersection of fig. 3 with the Fig. 3. conjugation lines liquid-gas. We have noticed previously that in some systems occurs only an infinitesimal quantity of L or G; of a similar complex L°-+ G or L+ G® the gas is 1322 represented by a point of the diagram in the first case; the liquid in the second case. The line of demarcation of the regions 1 and G represents the vapours which can be in equilibrium with solid /, that of the regions 2 and @ those which can be in equilibrium with solid #”. The line of demarcation of the regions 5 and G represents the equilibrium L°+ G, that of the regions 5 and 6 the complex 1+ G of the system /’+ L-+ G and that of the regions 5 and 7 this same complex of the system /#” + L+ G. If in agreement with fig. 1 we take a temperature higher than the minimum melting point S of the complex “+ /” and lower than the maximum sublimation point A’ of the substance /” we obtain a diagram as in fig. 4. If in agreement with fig. 1 we take a tem- perature higher than the maximum sublimation point A’ of the sub- stance F and lower than the minimum meltingpoint /” of the com- Fig. 4. Fig. 5. Fig. 6. pound /” we obtain a diagram as in fig. 5. If finally we take a temperature higher than the minimum melting point /’ of the com- pound /’ we obtain a diagram as in fig. 6. Between the diagrams figs. 2—6 exist different transition forms ; we must also consider the possibility that, in fig. 1, we ean draw, lines parallel to the P-axis which cut the curves DA, DK’, SF and S#” in two points. We will not, however, discuss here these transition forms. When deducing the diagrams it has also been assumed that the points D, K’, K, S, #” and F are situated in regard to each other as drawn in fig. 1. But this may be different. As a rule, the points S, #’, and F and also the points D, A’ and A will lie in regard to each other as assumed in fig. 1. The minimum melting point of the complex /’-+ #” is therefore, as a Ee 1323 rule situated at a lower temperature and pressure than the minimum melting point of each of the substances /’ and /” separately. For in fig. 1 we have assumed that curve S/’ corresponds with branch ZF of fig. 4 (IV) and that S is situated on the rising part of this branch and is removed far from the point with the maximum pressure. If, however, S lies on this branch somewhere between the point with the maximum pressure and that with the maximum tem- perature the curve S/’ in fig. 1 no longer exhibits a pressure maxi- mum but only a temperature maximum; the pressure in the minimum melting point of /7+ /” is then higher than that in the minimum melting point of 1. If S is situated on branch Z/ somewhere between the point with maximum temperature and the point /’, curve S/’ in fig. 1 proceeds from SS towards lower temperatures and pressures. In that case not only the pressure but also the temperature of the minimum melting point /-+ #” is situated higher than that of F. From our previous considerations as to curve Z/'Z, of fig. 4 (IV) it follows that the latter case can occur only then when the liquid formed at the minimum melting point of /’-+- /” differs but little in composition from the substance /’. From these considerations follows: at a constant pressure the melt- ing point of the complex /#’+ /” is always lower than that of each of the substances and /” separately. As a rule the minimum melt- ing point of #-+ F” is also lower than that of each of the com- pounds individually. By way of exception, the minimum melting point of /’-+ /” may, however, be somewhat higher than that of one or even of both of the substances / and F”. We shall see later that in this case at the temperature of the mini- mum melting point of /-+ #”, the saturation curve of / or LF” under its Own vapour pressure is exphased. A similar consideration applies to the maximum sublimation points of the complex /’-+ /” and the compounds /’ and /”. Let us now bring a complex /’+ /” of a detinite composition c, to a temperature 7, and a pressure P,. In order to investigate in ‘which of the 10 possible conditions this complex will now oecur we take a pressure concentration diagram of the temperature 7, and place in this the concentration c, and the pressure P, of the complex. If now the figurating point lies for instance in region 7, /”+L+G is formed, if in region 3, /-+ ZL is formed, if it lies in region G it is converted wholly into gas, in region L wholly into liquid, ete. Besides the pressure concentration diagrams considered above we may also deduce from fig. 1, or its corresponding spacial represen- 1324 tation, temperature concentration diagrams for a complex ofa definite composition ; I will, however, not go into this any further. 2. The complex / + /” has an incongruent sublimation line, four- phase line, and melting point line. We will assume that both liquid and vapour have such a com- position that on the sublimation curve a’ D (fig. 1) occurs the reaction I’2F+G, on the four-phase curve. DS the reaction “2+ L+G and on the melting point curve Sd” the reaction #” S / + L. Hence if #” is placed in an evacuated space and if gas is generated, then according to the capacity of this space /&+ 7’ + G or F+ G is formed or merely a vapour G of the composition /” ; if liquid and vapour are generated /’+ #’ + L + G is formed, or / + L + G, or L+G; if liquid is generated / + #” + L is formed or + L or merely a liquid of the composition £”. From /” according to the conditions chosen, one of the complexes FtP+G6, F+6,G6, F4+6, F+P+AL+G, F+L4+46, Ltd, F+lh’+L, F+ L or L will form or else the compound Ff’ may remain unchanged. If only LZ or G is formed these will, of course have the same composition as the compound F”. Hence, we can never obtain from the compound /’ one of the complexes +d, k’+L+4G or l’+ TL unless these appear in a meta- stable condition. In fig. 1 all curves relating only to the compound /” (a’ A’ , A’ FE’, Fd’ Fe’ and K’‘/’) and the regions encompassed by them, therefore represent only metastable conditions of the compound £” ; hence, they cannot be realised in the stable condition. If, therefore, the compound #” is introduced into an evacuated space it will not occur in the conditions which correspond with the P, 7-diagram of iI’, but with those corresponding with the P, 7-diagram of the complex /’+ 4”. : The terminal point D of the sublimation curve a’D is here not only the highest sublimation point of the complex /-+ /”’, but it also represents the highest pressure at which the conversion of /”~ into takes place by the side of gas; the initial point S of the melting point curve Sd" is here not only the lowest melting point of the complex /’-+ F”, but represents also the lowest pressure at which the conversion of 4” into /’ takes place in presence of liquid. From a consideration of what happens with the complex /’ + /” on supply or withdrawal of heat or on a change in volume we deduce : 6 aE 1325 At the left of and above a’ DSd" is situated the region /’ + +” >» » kighti;, >. below a’D E nA “i = FG oN ei Gee a at ix RS Weipa ts go ee eS rr ae 0 20 22 These regions are, therefore, situated, with regard to the curve a’ DSd", in the same manner as in fig. 1. It is also evident there- from that in the P,7-diagram the regions /” + G, 1” + 1+ Gand i’ + L are wanting. In order to survey the connection of these regions we might draw a representation in space by now also placing perpendicularly to fig. 1 the composition of the complex /’+ 4”. From this spacial representation wé might then deduce the pressure concentration the temperature concentration and the P,7-diagrams for definite concentra- tions. We will, however, not go into this matter any further just now. 3. Some other cases. Up to now, we have supposed that / and /” melt with increase in volume and that this is also the case with the congruent and incongruent melting of the complex /’+ #”; in agreement there- with, the temperature on each of the three melting point curves in fig. 1 increases with elevation of pressure. We now see at once that there are many cases to be distinguished; the reader himself can easily introduce the necessary alterations. Further, we have supposed sub 1 that in each point of the curve a'DSd' occurs a congruent reaction and sub 2 that in each point of this curve an incongruent reaction appears. It is evident that in this respect also many cases may be distinguished of which I will briefly mention a few. We imagine on the sublimationcurve a point /; on the part a'/ occurs, between the phases of the complex /’+ /” + G, the con- gruent reaction /#” + F/2G; on the part /D the incongruent reaction /” 7 F+G. In the point / itself the compound /' will then take no part in the reaction but the reaction /”= G' takes place in which G has the same composition as /”. Hence, in the point / occurs the complex / + #” + vapour LF”; in / therefore, also exists the complex /”’ + vapour /”. From this follows that / is not only a point of the sublimation curve a’) but also of the sublimation curve a‘ K’. Now, the direction of these curves in each point, therefore also CHE (is a Ls reaction in the two systems /’-+ /” + vapour #” and /” + vapour in / is determined by As, however in the point / the 1226 I” is the same (namely, /’= vapour /’) 4 Wand AV are also the same for both systems. The curves a'D and a’K’ must, therefore meet in the P, 7-diagram in the point /. A corresponding property holds when a corresponding point / is situated on the four-phase curve, or on the melting point curve of the complex /’ + F’. Hence, if the sublimation line, the four-phase line or the melting point line of the complex # + /” is in a part a congruent and in a part a transition curve, the curve of the complex in the P, 7-dia- gram will meet in its transition point the corresponding curve of that compound which is being converted. If there are iwo transition points, many cases may present them- selves, according to their situation, the compound converted ete., which we will not discuss here any further. (To be continued). Chemistry. — “The system sodium sulphate, manganous sulphate and water at 35°'). By Prof. F. A. H. Scureinemakers and D. J. van PROOWE. In this system oceur as solid phases, which can be in equilibrium at 35° with saturated solutions: anhydrous Na,SO,, the hydrate MnSO,.H,O and the two anhydrous double salts : Doo = (Mn SO4)p . (Naz SO4)10 and D,.3 = Mn SOq. (Na, SO4)s. The double salts previously deseribed : Mn SO,. Na, SO, , 2H20 and Mn SO,. Na» SO,. 4 H.O have not been found by us, whereas on the other hand those now noticed have not been described up to the present. Moreover, the accurate preparation and solubility of the salts previously described are but insufficiently known, so that it is difficult to decide whether these are perhaps metastable or whether the presence of two meta- stable salts was, perhaps, due to accident. The equilibria occurring at 35° are indicated schematically in the figure; the two double salts are represented by the points Dojo and D,5, the salt MnSO, . H,O is represented by the point Mn,. The isotherm consists of four branches, namely 1) Maricnac and Geiger, A. Min. [5] 9. 15. Mag. Pharm. 11 27, 1327 ab the saturation line of Na. SO, Gcuee ss ee Dans (Hal pe = oe Re Dir de ,. xs Mn SO,.H_O The exact position of these branches can be drawn with the aid of the determinations recorded in table I. TABLE T. Composition in °/, by weight of the solutions saturated at 35° and of the residues. ee Solution | Residue - ; — - Solid phase | = Of MnSO, 0 0 Na;SO, % MnSO, 05 Na,SO3 39.45 | 0 ee | = | MnSO, . H,0 aoe 523 43.84 | 4.50 | : 33.06 | 7.97 50.85 | 23.22 | MnSO, . HO + Do jo 32.76 7m | 49.35 | 14.71 4 32.92 7.42 | 43.49 | 7.76 ‘ 31.05 9.20 7) a I Data 27.67 10.76 33.44 | 21.81 | : 22.14 14.28 37.44 | 35.46 | . 14.58 20.01 31.08 | 35.50 | z 13.96 21.91 ei al Meares ee eione 12.19 22.49 18.63 aris _| Das 10.45 23.41 18.40 49.53 7.43 26.58 18.53 55.45 ‘ 5.69 | 29.31 17.02 | 55.00 = 5.11 30.52 9.11 | 61.58 | Dys+Na,S0, 2206) |. —-31-33 | 1.46 67.40 | Na,SO, 0 | 33 ey , | From the table it is shown that the composition of the solution saturated with Mn SO,.HsO + Doi) has been determined three times. In order to be able to deduce the composition of the solid sub- 1328 stances with which the solutions are saturated, the composition of such a solution has been determined and in addition that of the correlated residue. W As shown in the table, four solutions of branch cd and their correlated residues have been determined besides the two terminal points; if these are introduced into the figure and the conjugation lines are drawn, these intersect the side MnSO,— NasSO, in a point indicating 48.89 °/, of MSO, and consequently 51.11 °/, of Naz SOs. The double salt MnSO,.NagSO, contains, however, 51.53 °/, of Mn SQ , therefore, 48.47°/, of Na SO,, so that the solid substance with which the solutions of branch cd are saturated cannot be the double salt MnSO,.Naz:SO, or one of its hydrates. If from the composition (°/, by weight) of the point of intersection we calculate the molecular composition we find: (Mn SO4)y (Naz SOs)i0 = Dao. As shown in the table, four solutions of branch dc and their corre- lated residues have been determined besides the two terminal points b and c; these four conjugation lines intersect the side Mn SO;—Nas SO4 in a point indicating the composition of the double salt: MnsSO4 (Na2SO4)3 = Di 3. This double salt contains 26.16 °/, of Mn SO, and consequently 73.84 °/, of Naz SOs. The behaviour of both double saits in regard to water is shown at once in the figure if we connect therein the apex W with the points Dj.3 and Dgio. As the line W.D)5 intersects the curve dc and the line W.Do1jo the curve cd, it is evident that at 35° both double salts are soluble in water without decomposition. 1329 Botany. — “On intravital precipitates”. By Prof. C. van WisseLincu. (Communicated by Prof. Mott). (Communicated in the meeting of February 22, 1913). The precipitates caused by basic substances in living plant cells have long attracted the attention of investigators and the literature on this subject is already voluminous. Cuartes Darwin was the first to investigate these precipitates. He *) first mentions the phenomenon in his work on insectivorons plants, and calls it aggregation. As pg Vrres*) has pointed out, Darwin includes two different pheno- mena under this name: in the first place, the movements which he discovered in the protoplasm of the cells of the glands of Drosera rotundifolia and other insectivorous plants, movements which occur whenever stimulation causes an increased secretion, and in the second place the precipitates which occur in the protoplasm when ammonium carbonate is used as a stimulus. As Cu. Darwin*) has shown, precipitates with ammonium carbonate and with ammonia are also formed in many other cases in living plant cells. He stated that the precipitates no longer occur when the preparations are heated in water for 2 to 3 minutes to the boiling point and on this account he was inclined to consider the reaction as a vital one. With regard to the chemical nature and physiological significance of the substance of which the precipitates are composed Darwin expressed himself very cautiously. He supposed that they consist of protein and considered that we have to deal with an excretion product. He concluded his last-mentioned paper as follows: “But I hope that some one better fitted than I am, from possessing much ‘more chemical and_ histological knowledge, may be induced to investigate the whole subject”. From this it follows that Darwin may have thought that another explanation of the phenomenon he had discovered was also possible. Fr. Darwin‘) defends his father’s views, as far as the chemical nature of the precipitate is concerned, which ammonium carbonate produces in the tentacles of Drosera rotundifolia. Dr Vrirs*) is 1) CuaRLes Darwin, Insectivorous plants. 1875, p. 38. Chapter LIL. *) Huao pr Vriss, Ueber die Aggregation im Protoplasma von Drosera rotun- difolia. Bot. Zeit. 44. Jahrg. 1886, p. 1. 3) CHARLES Darwin, The Action of Carbonate of Ammonia on the Roots of certain Plants. The Journal of the Linnean Society. Botany. Vol. XIX. 1882, p. 239. 4) Francis Darwin, The process of aggregation in the tentacles of Drosera rotundifolia. Quarterly journal of microse. science. Vol. XVI. 1876, p. 309. 5) lic. p. 42 ff and 57 ff. also of the opinion that the precipitate belongs to the group of the proteins. as far as its behaviour towards reagents is concerned. The precipitates caused by ammonium carbonate in the cell-sap of Spirogyra and of ‘other plants, have also been investigated by Prerver’). In his opinion they are composed of protein tannate and give reactions both with protein- and with tannin-reagents. Lorw and Bokorxy?) have written numerous papers on the subject of precipitation in living plant cells by various basic substances. In these publications, the same points generally have been stated, so that they can here be dealt with together. In the opinion of these two investigators the precipitates which have been caused in the cells by ammonium carbonate, antipyrine and caffeine consist of active protein. The bodies of which the preci- pitates are composed, called by these writers proteosomes, can be formed both in the protoplasm and in the cell-sap. According to Lorw and Boxkorny the formation of proteosomes is a real vital reaction. When the cells have been killed, the reagents mentioned cannot any longer bring about the phenomenon, because the active protein has been changed into passive protein. The two authors describe peculiarities of the precipitates and mention positive results which they obtained with various protein reagents. The precipitates are siated to be composed either exclusi- vely of active protein or they contain also other substances, such as tannin, but it is emphatically declared in this connection, that the admixture of other substances is “unwesentlich”. > 1) W. Prerrer, Ueber Aufnahme von Anilinfarben in lebenden Zellen. Unter- suchungen aus dem botan. Institut zu Tiibingen. 2. Bd. 1886—1888. p. 239 ff. 2) O. Lopw und Tu. Boxorny, Ueber das Vorkommen von activem Albumin im Zellsaft und dessen Ausscheidung in Kérnchen durch Basen. Bot. Zeit. 45. Jahrg. 1887. p. 849. — Ueber das Verhalten von Pflanzenzellen zu stark verdiinnter alkalischer Silberlésung. Bot. Centralblatt. 10. Jahrg. 1889. XXXVIIT. Bd. p. 581 and 614, XXXIX. bd. p. 369. XL. Bd. p. 161 and 194. — Versuche tiber aktives Eiweiss fiir Vorlesung und Praktikum. Biologisches Centralblatt. 1891. XI. p.5.— Zur Chemie der Proteosomen. Flora. 1892. Erginzungsb. p. 117. — Aktives Eiweiss und Tannin in Pflanzenzellen. Flora. Cl. 1911. p. 1183—116. Autoreferat. Botan, Centralblatt. 32. Jahrg. 1911. I. Halbjahr. Bd. 116. 1911. p. 361. Tu. Boxorny, Neue Ustersuchungen iiber den Vorgang der Silberabscheidung durch actives Albumin. Jahrb. f. wiss. Bot. XVIII Bd. 1887. p. 194. — Ueber die Einwirkung basischer Stoffe auf das lebende Protoplasma. 1. c. Bd. XIX. i888. p. 206—220. — Ueber Aggregation, |. c. Bd. XX. 1889. p. 427. — Zur Kenntniss des Cytoplasinas. Ber. d. d. bot. Gesellsch. Bd. VII. 1890. p, 101. — Zur Pro- teosomenbildung in den Blattern der Crassulaceen. 1. c. Bd. X. 1892. p. 619. — Ueber das Vorkommen des Gerbstoffes im Pflanzenreiche und seine Beziehung zum actiyven Albumin. Chemiker-Zeit. 1896. No, 103. p. 1022. The views of Louw and Boxkorny that precipitates caused in living plant-cells by ammonium carbonate, ammonia, antipyrine, caffeine and other basic substances are protein precipitates have been contested by Av Kuiercker’), Kirmm ’) and Ozaprx *). All these consider that the precipitates are in reality tannin precipitates. On treating these and the cell-sap with protein reagents they always obtained negative results, while on the other hand tannin reagents gave positive ones. It is worthy of notice that Kiem in connection with his experiments with methylene-biue regards tannin as of secondary importance in the case of Spirogyra. Here another as yet unknown substance might cause the precipitate. Czaevk states that the precipitates may sometimes take up other substances, such as colouring-matter from the cell-sap and_ lipoids. Also, in spite of the negative results of experimental investigation, he thinks that the precipitates sometimes may contain protein sub- stances, because the latter occurs in the cells. There is a divergence of opinion between the last-mentioned inves- tigators as to the place where the precipitates occur. Ar KLErcKER holds that they occur in the cell-sap. Kiemm thinks that detailed study will probably show more and more, that they are formed exclusively in the cell-sap and not in the protoplasm or in both, as Boxorny wrongly asserts for the Crassulaceae. On the other hand Czarek believes, that they can occur in the cell-sap and in the cyto- plasm as, inter alia, may be the case in the leaf of Echeveria. In 1897 an interesting investigation by Ovurton ‘) was published. He experimented on Spirogyra with ammonia, amines, caffeine, pyri- dine, quinoline, piperidine, and alkaloids. He has no doubt at all that the precipitates which are’ found in_ the cell-sap are compounds of tannin with the above substances. He describes in detail the phenomena which are brought about by solutions of caffeine of different strength, namely, when successively stronger or weaker solutions are added. In explanation it is said that the compound of tannin and caffeine are in a condition of hydrolytic dissociation. 1) J. E. I. Ar Kiercker, Studien tiber die Gerbstoffvakuolen. Inaug. Diss Tiibingen 1888. *) P. Kuemm, Beitrag zur Erforschung der Aggregationsvorgiinge in lebenden Pflanzenzellen. Flora 1892, p. 395. —Ueber die Aggregationsvorgiinge in Crassulaceen- zellen Berichte d d. bot. Gesellsch. Bd. X. 1892, p. 237. 5) F. GzapeK, Ueber Fiillungsreaktionen in lebenden Pflanzenzellen und einige Anwendungen derselben. Ber. d.d. bot. Gesellsch. Bd. XXVIIL. 1910. Heft V. p. 147. 4) EK. Overton, Ueber die osmotischen Eigenschaften der Zellen in ihrer Be- deutung fiir die Toxikologie und Pharmakologie. Zeitschr. f. Physikal Ghemie XXL. Bd. 1897, p. 189. 1332 Shortly before the appearance of Czaprxk’s publication quoted above 1‘) made a preliminary communication on the demonstration of tannin in the living plant and on its physiological significance. While searching for a method of studying the physiological significance of tannin in Spirogyra my attention was also drawn to antipyrine and caffeine, substances which had not then been used for that purpose. Like Overton I described the precipitates as tannin precipitates and have never for a moment thought of regarding them as protein precipitates. All the results were in agreement with the view that they were tannin precipitates. In the paper referred to above I drew attention to the fact that they were earlier described erroneously by Loew and Bokoryy*) as protein precipitates. To this these authors *) soon replied. In connection with the various views on the chemical nature of intravital precipitates, I have further considered whether protein might occur in them and subsequently performed some experiments on Spirogyra maxima (Hass.) Wittr. which in my opinion render much more certain the view that the precipitates contain no protein, than was already the case. It follows moreover from these experiments that the precipitates occur in the cell-sap and not in the cytoplasm. 1 will first explain this point. Boxorny*) assumes that in Spirogyra proteosomes are formed in the cytoplasm as well as in the cell-sap. He thinks he has furnished proof of this by combining the formation of proteosomes with abnormal plasmolysis. He placed Spirogyra in a mixture of equal parts of a 10°/, solution of potassium nitrate and a 0.1°/, solution of caffeine. After the action proteosomes were observed in the cytoplasm as well as in the con- tracted vacuole. KiemM‘) agrees with Bokorny with respect to the localisation of the precipitate in Spirogyra. Kiem first allowed the precipitate to occur and then to be plasmolysed. When Bokorny‘) first brought about abnormal plasmolysis with a 1) ©. van WISSELINGH, Over het aantoonen yan looistof in de levende plant en over hare physiologische beteekenis. Verslagen der Koninkl. Akad. van Weten- schappen te Amsterdam, Maart 1910. On the tests for tannin in the living plant and on the physiological significance of tannin. These Proc XII, p. 685. 2) O. Lorw and Tu. Boxorny, Aktives Eiweiss und Tannin in Pflanzenzellen. 1.c. 3) TH. Boxorny, Neue Untersuchungen iiber den Vorgang der Silberabscheidung durch actives Albumin. l. c. p. 206. ‘) P. KuemM, Beitrag zur Erforschung der Aggregationsvorginge in lebenden Pflanzenzellen. 1. c. p. 407. 8) Tu. Boxorny, Ueber die Einwirkung basischer Stoffe auf das lebende Proto- plasma. |. ce. p. 209. 1333 10°/, solution of potassium nitrate and subsequently allowed basic substances to act, he found only proteosomes in the contracted vacuole and explains this by assuming that on the death of the protoplasm the active protein is changed into passive and that then no more proteosomes can be formed, so that a vital reaction is given no longer. Without considering this explanation for the present, I content myself with pointing out that, when the above experiments are repeated, careful observation already shows that so far as the localisation of the precipitate is concerned, Bokorny’s view, accepted by Kiem, is incorrect. When first abnormal phasmolysis is produced with a 10°/, solu- tion of potassium nitrate and this is followed by application of a 10°/, solution of potassium nitrate which contains in addition 1°/, antipyrine or 0.1°/, caffeine or if a rod with ammonia is then held above the preparation, precipitation takes place exclusively in the contracted vacuole. If the reagents are allowed to act simultaneously or in reverse order, i.e. if the precipitation is first produced by the antipyrine or caffeine solution and’ is followed by abnormal plasmo- lysis, then it is seen that the contracuon of the vacuole is accom- panied by continued expulsion of the precipitate which is surround- ed by cytoplasm. If the whole process is not followed under the microscope, but if the final result alone is observed, then it is easy to imagine that precipitation has also taken place in the cytoplasm and thus-to draw an erroneous conclusion, as did Bokorny. As already mentioned, some investigators have obtained all possi- ble protein reactions with the intravital precipitates, whilst others have only got negative results. [| may remark that protein reactions at our disposal are in general not sensitive as microchemical reactions. When these reactions, namely, the test with sugar and sulphurie acid, the biuret test, Minnon’s test and the nitric acid test, are tried on minute pieces of coagulated egg-white, the various colorations can indeed be easily seen, but yet it is noticed that most of the reac- tions can have no great value for microscopic. investigation. With Mituon’s reaction, and the mitric acid and biuret tests the colour with very thin pieces of egg-white is very faint. With a minute object such as the protoplast of Spirogyra which in addition to protein contains also other substances, little is to be expected from the three last-mentioned reactions. In accordance with this I did not obtain favourable results, but the reaction with sugar and sulphuric acid yielded better ones. The objects were left in a sugar solution for some time and then sulfuric acid was allowed to 87 Proceedings Royal Acid. Amsterdam. Vol. XV- 1334 flow in. I used a mixture of 9 parts by weight of concentrated sulphuric acid and one part by weight of water, therefore sulphuric acid of 85'/,°/,. This- mixture has a much smaller carbonising action on the sugar than concentrated sulphuric acid and is. therefore to be preferred. With small pieces of egg-white the reaction is very striking. At first the colour is red (compare Klincksieck et Valette, Code des Coleurs, 1908, N°. 16 and 21), sometimes with a very weak violet tint, then pure red (KL. et V. N°. 41) and afterwards orange-red (Ku. et V. N°. 51). With very thin pieces the colour is still observable. The reaction is also very suitable for microchemical use. In Spirogyra the protoplasts are coloured a distinet light red, the nucleus with the nucleolus and the pyrenoids are darker. At this point I mention a reaction which is indeed not a real protein reaction, but which may sometimes serve for the indirect microchemical demonstration of protein, namely, the test with tannin and iodine in potassium iodide solution. In botanical papers I have found it stated that iodine in potassium iodide solution gives a pre- cipitate with a tannin solution and can be used to demonstrate tannin microscopically. I have not been able to confirm this and it is more- over in conflict with what is generally stated in chemical handbooks, namely, that a tannin solution is coloured violet by means of an iodine solution such as iodine in potassium iodide. Of course care must be taken that the violet colour is not masked by the addition of much iodine. In chemical books I have found no mention of a precipitate. When hide-powder or pieces of egg-whiie are brought into contact with a tannin solution, washed with water after some time and then treated with iodine in potassium iodide solution, they usually show a dirty brown colour; after repeated washing with water a fine violet colour (KI. et V. 591, 596) appears, however. This reaction can also be applied to Spirogyra, but in this case the tannin solution is unnecessary, because Spirogyra itself contains tannin in solution in its cell-sap. The filaments of Spirogyra are warmed to 60° in water. They are then killed, the tannin leaves the vacuole and partly combines with the protein of the protoplast. If ihe filaments are now treated with iodine in potassium iodide solution and afterwards washed with distilled water until the iodine reaction of the starch disappears, it is then found that those parts of the protoplast which are rich in protein, are coloured violet. The nuclei with the nucleoli are finely coloured, ihe pyrenoids more faintly. I have been no more able to find protein in the intravital pre- cipitates with caffeine, antipyrine and ammonium carbonate than were Ar Kirrckrer, Kivmu and Czarek; neither when the precipitates 13385 with caffeine and antipyrine had been treated according to Bokorny’s' method with '/,,°/, ammonia and had thus become insoluble. Nor have I been able to obtain a protein reaction when the precipitates were some weeks old and had become insoluble. Spirogyra can, it should be noted, remain alive for several weeks in a 1 °/, antipyrine-solution and in a 0.1 °/, eaffeine-solution, At first the precipitates aggregate and form globules; gradually their solubility diminishes. When the filaments are then transferred into water, the globules leave vesicles behind, which have disappeared after some days. After a few weeks the globules seem altogether insoluble. In dead cells brown globules are found, which are also insoluble in water. Neither the globules nor their insoluble residues gave even a protein reaction with sugar and sulphuric acid, whilst the proto- plast became distinctly coloured red. On the other hand the globules gave tannin reactions. It is remarkable that Lozw and Boxorny*), who have repeatedly insisted on the protein nature of the precipitates, assert in one of their latest publications that the colowr-reactions for protein sub- stances, such as that of Mitton and the biuret reaction, are not the most important protein tests, although they formerly relied on these. Now they prefer coagulation by rise of temperature, by alcohol and by acids. I treated Spirogyra-tilaments, with precipitates produced by 1°/, solution of caffeine, by Boxkorny’s method with a saturated caffeine solution containing 20°/, aleohol or I exposed the filaments for a short time to the action of 10°), nitric acid or warmed them to 60° in a 1°/, solution of caffeine. In the first two cases I observed solution, in the last case coalescence. The results by no means proved the protein nature, as is especially evident from the following experiments. When I mixed 1°/, sointions of gallnut- or of Spirogyra-tannin with an equal quantity of a L°/, caffeine-solution and heated the mixture to 60° or added 10°/, nitric acid, the precipitate which was formed underwent a modification. It agglutinated more or less and a portion had clearly become much less soluble in water, so that after some days in an excess of water there was still a con- siderable resinous residue undissolved. It is possible that Lonw and Bokorny succeeded by heating and by the action of nitric acid to transform part of the precipitate in the cells into an insoluble modi- fication, but this is by no means a proof of its protein nature. Gy) Te BoKorny, Zur Kenntnis des Cytoplasmas. |.c. p. 106. 2) O. Lorw und TH. Bokorny. Aktives Eiweiss und Tannin in Pflanzenzellen. |.¢ Sy* 1336 Lorw and Boxorny') declare the formation of protosomes with ammonium carbonate, antipyrine and caffeine to be a true vital reaction. They say that when the ceils are dead, formation of proto- somes can no longer take place, because the active protein has become passive. 1 shall proceed to show how, starting from dead material, precipitates can be produced with antipyrine, caffeine and other basic substances, which completely agree with those observed in living material. That in dead cells of Spirogyra no precipitates occur with the above basic substances, is simply due to the fact that the dead protoplast and the cell-wall allow the tannin to escape. A portion of the tannin gets outside the cell and another portion enters into combination with the protein-substances present in the cell. It is specially fixed in the nuclei and the pyrenoids. Now antipyrine, caffeine and other basie substances can obviously no longer cause any precipitate in the vacuole. It can be proved as follows that in dead Spirogyra part of the tannin passes out. Pieces of Spirogyra-filaments are placed between slide and cover-slip in a 1°/, solution of egg-white or in a '/, °/, gelatin or glue solution. These colloids do not penetrate into the cells and cannot therefore form any precipitate with the tannin of the cell-sap. When carefully beated above a micro-flame, the cells are successively killed. The tannin passes through the protoplasmic layer and cell-wall and forms a precipitate in the egg-white-, gelatin- or glue-solution. On careful heating the precipitate lies immediately against the Spirogyra-filament. The cells which are still alive are not surrounded by a precipitate. It can be established by using solutions of ferric salts, and other tannin reagents, that the precipi- tate formed outside the filament is a tannin precipitate. When Spirogyra has been slowly heated in water to 60° in a test-tube placed in a water-bath, it dies. In this case much tannin usually combines with the protein present in the protoplast and only a little leaves the cell. When a large quantity of Spirogyra was heated to 60° in very litthe water, the liquid sometimes gave after filtration only a very weak tannin reaction with ferric salts, whilst the nuclei and pyrenoids always gave a distinct reaction. The nuclei and pyrenoids also gave a distinct tannin reaction with iodine in potassium iodide solution. When sufficiently- washed out with water they show a fine red violet coloration. When starting with dead material, it is desired to produce with 1) 0. Loew and Ta. Bokorny, Ueber das Verhalten von I'flanzenzellen zu stark vordiinnter alkalischer Silberlésung. Bot. Centralbl. Bd. XXXVIIL p. 614. antipyrine, caffeine and other basic substances precipitates which agree with those occurring in living cells, the following method may be adopted. A number of Spirogyra-filaments are taken, washed out with distilled water, which is allowed to drip off as much as possible and then they are heated to 60°, dried as well as possible by means of gentle pressure between filter-paper, and extracted 2 or 3 times with a mixture of 4 parts of ether and | part of alcohol, such as is used in the extraction of tannin from gallnuts; the fluid obtained is filtered and evaporated in a vacuum. The residue, which resembles gallnut-tannin, is dissolved in a little distilled water and filtered. We thus obtain a solution, which gives all the possible tannin reactions, with ferric salts, potassium bichromate, egg-white and gelatin solutions, caffeine, antipyrine ete. The precipitates with antipyrine and caffeine solutions, with pyridine and quinoline-vapour, and other basic substances completely resemble those occurring in living cells: little spheres or globules which show Brownian movement and gradually aggregate to larger masses, which on the addition of water dissolve and behave towards reagents as fannin precipitates, all of which completely resembles what we observe in living cells. From the above experiments it is evident that what Lorw and Boxorny take to be reactions of active protein are in reality none other than reactions of tannin and the proteosomes none other than precipitates of different basic substances with tannin. It is further evident that after death these precipitates can be as distinctly produced as in living cells and can therefore hardly be called vital reactions. The question what substances the precipitates can contain in addition to tannin-compounds is more difficult to answer than it was to demonstrate the tannin character of the precipitates in living cells. That other substances may be present in the precipitates, is already clear from observations on cells containing red colouring matter as well as tannin in solution in the cell sap. The precipitates take up the red colouring-matter and large red-coloured spheres finally arise through the aggregation of many globules. The question whether the intravital precipitates can contain protein will now be dealt with. As already stated Pykrrrr ') assumes that the precipitate which is produced in Spirogyra by ammonium carbonate, consists of protein and tannin, which, according to him, both oceur in solution in the cell-sap. The acids present in the 1338 cell-sap are supposed to prevent the precipitation of the protein by the tannin, When these acids are neutralised a protein-tannin precipitate is produced according to PrErreEr. Prerrer thinks that the formation of the precipitate in Spirogyre must be explained otherwise than the precipitation of tannin by ammonium carbonate, because in Spirogyra filaments a precipitate occurs with ammonium-carbonate at greater dilution than in solutions of tannin. Af Kiercker*) bas erroneously considered this observation incorrect. I have indeed found it to be correct and | have also come to the conclusion that organic acids ean entirely or partly prevent the precipitation of protein and gelatin by tannin. On the other hand, in order to explain his observations PrErrER assumes various factors, without proving their existence, whilst he takes no account of other existing factors. In the first place Prerrer ought to have considered whether the tannin in Spirogyra is really identical with gallnut-tannin. It is quite possible that the tannin in Spirogyra is a different chemical body from gallnut-tannin and behaves rather differently towards ammonium-carbonate. Then Prrrrrr has failed to demonstrate the presence of organic acids in the cell-sap. Also he has not proved the presence of protein in the precipitate and moreover he has not investigated whether the formation of the precipitate may be influenced by other substances. As to the first point, | have found that gallnut-tannin and Spirogyra- tannin in general behave similarly towards reagents and solvents. Also a solution of ammonium-carbonate must be more concentrated in order to produce in a solution of Spirogyra-tannin a precipitate than is necessary to produce it in the living cells of Spirogyra. The first point may therefore be left. It is otherwise with the presence of acids in the cell-sap. When Spirogyra is washed out and then disintegrated, the mass has a faint acid reaction to litmus paper but a solution of gallnut-tannin and of Spirogyra-tannin are likewise acid. A suitable microchemical method for demonstrating free acids in the cell-sap, does not appear te exist. No value can be attached to Lonw and Boxorny’s*) method. They lay filaments of Spirogyra in a potassium iodide solution and seeing that no iodine is set free, they infer the absence of free acid in the cell-sap. The liberation of iodine by free acid cannot be explained chemically, for although dilute acids might set free hydriodie acid from potassium iodide, they cannot liberate iodine. “Le. p. 37 ff 2) O. Logw and Tu. Boxorny, Ueber das Vorkommen yon activem Albumin im Zellsaft und dessen Ausscheidung in Kérnchen durch Basen. 