WH. OF ORONTO \BRARY Digitized by the Internet Archive in 2009 with funding from University of Toronto http://www.archive.org/details/proceedingsofsecO2akad Koninklijke Akademie van Wetenschappen . te Amsterdam. PROCEEDINGS OF THE Sao ?rtOn OF § € 1 EN CES. WO) EWP AMs at) ee AMSTERDAM, JOHANNES MULLER. July 1900. (Translated from: Verslagen van de Gewone vergaderingen der Wis- en Natuurkundige Afdeeling van 27 Mei 1899 tot 21 April 1go0. Dl. VIII.) Q O7 AL,S V2 Proceedings of the Meeting » » CLOeN KON T'S. » of May 27, » June 24, September 30, October 28, November 25, December 30, January 27, February 24, March 31, April 21, Or 1900 : , _ : J °° - 7 - : 7 , Fs. a 7 te, a an erry om , a - . KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday May 27th, 1899. DCG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdecling van Zaterdag 27 Mei 1899 Dl. VIII). Contents : “On the system: water, phenol, acetone.” By Dr. F. A. H. Scurememakers (Com- municated by Prof. J. M. van Bemmeven), p. 1. — “On the nitration of benzoic acid and its methylic and ethylic salts.” By Pret. A. F. Hotteman (Communicated by Prof. C. A. Losry be Bruyn). p. 4. — “The system of Sirius according to the latest observations.” By Mr. H. J. Zwiers (Communicated by Prof. H. G. van pk SanpE BAakHUYZEN). p- 6. (With one plate). — “Measurements on the magnetic rotation of the plane of polarisation in oxygen at different pressures.” By Dr. L, H. Srerrsrma (Communicated by Prof. H. KameriincH Onnzs). p. 19. The following papers were read: Chemistry. — “On the system: water, phenol, acetone.” By Dr. F. A. H. SCHREINEMAKERS. (Communicated by Prof. J. M. VAN BEMMELEN.) Two cases may, in general, be distinguished in which plaitpoints appear or disappear on the ¢-surface (by the ¢-surface without further qualification, is meant, both here and in what follows, that area of the ¢-surface which relates to the liquid state). 1. The plaitpoint appears at the margin of the ¢-surface. 2. The plaitpoimt appears, on the ¢-surface itself and not at its margin, Mr. SCHREINEMAKERS has already found experimentally various examples of the first case; for example, in the equilibria between water, succmonitrile and sodium chloride salt or ethylic-aleohol and 1 Proceedings Roya] Acad. Amsterdam. Vol. IL. (2) also in the systems formed from water, and phenol with common salt or aniline or ethylic-alcohol. The second case, viz. the appearance or disappearance of a plait- point on the area of the ¢-surface itself and not on its border, may arise in different ways. It occurs, for example, when a plait divides into two other plaits so that it also occurs with the connodal line which represents the equilibrium between the two liquid phases. According to the resear- ches of Mr. ScHREINEMAKERS this case occurs, most probably, in the system: [water — alcohol — succinonitrile] at about 4°. There is however, another case which Mr. ScHREINEMAKERS has now discovered experimentally. Let us suppose that at a certain temperature T the ¢-surface is at every point convex from below. On changing the temperature a plaitpoimt may now appear on the C-surface, which, on a further change of temperature, may develop into a plait in such a way that connodal lines with two plait- points are produced. We then have the case that at this tempera- ture the three compo- nents, taken in pairs, are completely miscible, but that ternary mixtures exist for which this is not the case. Mr. SCHREINEMAKERS has realised this in the system: [water (W) - phenol (Ph) — acetone (Ac)| for which the con- nodal lines for 30°, 50°, Ac, 8°; 80°, 85° and 87° are diagrammatically repre- sented in figure 1. Their lig. exact positions can be found by means of the following tables. Composition of the solutions on the connodal line at 30°. o/, W 92"-92.3 91 “88:4; ¥81 ~ 7079" 16251) 151-6 ~ 39:8) 28:9" (21-8 Ac 0 Le ee 7.6 15 23.1 28.9 349 40.2 43.1 40.2 foil) Tomes) 6 5 4 a 9 13.5 20 28 38 1 ) lor) ole W 18.4 17.2 17.9 19.1 21.1 22.6 25.2 27.1 28.7 30 31 0/, Ac 34.1. 25.8 81.1 12.9 (4 4:65 92:3 1.3 O:5 aU pe 47.5 57 64 68 695 720 70.2 70.6 70 69.5 69 (3) Composition of the solutions on the connodal line at 50°. 07,W 89 90.3 90 87.5 §3.8 69.4 60 49.3 37.8 23.3 0,, Ac 0 Alias ee Om ON 522.65 828 33.2 38.2 34.7 Q/)Ph 11 8 6 5 5.5 8 12 17.5 24 42 7,W 20.9 22.7 246 26.4 29.1 32.2 34.4 36.3 38 OAcmeatetee V5.3) ek 4s 86, 0.4. 2.8 16° 0.7 60 %/)Ph 58 62 64 65 65.5 65 64 63 62 Composition of the solutions on the connodal line at 68° %% W 66 50.1 45 39.6 34.6 31 28.6 26.9 26.4 % Ac 0 WM 22 eda) O41 eal 13.4 18.1 26.6 0/,)Ph 34 AQ 53 57 59 59 58 55 47 07 W 33.9 46 56.6 66.5 77.6 847 87.6 86.4 66 9, Ac 34.1 31 2O4e taieoe ta A Noy 3.96. L.Os 0 O/Ph 32 23 17 12 8 8 8.5 12 34 Composition of the solutions on the connodal line at 80°. 7, W 83.3 82.9 74.7 61.8 52.5 40.6 32.2 33.4 35.4 OT ACMO(gnmid(lge td Sama OKe 2405) ata 2i-8) 556) “ICG phe do) 107 aohithe ISS 230 Ble 146 Abd «IE owe «4.0.5 49S 262.7 baNes Vb do. 2.8 Ph 52 46 384.5 Composition of the solutions on the connodal line at 85°. OW SOL Wi 58:4 49:50 87:2. 39:2) 44.3 58.9 OAc, 9:9) 03.35 191. 922.9 17.8 12:8 © 818.151 % Ph 13 15 22.5 28 45.5 48 47.5 36 Composition of the Want he Ae Of Ph 78.3 70.1 Oe 2.9) 15 17 6. 8.5 5 1 25 solutions on 44.3 41.5 46.4 64.5 Ont Udion 826) ) 5.5 35 45 45 30 the connodal line at 87°. 1* (4) The preceding tables are obtained by interpolation. Varying quantities of phenol are added to mixtures of water and acetone containing 1.83, 4.24, 7.94, 15.6, 24.6, 31.8, 40.4, 50.2, 59.9 and 64.9 percent of acetone, and the temperature was determined at which the two liquid phases which form are converted into a single phase. Let us now examine the different connodal lines in figure 1. Below 68° they terminate in two points on the side W-Ph. of the triangle; these two points represent two binary solutions which are in equilibrium with each other. The positions of the conjugate points on the connodal line itself is still unknown. At 68° the connodal line touches the side W. Ph. in a point, at which the two liquid phases of the binary system W. Ph. become identical. As is shown in the figure at 80°, 85° and 87°, the connodal lines at higher tem- peratures lie wholly within the triangle and approach each other as the temperature rises, disappearing finally at about 92° in the point F. The composition at the point F is approximately 59 °/, of water, 12°/, of acetone and 29 %, of phenol. Above 92° the ¢-surface is convex at every point when regarded from below; as the temperature falls a double plaitpoint therefore appears at the point F, when this temperature of 92° is reached. On further depression of the temperature the point F develops into a plait with two plaitpoints, of which one moves towards the side W. Ph. where it disappears at 68° in the point at which the con- nodal line of 68° touches the side W. Ph.; at still lower tempera- tures therefore one point of folding alone remains. A further investigation will show whether it is possible in some measure te learn the course of the plaitpointcurve. . Mr. SCHREINEMAKERS has thus shown experimentally that connodal lines with two, one or no plaitpoints may appear on the ¢-surface. The first example with two plaitpoints has been communicated in the preceding paper; in previous investigations connodal lines with one and with no plaitpoint were referred to. Chemistry. — ‘On the nitration of benzoic acid and its methylic and ethylic salts.’ By Prof. A. F. Hotueman. (Communi- cated by Prof. C. A. Lopry pr Bruyn.) Some time ago (Recueil 17.335) I described a process for the quantitative determination of the three isomeric mononitrobenzoic acids in mixtures of them. This process has been simplified and improved so that the results obtained by it now attain an accuracy (5) of about 1°/,; by this means an answer to the following questions is obtainable : 1. To what extent does the proportion in which the acids are formed in the nitration of benzoic acid depend on the temperature at which this takes place? 2. How do the methylic and ethylic salts of benzoic acid behave in this respect? These two questions being answered we find at once, (3). How this proportion is modified by the replacement of the hydrogen of the carboxylgroup by methyl or ethyl. This appears from the following table: Nitratiou at — 30° ge -+ 30° () 14.4 18.5 29.3 Benzoic acid ¢ m 85.0 80.2 76.5 p| 0.6 1.3 1.2 to) 23.6 257 Methyli ag 74.4 69.8 benzoate. p 2.0 4.5 —40° t) 25.5 28.3 27.7 Ethyli ay, m| 73,9 | 68.4. | 664 benzoate. peers 3.3 5.9 From this it is obvious that the characteristic of the process of nitration, the preponderant formation of the meta-acid, is retained throughout the interval of temperature of 60° and is unaffected by the substitution in the carboxyl group, but that the quantity of secondary products is considerably increased both by raising the temperature and by the substitution. The details of this investigation will shortly be published in the “Recueil”. Groningen, May, 1899. (6) Astronomy. — ,7he system of Sirius according to the latest obser- vations”. By Mr. H. J. Zwiers. (Communicated by Prof. H. G. VAN DE SANDE BAKHUYZEN). In N°. 3336 of the ,Astr. Nuchr.”’ I have deduced the system of elements of the companion of Sirius so as to have an example for the application of my new method of computing the orbits of double stars. I have found : Elements I. T = 1893.759 “ = — 7°.04486 (Period = 51.101 year) e= 0.6131 i= 44° 56'.0 d= 37 3.6 (1900.0) A=n2—S = 223 36.6 t— a The observations which served as a basis for this orbit, extend from 1862 till the spring of 1890, when the companion was seen for the last time at Lick-Observatury by Burnuam. For about six years it then disappeared in the rays of the principal star, till, towards the end of 1896, new measurements could be obtained again at Mount Hamilton. The absolute positions of Sirius, as observed in the meridian of Leyden, were reduced to the centre of gravity of the system by aid of the elements just given, combined prelimina- rily with the distance of the principal star to this centre, as found by Auwers. In pursuance of the same object I immediately after the reappearance of the component took the computation once more in hand. For the computation of the final values I thought it advisable however to await a few further oppositions. As soon as Messrs. KEELER and AirKen of Lick-Observatory had kindly communicated to me by letter, in February and March of this year, the results of their measurements in the recent winter, I have deri- ved the final equations!). The error of my ephemeris amounting 1) An observation received iu the beginning of May from Prof, Hussgy arrived too late to be included in the computation, = Cm) in the winter of 1896—97 to over 4° and decreasing the following winter to somewhat over 2°, now proved to be reduced to 0° in the last opposition!). A total of 16 serviceable measurements after the periastronpassage seemed sufficient to venture on a correction of the elements of this interesting system. The space not allowing me to enumerate here all the separate measurements, I must refer to the Astv. Nachr. 3084—85, for the observations up to 1890, where Prof. AUWERS communicates them in extenso. Here and there only do the positions used by me differ a little from his on account of assigning slightly different weights to the results of the separate nights. Just as Prof. Auwers I had formerly been obliged to derive a measurement of Haxn in 1888 from the compilation given by Prof. Burnuam in Monthly Notices lviii 6 without knowing its source. In the 2nd part issued since then of the Observations of double Stairs, made at the U. S. Naval Obser- vatory by AsaPpH Hatt, | find: 1888.248 p = 23°27; s=5"177, with remarks as faint, very faint, extremely faint for the separate nights. Not being able however to make the angle of position agree in any way with the surrounding measurements I have now also excluded this measurement. Farthermore Mr. Hatt gives a few yearly means differing slightly from his previous statements in WM. N., A, N., and A. J. I considered the last values the best and have modified the previous data accordingly. The communication of the separate measurements after the peri- astron-passage would demand too much space; I therefore restrict myself to the following table of the mean numbers for each observer *). The observed angles of position have already all been reduced to the meridian of 1900.0 by applying the correction for precession. 1) It may be mentioned here that the orbit of Prof. Auwrrs leaves the following deviations (Os. — Comp.) : 4+ 15°.24; + 13°.87;-+1 11°53. These are indeed greater, but they also indicate that the assumed time of revolution is nearer the truth than mine. 2) As a rule all the observations of one and the same observer during one opposition are contracted into a single mean. With the relatively great changes in 7 however, the motion of the angle in this part of the orbit is far from regular and the 2nd differences (with an ephemeris from year to year) amount to several degrees. I have therefore not dared to join into means the observations 5 and 11, 7 and 12, 13 and 15, 14 and 16; in every case the difference in time amounts to half a year nearly. Un passing the proofs through the press). In M. N. lit 6 is still communicated the following measurement of Lewis at Greenwich with the 28-inch: {89*.21l4, §= 179°2, +=4"68 (1 night). This had been overlooked but would have received at all events the weight 0, the deviation in the angle of position amounting almost to 10°, 7. e to more than 05 in are of the great circle (according to elements II: Ab=+ 9°93; Av = + 063). (8) ; | Observation. | Number ay Ae N°, | Date. Observer. —= of n a ee D rs nights. P r i r | | | 1 | 1896.920 | Schaeberle ') | 189920 [373 4 3 ]+4°60 —0"35|—0°27|—0''06 2] 97.017 | Aitken %) | 187.03 |3.84 8:5 |4]4+8.81/—0.27|0.83)|-+0.03 3} 206 | Hussey *) | 186.62 [3.78] 1 |1146.04/-0.3914+1 84|—0.06 4| 916 | Brenner *) | 189.07 13.68, 2 |0]+8.63|—0.49|4-4.46\—0.16 5 | 1897.802 | See 6) | 173.89 |4.63} 4 |3[41.19|+0.99|-1.52|-+0.67 6 .818 | Aitken 6) | 174.78 |4.03) 4:3 |3]49.98|—0.32 ~0.38-+0.07 7 -828 | Boothroyd 7) | 173.66 4.95] 2 | 2 41.29 +0.60|—1.35) +0.99 8 839 | Schaeberle *) | 175.18 3.95 3 | 2]4+2.94|—0.401-++0.34|—0.02 9 940 | Hussey *) | 175.04 [4.03] 8:2 |2[44.07\~0.37]41.72140.08 10 | 1898.151 | Aitken 9) | 170.82 4.29] 2 | 2[42.44\—0.2914-0.63 +0.18 1 .273 | See 11) | 168.93 /4.79| 3 le +2.02)-+0.31]4+-0.52 40.73 12} .276 | Boothroyd ) | 170.74 [4.86 3 |2|+8.87/+0.38|+2.37/+0.79 13 | 1898.737 | Aitken 10) | 161.68 |4.22 3 |? +0.14/—0.40]/—0.21)+0.04 14 .785 | Hussey ) | 162.10 4.18) 2 |2]4+1.10/—0.45]+-0.86\—0.02 15 | 1899.177 | Aitken —!°) | 154.30 4.55 1 |1]—2.44|—0.90]—1.76/+0.94 16 .286 | Hussey 1°) | 154.63 pe 3 | 2]—0.96|—0.3S}-0.04/+0.06 A. J. 394; mean having regard to the weights. — 2) A. N. 3465; Ist, 7th and Sth nights weight 2. — 3) A. J. 427. — 4) A. N. 3421; excluded for unreliability of the method — *) A. N. 3469; every night weight 1. — %) A. J. 424 and 429; mean having regard to the weights. — 7) A. N. 8469; the two nights equal weight. — 8) A. J. 420, — %) A. J. 427; every night weight 1. — 1°) Received in MS.; mean having regard to the weights. — 1) M. N., Iviii 7; all the nights weight 1. The manner in which the weights have been deduced shall be stated farther on; in both eclumns A, are contained the differences from my elements of A. N. 3336 in the sense Obs. — Comp. My first work was to investigate anew the personal errors of the observers. These attaining considerable amounts especially in the distances I resolved to found the correction of the orbit exclusively on the angles of position. With the exclusion of the evidently un- successful measurements the means were taken of the differences Obs. — Comp. for every opposition, a diagram of these was made, the points being connected by a curve in the best way possible. Ac- cording to the method of Prof. Auwers I aiso assigned weights of the form q¢= mn, where m depends on the telescope and » on the number of nights. I assumed preliminarily : (9) m=—2 for: Dearborn Obs. (7, Hoven), Mt. Hamilton (both refractors), Princeton (23-inch), Virginia Univ., and the 26-inch of Washington. m=—=1.5 for: Cambridge (Mass.), Cincinnati, Glasgow (Mbo.), Malta, Ruruerrorp & Wakery, PerRRotIN, BiGouRDAN, OZ, Russet and the small refractor at Washington. m= for all the other observers at refractors of at least 9-inch or reflectors of at least 20-inch aperture. Farthermore : n= 4 for more than 6 nights. n= 3 for 4, 5 or 6 nights. n = 2 for 2 or 3 nights. n= 1 for 1 night. =q was multiplied for every yearly mean by the (computed) distance 7 in order to reduce to ares of the great circle and so to obtain comparable weights. Finally to every yearly mean Obs. — Comp. a weight p= , rounded off to tenths, was assigned. gi 100 Observations deviating more than O”5 (in are of the great circle) were always excluded. By comparing Obs.—Comp. for every observer with the corres- ponding ordinate of the curve, corrections were deduced whose mean furnished the following personal corrections (the weights, according to the number of nights, being taken into consideration). Observer. Ab S Observer. AS 5 Observer. Ab S E E E sigourdan +0°77| 3 | Hall —0°33)2 and 4] Stone +1°79| 3 Bond —0.09) 3 | Holden +] 12) 4 Struve —0.53) 3 Burnham —0.28) 4 | Hough +0.24| 4 Wilson +1.10) 3 Dunér +0.16) 2 | Howe +0.07) 3 Winlock +0.56) 3 Engelmann |—0.45) 2 | Newcomb 40.09 2 and 4] Young —0.15)2 and 4 Foerster +0.05) 2 | Peirce —0.94) 3 Frisby —0.96! 4 | Pritchett (C.W.) |—0.71) 3° The measurement of STRUVE at Rome gets the weight 2. Burn- HAM’s measurement in 1881.85 at the 12-inch at Mt. Hamilton is united to his measurements at Dearborn Obs.; likewise the measure- ments of ENGELMANN at the 74-inch and the 8-inch at Leipzig and those of Newcomsp at the small and the great refractor at Washington. For Youne and Hau the corrections obtained for the (10 ) small refractor were united with half weight to those for the great one. Wherever in the last column two weights are given, the former refers to the smaller instrument. Observers whose personal corrections could not be deduced received as a rule a weight that was 1 smaller than otherwise would have been their due with a view to the nature of the instrument. A weight 3 was assigned to LEAVENWoRTH, Prerrotin, Prerers and Watson; 2 to Cuacornac, Fuss, LassELt, Martu, H.S. Prircnert, RUTHERFORD & WakELy, SEARLE, Upton and WINNEcKE; the others received a weight 1. After applying these corrections we could pass to the formation of the definitive yearly means Ols.—Comp. The assigned weights were again of the form gu, where was assumed as before. The following table contains in the first column the mean date, in the second the preliminary means Obs.—Comp. which have served for the construction of the curve of the errors referred to before, in the third the definitive means corrected for personal error. The last column furnishes in the same way as before the value of r= (gn), 100 Date. | Ai § | Az $ | P l l 1862.21 | 40°57 | +0°49 21 fasts. ; —0°02 | +0°12 | 6.8 1863.92 | -+0.13 | +0.33| 1.7 | 1879.13 lsiriner| Soraoc| tere 1864.90 | —0.74 | —0.93 | 9.8] 1880.16 | +0.98| +0.38| 8.8 1865.91 | —0.91 | —-0.14 | 2.3] 1881.17 | +0.18| 40.04] 9.0 1866.91 | —0.02 | +0.10 | 9.3 | 1882.21 | —0.27 | —0.07 | 10.1 1867.90 | +0.93 | --0.21 | 9.8 | 1883.15 | —0.14| —0.32| 7.5 1868.19 | —0.49 | —0.54 | 3.6] 1884.18 | —0.46 | —0.43 | 7.2 1869.19 | 0.00] —0.96| 9.9] 1885.19 | —o0.91 | —o.15| 4.4 1870.17 | —0.65 | —0.73 | 3.7 | 1886.14 | —0.32 | —0.93| 4.0 1871.22 | —0.70 | —1.12 | 1.3] 1887.19 | —1.12 | —1.07] 2.8 1872.18 | —0.03 | —0.55 | 3.0 | 1888.970 | ...... =0:16\) 0:6 1873.99 | —0.74 | —0.92 | 1.4] 1890.975 | ...... ==ieaaal 1088 1874.18 | —0.49 | —0.47 | 4.2] 1897.004] ...... | 44.38 | 1.3 1875.99 | —1.14 | —0.89 | 4.7] 197.971 | ...... 42.43 | 3.2 1876.14 | —0.48 | —0.19 | 4.0 | 1898.844 | ...... +001} 0.9 1877.19 | —0.44 | —0.22 | 4.4 2 (Coie) For the last position the measurement of Hussey in April 1899 could not be taken into account. Of all the measurements after 1888.0 the means are taken without regard to personal correction, this not being independently deducible and the use of the value deduced above for Burnuam being prohibited on account of the entirely different appearance of the system. That the number of the normal positions might not be unneces- sarily great 1 formed normal places by uniting the yearly means two by two according to their weights for the whole of the period 1862—1880 when the changes in distance were still very slight and the motion of the angle therefore pretty regular and moreover very small. An exception was only made for the first three, of which only one position was formed. In order to simplify still further the following computations, the value of log ,/p was rounded off to tenths; these modified values are indicated by log /p' to distinguish them from the preceding. In this manner the following 21 normal deviations were obtained: N°.| Date Ab [4 ve N°.| Date A$ | L. ve N°.| Date Ab |2.Yp! 1 |1863.31 ;—0°154) 0.4 | 8 1877.75 0°01 4 0.5 | 15 ‘1886.14 /—0°23) 0.3 2 |1865.71 |—0.020) 0.38] 9 {1879.84 |10.217| 0.6 | 16 |1887.19 |—1.07) 0.2 3 |1867.76 |—0.219| 0.4 | 10 |1881.17 |40.04 ee) sbsbeli l1sss.970|—0.16 959 4 |1869.80 |—0.555| 0.4 | 11 |1882.11 |—CG.07 | 0.5 | 18 1890.275 —1.44 Sori 5 |1871.89 |—0.722| 0.3 | 12 |1883.15 |—0.32 | 0.4 | 19 |1897.004/ 44.38) 0.1 6 1873.94 |—0.582} 0.4 | 13 |1884.18 |—0.43 | 0.4 7 20 |1897.971|-+2.43) 0.3 7 \1875.64 |—0.568! 0.5 | 14 1885.19 |—0.15 | 0.3 | 21 11998. 844 +0.01) 0.0 | | As has already been stated the observations after the periastron- passage could not be treated in the same way as the previous ones, because for that part of the orbit the data are far from sufficient for a satisfactory deduction of the personal corrections. This statement however does not imply that the corrections found before 1888 are not at all subject to doubt. Whoever’s task il was to investigate the critical problem of these corrections will immediately admit, that in a part of the orbit where e.g. two of the observers have a predominating influence, there can be no question about a complete elimination of the personal errors, even apart from the fact that the accidental errors are often many times greater than the constant ones. Hence the determination of the latter may be very uncertain, ( 12 ) Moreover it is a fact that the personal error often varies greatly with the angle of position itself, especially when the latter, as is the case with Sirius, gradually falls from 90° to 0°, so that the con- necting line passes from the horizontal to the vertical position. However I did not feel at liberty to pass over the entire question ; the indications of systematic differences were often too clear for doing so. With regard to the last three normal positions I have still to remark that to the 24-inch refractor of Lowell Observatory the same weight 4 is assigned as to the 36-inch of Mt. Hamilton. The diffe- rences A @ have been laid down in the following diagram and have been joined by right lines. That the remaining errors might vanish as nearly as possible the differential relations were derived between the differences in the angle of position @ and the several elements. Without difficulty we find: ae on MOA Ret cost AA a cot w + tg w cos*i 2 2 ae eS) sin Ecos i(2 — e® — ecos E) A p+ (=) costcos (p A My + r . 2 a (=) cosicosp(t—T)Au. - In this expression w indicates the distance from the node, measured in the plane of the orbit, E the excentric anomaly, r the apparent, and / the true distance of the companion, g the angle of excentricity. The epoch 7), for which 4, stands, may be chosen arbitrarily; I have placed it somewhere in the middle of the period of observation namely at 1880.0. The equations of errors obtained were treated in the well known manner according to the rules of the method of the least squares; to make the coefficients less unequal the following substitutions were made (logarithmically) : r= 006A Sd; y = 0.0 Ai; z=0.7 Aq; Toma) BSI 0975 vi 0.4 Pye w= 0.5 A My; n= 0.7 degrees. ( 13) For the sake of brevity I state only the normal equations found (numerical coefficients) 47.54570 2 — 5.397497 +2.90792z +0.63518 ~ + 9.67691 » +4.10538 w = —0.39533 —5.39749 2 +10.82040 7 —2.44634 2 +2.60262 « — 7.12051 » —0.31185 w =-+2.69237 +2.20722% — 2.446347 +-3.76221 2 —1.35865 ~ + 2.10846 v —0.23716 w =—2.15710 +0.63518 2 + 2.60262 y —1.35865 2 +1.89029 w + 1.00294» +1 96019 w =-+1.73341 +9.67691 2 — 7.12051 y +-2.10846 z +-1.00294 « +-12.66065 » 4-5.51165 w ——0.26101 44,10538 2 — 0.31135 y —0.23716z +1.96012 u + 5.51165 » +3.72403 » =-11.34712 These equations furnished the following values (logarithmically) : v= 0.820019 z= 0.330168, v = 0.790540, y == 9.055875 u = 0.615761, w = 0.628364 from which were deduced: Reade? 227” ees — 7°. 87278 System I pa 4do 1012) = 10876656 (T= 1894.0696) e = 0.5832 7), == IE ayes I thought it more advisable however to deduce the two elements “# and 7 directly from the observations, rather than from the above values. With the corrected elements §%, 7%, e and 4 the mean ano- malies were deduced from the first and the last three angles of position; these were then united with suitable weights into 2 mean numbers, from which was easily deduced : [b, f= — 7°.814775 T= 1894.0367 With these elements the following errors were left in the normal positions: 1: —0°.131 7: —0°.422 13: +0°.008 19 ; —0°.207 Pee KORO este Onii4e edd 0.45] 20°: 280.151 Sera e0y 0250 19.5 20).862) 15: 420.597 ~ 21-0: .220 4: —0.319 10: +0 .224 16: +0 .119 Or Oeste: 0163.9 17 = --2 2108 ( 14 ) These errors are also represented in the lower diagram and con- nected by interrupted lines. Especially the last two positions before the periastron are now badly represented, a fact not to be wondered at, considering the large amount of the corrections of the elements. Although these positions have but the weights 0.6 and 0.3 I have yet proceeded to a second approximation. For the new 2nd members of the normal equations [I found : 4+0.32052 -+0.66856 +0.51950 +0.20554 +0.30590 +0.37168. After a new solution of the normal equations sand 7 were again determined as above; the system of elements obtained is: \ T = 1894.0900 AG 9 System II. we = —7°.37069 So= 4430.2 (1900.0) A=212 6.4 The deviations left by this system in the normal positions are as follows. They have been connected by dotted lines in the diagram. 1 : —0°.203 7: —0°.433 13 ; —0°.521 19 : —0°.300 2: +-0 .209 8: +0 .034 14 : —O .205 20 : +0 .158 3: +0 .082 9: +0 .182 15 : —0 .218 21 : —0 .087 4: —0.250 10: —0.032 16 : —0 .925 5: —0.455 11: —0 .161 17: +0.773 6: —0.880 12 : —0 .420 18 : +0 .098 The outstanding errors are unimportant, but a certain regu- larity is unmistakable. The characteristic curvature in the original curve of errors before the periastron, is found back all but unchanged in the diagram of systems 1> and II. The cause may be sought in a perturbation by a third (invisible) member of the system ; the suppo- sition however that not entirely eliminated personal errors have been at work seems to me more plausible. A third possibility remains : the not perfect accuracy of the coefficients of the equations of errors in the 2nd approximation might be the cause. Strictly speaking these ought to have been recalculated with the elements of system I>, (15 ) But this supposition is already very improbable @ priori. To arrive at certainty on this subject without an entirely new and prolix com- putation, I made use of the method of KLINKERFUES based on six angles of position. The ratio of the planes of triangles in the appa- rent orbit to those in the true orbit being always as cosi: 1 we have sin (vg—v) sin (vg—v¢) sin (Og—O) sin (O;—Og) sin (vg—v}) sin (vg—vg) ste (G3 —O4) sin (Ag.—Og) and two other similar equations in which the indices 4 and 5 are successively to be substituted for the index 5. For the epochs of the normal positions 2, 6, 10, 14, 17 and 20 the deviations of these normal positions were united with those of the two neighbouring ones according to the weights. We thus -obtained : O,= 76°.219 0,=59°.650 63 = 45°.476 0, = 33°,573 Galore Opa 1937.009. The second members of the equations may be denoted by @, /? and y: a@ = + 0.481680 (P= + 0.297904 y = + 0.120061 Istarted successively from 4 hypotheses : 1° system II; 2°A M,=-+1°; ? 3° A w==-+ 0°.03; 49>Ac=-+ 0.01. From the three anomalies deduced from these I computed : Ist hypothesis. 224 hypothesis. 3°¢ hypothesis. 4th hypothesis. a + 0.468089 + 0.465082 + 0.464792 + 0.474842 R ++ 0.294009 + 0.290553 + 0.290125 + 0.304140 y +0.119778 + 0.117508 + 0.116272 + 0.135123 from which the following equations ensued : — 0.003007 A VM, — 0.003297 A uw + 0.006753 Ae == +-0.013591 — 0.003456 AM, — 0.008884 Aw + 0.010181 Ac = + 0.003895 — 0.002270 A M, — 0.003506 A « + 0.015346 Ae = + 0.000283 (16 ) The solution of these equations furnished the following entirely improbable values: A M, = + 51°.8590 A w= — 2°.011252 Ae= — 0.07627 The question of course remained in how far these values might be brought within admissible limits by small allowable modifica- tions in the assumed angles of position. Moreover, on account of their being arithmetical means, the corrections assumed for the six epochs were rot exactly situated on the curve which connects the deviations in the best way possible. I have constructed therefore the curve of errors for the Elements II on a relatively large scale and I have deduced by its aid, for the same epochs as above, the following angles of position: O,=76°.281 0,=59°.581 O,== 45°.446 0, = 33°.503 0; = 138°.029 Og = 172°.924 From these I computed: @=+0484570 B= +0.299769 y= + 0.120473. The solution of the equations now led to: A M, = + 57°.0261 Ag=— 2°.23501 Ae=— 0.0854 It seemed to me that this proved sufficiently how impossible it is to cause the disappearance of the observed systematic course by a purely elliptic motion and I therefore stopped at System II, taking this to be the best which can be deduced for the present from the observations. Finally I have determined the semi-axis of the orbit for each observer who had given more than three measurements of distance. As a rule measurements leaving a greater error than 0”.5 were excluded. This fate befell, besides one unsuccessful observation of SEeccH! in 1863, only 5 other measurements of OX. This is not to be wondered at, if we consider the low position of Sirius at Pulkowa. The results obtained are compiled alphabetically in the following table where the column n» gives the number of measurements from which @ is deduced. (17) Observer. a | 2 Observer. a n | Aitken 7.805) 5 |Hussey ; 7.594 4 Bigourdan 7 507) 5 [Newcomb 7.747) 4 Burnham 7 404 10 |Peirce \7 576) 4. Denér |? .417| 5 |Pritchett (C.W.)|7 .668) 5 Frisby \7 .776| 4 [Stone 7 .423) 5 Hall (7.533) 18 |Struve 7 .812} 14 Holden 7 .911! 7 |Wilson vii 314 4 Hough 7 .3858) 8 |Young 7.579) 7 From all the measurements of the above observers I find in the mean 7594 for the semi-major axis. The complete system of elements by the side of which I introduce for the sake of comparison the one found by Prof. Auwers in 1892, runs as follows: System IT, System V*, ZWIERS AUWERS a 1894. 0900 1893. 615 fe —7°37069 —7°2877 IZ 48.8421 year 46.599 year e 0.5875 0.6292 i AG° 1'9 42° 25'6 Sb 44 30.2 (1900.0) 37 30.7) (1850.0) m—Sb 212 «6.4 219 56.5 a 7594 7568 I have also investigated for systematic deviations the distances found in the various years. To each observer of the above table the weight 1 was given (with the exception of the 6 measurements, men- tionned above), the remaining ones were given the weight 4, evident failures being excluded. After the periastron-passage the observations of Sex and Boornroyp were omitted. As appears from the table ) Reduction to 19)0.0 + 167.9. Proceedings Royal Acad. Amsterdam. Vol. II. (18 ) on page 8 where in the columns A, the various values of Obs.— Comp., as resulting from a comparison of the observations with System IT, have been given already, these observations deviate in distance from 067 to 0"99 (in the same direction) from the com- puted ones, whereas the other distances, measured at Mt. Hamilton, fairly oscillate round them. The following consideration proves a priori that the latter must come nearer to the truth. The area of the sector traversed yearly is already known with great approxi- mation from the first part of the orbit. So in each new orbit 11% are (0,—O,) must have about the same value as in the old one. Now 0,—0, is equal to 27°424 as appears from the normal posi- tions 19 and 21, and equal to 23°052 according to the old orbit. Half the difference of the logarithms is 9.96229 = log. 0.9168, so that the old distances must be diminished on an average by 8.32°/,. This gives for 1897.0, 1898.0 and 1899.0 respectively 3”8, 40 and 4"3 (compare the ephemeris below), whilst the observations at Lowell Observatory gave much greater values. The following table gives the yearly means obtained for a with their weights. It is easy to understand that from 1887 an error in r must appear magnified in a. 1862 8"33 (1}) 1873 7"33 (4) 1884 750 (74) 1863 7.65 (2) 1874 7.63 (34) 1885 7.42 (4) 1864 7.81 (2) 1875 7.49 (5) 1886 7.47 (5) 1865 7.49 (24) 1876 7.75 (44) 1887 7.62 (3) 1866 7.69 (64) 1877 7.64 (4) 1888 7.47 (2) 1867 7.57 (3) 1878 7.66 (5) 1890 7.74 (1) 1868 7.58 (44) 1879 7.61 (74 1897 7.58 (5) 1869 7.53 (44) 1880 7.49 (8) 1898 7.72 (3) 1870 7.69 (3) 1881 7.53 (104) 1899 7.85 (2) 1871 7.65 (4) 1882 7.51 (8) 1872 7.67 (54) 1883 7.62 (6) In the upper figure of the diagram accompanying this paper these values are laid down for the middle of the year and have been connecied by right lines. One can see that the deviations are but — (aig) relatively very small (the weight of the value found for 1862 is in fact about zero) and that the values continually oscillate round the horizontal line of 759. Sixteen times the latter is intersected by the connecting lines, fourteen times this is not the case. There is no indication of systematical errors of any importance and I believe I am justified in declaring that system II satisfies all just claims. For a comparison with future observations I have deduced an ephemeris, an extract of which follows in the subjoined table: Date 6 r Date 6 r Date 4 r 1896.0 | 205953 | 3”60 | 1900.5 | 140964 | 4"77 | 1905.0 | 107°17 | 6”80 .5 | 196.61 | 3.71 | 1901.0 | 135.60 | 4.97 5 | 104 67 | 7.03 1897.0 | 188.14 | 3.80 5 | 130.97 | 5.18 | 1906.0 | 109.34 | 7.96 5 | 180.08 | 3.90 | 1902.0 | 126.71 | 5.40 .5 | 100.14 | 7.49 1898.0 | 172.42 | 4.00 5 | 199.78 | 5.63} 1907.0 | 98.07 | 7.71 .5 | 165.17 | 4.12 | 1903.0 | 119.16 | 5.86 5 | 96.12 | 7.93 1899.0 | 158.36 | 4.26 5 | 115.82 | 6.09 | 1908.0 | 94.97 8.14 5 | 152.00 | 4.41 | 1904.0 | 112.72 | 6.33 5 | 92.52 | 8.35 1900.0 | 146.10 | 4.58 .5 | 109.85 | 6.56 | 1909.0 | 90.85 | 8.56 The parallax of Sirius has been determined very accurately by the heliometer measurements of Ginn and ELKin at the Cape in the years 1881—83 and 1888—89. If we take with Grin 0"374 + 0006 for the mean according to the weights (M. N., Jan. 1898, p. 81), we shall find for the sum of the masses of the two stars 3.51 times that of the sun, of which, according to Auwers (l.c. page 231) somewhat over ?/, is due to Sirius itself. Physics. — “Measurements on the magnetic rotation of the plane of polarisation in oxygen at different pressures.” By Dr. L. H. Srertsema. (Communication N°. 49 from the Physical Laboratory at Leiden, by Prof. KAMERLINGH ONNES). The results of my measurements on the magnetic rotation of the plane of polarisation in some gases, made at a pressure of about 100 atm., agreed fairly well with those made by Kunpt and Rén?GeEn '). 1) Arch, Néerl. (2) 2, p. 378 (1899); Comm. Phys. Lab. Suppl. 1. ( 20 ) If we want to compare them with those made by H. Becqueret, who has worked at a pressure of 1 atm. we must make use of a supposition on the relation of the rotatory constants at 100° and at 1 atm. The simplest supposition already made in the treatise men- tioned is, that the rotation is proportional to the density of the gas!). But then differences will be found between Becqueret’s results and mine, which in the case of oxygen amount to over 10 °/) and even more than that in the case of other gases. These differences might make us doubt the validity of our supposition *), and this caused me to make some measurements on the rotatory constants in oxygen at different pressures, in order thus to put to the test the propor- tionality of rotation and density. Till now the pressures were read on a metal-manometer, the corrections of which had been previously determined *). In order to obtain also a sufficient precision especially for lower pressures, the pressure was measured with the hydrogen manometer, used by VERSCHAFFELT in his investigations on the isothermals of mixtures of CO, and H,*). I used this manometer in the same way as he did when he compared its indications with those of the standard open manometer °). The copper connecting-tube mentioned there was now fixed to my apparatus. Mr. Harrman kindly took upon him to take the readings of the manometer. The pD’ARSONVAL galvanometer®) has now been clamped in a stand suspended as invented by JuLius, to protect it against vibrations’), so that the readings could be taken with greater accuracy. For the rest, everything was used in the same way as before. The observations are made with commercial oxygen at four pres- sures, at each of which three or two sets of adjustments have been made, in the same order as before®). The calculation®) then yields é Q@ : for each a number proportional to ie! where @ is the rotatory ; constant and d the density, borrowed from AMAGAT’s !°) observations. These numbers are: elec. yp. 1328. Vl iex ps, 39. 2) 1. ¢. p. 300. ‘) ‘Lhesis for the doctorate, Leyden 1899, p. 15. Comm, Phys. Lab. No. 45 and 47. 5) Thesis for the doctorate, p. 17. ®) Arch. Néerl. p. 305, 7) Wied. Ann. 56, p. 151 (1895). 8) 1. c. p.320, 9) lc. p. 325—330. ) Ann. de Ch, et de Ph. (5) 19 p. 375 (1880). Pressure in atm. ia x const. means. 97.38 1565 | 96.68 1560 1559 96.13 Isha} | 73.04 1571 | 72.82 1548 \ 1555 72.50 1545 | 49.33 1555 } 1555 49.15 1557 38.47 1546 | 38.44 1545 \ 1550 38,12 1558 | i All measurements are made at a wave-length of 0.608 «. The means can be esteemed equal, because the differences lie within the errors of observation '), and we find our supposition confirmed for pressures ranging from 100 to 38 atm. If at 1 atm. variations of 10°/, would appear, we could expect them to be per- ceptible at least at 38 atm. This not being the case, we shall have to look elsewhere for the cause of the difference between BecQUEREL’s results and mine. With N,O and with CQO, the differences 2) alluded to are much greater and it might be possible that with these gases, which diverge more from an ideal gas than oxygen, deviations from the proportionality im question would be perceptible. Therefore I intend to make the same measurements on the mag- netic rotation of one of these gases also. (June 20th, 1899.) KONINKLUKE AKADEMIE VAN WETENSCHAPPEN TH AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday June 24th, 1899. — EG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 24 Juni 1899 Dl. VIII). Contents: “On the influence of water upon the rapidity of the formation of ether from me- thyliodide and ethyliodide and from sodiummethylate and sodiumethylate.” By Prof. C. A. Lopry DE Bruyn and Dr. A. Srecer, p. 23. — “On an instance of conversion of mixture- erystals in a compound.” By Prof. H. W. Baxuurs Roozesoom, p. 23. —‘On the enantio- tropy of tin.’ By Dr. Ernst Conen and Dr. C. van Eryx. (Communicated by Prof. H. W. Baxuvis Roozepoom), p. 23. — .,The continuation of a one valued function represented by a double series.” By Prof. J. C. Ktuyver, p. 24. — “On standard gas- manomcters” (With 2 plates). By Prof. H. Kamertinca Onngs). p. 29. — “The deter- mination of isothermals for mixtures of HCl and C,H.” (With one plate). By Mr. N Quint Gzn. (Communicated by Prof. J. D. van DER Waats, p. 40.— ,,The elementary Theory of the Zeeman-effect. Reply to an objection of Porncart.” By Prof. H. A Lorentz, p. 52. — ,,On the finding back of the comet of Hormes according to the computations of Mr. H. J. Zwizrs.” By Prof. H. G. van pk Sanpe Bakuuyzen, p. 69. The following papers were read: Chemistry. — ,On the influence of water upon the rapidity of the formation of ether from methyliodide and ethyliodide and from sodiummethylate and sodiumethylate”. By Prof. C A Lopry DE Bruyn and Dr. A. STEGER. (Will be published in the Proceedings of the next meeting.) Chemistry. — ,On an instance of conversion of mixture crystals in a compound”. By Prof. H. W. Bakuurs Roozesoom. (Will be published in the Proceedings of the next mecting.) Chemistry. — ,On the enantiotropy of Tin”. By Dr. Ernsv Conen and Dr. C. van Eyx (Communicated by Prof. H. W. Bakuurs Roozrpoon). (Will be published in the Proceedings of the next meeting.) 3 Proceedings Royal Acad, Amsterdam, Vol, IL. ( 24 ) Mathematics. — ‘The continuation of a one-valued function, repre- sented by a double series.” By Prof. J. C. KLuyveEr. In his paper ,Ueber die Entwickelungscoefficienten der lemnisca- tischen Functionen” (Math, Ann., Bd. 51, p. 181) Mr. Hurwitz ‘alled attention to the perfect analogy between the Bernoullian numbers %, and another class of rational numbers /, occurring as coefficients in the expansion of the particular elliptic funetion pu, whose fundamental parallelogram of periods is a square. It is possible to carry still somewhat further this analogy. In fact, the numbers £, are closely connected with the values of the integral transcendental function (1 -+- e-7%)f (2), which correspond to positive integer values of z, and we will show that the numbers of Hurwitz admit of a similar interpretation. If we consider the doubly infinite series : 1 fo (me + m'eor'r * = m =O) ae aeieprrciacine + m’ the ratio o'/m being a complex quantity the imaginary part of which we assume to be positive, it is known that this series con- verges absolutely as soon as the integer n»>2. Changing the integer n into an arbitrary real number a>2 the series is still convergent, a determinate value however cannot be attached to its sum, until the amplitude of each separate term is fixed in some way or other. In order to define this amplitude without ambiguity we draw across the plane, containing the network with the vertices mo-+-m'o', a straight line or barrier leading from the point 0 to # and passing through the points @, 2@, 30,... Then, having fixed once for all the amplitude @ of the stroke w, we agree to under- stand by the amplitude of mo + m'o' the angle 6, augmented by the angle through which the barrier is to be turned in a positive direction till it coincides with the stroke m@-+m'o'. According to this agreement to every real value of a> 2 belongs a determinate value of the sum of the series, moreover it is easily inferred that its convergence and its one-valuedness are not impaired when the real exponent @ is replaced by a complex quantity z= x + 7 y, pro- vided we have x > 2. Hence we may put Z (2; @, o') = Z(z) = S' (ma + m'a')-= , and we have thereby arrived at a one-valued function Z (2), as yet merely existing in that part of the e-plane where « > 2. It will be at once noticed, that the agregate of values through which the thus defined function 7(z) can be made to pass, essen- tially depends upon the convention made concerning the amplitude of mo-+ m'o'. It is only when < acquires positive integer values > 2, that this convention becomes wholly immaterial. The question now arises whether the function Z(z) can be con- tinued across the limit of the domain in which it is originally defined by means of the double series. This question may be answered in the affirmative, indeed, it- will be found that by converting the double series into a definite integral the required continuation readily presents itself. Let 2@ and 2’ denote a pair of primitive periods of an elliptic function »u and let us put x (" —— W (wu) = pu — . ° E A@ | 4% sin~ - 20 Then, we consider the integral 1 (yu) [= — du 20% uel L aud take it along a loop / beginning and ending at uw = o, going posi- tively round the point «= 0 and enclosing the points »,20,3@,... its double linear part being drawn as closely as possible along the right line 0, w, 2... Under the restriction that the real part of 2 > 2 it follows from the application of Caucny’s theorem, that the integral J is simply equal to the negative sum of the residues corres- ponding to the poles (2 of w(u). For. these poles constitute the system of singular points that the subject of integration possesses in the region outside the loop. Thus, as we have in general P=2mo+2m'o’, 2S SS IS Be see Sot ie oo Aa aere 3% ( 26 ) we must conclude poe tip (EO OY a 2nmt ej) uel 21 p uz—! (u — 2)? 1 ' ' ' = (e—1) 2<— = — (e—1) "(mo 4 mo) . p [3 22 SW E— AO Mill tye 25 i — tres The aboye double series still differs from that which served to define Z(z) because it does not include the terms of the simple series ='(mo)—* . = hy ea Hence’ replacing this series by the equivalent expression (1 + e-7* ) w—* € (<) there results 1 2 - T= = (2-1) [4 (; 0, ') — (1 + e-7#) w= 0 (2) - We will now seek to express the integral J in a different way, The function yw (u) can be expanded in a trigonometric series. By a known formula we have 2 72 kag2h k wy (u) = — Ul an 1 = q a = cos o a % 1— qk ) ziw! eae ¢ ) and owing to the fact that along the path of integration the ratio u/ remains real, we are at liberty to substitute in the integral J the cosine-series for the function w(u). So we are led to a series of integrals, each of which of the form 1 1 k fh [Ss oi ee du. uz—l 22. z a L Always supposing the real part of «> 2, we find by the usual methods of integration whence it follows that == ON ote cos = (4 J post k2—1 Ie a zt 1— qk Combining this equation with the one we got before, we finally have Z (2; @, ') = (1 + e~7®) w— C (z) + 2 2 qt \* Tz 2k aL ( ) PRE ip I I D(z) 2 % 1—q** Now, in deducing this equation we postulated that the real part of 2 was greater than 2, but as the right hand side defines a one- valued function of <, holomorph all over the z-plane, we may regard this equation as the proper definition of Z(z), thus establishing the existence of an integral transcendental function that is only partially represented by the doubly infinite series. The resemblance between the functions Z(z) and (1 + e—7%) w= € (<) is manifest. The former is evolved from the doubly infinite system ma + m’o', the latter arose entirely in the same way from the simply infinite system me. Therefore we may conceive Z(z) as an extension of the function (1te—7) w-= &(z), the relation between these functions finding its analogue in the relation between the elliptic functions and the simply periodic ones. Seeking for the values of 7(2) corresponding to integer values of its argument, we find in the first place that Z(<2), therein behaving as (1 +e—7)@—= C(z), vanishes whenever 1. For z=0, we get Z (0) = 26(0) = — 1, for z= 1 there results Z (1) = Lim (l—e—7*) o-1F(1+0)= ee p 6 3=0 ” As for positive and even integer values of 2 we have Z (en) = 2o-ME (Bn) + Fy, al ae SL ea ( 28 ) ind from this formula for n= 1 7 2 4 ms 4 “ Z()=—4+4y0)+—=—, I~ a) (77) whereas for larger values of » we can write in general 92n — ywn—2) (0) , I’ (2n) ia ( ) Z (2n) = 2 @-2n ig (2n) a. Now considering the expansion 1 je yon—2 += : ue en : (2n—2)! pu : where the leading coefficient 4, is zero and the other 4’s stand for certain known polynomials in the invariants gy and g., we deduce from it a 1 2n—1 wy (u) = LZ u2n—2 Ge =. 2n) —— - 2n (2n—2)! (2@)?" and an (2 n—2) — =— a y) 74 Qn ; Ver =O" aim PON) En) so that we find : 92n 7 Z (2n) —- (Qn)! provided x be greater than 1. In order to obtain an expression of the numbers 2, of Hurwitz we take nD 3 as Oe) = eee i a = ==12,622 05ileerd 9 Ooi 4, gg == 0. V4s°9—4s . 1 In this special case we have hon le —— 0, dog acne, where /, is a rational and positive number, obeying the relation this relation obviously being the analogue of the well known formula for the Bernoullian numbers (2n)! By = ory (LE mM T)E On). (29 ) Physics. — Communication N°. 50 from the Physical Laboratory at Leiden by Dr. H. KaMernincu Onnes: “Standard Gas- manometers.”’ (Precision-piezometers with variable volume for gases.) § 1. Purpose. Further progress in the knowledge of the laws from which we derive the equation of condition for the gaseous and the liquid state, depends for a great deal on accurate determina- tions with perfectly pure gases and their mixtures in proportions exactly known. In these determinations the principal thing is to measure the pressure and volume of a precisely known quantity of gas at constant temperatures. ‘The standard open manometer '!) of reduced height formerly described offers us a means of attaining great accuracy in measuring the pressure. In the following pages I intend to describe piezometers in which (at temperatures above the freezing-point of mercury) the volume of a gas, shut off by mercury and compressed to different pressures, in proportion to the volume which it would occupy at 0° and 760 m.m. (the normal volume) can also be read with great accuracy. These apparatus enable us to determine the isothermal lines for gases to within ——_, at temperatures (above the limit mentioned) which can be 5000 kept sufficiently constant to allow measurements with the standard open manometer of reduced height. If the piezometer-tubes are filled with a standard gas, of which the equation of condition for ordinary temperatures has been deter- mined by means of the open manometer, or if their indications have been compared immediately with the open manometer indepently from a determination of constants, they can also conversely be used to replace the open manometer when the measurements have to be made in a shorter time than is required for reading the standard open manometer of reduced height at high pressures. This method has been followed by me in an investigation taken up a long time ago on the isothermal lines of hydrogen (now to be ex- tended of course to the since discovered argon and helium) together with those of different mixtures of gases at low temperatures (for the obtaining and keeping constant of which the cryogenic laboratory was devised ”) ). 1) Comm. from the Physieal Laboratory at Leiden N°. 44. *) Comm. Phys. Lab. Leiden N°. 14; the means for the accurate measuring of the low temperatures are treated of in Zitt. Vers], 30 Mei and 27 Juni 1896. Comm. Phys, Lab, Leiden N°, 27, ( 30 } It would be very difficult to keep the temperatures at which those isothermals are to be determined so constant that during the time required for a determination with the open standard manometer no variations can occur which would influence the pressure to be measured more than the errors of adjustment. The best thing to be done seemed to measure the pressure in the piezometers of constant volume filled with gas at a low temperature (a following communication will treat of its construction and use) by means of gas-gauges which have themselves been compared with the open manometer of reduced height, and to construct these closed mano- meters so that they are not much inferior either in sensibility or reliability to the standard open manometer. Ip order to render the indications of the piezometers or mano- meters as reliable as possible the glass tubes in which the gas is compressed have been taken so wide as appeared to be compatible with a sufficient power of resistance and would not render too diffi- cult the handling. The chance that a perceptible quantity of the gas, albeit in extremely small bubbles, should adhere to the walls when the mercury rises, as well as the influence of a deviating behaviour of the gas-layers at the surface of the glass, becomes less as the tube is wider. Moreover the more regular shape of the me- niscus renders the determination of the volume more accurate and diminishes the influence of capillary disturbances on the measure- ment of the pressure. The manometer-tubes may be cleaned and refilled without in- validating the determination of constants once made. This is of great importance, also because it enables us to apply a differential method when comparing the isothermals of two gases or mixtures of gases. For if we dispose of two manometers of the kind to be described, we can compress these gases simultaneously under the same pressure, and interchange them in the two sets; so the errors which the apparatus might still show, are eliminated for the greater part. For the rest the closed manometers are so constructed that the normal volume can be very accurately determined not only at the beginning of the measurements made under pressure, but at any time we should want to. In order to do so the manometer-tube filled with gas may be taken from the apparatus, placed in a space of constant temperature, — where the difference between the pressure of the enclosed gas and the atmosphere can be measured, taking into account the capillary depression —, and may be replaced in the appa- ratus being still as clean as before while the quantity of enclosed gas does not undergo the least change during this operation. The ( 31 ) data for the necessary corrections can also be determined with great accuracy. Lastly care has been taken that the mercury in the apparatus does not come into contact with anything but carefully cleaned glass or iron and cork or solidified cement. Accordingly the menisci in the manometer-tubes remain perfect. All this entitles us to call the apparatus described in the following pages when used as gasmano- meter, a standard manometer. § 2. General arrangement. The apparatus now used in the Leiden Laboratory is designed for measurements with 4 piezometers ranging from 4 to 64 atmospheres. In the construction of the apparatus, I have successively been ably assisted by Dr. Leprer and especially by Mr. ScnaLtkwisk, both assistants and Messrs. CurRvEeRsS and Fum, instrumentmakers, to all of whom I render thanks. It contains, when used for measurements of pressure, and as repre- sented in Plate I, four closed manometers placed in a row, on each of which a definite range of pressure is read, viz. 4—8, 8—16, 16—32, 32—64 atm.; each following manometer has a small range of pressure in common with the preceding, through which proper continuity and mutual testing are obtained. The piezometer-tubes are placed in compression-cylinders, each of which can be connected separately with the apparatus in which the pressure is to be mea- sured, while all can be connected mutually. The whole apparatus is mounted usually in a definite place. The pressure is transferred from the apparatus, in which we want to measure it, to the manometer through a narrow tube filled with compressed gas. This method offers many advantages in a research laboratory like that at Leiden. The choice of the stages of pressure agrees with the division into pieces for 4 atmospheres of the standard open manometer which ranges as far as 60 atm., and with which the closed manometer is used as an auxiliary apparatus in order to attain a pressure higher than 60 atm., in the way described in Comm. n°. 44. As the closed manometer for the next stage made after the same principle is not yet ready (it requires a compression tube with a thicker wall and greater volume than those existing) we use for pressures above 64 atm. closed manometers of simpler construction !), The mutual testing of the various closed manometers will be described when the observations made with the apparatus are com- 1) Comp. VerscHarrett, Thesis for the doctorate, Leiden 1899, ( 32) municated, together with the measurements made in order to test the accuracy of the standard open manometer of reduced height by divi- ding it into two parts, which are equilibrated with each other or simultaneously with one or two closed manometers. § 3. The piezometer- or manometertubes. These are made of Jena normal glass and recall in so far as the general form is concer- ned the type used by CaiLLerer (comp. fig. 3 and 4). On to the upper end of the stem a wider reservoir has been blown of about the same volume as the divided stem in order that on each manometer the range of the pressures extends only so far that the highest pressure at which an adjustment in that tube can be made is twice the lowest. In this way we ensure the sensibility to be about the same at the different parts of the graduated scale. The diameters of the reading-tubes (comp. fig. 3 and 4) are for the four manometer-tubes 8, 6, 4 and 3 mm. respectively. The diameters of the upper reservoirs and the thickness of the reading tubes and of the upper reservoirs have been chosen so as to be in accordance with these (comp. fig. 6). A very accurate determination of the volume of the enclosed gas when compressed is rendered possible by fixing a very fine capillary tube of known volume (diameter about 0.3 mm.) on to the upper reservoir just as with AMAGATs’s piezometer (e, comp. fig. 6). After sealing off we can, by measuring the length of that part of the capillary tube that has remained unchanged and by estima- ting the volume of the conical part formed by the sealing off, com- pute its whole volume from a definite mark. The error thus remai- ning may be entirely neglected. A wider capillary e' (fig. 7) carrying a small cock has formerly been welded on to the capillary tube at the place where it will be sealed off. By means of this cock we can connect the tube with the vacuum pump, suck up liquids in the manometer-tube, supply dry air, ete.; moreover it is useful in calibrating. The tube, dried and ready to be filled is sealed off at the place where the wider capillary tube has been welded on to the narrow one. If the tube has afterwards to be cleaned again, which can not but imperfectly be done without opening it and sucking liquid through, or if the tube has to be calibrated anew, the fine point is filed off and at that place a new tube resembling the one sealed off is joined on, In this way we lose in each operation only a few mm. of the capillary tube e and we can use the same manometer for numerous sets of measurements before it is necessary to weld on a (33) new capillary to the upper part of the reservoirs. If this happens to be the case we can no longer calculate the new volume of the reservoir from the old one by means of an insignificant and perfectly sure correction, which is possible as long as we preserve the same eapillary tube. The graduated stem ¢ is made from a carefully selected perfectly straight and almost cylindrical tube. The graduation extends from 0 to 50 em., continued on either side over some em. in order to make sure that the diameter of the tube in the neighbourhood of 0 and 50 does not show any particular change. It did not seem desirable to make the graduation extend over more than 50 cm. as it is necessary to keep the whole length at a constant temperature. The divisions are at distances of 1 mm. and the readings are taken by means of a kathetometer. It is of great importance that the whole tube should be perfectly vertical. Therefore care is taken that the stem and the cylinders of the manometer-tubes are well centred, and that the tube is truly centred in the steel tube with flange O (fig. 3. Pl. I) the whole apparatus being placed vertical by means of the plummet (compare also § 5). The reading tube is connected with the lower reservoir a by means of a wider tube, } fig. 3. By means of this wider part the manometer-tuke is cemented') in the flange 0, which for this pur- pose must be made so that it can be pushed over the upper reservoir. The outer diameter and the thickness of the wider part are taken a little larger than those of the upper reservoir, and the bore of the flange belonging to it so much larger that between the glass and the flange space remains for a thin layer of cement (about 0.5 mm.). The lower cylinder a is thin, as in the manometers of the type used by Cat~terer and Amacar. At its lower end however the manometer-tube terminates differently; it is provided with a U-shaped tube placed under the lower reservoir, of which the branch f con- nected with the reservoir is graduated. The purpose of this tube is to enable us to determine accurately the normal volume or to test it (as has been mentioned in § 1) at any time we should wish. Before we proceed to the filling with gas we, in the manner in- ) In some cases, when for instance we should want to heat the piezometer-tube, it may be desirable not to cement the piezometer but to enclose it in the flange by packing. But as we have principally in view its use as gasmanometer we need not dwell on this particular, (34) dicated by CArLLeTEeT, introduce in the lower reservoir, held in a sloping position, a quantity of mercury sufficient to fill this U-tube. After the manometer has been filled with gas in the said position, we cause the mercury to enter the U-tube by turning the manometer into the vertical position..Then by reading the posi- tion of the surface of the “mereury in the divided and calibrated branch f, after the manometer-tube is detached from the filling appa- ratus, we can determine the volume of the enclosed gas, while the difference in level with the other branch g indicates the excess ot pressure, above the pressure indicated by the barometer. And this determination can be made with great accuracy because we could allow the diameter of both the branches of the small manometer to be 8 mm., so that the correction for the capillary depression ean be deternined with sufficient accuracy from the form of the menisci. The length of the U-tube warrants that the gas remains shut off even when changes of temperature and atmospheric pressure occur. The peculiar position of the U-tube with regard to the mano- meter-tube leaves room under the lower reservoir for the tube 4, which acts a very important part in different operations, viz. the exhausting with the mereury-pump, the filling with pure gas and the shutting off of a definite quantity of gas. This tube % is bent downwards slantingly and backwards and carries at the end a ground tap which fits in a ground cap, welded on to the glass 0" 5 conduit of the mercury-pump and the gas-generating apparatus (Comm. N°. 