1. ¢. I attempted to demonstrate free acid in the living cells of Spirogyra as follows. I placed Spirogyra in a solution of potassium iodide (0.1°/,) and of potassium iodate (0.025°/,), but no separation of iodine by free acid was indicated (5KI-+--K10O,+6HCl +> 6KCI--61-+-3H,0). On heating Spirogyra for some time in a 0.1°/, solution of citric acid, before placing it in the solution of potassium iodide and iodate a very faint blue colour in the starch and faint violet coloration of the nuelei was to be seen; the latter had taken up tannin from the cell-sap, for in the meantime the cells had perished. This result points to light absorption of citrie acid and separation of iodine by this acid. The method seems to yield useful results and probably in the first experiment iodine would also have been liberated, in ease Spirogyra contained free acid. It should be noted that Spirogyra is very sensitive to dilute solutions of organic acids. In a O.1°/, solution of citric acid, tartaric acid, malice acid, quinie acid, it quickly dies. On these grounds it is very improbable that Spirogyra contains so much acid that protein and tannin should be able to appear together in soluble form in the cell-sap. The experiments which I am about to describe, also show that Prerrer has incorrectly interpreted his observations. Whilst with many reagents it is quite easy to demonstrate tannin in the cell-sap of Spirogyra because the cell-wall and protoplasm are permeable to these reagents, the most important tannin-reagents, namely, those which belong to the protein group cannot permeate. For this reason I heated Spirogyra in egg-white-, gelatin- or glue- solutions. On the death of the protoplasts the tannin passes through the protoplasmic layer and the cell-wall and a_ precipitate is formed outside the cell. If, instead of allowing the tannin to pass ont, a little protein solution could be introduced into the cell-sap which contains the tannin and if we could investigate the result, this would go a long way in my opinion towards solving the problem of whether in the cell-sap protein exists in solution as well as tannin. Should the cell-sap remain clear, one might be able to assume that the cell-sap, was of such composition as to contain dissolved tannin and protein side by side. If, on the other hand, a small amount of protein- solution produced a precipitate, then this might be taken to exclude the simultaneous presence of the two substances. I will proceed to explain how I succeeded in introducing a protein- solution into the cell-sap, causing a precipitate which on closer investigation was found to be a compound of tannin and protein. 1°40 As I) have previously described, the cytoplasm in Spirogyra possesses an alveolar structure. The hyaloplasm forms the walls of the alveoli, which are filled with a watery solution. By the action of reagents the structure is destroyed without the immediate onset of death. Often the hyaloplasm is seen to form a wall, which separates different portions of the contents. If abnormal plas- molysis is produced with, for example, 10°/, potassium-nitrate solu- tion then the hyaloplasm forms a wall round the contracted vacuole. As 1*) have previously stated, it may not be assumed that this wall is a special organ and accurately represents that part of the protoplast wlich in the cell constitutes the lining of the vacuole. If dilute chloral-hydrate or phenol solutions act on the living cells, other phenomena are again observed‘). Cytoplasm collects round the nucleus and, taking up water, forms a vesicle whose wall again consists of hyaloplasm and whose content except for the nucleus is chiefly an aqueous solution. Smaller vesicles are formed on the suspensory threads. If instead of the last mentioned solutions a 5°/, solution of ether (5 parts by weight of ether and 95 parts by weight of distilled water or ditch water) is used, then the death of the protoplasts is accompanied by the following phenomena. Cytoplasm flows towards the nucleus and collects there; the suspensory-threads are detached and are taken up by the protoplasmic mass, which has a granular appearance; round the nucleus a vesicle forms, which lies quite free in the cell sap. The wall of the vesicle is again composed of a hyaloplasmie layer; the nucleus is seen lying inside the vesicle and between the protoplasmic wall of the vesicle and the nucleus there is an aqueous solution, in which some granules can be distinguished. The protoplasmic wall is at first fluid ard stretched. When the protoplast dies, this changes; the protoplasmic-wall becomes rigid and often acquires folds and creases. The nuclear-wall also, which is stretched as long as the protoplast lives, contracts irregularly. By the walls different fluids are at first separated; this also is changed by death. When the nuclear wall contracts, we may assume that its content comes into contact with that of the vesicle, but this is not aecompanied by any noticeable phenomenon. It is otherwise when the content of the vesicle and the cell-sap 1) GC. van WhissetineH, Zur Physiologie der Spirogyrazelle. Beih. zum Botan. Centralblatt. Bd. XXIV (1908). Abt. I. S..190 ff. 2) |. c. p. 185 ff and 192 ff. ; 3) G. van WissetincH, Untersuchungen tiber Spirogyra. Botan. Zeitung. 1902. Heft VI. S. 121 ff. 1341 come into contaet. This takes place at one or more points on the circumference of the vesicle. At these points precipitates are produced, but it cannot be seen whether at first small openings or tears occur in the vesicle. It is often possible to distinguish two parts in the precipitates: the one is compact and seems to lie within the vesicle ; the other is looser and occurs outside the wall of the latter. When the precipitates are investigated with reagents, they are found to consist of protein and tannin. With sugar-solution and 85'/,°/, sulphuric acid they become very distinetly red, especially the mure compact portion; after treatment with iodine in’ potassium iodide solution and washing ont with water they show a reddish violet colour. With ferric acetate they become blue-black, with potassium bichromate brownish-red. From these results [ think the following conclusions may be deduced. The vesicle contains a solution of protein, which is derived from the cytoplasm and probably oceurs there in soluble condition in the alveolar fluid. When the protein-solution and the cell-sap containing tannin come into contaet with each other, the above mentioned precipitates are formed, from which it follows, in my opinion, that in addition to tannin protein in solution cannot be present in the cell-sap. They would at once form an_ insoluble compound with each other. It is thus impossible that, as Lonw and Bokorny assume, the precipitates, which are formed in the cell-sap by basic substances, are protein-precipitates or, as Prerrer assumes, precipitates of protein and tannin. In reality they are tannin precipitates. Although the possibility is not excluded that other substances are sometimes present in small quantity, experimental investigation yields the proof, that there can be absolutely no thought of protein-substances in the first place. Tannin and protein’ are’ separated in the living cells in a remarkable manner. Tannin in solution occurs in the cell-sap ; proteins can be demonstrated in the nucleus, the chromatophores and the cytoplasm. They are either solid, as for example, the pyrenoids of the chromatophores or dissolved, as in the cytoplasm. The nucleoli whiek contain a viscous substance, in which the two nucleolus-threads lie ') There still remains the question why a solution of ammonium- carbonate which causes a_ precipitate ‘in the cell-sap of Spirogyra, give specially clear protein-reactions. may be much more dilute than that which produces a precipitate in a solution of gallnut-tannin or of Spirogyra-tannin. 1) G. van WisseLincH, Ueber den Nucleolus von Spirogyra. Bot. Zeit. 1898, p- 202 — Ueber abnormale Kernteilung, 1. c. 1903, p. 217, * 1342 It is obvious that in the water in which Spirogyra grows and also in the cell-sap salts are present and I have on this account traced the influence of various salts on the precipitation of gallnut- and Spirogyra-tannin by ammonium carbonate. I found that precipitation is favoured by salts; expecially is this the case with calcium salts. The formation of a precipitate in the cell-sap at greater dilution of ammonium carbonate is therefore readily explicable. Intravital precipitates can in many case also be brought about by aniline dyes. Prerrer ') has described this in detail. In parti- cular he recommended imethylene-blue which gradually produces a precipitate in the living cells of Spirogyra with a very dilute solution. In Prerrer’s *) opinion the tannin is completely precipitated as a methylene-blue compound. The precipitate is also supposed to contain protein. When the solution of metbylene-blue is sufficiently dilute, the precipitation is regarded as innocuous to the vital processes. The explanation which Prrrrer gives of the phenomenon he has observed is incorrect, whilst he greatly overestimates the value of the results obtainable by his method. Prerrer *) writes: “In allen Fallen werden also Methylenblau und an- dere Farbstoffe wertvolle Reagentien sein, mit deren Hilfe, ohne Scha- digung, Aufschliisse iiber Vorkommen und Verteilung gewisser Koérper in der Zelle zu erhalten sind. Mit soleher vielseitig ausnutz- baren Methode lasst sich unter richtiger Erwagung nach vielen Richtungen hin eine Kontrole des jeweiligen Zustandes des Zellsaftes und der Veranderungen dieses im Laufe der Entwicklung erreichen.” Prerrer frequently writes of the harmlessness of his method to life. As a proof of this he cites for instance the growth of Spirogyra- filaments. In two cases this amounted in four days to 12 and 26°/,. 1 must here remark that Prerrer has made no compara- live experiments. If the rate of growth of Spirogyra cells in ditch water is studied, it is seen to be much greater. After two days the increase in length in 14 cases was found to be 25 te 75°/, and after four days in 18 other cases 40 to 75°/,. From Prerrgr’s results it is therefore clear that dilute solutions of methylene-blue also are harmful. My own experiments on Spirogyra maxima with methylene-blue (methylene-blue pro usu interno, the hydrochloride), indicated that it was very harmful. In a solution of 1 part in 10000 parts of . 183 and 218. ditch-water all the cells perished in one day. In sotution of 1 part in 500.000 parts of ditchwater or Knopp’s fluid many dead cells were seen after one day and in a solution prepared with distilled water of the same strength the number of dead cells was still greater. No growth was observed. The poisonous action of methy- lene-blue is the reason why there can be no question of ‘‘Kontrole des jeweiligen Zustandes des Zellsaftes und der Veranderungen dieses im Laufe der Entwicklung’, as Prnrrer imagines. It has been already demoustrated above that the cell-sap of Spiro- gyra contains no dissolved protein. The precipitate with methylene- blue cannot therefore as Prurrer believes, contain protein. In his opinion the precipitate is actually a compound of tannin with me- thylene-blue, which cannot be brought into agreement with the fact that solutions of methylene-blue, even stronger than those used by Preerer remain clear with solutions of gallnut- and Spirogyra-tannin. This is not explained by Prererer. It is noteworthy that when Spirogyra is placed in a dilute methy- lene-blue solution (1 in 500.000) there is no gradual formation of a precipitate which is coloured blue from the beginning, but there is first a colourless or almost colourless precipitate and that this is then gradually coloured a deeper and deeper blue. Of this Prerrer makes no mention. On examination of the precipitate with reagents tannin reactions eould be obtained, for example, the black coloration with ferric acetate. It may therefore be assumed that tannin is precipitated. The quantity of the precipitate even in Spirogyras with much tannin was however, small compared with other tannin precipitates. Henee I doubted whether the tannin is completely precipitated. After one day I could not, indeed, demonstrate any tannin in the ‘cell-sap in addition to the precipitate, but it seems that the cells may lose tannin by exosmosis. For when, for example, pieces of Spiro- gyra-filaments were placed in a dilute solution of methylene-blue, containing ‘/,°/, gelatin, a precipitate was formed outside the cells and between the layers of the cell-wall which separated from each other. The precipitate was a compound of gelatin with tannin and became coloured black with ferric acetate. | cannot therefore venture to assume with Prrrrer, that a complete precipitation of tannin takes place in the cell-sap. It seems to me that various factors play their part in the pro- duction of the precipitate. In the first place the harmful action of the methylene-blue, of causing great modifications in the organism. Further the presence of salts appear to assist the formation of pre- 1544 cipitate. In a solution of one part of methylene-blue in 500,000 parts of distilled water the phenomenon was not so clear as in a solution of the same strength made with ditch-water or Knopp’s fluid. A number of experiments in test tubes with methylene-blue, salts, gall- nut- and Spirogyra-tannin led to the conclusion that the appearance of a precipitate is not only affected by the presence of salts but that also atmospheric oxygen comes into play and finally, that me- ihylene-blue itself has no precipitating action, but that in one way or another a tannin precipitate is formed which gradually takes up more and more of the dye. How the precipitate is produced I cannot definitely say, but its formation does certainly not depend on a simple precipitation of tannin by methylene-blue, as Prerrer assumes. Chemistry. — “Vhe influence of surface-active substances on the stability of suspensoids”. By Dr. H.R. Kruyr. (Communicated by Prof. P. van RomsureH.) In the chemical literature of the colloids it is generally stated that electrolytes exert a great, and non-electrolytes no action on the stability of suspensoids, at least when those non-electrolytes are not colloids themselves. BopLANpER') found that the formation of sediment in a suspension of colloids was much accelerated by electrolytes, “dagegen sind die Nichtleiter wirkungslos’. And Freunpiicn’) states of a series of organic substances that they “in grossen Ueberschuss selbst bei tagelanger Einwirkung, keinen Einfluss auf die Bestandig- keit des Arsensulphidsols ausiibten.”” This, however, merely shows that these substances themselves do not cause a coagulation in a | direct manner. If, however, we take the standpoint of the ingenious theory developed by Freunpiicu*), the complete absence of any influence on the stability is absurd. For when the stability is determined by the eleetrie charge of the particle (Harpy‘), Burton*)) and when _ this charge is formed by the selective ion-adsorption (FREUNDLICH Le.) — a cause which exerts an influence on the adsorption cannot be inert towards the stability. 1) Nachr. Géttingen 1893, 267. ®) Diss. Leipzig, 1903, p. 13, Zeitschr. f. physik. Chem. 44, 129 (1903). 3) Consult his Kapiliarchemie, Leipzig 1909. 4) Zeitschr. f. physik. Chem. 38, 385 (1900). 5) Phil. Mag. [6] 12, 472 (1906). Now an adsorbed substance is displaced by another adsorbed substance; this is dependent on the degree to which that second substance is itself adsorbed‘); if to a suspensoid system is added a substance which itself becomes strongly adsorbed it would be asto- nishing indeed if it left the stability of the system unmodified. As a rule, we possess a measure for the stability of a system in the limitation value.*) Meanwhile it is as well to consider in how far we must attach value to this relation. A complete coagula- tion in a short time oceurs when of an added electrolyte so much gets dissolved that the colloid has become isoelectric. But this adsorption will also be modified by an added substance. If, for instance, we have a As,S, sol this consists of particles of arsenious sulphide dispersed in water; these particles at their preparation have adsorbed hydrogen sulphide in such a manner that an electric double layer has formed in such a way that the layer of S'-ions lies at the side of the solid particle and the H-ion layer at that of the liquid. If now we add a substance A which is adsorbed _posi- tively, the condition of that double layer will be modified because A displaces H,5, S" as well as H-. When effectuating coagulation by means of an _ electrolyte such as BaCl,, adsorption also takes place-of BaCl,, Bas and Cl’ and the limitation value will be attained when the quanuties of Bay and S: are equivalent.*) But this adsorp- tion process also experiences a similar influence from the substance A. The change in the limitation value under the influence of A is therefore the resultant of those two actions. Perhaps these might just neutralise each other? This seems to have always been an assumption not mentioned. Although we know as yet but little about the displacement in the capillary layer, such a symmetry did not seem to me probable and therefore the subjoined investigation was carried out, provisionally for the purpose of orientation. The substance to be admixed should give rise to a strongly posilive adsorption and hence, according to Gipss’s principle it must strongly reduce the surface tension. In this relation account must, of course, be taken of the surface tension solid-liquid; the measurement thereof is, as yet, almost impracticable, but experience has taught us up to the present (and theoretically this may be expected) that the surface tension must as a rule proceed similarly to that for liquid gas. Hence, as strongly adsorbable components were chosen those which strongly lessen the surface tension of water. 1) Cf. FREUNDLICH and Mastus, Gedenkboek vAN BeEMMELEN (Helder 1910), 88. 2) A version of the German word “Sehwellenwert’’. 5) Gf. Wuirney and Osrr, Zeitschr, f. physik. Ghem, 89, 630 (1902). 1346 The subjoined investigations were, therefore, carried out to demonstrate in the first instance the existence of the influence of surface-active substances on the limitation value. Hence, they were carried out by means of an arbitrary colloid As, 5, sol with an arbitrary electrolyte BaCl, with addition of substances, which in diverse degrees lower the surface tension of water, namely first of all, isoamyl alcohol, isobutyl alcohol, propyl and ethyl alcohol the o-c lines of which (6 surface tension, ¢ molecular concentration) had been determined by Travse ‘). TABLE I. Jsoamyl alcohol. SR CS ES) CR a ec Goresiaten | a) OR a ea ieantatipn the alcohol, ater alc. mixture | Value relat. 0 1.08 _ 1.00 66 1.08 1.16 | 1.07 78 1.07 1-32 23 92 1.07 1.38 1.29 TABLE Il. J/sobutyl alcohol. 0 0.87 _ 1.00 101 0.87 | 0.96 1.10 201 0.87 1.02 Wi Us/ 302 0.87 eS | 1.30 TABLE Ill. Propyl alcohol. 0 0.92 Load He 197 0.92 | ee) eet gi bals 393 0.92 | 1.14 1.24 , gave sl), G:G2 | 1.30 | 1.41 TABLE IV. Ethyl alcohol. OG, |), orer, elt Satecs 1560 0.87 | 0.97 | 1.12 1) Lieb Ann. d. Chem. 265, 27 (1891). 1347 To 10 ce. of the sol were added with constant shaking 5 ee. ofa solution of the organic substance (or water for the blank experiments which were repeated each time) and about 15 minutes later 1 ce. of a BaCl, solution. The whole was then again shaken and then once more two hours afterwards; the BaC!, concentration, which was just incapable to cause a complete coagulation, represented the limitation value. Those valyes may be taken as being accurate within two units in the second decimal. In the tables are given the concentrations relating to the final total volume in millimols. per Litre. In the last column the limitation values have been recalculated so as to make the value for pure water = 1.00. From these tables it is indeed evident that the aleohol concen- tration has an influence on the limitation value; this influeace appeared to vary for the different aleohols and therefore it was thought desirable to make a comparison of their influence on the capillarity of water, with their adsorbing properties, and consequently with their power of displacement. This comparison may be readily effected with the aid of the subjoined figure constructed from data obtained by Travse lc. (The line for phenol will be discussed presently). 6j,9 is taken therein as 76.0. 80 Cae: 70} 2 acthylale. 7 este Babes 40 phenol 30 EEG UL Blab late. Cin m.MN ol b. fi. 100 = 200 300 400 500 600 700 800 900 1000 Fig. 1. From the tables I—IV we now notice that the order of the admixed substances in which they effectnate an inerease of the limitation value is: tsoamyl, isobutyl, propyl, and amyl alcohol, 4348 while, according to the figure the order for the power of lowering the surface tension is the same. This result is, therefore, undoubtedly in barmony with the adsorp- tion theory. The only question still to be answered is why the added substances increase the limitation value. This however, was to be expected on account of the manner in which displacement takes place as shown from the research of FreonpLich and Masivs (l.c.). What they found is as follows: Let substance A be adsorbed according to the equation : ae m or expressed in logarithms = aj log — = log a 4+- —loge m nr (z the quantity adsorbed, m the amount of adsorbent, ¢ the concen- tration of the liquid in equilibrium, «@ and 7 constants). If now a substance B is added in definite concentration, the adsorp- tion of A takes place according to the equation : a 1 log — = log a' + — loge m n ' ; che ae 1 The investigation always showed that —- is smaller than —. As : n n v the dependency of log — on /og c is represented by a straight line, m we readily perceive that the reduced coefficient causes a stronger displacement of A’ by B in the higher concentrations of A than in the lower ones. If now in the experiments described above the alcohol is added to the sol the concentration of the liquid in’ stability-promoting ions will be exceedingly small in comparison with the concentration of- BaCl, when the limitation vaiue is attained. If now we assume that the adsorption of each of these substances by ifself is about the same, it will be readily perceived that the displacing influence will hinder . the charge of the particle in a much lesser degree than the discharge. Hence an cncrease in the limitation value. Meanwhile it will be as well to dispense with further theories until the matter cited above las been extended by the investigation of more colloids and other organic substances as well as of other (particularly uni- and trivalent) coagulating ions. With this investiga- tion | have already made a start. The following fact has already been disclosed : aromatic substances 1349 are always adsorbed much more strongly than might be surmised from their influence on the surface tension '). [| determined stalagmo- metrically the o-c figure for phenol (also given in the figure): although it appeared to lie between that of isobutyl and propy! auecohol, the influence exerted by addition of phenol is greater than that caused by isobutyl alcohol, exactly as was to be expected. This investigation is being continued, also in connection with a direct investigation as to the adsorption of the substances added. A more extended investigation in various directions appears to me desirable all the more because the results may elucidate several other problems in the chemistry of the colloids. I will again refer to this matter in due course. Meanwhile the results obtained are interesting when taken in connection with the researches of H. Lacus and L. Micuaénts*), who found that surface-active non-electrolytes exert no influence on the adsorption of electrolytes: the above described investigation, however, makes us surmise that although these two kinds of substances should not be put on a par with each other without further evidence, a displacement takes place nevertieless. The effect of the displacement, however, seems to elude the direct measurement, but it may be demonstrated by measurements of the limitation values. Hence, the said investigators could find a displacement effect for isoamylalcohol only, just the very aleohol which according to our research exerts the strongest power of displacement. Utrecht, March 1913. van ‘Tt Horr- Laboratory. Microbiology. — “Potassiuin sulfur, and magnesium in the meta- bolism of Aspergillus niger.’ By Dr. H. J. Waterman. (Com- municated by Prof. M. W. Betsertnck). In earlier investigations I have shown that the elements éarbon, nitrogen, and tosfor occur in large quantities in young mould material, but that, when it grows older, a considerable portion is again excreted as carbonic acid, ammonia, and fosforic acid *). During the develop- ment the plastic aequivalent of the carbon lowers to the half; as to the nitrogen, there is a threefold accumulation, whereas the quan- tity of fosfor in a young mould layer is ten times as large as that a) ‘Compare for instance I. TRAUBE, Verh. d. deutschen physik. Ges 10, 880 (1908). In the Table on p. 901, Aniline the only aromatic compound, occupies a quite special position. *) Zeit-chr. f. Elektrochemie 17, 1 (1911) 5) Folia microbiologica Bd. 1 p. 422, 1912. These Proceedings 1912. 88 Proceedings Royal Acad. Amsterdam, Vol. XV, TABLE & POPASSIae. 1, Nutrient liquid: Distilled water, 24 glucose, 0,2%) ammoniumnitrate, 0,19) magnesiumsulfate (7 Aq.), 0,1% ammonium pees, 0,029 9 calciumnitrate (free from water), 0,04°/) manganesechloride (MnCl,.4Aq.). f= 34° a Addition of KCl Growth and spore formation after Nr. |— | gram- ik =e) al : a milligr.! mol. |1 2 3 5 | 10 | 30 days pL: | | | | | a ‘GG 29 1 0 DN a fe = few spores few spores few spores {hardly any spores 1 re ++, beginning +++, +44 oe 37500 |t| +4 | sp. formation rather many sp. rather manysp.| few spores a el enee | ee = +4+++4, beg +++, | | 3 (0,6 : trl alee f ; 37500 £2 sp. formation many spores | many spores [rather many Sp, ° = u h UD Bhs mice pees) see eee a EL e 3750 iy ALF sp. formation many spores he | many spores | a 5| 20 Se Same | SSqeee | 4 eS 3750 few spores rather manysp. > i | | many spores b. Nutrient liquid: Distilled water, 29 glucose, 0,159 ammoniumnitrate, 0,19 magnesiumsulfate (7 Aq.), 0,05%9 fosforic acid (crystallised), 0,01%) MnCl,.4Aq. f=34° C. — ; | Addition of KCI Growth and spore formation after Nr. | ee | gram- | | | : | milligr. | mol. iy 2 3 4 8 days pils | ————— ee 1 0 0 ae 7 == tml | , ++, | no spores no spores few spores hardly any spores 1 | | 2 0,001 3750000 | » » | ” ” | ” » » ” ” | | | | 1 | 3 0,01 | 375000 ” ” | ” » ” ” SS no spores 01 1 ++, beginning | +++, beg. Ss) +-+-+-+, beginning 4 3 37500 spore formation sp.formation rather many spores} spore formation 514 pate +4 very | | ett bee | ee | 3750 | few spores fewspores | spore formation |rather many spores Pe tree me | REE very | Au 2 3750 =a}, dew sporess =) n y few spores many spores 5 7 4) 3750 ” ” ” ” ” ” » ” 12 8 12 3750 ” ” ” ” ” ” ” ” 15,5 9 15,5 | 3750 ” ” | ” ” ” ” ” ”» | 35,5 10 35,5 3750 ” ” » ” ” ” ” » | 85,5 | 11 85,5 | 3750 J | ” ” ” ” | ” » » ” contained in a similar old one. Various influences on the metabolism, such as temperature, concentration, hydrogenions, boric acid, man- ganese, rubidium, ete., were studied, in which only changes of velocity were observed. I have now continued these experiments, more qualitatively, with potassium sulfur, and magnesium and obtained the following results. a. Potassium. 1 used a nutrient liquid of the composition given in ’ Table [. The constituents of the soiution in the series of experiments b were the same as those of @, only no caleium had been added, because, as I have shown before, the non-addine of this element under the mentioned circumstances, has no influence on the velocity or the nature of the metabolism. This was also the case with chlorine. The cultivation was always effected in ErLenmeyer flasks of Jena glass and of 200 em’. capacity, the volume of the medium being 50 em*. The distilled water was once more purified in an apparatus of Jena glass. These experiments prove that the quantity of produced mould, even in the Nrs. @1 and / 1, where no potassium was added, is not inconsiderable. This may be ascribed to the difficulties aecom- panying the exclusion of traces of this element. Further we see that by excess of potassium the spore formation is temporarily inhibited. Compare Nr. 5 with Nr. 4, after 4 and 5 days (Table a), and Nr. 6 and following Nrs. with 5, after 4 days (Table 6). This inhibition of spore formation by an excess of a necessary element finds its cause in the cells being able to accumulate reserve food. *). Finally Table I shows that deficiency of potassium does provoke production of mycelium but no spore formation (Nrs. 1—38, Table I 4), Only at = er. mol. KCl. p. L. spore forming begins after 8 days. Formerly *) I have shown that potassium can but partly be replaced by rubidium. Whereas the production of mycelium is possible as well with potassium as with rubidium, spore formation takes only place with a certain percentage of potassium and not at all with rubidium, It was likewise proved that manganese is necessary for the latter process. The results given in Table I prove that at very low con- centrations the action of potassium is quite analogous to that of rubidium: mycelium is formed, but hardly any spores, and this in spite of the presence of large quantities of manganese. In the physiological action of potassium thus, two functions are to be distinguished, one corresponding with that of rubidium, the other with that of manganese. . i) These Proceedings, 1912. *) These Proceedings, 1912. (@ 6) CO # 1352 }. Sulfur. The results of the experiments on the action of different sulfate concentrations are found in Table II. Here we see that in the culture tubes (N° 1), where no sulfur was added, development takes place, just as had before been observed for the nitro- gen, the fosfor, and the potassium. A considerable spore formation took place after 2 days already in Nrs. 1—7, which had a deficiency of sulfur, whilst in the experiments with more sulfur the production of spores was at first slackened. Nrs. 8—20 had only few spores. After 3 days Nrs. 14—20 had hardly any, whilst in all other culture tubes an important spore formation had already occurred. After 4 days these differences were less marked; after 40 days all the mould layers were covered with a considerable number of spores. The explanation of this temporary inhibition of the spore production is ihe same as for the elements treated before. In other respects, too, the sulfur quite corresponds with the other elements. Like the carbon, nitrogen, and fosfor, the sulfur accumulates in the cells and is after- wards partly excreted. Indirectly this could already be shown by the following consider ations. We see that in Nr. 8, after 3 days only 34,5 °/,, after 3 days in Nr. 9, 36°/,, after 40 days already 48°/, of the glucose has been assimilated, notwithstanding after 3 days no sulfate was left in the solution. Evidently during the development of the organism by the dissimilation of an intermediary product, sulfate is set free in the liquid so that the assimilation of the glucose can go on. This is still more obvious in Nrs. 11—13. After 3 days the assimilation of ‘the glucose was 49°/,, after 4 days it mounted to 61°/,, and after 40 days already 82°/, of the glucose had been used, whereas, here too, after 8 days already, all the sulfate had disappeared from the solution. By direct analysis was shown that an old, mature mould layer indeed contains less sulfur than a young one obtained in quite the same way and under the same conditions. To this end the mould was, after frequent washing with distilled water, destroyed by fuming nitrie acid, in a closed tube at 300° C, The sulfate was precipitated in the usual way. It was here proved that of 4 mature mould layers (70 and 40 days old), treated in this way, after 3 to 4 hours’ heating on alow flame, no precipitate was formed, whereas 4 young moulds (3 and 4 days old) '), likewise treated, did give a precipitate after heating. In what condition the sulfur, temporarily withdrawn from the liquid, exists in the organism, must for the moment be left undisecussed. z) These were-the mould Jayers of Nrs. 14, 18, 15, 16 (Table IL). TAB Evy. 1358 Activation of magnesium by sinc, Nutrient liquid: 50 cm of distilled water in a Jena glass apparatus, in which dissolved 2%) glucose, 0,15 % ammoniumnitrate, 0,1) potassiumsulfate, 0,05 9, potassiumchloride, 0,05) fosforic acid (crystallised), 0,01 %) manganese sulfate. nn EEEEEEeeeeEeeeEeEEss—sC“*?D Development after NO, | Added ——__—___—— - 1 3 4 12 days 1 = | = = ? 2 - —_ a = | 3 = = | — — 4 | 0001 mgr. ZnSO,.7 Aq Germination + +--+ 4 5 0,01 ” ” ” 1 + a -6/ 0,001 , MgSO,7Aq — = = 7| 0,001 , MgSO,.7Aq-+ 0,001 mgr. — -- Germination ZnSO, 7 Aq 8 | 0,001 , MgSO,.7Aq-+0,001 mgr. — aa = Cadmiumsulltate 9 | 0,001 , MgSO,.7Aq+0,01 mgr. | |__ as 2 strontiumnitrate | ‘10 | 0,001 ,, MgSO,.7Aq--0,001 mgr. _ = 11 | 0,005 , MgSO,.7Aq = _ = 12 | 0,005 , MgSO,.7Aq-+0,001 mgr. = -+ (slight) + ZnSO,.7Aq : 13 | 0,005 , MgSO,.7Aq-+0,01 mgr. _ 2 Germination | : ZnSO,.7Aq | 14 0,01 +, MgSO,.7Aq 2 | + (slight) | of 15| 0,05 , : t Germination as +4, no spores 16) 0,1 ” ” ” a 44+, no +++, no | spores spores 17 | 0,3 » ” ” | Saale desta! Sess, beg. aes beg. | sp. formation | sp. formation | sp. formation 18 | 0,5 ” ” ” | -s Simateata beg. | ie beg. stalaciestaste sp. formation | sp. formation rather many sp. 19 | 1 » » ” Pt SSSaae no SSS SSa <5 ++-++ T , spores | beg. sp. form. many spores 20 | 5 ” ” ” ae +t tt++,| At =f = =55 se5= i few spores rathermanysp. many spores 1354 It may finally be called to mind that with deficiency of a necessary element the metabolism of Aspergillus niger remains unchanged. This follows from the amounts found for the plastic aequivalent of the carbon. The table shows, namely, that only trifling differences are found for all the simultaneous determinations. We see, moreover, that those mould layers, which are more developed, possess a corre- spondingly lower plastic aequivalent. c. Magnesium. Whilst in the study of the other required elements it was found that even the slightest quantities cause a perceptible growth, magnesium behaves quite otherwise. Relatively great quantities ( ie - or, mol. Mg SO, 7 Aq. per 1. did not, even after a pro- 2170000 longed cultivation, produce any macroscopically perceptible mycelium, 2 : whereas stronger concentrations ae gr.mol. Mg SO,7 Aq. p. L.), only after some days caused a considerable growth. This result warns us to be cautious in the computation of a production in a way as suggested by Mirscueriicn *) even in a rela- tively simple case such as the present. The results of the referring experiments are fonnd in Table IIL. The explanation of the above fact has not yet been found. It might be supposed that the metabolism of the magnesium is extremely slow; whereas for each individual cell mach magnesium should be wanted. More acceptable, however, is the supposition that by absence or deficiency of magnesium some unknown factor in the medium is allowed to exert ifs noxious influence which may be counteracted by addition of more magnesium. Beryllium, lithium, manganese, and calcium cannot replace magnesium. (See Table Il). Zine can replace it, as is shown by the experiments, whose results are exposed in Table IV. For cadmium, strontium, and mercury I have not as yet been able to find an action analogous to that of zinc. Nrs. 12 and 13 are in particular convincing as they show that even the slightest quantities of zine are sufficient to activate magnesium (0,02 mer. Ms Me P Aqep., Lx): The abundant growth in Nrs. 4 and 5 is also remarkable as not any magnesium was added there. This does not, however, prove thai the magnesium is here replaced by zine, as it is always possible that slight quantities of magnesium are present in the solution, so that in this case, too, the influence of the zine may be only an ®) MivscHervicn, Bodenkunde fiir Land- und Forstwirte, 2te Aufl. Berlin 1913. [355 activating one. This effect is the mere important as hitherto I have not succeeded in the usual way to demonstrate a favourable influence of zine. Laboratories for Microbiology and Organical Chemistry of the Technical University Delft, March 1913, Physics. — “On the law of partition of energy’. Ul. By J. D. van per Waats Jr. (Communicated by Prof. J. D. van per WaAats). § 6. It is obvious that the chance that the value of one of the variables p or q¢ lies between specified limits cannot be represented by a normal frequency curve. If however we investigate a region of the spectrum, which is very narrow, but yet contains many elementary vibrations, then we find another probability curve than for one single elementary vibration. If the region is sufliciently small, then the radiation will appear to us to be homogeneous. Only an observation during a long time (i.e. very long compared with one period) will reveal the want of homogeneity by the increase and decrease of the amplitude in consequence of beats. In order to describe the momentaneous condition we can represent one elementary vibration by : 2at 2at a sin —— +- b cos - iE ily and the total vibration of the spectral region by : _ ant 7 2a (Xa) sin 7 + (Xb) cos - T In this expression the separate a@’s and é’s may have all kinds of values. The chance that they lie between specified limits is not represented by a normal frequency curve. But. this does not detract from the fact that the chance for a specified value of (Ya) = A, is represented by a normal curve, at least if the sum contains a sufficiently great number of terms. Let us imagine that the decrease of the amplitude of the vibrators in consequence of the radiation has such a value, that they are perceptibly set vibrating by a great number of elementary vibrations whose period does not differ too much from the fundamental period of the vibrators, then Maxwen1’s law will hold for the chance that the velocity of a vibrating particle lies between specified limits. The mean energy of a linear vibrator is probably rightly represented by the formula of PLANCK: = ey, gh oe eee so the chance that the velocity of a vibrating particle has the value s will be represented by : , ms 1 Yr C 3 E Is her Ty eam yee 1 U 1 hy € ds where */,ms* = a m= Bae ~ 20 = l It is true that the formula (11) has been calculated with the aid of an equation of the form. (1) p. 1177 and that such an equation cannot hold good. But here a difference between the theory of PLANcK and the conception indicated in this communication comes. to light. For if the quanta-hypothesis is right, the equation (1) cannot even approximately be fulfilled, and it is to be considered as the merest chance if it leads to the exact value for U. According to the here developed conception however, the equation (1) cannot be rigorously satisfied, but it can hold with a rather high degree of approximation, and the sharpness of the lines of the spectra seems to indicate that this is really the case. For this reason it seems to me that we have reason_to expect, that we can find the average kinetic evergy of rotating particles, or of particles describing paths disturbed by collisions, with the aid of the ordinary fundamental equations of classical mechanies and electromagnetics. For this purpose we have to investigate the motions which those particles would perform according to those equations in an electromagnetic field whose partition of energy is that of the normal spectrum. According to the quanta-hypothesis it would seem doubtful whether such a calculation would yield the right value for the velocity of the particles. These conclusions would not be justified, if it should appear that the equations of motion of the electrons cannot be approximately represented by equation (1). In this case we should have no reason to expect that the velocities of the vibrating particles are distributed according to Maxwetn’s law for the partition of the velocities. It seems probable to me that the normal probability-eurve will rather apply to the momenta than to the velocities. If the mass is constant we have no reason to make this difference, but in the ease that 1357 the mass of the particles is variable, the fact that the normal pro- bability curve did hold good for the momenta would involve that it could not apply to the velocities. For Lorentz-electrons the deviations from Maxwe.u’s law for the distribution of the velocities, occasioned by the variability of the mass, would remain small for temperatures which are practically reached. The average kinetic energy of electrons of that nature in the normal radiation field can probably be calculated as if the mass were constant. When we differentiate the value of the kinetic energy which we tind in this manner, according to the temperature we find ¢, as is well known, if only we add to it another term which accounts for the potential energy. § 7. The potential energy. The distribution in space. For the distribution in space of particles of mass we have according to classical mechanics the following law: if 2 represents the number of particles per unit volume and ¢ the potential energy of one particle, the expression ne’ =a constant throughout the space. . (12) For a mixture an expression of the same kind holds good for each of the components. If we wish to take into account the volume of the particles we may write that Fag) = constant Se ae 8 ee = De) where J) represents the volume of the molecular weight in grams of the substance, and V—2h the “available space” present in this volume. The logarithm of this expression is, as is well known, equal to the thermodynamical potential ‘) of the component, to which the expression has relation. All thermodynamical equilibria, as well those for simple substances as those for mixtures, and also those in which electrically charged particles play a part, can be derived from the equation (12a), which was for the first time used by BottzmMany. We will now consider the question how the space-distribution must be according to modified mechanics. Will this law of Bourzmann hold also according to them? This question must be answered negatively. Let us imagine two coexisting phases e.g. liquid and vapour. Even if we assume that in each of the two phases Maxwett’s law for the distribution of the velocities is satisfied, the mean kinetic energy of the molecules in the two phases will be different. Of 1) Or at least it differs from it only in a function of the temperature which is immaterial for the existence of thermodynamical equilibrium. 1358 course this difference will be exceedingly small at ordinary tempe- ratures and will only get a noticeable value at extremely low tempe- ratures, at which the molecules in the liguid phase which can be regarded as vibrators of a shorter period than those of the vapour, have less kinetic energy than they should have according to the equipartition-law. This will of course have influence on the density of the vapour phase, which will be found to be smaller than we should expect according to classical statistical mechanics. Corresponding considerations apply to the contact difference of potential at very low temperatures. , Besides the distribution of particles in space there are other problems which may be treated with the aid of considerations of the same kind, e.g. the orientation. of the axes of polar particles under the influence of directing forces. The probability that the axis of such a particle, with moment m, in a field of forces, whose intensity is §, forms an angle « with the direction of this force, is according to classical statistical mechanics equal to mS) cos 6 sin @ 2 “= de, .. 2) 3a ae é According to our considerations the probability that it has a con- siderable amount will at low temperatures be smaller than is indicated by this formula. Accordingly we find e.g. the Curik-point at a higher temperature than would be deduced from this formula, at least for those substances, for which this point lies so low, that at the Curix-temperature the mean kinetic energy of the rotations of the molecules is smatler than it should be according to the equi- partition law. § 8. It is obvious that the above considerations have an exceedingly provisional character. Many problems are referred to, but not for a single one have we found a sufliciently conclusive solution. I hope to be able to treat some problems more in detail on a later occasion. In the meantime I think that [ have shown that the drawing- up of a new system of mechanics as aimed at in my former com- munication upon this subject is of the highest importance for all thermodynamic questions. I have done this with a view to draw the attention of the mathematicians to the problem and more in particular to the integral equation (5a) or a corresponding equation *), 1) I say a corresponding equation because, as I have already remarked on p- 1180 | was not perfectly sure that | was right in leaving the “proper coordi- nates” of the electron in this equation out of consideration. It is possible that the 1359 the solution of which would bring us an important step nearer to the drawing up of the new system of mechanics. Some phenomena are at present often considered in connection with the quanta-hypothesis of which it is not clear from the above how they are connected with the new system of mechanies, from which we expect the solution of the question concerning the partition of energy. Specially this is the case with the question of the emission of electrons under the influence of light- or R6NTGEN rays. In the thermodynamical applications it appears to me that we may expect from the quanta-hypothesis, that it will yield results which are sometimes quantitatively and always qualitatively accurate. For it has the tendency to lower the kinetic energy of vibrators of short period in agreement with the observations to an amount smaller than would agree with the equipartition law. And it is only this mean energy which is observed in thermodynamics, or the distribution in space which is closely connected with it. Whether on the other hand the application of the quanta-hypo- thesis on the emission of electrons is justified seems doubtful to me. From a theoretical point of view it appears to me that no reason for the accuracy of the considerations can be found. And whether the agreement with experiment is sufficient to warrant the validity of the considerations seems to me to be still doubtful. If in particular we take the theory of Sommerre.p for these pheno- mena with the aid of the quanta of “action”, then it appears to me that this theory (though perhaps accurate in itself) ean be in no way connected with any possible theory for the normal spectrum. Let us imagine e.g. two equal guns with equal projectiles but with unequal charges of gunpowder. The projectile with the greatest gun- powder charge will obtain the greater kinetic energy and that in the smaller time. And so we can assume that the molecular action is of such a nature that always the greater change of energy requires the shorter time in the way as is assumed by SomMerFELD. This is a question of the law of action of molecular forces; it has nothing to do with the laws of mechanics, and in particular it is not con- tradictory to the laws of classical mechanics. I at last cannot discover any contradiction. But if indeed the theory of SommerrELD can be reconciled with classical mechanics then it can also be reconciled with the spectral formula of RayLeiGn and leads by no means to the spectral formula of PLancx. function ¢ must depend besides on the p’s and the q’s also on the “proper coordinates’ and that we, in connection with this, must add the differentials of the proper coordinates to the prdduct of the differentials dp, ...dq,. 1860 Physiology. — ‘The electrocardiogram of the foetal heart.” By Prot. J. K. A. WERTHEIM SALOMONSON. In 1906 Cremer published an electrocardiogram of a buman embryo in utero, taken in a healthy woman during the last period of pregnancy. The curve showed oscillations caused by the heart of the mother, between which less conspicuous deviations could be seen, caused by the foetal heart-action. These latter had the form of monophasic deviations, but probably they should not be considered as a true representation of the actual electrical potential differences. Cremegr’s investigations were repeated by Foa, who was not able to extend our knowledge in this respect and could only confirm Cremer’s statement. | have tried to get some further insight in the peculiarities of the foetal electrocardiogram by investigating it in the embryo of the chieken. This very obvious way was clearly indicated, as Zwaarpk- MAKER had shown that an electrocardiogram could be taken from partly-hatched eggs. He published a foetal electrocardiogram in his Treatise of Physiology. Though my researches on this subject were commenced about a year ago and are not yet completed owing to a lengthy interval during the autumn and winterseasons, I may be permitted to show some of the results of my experiments. Long before the conclusion of the first 60 hours of the incubating period, we can see in the chicken’s embryo a strongly pulsating tubular heart, slightly curved to an s-form. In this early condition I have not been able to register any electrical potential difference *). The reason is that probably at that time the potential differences caused by the heart beats are exceedingly small. The electrical resis- tance of the substance in which the foetal heart is embedded and which contains albuminous and fatty matter is rather high. This combination of a low potential difference acting on a high resistance makes it very difficult even with an instrument so delicate as the string-galvanometer to detect the potential difference. The string-” electrometer gave me no better results. In the end of the first week we can generally without any par- ticular difficulty lead off electrical oscillations from the foetal heart. These are very regular, isochronic with the heart beats, and show a simple monophasic deviation. Generally the ascending part has a slighter slope than the descending part. The descending part .is fol- lowed immediately, without an isoelectric interval, by the next 1) I have since succeeded in doing so. 1361 deviation, so as to give a regularly rising and falling line. No eNO Eig) lis difference between the different beats could be cbserved. The maximal P.D amounts to about 20-—30 microvolts. On the 8" day we get a curve which is perfectly differentiated. Instead of a series of continuous simple, nearly sinusoidal deviations we get deviations which may be grouped in series of 3 each, each group belonging to one heart beat. In each group the first and second deviation have the same polarity and are followed by a third peak of opposite polarity. The first peak seems to be somewhat higher than the others. I suppose that we may consider these three deviations as identical with the summits P, R, and T in the normal human electrocardiogram. The largest potential difference, that of the ——————$— SS -wnnnm_-—~- Fig. 2. P-deviation, amounts to some 50 or 60 microvolt. The duration of P is of the order of 0.07 second. The R-peak has a shorter duration. In a few records I believe I have also found slight indications of a Q and an S-peak. The electrical activity represented by the T-peak extends over 0.15—0.18 second. T am not yet prepared to speak about the extremely important question as to how the differentiated electrocardiogran: of the 8 day develops from the undifferentiated curves derived before the 6' day. After the 8" day, as the foetal heart grows stronger, the electro- cardiogram also grows stronger. It shows more markedly all the points generally visible in the electrocardiogram of the full-grown embryo and in that of the new-born chicken. This latter shows some similarity to the mammalian or human electrocardiogram. On the 12" and 14% day electrocardiograms with higher potential oscillations, up to 0,5 millivolt, can easily be recorded. After that Fig. 3. time the maximal PD rises very slowly till the chicken is fully 1362 hatched. In the last week no further changes in the form of the curve are to be found. Fig. 4. During my experiments, the results of which have been here broadly summarized, | found a few other noteworthy details. So a record taken on the 14'* day gave a definite biphasic oscillation instead of the ordinary monophasic P-peak. Another complication in the form of the curve was caused by an unusual form of the T-peak, which also showed a tendency to alter into a diphasie Fig. 5. deviation (figs. 4 and 5) and to start before the R-deviation had completely subsided (fig. 5). Contrasting with these rather complicated forms, I sometimes found more simplified ones in which it was not possible to differen- tiate with certainty more than two elementary summits. Lastly I found no small number of complexes which had to be considered as pathological forms. The principal of these were caused by block; even isolated P-deviations could be found. The form represented in fig. 6 seems to me to be also a pathological form. Fig. 6. The pathological processes in these cases are probably caused by changes in the temperature, by lesions occurring during the prepa- ration, or by the gradual death of the heart itself. 13638 Mathematics. “On a class of surfaces with alyebraic asymptotic curves.’ By Prof. W. A. Versiuys. (Communicated by Prof. J. CARDINAAL). Ps qq 8 a, 0, § 1. Let a twisted curve ae ) be given by tbe equations: (OES Ue of aes tll aR unicycle (Gl) ¢ being the arbitrary parameter, a, 6,¢ constants and p,q, s positive integers not admitting a common divisor. In general we suppose r Je 2 — Gea) admits in the point /, (v,, ¥,,2,) corresponding to the value wu, of wu the plane (2) as osculating plane. The twisted curve g under discussion has to cut the plane (2) thrice in the point w= u,, i.e. the equation rd ') .9(2@ ) f (20 - 1)=0 x. Y, a must admit three roots «= w,. This gives the conditions : £, (™,) o's (u,) Ss v's (u,) cs: gy, (4) f2 (4) fs (%) PP) , o's), g's) é GP, (u,) P2 (%;) Ps (us) As the equation (5) must hold for any value of wu, the first diffe- rential coefficient of the first member must disappear. This gives by taking (6) into account : rien, . ght ol + s {Oe o == 7 Ch eee CC v.00) 4 @ As the equations (5) and (7) must hold for any value of u, they lead to the two seis of solutions : p(w) : iw) = te "a(u) : G2(u) eye '3(t) : g (u) Pp q 8 ; 0 eee and y wg — Y's: Ls =< Bs Fs 3) el Te ouee OP =.9' 4; Deane 4-08 ee By representing the three equal ratios (8) by w(w) we find D fe (uj du YG, ae) ae which passes, by replacing f w(u) du by 4 into op (u)\ a 5 04 2 i. e. into a curve of the system C(p, q, 5). Likewise the ratios (9) furnish tar =, Yi IPT ee — TA i. e. a second curve belonging to a system C(p,,q,,5,) determined by the relations 1365 Pi=p(—p+ q+ 4) %1=97 (p—q+s) oe eee es (LO) 8, =38 (p+ q—s) So we have the theorem : The equation (2) represents the osculating plane in the arbitrarily chosen point P, (x,,4;,2,) to both the curves Cp, (p, q, 8) and Cp, (p,,9,8,)- We also find easily for the equation of the osculating plane in P, to the curve Cp, (p,, G15 5;) ah (- 3 1) antes (2 fe 1) stirs (- ss 1) =f Py wc, vi YW S| ey so that and likewise eee ese te gma 20s) ENDS SS CLT § 3. Definition. We call C(p,,q,,58,) the complementary system of C'(p, q, 8). By determining the complementary system of C(p,, q,,s,) we find again the original C'(p, q, 5), as we have Pi (—Pi + Ua +4) = P(- pt+qts) (p—a+s) (p-+q—s), (P= +81) = 9 (—p +9 +s) (p—at+s) (P+ 9—8)s 8 (Pi+%—s) =s8(—p+qts) (p—ats) (p+ 4q—s)- Therefore an exception presents itself if and only if we have (—p+4+8) (p—9+s) (p—g+s) = 0. For p<.q0 for sp+q;p, and q, are always positive. For p=0O we also find p,=0O; then the two complementary systems C(p,q,s) and C(p,,q,,8,) are both systems of plane curves situated in planes 2 = constant. If two of the three numbers p, q,s, e.g. p and qg are equal, we find p, =q, = ps and both systems C(p,q,s) and C(p,, q,, s,) con- sist in plane curves complanar with the axis OZ. The identities pP + qQ +8 =0, (12) peeaeO es 0, ) = — © 89 Proceedings Royal Acad. Amsterdam. Vol, XIV. 1366 can immediately be verified. Likewise one finds PP, = i 12) ai 8,5, = 0 and as according to (11) P, =— P, ete. we find p,P =5 7:9 ae 35= 0, and also oo. Te) tn Se aalee PVP + 9,7Q + s7S=0. § 4. Let O,,, be a surface determined by the equations \ ic = auPvPi 7 A OUI UN tet 0S ae ee eee ee ee z=cus vi, where the coordinate limes v=constant are curves of the system C(p,q,s) and the coordinate lines w= constant curves of the com- plementary system C(p,,q,,5,). The two coordinate lines passing through any point P, (@,,y,,2,) of O.., admit in this point the same osculating plane. This common osculating plane contains the tangents in P, to both the coordinate lines and as the director cosines of these tangents are proportional to BOY TOE ot De ee and RUB Ew TED) these tangents do not coincide and the common osculating plane is at the same time the tangent plane of 0... in P,. This proves the theorem: . The two systems of coordinate lines are the systems of asymptotic curves of the surface Occ, gwen by (14). In any point P, of O,., the tangents to Cp,(p,g.s) and Cp,(p,.q,,51) are the principal tangents as these curves are the asymptotic curves, So in any real point of O., the principal tangents (see (15)) are real and different from one another; so we have the theorem: All the points of Oc, are hyperbolic. The equation of the surface O,,, is: Gxonen i: being the lowest common multiple of the numerators P, Q, S of (3) after reduction of these fractions to their simplest values. In- deed the values (14) of the coordinates of any point of Ovo, satisfy the equation (16) for arbitrary values of w and. v, as according to (12) and (18) we have the identities pP + 9Q+sS=0, PP+7,94 3, S= 0. 1367 On account of p< qgo, pee a @. Corollary If. The surfaces O.-, on which the lines of the systems C(p.q.s) and C(p,,q,,5,) are the asymptotic curves form a pencil. Corollary III. The base curve of the pencil of surfaces O,,, is formed by the sides of the skew quadrilateral OX. YaZ.O, each of these sides counted a certain number of times. Corollary [V. The complex of the principal tangents of the pencil of surfaces O.., is formed by the tangents to the curves of both the systems C(p,q,s) and C(p,, q,, s,): § 5. Reversely we start from the equation Bese ala — ee Ae aod Lan Caan Pa. ee oho) where L, M, N are integers admitting no factor common to all three, in order to investigate under which restrictions with respect to these numbers the surface represented by (18) admits as asymp- totic curves the lines of a system C( p, g,s) and therefore also those of the complementary system C(p,,q,,5,)- This will be the case if the surface (18) contains curves of both systems; to that end we must have : pL + qW@ + sN=0 19 and pP.L+9¢,M+s,N = 0, ( 2 or (p+q+s)(pL+qM+sN) — 2 (p*L+q°M-+s'N) = 0, what can be replaced, on account of (19), by pL +. gM + s?N == ()) . . . . . . (20) where p, q and s are integers. From (19) and (20) we deduce: p __ —LIM + \{— LMN(L+M+N) As p and q have to be integers the expression — LIN (L4+M+N) under the root sign must be positive and a square; so L, M, N cannot have the same sign. Let a* be the highest integer square by which LAN and 4? the highest integer square by which 2+ 1+ NV ean be divided, so that LWN:a* and (L+ M+ N): 0}? contain 89* 1368 prime factors only occurring only once in each expression; then we must have LMN: a? = —(L4+M4N):88. . . . . (1) By substituting the value of —(Z-+ M+ N) following from it into the expression for p:q given above we easily find: P q s M(atbN) —a(L+N) M(axbL) So, as soon as L, M, WN satisfy the condition (21) we find sets of numbers (p,q, 8), (p,q. s’) and therefore also two sets of curves C(p.q.s8). C(p',q'.s') lying on the surface (18). After some reductions we find p': q':s' = p,:q,:5, as the deduction of (p, q, s) and (p’, q’, s') requires. So we have proved the theorem: A surface (22) alyM2N — B admits as asymptotic curves the curves of the systems C (M (a+4N), — a(L4-N), M(a—bL)), and C (M (a—bN), — a(L+-N), UM (a+bD)), as soon as L, M, N satisfy the condition b? L+M+N=——LMN, a and b being integers. The simplest example of a surface 24 y”%2N = B, where the con- ba dition L+ M+ N=— — LMN, holds, is the hyperbolic paraboloid a te ate In this case the equations (22) become p= 0} gs endo se — 0 — ae The systems C(0,1,1) and C (4,1, 0) are systems of right lines forming on the paraboloid the asymptotic lines. § 6. Any surface O.., contains besides the two systems of asymp- - totic lines C(p,q,s) and C(p,, g,, s,) other systems of curves belonging to the systems C(p + Ap,,9 + qs + 4s,) and this holds for any rational value of 4 either positive or negative. Let, in order to show this, P, (v,,%,,2,) be any point of O,,,, so that we have w, Pkz Sk — By,—@&, then QO... contains any point of the curve 1369 C— vtPPa , y = yn, — zt as from the identities (12) and (18) we can deduce P(p+Ap,) + Q (q+49q,) + S(s-+As,) = 9. If A, and A, represent any two definite values of 4, the cross ratio of the four tangents in a point P, of O.., to the curves through P, of the systems C (P, 7 8), C (Pi: qi 81); C (Pp +4, Py) q F495 3 FA8i)s C (p+ AP d+ 4.91 8 +4,8,); is always equal to 2,:4, and therefore independent of a, 7, ,2,. So this cross ratio is constant all over the surface. If we put e.g. 4,=1:(p+¢q-+s) A, =(Pit+n+s)?(—pt+9+s) (P—a+s) (pt+a—4), the two systems of curves corresponding to these two values of 2 are the systems C'(p’, q?, s?) and C(p,?, q,”, 5,°). So the cross ratio of the tangents in any point of O,,, to the four curves through this point belonging to the systems C(Pig 8), CCP dss CCP 9gs8) (P7071 847) is therefore pee eet ata Pe NT ee) pee Ore) Ons) This cross ratio becomes zero or infinite if two of the four tangents coincide with each other; then the curves touching these coinciding lines also coincide. For p, g, and s positive and p and C\p,,,,8,) being the asymptotes of the indicatrix. So the two systems of curves corresponding to 4, and — 4, are conjugate on One. So the developable enveloping Q,,, according to a curve of the system C\4,) is represented by the equations v2, (1+ v(p—a4,p,) teria, | y=y, (1+ 9 (g—AzQ,)) th, fe ee ¢= 2, (1+ v(s— A, s,)) ests, 1371 Indeed this ruled surface proves to be developable, as it is possibe to determine v in such a way that the director cosines of the tangent to the curve of the system C(A,) situated on this surface /// and corresponding to this value of v become proportional to the director cosines of the generatrices. Indeed it is possible to find values » and vw satisfying the equations } P 55 A, Pr = v (p* a i,? Pr.) te w (p A, P1) == (ly a+4.g, + 2 (Q?—4,’ 9,7) + w(q— 4, 0,) = 9, s+, 3, + v (s? —A,? 3,7) + wls — A, s,) = 0, as the sum of the three first members, multiplied respectively by P, Q, and S disappears. This developable also cuts O,,. according to curves of the system ((a,) to which also belongs the curve of contact, . $ . A § 8. By assuming for a, the value — — we find s—a, s, = O and mit the system C(A) becomes the system C(p(s—p), g(s—q), 0). The con- Jugated system, i.e. the system corresponding to the value A,—=—2,=s:s,, is then the system C(pq, pq,s,). Then the first system consists of curves lying in the planes z= constant and the second of curves lying in planes through the axis OZ. The developable D circumscribed to Q,,. along a curve of the system C(p(s—p), g(s—q),9) is generated by the tangents to the curves C(pq, pq, s:) and admits therefore the equations : & =x, (1 + pqvr) tPs—P), y = yy (L + pgu) 9s), 2=2z,(1 + 4,»), @,,Y,, 2, Satisfying the relation w,Pk z Sk —= By—&, As the system of curves conjugated to the curves of contact consists of curves situated in planes through the axis OZ, the developable must be a cone (according to the theorem of Kornics’), the vertex of which lies on OZ. It is easily verified that all the Ce eee NG pa) \ The developable D’ circumscribed to O,,, along a curve of the system C(pq, pq, s,) is represented by the equations : generatrices of D pass through the point 1) G. DarBoux, Théorie gén. des surfaces T. 1 § 91. 1372 xa, {1+ p(s—p)v} 0, Y= ntl+ gb—gvjey, 2s, ie The direction of the generatrices of this developable being constant, D’ is an enveloping cylinder. For 4, = —p:p, and 2, =— q:¢, we obtain analogous results. So the theorems hold: ; I. The plane sections of Occ, by planes through any edge of the tetrahedron of ceordinates are conjugated to those by planes containing the opposite edge. H. The developable circumscribed to Occ, along a plane curve, the plane of which contains an edge of the tetrahedron of coordinates is a cone the vertex of which hes on the opposite edge. HI. Any of these enveloping cones cuts Occ, according to curves of the system C(a) to which belongs the curve of contact. § 9. Let A(a,b,c) be an arbitrary point. Then the curve of contact of the enveloping cone of OQ... with A as vertex lies on O,., itself, the equation of which surface is wPk y Qk Sk — B, and on the first polar surface of A with respect to O.., with the equation PawPk-1 yQe2Sk 4+ Qbe Pky Q—l 28k 4. SexPky ar 2gp—1 —(P4+Q45) B=0. By eliminating 5b between these two equations we find : Payz + Qbaz + Sexy —(P+Q4S8S)ayz=0.. . (23) So the curve of contact always lies on a cubic surface O'4 repre- sented by (2:). The equation (23) of O'; being independent of B, this surface O% is the same for all the surfaces Ojo; so we have theorem : The locus of the curves of contact of all the surfaces Occ, with- the enveloping cones with common vertex A is a cubic surface O's. The tangential planes of O,,.. being at the same time the osculating planes of the systems C(p,q,s) and C(p,,q,,5,), the surface O%4 is also the locus of the points P for which the osculating planes to Cp(p.q.s) and to Cp(p,.q:5,) pass through A; this can easily be proved directly by making use of the equations (4). The surface O% containing the six edges of the tetrahedron of coordinates, four of which also lie on Ovo, the intersection of Ons, 1373 and OW, breaks up into the curve of contact and these four edges. The tangential plane of O4 in any point of one of these edges is the same for all the points of this edge and different from the faces of the tetrahedron of coordinates. As we always have S<— Q and we suppose provisionally that ? > — Q, the tangential planes of O.., along the four edges coincide with faces of the tetrahedron of coordinates. So each of the four edges belongs to the intersection a number of times indicated by its multiplicity on O,,,. Now the edge OX, is always Sk-fold on O,., and Y, Z,, is always (S+Q+P)k-fold, while for P>>—Q the edge X, Y,, is Sh-fold and the edge OZ, is — Qk-fold. So the four edges represent together (BS+P)k common right lines. The total intersection of O% and O,,, being of the order 8(P?+-S)k, there remains a curve of contact of order 2Pk. In the case P< — Q the edge X, VY, counts (P+Q+S)k times on Q,,. and the edge OZ, counts P& times. Then the four edges represent (8S+38P?+2Q)/ commen right lines belonging to the intersection and therefore the curve of contact is of order — 2Qk. For ?=— Q which implies S=S+ P+ Q the tangential plane of O.., along OZ, is no more constant and therefore this plane does not coincide with the tangential plane of Or along this edge which is constant; likewise for the edge Y,Z,. So the multiplicity of these edges as parts of the intersection still remains equal to their multiplicity on Occ, « Now the edge YX, Y, is. Sk-fold on O,.. and the edge OZ, is Pk-fold. The order of the curve of contact is 2P4 = — 2Qhk. From P= — Q we deduce Cae d) (Gp). — 9, i.e. either s=q-+p, or p=q. In the first case O,,, is a ruled surface (see § 3, § 14), in the second a plane (see § 3). As in general the point A does not lie on the surface 0,,, it neither lies on the curve of contact and the order of the enveloping cone to Q,,, with vertex A is equal to the order of the curve of contact. So we find the theorem: The order of the enveloping cone to Ov, with an arbitrary vertex A is the larger of the two numbers 2Pk and — 2Qk. If A lies in one of the faeces of the tetrahedron of coordinates, O* breaks up into the plane of that face and into a quadratic cone the vertex of which coincides with the opposite vertex of the tetrahedron. If A lies on one of the edges of the tetrahedron of coordinates, 1374 O% breaks up into the two faces through A and into a third plane. Then the curve of contact is plane (see § 8). § 10. The class of the enveloping cone is equal to the class of Ovo; the class of O., being (P-+-S)k, as we shall see immediately, the class of the enveloping cone also is (P+ 5S) &. The class of O,., is equal to its order, the reciprocal polar figure of O., being also a surface O.,. The homogeneous plane coordinates («, 3, 7,4) of a tangential plane to O,,,, i.e. of an osculating plane to a curve C(p,q,s) satisfy the conditions (see § 1, equation 4): a i B ee Y ee) P:ajuPvPi — Q: bun ~~ Sz cu,sv,. PQS’ where (2, ¥,,2,) are the coordinates of any point of O,., and w,, the parameter values eae to the point of contact. By replacing 1:4, and 1:v, by wu’ and v’ we find: ulPv Pi a0 — QSe,’ E wn a —— PSy, “ u'sy's: Nt oe PQ, 4 So, but for constant factors, the coordinates of the pole of the tangential plane to O,., with respect to the quadric ep ga b= 05 2 2). ee are equal to the coordinates of a point of O.., (see §4, equation 14). So, if the equation of Occ, is x Pky Qk 2Sk — B, the equation of the reciprocal polar figure with respect to (24) is oe. B{PS+Q QP+S SP+Qk So the product of the parameters corresponding to two reciprocal. polar surfaces of the pencil QO... is constant, viz. {PAt+S QS+P SP+Q—k, Pk y Qk 2Sk — § 11. In the case s,=0O the asymptotic lines of the system C( py. 5) are right; so according to a known theorem four arbi- trary asymptotic curves of the system C(p, q, 8) must intersect all the generatrices in four points with a constant cross ratio. This theorem not only holds for the ruled surfaces on which the curves esa) C(p, q, 8) are asymptotic curves, buf also for any ruled surface generated by these curves. Proof: Let the ruled surface be represented by the equations v=(a+ av) Aid (Det a2) 6g atte fons te? ae. ep fers Ss, (ad) z=(c + yv)t 2 P,, Let iz ’ curves C(p,q,s) ecrresponding to the four parameter values v,, v,, P,, P, be the four points of intersection of the four v,, v,, With the generatrix corresponding to the parameter ¢,. The cross ratio of these four points is equal to that of the four projee- tions of these points on the axis OX and in its turn this cross ratio is equal to that of the four points of OX for which the v coordinate has the values a-+av, , a+av, , afar, , a--+ ay,. These four coordinates being independent of ¢, the cross ratio of the last group of four points does not vary with ¢,. So the cross ratio of the four points P,, P,, P,, P, is independent of 4, i.e. this cross ratio is the same for any group of four points determined by the four eurves C(p,q,s) corresponding to the parameter values V,, V4; U3,V, ON any generatrix. Example. The curves of the system C'(1, 2,3) intersecting a given right line lie on a ruled surface of order four, for which one of the twisted cubies C(t, 2,3) is double curve (nodal curve, isolated curve or cuspidal curve). According to the theorem just proved any definite group of four curves of the system C(1, 2,3) cuts all the generatrices in four points with a constant cross ratio. § 12. In the case of a rectangular system of coordinates we easily find for the first differential coefficient of the length of are 6 in the point P (w, y, 2) of the curve Cp (p, g, s) corresponding to the parameter value ¢ the expression do 1 Coan tol- pix? ais gy? as g222 | Let 464 be the angle between the binormals of the curve C(p, q, s) in the points corresponding to the values ¢ and t+ A‘; then we easily find : dO PQS | p?c? + g?y? + 8727 3 dt Pony ss + tuys So the radius of torsion @ becomes : 1376. dé rye Q? =—=-— =+5 dé = POS\: For the radius of torsion 0, y ne curve cat es the same point we get BEN fl Py os oO — Si =p 1 Ss. (= ae soit =) and, as P, =—P, Q,=—Q, 8S, =—S (see § 2, equation 11), lel=le.}”)- Of the serews osculating the asymptotic lines of the surface O,., in any point the cne is righthanded, the other lefthanded, as the determinant | CUM ee ey: one) ea ee “Pgs (P+Qt+S) | at Bil " 2 assumes Opposite signs for the two asymptotic lines. Let X, ¥, Z represent the director cosines of the binormal and d the distance of the origin to the osculating plane in the point (w, y, 2); then we easily find: 12 Pee Se) S 12 1:9=x¥7 | o+5|'=ar lara t=ax4, 3? 2 z ec y d __ awyz PQS ORY ZEP@Se tas Let Ay be the angle between the tangents to a curve of the sysfem C\p,q.s) in the points corresponding to the values ¢ and t+ At; then we have: a+? Q: +5] UVYZ == rite ees ; dt t (p*a = Vidic ot Paes) by means of which we find for the radits of curvature PR: 3 do a (pte? + gy? att ie) dp E Pgs we (5 TF : =F ae or, if @, 8, and y are the angles ae ne tangent and the axes of coordinates i > Fy 08 e008 B e087 I~ 44 =|" So we get: ') Pascan, Rep. di Mat. Sup. Cap. 16; § 9. : d i —— : PQS COSA cos3 cosy and R AYZ Q cosa cosB cosy Likewise, if «@,,8,,y7, are the angles between the tangent in the point P (v,y,2z) to CP (p,,q,,%,) and the axes of coordinates, and Rk, is the radius of curvature of this curve in this point, we find: d LS SSS —, P,Q, S, cosa, cos, cosy, and therefore ci fae eal eel R,| =| cosacosBcosy | § 13. The tangent in the point P, to the curve Cp (p,, q,, 8) admitting the director cosines Po, > TY» 8% » this line is normal, in the case of rectangular axes, in P, to the quadrie of the pencil joie SGP ALC? Site ote oe Be 8 (FD) passing through P,. So the surfaces of this pencil (26) cut all the curves of the system C'(p,g,s) and consequently also all the sur- faces generated by curves of the system C(p, q, s) under right angles. Moreover the pencil (26) cuts any surface generated by curves C(p, q, 8) according to the orthogonal trajectories of these curves. The surface QO.-, being generated by curves of any system C’ (7), see § 7, we find the theorems: I. Any quadric of the net px* + gy* + sz* + A(p,2?+9,y?+5,27)) =u. . . (27) cuts any surface Op, under right angles. I. The orthogonal trajectories of the curves C (4,) situated on Oco, are the intersections with surfaces of the pencil. px + gy + s2* + A, (pe? + gy? + 8,2°) = pe Il. Any curve of order four forming the base of a pencil of quadrics belonging to the net (27) cuts any surface Ove, under right angles. IV. In particular the orthogonal trajectories of the asymptotic curves of Occ, are determined by the intersection with the two pencils of quadries pe+tqytsz2=u, Pp? + gy’? +327 =, 1378 § 14. We now suppose s=p-+q; then the numbers p, q, s are mutually prime two by two. We then find p,=g, =2pq,s,=0; so the complementary system C'(p, ,q,,5,) is a system of right lines resting on the axis OZ and on Xz Yz. The surface O.:, is a ruled surface with two right director lines. Furthermore we find: PSELo=—4,5=-—3 he 2 so the lowest common multiple of the denominators of P?, Q,S is either g-+ p ov (¢-+p):2 according to the numbers g and p being either one even and the other odd, or both odd. We suppose in the first place that one of the numbers p, q is even (see § 15, examples I and III). Then the equation of the ruled surface O,,, is: wItPzI—P = ByltF ; so the ruled surface is of order 2g. The enveloping cone is of order 2Pk=2(qg+p), see § 9, and of class 2¢.. If p and q are both odd and therefore p—- g and p+ q both even (see § 15, examples II, IV and V), the equation of Q.., is xiP+q):2 2p—9):2 — ByP+9):2, so Op, is a ruled surface of order g. The enveloping cone with arbitrary vertex A is of order q+p, see § 9, and of class q. The ruled surface osculating O.., along a generatrix /is generated by the principal tangents of O,., in the points of 7 which do not coincide with J, i.e. by the tangents of the curves of the system C(p. q p+q). So this osculating ruled surface is represented by the equations : «=a, (1+po)t y=9, 0 +9u)t, == 2, {1 +(p+9) 4: or by the equation TY, — YX, meal Pty — qe (p+) § 15. Example I. Suppose p=1, g=2, s=3; then we have 1 s=pt¢@ i 7 Su P= =) — 1, eure So the equation of the ruled surface with the twisted cubies of the system Cd, 2, 3) as asymptotic lines is es By*. Example lf. For p=1, q=3, s=4; we find s=p+4q, 1 Gop = 0; sO} PSS VE, i= So the surface admitting as asymptotic lines the twisted quartics of the system C(1, 3,4) with two stationary tangents, is the cubic surface ke = IT The section of O... by a plane «= constant breaks up into the line at infinity of this plane and a curve of the system C(O, 1, 2). The ruled surface osculating QO,,. along this section is represented by the equations : = 2, (1-+2), y = y, (1430) ¢, = z, (1+ 40) @. The equation of this osculating ruled surface is yz, (4a—32,) = zy,° (Ba—2z,)’. The intersection of this cubic surface and O,,, consists of the conie of contact counted thrice and of the two right directors of Oc... Example III. Suppose p= 2, gq=3, s=p+q=5. Then Occ, is a ruled surface of order 2g = 6, the equation of which is eee _So this ruled surface admits a system of asymptotic lines of order five. Example IV. Suppose p=1, q=5, s=p+q=6. Then 0,, is a ruled surface of order ¢=5 with the equation Pe = 1BiIM So this ruled surface of order five admits a system of asymptotic lines of order six. Example V. Suppose p=3, q=5, s=p+q=-8. Here Occ, is a ruled surface with the equation pepo —— Jovian Example VI. If the first system of asymptotic lines is formed by curves of the system C(1,3,6), then the asymptotic lines of the second system belong to the system C'(2,3,—8). So both systems are curves of order six. The equation of O,., is Zoey. Example VII. It the first system of asymptotic lines belongs to the system C (41, 2,4) the second system belongs to the system C5, 6, —4). Then the equation of 0... is aces 1380 Physies. — “On piezo-electric and pyro-electric properties of quartz at low temperatures down to that of liquid hydrogen.” By H. Kamertincu Onnes and Mrs. Anna Beckman. Communication N*. 1327 from the Physical Laboratory at Leiden. (Communicated in the meeting of February 22, 1913). § 1. Introduction. As many qualities of solid bodies are much sim- plified at very low temperatures by the considerable decrease of the calorie motion, it seemed desirable to examine also the piezo- and pyro-electric effects under these probably favourable circumstances. In order to make a preliminary inquiry into this branch of the subject we have measured the- piezo-electric modulus of quartz, per- pendicular to the axis, down to the temperatures of liquid hydrogen. Then we have also, at the temperatures of liquid air and liquid hydrogen, observed the pyro-electric phenomenon of quartz, which FriepeL, Curie and others have examined at higher temperatures. § 2. Measurements of the piezo-electricity of quartz at low tem- peratures. The measurements were effected by the generation of electricity on a quartz plate, which was kept at low temperatures and compared with a similar plate at ordinary temperature. Thre generated charge was measured with a quadrant electrometer. Both ihe plates were of the same sort as is used in the ordinary Curir’s instrument, that is to say, they were cut out of the crystal parallel to the optical axis and with the broadest side perpendicular to one of the electrical axis. ’, They were 7—8 cm. long, 2 em. | broad and 0.06 em. thick. The two I+ broad, sides were coated with tin‘). é CD Py One of the*tin coatings of each plate Be was earthed, the two others were metal- eA lically connected with one another and. all with one pair of quadrants of the elee- trometer, as is shown in the figure. The other pair of quadrants was earthed. All the connections were enclosed in brass tubes, which were in 1) The tinfoils were apt to get loose from the plate in the liquid oxygen, which gave rise to blisters; it would of course be better to employ a platinized quartz plate, silvered: Then, too, the use of cementing material between the metal coating and the quartz would be obviated. 