27 p. 15). After the piezometer-tube is cleaned and dried, the capillary end at the top of its upper reservoir has been sealed off, and the wider part of its stem has been cemented in the flange, it can be suc- cessively exhausted and filled with gas by means of this tube h. Then by revolving the piezometer-tube round the axis of the joint we can admit the mercury from the lower reservoir into the U-tube and so shut off the gas perfectly sure, after which the tube may be separated from the gas-generating apparatus. It needs no comment that the operation described must be done with great care in order to prevent that the tube 2 breaks off, as the manometer is already burdened with the heavy flange. In order to facilitate any repairs to be made in the U-tube, its branches are connected by a narrower tube that can easily be straightened in the flame and after the repair is finished can be bent again into the original form without any damage to the calibrated tube. (35 ) § 4. The compression-cylinders and stopcocks. (Pl. I, fig. 1, 2, 3.) The manometer-tubes filled with gas and closed by the mer- eury in the U-tubes are introduced into the compression-cylinders A previously filled to the rim with mercury. In order to prevent the air from getting into the U-tube, care is taken that the mercury is flowing out of the tube (by heating the manometer reservoir) at the moment that its opening is immersed below the mercury surface in the compression-cylinders. When the compression-cylinder is closed by the flange in which the manometer is cemented, the mercury pushed up by that part of the flange which fits in the compression-cylinder, drives the air out. The superfluous mercury escapes until by firmly screwing on the nut NV we obtain a tight fit on the washer p. Then the reservoir of the manometer-tube is contained in a space wholly and exclusively filled with mereury. By means of this contrivance we can take the manometer-tube from the apparatus without its coming in contact with any liquid but mercury, and avoid the great number of difficulties which always arise when we transfer, as usualy is done, the pressure by another fluid on the mercury in the compression-cylinder. It is desirable that we should have at hand a greater number of manometer-tubes with flanges in order that we may successively place several piezometers previously prepared into the compression- cylinders. The 4 compression-cylinders of the apparatus on PI. I consist of well-drawn iron tubes, carrying taps welded on at both ends !). They are mounted together on a stand V, in the notches of which they fit in with the parts of the two taps that are filed sexangularly ; they are shut up by a counter plate, in which likewise notches have been filed. These notches together with those in the stand hold the sexangular taps, as clearly shown in fig. 1 Pl. IT. Thus it is easy to place into and to take out of the apparatus each of the compression-cylinders separately, while the tubes with the stand form a whole and are kept as it were in a large wrench, which can be held firmly so as not to meet with the difficulty, which else so often occurs, whenever we want to screw the nut ofa compression-cylinder tightly by means of a wrench with a long lever. The whole stand is placed in a wooden receptacle for the mercury that might flow out. The compression-cylinders can be opened on both sides. In 1) The boring of a bar is very expensive and it is difficult to get smaller pieces of tubing with walls sufficiently thick to be provided with screw-thread and a sexan- gular tap. ( 36 ) cleaning the inner surface we therefore do not meet with the difficulty, which generally is occasioned by the bottom part. At their lower ends the compression cylinders are closed by nuts /, similar to those at the upper ends; through these they are coupled to steel tubes 1), /),/3,/, bent rectangularly, terminating in the stopcocks hy, kay kg. ky) which serve to couple each manometer (sometimes two) to the pressure-conduit or to disconnect them according as_ to whether or no the pressure to be measured is within the range of the manometer. These stopeocks are below the upper rim of the compression cylin- ders so as to allow us to fill without difficulty the compression- cylinder and the tube entirely with mercury; as they are provided with cork stuffing the mercury cannot become dirty by streaming along, in or out. The pressure is transferred on to the mercury in the compression- cylinders by means of mercury in the tubes s;. The stopeocks of the different compression tubes are mounted on a board, screwed on to the stand V (see Pl. I fig. 1 and 2) together with a system of supply-tubes. These supply-tubes filled entirely with mercury con- nect the compression-cylinders with: 1°. a mercury-reservoir /’), serving to supply mercury and to gua- rantee that, when the apparatus is not watched there still remains in case of change of temperature and atmospheric pressure a sufficient excess of pressure in the apparatus even if the stopcocks were open. This reservoir is always closed by the iron stopcock 4; when determinations of pressure are being made. 2X. the principal tube s; through which the pressure is trans- ferred on to the mercury in the tubes, and which may be closed by an iron stopcock 4g 2). The tubes s; are entirely filled with mercury by exhausting them and then admitting mercury from /,; the stopeocks, like the other ones are provided with cork stuffing. Through the supply-tube s;, immersed in the mercury down to the bottom of the reservoir 2, we supply from the mercury in 7, as much as is required to compress the gas in the manometer tubes. The pressure to be measured is transferred on to the mercury in the reservoir by means of compressed gas. In order to apply the 1) The construction of steelwork of this kind is described in Comm. N°. 27 and 44. 2) These stopcocks did not require the same great care as bestowed on the steel stopcocks of the single manometers (which must be perfectly reliable) as not all mano- meter-tubes may be exposed to the highest pressure. (3%) correction resulting from the difference in level between the surface on which the pressure to be measured is applied, /7, and the top of the meniscus of the mercury in one of the manometer-tubes 0, it is necessary to know the level of the mereury in the reservoir R,. This is indicated by the gauge-glass P, beside the reservoir 2. It consists of a thick-walled tube, drawn out on both ends and provided with steel caps and steel capillary tubes ¢), t:, as described in Comm. n°. 44, which form at the higher and lower ends the connection with the mercury-reservoir 2, (or what comes to the same with the siphon tube s;). The stopcock &; serves to close the gauge-glass when the reservoir has been exhausted and we want to let mercury flow into it through the tube s3. The correction just mentioned for the vertical distance between the level of the mercury in the reservoir (as indicated by the gauge-glass) and the meniscus in the manometer where the reading is taken, which in the case of many manometrical measurements could but very roughly be applied, is accurately determined here with a kathetometer. A divided scale on which we can immediately transfer the rea- dings is placed at the side of the gauge-glass. With the aid of the kathetometer we compare the level of the graduations with the level of the graduations on the manometer-tubes to be read. This is done before and after they have been provided with the waterjackets m, mg, mz; and my. To protect the observer the gauge-glass is provided at the back and on the sides with iron plates and in front with a thick plate-glass. On a board near FR stopeocks and tubings are fastened which are represented in Pl. [ fig. 1 and 2 require no separate descrip- tion. by means of these we can: 1°. close (by means of %) the conduit s, through which the pressure is transferred!) by means of compressed gas ; 2°. read the pressure (ts being shut) transferred through this conduit, on an auxiliary manometer J/, before the compressed gas is allowed to transfer the pressure into the measuring apparatus, in order to get to know, which manometer is to be connected; 3°, make and break arbitrarily the connection with the auxiliary manometer, whenever this seems desirable, while making the measu- rements of pressure ; 1) As for instance a tube which forms a connection with an apparatus like that ot Dr. SiertsEma’s Comm. N°. 49, or a tube, which connects the manometers with the piezometer for gases compressed at low temparatures, mounted in another room. 49, exhaust the conduits (through %) and &,, before the con- necting of s, and ss) and to fill fhe reservoir 2, with mereury through &% and fs) ; 5°. To connect the apparatus with the standard open manometer (through 4). When the apparatus is used as a manometer the bottoms of the waterjackets on to which the glass waterjackets are fastened with india-rubber, are screwed on to the flanges O at A (seefig. 3). The temperature is kept constant by means of circulating water) and of the stirring rods 1, 79, 73, 74, While thermometers (not repre- sented in the figure) enable to read the temperature at differents heights. The stirring rods are suspended from the stand S,, which is constructed so that it can easily be removed. § 5. Some remarks on cleaning, cementing and filling. The cleaning of the tubes is of great importance. Only when this is done with the greatest care, it is possible that the menisci remain perfect. As for the precautions to ensure this, I refer to Comm. No. 27. Attention must be drawn however to the fact that, without particular precautions it would be impossible to clean the tubes by boiling for instance with nitric acid. In the first place different parts of the walls are very thick; moreover they are very long and terminate on one end in a comparatively narrow tube, on the other end in an extremely narrow capillary tube, which almost closes them. The difficulty arising from this, was removed by placing the tubes, as shown in Pl. IL fig. 2, in expressely made boiling-tubes of ordinary size in which the cleansing-liquid is poured also filling the manometer-tube (being not entirely shut on both sides), and is heated until the liquid begins to boil within the manometer- tube. Round the manometer-tube a platinum wire is slung, which prevents contact between manometer-tube and boiling-tube, and serves to take the manometer-tube out of the boiling-tube. In cementing the manometer-tubes in the flanges, we must take care that the axes of the two coincide. Therefore it seemed desirable to make special moulds in which the tube and the flange are fastened. (Compare fig. 3 Pl. II). 1) I shall not dwell on this cireulation. When the piezometers are used at tempera- tures much differmg from that of the room we must surround them with liquid- or vapour-jackets (or liquid-jackets enclosed in vapour-jackets). (39 ) On to the part A of the flange provided with a screw-thread, we screw a brass tube in which two openings e¢ have veen cut, and in which the stem of the manometer-tube may be fastened by means of the wooden stopper 2 cut in two. Over the wider lower-part of the flange, we slide the tube consisting of a narrow and a wide piece in which openings have been cut at b, d and also at e, and which fits at 4 round the former tube. By means of a tight ring at f the two tubes are kept in a coaxial position. In the wide end of the second tube the lower cylinder of the manometer-tube may be fastened at « by means of a wooden stopper likewise cut in two. The cementing is done in the following way: the manometer-tube is heated to a little above the melting-point of the cement, a thin layer of which is spread on the tube. In the meantime the steel piece with the brass tube screwed on to it is heated also to about the same temperature. Then the manometer-tube (in the reversed position of fig. 3) is slid into the steel piece, over this the second tube is slid and then the halves of the wooden stopper are put in their places. In this way the manometer-tube is truly centred and the space between manometer-tube and flange is entirely filled up with cement. Through the openings we may pour in additional cement. After this is solidified we turn the apparatus upside down (position of fig. 3) so that the glass-reservoir rests on the collar ¢ of cement oozed out. The superfluous cement is washed away with benzine. For the filling with pure hydrogen I refer to Comm. N°. 27; for the revolving of the manometer-tube round the axis of the tube A, in order to shut off the gas by means of mercury admitted before- hand into the reservoir, I refer to § 3 of this paper. § 6. Calibration, determination of the volume of the tube and measurements of the normal volume of the enclosed gs. In order to calibrate the graduated tubes and to determine the volumes of the reservoirs, we weld a wider tube with a glass stopcock on to the capillary tube where the manometer-tube is to be sealed off. On the other side of the stopcock, this wider tube terminates ina fine point. After being cleaned and dried the manometer-tube is entirely filled with mercury. The calibration and gauging is done by weighing the mercury which we let flow out. I will not dwell on these ope- rations and the corrections they require as they can better be treated of when the observations made are communicated, but here I will only mention that in these operations much time was saved and the degree of accuracy was greatly increased by placing the tube in a 4 Proceedings Royal Acad, Amsterdam Vol. I. ( 40 ) double walled copper box lined with thick felt, the inner and the outer wall being provided with plate-glass windows in order to enable us to take readings along the whole scale of the tube (comp. PI. {I fig. 4). The space between the two walls was filled with water and the constaney of the temperature was promoted by stirring. The tube to be calibrated rests on a wooden ring and the lengthening- piece with stopcock, welded on to the upper-reservoir, passes through an india rubber stopper cut in two. The point of the manometer- tube through which the mereury flows is protected from variations of temperature by a copper felt-lined cap fastened to the box by a bayonet-adjustment; this cap can easily be removed (for a short time) whenever we want to let a quantity of mereury flow out from the tube. The readings for determining the normal volume are made while the manometer-tube is placed in a double-walled box as described above, (comp. PI]. II fig. 5) but in which the windows were only small, as we wanted to read only the position of the mercury in the U-tubes and of the thermometer. These readings and_ that of the standard barometer (the box communicating with the atmo- sphere by a small tube) yield a perfectly accurate determination of the normal volume, which is of the greatest importance for the investigation of the isothermal lines. Physics. — Prof. vAN per Waatzs presents on behalf of Mr. N. Quint Gzx. a paper on: , The determination of isothermals for mixtures of HCl and C,H,.” Introduction. At the commencement of this investigation there were but few observations made, which might be used for testing Prof. vAN DER Waats’s theory on the behaviour of mixtures of two substances. At that time Mr. KuENEN was the only one who had examined some mixtures and his observations agreed with that theory. In order to add to the material on this subject (to which also Mr. VAN per Leg, Mr. Verscuarrent, Mr. Harrmay have since contributed), I have examined mixtures of HCl and CyHy. The results of the determinations of the isothermals and a short description of the experiments follow; I hope soon to publish some further details and a calculation of volume-contraction ete. ( #1) The substances. From the theory follows that some mixtures, when being condensed at a certain temperature will show the phenomenon, indicated as retrograde condensation second type. Mr. Kurenen had not been able to observe this phenomenon; therefore it was desirable to select substances, in which at least theoretically, the phenomenon of r.c. II was to be found. As Mr. Kuenen states in Phys. Soc. (13) 10, 1895, this is the case with some mixtures, if the component that has the higher vapour-pressures, has also the higher critical temperature. We settled therefore on HCl and C,H,, because each of these substances has also a critical pressure which may be easily attained. HCl was obtained by adding drops of concentrated sulphurous acid to pure HCl, to which some Fe.SO, had been added. When the gas obtained in this way, was dried, it was very pure, as appeared from the slight increase of pressure (at 12° about 0,2 atm.), when condensed and from the agreement of the critical data with those found by ANSDELL. In order to obtain ethane, acetate of sodium was subjected to electrolysis; the gas which was developed, was condensed at a low temperature (about —50°), the vapourphasis was removed, and from the liquid phasis a quantity of gas had been collected. Though this method is the same as had furnished good results to Mr. KuENEN, I have not succeeded in making the gas as pure; this C. Hg pre- sented in being condensed at 21°, an increase of pressure of 1,4 atm. As however the values for the critical data as found by me (crit. temp. 31°,88; crit. pressure 48,94 atm.) did not differ much from those found by Mr. Kurnen for his ethane (crit. temp. 31,95 & 32,2; crit. press. 48,64 & 48,91) and as moreover it is difficult to obtain perfectly pure ethane, as clearly appears from the obser- vations of others (Dewar, OLszewsky and HAENLEN found resp. for crit. temp. 35°, 34° and 34°,5 and for crit. press. 45,2; 50,2 and 50 atm.) I resolved to continue the observations with the ethane I had obtained. The Method. The compressibility of the two substances mentioned and also that of four mixtures (prepared in a mixing-apparatus made completely of glass), was compared with that of dry air, free from carbonic acid, at temperatures which were the same for the two substances and for 4* ( 42 ) ile mixtures. The gas was compressed in a calibrated tube of CAILLETET, on which the mm. were marked, and the thickwalled part of which was placed in a waterbath of about 35 L. After this water had reached the desired temperature, the temperature was kept constant by means of an alternating current, which passed through two tubes filled with a solution of NH,Cl, which were placed in the bath. Moreover in this bath were found the coil, serving to move the electro-magnetic stirrer in the CalLLeret-tube, and a stirrer, kept in motion by the flow of water. The temperatures between 15° and 35° were read from a thermo- meter, which was divided in 1/2)°; the others from thermometers with a division of !/,,° ; now and then the thermometers were tested by means of a normal thermometer, which had been compared with an air thermometer at the Reichsanstalt. The pressures were calculated by making use of the table which Mr. AMAGar gives for the compressibility of air in Ann. de Ch. et de Phys. 6¢ série 1898. The Results. It appeared already in the observation of the first mixture, that I, no more than Mr. Kuenen, should succeel in observing the retro- grade condensation 22¢ type. For the critical temperature of the point of tangency and of the plaitpointeurve were so near each other, that I could scarcely state a difference between these tempe- ratures. Moreover, also in these mixtures the phenomenon of a maximum pressure and a minimum eritical temperature appeared, which made the region, where r.c. LI was possible, still more limited. (See KUENEN, experiments on mixtures of N,O and Cy Hg ete. Zeitschr. fiir phys. Chem. XXIV, 4, 1897). This maximum pressure occurs when # = 0.44 and this minimum critical temperature when 2=0,62 (ethane is considered as the solved substance, N,O as the solving substance), as appears from the gra- phical representation, in which the course of the plaitpointcurve, of the curves of the vapour pressure of the simple substances and the border-curves of the mixtures are indicated. This diagram, drawn up according to the initial and final points of condensation, occur- ring in the tables, is founded on the foliowing tables. HCl C; He Mixture f. = 0,1388 t Pa t Pa t Pa Pb 1455 38,03 | 13,2 32,21 13,7 40,42 42,33 21,3 44,25 21,3 38,75 21,3 48,11 49,97 30,23 53,82 | 25,4 42,19 | 25,4 52.74 54,48 41,45 68,47 | 30,23 46,92 | 30,23 5836 59,93 51,3 84,13 31,88 48,94 41,45 74,37 75,26 43,1 Gp Mixture IT. a=0,4035 | Mixture IIT. 20,6167 | Mixture 1V. 20,7141 t Pa Pb t Pa Pb t Pa Pb 14,1 45,72 46,94 | 14 43,96 45,83 | 14,5 42,18 44,60 D2) 58486" 54:95 | 21538 851,64 53.18 | 21,3 49508 51,10 25,4 58,42 59,19 | 25,4 56,55 57,57 | 25,4 53,87 55,25 30,23 64,80 65,11 | 27,25 59,15 27,33 56,49 56,92 30,43 65,30 | 27,25 59,30 27,37 56,84 30,53 65,42 The results of the determinations of the isothermals are repre- sented in the tables from A to F. The following remarks may be added : The values represent the observations, so that the corrections, which might be drawn from the graphical representation, have not been applied. The isothermal of 25°,4 for HCl and that of 52°,5 for mixtures II are not given, as the former was most likely not reliable, and as the latter could not be determined, because the CarLLEetnr-tube was broken. When the substance was divided into heterogeneous phases, the vapour-volumes then present were also repeatedly measured ; they are, however, less accurate than the total volumes on account of the uncertainty of the correction, which is to be made for the meniscus. All volumes are expressed in the theoretical normal volume (i. e. the volume at 0° and 1 atm. multiplied with (1-+ a) (L—d)) as unity ; moreover the volumes, at which for the first time liquid is to be observed, are underlined, and those at which the vapour phasis dis- appears, are doubly underlined. The pressures are expressed in atmospheres, the error will seldom exceed 1/j990, at least for the lower pressures. 2) A. Hydrochloric acid. Vj; = 54,348 eM. | ‘Tot. Vol [Vapour Vol | Wot. Vol. Temp. 0,0 | 0,0 | Pressure. Temp. 0,0 | Pressure. 14°85 | 1890 | 38,03 | 30°23} 2170 | 39,08 1738 | 1717 | 38,09 |(contin) | 2112 39,81 1615 1584 38,09 2077. «| ~—40,29 0902 0796 38,09 2041 | 40,74 0420 | 0258 38,14 1990 41,36 0190 38,21 1930 4216 0189 38,25 1820 43,84 ee 1733 45,20 219,30 | 2157 37,18 ne fees a Sige? 1505 | 43,94 ig ae 1402 50,75 2A05 37,81 1230: 53.89 2086 38,01 ai 53,95 2065 38,23 0207 64,10 2043 38,46 ete 2023 38,69 JAAS | 9347 39,32 1897 40,24 2200 MA A4 1885 40,38 2069 43.05 | 1804 | AAAS 1951 44,78 1792 | 44,64 1840 46,64 1780 | ast 1712 48,88 1710 | 42.74 1584 31,17 1686 | 43,07 1431 54,64 1613 | 44. 1261 38,47 44,16 | 4663 1148 61,20 44,25 1566 1027 64,18 AAAT 19% 0913 66,96 — 0830 68,47 30°,23 | 2318 37,44 0239 68.63 2269 37,96 TF 221) 38,50 ( 45) Temp. orc Presa | Temp. Tees Pressure, 0,0 a 51°,3 OALA 84,13 52°,5 1986 47,05 crit. point} ——| (contin.) 1807 50,34 52°,5 2706 37,22 1638 53,72 2546 39,08 - 1450 58,28 2358 AAAS 1260 63,42 2168 44 AK 1075 68,88 Bo EKthane, V, = 54,491 cMs. Temp. are bey M 2 Pressure. Temp. parc ues Pressure. 1392 1968 32,21 25°, 4 {822 37,02 1818 1781 32,29 1599 39,19 1599 1521 32,36 1414 40,88 1321 1178 32,48 1265 42,10 1032 0822 32,72 1255 42,19 0725 0443 33,05 OSSO 0696 42.56 O34 0072 33153 0665 0362 42,89 0387 33,71 OAT7 0067 43,29 0368 33,89 0430 43,54 2153) 1876 35,26 30°23 1785 38,86 1785 36,05 1599 49,86 1692 36,91 1414 42.88 1599 37.70 1228 44,88 1506 38,38 1042 46,39 1488 38,59 0949 46,90 1479 38,66 0940 46,92 1469 38,72 0930 46,94 4464 38,75 0498 £7.76 0526 O173 39,76 = 0404 40,13 Temp. Temp. pier Pes Pressure. lemp 0,0 Pressure. | 319,38 0759 48,26 | 44945 | 1210 50,48 31°,63 0759 48,79 | (contin.) 1191 50,73 31°,63, 0563 49,06 | 4172 54,05 31°,83 0669 83). 31°86; 0697 | 4893 | >| 16 oS 319,88; 0688 | 48,94 1767 43,08 E73) ONS | BAL Peed) ea 1730 AG,A4 A1o45)|) « ATS5 ye 4043 1711 46,50 1767 42,34 1526 49,73 1748 42,63 1507 50,02 1730 | 4283 1489 50,26 711 | 43,40 1470 | 80,68 1526 15,74 | 1998 | 88,47 1307 45,99 | 4210 53,81 1489 46,23 1191 | 56,11 1470 | 46,52 1173 | 56,65 1228 | 50,12 ( 46 ) Mixture Tot. Vol. Vapour Vol. I. x == 0,1388. Tot. Vol. | Tot. Vol. \VapourVol.| | | 0.0 | 0.0 00 Pressure Temp. | 0.0 -ressure. : H | 7 | 13°,7 | 2019 | 37,20 | 13°,7 1110 1031 40,96 | | | | 1937 | 37,88 |(contin.)| 0868 0739 «| 44,24 1897 | 38,54 OG1T7 0465 AA,51 1840 39,22 0348 0015 41,90 1783 39,91 0217 42,13 | 1728 | 40,4 0213 42,33 1704 40,42 a ee 21S 3 2132 37,84 1548 1529 40,60 | i - 2020 | 39,20 1367 1324 | 40,72 | 1897 40,74 (Ets) Te | Tot. Vol. Vapour Vol. Preseare mantel Tot. Vol. | Vapour Vol Presence emp. 00 0,0 ressure, em] | 0,0 | 0,0 | ressure. 21°,3 | 1783 | 4297 | 30°32 | 1032 ‘| 58,36 (contin.) | 1655 Ait [(contin)) 0808 | 0742 | 58,78 | | 1548 45,66 | 0479 0312 | 89,38 1428 ATA8 1) 0259 |! | 89,93 |= 1382 POS | so Da ee — MA°,43 | 2559 37,10 1064 | 48,48 | eee | | | 2406 lay) assho | 0760 0642 | 48,86 | | | | 9301 | 41,20 | 0480 | 0274 | 49,52 | | | | | 9031 43,88 | | | 1854 46,71 l | | i 1675 50,07 | 11 | 53,36 | ee 2020 | | 40,97 1316 | 57,81 | 2 | 1893 | 1,94 reais Iq <82:28 | | : = 1773 | | 43,65 | 0953 67,09 | 1 | 9 OF 1635 | 48,43 eee oe | | Wes Lhe | 4340 47,29 | 0613 74,37 epee 49,34 0515 | 74,72 Aaon stk | 0428 74,95 1212 52,74 ) 9313 | B20 0961 0907 53,10 | | | | 43°,4 0420 | 77,54 0643 0515 | 53,57 |_pl.p.t. | | 0408 0216 og | ecco ite TA ke 0236 5448 2690 | 37,62 534 3918 | | | | 30°,23 | 9369 | | 37,10 2342 | AA,96 2939 | 38,71 46 | 44,78 2045 | | 40,98 1959 | 47,92 i} | | 1863 | 43,54 | 1769 | 51,63 1707 | 45,99 | 1885 35,55 1569 18,34 | 1406 60,11 4404 | 51,35 1234 65,06 1237 | 54,25 1049 i “74108 |, 1238 54,28 0878 | | 77,04 Temp 0.0 0,0 Pressure. Temp. 0,0 0,0 * ressure. U288 14°, 216 36,29 | 23°4 Ostf 58,72 1918 38,51 |(contin.)! 0332 59,19 1745 40,63. | | 30°,23 ) | 36,82 1573 | 42.84 ; as iz 2235 eee 1398 45,11 Panic} se 059 40,83 1345 45,72 Z : 867 43,5 0949 0847 43,86 S03 a 698 46,2 | 0609 O404 46,10 os) a 1528 49,20 0282 | 46,94 ‘acay = 13 52,80 91°2 | 994 | 36,55 1162 56,46 2056 38,67 O86 62,20 1867 | 41,03 0610 64,80 1697 | 4344 0528 0378 64,99 1523 43,98 0463 0178 63,10 1340 48,95 OMT 63,14 | | — | | 1161 | 479 are eee 30°43 | 0439 63,30 1045 | 53,36 = | ae | E ue ee. | 309,53 0471 63,42 0839 | 0667 53,57 plaitp. | | Noe 0234 | 53,76 | so038 | 0488 | 63,45 ¢ > | we Pry ) peas 525 | teas | os37 | 37,29 D335, 946 25° 4 2294 | 36,83 2338 lagers : | 73 83 2098 | 39,16 : 1976 | 44,75 1914 | | 44,60 = | ig 1799 47,70 1754 | 643,87 1644 50,80 1583 46,39 © 146 54,60 1401 | 49.73 Rass | 1292 58,58 1208 53,18 1105 63,49 1039 36,18 “e 0872 70,24 0877 | 58,42 : 0582 78,02 732 0647 | 58,48 ‘ D; ( 48 ) Mixture II. V. 0 — 55,887 cM. a = 0,4035. | Tot Vol. Vapour Vol. Vapour Vol. ] ( 49 ) bee vMeix ture Ill: V, = 54,207 cM’. } x = 0,6167. TOMEVole VanounVoll a. Note Vol. | j Tok NG): Varner Pressure. | Temp. ar air oo Vol,| Brossures 2015 36,53 25°, 4 1778 42,50 1854 38,28 | (contin.) 1550 45,83 1651 40,61 1306 49,65 1490 42,56 1122 52,66 1355 43,96 0926 55,39 1177 1121 LAAT 0799 56,55 0969 0850 4A4,A3 0662 0517 56,87 0520 0216 57,17 0775 0588 44,70 0416 57,57 0531 0266 45,13 = 0361 64,38 0327 45,83 == |S A 0347 54,33 | 97°95 | 9971 36,79 0305 66,94 2152 38,16 J = Ae | ee 1928 40,96 2160 36,69 173% 43,614 1974 38,81 1554 46,40 1786 44,18 1336 49,97 1612 43,33 | 1119 53,65 1422 46,18 O893 57,14 1243 48,73 0772 58,35 1015 51,64 0744 58,68 0857 0768 51,92 0684 58,88 0662 0459 52,27 0666 58,91 OA84 018% 52,75 0629 59,10 0365 53,18 = 0612 59,15 0337 63,01 0583 0525 59,19 0326 | 69,15 0562 0460 59,23 2245 | 36,72 0546 0296 59,28 234 | S014 pl. p. | 0:40 0296? 59,30 ( 50) en EUEEEEEEEIE SEES Tot. Vol. Tot. Vol. Temp. 0,0 Pressure. | Temp. 0,0 Pressure. 279,25 | 0498 59,34 | 44945 | 24413 | 41,85 (contin. |. 0469 | 89,54 (contin.)| 1920 44,70 | 0439 60,06 | 1740 A767 0406 61,56 1553 51,26 | 0384 | 63,98 | 4372 54,99 | 0366 | 67,80 1192 59,26 97°,30 | 0387 | 39,21 | 1185 | 59,40 | 0364 59.25 | 4043 | 62,97 — | O81 4 69,11 B0°:23i5 |) s29a7iee) o S3670 | 0379 =6.07 a 38,02 | 0469 81,32 | 174 | 38,60 | 1984 40,96 | 52°5 | 2665 | 37,20 | 1798 | 43,63 | 2445 39,80 1618 | 46,38 2195 13,18 1432 | 49.60 | 2006 46,07 1256 52,70 1830 49,13 1037 3644 | 4817 49,42 0796 60,57 | 1624 | 53,38 | 0493 63,64 4391 58,90 | o363 | 74,91 | 4192 | 64,42 1017 | 70,19 HA°A5 2518 | 36,89 eer 163 2285 39,63 ( oy) Keep Mer xabat res LV), = 54,505 icM8. 1p == 0,7141. | Tot. Vol. |Vapour Vol.| Pyersine Tot. Vol. | Vapour Vol. Temp. 0,0 | 0,0 Temp. 00 00 Pressure. 195 | 1993 | | 3713 | 2804 | 1496 46,54 1735 | | 38,81 | (contin) 1237 | | 19,35 1598 | | 40,31 1082 | 518% | 1451 | 44,92 | 0853 | 53,87 ais | 44,96 0709 | o574 | 54,96 1422 | | 42,18 0386 = O310 54,72 | 4183 | 1072 | 42,64 | 01s | 88,25 oss2 | 0710 | 43,18 _--————— —_——_. O611 | 0347 | 43,77 2138 | peed Bod | 0606 | 0339 | Laerouene, oo Soe he 2842 O87 | eerie D72:35 | Osi. | 55,69 | | | SRT 0576 0271? 56,84 20,3 2066 | | 937.43 eae | 066% 56,62 | 62 1905 | | 38,85 | 0643 | 36,68 | 1709 | | 41,26 | 624 56,75 1539 | | 43,43 | 0390 | | 56,87 | 4387 | | 453,81 | 27040) 0617 | 56,83 1079 | | 49,08 —_———— | 0838 | Grae. | 19,62 | 39°23 | 2266 37,03 | 0582 0300 | 80,44 ary [eee 0385 31,10 estate at == 1744 | 43,96 25°, 42 | 37,24 | 1542 | 46,36 | 197% | | . 39,17 | 1361 | 19,51 | 1774 | | 69 | | | 1589 | | 14,20 | Temp. may A | Pressure. | Temp. | ea Pressure. 30°,23 | 1182 52,51 41°45 | 1179 58,10 (contin.)| 0993 55,61 |(contin.)| 0993 62,47 0797 58,24 0800 67,27 0560 60,48 0574 73,93 0399 | 6804 > | 20,5 2613 37,40 AA°,43 | QS 37,29 2428 39,59 2283 39,12 2168 43,03 2100 AAAS {921 46,90 1910 44,18 1662 51,70 1727 47,04 1187 63,13 1545 50,42 0936 71,12 1362 54,08 0758 77,17 Physics. — “he elementary theory of the Zeeman-effect. Reply to an objection of Potncarh.” By Prof. H. A. Lorentz. § 1. In a recent article in L’Eclairage Electrique !) Porcart comes to the conclusion that the well known theory of ZeEMan’s phenomenon, according to which every luminous particle contains either a single movable ion, or a certain number of such ions whose vibrations are mutually independent, can account for the doublet which is seen along the lines of force, but is unable to explain the triplet which one observes in a direction perpendicular to these lines. This result is obtained by treating, not the emission but the absorption in the magnetic field, and it is curious that the same mode of reasoning has led Vorer®) to formulae implying the existence of the triplet. I believe this discrepaney to be due to PoINcaRE’s erroneously omitting the term £ ~ ne Po 4 1) Porncart, La théorie de Loruntz et le phénomene de Zeeman, Eclairage Elec- trique, T. 19, p. 5, 1899. 2) Voret, Ueber den Zusammenhang zwischen dem ZpEMAN’schen und dem Fa - Rapay’schen Phinomen, Gottinger Nachrichten, 1898, Heft 4, p, 1. in his equation (6) on page 8. In order to explain this, I shall in the first place compare the different formulae that may be applied to the propagation of light in an absorbing gaseous body, placed in a magnetic field. § 2. The equations of Vorar contain the following quantities: 1°. The components w,v,w of a vector (the vector of NEUMANN) which comes into play in all media, the aether itself included, which are traversed by light-waves. 2°. The components §, 7, ¢ of a second vector (the vector of FRresNEL), which is related to the former in the way expressed by the equations ge de dude pte ae Ayine Ozhitas SuGzulnda te Soe Sumi es © 3°. , H, Z), which is defined as follows: o eo Sl 60, Hv 2 a, Vi, 2 Wei + =e, Wi. (2) Here, the coefficients « are constants, and v is the velocity of light in the aether '), Between the vectors (7, (7, Z) and (u, v, w) there exists a relation, expressed by du dH 04 du 04 OF dp 0 oH 202 oy’ 08 or de’ d® dy oe ° °®) Finally there are a certain number of equations — three for each 1) In order to ayoid confusion, I shall depart a little from the notation of Voter and from that which I myself have used on former occasions, ( 54 ) vector P, — which are to be considered as the equations of motion for the ponderable matter. They are of the form 0? U) : _ oh, OW; OV; % ae + dy Un + fi vi + yh (2 airs C aca) + e,§&=9, ete.) (1) in which d, f and g are constants. The terms with the first coeffi- cient depend on the elastic forces acting in the ponderable particles, the terms with f serve to introduce a resistance and consequently an absorption of light, while the terms with g are due to the forces produced by the magnetic field. The field is supposed to be homogeneous; the components of the magnetic force in the field are A, B, C. In the simplest case there is only one veetor P. The signs of sum- mation (in (2)) and the indices / are then to be omitted, and there will be no more than three equations (4). § 3. On the basis of the electromagnetic theory of light I have established the equations of motion in the following way *), Let there be N equal molecules per unit of volume, each of them containing a movable ion of charge ¢ and effective mass z. Let x, y, z be the displacements, in the directions of the axes, of one of the ions; then ex, ey, ez wiJl be the components of the electric moment of a molecule, and, if a horizontal bar over the letters is employed to indicat mean values taken for a large number of particles, the components of the electric moment per unit volume will be M, = Nex, M,= Ney, M,=WNez, If the ions are in a state of vibration, they will excite in the aether a certain periodic dielectric displacement and a similar mag- netic force; besides these, there may exist, independently of the ions, a disturbance of the equilibrium in the aether, in which there is a dielectric displacement, say (f,, Yo, /o)- Now, in order to obtain the equations of motion for one of the ions, I conceived a sphere BL, whose radius, though very small in comparison with the wave-length, is very much larger than the 1) The sign vetc.” will always be used to indicate two equations similar to the one that is written down and relating to the axes of y and z. *) Lorentz, La théorie Glectromagnétique de Maxwru1 et son application aux corps mouvants, Leiden, Britt 1892. Also in Arch, néerl. T. 25. (55 ) molecular distances, and the centre of which is occupied by the mole- cule to be considered. I denoted by ¥, DY, 3 the components of the electric force at the centre of the sphere, in so far as it is due to the molecules within the surface, by the components of the elastic force by which the ion is driven back to its position of equilibrium, and by M,, M,, M three auxiliary functions, satisfying the equations 1 0 : (a = cate =—47M,, \ v* oe? 1 0? | (4-3 5)™ =—4 = My, napa curso kD) 1 32 (a == om. =——4 My. v2 de? In these the velocity of light in the acther is again represented by v. Finaily, I found for the first of the three equations of motion ') ix e dx 4 s—_ = fx ~+—av’eM, + dt? vy dt? 3 0? Ma 0? My ine | eM. 1 Me Pal ica 8 pal pa du dedy dede vv? dt? -|t4avefotedk'. . (6) The term e d®x vy de’ which corresponds to the damping of the vibrations by radiation, was shown to be so small that it may be neglected. Tf, in (6), we replace some of the terms by their mean vaiues, we shall find after division by ¢ and after replacing 2’ by M,, mul- tiplied by a constant, Nelress § 128: Proceedings Royal Acad, Amsterdam, Vol, U. ( 56 ) Vv Z 0” M, — Me = ri a + Ne 2 E MM, 0” My hd M- 1 he Mr} { 97 t af = y? ae : hy, aL er Aae Ox oy Ou Ae v2 Ale | a | Jos elc. . (7) where g is a constant coefficient. If the ion experiences a resistance, proportional to the velocity, we must introduce a term dx pi dt on the right-hand side of (6), and in the case of a magnetic field with the magnetic foree (A, B, C), there will be a term a( Os pee dt Hence, the equations (7) will change into Vv zx 0? Mz ec 0 M, 1 aM do M. SMe Sey ILS Shp pea (pict a | ae ere Nee q T We Ale T We Ot ae dt e i) | (8) |e a d* My | oF Me 1 AM, — Wie > da? ' Qedy | dedz we dt? ie a | ete. § 4. The above formulae may be put in a form better known in the theory of electro-magnetism and admitting of direct compa- vison with the equations of Voigt. We shall arrive at it, if we observe that there will be a magnetic force 0, which may be decom- posed into two parts, the one §, being produced by the vibrations of the ions, and the other . belonging to the same state of motion as (fos Joy ho). The components of the first of these parts are found to be ') 2M. d?M, O7Mz OM. | O2My d2Me eo by a dydt — dede dsdé dudt dvdt dot” and those of , satisfy the equations Yle, § 124. 4 (57 ) he 8 ( 3 0 ) Sa v2 ( a) ; Doz ( 0 2z 4 v2 (oho ee) . . . . ° (10) Now, if we put 7M aM, aM 1 3M, 0° Mr 0? My , a? M. 0° a | +4 fo: ete. (11) 0 v2 Ow On] Ou 0c v~ 0 i €.=¥| we shall find 0 &, 0 &- at 0” {0 M- 0 My Q 0 Io 0 hy am mater deen onl 8 yee ag or, by (9) and (10), aEy 2G, 20 VE, IG Aly IG AG, IH de midgumman “or TL clzery Gee “oy, Pow oer The form of these equations shows that © is precisely the “electric force.” In virtue of (11) the equations (8) become ae 2 0M, c¢ OM; ig poe se! a @ Undo e Me Sail ae “in aa Pe OY As we see, they express the relation between the electric force and the electric moment. ina rom (¢ né he formula Finally, from (9) we may deduce the formul dH. dD, 0 pee a? My | dM. : Se ll aera —-—AM| , dy os délda® | drdy | dwoz or, if (11) be taken into account, 1}. fs ; 2M, Om 3 d nies 3 Oly oO EE 3” te fh mi, | a i OS —dz7 0 So Oy z otlvw gv : v- O¢ ot Combining this with 4 s 0 fo re 0 D2z r4 3 Doy Side > Oy dz | ( 58 ) and attending to (5), we see that 0D: 0Dy dM: 1 @&. ~— ———_ =40n --+-—. 4 Oy Oz Ot v> Ot Now, let a new vector D be defined by the equation $ S ar eee.) Pee (2') 4 vy” then: 0h. 0 Dy 0D. d0f2 0 Dz aD, i sa A 97 TS == =4a ’ dy dz dt de 04 ot SH, De Oe é Cay ata Oe ae Oat Oy dt Since € is the electric foree, €/4 av? will be the dielectric dis- placement in the aether; D will therefore be the total dielectric dis- placement and ® the displacement-current. Thus the equations (1’) are seen to contain the well known relation between the magnetic force and the electric current. In (1), (2), (3) and (4') we have got the complete system of equations of motion. We might have obtained them also by starting from the relation between € and M, which I have assumed in my » Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Kérpern”; it would only have been necessary to add the terms which arise from a resistance and from the action of a magnetic field. The above method is less simple, but it goes farther in explaining the mechanism of the phenomena. § 5. Now, it is easily seen that the equations of the electro- magnetic theory are identical with those of Vora, if in these latter only one vector P is assumed. Indeed, if, in the formulae of Voter, we replace du dv dw s ras P a? ap? va E59, 1G; Vee eZ by Dy SD y i Zo Dr D, ADs Anv?’ 4av2’ dav?’ y27 vy” ye’ M,; M, M. ¢, €, Ce ae Rm Miers cet 5 2? (CEE) 9) the equations (2) and (3) change into (2') and (3’), and the formulae (1), if first differentiated with regard to ¢, take the form (1). As to the equations of motion (4), these become io2Mee ad f oMz g ( , oM- coMy Fa Apaiie cha Sere On ry aa TAG EDy ) Hee 2 ete (12) v2 : ; 4 nv* or, if we put for D the value (2'), and multiply by , é 2q 4 v4 02M, Rae) (“a —1)Me+ SERRE ae Ee e2 0 t? 42 ; 4 ‘i sve TOM, _ Any ioe Bo One Nees stew at (13) ae Ot & at Olt This agrees with (4')1). At the same time we are led to the fol- lowing relations between the coefficients ved 1 4 x vi z tav(“~—1)=-, —_—_ = —; &° q &* Ne? Anv' f c Anv«g 1 => , © ? ‘ — ale Fd Ne? ge Ne (14) § 6. If we suppose a molecule to contain a certain number of ions, each of which can be displaced from its position of equilibrium, the total electric moment M may be split up into the parts M;, Mo,..., corresponding to the displacements of the separate ions. In this case, the equations (1'), (2') and (3') will still hold, but instead of (4') we shall have as many times three equations, as there are ions in the molecule. For the sake of brevity, I shall put %'=9'=3'=0 2). If, now, we wish to write down the equation (6) for the ™ ion, 4 : : we have to replace x by x;, but the term uae will still con- tain the total moment Mz. Instead of (4) we shall therefore get 1) Vorar’s formulae in Wied. Ann., Bd. 67, p. 845 are likewise of the same form. 2) lc. § 106. ( 60.) fh 4 Zh 2M Le Oo a ee eee. } Ne 3 Ne Oe | : | -. 4) Ch OMe iL ch oMny , oM;- = : —— (¢ SY 5 ae =) = €,, ete: i er at Ne; Ot 0 t The equations (1), (2) and (3) of Voter, taken this time im their general form, may again be written in the form of (1'), (2’) and (3'); for this purpose it will suffice to replace as before Ou = at > § ty ete by HD, Der €.. a ia ui faa 1 ° ’ ete 47 Vv" Vie ek TUR and L hy Vis Wi, by Mix Miy M;- matt ARE PSS et Le oe €h eh Eh From (4) we shall get equations, similar to (12). They will however contain the indices #, and if we use the value € : 9% 4 mv” DS=M+ we obtain an equation which is only slightly different from (13). The first term in it will be 4a v* dh Miz — 4a v? Mz, instead of in (13), and in the following terms M as well as the coefficients must be written with the index h. Finally, by assuming similar relations between the coefficients as in § 5 above, this new equation will become nearly, but not quite identical with (4"), the difference consisting in this, that it will not contain (61) 4 9 SEN ME v but — Any? Mp. For our purpose this is of no consequence. We shall confine ourselves to the case of molecules with a single movable ion or a single vector P, and even if we were to consider a more general case, our conclusions would not be materially altered. § 7. PorncARE investigates the propagation of plane waves in the direction of the axis of ze. He introduces no resistance, but he assumes the existence of several ions in each molecule. In his paper (X, Y, 7) denotes the total dielectric polarization,” (X7, Yn, Z) one of its parts, (f, g, 4) the dielectric displacement. His equations, if written partly in the above notations, are 02 Xp, , Xn 1 0 Vi; 0 Z), A n — Pp - = xX nd ae Cc ae B ) ’ t < 15 teases Maye) eg Pen a at eter at) with the constants a, , Z;, and &,, and?) ee ay 1 ex 2 vot vw Oo og Oe me Oe eure tise ta en ¥ LG) g2 ve ot ve de” h+Z=0. i Now, if 6 and & do not contain x and y, we shall have by our equations (1') and (3’) and 1) By a typographical error, the formula of Poincaré which corresponds to the first two of the equations (16) has on the left-hand side the sign -+. Hence a? , Op | = zl =i fi : Z 0 t Dies cay ee emer MEMO ah ae CS) 022 Ot? ’ \ Do=10 / Let the components of the dielectric displacement in the aether be /, g, h. Then G,=4avwo, CoS 4a veh; and if, instead of (M,, M,, M.), we write (X, Y, 7) for the electric moment per unit of volume, D-=f++-x, yo=gtY, De=ahtZ. Putting this in (17), we are led to the equations (16), which I have just taken from Porncann. Again, if there be no resistance, our equations (4') may now be replaced by fi = A ae Zh 0? Xh = h — —— Tt fo dl Ss — Ne}? 3 a N en Ot 1 a O¥n 0Z), a | OS ae St! 2p webes ae Ct ae. pes a Dividing this by 4a v*, and putting Zh ; PSE Vise) ae 4 A nv? Ne)? ra fh aa 1 Anve Ne? Lp’ 1 ea ee 0 4a v2 Nen we find the above formulae (15). Porncart’s equations are thus found to be identical with mine. ( 63 ) e question, I shall follow Vorat’s treatment of the case of a single vector P. In the first place VotaT examines the propagation of light along the lines of force, which are supposed parallel to the axis of @. He denotes by “ the strength of the field, by # the time of vibration, divided by 2a, by @ the velocity of propagation, and by xz the coefficient of § 8. In the application of the equations to the phenomena in absorption, in this sense, that over a distance equal to the wave- : : we aes : : : wk) length the amplitude is dimimshed in ratio of 1 to e~*7*, Further he puts: Si ov, Yd 8, fia, g/d=—k *)). =. (18) The values of by Vorer’s formulae (24) and (25), in which the upper signs are to be taken if the polarization is right-handed, and the lower signs if it is left-handed. ‘To simplify these formulae, I shall put @ and z for cireularly polarized light are given PEKRI — a2 =Siy we have then a (1—z*) 2/4 GPRS = SSS SNE eae (1 + #2)? ( S24 y? ae 20@°% v2 g? H 9 +2P S24 9292" Now, we may suppose that even the maximum value of z is a very small fraction. The left hand members of the equations may therefore be written wo? and 2 wz; hence, by division, g2 iW! 98 Iv— ar eA ee DA 970a29d0 Gl G9 SOUS tenes 1) 2 x 9% is the period of the free vibrations of which the ions are capable. As to the time 3/, it depends on the magnitude of the resistance, ( 64) Our next question is, for what value of this will be a maximum. At all events this value will lie in the neighbourhood of i), and if the absorption bands are narrow, it will be permitted to replace % by J in the numerator of (19). Consequently, the denominator, for which we may write g ] 9 go Ne oo a2 i 4 94 r0 (. — ai qr oe ) + 3? HF — wi OR eed shoe on (CAG) must become a minimum. I shall neglect the variation of the two last terms, and replace in them by J). Then, the minimum will be reached if S14 97 02 Sea ees ee eee ely and the maximum of absorption will be determined by 5. vi wy 75° 4 %max. = — . ye aed — ft qf ae In order that this may be very small, I shall suppose that g? is ere i ; ; : greatly inferior to at In this case, the last term in the denomi- wv : 0 nator may be neglected, so that At the same time we see that the last term in (20) may be neglected in comparison with the preceding one; consequently our result will be true, provided that we may neglect the variation of the second term in (20), while the first term passes through its minimum. This condition will always be fulfilled, if the absorption bands are suffi- ciently narrow. The equation (21) may be replaced by Ps Rap Foe = 4 Gg Fo We shall suppose % much smaller than %. Then, from what has been said, g? will be much smaller than 1, and in the absence of a magnetic field, i.e. for R= 0, the maximum of absorption will lie in the immediate neighbourhood of 5. If, moreover, k RJ, be very large in comparison with 3 4°?°, we shall have approxi- mately (65 ) PERS — a, =205 or F=9 SER, since & R must be small with regard to o>. Now, in order that a distinct doublet may be seen, the distance of the components must be large as compared with the breadth of the absorption bands. Replacing (19) by gH I,3 (S— 3g? P24 97292 bo XN I ’ we see at once that for a value of %, such that S—i7P KR == ud’ I the value of x will be 4%max 1 + We may therefore consider the borders of the absorption band to be determined by the last equation, if in it we take for « a moderate number, say 5. Hence, the necessary condition for a distinct doublet is seen to be KR > ws’. Tf it is fulfilled, our above sup- position as to the value of & Ri) will likewise hold good. Indeed, we shall have kRA> ku we Gia; 9 whereas g° Jy? is much smaller than 9 Ao. § 9. We now come to the propagation of light in a direction perpendicular to the lines of force. Let the vectors P be also per- pendicular to these lines, i. e. in the language of the electromagnetic theory of light, let the electric vibrations take place ata right angle to the direction of the field. Then, according to Vora, the velocity of propagation @, and the absorption z will be determined by his formulae (50) and (51), or if we neglect #*, by 4g? 2S, ig? 2S, w? = we 1 a y "9 2 19 c 1" ) ~~ 0 J (22) Sy + a? 9 Sy? + oh? FP! and 9 Se tada 1 ] CO gibi Vi Ue =s : - S)? -}- yp? 92 S,? 4 2 92 | Here I have put 92 —k RF — aan = 7 and +E RI — G2 = Sp. It is easily seen that, with the assumptions we have made concer- ning the magnitude of the different terms, the equations (22) and (23) imply the existence of to absorption-bands, corresponding to S57 —0e ‘andiitso'— 0: These. bands are precisely the outer components of the triplet, one is led to by the elementary theory of the ZmrMan-eftect. ‘The breadth of each of these lines will be equal to that of the original absorption-band; in virtue of our assumptions it will be much smaller than the distance of the two lines. Now it is clear that such a thing would be impossible, if the modification of the propagation of light were so small as Porncaré finds, namely of the order of #°, if & is the strength of the field. If, by the action of the magnetic field, the maximum of absorption is shifted to a place, where the absorption was originally insensible, we have to do with a finite change at this point of the spectrum. § 10. In order to examine this more closely, we must return to the equations of motion themselves, from which the formulae (22) and (23) have been deduced. Let the magnetic force be parallel to the axis of = (4A=B—0, C= R) and let the propaga- tion of light take place along the axis of « Then the complex expressions, which satisfy the equations of motion and whose real parts are the values of U, V, W, &, 7, ¢, ete., will contain the common. factor pair og 1 : 0 —_— — 7—(t——). ’ Iw iy ( 2) ) There will arise no confusion, if we use the letters U, V, ete. themselves to represent these complex expressions. Let the vector P be perpendicular to the axis of 2. Then W = 0, and = 77—0. ( 67 ) By the equations (3) we find: iF a=, OSS SAE @ by (@): 1 = 0) 7S — = (wy, C= 90; @~ and by (2): ee Ue ne ee ice Ve @-~ Hence eV H=———_ Ve oO Do = Py? @~ and = ie nai Ne w® + v? (z +7)? (= Consequently, the two first of the equations (4) beeome (day Ho Bra J* i} vA and et ie al Ney Y J o® + v2 (z + ip or, if we introduce the quantities %), #, ete., (P69 9 —G2)U—ikRIVaO0 . .. (24) (x + 1)? (P2 Lid} — Br) VtikRs U— = These equations correspond to the two last of Porncart’s formulae (6), and if we were to follow his mode of reasoning, we should say that, in virtue of (24), U mast be a small quantity of the order R so that the second term in (25) becomes of the order of R?. We should then omit this last term; all influence of the magnetic field would thereby disappear from (25). There is however an error in this reasoning, because, as I shall now show, the coefficient of U in (24) may become of the same order as that of V. ( 68 ) We saw already that the place of the absorption-lines is deter- mined by the conditions S; = 0 and Sr — US i. c. by f—I2X=ELRG. We have further assumed that 2»? is much larger than & # Hence, in the equation (24), the coefficient of U is approximately +thkRd, so that UAW ee ge S26) On the other hand, we may neglect in (25) the last term, at least if has a value for which the absorption is a maximum. For, neglecting #*, we find for that term 1— 2iz Z § ———— MOON Ves. 6. oe in yess) (a? —v*)+ 2 viz The equations (22) and (23) show that, in the middle of one of the absorption-bands, @?—v? is much smaller than 2v?z. We may therefore neglect the first term in the denominator, Omitting like- wise in the numerator the second term, which by our assumption, lies far beneath 1, we find for (27) Ti 3,2 v2 V ig’ Jo vy Seon ea ati 2; ? VrU%s Z But, according to (23), the maximal absorption is given by 2. .¢ 7 Fo. ro Lo XN | wie (27) may therefore be finally replaced by = 2709) V., a quantity that may be omitted in (25) as well as i? # V in the first term of that equation. In this way (25) reduces to AES eater, which agrees with (26). Translated into the terms of the electromagnetic theory of light, our result becomes ( 69 ) M,=+iM,. The meaning of this is that the ions move in circles perpendicular to the lines of foree, the direction of this motion being opposite in the two cases, represented by the two outer lines of the absorption- triplet. The assumptions we have found necessary in the foregoing con- siderations, viz. that the inequalities we C Uy qa andes kyu exist in a high degree, imply that %£& is much larger than g? J,. Ee) de Ne ; : g If this is to be the case, it follows from (18) that — & v? must ) far surpass *,; in the language of the electromagnetic theory of light this means — as may be seen from (14) — that Rk en A OOP re OPS RON tes 4zv? Ne oe must largely exceed the time /,. Of course this condition can always be fulfilled if only the num- ber of molecules N can be made small enough. This was to be ex- pected because at very smail densities the molecules must become independent of one another, and this is precisely what is assumed in the elementary theory. It would be difficult to state accurately at what density the expres- sion (28) becomes so large that distinct triplets may be seen. The preceding considerations show however that the triplets must appear in all cases where the observations along the lines of force give < good doublet. Astronomy. — ‘On the finding back of the Comet of Houmes according to the computations of Mr. H. J. Zwiers.” By Prof. H. G. vAN DE SANDE BAKHUYZEN. In the Transactions of the Royal Academy of Sciences 1s* Section Vol. III appeared a paper by Mr. H. J. Zwiers on tiie orbit of the comet of Hones, observed from Nov. 8 1892 till March 13 1893. From these observations Mr. Zwiers has deduced with great care the most probable orbit, which proved to be an ellipse, in which the comet at its greatest distance from the sun approaches ( ‘70)) Jupiter’s orbit very closely and at its shortest distance to the sun remains still outside the orbit of Mars; the period of revolution amounts to about 6 years and 11 months. In 1898 and 1899 the comet would probably again come so near to the earth, that it can be observed. In the above-named paper Mr. Zwiers has computed the pertur- bations which the comet would undergo till the end of 1898 and later on in a paper in the “Astronomische Nachrichten” Vol. 149, page 9, he has continued those computations till Sept 9% 1899. In an ephemeris added to it he has given the positions which, according to his computations, the comet would occupy on the celestial sphere. By the aid of this ephemeris the comet has been found back as a faint nebula by Pprrine at the Lick-observatory on June 10th, Its position deviated for the computed place 22%,2 in right ascension and 4'17" in declination. Furthermore it appeared that the comet was exactly in the orbit which it had to deseribe according to the computations of Mr. Zwirrs, and that a perfect correspondence was obtained between the observed and the computed position by adding 0.379 days to the period of revolution. Mr. Zwiers having taken the mean error of the period of revolution to be + 1 day, the accuracy of the computations proves to be still greater than he had surmised. Probably of the elements computed by Mr. Zwrers only the pe- riod of revolution will have to be corrected a little; this cannot be stated however with certainty until more observations will have been made. For the present Mr. Zwiers has computed a corrected ephe- meris supposing only the period of revolution to be increased by 0.4 day. An ephemeris corresponding entirely with this one has been given in n° 464 of the Astronomical Journal. (August 9th, 1899.) KONINKLUKE AKADEMIE VAN WETENSCHAPPEN TH AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday September 30th, 1899, Dt Ce = Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige to} te] So ro) c Afdeeling van Zaterdag 30 September 1899 Dl. VIII). Conrexts: “On the influence of water on the velocity of the formation of ether’. By Prof. C. A. Lopry pe Bruyn and Dr. A. Srecer, p. 71. — “An example of the conversion of mixed crystals into a compound”. By Prof. H. W. Baxuvis RoozeBoom, p. 74. — “On the Enantiotropy of Tin”. By Dr. Ernst Conen and Dr. C. van Eyx (Commani- eated by Prof. H. W. Baxuurs RoozpBoom), p. 77. — “On the Enantiotropy of Tin dI)”. By Dr. Ernst Conen and Dr. C. van Eyx (Communicated by Prof. H. W. Baxuvis Roozepoom), p. 81. — “The mixture crystals of Hg J, with Hg Br,”. By Prof. H. W. Baknuis RoozEBoom, p. 81. — “On a new kind of Transition Elements (sixth kind)”. By Dr. Ernst Conen (Communicated by Prof. H. W. Bakuuis Rooze- Boom), p. 81. — “On Isodialdane”. By Prof. C. A. Lopry DE Bruyn and Mr. H.C. Byv, p- 81. — “The results of a comparative investigation concerning the palatine-, orbital- and temporal regions of the Monotreme-skull”. By Dr. J. F. van BemmeLen (Commu- nicated by Prof. A. A. W. Husrecur), p.81. — “On the Formation of the Resultant”. By Mr. K. Bes (Communicated by Prof. J. Carpinaau), p. 85. — “Investigations with the Micromanometer”. By Dr. A. Smirs (Communicated by Prof. V. A. Juius), p- 88. — “The determination of the refractivity as a method for the investigation of the composition of co-existing phases in mixtures of acetone and ether’. By Mr. E. Wi. J. Cunarus (Communicated by Prof. J. D. yaN DER WaaLs) with one plate, p- 101. — “On the Theory of Lirpmany’s Capillary Electrometer”. By Prof. W. E1nt- HOVEN (Communicated by Prof. T. Zaayer), p. 108. — “On the formation of Indigo from the Woad (Isatis tinetoria)”. By Prof. M. W. Betserincx, p. 120, — “Methods and Apparatus used in the Cryogenic Laboratory (1)”. By Prof. H. Kamervinen Oxnxes (with 4 plates), p. 129. — “The diclectrie constants of liquid nitrous oxide and oxygen”. By Dr. Frrrz Hasenozrnri (Communicated by Prof. H. Kameriincu Onnes), p. 140. — “On Spasms in the Earth’s magnetic force”. By Dr. W. van Bem- MELEN (Communicated by Prof. H. KamMeriincu Onnegs), p. 141. — Erratum, 141. The following papers were read: Chemistry. — ,On the influence of water on the velocity of the formation of ether.’ By Prof. C. A. Lopry pe Bruyn and Dr. A. STEGER. (Read in the meeting of June 24th 1899), In a previous communication ') we drew attention to the influence of water on the velocity with which oxyethyl or oxymethyl is sub- ) Proceedings 1898 p. 166. 6 Proceedings Royal Acad, Amsterdam, Vol. LI. (72) stituted for the nitrogroup in orthodinitrobenzene by sodium aicohol- ate. It appeared that the existence of constant coefficients of velocity was not at all, or very little affected by the presence of water in the methyl- or ethylaleohol, a fact which was explained by the circumstance that by far the greater part of the sodium is present as alcobolate in mixtures of water and alcohol containing even 50 °/o of water. The influence of the water present was however felt in the alteration of the numerical values of the constants due to the change of the medium; with ethylaleohol the change consisted of a diminution of the constants as the quantity of water present in- creased, with methylaleohol exactly the contrary took place. The influence of water on the reaction under discussion could not be followed further than a 50°/) mixture of water and alcohol, owing to the ever decreasing solubility of the dinitrobenzene. We pointed out therefore the desirability of finding a reaction, which would allow velocity determinations to be made, for both alcohols, from the absolute alcohol to pure water; the two different curves for the two alcohols must necessarily meet in the point correspond- ing to pure water, that is to the reaction with Na OH. We have discovered such a reaction in the process of the forma- tion of ethers from aikyliodides and alcoholates, in the special case in which methyliodide is employed; the solubility of this iodide in water being sufficient to permit of a determination of the velocity. With ethyliodide it was found that, owing to its smaller solubility, it was impossible to go further than 30°/, ethylaleohol (70°/, water) and 40 °/, methylaleohol (or 60 °/) water). The reactions studied are thus: I. NaOC;H, + CH;I , Il. NaOCH, + C HI Ill. NaOC,H; + C,H,I, IV. NaOCH; -+ C,HI ; to which the change, CH; + NaOH =CH;ONa-+ Nal, must be added. The composition of the mixtures of water and alcohol was changed by equal steps of 10°/, between absolute alcohol and water. It was at once evident that the reaction-coefficients obtained in each experiment might be regarded as constants; with methylalcohol, the numbers are very satisfactory, less so with ethylalcohol, but still more than sufficiently so to show the change of velocity with the quantity of water present. For reaction I the numbers diminish from 0,189 for absolute aleohol to 0.0040 for water; for reaction . . (73) III, from 0,0168 to 0,005 ; for the reactions in methylaleohol (II and IV) an increase at first occurs with increasing content of water, for [I there is a maximum at 70 °/, (0.032 to 0.0435) after which the numbers diminish to 0.004, for reaction IV the increase continues as far as the decomposition in 40°/, alcohol (0.00525 to 0.0098) which was the extreme limit to which it was possible to go. The subjoined figure shows the change of the constants with the content of water. AE; Si ss IL I L CHS r 7 f 1 M sia a iB | Ale 80 60 40 POM HIO 2 It is thus evident that, as in the case of the reaction between o-dinitrobenzene and sodium alcoholate, the addition of water to ethylaleohol diminishes the velocity of the reaction, whilst with methylalcohol an increase first occurs which (reaction II) is followed by a decrease. Attention may be drawn to some other conclusions. First, it appears that whilst for both iodides in methylaleohol there is a maximum for the mixture containing about 70 °/, of alcohol, the constants diminish regularly with methyliodide II, whilst with ethyliodide (IV) they remain practically constant between 40°/, and 70°). It is further seen that in the aleohol in which the electro- lytic dissociation is the greater (methylalcohol) the velocity of 6* ( 189) reaction is the smaller, notwithstanding the fact that according to the researches of MpNnscHUTKIN and Carrara, methylalcohol itself accelerates similar reactions to a greater extent than ethylalcohol. It appears to us therefore that it follows from this case, as in the case of the reaction of o-dinitrobenzene and alcoholate, that reactions taking place in solvents other than water depend on circumstances which are as yet unknown, in addition to the degree of dissociation into ions. From our earlier research we had concluded that the sodium dissolved in a 50°/, mixture of alcohol and water is present mainly as alcoholate. The same conclusion may be drawn from an experi- ment in which a solution of 5 grams of Na in !