1381 connection with the earth. The electrometer needle was kept at a constant potential of 120 volts. The quartz plate @, was suspended in an earthed meta! case and carried a scale pan, on which weights could be placed, in order to stretch the plate; Q, was put in a Dewar glass; its lower end was fastened in a brass support, which was carried by the .cap of the vacuum vessel; the uppermost end was suspended by a brass rod to one arm of a balanee, whose other arm carried a seale, which could be loaded with weights. In order to be able to close the vessel hermetically (which was quite necessary), and at the same time make the free movement of the rod through the cover possible, it was simplest, for these preliminary measurements, to use an elastie india rubber tube which closed round the rod and the tube in the cap. As we shall see this had only a slight effect on the relative measurements. Within the glass the quartz plate and the support were surrounded by a brass net in connection with the earth. The measurements were made in the following way : first the plate Q, was stretched by a weight (500 gr.) and the deviation of the electrometer needle was observed. Then this plate was earthed, and when the connection with the earth was broken, the weight was removed and the deviation ot the electrometer te the other side was observed. The sum of these deviations is proportional to the quantity of-electricity generated. Then the electricity which was generated on Q, was measured in the same way. Immediately before and after the measurements the electrometer was calibrated with a Weston element. The sensibility changed very little. The insulation was generally very good, so that there was seldom any need of making corrections for leakage.. " Always five or seven turnings of the electrometer needle were observed. From these the eventual corrections for incomplete insula- tion could be calculated. § 3. Results. I. Both the quartz plates at room temperature (TP =.-280° K.): The deflections were mean values Q, 126.7 127.2 127.0 127.6 127.4 127.2 Q, 163.7 164.0 163.6 163.2 163.3 163.6 The Weston element (1.018 Volt) gave 34.4. The capacity of the electrometer, of the connections to Q, and of Q, itself was about 150 em.; that of the connection to Q, and of @, was about 100 em. By the cooling of Q, its capacity changes. 90 Procecd:ngs Royal Acad. Aii.slerdam. Vol. XIV. 1382 II. , in oxygen boiling under a pressure of 21 em. 7’ = 78°.5 K. mean values Q, 130.6 130.1 130.3 Q, 165.2 165.7 165.4 One Weston element 34.4. III. Q, in boiling hydrogen, 7'’= 20°.3 K. mean values Q, 129.6 130.5 130.0 130.0 Q, 165.4 165.5 165.4 165.4 One Wrston 34.4. IV. Q, at ordinary temperature, 7’= 290° K. mean values Q . Agta 127.4 127.1 126.8 127.0 127.0 Q, . 1625 163.0 162.8 1631 162.7 162.8 One Weston 34.3. In order to examine the influence of the elastic connection between Q, and the cap of the vacuum vessel, two measurements were made without the elastic tube, one at ordinary temperature and the other in liquid air. These gave V. Q, at ordinary temperature, 7’ = 290° K. mean values OQ) 126.2 126.8 AOA Le) eee 127.0 Q, 167.4 168.1 168.1 AGieoe a llGere 167.9 One Weston 34.3. VI. Q, at the temperature of liquid air, 7’= 80° K. ; mean values Q, 129.3 129.6 129.8 129.7 -1129:9 2957 an 168.8 169.3 170.1 169.2 169.4 169.4 One Weston 34.3. 3y immersing Q, into the bath of low temperature the deviations are thereby changed for both the plates. The change was at the measurement ; LL (0 378 se) Q, + 2.4°/, Q, +41.1°/, Hl 20.3 2.2 1.0 VI 80.0 2.1 0.9 1383 The electricity generated on Q, was thus at all events less than at ordinary temperature. The decrease was 1.3°/,, 1.2°/,, 1.2°/,. The influence of the elastic connection falls within the limits of errors of observation. In the absolute measurements the connection causes a decrease of about 3 °/,. Thus we may conelude that the cooling from 290° K. to 80° kK. causes a decrease of 1.2°/, in the piezo-electric modulus. A further cooling from 80° to 20° causes a much smaller change, it appears even less than 2°/,,. The importance of this result is perhaps that the change in the piezo-electricity by cooling to low temperatures 0 seems to take place chiefly above the temperature of liquid air. § 4. Pyro-electricity of quartz. As has already been said, we also made some observations on the pyro-electricity of quartz at the _temperatures of liquid air and hydrogen. The pressure under which the liquid round Q, boiled was changed. By the change of tempe- rature, which is the consequence thereof, a pyro-electric charge is generated on Q,. The deflections of the electrometer were ° ° for 90 K to 86.5K + 27.5 mm. or per degree + 8.5 mm. , mean value Sede Oper ata Oe ss a Se) BS KE §.B 1. per 82.5 PUN Lt Oma aris eD/tl px oe tore ts As +85 ,, degree 78.5 » 2 == fo8)40)) arte ae ei waits gy 7.8 mm. fo} fo} Pak ae Gh gy, sss + 1.4mm. TIEN LOS) ear Ceo or —1.6 ,, 1.6 between 20.3,, and 15.8,, + 14.3 (double deflect.) 141.7 ,, The deviation 7.8 per degree at the temperatures of liquid oxygen 1.6 per degree at the temperatures of liquid hydrogen has by an increase of temperature the same direction as by a stretching of the plate. We note that the generated pyro-electric charge is about propor tional to the absolute temperature. We wish to record our heartiest thanks to Mr. G. Horst, assistant at the physical laboratory, for his assistance at our experiments. 90~ 1354 Physics. — “Measurements on resistance of a pyrite at low tempe- ratures, down to the melting point of hydrogen.” By Bener BreckMAN. Communication N°. 132g from the Physical Labo- ratory at Leiden. (Communicated by Prof. H. Kameruincu ONNES). (Communicated in the Meeting of February 22, 1913). In an earlier publication’) I examined resistance as a function of temperature in the case of a pyrite erystal from Gellivare, Malm- berget, Sweden. Those measurements embraced the temperature interval + 100° C. to — 198° C. The resistance was well represented by the formula Wi Wet, . go so. where IV, is the resistance at 0° C. and ¢ the temperature on the centrigrade scale. The spec. resistance at 0° C. in ohms per cube of 1 cm. was w, = 0,00294; a was 3.53 x 10-%. The measurements were made with a Wueatstone bridge. The ends of the erystal were galvanized with copper; as electrodes amalgamated copper plates were used. The resistance at 0° C. was 0.101 ohms. To determine the magnitude and the variation of the contact resistances and of the connections with the temperature, a little copper prism of the same dimensions as the crystai was placed between the electrodes and short-circuited, and the resistance of the short-circuited crystal support and the connections were measured at the various temperatures. I have now had an opportunity of continuing these measurements on a pyrite through a larger temperature interval (down to — 258° C.). This last investigation was made in the eryogenic laboratory of the University of Leiden, and for the opportunity I owe the director of the laboratory, Prof. H. Kamurninca ONNEs, great thanks. To obtain these measurements | have used another method, which eliminates the possible errors of the contact resistances. The erystal- was pressed between two copper electrodes, through which the current was conveyed to it. Two other electrodes were firmly pressed against the longest side of the crystal. The voltage between these was measured with the compensation apparatus *). In. Table I the results of the measurements in Upsala 1910 are !) Bexar Beckman: Uppsala Univ. Arsskrift 1911. Mat. o. naturvetenskap 1, p. 28, *) See H. Digsseruorst, Zeitschrift f Instrumentenkunde 26, p. 182, (1906), where Fig. 2 gives a survey of the mounting. 1385 TABLE I. Change of the resistance of pyrite with the temperature. Measurements in Upsala 1911. E | Ww W jobs. | [ We leate —<—<—$———— =— = | + 100°.9 C. 1.422 | 1.436 | pe | 1.223 | 1.215 | + 44 .5 1.180 | 1,173 | | 0 1 1 | ne .6 0.726 0.754 | | — 193 0.508 | 0-495 TABLE II. | Change of the resistance of pyrite with the | temperature. Measurements in Leiden, 1912. | pws | pw E lw ‘ll obs. W | calc. a a aoa = === 2S SSS + 15°.8 C. 1.063 | 1.058 — 183 0.519 0.520 | — 252.8 0.405 | 0.404 — 258 0.390 0.396 | given and in Table Il these 'ast results of 1912. The values lz . are calculated from the formula (1), where now = i— sor lO Ss: The results are well represented by this formula. The values of Ww : ; : at low temperatures that were found in the last observations W, are in better agreement with the formula than the earlier ones. The results for = —78°.6C. and —193°C. in these deviate a little from the ecaleulated values, but in different directions. The 1386 deviations do not exceed 4°/,, which corresponds to a difference of 0.004 ohms at the most. The last measurements may also serve to control whether the results of the earlier ones were not fully accurate owing to the contact resistances. The deviations that I have just mentioned might arise from this souree of error, but, as they go in different directions at ¢= —78°.6C. and ¢—=-—-193°C. one is inclined to think that these deviations may originate in other errors too, for instance in variations of the temperature bath at t= —78°.6C. (solid carbonic acid and ether). QO. Reicuennem') and J, KorniGsserGer*) have examined pyrite from Val Giuf, Graubiinden and have found a minimum of resistance at about ¢=—10° C. This pyrite has a specific resistance of 0.0240 at O°C., thus eight times larger than mine. An explanation of this difference of the conductivity is given by J. KoENiGsBEerGer *). My pyrite shows no minimum of resistance above —258° C. The resistance throughout the whole temperature interval follows the formula (1), which is the same, mathematically, as 1 dW W dt It seems very probable that there does not exist any minimum below — 258° C., but that the resistance at still lower temperatures approaches asymptotically to a limit value, as is the case in, for instance, not perfectly pure gold and platinum. A. Wesety*) has recently examined a pyrite crystal from the same place af origin, Malmberget, Gellivare. He found a still smaller spec. resistance, w, = 0.00247 and a temperature coefficient at 0° C. of 0.00228. 0? = const. Physics. — “J/nvestigation of the viscosity of gases at low tempera- tures. 1. Hydrogen.” By H. Kamertincn Onnes, C. DorsMan and Sornus Weber. Communication N°. 134a from the Physical Laboratory at Leiden by H. Kameruincu ONNEs. § 1. Jntroduction.*) The investigation of the dependence of the viscosity of gases upon the temperature at densities near the normal, 1) O. RetcHENnHermmM, Inaug. Dissert. Freiburg 1906, 2) J. Kopniaspercer, Jahrbuch der Rad. u. Elektr. 4, p. 169, 1907. 3) J. KoENIGSBERGER, Phys. Zeitschr. 13, p. 282, 1912. — 4) A. Wesexy, Phys. Zeitschr. 14, p. 78, 1913. 5) This Gomm. includes the paper on the same subject by KAMERLINGH ONNES and DorsMan, which is veferred to in Gomm. Suppl. No. 25. (Sept. 1912) § 6, note 1. 1387 is chiefly of importance for the knowledge of the mechanism of the impact of two molecules, or, more simply in monatomic gases, of two atoms. In the nature of the case it is desirable to extend this investigation with one substance over the largest possible range of reduced temperature. This gives a particular significance to very low temperatures and substances such as bydrogen, neon, and helium. The pupils of Dorn’) at Halle have made systematic researches into the viscosity of different gases. By these both absolute values and temperature coefficients have been determined, and they have gone as low as the temperature of liquid air. In our researches we particularly wished to investigate hydrogen temperatures, while the viscosity apparatus was so arranged that it could be used without alteration for helium at helium temperatures. ZG) But it was natural for us to extend our in- vestigation to the viscosity of our gases at xe) 7—* less low temperatures. It then appeared that besides being of value for the confirmation of the above mentioned researches as far as the temperature of solid carbonic acid, it was also of value for the knowledge of viscosity in the field of the temperature of liquid air. In the field of hydrogen temperatures we found the viscosity of hydrogen while flowing Ww|] || @ through a capillary tube dependent upon the mean pressure. From MAxweE.’s') resear- ches we know that the viscosity of gases at normal density is independent of the pressure, and WarsurG and von bazso have shown in the investigation of carbon dioxide, that in dense vapours, it increases with the density. There is, therefore, every reason to further investigate the dependence of the viscosity upon the pressure in hydrogen vapour. ' § 2. Method. The measurements were . Seite Ne TA sp 3. 9 made according to the transpiration method. ° 5 wem This presents experimentally perhaps the Fig. 1. greatest difficulties, but it seems to allow 1) There is a survey of these researches by K. Scumrrr. Ann. d. Phys. (30). p. 393, 1909. *) For the older litterature see H. KAMERLINGH ONNES and W. H. Keesom. Leiden Comm. Suppl. N°. 23, page 86. 1388 better than any other the fulfilment of the conditions which are assumed in the theoretical deduction. The form which we choose (diagrammatically represented in fig. 1, compare further fig. 2) is distinguished by the following special features : 1. the pressure at both ends of the capillary tube through which the gas flows, can be kept constant as long as desired at any height. 2. the mean pressure and the difference of pressure are imme- diately measured at both ends of the capillary. 3. before it enters the capillary the gas flows through a copper tube (in our case 70 em. long) where it acquires the desired tempe- rature. The calculation of the measurements got by the transpira- tion method was made by the formulas of O. E. Meyer and M. Knupsen ‘); for the amount of gas that passes through a capillary they give: Tid Se 46 Q= 8° Be ae) A 3 (: Te a) ' in which ¢ . 1 Es or 1 7) 2 1105) = = — al pi = — ,.—____.. —— A : Tienes es 8 0,30967 Wo. 5 -|- v1 y = coeflicient of viscosity. R=radius of the capillary. L = length of the capillary. t= time of flow. cia Pega 4 3 a Mean pressure. Pp, = pressure at beginning of capillary. p, = pressure at end of capillary. (J= the quantity that has flowed through, measured by the product of volume and pressure, and corrected for the temperature — of the capillary. $= the gliding coeflicient which is determined by the two last equations, in which g, is the density of the gas. The units are those of the C. G, WS. system. § 3. Arrangement of the apparatus. The manner in which the various quantities in these formulas were determined in the measure- ment, will easily be understood with the help of fig. 2. 1) M. Knupsen; Ann. d. Phys. 28, 1909. p. 75, 1389 The pure gas‘) from a store cylinder is first let into a pipette P, in which it can be brought to a suitable pressure by means of mercury. By a high pressure regulating fap it is then conducted by a brass capillary to A, where the capillary forks. One branch leads to a mercury-water differential manometer, in which the !evel of the water is kept constant by the regulation of the tap C. At first we worked with oil manometers, which allow an easy adjustment at any pressure required. With these no constant values were found for the viscosity coefficient, which was perhaps in consequence of oil vapour solidifying on the capillary. On this account the oil manometers were replaced by mercury-water differential manometers. The other branch of the capillary at A leads the gas through a steel capillary H/’G to the viscosity apparatus in the cryostat. Between D and F is a U tube of charcoal immersed in liquid air, by means of which the last possible traces of air would be kept hack. A vertical glass tube carried the gas further. To this was soldered the spiral copper capillary of about 70 em. length, in which the above mentioned cooling of the gas took place, which had been shown to be indispensible. This terminated at A, from where the eas was carried to L. In “4, which was a small reservoir, the tube divides into two branches viz. the capillary and the tube LJI/N to the mercury manometer (0. ZL and P could be directly connected by a tube in parallel with the capillary and provided with a stop- cock. This was necessary during the exhaustion. The transition from the capillary tube into Z, in which the gas may be considered as at rest, is very gradual. This is of importance for the correction of HaGenpacn, which can be omitted in these circumstances. From S a branch TO leads further to a second mercury manometer V7, which registered the pressure p at the beginning of the capillary tube. Through the capillary tube, (about 65 em. long, with a diameter of 0.122 mm.) the gas flowed into P. As at Z a tube PQR leads from here to the other end of the mercury manometer Y. By means of this manometer we could thus read the difference p,—p,. Another tube WMYZ leads the gas from P to 7% Z is connected on one side to the mercury-water differential manometer 4, and on the other side by « to c. At a there is a regulating tap, which enables us to keep the level of the manometer 4 at a constant height during the experiment. By doing this during the experiment we can keep p,—p, 1) The gas was purified by passing over a spiral cooled by liquid hydrogen (Comm. N°. 83). A trace of air was afterwards found in the gas, this may have been absorbed during the compression in spite of the precautions taken. § 2 ‘Bq > Tn! Ile — Mil) LTE 1391 and p, steady, except for the small irregularities due to the regulation of the taps. The tube ¢ is connected to a vessel ¢ of about 4 L. placed in ice, intended for the determination of the volume. The gas pressure in this reservoir was determined before and after every experiment, by reading the manometer g. As can be seen, a small portion of this volume is not reduced to 0° C., it remains at about the temperature of the room. This portion is only about 1.5 °/, of the whole volume. The three manometers were read by a kathetometer, and were so placed that they could all be viewed by turning the kathetometer. The temperature of the viscosity capillary was determined by a platinum resistance thermometer placed beside it, which was reduced to the hydrogen thermometer of the Laboratory by comparison with a standard resistance thermometer. For the arrangement of the cryostat with stirrer see Com. N°. 123. The measuring apparatus were immersed in a cryostat glass exactly like that of the helium eryostat. As we said in 4 J, it is our intention to determine the viscosity of helium at helium temperature with the same apparatus. The cryostat glass was covered by a cap, which is like that of the helium cryostat, but simplified in an obvious way. In fig. 2 the cryostat glass with stirrer and thermometer are omitted. § 4. Course of the experiments. When the tightness of the apparatus had been properly tested and all found to be in order, the experiment was made in the following way. The volumenometer and the whole apparatus were pumped out and the tap a@ was closed. Then tap ¢ was opened, and regulated so that the manometers 4 and d were at the desired height. When this was attained the experiment was begun, and simultaneously with the beginning of the regulation of tap a the knob of achronometer was pressed. During the experiment, as already said, the taps a@ and ¢ were so regulated that the diffe- rential manometers which acted as indicators, kept constant, at the same time the manometers 0 and V were read, and the small irregularities which at the most were 1°/, were noted as well as was possible. By the determination of a mean-value we find from these readings the pressure difference, which existed between the extremities of the capillary tube during the experiment. If we reduce the readings of the manometer v_ by —- we find the mean pressure p. The chronometer was compared with the standard clock of the laboratory immediately after pressing the knob. The latter served 1392 as the actual time measurer. The end of the experiment was regis- tered in the same way. At the same time tap a was closed. Then the pressure in the volumenometer was read, and herewith the necessary data were obtained. The distribution of temperature in the cryostat during the evapo- ration of the bath, may be a source of error, as it affects the distri- bution of the density in the tubes leading to the capillary tube. These tubes and the time of flow were therefore so chosen that the errors which might arise from this were negligible. The experiments were usually made at a mean pressure of about ‘/, atmosphere. Ruckrs*) has preved that ReyxoLps’ criterion applies also to gases. When we determine the critical velocity for our experiments at hydrogen temperatures, we find 8253 em./see. while the greatest which occurred in the experiments was 419 cm./sec. § 5. Results. In the first measurements made with hydrogen in the manner described above, the viscosity became higher and the higher, which ean be expiained by the hydrogen still containing some traces of air which froze in the capillary tube. On this account we intro- duced the tube with charcoal described above. The later determinations gave constant results. The whole observational material is collected in Table I. The first column contains the temp. in Kelvin degrees, the second and third the difference of pressure and the mean pressure. These results, as already said, are calculated from a great number of observations, the deviations from the mean were about 2°/,,. The fourth column contains the time of flow in seconds, the fifth the increase of pressure in the volumenometer. This increase of pressure combined with the volume, gives the amount of gas which flows through, and: this must be reduced to mean pressure and temperature of the tube through which it flows. For this purpose the equation of state was used, which had been deduced from the measurements of KampriincH Onnes and pr HAAs (Comm. N°. 127) and Kamerninen Onnes and Braak (Comm. N°. 97a). The two first observations were used to calibrate the apparatus, in which we assumed with Markowsk1?) 7, = 841.10—7, while for Cin Surnertann’s formula 83 was taken. By this means the values were determined which are given under 1) W. Rucxes. Ann. d. Phys. ae) 1908 pag. 983. 2) H. Marxowski loc. cit. and K. Scumirr loc. cit. 1393 AB aE wl rAN Pe Pom.Hg | Pom.Hg Tec mHg 293.90 | 11.455 | 41.83 | 12739 | 1.479 993.88 | 10.750 | 42.61 | 16814 "866 i 5 887.2 | — 170.2 10.315 43.42 | 4755.5 1.282 616.8 609.2 170.2 10.310 43.43 | 6600.5 | 1.777 617.0 609.4 89.60 6.020 | 39.47 | 4760.0 | 1.999 | 399.4 | 392.1 89.65 5.545 | 40.39 | 3472.5 | 1.374 | 399.4 | 392.1 89.65 8.485 | 38.86 | 3045.0 | 1.773 | 399.8 | 392.5 | 70.9 | 6.010 | 39.48 | 2610.0 | 1.711 | 323.1 | 316.7 70.9 |- 8.385 | 38.91 | 2301.5 | 2.056 | 326.2 | 319.8 70.9 8.300 | 38.92 | 1834.0 | 1.614 | 327.7 | 321.3 | 20.06 | 4.648} 39.08 | 1264.2 | 6.565 | 114.1 | 111.5 20.04 4.651 | 39.16 | 1264.0 | 6.628 | 113.5 | 110.9 20.03 4.630 | 39.70 | 1265.5 | 6.694 | 113.5 | 110.9 | | ; 20.04 3.945 | 20.40 | 1684.1 | 4.021 | 108.5 | 106.0 20.04 4.190 | 19.12 | 1576.3 | 3.799 | 107.0 | 103.5 | 20.04 4.580 | 20.71 | 1625.0 | 4.575 | 108.4 | 105.9 | 20.04 4.603 | 20.37 | 1357.6 | 3.787 | 108.2 | 105.7 7/.10?. They were corrected for the change of R/L with the temperature and for the gliding. The corrected values are in column 7 under 7.10°. From Table I we can immediately see the degree of accuracy that may be ascribed to the measurements with regard to accidental errors. As we have said before the determinations were usually made at a mean pressure of half an atmosphere. At and above oxygen temperatures a determination at one pressure is sufficient, at hydrogen temperatures this appeared to be no longer the case. Table I shows that there the viscosity changes with the density, and in the same direction as was found by Warsere and Baso tor carbon dioxide. Our differential manometers were not yet arranged, as we intend to do, for working with different mean pressures, and the apparatus was thus not very suitable for determining the in- fluence of the pressure. In order to perform a few experiments with a different pressure, the two differential manometers were con- nected to an artificial atmosphere /, as can be seen in the plate. For the further experiments which we intend to make (see § 1) concerning the dependence of the viscosity upon the density, it may appear that where it is a case of relative determinations only, the oscillation method is perhaps the most suitable. 1394 TABLE Il. T?K Mops 107) Ms + 107 /icate. 107 457.3" | 1212 | 1203 1207 373.6" | 1046 | 1050 1052 293.95 | — 887.2 | 886 287.6* | 877 874 875 273.0* | 844 843 843 | 261.2" | 821 814 816 | 255.3° | 802 800 803 | 233.2* | 760 741 1 | | 212.9° 710 697 709 | 194.4" | 670 648 666 | 170.2 | 609.3 | 582 608 | 90.63 | 302.2 | 326 389 [78.2* | 374.2 | 284 | 354] 70.87 | 319.3 | 257 329 20.04 51 58 137 In Table II our results are put together with those of Markowskt and of Kopscn') (the last are marked with an asterisk). Fig. 3 shows that our measurements correspond well with the previous ones. Koprscn’s determination in liquid air forms an exception. The cause of ‘this is probably an insufficient fore-cooling in Kopscn’s apparatus, as it is improbable that the density should have an important in- fluence’) here. In column 3 under »,.10’ are given the values calculated by ScTHERLAND’s formula with 1, = 841.10? and C= 83. The differences become very great at the lower temperatures, in liquid hydrogen more than 100 °/,. Koprsch has already pointed out that Suraerianp’s formula no longer holds for hydrogen at the temperature of liquid air, and although the deviation which he found seems to be partly ascribable 1) H. Markowskt. Ann. d. Phys. 14. 1904 pag. 742. *) Observations for He which will be treated in a following paper, show that there is no such dependence on the density, 1395 1300 1100 + — + al | 900 00 500 ‘ ; ad ie 0 0 100 200 300 72) 506 — OF Fig. 3 to insufficient fore-cooling his conclusion remains correct, as the amount of the deviation of the observations from the formula even at the temperature of liquid air is larger than that of the deviation which is due to insufficient cooling. We endeavoured to find a simple relation between /og 4 and log T, whieh would correspond to the observations better than SurHernANd’s formula. Column 4 under 3.9; 107 contains the values of 4 calculated by the formula T \0.695 — Yo (<3) 1396 The correspondence is satisfactory as far as the temperature of reduced oxygen. We shall return to this question in the following paper about the viscosity of helium, in which we shall farther deal with the change of the nucleus volume 4, with the temperature, as it follows from our experiments. Physics. — ‘‘/nvestigation of the viscosity of gases at low tempera- tures. Il. Helium’. By Prof. Kamrruincu Oxnes and Soprvs Weser. Communication N*. 1344 from the physical Labora- tory at Leiden by Prof. H. Kamertincn Onnes. § 1. Results. With the same apparatus as was used for the investigation of the viscosity of hydrogen *), a series of measuye- 2,15 2,40 2,05 2,90 1,90 1,65 1,40 > fog F i Ee e 1) H. Kamertincu Onnes, GC. DorsMAN and Sopnus Weser: Comm N?®. 134a. 1397 ments were made for helium. According to Reyxo.ps the eritical veiocity would be 2960 ©™/,...; in our experiments the greatest velocity was 105 °m/,.. All our observations are brought together in Table I. The notations are the same as in the previous paper about hydrogen. Again the first two experiments were used for the calibration of the apparatus, for which purpose we assumed as K. Scart ') does, 7, . 10’ = 1887 and C in Sutnerianp’s formula = 78.2. In this way we got the values given under 4, .10°. These were corrected td for the change in — with the temperature and for the gliding. The p corrected values stand in column 7 under 9.10%. As can be seen, most of the measurements were made under a mean pressure of 40 em. mercury. At 20°.1 K. we also took some measurements at 12 cm. mercury pressure. A glance at the table shows that the viscosity does not depend upon the density. TABLE I. Viscosity of helium at about normal density, observations and results. | | eer Te K. | 6 PoemHg PcmHg Fsec. | 4 PomHg (ed Mil in zaseson| 10.63, || 36.81 | 13475 | tse |). — | 1004 294.55 | 7.892 | 44.43 | 13372 | 1.370| — |t | | | | | 250.3 | 9.870 | 42.08 | 9540.5 | 1.539 | 1806 | 1788 | 203.1 | 8.471 | 45.65 | 7828.5 | 1.622 | 1591 1564 | | 170.5 | 8.522 | 42.60 | 7191.2 | 1.851 | 1420 | 1392 ‘| | 89.7 | 10.173 | 41.07 | 3201.0 | 2.709 | 943.7 | 917.9 89.8 | 8.480 | 44.60 | 2933.4 | 2.241 | 945.6 | 919.2 | | | 75.5 | 9.744 | 42.57 | 1828.1 | 1.999 | 9841.8 | 9817.6 | 74.7 | 7.037 | 45.30 | 3220.0 | 2.810 | 938.2 | 813.2 20.17 | 5.121 | 41.61 | 921.1 | 4.600 | 362.5 | 349.9 20.15 | 5.566 | 39.49 | 881.0 | 4.516 | 364.6 | 352.0 20.20 | 4.540 40.10 846.8 | 4.540 | 360.0 | 347.6 | 20.16 | 4.528 | 11.15 | 1788.8 | 2.113 | 362.9 | 351.5 | 20.16 | 4.530 | 12.28 | 1967.2 | 2.573 | 362.0 | 350.7 15.00 | 3.374 | 42.73 | 922.8 | 5.010 | 304.1 | 293.1 | 15.00 | 3.962 | 40.31 | 821.4 | 4.921 | 305.2 | 294.2 15.00 | 1.270 | 41.55 | 1514.1 | 2.981 | 307.5 | 296.4 1) K. Scumirr: Ann. d. Phys. 30, 1909, p. 393. 91 Proceedings Royal Acad. Amsterdam. Vol. XV. 1398 In Table IT our measurements are placed together with those made at Halle by Scnterton and Scamirt, which are marked with an asterisk. From this table and from fig. 1 it can be seen that our results correspond very well with the previous ones. Only Scumirt’s result in liquid air seems to be too high, which perhaps may be explained, as in Kopscu’s experiments with hydrogen, by the gas not being sufficiently cooled before it came into the capillary tube. TASB aU Eas: Viscosity of helium at about normal density and representation of the dependence on the temperature by empirical formulae. TOK Mees 107) Me 107 | Neale: 107 456.8° 2681 2682 | 2632 372.9* 2337 9345 | 2300 294.5 — 1994 | 1982 291.8* 1980 1979 1970 290.7* 1967 1974 1965 250.3 1788 1771 1783 212.2* 1587 1563 1603 203.1 1564 1513 1558 | 194.6" | 1506 1460 1516 | | 170.5 1392 | 1317 1389 | 89.75 | 918.6 | 745 918.5 \[79.9* 894.7 659 852.1] T5o5 817.6 | 628 821.3 74.7 813.2 | 621 815.5 20.17 349.8 | 135 348.9 | 15.00 294.6 | 92 288.7 § 2. Representation of the observations by a formula. In the same table under 2,.10’ the values are given which SuTHERLAND’s for- mula gives with the assumed values of 4, and C. Scumirr has already found that at the temperature of liquid air a distinct deviation appears. For this observation the same is true as we said about that of 1399 Kopscu with regard to the deviation from Sutipruann’s formula of the observations on hydrogen at liquid air temperatures. At hydrogen temperatures Suruerianp’s formula is shown to be entirely unsuitable for expressing our results. It gives a value two or three times too small. We have tried to represent the series of measurements by another formula, and in column 4 under Yay, . 107 we have given the values which we have calculated by the following formula. y ( T ose Meme D7sel As can be seen, this empirical formula agrees remarkably well with the values found over the whole extensive field of temperatures. In a following paper we sball discuss the values for nla Nt ii which follow from our experiments, and further the viscosities at various temperatures for different substances in connection with the law of the corresponding states. Physics. — ‘“Jnvestigation of the viscosity of gases at low tempe- ratures. IIT. Comparison of the results obtained with the law of corresponding states’. By H. KamertincH OnnEs and Sopnus Weser. Communication N°. 134¢ from the Physical Laboratory at Leiden by Prof. H. KameriincH OnnEs. § 1. Dependence of the viscosity upon temperature. We have already discussed this in our previous papers. It was shown that SUTHERLAND’s formula in no way corresponded to the observations at low temperature, either for hydrogen or for helium‘). RermnGANnum’s formula although founded upon acceptable hypotheses about the constitution and mutual action of the molecules, is even worse so long as we regard C in it as constant. This can be easily understood when we consider that SurHerLANp’s formula can be taken as a first approximation to Reincanum’s, and that the terms left out must lead to a further divergence from the observations. Neither is it possible to come to an even approximate agreement at low tem- 1) Shortly after our paper an important article by EvckEn appeared in the Phys. Zeitschrift (April 15th 1913) in which observations concerning the visco- sity of helium and hydrogen taken from an as yet unpublished paper by Voce. were communicated. Within the limits of accuracy, which in Voget’s observations are given at 5°/) at hydrogen temperature, these confirm ovr measurements, of which the accuracy at hydrogen temperatures is to be put at about 1°/). 91* 1400 perature with the empirical correction of Reincanum’s C which RAPPENECKER has suggested. ‘ We might for instance with helium take C= C' 7’ log T, to come io agreement with the observations. But then Remeanum’s formula would simply be converted into our interpolation formula. Krrsom, in Suppl. N°. 25 and 26 of these communications has shown, that the second virial coefficient in the equation of state for hydrogen, at temperatures at which this gas may be regarded as di-atomical, can be very statisfactorily explained by the supposition that hydrogen molecules are hard spheres with electric doublets in the centra. His formula for the virial of the collisional forces under these circumstances gives a change of the radius of the molecule with the temperature, which for higher temperatures agrees fairly LUE At lower tem- yVT peratures at which hydrogen behaves like a monatomic gas, the formula for hard spheres with a central foree according to the law r—¢ becomes applicable, and Krrsom finds this again confirmed by well with that deduced from the viscosity by the change of the viscosity with the temperature. But when we go down to —193° C. deviations appear, in aceord- ance with what we said above about SurHerLAND’s formula, and at lower temperatures the value of the viscosity becomes much too small. : None of the formulas deduced from theoretical suppositions can represent the observations for helium; for the present we can only use our empirical representation for this substance, which for hydrogen also holds good for lower temperatures than the theoretical formulas, viz. as far as the temperature of reduced oxygen. As regards the formula for helium, it is not impossible, that the straight line in the logarithmic diagram must be replaced by one that at low tem- peratures, and perhaps ai higher ones also, curves somewhat towards | greater values of the viscosity. § 2. Application of the principle of inechanical similarity upon the comparison of the viscosities in corresponding conditions. If two substances may be taken as mechanically similar systems ) that the viseosities for both in corresponding conditions must be in a constant ratio which may be calculated from the ratios of the units of length, time, and mass in both systems. On the other hand from the values of of molecules, it follows ' 1) H. Kamertinen Onnes. Verh. Kon. Akad. Amsterdam 21, p. 22. 1881 Beibl. 5. p. 718. 1881, 1401 1 yj — loa 2 °° YT YM where J/ is the molecular weight, 6 the mean radius of a mole- = log 6 — loge cule, as it is effective in viscosity, and ¢ a constant, the same for all substances, we may, when the curves which express the connection between 7 and — are the same, infer the ratio between k the units of length which have to be aseribed to the two mechani- cally similar’) systems. With the help of the viscosity we ean, there- fore, make a comparison of the just defined mean molecular radii and we may inquire how far the ratio found corresponds to that of the mean molecular radii, determined in the way that is necessary in the deduction of the equation of state. If this correspondence were complete, then, when the expression of 6 given above, is ex- pressed in reduced quantities, the curves which express the logarithm of the reduced o as a function of the logarithm of the reduced tem- perature for the various substances, would coincide. The accompany- ing diagram shows in how far this is the case. In the construction Mh Ty's pe/s has been used as the ratio by which the viscosities *) are deduced to the same imaginary system. In this we have taken pe and 7; which hold for the critical state *), as determining quan- tities, and postponed the consideration of deviation functions still later‘). The first thing that strikes one is the great deviation of helium. In § 1 we remarked that the character of the viscosity of helium can be expressed by replacing the constant ce, which may be under- stood as a measure for the attraction between the molecules, in Reincanum’s formula (differing by a constant factor from v in KERsOM’s formula) by c’ T’log 7. Perhaps this points to an increase with the temperature of the quantity which determines the attraction of helium, 1) More correctly : mechanically and statistically similar. 2) H. Kamerunen Onnes Leiden Comm. No. 12, p, 9. 8) The cristical dates we have used are the following. pk (Atm.) Tk Hy 15.0 32°.0 K. He 2.26 5 25 Ox 50.0 155 .U Ng 33.0 127 1 Ar 48.0 150: .7 CO 35.9 132 0 [Note added in the translation], 4) KamertincH Onnes and Keesom. Suppl. No. 23, § 38. The ratios found by Keesom in Suppl. No. 25, p. 12, note 3, give 6°/) deviation for hydrogen and argon, those used here 9 °/o. 1402 KAMERLINGH ONNES was also led to assume a similar increase of the attraction with the temperature, to explain peculiarities in liquid helium, and Keresom in discussing the second virial coefficient of lelium at higher temperatures, found that peculiarities of this coeffi- 0650-1 0250 2,550 0,850 6150 4x50 1408 cient might be ascribed to the same cause; in this case the receding of the attraction sphere (or the greater receding than in other sub- stances) might be the cause of a slighter decrease of the viscosity at the reduction to lower temperatures. There might, however, also be an expansion of the molecule (in this case the atom) with tem- perature, and finally both phenomena might be dependent upon one cause, and go together. The possible small curvature for helium of the line in the logarithmic diagram {that we mentioned in § 1} in the opposite sense to that of the other lines whici expresses the difference between helium ‘and other substances, could be ascribed to this change in the attraction. That which might explain the deviation for helium of the slope of the line from that which holds for a large range of temperatures for other substances, may also possibly help to explain the deviation from Reincanum’s formula at low temperatures, by the quantity which determines the attraction becoming smaller. With hydrogen at the temperature of liquid air there is a distinet change in the slope of the curve. It is remarkable that the same is found with nitrogen, and perhaps also with oxygen and carbon monoxide, and that the point at which it occurs seems to lie at the same reduced temperature for hydrogen and nitrogen and perhaps also for oxygen and carbon monoxide. If this is the case, then the change which in the hydrogen molecules may according to Krrsom be taken as a change from hard spheres with electric doublets into hard spheres’ with a central foree r—q as far as the vis cosity, is concerned would be a similar process for all these different substances, determined by the same units of length, time, and mass as hold for the critical quantities, while this point only coincides with the point of transition in the specific heat of diatomic substances in the special ease of hydrogen. We must further notice the systematic differences between the different substances which appear from the non coincidence of the curves. It is remarkable that most of them (except a part of argon) can be removed by shifting the curves. The mean value of the molecular radius which comes into consideration for the viscosity seems thus to differ from the mean value which comes into consi- deration for the equation of state at the critical temperature, but both are in a fixed relation for the various materials over the whole field of temperature. This might be ascribed for instance, to a more vive the elongated shape of the molecules in substances which g¢ smallest viscosity. 