/, litre of a 50 °/, mixture of alcohol and water was warmed to 25° for 8 days with 32 grams (1 mol.) of ethyliodide. By means of several fractional distillations about 11.5 grams of ethylether were obtained, the theoretical quantity being 15.5 grams. Considering the unavoidable losses it may therefore be said that by far the greater part of the iodide was converted into ether. It is still necessary to examine reactions such as those here studied, in mixtures of aleohol and water containing a Jarge pro- portion of water, since in these there cannot be much alcoholate. The details of this research will shortly be published in the “Recueil des travaux chimiques.” Chemistry. — Mr. Prof. 11. W. Baknuis Roozesoom speaks on: ,»An example of the conversion of mixed crystals into a compound’. (Read in the meeting of June 24!» 1899.) In the meeting of the 25 February 1897, page 376, I gave an explanation of the solidification of mixtures of optical isomers, when the solidification results in the formation (1) of a conglomerate (2) of mixed crystals, (3) of a racemic compound. In a more complete paper, Zeitschr. phys. Chemie 28, 512, I have further developed the theory of the phenomena which must oceur when these three types pass into each other when the solid mass is further cooled. As one of the most interesting cases, Mr. ApriaANI, has at my request, studied an example of the conversion of mixed crystals into a compound below a certain temperature. The example was camphoroxime. Mr. ADRIANI prepared the . ( 75 ) d-oxime; we owe the Loxime to the kindness of Pref. BeckMANN of Leipzig. 1. The melting points of the pure oximes and of mixtures of them were first determined. Both melt at 118°.8; the inactive mixture, containing 50°/o d- and 50°/) /-oxime melts at exactly the same temperature as aiso a number of mixtures containing excess of d- or /-oxime. No difference could be discovered within the limits of attainable accuracy. The accuracy here is not more than 0°.1, because it is very difficult to determine the melting- point exactly, owing to the small difference in the refractive indices of the solid and liquid. Very satisfactory results were obtained finally by using very thin walled tubes in which a thin cylindrical ring of the solid mass was placed just above the lower end. The solid mass is, in all proportions, microscopically homogeneous and regular. Forster and Popr’s view (Journ. Chem. Soc. 71.1049) that we are here concerned with mixed crystals is confirmed by the discovery of one melting-point line alone. At the same time the existence of mixed erystals of optical iso- mers, the probability of which was pointed out by KipprnG and Pope, is confirmed. 120° In the figure, the horizontal = ka wi “ line AB represents the melting 115° ~= point line. The view that the melting points of all the mixtures loc ~=6rwould be the same is thus con- firmed in this case. I have already pointed out that this is possible in no other series of mixed crystals than those containing optical isomers. A consequence of the hori- zontal melting-point line is that each mixture solidifies to a homogeneous mass. The melting point line therefore represents the compositions both of the liquid and of the solid phase. 2. According to Pore the two isomers, as well as mixed erystals containing them, undergo a change from regular to monosymmetric crystals shortly after they have solidified. ld (76) The temperatures at which this change took place were however unknown. They were therefore determined. Change [rom regular to monosymmetric crystals. 100°/5, d or be 212556 90°), Vi 1 | 0°.6 ” ” 709/, 109°.7 ” n 7” 50/, » » » 109°%4 These values are shown by the line CDE, which is completely symmetrical and has a minimum of temperature at the transition point of the inactive mixture. Since here again only one curve is obtained for all the transition temperatures we must conclude that the regular mixed crystals change into monosymmetric mixed crystals. When the change takes place with falling temperature it may be much delayed; in the other direction however it is very sharp. With the microscope it may be observed clearly, with the thermo- meter with great difficulty, and very distinctly by means of the dilatometer. With the non-racemic mixed-crystals it is possible that the transition takes place through some interval of temperature. In any case this is very small. 3. A further change takes place in the monosymmetric mixed erystals when they are cooled still more. Pope has observed this, only in the inactive mixtures, and ascribed it to the formation of a racemic compound (which may be obtained from a solution of the inactive mixture at the ordinary temperature). In that case the con- version of the mixed crystals into the compound should theoretically oceur in other mixtures also but at lower temperatures. This has been shown to be the case. Conversion of mixed crystals into a compound. 50%, @ or 1 103° 60°/ ‘0 4” » 7 QE 10°/, ya) 86° These points are indicated by the line /G// which has a maxi- mum at 50 °/o. (02) The change occurs less readily the greater the excess of d or / which is present and proceeds very slowly. At 75 °/, it could not be observed even at the ordinary temperature. The monosymmetric crystals change to a granular mass; when excess of d or / is present this is of course only partial. The transition temperature in this case could not be detected by means of the thermometer or of the dilatometer but only by means of the microscope and then only when the temperature was rising. With 50°, the change is complete at the maximum tempe- rature; with the other mixtures the change is gradual; the line FGH represents the temperatures at which the racemic compound in a given mixture has just disappeared. All points between the two branches represent conglomerates of the compound with mixed crystals. The course of the conversion of mixed-crystals into a compound, deduced by me on theoretical grounds, is therefore completely con- firmed by this first example. Chemistry. — ,On the Enantiotropy of Tin”. By Dr. Ernst CoHEN and Dr. C. van Eyx (Communicated by Prof. H. W. Bakuuis Roozrpoon). (Read in the meeting of June 24th 1899). 1. That pure tin falls into a grey powder when exposed to great cold is a phenomenon with which the tin traders of Russia espe- cially have been long familiar. The phenomenon is, in that country, so common that a special name has been given to the tin powder which may be translated as tin which may be scattered. The phenomenon has been very frequently referred to in scien- tific literature; the first description of it is due to ERpMANN ') in 1851. Ile is followed by Frivscie*), LEwALD *), RaMMELSBERG ‘), Ouvemans °), Watz °), Perri’), ScHERTEL ‘), RAMMELSBERG ay 1) Journ. f. pract. Chemie 52, 428 (1851). 2) B. B. 2, 112 en 540 (1869); Mém. de P Académie de Pétersboure, VIT Série N° 5 (1870). 8) Dinglers polytechn. Journal 196, 369. (1870). ‘) B. B. 3, 724 (1870). Zeitschrift fiir Chemie 1870. 735. *) Processen-Verbaal der Kon. Akad. v. Wetenschappen te Amst., veread. 28 Oct. 1871. °) Waaner’s Jahresbericht 1873, 207 uit: Deutsche Industriezeitune 1872, 468, 7) Wrepemanys Ann. (2) 2, 304. (1877). *) Journ, fiir pract. Chemie 19, 322 (1879). *) Berl, Akad. Ber, 1880, 225, ( 78 ) MarkownikorF !), Emevsanow®), Eoy. Hserr*), Horve er *), Srock- MEIER °) and ScHaum °). The phenomenon has been observed on articles made of tin such as organ pipes, buttons of uniforms, coffee pots, medais, rings ete. and not only on blocks of pure Banca tin. Whilst tin in the ordinary, well known condition, is silver-white, it becomes grey under certain circumstances and loses its coherence. 2. The different authors by no means agree as to the cause of the change. Some ascribe the change to great cold, others to the combined influence of cold and vibration, whilst a third group of observers speak somewhat vaguely of an influence which the greater or smaller rate of cooling of the tin after it had been melted might exert on the occurrence of the phenomenon. 3. FrirzscHe proved qualitatively that a considerable expansion accompanies the transformation of the silver-white into the grey condition. SCHERTEL and RamMELsBEeRG found later that the specific gravity of the grey modification at 19° is about 5,8 whilst the silver-white form at the same temperature has the specific gravity 7,3. 4. The facts enumerated remained up to the present isolated ; many points in the different memoirs could not be brought into harmony with each other. A more accurate, quantitive treatment of the subject, based on the newer physico-chemical conceptions, may perhays throw some light upon it; at the request of Prof. Baknuis RoozeBoom we have undertaken this and give in what follows a very brief account of some of the results thus far obtained. 5. The material used was obtained from Prof. Epy. Huei of Helsingfors, who was kind enough to send us 25 grams of grey tin. This tin was part of a piece of Banca-tin which had falien into powder in the warehouse of a Helsingfors firm. 1) Journ. russ. phys. chem. Gesellschaft 1881, 358; Bulletin de la Société chimique de Paris (2) 37, 347 (1882). *) Congress russischer Naturforscher und Aerzte Petersburg 1890. 5) Chemiker Zeitung 16, 1197 (1892); vOfversigt af Finska Vetensk: Soc. fSr- handlin”. 32. *) Chem. Zeitung 1892. 1339. ®) Verh. d. Ges. Deut. Naturf. v. Aerzte. Niirmberg 1893. *) Die Arten der Tsomerie. Habilitationsschrift, Marburg 1897, ( 79 ) If the tube containing the grey tin is immersed in warm water the tin immediately takes on the colour of ordinary tin. The recon- version into grey tin occurs when the tube is cooled. At — 83°, in a paste of solid carbonic anhydride and alcohol the change from white to grey tin took place in about 24 hours. Prolonged cooling to a temperature not lower than —20° was fruitless. On the other hand the change of grey into white tin was only observed at tem- peratures above + 30°. From this point, however, the velocity of the change increased very rapidly with rising temperature. It appeared therefore to be difficult to find a transition point. It is, however, known that transition phenomena are accelerated when the materials undergoing the change are present in a finely divided state, and also that solvents accelerate the change !). After a number of preliminary experiments we found that a so- lution of ammonium stannic chloride aiforded an excellent means of causing the change to take place readily in either direction. For example, the change white tin — grey tin, which without the ammonium stannic chloride solution required 24 hours at —83°, took place in 6 hours when a few drops of a 10°/, solution of the salt in water were added to the tin. When the change has been carried out in both directions several times with the same quantity of tin, it takes place more and more readily. In general, it may be said that the phenomena are here quite analogous to those observed with salts containing water of crystallisation when they are heated above their transition points and again cooled. 6. In order to determine the transition point of the change erey tin 2 white tin we used the dilatometrie- and the electric methods. a. Determinations with the dilatometer. The dilatometer contained about 2 cc. and was filled with white tin; a 10°/, aqueous solution of ammonium stannic chloride served as measuring liquid. The position of the liquid in the very narrow capillary was read on a porcelain millimeter scale. The following table contains the observations. 1) See for example: L. Tu. Reicuer, De temperataur der allotropische verandering van de zwavel. Disseitatie. Amsterdam, 1883 ( 80 ) Tos Bul bie A. ‘Temperature. ‘Time in hours, Rise of the ievel in the Rise per houc. eapillary in mm. in mm, en) 23 104 4,5 0° 20 48 2,4 55-0 17 2 0,1 10°,0 13 0,9 0,0 15°,0 11 0,0 0,0 17°,0 23 0,0 0,0 20°,0 244 — 2,0 — 0,1 From these observations follows that the transition point lies between -+ 10° and -+ 20°. More exact results would be obtained by prolonged observations at constant temperature. b. Electric determination. A transition element was set up as follows: white tin — 10°/, ammonium stannic chloride solution — grey tin, and its E.M.F. at different temperatures determined by PoGaEn- porFF’s method. A Weston-cell was used as standard and a small accumulator as the working cell. Our transition cell stood in a thermostat. The change of pole oceurred at 20°, 7. The two methods thus lead to the result that the change grey tin = white tin has a transition point (at 1 atmosphere) at 20° C. Since all tin articles in every day use, consist of the white mo- dification, the above research leads to the striking result, that our whole tin-world exists, except on a few hot days, in the metastabile condition. Amsterdam, Chem. Laboratory of the University, June 1899. (S08) Chemistry. — ‘On the Enantiotropy of Tin (11).” By Dr. Ernst Conen and Dr. C. van Eyx. (Communicated by Prof. H. W. BakHuts ROOZEBOOM). (Will be published in the Proceedings of the next meeting.) Chemistry. — “The mixture crystals of Hg J_ with Hg Bro.” By Prof. H. W. Baxknurs Roozesoom. (Will be published in the Proceedings of the next meeting.) Chemistry. — “On a new kind of Transition Elements (sixth kind).” By Dr. Ernst Conen. (Communicated by Prof. H. W. Bakuvtls RoozEBoom). (Will be published in the Proceedings of the next mecting.) Chemistry. — “On Isodialdane.” By Prof. C. A. Lopry pr Bruyn and Mr. H. C. Brgz. (Will be published in the Proceedings of the next meeting). Zoology. — Mr. Husrecur presents on behalf of Dr. J. F. van BremMeLen: “The results of a comparative investigation con- cerning the patatine-, orbital. and temporal regions of the Monotreme-skull”’, Ii Palate: In both Ornithorhynchus and Echidna the palate has been secon- darily prolonged backwards, in consequence of their mode of life, and therefore independently of each other, and in two different ways. The palatine bones of O. are as broad behind as in front, the pterygoids being situated entirely along their lateral borders, quite un- connected with the bones forming the wall of the cerebral cavity. In the E. skull on the contrary, the palatines are prolonged backwards into slender points, which causes’ the pterygoids to find a place at the roof of the mouth much nearer to the middle line, between the oblique postero-exterior border of the palatines and the petrosa, thereby allowing them to enter into the formation of the cerebral skull-wall. The horizontal mouth-plates of the Echidna-palatines are provided at their lateral border with two vertical wings: a larger one in front, forming the basal part of the wall of the orbital cavity, and a ( 82 ) smaller one behind, stretching upwards in the temporal groove and separating the foramen ovale from a large bipartite opening at the border of the orbita, which represents the united foramina rotunda, optics and spheno-orbitalia. In O. tie first mentioned of these apertures is separated from the two following by a short bone-column. At the ventral side of this temporal palatine-wing in KE. we notice the front end of a tiny canal, which may possibly represent the homologue of the well-developed canalis pterygoideus seu vidianus of O., this latter running longitudinally along the margin of the palatine-plate, between for. ovale and for. rotundum. The difference is explained by the occurrence of a large artery in O., branching off from the carotis interna, crossing the tympanic cavity externally to the stapes, and entering the vidian canal to reach the orbital cavity. This artery, called art. stapedia by TANDLER, is absent in E., where the orbits are provided with blood by the earotis externa, but perhaps the small artery occupying the above-mentioned tiny canal is the last remnant of the art. stapedia, Il. Sphenoid. The corpus sphenoidei in E. appears iong and slender, owing to the want of connection with ali-sphenoidea (alae magnae). It shows a coneave ventral side, caused by its curving down at both sides in slightly elevated but very elongated. pterygoidprocesses. At its hinder margin it is pierced by the foramina carotica, and laterally to these it is provided with backward prolongations of the processus ptery- gotdales, viz. the spinae angulares. These latter are much more developed in O., where they extend over tie ventral surface of the petrosa. In this animal they form a narrow partition dividing the foramina ovalia from the choanae, whereas in E these two are separated from each other by the whole diameter of the pterygoids, which also hide the spinae angulares under their projecting median edge. The sclla_tureica of O. is much more elongated in a sagittal direction than that of E. This contrasts with the extraordinary development in the latter animal of the lamina cribrosa ethmoidei, which totally anchyloses with the sphenoid. In O. no trace of such a cribrous plate can be detected. The space of the ali-sphenoids is occupied in E. by thin bony plates, separated by suture from all the surrounding bones: the basi-sphenoid as well as the others. These plates ossify at a very late period, so late indeed that even in the almost adult skull a large fontanella is found in this spot, leaving the for, ovale not = ( 83 ) encircled by bone at its lateral border. In the partly-ossified skull of a young E. removed from the pouch, this fontanella even extended to the foramina rotunda, optica and spheno-orbitalia, which all confluated into one large vacuity in the lateral skull-wall. The same fact occurred in the skull of an Ornithorhynchus-foetus: the bony plate that was going to close up this open space, was growing out from under the squamosal as a dermal bone. In this character it resembled the post- jrontale, which is destined to anchylose with the orbito-sphenoid. In consequence of this latter occurrence the orbital wings of the sphenoiad reach an enormous size in Monotremes. The presence of postfrontals in these animals, resembling those of Sauropsids, already mentioned by SEELEY, is proved beyond all doubt by the investigation of the skulls of new-born individuals. The orbital wings of the sphe- noid anchylose with the median corpus, in KE. as well as iv O., thus contrasting with the alisphenoidplates in the former animal. II. = Petrosum. The petrous bone of O. is separated from the surrounding bones by three large perforations of the skull-wall; 1st. an anterior one, the foramen ovale, dividing it from the alisphenoid, 2°. a posterior one, the for. pro nervo vago et glossopharyngeo, separating it from the exoccipital (occ. later.); 34. a median one, through which no structures enter or leave the cerebral cavity and which separates the petrosum from the basi-occipital. In E. these holes are apparently wanting, but in reality they are all present, only they are lying much farther apart, and more- over the anterior and median ones are separated from the petrosum by the large pterygoid. The posterior opening is divided into two orifices, an anterior one which serves as an outlet to the nerves and is situated within the borders of the petrosum, and a posterior one, which is nothing but a fontanella, closing up in the full-grown animal and surrounded by the exoccipital. In O. the large size of the corresponding single opening is also due to incomplete ossifica- tion in the neighbourhood of the nerve-foramen. This scattered position of the three apertures around the petrosum in Kchidna brings this bone into an all-round contact with other bones viz. the alisphenoid, pterygoid, basioccipital, exoccipital and squamosal. At the lateral wall of the skull the petrous bone of E. appears to be continued in a dorsal direction as a large patch of bone, but in ( 84) reality it is separated from this patch longitudinally by a suture that runs through the Jateral part of the tympanic cavity. By its form and position this patch resembles the mastoidal part of the temporal of other Mammals, but as for its size and independence, it may be compared to the opisthoticum and epioticum, taken conjointly, of Sauropsida. This mastoidal part of the skull-wall is a chondrostosis, which fact is in itself sufficient to forbid its comparison with a squamosal, a comparison one might otherwise be much inclined to make, consi- dering that the dermal bone which is situated on its outer surface might easily be mistaken for the jugal, with which it shows many points of resemblance, and which, but for this hypothesis, must be con- sidered as absent in the Monotreme-skull. IV. Areus zygomaticus. The malar arch of Monotremes is made up of two bony processes, running side by side for the greater part of their length. The anterior belongs to the maxillary, the posterior to the above-men- tioned dermal bone, that I take to be the squamosal. A jugal bone is totally absent in E. In O. on the contrary a little prominence oceurs on the dorsal side of the arch, marking the limit between orbital and temporal fossae. In some skulls this prominence was found separated by a suture from the underlying zygomatic process of the maxillary. Most probably we may look upon it as the last remnant of a disappearing jugal. The foetal O. skull did not show any trace of it. V. Canalis temporalis. Between the squamosal and the wall of the primordial-cranium (mastoidal bone), a canal is left open from betore backwards in both E. and O. In no other Mammalian skull a trace of such a canal was found. In E. it is longer but narrower, in O, shorter but wider. Its lumen is filled up with fibres of the temporal muscle. Moreover in E. an artery penetrates into the skull-wall by the posterior opening of this canal, but immediately leaves it to con- tinue its way through the diploé of mastoidal, parietal and frontal as far as the ethmoidal region. Hyrrrn calls it art. occipitalis. ( 85 ) Mathematics. — On: “The Formation of the Resultant”. By Mr. K. Bes. (Communicated by Prof. J. CARDINAAL.) The method of elimination by means of the Brzour function as shown by me in my treatise “Théorie Générale de Elimination” (Verhand. der Kon. Akademie van Wetensch. te Amsterdam 1° Sectie, Dl. VI, N°. 7) offers a means to form the resultant that is to be obtained, if between » — 1 homogeneous equations of arbitrary degrees with n variables » — 2 of those variables are eliminated. I intend shortly to treat this subject in extenso; but looking forward to the time necessary for this work I thought it my duty at present to acquaint your assembly with the obtained result. For this the special case is taken of two homogeneous equations of the degrees / and m with three variables, viz.: Pp (x, y, 2) = a, al + agal—ly + ag al—lz + ay vi? y? + a; a!—2y = + | cpap gees | Oy Oh Sy ieee ay 24 — 0) 2 /(1). y (a, Ys 2) — by qm a by qm - ly a bgam—! 2 a by qm—2 y? “f+ b; am —2 ys -f ( ) + bg am—2 2? bp am—Sy3 + 2... wt L(+) (m-42) =" = ( unr It is known that in this case the resultant is of the degree lm. If we form an homogeneous function / of the degree /m as follows : J ee Dre 8 Uae ate Oe ec? Copa Woe (2) ir where ® and ¥ are respectively homogeneous functions of the degrees Jim —Jl and lia — m with provisionally undetermined coeffi- cients s the equation 1S Vioiig “Si eehe tone so 8 a (8) will represent the resultant, if we can determine the coefficients s in such a manner that all the terms containing one of the three variables disappear from the equation. The function & can be developed in two ways, as was shown in the above-named treatise on the theory of elimination: Ist. according to the successive arguments of an homogeneous function ; 24. according to the undetermined coefficients s), sy) ss, ete. (86 ) Thus it gives rise to the formation of an Sassemblant” consisting of UK + 1)(lm + 2) — rows and v, == @, + ag columns, 9 2 where (i 0) (in ee) (Lm — m +- 1) (Um — m+ 2) Cae aa mer ; and @) = 9 . The columns of this “assemblant” are in general not independent of each other but connected by (lm —l—m + 1) (Um — 1 — m + 2) Vg = —-— ——-— — 2 independent linear relations. We now see that between the numbers 2, v;) and vs the relation Upto once oe te, etcetera) exists, as is easily shown by substituting the values. We determine the v; undetermined coefficients s in the following way: In the function /” we make equal to zero the coefficients of cs : ' Lm (lm + 1) all the terms containing the same variable. This produees ——~—— linear homogeneous equations between the coefficients s which are moreover, as was said above, connected by ro linear relations of dependence. So the difference between the number of undertermined coefficients and that of the mutually independent linear homogeneous equations existing between them is: Lin (Lm + 1) lm (lm + 1) vr —= 0h) oe = OS SS 2 2 __ (tm + 1) (lm + 2) CHS 2) ay yr ges ar ea which proves that the v undetermined coefficients s can be deter- mined quite unequivocally out of the indicated homogeneous linear equations. By substitution of the obtamed values in the equation “= 0 the demanded resultant is arrived at. The given method is rather simple to apply. ( 87 ) As an example we take the system of two homogeneous equa- tions of the second degree with three variables: aya? +agry + ase2+ ay? + asy2 tage =0, PS(08 + qaytogezt yy? + oy 2+ 52%) ry +azxvz2+ ayy? + sny@ + S12 2°) (bya? + dyvy + bse2 + byy? by x + byvy + bgwe + by y? The function / is represented by (a, a? + as + (ya fogey fay ee soy? From this follows the ++ bs yz + O62? “assemblant”’ Proceedings Royal Acad, Amsterdam, Vol. LI. eile Eb OB) EEG BEI Chi Cha ety ahah coll yea) Pa: : n Ce nec by | ay dg ay b 2 b 1 wz | ay ay b., by ae eG vas uy by bo by aye | ds ag ay ay b; bg by by | vent) ay ay ay by bs by | ay ay, ily by by ayrs Gz) Gq Gah lay bz by bg bg CUES: ag ds Coico bg bs bs; bg |. Oe 38 ay Us by by y" thy by ys Ws Ay b; by yee dg ds a bg bs by ya? ag as bg OU; zt a bg to which ty b) by bg by bs bg -a, -ag -ag -ay -a; —ag 5 0((7E belongs as supplementary “assemblant”’. If we omit one of the columns from the “assemblaut” (6) the determinants in the remaining columns (see Chapter I of the above- named paper) are divisible by the supplementary determinant of the assemblant. From this “assemblant” the coefficients of the resultant follow immediately. Thus we find for the resultant between y and <: 32 2.9 Sores P12,13,14,15 9" F pi,i31415 92 + Pir,i2145 9%" + piiagis,isy 2 + pit iisis oe Ye eae) ly for the resultant between « and <: 4 3> 2-2 See P3,6,10,15 at P1,6.10,15 22 + P1,3,10,15 ts" + p1,3,6,15 t=? + pig610e*=0 . . (9); for the resultant between « and y: pat t+ pian @y + pier #y?+ piaau ty? + p47 y'=0.(10), where the coefficients represent determinants contained in “assem- blant” (6) after one of the columns having been omitted and where the indices indicate which rows must be left out of the “assemblant”’ to obtain the determinant represented by the symbol. All the coef- ficients of the equations (8), (9) and (10) are now still divisible by the same linear factor, namely by 4, if we leave the sixth column out of the “assemblant’’, in general by the supplementary determinant of the “assemblant” (7). Chemistry. — Prof. V. A. Junius presents on behalf of Dr. A. Surrs of Amsterdam a paper on ,lnvestigations with the Micromanometer.” After I had published in 1896 the first results obtained with the micromanometer !), I continued my investigations to inquire whether the course observed for NaCl, KOH and cane-sugar would also appear in other compounds. ') Dissertation Untersuchungen mit dem Mikromanometer” 1896. Verslag Koninkl. Akad. vy. Wetensch. te Amsterdam, Wis- en Natuurk. Afd. pag. 292, 1897. Archives Neerl. Série IJ, Tome I, p. 89, 1837. (89 ) Before, however, examining other compounds, T wished to make some further experiments with NaCl, KOTI and sugar solutions, because I had made a slight improvement in the apparatus ; I had namely brought the legs of the manometer nearer together, so that they were only 2 m.m. distant, which diminished the error in the observation. Before communicating the results of those observations, I shall first shortly state my former results, to facilitate a compa- rison. The meaning of py»; ps) pm N and n is as follows. pw = tension of the gas of pure water expressed at 0° in m.m. He. Da es Stik s peehe SS ssolution ‘ ete Rs 7 - Pm = Mol. deercase of the tension of the gas, os Sy ERE oe. Ant N and n indicate the number of mol. of water and solved substance found in the solution : Na Cl. i Concentration in gr Pw —ps pm _ Pw —ps N 4 F i=: mol. per LOOD er. H,O. in mm. He. in mm. He. hyp fun 2 a —____ 0.02842 © 0.00844 0.121 | te 0.03546 | 0.00477 0.134 | 1.6 0.08813 0.01223 0.139 1.67 0.17680 0.02477 0.140 1.69 0.35587 0.05026 0.141 1.70 O.SS54 0.12646 143 1.718 1.8228 0.26757 ().147 1.765 KOH Concentration in gr. Pu—Ds pm |. pops NV mol. per 1000 gr. 1,0. in mm. de. | in mm. Hg. eekiae po 2 0.08035 0.00409 | 0.135 | 1.6 0.05564 | 0.00763 | 0,137 | 1.65 0.09992 0.01382 0.138 1.66 0.16626 | 0.02321 0.140 | 1.68 0.33464 0,04786 | 0.143 72 0.51342 0.07504 0.146 1.76 0.75044 | 0.11170 | 0.149 | 1.790 1.0356 | 0.15867 | 0.153 | 1.842 26422 | 0.47601 | 0.180 | 2.166 | (90 ) CANE SUGAR. Concentration in gr pwo- Pps pm . po—ps N mol per 1000 gr. HO in mm. He in inm. He. a Pwo n 0.02138 0.00178 0.083 1.0 0,046380 0.00388 0.084 L.0 0.08488 0.00705 0.083 1.0 0.17287 | 0.01440 0.083 1.00 0, 28340 0.02366 0.084 1.00 0.77912 0.06485 0.083 1.001 1.8821 0.17453 l 0.093 1.115 For NaCl and KO H-solutions I found that the molecular depression of the vapour tension, and so 7, became greater, when the concen- tration increased. For cane sugar svlutions the molecular depression of the vapour tension and so 7, was found constant between the concentration 0,02138 and 0.77912 gr. mol. per 1000 er. H,O. Only for the last concentration 1.8821 gr. mol. per 1000 gr. H,O a higher value was found for the mol. depression of the vapour ten- sion and for 7 than for the other concentration. The results of the observations with the improved manometer follow. As the determination of the course was my principal object, I chose some solutions with a great difference of concentration. Na Cl Concentration in gr. pPw—ps pm -__ pw —s N mol per 1000 gr. 1.0. in mm. He. in mm. Hg. ne pumwin 0.033028 0.00435 0.132 | 1.6 | 0.34057 0.04793 0.141 1.69 1.7533 0.25724 0.147 1.764 FEIN PI 0.33406 0.153 1.832 1.6362 0.78345 0.169 | 2.032 KOT Concentration in gr. Pos pm j— Pups N mol. per 1000 gr. HO. in mm. Hg. | in mm. Hg, Tot in | 0.03476 0.00470 0.135 1.6 0.42374: 0.06454 | 0.152 1.83 1.1912 0.19505 | 0. 164 1.969 2.5995 | 0.48440 0.186 9.94) > Ces) CANE SUGAR. Concentration in gr. Pw —ps pm + Pops N mol. per 1000 gr. H,0.) in mm. Hg. in mm. He. Bae Ye: 0.02602 0.00219 0.084. 1.0 0.17225 0.01479 0.086 1.03 0.45413 0.03972 0.087 1.05 1.0811 0.09074 0.090 | 1.08 These few determinations were sufficient to prove that for Na Cl, KOH and cane sugar the molecular depression of the vapour tension, and so 7, increases with the concentration. The second series of KOH solutions is more reliable than the first, because great care has been taken to keep the second series of solu- tions free from carbonic acid. Probably this is the reason, that the values for ¢ in the second table of solutions of KOH are a little higher than in the first. The second table of solutions of cane sugar is also more accurate than the former, because the temperature of the waterbath in which the manometer is placed, was about 10° lower in the second series than in the first. At a lower temperature the accuracy is greater, because the manometer then reaches its position of equilibrium sooner than at a higher temperature. It is evident that it is not much use to calculate the value for / for concentrations above 1 gr. mol. per 1000 gr. water. Nevertheless this calculation has been made here to facilitate a comparison with my former observations. After this repetition of my former observations, experiments were made with solutions of the following substances : Hy SOL) CrS0.25 HyOr and) KN O; The results are given in the following tables. Hi, 80, Concentration in gr. | _ Dw—ps | pu ~— pw—ps N mol. per 1000 gr. H,O in mm. He. in mm. He. ea jie i 0.02090 0.00336 0.161 1.9 0.04968 0.00819 | 0.165 2.0 0.24960 0.04204 | 0.168 2.03 0.50418 0.08713 | 0.173 2.08 1.11431 0.21057 | 0.181 2.215 2.1795 0.44246 0.203 2.441 Conceutration in gr. mol per 1000 gr T1,0 0.023848 09860 0.24519 0.49378 99612 | 1.2162 | Puo—ps in mm He, 0.00086 0.00525 0.01585 0.03276 0.06790 0.09656 ( 92) CusO, | | | _——S— ip m in m.m. Hg. 0.037 0.053 0.065 0.066 0.068 0.079 co Pw—Ps N Pw a 3y concentration the number of gr. mol. CuSO, per 1000 gr. HO is represented. KNO, Concentration in er mol. per LOCO gr. H,O. Pwo—ps Pia ' in mm. He. in mm. He. pw 0.02051 | 0.00287 0.140 1.7 0.25349 | 0.03241 0.130 1.54 0.51074 | 0.05569 0.109 ESB 1.0465 0.08671 0.083 0.996 It appears from what precedes that of the examined compounds K NOs; is the only exception with regard to its course. If the concentration of H,SO, and CuSO, increases, the molecular depression of the vapour tension, and also 7, becomes greater, whereas for K NOs, the reverse takes place. It is remarkable, that the values for ¢ of CuSO, always remain below unity, if we assume that there are in the solution CuSO, molecules, whereas the values for ¢ caleulated from the conductivity have been always found to be larger than unity. 1) The most interesting result, however, is that of K NO,, for it shows that the course of NaCl ete. is probably not general. When I was occupied with these observations, Mr. Drrerertcr®) ") Prexertna, Berl. Ber. 25 pe. 1315, 1892. *) Wied. Ann. 62, pg. G1, 1897, os (93 ) published a treatise ,Ueber die Dampfdrucke verdiinnter wiisseriger Lésungen bei 0° C.” He describes there in what way he has succeeded in making his aneroid more sensible, so that he could also examine diluted solu- tions with it. The results obtained for solutions which I have also examined, follow. To facilitate comparison some of my results are also mentioned. Na Cl DIETERICI SMITS Concentration in gr. pm Concentration in gr. pm mol. per 1000 gr. H.O in mm. Hg. fies per 1000 gr. HO. in mm. Hg 0.0732 0.121 0.02842 Q).121 0.154 0.131 0.03546 0.134 0.294 0.146 0.CSS13 0.139 0.454 0.144 0.17680 6.140 0.964 0.147 0.35587 0.141 0.SS54 0.145 1.8228 0.147 H, SO, DIETERICLI | SMITS Concentration in gr. | pm Concentration in gr. pm mol. per 1000 gr. H,O in mim. Hg. mol. per 1000 gr. HO. in wom. THe. 0.0542 0.144 0.02090 0.161 0.0871 0.127 0.04968 0.165 0.1088 0.145 0 24960 0.168 0.1771 0.143 0.50418 0.173 0.221 0.156 1.41131 O.1S4 0.263 0.159 2.1795 0.208 0.350 0.159 0.436 0.167 ( 94 ) CANE SUGAR. DIETERTICI. Smits Concentration in gr. Pn Concentration in gr. pm mol. per 1000 gr. H,O. in mm. Hg. mol. per 1000 gr. HO. in mm, Hg. 0.116 0.067 0.02602 0.084. 0.255 | 0.078 0.17225 0.086 0.506 | 0.080 0.45413 | 0.087 0.99] | 6.C8S 1.0811 0.090 It appears from these tables that Mr. Diererici’s results for Na Cl and cane sugar agree very well with mine. The same might be said of H, SO,, but that Mr. Drmrericr found a lower value for p,, for the concentration 0,087L than for the con- centration 0,0542. Tle makes the following remark about this : ,Die Lisungen der Schwefelsiure zeigen eine deutliche Abnahme der molecularen Dampfspannungsverminderung mit der Verdiinnung in dem Concentrationsintervail 1 bis 0.1 gr. mol.; unterhalb dieser Verdiinnung scheint wieder eine Zunahme einzutreten; indessen liisst sie sich aus den Dampfspannungsbeobachtungen allein nicht sicher constatiren und ich wiirde die Zahlen iiberhaupt nicht mitgetheilt haben, wenn nicht die Gefrierpunktsbeobachtungen von Loomis ') und Ponsor?) auch eine Zunahme der molecularen Gefrierpunkts- verminderungen bei grésserer Verdiinnung als 0.1 gr. mol. ergeben.” By repetition of his experiments, which will be discussed presently, Mr. Diererict found no decided increase of p, for concentrations telow 0.1 gr. mol., but oscillating values, so that we may say, that also for H,SO,4 qualitative agreement exists, as the oscillations just mentioned are due to the influence of errors of observation. Mr. AbEGG ®) has tested Mr. Dirrertici’s observations by compa- ring the tatter’s results quantitatively with those obtained by the determination of the lowering of the melting point. In doing this Mr. Abeaa came to the conclusion, that there must be a fault in Mr. Dirrerici’s method of observation, which induced ') Loomis, Wied. Ann. 51, pag. 500—524, 1894; 57, pag. 465—529, 1896; 60, pag. 528—547, 1897. 2) Ponsor, Recherches sur les congélations, Gauriipr et Vittars, Paris, 1896, 8) R, Apeca, Wied. Ann. Gf, pag. 500—505, 1898, 95 ) Mr. Drerertcr!) to repeat his experiments once more, now making use of an aneroid which could give a deviation not to one side only as before, but to both sides. As changes of temperature exer- cise a great influence on the zero position of the aneroid, it was placed in a waterbath. After having determined the constant of this aneroid, he repeated his observation and obtained the following results. To facilitate comparison I shall again add some of my results, Na Cl DIETERICI. SmITSs. Concentration in gr. | Dm Concentration in gr. pm mol. per 1006 er. H,O. in mm. He mol. per 1000 gr. HO. in man. He. ee ——————— 0.0690 0.152 0.02812 0.121 0.0976 0.156 0.03546 0.134 0.1500 0.150 0.08813 0.139 0.2176 0.148 0.17680 0.140 0.2996 0.1505 0.35587 0.141 0.4900 0.1515 0.88510 0,145 0.9788 0.1515 1.8228 0.147 1, SO, DIETERICL. Tan teh co ee ne SMITSs. Concentration in gr. Pn Concentration in gr. Pm mol. per LOW er. HO. in mm. Ig mol. per L000 gr. Il, 0. in man. He. 0.0621 0.168 0.02090 0.161 0.1106 0.180 0.04968 0.105 0.1472 0.167 0. 24960 0.168 0.2323 0.168 0.50418 0.173 0.4483 0.171 L.11431 O.1S4 0.9505 | 0.177 1) Dinvericr, Ann. der Phys. und Chemie, 27, 4, 1898, (96 ) CANE SUGAR. DIETERICL SMITS. Concentration in gr. | pm Concentration in gr. pm mol. per 1000 gr. HO. in mm’ Hg. mol. per 1000 gr. H,O. in m.m. Hg. 0,1506 0,084 0.02602 0.086 0.2653 0.084 0.17225 | 0.086 0.4993 | 0.087 0.45413 | 0.087 | | 1.0122 0.0905 1.081] | 0.090 It is remarkable that the agreement of Mr. Dierertct’s_ results with mine for Na Cl-solutions, which was closest before, is now least perfect, while the agreement for cane sugar may be said to be absolute. If we leave the oscillation for the two smallest concentrations out of account, the agreement of the H,SO, solution is also very close. It is very difficult to find an explanation for this fact, as an error in the constants of our apparatus cannot cause this difference. Mr. Drerericr puts the solutions and the water in small platinum tubes, 3 em. high and with a diameter of 1,2 ¢.m., which are connected with the apparatus in such a way (cemented), as to exclude shaking, whereas I put the solutions and the water in glass bulbs connected with the apparatus by means of mercury valves, in order to be able to shake them thoroughly. I consider this of the highest importance, both when freeing the solution and the water from air and during the experiment. I consider shaking as necessary for preventing differences of temperature, Mr. Dinterici, on the other hand, fears to bring them about by shaking. If, however, I read the manometer ten minutes after having shaken the bulbs carefully, I get always the same results by repetition of the experiment. Moreover in Mr. Diererict’s experiments the platinum tubes which lead to the bottle and are cemented to glass tubes, are not quite immersed in the icebath, which may cause slight differences of temperature, specially because these small platinum tubes have a small thermal capacity. Mr. Drererici, who himself, makes the preceding remark, thinks it possible thet a difference of temperature of 0,0025° may occur, in spite of this careful protection of the icebath against absorption of heat. As a difference of temperature of 0,0025° agrees with a . ia (97 ) difference of tension of 0.001 mm. Hg., Mr. Drrerericr takes as limit of his accuracy 0,001 mm. Hg. Therefore he states clearly, that he draws only qualitative conclusions. I am, however, convin- ced, that the difference in temperature in my bulbs, which have a volume of 100 eem., is less than 0,0025°, which also appears from the fact that when I read the manometer, when comparing water with water, the manometer indicated accurately to 0,1 mm. the same difference of position, as when there was communication between the two sides of the manometer, and the bulbs were closed. As a deviation of the manometer of 0,1 mm. agrees with —- 0,00025 mm. Hg, the difference of temperature of the two bulbs must be exceedingly small. Some time ago prof. Jann at Berlin wrote to me to ask, whether I was sure, that my solution had been perfectly free from air and if I would repeat some of my experiments once more, after haying first reduced the solutions in vacuum to half of its original volume by means of evaporation. First I tried to comply with Prof. Jann’s wish in the following way. The bulbs with water and solution were successively shut off from the apparatus by turning a tap and the air was exhausted by means of a velocity pump, while they were heated softly. During this the tube, connecting the bulb with the apparatus, was moistened with condensed vapour of water. Threugh the rise of the temperature the grease with which the tap (by means of which the communi- cation of the bulb with the apparatus was broken off or restored), was greased, spread over the mside wall of the tube, and this is the reason why I could not make use of this way of boiling. It seems namely, that the vapour tension of a layer of water on the greased part of the tube is so small, that the water was not distilled into the bulb, though the bulb was cooled to 0° and the temperature of the room was + 20°. I was therefore obliged to apply another method, by which rise of temperature was excluded. The most practical method appeared to be the following. When at the ordinary temperature most of the air was exhausted from the bulbs with water and solution by means of the velocity- pump, all the remaining air was expelled by bringing about the communication of the bulbs with the apparatus, after first having closed the bulbs for drying. The communication between the bulbs and the apparatus was interrupted after some moments, and when the vapour of water had been absorbed by the drying bulbs, the ( 98 ) air of the apparatus was exhausted by means of an automatical mercury airpomp. This was repeated till the bulbs were free from air. In order to comply with Prof. Jauy’s wish, I brought about a communication between the bulbs with water and solution and one of the drying bulbs (filled with H,S50,). When the air is greatly rarefied, H,SO, absorbs the vapour of water quickly and the water and the solution, having the temperature of the room + 20° (the bulbs being continually shaken), evaporated quickly, in consequence of which the temperature of the water and the solution fell consi- derably. To prevent congelation the bulb was now and then warmed with the hand, The temperature of the bulb with H,SO, rose con- siderably during this absorption of water, and it was also frequently shaken. When the water and the solution had been reduced to the half of their former quantity by evaporation, the bulbs were shut off from the apparatus. Every solution was first treated in this way, after which the bulbs were placed in ice, and the experiment began. The concentration of the solutions was determined by weighing + 50 gr. solution in a flask with a long neck, and then the water was evaporated according to the method applied by Mr. ANDREAE !) While the flask was being heated in a waterbath, a weak current of air was drawn over the solution. After all the water had been evaporated, the flask was placed in an airbath of 170°, while all the time a stream of air was drawn over it. In this way it is also possibie to expel the water from NaCl-solutions without any loss of weight of salt. I may further add that I had altered the apparatus somewhat for these experiments. Instead of two bulbs, I used three; one filled with water and the two others with solution. One of these bulbs with solution remained untouched during the whole series and served as a test. These three bulbs were placed in a copper trough, which was surrounded by a larger wooden one in such a way that there remained a space of 6 cm. all round. This space was filled up with small pieces of ice, while the copper trough was filled with a paste of fine ice and water. Two pieces of paste board, which could move across each other and were provided with slits, served as a lid. In this way I was quite sure of a constant temperature and yet I could shake the bulbs thoroughly. In order to make it possible to read the manometer more accurately, ‘) Journ. f. prakt. Chem. 22, p. 456, 1884. (99) a glass scale divided into m.m. was adjusted behind the legs of the manometer. The error of reading amounted to less than 0,1 mm, so 1 to less than —— mm. He. 4000 ‘ The results of the research with NaCl solutions follow. Na Cl Concentration in gr. Pu—ps pm -— Pw—ps N mol. per LOO0 gr. 11,0. in mm. He. in mm. He. ; po 7 | 0.05185 0.00675 0.130 1.6 | 0.10735 | 0.01476 0.188 1.65 0.25770 | 0).03650 0.141 1.70 1.0307 | 0.14626 0.112 1.706 1.6075 0.23082 0. 14-4. 1.726 From this table follows that the changed method of experimenting has had no influence on the course of the molecular depression of the vapour tension. ‘The differences of the absolute values are due to the use of a new manometer, the sensibility of which was to be determined anew. As to the results obtained by another method, we have to mention, that Loomis and Ponsot have found that in general the molecular lowering of the freezing point of greater concentration to the con- centration of 0,1 gr. mol. decreases in case of rarefaction as well for electrolytes as for non-electrolytes, whereas below these concen- trations both investigators observed an increase of the molecular lowering of the freezing point, when the rarefaction increased. Mr. Loomis expresses his astonishment, that other investigators have not discovered this minimum, as this is so evident for binary chlorides, that: it may be easily shown with an ordinary thermometer divided into 3/,;5° and with a beaker. Mr. R. ABEGG, who points out some inaccuracies in his eviticism on the researches of Mr. Loomis, doubis of the results of Mr. Loomis and also of those of Ponsor. Mr. Aseaa finds tor KCl between the concentrations 0.009 er. mol. and 0.4007 gr. mol. per 1000 gr. water a mol. lowering of the freezing point, increasing with the rarefaction. He has not observed a minimum. ( 100 ) Nor has Mr. Raoutr!) found a minimum, but he found nearly constant values down to 0,1 gr. mol. for the molecular lowering of the freezing point. They did not differ more than 0,1 pCt. In my opinion, however, the question remains, whether at this moment the highest degree of accuracy has already been reached in the method of the lowering of the freezing point. it is quite possible that the air which is solved in the water and the solutions, causes the results, obtained for the determination of the lowering of the freezing point, to be faulty. If e.g. the quantity of air in a solution depends upon the quantity of salt solved in it, the error made is not constant, and it can even render the course of the mol. lowering of the freezing point, quite faulty. Mr. Raounr has tried to reduce the error caused by solution of air in water and solution to a minimum by saturating at the tem- perature af the room the water and the solution with air. Mr. Raouur states further that diluted solutions absorb the same quantity of air as pure water. Prof. Jann, however, communicated to me in a letter that the coefficient of absorption of air for diluted solutions depends on the concentration and increases by diluting. It is therefore of the greatest importance for the determination of the freezing point to examine accurately the influence of the concen- tration on the coefticient of absorption for air. As long as this influence is not sufficiently known, Mr. Raou.t’s determinations, however accurately made, are in my opinion not quite reliable. In connection with what precedes, it seems to me, that Mr. ABEGG *), who, led by the differences between the results obtained by means of the lowering of the freezing point and the decrease of vapour tension, came to the conclusion that there must be a fault in the method of the determination of the decrease of the vapour tension of Mr. Diererict, has attached too much importance to his deter- minations. In the first place the influence of concentration on the absorption of air has not yet been fully ascertained, as [ said before, and secondly, even though this influence were perfectly known, a quan- titative comparison between the results of the determinatioa of the decrease of vapour tension and the lowering of the freezing point is not yet raised above doubt, when the solutions and the water are not in exactly the same circumstances in both methods. There would, however, be no objection to a comparison, when the lowering 1) Zeitschr. f. Phys. Chemie: 27. pg. 617. 1898. 2) Wied. Ann. 64, pag. 487, 1898. ( 101 ) of the freezing point was determined of solutions quite free from air, I regret that Mr. Dierertct, who was acquainted with my inves- tigations, has not mentioned, that in 1896 I published results which agreed perfectly with those he found with his aneroid and which he published in 1897. I intended to investigate other substances than NaCl in the way Prof. JAHN recommended, but my manometer got defect while I was engaged with experiments on KCl, so that I had to put off this investigation. At the end of this treatise I feel obliged to express my thanks to Prof. H. C. Drssrrs for the great kindness with which he placed at my disposal the apparatus required for my researches. Physics. — Prof. van Der Waats presents on behalf of Mr. K. HW. J. Cunauus a paper on: “The determination of the refractivity as a method for the investigation of the composi- tion of co-existing phases in mixtures of acetone end ether”. Introduction. The aim of this investigation was to examine the relation between the compositions of the co-existing vapour- and gas phasis and to find out the relation between the composition of the vapour and the pressure. When I began my experiments only the investigation of Linr- BARGER!) had been published; since then those of Luargetpr?) and ITaARTMAN *) have also appeared. The great difficulty of the investigation of this relation lies in the determination of the composition of the vapour; I have tried to do so without first condensing the vapour, and without chemical analysis, by means of the determination of the refractivity. I was induced to use this method by the experiments of Ramsay and TRAVERS on the refractivity of gases and some gaseous mixtures *). 1) Journ. of the American Chem. Soc. Vol. XVIL N°. 8; Aug. 1895. Chem. News, Vol. 72, N°. 1871, v.v. Oct. 1895. *) Phil. Mag. (5) Vol. 40, 46. 8) Dissertation for a doctor's degree, Leyden 1899. *) Proce. Roy. Soc. Vol. LXII, p. 225, 1897. ( 102 ) The Method. In their investigation Ramsay and Travers found that the refractivity of a mixture of gases may be found, not accurately indeed, but yet with a high degree of approximation, from the molecular proportion of mixing and the refractivity of the compo- nents. In order to determine whether this deviation occurs always, or must be attributed to accidental circumstances, but at the same time in order to try and find the cause, I have first examined a series of mixtures of gases; viz. carbonic acid and hydrogen in different proportions. These gases were chosen, because their refrac- tivity differs considerably and because they may be prepared suffi- ciently pure in a simple way. The carbonic acid was prepared according to the method described by Mr. Kurnen !), by dripping a solution of NaHCO, in Hy. SO, and by drying the gas by means of H,SO, and P» O3. Hydrogen was obtained by electrolysis of diluted HCl with an apparatus similar to that used by Prof. KaMeRLINGH ONNES for filling the hydrogen-thermometer. ”) The determination of the refractivity was made according to the method of Lord Rayieign®), which was also followed by Ramsay and Travers. A nearly parallel pencil of light is split into two parts, which pass through tubes of equal length closed by plate glass and which are made to converge by an achromatic lens. The interference phenomenon obtained in this way was observed with an eye-piece, consisting of two cylindric lenses. These tubes (4 and B fig. 1) are respectively connected with the open manometer and / and with the reservoirs C and G; the latter are partly filled with mercury and the pressure in them may be changed by moving the bulbs D and JZ up and down. The right half of this apparatus is filled with dry air freed from CO,. The left side was filled with the gases and gaseous mixtures which were to be examined. To this end G was connected with another reservoir H with a bulb XK filled with mercury, by means of the three-way cock ¢, and it was also connected with the tube V, which may be connected by means of the taps gy and 4 with two gas- reservoirs L and M; by means of i with the air pump; and by means of with the apparatus for the preparing of gas. G and // serve for preparing the mixtures. 1) Phil. Mag. (5) Vol. 44, p. 179. *) Versl. Kon. Akad. 30 Mei 1896. 5) Proc. Roy. Inst. Vol. XV Jan. 1896. ( 103) {f the substances used followed the laws of BoyLe and Gay- Lussac, the refractivity would be directly found from the pro- portion of the changes in pressure, which the gas and the air must undergo, when the interference phenomencn is twice brought into that position which it occupies when the two parts of the pencil of light pass through equal ways; so for instance when the two tubes are filled with air of one atm. So if p and p’ are the press- ures for air; p,; and p’, those for the gas whose refractivity B is is to be determined, we get: B= Aiee ; Pie Pi The gases, however, do not follow these laws, and therefore the refractivity is not to be found from the proportion of the change of the real pressure (p,p',p; and p';), but from that of the pressures which would prevail, when the gases followed the laws of BoyLE and Gay-Lussac and had the same volumes and temperatures (P, P', Pi, P')). So that we may put: Biel a) a6). sae V(V — b) 278 v2 Tip from which follows with some approximation : 1 ; (= a 5 =) P—P' p—p' ae (p == P) T ) OS 273 PP p—p' 1) ( 278," r , 1— (nite) (=) Can) 3= B= 8114 (7) [ote (as g,) —@t0) («0 3)I}- This correction was also applied in calculating the composition of the mixtures. Y In order to find the values a and 6 for the mixtures CO, and Hy, I made use of the formula, deduced by Prof. vAN DER WAALS from the experiments of Dr. VeRscHarrE.t !). y = 0.999546 + 0.001618 (1 — z) + 0.00497 (1 — a2 this gives for 18°C. (£=291) at once the value of az—bz ee ") Proc. Roy. Acad, April 1899, Proceedings Royal Acad. Amsterdam. Vol. II. ( 104 ) In this way I obtained from my experiments the results given in Table I (hydrogen considered as the solved substance). TP Ar er as eo a B 6 | 8,0—+8,¢| 2! 0. | 1.53985 | 1.5398 | 0.2082 | 1.3057 | 1.8095 | 1.3183 0.2165 0.30001) 1.9052 | 1.2080 1.2206 0.3118 0.4192 1.0826 | 1.0843 1.0938 0.4281 0.5077 | 0.9884 | 0.9891 | 0.9997 0.5176 0.6498 0.8399 | 0.8400 0.8485 | 0.6577 0.7085 | 0.7799 | 0.7796 | 0.7850 0.7145 1. 0.4765 | 0.4759 There is evidently a difference between the observed values (co- lumn 3) and the calculated ones (column 4), the difference amounts at the utmost to about 1 pCt.; when from the observed refracti- vity the composition (2’, column 5) is calculated, the difference amounts at the utmust to a unity in the 2.¢ decimal. So I consi- dered the method as suitable for the purpose. IT hope soon to publish some further details about the difference found and the probable cause. Investigation of the vapour-mixtures. For the investigation of the vapour-mixtures an apparatus may be used of nearly the same construction as has been described above. The apparatus was modified only in so far that a branch-tube Q (fig. 2) with bulb P was added to tube B (fig. 1). The bulb was provided with a neck R with astopper S well ground in and closed by mercury. Two platinum wires, 7 and 7", passed through the stopper; they were one m.m. in diameter and connected inside the bulb by a bent kruppin-wire U with an electric resistance of + 4 Ohm. The liquid or the mixture of liquids which was to be examined, was fused in a thin-walled glass tube, which was suspended in U; then the air 1) The accuracy which might be expected of the 2nd mixture is smaller than that of the others on account of a deviation in the experiments. ( 105 ) was exhausted from the whole apparatus, and by passing an electric current through the wires TU 7", the tube was heated till it burst. While the bulb P was constantly kept at 0°, the refractivity of the gas could be determined, by changing the pressure of the gas in the other side of the apparatus, till the interference phenome- non reached again the normal position and by reading this pres- sure and that of the gas. On account of the great refractivity of the gases, air could not be used as the gas, serving for comparing them; I have therefore used carbonic acid. The investigation was made with ethylether and acetone; both from Merck in Darmstadt. These substances were chosen because at 0° they have a vapour tension of less than one atm., and yet it is large enough to be measured pretty accurately; moreover the refractivity of the gases had to differ as much as possible. The compositions of the liquids was obtained by weighing, while the weights of the quantities of each of the two substances in the vapour were afterwards subtracted from the original quantities. The results are given in Table II (see also fig. 3) ether being considered as the solved substance. TAB cio Bee Refractivity. | | wd | p in mm. 3.7788 | 0. 0. | 69.6 4.4956 | 0.156 | 0.446 | 110.5 4.7709 0.364 | 0.617) 149.4 4.8552 0.510 | 0.670) 159. 4.9497 0.617 | 0.728 | 166.8 5.1636 0.835 | 0.861 | 181.2 5.3869 il, 1 | 185.6 They give rise to the following observations. There is no maxi- mum or minimum pressure; so the mixture belongs to what Harr- MAN calls the first type. There is greater difference in the composition of the liquid and the gas when a little ether is mixed with acetone, than when a little acetone is mixed with ether. The curve representing the pressure as function of the composition of the vapour (p=/f (7g) im fig. 3), shows a point of inflection ( 106 ) at « = 0.65; which has never yet occurred in former experiments. I have not succeeded in finding a simple meaning of this; the con- dition for the occurrence of such a point of inflection leads to an intricate relation, in which also the unknown relation between za and 2, occurs. That the point of inflection really exists and that it is not due to an inaccurate method follows, in my opinion from the following considerations : Ist the deviation from the observed curve, required to get a curve without a point of inflection is much greater than the investigation of the method would give us cause to expect. 