1404 Physics. — “Maynetic Researches. VIII. On the susceptibility of gaseous orygen, at low temperatures’. By H. KAMERTANGH ONNES and E. Oosrernurs. (Communication N°. 134d from the Physical Laboratory at Leiden.) Communisated by Prof. H. KamERLINGH . ONNES. § 1. The susceptibility of compressed oxygen between 17° C. and temperatures near the critical temperature of oxygen. In our last paper in connection with our investigations of various cases in which a molecular field of Wess with opposite sign can be assumed with paramagnetic substances, we mentioned the continuation of the experiments by KamertincH Onnes and Perrier whieh have already been projected and the continuation of which may soon be expected, and which have for their object to investigate the influence, with oxygen, of bringing the molecules to various densities upon the deviations from Ctrie’s law. Working in the same direction, we have endeavoured to ascertain whether in gaseous oxygen below the ordinary temperature and above the critical temperature a 4 appears. For this purpose we have measured the susceptibility of oxygen between 17°C. and — 126°.7C. We used the attraction method in the same form as described for the paramagnetic salts in our previous paper. A copper tube, closed underneath, 10 em. long, 8 mm. external and 6 mm. internal diameter, provided with a capillary tube above, by which it could be filled with oxygen under pressure, and closed, one time with a fine tap in which the capillary tube ended, another time by pinching this capillary, and then soldering up after it had served for filling, was filled with oxygen at ordinary temperature to 100 atmospheres. The experiment was then repeated with the evacuated tube in the same baths. For results: (see table I p. 1405). The experiments should be regarded as comparative for the question under consideration, but the absolute value of the susceptibility was- also determined at 289°.9K. It corresponds pretty well to that of Weiss and Piccarp. As manometer we used a metal manometer which was compared with a hydrogen manometer going to 120 atmospheres. The density of oxygen was taken from Amagat. 47 appears to be constant, within the limits of accuracy (which is about 1°/,.) as far as the boiling-point of ethylene (169°.6 K.). The two points in ethylene, evaporating under reduced pressure, deviate a little, but this need not be considered as of much importance, as these temperatures were not accurately known. Moreover the proximity “1405 of the critical temperature made the distribution of density in the tube uncertain. We may draw the conclusion that within the limits of accuracy TABLE I. Gaseous oxygen ( N= 100) H=10 to 18 kilogauss. | T 7.108 | x. 7.108 Bath. | 280.9 K, 105 | $04 | In air. | | } 249.7 121 302 | Liquid methyl], PNA | 142 301 chloride. 169.6 179 304 | | Liquid [157.7 188 296) | | | \ ethylene. [146.6 | 201 295] | 1406 in the measurements a 4 does not yet appear in oxygen above the critical temperature at densities which are 100 times the normal. From this it seems all the more probable that 4 only appears for oxygen at great densities, and in liquid oxygen can rise to the considerable value of 71° as the density rises to 1000 times the normal. In the accompanying figure our observations concerning gaseous oxygen and those of Kamertinca Onnes and Perrrmr which we confirmed in our last paper, are combined in a graphic represen- tation; the uncertain points near the critical temperature are not given. The point of intersection of the line for gaseous oxygen with the production of the line for the liquid state, appears to have no physical meaning; as we supposed in our last paper, it is due to the value of the constants, that the temperature which indicates the intersection of these lines happens to be about the ordinary one, at which amongst others, the observations of Wetss and Piccarp fall, and helow which as yet no observation had been made for gaseous oxygen. (To be continued.) Physics. — “Further experiments with liquid helrum. H. On the electrical resistance of pure metals ete. VUL The potential difference necessary for the electric current through mercury below 4°19 Kk.” By Prof. H. Kamertincu Onxes. Communica- tion N°. 138a and 1334 from the Physical Laboratory at Leiden. (Communicated in the meetings of February 22 and March 22. 1913). § 1. Difficulties involved in the investigation of the galvanic pheno- mena below 4°19 K. In a previous Communication (No. 124¢ of Nov. 1911) we related that special phenomena appeared when an electric current of great density was passed through a mercury thread at a temperature below 4°.19 K., as was done to establish a higher limit at every temperature for the possible residual value of the resistance. Not until the experiments had been repeated many times with different mercury threads, which were provided with different leads chosen so as to exclude any possible disturbances, could we obtain a survey of these phenomena. They consist principally herein, that at every temperature below 4°.18 K. for a mercury thread inclosed in a glass capillary tube a “threshold value”, of the current density can be given, such that at the crossing of the “threshold value’ the phenomena change. At current density below the “threshold value’ the electricity goes through without 1407 any perceptible potential difference at the extremities of the thread being necessary. It appears therefore that the thread has no resi- stance, and for the residual resistance which it might possess, a higher limit can be given determined by the smallest potential difference which conld be established in the experiments (here 0.03.10~-§ V)and the “thresbold value” of the current. At a lower temperature the threshold value becomes higher and thus the highest limit for the possible residual resistance can be pushed further back. As soon as the current density rises above the “threshold value’, a potential difference appears which increases more rapidly than the current; this seemed at first to be about proportional to the square of the excess value of the current above the initial value, but as a matter of fact at smaller excess values it increases less and at greater excess values much more rapidly. It appears that the phenomena at least for the greater part are due to a heating of the conductor. It has still to be settled whether this heating is connected with peculiarities in the movement of elec- tricity through mereury, which for a moment I thought most pro- bable in connection with various theoretical suppositions (comp. § 4), when this metal has assumed its exceedingly large conductivity at low helium temperatures; or whether it can be explained by the ordinary notions of resistance and rise of temperature of a conduc- tor carrying a current, perhaps with the introduction of extra nume- rical values for the quantities that influence the problem. A further investigation of this with mercury in the most cbvious directions, such as cooling the resistance itself with helium, presents such diffi- culties that I have not pursued if, as it would not be possible to prepare the necessary mercury resistances by the comparatively simple process of freezing mercury in capillary tubes. When I found (Dee. 1912) that, as 1 shall explain in a following Comm., (see VIII of this series Comm. N°. 132d) tin and lead show properties similar to those of mercury, the investigations were continued with these two metals. Thus the experiments with mercury which are described below may be regarded as a first complete series. Various circumstances combined to make even the investigation of the mercury inclosed in capillary tubes difficult. A day of experi- ments with liquid helium requires a great deal of preparation, and when the experiments treated of here were made, before the latest improvements in the helium circulation were introduced, there were only a few hours available for the actual experiments. To be able to make accurate measurements with the liquid helium then, it is necessary to draw up a programme beforehand and to follow it 1408 quickly and methodically on the day of experiment. Modifications of the experiments in connection with what one observes, must usually be postponed to another day on which experiments with liquid helium could be made. Very likely in consequence of some delay caused by the careful and difficult preparation of the resistances, the helium appa- ratus would have been taken into use for something else. And when we could go on with the experiment again, the resistance sometimes became useless (e.g. § 3) because in the freezing the fine mercury thread separated, and all our preparations were labour thrown away. Under these circumstances the detection and elimination of the causes of unexpected and misleading disturbances took up a great deal of time. § 2. Confirmation of the sudden disappearance of the resistance at 4°.19 K. and first observations concerning the potential phenomena at low temperature. The first experiments which showed the pheno- mena to be discussed were made in October 1911, with the resistance described in the previous Comm. (N°. 124c). «. Before discussing them let us consider for a moment the measurements which were made with this resistance at 4°.23 K. and add something to what we said about them in the previous Comm..). In the measurements which we are considering we could take ad- vantage*) of the presence of Hy, to measure the portions between Hg, and Hg, and between Hy, and Hg, separately and afterwards the two in series. The result was Hg,Hg,=0.05182, Hqg,Hg,=0.06172, together 0.1185 2. This gave a necessary check on the determination of the twoin series Hg, Hg, = 0.1142 2%). These values, considering 1) For a survey of the observations concerning mercury at the lowest temp. in three figs. with rising scale the reader is referred to Rapport du Comité Solvay, Noy. 1911, fig. 11, 12 and 13 (in which read 13 for 12, and 12 for 13, Leiden Comm. Suppl. N 29). ; 2) The measurements with a view to which the tube Hg, was added (see Plate I in Comm. N° 124c) were not made then, but postponed till later. (See § 5%. They were to enable us to judge of the dependence on the section. 8) The resistance at the boiling point of hydrogen was 3.27 ©. A further Comm, will refer to the difference of the ratio of the values at 273° K. and 20° K. to those in previous measurements, which is here of no consequence and is due to different ways in which the mercury freezes. In the experiments described here. similar differences were constantly found. It should be mentioned that the glass was tested at all temperatures for its insulation and also that when the potential difference at the terminals was found to be zero, it was always ascertained that the resistance of the galvanometer circuit which served to measure the P. D. had not changed materially. 1409 that they belong to about 65 2 (calculated for solid mercury at Oo C.) correspond pretty well to the results obtained in the experiments in May 1911 Comm. N°, 1224, July 1911, viz. that a resistance of about 40 2 (ealeulated for solid mercury at 0° ©.) becomes 0.084 2 at the boiling point 4°.25 Kk. 8. In these experiments the validity of Onm’s law was confirmed above the point where the almost sudden disappearance of the resistance begins which was treated in the previous Comm. by one measurement at a current strength of 3 and another of 6 milliam- peres which within the limits of accuracy gave the same result (0.0837 at 3, and 0.0842 at 6 m.A.). In connection with the expe- riments in Comm. N°. 1224 July 1911 we may mention that they were made with a resistance of a different kind from that’) which was used for the experiments in Oct. 1911, viz. the one which appears in the Plate of Comm. N°. 123 as Qy, (of about 40 2 calculated for solid mercury at 0° C.). Narrow tubes alternately going up and down were connected by expansion heads (as in the Plate in Comm. N°. 124+) and connected to platinum leading wires by fork-shaped turned down wide pieces*), which can be seen distinetly on magnification on the Plate in Comm. N°. 123 (where the resistance is shown in the cryostat). y. After this digression about the change in the resistance between ordinary temperature and the boiling point of helium, let us return to the experiments in and below the region of the sudden fall of resistance, which as has been said at the beginning of this § were made with a mercury resistance with mercury leads, and which were treated of in § 3 and fig. 1 of the previous Comm. (Dec. 1911) about the resistance at helium temperatures (experiments of Oct. 1911). 1) This was a ramification of solid mercury threads consisting of a U divided at both ends, allowing measurements as well by the method of Carenpar as by the potentiometer method. (Note added in the translation). 2) In the resistances which were used for the first experiments with mercury, the platinum leading in wires were simply sealed into the wider portions of the resistance tube at the ends (the expansion heads). When the mercury cannot be poured into the tube in vacuo but has to be boiled in the tubes in order that they may afterwards be exhausted without any chance of the mercury separating there is some fear of platinum amalgam being formed which might penetrate into the current circuit. In order to prevent this the wide ends of the tubes are according to a suggestion of Mr G. Housr, made fork-shaped, the prongs which contain the sealing place being turned down. In this manner mercury leads may in general be replaced by platinum leads without any trouble being experienced with regard to the resistance of the current circuit. By a comparison with experiments with mercury leads it had been found that the mercury-platinum contacts could be allowed in the potential circuit 1410 At 4°.20 K. we find ourselves in the higher part of the almost sudden change. In the case that we are now about to treat it had almost become complete. With a current of 7.1 m.A. it was a con- siderable time before the condition became stable. When this had taken place, the resistance of Hy, Hy, was found to be 0.000746 & °). At a further cooling of the mercury to 4°.19° K. with the same strength of current the result was only //y,Hg, << 14.10 &. J. At 4°.19 K. we come into the lower part of the region with which this Comm. deals in particular. The strength of the current had to be increased to 14 m.A. to give a perceptible potential difference at the ends of the resistance but even then it remained doubtful. It became distinct at a current strength of 0.02 amp. and was then 2.5.10—-5 V. At 0.023 amp. it became 5.10—° V, and at 0.0288 amp. 163022; When the mercury thread was cooled by helium which evaporated at a mercury pressure of 40 cm. that is at about 3°.65 K., with a strength of current of 0.49 amp. there was no potential difference to be observed at the extremities, the current had to be increased to the threshold value of 0.72 amp. to make the potential difference observable. «. The highest limit of the value which the residual resistance ‘an have in the case of the lowest temperature, is therefore in these last experiments again considerably reduced by the application of stronger currents, viz. in this case (3°.65 K.) to 10—-° of the resistance at O° C. (ecalenlated for solid mercury) while in Comm. N°. 1225 June 1911 at 3° K. it could only be put at << 10—". § 3. Appearance of the same potential phenomena in a revised arrangement of the experiment. The appearance of the peculiar pheno- mena immediately above the “threshold value” of the current, gave rise to the question whether the just established limit would not have to be put lower when it should be possible to avoid the dis- turbanees, which might still exist, and perhaps showed themselves in the above mentioned phenomena. The most obvious thing in the first place was to prevent the possibility with great current density of heat, developed in places in the main circuit where the temperature is higher, penetrating to the resistance that is being measured. By this, from both ends, the thread would be brought over part of ') Here and in the following we speak repeatedly of resistance, without wishing to give it beforehand any other meaning than: calculated by Oum’s law from the strength of current and the potential difference observed, 1411 - its length above the vanishing temperature, which would immediately ‘ause considerable potential differences. In this connection we thought particularly of Jove heat. PeLtier heat, which we had noticed before (Comm. N°. 124c) but which for the present we attributed to impurities in the mereury in the legs, and assumed to be present only in the neighbourhood of the transition from solid to liquid, I took to be as far as possible excluded by the fact that the whole current system was of pure solid mercury at the very low temperatures. Now this belief may be untrue, because owing either to tension caused by a difference of expansion to that of glass which it seems can be fairly great as the mercury sticks to the glass, or through the contact between crystals of different kinds or sizes, even in the purest mer- cury considerable thermopowers may possibly appear. But then they have their seat, as shown by the previous experiments, chiefly in places above the temperature of liquid air and Perrier heat in these places need not be feared. To avoid disturbances of the sort to whieh we referred the experiment was repeated with resistances of such a kind that the conduction of any kind of heat from a part of the apparatus where there was higher temperature was made very difficult. The accompanying figure, which should be compared with figs. 1 and 2 on the Plate in the previous Comm. N°. 124¢ (VL of this series) shows the form chosen. The mercury threads which lead the current to and from the apparatus, run first through the liquid helium downwards, before they come out into the widened parts of the resistance. The potential wires do the same‘). Close to the surface of the liquid the leading 1) Corresponding parts are indicated by the same letters, modified parts by the addition of an accent A small additional improvement was further introduced into the contacts at the upper end, the four leading tubes were simply left open 1412 wires can be thin on account of the low temperature. There were two resistances of the same kind in the cryostat, one of 50 2 and the other of 1380 2,. the section of the tubes was about 0.004 mm? and 0.0015 mm?*. They were intended to investigate the influence of the section of the tubes upon the phenomena examined, a thing that had been aimed at already before (see § 2) but did not succeed and the preparation of the narrowest one in particular had given great difficulties. It gave way during the experiment, so that the question of the influence of the section had again to be solved later on (see § 5). The experiments which were of chief importance for the matter under consideration were made in Dec. 1931 with the sinallest of the two resistances, the section of the narrow resistance tube was here a litthe smaller than the mean in the resistance which was used for the experiments in Comm. N°. 124c. On the whole the results were the same as by previous measure- ments. Although great care’) was again given to the distillation of the mereury with the help of liquid air?), the mercury legs, as has (which made it easy to add mercury which the contraction during the freezing made necessary), and bell-shaped tubes Hgt were placed over the extremities in which the platinum wires Hg' ete. are sealed, which connect the resistance to the current sources and the measuring apparatus. Platinum amalgam (see note 2, p. 4) need not be feared in this case, so that the complication of the inverted forks was superfluous. We do not need here to enter into particulars of precautions such as the protection of contacts against changes of temperature, and others which have reference to the special circumstances under which the resistance measurements were made () () 1) In § 9 it is demonstrated that in repeating the experiments | 16 A . } a} |é rot so many precautions would have been sufficient. 2) In the distillation the mercury was not heated above 65° and 70° C. while the cooling was effected with liquid air. In order not to have to wait too long to procure a sufficient quantity it was done in an apparatus shown in fig. 2 at 1/g of the actual size. The mercury is brought into the double walled tube a b wer (with the reception beaker c), which was sealed off below at e. — It is exhausted through tube @, while the mercury is warmed and then sealed off at f. .— The lowest part is immersed in warm water; in the hollow a liquid air is poured. In 3 hours about 2 cm® goes over; the Fig. 2 condensed mercury in ¢ is afterwards poured out at /. g. 2. 1415 been observed, gave considerable thermo-power; the legs with the smallest thermo-power were chosen as potential wires‘). There was some indication that the resistance of the mercury in narrower tubes falls a trifle less than in wider ones, when the tubes. are cooled to 4°.25 K. (boiling point of helium). The new experiments also raised the question whether the almost sudden changes were found at a slightly different temperature of the bath in the narrower than in the wider tubes. But all this concerns particulars which can probably be explained by differences of erystal- lization and of heating by the current. That the almost sudden change begins at 4°.21 K.*) and ends i ASB Bt Potential difference of the extremities of mercury threads carrying a current. Current eerie amperes Potential difference in microvolts epee Wee ek leaks || October 1911 December 1911 October 1911 | December 1911 1=1><20em | 1= 20cm 0.49 S< 190 0 0.510 < 260 0 0.56 0 3°.65K. 0.665 | 0.5 0.72 71.14 | | 0.890 | 4.7 1.10 AL 0.010 0 0 0.014 7X 0.017 0.016 | 0.4 4°. 19K. ¢ 0.020 1X 0.36 0.023 w> enter through the sentinel wires, and these could only become dangerous to the experiment after betraying a heating above the vanishing point by showing a potential fall. On the ground of the experience in the last experiments, the connecting wires carrying the current in to the resistance (compare ihe diagrammatieal fig. 4 and the perspective fig. 5) were again of mereury, in order to prevent Jovy heat being transported to the resistance, while sealed in platinum wires to which copper wires were soldered served as potential wires. The sentinel thread A had 1421 at the ordinary temperature about 35 2, the sentinel thread 4 about 36 @ resistance, the resistance C’ consisted of five threads in series of about 80 @& resistance each and with a combined resistance of about 390 2 at ordinary tempe-:ature. At the boiling point of helium Ws, = 0,01831 2, Wz = 1.01285 2, We = 01773 &. The observations were as shown in Table IV. We had therefore not sueceeded, as had been our intention in giving a larger section to A and & than to C, in managing that if C should show potential difference, it would do so before A and Lb did it. Only if this had-happened it would have been shown that the heat that brought C’ to a temperature above the vanishing point was developed inside C. And the potential which now appeared in C can again be ascribed to heat conduction through A. The expe- riment shows very clearly that accidental circumstances in the freezing of the mercury threads play a part in the determination of the “threshold value” of the current density, and that in caleu- TABLE IV. Resistance of a mercury thread just below 4°.20 K. =r2 = 0.0025 mm2 for We | Ysa | “sp | We (femp:|—————__ | |current density 2.5 Amp. p. mm2 in We | == 1 4°,24 | | 0.163 2 | 4 .234 | 0.161 | 4 .230, 0.011 0.158 4 .222) 0.0078 0.0774 | 4 .208 0 0022 0.0025 0.00775 | 4 -192) 0 000024 0.000024 | 4.185 0.000012 < 10-6 | current density 12 Amp. p. mm2 in We | posal Sa ae | 4 .185) 0.000071 | 0.000153 | <10—* ‘current density 20 Amp. p. mm2 | in We “4.185, 0.000117 “0.000048 1422 lating with the average section of the tube in which the thread is frozen, only a lower limit can be given for this. Possibly the mereury in A and & was only frozen in an unfa- vourable form, and therefore greater local current densities or worse exchange of heat had arisen than the average. § 7. Repetition of the experiment with the same apparatus. We obtained more favourable results from another freezing. First a few results may be given, which were obtained by measurements at different strengths of current at 4°.25 K., that is at a temperature above the vanishing point. These results gave an opportunity of judging to what degree heat can be given off by the mercury thread closed up in a glass capillary or flows off along the extremities. From the increase of resistance at greater current strength, the rise of temperature was deduced on somewhat simplified suppo- sitions, at which the equilibrium between the JouLe heat and the heat given off to the outside is established. The result for the resis- tance and the average rise of temperature of C was: current resisiance rise of temp. 0,006 amp 0,1928 O27 0,006 ,, 0,1932 0°, 0,306" 5: 0,2149 0°12 0,500, 0.2410 0°,25 The average rise of temperature was calculated by the formula got by separate determinations Wr= Ws( + 0.9(T — T,))) in which 7; represents the boiling point of helium. It follows from these determinations that per degree of difference of temperature between mercury thread and bath 0.057 calorie is given off per second. If we assume that all the heat goes through the glass, that the mercury touches the glass everywhere, and that we only have to consider the narrow capillary, then we find with d; = 0.056 mm, d= 2.07 mm, /=100 em, for the conductivity of glass (= 0.00033, while at ordinary temperature 4 = 0.0022. The loss of heat through the glass must therefore by cooling to the boiling point of helium have become much less than at ordinary temperature, which might possibly be the consequence of the mercury only touching the glass at a few places besides in the bends. 1) See the fig. in Comm. No. 124. Dec. 1911. 1425 The application of the data obtained at temperatures below the vanishing point is in the nature of the matter uncertain, as we do not know whether, with the galvanic change in the mercury, there may not be another change in the thread, which would bring about a further change in the giving off of heat. With regard to the appearance of potential differences at the extre- mities of the thread, we found the data contained in Table Y. At 8°.6K. the current at which a potential difference would appear in the sentinel wires could not be measured, as, before the eA Bek Ew Vs Strength of current at which the potential difference appears at the extremities of a mercury Wire carrying a current below 4°.2 K. xr2— 0),0025 mm2 for C. | Temp. A B (S 42.18 K | 0,0535 0,0615 0,084 4. 10 | 0232 | ogi7 | o72 | 3. 60 | 1.068 | 3, 28 1,646 | 2, 45 | e256 | current had reached this value, the resistance C was heated toabove the vanishing point along too great a length. What we were aiming at was however attained in these experi- ments of Feb. 1912. It is established that heat is produced in Cby raising the strength of current sufficiently, and that the heat is not conducted to it from A and JB, since A and B were at a lower temp. than the vanishing point as appeared by the absence of poten- tial fall in them. It is developed in the thread Jtself, Table VI may be subjoined concerning the experiment at 2°.45 k. corresponding to Tables I and IIL. At the same moment that the galvanometer which measures the potential difference at the extremities of the thread is deflected, the strength of current in the main circuit falls from 7 = 2.84 amp. to ¢= 1.04 amp. which corresponds to an increase of resistance A W = 2.44 2 in the circuit, from which it appears that the resistance is heated nearly to the temperature of hydrogen by the remaining current, of 1 amp. nearly. 1424 If we take the last described experiments together, we have been able by them on the one hand to raise the current density to the enormous value of about 1000 amp. per mm*, without any heat being developed in the wire. This threshold value for TABLE VI. Potential difference at the extremity of a mercury thread carrying a current below 4.°2 K. =r2 = 0,0025 mm2 current density | potential diff. Temp. in amp. per mm. in microvolts 20.45 K. 944 < 00 A 1024 0.56 | » | 1064 | 1.5 | | 5 1096 6.3 “n 1120 very large | the current density brings the highest limit for the possible resistance of mercury in the peculiar condition into which it passes below 4°.19 K. and particularly when it is cooled to 2°.45 K. still further back, and the ratio of the resistance at 2°.25 K. to that of solid TEASE 910-0, 2730 K On the other hand it is proved that the development of heat which appears at a still higher strength of current, has its origin in the thread itself. mereury at 273° K. becomes . § 8. Influence of the current density upon the manner in which the resistance in mercury threads disappears. What has been related - above can all very well be reconciled with the view (see § 5) that the disappearance of the ordinary mercury resistance at 4°.19 K. occurs quite suddenly, and in a thread that has been cooled to below that temperature, as soon as the “threshold value” of the current density is exceeded, somewhere heating occurs. which carries the thread at that place to above that temperature, at first over a scarcely perceptible length but at higher currents over a rapidly increasing distance, by which ordinary resistance is generated in this part of the wire. With these larger currents the thread then comes in astate 1425 On which there is no uncertainty, it assumes over its entire length the new temperature equilibrium of a thread carrying a current, which equilibrium is determined above the vanishing point in the usual way. In order to improve the comprehensive view that may be formed on the ground of Table IV combined with Table IL in which latter the different current densities do not refer to the same wire, further experiments were made in June 1912, which show how with the same thread the resistance disappears at different current densities. The thread had a_ section of about ae mm?*., at the boiling point of helium the resistance was 0.1287 £. The experiments were made with a falling temperature, with current densities of 1.2, 000.10 aa amp 1 uel | = — $00} + 7 i | | ay | Nog aan i | 4a 1 | — = | | | | | |} Id! | so} — Pele te a haa tae | | J on ctinya, fa-gusamnge SQvamyp —|d4gnvamg i | 200 = =I } lp ear irae ee 5 a A | ii | t | (ay a a Et AE Wee Se 100 p—j+ | | | /\ / | } | yp d | | Spe l 0 Ae | —=} ° Peeot 1. i ;, Pe} 30 00 10 0 r=) 40 20 0 ae foots 5” 1000 F8-F ) ) : Fig. 6 Fig. 7 13 and 130 amp. per mm’. (sirength of current 4, 40 and 400 milliamp.). The phenomena are shown in the accompanying figs., upon which the numerical values are distinct enough to make it unnecessary to print a table. Fig. 6 allows a comparison between the phenomena at 0.004 amp. and 0.04 amp., fig. 7 at 0.004 amp. and 0.4 amp. The ordinates represent the potential fall in microvolts divi- ded by the strength of the current, expressed in 0.004 amp., the abseissae the difference of the temp. 7’ with that of the boiling point 7, = 4°.25 K. in thousandths of a degree. The unit of the scale of the abscissae in fig. 7 is five times as large as in fig. 6. At 0.04 amp. the curve continues with diminishing values of the ordinate to lower temperatures than are shown on the fig.; at 4°.11 K., when the experiment had to be stopped, the resistance was not quite 0, we found 0.2.10-6 V7. The intersection with the 1426 horizontal axis in fig. 7 is probably drawn too sharp; at 3°.96 K. the potential difference was < 0.03 .10-° V. The whole gives’ one the impression that the lower temperature of the bath at greater strength of current is required (a comparison of 0.004 and 0.04 amp. shows that an almost constant shift of temperature would change the potential differences per unit of current in the one case into those of the other) to cool the part of the thread that has an ordinary resistance strongly enough to prevent it imparting its temperature to the part which is below the vanishing point, and to prevent the temperature in the latter part from being raised above the vanishing point by the greater local development of heat. With the same thread in the manner of table III the results of table VII were found, in which experiments are included with a second thread with a section of about 0.012 mm’. It appears that in the thread I7,, to which the experiments just quoted refer, local heating takes place more easily at the same current density than in W,,, (see § 5). The fact that the latter thread gives off heat more readily also explains why in JW,,, a greater current density checks the disappearance of the resistance less than in the case of W, (June 1912). As regards the threshold value of the current density for different temperatures with the same thread, it would seem from Table VII and Table V roughly speaking to change linearly with the temperature, TABLE Vit Potential differences at the extremities of mercury threads carrying current Current density in Potential difference amp. per mm?®. in microvolts Temp. : = | , | , | i LA Wi a i | —_———| 3.°6 K 129 e065 141 very large 363 0,3 412 3,8 | 429 12,1 431 very large a | — et 1427 if the fall below the vanishing point is not too small, and if we leave out of account a term for Jounk heat which only appears distinetly at a higher current strength. This naturally suggests that we are dealing with a Prrripe-effect raising the temperature to the vanishing point of resistance (e.g. connected with different forms of crystallication or tensions); (the simultaneous cooling of the opposite contact has no effect on the resistance which is already practically zero and remains zero when further cooled). As regards the threshold value of the density at a given temperature for different threads this appears (comp. § 6 and Table IV) to be rendered uncertain by accidental cireumstanees. But it deserves notice that it was also found very high in very narrow capillaries. § 9. Experiments on impurities as a possible source of disturbances. Although the greatest care was always bestowed upon the purifica- tion of the mercury, the explanation of the appearance of a residual resistance that offered itself the first for closer investigation was the influence of impurities. These may give an “additive mixture resistance’ to the metal which changes little with the temperature and is proportional to the amount of impurity. To such an additive resistance I ascribed the fact (Comm. N*. 119 and Leiden Suppl. N°. 29) that the resistance of very pure platinum and very pure gold did not disappear at helium temperatures as I expected with absolutely pure metals. Now the experiments had realized the expectation, that mer- cury could be so far freed from impurities, as to make the resistance practically nothing. but if one may judge by the additive resistance which even very pure gold exhibits, then with the residual resistance of mercury which is only perceptible at the threshold value ot current density for the lowest temperatures, it would be a question of an impurity of the order of a millionth of the trace that could possibly be present in the most carefully purified gold. And it was a priori doubtful if the mereury could be procured in so much ereater a state of purity than gold. ’) The experiment was therefore repeated with solid) mercury in which I believed a very small quantity of an other metal to be present. After being distilled in a vacuum by means of liquid air, the mereury was in one case brought into contact with gold and the other time with cadmium, after which if was mixed with a larger quantity of pure mereury. To my surprise with the mercury 1) For difficulties inherent in the supposition of a resistance equally distributed throughout the thread which apply also to our present case of additive mixture resistance see § 11. 1428 that had been treated in this way, the resistance disappeared in the same way as with pure mercury’); much of the time spent on the preparation of pute -mercury by distillation with liquid air, might therefore have been saved, without the experiments on the sudden disappearance of the resistance which were made with mercury prepared in the ordinary way with double distillation giving other results. Even with the amalgam that is used for the backing of mirrors, ihe resistance was found O at helium temperatures. (Later Dec. 1912) it was found that it disappeared suddenly, as with the pure mercury but at a higher temperature. *) Where the influence of impurities, in the form of mixed erystals in the solid mercury, seems to retire into the back ground, the next most natural supposition is that less conductive particles, sepa- rated out of the mercury during the freezing, or coming amongst the mereury erystals in some other way, bring a resistance into the path of the current. But if we do not assume that a thread of per- fectly pure mercury can possess a residual resistance itself, this theory of ‘the origin of the potential differences is not very probable, because in a resistance-free path of current, only by a closing of the whole section by an ordinary conductor resistance is produced. Particles of the sort we mean, as also other casual circumstances, for instance the manner of freezing and small cracks, can influence the magnitude - of the threshold value of the current density derived from the ex- periments, but the values found for this quantity. although they vary, differ so little, that in addition to the causes mentioned we must assume for a /hread of pure mercury the existence of a residual resis- tance which we will eall a “microresidual” resistance, to distinguish it from the ‘additive mixture” resistance to be attributed to impurities. § 10. Experiments on the possible injluence of contact with an ordinary conductor upon the superconductivity of mercury. In the reasoning that we have just given it is assumed that the laws of current division between two conductors which touch each other also hold when one of the conductors consists of mercury below 4°19 K. But this assumption might not be correct. In the line of 1) Perhaps nol even a quantity of the order of a thousand millionth of zine or gold is absorbed in solid mercury. The application of the sensitive test of the disappearance of the resistance may be of value for the theory of solid solutions. Of course in our argument we only deal with absorption in a form which comes into consideration for the resistance (mixed erystals). 