2ud When we calculate the composition of the gas by means of the approximated formula given by Prof. van per Waats im his ,Théorie moléculaire” ') we find the points indicated by © in fig. 3, which points agree very well with the observed curve, at least at the ends; that the deviation is greater in the middle was to be expected, according to the approximations used in the deduction. A curve drawn through these points, shows also a point of inflection. If we draw a tangent at a point of the curve p= f(,), we arrive by means of the former formula at the values which are given as calculated in Table III. fA B GE oir dz | ale. observed. | ale. | observed. 0.05| 85.5] 301 | 0.167 | 0165 | 0.917 | 0.915 0.1 99.5 | 264 | 0.297 | 0.953 | 0.327 0.353 0.2 120.6 | 179 | 0.287 0.305 | 0.437 0.505 0.3 | 134.4] 187 0.215 | 0.980 | 0.515 | 0.580 0.4 | 17.1] 115.5| 0.180 | 0.982 | 0.580 | 0.632 o.5 | 158.0] 94 0.150 0.170 | 0.650 0.670 0.6 | 166.7] 74.5 | 0.107 0.15 | 0.707 | 0.75 0.7 | 173.7} 63 | oor 0.08 | 0.777 0.78 0.8 | 179.2) 50.5| 0.04 | 0.042 | 0.845 | 0.842 O00 aeae4.| 831, | pore o.o2 | 0.916 | 0.99 1) Arch. Néerl. 24. p. 44. ( 107 ) 34 Some observations made at + 15° make it very probable, that the p=/(«a) curve will show a point of inflection also at that temperature, and even at about the same rq as that at 0°. If it was not our intention to make the existence of a point of inflection probable, it would be better for testing the results at the theory, to use instead of the former formula, the formula as this formula may be expected to hold good with much greater approximation, also for the values of 7g which are not near Oor 1. It appears, however, from Table IV and the points (x) of fig. 4 which are derived from it, that the agreement is not much closer TOA Be ake Ve - | ? | c dp | wd art | i 0 | | dca cale. | observed. | cale. _—_|_ observed. OealeaTe i 73 0.086 | 0.082 | 0.014 | 0.018 0.2 | $4 | 84 0.160 | 0.155 | 0.040 0.045 0.3 | 93.5] 102.5) 0.930 | 0.924 | 0070 | 0.076 0.4 | 105 128.5 | 0.994 0.273 | 0.106 0 127 0.5 | 1299.5 | 168.5 | 0.395 | 0.295 | 0.175 0.205 0.6 | 139 204 0.352 0.270 0.248 | 0.330 0.7 | 163 171 0.920 | 0.155 | 0.480 | 0.545 0.8 | 176 | 103 0.094 0.075 0.706 | 0.725 0.9 183 50.5 0.025 | 0.020 0.875 | 0.880 This is the first time that the formula, derived from the theory of the mixtures, has been used for the attempt of deducing one of the two curves p==/ (av) and p=/(a) from the other, when both have been determined experimentally. Only when « and 1—z are small, the result is satisfactory. Further investigation will have to prove, whether the great differences for x near '/, are to be attri- buted to the observations or to the formula, ( 108 ) Physics. — “On the Theory of LippMann’s Capillary Electrometer”’. By Prof. W. EryrHoven (Communicated by Prof. 'T. ZAA WER.) In a paper on the capillary electrometer and on the action currents of the muscle Hermann?) has put forward the statement, that the results obtained by Burcu *) and myself®) in the investigation of the motion of the mercury in the capillary electrometer are imme- diate consequences of his theory, and that since Burcu and I should have obtained empirically our results, they ought to be regarded as a ,schine Bestiitigung” of his theory. An answer of Burcn*) here- upon has already appeared. In answering Hermann I will try by means of some new expe- riments to advance somewhat our knowledge of the laws governing the motion of the mercury in the capillary electrometer. On a former occasion I have given the equation: Ys GG Seay ait Ss ee ey where C is a constant, y the distance the meniscus has moved from its zero position at the time 7 and y* the distance the meniscus would have moved if the P.D. of the poles of the capillary electro- meter at the time Z had been constantly applied. In order to obtain for all capillary electrometers comparable values of the constant, we shall in this paper always measure the time 7 in seconds °), whereas y and y* will be given in arbitrary but equal units. The value of C is apparently unaffected by a change of the unit in which y and y* are measured. The constant C is, as I re- marked on a former occasion, determined by the properties of the instrument, especially by the mechanical friction in the capillary and the ohmic resistance w in the circuit; the precise relation between C and w I did not mention till now, but it will be given in the following. HerMann thinks that the mentioned relation is very simple, and assumes that C varies as the inverse of w. The equation his theory *) Pruiicrr’s Arch. f, d. ges. Physiol. 1896, Bd. 63, 8. 440. ?) Philosoph. Transact. of the Royal Soc. London, 1892, Vol. 183, p. 81. 8) Prniiger’s Arch, f. d. ges. Physiol. 1894, Bd. 56, 8. 528 und 1895, Bd. 60, S. 91. *) Proceedings of the Royal Soc. London, 1896, Vol. 60, p. 329. 5) In formerly given calculations of the constant, the time was given in twentieth to fiftieth parts of a second dependent on the velocity of the photographic plate, on which the normal curves were recorded, being 20 to 50 mm. per second. ( 109 ) : ; pean arrives at, differs from formula (1), in having —— instead of C, h Ww being an instrumental constant. Aceording to Hermann formula (1) must be: !) dy h aS) = (0 dT w J y) This formula represents the facts in so far as the cmcrement of tee the resistance varies directly as the énerement of pi accordance with what I have said in a former paper and as will be discussed further on. This is occasioned by the fact, that the mechanical friction in the capillary has a similar influence on the motion of the mercury as the ohmic resistance in the circuit. HERMANN ; 1 wrongly concludes that the constant must be proportional to — , w whereas from the experiments is to be inferred only, that it is pro- portional to —. Differentiy stated HERMANN wrongly assumes a+ bw thata= 0, The error of his formula is to be ascribed to a misconception of the action of the capillary electrometer. He neglects entirely the influence of the mechanical friction in the capillary on the motion of the meniscus, whereas this mecha- nical friction is with most capillary electrometers of the foremost importance. his may be inferred from the following. Using capillary @ 103 and suddenly applying a P. D. remaining constant, a normal curve was described, no additional resistance being inserted in the circuit. This curve was measured and the con- stant, which we will! cail C,*), determined according to formula (1). Then a normal curve was taken with the same instrument, a resistance of 0,1 Megohm now being inserted in the circuit, and the value of the constant, now indicated by C,, was determined again. 1) Hermann’s formula in his own symbols is: OYE ar poe a Oe i E being here identical with y* of formula (1). *) The manner in which the constant @ is calenlated from the normal curve was given formerly, vid. Pruiiger’s Arch. 1, c ( 110 ) wesequal.to-/ ize: -8)--t Henby era. Mlk ete au JOAN ae ‘a 1 = 7 a gcopy ROMLcche # Reteretle Pot ay nce 2 ey owl Cy According to HErRMANN’s theory it must be possible to calculate from these data the internal resistance of the capillary electrometer. Let the internal ohmic resistance of the capillary electrometer be denoted by ~;, the resistance intentionally inserted in the circuit wy, then w= wi + Wy h h GZ=—; and: .C, =——_ 3 Wi wi + wy hence we must have Ww 2) (HERMANN) —— rs 1 1 Ga) Ca: Substituting the values of C,, Cj and w, we obtain wi = 0,320 Megohm. Now w; may be calculated also from the dimensions of the ca- pillary, in which case a knowledge of the dimensions of the sul- phurie acid thread is principally necessary. Calculating the resistance from the dimensions, ~; was found 0,029 megohm; hence more then 11 times smaller than the amount required by HeRMANN’s theory. Here follows a table with the correspondent calculations for four capillary electrometers. A Bal ale Number wi as calculated wi as calculated of the _ according to from the dimensions capillary. | HERMANN’s theory. | of the capillary. G. 103 0,320 Megolim 0,029 Megohm B. VOL= i as545 ¥ 0,124. ” B. 102 | alive ae | 0,101, B. 108 0,665 ” 0,026 , ( itt ) We see that HrrMann’s theory gives far too high values of w;y with the above mentioned four capillary electrometers 11 to 25 times greater than is to be calculated from the dimensions of the apparatus !). The value adopted for the length of the sulphuric acid thread in the calculations was one never exceeded in recording the curves, hence the figures in the last column of our table are maximum values. It seems difficult to misinterpret the results described above and they are certainly sufficient to refute HerMmann’s theory. That really the mechanical friction neglected by HeRMANN is of primary importance with most capillary electrometers, will be clear from a series of experiments of entirely different character, in which the mechanical friction in the capillary was measured in a direct manner. A capillary tube, after having been used for the recording of normal curves, is placed above a small glass vessel filled with mer- cury in such a manner that the end of the capillary is below the surface of the mercury. For a short time the air above the mercury in the tube is highly compressed so that it flows in the vessel, the free air being admitted however immediately again. The mercury continues flowing if there has been but once a direct mercury connection between the interior of the tube and the vessel. The total quantity of the flow in a given time varies according to PoIsEUILLE’s law directly as the pressure, in our case the difference of level between the mercury in the tube and the mercury in the vessel. The flow is continued during some hours and the vessel is weighed before and after the experiment. From the difference of weight, g grams, the duration of the flow, 7 seconds, the mean difference of level, D centimetres, can be calculated how many grams of mercury G are pressed through the capillary tube under a pressure of 1 cm. in one second, Gast wi Le Let the radius of the capillary tube at its point be = r em., then the mean velocity in a section near the end is 1) In this communication a short account of our results must suffice, more parti- culars concerning the mentioned and yet to be given measurements and calculations will be published elsewhere. ( 112 ) G "0 eee centimetres per second under 1 em. of mercury pressure; in this formula s is the density, whereas vx) is dependent only on the mechanical friction. Let us suppose that in a capillary electrometer the ohmic resis- tance in the circuit is reduced to zero, then in our formula (1) the constant C is determined only by the mechanical friction in the capillary '). We will call the constant, when this is assumed, &. For a given value of y*—y= vu the formula can then be put 2) in the form du dT — KU. If u represents the displacement of the mercury meniscus for 1 cm. change of mercury pressure, then du Sik = % 9 dT hence also Opis IR Sor tes ooh Molise: awd. on du (CA) The constant & is, as appears from formula (2), determined only by the magnitude of the displacement of the meniscus with a given change of pressure and the mechanical friction in the capillary; & can be calculated from u and v°*). Moreover & can be calculated in an entirely different manner viz: from 1s. the constants of the normal curves, recorded without and with resistance purposely inserted in the circuit, 24. the internal resistance of the capillary electrometer. For & is the con- *) Vid. on this point a former paper l.c. We remind the reader that y and y* denote the displacements from the zero position of the meniscus. In formula (1) we indicated as the cause of these displace- ments the change of P. D. between the poles of the capillary electrometer, the pressure in the capillary remaining constant. The formula remains unchanged if with a constant P. D. the displacements of the meniscus are caused by a change of pressure in the capillary. *) In caleulating & the difference between the friction of the sulphuric acid and of the mercury in the inferior part of the capillary has been neglected. It was supposed that the friction im the capillary electrometer equalled that in the capillary when totally filled with mercury. The error hereby introduced is but small and amounts only to a small percentage of the final result, see the more detailed publication. a ( 113 ) stant of a normal curve that would have been recorded by a capil- lary electrometer if the internal resistance could have been annulled. The double calculation of & has been made for two electrometers, and the results are united in Table II. A Bor, Sle il Iie aes — a | a ] Wj u P Re IOG Bes Nenaer Ca 0,1 calculated from friction of | caleulated from the normal in capillary and magnitude capillary- | curves and internal of displacement of electrometer. | . : : : | resistance of capillary | meniscus by change of | electrometer. | pressure, | B. 102 4,59 | 4,95 B. 103 2,92 | 2,78 | The agreement between the values of & in the two columns, obtained in so different a manner and which have required inde- pendent series of measurements is certainly quite sufficient. : , h According to HerRMANN’s theory we must have C = —— Ww , henee y= 00% Let us now consider more closely formula (1) and let us see in what manner the resistance in the circuit influences the value of C. Already on a former occasion ') the normal curves of capillary G 103 were examined, recorded with several resistances, purposely inserted in the circuit. An increase of the resistance with 0,01 megohm 1 Pave AN INCLEABOL Ol see. Ve tet) uth) ay) oe a O00 25 Cc ; : 1 my An increase of 0,1 megohm increased ves 0,0255 1 An increase of 1 megohm increased Gi ees 0,2545 1) 1c. Bd. 60. (114) ' 1 sy dat We see, that the increase of the value of q varies directly as the J increase of the resistance. Hence it follows immediately that, 1 C =a-+bu , a and > being constants, determined by the properties of the instru- ment independent upon the internal ohmic resistance. w represents the resistance in the circuit in megohms. Hence our formula (1) 1 = = C(7* — y) now becomes eo we (3) igen ee Seca toy om momare tents 7m ((c 1 1 For w~=0, is -—___——,, hence the constant & is equal to —. a + bw a a 1 : The constant 6 is the increase of ra when the resistance in the circuit is increased with 1 megohm. In the subjoined table the values of a and / are given for four capillary electrometers. EAS Bl; aie Number of a b the capillary. | | | G. 103 0,0741 | 0,295 B. 101 0,1599 0,1124 10952 12)? Wosist | 0,166 | B. 103 0,3429 0,5365 We may obtain a_ better insight into the action of the capillary electrometer in considering in which manner and to what amount the different forms of energy are transformed with a given displa- cement of the meniscus. For this purpose the following representa- tion may prove of use in this connection. ( 115 ) Suppose that the drawn-out tube of the capillary electrometer, see fig. 1, is connected with two vertical tubes, a and 4, filled with mereury and widened at the upper end. By means of the stop-cocks a and (? the communication of a and b with the capillary tube can be stopped. Fig. I. The poles of the capillary electrometer are connected by the con- ductor G. W is a resistance box, CZ a cell and P a Pont’s mer- cury key insulating at the beginning the cell from the capillary electrometer, so that at / there is no P. D. We think at the beginning stop-cock @ opened, # closed: 1st po- sition of stop-cocks. Let the meniscus have its equilibrium position at the height m,. Suddenly the position of the stop-cocks is intev- changed ; 2¢ position of the stop cocks. The meniscus will move, at first fast, then slower and will at last attain the equilibrium position my. If now the stop-cocks are placed again in their first position, then the meniscus will return also to its initial level mm. ( 116 ) The work done in displacing the meniseus up and down is easily cal- culated. For the only final change in the apparatus is the passage of mercury from toa. The quantity of mercury passed can be calculated from the section of the capillary tube d, the distance m, — mg, and the specific gravity of the mercury s This quantity is M==ds(m,—my), M being given in grams d in square centimetres and m, and mg in centimetres. Let the difference of level between a and b be x centimetres, then the work done is A =2M gram- centimetres. The potential energy of the displaced mercury is transformed into heat, partially by means of electric currents, partially by mechanical friction. It merits attention that the amount A is not changed by changes in the resistance of the circuit G. An increase of the resistance causes retardation in the movement of the meniscus; the energy of mechanical friction is diminished, whereas that of electric currents is increased with the same amount. If the stop-cocks have only changed the first for the second position and the meniscus ae moved from m, to m,, the energy of the heat produced is = ‘/, A; for the motion of the mercury in the capillary — viz. the cause of the mechanical friction and of the electric currents — is, while the meniscus returns from mg to m, in all phases perfectly equal — but of contrary direction — to the motion of the original displacement from m, to my. Hence in first changing the position of the stop-cocks a quantity of energy must not have been transformed into heat, but must have accumulated as elastic tension in the meniscus. It is only in returning from m, to m,, that the meniscus delivers its energy. An analogous reasoning can be used if the meniscus is displaced by the sudden application of a constant P. D. between the poles of the capillary electrometer, the pressure in the capillary remaining unchanged. If the P. D. £& is applied by closing the key, see fig. 1, then there will be a temporary current in the circuit G. The work done by the current will be Q= # = idT Joules, if Z, i and T are, as usually, expressed in Volts, Ampéres and seconds. 1, Q is transformed into heat, whereas 1/, % is accumulated in the meniscus as in a condensor in the form of an electric charge. If with circumstances as for the rest unchanged the applied P. D. — by opening of the key — is removed, the meniscus returns to OO aa ( tt its original position and delivers its energy, which once more is partially transformed into electric currents. The amount of 2 iT in returning must be equa! to Sid7 in the original displacement. This was easily controlled experimentally. The experiments which we have made with a sensitive high- resistance THOMSON-galvanometer, used as ballistic galvanometer, and kindly lent by Prof. KamertincH OnNes, perfectly confirmed the statements given above. The theoretical conclusions, that the value of the integral current increases directly as the P. D. used and that it remains unchanged with variation of the resistance of the circuit we could not rigo- rously prove by experiment because the time of oscillation of the calvanometerneedle was too small. The duration of a displacement of the meniscus was with some of the capillary electrometers a con- siderable part of the oscillation time of the galvanometer }). Yet the results of the galvanometer experiments are far from unsatisfactory as may be proved from the data concerning capillary B 102 in the subjoined tables IV and V. AS BS ln Eel Viz Mean deflection Mean deflection | Mean deflection Difference of j with suddenly with suddenly calculated per Poel: | applied P. D. removed P. D. 1 millivolt. e;. 40 millivolt. | 19,5 mm. 10,6 mm. 0,264 mm. 100 ” | 2830 ¢ 28,5 4 0,284 » | | A Teeets\ ed Be Eyes Dery Resistauves introduced in the Mean deflection of the galvano- circuit. meter with applied coustant P. D. : | oe 6000 Obm | 35,5 mm. 0.4 Megohm | 34 w 1 y | 315 -f ’) It proved unpracticable to arrange the galyanometer for large period. The damping soon became excessive. ( 118 ) The columns 2, 3 and 4 of Table IV give the mean values, obtained from experiments with the mercury as positive pole and the sulphuric acid as negative pole and reciprocally. Usually the deflections, caleulated for 1 millivoit at first slightly increased with increasing P. D. then reached a maximum and further decreased. On account of the above mentioned relatively too short oscillation time of the galvanometer, the maximum value of e probably will be the most accurate for calculating the work done, we therefore will make use only of the maximum. The values in column 2 of Table V are obtained only with mercury as the positive pole, sulphuric acid as negative pole. They represent the means of observations with suddenly applied and suddenly annulled P. D. For three capillary electrometers I have calculated the work necessary for the motion up and down of the meniscus, the difference of potential being “= 1 millivolt. The calculation always was made in two different manners, in the first place from mechanical principles using the difference of ‘pressure, necessary for the displacement and the dimensions of the capillary; in the second place from electrical principles using the deflections of the galvanometer, see Table VI. AGB EUHE Savile | Work doue as calculated from dimen- | Work done calcu- Number | Sions of the capillary-electrometer and | lated from galvano- ofttlic | the manometer readings | meter readings Ub 6) | in in gram-centim. | in Joules. Joules. | ] l sig | 115} | —13 B. 101 1,282 x 10 | 1,958 x 10 1,405 % 10 B. 102 2,209 » «» 2,162 » |e 2sloe eer B. 108 805 4 4 me year | 616 + e | The agreement between the values of columns 3 and 4 of the given Table VI, though not very beautiful may yet be called satisfactory considering the different measurements necessary in calculating the result. Concluding, we will see what part of the work done is spent (119 ) in surmounting the mechanical friction, what part for the production of electric currents. Let the total quantity of heat developed in a complete up and down motion of the meniscus by the sudden application and annulling of a given P. D. be A, the heat produced by mechanical friction A), by electric currents 4», then A =A,+ A, . ° . ° ° . ° ° (4) Let the initial velocity of the meniscus after the application of the given P. D. be w%, then is _ dyy SUE ia Formula (3) reading dy 1 (y ai Pee bo — > becomes for y = 0 dy 1 : een dil a + bw A, varies directly as v, hence with a given value y*, also as 1 —-—, Therefore we write a+ bw 1 AR a S a + bw ¢ being a constant. For w=0 the heat produced by mechanical friction becomes equal to the total work. The last remains the same for every value of w, hence we may put From the formulae (5) and (6) follows A, a a A a + bw Proceedings Royal Acad, Amsterdam. Vol. IL. ( 120 ) and from (6) and (7) Ag po bw F Agate Seine Sdetreccer fda vos (GS) In the subjoined table are given for a few capillary electrometers, examined without purposely inserted resistance the values of 4, and A, in percentages of A. AC Bie ivell, ana | 100 x 4 | 100 x 2 G. 103 91 9 B. 101 92 8 B. 102 93 7 B. 103 96 4 In the course of these experiments valuable assistance has been given by Mr. H. W. Buore and Mr. H. K. pe Haas. Botanics. — Prof. Betserinck speaks: “On the Formation of Indigo from the Woad (Isatis tinetoria)” 3). Some years ago I wished to become acquainted with the so-called “indigo-fermentation”’, about which nearer particulars had been communicated by Mr. ALvarez. He examined /ndigofera and says:*). “If a decoction of the plant is prepared and_ sterilised atfer passing it into test-tubes or PasTruR’s-flasks, the reddish colour of ) It was first my intention to treat ,On the function of enzymes and bacteria in the formation of indigo.” I have declined this plan for the moment, and give now only part of my experiments, because I see that also Mr. HazewinkEL, of the Experi- mentstation for Indigo at Klaten, Java, has obtained important results about that very subject, which results, for particular reasons, have however been imparted till now to a few experts only. Yet I cannot avoid mentioning some facts, found by me, the priority of which perhaps pertains to Mr. HazBwINKEL, without my being able to acknowledge his claim. One indiscretion, however, I am obliged te commit: Mr. Hazn- WINKEL has, already before me, established the fact, that by the action of the indigo- enzyme and of acids on indican, indoxyl is produced. *) Comptes rendus T, 105, pag. 287, 1887. aie (ELa is) the liquid remains many months unchanged without the appearance of indigo. But if some microbes of the surface-membrane of an ordinary indigo-fermentation are added, as also the special active bactery of it in an isolated condition, after some hours an abundant indigo-formation is observed,” I then tried to make from woad (Isatis tinctoria), in which, according to the literature, indican, i.e the same indigo-producing substance as in the other indigo-plants should be present, a decoc- tion with which I might repeat the experiment of ALvarez. But I could, neither by boiling, nor by extraction at low temperature, obtain from this plant a sap which remained unchanged at the air. Constantly, after a short time, indigo will separate out of it, without there being any question of the influence of bacteria or enzymes, so that the word “indigo-fermentation” would here be quite mis- placed. Neither do purposely added bacteria or enzymes favour the indigo-formation from woad-decoction. Later, however, I was enabled to convince myself that the state- ment of ALVAREZ is correct, as well with regard to the decoction of Indigofera leptostachya as to that of Polygonum tinctorium }), for which latter plant the same fact as described by ALVAREZ, has also been established by Moutscu ’”). So it was evident that the indigo-plants must belong to two phy- siologically different groups, and I subjected the concerned chromogenes to a further examination with the following results. 1. The Chromogene of the Indigo-plants is Indoxyl or Indican. The chromogene of woad is not as is usually accepted indican, but the very instable indoxyl C*’H™NO. Indigofera leptostachya and Polygonum tinctorium, on the contrary, contain the constant glucoside indican, the constituents of which are, in accordance with the supposition of MARCHLEWSKI and RabcLirre *), indoxyl and sugar, 1) Much material of this Zudigofera, as well full grown plants as seeds, I owe to the kindness of Mr. van LookereN CampaGne of Wageningen. This interesting plant, a native of Natal, has been cultivated, very rich in indican, in the open ground in the Laboratory-garden at Delft; at Wageningen several specimens had grown this summer to more than 1.5 M. height. Polygonum tinctoriwm comes from China and is, as the woad, in the seed-commerce of ViuMORIN in Paris. 2) Sitz.ber. d. Akad. d. Wiss. zu Wien. Math. Naturw. Klasse Bd 107 pg. 758, 1898. ‘) Journ. Soc. for chem. Industry T. 87 pag. 436, 1898; Chem. Centralblatt Bd 65 pag. 204, 1898. With thankfulness I remember the aid lent me by my chemical colleagues Hoogewerrr and Brnreys in the determination of indoxyl. ge which has first been brought to certainty by Mr. HAZEWINKEL, and, without my knowing of his experiments, by myself. Woad, as an yindoxyl-plant” containing no indigo-glucoside, wants also an enzyme to decompose it. The two mentioned ,indican-plants’, on the other hand, do contain such an enzyme, which had already in 1893 been rendered probable by Mr. vAN LookeREN CaMPAGNE with regard to Indigofera'). I have prepared this enzyme, albeit in a very impure state, in rather great quantity and I hope afterwards to describe the experiments made with it. The important difference between ,indoxyl-” and ,indican-plants” becomes particularly clear when comparing the different extraction methods. ‘Thereof what follows. If ,indican-plants” are extracted with water below the tempe- rature at which the indigo-enzyme becomes inactive, for instance below 40° C. or 50° C. (,cold extraction’’), and under careful exclu- sion of air, an indoxyl-solution is obtained. If, however, the same ,indican-plants” are extracted by boiling (,decoction”), the indigo- enzyme will be destroyed, and independently of removal or access of air, an indican-solution results, which ean be kept perfectly unchanged when microbes are excluded, but either by the separately prepared indigo-enzyme, or by certain bacteria or yeasts, or also by boiling with acids, it can be converted into the constituents indoxyl and sugar. I have prepared from it the crude indican in a dry state, by evapor- ating to dryness the decoctions of both Zndigofera leptostachya and Polygonum tinctorium. 'The brown matter, thus produced, resembles sealing-wax, is very brittle and can quite weil be powdered. Woad on the contrary, as an ,indoxyl-plant’, both by ,cold extraction’ and by ,decoction” always gives the same produce i. e. an indoxyl-solution. Here, in both cases, the greatest care must be taken to exclude the air in order to prevent that the indoxyl, which is so easily oxidised, is converted already in the leaf itself, for then the iudigo-blue is lost. Besides, access of air in a dying wood-leaf gives still in another way cause to loss of indoxyl under formation of tinknown colourless and brown substances. A sufficient removal of air during the preparation of the extracts is easily effected in the following way”). A well closing, wide- mouthed stoppered bottle is quite filled up with woad-leayes, hot ) Verslag omtrent onderzoekingen over indigo, pag. 12, Samarang 1893. *) The technical preparation of indigo from woad is described in Grospert, ‘Traité sur Je Pastel, Paris 18138, and in Dr Puymaurin, Instruction sur lart d’extraire VIndigo du Pastel, Paris 1813. ( 123 ) water is poured in, the leaves are pressed together until all air is replaced, and the stopper is put on so as not to leave the smallest air-bubble. By the exclusion of the air, together with the high tem- perature, the leaves soon die and already after a few hours a clear, light yellow liquid can be decanied, which is rich in indoxyl. If some alkali is added and air blown through, the indigo-blue precipi- tates, the colour of which appears only pure after acidification. In a sufficient time of extraction there can be thus obtained from woad a liquid of which the proportion of indoxyl, according to Rernwarpt ') who in 1812 applied the decoction-method on a rather large scale, answers to 0.3 pCt. “pure indigo” for the fresh leaves, which, as he remarks, might rise to the double amount in the South. If we consider that the indoxyl is especially concentrated in the youngest organs still in a state of cell-partition, that it diminishes considerably in full grown parts, and is almost or wholly absent in old leaves, we must conclude that the youngest organs may contain more than 0.3 pCt indigo. As the woad-leaves contain about 85 pCt water this would correspond to a little less than 2 pCt indoxyl in the dry matter *). The indoxyl-containing sap, whether prepared by “cold extraction” from the indican-plants or by decoction from the indoxyl-containing woad, has the following characteristics. It is a light yellow, in cold greenish fluorescent fluid; at warming the fluorescence diminishes and comes back at cooling. The reaction is feebly but distinctly acid, of course not by the neutrally reacting indoxy] but by organic acids. At the air a copper-red film of indigo-blue is formed at the surface of the liquid. 2(C8H7N 0) + 0? = Cl HN? 02 + 2 H?0, but this oxidation follows so slowly in the feebly acid solutions, that evaporating to dryness at the air is possible without too much loss of indoxyl. The indoxyl itself is soluble in water, ether, alco- hol and chloroform, in the two last under slow decomposition when the air finds access. 1) In a report of 6 December 1812 to the President of the Agricultural Comittee for the Department of the Zuiderzee, present as a manuscript in the library of the Academy of Sciences, Amsterdam. 2) But according to Grorcrvics, Der Indigo, pag. 2 and 18, Wien 1892, the rate of indigo for woad would only amount to 0.03 pCt. In my laboratory Mr. van Hasse found in three special cases 0.05 pCt, 0.07 pOt. and 0.09 pCt. indigo-blue in relation to the weight of the living leaves, which latter amount corresponds to ca 0.6 pCt indoxyl with regard to the dry weight. ( 124 ) As soon as the liquid becomes alkaline, however feebly, the indoxyl oxidises at the air with much greater quickness to indigo-biue. The statement of Britaupar?), that in the sap of /satis there would be present an oxidase, by which this oxidation is effected, is not proved; in none of the three indigo-plants I have been able to find an oxidase producing indigo-blue from indoxyl. For, by preparing from the woad-leaves “crude enzyme” by finely rubbing them under, and extracting them with strong alcohol, whereby, after pressing and drying, a completely colourless powder is obtained in which all the enzymes must be present, it is found that the oxidising effect of this “crude enzyme” on an indoxyl-solution is very slight, ceases soon, and does not change by boiling, from which must be concluded that the oxidation cannot be attributed to oxidase, but is of a purely physical nature ®). The leaves of the indican-plants give quite the same result. Though there originates during the slowly dying of woad-leaves at the air, a substance which gives rise to a total destruction of the indoxyl, yet about the nature of it I cannot express a sup- position. If it might prove to belong to the group of the oxidases, 1t is surely in no other relation to the formation of indigo from indoxyl, than that it is very pernicious to it. For the indican-plants the same has been observed. In Indigofera this destructive influence is so strong that the ,alcohol-experiment”, of which later, wholly fails with this plant. Hydrogen-superoxyd, too, causes the indoxyl gradually to vanish from the solutions, without any coloured products originating. Strong acids, just as alkalis, {though in far less degree, favour the formation of indigo from indoxyl, but then part of this sub- stance constantly changes into a brownish-black matter. In feebly alkaline and in moderately acid solutions, indoxyl, war- med with isatine gives, in absence of air, a precipitate of indigo-red, which is isomeric with indigo-blue C*H7 NO + C>H* NO? = Cl HN? 0? + H?0, This precipitate separates quickly out of alkaline solutions as fine red, from acid ones as coarser dark erystal-needles and can easily be filtered. It is soluble in alcohol and so can be separated from 1) Comptes rendus T. 127, pag. 769, 1898 en T. 128, pag. 1478, 1898. 2) In a small porcelain vessel the menisc of the fluid furthers the oxidation of indoxyl to indigo-blue just in the same way as vcrude-enzyme”, strewed as a powder on the surface of the liquid. nama pee es (125°) the indigo-blue. On warming an indican solution with isatine and dilute hydrochloric acid, all the indoxyl which is set free precipi- tates as indigo-red, and I presume that a good quantitative indican determination may be based upon this reaction. All the here mentioned characteristics of the indoxyl-containing plant-saps are also announced in the literature of the chemically prepared indoxyl, except the conduct towards isatine and hydrochloric acid which has perhaps not been examined. Natural indigo prepared from woad, contains a small quantity of indigo- red; but whether this originates from the same indoxyl as the blue, or from an isomeric indoxyl, I cannot decide. Indigo-red I could also find in the indigo made from indican, whether chemically by boiling with acids, or by bacteria, or by enzymes. Consequently, if two indoxyls should exist, there should also exist two indicans. 2. Demonstration of Indigo in the Indigo-plants themselves. For the demonstration of indigo in the plants themselves, Mr. Motiscu described in 1893 his ,aleohol-experiment’’ to which he afterwards repeatedly recurred '). In this experiment the parts of the plants to be examined are exposed, in a confined atmosphere, to alcohol- or chloroform-vapour, for instance by putting them into a glass-box, in which a small vessel with these substances is placed. Thus slowly dying all the indigo-plants become more or less blue, which is perceptible after the chlorophyll has been removed by extraction with alcohol. I found, however, that never all the present indoxyl or indican changes into indigo. The ,alcohol-experi- ment” succeeds the best with Polygonum tinctorium, where at least most of the indoxyl changes into indigo. For woad the result is greatly dependent on the length of time which the experiment requires, even on the season, but invariably only a part, though it may be a great part, of the indoxyl passes into indigo. With Indigo- fera only a little indigo precipitates in the youngest leaflets and buds, while the older leaves become quite colourless by the alcohol- extraction though they are extremely rich in indican, so that, for this plant, the ,alcohol-experiment” is without any value *). ‘) Sitz.ber. der k. Akad. d, Wiss. zu Wien Bd. 102, Abt. 1, pag. 269, 1893; Bd, 107, pag. 758, 1898, and Berichte d. deutschen Botan. Gesellsch. Bd. 17, pag. 230, 1899. *) Quite wrongly Mr, Moniscu declares: /Die pracisesten Resultate erhilt man bei Indigofera mit der Alkoholprobe,” and as wrong is his assurance ”Durchwegs war zu bemerken, dass die in Kuropa gezogenen Pflanzen (von Indigofera) auftallend viel weniger Indigo lieferen wie die tropischen” (Berichte d. deutsch. Bot. Ges. Bd. 17, pag. 231, 1899). (¢ Tar) For woad, as an indoxyl-plant, the alcohol-experiment can be improved by changing it into an ,amoniac-experiment”’, by which the percentage of indigo is much heightened. If near the woad- leaves in the glass-box a vessel with ammoniac instead of alcohol is placed, death follows almost instantly. The leaves then first become of an intense yellow and afterwards, by the indoxy]-oxidation, of a deep blue colour. By subsequent extraction with alcohol the leaves become deeply blue as compared to the lightly coloured »alcohol-leaves”. The ,ammoniac-experiment” proves that all growing parts of the -woad, even the roots, the rootbuds !), the cotyledons and the hypocotyl, contain indoxyl. The explanation of the ,alcohol-experiment” is, of course different for the different indigo-plants. This explanation must at the same time elucidate the following fact: Suddenly killed leaves, for instance leaves, which have been kept in vapour of 100° C., do not colour at the air, neither of woad, nor of Polygonum, nor of Indigofera, why then do they become blue when slowly dying off? The answer for Polygonum and Indigofera lies partly at hand. By the temperature of the boiling-point, the indigo-enzyme has been killed, so the indican can no more be decomposed. If slowly dying, on the contrary, the indigo-enzyme can become active and indoxyl is formed *). But the explanation of the second part of the process, that is the transformation of indoxyi into indigo, — at the same time the only point which for woad, as an indoxyl-plant, requires our attention, — is less clear. I think that the course is as follows. In slowly dying leaves the indoxyl changes into indigo-blue, because, in this form of death of the cells, some alkali originates. In suddenly killed leaves, on the other hand, alkali-formation does not occur, they do not grow blue, and the indoxyl disappears in another way. If im the leaves of indigo-plants the presence of an oxidase, acting on indoxyl, could be demonstrated, this would certainly explain quite well the action of higher and lower temperatures. But, as I said, I could not convince myself of its existence, so that I am necessarily led to the alkali-hypothesis. The cause of the great lack of indigo-blue which, as above obser- ved, diminishes the value of the ,alcohol-experiment’, lies in the ') The production of leafbuds ou the roots of the woad seems nowhere else men- tioned, Other biennal Cruciferae produce also rootbuds, for exemple Brassica oleracea, Sisymbrium alliaria and Lunaria biennis. ) Also a slow death of the leaves by drying or by frost renders the protoplasm permeable and the indigo-enzyme active. (19%) fact, that during the slowly dying of the leaves at the avr, a consi- derable quantity of indoxyl is lost in an unknown way. And in this circumstance I see one of the reasons why, in woad-leaves, there is produced so much more indigo by the ,ammoniac-experiment”’ than by the ,alcohol-experiment”, because in the former the leaves die almost instantly, whilst the latter requires much more time. With . /ndigofera, as said above, the ,alcohol-experiment’’ produ- ces hardly any indigo. I have therefore tried to substitute for it a better one, which is effected in the following way, and by which, also excellent results are to be obtained with Polygonum. At the direct action of ammoniac, indican-plants form no indigo at all, for thereby not only the protoplasm is killed, but the indigo-enzyme, too, is so quickly destroyed that it cannot decompose the indican. But we can, before exposing to the alkaline vapour, decompose the indican and free the indoxyl, by making the plants die by complete exclusion of air, but which in this case should occur in such a way, that the indoxyl remains within the plant itself. Indican-plants turn then into ,dead indoxyl plants’ and can in this condition, quite like the living woad, be subjected to the ,ammoniac-experiment” with a very good result. The simplest way by tar to reach the double aim of killing the plants by exciusion of air and leaving the indoxyl in the cells, is by entirely plunging them into mercury, whereby asphixion follows with surprising quickness, the protoplasm becoming permeable and the indigo-enzyme and the indican mixing together. At a proper temperature !) the indican is then decomposed after a few hours and the freed indoxyl remains in the leaf, albeit not exclusively in the cells in which originally the indican was localised. The leaf is then taken out of the mercury, ammoniac-vapour is allowed to act upon it, and at last the chlorophyll is extracted by boiling with alcohol and some hydrochloric acid. Even old Indigofera-leaves, which by the “aleohol-experiment”” become quite colourless, take a brilliant blue colour by this “mercury-ammoniac experiment.” Before L had worked out the mercury-method, I examined the results of killing the leaves by the asphixion in hydrogen, carbonic acid and the vacuum, in each case followed, in the same manner as in the mercury-method, by subsequent exposition to ammoniac- vapour and extraction of the chlorophyll with alcohol. When the hydrogen was mixed with air a singular phenomenon ') The influence of temperature on the action of the indigo-enzyme is interesting, I hope on another occasion to return to it. ( 128 ) was observed: the indoxyl disappeared so completely from the leaves, that, after the said treatment, they became quite colourless, whilst pure hydrogen produced intensely blue leaves. In the carbonic-acid atmosphere there appeared, with the indigo, a small quantity of brown pigment, probably because the carbonic acid was not wholly free from air. The action of pure carbonic acid I have not yet examined. The vacuum in a barometer-tube, above mercury, gives the same result as the submersion in mercury itself, but this method is, of course, more complicated. 3. On the coloured strip” in partly killed leaves. The following phenomenon is in near relation to the preceding. In many Jeaves, when partly dying off, a coloured matter will appear, just on the border between the living and the dead tissue ; with woad and with Polygonum tinctorium, the chromogene of this coloured strip is indigo }). The experiment succeeds best if the leaf is partly killed by keeping it for a moment in the vapour of boiling water. The killed part remains green, although it may be a little more brownish than the living one. As for woad I think the phenomenon should be explained as follows. On the border between the dead and the living tissue, a strip of cells must occur which are in a condition of slowly dying. Accord- ing to the preceding description, alkali will be formed in these cells and the indoxyl quickly oxidises to indigo-blue, nothing of it finding time for disappearing in another way. If the partly killed woad-leaf, immediately after death sets in, is exposed to ammoniac- vapour, it becomes, as might be expected, over its whole extent deeply blue. If it is, before the action of the ammoniac, left for some time to the influence of the air, then some indoxyl gets lost from the killed part which colours with ammoniae, a little less strongly than what remained living. For Polygonum tinctorium the explanation is somewhat different, because the indoxyl must first be originated by the action of the indigo-enzyme. But this enzyme is destroyed by the hot vapour in the quickly dying part, whilst on the border between the living and the dead part there must be a number of cells in which the 1) With woad this experiment succeeds best with leaves from the rosettes of the first year in June; with Polygonum always equally well. In many other plants the veoloured strip” does not contain indigo but a black or a brown pigment. (1299) protoplasm is killed or hurt, but in which the enzyme remains active. During the dying the protoplasm becomes permeable, indican and enzyme are mixed up, and indoxyl-formation is the result. But in the same cells there occurs, in consequence of the slowly succeeding death, an alkaline reaction, by which the indoxyl soon oxidises to indigo-blue, which therefore precipitates in these cells alone, and not in the quickly killed nor in the living cells. Put into ammoniac- vapour the living, as well as the dead part of the Polygonum-leaf remain uncoloured, in opposition to the woad-leaf, this, after the preceding, requires no further elucidation. Of course, these phenomena would find a somewhat simpler explan- ation if they could be brought back to the action of an oxidase, present from the beginning. But an oxidase, producing indigo from indoxyl is, as said, not to be found. To conclude I wish to observe, that some other phenomena, which are attributed to the effect of a ,wound-irritation”, for stance, the formation of starch and of red pigment, as also the development of warmth in hurt parts of plants, possibly repose also on alkali- formation in or near the damaged cells. Physics. — Communication N°. 51 from the Physical Laboratory at Leiden by Prof. H. Kamertincu Onnes: “Methods and apparatus used in the cryogenic laboratory”. I. 1. Last year the completion of the safety-arrangements, thought desirable for the cryogenic laboratory by the Privy Council, in accor- dance with the Report of the committee appointed by the Academy, enabled us again to take up the work. I intend now to publish, whenever the completion or the progress of researches allow, something about the methods and apparatus used in working at low tempe- ratures and with liquefied gases. In this way the short survey (Comm. N°. 14) of the arrangement of the cascade formed by the methylchloride-, ethylene- and oxygen- cycles will be continued or elaborated. 2. Cryostat (boiling-glass and botling-case) for measurements with liquefied gases (especially with liquid oxygen). In the above mentioned communication a method was described (§ 8) for using liquid gases in measurements. A sketch, shown on plate I of Communication N°. 27 '), may serve in some way to ‘) Verslag der Vergad. Kon. Akad. 96/97. pg. 37, Comm. Leyden, N°. 27. ( 130 ) illustrate that §. For that purpose however the drawing, to be found in the description of the eryogenic laboratory by Prof. Marutras !) is better adapted. Whereas the apparatus described by him was made for measurements in a permanent bath of oxygen with a capacity of from '/, to '/y Litre, in the experiments of Dr. HaseNnornRt, treated of in Communication N°. 52, a cryostat (boiling-glass with boiling-case) was used, designed on the same principle, but which contained a bath with a capacity of from !/, to */, Litre *). This also offers the advantage of being more quickly and easily mounted, and being more certainly air-tight, thus being better able to keep the enclosed gas pure and dry. It was built by Mr. J. J. Curvers, head mechanic of the cryogenic laboratory, to whom I owe my best thanks for the care and ingenuity displayed in these works. Plate I gives an elaborate drawing (1/; nat. size) of the apparatus together with the electric condenser for measurements with liquefied gases *), which was fastened in it in the experiments of Dr. HasENOERHL. Hence this plate may serve at the same time to illustrate the description of his research. The gas liquefied under pressure e.g. liquefied oxygen at —140°C. from the ethylene boiling-flask, (Comm. N°. 14 § 5) is introduced by means of the tube a, which is wound in numerous turns b round the piece of wood carrying the cock. When the apparatus has been working for a short time, part of the gas streaming out in drops and clouds passes along these turns and so even further cools the liquefied gas before it escapes. The cock-pin v having been opened by means of the handle Ay, the gas passes through a filter J filled with glasswool enclosed by gauze, and flows out through the tube ¢ against the cylindrical glass C, which fits exactly round the turns of the spiral 6. If we apply the eye to the observing tube A, *), and the light obtained by means of the illuminating tube Vy is sufficient, as long as liquid flows out from the tube ¢ we see the jet spread out in a fan over the glass C, the jet-catcher °). Part of the cooled liquid escapes along the spiral b, as remarked a / 1) Mavutas, le laboratoire cryoge¢ne de Leiden, Revue générale des Sciences, 1896, p. 387 fig. 3. 2) By placing other beakers in the boiling-glass the apparatus may be used for baths of almost twice that volume. ’) For this compare the section Pl. I of Comm. N®% 52. 4) The construction of VY, is exactly like that of A,; in the drawing the front-view of K, or V, is given near 7. °) The disappearance of this fan-shaped form indicates that no ‘more liquid is supplied by @ and that we must therefore shut the cock. (sit) above, but by far the greater part flows down along the inner wall of this cylindrical glass; it is conducted further by an exceedingly thin brass continuation D, and flows out over the lip 2, into the beaker 2, destined for receiving the liquid. Applying the eye to the oval observing-tube 4, and securing a sufficient illumination by means of the opposite oval illuminating-tube V, we may see the liquid descending in a little jet or in drops and gathering in the beaker. The cylindrical glass C, suspended by means of thin copper strips !), as well as the continuation ), which is kept in its place by means of little pieces of cork y, are almost unaccessible for heat by con- duction, especially when the cold vapours of the liquid which ascend from the receiving vessel 6, have exerted for some time their refrigerating action on the surroundings *). Again the beaker A, is screened from external heat by a double gas-layer between the beakers 6,, B, and B, round which the escaping vapours are con- ducted in a manner to be described presentiy. By means of a glass ring, &, and a border of ebonite R, the beaker is fastened to the inner of two thin copper pieces 2, and /,, constituting together a double cover. In this cover are placed, as in the model described in Dec. ’94, two tubes 7 and G), one of which receives the jetcatcher C, whilst the other one serves to admit the measuring-apparatus, to be immersed in the bath of liquefied gas. In the case depicted this latter is the covering of Dr. HASENOEHRL’s condenser, the glass tube y of which is fastened by means of a tube of caoutchouc g and brass tightening bands g; in the tube F, which is on the right hand of the boiling-glass. By this means the boiling-glass is closed on this side. The vapours evolved from the liquid escape through the tube G, on the left hand, which is covered by a second, wider tube .@,. This latter tube, which by means of a caoutchoue tube G; and a brass band is fastened to the wooden cock-box S3, prevents the gas from escaping and conducts it towards the outer piece 2 of the double cover. The glass tube *) is fastened to this by means of a cork ring H,, and the two pieces of the double cover are united by the caout- choue ring £,. The outer cover fits by means of 2, on to a beaker B,, a little wider than the receiving beaker B, together with its surrounding glasses. Besides these beakers, which moreover are sus- ') To the glass G,; (the strips are omitted in the drawing). *) Silvering the glass where it does not need to be transparent was not yet necessary and was therefore omitted for the sake of simplicity. ‘) G, serves to screen Gy from external heat. ( 132 ) pended to the cover by means of fiddle-strings strained round them, B, also rests, by means of a ring J; on a very thin supporting-board Lo, which is itself suspended by means of fiddle-strings L, and Z;. The gas escapes from the boiling-glass through the holes in the supporting ring Z, and the supporting board Z, into the boiling-ecase and leaves the apparatus through the exit tube 7, which leads through the cover of the boiling-ease and the caoutchoue cap stretched over it. In this way the cold vapours are forced to follow the route indicated by the arrows and so to prevent the passage of heat to the bath. The whole boiling-glass with the supportingboard L, is suspended to the cover of the boiling-case as appears from the description given above. This cover has the shape of a cap with three holes in the upper sheet of thin copper, strengthened by ribs). Through one of these holes leads the above mentioned exit tube 7,. The two remaining holes serve to admit parts of the boiling-glass. The left hand one beneath Q, is for the wooden cock-box, consisting of two pieces screwed on to each other and to which the left hand part of the boiling-glass is suspended; while the right hand hole beneath P is for the tube admitting the measuring-apparatus. The latter is also connected to the cover by means of a wooden ring, consisting of two pieces J; and Jj, which are screwed on to the cover from both sides. The closure of the holes in the cover is obtained by means of a caout- choue cap, having on its upper surface three tubes, which fit on the tubes emerging from the case and are pressed on to these by means of brass bands (C. f. Q), Qo). From the more detailed description of the mode of connecting it will appear, that the cock-box and the experimenting tube together with the. cover are permanently united into a frame, to which the rest of the boiling-glass is suspended. In order to build up the apparatus, we first connect to this frame the double cover 2, £, of the receiving beaker by means of the above described glass-tubes /) and G). Then we should generally adjust in its place the apparatus to be immersed in the liquefied gas. So in Dr. HasENOEHRL’s case the glass-tube g, carrying the cover m of the condenser, was introduced into the* experimenting tube and fastened by means of the caoutchouc-tube ) g, and the brass band g; *). The thin wire gy, which is to put the 1) See section through upper surface of cap next to it. *) g is pushed through the cover from beneath, the side-tube ~, is then connected to g as follows: the brass 7:piece ~, w, (comp. Pl. I, Comm. N°. 52) is slid from above over g, and fastened by means of the caoutchoue-tubes , and wz, and brass bands so that w. comes opposite to a hole made in y. a vies ( 133 ) brass cover of the condenser to earth was connected to the tube a, and then the beakers B, 6, B; B, were mounted in their places and together with the supporting-board 2, suspended to the cover by means of Zg. Into the cock-box S$, we place the cock-piece of wood Sj; this fits in it first by means of the caoutchouc-packing 4, which serves only to prevent the gas from taking the way upwards and also by means of the caoutchouc-packing //;, which is compressed by the screws S, till an air-tight fit has been obtained. In the cock-piece the supply-tube a and the glass cock-tube p 1) are also introduced. The design of the cock is for the rest exactly like that of ’94 (see also Marutas l.c.). At the lower end of the glass tube p a hexagonal brass cap has been cemented, in which is a nut, turning together with the glass tube p and screwed on to the brass cock-piece hy which contains the washer. When the washer has been screwed on sufficiently, the hexagonal portions of nut and cock-piece are fixed together by means of a hollow hexagonal piece. Then the tubes a and p are fixed hermetically into with elastic cement. The pin v is moved by a wooden stem A;, ending at the upper end also in a pin, which goes through the packing 4s. Sideways a tube j is placed, serving to test the cock for leakage of the packing hy and to lead away the gas possibly escaping at high pressyre through that packing, as otherwise the glass tube p’ might burst. It is very con- venient that the cock-piece with the cock can be taken out of the appa- ratus, if the packing, the filter or one of the tubes has gone wrong. By pressing the packing \, by means of the screws 1; between the flanges of the cover NW, and of the boiling-case NM, we obtain an air-tight fit of the cover on the case. The conical ring Z,, supported by felt, guides the ring Z; when the boiling-glass is lowered into the case, until through the fitting of the ring Z; into another similar ring fastened into the bottom of the case a centric and elastic mounting is obtained. The case itself consists of two thin copper cylinders strengthened by rings, the lower and somewhat narrower of which cylinders, U has been soldered excentrically into the bottom U, of the upper and somewhat wider, JU). A sufficient rigidity in the connection of both cylinders has been secured for by inner strengthening-bars Uj, The case carries at the upper part two circular and at the lower part two oval opposite flanges 4, and A, on to which the observing and illuminating-tubes are ciamped air tight by means of flanges ") Constructed exactly like the cock, depicted Pl. | Comm. N°. 