2) This part of the text is changed in accordance with the facts see § 13 y in VILL of this series, 1429 thought of § 4 and taking into account the heat motion which takes the electrons now to the inside and then to the surface of the conductor, a pushing forward of the electrons in the galvanic current through a super-conductor without performance of work seems only possible, when its surface only comes into contact with an insulator, which reflects the electrons with perfect elasticity. If the electrons can hit against the atoms (or more accurately the vibrators) of an ordinary conductor, they will of course give off work in this collision. Thus a thread of super-conducting mercury, if an ordinary condueting particle were present anywhere in the current path, could show resistance at that spot, even although the particle did not entirely bar the section which was otherwise free from resistance. These considerations lead to the following experiment. A steel capillary tube, supplied with connecting pieces in which were platinum wires for measuring the resistance, was carefully filled with mercury at the air pump. The measuring wires were immersed in the mereury, without touching the current wires. According to the ordinary laws of current distribution the resistance of this composite conductor should disappear below 4°.19 K. Whether the mercury is in a glass or a metal capillary makes no difference to the conduction. Thus for instance, if one was to coil up such a steel capillary filled with mercury, and press the coils against each other without insulating them, the coil could still serve as a magnetic coil below 4°19 K.; the coiled up mercury thread would be resistance-free, and the steel would take the part of the insulator, which otherwise separates the different windings of the current path in a magnetic coil. On the other hand if the above reasoning is correct, a mercury thread, that is provided with a close fitting steel covering should retain its resistance below 4°.19 K. though the current is lowered below the threshold value. In several experiments with the above mentioned steel capillary, in accordance with the last conclusion, the resistance of the mercury thread did not disappear. Yet we must not conclude from this that the remaining resistance is given to the mercury by the contact with the steel. There only needs to be one little gap in the mereury which extends over the whole section, to cause the appearance of ordinary resistance of the amount according to the potential diffe- rence. If the resistance had disappeared in the experiments, there would on the other hand have been room for the question whether there had been contact between the steel and the mereury. With mercury in a steel capillary the result of the experiment remains always doubtful. We may therefore mention here, that afterwards 9 Proceedings Royal Acad. Amsterdam. Vol. XV. 1430 when it was found that the resistance of tin disappeared suddenly too, we succeeded in making a less doubtful experiment than is possible with mercury, with a flattened out constantan wire, which was covered with a thin layer of tin’). The resistance of the layer of tin disappeared with a weak current and at a low temperature, while the constantan remains an ordinary conductor at that tempe- rature. Thus we may for the present adhere to the usual laws of current division, and in this extreme case continue to assume that in so far as the appearance of the potential difference is to be explained by a local heating in consequence of a local change in difference of the chemical nature of the conductor from pure mercury this disturbance must extend over the whole section of the current path. Thus the conclusion drawn in § 9 concerning the probability of the existence of a micro-resistance remains valid. (To be continued). Physics. — “The radiation of Radium at the temperature of liquid hydrogen’. By Madame P. Curie and H. KAMERiINGH ONNEs. Communication N°. 135 from the Physical Laboratory at Leiden. One of the most remarkable peculiarities of radio-active substances, is that the radiation is independent of the temperature. Neither do the radio-active constants change with the temperature. These two facts are related to each other; they prove that the radio-active transformations are net affected by the influence of temperature, Which plays such an important part in the chemical transformation of the molecules. According to the theory of radio-active transformations, the intensity of radiation of a simple substance is proportional to the rapidity of the transformation, so that a change in one of these quantities involves a change in the other. The experimental investigations of the influence of temperature have been concerned with the measurement of the radio-active constants and the intensity of radiation of certain substances. P. Curie has shown that the law of transformation for the emanation does not change at a temperature of 450° C. nor at the temperature of liqnid air*). Various observers have proved that the penetrating ') It is to be noted, however, that the current density in the thin layer had to be made very weak Comp. the following part of this Communication VIII, § 16, ) P. Uurte, C. R. 1908. 1431 ‘adiation of radium and uranium have the same value at ordinary temperature and at the temperature of liquid air’). The influence of high temperatures on the radium emanation and its transformation products, particularly Radium C, has also been the subject of various investigations. The results have given rise to differences of opinion. Nevertheless it would seem to be justifiable to conclude that the dependence upon temperature which was observed in some cases must be attributed to secondary phenomena of less importance, and that the radioactive constants of the above substances are not appreciably altered when the temperature is raised to 1500° *). As the question is of great importance it was desirable to extend the results already obtained, by exiending the experiments over a wider range of temperature and by increasing the accuracy of the measurements, which in the above mentioned investigations could not have been greater than 1°/, at the most. Our object was to descend to the temperature of liquid hydrogen. By using 2 compensation method we were able to determine very slight changes in the radiation intensity. Our measurements were concerned with the penetrating radiation of radium. The results, within the limits of accuracy which may be placed at 0.1 °/,, do not confirm the existence of a quickly acting influence upon the radiation, in consequence of this strong decrease of temperature. The investigations were made in the first part of 1911. The preliminary measurements were partly made in Paris, and partly in Leiden, while the final measurements took place in Leiden in July 1911. We intend to continue and extend the experiments, which is the reason of the publication having been postponed. But as the continuation of the work has been prevented so far by the long indisposition of one of us, we thought it best not to wait any* longer in publishing our results. Apparatus and arrangement of the measurements. After some preparatory experiments we decided to vse the following apparatus. The apparatus consists of a vacnum glass A, in which a copper vessel £ is placed, which contains the low temperature bath. The vacuum glass, which is fairly wide at the top (a,) consists underneath of a tube-shaped portion, the length of which is about 16 cm. and the two diameters 8,5 and 138 mm. The copper vessel - which fits into the vacuum glass, is also provided with a tube- 1) BecqueweL, Curte, Dewar, RutHerrorp. 2) Cure and Danne, C. R. 1904. Bronson, Phil. Mag. 1906. Maxower and Russ, Le Radium, 1907. Exeuer, Ann. d. Phys. 1908. Scumrpt, Phys. Zeitschr. 1908. 93* 1432 shaped portion, which is shorter than that of the vacuum glass. This copper tube is closed underneath (4,) by a metal stopper C, to which a tube C, of thin aluminium is attached (thickness 0.3 mm.); this tube contains a sealed glass tube with the radium. The narrow space at the bottom of the vacuum glass in which this tube is placed, is cooled to a temperature that differs very little from that of the bath: the difference could hardly be established, when the copper vessel was filled with liquid air. This = eT 1433 method of cooling seemed to us to be preferable to placing the tube itself into the liquid gas, which is always a little dangerous. The rays that the radium in the tube sends out are partly of a penetrating nature. They go through the walls of the aluminium tube and those of the vacuum giass, and penetrate through a metal wall into the ionisation space. This consists of a cylindrical box D,, which is connected to a battery; in the middle of the lid of this space a tube is soldered, which is closed at the lower end. The insulated electrode 4, which is a hollow cylinder, is connected with the electrometer. The metal case /’, which is connected to earth, serves for electrostatic protection. When the apparatus is mounted the tube-shaped portion of the vacuum glass is inside the tube D,, which is placed centrally in the box D,, while it is closed by a thick piece of india-rubber tubing round a piece of amber G which is sealed to the vacuum glass. When the tube containing the radium is in its place, ions are formed on both sides of the electrode £, in the air that fills the box D,. The current that is taken up by this electrode is measured by an electrometer and a_ plate of piezoquartz. The experiment consists in measuring the ionisation current gene- rated by the rays of the radium: 1. when the radium is at the temperature of the room, and 2. when the radium is cooled to the temperature of liquid hydrogen. The ionisation chamber, which is outside the vacuum glass remains at about the temperature of the room. The chamber is airtight, and the quantity of gas that it contains does not alter during the experiments. The accuracy of the measurements is greatly increased if instead of measuring the total current, a compensation method is used. This consists in compensating the current to be measured by a current in the opposite direction, which is generated in a second ionisation chamber by a tube containing radium, which is kept at constant temperature during the experiments. This current compensator is of a type which is greatly made use of in radioactive measurements. The insulated electrode G is in the form of a tube which is closed at the bottom; it is connected by means of copper wires (electrically protected in brass tubes filled with paraffin wax) with the electro- meter and with the electrode /,. This tube reaches into a eylindri- cal box H, which is connected to a battery and which forms an ionisation chamber. The outside case A’ serves for electrostatic pro- tection. The electrodes G and £, are protected in the usual way by a protecting ring connected to earth. The tube G contains a sealed glass tube with radium salt. The boxes D, and H are kept 1434 at high potentials of opposite sign. Under these circumstances the difference of the two ionisation currents is measured which are generated in the two chambers. With sufficiently strong currents great accuracy can be attained in this way. fil i 1} S oS \\ ; & sy \ +2 ae } St J 13 ep 2\\ (l= i = i Nae | : dee a eee 4 i Rar = VA q R H 3 = 3 Roos It is worth noticing, that the various small imperfections in the method of measuring, which are usually unnoticed, become appa- rent when the method described above is followed. E. g. when each current is measured separately, the saturation appears to be complete at a potential of about 500 volts. But when the difference between the currents was measured, which was usually under 5°/, of each current separately, it was found that the current under these circumstances increased with the voltage. When the potential 1435 increases from 500 to 800 volts, the current increases by 2 to 3 thousandths. Constant potentials must therefore be used. The accuracy is limited by the stability of the apparatus and by the oscillations in the radio-active radiation. The investigations were made with radium salts in the solid state, contained in sealed glass tubes; the salt was finely granular, and the tubes were not quite filled. When they are shaken the grains can move to a certain extent, which causes a slight change in the distribution of the radiation inside the ionisation chamber. The danger of this is lessened by giving the grains a definite arrange- ment beforehand by tapping the tube. But in spite of this, small perturbations of this nature remained in our experiments of not more than 1 in 1000 The very greatest care is, therefore, necessary in the manipulations which must be made during the experiments. The radio-active oscillations of the ionisation current become apparent when the sensitivity of the measurements is raised suffi- ciently. They cause irregular deviations which can only be eliminated by a great number of measurements. They are least to be feared When gamma rays are used, as was the case in our experiments. In our case they could not do any harm to the determinations. It is important that the ionisation chambers should contain an unchangeable quantity of air. When working with penetrating rays, the current is approximately proportional to the amount of ionised air. If one wishes to keep the current constant with great accuracy, we must, therefore, take care that the ionisation chambers are properly closed. Each chamber is supplied with a tap. By changing the amount of air in the compensation chamber, the current in the chamber could be so regulated as to get a compensation of the amount required. Both the compensation chambers are filled with dry air by a tube filled with cotton wool, which can be connected to the tap of the chambers by a ground joint, and to an air pump and a manometer to regulate the supply. We had to take very great precautions to prevent the cryogene operations from causing insulation errors in consequence of the precipitation of moisture from the surrounding air on the strongly cooled parts of the apparatus. The cryogene apparatus used by us enabled us to avoid all difficulties of this sort. This instrument, which was arranged for working easily and safely with liquid hydrogen, had moreover the advantage that the radium tube could only come into contact with the gaseous phase of the liquified gas, so that when this was hydrogen there was no fear of solid air being deposited on the tube. 1436 The eryogene apparatus is completely closed. The vacuum glass has a lid / of thin new silver, which is fastened air tight to the glass by means of an indiarubber ring, so that when the radium tube is in its plaee, the apparatus can be evacuated, and can be filled beforehand with pure, dry gaseous hydrogen (by Z). A small hole in the stopper C,, upon which the radium tube in the alumi- nium tube rests, ensures the pressure equilibrium, which establishes itself easily during these operations, so that the radium tube is not exposed to any danger. The liquid hydrogen is poured into the vessel B through the new silver tube /, and through the india-rubber tube /,. For this purpose the vlass stopper is removed which closes the india-rubber tube, after the tube with the stopper A, has also been taken away, and the india-rubber tube is connected to the syphon A, of the large vacuum class IW, containing the liquid hydrogen that bas been previously prepared. Before the syphon and the india-rubber tube are connected, the apparatus and the vacuum glass are connected to a gasometer with pure hydrogen, by the tubes Z, and Z,. When the first mentioned connection has been made, the connection of the vacuum glass with the gasometer is broken, and the liquid hydrogen is poured into the apparatus by means of pressure from a cylinder with compressed hydrogen, admitted by the cork m, and controlled by the mercury manometer n. The supply-glass and the gasometer are then again connected. The syphon is taken off the inlet tube afier the connection tube has been warmed, and this latter tube is immediately closed by a glass stopper. To prevent these manipulations from shaking the apparatus, we mnade the indiarubber tube ./,, which is usually as short as possible, rather long; but as the great cold makes the india-rubber very brittle, and the breaking of it might cause great inconvenience, we used only a length of 7 ¢.m. In this way the shaking remained below the limits of stability in the apparatus which we used for these experiments. In a larger apparatus, intended for experiments that take longer, more than 24 hours, bat with which we have only been able to make preliminary determinations so far, we were able to attain a greater amount of stability, and we were more independent of the shaking caused by the manipulations. Care must be taken in filling the copper vessel 5, that the liquid. eas does not overflow, as it might penetrate into the cooling chamber, which would give rise to irregularities, and might injure the radium tube. On the other hand it is necessary to know when the liqnid gas has evaporated, otherwise the experiments might be 1437 continued without our being certain of the temperature. The height of the surface of the liquid gas can be read by means of a float. This consists of a new-silver box p,, suspended from a weak Spring p,, which spring is attached to a rod p,. This rod_ is movable in a packing tube, which is fastened to the upper end of a glass tube g, carried by the lid /. Beside the spring and also hanging from the rod, is a flat rod which is provided with a seale at its lower end. [n consideration of the very small density of the liquid hydrogen ('/,,), the float is made very light. When the float reaches the surface of the liquid by the moving down of the spring, this is indicated by the shortening of the spring, and the height of the liquid can be read on the seale and on the rod. é Before pouring in the liquid gas, the float is regulated to the height to which the vessel is to be filled. Before beginning the measurements, the spring is pressed down as far as is necessary to make the lengthening of it show when the liquid is so far eva- porated that the measurements must be stopped. The evaporated hydrogen is carried off by L,. The tube R, the extremity of which is placed in mercury, serves as a safety. In order to be certain of the insnlation of the vacuum glass, and to avoid currents which might be injurious to the constancy of the tension of the battery, a piece of amber is interposed in the tube Z,. To prevent the amber from being cooled too much by the filling, the cold vapours are carried off by a supplementary tube Z,, which is coupled off as scon as the filling is completed. When the evaporation of the bath has become stationary, a current of air a litthe warmer than that of the room directed upon the amber is sufficient to maintain the insulation. This current cf air is given by a reservoir of com- pressed air, the air flows through a long tube, part of which is warmed by hot water. The connection of the piece of amber, g, Which is sealed to the vacuum glass, with the tube D, of the principal ionisation chamber, is very carefully made, to insure an airtight closing, and thereby to prevent the possibility of moisture penetrating to the space between the tube and the vacuum glass. The currents of cold air that come down are kept away by a paper screen. The water that runs down the glass from the lid must also be disposed of. The very low temperature of the vapours inside the lid causes frost to settle on it during the filling, wkich thaws afterwards. After the filling is finished, the condensation of water vapour out of the air continues; the water thus formed, is absorbed by cotton wool above the paper screen we mentioned, and below it by filter-paper. A current of dry slightly 1438 warmed air is directed upon the amber, which at the same time dries the lower part of the vacuum glass. Finally, the cooling of the parts of the connection of the main electrode #, with the electrometer must be prevented. To attain this a current of dry and slightly warmed air is also directed upon the amber stopper between the stem £,, and the protecting ring &, at the bottom of the main ionisation chamber. The cold currents of air, which come down from the tubes that lead off the gases, are diverted from the apparatus by suitable screens, and large currents of air in the room are avoided as far as possible, so as to prevent the ionised air around the contacts from being displaced ; these contacts were further protected by various lead protecting mantles (in the figure diagrammatically represented), by tin foil, ete. The influence of the warm currents of air already mentioned was tested at the temperature of the room: they did not cause any electrostatic phenomena. n Preparatory Experiments. The experimental method was first studied in Paris, using liquid air as cooling bath. The current in the main ionisation chamber was procured by using a tube with about O.1 gr. of radium chloride. In the com- pensation chamber a tube with about 25 mgr. of radium chloride was used. In the first experiments the first tube was contained in an aluminium tube with walls of 0.8 mm. thickness; the central tube D, in the chamber D, was also of aluminium, with walls of 0.5 mm. thickness. The rays, before penetrating into the ionisation chamber, passed through a layer of aluminium of about 0.8 mm. and moreover a glass layer about 2.5 mm. (wall of the radium tube and both walls of the vacuum glass). During the cooling a diminution of the current in the main chamber could be observed. It was not very regular, and amounted to about _ 2°/,, it was perceptible immediately after the liquid air was poured into the copper vessel, and reached its maximum in about half an hour. “When, however, the liquid air was quickly taken out of the vessel, and the temperature of the radium tube was followed witha thermoelement, it could be observed that while the temperature of the radium tube was still constant, the strength of current already began to rise, and reached about its original value, by the time the whole apparatus had returned to ordinary temperature. From this it was evident that the decrease of strength of current which we observed a 1435 was noi attributable to a change of radiation in the radium tube, but to some other cause. Various test experiments seemed to show that it was caused by change in the power of absorption of the screens, due to their con- traction at low temperatures. It was therefore necessary to make use of heavier and thicker screens, to make sure that we only worked with the most penetrating rays, which are less susceptible to phenomena of this kind. After the radium tube had been inclosed in a copper tube of 1 mm. thickness, we found that the decrease of enrrent when the liqnid air was poured in was reduced to 0.1°/,. The decrease was completed in 10 minutes. Three successive expe- riments gave this result. We found that we could make the circumstances even more favourable, by changing the arrangement of the apparatus in such a way that the screens in which the absorption of the rays took place were not cooled at all. In order to do this, the radium tube was once more put into the aluminium tube of 0.3 mm., while the central tube D, of the chamber D, was replaced by a brass tube of 2 mm. wall thickness. The decrease of the current became by this means less than 1 in 1000. This arrangement was used in the final experiments. Final Experiments. The experiments were made in Leiden from July 20th to 25th 1911. The ionisation current in the main ionisation chamber was 1100, expressed in arbitrary units (about 10 electrostatic units). The strength of the compensation current was so regulated that it was a little larger. The difference was at most 20 units, about 2°/, therefore. The rays used for the experiments were gamma rays. | We were able to make two experiments with liquid hydrogen. [In the experiments the cold ionisation chamber, as we said above, was filled with dry gaseous hydrogen, and by this we made sure that no deposit could come on to the radium tube. In the first experiment the current of originally 10.9 units, attained the value of 14.7 units after the pouring in of the liquid hydrogen, which took 15 minutes. This change corresponds to a change in the main current of 0.384°/,. In the second experiment the current measured had a strength of 18.3 units, and was very constant, the irregularities measured during an hour were less than 1/10000 of ihe main current. After the liquid hydrogen had been poured into the apparatus, measurements which agreed very well with each other gave for the value of the current during half an hour 18.5 1440 units, and after an hour 18.2 units. We can thus assert that in this experiment, which was evidently conducted under very favourable circumstances the cooling had not caused a change in the main current of as much as 1 in 5000. We made another experiment at the temperature of liquid oxygen. The current measured had a strength of 1.8 units. Measurements made during an hour at the temperature of liquid oxygen gave a value of 2.6 units for the current measured, which corresponds to a decrease of 0.7 in LOOO in the main current. It would have been desirable to have made a greater number of experiments and to continue these during a greater length of time; nevertheless it would appear to be justifiable even now to state, that cooling of radium down to the temperature of liquid hydrogen (about 20°.3 absolute) during a period of not more than 1°/, hours does not cause a change in the gamma radiation of 1 in 1000 and pro- bably not even of 1 in 5000. It is thus probable paying due regard to the degree of accuracy attained, that this decrease of temperature has no immediate or quickly discernable influence upon the emanation or the active deposits of short period (radium A, 6 and C). But in these expe- riments there was no opportunity for detecting an eventual effect upon the radium itself, or a slowly developing effect upon its evolu- tion products. Experiments with polonium. A few preliminary experiments on the influence of low tempera- tures upon the radiation of polonium have been made in Paris. The experiment which was made only with liquid air, gives rise io some difficulties. A plate on which was some deposit of polo- nium was placed at the bottom of a long glass tube, which could be immersed in liquid air. This plate radiated through a thin alu- minium plate that closed the tube, into an airtignt ionisation cham- ber, where the polonium rays were absorbed by the air. The polo- nium tube was as far as possible exhausted; and the vacuum was further improved by iminersing a side tube containing a little charcoal in liquid air. The radiation was measured at ordinary tem- perature, and later, when the bottom of the tube was immersed in liquid air. In these experiments changes of current of inconstant amount were observed when cooling was applied. These changes were smaller in proportion as the vacuum was made more com- plete and kept more constant. It is thus highly probable that they 1441 were entirely due to the influence upon the polonium of the con- densation of gases still present in the apparatus. Experiments made in Leiden in liquid hydrogen with a provisional apparatus have convinced us that one might get rid of the conden- sations completely, even with liquid hydrogen, by using a ionisation chamber filled with pure gaseous hydrogen and a side tube with charcoal, immersed in liquid hydrogen. Conclusions. All these experiments which unfortunately are not so complete as we could have wished, confirm the independence of the radiation from the temperature, over a larger range of temperatures than had heretofore been done. Moreover these experiments have brought to light sources of error which must be taken into account, if one wants to make very accurate measurements at low temperatures. Astronomy. — “The periodic change in the sea level at Helder, in connection with the periodic change in the latitude’. By Prof. H. G. v. p. Sanne BakHuyzEn. At the meeting of the Academy in February 1894 I read a paper about the variation of the latitude, deduced from astronomical obser- vations, and added to this a determination of the change in the mean water level in consequence of the variation of the: latitude. Roughly speaking, one may regard the variation of latitude, as consisting of two parts, a periodic variation which takes place in one year, probably due to meteorological influences, and a periodic varia- tion which takes place in about 431 days, which depends amongst other things upon the coefficient of elasticity of the earth, its resistance to change of shape. As a consequence of these changes of position of the axis of the earth oscillations of the same periods must take place in the mean sea level and if we eliminate the annual oscillation, the periodic variation of 431 days remains. For the determination of the latter variation, I bad made use of the mean sea level during the different months of the years 1855—1892, taken by the tide gauge at Helder. The results attained then for the amplitude and the phase of the periodic variation confirmed the opinion that such variations actually existed in the water, but as the changes in question are very small, it was desirable to extend the investi- gation in order to increase the accuracy of the results. I resolved therefore to submit to the calculations all the tidal observations made 1442 at Helder in the years 1855 -1912, and as the results of the years 1893—1912 were not at my disposal, Mr. Gockinca, Chief engineer Director of the “Waterstaat’”, was so good as to let me have the monthly averages of these years. 2. Before I give an account of how the monthly averages were used by me, it is desirable to explain the exact significance of the observation material. The tide curve of Helder, with its double maximum, has an asymmetrical form, which differs considerably from a sinecurve, so that to deduce the exact mean sea level during a day trom the observations, one must either determine the area of the surface enclosed by the tide curve with a planimeter, or, as will also be sufficiently accurate, determine the average value of the 24 hourly heights. From the daily means one can then deduce the monthly means. It will be clear that the work which is necessary to calculate all the observations in this way for the more than 21,000 days from 1855 to 1912 is very great; fortunately for our purpose we can use an easier way, as we do not need to know the actual mean heights, but only their mutual differences. If the tidal curve were symme- trical with respect to the mean sea level, the half of the sum of high and low water would correspond to the mean sea level of that day ; but the form is not symmetrical, and even changes periodically, so that there is not only a difference between the half of the sum of high and low water, and the mean sea level, but this difference changes from day to day. If, however, we determine the average form of the tide curve during the period of a month, then we get a fairly constant shape, and for such a period one may assume, that the difference between the half sum of all the high and low waters and the mean sea level is almost constant. This assumption will differ even less from the truth, if we take the average of a great number of monthly means from different years, which is the case with my calculations. On these grounds I have taken as the monthly means of the sea level the half of the sum of the high and low waters during these months, deduced from the registered tidal curves in the years 1855—1912. These monthly means show rather marked deviations from the annual mean, due partly to the yearly and halt-yearly sun_ tide, and partly to the regularly changing meteorological conditions. From 58 years, | found for Helder the following mean values for yearly means—monthly means in millimetres. 1443 January, February, March, April, May, June, July, August, —178 +285 + 60.9 +1024 + 92:9 +480 —16 — 384 September, October, November, December. — 42.6 85.2 75.4 72.5. By the introduction of these corrections I have eliminated the influence of the yearly periodic variations in the water level. In order to increase the accuracy of the values from which the results must be deduced and to remove entirely or partially the error that might arise, if the number of low waters in a month should be one less or more than the number of high waters, I have always taken the averages of two consecutive months: Jan. and Febr., Febr. and March, ete. The further caleulations are based upon these two-monthly means. Corrections for known tides are not introduced into these values. The influence of tides of short period is very slight upon the two- monthly means, and if, as is the case in my calculations, the average is taken of nearly 50 such means, it may be altogether neglected. Of the tides of longer period we must mention, besides the yearly and half-yearly sun tide, the influence of which has been taken into account, the tide Mm, with a period of over 27 days. It appears from the calculations that the influence of this tide upon the two- monthly means can rise to about = 6 mm. but as the amplitude and pbase constant of this tide are very littke known, we cannot calculate the exact value of the correction. We may, however, assume that in an average of about 50 of these values, for dates thaf cor- respond to very various phases of this tide, its influence may be neglected. 3. The length of the period of the latitude variation of about 431 days (CHANDLER’s period) was deduced from long series of astronomical observations, by E. F. v. pb. Sanne Bakuuyzen, Dr. Zwigrs and me; the results obtained by us differ very little, but | take as the most accurate that deduced by Dr. Zwirrs in a paper in These Proceedings of June 24%, 1911, Vol. XIV, p. 111, that is 431,24 days. In order to determine whether a variation in the sea level takes place in that period, I have, starting from the first bi-monthly mean for 31 Jan. 1855, determined the dates of the days, which fall 431,24 days later, or a multiple of that interval and then selected the bi-monthly means which are nearest to these dates, sometimes a little earlier and sometimes a little later, with a difference at most 1444 of 15 days. From all these mean sea levels, 49 in number, corre- sponding to the same phase of the latitude variation, an average is then formed. In a similar way the averages are taken from the series of sea levels which correspond to the phases of the latitude variation 1, 2, 3,...13 months later than 31 January 1855. These 14 months contain over 426 days, almost the entire CHANDLER period therefore. | found for the deviations of these 14 values from their general mean : — 10.1 mm. — $)ir 7.4 44 S38 These numbers with the exception of the 4% and 5" seem to show, a periodic variation, and the assumption is permissible that the sea level at Helder undergoes a periodic change in the course of 431.24 days, and that the height, ¢ days after the end of January 1855 is represented by t , f : n h=asin = vie 360°-+ «,)=a sin (pf +a@,) =a cos @, SING + Asin A, COs P =psing + q csp. The heights given in the above column are got by taking the average of the bi-monthly means; if at the beginning of the period y=, and at the end y= g,, then that average is (O08 YJ, — COS f sin P, — sing, i - - €08 a, + a ——— ——= 8 Mt, T, Ls Pro or COS J, — C08 &, sin J, — sin &, H=p —— -+- g —— —. So =a Po Disa Pe 1445 108 P, — CO8 sin P, — sin G—, . ; forthe eubstitution of — eee and — Cee OE in whieh f -— QP, Pf, — Po 1 9-7, = 11278" we get the following equations gla oa oo 0.415 p oo 0.874 4 =—— ——h\() 1 + 0.750p + 0.611g=— 9.6 + 0.940 P + 0.230 q=— 5.8 + 0.948 p —0.195q¢=-+ 1.7 + 0.772 p — 0.529 ¢ = 4+ 11.0 + 0.447 p — 0.858¢ = — 4.2 + 0.036 p — 0.967 ¢ = — 13.4 — 0.382 p — 0.889¢=-+ 2.9 — 0.727 p —0.639¢=-+ 1.6 — 0.930 p — 0.265¢ = -+ 1.2 — 0.954 p + 0.160¢g=-+ 9.0 — 0.793 p + 0.554¢ = + 7.4 — 0479p + 0.841g=-+ 4.1 — 0.072 p + 0.965¢ = + 3.3 Solving these by the method of least squares, we get p= — 4.40, qg= + 0.42, therefore h = 4.42 sin (p + 174°88)). The mean error of the unit of weight (mean of two consecutive months) is + 51.5 mm., the mean errors of p and q are + 2.86 and + 2.89, and the probable errors + 1.93 and = 1.95 millimetres. 4. So far, we may deduce from this that the periodicity of the sea level in a period of 431.24 days is presumably real, although considering the small amount of this variation and the comparatively large value of the mean errors, a more detailed investigation as to the probability of the results is desirable. For this purpose I have in the first place calculated the mean error of the unit of weight in another way, namely by taking the yearly means, and in the assumption of a small change in the sea level, proportional to the time, determining the mean error of a yearly mean and therefrom the mean error of the unit of weight ; I found for the latter value + 95.3 mm., much greater than the first value given. This shows that there are fairly large systematic o4 Proceedings Royal Acad. Amsterdam. Vol. XY. 1446 errors in the sea levels, probably to a large extent caused by the circumstance, that the causes of deviations in the normal sea level are of lengthy duration, and thus can cause abnormally high or low sea levels during a long time. In order to investigate this, I have taken the means of a series of 12 months in a different way, by combining the heigbt in Jan. of the year a, with that in Feb. of the year a+ 1, in Mareh of ihe year a+ 2 ete. From this follows for the mean error of the unit of weight + 60.2 mm. which agrees much better with the value we found + 51.5. The real mean errors of p and q therefore probably do not differ greatly from the values calculated. . 5. A second way of judging of the reliability of the results obtained is the calenlation of the ‘same quantities from another combination of observations. For this purpose I chose the observations of 1855— 1892, which I had calculated in 1894, but had now redu- ced to the yearly means with better values for the deviations of the monthly means and further the observations of 1893—1912. I found from both series of observations : h = 4.50 sin (p + 168°.59) . . . (1855—1892) and é h = 3,74 sin (p + 176°13') . . . (1893—1912). By the change in the reduction numbers and a more accurate calculation, the formula for the sea level during the period 1855— 1892 differs somewhat from the formula found in 1894. The striking correspondence between the three formulas now found for the periods 1855—1892, 1893—1912 and 1855—1912 is certainly largely due to accident, but it: confirms the view that the variation in the sea level is real. 6. In order to test the efficiency of the method that I had fol- lowed, | applied it to two cases in which one could not a priori expect a periodic variation, and to another case in which the existence of such a variation was certain. First 1 arranged the bi-monthly means in a period of 13 months or 395.75 days which is not a multiple of any period of a sun or moon tide, and in which therefore we could not expect any periodic variation of level. For this purpose I used the observations of 1855—1592, and got the following deviations of the sea level from their general averages. 1447 4.0 m.m. — 14.8 4.1 8.4 Al 2.0 Qs 2.8 0.8 29 9.8 4.6 a 448 I++) ++4++4 | A periodicity looks less likely here than in the first case. Further I arranged the bi-monthly averages according to the period of 438.096 days, which, according to a paper by Scuumenn from Vienna, should represent the length of the CHANDLER’s period. This value differs very greatly from the results obtained in Leiden, and is a priori improbable as it is only theoretically deduced from the elements of the moon’s orbit, without taking into account the elasticity of the earth, which certainly has a great influence upon this value. From all the observations from 1855 to 1912, arranged according to the phases of a periodic variation in 488.096 days, in distances of a month, I got the following figures for the sea level. — 18.0 m.m. — 48 + 13.9 + 8.6 — 44 — 0.7 — 5.3 2.9 o4* 1448 In this series there is again little trace of a periodicity in a period of 488 days. Finally | arranged the mean sea levels according to the phases of a period of 440.872 days, which is 16-times the period of the monthly moon tide Mm. the length of which is 27.5545 days. It is plain that the influence of this tide will only be felt to a very small degree in the bi-monthly means, as these are the means of two complete periods or 55.11 days and 5.7 days. The periodic variation in the bi-monthly means will be about ‘/,, of that which is due to the actual tide Mm. Afier arranging and combining the bi-monthly means I got for the sea level at 14 different epochs with intervals of one month — 2.6 mm. | ~ bw J +++++44 | The periodic character is here undeniable, and if we determine the amplitude of the Mm.-tide itself from these figures, we get for the amplitude 118.0 mm., whereas from the. observations in 1892 I formerly got for the amplitude 83.4 mm. (Versl. Kon. Akad. v. Wet. Vol Ill, p. 197). The correspondence is satisfactory, if we consider that the error in the observations made in the above series appears in the amplitude multiplied by about 16 These different considerations give me reason to take the value found above for the periodic change of the mean water levels in the time of 431.24 days as correct within the limits of the probable errors. The probable error of the amplitude 4.42 is + 1.93, the probability that the amplitude lies between O and 8.84 mm. may therefore be put at 7. (. We have next to discuss the question what the connection is 1449 between this variation in the sea level and the change in the position of the pole. If the sea level always corresponded to the position of the pole, the lowest sea level at a given place would always correspond to the maximum of the latitude at that place. In the formula for the periodic variation in the water level gy=O for 1 Jan. 1855 = 2398585 Julian date, and as the change of y per day is (0°. 