52, where the drawing is more distinct, ( 134 ) @, a@ and caoutchoue packing. The line joining the upper couple has been turned about the axis of the case with respect to the line joining the lower couple, in order to obtain a sufficient illumination of the issuing jet '). The loose bottom W , which may be pushed outward by inner pressure, rests on exhaustion with the border W, on the border of the case, and is sufficiently strengthened by ribs to be able then to resist the outer pressure. By means of the caoutchoue cap W,, which is stretched over the bottom and fastened air-tight to the borders once for all with the utmost care, a fitting is obtained, whilst nevertheless in case of accident the whole bottom would act as a safety-valve. The whole apparatus can be exhausted through the cock X;. This is connected together with the vacnum-manometer X, to the case at the flange X; (dotted in the section, and depicted beside the case separately in section), to which the glass tube X; has been fastened in the same manner (by means of X,) as the observing tubes. In this tube P, O; is introduced for drying the apparatus. The whole inner wall of the case 1s coated with a layer of felt and the bottom with several layers while the inner surface of this layer has been rendered reflecting by lining it with nickel-paper. The thin layer of nickel however has been removed over‘a length of a few eentimeters at all places where heat might be supplied to it by conduction. Where the inside of the case or of the observing and illuminating-tubes has not been coated with felt, or a layer of felt would not be rigid enough, insulation has been secured by intro- ducing wood or caoutchouc, as appears sufficiently from the drawing *). The dust-box Y, provided with an extremely light valve Y, opening outward, and made of cotton wool enclosed between gauze with a border of wash-leather, allows the gas to escape without appreciable fall of pressure and prevents the gas, which might flow 1) Further explanation of symbols: 7,, x, loose-fitting, thin plate-glasses, separating the back observingtube-chamber from the case, while nevertheless the pressure of the gas in the case and the observing tube remains equal; ¢,, ¢. wooden packing tubes, in order to supply as little heat as possible to the gas in the observing tube- chamber; ¢,, p. thick observing glasses, fitting air-tight in js, and further fastened by means of bands y, v5; 9), @: caoutchouc-tubes, fitting round the brass-ring of foremost observing tube-chamber; ,, w, observing-glasses cemented in border, with packing fitting on 7), 7,3 &, @ tubes serving for sucking dry, heated air through foremost chambers (commonly cicsed). In the various chambers stand drying-dishes with P, O;. The tube at +, should have been drawn broken off. *) The case has room to place still another athermanous layer between the wall and beaker B,. ms ( 135 ) back from the conduit Y,, from introducing dust into the apparatus. For the tube Z, through which in the experiments of Dr. HAsENOEHRL the gas escaped which evaporated from the electric measuring-con- denser, a simpler dust-box Z, (filled only with cotton wool between gauze) was sufficient, as this has not to transmit so much gas at once. It has already been pointed out above, that the arrangement of this cryostat offers a great advantage as concerns easy mounting and dismounting. ‘This is especially due to the use of flanges with packing for all the air tight joints that have to be made and tem- porarily broken in working with the apparatus. The copper wall with flanges soldered to it will of course occasion no leakage, and can be tested previously by means of a temporary bottom soldered into it and temporary closing plates on the flanges. When we are quite certain everything is tight, the caoutchoue cap, which is to close the bottom, is spread over with rubber-solution, and by means of bands W, once for all united with the case. In the same manner the cap YN, is fitted onto the cover and the parts going through the holes. When all this has been done carefully, the joints are tested by immersing the case with bottom and cover, closed with temporary plates on the flanges, in a tub filled with water, and protecting the eaoutehoue caps from without against inflation; then admitting air into the case under a little excess of pressure (0,2 atm.), and seeing whether any air bubbles escape. These fittings which demand much eare are permanent, so that if they are found in this manner to be secure, they will not generally require any more attention. In the same way we may also carefully cement once for all the thick plate glasses @), Yj and the flanges of the observing and illuminating-tubes in the caoutchouc-tubes sy 4, and test the joints by means of tem - porary flanges before fastening them to the apparatus. In commencing to use the cryostat we need only screw the case on to the cover Ny and the observing-tubes onto the side-flanges, and secure an exact fit of the packing between the flanges, a thing which can always easily be attained. This is the case also if we wish to lift the boiling-glass with the cover for a moment out of the case, or if we must renew the P,O; in the drying-dishes in the observing- and illuminating-tubes. The cryostat rests with N, on a wooden ring supported by three legs and is packed up in wool. It was described above how in the experiments of Dr. HASENOEHRL the measuring-apparatus was mounted in the boiling-glass. We may add here only that, as explained by him in Comm. N°, 52, the beaker B, was filled with liquid oxygen from the ethylene-boiling- 10 Proccedings Royal Acad. Amsterdam. Vol. II. ( 136 ) flask (Comm. N®. 14 § 5), the liquid was sucked over partly into the condenser through the tube r by means of the cock h, and the beaker B,; was then filled up with liquid oxygen and remained so ’). All these operations were watched through the observing-glasses and proceeded without offering the least difficulty. 3. The arrangement of a Brotherhood air compressor for the compression of gases, to be kept free from admixture with air. In Communication N°. 14 this was dismissed in a few words. Plate II gives a view of the compressor with its separator and the newly devised accessories ('/, nat. size). As for the pump itself, in Plate III (4/, nat. size) figs. 1 and 2 what has been newly added is indicated with thicker lines. By means of figs. 1 and 2 together, completed by fig. 3, the construction and working of the compressor may be understood ®), As explanation we may remark, that the cock B, supplies the steam, which drives the miniature steam-engines By, By placed at both sides of the body of the pump. When working at full speed the shaft 6;, which moves the plunger of the compressor up and down makes up to 500 revolutions per minute. Usually the air to be compressed is drawn directly from the atmosphere, through the suction-valve d, d — which is in the shape of a flat ring en- closed between two concentric circles —- in which process it becomes mixed with water and a lubricant. To suck a gas which must be kept free from air this valve is covered with a head, consisting of a brass ring ¢, a thick observing-glass e, and a caoutchouc-tube e5 which is firmly and hermetically fixed to both by means of bands e; and e, and cement). The lubricant mixed with water, which in the case of the compression of NO (and also of Oy) was glycerine with */s of water, drops from the tube f; *) and the gas is supplied through the tube g, (Pl. IID. It also sometimes happens as will appear later on, that liquid is let off through this supplying tube. In order to prevent in such case the observing glass, through which we wish to watch the regular working of the valves, from becoming dull the screen g, has been introduced. Received through the sucking-valve 1) Through z, the measuring-condenser is exhausted, by means of Z, and X; we may judge of the difference of pressure required to suck over the liquid from B, into m. 2) E. g. by following the letters ag the circulation of cooling water may be traced. *) The metal-cage fig. 4 serves to prevent the projection of the glass in the possible case of accident. *) In compressing air we might use spermaceti oil with water, but in the case of oxygen and nitrous-oxide explosions might then be dreaded. oy ¢( 137) in the room a the gas is compressed in three steps, first in the room a itself, whence it escapes through valves, then in the annular space b, and lastly in the narrower and also annular space c, which it enters also through valves, and whence it goes over the cooling spiral *, through a feeding valve and passing a safety valve to the separator S. When the cock % of this is shut, the gas may escape along a little screw!) as well as through the safety-valve. The safety-valve comes into use only when the former is screwed tight and with the Leiden arrangement the gas, mixed with liquid, escaping from it is conducted back to the sucking-tube /,. When the gas has reached a sufficient pressure by opening /, it is admitted into the separator, where the liquid gathers below and from which the gas may be conducted through the cock é. Thence it reaches first the wide drying-tube P, and then the narrower one Dg. In both it passes through P,O;, shut up between glass-wool and asbestos by means of gauze and little sieves *). Through cock A, and tube S,, the com- pressed and dry gas may be led to the apparatus where we wish to bring it; generally a tube like Dy, filled only with glass-wool, is added in order to arrest the P,O; possibly carried over as dust. The lubricating liquid flows in at the sucking chamber through the tube jf, from the reservoir f;. Care should be taken that this reservoir remains filled, (the best way is to keep the level constant) and to watch by means of the glass tube /,, partly enclosed in brass, the regulation of the little jet by the cock /,. (Compare for the construction Pl. I{I fig. 5). The liquid from the separator is forced through the cock 4%. and the tube Ss into the reservoir V, whence the gas dissolved in or escaping after the liquid returns along A (Pl. 1V) to the sucking tube g,; °). This arrangement besides that at the safety valve described above is intended to prevent the loss of pure gas, which usually is costly. The glass tubes cemented in brass-pieces 4, /2 with taps (see Pl. III fig. 5). allow us to see whether chiefly liquid or gas is forced out. A gauge-glass indicates the level of the liquid and a }) This little screw is not to be seen in the section represented, it is useful when starting the compressor, especially as it allows liquid to escape from the cooling- spiral, *) Fig. 6 gives a section of these frequently used drying tubes, mentioned in N®. 14, and to be found in the drawing of Maruias and in other of these communications. The construction is cheap and fit for pressures up to 80 atmospheres. The brass nuts have been screwed and soldered onto a gaspipe tested up to 290 atm. and provided with a screw thread. The drawing should require no further explanation. *) The cock Ay is always opened while working with the apparatus but is useful to test the tightness of the apparatus. ( 138 ) safety-valve v beneath the liquid regulates the out-flow without permitting air to be sucked in. Into this reservoir may escape also through the tubes S, and S;, the cock K; and the tube S,, the contents of the joining-tube S), and the mixture of gas and liquid contained in the pump itself. The contents of each of the reservoirs S, D,, Do, which enclose gas under pressure, may likewise escape into the reservoir V, or directly into the sucking-tube on opening the cocks Ay, K; intro- duced for that purpose. Moreover the various parts of the arran- gement may be connected through the cocks A, and 4% to an air- pump, to the open air or to a gas reservoir. 4. Pouring out little quantities of liquid nitrous-oxide. Nitrous- oxide is a very important means for operating with low temperatures. The boiling point lies lower than that of carbon dioxide. It has further an advantage over carbon dioxide in remaining liquid at the boiling- point. Hence it may be used for transparent (liquid) baths, which for most experiments will be preferred to a snow-like substance. In physical and chemical laboratories however the free liquid is relatively seldom used for this purpose. One of the causes of this may have been that, on trying to pour out the liquid directly from the com- mercial cylinders, the cock was frozen. Or that, by neglecting to sufficiently close the glass-vessel (a vacuum-glass for instance) in which the liquid was poured out, part of the N.O, the melting point of which lies very near the boiling point was allowed to congeal by evaporation in the air!) and so to form a solid mass in front of the orifice. However the principal reason will probably have been, that im all cases the quantity poured out was very smail in proportion to the quantity employed, and hence the price of the free liquid thus obtained was far in excess of the moderate price by weight of the N.O in the cylinder. The N,O may however be csoled easily and with little cost by means of carbon dioxide so much, that almost all the nitrous-oxide flowing out is received as liquid if the glass into which it is poured has been also closed sufficiently. For many experiments then the advantages enumerated above will outweigh the smaller cost and danger of the solid carbon dioxide. In such cooling experiments the gaseous N,.O is conducted through a drying tube with P.O; (as in plate III fig. 5) which is connected with the reservoir of liquid gas, to a thick copper condensing spiral (7,5 mm. outer 4 mm. inner diameter) consisting of 24 turns, 12 with diameter 8 and 12 with ') See Natrerer, Pogg. Ann. 62 p. 134, (1844). (139 ) diameter 11 cm. contained in a felt-coated copper vessel (height 14, width 12, 5 cm.), which is packed with solid carbon dioxide. The condensing spiral is provided on both sides with a regulating-cock (for the model see SreRTSEMA, Comm. Suppl. No. 1, Pl. IL, fig. 9) and To the latter of these a narrow discharging tube is fastened. 5. Boiling nitrous-oxide in large quantities. Cycle of nitrous- oxide. If we wish to cool apparatus with larger volumes or capaci- ties for heat in a bath of nitrous-oxide, it will be necessary to receive the gas evolved by the liquid and to compress it by means of a compressor with or without cooling. As at Leiden a methyl- chloride-cycle is at hand, the proper way was not to compress the nitrous-oxide at the ordinary temperature, but in the methylchloride refrigerator (Comm. N°. 14 § 3, see also Pl. I, Marutas l.c.). As compressor a Brotherhood-pump could be used, arranged as described above § 3. If we condense the N,O at a very low temperature, the vapours escaping from the refrigerator are very rare and the vacuum-pump, which sucks them up, can only moye a small quantity of methylchloride. If we condense the N,O at a higher temperature, more methyl- chloride will certainly evaporate and more nitrous-oxide will be condensed, but the latter will evaporate to a much greater degree on flowing out than more cooled N,O. Usually we operated at the temperature — 45° C of the methylchloride-refrigerator and the safety-valve of the Brotherhood (see § 3) was adjusted for 25 atm. The separator in order to work well, should have a rather large capacity in which therefore a large stock of N,O0 would be stored up at high pressure. This alone would make it desirable not to proceed to tco high pressures, and moreover at the discharge of the gas, which deviates strongly from Boyte’s law, from the separator water might be frozen and so cause accidents. Plate [V +) represents a scheme (the parts nearly 1/3; nat. size) of the arrangement of the apparatus in Dr. HaseNOEHRL’s experiments with liquid nitrous-oxide (Comm. N°. 52) as an example of operations with the nitrous-oxide cycle. B is the Brotherhood-pump, with acces- sories, of which the principle may be understood from plates IT and IT together with ¢3. The compressed gas is conducted through the regu- lating-cock (k, Plate Il) along D (Plate IV) to the methylchloride- refrigerator, where it is cooled first by the cold methylchloride vapours *) For simplicity a case was here selected for which the refrigerator had been formerly described; but a refrigerator, wholly independent of the triple-cascade might be used, ( 140 ) in the spiral £ of the regenerator (Comm. N°. 14 § 3), whence it flows through the condensing tube and a cock to the cryostat which is indicated only diagrammatically, but may be understood from Plate I together with § 2; the evaporated gas escapes through the dust-box Yj, to the sucking-side of the pump, which communi- cates with the gas-sacks G, and G3, into which also the gas from the condensor escapes through 2Z;. The cocks indicated in these conduits are required to cut off and to test the separate apparatus. Besides the possibility of closing these we should be able to shut off the gas-sacks G, and G, and to stop the Brotherhood. Therefore a safety-tube has been connected to the tube conducting the gas. The observer, who regulates the influx of liquefied gas by means of the observing glasses of the cryostat, keeps in view at the same time the vacuum-manometer. The entire cycle could be operated in the experiments of Dr. HaseNnoEHRL, where only a beaker containing */4 Litre had to be kept full, with about 2 kg. of N,O, which was admitted into the apparatus through the cock 4, (Plate 111) from a reservoir of compressed nitrous-oxide. With the first experiments little care was bestowed upon the exhausting etc., and therefore a mixture of NO and air circulated. A remarkable phenomenon then occurred. While the observer looked through the observing glass at the jet, the jetcatcher was suddenly obscured by solid substance, and thick flakes of snow and accumu- lated snow heaps rushed down into the beaker B, (PI. I, where they took some time to melt. ; This singular phenomenon, for a moment suggesting the doubt as to whether something had gone wrong with the P.O; or the circulation of water, could be simply explained as follows. From a mixture of NO and air a liquid phase is separated, which contains chiefly N,O, the gas available in the cycle becomes then very impure N,O. In the methylchloride refrigerator this on a sufficient increase of the pressure is condensed into a solution containing much air, which on being poured out sets free the air in a gaseous phase in which the partial pressure of the nitrous-oxide is less than that of solid nitrous-oxide, so that the liquid phase, consisting almost solely of pure uitrous-oxide, congeals. Physics. — “The dielectric constants of liquid nitrous oxide and oxygen.” By Dr. Fritz Hasenoenru. (Communicated by Prof. H. KaAMERLINGH ONNES). (Will be published in the Proceedings of the next meeting). ( 141) Magnetism. — ‘On Spasms in the Earth's magnetic force.” By Dr. W. van BeMMELEN. (Communicated by Prof. H. KAMERLINGH ONNES). (Will be published in the Proceedings of the next meeting). (Octobre 25th, 1899.) BR CAS OMe Page 41 line 13 for Fe,SO, read FeSO, Waa ero | aNSO Pare GGA eee NAL IG 1603). e603...) s A416 Coen 44.05 b M56G., «1 1566 4nd 95 | 26U 4d 474 620194 0194... 44,47 KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday October 28th, 1899, CS er nme (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 28 October 1899 Dl. VIII). Contents: “On Isodialdane”. By Prof..C. A. Losry pe Bruyn and Mr. H.C. Byt, p. 143.— “Mixed Crystals of Mercury Iodide and Bromide.” By Prof. H. W. Baxnurs RoozEBoom, p. 146. — “On the Enantiotropy of Tin (IT}”. By Dr. Ernsr Conen and Dr. C. van Eyk (Communicated by Prof. H. W. Baxnurs Roozeroom), p. 149. — “On a new kind of Transition Elements (sixth kind)’. By Dr. Ernst Conen (Communicated by Prof. H. W. Baxuvis Roozrroom), p. 153. — “On mixed Crystals of Sodium nitrate with Potassium nitrate and of Sodium nitrate with Silver nitrate”. By Prof. 1. W. Baxnurs RoozeBoom, p. 158. — “The Nature of inactive Carvoxime”. By Prof. H. W. Baxkuuis Roozepoom, p. 160. — “On Isomorphous Compounds of Gold and Mercury”. By Prof. Tu. H. Benrens, p. 163. — “A Remark on the Molecular Potential Function of Prof. VAN DER Waats”. By Dr. G. Bakker (Communicated by Prof. J.D.van DER WAaLs), p- 163. — “Tidal Constants in the Lampong- and Sabangbay”. By Dr. J. P. van per Stok, p- 178. — “On the Relation of the mean Sea-level and the Height of Half-Tide.” By Mre H. E. pe Bruty, (with 2 plates) p. 189. — ‘“tNew Theorems on the Root of the Functions C (x)”. By Prof. L. Gecrnspaver (Communicated by Prof. JAN pE Vrigs), p. 196. — “Spasms in the Terrestrial Magnetic Force at Batavia’. By Dr. W. van BrmMMELEN (Communicated by Prof. KamERLINGH ONnNEs), p. 202. — “The dielectric Coefficients of liquid Nitrous Oxide and Oxygen”. By Dr. Frirz Hazenorurt (Communicated by Prof. H. Kameriinen ONNeEsS) (with one plate), p. 211. — “The Harx-Effect and the increase of Magnetic resistance in Bismuth in very low Temperatures.” By Dr. E. van EvEeRDINGEN JR. (Communicated by Prof. H. Kamerrincu Onngs), p. 228. The following papers were read: Chemistry. — ‘On Isodialdane.” By Prof. C. A. Lopry pu Bruyn and Mr. H. C. Bust. (Read in the meeting of September 30th 1899). In his interesting and prolonged researches on aldole, Wurtz has described two condensation products of this substance, formed by the separation of a molecule of water from two molecules of aldole, One of these, dialdane, which is formed along with aldole from 11 Proceedings Royal Acad, Amsterdam. Vol, IU. ( 144 ) aldehyde, was more fully studied. The results of this study led Wurrz to propose a formula for dialdane according to which it still contains one aldehyde group, exhibits the properties of an alcohol twice and contains two carbon atoms united by a double bond. From two mo- lecules of aldole CH, CHOH CH, COH dialdane CH, CHOH CH, CH : CH CHOH CH, COH is therefore formed by the separation of water from the methylgroup of the one molecule and the aldehyde group of the other. ‘The second condensation product, which Wurtz called isodial- dane, was only obtained by him in very small quantities, and was not further examined. He obtained it, along with other substances, by heating aldole to 125°; it melted at 112°. In an attempt which one of us made long ago !) to combine aldole with bydrocyanic acid, pure hydroecyanie acid was mixed with aldole and the mixture left to itself for some months. It was found that the hydrocyanic acid had not combined with the aldole, or only to a very small extent; it had, however, acted as a dehydrating agent so that two molecules of aidole had formed one molecule of isodialdane. As a result of this observation isodialdane was readily obtainable and a proper study of it was taken in hand. The result of the investi- gation possesses a more general interest because it leads to the con- clusion, that isodialdane is to be regarded aes a substance in some measure analogous to ordinary cane sugar, in the sense that the relation between isodialdane and the two aidole molecules, from which it is formed, is the same as that between cane sugar and glucose and fructose (laevulose). It is known that cane sugar does not possess reducing powers and therefore does not contain an aldehyde group, but that under the influence of dilute acids, it very readily takes up a molecule of water, being converted into the two above mentioned reducing hexoses ; the aldehyde group of glucose and the carbonyl group of fructose are therefore absent in the saccharose molecule. At the same time two of the ten hydroxyl groups of the two hexoses disappear, for saccharose only gives an octo-acetate. Let us now turn to the results of the study of isodialdane. It has no reducing power, but with dilute acids it at once obtains this; it is thus very readily inverted. 1) Bull. Soc. Ch. (1884) 42. 161 ( 145 ) Tsodialdane contains no unsaturated bond, bromine is not taken up and alkaline permanganate is not decolorised. The two hydroxyl groups of the two aldole molecules have disappeared; the solutions in benzene and xylene giving no hydrogen when boiled with sodium and acetic anhydride and sodium acetate having no action on iso- dialdane even on boiling; acetic anhydride with a trace of sulphuric acid or of zine chloride gave rise to resinous products from which an acetate could not be separated. The application of ScHorren— BauMann’s reaction with benzoylchloride also gives a negative result. Phenylhydrazine is quite without action even after boiling the alcoholic solution, so that a carbonyl group is not present in iso- dialdane. Sodium amalgam does not effect reduction or acts very slowly, since after four days reaction, partly at the temperature of the boiling water bath, almost the whole of the isodialdane was recovered unchanged. We consider that the structural formula, which satisfactorily re- presents the results obtained, must be that in which each of the three oxygen atoms still present in isodialdane are supposed to be connected to two carbon atoms. This leads to the hypothesis that two aldole molecules CHy Pe eOr, | | CHOH CHOH | | CH, CH | | (0: aE lose one molecule of water, yielding CH, CH, | CH —0O—CH | | CH, GH, | | ae CH 6 / CH This system is apparently very stable, except under the action of dilute acids. 13 bs ( 146 ) We consider that there is some justification for the assumption of the existence of the group of carbon and oxygen atoms, found in isodialdane, in the saccharose molecule, the constitution of which is as yet unknown. Making this assumption and using the stereochemical formulae of glucose and fructose the following formula is obtained. The left half represents the fructose molecule, the right the glucose molecule. OH,OH | ke C oH “at HCOH me a o— oH HCOH HCOH bH,OH HOOH bHLOH The investigation of isodialdane, which crystallises in two modi- fications and is inactive, is to be continued. Chemistry. — Prof. H. W. Bakuuts Roozesoom _ presents Dr. W. Rerpers’ Dissertation on ‘ Mixed Crystals of Mercuric Iodide and Bromide” respecting which be makes the following communication. (Read in the meeting of September 30th 1899). This research is a second contribution to our knowledge of the phenomena which may be observed during the solidification of fused mixtures of two substances to mixed crystals and the transformation of the mixed crystals into another modification. Of the many types, which, according to the theoretical develop- ment of the subject given by the speaker, (See Report of the meeting of the Academy of Sept. 24th 1898, p. 134) are possible, one of the simplest is here realised. The meltingpoint line is a continuous curve, showing that only one set of mixed crystals is deposited, the composition of which changes gradually with that of the fused mass. The meltingpoint line, which extends from 236°.5, the melting * | ' ( 147 ) point of Hg Br, to 255°.4, the meltingpoint of Hel,, possesses a minimum at 216°.1 and 59 pCt. (molecular) of Hg Br,. In this minimumpoint the mixed erystals have the same composition as the fused mass. To the right of this point the erystals contain more Hel,, to the left of it more HgBry than the fused mass. The differences are, however, not large; the line of the crystals (lower curve “99,4 ACB) lies close beside the 249 meltingpoint line (upper curve ACB). Below 216° — therefore, mixed crystals of any com- 999 position are capable of exis- tence. ‘hey belong to the rhombic system. At 127° pure Hel, is transformed 169 into red, tetragonal crystals, (point DP). This transition point is ane depressed by admixture of 120 UgBro. Further, it develops into a transition interval, 199 bounded by a line DE for the yellow crystals, which runs from 127° and 0 pCt. Hg Br, to 0° and 33 pCt. Hg Br, and by a line DF for the red erystals which 4g runs from 127° to 0° and 8.6 percent. He Br,. (in 97 molecules). The significance of these two lines is as follows. Be- low a temperature given by the line YE, mixed erystals 236,5 220 200 80 60 g° He br, Mol.9/, Hel, Of a certain concentration must separate red mixed crystals belonging to the line D’, The compositions of the two change as the temperature falls, until, at a sufficiently low tempe- rature, homogeneous red crystals remain. Since the two lines lie somewhat far apart, even when a small ( 148 ) quantity of Hg Brg is present, the interval of temperature through which the transformation takes place is very considerable. The change, further, is subject to great retardation. For this reason the determination of the transition interval was not possible either by the dilatometric or by the thermometric method. By observing the change of colour it was possible to determine the composition at which the red crystals were completely converted into the yellow crystals at a given temperature. The circumstance that yellow mixed erystals containing up to 20 pCt. in molecules of Hg Br, may be converted into the red modification by grinding at the ordinary temperature was here used. The beginning of the change of the red into yellow crystals could not however be observed in this way. In order to do this the erystals which are deposited from mixed solutions at constant tempera- ture were studied. By ailowing mixed crystals to deposit from a sufficient number of solutions, a solution is finally found from which both red and yellow mixed crystals are deposited and which therefore represents the two points of DE and DF which lie on the same temperature line. Theoretically, the nature of the solvent should have no influence on the result. This conclusion was confirmed by the results of experiments with alcohol and acetone as solvents. In spite of the fact that the solubilities of the two mercury salts and their ratio were very different, the same values were found for the coexisting yellow and red crystals. Even by this method, however, it was impossible to determine points on DE and DF below 0°. The direction of the two lines indicates that if HgBr, possesses a transition point, it is probably at a very low temperature. Experiments in this direction gave no indication of a transition down to —83°. It is to be remembered that even at ordinary temperatures, and much more so at higher temperatures, solid Hg Br, and Hgl, diffuse into each other, so that the transition temperature of a finely ground mixture agrees closely with that which would be found for mixed crystals containing the same proportion of Hg Bry. Finally it was possible to show, by means of the known heat of transformation of mercuric iodide, that for moderate admixtures of Hg Brg the course of the lines DE and DF agreed with a formula which RorumunpD has recently given for the case that the concen- trations of the two coexisting phases are known. This is the first case in which it has been possible to verify the laws of dilute solutions in the case of the relationship between two solid solutions. ( 149 ) Chemistry. — ‘On the Enantiotropy of Tin (11). By Dr. Exnst Conen and Dr. C. van Eyxk. (Communicated by Prof. H. W. Bakauts Roozesoom). (Read in the meeting of September 30‘ 1899.) 1. Continuing our researches on grey (stable) and white (meta- stable) tin!) we first attacked the question of the velocity of change of the white into the grey modification. According to our first communication the velocity is zero at + 20° C, the transition point. In the course of our experiments we had received the impression that the change white tin — grey tin, took place more slowly at — 83° than at somewhat higher temperatures. Such a phenomenon recalls the solidification of super-cooled fused substances where the rate of crystallisation increases as the tempe- rature falls below the melting point until a maximum is reached after which it decreases again *). 2. A dilatometer, of 2 cc. capacity, was filled with grey tin which had already repeatedly undergone transformation in both directions. By warming the dilatometer for a few moments to 50° a part of the contents was converted into white tin. The dilatometer was then filled with a solution of pink-salt in alcohol, in order to avoid complications which might arise from crystallisation of the salt at very low temperatures. The dilatometer was then placed successively in different baths at constant temperatures. Since the conversion of white tin into grey tin is accompanied by a considerable increase of volume the rise (per minute) of the liquid in the capillary of the dilatometer is a measure of the velo- city of transformation. It is necessary, of course, to take care that the quantity of white tin undergoing change remains constant during the whole course of the experiments. For this reason the capillary tube of the dilatometer was made very narrow; the conversion of a very small quantity of white tin then gives a sufficient rise. One mm. of the capillary = 0,00028 ce. Taking the specific gravity of white as 7.3, and that of grey tin as 5.8 the transformation of 8 mgrm. of white tin into the grey modification gives a rise of 1 mm. In this way the following results were obtained. ~1) These Proceedings, June 24 1899. 2) Compare Gernrz, Journal de Physique (2) 4. (1885) p. 349. Tammann, Zeitschr. fiir phys. Chemie 23, 326 (1888). Couen, ‘These Proceedings, February 25 1899. ( 150 ) Temperature —85° (Paste of solid carbonic auhydride and alcohol). Time Height of the leve! of the liquid Ah in minutes in the dilatometer (in mm.) At 0 100.2 2.3 1 102.5 2.5 2 105.0 2.5 3 107.5 Mean rise 2.5 4 110.0 2.5 per minute 5 112.5 2.5 6 115.0 2.5 mm. 2.6 8 120.2 2.8 9 123.0 2.7 10 125.7 Temperature —48°. 0 4470 f 5.0 1 249.0 4.5 2 253.5 Mean rise ; 4.5 3 258.0 5.0 per minute 4 263.0 4.0 5 267 .0 4.5 mm 4.0 6 271.0 4.0 8 279.0 Temperature —15° (Cryohydrate of NH, Cl.) 0 232 0.40 3 233.2 0.45 Mean rise 7 235.0 : 0.44 ; 12 237.2 per minute 0.43 15 238.5 0.50 0.4 mm. 24. 243.0 0.33 30 245.0 Temperature — 5° (Cryonydrate of Mg SO,). 0 82 Mean rise 0.07 per minute 1200 167 0.07 mm. Temperature 0°. 0 186 Mean rise 0.03 per minute 1230 234 0.04 m.m. ( 151 ) The curve in the figure is obtained by means of these data, the velocities of transformation being taken as ordinates and the tem- peratures as abscissae. Transitionvelocity —> —80° —70° —60° —50° —40° —30° —20° —10° oe +10° +20° This curve shows precisely the same course as that above mentioned. There is a maximum at about — 48°; this agrees well with the fact that we had received the impression that the change took place more slowly at — 83° than at a somewhat higher temperature. If it is desired to convert common white tin into the grey modi- fication a temperature should therefore be selected for the conversion, lying not far from — 48°. 3. So far our experiments had been made with grey tin received from Prof. Hsevr of Helsingfors. This was Banca tin which had fallen to powder in a tin store in Helsingfors. The question arose whether the transformation was completely mastered, whether it would be possible to convert any piece of white tin completely in- to the grey modification. Our researches in this direction have been crowned with success. We would here express our thanks to Mr. W. Hovy of Amsterdam, who permitted us to make use of one of the so called “evaporators” ( 152 ) in his brewery; this is a reservoir through which a current of brine passes without interruption the temperature of which during our experiments varied between — 7° C. and — 4° C. ‘The result of the experiments is briefly as follows: (The tin employed was part of a block of Banca tin belonging to the collection of the laboratory). a. Quite dry, white tin, in the form of a block, was converted into grey tin at the temperature mentioned. The process takes place slowly and begins at the edges. b. Quite dry white tin, in the form of a block, in contact with traces of powdered grey tin, undergoes change more rapidly. The change begins at the places where the white tin is in contact with the grey tin. c. White tin in the form of a block immersed in a solution of pink salt undergoes more rapid change than the combination Ob. d. White block tin, immersed in a solution of pink salt and also in contact with traces of grey tin, is transformed more rapidly than ec. e. When the white tin is exposed to the low temperature in the form of filings the process takes place much more rapidly than when the tin is in coherent lumps. The velocities of change under the circumstances mentioned under a, b, ¢ and d retain the same order as before. 4. Grey tin, therefore, behaves under all circumstances as if it was infectious. If the change is once started it goes on at higher temperatures (up to 20° C.). Jt is thus necessary in these investi- gations to exercise caution and to take care that traces of grey tin are not imported into tin stores, where their presence might, as it were, give rise to a tin plague. Grey tin and the finely divided white tin formed from it above 20° C. can hardly be fused together to a coherent mass, a part becoming useless owing to the violent oxidation which it undergoes in the finely divided state. 5. We have already converted large quantities of white tin into the grey modification. In order to attain this result quickiy, 500 grams of tin filings were divided between several bottles and some grams of grey tin, which we possessed at the time, were added to the contents of each bottle. The solution of pink salt was also used in the transformation. At —5° C. a hundred grams of grey tin were obtained in this way in eight days. 6. The destruction of the white tin due to the formation of the ( 153 ) grey modification is enormous. One of our tin blocks is entirely fissured and eaten away on the lower side whilst on the upper surface a number of grey protuberances are visible which gradually become greater finally developing into large cracks. We shall shortly report on some physical constants of grey tin and on its erystalline form. We shall be pleased to send a sample of grey tin to any one interested in the matter. Amsterdam, Chemical Laboratory of the University, September 1899. Chemistry. — “On a new kind of Transition Elements (sixth kind).” By Dr. Ernst Conen. (Communicated by Prof. H. W. 3AKHUIS ROOZEBOOM). (Read in the next meeting of September 30th 1899.) 1. The name, sixth kind of transition element, will be applied to elements built up in accordance with the formula : Electrode of a metal 17| Solution of a salt of | Electrode of the metal in the modification @ the metal JZ. M inthe modification 7 (stable modification). (metastable modi- fication). Since, up to the present, no metal was known which, at suitable tempe- S ratures, occurs in two modifications, it was impossible to realise an element of this kind. As Dr. van Eyx and [ have shown!), the metal tin has a transition point at 20° C. Below this temperature the socalled grey tin is the stable form, above it the white. Since the white modification may Z g Z Z Z Z Y A g Z g YZ Y Z Z y 4 yj y g g G Z y be considerably supercooled we may put together, below 20° C., an ele- ment (see Fig.) of the form 1) Report of the session of June 24th, 1899, p. 36, and of this session, p. 149. ( 154 ) Electrode of grey | Solution of a tin | Electrode of white tin. salt. tin. In the figure, @ and > are glass tubes, 7 cm. long and 14 em. wide united by the wide middle-piece c. The grey modification of the tin is placed in a, the white in 0. In contact with the powder in each tube is a platinum wire, 7 and 7., Which is fused into a glass tube and bent into a ring at its lower end. An electrode made in this way has many advantages in practice !). An aqueous solution of a tin salt is poured into a, 6 and e, and a and 6 are closed with corks, 4; and %:, which allow the wires 7 and ro to pass. The whole element thus formed may be suspended in a thermostat by means of the glass rod g which is fused to it. 2. The theory of this element is easily given and offers, as will appear, many points of interest. If an electrode of grey tin is placed in a dilute solution of a tin salt, in which the tin ions have an osmotic pressure p,, the poten- tial difference between the electrode and the solution at the tem- perature T is nN Ep Pl where » is the valency of the tin, «, the number of coulombs attached to 1 gramion, F, the electrolytic solution tension of the grey tin at the temperature T and R& the gas constant. If an electrode of white tin is now placed in the same solution we obtain RL Pw EL, = log. — . n €o Pi The E.M.F. of the transition element so obtained is then repre- sented by the equation ae 1k i 12 0.0061983 if E= h-hh, = log. ’ Volt = logyo ——- Volts. . (1) n Eo » n Py 0,0001983 7 . Since —_————. is a constant at a given temperature we see n 1) See Ricnarps and Lewis, Zeitschr. fiir phys. Chemie, Bd. 28, S. 1 (1899). ( 155 ) from this that the E.M.¥. of the element is simply a function of the electrolytic solution tensions of the two modifications of tin. The employment of the element described as a transition element depends on the fact that at the transition temperature the two modi- fications become identical, the grey modification being transformed into the white. In equation (I), P, and Fy are then equal and Z = 0, In order to discover the transition poimt of the change grey tin = white tin it is therefore only necessary to find the temperature at which E=0, The application of this method is to be found in the com- munication which Dr. vAN Eyxk and I made some time ago on the Enantiotropy of tin !). We can now go a step further and investigate the electrolytic solu- tion tensions. We require the equations RE 2) Pp RT P, EE, = —— log. — and EL, =--—— log. —— . n Eo Py n &o Pi By placing an electrode of grey or of white tin in a dilute solution of a tin salt and combining it with a normal (Hg—-HgCl—!/,,N . KCl) electrode, /, and Ey may be separately determined. If the dissociation of the tin solution is known, all the quantities required to calculate P, and Fy are then known. From the equations we obtain n Ey n By 0.0001983 7" 0.00019837" Ti pies LO andite Eig ==" lO 4, In the first place an element was prepared with a sample of Sue ; ; bbe Mee cE, grey tin from Prof. Hyetr of Helsingfors and the ratio - a deter- : sing g mined at different temperatures, Recently we have succeeded in converting ordinary Banca tin into the grey modification in any desired quantity *). The measure- ments here described are to be repeated with this material which is particularly pure and the results together with the details of manipulation will be described in a later communication. 1) See note 1 on pag. 149. 2) See pag. 152, ) w ‘Temperature. Ratio Py ae 1,067 10° 1,043 lay 1,017 20° 1,000 The ratio is calculated by means of the equation Pp an E. fat 1.9 20001988 L ; Po 5. Below the transition temperature the modification which is metastable (the white) should have a greater solution tension than the grey (Pv > P,). From this it follows that grey tin must be precipitated from tin solutions below 20° C. when white tin is brought in contact with them, just as copper is precipitated from a copper solution into which a zine rod, for example, is dipped. The metal with the greater solution tension goes into solution whilst that with the smaller is precipitated. 6. In our researches on the Enantiotropy of tin!) it was found that the conversion of white tin into the grey modification is highly favoured by the presence of traces of grey tin. What has just been said about the solution tension of the two modifications explains the fact that the presence of a solution of a tin salt is also very favorable to the conversion of white tin into grey tin. Below 20° C. grey tin is always precipitated from the solution of a tin salt by white tin; this process takes place, by analogy with what we know of other metals, very fast. In contrast to what so often happens with salt solutions, supersaturation does not occur. If traces of grey tin are once present, they have a further acce- lerating action on the process. (According to experiment.) 7. We may now deduce another relationship which must exist between the displacement of the transition point of the reaction grey tin = white tin with the external pressure exerted on the system and the tempera- ture coefficients of our transition element. For the grey tin electrode we have 1) See note on pag. 149. ( 157 ) Te 4 ee (1) gers CRS, Pik ees Here £, is the difference of potential, at the absolute temperature T, between the grey tin and tke tin solution in which it is im- mersed, 7, 18 the heat of ionisation of the grey tin, » the valency, and ¢, = 96540 Coulombs. For the white modification we have: a L Ll Ey ol Se UIC Ni cpt 23 TR Ne sen (2) NE dl in which r represents the heat of transition. From (1) and (2) we obtain, since £, = Fy at the transition temperature, 4 d Ey bora ay ae pits i ee ee N Eo ayy n Ey dT of T hes = (3 inert sooo gm ak agp) * Now we know that _, aD r) Seep RE RG NE 4s cae) diy. Wai2Vg where T is the absolute transition temperature, D the external pressure, 7; the quantity of heat which is evolved when 1 ke. of white tin is converted into the grey modification, that is the heat of transition for 1 kg., and V, and V, are the volumes of 1 kg. of each modification in cubic metres. Since r in equation (3) relates to one gram atomic weight and 7 in (4) to 1 kilogram, we have n= =, where 4 is the atomic weight of the metal forming the electrode. From (3) and (4) 7dE, dE, ap 006 Var 7a, ge er ames (5) I ee ae The quantity to the right of the sign of equality is now expressed in Volt-Coulombs, or ergs < 107. If we wish to ascertain the change of the transition point produced by a change of pressure of 1 atmo- sphere, we may write (5) as follows: ( 158 ) dE, dEy dD 8 on war df 101.4 A (Vy—Vy) or: : iT’ 101.4'A(Vn— Vz A VeVi \ D = 000105 — dD dE, dEy qe. en A a ry A dT dl dT di The advantage of this equation, which so far as I am aware is deduced here for the first time, is, from the practical point of view, that it is possible to determine the displacement of the trans- ition temperature by external pressure by means of electrical mea- surements, if the specific gravities of the two modifications forming the electrodes have been determined. For the electrical determinations of the temperature coefficients of the two electrodes of the transition element in the neighbourhood of the transition point quite small quantities of the electrode material (1 or 2 grams) suffice, whilst for calorimetric determinations, which in the nature of things are less accurate, considerable quantities are required. The result of the measurements will be communicated as soon as the specific gravity of the grey tin has been determined in a com- pletely satisfactory way. Amsterdam, Chem. Lab. of the University, September 1899. Chemistry. — Prof. H. W. Baxkuuis Roozesoom in presenting the dissertation of Dr. D. J. Hisstnk: “On mixed Crystals of Sodium nitrate with Potassium nitrate and of Sodium nitrate with Silver nitrate’, makes the following communication with respect to it. This research is a third contribution to our knowledge of the phenomena observed in the solidification of fused mixtures of two substances which form mixed crystals and in the transformation of the mixed erystals into another modification. With respect to the system KNO; + Na NOs the fact is mentioned that mixed erystals are formed on solidification ; the limits within which these can exist are, however, so narrow that it did not appear to be worth while to investigate the exact connection between the phenomena. The solidification of the system NaNO, + Ag NO; belongs to a type of which no example was known. The meltingpoint line rises continually from the meltingpoint of AgNO, (208,°6) to that of NaNO; (308°). It consists, however, of two branches, AC and CB, - ( 159 ) which join each other at an angle at 217,°2. Although all the mixed erystals are rhembohedral, the series of mixtures is discontinuous ; at 217°2 there is a sudden transition from mixed erystals with 38 °/, (in molecules) NaNO, (/) to those with 26 °/5 (DP). The fused mass which is in equilibrium with both contains 19.5 °/, (in mole- cules) of Na NO, (€). On cooling the following transformation takes place at 217°, Fused mass C + crystals 2 crystals D. 140 120 100 80 60 40 20 4y NO, Mol.°|, This temperature possesses all the characteristics of a transition temperature. The points on the lines EB and 4D represent the compositions of the mixed crystals which are deposited from a liquid having the composition represented by points on the lines CB and AC corresponding to the same tem- perature. Below AD a series of homo- geneous mixed crystals containing from 0 to 26°/, Na NOs exists, and below £B a similar series from 38—100°/, Na NOs. The mixed erystals containing 26 and 38°/) which coexist at 217°, gradually change in composition as the temperature falls, in such a way that the limits between which no mixture exists become more widely separated, so that at 138° they are 4.2 and about 50 %/,, NaNO, (H and J). The region within which homogeneous mixed crystals exist, becomes smaller and smaller. Below 160° a change occurs in the series which is rich in silver, in consequence of which the rhombohedral crystals are con- verted into rhombie crystals. With pure silver nitrate this takes 12 Proceedings Royal Acad. Amsterdam. Vol. I. ( 160 ) place at 160°, the addition of sodium nitrate depresses this tem- perature. The limiting mixed crystal of the series which is rich in silver undergoes the change at 138°. Below 138° only rhombic crystals, containing much silver, and rhombohedral crystals, containing much sodium, are capable of existence. No transformation has been observed in the latter down to — 50°. The limits of composition of the two kinds of crystals become more and more restricted as the temperature falls below 138°, so that at 15° they are 0—1,6"/, (in molecules) Na NOs and 64.4— 100 °/, Na NOs. The compositions of the coexisting limiting crystals were determined by allowing them to deposit beside each other from suitable solutions. The transformation of the rhombohedral into rhombic crystals on the lines /H and £G was determined by means of an air dilatometer. Chemistry. — By Prof. H. W. Baknuis Roozesoom: * The Nature of inactive Carvoxime.” In continuation of the investigations of Mr. ADRIANI on the phenomena of fusion and solidification of mixtures of optical anti- podes, carvoxime has been examined. Samples of the d- and /-oximes were prepared for us through the kindness of Prof. GoLDscHMIDT of Heidelberg. Up to the present time the inactive carvoxime has been regarded as a racemic compound. This view rested on the facts that the melting point is higher than that of the active substances and that the density is greater (1.126 against 1.108). The investigation of the melting and solidifying points gave the following results. Composition of the | Commence- End of ment of fused mass. solidification. | solidification. 100%/, d of Z 72° 72° 99 » y 72°4 —- 98S y 73°0 — 95 ” ” 75°4 73° 90 v y 79°0 15° 80 v 7 | 84°6 80° Ti Ni ae Si, 86°4 820 TO uv 88°2 85° 60 v 90°4 — 507 ow } 91°4 91°.4 ( 1619 The results of these determinations are reproduced in the accom- panying figure. The line ACB represents the beginning, ADB the end of the solidification. To begin with, it is to be remarked that, setting out from the end points, the first line at once rises on addition of the active compound of opposite sign. There is therefore only one meltingpoint line and, consequently, the solid mass must consist of mixed erystals, and the inactive substance (50 pCt. d of 2) is not a racemic compound but a pseudo- racemic mixed crystal. It were however conceivable that from 4 or B a small fall occurs, which escapes observation, because the rise begins at a very smal! concentration of the second oxime. If this were the case the inactive oxime would really bea racemic compound. The matter can, however, be readily decided. If it is a racemic compound the solidification of ad/ mixtures, from 0 to 50 pCt. dor /, must terminate at the temperature of the eutectic point, which exists where the short falling lines from A and B meet the line of the racemic compound. In our case therefore the solidi- fication of all mixtures between Q and 50 pCt. would have ter- minated just below 72°. The final solidifying points, which were susceptible of very accurate observation, lie however on the line ADB and change continuously with the concentration. For some concentrations the end point was determined by obser- ving the course of the cooling as a function of the time in a bath at constant temperature. By this means the time, and therefore also the temperature, at which the solidification is complete may , be observed with great accuracy. The curve ADB confirms the view that mixed crystals are formed on solidification at all concentrations. Thirdly it is supported by the analysis of crystals which were deposited from a fused mixture containing 20 pCt. of /-oxime. If the line ACB were the melting point line of a racemic compound, this compound would be deposited from the fused mass; if mixed 12* 95° 90° ( 162 ) crystals are formed they must have the composition given by the point on the line 1B, which lies on the horizontal line drawn through the point on CB which corresponds to 20 pCt. of /-oxime. The solid mass, weighing 0.69 gram, which was deposited from 7 grams of liquid, containing 21.7 pCt. of oxime, was found to contain 32 pCt. The composition of the solid was determined by polarisation and corrected for the adhering mother liquor. The quantity of the latter was determined by adding some CH Br, and determining the bromine in the liquid and in the drained crystals. The result agrees very well with the position of the line 6 determined from the final solidification points. Not only do we obtain thus a continuous series of mixed crystals on solidification, but we have here the first example of such a series with a maximum meltingpoint, which naturally lies at 50 pCt. In agreement with the theory the composition of the fused mass and of the mixed crystals is the same at this point and the interval of solidification therefore vanishes. The opinion, which I expressed, that even in the case of mixed erystals of optical isomers the equality of melting points, looked for by Kuipprnc and Pops, does not necessarily exist, is confirmed by this example. It is worthy of attention that the rule, that racemic compounds with a higher density than their active components also have a higher meltingpoint, appears to be applicable also to mixed crystals ; always providing that the difference in density observed at the ordinary temperature still exists near the melting points. Probably this will remain, at least qualitatively, unchanged. The possibility still exists that carvoxime forms mixed crystals on solidification, which change at lower temperatures wholly or partially into a racemic compound. Between 10° and 90° however no indication of such a change could be found by means of the dilatometer with an inactive mixture. That at jower temperatures the inactive oxime, obtained from solutions for example, is a mixed crystal and not a compound is supported by the great crystallographic similarity between the in- active and active crystals which Bryer has observed (Zeits. Krystall. 18, 296, 1890). The density rule of Rerarrs would, therefore, not hold good for this kind of mixed crystals. ( 163 ) Chemistry. — “On Isomorphous Compounds of Gold and Mercury.” By Prof. Tu. H. BEenrens. In his Manual of Microchemical Analysis the auther has pointed to analogies between thiocyanates of gold and mercury. Renewed investigation of this subject has shown, that the iso- morphism of these double thiocyanates cannot be fully established by means of compound crystals. Halogen compounds have then been tried, and from these complete series of compound crystals have been obtained. They were prepared by adding to mixed solutions of the chlorides and bromides of gold and mercury chlorides or bromides of thallium, caesium and rubidium. Thallous compounds act promptly; the compound crystals are interspersed with flakes of trichloride or tribromide of thallium. The action of caesium and rubidium compounds is slower and less energetic. It can be hastened and furthered by adding about one tenth part of alcohol. This takes up one third of the halogen, that was combined with gold (shown by a change of colour in the solution of bromides) while gold dichlo- ride or — dibromide is fixed in the compound crystals along with dichloride or dibromide of mercury. If no alcohol is added the halogen, split off from the gold trihaloid must form trihaloid of caesium or rubidium, which is also readily attacked by hydrolysis. Finally it may be mentioned, that the compound crystals of bromides will be found useful in testing for gold. With caesium the solubility is small, and the yellow colour of the crystals is seen without difficulty with a proportion of one part of gold to fifty parts of mercury. Physics. — Prof. J. D. van DER WAALS presents on behalf of Dr. G. Bakker of Schiedam a paper on: “A remark on the Molecular Potential Function of Prof. VAN DER WAALS.” In his ,Thermodynamische Theorie der Capillariteit in de onder- stelling van continue dichtheidsverandering” Prof. vAN DER WAALS finds for the potential of two material points at a distance r the expression r a Capek r in which C, f and 4 represent the constants. ( 164 ) Some time later!) Prof. van DER WAALS pointed out a remark- able property of that function. He found that if a coefficient depending on the radius, is left out of account, in consequence of this function the potential of a homogeneous sphere for an exterior point is determined by the distance between the point and the centre of the sphere in the same way as if the whole mass were concentrated in the centre. On account of the great importance, practical as well as theore- tical, of such a funetion for a theory of gases and liquids, which assumes spherical molecules (by which the potential energy might be determined in a simple way by the configuration of the centres of the molecules), I examined the question whether there are more potential functions, which possess this property. As a solution I found the general function: tO ee in which A and B are arbitrary positive and negative constants. For a spherical shell the coefficient depends on the radius in the following manner: eg Rh —e-gR 2q R- If however, we restrict ourselves to attractive forces, which decrease according to the distance, the most general function is that of VAN DER WAALS, Viz: or p(r) = C— fe $ If for this potential function a spherical (homogeneous) mass assumes this property, it will also be the case for a spherical shell and vice versa. Let & be the radius yi of a spherical shell which is thought infinitely thin, P the AA point on which the P sheli acts, dk the thickness and MZ the centre of the shell. Let us imagine a cone with an infini- Fig. 1. tely small aperture 1) See vZeitschrift fiir physikalische Chemie”, XIII, 4, Seite 720, 1894. _ ( 165 ) do, of which M is the vertex, then this cone will cut from the shell a volume #?dR<’w. If vg is the density, the mass of the element in 4 is: &@dkdwg. If ~(r) represents the form of the potential function, the potential energy of a unity of mass in P in conse- quence of the element in A is: A? dRkdog p(p), p representing the distance between A and P. If we turn the figure round MP as axis, the element in A describes an annular space, so that fro= 2 sinO dO; O representing “AMP. In consequence of the annular space the potential energy in P is: 20 Rd sin O db 0 p(p) = —2aRdRdcsO og (p) . Now p?= R? 4+ r? — 2 Rreos 6, in which r= MP, so 2pdp=—2RrdcosO. The expression for the potential energy becomes therefore : 2 a0 RdkR ae dp p (p) ve or because 4 R* dk g represents the mass of the shell: 1M pee PP)® « The integration over the whole of the shell gives: r+h 1 M 2 pe) PP)? - r—R If F(A) represents the before mentioned coefficient and F(R) a function of & which is also to be determined, we may write: r+-h 1 M Pp (p) dp =F(R) Mp) + F(R) M , 2 ine r—R If we leave an absolute constant out of account, this equation furnishes the potential function, belonging to a force acting in the required manner. Let us put: ( 166 ) r+ Rh Pep (p)dp=2RrF (Rk) g(r) +2RrF(R). . . (a) r—R If we differentiate this identity twice with respect to r and also twice with respect to /, and put f rp(r)dr=wywi(r), we get: w" (r+ R) — y" (r — R) = 4 RE (R) g(r) +2 Rr F(R) gp" (r) and wrt Rw r—R=4re@F(R) +2hre MM RH+ 4+ 4rJ]"(R)+2RrF"(R). The left side members of these equations are the same, so also 2 RE(R)@' (r) + Rr F(R) g" (7) = 2 7r g(r) F(R) + + Rr p (7) BY (R) $27 F(R) + Ker F(R) or 2 yr) + ret) _2F(R)+RE(R) | 1 2P (A+R) ro) - RF (2) 9 (7) RE(R) R and r not being dependent on each other, we get separately 2F'(R) + RF" (R) een =C), in which C) isan absolute constant RE(R) 2F'(R RE"(R rhe ar ( NG, also absolutely constant RE(R) A aaa el Me LaN I © , rp (r) pr) The solution of equation 3 will furnish the general form for the required potential function. If we write r= and g(r)=y, the last equation becomes ay 2 dy ~ — —— y=, anes Sr etaCwnr Pe (4) dx? @ dr or ren di v CE iy AP Gh RO dx* dx or ( 167 ) This equation has, according to C, being positive or negative, the solutions : (5 — c x c CU nrg oy Vici ae Ver Ail or OF ry + a v= A, sin (w Y-C, + @) 1 in which A, &, 4; and «& are arbitrary constants. The potential function becomes therefore: 1G ot tr pr) ; C, (9) or A, sin (r Y-C C. ore 1 sin (rT Y-C, + @) _& (6) 7: Cy {f we put C;= 9° in the first case and ©, = — q? in the second case, the potential functions become : ! Heme eee Be Os i CON) a a Cui Moma eh (GE) r q or A, st y+ @ G Pp (r) —— 1 sin (gr = ‘) — <2 (6a) 2 , q % If we restrict ourselves to functions which relate to forces as they occur in nature, the second potential function must be excluded, and according to an above mentioned remark, the most general expression becomes: (ONO) Na aes rE 6: 1 90 Be dom “Ge (1) The factor F (2) is determined by equation 1. This equation be- comes identical with equation 4, if we put C,=0. The general so- lution becomes therefore: F(R) = ———.—__ . ... . . . (7) ( 168 ) According to equation (2) the following equation holds good for function F(R): 2F'(R) 4+ RF" (R) = C,( Met” + Ne ) 2 le We find easily : ry Us qh —gR RF(R)= = (ae 4 Ne M\LERLD. se" (3) ? in which # and D represent constants. If in equation a we substitute the expressions we have found, for g(r), F(R) and F(R), we find the relations which must exist between the constants. We shall easily find: 1 M=— ee q 29 Therefore Ae LE Be” (ey g (*) = ——+— — io so osc .o (@) r q and gk — qk i (eye ee AL) 2gh The potential. for a spherical shell in point P (see fig. 1), becomes therefore !) : QR ee gale 2) ee NRE e e ) R — WV MF (R) g(r) = M 2 gh z If g is the density, then 42 R?dRg=M. For the whole sphere we get therefore for the potential in an outside point: R 5% Ae aos Be? a dno pO) {FO Rah=4ng— R( ee *\iR= qr 0 Ap are Ree ae 1 1 ee = ong} (n=) eo + (K+) ei qr CPS q q 1) We put the constant of the potential function = 0, ('169.) 