83478, we may represent the formula for the height of the sea level on a day for which the Julian date is ¢ by h—= 4,42 Sin {(t — 2398585 -} 209,1) 0°,83478} h = 4,42 Sin {(t — 2398375,9) 0°.83478}. The height of the sea level is a maximum when the expression under the sine is 90°; thus we find Maximum height of sea level for ¢ = 2398483,7, Minimum Me —— = 897000 occurred 33”38° before second 1) Cf. Astrophysical Journal, 37, p. 232, 1913. *) Astrophysical Journal Vol. 23 p. 312, 1906. PR ss 24 1459 contact and 33m48s after third contact; so, on the average, 337/, minutes were required for the moon to cover the second effective half of the solar disk. Now, at Burgos the moon’s edge took 77*/, minutes to cross the whole solar disk; at Maastricht, in 1912, it took 50*/, minutes. If, therefore, the ratio of the radius of the moon’s disk to the radius of the sun’s disk had been the same in both cases, then the time necessary “ for covering the second effective half of the solar , A yey disk would have been, at Maastricht, 337/, x ——— = very nearly 77"), 35 minutes. But at Maastricht the moon’s radius was practically equal to the sun’s radius, whereas at Burgos the radii were in the propor- tion 152,8:126,8. This difference between the two cases implies that the interval of 35 minutes, calculated for Maastricht, is a little too great. Indeed, when drawing circles representing the sun and the moon in the right proportion and position, and taking the distribution of. brightness on the disk into consideration, one easily concludes that the interval has to be taken about 25 seconds smaller say 34'/, minutes. Consequently, the results obtained in 1905 required that in 1912, at the epochs 0'0™20s and 1'9™20s (i.e. 34'/, minutes before and after centrality), the radiation should have shown half its maximum 4960 intensity, or —.— = 2480 scale divisions. This is indicated by the points 5. The agreement with the actual observations of 1912 is indeed very satisfactory. During the middle phase of the Burgos eclipse the conditions were, on the contrary, so unfavourable, that the central part of the radiation curve, there obtained, claims no confidence. It was worth while, therefore, to found on our present eclipse-curve a renewed application of the method, formerly devised '), of determining the rate of decrease of the radiating power from the centre toward the limb of the solar disk. Discussion of the thermopile results. On a homogeneous piece of paper a circle of 40 centimeters in diameter, representing the sun, was drawn, and divided in the man ner shown by the adjoined figure *), There are conceniric zones, 1) Astrophysical Journal 23, 312, 1906. 2) The figure is not a copy of the original drawing, as this could not be so much reduced on account of the delicacy of the lines, 1460 indicated by the numbers 1 to 12, and ares representing the moon's limb in a series of positions. The width of the sickle-shaped strips bounded by these ares, is ‘/,, of the sun’s radius, excepting the strips a, 6, ¢, d, for which it is */,,. In 40°/, minutes the moon’s limb accomplished a distance equal to the sun’s apparent radius; so the strips a, 6, c, d, required “/4o 40°/, minutes each for reappearing from behind the moon, the strips e to w took '/,, X 40°’, minutes each. On our curve (Plate XI l.c¢.) we read the successive increments of the radiation, corre- sponding to the series of sickle-shaped strips. We shall denote these increments by the same letters as the strips. The increment a is entirely due to radiation from zone 1; the increment 6 to radiation from the zones 1 and 2, ete. Let us indicate by 2, the average intensity of the radiation with which a unit of disk-surface, belonging to zone », supplies our thermopile. Then the increment /, for instance, will be composed as follows: ; == 05 BO sa ome cusrens 0,2,. 6,,4, etc. being the surfaces of the parts that the corresponding 146] zones contribute to the strip 4. Though possible, it is extremely tedious to calculate these surfaces. We therefore determined them by cutting out and weighing the pieces of each strip. So the unit of area, adopted for measuring the surfaces, corresponds to a piece of our drawing-paper weighing 1 milligram. Expressed in that unit, the coéfficients 6, ,6,...0@. were found to be 6,1, 11,9...... 298. Table If contains all the coéfficients of 2, ,2, ,@,.....« v,, thus AB Ee Coéfficients of: | x I 2 | 43 | 44 | 45 | te | 27 +3 % io) Ti | V2 a AG 251.0 > | oOo we or 83.0 168.4 G—osro! P25.) OS. Ol Seo 8 34.5 78.5 123.0 e— 130 15.7 37.5 59.6 113.0 264.0 9 5 f=135 | 10.9 21.0) 31.1 45.0163.0217.0 g=140 | 8.5 15.0 19.5\ 27.0 80.0146.01192.0 A=144 | 8.1] 11.9] 15.8| 21.1| 55.3| 77.01298.0 eer 7.7) 10.3 12.3) 15.9| 42.0) 55.5/198.0 146.5 j=150 | 7.4) 9.3 11.0 13.2 33.0 42.0123.5/247.0 k = 152 7.1] 8.4| 9.2) 11.9| 28.7) 34.8) 93.51168.5 120.0 1=153 | 6.9| 8.2 8.8 10.2 25.4 30.2| 76.6108.2204.2 m=154 | 6.9 8.1) 8.5 9.8 22.4) 27.5) 66.0 86.5142.0| 98.2 m=154.5 | 6.8 8.0) 8.3) 9.5| 20.8 24.9] 58.0| 73.4. 96.4)165.3 o=154 | 6.8 7.7) 8.1| 9.2) 19.8| 22.6] 52.5| 63.6) 77.81119.7] 77.7 p=154 | 6.8] 7.6] 8.0 9.0) 19.1) 21.1) 49.1) 57.3 66.2 82.2134.0 g—=154 | 6.1] 7.5|-7.8) 8.8! 18.3| 19.7] 44.9] 53.0) 57.7] 68.9 164.7 r= 153.5 | 6.7; 9.4] 7.6 8.6] 17.6, 19.0) 42.4) 49.7] 53.4| 69.0)181.2 C= 1188) 6:8) Te5) 7-6) 824) 17.0) 18-2) 40.3) 45.5) 49.2) 54.5)143-0) 50.3 f=151.5 | 6.8} 7.5| 7.5 8.2| 16.7 17.5| 39.2) 42.9) 46.5| 51.1/115.3| 83.6 “=—149.5 | 6.8| 7.4) 7.5. 8.1| 16:5| 17.1| 38.0) 41.7, 45.1| 48.3.102.0| 97.0 obtained. The first column gives the values of the increments of the radiation as read on the eclipse-curve. Every horizontal row 95 Proceedings Royal Acad. Amsterdam. Vol. XV. 1462 defines an equation. From the first equation we obtain z,, from the second equation z,, ete. TAB LEE ‘ Average Radiating Power per Unit of Distance of Zone Surface Zone from —— from Centre = : Reduced to Found b Centre of Found directly from the ‘value 100 | Sraphicat. of Disk. pa Equations at Centre Interpolation Distance 0.9875 x, — 0.18725 48.6 || 40.0 | 1.0 0.9625 | x, — 0.2054 | 585° | | 61.0 | 0.95 0.9375 x3 — 0.2457 63.9). | 5 0.9125 xy — 0.2631 68.4 6.0 | oS 0.875 Xs — 0.2813 73.0 74.2 0.85 0.825 Xs — 0.2900 cE 0.3038 71.8 0.8 0.75 ee) =O: 50710 a wes6 10.3103 ate ie 0.3221 ; 0.65 tn | _ 9.3963 84.8 19.3305 83.3 0.7 0.3463 0.55 x = — 0.3447 89.5 87.4 0.6 10.3432 \ 0.3519 91.0 0.5 0.45 ines — 0.3540 92.0 10.3562 93.8 0.4 0.3656 Nn eat 96.5 0.3 0.3 a } 0.3691 | 95.9 | ).3681 aa 98.3 é 0.3934 het 99.5 0.1 0.125 oo oe — 0.3840 99.8 , a 100. hes, The results are collected in the second column of Table II. The third column shows the same values converted into percentages of the intensity prevailing in the centre of the disk. After they had been plotted on millimeter paper, a smooth curve was drawn, fitting the points as well as possible. On this ‘“distribution-curve” the numbers of the fourth column were read as ordinates, belonging 1465 to the places defined in the fifth column. Our results are thus made more easily comparable with those obtained by other observers. It is not surprising to find the shape of our distribution-curve sensibly different from the shape of any of the curves that repre- sent Vocri’s spectrophotometric measurements. Indeed, the latter show the distributions characteristic of special groups of rays, each covering a narrow part of the spectrum; they are germane, but yet vary considerably with the wave-length. The combined effect of all waves (invisible ones included), that are absorbed by our ther- mopile, must give a distribution-curve of another type, less simple than that to which Voerr’s curves for nearly monochromatic light belong. Summary. During the annular eclipse of the sun on April 17 1912 the variation of the total radiation has been observed near Maastricht under exceptionally favourable sky-conditions, with two mutually independent sets of apparatus. One set, comprising a bolometer and a_ short-period recording galvanometer, served the purpose of finding as accurately as_possi- ble the proportion of the minimum to the maximum radiation. The ratio was found to be nearly '/,,,,. On this result we based an estimate of the total amount of energy radiated and scattered by the entire solar atmosphere; we thus obtained a very small fraction of the solar output (about 7/,,,,). It is impossible, therefore, to ascribe the fall of the sun’s bright- ness from the centre toward the limb of the disk to absorption or scattering of the light by an atmosphere, enveloping a body that otherwise would appear uniformly luminous. The cloud-theory of the photosphere is not borne out by the facts. With the other set of apparatus, consisting of a thermopile and accessories, we obtained a sufficient number of reliable readings for constructing the whole radiation-curve, from the first until the fourth contact, with a fair degree of exactness. Besides confirming the value of the minimum as found with the bolometer, this curve procured the data necessary for once more determining the rate of decrease of the radiating power from the centre to the limb of the solar disk. 1464 BRR Ae T UM: Pioceedings of Dec. 28, 1912 and Jan. 25, 19138. . 952 1. 20 from the top: for 133¢ read 131c. | | (July 15, 1918). CONTENTS. ABEL’s functions g,(«) (Expansion of a function in series of). 1245. ABSORPTION LINES (A method for obtaining narrow) of metallic vapours for investi- gations in strong magnetic fields. 1129. ATR-TEMPERATURE (On the interdiurnal change of the). 1037. ALLoTROPY (Hxtansion of the theory of). Monotropy and enantiotropy for liquids. 36). — (Application to the theory of) to the system Sulphur. U1. 369. — (The dynamic) of sulphur. 5th communication. 1228. AMMONIUM-Sulphoeyanate-thioureum—water (On the svstem). 683. ANATOMICAL sTRUCTURES (The Linnean method of describing). 620. Anatomy. E. W. Rosrnsere : “Contributions to the knowledge of the development of the vertebral column of man”. 80. — G. P. Frers: “On the external nose of primates”. 129. — G. P. Frets: “On the Jacospson’s organ of primates”. 134. — C. T. van VaLkensurG: “On the occurrence of a monkey-slit in man”. 1040. — J. Borxe: “Nerve-regeneration after the joining of a motor nerve to a receptive nerve’. 1281. ANGIOSPERMS (Petrefactions of the earliest European), 620. ANTAGONISM (The) between nitrates and calcium-salts in milkeurdling by rennet. 434. ANTIMONY (Series in the spectra of Tin and). 31. ARGON (The empirical reduced equation of state for). 273. — (Calculation of some thermal quantities for). 952. — (The rectilinear diameter for). 667. 960. ASPERGILLUS NIGER (Mutation of Penicillium glaucum and) under action of known factors. 124. — (Action of hydrogenious boric acid, copper, manganese, zine and rubidium on the metabolism of). 753. — (Metabolism of the nitrogen in). 1047. — (Metabolism of the fosfor in). 1058. — (Potassium sulfur and magnesium in the metabolism of), 1349. Astronomy. H. J. Zwrers: “Researches on the orbit of the periodic comet Hotmes and on the perturbations of its elliptic motion”. V. 192. — N. Scurnrema: “Determination of the geographical latitude and longitude ot Mecca and Jidda, executed in 1910—11”. Part I. 527. Part 11.540. Part IL. 556. —- W. ve Srrrer: “On absorption of gravitation and the moon’s longitude”. Part 1. 808. Part 2. 824. 96 Proceedings Royal Acad. Amsterdam. Vol. XV. 11 oO N TN TS, Astronomy. A. PaANNEKOEK : “The variability of the Pole-Star”. 1192. — W. ve Sirrer: “A proof of the constancy of the velocity of light”. 1297. — H. G. van ve SanprE Bakuuyzen: “The periodie change in the Sea-level at Helder, in connection with the periodie change in the latitude”. 1441. — W. H. Junius: “The total solar radiation during the annular eclipse on April 17th 1912”. 1451. ATEN (a. H. W.). On a new modification of sulphur. 572. ATMOSPHERIC PRESSURE (The correlation between) and rainfall in the East Indian Archipelago, in connection with the 3,5 yearly barometric period. 454. atropHy (On localised) in the lateral geniculate body causing quadrantic heminopsia of both the right lower fields of vision. 840. AVENA SATIVA (The influence of temperature on phototropism in seedlings of). 1170. paawv (Miss w. c. pe) and F. A, H. Scurernemaxkers. On the quaternary system KCl—CuC)],—BaCl, —H,0. 467. BABPER (On the freshwater fishes of Timor and). 235. Bacteriology. C. Eyxman: “On the reaction velocity of micro-organisms”. 629. BAKWUYZEN (E. F. VAN DE SANDE) presents a paper of Dr. H. J. Zwiers: “Researches on the orbit of the periodic comet Hormes and on the perturbations of its elliptic motion”. V. 192. — presents a paper of Mr, N. Scuetrema: “Determination of the geographical latitude and longitude of Mecca and Jidda, executed in 1910—1911.” Part. I. 527. Part. Il. 540. Part. III. 556. — presents a paper of Dr. A. Pannexork: “The variability of the Pole-Star”. 1192. BAKHUYZEN (H. G VAN DE SANDE). The periodic change in the Sea-level at Helder in connection with the periodic change in the latitude. 1441. BEAUFORT (L. F&F. Dz) and Max Wepzer. On the fresh-water fishes of Timor and Babber. 235. BECKMAN (ANNA) and H. Kamertmca Onnes. The piezo-electric and pyro- electric properties of quartz at low temperatures down to that of liquid hydro- gen. 1380. BECKMAN (BENG T). Measurements on resistance of a pyrite at low temperatures down to the melting point of hydrogen. 1384. — «and H. Kamertincn Onnes, On the Hatt-eflect and the change in the resistance in a magnetic field at low temperatures. L 307. II. 319. ITT. 649. IV. 659. V. 664. VI. 981. VII. 988. VIII. 997. — On the change induced by pressure in electrical resistance at low temperatures. I. 947. BENZENE (Oxydation of petroleum, paraffin, paraffin oil and) by microbes. 1145. BENZENE NucLEUs (On the velocity of substitutions in the) 1118. BEIJERINCK (M. W.) presents a paper of Mr. H.J. Wavrerman : “Mutation of Peni- ciliium glaucum and Aspergillus niger under the action of known factors.” 124. — presents u paper of Prof J. Boesexen and H. J. Waterman: “A biochemical method of preparation of d-tartaric acid” 212. CON TEN TB, im BEIJERINCK (M. W.) presents a paper of Mr. H. J. Waterman: “Action of hydro- genious borie acid, copper, manganese, zinc and rubidium on the metabolism of Aspergillus niger”. 753. — On the composition of tyrosinase from two enzymes. 932. — presents a paper of Mr. H. J. Waterman: “Metabolism of the nitrogen in Aspergillus niger.” 1047. — presents a paper of Mr. H. J. Warerman: “Metabolism of the fosfor in Asper- gillus niger”. 1058. — Penetration of methyleneblue into living cells after desiccation. 1086. — presents a paper of Dr. N. L. Somneaen: “Oxydation of petroleum, paraffin, paraffin-oil and benzene by microbes”. 1145. — presents a paper of Mr. H. J. Waterman: “Potassium sulfur and magnesium in the metabolism of Aspergillus niger’. 1349. BINARY MIxtuRES (Isotherms of monatomic substances and of their). XIII. The empirical reduced equation of state for argon. 273. — (Isotherms of diatomic gases and of their). X Control measurements with the volumenometer of the compressibility of hydrogen at 20° C. 295. XI. On deter- minations with the volumenometer of the compressibility of gases under small pressures and at low temperatures. 299. — (Isotherms of diatomic substances and of their). XII. The compressibility of hydrogen vapour at and below the boiling point. 405. BINARY SYSTEMS (On vapour-pressure lines of the) with widely divergent values of the vapour-pressures of the components. 96. — (Contribution to the theory of). XXI. 602. Biochemistry. J. BorseKen and H. J. WavermMaN: “A biochemical method of prepa- ration of /-tartaric acid”, 212 — J. R. Karz: “The antagonism between nitrates and calcium-salts in milkeurdling by rennet”. 434. — J. R. Karz: “The laws of surface-absorption and the potential of molecular attraction”. 445. BOEKE (J.). Nerve-regeneration after the joining of a motor nerve to a receptive nerve. 1281. BOESEKEN (J.). On a method for a more exact determination of the position of the hydroxyl groups in the polyoxy compounds. 216. BOESEKEN (s.) and S. C. J. Ouivier. Dynamic researches concerning the reaction of Frrepen and Crarts. 1069, — and H. J. Warerman. A biochemical method of preparation of /-tartaric acid. 212. BOTS (H. DU) presents a paper of Mr. Prerre Marni: “The magneto-optic Krerr- effect in ferromagnetic compounds and metals”. IIL. 138. — presents a paper of Mr. D. E. Rosserts: “The effect of temperature and trans- verse magnetisation on the resistance of graphite”. 148. — A theory of polar armatures. 330. BOKHORST (s. CG.) and A. Smrrs. The phenomenon of double melting of fats. 681. B OLX (1) presents a paper of Dr. G. P. Prers : “On the external nose of primates”. 129. — presents a paper of Dr. G. P. Frets‘ “On the Jacobson’s orgin of primates”. 124. 96* 1V CONTENTS. BOLTZMANN’s entropy principle (On the deduction of the equation of state from), 240. — (On the deduction from) of the second virial coefficient for material particles (in the limit rigid spheres of central symmetry) which exert central forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre. 256. BoRIC actD (Action of hydrogenious), copper, manganese, zine and rubidium on the metabolism of Aspergillus niger. 753. Botany. ©. van WusseLiNcH: “On the demonstration of carotinoids in plants. Ist Communication. 511. 2nd Communication. 686. 3rd Communication. 693. — J. W. Moun and H. H. Janssontus: “The Linnean method of describing ana- tomical structures. Some remarks concerning the paper of Mrs. Dr. Marir C. Stops: ‘Petrefactions of the earliest Duropean Angiosperms”. 620. — J. GC. Schoute: “Dichotomy and lateral branching in the Pteropsida”. 710. — Miss T. Tammes: “Some correlation phenomena. in hybrids”. 1004. — Jon. van Burxom: ‘On the connection between phyllotaxis and distribution of the rate of growth in the stem’. 1015. — ©. yan Wissetincu: “On karyokinesis in Eunotia major Rabenh.”. 1088. — Miss M. S, pr Vries: “The influence of temperature on phototropism in seed- lings of Avena sativa’. 1170. — ©. van Wissetineu : “On intravital precipitates’. 1329. Braaxk (c.). The correlation between atmospheric pressure and rainfall in the Hast- Indian Archipelago, in connection with the 3,5 yearly barometric period. 454. — A long range weather forecast for the East monsoon in Java. 1063. BROUWER (H. A.). On the formation of primary parallel structure in lujaurites. 734. — Leucite-rocks of the Ringgit (East Java) and their contact metamorphosis. 1238. BROUWER (L, E. J.). On looping coefficients. 113. — Continuous one-one transformations of surfaces in themselves. 5th Communi- cation. 352. — Some remarks on the coherence type y. 1256, BUCHNER (kg, H.). The radio-activity of rubidium and potassium compounds. IT. 22. BUCHNER (kf. H.) and L. K. Woxrr. On the behaviour of gels towards liquids and their vapours. 1078. BURKOM (JOH. H. VAN). On the connection between phyllotaxis and the distri- bution of the rate of growth in the stem. 1015. caLciuM-sAaLrs (The antagonism between nitrates and) in milkeurdling by rennet. 434. CALCULUs rationum. 2nd part. 61. CARDINAAL (J.) presents « paper of Prof. W. A. Versbuys: “On a class of surfaces with algebraic asymptotic curves’. 1363. carotinors (On the demonstration of) in plants. 1st Communication. 511. 2nd Com- munication. 686. 3rd Communication. 693. ceLLs (Penetration of methylene-blue into living) after desiccation. 1086. Chemistry. J. W. 1e Hux: “On some internal unsaturated ethers”. 19. — Lk. H. Bictxer: “Lhe radio activity of rubidium and potassium compounds” II, 22. CON VEN 2 8) Vv Chemistry. F. A. H. Scureinemakers and J. Minikay: “On a few oxyhaloids”’. 52. — F. E. C. Scnerrer and J. P. Trevs: “Determinations of the vapour tension of nitrogen tetroxide”. 166. — A, Smurs: “On critical end-points in ternary systems”. II. 184. — A. P. N. Francurmonr and J. V. Dussky: “Contribution to the knowledge of the direct nitration of aliphatic imino compounds”. 207, — J. Bowsexen: “On a method for a more exact determination of the position of the hydroxyd groups in the polyoxy compounds”. 4th Communication. 216. — A. Smits: “Extansion of the theory of allotropy. Monotropy and enantiotropy for liquids”. 361. — A. Smits: “The application of the theory of allotropy to the system sulphur”. II, 369. — A.Smits: “The inverse occurrence of solid phases in the system iron-carbon”. 371, — F. E. C. Scunrrer: “On the system ether-water”. 380. — F. E. C. Scuerrer: “On quadruple-points and the continuities of the three- phase lines”. 389. — F. A. H. Scurernemaxers and Miss W. C. pe Baar: “On the quaternary system : KCl— CuC],—BaCl, —H,O”. 467. — F. A. H.Scureinemakers and J.C. Taonus: “The system HeCl,-CuCl,-H,0. 472. — W. Retypers and S. pe Lance: “The system tin-iodine”. 474. — W. Reinpers and D. Lety ue.: “The distribution of dyestufls between two solvents, Contribution to the theory of dyeing”. 482. — A. H. W. Aven: “On a new modification of sulphur’. 572. — H. L. pe Leeuw: “On the relation between sulphur modifications”. 584, — A. F, Hotieman and J. P. Wisavv: “On the nitration of the chlorotoluenes”’. 594. — A. Smits and H. L. pe Leeuw: “The system tin”. 676. — A. Smits and 8S, C. Boxuorsr:; “The phenomenon of double melting for fats”. 681. — A. Smits and A. Kerrner: “On the system ammonium-sulphocyanate-thioureum- water’. 683. — Ff. A, H. Scorernemakers: “Equilibria in ternary systems”. I. 700. [I. 853. Ill. 867. IV. 1200. V. 1213. VI. 1298. VIL. 1313. — Enrnsr Conen: “The equilibrium Tetragonal Tin = Rhombic Tin”. 839, — L. van Ivattre and J. J. van Eck: “On the occurrence of metals in the liver”. 850. — A, Smits, J. W. Terwen and H. L. pe Leeuw : “On the system phosphorus”. 885. — 8. C. J. Ovivier and J. Borsexen : “Dynamic researches concerning the reaction of FrrepeL and Crarts’”. 1069. — L. K. Wourr and E. H. Biicuner: “On the behaviour of gels towards liquids and their vapours”. 1078. — F. E. C. Scuerrer: “On velocities of reaction and equilibria”. 1109, — F. E. C. Scuerrer: “On the velocity of substitutions in the benzene nucleus’’, 1118. — P. van Rompuren: “On hexatriene. 1, 3, 5.”. 1184. — H.R. Kruyt: “The dynamic allotropy of sulphur’, 5th Communication. 1228, vl GONTENTS. . Chemistry, F. A. H. Scursixem\Kkers and D. J. van Proowe: “The system sodium sulphate, mangane sulphate and water at 35°”. 1326. — H. R. Krvyr: “The -influence of surface-active substances on the stability of suspensoids”’. 1344. CHLOROTOLUENES (On the nitration of the). 594. cLoups and yapours (Electric double refraction in artificial). 178. COEFFICIENT of diffusion (Lhe) for gases according to O. E. Merger. 1152. COEFFICIENTS (On looping). 113. COHEN (ERNST). The equilibrium Tetragonal Tin <> Rhombie Tin. 839. COHERENCE-TYPE * (Some remarks on the), 1206. COMET HOLMES (Researches on the orbit of the periodic) and on the perturbations of its elliptic motion. V. 192. COMPONENTS (On vapour-pressure lines of the binary systems with widely divergent values of the vapour pressures of the). 96. compounps and metals (The magneto-optic Kerr-effect in ferro-macnetic). IIT. 138.2 COMPRESSIBILITY of gases (On determinations with the volumenometer of the) under small pressures and at law temperatures. 299. — of hydrogen-vapour (On the) at and below the boiling point. 405. CONGRUENCES (On loci), and focal systems deduced from a twisted cubic and a twisted biquadratic curve, I. 495. II. 712. ILL. 890. copper (Action of hydrogenious boric acid), manganese, zine and rubidium on the metabolism of Aspergillus niger. 753. CORRELATION (The) between atmospheric pressure and rainfall in the East Indian Archipelago in connection with the 3,5 yearly barometric period. 454. CORRELATION PHENOMENA (Some) in hybrids. 1004. CORRESPONDING states (The law of) for different substances. 971. crarts (Dynamic researches concerning the reaction of FrrepEL aud), 1069. CROMMELIN (c. a.) and H. Kampruincu Onnes. Isotherms of monatomic sub- stances and of their binary mixtures. XIII. The empirical reduced equation of state for argon. 273. XIV. Calculation of some thermal quantities for argon, 952. CROMMELIN (c. 4.), BE. Matatas and H. Kameriinea Onnes. On the rectilinear diameter for argon. 667. 960. CRUSTAL MOVEMENTs (On recent) in the island of Timor and their bearing on the geological history of the East-Indian Archipelago. 224. crysraL (The diffraction of electromagnetic waves by a). 1271. cunR1e (Madame P.) and H. Kameruineu Onnes. The radiation of Radium at the temperature of liquid hydrogen. 1430. curves (On a class of surfaces with algebraic asymptotic). 1363, — of order 32 (On Steinerian points in connection with systems of nine ¢-fold points of plane). 938. pensity (Accidental deviations of) in mixtures. 54. DIAMETER (On the rectilinear) for argon. 667. 960. picuotoMy and lateral branching in the Pteropsida. 710. pirrRActiON (The) of electromagnetic waves in a crystal. 1271. CrOP sel Cen TS: Vit DORSMAN (c.), H. Kampriincu Onnes and Soruus Weper. Investigations on the viscosity of gases at low temperatures. 1. Hydrogen, 1586. puBs«y (J. v.) und A. P. N. FPrancuimont. Contribution to the knowledge of the direct nitration of aliphatic imino compounds, 207. pyresturrs (The distribution of) between two solvents. Contribution to the theory of dyeing. 482. ' DYNAMIC researches concerning the reaction of I’rimpeL and Crarrs. 1069, EAST-INDIAN ARCHIPELAGO (The correlation between atmospheric pressure and rainfall in the) in connection with the 3,5 yearly barometric period. 454. EAST MONSOON in Java (A long range weather forecast for the) 1063. Eck (J. J. Van) and L. vaw Ivautie. On the occurrence of metals in the liver, 850, uciipsn (The total solar radiation during the annular) on April 17th, 1912. 1451, EHRENFEST (e.) On Ernsrery’s theory of the stationary gravitation field. 1187. EINSTEIN’S theory (On) of the stationary gravitation field, 1187. EINTHOVEN (w.) presents a paper of Prof. L. van Ivautre and Dr. J. J. van Eck: “On the occurrence of metals in the liver’. 850. ELECTRIC PRopERTIps (The piezo-electric and pyro-) of quartz at low temperatures down to that of liquid hydrogen. 1380. ELECTRIC‘L RESISTANCE (On the change induced by pressure in) at low temperatures, I. 947. ELECTROCARDIOGRAM (The) of the foetal heart, 1360. ELECTROMAGNETIC Waves (The diffraction of) by a crystal. 1271. ELTE (&£. L.). The scale of regularity of polytopes. 200. ENANTIOTROPY (Monotropy and) for liquids. 361. END-POINTS (On critical) in ternary systems. II. 184. ENERGY (On the law of the partition of). 1175, IL. 1355. ENTROPY PRINCIPLE (On the deduction of the equation of state from Bourzmany’s), 240, — On the deduction from Bottzmann’s) of the second virial-coefficient for mate- rial particles (in the limit rigid spheres of central symmetry), which exert cen- tral forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre. 256. ENZYMES (On the composition of tyrosinase from two). 932. EQUATION (On a differential) of ScHLirxr. 27. EQUATION OF STATE (On the deduction of the) from Botrzmann’s eniropy principle. 240. — (The empirical reduced) for argon. 273. — (Some remarks on the course of the variability of the quantity 4 of the). 1131. EQuations (Homogeneous linear differential) of order two with given relation between two particular integrals (5th Communication). 2. — (New researches upon the centra of the integrals which satisfy ditlerential) of the first order and the first degree. 2nd part. 46. EQUILIBRIA in ternary systems. I. 700. IL. 853. LIL. 867. LV. 1200. V. 1213. VI 1298. VIL. 1313. — (On velocities of reaction and). 1109, EQuiLisRiuM (The) Tetragonal Tin Z Rhombic Tin. 839, ‘ vu CONTENTS. ERRATUM. 43]. 673. 1464. ErYTuROCYTES (Comparative researches on young and old). 282. ETHER-WATER (On the system). 380. erners (On some internal unsaturated). 19. EUNOTJA MAJOR RABENH. (On karyokenesis in). 1088. E1JK MAN (c.), On the reaction velocity of micro-organisms. 629. — presents a paper of Mr. C. J. C. van Jloocennuize and J. Nreuwennuize : “Influence of the seasons on respiratory exchange during rest and during mus- cular exercise’. 790. FascictE (The posterior longitudinal) and the manege movement. 727. rats (The phenomenon of double melting of). 681. ratty acrps (The eilect of) and soaps on phagocytosis, 1290. risHes (On the freshwater) of Timor and Babber. 235. rocaL systems (On loci, congruences and) deduced from a twisted cubie and a twisted biquadratic curve. I. 495. il. 712. ILI. 890. rosror (Metabolism of the) in Aspergillus niger. 1058. FRANCHIMONT (a. P. N.) and J. V. Dussxy: Contribution to the knowledge of the direct nitration of aliphatic imino compounds. 207. FRETS (G. P.). On the external nose of primates, 129. — On the Jaconson’s organ of primates. 134. FRIEDEL and Crarts (Dynamic researches concerning the reaction of). 1069. FUNCTION (Expansion of a) in series of ABEL’s functions ¢p(n). 1245. Gases ({sotherms of diatomic) and of their binary mixtures. X. Control measurements with the volumenometer of the compressibility of hydrogen at 20°C, 295. XI. On determinations with the volumenometer of the compressibility of gases under small pressures and at low temperatures. 299. — (On the second virial coefficient for diatomic). 417. — On the second virial coefficient for monatomic), and for hydrogen below the Boyle-point. 643. — (Measurements on the ultraviolet magnetic rotation in). 773. — (Determinations of the refractive indices of) under high pressures. 2nd Commu- nication. 925. : — (The coefficient of diffusion for) according to O. E. Menger. 1152. — (Investigations on the viscosity of) at low temperatures. I. Hydrogen. 1386. IL Helium. 1396. III. Comparison of the results with the law of corresponding states, 1399. Geis (On the behaviour of) towards liquids and their vapours. 1078. GEOGRAPHICAL latitude and longitude (Determination of the) of Mecca and Jidda, executed in 1910—711. Part [. 527. Part IL. 540. Part ILl. 536. Geology. G. A. f. Monencraarr: “On recent crustal movements in the island of Timor and their bearing on the geological history of the East-Indian archipelago”. 224. — A. Wicumann: “On rhyolite of the Pelapis-islands”. 347. — L. Rurren: “Orbitoids of Sumba”. 461, — H. A. Brouwer; “On the formation of primary parallel structure in lujaurites”. 734. ClOeN Dl BON 2s. iX Geology. H. A. Brouwer: “Leucite-rocks of the Ringeit (Hast-Java) and their contaet- metamorphosis”. 1238, GRAPHITE (The effect of temperature and transverse magnetisation on the resistance of). 148. GRAVITATION (On absorption of) and the moon’s longitude. Part 1. 808. Part 2. $24. GRAVITATION FIELD (On Erystern’s theory of the stationary). 1187. HAAS (W. J. DE). Isotherms of diatomic gases and of their binary mixtures. X. Control measurements with the volumenometer of the compressibility of hydrogen at 20° C. 295 XI. On determinations with the volumenometer of the compressibility of gases under small pressures and at low temperatures. 299. HAAS (W. J. DE) and H. Kamertincn Onnes. Isotherms of diatomic substances and of their binary mixtures. XII. The compressibility of hydrogen vapour at and below the boiling point. 405. HALL-EFFECT (On the) and the change in the resistance in a magnetic field at low temperatures, I. 307. II. 319. IIT. 649. IV. 659. V. 664. VI. 981. VII. 988. VIII. 997. HAMBURGER (H. J.) presents a paper of Mr. J. SNapeer: “Comparative researches on young and old erythrocytes”. 282. HAMBURGER (H. J.) and J. pe Haan. The effect of fatty acids and soaps on phagocytose. 1290. HEART (The electrocardiogram of the foetal). 1360. HELDER (‘The periodic change in the sea level at) in connection with the periodic change in the latitude. 1441. HELIUM (Further experiments with liquid). H. VII. 1406. HEMINOPsIA (On localised atrophy in the lateral geniculate body causing quadrantic) of both the right lower fields of vision. 840. HEU X (J. W. LE). On some internal unsaturated ethers. 19. HEXATRIENE |, 3, 5. 1184. HOLLEMAN (a. F.) presents a paper of Dr. E. H. Bécuner: “The radioactivity of rubidium and potassium compounds”. I]. 22. — presentsa paper of Prof. A. Smrrs: “On critical end-points in ternary systems’’. [I. 184. — presents a paper of Prof. J. Borsrken: “On a method for a more exact deter- mination of the position of the hydroxyl groups in the polyoxy compounds”. 216. — presents a paper of Prof. A. Smits: ‘‘Extansion of the theory of allotropy monotropy and enantiotropy for liquids”. 361. — presents a paper of Prof. A. Smits: “The application of the theory of allotropy to the system sulphur”. IT. 369. — presents a paper of Prof. A. Smirs: “The inverse oceurrence of solid phases in the system iron-carbon”. 371. — presents a paper of Mr. J. R. Karz: ‘The antagonism between nitrates and calciumsalts in milkeurdling by rennet”. 434. — presents a paper of Dr. A. H. W. Aven: “On a new modification of sul- phur”. 572. — presents a paper of Dr. H. L. pe Leruw: “On the relation between sulphur modifications”. 584. — presents a paper of Prof. A. Smrrs and Dr, H. L, pe LeEuw: “The system tin”. 676, x CONTENTS. HOLLEMAN (a. F.) presents a paper of Prof. A. Surrs and S. C. Bokuorsr: “The phenomenon of double melting of fats”. 681. — presents a paper of Prof. A. Smrrs and A. Kerryer: “On the system ammonium sulphocyanate thioureum water”. 683. — presents a paper of Prof. A. Surrs, J. W. Terwen and Dr. H. L. pe Lezuw: “On the system phosphorus”. 885. — presents a paper of Mr. S. C. J. Oxtvier and Prof. J. Boeseken: “Dynamic researches concerning the reaction of FrrepEL and Crarts”. 1069. st presents a paper of Dr. L. Kk. Woxrr and Dr. E. H. Bicuner: “On the behaviour of gels towards liquids and their vapours”. 1078, — presents a paper of Dr. F. E. C. Scuerrer: “On velocities of reaction and equilibria”. 1109. — presents a paper of Dr. F. E, C. Scuerrer: “On the velocity of substitutions in the benzene nucleus”. 1118. — and J. P. Wrsaur. On the nitration of the chlorotoluenes. 594. HOLMES (Researches on the orbit of the periodic comet) and on the perturbations of its elliptic motion. V. 192. HOOGENBOOM (c. M.) and P. ZEEMAN. Electric double refraction in some artificial clouds and vapours. 178. HOOGENHUYZE (Cc. J. c. vAN) and J, Nreuwenuuyse. Influence of the seasons on respiratory exchange during rest and during muscular exercise. 790. uyBrips (Some correlation phenomena in). 1004 uypkoGEN (Control measurements with the volumenometer of the compressibility of) at 20° C. 295. — (On the second virial coefficient for monatomic gases and for) below the BoyLE- point. 643. HYDROGEN: VAPOUR (The compressibility of) at and below the boiling point. 405. HYDROXYL GROUPS (On a method for a more exact determination of the position of the) in the polyoxycompounds. 216. IMINO coMpouNDs (Contribution to the knowledge of the direct nitration of aliphatic). 207 INTEGRALS (Homogeneous linear differential equations of order two with given relation between two particular). 5th Communication. 2. ; — (New researches upon the centra of the) which satisfy differential equations of the first order and the first degree. 2nd part. 46. INVOLUTION (An) of associated points. 1263. TRON-CARBON (The inverse occurrence of solid phases in the system). 371. ISOTHERMS of monatomic substances and of their binary mixtures. XLII, The empirical reduced equation of state for argon. 273. XIV. Calculation of some thermal quantities for argon. 952. — of diatomic gases and of their binary mixtures. X. Control measurements with the volumenometer of the compressibility of hydrogen at 20° C. 295. XI. On the determination of the compressibility of gases under small pressures and at low temperatures, 299. Cro; Nf E NTS; XI IsoTHERMS of diatomic substauces and of their binary mixtures. XIL The compressi- bility of hydrogen vapour at and below the boiling point. 405. ITALLIE (&%. van) and J. J. van Ecx. On the occurrence of metals in the liver. 850. , JACOBSON’S ORGAN (On the) of primates, 134. JANSSONIUs (Hd. H.) and J. W. Motz. The Linnean method of describing anato- mical structures. Some remarks concerning the paper of Mrs. Dr. Marte ©, Sroprs: “Petrefactions of the earliest European Angiosperms’’. 620. Java (A long range weather forecast for the Hast monsoon in). 1063, Jippa (Determination of the geographical latitude and longitude of Mecca and), exe- cuted in 1910—’11. Part I. 527. Part IL. 540. Part ILI. 556. JuLtus (w. u.). The total solar radiation during the annular eclipse on April 17th 1912. 1451. KAMERLINGH ONNES (H.). V. Onnes (H. Kamertinan). KAPTEYN (w.). presents a communication of Dr. M. J. van Uven. Homogeneous linear differential equations of order two with given relation between two particular integrals, 5th Communication. 2. — New researches upon the centra of the integrals which satisfy differential equa- tions of the first order and the first degree. 2nd part. 46. — Expansion of a function in series of Apnu’s functions g(x), 1245. KARYOKINESIS (On) in Eunotia major Rabenh. 1088. Katz (J. R.). The antagonism between nitrates and calciumsalts in milkeurdling by rennet, 434. — The laws of surface-adsorption and the potential of molecular attraction. 445. KHESOM (Ww. H.). On the deduction of the equation of state from BoLtzMann’s entroply principle. 240. — On the deduction of Bonrzmann’s entropy principle of the second virial- coefficient for material particles (in the limit rigid spheres of central symme- try) which exert centrai forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre. 256. — On the second virial coefficient for diatomic gases. 417. — On the second virial coefficient for monatomic gases and for hydrogen below the Boy.E-point. 643. : KERR-ErrECT (The magneto-optic) in ferro-magnetic compounds and metals. ILI. 138. KETTNER (a.) and A. Smrvs. On the system ammonium sulphocyanate thioureum water. 683. KLESSENS (J. H. M.). Form and function of the trunkdermatome tested by the strychnine-segmentzones. 740. KLUYVER (J. c.). On a differential equation of ScHLAFLI. 27. KOHUNSTAMM (PH.). On vapour-pressure lines of the binary systems with widely divergent values of the vapour pressures of the components. 96. — and J. Timmermans. Experimental investigations concerning the miscibility of liquids at pressures to 3000 atmospheres. 1021. x1 CONTENTS. KORTEWEG (pb. J.) presents a paper of Dr. L. E. J. Brovwer: “On looping coeflicients”. 113. KRUYT (H. B.). The dynamic allotropy of sulphur. 5th Communication. 1228. — The influence of surface-active substances on the stability of suspensoids, 1344. KUENEN (J. P.). The coefficient of diffusion for gases according to O. E. MEisEr. 1152. LAAR (J. J. VAN). The calculation of the thermodynamic potential of mixtures when a combination can take place between the components. 614. LANGE (s. DE) and W. RernpeErs. The system Tin-Iodine. 474. LATERAL BRANCHING (Dichotomy and) in the Pteropsida. 710. Law (On the) of the partition of energy. 1175. II. 1355. — of corresponding states (The) for different substances. 971. |, EE Uw (H. L. D#). On the relation between sulphur modifications. 584. —, A. Sirs and J, W. Terwen. On the system phosphorus. 885. — and A. Smits. The system tin. 676. LELY gr. (D.) and W. Reryogrs. The distribution of dyestuffs between two solvents. Contribution to the theory of dyeing. 482. LEucitE-rocks of the Ringgit (East-Java) and their contact metamorphosis. 1238. ticut (On the polarisation impressed upon) by traversing the slit of a spectroscope and some errors resulting therefrom. 599. — (A proof of the constancy of the velocity of). 1297. LINE COMPLEX (On a) determined by two twisted cubics. 922. LINE SPECTRA (Translation series in). 156. LINNEAN METHOD (The) of describing anatomical structures. 620. Lipase (Influence of some inorganic salts on the action of the) of the pancreas. 336. L1guIvs (Monotropy and enantiotropy for). 361. — (Experimental investigations concerning the miscibility of) at pressures to 3000 atmospheres. 1021. — (On the behaviour of gels towards) and their vapours. 1078. LITHIUM-LINE (‘Tbe red). 1130. LIVER (On the occurrence of metals in the). 850. oct (On), congruences and focal systems deduced from a twisted cubic and a twisted biquadratie curve. I. 495. IL 712. HI. 890. LOH UIZEN (%, VAN). Series in the spectra of Tin and Antimony. 31. — Translation series in line spectra. 