1 or, if we substitute 4 for —: q Cam x Bex R pee Be im —nert Se (RAED ea at ; é =F Starting from the function (7) = ah eer : (Thermodynami- sche Theorie der Kapillar. Zeitschrift fiir phys. Chem. XIII, 4, 1894 p. 721) Prof. van per WAALS finds: PEL Sg ois A | P=— 2xnfok— p(B Aer + (R+ dye 4h ; The coefficient is the same as in the more general form of the potential re If we take the more general expression Ae™ amen Ber g oof ae aly, and A — f , we get the function g(r) = of VAN DER WAALS. The theory of capillarity requires forces, which decrease with the distance and are attractive. The latter condition furnishes: — '(r) negative or ~'(r) positive. We have: giry=— ae are + —_____ ae for all positive values of ,. If we take r=A, we get: 2A SEZ BE 0) é from which follows that A must be negative. Put A == —/, in which / represents a positive value, the last inequality but one becomes : -rA14 F< mF (E-1) (170 ) or 1 1 re Tie Ee ae ae r 2 POSH For always iereasing values of r, the left hand member tends to zero and the coefficient of 2B becomes infinite. Therefore (sym- bolically) : —0< BXow So B cannot be negative. The former condition furnishes: d g' (r) 0 dr —2fe *+12Ber fe~x+ Bex fe x+ Bex —fe *1Ber a ae oo : 2 -< 0 7? Ar her hr or BY LOA er cf Oa ems (A is replaced by — /). If * is always more increased, the left hand member becomes infinite, whereas the right hand member decreases infinitely. Therefore symbolically BX+e2 B mtd) = — e-y + a er aiey Cr-. q So = tak Wa < e~ g(h+r) 4 na eq(h+ r) 1 ual C(k + r)? + 2 Rr q q 2 4. abt e—1k —7r) — z Baal (er) oR —r) | 2 ; : 2 The expression must now depend on r. It is easy to see that we have only to take A= je? and B=— fei. to get (f= con: stant): v— M Cre a 5 ; f . = —e- 7 — J gry Tae —e-7 4- 2°C Rr! = Mm. G 2 Rr ( q q q q j in which we have also fulfilled the second condition. The potential function becomes therefore: —9r eq — fe—vk +C. 7 ep (r) = fev d Considered superficially we now get in contradiction with the theorem of Lapiace, which states that the law of Newron is the only law which fulfils the condition, that the spherical shell exer- cises no force on a point inside it. In reality this theorem includes more. The function of forces must namely keep this property without change of the constant, whatever the radius of aspherical shell may be. However in the case discussed by us the radius of the shell is given and in the potential we have therefore introduced constants depending on the radius of the shell. As solution of equation (4) we found two integrals. If we had substituted function (6a) in equation a@ and if, in the same way as before, we had sought the conditions which the different coef- ficients must fulfil, we should have found that C=0 and further F(R) = sing R gk ( 175 ) The potential of a spherical shell in point P becomes therefore : sing RA, sin (gr + @) M aye gk r ) ' A, sin(gr +@) . ; : Though the function set NE SE ig OR nO importance for the wT theory of the molecular forces, it has nevertheless another remarkable physical signification. By twice differentiating with respect to 2, we shall easily find: ap Ajsin(gr-+a@) 3 4,sin(qgr+e@)a? 3A, ¢ cos(qr+a)x? =a) = = 3 —- 5 ¥ F722 ni i 7 ie da* ; , 7? , A, gcos(qgr + @) A, q? sin (qr + @) 2? 1 x) ‘ PEER ues r r A ep Ep : In the same way we find for AG and rs corresponding expres- ay~ az sions. By adding these equations, we get: — Th Pp. . . . (11) ts A, q® sin (qr + @) Cp ae 7 As is well known this differential equation is of great importance in the theory of the conduction of heat. The function found is an extension of the caloric potential of Marnrev. ; , 5 : Ae-v + Bey If we had deduced for the first found function ~ (r) =~" — ee 5 the second differential coefficient according to x, we should have found : dp AGH STE ie 3 g( Ae-7"— Bel) x? i 3 (A e—9" + Bet) x? da? 7 r Pr me! (Ae—a" — Bes’) 4 g? (Ae—a + Bes) a? 2 2 r~ 7? If we calculate in the same way the corresponding expressions for dp Pp : we —, and —-, we find by putting the three quantities together: ade ) In putting g=0 we refind the potential which we should have found according to the law of attraction of Newzon. ales Proceedings Royal Acad. Amsterdam, Vol, LI. (176 ) > Ae + Ber VE aa ere — i ) aaee ie eee) ; 1 1 ; In the particular case that A = —— and B=—., the relation 29 2q between the two equations (11) and (12) is evident. The function Ae~vr + Ber ev — e— : 9 (r) = — Paee becomes: Sees If we substitute ¢Y—1 2 qr for g, the latter expression becomes: ey'V ee e—-V'V- 1 sin qr 2gri/—1 © ior This function is a special case of the more general A, sin(qr + @) g (r) = ——___—_.. 4, => — and a@=0. Tr qY By substituting in equation (12) ¢V—1 for g, we get equation (11). If y= 9 the two equations yield the well known equation: Vv? ——a ie The funetions g (r) => —————_- and g(r) = - 7 us Ae-v + Ber A, sin (gr + @) are solutions of two different partial differential equations of the 2nd order, but we have seen that they are also common solutions of the same probler. We might also have deduced the partial differential equation (12) in the following way: Ae—# A gr 3 8 == (1—+! eee +..)= , r m2 m3 iy: { i A yr A q Sp? =< ag m2 om aie and Bev B Th a q? re = a a Le a +. — 7 7 Tt wd ( i } So: A B gr BA ge rd is eee ee Sane To by ae) Acv+ Ber A+B yp r If we apply to the two members of this equation the operation 7°, we find Ae-@? Bev B yt | at [A$ B= A + mt 2 A B) q* p (A + B)q +| , Ae—a + Ber == q~ -_O Fs In the same way equation (11) may also be deduced. On the other hand, if 2? + y?+ 22 = °, it is possible to show that the solutions of the differential equations 7? y = + 9’ g, give exactly those functions that possess the property found by Prof. van . . Cele . DER WaaLs for the potential function — /——., We have, viz: r dg dp adr Pp Pp eS) dp @r dx dr du de® ~ di? \dx dr da and because r? = 2? + 9? + 2; dy r da 1 {hed da | r dae rp therefore Pp Pp x dg (1 x? dx? dr® 72 Fe h 78. ) 2 2 If we deduce the expressions for ze and at in the same way dy” dz” 4 we find by additien: dp 2 dp _ 0 dr? Pawn 4 ox The differential equations V* g = + g’?g may therefore be written in the following way: -{- == ESM Giets och ol Sen (13) ( 178 ) We get these equations, when for C, we substitute -+- 4? and —? respectively in equation (4) and when we put C;=0, and this proves that the solutions of (13) fulfil the condition in question. In a further paper I hope to prove the two following theorems : I. If in a region of space g and v are functions of x, y and <, and v satisfies the three following conditions: Ist » and its differentia! coefficients with respect to «, y and z are everywhere continuous 5 2ud with the exception of some points or surfaces in this space Pv dy dv 2 4 J B dx® ' dy? Wie te gee (A+ Bo; 9 4 dv dv 5 dv 3 the products av, yer, cv, 2® > y* — en 2 are nowhere du du: dz infinite ; then v is the potential with respect to the point #, y and z of an agens, the density of which is gy, while the potential function is expressed by : Ae-v + Ber g (1) = — aes F3 Il. If the same conditions as in 10ld for g and v with this IWS Soe an ndit I hold for g and v with tl modification that — g® is substituted for g? and Asina@ for A+ B; then v is the potential with respect to point #, y and < of an agens, the density of which is g, while the potential function is expressed by A sin (qr + @) gaa. Hydrography. — Tidal Constants in the Lampong- and Sabang- bay, Sumatra. By Dr. J. P. VAN DER STOK. I. Telok Betong. a. From April 23,1897 to April 22,1898 tidal observations have been made in the Lampong-bay on the road of Telok Betong, sit- uated in 5° 27' Lat. 8. and 105° 16’ Long. E. at the 6 hours of 8 and 10 a. m., noon 2, 4 and 6 p. m. As in the eastern parts of Sunda-strait the normal (i. e. oceanic) tides of the Indian Ocean must show a more or less gradual trans- ition to the peculiar tidal régime of the Java-sea, the cotidal lines run here very near to each other, by which reason two places, situated at no great distance may show very different tidal constants. For such stations a simple interpolation with respect to intensity or time of occurrence is not allowed, and the determination of the characterising constants is of great importance because it is the only way of obtaining exact data concerning the manner in which tidal waves progress and mutually interfere. The observations have been made at the request of Major J. J. A. Munrer of the Topographical Service, who wanted an exact determination of the general water-level in the bay in behalf of the Topographical Survey of South-Sumatra. b. The constants of the partial tides M1/,, 0 and N have been computed in the ordinary way by arrangement of the records according to the different periods; the constants of the other tides Sj, Sy, 4), K,, Sa, Ssa and the value of the general mean W have been cal- culated by means of the monthly means. The problem, therefore, consisted in computing 15 quantities from 73 equations in the simplest and most advantageous manner; it would have been a tedious work to apply directly to this problem the method of the l. sq. and the results would not have been more accurate than by using the following abbreviated method. c. The constants of the tides S, and S;, as also the general mean value W, are deduced from the 6 equations given by the hourly means taken over the whole year. These equations are for the given hours: (1) Sam. = W-+ 8S, cos (300°—C}) + Sp cos (240° — C,) (2) 10 ,, = W-+S, cos (330°—C,) + S, cos (300°—C,) (3) noon = W-+ 8S, cos C, -+- S3 cos Cy (4) 2p.m.= W +S, cos (30° — C,) + 8, cos (60° — Cy) (1) (5) A, = W-+S, cos (60° — C,) + S, cos (120°—C,) (6) 6 , = W-LS, cos (90° — C)) + Sy cos (180°—G,) Mean : W + 0.644 S, cos (15°—C)). } By combination of (1) with (4), (2) with (5) and (3) with (6) S, is eliminated, the result is: ) = 220.2 o.M. = 28, sin (75° — C)) sin 45° + 2W (2) + (5) = 219.1 ,, = 2S, sin (105°—C)) sin 45° + 2W ) = 218.7 ,, = 28, sin (135°—C)) sin 45° + 2W ( 180 ) These three equations are satisfied by the values : W=111.17eM., S,=2.70cM., C,= 207°8' Substituting these values in equations (1), we find, on putting: Geen eS P:S— TRO (1) 0.5 X + 0.866 Y = 12.731 cM. (2) —0.5 X + 0.866 Y = 10.801 ,, (3) 2k = 1.634 ,, (4) 0.5 X + 0.866 Y= 12.731 ,, (5) 0.5 X + 0.866 Y = 10.802 ,, (6) x = 1.636 ,, and from these (1) + (2) + (4) 4 (5) = 3.464 Y = 47.065; Y= 13.587 eM. Substituting this value of Y in (1) (2), (4) and (5) we find: Ke=17930 eM. and in (3) and (6) X = 1.634 cM. The difference is small, but it points to a systematic error, e. g. in the assumption that the diurnal variation may be represented by only two periodic terms instead of by three or more, owing to the somewhat aperiodic description of the influence of land- and seabreezes. As a final value we take: 1.930 X 4 -+ 1.634 X 2 DC ~ —— Sa 21cm. 6 S, = 13.71 eM. Cy = 82°20’. d. With a view of calculating the constants of the tides K, and P the following sums and differences of the monthly means are used. a b ¢ (3)+(10) (12)+(2) (4)4(6) ab = ae April 210.1 212.6 215.6 — 2.5 Deo May 155.8 218.2 237.5 — 62.4 —81.7 June 184.5 247.9 269.4 —6§3.4 —84.9 July 198.8 263.6 283.9 —64.8 =e! August 220.2 290.9 294.8 = Que —74.6 (181) a b c (8)-+(10) (12-4) (+62) ab ae September 218.4 278.5 252.3 —60.1 — 33.9 October 203.4 234.7 196.6 —31.3 6.8 November 206.4 212.0 170.4 — 5.6 36.0 December 197.9 182.6 161.6 15.3 36.3 January 210.1 199.2 201.8 10.9 8.3 February 189.2 207.5 217.0 —18.3 —27.8 March 179.9 217.8 231.8 —37.9 —51.9 April 188.8 245.3 231.2 —56.5 —42.4 (—42.1) (—82.6) The differences (2—b) and (a—c) are independent of W, the general mean, of the annual and semi-annual variations and of disturbing influences as far as they may be considered to be the same at the different hours of the day or i. 0. w. jast for some days. The influence of S,; and S, is the same for every month, so that the periodic variation, which is evident in the differences, is caused exclusively by the tides Ay, P and 4g. The figures in brackets —42.1 and —32.6 are obtained by combining the two values for the month of April in such a way that to each value is given a weight equal to the number of days of observation resp. 8 and 22. The series is considered therefore to commence with May Ist, a fact which must be taken into consideration in applying the astro- nomical argument. Representing the single-periodic variation of the differences (a—b) and (a—c) by the expression: a—b= Acos 30° 2 +- B sin 30° « } (2) a — ¢ = A, cos 80° «+ B, sin30° x J i we find by the method of the I. sq.: A = — 26.58 B= — 28.68 A, = — 51.88 By = — 25.62 The influence of- the tides A,, P en Ay in the monthly mean values may be represented by the expressions: (1) Ky Rgcos (30° x +-315° — Cy) + PRy cos (30° # + 75° + G) \ (2) Ky, Rg cos (30° x 4-345° — Cx) + PRg cos (30° « + 45° + C,) (8) K; Ro cos (30° x 4. 15° — C,) + PR, cos (30° x + 15°+ 6) | (4) Ki; Ry cos (80° 2+ 45°— Cy) + PR, cos (30° x — 15° + C,) | ©) (5) Ky, Ry cos (30° « + 75° — Cy) 4+ Pha cos (30° « — 45° + G) (6) K, Ry cos (30° # +105° — C,) + PR, cos (30° x — 75° + ©) Mean. 0.644 K, Ry cos (30° x + 30°—C,) + 0.644 PRe cos (30°x + C,) ( 182 ) (1)* Ky Rz,cos (60° « — 90° — Cox) (2) Ky Rs cos (60° « — 30° — Cz) (35) Ky Rs cos (60° a + 30° — Coz) (4) (4) Ky Me cos(O0s a} 90° — Coin irs eee (5) Ky Rs cos (60° a+-150° — Coz) (6) Kg Rez cos (60° +-210° — Cox) From the formulae (3) we deduce: a—b=p}K, cos Cy — P cos (C, + 30°) } sin SO mat — p} Ky sin C, + P sin (C, + 30°)} cos S0cet a — ¢== q} Ky cos (30° — Cy) — P cos C,} sin 30° ¢ + 7} Ky sin (30° — C,) — P sin C,} cos 30° t in which p=4X 0.966 X 0.5 X Ry q= 4X 0.966 X 0.866 X R, and #, denotes the coéfficient of decrease, due to the fact that average values are used for a period of one month. By equating the corresponding coéfiicients of these equations and formulae (2) and putting: Yo phevsin Ge X = Kj cos Cy Y= P sin G XP cos Cp We find: A/p = — Y— X'sin 30° — Y' cos 30° Blp= X— X'cos30° + Y' sin 30° Aj/q= Xsin30° — Y cos 30° — Y' Byq= Xcos30° 4+ Y sin 30° — X' which are satisfied by the values: Yeas Se dae N X= — 11.14 eM. Y= = 0.48 > a 4.21 » K, = 16.54 eM. a 4.24 eM. Cp S1022 19 Cp = 353°30' » In order to obtain a serviceable combination for the calculation of the constants of the tide A, the values are formed. a ae Se or tee ed ( 183 ) In these values again the annual variations and the aperiodic disturbances are eliminated. (a +b — 2c) May —101.0 eM. June —106.4. » July —105.4 » August — 13.5 » September — 7.7 » October 44.9 » November 77.6 » December Eyes b> January 5.7 > February — 37.3 » March — 65.9 >» April — 22.8 » The double-periodic variation of these values, as computed by the method 1. sq., may be represented by the expression: QD: cos) GOL a = VALObsin GORA et (9) From (4) we find: (1) + (2) = @ = 2 Ky Ry cos 30° cos (60° 2 — 60° — Cox) (3) + (4) = b = 2 Ky Rez cos 30° cos (60° x + 60° — Cyr) (5) + (6) = c = 2 K, Ry cos 30° cos (60° + 180° — Cox) a+b —2¢=6 K, Rs cos 30° cos (60° x — Cx) . « - (6) This equation shows that, by this method, the constants of Ay can be determined from a periodic formula in which the amplitude is about 5 times larger than the value which has to be calculated. By equating the coefficients of (5) and (6) we find: Ky cos Coy, = 5.558 Ky sin Cy, = — 2.825 K, = 6.24 em. C3. 333%! e. The average monthly values of the water-level are found by correcting the mean values as obtained by direct computation for the influence of the tides S;, Ay and ?. From formulae (1) and (4) it appears that (for the actual hours of observation) the correction due to the influence of S, and Ky, is nil; that for the single period- ical tides is given by the average values of formula (1) and (3) and is to be applied with inversed signs. ( 184 ) Correction for S; K, P Correct. values em. em. May 101.9 1,70 2,27 —2.72 103.2 June 117.0 1.70 — 3.2 —2.50 113.0 July 124.4 1.70 — 7.88 — 1.62 116.6 August 134.4 1.70 —10.41 —0.31 125.4 September 124.9 1.70 —10.15 L.09 117.5 October 105.8 1,70 — 7.17 2.20 102.5 November 98.1 1.70 — 2.27 2.72 100.3 December 90.3 1.70 3.24 2.50 UBC January 101.8 1.70 7.88 1.62 113.0 February 102.3 1.70 10.41 0.31 114.7 March 104.9 1.70 10.15 —1.09 115.7 April 109.7 1.70 Leilel — 2.20 116.4 Mean 109.6 1.70 111.33 The corrected monthly means exhibit a principal maximum (low water) in August and a principal minimum (high water) in Decem- ber; owing to the abnormal low value in May the position of the secondary extremes is doubtful. The constants for Sa and Ssa, computed from these data, therefore do not give more than a rather rough approximation of the actual state of affairs. The following expression is found: W = 111.38 + 5.54 cos (30° t — 28°55’) + 9.48 cos (60° t — 190°50') in which the origin of time coincides with May 16". As might have been expected the accordance between the observed and calculated monthly departures from the annual mean leaves much to be desired: Observed. Calculated. em. cm. May — 8.1 — 4.03 June 7 — 0.37 July 5.3 Uethh August 14.1 11.56 September 6.2 5.81 October — 8,8 = Ss November —11.0 —13.73 December —13.6 —11.45 January Nez — 1.78 February 3.4 6.20 March 4.4 6.02 April 5.1 — 0.11 (185 ) A systematical investigation of the normal and abnormal motions of the mean water-level, if extended over a large area and over some years, might prove of great importance with respect to two interesting problems. In the first place it would appear from such an inquiry that it will be always impossible to predict with great accuracy the absolzte water-level at a given place even when the periodic terms of the tidal components are fully known; therefore it can be of no use to earry on the calculations in behalf of tidal prediction to an astro- nomical degree of accuracy; in the second place an inquiry into the aperiodic departures from the average normal values might lead to a better knowledge of the important and varying meteorological influences which prevail on the ocean, than by means of the in- complete and scattered observations taken on board ship. It is not improbable that the variations of the water-level e.g. in the Gulf of Bengal and the Arabian Sea, which must be dependent on the “vis a tergo” in the Indian Ocean in and south of the area of the trade-winds, might give a clue to the prediction of the periods of drought to which the climate of India is subject. f. In recapitulating the results obtained, it must be kept in mind that the zero-point of the tide-gauge is on the upper end, so that low figures denote high water. If positive numbers are to correspond with high, negative numbers with low water, the argu- ment of the formulae must be augmented or decreased by 180° and the corrected monthly values subtracted from an arbitrary number. After reduction to the conventional origin of time, application of the augmenting factor '/R% to the amplitudes of the annual variations, reduction to average values of the constants in so far as they are dependent on the moon’s declination and, finally, inversion of the sign, the following tidal constants are found for Telok-Betong: Telok Betong. Java’s 4th Point H z H % Sy 2.7 ¢.m. 27° — — Sg 13.7 262° 1258 cm. 280° My, 32.1 222° 24,2 210° Ky 15.5 269° 6.8 226° O 7.8 265° 0.4 21165 E 4.2 231° ea WCAae N 5.6 192° 4.1 190° Ky 5.3 246° 2.9 299° Sa 5.6 263° 14 220° Ssa 9 120° 5.6 149° a3) W 111.3 53.9 ( 186 ) Besides the constants for Telol-Betong these quantities are given also for the tidal station Java’s 4” Point, situated too in Sunda- strait; they have been computed from a five-year series of observations. A comparison between the data for the two places exhibit some important differences, whilst a look at the chart would show that their situation with respect to the tidal wave, progressing from the Ocean in the strait, is about the same. For the differences of time, Velol-Betong minus Java's 4% Point, we find: Sz — 18° = —0.6 hours. My -+ 12° = 0.4 » Ky + 43° = 2.9 » O + 49° — 32D es, The single diurnal tides in the Lampong-bay therefore lag behind those near Java’s 4 Point in quite another way than the moon’s semi-diurnal tide My and this again in another way than the semi- diurnal solar tide S,, which is in advance. An estimation of the tides for the one place based on those of the other by assuming a constant difference of time — as is usually done along a coast — is therefore quite inadmissable here, as the differences of time are by no means constant, but variable according to the moon’s phase and declination. If we look at the hindrance which Sumatra’s most southerly neck of Jand offers to the free propagation of the mono-diurnal tide-wave from the Java-sea into the Lampong-bay, we should expect a stronger influence of the A, wave near Java’s 4t Point than on the road of Telok-Betong, but, on the contrary, the tide near the latter place may be regarded as twice as “monodiurnal” as the tide in the strait, as in shown by the proportion: RESO Ampl. ————- == 0,51 near Telok Betong, My + Sy = 0.28 near Java's 4% point, This prevailing influence of the Java-sea on the tides in the bay does not, however, give an explanation of the peculiar fact, that the S; tide in the bay causes high water earlier than in the strait proper, whereas the other tides occur /ater. If we assume that the S, wave finds its way into the bay in the same way as the other waves, it ought to have rather a retarding effect, because near Duizend-eilanden the kappanumber of Sj is 11°. ( 187 ) It is, therefore, as yet impossible to offer an explanation of this peculiar behaviour of the S, tide and we can only state that spring and neap near Telok Betong occur 1,64, and at Java's 4%” Point 2,87 days after New and Full Moon and First and Last Quarter. It must be remarked however, that the constants S, near Java's 4th Point are not quite exact owing to the fact that they had to be ealeulated from observations taken thrice daily, whilst (as appears from formulae (1)), for the complete determination of W, S; ands, at least five independent — 1. e. not 6 or 12 hour distant) data are required. In calculating the S, constants, therefore, it is assumed either that S,; is small with respect to Sj, or that the kappa-number of S; (land- and seabreeze) is about 65° or 245°, in which case, for the hours of 9 a.m., 2 and 6 p.im., the influence of S, disappears altogether. In fact the seabreeze at most places causes high water about 4 or 5 p.m. and, with the exception of only a few places, e. ¢. Semarang, the amplitude of S, is insignificant everywhere in the Archipelago. The neglect of S, therefore, cannot in most cases have any appreciable influence on the determination of the S.-constants and it is principially for this reason that, for the greater part of the tidal stations, the above mentioned hours of observation have been selected. In this special case, moreover, it is highly improbable that the kappanumbers of Sj for Java's 4“ Point would undergo a decrease if it were possible to correct for the neglect of S,, because, if we assume for S, the same kappanumber as near Telok Betong, viz. 27°, the kappanumber of S, becomes 285° instead of 280° so that the difference would increase rather than decrease. The tides of long duration Sa and Ssa may be considered to run pretty well parellel if allowance is made for the fact that the constants have been calculated from observations made during different periods. II. Sabang-bay. In this bay of the isle of Weh or Waai situated north of Sumatra’s most northerly point in 5°54’ N. Lat. and 95°20' KE. Long., tidal observations have been made since June 1* 1897 at the hours of Tam., 11 am. and 4 p.m. The results calculated from the first year-series may be given here and, for the sake of comparison, also the constants for the road of Oleh-leh. ( 188 ) As the hours of observation are not the same as those at which the observations have been made at T'elok- Belong, new formulae had to be applied; the method however being essentially the same, the results of the computation only may be given here. Sabang. Oleh-leh. H z H z Sy 24.1 cM. 310° 3.3 cM. 329° M, 46.6 266° 23.0 285° ky 9.1 291° 6.5 318° O 3.5 274° 2.3 323° Pp. 2.1 10° ? 2 N 8.3 265° 3 286° Ky 4.9 312° 2 333° Sa 9.2 165° 8.8 65° Ssa 8.5 114° 6.8 145° W 202.8 118.5 The tidal constants for Oleh-leh have been computed from three series of observations made during three years from 1895 to 1898; it appears that the tide P is so small that it cannot be calculated with any degree of accuracy from the given data, which is proved by the fact that the three determinations for the different series widely differ. No more importance can be attached to the constants of P in Sabang-bay, because its argument cannot possibly be 10°, but must be somewhat smaller than 291°, the argument of 4). For the rest the conformity of the arguments of S, and Ay, M/, and N, and the differences between those of S, and My, A; and O are to be considered as so many proves of the reliability of the results. The influence of the wind cannot be determined, as for neither station a calculation of S, can be effectuated from the available data; it cannot be of great importance because otherwise the differ- ence between the arguments of S, and Mg, which is 44° = 1.80 days, i.e. quite normal, would be sensibly affected. As, for all practical purposes, both tides may be considered as almost exclusively semi-diurnal, it is possible to assume a constant difference of time; this difference Oleh-leh minus Sabang is: . ( 189 ) So 19° = 0.6 hours, M, NGS 0 Sas N Nic OS Ky 21°=0,7 » so that the difference amounts to 42 minutes of time, whilst the amplitude may be assumed to be twice as large at Sabang — at least in the back parts of the bay — as on the road of Oleh-Ieh. The mono- and semi-annual variations are for both places some- what different; from the three series of observations at Oleh-leh it appears however that in these regions the monthly mean values of the sea-level widely differ for different years, so that a better agree- ment might be expected only if the observations extend over a long series or at least over simultaneous periods. It is of some importance to remark that, whereas the semidiurnal tides at Sabang are nearly twice as strong as near Oleh-leh, the mono-diurnal tides seem to be amplified in a far less degree. This point, concerning the way in which both tides propagate and are enlarged or diminished, is of great importance for the understanding of the mechanism of tides and requires a thorough investigation. With a view of elucidating this point tide-gauges ought to be established at the entrance and in the back parts of bays and estuaries: for these experiments however stations should be chosen where the mono-diurnal tides are better marked than at Sabang so that an accurate determination of the characteristic constants is possible. An analysis of tides at different parts of a river in which a tidal wave of mixed description propagates would also afford useful data for this purpose. Hydrography. — ‘On the relation between the mean sea-level and the height of half-tide.’ By H. E. De Bruyn. The mean sea-level is the mean of the height of the water ob- served at short intervals i.e. every hour. Observations have proved, that the mean of 3-hourly observations does not practically deviate from this; in this way the mean sea- level in the years 1884—1888 has been determined by the Royal Geodetical Commission (Annual report of the Commission 1889). Generally it is admitted that there isa constant difference, between ( 190 ) the mean sea-level and half-tide (the mean of high and low water), during several years or months. This has been done by the above-inentioned Commission, in their calculation of the mean sea-level for several years for Den Helder. Dr. H. G. van bE Sande Bakunuyzen also in his communication “On the variation of latitude,” to the meeting of the Royal Aca- demy (24% of Febr. 1896), assumed that the mean value of that difference during a month was a constant quantity at Den Helder. In both cases this was perfectly justified, as this value for the annual means is very nearly constant at Den Helder, and in the last ease differences that may exist, are eliminated by the method of determination. However, the supposition that the difference is con- stant is not true for the annual means at all stations, and is certainly not so, for the monthly means at some stations. I intend to trace those causes, which produce a difference in this value, and to find its range for one tide-gauge. I took Delfzyl for the observation-station, as at Delfzyi the difference between half-tide and the mean of the sea-level, is greater and more variable than at any other station in our country. From another point of view, Delfzy] would not be so advantageous, as there a comparison with tide-gauges in the neighbourhood is not possible. Before proceeding further, a few words, to point out the impor- tance of the Jaw of the variation of that difference, are necessary. The knowledge of the mean sea-level is not only important for the annual ‘means, but also for the monthly means, as we can deduce from them the annual variation, and also because an exact knowledge of the monthly means, assists in the detection of the unavoidable changes of the zero’s in the automatic tide-gauges, and the deter- mination of their values. As the high and low water marks are always determined in the first place, their mean is naturally known; therefore it saves much trouble, if it is possible to deduce from that mean value, the true mean sea-level, as the hourly observations can be then neglected. Besides, in the event of interruptions, which happen frequently in using the automatic tide-gauges, it is much easier to guess, the positions of high and low water, than the hourly heights, as high and low water are independent of the exact time. Moreover meteorological circumstances have, by the retardation or the acceleration of the tide, a greater influence on the hourly heights than on high and low water. The mean sea-level can therefore be deduced more exactly from the height of half-tide, the difference of both being known, than from the hourly observations when some of these must be guessed. — ae ea (191 ) Further Jet the difference between the mean sea-level and the height of half-tide be 4, the mean sea-level Z, high water V, low water E. Half-tide is }(V + £) and the range of the tide(V — £). The causes, which have an influence on the value of A, are four in number: 1st. the range of the tide (V— £); 2nd, the mean sea-level (72); 3'4. the time of the year; 4th, the presence of ice. In the last mentioned case, I am not alluding to the fact of the ice preventing the working of the tide-gauge, for I consider this to be an interruption, but to the fact, that the presence of ice at a certain distance from the tide-gauges, deforms the tide-curve. This defor- mation is, in my opinion, one of the most interesting researches on tides. I propose to solve the following question. What corrections are wanted for Delfzyl in the value A, deduced from a certain number of years, in order to find that quantity for separate months ? The data, which I had at my disposal were the values of V and E for 18 years (July 1881—July 1899) the values of Z for 7 years (1884—1890) viz. the height at 2, 5, 8 and 11 o’clock, and in addition the height at 2 and 8 o’clock for 8 years (1891—1898). The mean range of the tide at Delfzyl is, according to these data. 2750 m.m., the mean sea-level 7 is according to the caleula- tions of the above-mentioned commission 128 m.m., reckoned from the zero of the tide-gauge during the years 1884—1890. The mean valne A during these 7 years is 193 m.m., so we find that the mean of half-tide is 128—193 mm. = — 65 mm. Tide-curves of spring and neap-tides accompany this paper. It is difficult to determine, how much each of the four causes, influences A at Delfzyl, as they often modify 4 in the same direction. So, during the year, the correction for each of the three first-named causes, is generally a sinusoide of about the same amplitude and the same phase. It is therefore necessary, to adopt a certain definite value for one of these causes. I assume that the correction, due to the first cause, is proportional to the difference of the mean range of the tide and the observed value of that range V—Z and that their proportion is equal to the ratio of the mean values 4 and V—Z, or ceteris paribus, A is always proportional to V—#. In substance this will be 14 Proceedings Royal Acad. Amsterdam, Vol. IT. ( 192 ) he case. I adopted as this proportion 1/,;, the correction is therefore WN); (V —E—2750) mm. As coneerns the second correction we see that when the sea-level is higher, A is smaller than the mean value, and vice-versa. ’ We do not know exactly the law governing these small changes, because various unforeseen circumstances e.g. storms influence them. The only thing that can be done, in my opinion, is to take for this correction a quantity proportional to the deviation of the mean sea-level. As it was my intention to deduce the value of 7 from that of half-tide, which is known, I adopted for the value of that correction a quantity proportional to the deviation from the mean height at half-tide (— 65 mm.). After comparing the same months of different years, I found that this correction amounts to about */s9 or ?/s9 of the value of that deviation i.e. 4/2) or 4/s9 of (V+ £-+ 130). I have adopted Vg (V-- E-+ 130). That the height of 7 has an influence on the form of the tide- curve, is probably due to the mud-banks in the Dollard. The surface that must be covered, constantly changes with the level of the sea, and so for equal tide-ranges, the quantity of water flowing in and out of the Eems at Delfzyl, is much greater for high sea-levels than for low. Both corrections being applied another annual correction is still wanted. For this correction I adopted an annual sinusoide, the amplitude and the phase of which can be easily determined, The amplitude is in round numbers 10 mm. and the greatest positive value occurs about the 1st of July. From the observations in the seven-yearly period, there is no evidence of the existence of a half- yearly sinusoide. Considering also the heights at 2 and 8 o’clock for the period 1891—1898, there appears to be a semi-annual sinus- oide, but the amplitude is very small, and it is questionable whether the sinusoide derived from those observations is not different from the meau sinusoide. It is better to entirely neglect this correction. After applying these corrections, the values of the sea-level for some months, still show great negative divergencies. It is obvious that these are exactly the months in which we have a very low temperature, and in which there must have been ice. But as the mean temperature of a month is not an exact proof of the presence of ice, I adopted as a datum the thickness of the ice according to the observations at Den Helder (see the Proc. Kon. Inst. van Inge- nieurs) as quoted in the following table. (193°) Thickness of the ice in mm. 1884 1885 1886 1887 1888 1889 1890 January 22 387 201 298 310 204 43 February 53 BEl 323 266 360 156 aLeAl March 6 24 ena 110 223 124 93 November 46 74 6 43 145 27 267 December 95 58 96 PAL 51 199 811 I took for the months in question the four ones in which the ice has the greatest thickness, and two other months in which the thickness too was great, following immediately on two of the for- mer, aS we may suppose the ice still existed during that time. The selected months are underlined in the table. I found that in these months A is too small. It is difficuit to find a cause for this, as, excepted at Delfzyl and Statenzyl, there are no tide-gauges in the Kems and the Dollard, and the gauge at Statenzyl does not work when the tide is low. Probably it is due to the ice on the mud-banks of the Dollard. Generally the effect of the ice is to raise high-watermark at the mouth of the river, but this is not the case at Delfzyl. On the contrary, the range of the tide is less in the months with ice. Probably both V and £ are increased, but “& more than V, and therefore the range is smaller and half-tide considerably higher, the mean sea-level is less increased than half-tide and hence the difference A is smaller. The heights at 2 and 8 o’clock in the months January 1891 and February 1895, when there was much ice, give also corresponding results. In the foliowing table are given the values A, the corrections and the remaining differences, for the 5 months in which A is a maxi- mum, the 5 months in which 4 is a minimum, the months with ice and two other months in which the error or the remaining diffe- rence is greater than 15 mm. 14* Value Remaining Mouth Tide- Time of A. Y. Difference. range. the year. Maximum values of A. April 1884. 2235 9 14° 9° 45 May 1886. 2205 75 9s 7 3 April 1888. 220 125 10 25 2 April 1889. 229 9 10 QF 146 May 1889. 9956 10 108 7 5 Minimum valie of A. October 1884. 148 —5 —23 —2 —145 December 1884. 158 —45 —15 —9 —6 February 1889. 158 — 3° —20° mall —4 January 1890, 160 —5 —155 —9° —3 October 1890 | M49 —)l —25 —2 15 Months with ice. January 1885. 178 —l 12 —9 —16° February 1886. 1885 4 We —7 —19 March 1886, 186 08 14 —28 —19 February 1888. 164. —1)° 15° —7 —36 March 1888. 183 —1l 10 —28 —16° Deceimber 1890. 167 —7 21 —95 —30° Months with differences greater than 15 mm February 1890. 189 08 23° —7 —2) December 1888. 1995 —2° —5* —9° 24 (194) Correction for From this it appears that the corrections and the errors are positive in the months with maximum values of A, negative in those with minimum also nas been values. We find concerning February 1890 that there ice during a portion of this month, that the mean height was lowest of all months and that as low water occurred on the 28th a few minutes before midnight, it had to be considered as occurring in March. The great negative difference can probably be explained by these circumstances. H. E. DE BRUYN: On the Relation of the mean Sea-level and the Height of Half-Tide. Tidecurve at Delfzyl (Spring-tde). i 7120 140 HH 160 a u LL | UJ 280 eet At Pe Rae SEMIS, © | 200 — —-—-— Mean Sea-level. —..—..— Half-tide. Proceedings Royal Acad. Amsterdam. Vol. II. H. E. DE BRUYN: On the Relation of the mean Sea-level and the Height of Half-Tide. Tidecurve at Delfzijl (Neap-tide). re Goll 160 —— ; a 140 eee ee — | 120 a =; —_— + 100 Al 80 ‘lie \ (a) r 4o 4| \\ i f 20 aa yo" \yo" ee y 6 = SS === ee —o == a — — — — Mean Sea-level. —,.—..— Half-tide: Proceedings Royal Acad. Amsterdam. Vol. IT. (195 ) The remaining differences for all months are given in the following table, in which half mm. have been neglected; the months with ice are underlined. Month 1884 1885 1886 | 1887 | 1888 | 1889 | 1890 ae ! a | January I. | sail | a 5} —2}—13| —3 February 9 | 2) Silt) — e200 =e | — oll Mareh 6.) —13)| —19 nf esky eee ee April A= OmiiieOs We Bylivie, walt | 9 May 1 1 Balt salts OM Me BIE ME June —1: —11 —1 | =) —-] | ==6 | +—=3 July fi = abel She eB eM] 7 3 —6 August | 5 sal eo eee 4 | Mee a September Da epee Fee LOM Odie Oe | yd October | —14 Del ) — 2 | Gye lo November | == (5) | —2 | a | 4 —9 | 3} | 3 December | —6 3 A etek 24 | O30) The mean error of the sea-level for all months, those with ice excepted, is 6,0 mm. | computed this mean error also on the sup- position that the second correction is !/., or 4/3, of V + & + 130. The mean error was found to be respectively 6,3 and 6,1 mm. When the value of Z is deduced from the heights at 2 and 8 o’clock and a mean correction 1/, (height at 5 + height at 11 — height at 8 — height at 2) is applied, the mean error of Z has been found to be 8,8 mm. It seems therefore that the deduction of Z from the height at half-tide gives more exact values, than the deduction from the heights at 2 and 8 o'clock. Hence the value A for Delfzyl, after applying the above-mentioned corrections, the sun’s longitude being g and the correction for the presence. of ice Y, is: A = Z—1,(V + BE) = 193 + 1/,,(V—E — 2750) — "es (V + E+ 130) + a, cos(p—y) + FY, y being a constant angle. Or: A=5 42/95 V — 8/75 H+ ay cos (p—y) + Y. ( 196 ) Partly neglecting the variations of the monthly tide-ranges in different years, which are at a maximum 120 mm. and give only a maximum error of 3 mm, in the value of A, we can put "ly, X 2750 + ay cos (p—y7z) instead of 2/,, V — %/,, EH mm. The formula then becomes : A = 78 — 0,08 E+ az cos (p — yz) + VY. The errors caleuleted from this formula do not differ much from the above-mentioned, for now the mean error is 6,4 mm. and the formula is therefore as exact, while the computation is much more easily carried out. In conclusion I will add the following remarks. First I should mention that I found some errors in the tables containing the observed height of the sea-level at Delfzyl during the months in which the greatest differences occurred and in those of two other tide-gauges during five months. For instance at Delfzyl I found a month in which one height had been read from the half hour-mark instead of the hour-mark, and also one reading with a wrong sign. After making the correction the great divergence was very much reduced. Although this is no proof, we may suppose that the greatest differences very nearly give the limit of precision. Further I notice that the second correction mentioned above does not agree with the principle on which the method of harmonic analysis is founded, so that this method cannot give exact results in the reduction of the observations at Delfzyl. Still, I do not affirm that any other is better. This want of agreement is demonstrated by the term 0,08 / in the preceding formula. For the same month in two different years (February 1889 and 1890) the difference of the two values of / is 083 mm., so that 0,08 # = 47 mm., and although this difference would not be of much importance for a single observation, it is far too great for an error of the monthly mean. Mathematics. — Prof. Jan pe Vries reads for Prof. L. GEGEN- BAUER at Vienna a paper entitled: “New theorems on the roots of the functions CO" (z)”. n Up to this moment we know of the roots of the coefficients CH (x) of the development of (Ll —2q@ + @*)~* according to ascending 3 powers of @ only this, that they are all real and unequal, are situated (0975) between +1 and —1 and — apart from the root 0 appearing in the case of an uneven n — have in pairs the same absolute value ; finally that the roots of C (x) and om AC) as well as those of GC (x) n (— n oH C @) mutually separate cach other. In the following lines some new theorems on the roots of these functions will be found in a highly simple manner, one of which including as a special case a well known theorem of the theory of spherical functions. eye > : Cl ay, . 1. From the addition-theorem of the functions C (x) arrived n at by me ‘ ; Qn I] (n-+-y—1) 72 C [ary +V (l—2)V ay’) cos g] = U(2v—2) | Ul — 7 | pn ey—1 ee 2y+2o0—1 v5 mee 55 =i) a N Cia OG Ae vy De ( ) H (n—e) W(n+2rv+e—1) 2» (x} oy (x) c (cos p) BO (1 2% ty Ca 1) where the square roots are taken positively and Ys p IT (n—v) Hv + @ — 1) ree, CAe)= : Se gs 20 - n gn—p TT (n+ y — 1) pe we find the relation { C [ray + /(L—2?) (1 —2,”) cos g] sin?’—! pdp = n 0 92y—1 [IT (vy — 1) 2 HT (n) tel (n+ 2y = 1) v v C (x) Cs (2) . v By putting «, equal to a positive root 2, of the function Cc (x) the equation is transformed into Ie [xen + YY (1—2?) (L—zn?) cos p] sin” 1p dp=0 , “ n 0 é < . ew . > showing that the function C (x) vanishes at least for one value of its argument lying between #2,-+ /(1—2*)/(l—<«,”) and @ en—YV (1—2”) V (L—en?), as otherwise the function to be integrated ( 198 ) would not change its sign in the entire region of integration, and hence the integral could not be equal to 0. This value certainly (differs from z, when 2n > Len + //(1—2?) Y(1—z,) , which can only be the case, if aa2z—1, and this leads, in case « might also be positive, to the supposition 1 Zn > y2 The entire interval under discussion being a positive one when w is taken greater than 4/(1—<,*), we find the theorem: If 2n be a positive root of the function C; (x) surpassing 1:2 and a a positive root lying between |y (1—2n)] and 2 z,2—1, then there must be in the interval az,—y/ (1— ea’) / (1—2n2) to &in+VY (l—a@)Y (L—2zn*) at least one other positive root of this function (smaller than 2n). A corollary of this theorem is the following: v The smallest positive root of the function C (a) is smaller than 1: \ 2. n . v ‘ . . 2. In my paper “Some theorems on the functions Gi (x)” (“Einige Siitze tiber die Functionen C (z)’’) contained in the 47" vol. of n “Denkschriften der mathematisch-naturwissenschaftlichen Classe der Kais. Akademie der Wissenschaften in Wien” I have given the four following equations : y CO (cos\x)\ = (cos g — cosz)¥—} n a L 2-1 V/a HT (y—1) sin?y— 5 ( 199 ) eS. y 2 C (cos r) = — - - fo x—cos ¢)¥—1 ; 2-l v/a HN (vy—1) costv—t 5 (1) 2 (= Vir : G: Se) = —— ; form 2) Vigo i 2¥—-1 1 /a ID (v—2 Fee “1 3 2y—1 @ Cock (: sin =) sin p dp (y Zi 4) ’ Qy zi n(— y 2 CoA) = —— = 2 Je xv—cos g)¥—1 2 29-1 a IT (v—2) cos2¥—! — 2v—1 WH ; (cos =) sngdp (Y> \), ’ which are a generalization of the integrals: ames di pos (cos @ — cos 2)’ as 2 Ie sin (n ai 4) ¢ dp Xho) = |= ———— * 7 V 2 (cos x — cos g) x given by MEHLER in his communication “Notice on integralforms of Dirichlet for the spherical functions P, (cos #) and an analogous integralform for the cylindrical functions JZ (2), ‘“(Notiz iiber die Dirichlet’schen Integralausdriicke fiir die Kugelfunctionen P,, (cos #) und eine analoge Integralform fiir die Cylinderfunctionen 7 (2))”. By putting « equal to the root of the function C (cos x) lying be- n tween 0 and > we transform them into the following relations: - ( 200 ) yn y oo abl i 0 ~ | (cos p — ¢08 Yn)! C, ( sin 7 )e08 = an 0", nm \ 2Qy gq . gE (cos y, — cos g)¥—! C, cos ain = din One on te s yn Ya 2y—1 af [oo GF — C08 Yn)¥— Ca (sin =a) sngdp=0O, 0 2y—1 Q ty a one MYL. CO. 08 — 27 — } (cos yn — cos f) Ca, (cos 5 ) stagpdpy=0O0, Yn Bd 2 k , 3 isha? KB Pp which relations show that the functions C. (sin =) and C, (cos ) vanish at least for one value of » within the respective interval of. integration. This gives rise to the following theorems: The smallest among the roots of on (cos x) lying between 0 and n J 2y Zz = is larger than the smallest of the roots of C,, ( cs ) ful- filling the same conditions and the greatest among the above named roots of C (cos x) is smaller than the greatest among the roots of n 2y onl cos a belonging to this region. The smallest among the roots of Cc (cos x) lying between 0 and 2v—1 > is larger than the smallest of the roots of C _ (sin) ful- 2n+ filling the same conditions, and the greatest among the above named roots of CG (cos x) is smaller than the greatest among the roots of n v—1 z F : C (cos) belonging to this region: 2n--i 2 By putting in the first proposition ” equal to 4 and by marking that ( 201 ) 1 C2 (cos x) = Py (cos x) , n 1 sin (2 MN) 9 C (cos 7) = aE ant ) x : 2n sin ZX 08 (2 3 ID G (sin X) — (— 1) 698 (2:0 ahs Nx Qn cos X and that sin @ increases, cos @ however diminishes with @, we arrive at the theorem: The positive roots of the nt® spherical function P, (av) le hetween cos — "and cos ——— where n, is the greatest even number 2n+1 2n-+ 1 contained in n. This theorem is a corollary of the one deduced by Bruns in his treatise “On the theory of the spherical functions” (Zur Theorie der Kugelfunctionen) published in the 90 yol. of Crelle’s Journal and recently proved by Markorr!) and STIELTJES *): The roots of the spherical functions le one by one in the intervals Qin (2i—1)a One 1 ee ay 2n-+ 1 From the preceding theorems we can easily deduce the following: cos The difference between the greatest positive voot of the function v C (x) and unity is less than two times the square of the smallest n 2Qy positive root of C, Gaye The difference between the greatest positive root of the function C (x) and unity is less than two times the square of the smallest n 2—1 positive root of C_ (a). 2n+ 1 The difference between the greatest positive root of the n‘” spherical ny function and unity is less than 2 cos® a : 2n+ 1) On the roots of certain equations”, (/Sur les racines de certaines ¢quations’’) Mathem. Annalen, 27th Vol. 2) wOn the roots of the equation X,—0,” (wSur les racines de l’équation X,= 0”) Acta Mathematica, 1X Vol. “On the polynomia of Legendre”, (Sur les polynomes de Legendre”), Annales de la Faculté des Sciences de Toulouse. Vol. IV. Markorr and Stietryes deduce in the cited treatise also the narrower limits in (Qi—l)a cos ————... . COS —— n+l 2 ( 202 ) By Two times the square of the smallest positive root of C, () is smaller than the smallest positive root of C (x) increased by 1. nm - ° . Wate 27—1 Two times the square of the smallest positive root of C, | (x) 2n+1 is smaller than the smallest positive root of C (x) increased by 1. n The two latter theorems furnish us with a less narrow limitation Gale . _ . ¥ for the smallest positive root of the function C (x) than the theo- n rem at the conclusion of § 1. Terrestrial magnetism. — Dr. W. van BemMeen. ‘ * Spasms” in the terrestrial magnetic force at Batavia.’ (Communicated by Prof. H. KaMERLINGH ONNES). (Read September 30th 1899). Since the great development of Seismology, the instruments, which record photographically the quantities determining the earth’s mag- netism have also rendered good service as Seismographs in the researches on the propagation of earth-waves in the surface of the earth. During half a year I had the opportunity of tracing the seismic disturbances in the Magnetograms at Batavia, and this under very favourable circumstances; for, not only was the fear of local distur- bance very small, the temperature constant and the damping large, but since June 1%* 1898 a new Milne Seismograph had been working and furnishing accurate information about seismic disturbances. When an earthquake is near, these appear in the curves of the Magneto- grams as discontinuities, viz. the needle suddenly starts vibrating and continues doing so for some minutes; when at a greater distance, on the contrary, only a more or less considerable regular broadening of the curves appears. Comparison with the Milne-Seismograms quickly taught me that the seismic disturbances at Batavia seldom are large enough to appear in the Magnetograms, but also conversely, that no trace of a large number of analogous disturbances in the Mag- netograms could be detected in the Seismograms. Hence there is danger of considerable confusion: if for instance an earth-wave has passed at Batavia at 11.10 which has not appeared in the Magnetograms, then very likely a non-scismic disturbance, occur- ring at 11.5 for instance, will be mistaken for an earth-wave and an error of minutes will be made. Moreover it is necessary to inquire whether a new phenomenon does not mingle with those just mentioned. ( 203 ) I have given the name “Spasms” to these little motions. These appear as broadenings of the curves of the Bifilar-Magnetometer, which may be caused by vibrations of the magnetic force with an amplitude of from 3 to 15 g. (g = 0.00001 C.G.5.). during about 1 to 8 minutes. On the scale of the bifilar-magnetogram 1 m.m. represents 4 minutes and 5 g. On trying to find an answer to the question, whether there is really evidence of a new kind of small disturbances, I employed two methods, that of statistics and that of direct observation. After the example of Escuennacen I constructed a Microvario- meter for the Horizontal Intensity, in which a light magnet is held perpendicular to the magnetic meridian by the torsion of a German-silver wire. The period of a complete vibration was 9 seconds, the damping ratio 2—7, the value of the tenths of divisions, which could be estimated very easily, 0,06 ¢. With this instrument I observed continuously during one or two hours for many nights, and often took readings every fifth second, but unfortunately I have not yet been lucky enough to observe an undoubted Spasm. It occurred on only one occasion and was even then not a striking one. Notwithstanding this adversity I have been able to learn much from these observations. For instance I happened to be behind the telescope when a series of faint earth-waves, distinctly registered by the Seismograph, passed Batavia, and though wholly unconscious of this, I nevertheless noted three times horizontal and vertical motions of the inagnetic needle. Their period was 2,5 seconds, half that of the free vibration of the magnet. This observation during the occurrence of a Spasm in the Mag- netogram indicated that really a kind of miniature disturbance had passed, and not a prolonged motion, caused by an earthquake. On one occasion I noted, while everything else was quiet, a strong impulse three times in one minute, which caused deviations of 20 to 40 g. The Magnetograms did not show the least signs of these, as the damping of the magnet is too rapid and the paper is not sensi- tive enough to light. Although my direct observations have not until now met with much success, they nevertheless make the existence of very small magnetic disturbances appear probable in this case. Here at Batavia only the curves of the Horizontal Intensity show the Spasms, never those of the Declination which rarely exhibit perturbations at our tropical station. In compiling the statistics we met with three difficulties ; ( 204 ) Ist. The number of Spasms detected depends upon the breadth and distinctness of the curves, which are very variable during the registering-period 1883—’99. 2nd, During a very unsettled state of the Magnet it was often impossible to distinguish between the various kinds of disturbances. 3'¢, The possibility exists, that many earthquakes have not been noticed, though I had made extracts formerly from the statistics of earthquakes published in the *Natuurkundig Tijdschrift voor Neder- landsch Indié”. Only the difficulty mentioned under 1 is unevitable, and indeed its baneful influence has been keenly felt. I searched the Magnetograms of the continuous series from March 27 1883 till March 27 1899; for the undulations only the years with narrower curves. ANNUAL NUMBERS. eae sl Soames: bf, PE lg eran Sun-spot maximum (27 IIL-31 X11) 1883 (87) | 27 111 1883-27 1111884. | 55 ‘ Siiul/ 2-482. ily: =i) GB MeoleeS5i eaeD > S53) 64s @ pee Socom mee 58 | » 86 | 74 } > 86- > s7 | 81 » 87 | 63 » 87- » 88) 54 ) ss. | 43 se eho Sh PED 36 (1889.6) | » Soule esi 5. BOE >) 490 51 Sun-spot minimwe > QOH) e5/ieu| queer 902) aaa) 46 » Biel 4a pee ON) Vy ae 99 44 > 92 | 37 » 92- » 98 53 » 93 | 83 Pe 98—\..d: WANDA gt88 (1894.0) | » 94] 75 ge Oat ny 95 9/hnera Sun spot maximum | | » 95 | 103 » 9- » 296 | 122 | > 96 114 ye 96— 0 <0 we OL > 97 | 105 tO 7 = eeOS | 96 ) gaii'sal |S y%. (ose of Mogmaimmas > 99 | (80) “113° Total 1130 If we take into account, that especially in the years 1888—91 ( 205 ) the curves are very broad and during the years 92—97 almost invariable in breadth, then a concordance with the number of sun- spots appears rather dubious. ANNUAL VARIATION. It soon appeared that an annual fluctuation existed in the fre- quency of the disturbances. Hence I have calculated for a closer inquiry the twelve day and not the monthly means. (Five 13 days periods were made, distributed equally throughout the year.) se eas Period. peered Ge ae | 29. ==18 9 VIE —13 VIE | ier—116 13 tye okey 36, al 14 » —25 » | 25 —12 5 pe wearer DL 39 2 Gyo a= 7) VIIT Su—18 6917 > | 57-0 8 VIIL-19 » 27 —10 leary =e ITT 73°36 9» 21 » he PeTGE Py Sy | 64 27 (aires HQCEK S66 aaa 15s >) 960.3 al ole (Sey) Od > 35 aed Peery ake 1V age Cyst Obie Ga 49 12 Seven ——19) %> 41 4 Te Xee 19.0) 63 26 OO a) beet V Shenae 20 » —8l » 47 «10 SNE E13" 5 29 —8 Nap dip aoa 300 ai 1th 8965 Nia) Tagheay 13) eh 94) 414 Ha) Sana 16 —21 25) payee 6 MIT 1 4 Gav =19) > | 26 —11 7 Xai 188 93 14 BO iy == DEVEL ee aly 19) yet = 31h. ob | Oe eet Mean 37 Hence the annual variation of the Spasms is very clear, and with two maxima. In order to determine even more accurately the dates of the maxima etc., I have calculated the daily numbers for the adjacent months and compared them by means of the formula 2+ 26+ e. A principal maximum certainly appears from these on February 22, a second smaller maximum on October 17; a minimum on Decem- ber 22 (close to Dec. 20, the mean of Oct. 17 and Febr. 22) and a second very uncertain minimum. Here the comparison of the daily numbers for the period May 23—August 7 by means of the formula a+2b+4c+6d-t+4e12ftga 20 ( 206 ) left the choice between June 22 and July 12; and as June 21 is midway between Febr, 22 and Oct. 17, we have good reason for choosing June 22. The harmonic analysis of the numbers for the 12 days periods yields : D = 37.14 10.2 coz (n X 12° — 24°15')+ 8.3 cos (n X 24° — 67°53') but this formula does not account for the steeply rising maxima, which demand the terms with 3m and 4 m and so reduce the cosine- formula to a mere result of calculation. I think it therefore more suitable to defer the deduction of formulae until an explanatory and acceptable hypothesis has been found. DIURNAL VARIATION. | No. of Hour. Spaams | Hour. See A 0—1AM 91 45 0—1PM 4g 159 72 6 1-9 45 —1 2— 3 | 59 13 2— 3 | 46 0 Baad yar ea ee! | 48 4— 5 19 —97 4— 5 | 39. = 7 5— 6 ll —85 5— 6 47 1 6— 7 8 —s8& 6— 7 2 —21 7— 8 7 —39 7— 5 43 — 3 s— 9 23 —23 S—- 9 66 20 9—10 27 —19 9—10 58 12 1o—11 46 0 10—11 103 57 l1—12 37 — 9 11-12 110 64 Hence mean 46 Principal maximum (110) 11 —12 PM. ” minimum (7) 7—8 AM. Secundary maximum (48) + 2 PM. y minimum (25) 6—7 PM. The harmonic analysis of the hourly numbers yields: S = 46.5 + 24.6 cos (n. 15° — 324°52') + 7.8 cos (n. 30° — 312°33') + 13.6 cos (n. 45° — 8°48') + 21.3 cos (n. 60° — 331°9') Again the term with 4 is very large. One receives the im- pression that in the daytime the height of the sun exerts a ( 207 ) certain influence for, the minima appear about sunrise and sunset and the maxima, as frequently happens, about midday. The mean diurnal variation calculated from four maximum and from four minimum months does not show any sensible difference, DIURNAL VARIATION FOR MAXIMUM AND MINIMUM PERIODS. The Nos. for HH. | Febr.-March Sept.—Oct. May-June July-Dee. minimum periods | multiplied by 2. 0O— 1 AM | 440 - 17 34 i= 3 37 18 | 36 gat sr 35 10 20 3— 4 12 13 26 4— 5 8 5 10 5— 6 6 2 4. G7 3 min. 4 min. $ 7— 8 3 2 4 8S— 9 | 11 4 } 8 9—10 10 7 14 (ESB 18 ul | 22 11—12 | 14 19 20 0— 1PM 24 12 24 } max, 1— 2 | 21 . = 22 > max. 3 12 12 24 j5— 4 21 6 12 4— § 7 9 1s 5— 6 20 12 24. 6— 7 12 min. 8 16 7— 8 22 6 12 Ss— 9 34 1s 36 9—1L0 31 9 1s 10—11 42 21 max. 42 Tae. 46 21 49 503 248° ! 4.96 15 Proceedings Royal Acad. Amsterdam, Vol. LI. ( 208 ) I further investigated whether any connection existed between the frequency of the Spasms and the tropical and the synodical revo- lution of the moon, respectively 29,5306 and 27,3216 days; and moreover with the sun’s rotation, for the periods: 25,787; 25,800; 25,815; 25,857; 25,929 and 26,071 days. In none of these cases however was a marked periodicity found, at all events nothing pointing to a direct influence of these revolutions. Such an influence would have been useful for the explanation of the phenomena we are now considering. It is not possible now to give an explanation; for that purpose we require, that 1st. The Microvariometer should furnish new material for research ; gud, The phenomenon is also investigated at other magnetic observatories ; 3, A theory of tbe variation of the earth’s magnetic force, of the Aurora borealis and of the electric currents in the earth and the high atmosphere has been established. I will only point out some analogies, which may perhaps con- tribute afterwards to an explanation. The deviations, calculated according to VAN DER SroxK’s method of reduction, can serve as an indication of the amount of distur- bance of the Horizontal Intensity at Batavia, especially for the shifting of the lines. The table +) for the period 1892—93 shows for these deviations Ist. A semi-annual period, with its maxima in March and Sep- tember, its minima in June and January. Qnd, A diurnal period, with its maximum at 3 P.M. and its minimum at 1 A. M. 3, A concordance with the number of sun-spots. Hence there is agreement between the annual variation of these devia- tions. with that of the Spasms, but not between the diurnal variations. The photograms giving the Potential of atmospheric electricity show nothing in particular during Spasms, the diurnal variation of the Potential is even reverse and is not semi-diurnal. The annual variation again only contains ove maximum and one minimum. Co- incidences in the variations of the meteorological elements are not to be detected. Important coincidences are found with the periodical fluctuations cf the Aurora borealis here, in the nightly maximum and the semi-annual periodicity characteristic of this. The observed numbers have shown, that the epochs of the maxi- 1) Observations, Batavia, Vol. XVI. ( 209 ) mum and the minimum are altered together with the geographical position, and that the daily variation has no secundary maximum at- noon. We should not forget however, how Jarge the influence of moon- and daylight is, and how difficult it is to choose an adequate scale for the Intensity. At lower latitudes the maximum is reached a little before midnight, the minimum about six o’clock in the morning. | The annual variation of the Aurora australis according to BOLLER !) is given by: Jan. Febr. March April May June July Aug. Sept. Oct. Nov. Dee. 63 104 119 77 44. 