156 LORENTZ (H. A.) presents a paper of Dr. L. S. Ornsrern: “Accidental deviations of density in mixtures”. 54. — presents a paper of Mr. J. J. van Laas: “The calculation of the thermodynamic potential of mixtures when a combination can take place between the components” 614 — presents a paper of Dr. L. S. Ornsvery: “On the thermodynamical functions for mixtures of reacting components”. 1100. — presents a paper of Prof. P, Earenrest: “On Exysrety’s theory of the stationary gravitation field”. 1187. — presents a paper of Dr. L. S. Ornsrein: “The diffraction of electromagnetic waves by a crystal”. 1271. CONTENTS, xiii Lusaurtres (On the primary parallel structure in), 784. MAGNESiUM (Potassium sulfur and) in the metabolism of Aspergillus niger. 1349. MAGNETIC FIELD (On the Hatt-eflect and the resistance in the) at low temperatures. I. 307. If. 319. IfL. 649. IV. 659. V. 664. VI. 981. VIL. 958 VIII. 997. MAGNETIC RESEARCHES. On paramagnetism at low temperatures. VI. 322. VII. 965. VII!. On the susceptibility of gaseous oxygen at low temperatures. 1404. MAGNETISATION (The eflect of temperature and transverse) on the resistance of graphite. 148. MALIGNANT GRANULOMA (On a micro-organism grown in two cases of uncompli- cated). 765. MAN (Contributions to the knowledge of the development of the vertebral column of). $6. — (On the occurrence of a monkey-slit in). 1040. MANEGE MOVEMENT (The posterior longitudinal fascicle and the). 727. MANGANE SULPHATE (The system sodium sulphate), and water at 35°. 1326. MANGANESE (Action of hydrogenious- boric acid, copper), zine and rubidium on the metabolism of Aspergillus niger. 753. MARTIN (PIERRE). The magneto-optic Kerr-eflect in ferro-maguetic compounds and metals, III. 138. Mathematics. M. J. van Uven: “Homogeneous linear differential equations of order two with given relation between two particular integrals”. 5th Communication. 2. — J. C. Kuvyver: “On a differential equation of Scuxiriy’. 27. — W. Kapreyn: ‘New researches upon the centra of the integrals which satisfy differential equations of the first order and the first degree”. 2nd part. 46. — G. ve Vrtss: “Calculus rationum”. 2nd part. 64. — L. E. J. Brouwer: ‘On iooping coefticients”. 113. — E. L. Etre: “The scale of regularity of polytopes’. 200. — L. E. J. Brouwer: “Continuous one-one transformations of surfaces in them- selves”. 5th Communication. 352. — Hk. ve Vriks: “On loci, congruences and focal systems deduced from a twisted cubic and a twisted biquadratic curve”. I. 495. If. 712. III. 890. — Jan ve Vries: “On metric properties of biquadratic twisted curves”. 910. — Jan pe Vrigs: “(On the correspondence of the pairs of points separated har- . monically by a twisted quartic curve’. 91S. — Jan pe Vries: “On a line complex determined by two twisted cubics”. 922. — W. van per Wouve: “On Steinerian points in connection with systems of nine g-points of plane curves of order 3)”. 938. — Jan ve Vries: “On bilinear null-systems”. 1156. — Jan pe Vries: ‘On plane linear null-systems”. 1165. — W. Karreyn: “Expansion of a function in series of ABEL’s functions ¢(n(x)”. 1245. — IL. E. J. Brouwer: “Some remarks on the coherence type +”. 1256, — Jan pe Vries: “An involution of associated points”. 1263. — W. A. Verstuys. “On a class of surfaces with algebraic asymptotic curves’. 1363. MATHIAS (8.), H. Kameriinco Onneés and C. A. Cromme.iy. On the rectilinear diameter for argon.. 667. 960. XTV CONTENTS. MEASUREMENTS on the ultraviolet magnetic rotation in gases. 773. —on resistance of a pyrite at low temperatures down to the meltingpoint of hydrogen. 1384. mecca and Jidda (Determination of the geographical latitude and longitude of) exe- euted in 19]0—’11. Part I. 527. Part 1f. 540. Part III. 556. MELTING of fats (On the phenomenon of double). 681. METABOLISM of Aspergillus niger (Action of hydrogenious boric acid, copper, manga- nese, zinc and rubidium on the). 753. — of the nitrogen in Aspergillus niger. 1047. — of the fosfor in Aspergillus niger. 1058. — (Potassium sulfur and magnesium in the) of Aspergillus niger. 1349. METALLIC varouns (A method for obtaining narrow absorption lines of ) for investigations in strong magnetic fields. 1129. METALS (The magneto-optic Kerr-etlect in ferro-magnetic compound and). Il. 138. — (On the occurrence of) in the liver. 850. j Meteorology. C. Braax: “The correlation between atmospheric pressure and rainfall in the East-[ndian Archipelago in connection with the 3,5 yearly barometric- period”. 454. — Jj. P. van per Srox: “On the interdiurnal change of the air-temperature”. 1037. — C. Braax: “A long range weather forecast for the East monsoon in Java”. 1063. METHYLENEBLUF (Penetration of) into living cells after desiccation. 1086. METRIC PROPERTIES (On) of biquadratie twisted curves. 910. MEIER (0. E.) The coefficient of diffusion for gases according to. 1152. Microbiology. H. J. Waverman: “Mutation of Penicillium glaucum and Aspergillus niger under the action of known -factors”. 124. — H. J. Warerman: “Action of hydrogenious boric acid, copper, manganese, zine and rubidium on the metabolism of Aspergillus niger’. 753. : : — M. W. Bewerrckx: “On the composition of tyrosinase from two enzymes”. 932. — H. J. Warerman: “Metabolism of the nitrogen in Aspergillus niger’. 1047. —M. W. Bewerinck: “Penetration of methyleneblue into living cells after desiccation”. 1086. — N. L. Séuncen: “Oxydation of petroleum, paraffin, paraffinoil and benzene by microbes”. 1145. — H. J. Warerman:: “Potassium sulfur and magnesium in the metabolism of . Aspergillus niger”. 1349. Micro-orGANIsM (On a) grown in two cases of uncomplicated Malignant Granuloma. 765. MIcRO-oRGANISMS (On the reaction velocity of). 629. MIEREMET (w. G.) and Hrxestine be Necri. On a micro-organism grown in two cases of uncomplicated Malignant Granuloma. 765. MILI1KAN (J.) and F. A, H. Scorernemakers, On a few oxyhaloids. 52. MILKCURDLING (The antagonism between nitrates and calciumsalts in) by rennet. 434. miscrpiLtry of liquids (Experimental investigations concerning the) at pressures to 3000 atmospheres. 1021. mixtures (Accidental deviations of density in). 54. CONTENTS. AV mixturEs (The calculation of the thermodynamic potential of) when a combination can take place between two components. 614. — of reacting components (On the thermodynamical functions for), 1100. MOLECULAR ATTRACTION (The laws of surface adsorption and the potential of). 445. MOLENGRAAFF (G. A. F.). On recent crustal movements in the island of Timor and their bearing on the geological history of the East-Indian Archipelago. 224. — presents a paper of Dr. H. A. Broower: “On the formation of primary paral- lel structure in lujaurites”. 734. — presents a paper of Dr. H. A. Brouwer: “Leucite-rocks of the Ringgit (Hast- Java) and their contact-metamorphosis”. 1238. MOL (J. W.) presents a paper of Prof. C. van WissE.incu : “On the demonstration of carotinoids in plants. Ist Communication 511. 2nd Communication 686 3rd Communication. 693. — presents a paper of Miss T. Tames: “Some correlation-phenomena in hybrids’. L004. — presents a paper of Prof. C. van WisseLincH: “On karyokenesis in Eunotia major_Rabenh.” 1088. — presents a paper of Prof. C. van WisseLinau: “On intravital precipitates.” 1329. — and H. H. Janssontus. The Linnean method of describing anatomical structu- res. Some remarks concerning the paper of Mrs. Dr. Marte C. Stopes: “Petre- factions of the earliest European Angiosperms”. 620. MONKEY-sLIT (On the occurrence of a) in man. 1040. MoNoTROPY and enantiotropy for liquids. 361. MOON’S LONGITUDE (On absorption of gravitation and the) Part 1. 808. Part 2. 824. MOTOR NERVE (Nerve-regeneration after the joining of a) to a receptive nerve. 1281. MUSKENS (L, J. J.). The posterior longitudinal fascicle und the manege move- ment. 727. mutation of Penicillium gluucum and Aspergillus niger under action of known factors. 124. NEGRI (ERNESTINE DE) and W. G, Mieremer. On a micro-organism grown in two cases of uncomplicated Malignant Granuloma. 765. NERVE-REGENERATION after the joining of a motor nerve to a receptive nerve. 1281. NIEUWENHUYSE (J.) and C. J. C. van Hoocennuwze. Influence of the seasons on respiratory exchange during rest and during muscular exercise. 790. NITRATES (The antagonism between) and calciumsalts in milkcurdling by rennet. 434: NITRATION (Contribution to the knowledge of the direct) of aliphatic imino com- pounds. 207, — (On the) of the chlorotoluenes. 594. NITROGEN (Metabolism of the) in Aspergillus niger. 1047. NITROGEN TETROXIDE (Determinations of the vapour tension of). 166, NosE (On the external) of primates. 129. NULL-systEMs (On bilinear). 1156. — (On plane linear). 1165. OLIVIER (s. c. J.) and J. Borsexen. Dynamic researches concerning the reaction of FrrepeL and Crarrs, 1069. Xvi CONTENTS. ONNES (H. KAMERLINGH) presents a paper of Dr. W. H. Keesom: “On the deduction of the equation of state from Bo.TzmMann’s entropy principle”. 240. — presents a paper of Dr. W. H. Keesom: “On the deduction of BoLTzmann’s entropy principle of the second virial-coefficient for material particles (in the limit rigid spheres of central symmetry) which exert central forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre. 256. — presents a paper of Mr. W. J. pe Haas: “‘Isotherms of diatomic gases and of their binary mixtures. X. Control measurements with the volumenometer of the compressibility of hydrogen at 20° C”. 295. XI. On determinations with the volumenometer of the compressibility of gases under small pressures and at low temperatures. 299. — presents a paper of Dr. W. H. Kersom: “On the second virial-coefficient for diatomic gases”. 417. — presents a paper of Dr. W. H. Kegsom: “On the second virial-coefficient for monatomic gases and for hydrogen below the Boyxe-poinv’. 643. — presents a paper of Mr. J. F. Srrxs: “Measurements of the ultra-violet mag- netic rotation in gases.” 773. — presents a paper of Prof. L. H. Sterrsema: “Determinations of the refractive indices of gases under high pressures” 2nd Communication. 925. ; — presents a paper of Dr. Bener Beckman: “Measurements on resistance of a pyrite at low temperatures down to the melting point of hydrogen’. 1884. — Further experiments with liquid helium. H. VII. 1406. — and Mrs. Anna Beckman: On piezo-electric and pyro-electric properties of quartz at low temperatures down to that of liquid hydrogen. 1380. — and Benet Beckman. On the Hawt-effect and the change in the resistance in a magnetic field at low temperatures. [. 307. II. 319. ILL. 649. IV. 659. V. 664. VI. 981. VII. 988. VIII. 997. — On the change induced by pressure in electrical resistance at low temperatures. I. 947. — and C. A. Crommexin: Isotherms of monatomic substances and of their binary mixtures. XI{f. The empirical reduced equation of state for argon. 273. XIV. Calculations of some thermal quantities of argon. 952. — and Madame P. Curr. The radiation of Radium at the temperature of liquid hydrogen. 1430. : — C. Dorsman and Sorpaus Weser. Investigations on the viscosity of gases at low temperatures. [. Hydrogen. 1386. — and W. J. pe Haas. Isotherms of diatomic substances and of their binary mixtures XII. The compressibility of hydrogen vapour at and below the boiling point. 405. — and E. Oosreruuis. Magnetic researches. VI. On paramagnetism at low tem- peratures, 322. VII. 965. VIII. On the susceptibility of gaseous oxygen at low temperatures. 1404. — &. Marvntss and C. A. Crommetry. On the rectilinear diameter for argon. 667. 960. _— CONTENTS XVIT ONNES (H. KAMERLINGH) and Sopnus Weper. Investigation of the viscosity of gases at low temperatures. II. Helium, 1396. ILI. Comparison of the results obtained with the law of corresponding states. 1399. OOSTERHUTS (£.) and H. Kamertinen Onnes. Magnetic researches. VI. On paramag- netism at low temperatures. 322. VII. 965. VIII. On the susceptibility of gaseous oxygen at low temperatures. 1404. orbit of the periodic comet Hotmes (Researches on the) and on the perturbations of its elliptic motion. V. 192. orBrrorps of Sumba. 461. ORNSTEIN (t, s.). Accidental deviations of density in mixtures. 54. — On the thermodynamical functions for mixtures of reacting components. (100. — The diffraction of electromagnetic waves by a erystal. 1271. oxyGEN (On the susceptibility of gaseous) at low temperatures. 1404. OxYHALOIWs (On a few). 52. PAIRS OF POINTS (On the correspondence of the) separated harmonically by a twisted quartic curve. 918. panorEas (Influence of some inorganic salts on the action of the lipase of the). 336. PANNEKOEK (A.). The variability of the Pole-star. 1192. PARAFFIN (Oxydation of petroleum,) paraffin-oil and benzine by microbes. 1145. PARALLEL STRUCTURE (On the formation of primary) in lujaurites. 734. PARAMAGNETISM (On) at low temperatures. 322. 965. Pathology. Exnestine DE NEGRI and W. G, Migremer: “On a micro-organism srown in two cases of uncomplicated Malignant Granuloma”. 765. PEKELHARING (c. a.). Influence of some inorganic salts on the action of the lipase of the pancreas. 336. — presents a paper of Dr. W. EB. Riyeer and H. van Trier: “Influence of the reaction upon the action of ptyalin”. 799. PELAPIS-ISLANDs (On rhyolite of the). 347. PENICILLIUM GLAUcUM (Mutation of) and Aspergillus niger under action of known factors. 124. periopic cHANGE (The) in the sea-level at Helder in connection with the periodic change in the latitude. 1441. PERTURBATIONS (Researches on the orbit of the periodic comet Hotmes and on the) of its elliptic motion. V. 192. PETREFACTIONS of the earliest European Angiosperms. 620. perroteum (Oxydation of), paraffin, paraftin-oil and benzine by microbes. 1145. pHacocytosts (The effect of fatty acids and soaps on). 1290. PHospHorus (On the system). 885. pHotorropisM (The influence of temperature on) in seedlings of Avena sativa. 1170. pHYLLOTAXIs (On the connection between) and the distribution of the rate of growth in the stem. 1015. j Physics. T. van Loaurzen: “Series in the spectra of Tin and Antimony”. 31. — L. S. Ornstein: “Accidental deviations of density in mixtures”. 54. 97 Proceedings Royal Acad. Amsterdam. Vol. XVI. XVIIT CONTENTS. Physics. Pu. Kouxstamm: “On vapour-pressure lines of binary systems with widely divergent values of the vapour pressures of the components”. 96. — Pierre Martin: “The magneto-optic Kerr-effect in ferromagnetic compounds and metals”. IIL. 138. — Daviv E. Rosserts: “The effect of temperature and transverse magnetisation on the resistance of graphite’. 148. — T..van Lonuizes: “Translation series in line spectra”. 156. — P. Zeeman and C. M. Hoocensoom: “Electric double refraction in some artificial clouds and vapours”. 3rd part. 178. — W. H. Keesom: “On the deduction of the equation of state from BottzMann’s entropy principle”. 240. — W. H. Keesom: “On the deduction from BottzMann’s entropy principle of the second virial-coefficient for material particles (in the limit rigid spheres of central symmetry) which exert central forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre”. 256. — H. Kamertincu Onnes and C. A. CromMeLin: “Isotherms of monatomic substances and their binary mixtures. XIII. The empirical reduced equation of state for argon”. 273. XIV. Calculation of some thermal quantities of argon. 952. — W. J. pe Haas: “Isotherms of diatomic gases and of their binary mixtures. X. Control measurements with the volumenometer of the compressibility of hydrogen at 20° C. 295. XI. /On determinations with the volumenometer of the compres- sibility of gases under small pressures and at low temperatures”. 299. — H. Kamertinch Onnes and Benet Beckman: “On the Hawi-effect and the change in the resistance in a magnetic field at low temperatures”. I. 307. IL. 319 II]. 649. IV. 659. V. 664. VI. 981. VII. 988. VIII. 997. — H. Kameruincu Onnes and E. Oosteruuts: “Magnetic researches. VI. On paramagnetism at low temperatures”. 322. VII. 965. — H. vu Bots: “A theory of polar armatures”. 330. — H. Kameruicu Onnes and W, J. bE Haas: “isotherms of diatomic substances and of their binary mixtures. XII. The compressibility of hydrogen vapour at and below the boiling point”. 405. — W. H. Kersom: “On the second virial~coefftcient for diatomic gases”. 417. — P. Zeeman: “On the polarisation impressed upon light by transversing the slit of a spectroscope and some errors resulting therefrom”. 599. — J. D. van per Waats: “Contribution to the theory of binary systems”. XXL 602. — J. J. van Laar: “The calculation of the thermodynamic potential of mixtures when a combination can take place between the components”. 614. — W. H. Kersom: “On the second wirial-coeflicient for monatomic gases and for hydrogen below the Boyxe-point”. 643 — FE. Marnias, H. Kamertincu Onnes and C. A. CrommeELin : “On the rectilinear diameter for argon”. 667. 960. — J. FP. Srrxs: “Measurements on the ultraviolet magnetic rotation in gases”. 773. — J. D. van per Waats: “Some remarkable relations either accurate or approx= imative for different substances’. 903. CONTENTS, XIX Physics. L. H. Sierrsema: ‘Determinations of the refractive indices of gases under high pressures”. 2nd Communication. 925. — H. Kamertincu Onnes and Benor Beekman: “On the change induced by pressure in electrical resistance at low temperatures”. [. 947. — J. D. van ver Waats: “The law of corresponding states for diflerent substan- ces”. 971. — Ph. Konnstamm and J. Timmermans: ‘“ixperimental investigations concerning the miscibility of liquids at pressures to 3000 atmospheres’. 1021. — L. S. Ornsrern: “On the thermodynamical functions for mixtures of reacting components”. 1100. — R. W. Woop and P. Zerman: “A method for obtaining narrow absorption lines of metallic vapours for investigations in strong magnetic fields”. 1129. — P. Zeeman: ‘The red lithium line”. 1130. — J. D. vaAN per Waats: “Some remarks on the course of the variability of the quantity 4 of the equation of state”. 1151, — J. P. Kuenen: “The coefficient of diffusion for gases according to O. E. Mryer”. 1162. — J. D. van ver Waats Jr.: “On the law of the partition of energy”. 1175. IL. 1355. — P. Euseyxrest: “On Winstein’s theory of the stationary gravitation field”. 1187. — L. §. Ornstein: ‘The diffraction of electromagnetic waves by a crystal”. 1271. — H. Kamertinch Onnes and Mrs. Anna Beckman: “On piezo-electric and pyre-electrie properties of quartz at low temperatures down to that of liquid hydrogen”. 1380. — Benet Beckman: “Measurements on resistance of a pyrite at low temperatures down to the melting point of hydrogen”. 1384. — H. Kameriinen Onneés, C. Dorsman and Soruus Weer: “Investizations on the viscosity of gases at low temperatures. I. Hydrogen”. 1386. — H. Kameriinch Onnes and Sopnus Weser: “Investigations on the viscosity of gases at low temperatures. II. Helium. 1396. ILI. Comparison of the results obtained with the law of corresponding states”. 1399. — H. Kamernineu Onnes and EF. Oosteruuts: “Magnetic researches. VIL. On the susceptibility of gaseous oxygen at low temperatures”. 1404. — H. KameruineH Onnes: “Further experiments with liquid helium’. H. VIL. 1406. — Madame P. Curie and H. Kamernincu Onnes: “The radiation of Radium at the temperature of liquid hydrogen”. 1430. Physiology. J. Sxarper: “Comparative researches on young and old erythrocytes”. 282 — ©. A. PrexeLuarine: “Influence of some inorganic salts on the action of the lipase of the pancreas”. 336. — L. J. J. Musxens: “The posterior longitudinal fascicle and the manege move- ment’. 727. — J. H. M. Kvessens: “Form and funetion of the trunk dermatome tested by the strychnine-segmentzones”. 740. xx CONTENTS. Physiology. C. J. C. vas lHoocrxuunze and J. Nrpuwennunse: “Influence of the seasons on respiratory exchange during rest and during muscular exercise”. 790. — W. E. Riycer and H. van Tarot: “Influence of the reaction upon the action of ptyalin”. 799. — C. Wivgier: “On localised atrophy in the lateral geniculate body causing quadrantic hemianopsia of both the right lower fields of vision”. 840. — J. K. A. Wertnem Satomonson : “On a shortening-reflex” 1092. — H. J. Hamepurcer and J. pe Haan: “The effect of fatty acids and soaps on phagocytosis”. 1290. — J. K. A. Werrnrim Sacromonson: “The electro-cardiogram of the foetal heart”. 1360. pLants (On the demonstration of carotinoids in). Ist Communication. 511. 2nd Com- munication. 686. 3rd Communication. 693. points (An involution of associated). 1263. POLAR ARMATURES (A theory of). 330. PoLARTsATION (On the) impressed upon light by transversing the slit of a spectro- scope and some errors resulting therefrom, 599. poLe-sTaR (The variability of the). 1192. POLYOXY coMpouNDs (On a method for a more exact determination of the position of the hydroxyl groups in the). 216. potytoprrs (The scale of regularity of). 200. potTassiuM compounds (‘The radioactivity of rubidium and). II. 22. POTASSIUM SULFER and magnesium in the metabolism of Aspergillus niger. 1349. poTENTIAL (Lhe calculation of the thermodynamic) of mixtures when a combination can take place between the components. 614. POTENTIAL of molecular attraction (The laws of surface-adsorption and the). 445. Precipitates (On intravital). 1329. PRESSURE (On the change induced by) in electrical resistance at low temperatures. I. 947. PRIMATES (On the external nose of). 129. — (On the Jacopson’s organ of). 134. PROOWJE (D. J. VAN) and F, A. H. Schtrernemakers, The system sodium-sulphate, mangane-sulphate and water at 35°. 1526. prenopsipA (Dichotomy and lateral branching in the). 710. pryaLtN (Influence of the reaction upon the action of). 799. pyrite (Measurements on resistance of a) at low temperatures down to the melting point of hydrogen. 1384. QUADRUPLE-PotNnTs (On) and the continuities of the three-phase lines. 389. auantity 4 (Some remarks on the course of the variability of the) of the equation of state. 1131. avartz (The piezo-electric and pyro-electric properties of) at low temperatures down to that of liquid hydregen. 1380. QUATERNARY systeM (On the) KCl-Cu Cly-BaCh-H,0. 467. rapio-activity (The) of rubidium potassium compounds. IT. 22. CONTENT S&S. XXI RabruM (The radiation of) at the temperature of liquid hydrogen, 1430, RAINFALL (The correlation between atmospheric pressure and) in the’ East-Indian Archipelago, in connection with the 3,5 yearly barometric period. 454. RATE OF GROW? (On the connection between phyllotaxis and the distribution of the) in the stem. L015. reaction (Influence of the) upon the action of ptyalin. 799. REACTION of FrrepeL and Crarrs (Dynamic researches concerning the). 1069. RPAUTION VELOCITY (On the) of micro-organisms. 629. RECEPTIVE NERVE (Nerve regeneration after the joining of a motor nerve to a). 1281. REFRACTION (Hlectric double) in some artificial clouds and vapours. L7S. REFRACTIVE INDICES (Determinations of) of gases under high pressures. 2nd, Com- munication. 925. REINDERS (wW.) and 8. pe Lanes. The system Tin-lodine. 474. — and D. Lery Jr. The distribution of dyestuffs between two solvents. Contri- bution to the theory of dyeing. 482. RELATIONS (Some remarkable) either accurate or approximative for different substan- ces. 903. RESISTaNce (On the Hant-effect and the) in the magnetic field at low temperatures OO Ue Ses LULw Gt. TVeGa9, Vobd. VIL 98, Vile 988 VILE 997. RESPIRATORY EXCHANGE (Influence ‘of the seasons on) during rest «und during muscular exercise. 790. RHYOLITE (On) of the Pelapis-islands. 347. RINGER (w. £E.) and H. van Tricr. Influence of the reaction upon the action of ptyalin. 799. rineoir (East-Java) (Leucite-rocks of the) and their contact-metamorphosis. 1238. ROBBERTS (DAaViD E£.). The effect of temperature and transverse magnetisation on the resistance of graphite. 143. ROMBURGU (P. van) presents a paper of Mr. J. W. te Heux: “On some internal unsaturated ethers”. 19. — presents a paper of Prof. Exnsr Cowen: “The equilibrium Tetragonal Tin Rhombie Tin”. $59. — Hexatriene 1, 3, 5. 1184. — presents a paper of Dr. H. R. Keruyr: “The dynamic allotropy of sulphur”. 5th. communication. 1228. — presents a paper of Dr. H. R. Kruyr: “Uhe influence of surface-active sub- stances on the stability of suspensoids”. 1344. ROSENBERG (£. w.). Contributions to the knowledge of the development of the vertebral column of man. §0. ROTATION (Measurements on the ultraviolet magnetic) in gases. 773. RUBIDIUM (The radio-activity of) and potassium compounds. II. 22. — (Action of hydrogenious boric acid, copper, manganese, zinc and) on the metabolism of Aspergillus niger. 753. RUTTEN (1L,). Orbitoids of Sumba. 461. SALOMONSON (J. K. aA. WERTHEIM). On a shortening-reflex. 1092. * XXII CONTENTS. SALOMONSON (J. K. A. WERTHEIM). The electrocardiogram of the foetwl heart. 1360. saLts (Influence of some inorganic) on the action of the lipase of the pancreas. 336. SANDE BAKHUIJZEN (E. F. VAN DE). V. BakuvuryzEN (E. F. van DE SANDF). SANDE BAKHUIJZEN (H. G. VAN DE). v. BaKHUIJZEN (H. G. van DE Sanrr) SCHEFFER (f. E. C.). On the system ether-water. 380. — On quadruple-points and the continuities of the three-phase lines. 389. — On velocities of reaction aud equilibria”. 1109. — On the velocity of substitutions in the benzene nucleus. 1118. — and J. P. Trevus. Determinations of the vapour tension of nitrogen tetroxide. 166. SCHELTEMA (y.). Determination of the geographical latitude and longitude of Mecca and Jidda executed in 1910-11. Part I. 527. Part IL. 540. Part IIL. 556. $CHLAF4LtT (On a differential equation of). 27. SCHOUTE (4s. c.). Dichotomy and lateral branching in the Pteropsida. 710. SCHOUTE (v. H.) presents a paper of Dr. E. L. Erte: “The scale of regularity of polytopes’’. 200. — presents a paper of Dr. W. van pER Wovupe: “On Steinerian points in con- nection with systems of nine g-fold points of plane curves of order 3 0”. 938. SCHREINEMAKERS (Ff. A. H.) presents a paper of Prof. W. Reixpers and S. vr Lance: “The system Tin-[odine”. 474. — presents a paper of Prof. W. Reixpers and D, Lery Jr: “The distrioution of dyestuffs between two solvents. Contribution to the theory of dyeing’. 482. — Equilibria in ternary systems. I. 700. IL. 853. III. 867. 1V. 1200. V. 1213. VI. 1298. VII. 1318. — and Miss W.C. ve Baar. On the quaternary system: KC]-CuC))-BaCls-H.0. 467. — and J. Minixay. On a few oxyhaloids. 52. —and D. J. van Prooyr. The system scdium sulphate, mangane sulphate and water at 35° 1326. — and J. C, Tuoxus. The system HgC!,-CuC!,-H,O0. 472. SEA-LEVEL at Helder (‘Ihe periodic change in the) in connection with the periodic change in the latitude. 1441. seasons (Influence of the) on respiratory exchange during rest and during muscular exercise. 790. SHORTENING-REFLEX (On a). 1092. SIERTSEMA (L. H.). Determinations of refractive indices of gases under high pres- sures. 2nd Communication. 925. S1RKS (J. F.). Measurements on the ultraviolet magnetic rotation of gases, 773. SITTER (W. DE). On absorption of gravitation and the moon’s longitude. Part 1. 808. Part 2. 824. — A proof of the constancy of the velccity of light. 1297. SMITs (A.). On critical end-points in ternary systems. II. 184. — Extansion of the theory of allotropy. Monotropy and enantiotropy for liquids. 361 — The application of the theory of allotropy to the system sulphur. II. 369. — The inverse occurrence of solid phases in the system iron-carbon. 371. CON REN TS, XXII sM1Ts (a4.) and S$. ©. Boxnorst. The phenomenon of double melting of fats. 681. — and A. Kerrxer. On the system ammonium sulphocyanate thioureum water. 683. — and H. L. pr Leeuw. On the system tin. 676. — J. W. Terwen and H. L, pe Leruw. On the system phosphorus. $85. SNAPPER (J.). Comparative researches on young and old erythrocytes. 282. soars (The effect of fatty acids and) on phagocytosis. 1290. SODIUM SULPHATE (The system) mungane sulphate and water at 35°. 1326. SOHNGEN (N. L.). Oxydation of petrcleum, paraffin, paraffin-oil and benzine by microbes. L145, : SOLAR RADIATION (The total) during the annular eclipse on April*17th 1912. 1451. SOLID piiasEs (The inverse occurrence of) in the system iron-carbon. 371. spectra of Tin and Antimony (Series in the). 31. se-crRoscorE (On the polarisation impressed upon light by transversing the slit of a) and some errors resulting therefrom. 599. SPRONCK (Cc. H. I.) presents a paper of Miss Erx. pe Neari and Mr. W. G, MIeREMET: “On a micro-organism grown in two eases of uncomplicated Majignant Granuloma”. 765. STETNERIAN PoINtIs (On) in connection with systems of nine v-fold points of plane curves of order 3. 958. steM (On the connection between phyllotaxis and the distribution of the rate of growth in the). 1015. STOK (J. P. VAN DER) presents a paper of Dr. C. Braak: “The correlation between atmospheric pressure and rainfall in the Kast-Indian Archipelago in connection with the 3,5 yearly barometric period”. 454. — On the interdiurnal change of the air-temperature. 1037. — presents a peper cf Dr. C Braak: “A long range weather forecast for the Kast Monsoon in Java’. 1063. STOPES (MAR1E Cc.) Some remarks concerning a paper of Mrs. Dr. (—): “Petrefac- tions of the earliest European Angiosperms’’. 620. STRYCHNINE-SEGMENT-ZONFS (Form and function cf the trunk dermatome tested by the). 740. SUBSTANCES (Isotherms cf menutcmic) and of their binary mixtures. XIII. The empirical ‘reduced equation of state for argon, 273. XIV. Calculation of some thermal quantities of argon. 952, — (Isctherms of diatcimic) and of their binary mixtures. XII. The compressibility of hydregen vapour at and below the boiling—point. 405. — (Some remarkable relations either accurate or approximative for different). 903. — (lhe law of corresponding states for different). 971. — (Ihe influence cf surface-active) on the stability of suspensoids. 1344. SULPHUR (On a new modification of). 572. — (The dynamic allotropy of). 5th Communication. 1228. — (Application of the theory of allotropy to the system). II. 369. SULPHUR MODIFICAIIONS (On the relation between). 584. suMBA (Orbitoids of). 441. LXIV CONTENTS. suRPACE-ADsorPTion (The laws of) and the potential of molecular attraction. 445. suRFACEs (Continuous one-one transformations of ) in themselves. 5th Communication. 352. — (On a class of) with algebraic asymptotic curves. 136%. suspensorps (The influence of surface-active substances on the stability of). 1344. sysrem He Cl,—CuCl, —H.0. (The), 467. — ammonium-sulphocyanate-thioureum-water (On the). 633. — ether-water (On the). 380. — iron-carbon (The inverse occurrence of solid phases in the). 371. — phosphorus (On the). 8S5. : — sodium sulphate, mangane sulphate and water (The) at 35°. 1326. — sulphur (Application of the theory of allotropy to the). IL. 369. — Tin (On the). 676. — Tin-Iodine (The). 474. systems of o-fold points (On Steinerian points in connection with) of nine o-fold points of plane curves of order 3). 938. 7AMMES (Miss 7.). Some correlation phenomena in hybrids. 100+. TaRTARIC acID (A bio-chemical method of preparation of /-). 212. TEMPERATURE (The effect of) and transverse magnetisation on the resistance of graphite. 148. — (The influence of) on phototropism in seedlings of Avena sativa. 1170. TERNARY SYSTEMS (On critical end-points in). Il. 184. — (lquilibria in). I. 700. IL. 853. ILL $67. LV. 1200. V. 1218. VI. 1298. VIL. 1313. TERWEN (J. Ww), A. Smits and H. L. pe Leeuw. On the system phosphorus. 893. yHeory (A) of polar armatures, 330. — of allotropy (Extansion of the). Monotropy and enantiotropy for liquids. 361. — (Appli:ation of the) to the system sulphur. If. 369. — of binary systems (Contribution to the). XXT. 602. — of dyeing (Contribution to the). 482. THERMAL QuantITIES (Calenlation of some) for argon. 952. THERMODYNAMICAL FUNCTIONS (On the) for mixtures of reacting components. 1100. THONUs (J. c.) and F. A, H. Schrernemskers. The system HgC]—CuCl,—H,0O. 472. THREE-PHASE LINES (On quadruple-poiuts and the continuities of the). 339. TIMMERMANS (J.) and Pu. KouNstamu. Experimental investigations concerning the miscibility of liquids at pressures to 3000 atmospheres. 1021. Timor (On recent crustal! movements in the island of) and their bearing on the geological history of the Hust Indian Archipelago. 224. : Timor and Babber (On the freshwater fishes of). 235. TIN (On the system). 676. — (The Equilibrium Tetragonal Tin S$ Rhombic). 839. — and Antimony (Series in the spectra of). 31. — 1op1Ne (The system). 474. TRANSFORMATIONS (Continuous one-one) of surfaces in themselves. 5th Communi. cation. 352. TRANSLATION-SERIES in line spectra. 155. CON TEN TS. XXV TREUB (J. PB.) and, F. , C. Scuerrer. Determinations of the vapour tension of nitrogen tetroxide. 166, TRIGT (Hu. vAN) and W. E. Rine@er. Influence of the reaction upon the action of ptyalin. 799. TRUNKDERMATOME (Form and funetion of the) tested by the strychnine-segmentzones, 740. TWisreD cuBrcs (On a line complex determined by two). 922. TWISTED CURVE (On loci, congruences and focal systems deduced from a) and a twisted biquadratic curve. I. 495. IT. 712. III. 890. TWISTED CURVES (On metric properties of biquadratic). 910. TWISTED QUARTIC cURVE (On the correspondence of the pairs of points separated harmonically by a). 918. TYROSINASE (On the composition of) from two enzymes, 932. UVEN (M. J. vAN). Homogeneous linear differential equations of order two with given relation between two particular integrals. 5th. Communication. 2. VALKENBURG (C. tT. vAN) On the occurrence of a monkey-slit in man. 1040. vapours (Electric double refraction in some artificial clouds and). 178. VAPOUR-PRESSURE lines (On) of the binary systems with widely divergent values of the vapour pressures of the components. 96. VAPOUR TENSION (Determinations of the) of nitrogen tetroxide. 166. veLocitiEs of reaction (On) and, Equilibria, 1109. vetocity of light (A proof of the constancy of the). 1299. veLociry of substitutions (On the) in the benzene nucleus. 1118. VERSLUWS (w. A.). On a class of surfaces with algebraic asymptotic curves. 1363. VERTEBRAL COLUMN of man (Contributions to the knowledge of the development of). 80. VIRIAL-COEFFICIENT (On the deduction of BoLrzmMann’s entropy principle of the second) for material particles (in the limit-rigid spheres of central symmetry) which exert central forces upon each other and for rigid spheres of central symmetry containing an electric doublet at their centre. 256. — (On the second) for diatomic gases. 417. — (On the second) for monatomic gases, and for hydrogen below the BoyLe-point. 643. vision (On localised atrophy in the lateral geniculate body causing quadrantic hemi- nopsia of both the right lower fields of). 840. viscosity of gases (Investigations on the) at low temperatures. I. Hydrogen. 1386. Il. Helium. [11. Comparison of the results with the law of corresponding states. 1399. vies (G. Dez). Calculus rationum. 2nd. part. 64. VRIES (HK. DE). On loci, congruences and focal systems deduced from a twisted curve and a twisted biquadratic curve [. 495. IL. 712. LI. 890. VRIES (JAN DE) presents a paper of Dr. G. pe Vures: “Calculus rationum”. 2nd. part. 64. — On metric properties of biquadratic twisted curves. 910. — On the correspondence of the pavis of points separated harmonically by a twisted quartic curve. 918. — On a line complex determined by two twisted cubics. 922. XYXVI ONE EN res. VRIES (JAN DE). On bilinear null-systems. 1156. — On plane linear null-systems. 1165. — An involution of associated points. 1263. VRIES (Miss M. s.), The influence of temperature on phototropism in seedlings or Avena sativa. 1170. WAALS (J. D. VAN DER) presents a paper of Prof. Pu. Koanstamm: ‘On vapoar- pressure-lines of binary systems with widely divergent values of the vapour pres- sures of the components”. 96. — presents a paper of Dr. F. E. C. Scuerrer and J. P. Trevs: “Determinations of the vapour tension of nitrogen tetroxide”. 166. — presents a paper of Dr. F. E C. Scuerrer: “On the system ether-water’’. 380. — presents a paper of Dr. F. E. C. Scurrrer: “On quadruple-points and the continuities of the three-phase lines”. 389. — presents a paper of Mr. J. R. Karz: “The laws of surface-adsorption and the potential of, molecular attraction”. 445. — Contribution to the theory of binary systems. XXI. 602. — Some remarkable relations either accurate or approximative for different sub- stances. 903. — The law of corresponding states for different substances. 971. — presents a paper of Prof. Pa. Konnsramm and Dr. J. Timmermans: “Experi- mental investigations concerning the miscibility of liquids at pressures to 3000 atmospheres”. 1021. — Some remarks on the course of the variability of the quantity 2 of the equa- tion of state. 1131. — presents a paper of Prof. J. D. van per Waals Jr.: “The law of the partition of energy”. 1175. Il. 1355. WAALS JR. (J. D. VAN DER). On the law of the partition of energy. 1175. IL. 1355. waTeR (The system sodium sulphate, mangane sulphate and) at 35°. 1326. WATERMAN (H. J.). Mutation of Penicillium glaucum and Aspergillus niger under action of known factors. 124. — Action of hydrogenious boric acid, copper, manganese, zine and rubidium on the metabolism of Aspergillus niger. 753. ; — Metabolism of tke nitrogen in Aspergillus niger. 1058. — Metabolism of the fosfor in Aspergillus niger. 1058. — and J. Bozsexry. A biochemical method of preparation of /-tartarie acid. 292, — Potassium sulfur and magnesium in the metabolism of Aspergillus niger. 1349. WEATHER FoREcAST (A long range) for the East Monsoon in Java. 1063. WEBER (MAX) and L. F. ve Beaurort. On the freshwater fishes of Timor and Babber. 235. WEBER, (sOepHUs), H. Kamertinco Onnes and C. Dorsman. Investigation of the viscosity of gases at low temperatures. 1. Hydrogen. 1386. — and H. Kamertinen Onnes. Investigation of the viscosity of gases at low tem- peratures. II]. Helium. 1396. ILI. Comparison of the results obtained with the law of corresponding states. 1399. CONTENTS. XXVII WENT (fr A. ® ©) presents a paper of Dr. Jon. H. van Burkom: “On the con- nection between phyllotaxis and the distribution of the rate of growth in the stem”. 1OL5. — presents a paper of Miss M. S. pe Vares: “The influence of temperature on phototropism in seedlings of Avena sativa”. 1170. WERTHEIM SALOMONSON (J. kK. A.). v. Sabomonson (J. K. A. WertTHEm™). w1Baur (s. P.) and A. F, Hontemay. On the nitration of the chlorotoluenes. 594. W1CHMANN (a.). On rhyolite of the Pelapis-islands. 347. — presents a paper of Dr. L, Rurren: “Orbitoids of Sumba”. 461. WINKLER (c.) presents a paper of Dr. L. J. J. Muskens: “The posterior longitu- dinal fascicle and the manege movement”. 727. — presents a paper of Dr. J. H. M. Kuessens: “Form and function of the trunk- dermatome tested by the strychnine segmentzones”. 740. — On localised atrophy in the lateral geniculate body causing quadrantic hemi- nopsia of both the right lower fields of vision. 840. — presents a paper of Dr. C. T. van VALKENBURG : “On the occurrence of a monkey-slit in man’. 1040. WISSELINGH (c. VAN). On the demonstration of carotinoids in plants. Ist. com- munication. 51]. 2nd. Communication. 686. 3rd. Communication. 693. — On karyokinesis in Eunotia major Rabenh. 1088. — On intravital precipitates. 1329. wourr (t. K.) and £, H. Bicaner. On the behaviour of gels towards liquids and their vapours. 1078. woop (kg. w.) and P. Zeeman. A method for obtaining narrow absorption lines of metallic vapours for investigations in strong magnetic fields. 1129. WOUDE (W. VAN DER). On Steinerian points in connection with systems of nine g-fold points of plane curves of order 39. 938. ZEEMAN (p.) presents a paper of Mr. T. van LonuizEN: “Series in the spectra of Tin and Antimony”. 31. — presents a paper of Mr. T. van Louvre : “Translation series in line-spectra”. 156 — On the polarisation impressed upon light by transversing the slit of a spec= troscope and some errors resulting therefrom. 599. — The red lithium-line. 1130. — and C. M. Hoocensoom. Electric double refraction in some artificial clouds and vapours. 178. — and R. W. Woop. A method for obtaining narrow absorption lines of metallie vapours for investigations in strong magnetic fields. 1129. zinc and rubidium (Action of hydrogenious boric acid, copper, manganese) on the metabolism of Aspergillus niger. 753. Zoology. Max Weser and L. F. pre Beaurort: “On freshwater fishes of Timor and Babber”. 235. %WIERS (H. J.). Researches on the orbit of the periodic comet Hones and on the perturbations of its elliptic motion. V. 192. rs oa Q Akademie van Wetenschappen, if Amsterdam, Afdeeling voor ALS de Wis— en Natuurkundige Vel) Wetenschappen pt.2 Proceedings of the Section Physical & Of Sciences Applied Sci. Serials PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY STORAGE [/87