25 39 52 58 67 63 65 which shows considerable analogy with that of the Spasms; but unlike the Spasms the Aurorae are more numerous during a disturbed magnetic state. It seems however that a connection exists with a series of wholly different motions in the curves of the Horizontal Intensity, in which for a time varying from a few minutes to several hours the Magnet regularly executes little oscillations with an almost constant period of about 1—4 minutes, and an amplitude of from 1 to 7 g. I had made these motions already the subject ofa careful inquiry, when a remark in the second paper 2) of Prof. EScHENHAGEN made it appear probable to me, that Dr. Arenpr had made already a similar investigation for the curves at Potsdam. Prof. ESCHENHAGEN writes (p. 679): “So far as has been observed until now, these vibrations appear principally in the daytime; at night they are very rare. But frequently at night larger oscillations occur, which are observed even macroscopically in the usual records and which usually occupy whole minutes, though the phenomenon itself seldom lasts for an hour, but usually only for a short time. Already at the beginning of the registering in 1890, attention was paid to this, as the greater distinctness and larger time-scale at Potsdam allowed the phenomenon to be observed there better and more easily than at other observatories. Since then Dr. ARENDT has studied this kind of waves, and he is inclined to the opinion, that they are connected with the phenomena of atmospheric electricity.” This paper of Dr. Arenpt’s “Beziehungen der Elektrischen Er- scheinungen unserer Atmosphire zum Erdmagnetismus (das Wetter ') W. Bouier. Das Siidlicht. Beitrige zur Geophysik. Bd. IIL. Heft 4. 8.554. 1898. *) Sitzungs Ber. d, Pr. Akademie d. Wiss. zu Berlin 1897. June 24. 15* (210 ) 1896, Heft 11 und 12)”, is, I regret to say, not at my disposal here, therefore I will only touch slightly on this matter now. I have given the name Pulsations to these wave motions in the curves, contrasting them thus with the Spasms, because of their resemblance to similar motions in the Seismograms, which were first detected by vy. Reseur-Pascuwirz and afterwards by MILNE and Eutert, and to which this name was given by VON REBEUR. I have compiled statistics of the oceurrance of these Pulsations in the years with narrow registering curves, which led to the following result: 1 Jan.—12 July 1885 278 series 1892 267» 93 169 » 94 97 » 95 241 » 96 230 » 97 949 =» 98 197 » Annual variation for the Period 1892—98. Jan. 127 July 99 Febr. 116 Aug, 115 March 142 Sept. 101 April 134 Oct. 96 May 144 Nov. 132 June 157 Dec. 87 820 Series 630 Series Monthly mean 121. DIURNAL VARIATION. Hou | No. of series rehee | No. of series | of pulsations. | of pulsations. o— 1 AM 223 0— 1 PM 42 Sie) 140 12» 45 3s 121 BB} | 42 3= 4) oy | 83 gue ty 37 fi 5)» 53 1s | 33 5a GL, | ot SES Glee 31 6— 7 » ale} 6— 7 » 45 [== 8) 6 7—8 » 70 S—9 » 11 Seon 1 9-10 26 9—10 127 OSI oy 36 10—11 » 162 11—12 » | 16 11-12 » | 199 Mean 72 (211) The frequency of the Pulsations was tested in vain like that of the Spasms for a concordance with the tropical or synodical revo- lution of the Moon. In the yearly values of the frequency of these Pulsations no parallelism with the numbers for the sun-spots can be found, and in the monthly values a not very distinct yearly undulation appears, which however is quite different from that of the Spasms. But, curiously enough, the daily variations in the frequency agree, without being however auite equal, as appears from the following table of the epochs of the maxima ete. Spasms Pulsations Principal maximum 11—12' PM. 0O—1l A.M » minimum 7— 8 A.M. 7—S8 A.M. Secundary maximum -t 2 BEMG asia P.M. » minimum 6— 7 P.M. 5—6 PM. The Electrograms at Batavia show nothing remarkable during the occurrence of Pulsations,, which means that no simultaneous changes in the Potential can be observed. As regards the slope of Electric Potential in the lower strata of the atmosphere, I think this will not have any influence on the magnet. In concluding this preliminary communication I will point out, that a magnetic calm favours the development of the Pulsations, which is connected directly with the quiet of might, as shown by the magnetograms at Batavia. This nightly calm is clearly indicated by the diurnal variation of the above mentioned ,deviations”, and the epoch of the minimum (1 A.M.) practically coincides with the maximum epoch of the Pulsations. But also the minimum epoch of the deviations (3 P.M.) coincides with the epoch of the secondary maximum, and this makes the connection less clear. Physics. — Dr. Fritz Hasexorurn. “The dielectric-coef ficients of liquid nitrous oxide and oxygen.” (Communication N°, 52, from the Physical Laboratory at Leyden by Prof. H. KaMgr- LINGH ONNES). (Read September 30th 1899), Measurements of the dielectric-coefficients of liquid gases have been made up to the present only by Linpr!) and by Dewar and 1) Linpp, Wied, Ann. 56 p. 546. ( 212 ) Fiewmca'). The measurements of LINDE are concerned with those gases which become liquid under high pressure at relatively high temperatures and are not in direct relationship with the following work. On the contrary Dewar and FLemina have sought the dielectric-coefficient of liquid oxygen under the same condition as J, namely at the temperature of the normal boiling point under atmos- pherie pressure. The gases were liquefied in the eryogenic laboratory of the University of Leyden, the arrangement of which is described in another place *). I shall hence confine myself to mentioning here the special arran- gements. used in the determination of the dielectric-coefficients. During the experiments the cryogenic apparatus was under the personal eare of Prof. KAMERLINGH ONN»Es, through whom alone my research was brought to a satisfactory conclusion. I wish to express here, for this and much other valuable assistance, my warmest and most sincere thanks. 1. The Method. Elccteo mele The method IT used was a modification of Gorpon’s, the principle of which is clearly and diagramatically shown in Fig. I. The in- ner surfaces of two condensors C, and C, are connected to the quadrant pairs of a THomson electrometer, and the outer sur- c, faces to one pole of an induction coil the F— other pole which is earthed together with the y needle of the electrometer, Then, if the / capacities C; and C, are equal, the needle will not be deflected on starting the coil. If C, is an adjustable condenser, then the capacity of C, with different media can be obtained and hence immediately the dielectric coefficients of these media. But this assumes that the electrometer is constructed symmetrically and that the capacity of the leads and also of the non-inductive parts of the condenser (i.e. other than the plates) are the same on the two sides. The simultaneous elimination of these two sources of error offers consi- derable difficulties. If we call vy; and yg the capacities of the quadrant pairs together OUiamfpe ff Fig. 1. 1) Dewar and Frpmine, Proc. R. S. Lond. *) KaMeRLINGH Onnus, Comm. Phys. Lab. Leiden N°. 14, Maratas, Le Laboratoire eryogtne de Leyde, Rey. Gén. d. Sciences, 1896 p. 381. And especially KaMERLINGH Onneés. Methods and apparatus used in the eryogenie Jaboratory [: loc. cit. No. 51. ( 213 ) with their leads; p, and py the characteristic constants of their action on the needle (the differential quotients of the mutual induction coefficients by the rotations); C; and C, the capacities of the two condensers to be compared; ¢; and ec, the capacities of the non-inductive parts of the condensors connected to the electrometer ; then the equation for the equilibrium of the needle is!) C 2 Cy os (—_) LZ (——) Ho as ween, 1m AG!) atn Co + 42 If however this equation is fulfilled the equality of C, and C, does not immediately follow. We can first make p; =p, by some known method. In this case equation (1) takes the form eae ft Tier Tue We can now reverse C, and C, thus changing their influence and, keeping p constant, alter y through a capacity such that the equi- librium of the needle is not further altered by this reversal. Hence besides (1') we have And from (1') and (2) it follows that we must have y; = yg and ¢;=cy if we wish to arrive at Cy — Cy > It would however be difficult te make these quantities p and y equal with the necessary accuracy. Further they alter with every change in the nullpoint of the electrometer needle, and hence these equalizations would have to be often repeated and would be certainly very tedious and lengthy. On account of these difficulties I have modified the method as follows. C, remains permanently unaltered, C) is an adjustable condenser, and is so arranged that the needle will not move when the coil is started. The condenser, of which the capacity is required, is now put in parallel with C). To bring the needle back to zero, the capacity C, must be decreased by a measurable amount which is equal to the required capacity. In this way the symmetry of the electrometer ete. requires no attention. The sole condition is that the wires, which put the unknown capacity in parallel with Cj, have not themselves ‘) See Maxwetu Electricity and Magnetism. Vol. I. p. 219. ( 214 ) a measurable capacity. Naturally this is not easily attained, but the respective corrections may be determined fairly simply as explained below. 2. Description of the separate apparatus. The electrometer was a THomson’s in its original form. When this is set up in the neighbourhood of the working pumps of the cryogenic laboratory it must be little sensitive to vibration. For this purpose I obtained the damping by air (after TopLER), instead of by sulphuric acid, and repli iced the bifilar suspension of two cocoon fibres by a platinum wire about 70 em. long and 30 4“ in diameter which can carry a much greater weight. After these changes had been made the vibrations were less than 0.1 mm. on a seale at 3.5 m. distance, even when the pumps of the cryogenic laboratory were working at a distance of 10 m., while with the original arrangement it was quite impossible to make obser- vations under the same conditions. The induction coil was worked by an alternating current making 200 vibrations per second, the spark distance at the ends of the secondary being about 0.05 mm. !). For the condenser an apparatus was used which was constructed according to NERNST*) yiz. two metal plates between which a glass plate can be displaced. Theoretically the alteration in the capacity is proportional to the position of the glass plate. In practice however the condenser must first be calibrated. This can be done with the help of a specially constructed condenser such as Nernst’s ‘Trough condenser *). The one used and shown in Fig. 2 only differs from this in that the ebonite cover has been replaced by a metal one; and the metal tube, to which the other plate is fastened, by a stiff wire D of 2mm. diam. The latter is insulated from the metal cover by a small thickness of ebonite. In a condenser constructed thus the non-inductive capacity is exceedingly small. In the construction of the experimental con- Fig. 2 denser there are two points to be primarily con- sidered; as large a capacity as possible must be introduced into a somewhat limited space, and the non-induetive capacity which is connected to the electrometer must be as small as possible. These 1) Preliminary “experiments showed that the passage of sparks of several mille- meters long did not explode liquid nitrous oxide though this is endothermic. 2) Nernst, Zeitschrift fiir physik. Chemie XLV. 4. 5) Nernst, loc. cit. conditions were fulfilled in the manner clearly shown in Plate I, which represents three different sections of the condenser together with the beaker of the cryostat, made to receive the liquefied gas, in which it is placed. The two outer plates p; and pz are connected by the nuts to one another and by the pin ¢ with the earth. The three screws s are placed in suitable glass tubes on which the five plate condenser is itself mounted. The plates themselves have a radius of 3 em. and are separated from one another by small glass rods 1 mm. long. To reduce the errors so introduced to a minimum these glass rods must be made as small as possible, and it appeared to be best to cut them from a 1 mm. glass tube with a wall of '/; mm. and then to grind them exactly equal. The above mentioned error cannot finally be more than 0.1 %/ since it enters equally into the numerator and denominator of the expression for the dielectric coefficient. The 1st, 3'¢ and 5 plates are connected with a pole of the induction coil, the 2"¢ and 4 with the electrometer. The necessary wires for this, d; and dg, are fastened to the 1st and 2n¢ plates respectively; they are drawn through small openings in the superimposed plates, and continue above through the glass tube g. By means of a pin t the whole condenser is fastened to the cover of a hollow eylinder of brass m in which the liquid to be investigated is placed. The hollow cylinder is earthed together with the two outer plates *). The method of fillimg the condenser with liquid gases must now be discussed, but some points should be first considered. The condenser and hollow cylinder must be protected as much as possible from external heat to prevent the formation of bubbles of vapour, whence they are immersed in the beaker B; under the liquid gas. The liquid gas must be employed in sufficient quantity to cool the condenser and to keep it cold, it must be kept from the deteriorating action of atmospheric air, and finally care must be taken that the vapours drawn off are not lost. All these conditions can be best obtained by the aid of a cryostat i.e. a boiling glass with its cases, such as is used in the eryogenic laboratory for measurements with liquid gases. The description of the latter can be found in another place °), The following must also be considered. The principle of the method 1) The section is taken partly through the tube g and partly through the tube \. *) By the wire g. See Plate I, Comm. N® 51. *) KamMERLINGH ONNEs, Comm. N® 51 § 3. ( 216 ) is to compare the capacity of the same condenser in air and in a given medium when all dimensions are kept strictly constant. When the capacity of the air condenser is obtained at the room tempera- ture, and that of the liquid condenser at the temperature of boiling gases the geometrical proportions are probably altered by thermic expansion and deformation, and in consideration of the large diffe- rence of temperature it is possible that an appreciable error may thus enter. For these reasons the condenser was arranged in the hollow cylinder so that this enclosed space could be evacuated and cooled in liquid gas. Then, in the manner described below, this evacuated space con- taining the condenser could be filled with liquid gas from the beaker. It must be noticed that, however thin the leads may be they always will represent a measurable capacity and hence that the smallest dis- placement of the apparatus will produce considerable errors. Especially to avoid this it is desirable to mount the apparatus as in ONNES’ method for the use of liquid gases in measurements. According to this method, the apparatus to be dipped in and filled with liquid gas is mounted in the closed boiling case, in which the liquid can be immediately poured out, so that the operations of exhausting cooling and filling with the liquid gas allow the position of the condenser and the leads to remain unaltered. The manner in which the above mentioned hollow brass cylinder is mounted with the experimental condenser in the boiling glass is given in Comm. N°. 51 § 21). The further arrangement of the covering of the condenser is shown in Plate I. The inside of the cylinder communicates with the exterior in two ways. One is the fine copper tube 7 which communicates with the part of the beaker un- occupied by the cylinder. This can be opened or closed at pleasure from without by means of a cock in which the pin 4 is moved by the rod hy and handie /4;. The other outlet is the glass tube g, through which the expanding vapours can be drawn towards wu to be collected in the caoutchoue bags ”). ") Plate I is a detailed drawing of the cryostat containing the condenser. Plate IV is a diagramatic representation of the nitrous oxide circulation and the cryostat, for the oxygen circulation see Marutas l.c. *) Vurther explanations: a, are small screws to fasten packing «,, 4 wooden block to support glass tubes 2, which the wires 7, and d, pass through, ¢ wooden block in two parts to support outflow tube without conducting of heat, f soldered in screw used in boring the canal for the liquid gas, 4, packing under the level, 4; brass mount for screwing on the same, *% leather cushion, e caoutchoue tube to connect the glass tube y with the brass covering of the condenser and protected by fishglue against the liquid gas. ¢ brass bands to make all tight with the help of the screws (217 ) Measurements are obtained with the above as follows. First the cock A is shut and the liquid gas allowed to stream into the boiling glass. When a sufficient quantity has collected there, and we may consider that the whole of the condenser has assumed the temperature of the gas, the inside of the hollow cylinder is evacuated through the glass tube g and the capacity of the conden- ser determined. The cock % is then opened so that the liquid gas streams into the inside of the cylinder in consequence of the pres- sure. When this operation is finished the cock / is again shut and the capacity of the condenser redetermined, this time with the liquefied gas as a medium!). In order to be certain that the cylinder was full of liquid gas the gauge N was found to be necessary, in which the level of the meniscus indicates outside the level of the liquid in the cylinder or the glass tube g adjacent to it. The glass tube / which connects g to V allows an equalization of pressure *). It was unfortunately impossible for the electrometer and above mentioned auxiliary apparatus to stand in the room where the refrigerating machinery is installed, partly from want of space and partly because of the ievitable vibration caused by the working of and attendance on the pumps. Hence I had simply the choice be- tween, placing the boiling flask containing the condenser in the neighbouring room where the electrometer already stood; or keeping the boiling flask in the cryogenic laboratory and connecting the condenser to the electrometer by adequately long leads. In the former case the liquefied gas would have to be conveyed to the boiling flask through about 5 m. of tubing into which it would be very difficult to prevent the entrance of heat, and a successful termination of the research would be doubtful. This consideration caused me to primarily favour the latter arrangement, although the sensibility of the method is undoubtedly diminished owing to the non-neglectable capacity represented by the long leads. Finally I considered that the advantages of the latter arrangement outweighed its disadvantages. It appeared to be necessary to eliminate the influence of the long indicated 3 7, p, 9, %, Ua, W, @y see Comm. N°. 51 § 2; ¢, ¢, copper mountings to fasten steel pins v,, v2. The lateral opening of the glass tube g can be clearly seen in front of the side tube uw, of the brass 7’ tube. 1) In the first of the three sections given the beaker and condenser are empty, in the second the beaker is full and in the third both are full of liquid gas. *) The gauge has been turned in the second section in order to show 7. As remarked above the gauge has not been drawn in Plate I. Comm. N°, 5t § 2, it is observed through K, (Pl. I, loe. cit.). ( 218 ) leads, for which auxiliary capacities were required. These were made on the same principle as the experimental condenser; metal plates which are connected by glass tubes and separated by small glass rings. The so formed condenser is then insulated by a layer of paraffin and placed in a card-board box coated with tin foil. The foil is put to earth so that the capacity is quite invariable and inde- pendent of the presence of neighbouring bodies. Such an auxiliary condenser is also useful when experimenting on a substance with a large dielectric-coefficient, for then the glass plate of Nerysr’s adjustable condenser may not be sufficiently long to give the required change of capacity. In such a case the auxil- lary capacity should be put in parallel with the adjustable condenser. 3. Arrangement of the apparatus. In order to avoid the errors arising from the change of capacity of the leads, the whole apparatus must be immovably and perma- nently fixed. For the same reason the condensers should be very carefully switched on and off. This requires the use of a switch board to which the taunt wires are fixed and the capacity of which is as small as possible. Indeed for this purpose I employed small ebonite plates provided with mercury cups which could he connected by small metal bars. A diagramatic representation of the arrange- ment is shown in Fig. 3. Fig. 3. From the two quadrant pairs of the electrometer two wires pro- ceed to the mercury cups a and 6, and then to the small key S, by which a metallic connection between the quadrants can be made and the zero reproduced. From the six other mereury cups ¢, d, e, fy g; h, leads go to the inner plates of six condensers y, No, A, B, C, D, of which Nj, Ng are adjustable NeRNst condensers and 4, B,C. D are auxiliary condensers as described above. The outer plates of these last four condensers can be connected as required to the earth or to the pole P of the Rumkorff coil to which the outer plates of N, and N, are always connected. When the key V is shut the condensers are earthed together. From H a wire proceeds into the neighbouring room, and can be connected by the key 7 to the experimental condenser £; the outer plate of which is always con- nected to the coil. Although only one adjustable condenser is required by the theory of the method, the second Vy is used partly for convenience, partly for the calibration of the former ') as described below. 4. Calibration of the adjustable condensers. The adjustable condenser was, as mentioned above, an instrument constructed after Nerwnst’s design. The alteration in the capacity would be proportional to the movement of the glass plate if the apparatus were theoretically exact. This is naturally not the case, so the condenser must first be calibrated. The method employed is also due to Nernst. The calibration condenser is put in parallel with the adjustable condenser as described above, and the displacement determined which is required to re-establish equilibrium. When this is done the calibration condenser is again cut off, and equilibrium re-obtamed with the help of the other adjustable con- denser. The former condenser is again put in parallel with the calibra- tion instrument, the necessary displacement measured and the process repeated until the glass plate is exhausted. In this way one finds the different positions of the glass plate which correspond to equal differences of capacity. The application of this method of calibration depends upou the supposition that the capacity of the non-inductive parts of the calibration condenser is negligible, as well as that of the wire which puts it in parallel with the adjustable condenser, The first condition is almost absolutely fulfilled by the condenser described above (see fig. 2). The use of the wire can moreover be avoided as shown by Nernst *), The condenser is insulated by an ebonite plate and is so arranged that the 2 mm. wire D, which projects above the cover of the condenser, stands at the same height as the wires of the adjustable condenser (Fig. 3). The cali- bration condenser can now be switched on and off by shifting it for about 2 mm. in a horizontal direction, so that the wire D is brought into contact with the lead. The respective positions of the 1) See Nernst 1. c. alls cee ( 220 ) leads, condenser plates ete. will be so little altered by this, that an error from this change is scarcely to be feared. The whole of the connecting wire is hence reduced to the above mentioned wire J? which has already a small capacity. The error is still further reduced, as VD is inductively affected by the metal cover of the calibrating condenser and hence may be considered as part of the inner plate of this. The results of a calibration performed in the manner described above are given in the second column of Table I. TABLE I. C; Position apa of the Diff. Gry: | glass plate 0 8.40 | ( 865.65 god 6.40 2 21.45 6.20 3 | 27.65 5.95 4 33.60 6.10 5 | 6939.70 6.20 6 45.90 6.35 Bal 52.25 6.58 8 | 58.83 | 6.70 9 | 65.538 | 6.78 10 72.31 | | 6.41 ll 78.72 | 6.16 12 $4.88 5.59 13 90.47 5.25 14 95.72 4.96 15 100.68 4,54 16 105.22 | 4.17 17° | 109.39 4.1 18 I13 .52 3.62 19 117.14 These numbers are the means of four series of observations in which the maximum difference was 0.2 mm. They form the basis of ( 221 ) the following measurements. As only the differences of capacity are required we put the capacity in the position 8.40 as 0, in the position 15.05 as 1 ete., i.e. we take that of the calibrating con- denser as unity. The corresponding numbers are given in the first column of the above table, from which intermediate values can be obtained by graphic interpolation. As a control of the accuracy of the calibration values given in Table I the following work was undertaken. Measurements were made with another condenser in the same manner as __ before with the calibration condenser, but the connecting wire was about 12 em. long and had hence a relatively large capacity. Let ¢ be the capacity of this condenser, d that of the wire and y that of the electrometer together with its leads, which were unaltered throughout the experiment. Further let 2, 7, 72.... be the capacities of the adjustable condenser which correspond to the different positions of the glass plate obtained in the calibration. Hence, when the condition that the needle is in equilibrium is fulfilled, we have tomes vy +e 4 wis np) + ¢ a = = aie Veter. (3) A ie Os Se ay a from which we have immediately Kae py Seca ape Ob = = Ss oor Ge as 7 NS LK vy — 7 hence the consecutive displacements of the glass plate are proportional to one another. The numbers given in Table IL were obtained in this manner and each is the mean of three values as satisfactory AGB Slik. ell: ee Eosttion | Capacity | Capacity of the Diff. | observed.) | calculated. | | | } glass plate. 5225 | 7.000 ey | 1.439 (age 61.80 8.439 8.440 0.001 1.473 | 71.80 | 9.914 | 9.933 | 0.019 | | 1.573 | | S77 | 11.487 | | 11.485 | 0.002 | | 1.612 | | 91.02 | 13.099 | 13.099 | 0.000 | 1.684 } 99.61 | 14.783 | 14.775 | 0.007 | 1.743 | 107.46 | 16.596 | | 16.516 | 0.010 ike 114.81 18.330 18.325 0.005 ( 222 ) as in the former observations. The second column contains the capacities corresponding to the respective positions and obtained by the above graphic interpolation. Column (3) contains the differences of the capacities in column (2) which should be proportional to one another. From the various consecutive quotients the geometric mean is obtained and_ the numbers caleulated which are actually proportional to one another and which also agree as much as possible with the numbers in column (3). From these “caleulated differences” column (4) is obtained by addition. The differences azain between columns (4) and (2) are found in column (5) which we may safely call errors of observation. The greatest is 0.019 of the capacity of the calibrating condenser and is equivalent to a displacement of 0.13 mm. of the glass plate in the adjustable condenser. We can take this as the highest limit of attainable accuracy, being that with which a single capacity is itself determined. Tables IIT and IV were obtained in the same manner. The former relates to the part of the glass plate which was not used in Table II, while the latter represents the results of an experiment in which the former method was carried out with a considerably greater capacity. In will be seen that these tables show “observation errors” of the same magnitude as Table II, and the remarks made above concerning the accuracy of the determinations hold also with these values. On the magnitude of the errors we may notice the following. The accuracy of a single adjustment was at a maximum 0.1 mm. as shown by a number of observations, in which the readings Mm -Ay Bela EK. SE: ore (Capacity Capacity of the | Diff. A Z observed. caleulated. | class plate. 52.25 7.000 | — — 1.445 43.15 BEY || 5.545 0.010 | 1.395 84.55 | 4.160 | 4.164 0.004 | 1.310 26.70 2.850 2.854 | 0.004 1.255 18.90 1.595 1.611 0.016 1.170 11.25 | 0.425 | 0.431 0.006 ( 223 ) TABLE IV. Position Capacity Capacity of the Diff. observed. calculated. glass plate. a 27.15 2.920 _ = 4.080 52.25 7.000 6.988 0.012 4.220 80.10 | 11.220 11.233 0.013 4 445 103.70 | 15.661 15.663 0.002 with one adjustable condenser were repeated ceteris paribus. Each of the numbers given in the above four tables is deduced from three readings, two with the condenser N, and one with N». The values which are given in the second column of Tables H, III and IV have a larger inaccuracy, since the errors of direct reading are added to the eventually similar errors of the calibration curve. But all the values are the mean of four series of three observations, so the required error is reduced to 0.12 mm. This is in accordance with the maximum error seen in the Tables Il to IV which is 0.13 mm., while most are much smaller. These considerations are not however very precise, for the caleula- tion of a capacity from the calibration curve implies the use of more than one observation, and the values ,Capacity calculated” are derived from all the observations. Hence the calculated error must be greater than 0.12 mm., and therefore the maximum error of 0.019 in the capacity — or of 0.13 mm. in the position of the glass plate — is entirely explicable from the reading errors. This result leaves no doubt as to the accuracy of the principle of the expe- riments. 5, Measurements. The final determinations were made in the following manner. The adjustable condenser NV, was set at 21.45 and the key T (Fig. 3) opened, equilibrium was then attained by connecting up the auxiliary capacity and adjusting M2. The key 7 was then closed and 4, readjusted until equilibrium was again established. If now we call 7) and 2 the capacities of Nj, in the first and second positions respectively, y the capacity of the electrometer and its leads including the wire from H to the key 7, d@ that of the wire from 7 to the Proceedings Royal Acad, Amsterdam, Vol. Il, = 224 ) experimental condenser, ¢ that of the experimental condenser. with vacuum as a medium, Then we have as above in equation (3) Xo ate Aas bat 2 or d Lyi Li —'C =! —~ he joy ae os) ee) if When the experimental condenser is now filled with a dielectric fluid its capacity will be altered to c’ and a considerable movement of the glass plate will certainly be required to compensate it. If we call the capacity of the condenser in this third position -g, then we have in analogy with the foregoing The differences 2) — 2,3 %— #2 can be immediately read off. In the same way we may express the difference c' — ec as a measurable quantity from (4) and (5). From this we can determine the value of ¢'/e if we know the value of ¢, which can be obtained by mea- surements in which the value of y is purposely varied. But we find that the differences of the readings occurring in the observations are so small that the value of ¢ cannot be determined to a greater accuracy than 10 °/o, and is hence useless. A determination of the value of «,d/y is required, and this can be made once for all by cutting off the lead close to the condenser and fixing it in almost exactly the same position as before by means of wax, but insulated from the condenser. One can now convince oneself that the error produced in fixing the wire does not reach 0.2 mm., by loosening and refixing it, moreover the error occurs equally in the numerator and denominator of the expression for the dielectric-coefficient. In the same way the capacity of the wire can be determined, by pro- eeeding with the lead in exactly the same way as with the whole condenser, and thus arriving at the equation and hence in which x’) is the capacity of the adjustable condenser after the last alteration. From (4), (5) and (6) one obtains immediately for the dielectric coefficient Ee (tae It srtolad iho ease 3} (7) ¢ (x — v)) == (wv 0) = 9) In the following account of the results of my measurements let y, be the position of the glass plate of the adjustable condenser after switching on the experimental condenser with a vacuum as medium and at the temperature of the liquid gas; y2 be the position when the medium is the liquid gas. The capacities corresponding to these positions are, as before, indicated by 2, and 72. Before the determ- inations the glass plate always stood at 21.45 (so 2) = 2.000). 1. Nitrous owide. 19 June: Of SS O8o se. 8 (This reading was omitted) yg = 106.2; 106.5; 106.2. 20 June: y= 58.85; 58.85; 58.90. ya = 107.90; 108.10; 107.95. These determinations are not however really trustworthy, as it appeared that the nitrous oxide became quite impure, The following results are final. 9 July: y= 56.30, 56.40; 56.35 Means 56.52 yp = 106.00; 105.90; 106.00; 106.20 106.03 (+ 0.17). The corresponding capacities are: (a, = 2.000). y= 7.640. aoe LOI: — DO no So ~— 2. Oxygen. LO July: fj — 00.10 OO elena Means 57.72 yo = 86.15; 86.10; 86.05; 8585; 85.95 86.02 (+ 0.17) The corresponding capacities are. (7) = 2.000) #, = 1.843 a, = 12.200 This gives the aboye defined difference. ro!—a) = 3.731. As the glass plate can only be moved from 21.45 to 8.40, an auxiliary condenser must be employed; it is however scarcely worth while to communicate the resulting data in extenso. From the above results and formula (7) we obtain the following values for the dielectric-coefficients : eee Oe eee M0 = F540 48.731 | Ree ead: (8) 10.200 + 3.731 [Gp nose 0 Deretesa SUN Ba gee > — "5.843 3.781 ‘ To these values we can make a correction; we must consider that not only the experimental condenser but also the leads were immersed to a definite height in the liquid gas, while the entire length of the leads was 88 cm. The value d ie = 3.731 ' — vo = Ea) = 7 only applies rigidly when the whole lead is in air. When the capacity of the condensers filled with» liquid gas is required the quantities d and (7) — 79) must be multiplied by 83 5 (= pe =) where K is the diclectric-coeffcient of the medium. For this cor- rection the approximate values given by (8) are quite sufficient, and ( 227 ) the influence of the surrounding tubes is negligible in view of the accuracy obtained. We arrive finally at the following values for nitrous oxide: 14.197 4+ 3.731 (2 + 1.912 = RaNcS Sev t 88 ine = 1988 De, 5.640 + 3.731 for oxygen: 83 20 ; i= 1.455 — 10.200 + 3.781 (<= + 1.455 ; aes es TS = 1465 ®. 5.843 +} 3.731 As one sees the values of yg are a little more variable than those which refer to our condensers when filled with air (see § 4). This may be due to variations of temperature or small impurities. When we take this into account and assume for the other numbers the accu- racy arrived at above, we find that the maximum error (if we assume that the errors are additive) in the dielectric-coefficient of nitrous oxide is 0.5 °/) and in that of oxygen 0.7°/, while the error probably can be smaller. The value 1.491 given by Dewar and Fiemine for the D-C. of . oxygen at the normal boiling point, differs from my value by 1.8 °/, an agreement which may be considered as satisfactory, if we take into account the deviations in the various values arrived at by different workers, even where the experimental substance can be more easily produced than liquid gases. 6. Application of the Cuaustus-Mosorti formula to the results. An obvious application of the above results is employing them to test the Crausrus-Mosorti formula. This is usually expressed RE 2 ny. a Const. 9) where & is the dielectric-coefficient, ¢ the density. This equation enables us to calculate the D.-C. of a substance in the liquid state when we know the D.-C. in the gaseous state and the densities of both aggregates. This is unfortunately not possible for nitrous oxide as the density at the normal boiling point is not accurately known. However as it is very interesting to see how my value agrees with the observations ( 228 ) of Lixpe!), we will take 1.15 for the density of nitrous oxide after Navrrerer *). Hence we obtain 4.85 as the value of D for liquid nitrous oxide at its boiling point, while Linpre found 5.42 for the same at 0° C. For gaseous nitrous oxide we obtain D = 5.103 assuming d= 1.969 10°, K == 1.001158 after Kiemencic. With oxygen also only an approximate test of the formula is possible as the required data are inaccurate. More especially the value of the D.-C. of gaseous oxygen is unknown, and there exists only a well grounded supposition by Dewar and FLEMING *) that it will not differ sensibly from that of air, which was found by both BotrzMaANN and KLemencic to be 1.00059 at 0° C. and 760 mm. The density of gaseous oxygen is 1.4292 « 10-3 at 0° C. and 760 mm.“), that of liquid oxygen is 1.124 after OLSzEWwskI °), 1.1375 after Dewar °) and 1.134 after LADENBURG and KrtGet *%). If we then assume 1.00059 for the D.C. of gaseous oxygen, and 1.1375 for the density of the liquid we arrive at 1.556 as the D.-C. for the latter, which value agrees as far as the order of magnitude with the values found by Dewar and Firmina. Conversely assuming the D.-C. of the liquid oxygen we obtain the value of 1.00051 for the gas instead of 1.00059. From the uncertainty of the data employed a better agreement ‘cannot be expected. The experiments are at least not contrary to the Criausius-Mosorr1 formula, while the further consideration of its application to oxygen must be deferred for the present. Physics. — “The Hatut-effect and the increase of Magnetic Re- sistance in Bismuth at very low Temperatures’. By Dr. E. vaAN Everpincen Jr. (Communicated by Prof. H. Ka- MERLINGH ONNES). (Will be published in the Proceedings of the next meeting.) 1) ee. 2) Pogg. Ann, 62 p. 134. \ desc. *) Lanpour and Bornstein, p. 116. 5) Ztsehr. f. phys. Chem. XVI, 383. 5) Proc. Royal Instit. 96. 7) Ztschr. f. Compr. Gase 99 p. 77. (November 22, 1899.) KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TH AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday November 25th, 1899. Ce (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 25 November 1899 Dl. VIII). CONTENTS : “The Hatt- effect. Pat the increase of resistance of anit in aN magnetic field at very low temperatures”, I. By Dr. E. van Everpincen Jr. (Communicated by Prof. H. Kamertmcu Onnxs), p. 229. — “The resorption of fat and soap in the large and the small intestine’. By Dr. H. J. Wampurcer, p. 234. — “An application of the involutions of a higher order’. By Prof. J. Carpinaat, p. 234. — “On some special cases of Monar’s differential equation’. By Prof. W. Kapreyn, p. 241. — “Two _ earth-quakes, registered in Europe and at Batavia”. By Dr. J. P. van per Stok, p. 244 (With one plate). — “The potential function ¢ (7) = A eis He and Fe A sin (qr + «) ¢(r) = ——_———— and the potential function of van per Waaxs”. By Dr. G, BAKKER wr (Communicated by Prof. J. D. van per Waats), p. 247. — “On the systematic corrections of the proper motions of the Stars, contained in Avuwers’-BrapDLey- Catalogue, and the coordinates of the Apex of the solar motion in Space”. By S. L. Veenstra (Communicated by Prof. J. C. Kapreyn), p. 262. — ,,On d-sorbinose and l-sorbinose (-tagatose) and their confignrations”. By Prof. C. A. Lopry pe Bruyn and W. ALBERDA VAN ExensTEix, p 268. — .,On the action of sodium mono- and -disulphides on aromatic nitro-compounds”, (Preliminary communication) By J. J. Branksma (Communicated by Prof. C. A. Lopry pe Bruyn), p. 271. — ,,The alleged identity of red and yellow mereure oxide”. (1). By Dr. Ernst Conen (Communicated by Prof. H. W. Baxuurs Roozenoom), p. 275. — ,,The Mnantiotropy of Tin”. (III). By Dr. Erxst Conen (Communicated by Prof. H. W. Bakuuis RoozEBoom), p. 281. (With one play ; The following papers were read: Physics. — Dr. E. van Everpincen Jr. “The Haut-effect and the increase of resistance of bismuth in the magnetic field at very low temperatures”. 1. (Communication N°. 53 from the Physical Laboratory at Leiden, by Prof. H. KAMERLINGH ONN#s). (Read October 28, 1899). 1. In the Proceedings April 21 ’$7, p. 500 and June 26 ’97, p. 74 measurements on the above subjects were just mentioned. These are 17 Proceedings Royal Acad, Amsterdam, Vol. LL. described at greater length elsewhere (Thesis for the doctorate, Chapt. VII). At that period however these measurements could not be very aceurate, in consequence of the work in the eryogenic laboratory being legally prohibited on account of its alleged dangers, so that we could not adequately use liquid gases for reaching low temperatures. Hence I resorted to a mixture of solid carbon-dioxide and alcohol; but then the temperature remained constant only for a short time, and the value given is not quite accurate. The difficulty mentioned being removed, I have taken this work up again, and am now able to communicate some figures, obtained by means of a bath of boiling nitrous oxide, i.e. at a temperature of about — 90° C. 2. The liquid-bath. Two forms of vessel for the liquid gas have been used. The first consisted only of a very narrow vacuum-glass, outer diameter 33 m.m., inner diameter 21 m.m., height about 35 c.m. This was filled to twe thirds of its height with liquid nitrous oxide by means of the spiral packed in solid carbon-dioxide, described in Comm. N° 51, § 4!). It was then mounted between the poles of an electromagnet. The experimental apparatus could be placed in the vacuum-glass before filling this, so that after filling only the necessary leads had to be connected; usually however it was lowered into the vacuum-glass after this had been placed between the poles, and was then quite ready for the experiment. A single filling, in which about 0.4 kgm. of nitrous oxide in all was taken from the cylinder, was sufficient to cover the apparatus for more than two hours. A draw-back of the use of vacuum-glasses is however the large space between the poles, which is required even with this narrow glass, and prohibits the use of comparatively intense fields. In order to meet this difficulty a second form without a vacuum wall 2) was constructed, drawn in fig. 1. The vessel for the liquid in the strict sense of the word consists of a cylindrical wooden receptacle a, in the bottom of which a vessel made of compressed paper with oval section and wooden bottom is glued. Externally 1) Verslag der Verg. Kon, Akad. v. Wet. Amsterdam, 30 September 799, p. 135. Comm. Phys. Lab. Leiden N° 51. 2) In the same way in the ethylene boiling flask (Comm. N® 14, Versl. Dec. *94) the condensed gas is only sufliciently protected against heat by air-spaces and wool wrapping. ( 231 ) these vessels are covered with shellac, internally with fish-glue. Round the paper wall about °/, m.m. thick a cotton thread has been wound forming a layer also */, m.m. thick ; while the inner minor axis 1s 12 m.m,, the maximum thickness is thus restricted to 15 m.m. ms ny By means of the conical caoutchouc ring ¢ the vessel a is connected to the glass tube d, which becomes narrower at the top. Onto this the brass T-tube e fits, which is connected to it by means of a caoutchouc tube. Through the caoutchoue stopper g lead four glass tubes h,...h4, containing the leads for the experimental apparatus. For pouring out the condensed gas a steel capillary tube &, covered by a rubber tube leads through the side-tube of e and is screwed on to the above mentioned condensing spiral. If it is desired to collect the evapo- rated gas, all connections may easily be made air-tight; for this purpose the glass tubes are drawn out at the top and the leads may be cemented there. Conduits leading to a pump or gas- sack can be then connected to the side tube of e. The T-piece e fits also on the above described vacuum-glass and may serve to close it, as will be necessary in further researches. Untill now there was no objection to leaving both baths open and allowing the gas to escape. In the observation of the Hatt- effect in an electrolytic plate of bismuth, to be mentioned directly, the vessel a was about half filled after a small quantity of liquid had evaporated. It took more than an hour, before the level of liquid was lowered to the opening of b. In these operations about 0.7 kem. of nitrous oxide was used. The space between the vessels a and b, the polepieces and the coils of the magnet was filled throughout with wool. 17% ( 232 ) 3. The Hawr-effect in electrolytic bismuth. The plate is obtained n the way described in Comm. N°. 42 !). The method of observation is the same as in all the previous experiments, and was described in Comm. N°. 26). The plate car- rier 1 is made of ebonite. The leads for the Haut-current n;%2 are only 0.1 mm. thick, in order that they may conduct as little heat as possible, the larger resistance being immaterial. The wires m, m supplying the primary current of about 0.5 amp. were chosen somewhat thicker, 0.25 mm., in order to decrease the heat produced in the liquid without in- creasing too much the heat conducted to it. The following results were obtained for the coefficient of HaLu R and the product RM (M = Magnetic force). MAGNETIC FORCE Temp. 1500 | 2600 3900 | 5000 | 5800 | 8100 | R | RM] R | RM] R na | R no R na | R | RM 4+. 15° |] 27,2 | 14,5 | 20,9 | 98,2 | 20,0 | 39,0 | 9,4 | 47,0 | 9,2 |52,7]— | — SEGOO si 2181 nO 74 |e | een | 2787016904) — sl = e381) Oller 7 GalaTS-0 > (RM was expressed in the unit 1000 C.G_8.) Hence in all fields the Haxt-effect has been increased, especially in the weakest field. The latter particular was also observed before *) with other bismuth for temperatures ranging from 20°C. to 100°C. The coefficient of Harn at — 90° C. in a field of 1300 C.G.S. units is 21,1 and exceeds by far the highest value formerly obtained. The question delt with in several earlier communications, as to whether or no a maximum HAtt-effect exists at low temperatures, is not definitely answered by these measurements at only two tem- peratures, but the rapid increase points to the contrary. A more decisive answer will be obtained I hope before long by repeating the experiment in a bath of liquid oxygen. The figures communicated for the temperature — 90°C. are not yet quite final, as the contact-resistance at the secondary electrodes 1) Versl. 25 Juni 98, p. 98. Comm. N°. 42, p. 7. 2) Versl. 30 Mei ’96, p. 47. Comm. N® 26, p. 3. 3) Versl. 30 Mei “96, p. 5. Comm. N°. 26, p. 20. ( 233 ) increased considerably during the experiments. Though the resistance in the cireuit of the Hati-current was measured several times during the experiments, some of the interpolated values may still contain a small percentage error. In future I intend to avoid this by altering the construction of the plate carrier. 4. Magnetic increase of resistance and crystallographic direction. The experiments made before on this subject with one of the bars (N°. 1) cut out of a crystalline piece from Merck !) have now been repeated at — 90° C. The method of observation was the same as described in Comm. N®. 48.%) The use of the above described vacuum-glass offered especial advantage in this case, for the bar could be rotated, together with the whole frame in which it was placed, about its greatest axis, which was vertical. In this manner the lines of magnetic force could be made-to coincide with different crystallographic directions, without altering anything in the adjustment of the electrodes etc. This easy turning had only one disadvantage, that it sometimes occasioned movements during the experiments. For accurate measurements therefore it will be necessary to fix to the frame a rigid stem provided with an index. The following results are therefore only mentioned because they evidently prove that the differences in inerease of resistance formerly observed in different positions of the bar were only caused by the change of the angle between the lines of force and the crystallo- graphic directions. In the following table column I contains the positions in which the direction of maximum resistance ®) coincided with the lines of force, II the positions in which this direction was perpendicular to the lines of force. Percentage increase of resistance, Temp. MAGNETIC FORCE, 2650 | 3800 1) Versl. 21 April °97, p. 498. Comm. N°, 87, p. 13. | I I *) Versl. 25 Maart ’99, p. 486. Comm. N®. 48, p. 6. %) Versl. 21 April 97, p. 498. Comm. N®, 37. p. 13. For the sake of comparison we may note, that formerly at the temperature 15° C. and in a field of 7700 C.G.S. units the increase was found to be: in the position I 6,5 II 14,9 5 Physiology. — “The resorption of fat and soap in the large and the small intestine”. By Dr. H. J. Hampurcer. (Will be published in the Proceedings of the next meeting). Mathematics. — “On an application of the involutions of higher order”... By Prof. J. CaARDINAAL. 1. One of the best known problems of the theory of the pencil of conics is the determination of the number of particular conics in such a pencil, where one rectangular hyperbola, two parabolae and three pairs of straight lines are obtained. The corresponding problem of geometry in space, namely the determination of the number of particular quadric surfaces in a pencil of those quadrics (pencil of S*), offers more difficulties. It is true, it 1s easy to prove that there are three paraboloids in a pencil of S*; but more difficult is it to trace the number of other particular groups of surfaces. The surfaces of revolution cannot be reckoned amongst these, having to satisfy two conditions. However, the orthogonai (rectangular) hyperboloids can be, as it will be proved that these are bound by one condition only. My purpose in this communication is to investigate first how many rectangular hyperboloids appear in a general pencil of S* and consecutively to prove that the construction may be brought back to a problem of synthetic geometry in the plane, a problem where the theory of involutions of higher order must be applied. 2. According to definition an hyperboloid is rectangular when the cyclic planes are normal to two generatrices. With Ciessca }) we however think it preferable to choose a definition, in which we make use of the section of the hyperboloid with the plane at infi- nity. To investigate the rectangularity we set to work as follows: 1) CuepscH-LinDEMANN: Vorlesungen iiber Geometrie, (‘Lessons on Geometry”), Vol. II, Part 1, p: 195, where we also find the literature of this subject mentioned. ( 235 ) first we determine the section (H2) of the hyperboloid with the plane at infinity, then we construct the chords of intersection of H? with the imaginary circle (C2) in that plane. If the pole of one of those chords of intersection in reference to C? falls in H?, the hyperboloid is rectangular. 3. By this method the problem of space is transformed into a problem of the plane; in the further treatment, however, we come across the difficulty of an imaginary conic C?. For a better insight into the problem, we substitute for the present an arbitrary plane for the plane at infinity, a real conic for the imaginary circle and then the problem is formulated as follows: Given a conic A? and a pencil of conics with the also real base points 1, 2, 3, 4; to determine a conic LZ? of the pencil, for which the pole of a chord of intersection with A? lies on L?. 4. If L* is found, we can still make the following remark about the solution: Let Z? intersect the conic A? in the points Z,, LZ, I, Ly; let Ly, be the pole of Z, ZL, in reference to K? and let L? be brought through Z,., then according to a known theorem LE? will also pass through the pole Z,, of the opposite chord LT; L,%). So the points 1, 2, 3, 4; Lio, La, lie on the same conic, After this remark we can pass to the construction of the locus of the poles, supposing that Z° describes the whole pencil. 5. Let A? be a conic of the pencil (1234): it intersects A? in the four pomts A,, 4,, 43, Ay. These four points will give rise to six common chords A, A,, A, 43, A, A,, AzAg, A, Ay, Az Ay which correspond to six poles Ay... . As,. If A® is replaced suc- cessively by all the conics of the pencil, every new conic gives rise to four new points of, intersection: on A? these quadruples form an involution of the fourth order. It is clear, that if 4, is chosen arbitrarily and conic A® is constructed, Ag, Az, A, on K® are also determined, and that reciprocally when one of the last points, take Ag, 1s chosen, A,, A, and A, are also determined. The six lines joining the quadruples of points by two envelop a curve C, of the third class ”). 1) Sremer-Scurorer: Theorie der Kegelschnitte, (“Theory of Conies”), II, 3rd edition, p. 526, problem 90. 2) RK. Sturm, Die Gebilde ersten und zweiten Grades der Liniengeometrie, (‘The figures of the first and the second order in the geometry of the straight line)’, [, p. 29. Miuinowsk1, Zur Theorie der kubischen und biquadratischen Inyolutionen, (‘Theory of cubic and biquadratic inyolutions”) Zeitschrift f. Math. und Physik, 19, p. 212 ete, ( 236 ) We can determine the order of this curve C; in the following way: Construct one of the common tangents t; of K2 and Cy; let 7, be the point of contact of ¢; with A®, then 7, is a double point of the involution. Through 7, still two tangents can be drawn to C;; they intersect A? in the branchpoints of the involution; these branchpoints are common points of K? and C;. We can conclude from the number 6 of the common tangents that there are 12 of these branchpoints; therefore ©, intersects the conic K? in 12 points. Hence €* is of the sixth order and may be called C°. 6. The locus of the poles of the tangents of C® in reference to K? is the reciprocal polar curve C® of C%; it is of the third order and of the sixth class. We imagine once more a point A). on C® as the pole of chord A, A, of A?; A, and Ay determine two points of the corresponding conic A? of the pencil which intersects K? moreover in A, and A,; A® also intersects C* in the six points A's, Alig» » + A'z4. Moreover five other poles will appear on C? besides Aj, the poles of the chords A,As, A,A4y, Agd3, Ao44, Ag Ay By assuming one point on C*, two groups, each of 6, are deter- mined on C®, the group A and the group A’. If one of the points A is taken arbitrarily no point of group 4 will coincide with a point of group A’. 7. The following conclusions may be arrived at from the preceding: a. If we assume successively the points Ajo, By, Cjg... on C3, as many groups of 6 points are formed; each of the points of the group can determine the whole group unequivocally, so the points A, B, C... form an involution of the sixth order on C3. b, The points of intersection A’, B', C'... of the conics with C® also form an involution of the sixth order. c. Each point of group A’ corresponds to any point of group A; reciprocally each point of group A corresponds to any point of group A’; so both involutions are projective. d. The points of coincidence of both involutions determine the conics which give the solution of the problem (3). 8. The projective involutions on the same bearer are both of the sixth order, so they have 12 points of coincidence !), These points may be indicated more closely in the following manner: 1) E, Korrer, Grundziige einer rein geometrischen Theorie der algebraischen ebenen Curven, (“Elements of a purely geometrical theory of the algebraic plane curves’’.) p- 88 ete. wo ( 237 ) C8 intersects K? in 6 points; these 6 points are at the same time the points of contact on A? of the common tangents of K2 and C®. From this we can conclude that for these points the end- points of the chords of intersection coincide; so in these points conics of pencil (1 2 3 4) will touch A*. If we imagine one of these points 7, to be given, a conic of the pencil passes through this point, and as it touches A*®, the corresponding pole falls in 7); from this we conclude that: The 6 points of intersection 7... 7; of C® and K? are 6 of the points of coincidence of both involutions; so we have still to account for 6 other points of coincidence. Let us call one of these points Aj, then the conic through Aj, will meet K*® in Aj, Ay, As, Ag and will pass through A.,, the pole of A, 4,. Hence these six points can be divided into three pairs of points (Aj) Ag) (By Begs) (Cig C54). By the way we remark that the obtained result is in accordance with the fact, that six conics of a pencil touch an arbitrary conic. 9. The found three pairs of points determine the three conics which will solve the problem. We however add a second deduction, ( 238 ) which is connected, as will be proved, with the theory of double points of curves of higher order. Tet A? again be a conic of the pencil (1 234); we imagine two of the points of intersection of A® with K? to be constructed, take A, and Ay, and moreover the pole Aj) of A, Ag in reference to K*® (see diagram). The tangents A, Aj. and A, Aj. intersect the conic A? for the second time in the points P, and P,; in the same way we can also determine the tangents in the points A, and A, with their second points of intersection P, and Py. If A® describes the whole pencil, P,, Py, P;, Py generate a locus; at the same time the poles A, ... Az, generate the locus C* found formerly. The conics forming the solution of the problem proposed sub (3) must now be brought through the points of intersection of the curve C® with the locus of the points P,, Py, Ps, Ps. 10. To determine the order of the locus lastly named, let us take a straight line / and determine how many points it has in common with it. We take a peint A, on J, draw from that point iwo tangents to A*® and construct the conic (1234) through each of the points of contact; as we can construct two conics, four points of intersection A‘, A’s, A's, A's on J will be found. So to one point A, belong 4 points A’ in the just found correspondence. Reversely if we construct the conic passing through A‘), then it also passes through one of the other points A’say A’,; it determines 4 points of intersection with A?; the tangents to A* through those points determine still three points A», ds, 44 besides A). Conse- quently 4 poimts A’ correspond to one point A and 4 points A to one point A’, So there exists a projective correspondence (4,4) between these points A and A’ which possesses 8 points of coincidence. So the required locus intersects / in 8 points, hence it is a curve of the 8th order. 11. However, this curve breaks up into two parts. It is clear that A? itself belongs to the locus of the points of intersection of the tangents to AK? with the variable conic A?. The remaining curve will be of the 6 order; we have now to investigate its particular points. These are the following: a. The points 1, 2, 3, 4 are double points of K*%. To prove this we consider point 1, from which we draw the tangents ¢, and t, to K2, There is a conic of the pencil (1234) passing through the ( 239 ) point of contact t; and a second through the point of contact 4; if the variable conic describes the pencil, then the jocus will pass two times through the point 1; so 1 is a double point and so are 2, 3 and 4. b. The points of intersection of A° and C® are double points. C3 is the locus of the poles Aj... . A343; im these poles two tangents concur; so the locus also passes two times through these poles. It is evident that we are dealing with points of intersection of C3 and AK“, not lying at the same time on A, so these are the six points (Aj., As4); (Bia, Bs), (Cis C34) formerly found. 12. It is now evident, that the curve K® has ten double points; so it is unicursal. Of these points six lie on C*%, the remaining 4 are 1, 2, 3, 4. The six double points representing 12 points of intersection of K°® with C%, there are still 6 points; these are evidently the points where C* also intersects K®, so that now all the points of intersection of ©% and K® are found. Moreover it is clear that the curve A® touches the curve A® in the six common points, so that it has no more points in common with it. Au additional remark is, that the 10 double points have a partic- ular position in reference to each other. They are situated so, that the points A lie in pairs with the 4 points 1, 2, 3, 4 on a conic. This corresponds with the geometrical truth that the ten double points of a curve of the 6 order cannot have an arbitrary position in reference to each other. 13. The algebraic reckoning comes to a similar result. Let the hyperboloid be: ed y 22 D ar = 2 9 = 1 : ay b* c* This is rectangular, if 1 1 1 1 1 Sa ieee OM, Fe a a ta b* m Ce a If we start from a general equation of a quadratic surface @ 1 @ + og y® + agge?> + .... = 0, ( 240 ) ! ] I ; ; ; then as is known . —— are given as roots of the equation ae’ bw * @ = ay, —A 9 (3 (5) ag9 — A Age, ane “3 a39 Cg, — A or B43AiM+43B14C=0, so that the condition, which must be satisfied by the 3 roots Ai Ag, Ag, is A, a As = ds ‘ Now we have A, + A. + Ag = — 8 A, Ay Ag + Ay As + Jods = 3 B, hy dg hg = —C, from which results after some deduction as a relation between the coefficients 27 AX? — 36 AB4+8C=0 Expressed in the coefficients of the general equation this becomes 3 27 (ay) ++ 499 -F 433)" — 2 2 2 — 36 (a); + aq + agg) { 411 92 + 499 33 + 433 411 — ws =) => + 8 (a1 99 a33) = 05 so we see, that this is a relation where the coefficients appear in the third order. If there is a pencil of quadratic surfaces of the second order, we substitute a); + 4b; for a; for & we obtain a cubic equation, which proves that there are three rectangular hyperboloids in the pencil, a result corresponding with that of the geometrical considerations. Up till now the treatment of the problem has borne a general character. For a complete insight the imaginary circle at infinity must be exchanged for the arbitrary conic A*; there are moreover many particular cases. This would however lead to too extensive discussions; so this communication must be concluded here. ( 241 ) > 0 Mathematics. — “On some special cases of Monen’s differential equation”. By Prof. W. Kaprryy. If as in general p, g, r, s, ¢ represent the first and second differ- ential coefficients of a function - of two independent variables « and y, the differential equation appearing in the title is Hr + 2Ks 4+ Lt + M=0, where H, K, 4, M are functions of 7, y, z, p and g. For the solu- tion of this differential equation MonGE has given a method based on the determination of two intermediate integrals of the form u=f(r), where uw and v are dependent on 2, y, z, p and g and f/ represents an arbitrary function. This method is however deficient, the existence of intermediate integrals depending on certain relations between the functions H, K, Z and M, thus far unknown. For the purpose of making this method more practical, { have tried to trace these unknown relations. However, these relations are very intricate; for this reason I have confined myself for the present to the simple cases where Monau’s equation consists of two terms only. For these cases I have succeeded in finding the necessary and sufficient conditions which the only remaining function must satisfy, if we suppose that the equation has two intermediate integrals. From these conditions I have then deduced the most general forms for the only remaining fanction and determined the two intermediate integrals belonging to it. The result of this investigation is the following, as for as concerns the most general forms of the function and the two corresponding integrals, /, », w representing everywhere arbitrary functions of the arguments indicated when necessary between brackets. Ae 05 In this case the form is | oe ee et q — ¥ (yp) and the intermediate integrals are ( 242 ) {2 dq —/" eS q . qe +f ¢ —dp = fly) A yw z—(p—y) —fo dij = f (p) IL.- r—A%+ = 0. For convenience sake we have represented the unknown function by the square of a function 4; we then find for the most gencral form of 4 A(AEN — Z2) + 2AXZp — A(X? — 1/4/3)p? i 2? — AE(X? — 1/43?) — AYZq + A® Nq? where SEN Z== Az + B, Sapna a ak =(y—7) ¥—y +P) and A, B, C, £, # and y denote arbitrary constants. To be able to express the intermediate integrals in a simple manner, we write aV aV A V — h aed ( ) oq op’ oV BV Aaa aV aV oy Seth hy) Ase ov A(V)= ae oV B(V)=o 4A 2 +p +49) S. Then the two intermediate integrals are AMA) . (| Bid) Me 8 ae A(ay)’ A) 732 })| ee me), =a ( 243 ) 0A 0A\? ae . when by A%(2) we understand = —A : and likewise by 4,°(A) 3 f) (2 ce. Ogee ops lee A —1 08 In this case it is only necessary that 4 is independent of g. The two intermediate integrals are found by determining the three independent integrals u, v and w of the system .of simultaneous differential equations da dz dp dy law DP at Ua.y,2,p) 0 and by uniting these to ui f(¥)) Ns — Ate 0: Here 4 must be equal to p»(g)-+ w(e, 4) and the two inter- mediate integrals are pe — [vay > —f dq | wdq = fo) « (= gay +29 + yd =A) Wee Shee Let U represent an arbitrary function of «, y and z, then 4 must be equal to z 0U oU 0U -— pg —=-p —~- + D aie aut 7; aes if ROU Sole Meo, ’ 10) = e~ 0 a -. = + 7) lz — e—-U Wa Bs Nae ay dady (ey) where W denotes an arbitrary function of « and y. This result was already given by Goursat, “Equations aux dérivées partielles du second ordre’, II, p. 88. ( 244 ) The two intermediate integrals become " ,0U : qe L — [. L Ay dz a. ( W(ay)de —a J (y, rae 6. eh ef grey. : peY —{e ; dz +{ W(ay)dy = f(z). Vleet — 2A —0 In this case the only condition is that 4 is independent of p: The intermediate integrals are found by uniting the three integrals u, v, w of div dy dz ee 0-1 g Alxyyes9) to a f(r). u = f(w). Remark. It seems that the form sub I may still be chosen more generally. Physical Geography. — ‘T7'wo earth-quakes, registered in Europe and at Batavia’. By Dr. J. P. VAN DER SroK. A. 1. In the night of 29 to 30 September 1899, a heavy earth- quake caused serious damage at the south coast of the isle of Ceram and in the Mollucco’s. The first official report, sent by the Resident of Amboina to the Governor-General immediately after the disaster, runs as follows: »ln the night of 29 to 30 September at 12 45™ a. m. a heavy earth-quake, followed by a series of sea-waves, caused considerable damage at the south coast of Ceram and, in a less degree, also at the isles of Ambon, Banda and the Ulias-isles. Several villages at Ceram’s south coast have been devastated ; in the Elpanutih-Bay all except two. The prison at Amahei has been completely destroyed, the fortifications partially, whereas the presbytery and the churches remained unhurt, as also the garrison and the civil officers at Amahei and Kairatoe. As the Government-steamer Arend proved incapable of doing all the work, the steamers Gouverneur-Generaal ’s Jacob and Japara of the Royal Pakketvaart-Company were chartered in order to convey victuals and medical assistance and for the transport of the wounded, whilst also the Resident of Ternate was requested to give assistance. ( 245 ) Provisions and material for building are to be had at Ambon in sufficient quantities and have been provided immediately; but in other respects there is still much sufferance. The steamer ’s Jacob brought over to Amboina 27 wounded, whilst the Japara, by which boat the Resident and first medical officer went to the place of the disaster, conveyed 49 wounded from Amahei and Saparua. From Banda, where the pier before fort Nassau has been destroyed, satisfactory information has been received. According to preliminary reports the number of natives, killed by the disaster, amounts to 4000 and that of the wounded to 500. The natives who survived have fled to the inland country and do not venture to come back to their hamlets: there is much agita- tion everywhere, where the effect of the earth- and seawaves has been felt. The petroleum-establishment at Bulobay has not suffered any damage.” 2. The seismograms, received from Dr. Ficer, show that this earth-quake has been registered very neatly at the Royal Observ- atory at Batavia. As far as I know this is the first case that an earth-quake, origin- ating in the Molucco’s has been observed at Batavia by means of Milne’s seismograph. The motion commences abruptly at 0 14™,6 Batavia time, which corresponds to 1' 43™,5 local time, the diffe- rence in longitude between Amahei and Batavia being 1! 28™,7. 3. On the 29 of September an earth-quake has been also reg- istered in the new Imperial Central-station for seismology at Strass- burg by the Rebeur-Ehlert pendulums and also at Dr. Scutrr’s seismic Institute at Hamburg. Professor GERLAND at Strassburg has kindly forwarded the fol- lowing dates, reduced to Greenwich time. Strassburg. Batavia. m m Beginning (about) 17 23,5 17) 7,6 ™m m Maximum 17 58,8 174 29,6 m m End (about) 18h 49,4 18h 23,0 m m Duration 1h 25,9 1h 15,4 18 Proceedings Royal Acad. Amsterdam, Vol. II. ( 246 ) As the seismograms bear an entirely different character as the waves proceed irom the centrum of disturbance, an exact comparison of the epochs of commencement, maximum effect and end offer, up to the present time, considerable difficulties. Moreover in most cases the epochs of beginning and termination cannot be sharply indicated, as the seismograms generally exhibit a gradual increase and decrease of motion. An exact measurement of the velocities of propagation will be possible only when a reliable method has been found of analysing the compound movement in its elementary constituents. With the hypothesis, that the vibrations have travelled along paths approximating the chords through the earth, we find that the velocity of prepagation has been about 10 K.M. per second; the distance between Strassburg and Amahei being 10402 K.M. As the distance between Batavia and Amahei is 656 K.M., the exact local time of the earth-quake can be fixed at 1" 42™,2. B. Concerning the other earth-quake, observed also at Batavia as well as at Strassburg, the following data are provided by the seismograms: Strassburg. Batavia. prelim- 20h 58,9 beginning. icy 21h 5,2 maximum, September 10 oo 1899. | 210 54,3 beginning, 220 7,0 Greenwich time 21h 58,9 maximum 22h 54,5 24h 28,9 end 23h 19,5 \ Duration 2h 34,6 1h 12,5 From these records we may conclude that the centre of the disturbance is situated at a greater distance from Batavia than from Strassburg ; firstly because preliminary tremors have been registered at the latter place about 21"; secondly because the epoch of maximum disturb- ance at Batavia is about one hour later than at Strassburg, and thirdly because the duration is considerable less at the former than at the latter station. The last argument is, however, questionable, owing to the diffi- culty of fixing the characterizing epochs. In ,Nature“ it is noted down, (presumably by Prof. Minne from the isle of Wight) that seismic disturbances occurred on the 3'4, 10% and 17% of September. No indications of the exact time of occurrence are given, but it is stated that the centre of disturbance is in Alaska. TI JOA “Wepdajstry “proy jpAoy SHtIpaIvo01g O16 , oe 668/ he vianipE mt TY ee ett ere slid bb athe, o¢ 141 iN C49 : Cah i. (as roe iv S91 ff HSS a in eager ae ren erent acre Nes a: 5) .BIARyVg yeV pue edoing uy posoystFe1 ‘soyenb-yjvo OMT“ “HOLS UIA NVA ‘d ‘£ 7 yy sree ar = ters _ Ton in rsreormir, z nee te a es Meese 2 : i Ree tea - | = “> i enti} Ip Rat ne) re ah ae Ss linn end ae ( 247 ) Physics. — Prof. J. D. van per Waats offers on behalf of Dr. G. Bakker of Schiedam a paper on: “The potential Ae—v + Bey A sin (qr function p(r)= - ip Cais td and op by es UE 2) and the Fs potential function of VAN DER WAALS’. In a previous paper I have pointed out that these potential func- tions lend to a spherical homogeneous shell or to a massive sphere, the density of which is a function of the distance from the centre, the property to attract an external point as if the mass were concentrated in the centre, if we leave a factor, depending on the radius, out of account. The differential equations, which are satisfied by these functions, are resp. : and If we substitute «?-+y?+ 2 for 7°, these equations may also be written: Win Ae Ott oudew reat Mrounds Musferern (LC) and VG a GPM as Wen we ele) (20) The resemblance of these differential equations with the well- known equation VY’ =O for the potential of Nuwron, made it probable that these potential functions would have more in com- mon. The analogy was even closer than I expected. I found e. g. that the action between two systems of agens, spread over arbitrary spaces and surfaces, may be substituted by a system of tensions in the medium in a similar way as MAxweELt did for electric agens. In the first place we state the following theorems: I. If w represents the potential in a point «,y,2 of an agens which fills several spaces continuously, and is spread over several ee Gi surfaces, the potential function being eQ=— we find for the potential, with the exception of some points and surfaces the differential equation: Vy=qy—4n(A+Bo....- . (3) in which g represents the density in that point. 18% ( 248 ) II. If % represents the potential in a point 2,y,z of an agens which fills several spaces continuously and is spread over several A sin(qr a surfaces, the potential function being 9 (r) = —— , we get J” for the potential the differential equation: Vwy=—gy—4naegAsina.... « (A) some points and surfaces being excepted; g represents the density in that point. It is easy to find equation : Aer + Ber A Bea Ay aa Or sis ane Oe 1(B © ay oe Dn )q°s A , mt 2 U3 Let us put: Ae + Ber A+B Tr rT iy ee Se (3d) By applying the operation V* to the two members of the last AB equation but one, taking into account that 7? = 0, we find: Aer + Bear 1 r A Bi (A+ B)q?r =Viu=_ + (B= Ayg + OE Aen 1. Bey = 01. aie or r Vo=Vu=7 Se tS. (6) The proof of the first theorem is based on this consideration. The potential w in a point 2, ye > of an agens with a cubic density 0 and a surface density ¢, becomes if the potential function is ¢ (r): w= log(r)dtc += |og(r) ds if 7 represents the distance from point 2,ys- to the elements of space or of surface for which the density is represented by @ or o. We have: AEB g(r) = + (eyuation 5) ( 249 ) The potential may be written: ALB A+B » vem - aa Ae dr + = sat ane ds +- = Joudr += [ou ds « r r xv wv or 6 ds (AB) \2/25 zt = |. oS |oude > fou ds ; If we apply to both members the operation V*, we get: act o dt o ds) LED Nar -—— +2 ceptor sae A r 5S r and because 7* u= 9° p (see equation 6): Qnd v= joudr + VE fou ds = = [ev udr + Sfovy?uds= =P = fopar +P 2 [ope wy Hence : VP Wem 9) ty — Ee (AS Bye on ey (0) To prove the second theorem, we point out that: A sin (qr + @) = A cos @ sin gr + A sin @ cos qr If we substitute a new constant A, for Acose and B for A sina we may write the potential function g (7) as follows: A, sin gr + Bos qr Da a We find easily : Ay sin qr + B cos qr B ———_—$ —_ ———— — — =A, q—- ——_ r r 7 2 A, gir? B gir A, g> r* uw 3 w4 5 B If we put ~,(r) — — =» and apply the opevation V*, we get: Tr ( 250 ) Bar Ay qr? mu 2 RO = | 7B Vo=—¢ (—+4r9 o B ° =~¢(—+u)=-¢o, r and on this the proof of the second theorem is based. Now we have for the potential in a point : Wis = fe Qf, (r)dt + J J 6 —y (r) ds B Now 9) (r)=—-+ 4. So also: - ‘Bud Be d: waz [Fp s[H"+5 gudt + = jovds. UP Vp (8) If we apply to both members the operation V* we find in a similar way as we did when proving the preceding theorem: Vy=—ta be tS fopoar+s 6 V*vds Now we get in consequence of (7): =]ev vdtr =— Pz ]egide and in the same way: £5 oVivds= —g = (om de or (9) =e V?vdr = fovted=—9(Sfendt3 (op )=— ey Equation (8) becomes: Vy=—4nBo—Gy or because B= A sina: Vw=—Pw—AnrdAsinag . Let us now prove the reversed theorem of Theorem I !). ) With that modification that B is put 0. (10) ( 251 ) Ill. If yw and g are functions of 2, y and z, wy satisfying the three following conditions : 1st yw and its first derivatives with respect to 2, y and < are continuous everywhere. 2nd some isolated points, lines and surfaces excepted, w fulfils in an acyclic region, the equation: Vyp=Pu—sadg. d d dw 3" the products ay, yy, zw, 2” — y? 2 and os become nowhere infinite; then the potential of an Oks ae density of which is @, is for that region w, the potential function being: In order to prove this theorem, we take into account that the : : : aL eae Agia potential of an agens, for which the potential function is - ; r fulfils the differential equation : FP ih Ue Arte A Ole he nal cco Potre,- eo Leh) which is a special case of equation (3). [f we can prove that on the given conditions cnly one solution of (11) is possible, the theorem is proved. We shall do so by proving that if there are two solu- tions, the difference of these functions will be zero everywhere. If w and wv are two solutions of equation (11) and if we put y—v=u, the new function wu will satisfy the equation: Fo 1 Gite. As yw and v and their first derivatives with respect to «, y and ¢ are supposed to be continuous everywhere, this is also the case with the function wu and we may make use for this quantity of the well-known theorem of Green. This furnishes the equation : F du du ae MCL (V7 u)udr= |u = cos @ + — cos (3 + —cos 7) ds — : de dy dz Z) (C du o if (a) u (S) i ets yi i de + tte) ( 252 ave If we subtract iG w dr from the two members of this equation, we get: 1 1 : 1 fv? u— q° u)udr= fu(S au cos a + — COS p +- = c0s 7) ds — J dy dz = [\(S)+ (Se (=) + ¢ ul dr J (\dz dy dz j Diricnter!) in his proof of a corresponding theorem concerning the potential function a has surrounded the spaces that present a r singularity by closely surrounding surfaces, and he construed a cube, the centre of which coincides with the origin of the coordinate system, while it compasses all the spaces that present a singularity. By doing so we may make use of the above equation for the space contained between the sides of the cube and the surfaces construed round the places which offer a singularity. The first term of the right-hand member consists of the sum of a number of surface integrals, which are reduced to zero for the surfaces of the cube, when the edges of the cube increase infinitely, while the surface integrals taken over the surfaces which enclose the places offering a singularity, furnish two values of opposite sign, so that the result for every surface is zero. Then V2u=g?u. The volume integral of the left-hand member is therefore also zero. So: -) du? du \* oH) ice y+ (S) a. &) -|- 9% ue, dr = 0 du dz j from which follows: i=) OW OL ey =v engudie: In these considerations the more general function : Ae—@ + Ber r g()= must be excluded as potential function. 1) Vorlesungen iiber die im umgekehrten Verhiltniss des Quadrats der Entferning wirkeriden Krafte von P. G. Lrynunr=Diricaier. blz. 32 ( 253%) In this case the following equation would hold for points which are at an infinite distance from the agens: Ae—ar + Ber , y= M M representing the whole mass. According to the third condition » yw will nowhere become infinite. Now ry = M(Ae—% + Ber) and cg become infinite, if r=. Only for B=0 this objection has no weight. We shall therefore confine ourselves to the function of VAN DER WAALS and a general reversion of theorem I cannot be proved in this way. Such a theorem, however, would not be of much importance here, as for Be 0 the potential function has properties, which are never found when examining molecular forces. Potential energy in the unity of volume. Let us seek the potential energy of an agens spread continuously over several spaces for the potential function of VAN DER WAALS, which we write: i Capea das g()=—f If w is the potential and g the density, we get for this quantity: 1 . = S[ved 5G oe Bide re 118) We consider this as being taken over the infinite space. Now we get according to equation (11) Vw=Pytinfe and so = SEG SS An f By substitution in (13): yl oa ‘fy 9 war furae Perse Sas. ( 254 ) Now we have: A : Py ly WY wat =| w——dr + fun ~ dv + fos dr . (15) a dx” dy” dz? By partial integration : ii — wdy dz — (=) fo ae J dx vara f dx ee d : F ; Because yw and = become!) zero at infinite distance from the H agens, the surface integral becomes zero and so: da?y > (dy? —— dt = — (+ in. ee be | AB) me 7. d*y By substituting in equation (14) this expression for | w AG dt x and the corresponding expressions for the other surface integrals of (15), we find: = (= (2+ (2+ C2). The energy in the unity of volume becomes therefore: Series Ey +a yt Let us put: tat (a Ro = (Sy dx then we may also write: 2 Q 9,2 2 cpr RB Se na fr 8af 1) If the members of the last equation are added to those of the corresponding equation for the other axes, we may consider the surface integrals together as being one surface integral over a sphere. If r=, this integral becomes 0. *) gy has the dimension of a force, for g is the reverse of a length. “s bo or or — ete L or substituting a for q: < (its) LDPE. Mh eves If f=1 and g=0, we find once more the well-known expression: R2 8a This expression is negative, because the constant of the potential function is equated to zero. So it represents without the — sign the work required to separate different parts of the agens at an infinite distance from one another, when the forces are attractive. Tension in the medium. MAXWELL has proved that the foree which two electric systems exercise on each other, may be considered as a simple system of tensions in the medium. The same applies to the general potential ; Aev + Ber ; p function g (r) = SET aud so also to the potential function of VAN DER WAALS. Imagine an agens spread over different spaces, for which the potential function g(r) holds good, and enclose a certain region by a closed surface. Call this region system I and all other space system II. The resultant of the X-components of the forces exercised by system II on system I is: iA a y=—| Tana tine t) According to equation (3): PRLS coe A O40 (A+B) so eieleatt oy) d 4n(A + B)X,= | Vw a dt — fuser c A dz , da 1) Here the same remark holds good as | have made repeatedly in such like caleu- lations. See e.g. Journal de Physique 1899, p. 546. Generally this expression for X, is proved in a iengthy way. ( 256 ) Now we get (see MaxweLL 1873, blz. 129, I): dy dy dy Py dy? ay (e dy? a) onan 2) ey ibd Ge 7 a ie dx dx (Sy d dy dy dz } dy\ dx aE Let us put: dy? dw 2 dw? ees ea a es ws i) — gy? =82(A+ B) pz dy? d,2 dy? Rep Ge a ( ) Fi (*) re ae ake ad fi! GG) d 2 ee — Py? = 84(A + B) pz dy ly d OY hn (A+B) py = 40 (A + B) py dy dz ly d ple eT CA 1) ne ee Ae dz dz aw d aU Am (A+ B) pry =40(A + B) pen dx dy then we get: I dy — 7? yw=(A+ B) (Pas, dys te dpex| du ( de dz J Aprx dp, yoo Apex a ( ee a ) dt : f RAE iar or as a surface integral on the surface, which encloses system I: and so: X= [Cpe + Pye +n pes) and in the same way: Y= fo Pay + ™ Pyy + 0 pzy) ds 4 = | (pe: of ™ Pyz aie P22) ds ( 257 ) In exactly the same way as MAXWELL we may conclude from this that, when a part of the whole system is enclosed by a poten- tial surface, we may consider the action of the other part on the enclosed part of the system as a tension (or pressure), normal to that potential surface, so in the direction of the lines of force, and a pressure (or tension) round the lines of force normal to them. The value of the tension is here: R— gu? ie se pelle -if B=0 and A=—/: 8a(4 4B) or if an 5) Saf The quantity g is the reciprocal value of 4 in the potential func- tion of VAN DER Waats. Hence: If R> = the expression becomes negative and the tension # 2 becomes a pressure. The value of this expression becomes: solo) Re ie tse 617) If we take the surface element for which the tension or pressure is to be determined, normal to the lines of force and represent by 1, m and n the direction cosines of the normal measured outwards, then the z-component of the force, acting on the element (considered as a part of a closed surface) is: L par + m pyz + 2 Paz + Now: 8 (A + B) El por + m pyz + 2 pre} = =| GY- C-ro fr satt a oe dz de dy dx dz and we get the relation: ( 258 ) By combining these two equations, we find easily : 82 (A+ B) fl per + m py: + 2 pez) = rps) (sey naiaennneaa aD dx dy \dz As we have taken the force as a vector in the direction of the normal measured outwards, the above equation indicates the force which acts on the element from the inside towards the outside. The expression between the bracesx in the right-hand member is always positive, and we get therefore a negative tension or a pos- itive pressure : 82 (A+ B) For the potential function of vay pER Waats B=0, A=>—/f 1 and g= TZ» £0 we find here a (positive) tension : ee Rae 8 a al i A For an electric system the system of forces may be described as a system of ¢ensons in the direction of the lines of force and a system of pressures normal to the lines of force, here however we see that we must assume both tensions and pressures in the direction of the lines of force. Normal to the lines of force there are only tensions, whereas for electric agens the reverse is found. For electric agens the numeric value of the tension is equal to that of the pressure; in our case the tension is not equal to the pressure, except where y and #& are zero. For the potential energy per unit of volume we found: te 7 2 weitere Pe 8a f Lo = from which follows that: the absolute value of the potential energy per unit of volume is equal to the tension normal to the lines of force. ( 259 ) The Surface-tension and the Molecular Pressure. Let us imagine a liquid in equilibrium with its saturated vapour. In the transition layer we may assume the lines of force to be normal to the surface separating the two phases. Let us imagine this surface to be horizontal, therefore the lines of force in the capillary layer as being vertical. If the above considerations are correct, and if we assume that the substance fills the space contin- uously with a mean density, we shall find for the surface tension exactly the same value as is deduced from the calculations of VAN DER WAALS in his “Theorie der capillariteit’’. Let us first calculate the molecular pressure; i.e. the force, with which a column of the surface layer with the unity of transverse section is attracted down- wards in the direction of the liquid by the surrounding substance. Per unit of surface we found a pressure, indicated by the formula : b= (# -F). The foree we are speaking of, which we shall call A, is nothing but the difference between the absolute values of the pressure D on the upper and the lower surfaces of the column of the surface layer. Let us call the potential in the vapour yw and in the liquid yw, and let us bear in mind that both in the vapour and in the liquid R may be put equal to zero, then we find: ) 2 Tig ree ey Su f a ) 1 - Betis fre eRe aS (— We" + Wr") = 1) The pressures in consideration are here negative and therefore properly speaking, tensions. For the rest the ideas tension and pressure are somewhat arbitrary. There is no objection to adding an everywhere equal amount to the pressure and the ten- sion through the whole mass. ‘The new system of pressures and tensions will give a representation of the system of forces as well as the original. This appears immedia- tely from the form of the space-integral, which represents the force between two parts of the system : "7d 1, I; Net [i eee ee Ne du dy dz The coefficient of dr consists of the sum of three differential coefficients. Therefore constant amounts may be added to pyr, pe, and pz,. If the hydrostatic pressure through the whole mass is equal to the external pressure 9 “1 . . l fi zs and if only the pressure of the air acts on the system, the pressure ~ ee =) 8x f is equal to the pressure with reversed sign, leaving a constant out of account. ( 260 ) As further y= —4n fhe, and y= — 40 fh? Qy or yw, = — 2a; and yy = — 2aQg we may also write: 4a? 9,? — 4a’ Q,2 4a K —="d (Oy 05.) oe ee 0) If we neglect g with respect to @, we get the well-known expresssion of LAPLACE: K =a 00 LApPLAcE, however, proved this relation only in the supposition that the density in the liquid (also in the surface layer) is constant everywhere. For the tension normal to the lines of force, so in our case in the direction parallel to the separating surface, we found: = (w+). This expression holds for a unit of surface. For an elementary- rectangle of transverse section of the capillary layer, (i. e. normal to the potential surfaces), two sides of which are parallel to the potential surfaces and have the length of a unit, whereas the other two sides have the direction of the tangents of the surface and a differential length dh, we get: The total tension in the capillary layer will be equal to the sum of these differential-expressions, 1. e.: 2 : [his 72 1 + syj= R? dh - Pee an a: (CB ) cal Ute [Om (23) 1 1 4) This quantity S is no¢ the quantity 2 of Lapuacs. —LSs- —_ —_——_ \ ( 261 ) The limits 1 en 2 relate to liquid and vapour. In the theory of VAN DER WAALS is: 2¢o de 2c, do : 2. dh? w4 dh? for eee a do st 2 eg #e 2 2 C4 eo dh 2 dh 7-24 dhd By substitution of the squares of these expressions in (23), making use of the expressions: 5 C4, C4 2 mu 4 mu 6 2 — — = = Se SS e . a Un) C4, 2 uw 4 we find easily: 9 2 2 S IE 2 dh — ai? ((y th + a Mt (ee “dl ai v Dh at ah rei “a tt 1 1 As the tension normal to the lines of force per unit of surface was equal to the potential energy per unit of volume with reversed sign, we have also found this energy. We can also easily derive the value of the energy directly from the equation for the energy, with which the energy of the unit of mass in a point of the surface layer exceeds that in a point within the liquid. Prof. van DeR Waats finds for this: ( tg do C4, dQ a CECH) mata as See aid For the whole separating layer we get per unit of surface a potential energy : fe ( C9 dy ¢ a dte —ajle?dhta n| » dh — | ee fe Sh = a “areas Jee ase Te i mu 4, dh* i 1 1 l fe dk = mass of the separating layer per unit of surface = m, 9 Proceedings Royal Acad. Amsterdam. Vol. II. if do 1) fs 108 a On ) = —— — I ae Je: dh i Gry ioe) 1 1 lL > di ais “Dp lo “do Po * Po? le S m= | gd “ =| ip h=— | Fa a (4 dh ‘ dh* J dhs J dh® dh ANP Mh? Ze ah? 1 1 1 1 l The potential energy per unit of surface becomes: ( , C9 ie do 2 C4. (ee tO 2 W=—alfordh+ag,m 4 | ( ) dh — ( -)dh+.. Y 2. dh m4. dh? 1 l 1 As zero position we have taken that of the liquid. If we take infinite rarefaction as zero position, we get «g,;m—=0 and so: s= -—- W Astronomy. — S. L. Veensrra: “On the Systematic Corrections of the proper motions of the stars, contained in AUWERS’- Brapury-Catalogue, and the coordinates of the Apex of the solar motion in Space”. (Communicated by Prof. J. C. Kapreyn.) The materials for these investigations have been taken from an yet unpublished catalogue, prepared by Prof. Kapreyn. This cata- logue contains for all the Bradley-stars, observed in both coordinates (with the exception of the Pleiades, the Hyades and the fainter components of physical double-stars) the position, the total proper motion «, its components v and +r, in the direction from the apex and perpendicular to that direction and the quantities 2 and 7 ®), respectively the distance from star to apex, and the angle between the great circle on which this distance is measured and the decli- nation-circle. The quantities v, 7, 4 and v have been calculated with different ba : d ; 5 1) The differential-quotients dh a ete. are zero outside the separating layer. 2) In the printed catalogue the quantities x have not been included. ( 263 ) sets of values for the coordinates of the apex and the precession. The set used by me is as follows: A= + 276° Det oiee i 1 precession = prec. of Auw.-Bradley [fe — ) 4 Besides to the proper motions in Declination of Auwrns, the following preliminary corrections had been applied: Declination. Correction. Southern Decl. — 0”.008 Decl. 0° tot + 20° — 8 4), 20 - > 4240 = 8 >» +40 » +60 _ 5° (mean) 3. E60! 9° 21590 = 1 According to the arrangement of the catalogue, I have caleulated the systematic corrections of the P. M. in declination for these five belts, separately for the stars of «) Spectral Type I and unknown spectrum, J) Spectral Type IT. They have been derived from the condition that 7 must be zero for each half belt, viz. for the halves, in wich sin 7 is only pesitive or only negative. The expression of this condition is : stt+A us = sn v= or where A ws, taken constant in each half belt, is the correction, to be applied to the P.M. in declination. In order to get reliable results, the stars with small six. 7, which evidently have small weight, were omitted. The calculations have further been performed separately for: Ist, sin 7 > + 0.80; ond sin 7 > + 0°60’ . 19% ( 264 ) Besides, the stars with a total yearly proper motion > 0".3 have been left out too. Combining the values of A ws for both parts of each belt, according to their weights, the result is: A. sin 4 >} Ar 0.80 Southern Declination Decl. 0° tot +- 20° + 40° + 60° + 900 » + 20° » » +40° » » -+ 60° » b. ail 0.80 S sin x» ar 0.50 South. Decl. Deel. 0° tot + 20° » +20° » + 40° » +40° » + 60° » -+ 60° » -++ 90° The combination of the values sub 4 and &, with corr. A (72) — 0".0093 (226 st.) | >) ») | >) +- numb. of stars 954 corr. A pd 0" 0024 (278 st.) | 90 (218 52 (131 5 ( 62 » ) 2 42 ( 32 ») numb. of stars 721 prel. corr. | total corr. Ax — 0".0080 —= 0".0173 80) ee 96 80 pad Dsl 55 a 57 10 a 7 | total ov.0080 | — ov.o104 80 = 170 80 Zz Spas 55 &2 60 10 ae 32 weights pro- portional to » six? 7 (n=number of stars), is given in the following table: C. «sin x > + 0.60 Sceuth. Decl. Decl. 0° tot + 20° + 40° -- 60° + 90° » +20° » » -+-40° » » + 60° » numb. What part is final values, is shown in the next table: Ap prel. corr. | Total A ws prob. err. — 0".0062 (504), — 0".0080 — 0".0142 0” .0015 = 45 (433) | — 80 — 125 23 et 38 (389) | — 80 | nee a | 16 aa 1 (222) | — 55 vas 56 13 zs 29 (197) | — 10 | a 19 20 of stars 1675 | due to each Spectr. Type in making up these ( 265 ) OTL 696 eld | 696 GOs 80F COF Les savys Jo qundm (Fg ) 9g +| (ep )eo +) Gador + (eo dee. +} (@rdest +) (er)s9 = — (@e)s —| (o)er +/.06 + « .09-+ « (s6 )9¢ +) (280) 68 =e (88) +| (FI)¢ —| (se ) er +) (LF ) 0g —| (09 dee +! (os ) 62 —009 + « of + 4 (S9L) Te —| (188) BF =| (991) 06 —| (888) Fs =|) 62, ing +) (Zs ) £9 —| (68 )98 —) (FEL) 6e —0F-+ « 0+ « (641) 8% —| (6s) 19 —| (661)SIl —| (Fes) Ft +! (68 ) FZ (SCALP ie sais (LGD 166 +} (281) ot +/008 +49..0 ‘9d (48 $16) £200" .0— (48 068) £900’ .0—|("48 Lez) €800° O—|(38 £98) 8F00".0—|(38¢6 ) FL00',0— (48 FFD FILO WO—|(48 TST) TL00°.,0--|(48 9FL) 000° ,0— ‘Poa wreyNog | {1 edgy, *T adky, —% us | + % as ‘Tr odfy, ‘T addy, ‘Ty eddy, ‘T addy, “404 40} 40} | 40} — % us + % us ——_ = = — ( 266 ) The values, found for Ags have been used in computing the corrections, to be applied to the P.M. in right ascension. This correction, A #,, supposed to be = 0, when A yw; was calcu- lated, is derived from the formula ZST+A 3 = sin x = cos y Ni — ? first for each speetr. Type, and each belt separately and taking A fz constant from 0" to 3%, from 3" to 6, a.s.o. Afterwards the different values for the same R.A., but different types and declina- tions, were combined, with weights proportional to the numbers of stars. The final values are | | | | | | hgh | 3h—Gh | Gh—9h | gh a came erat be Q]h—Oh 4-000 4-0004 00008 —1013| 05001 —Os000 | | | Au 0005-000 Putting the weight proportional to cos d instead of proportional to n, we get NU | | 1.0,0005,6 000008 02-0008. 0.001 3 _0,0009.7|—-0,0006.61 —0s.0000.7 | | | | | mean probl. err. 08.00042. As appears from the prob. errors, they are hardly to be consid- ered real. With these corrections to the proper motions, the coordinates of the apex have been calculated. The formulae used for the purpose, the derivation of which is easily seen, are sin (a — A) cos 0 sin? sin? 2d sin 0 — cosd sin D 5 ee ay a y= O = 0" eee) where «= AA= corr. to be applied to the R. A. of the apex. LS Dy) » 9 » »” ” Decl. ” ” n = (T+ A “4G sin 7) ig@Q=— —-- : = (vu +A “0 cos 7) ( 26%) when A «3 only was applied and Pei a sens DAA Attar 9 e082) Seay) SS (vu -+ A ws cos 7 + A uz cos 0 sin Z) ‘ on applying both corrections. Dividing each belt in eight parts, of 3h in R.A., and including all the stars (2503 in number) of which the proper motion does not exceed 0".30, six sets of equations of condition of the form (1), of 40 equations each, were obtained. From each set was derived a value for A A and AD. The weight of 9 proves to be proportional to the respective number of stars. The @’s, having negative denominator, evidently should be taken in the 2>¢ or 3"¢ quadrant. The coordinates of the apex, found in this way, are: A D Type I. corr. A “ts 268°.3 + 2°.4 aS Orel eeko A f,and Aus 272.1 + 2.3 oO: se ly! Type Il. Ams 273.5 + 4.3 33.9 + 2.8 A taand A us = 270.6 + 4.0 Syl a es) Ad ts Types I and I Ais) (2690 et NG 347.5) zeae 2 together Apweand Ams 274.2 £1.47 By glee alee Besides, values of A and D have been derived in perfectly the same manner from 151 stars with annual P. M. > 0'.3, after applying A ws to these P. M’s. For each of these 151 stars an equation of cond. (1) was con- structed. The result is: Al ODA: «aah BU ars Dim NAO, ae These results confirm what Mr. PaNNeKorK wrote in 1895 (Bullet. Astr. XII p. 196): “Si l'on a égard & ces corrections des apex caleulés, on peut en tirer Ja conclusion qu’ils ne montrent pas (indication évidente d’un monvement relatif entre les étoiles 4 spec- tres de types différents.” NewcomeB goes a little farther yet (Astron. Journal X VII, p. 390) : “The centres of gravity of two great classes of stars scattered through the celestial sphere will be at rest relatively. — I believe this hy- pothesis safe still when the classes differ by spectral type, as the positions of the apex in both cases are fairly well the same.” The calculations, of which the results only are given here, will shortly be published in extenso. Groningen, November 1899. ( 268 ) Chemistry. — ‘“d-Sorbinose and I-sorbinose (y-tagatose) and their configurations.” By Prof. C. A. Lopry DE Bruyn and Mr. W. ALBERDA VAN Exkenstein, communicated by Prof. Lopry DE Bruyn. The configuration of d-sorbinose, a substance which has been known for a long time, has not up to the present been made out with certainty. It is only known that this sugar is a ketose, that it yields d-sorbite on reduction and that it can be formed again from this latter aleohol by oxidation. d-Sorbinose which was formerly difficult to prepare in a tolerably large quentity, is now more easily obtained by the method of 3ERTRAND !). According to the interesting method of this chemist, sorbite can be oxidised to sorbinose by means of Bacterium xylinum (and B. aceti). By this method we have obtained yields of 25 to 30 pereent *); we are indebted to the courtesy of Mr. BryerincKk of Delft for the pure cultures of Bact. xylinum. The final experiments with d-sorbinose were brought to a conclusion in the beginning of 1898; they proved that, on reduction with sodium amalgam, d-idite is formed as well as d-sorbite. The former aleohol was recognised, in the form of its tribenzal-compound, as the optically opposite form of tribenzal-/-idite prepared from /-idonic acid. *) This result was obtained many months before the publication, at a meeting of the Société chimique, by G. BerTRaND from the fact that on reducing d-sorbinose a second hexite is produced, in addition to sorbite, which according to BERTRAND must be d-idite.4) The publication of our work was, however, postponed because in the course of an investigation of w-tagatose (a new ketose which is formed along with tagatose by the action of alkalis on galactose °) it was becoming more and more probable that this sugar was to be regarded as /-sorbinose. More than a year ago, the two ketoses were submitted to a comparative crystallographic examination ; Mr. van Lier was good enough to make this examination in the laboratory of Prof. SCHROEDER VAN DER KoLk at Delft. The result 1) Bull. Soc. chim. 15, 1196, 627. *) 200 gr. sorbite gave 50 to 60 grams of pure sorbinose. *) Recueil 18, 150 *) Report of the meeting of March 11. 1898; Bull. 19. 259. In the publication rela- ting to this communication (Bull. 19, 347) no details are given about the reduction of d-sorbinose to idite or about its configuration; Bertranp has also not returned to the subject. ) Recueil 16, 267. ( 269 ) was that the two substances behave crystallographically and optically in exactly the same way. At that time we still hesitated, however, to assume that w-tagatose was l-sorbinose; on reduction some /-dulcite was always obtained along with J-sorbite and J-idite. The specific rotatory power of y-tagatose to the right remained, even after repeated crystallisations from water, methyl- and ethylalcohols, about 4° less than that of d-sorbinose to the left; the crystals were never quite clear but always slightly turbid. After many attempts to convert w-tagatose into a crystalline compound from which the pure ketose could be regenerated, we attained our object by the employment of aniline. It was then found that d-tagatose crystallises together with w-tagatose in a very persistent way, but forms an anilide much more readily than its isomer so that the latter is deposited in well formed, clear crystals from an alcoholic solution containing aniline. The w-tagatose purified in this way was then proved with certainty.to be the optical opposite of d-sorbinose and it is therefore henceforth to be regarded as l-sorbinose. A short summary of the comparative experiments which place this view beyond doubt follows. The melting points are the same (about 154°); from a mixture of equal quantities of the two ketoses a well crystallised racemic compound is obtained with approximately the same melting point and a somewhat higher specific gravity. The specific gravities and the solubilities in water and methyl- and ethylalcohols are the same. For d-sorbinose, @n) = — 42°.7, for l-sorbinose em, = + 42°.3 (4 percent solutions at 17°). Both solutions show the same slight birotation. It has already been remarked that the two ketoses are crystallo- graphically identical; hemihedral faces will be again sought for. The osazones have the same melting point (150 to 151°), the sane solubility and equal and opposite rotatory powers. l-Sorbinosazone is, as a comparison shows, identical with l-gulosazone. ') On reduction with sodium amalgam, d-sorbite and d-idite are formed from d-sorbinose, /-sorbite and /-idite from /-sorbinose; these ') The statement in von LrppMann’s Chemie der Zuckerarten”, p. 534, that sorbin- osazone is not identical with eulosazone is, according to a communication from the author, a mistake. ( 270 ) hexites were recognised in the from of the benzal-!) and formal- derivatives. Both d- and Jl-sorbite have been prepared from the benzaleompounds and obtained in the crystalline form. Crystalline methyl-/-sorbinoside was prepared by E. Fiscner’s method from /-sorbinose; its specific rotation is equal and opposite to that of the known methyl-d-sorbinoside (88°.5). *) The results obtained, including the production of idite along with sorbite by reduction and the identity of /-sorbinosazone with /-gulo- sazone enable us to give the two sorbinoses the following config- urations : CHLOW CH,OH | | CO CO | | , HOCH . HCOH d-sorbinose : | and /-sorbinose : HCOH HOCH | | HOCH HCOU | | CH,OH CH,OH The formation of /-sorbinose from d-galactose under the influence of alkalis is an example of a direct transition from the dulcite series of the hexoses to the mannite series. This can be best represented by assuming the intermediate formation of d-tagatose; the OH and H attached to the third carbon atom must then change places in the transformation OOH CH.OH CH,OH | | | COTL CO CO | | HOC HOC CO ; — | a | | HOC HOC HOC | | | COH COT CO | | | CH,OH CH,.OH CH,OH d-galactose d-tagatose 7-sorbinose ') Recueil 18, 150. A tribenzalsorbite was obtained as well as the mono- and di- henzalsorbites. 2) BE, Fiscuer, Ber. 28, 1159. ( 271) We shall try to determine whether pure tagatose readily yields l-sorbinose under the influence of alkalis. We have also again taken up the investigation of the probable formation of a new ketose (called, for the present, y-fructose!) by the reciprocal transformation of glucose, fructose and mannose under the influence of alkalis. The following triplets of hexoses (two aldoses and a ketose) are now known which give the same osazone: d- and /-glucose, — fructose and — mannose d- and /-gulose, — sorbinose and — idose d-galactose, — tagatose and — talose. *) A complete account of this investigation will be published in the “Recueil”. Chemistry. — “On the action of sodiummono- and -disulphides on aromatic nitro-compounds.”’ By Mr. J. J. BLANKSMA. (Preliminary communication). Communicated by Prof. C. A. Lobry DE Bruyn. It has been shown for orthodinitrobenzene by LAUBENHEIMER *) and for paradinitrobenzene by Losry DE Bruyn *) that the nitrogroup can be readily replaced by other groups. The investigation of the behaviour of the alkalisulphides, although promised *), has not been taken up until the present. Some positive result may be expected from this study since Nietzk1 and Bornor®) have proved that the corresponding dinitrodiphenylsulphides are formed from o- and p-chlornitrobenzene and sodiummonosulphide. It has now been found that orthodinitrobenzene reacts not only with sodium monosulphide but also with the disulphide in a similar 1) Recueil, 16, 278. *) The d-tagatose has yielded ¢-talite along with dulecite. ’) Ber. 9, 1828; 11, 1155. ‘) Recueil 13, 121. 5) Reeueil 18, 105—106. ®) Ber. 27, 3261; 29, 2774. ( 272 ) way. In the first case o-dinitrodiphenylsulphide NO,C,H,SC,H,NOg, in the second o-dinitrodiphenyldisulphide NO .O,HsSSC;HyNOg, is formed, sodium nitrite being simultaneously produced. The monosulphide is readily oxidised, first to a sulphoside and then to a sulphone; the molecule of the disulphide on the other hand is broken up and converted into two molecules of o-nitroben- zenesulphonic acid, of which some derivatives were prepared. By means of sodium disulphide it is therefore possible to substitute the sulphonic group for a nitrogroup in the orthoposition. From p-di- nitrobenzene, neither the dinitrodiphenylsulphide nor the corresponding disulphide could be obtained; in this respect, therefore, it differs from its isomer. Both with Na,S and with NaS, reduction to p-dinitroazoxybenzene first occurs; this substance has already been obtained by the action of potash on p-dinitrobenzene. °) Small quantities of p-nitrothiophenol NO,Cj;HySH are also formed. ParachJornitroben- zene, the behaviour of which with Na,S has already been studied by Nierzx1 and Boruor, reacts also with NaS, forming paradini- trodiphenyldisulphide NO ,Cj;H,SSC;H,NO,. The crystals of this compound, which has already been prepared by Leuckart °) by another method, have the interesting peculiarity of flying to pieces when warmed to 134°, subsequently melting at 170°. Inversely, the solid mass formed below 170° changes at the same temperature into another crystalline modification in a clearly visible manner. We are here obviously dealing with a transition point characterised by a great difference in the specific volumes of the two modifications ; this is to be more carefully investigated. Like the isomeric ortho-compound, p-dinitrodiphenyldisulphide is readily oxidised to nitrobenzene sulphonic acid. By this means, therefore, halogen united to the benzene nucleus has been replaced by the sulphonic group. The results of some preliminary experiments make it probable that by direct substitution substances containing not only two, but also more sulphur atoms, connecting two benzene rings, may be prepared. The investigation is being continued. *) Recueil 13, 122. 5) J. Prakt. Chem. (2) 41, 199; see also WiLLeERopt, Ber. 18, 331; KEHRMANN and Baurr, Ber. 29, 2361. ( 273 ) Chemistry. — “The alleged identity of red and yellow mercuric oxide’, Part I. By Dr. Ernst Conen. (Communicated by Prof. H. W. Baknuuis RoozEsoom.) 1. Some years ago, (1895), in a review ') of Vargts’ thermo- chemical determinations”) concerning red and yellow mercuric oxide, OstTWaLD said that in his opinion it was doubtful whether the two modifications were isomeric. He added the remark: “probably they only differ in the size of their particles, that is mechanically”. Shortly after this review, OstwaLp published the results of some measurements 3), made at his request by Toor Mark with the object of seeing whether we are here confronted by a case of identity or isomerism. OstTWALD concluded that “the two kinds of mercuric oxide are no more different than crystallised and powdered potassium bichro- mate, which exhitit a similar difference of colour; they are not isomeric but identical’’. This conclusion rests on the following experiment: a galvanic cell, arranged as follows: | Red oxide | Yellow oxide | MUSVetL | in potash solution | in potash solution | Mercury showed, according to Mark’s measurements, a difference of po- tential of less than 0,001 volt, since, as OsTWALD said ,no deflec- tion could be observed with the electrometer used which was capable of measuring 1 to 2 millivolts”. Besides this electrometric determination of solubility, determinations of the solubility of the two oxides in solutions of potassium bromide, potassium iodide and sodiumthisosulphate were made. After satura- tion, the solutions, which had become alkaline“), were titrated with hydrochloric acid. Equal volumes of the solutions required the following quantities of acid : Potassium bromide Potassium iodide Sodiumthiosulphate solution saturated with solution saturated with solution saturated with Red oxide Yellow oxide Red oxide Yellow oxide Red oxide Yellow oxide 6,16 cem. HCl. 6,20 com. HCI. 49,82 com. HCL. 49,64 com. HCI. 51,84 cem. HCl. 51,98 cem. HCl. 51,75 as 51,80 55 BPs eo Slee 1) Zeitschrift fiir physikalische Chemie 17. 183 (1895). *) ©. R. 120. 622 (1895)., Ann. de chim. et de phys. (7) 8, 79 (1896). *) Zeitschrift fiir phys. Chemie 18, 159 (1895). *) Berscu, Zeitschrift fiir phys. Chemie 8, 383 (1891). ( 274 ) “It is proved by these experiments that the /7ee energy of the two forms of the oxide is the same; since the same thing has been proved for the total energy by the experiments of Varer, the above conclusion, that the two forms are identical, follows of necessity.” 2. In my researches on the difference in the free energy of the two isomeric forms of tin, the grey and the white'), of which I shall publish the details shortly, I had found that the difference between the forms is very small. Even at a considerable distance from the transition temperature (20° for example) the difference is only of the order of a few millivolts. If now, ir a case such as that of tin where the isomerism is so clearly marked, only such small differences in the free energy of the modifications are to be found, it is natural to assume that the scale with which OsrwaLD measured in the case of the red and yellow mercuric oxides (1 to 2 Millivolts) was much too large to permit of the definite conclusion that there is no difference in the free energy of the two modifications. I decided therefore to determine the difference of free energy between red and yellow mercuric oxides, choosing a scale a thousand times smaller than OsTWALD’s (?/;999 millivolt). 3. In 1892 an investigation by GLAZEBROOK and SKINNER ap- peared *) in which a number of observations is described which indirectly have an important bearing on the question with which we are here occupied. GLAZEBROOK and SKINNEP investigated the E. M. F. of the Gouy normal cell *), which is constituted as follows: Hg | HgO | 10 °/, solution of Zinc sulphate | Zn, and found a great difference between the E.M.F. of elements con- structed with yellow and with red mercuric oxide. For the E. M. F. of the Gouy cell containing red mercuric oxide they found 1,384 Volt, for that of the element with yellow oxide 1,391 volt at 12° C. 1) See Ernst Conzn, A new kind of transition element (sixth kind). Proceed. Roy. Acad. Amsterdam. Vol. II. 1899 p, 153. 2) Phil. Trans. of the Royal Society 183. 367 (1892). 3) Journal de Physique Tome VII (1888), p. 532. ( 275 ) From this it might be deduced that the difference of free energy between red and yellow mercuric oxides was of the order of 7 milli- volts, whilst OstwaLpD gives it as smaller than 1 millivolt. Here also a careful and exact investigation appears desirable. 4. In the first place it is rather surprising that neither OsrwaLp nor GLAZEBROOK and SKINNER say anything about the purity of the materials, which is nevertheless of the greatest importance owing to the great sensitiveness of the electrometric method. In determi- nations made by this method, traces of impurity may have an enormous effect on the HE. M.F. measured. Further, the preparation of absolutely pure mercuric oxide, whether red or yellow, is to be counted among the more difficult tasks of preparative chemistry, as may be seen from what follows. Four specimens (from different makers) of red mercuric oxide (hydrargyrum oxydatum rubrum praecipitatum pro analysi) and yellow oxide (hydrargyrum oxydatum via humida paratum pro analysi) could not be used on account of the many impurities which they contained. In the red and yellow oxides from Merckx of Darmstadt, I could not discover any traces of impurity by analytical means; these preparations were therefore used as the starting point of the in- vestigation. The water which served for making the solutions employed, was very pure and possessed a conductivity of 1 xX 10-8. It was distilled from a heavily tinned copper vessel a trace of phosphoric acid being added; the middle fraction was used, carbonic acid being removed by means of an air current in the well known way. The solution of potash used was made from potassium and this water, the carbonic anhydride of the air being excluded. The mercury was, after a preliminary purification, twice distilled in vacuo. All glass vessels, flasks ete. with which the substances came in contact were steamed out. 5. A cell was now put together of the form shown in the figure: aa and bb are glass tubes 73 em. long and 2 em. wide, connected below with capillaries, which are bent round and carried upwards to 2 cm. above the caoutchouc stoppers k k. In this way it is possible to submerge the whole apparatus in water without the platinum wires P; and P;, which must be heated to redness before each experiment, coming in contact with it. These wires terminate in the mercury which is placed on the bottom of aa and Dd. Upon ( 276 ) this a layer of 1 em. of yellow HgO is placed in aa and of red HgO in bb. The layer of oxide is made thick in order to prevent movement of the F000 550° Fe surface of the mer- Te De cury electrodes. According to the measurements of HELMHOLTZ, irreg- ular vibration of the surface of the electrodes may give rise to differences of potential between them, which must, of course, be avoided. The two limbs and the connecting piece Hod yell. cé With the tap & were filled witha so- lution of potassium hydroxide (about 15 Fig. 1. percent), the tap re- maining closed meanwhile. In this way the two oxides remain each in its own compartment whilst the cel! is being prepared. After filling them, the two limbs are immediately closed by india- rubber stoppers kk and kk. A small Anscutrz thermometer, (graduated in ¥/;°) passes through each, the air being allowed tu escape by means of capillary tubes 7 and /. These tubes are closed at once after filling in order to prevent entrance of water into the element when it is placed in the thermostat. The use of the thermometers is necessary, because small differences of temperature between the liquids or the mercury in the two limbs of ‘the element might give rise to thermocurrents which would interfere with the measurement of the very small differences ot potential which are being dealt with. KOH sol. KOH sol. | Hg0 red ——§ 6. The arrangement and course of the measurements may be somewhat fully described, since the value of the results is very closely connected with them. The elements, also the standard cells, were kept in the dark during the whole course of the research. The influence of light on red and yellow mercuric oxide is not yet suffi- ciently studied to permit one to decide whether this agency would have any effect on the E. M. I’. which is to be measured. ( 277 ) After the element has been set up in the way described, it is immersed in a thermostat, the temperature of which is maintained at 25° by means of a toluene regulator. By means of this regulator and a stirring arrangement (a small ships propeller kept in movement day and night by a Hetnrict’s hot air motor) it was possible to keep the temperature at 25° during the whole period of the observations (about 6 weeks); the greatest variations, measured by means of a thermometer designed for thermochemical work, did not exceed 0°,004 C. The variations which occurred within 15 minutes could not, of course, appear in the element itself. It was, further, only of importance that the two limbs of the element should undergo the same changes of temperature. The standard cells, which were used in the measurements by means of POGGENDORFF’s compensation method, were placed in the same thermostat. The standard cells were: 1. A Weston-cell made in April 1899. 2. A Cuarx-cell A , in January 1899. 3. A Cuark-cell B , in January 1899. A small accumulator ') was used as the working cell. Since all the measurements were reduced to the Westoncell, it appeared important to control it from time to time. This was done by means of the two Crark-cells; as will be seen the E. M. F. of the Weston-cell remained absolutely constant during the whole period of the measurements. (See Table I). TABLE I. E. M.F. Ciarx A 25° E.M.F, Cuark B 25° Date Ratio ———H— = Ratio ie Ss KE. M. F. Weston 25° E.M.F. Weston 25° 1 October 1.3946 1.3945 10 October 1.3946 1.3945 20 October 1.3946 1.3945 27 October 1.3946 1.3945 10 November 1.3946 1.3945 20 November ”) 1.3946 1.38945 1) These accumulators, having the very small dimensions 55 x 42 X 150 mm. capacity 5,5 ampere hours, (weight when filled 880 er.) are obtainable from the Berlin accumulator factory Andreas Str. 32, Berlin (O) at a cost of 3 Marks. They are to be strongly recommended for measurements of this kind. My friend Dr. BRreDIG of Leipzig drew my attention to these cells. *) The great reliability of the standards is further evident from the fact that in another test made on June 17, 1899 the same ratios 1.3946 and 1.3945 were obtained. 20 Proceedings Royal Acad. Amsterdam. Vol. IT. ( 278 ) If, in accordance with the completely harmonious determinations of Kanne?) and CaLLenpAR and Barnes?) we take the E. M. F. of the Crark-cell at 25°,0 as 1,4202 volts, then the E. M. F. of the Weston-cell at 25°,0 is, according to these determinations, 1,0184 volts. The comparisons made by Jarcer and Wacusmura *) also give the E.M. I. of the Wesron-cell at 25°,0 = 1.0184 volt. Our standard was thus very trustworthy during the whole research. An extremely sensitive THomMsON mirror galvanometer was used as zero instrument. The thermometers employed were compared with a thermometer standardised by the Physikalisch-Technische Reichs- anstalt. The thermometer which indicated the temperature of the ther- mostat was graduated in !/j9°. 7. A series of measurements was first made with the red and yellow oxides from Merck, which were used without further treatment, after it had been found that no impurities could be discovered in them by analytical means. I first determined the potential difference red HgO0 — red HgO by setting up an element arranged thus: Hg — red HgO — potash lye — potash lye — red HgO — Hg. The potential difference was less than 0,000001 volt *). In the same way the potential difference of yellow HgO — yellow HgO was measured. This also was less than 0,000001 volt. 8. The determination of the potential difference red HgO —- yellow HgO then followed. An interesting phenomenon, which might have been foreseen, was here encountered. It is known that the two oxides behave differently towards a number of reagents, the velocity with which they react being different. The yellow oxide, for example, dissolves in acids more rapidly than the red. If now, as might be anticipated, the equilibria of the two oxides with the solution in the cell are attained with different velocities, it is to be expected that the K.M.F. of the mercuric oxide cell, regarded as a function of the time, will increase to a certain maxi- 1) See Thiitigkeitsbericht der Physikalisch Technischen Reichsanstalt 1896/97. Zeit- schrift fiir Instrumentenkunde 17, 144 (1897); Wrepemann’s Annalen 64, 94(1898). Zeitschrift fiir Instrumentenkunde 1398. 161. *) Proc. of the Royal Society 62, 132 (1897). 8) Winp. Annalen 59. 575 (1896) en Zeitschrift fir Instrumentenkunde 1898. 161, 4) The smallest quantity measurable. ( 279 ) mum, after which it will fall until a constant value is reached, which would indicate the attainment of equilibrium. It was to be expected that the attainment of the final condition would be slow, considering that the contents of the cell were not . stirred and that the saturation of the liquid with HgO was brought about by diffusion. The correctness of these views was proved numerically by all the experiments. In the following table the time in hours, from the first filling of the cell, is given under t, the E. M. F. of the element (at 25°,0) at the time mentioned is given under Z in millivolts. TABLE II. t. (hours) EF. (Millivolts) t (hours) FE (Millivolts) 0 0,585 61 1.037 Bf, 0,759 73 0,876 11f, 0,843 97 0,756 5M, 1,066 eH 0,721 24 1623 147 0,703 293), O37 171 0,686 49 1,169 194 0,685 24] 0,685 Representing the E.M. F. graphically as a function of the time, the curve in fig. 2 is obtained. A maximum is attained in 24 hours, 1 [a See Tse 2 Cees COCR Eee Svea Sa Sh aCSine 2 [ ve || Bal | : pen a ‘Sim S Sea Me ies eats |: ( = 05424529 49 61 73 97s 147017194 241 Time in hours —> Fig. 2. the condition of equilibrium being reached only after the lapse of 171 hours; this was observed for a further 70 hours. According to this experiment the difference of potential between red and yellow mercuric oxides at 25°,0 is equal to 0,685 millivolts. 2. Although, as above mentioned, impurities could not be discoy- ered by analytical methods in the specimens of red and yellow mercuric oxide used yet, considering the great delicacy of the electric 20* ( 280 ) measurements, it appeared to me to be of importance to obtain further confirmation of this result. The red and yellow oxides from Merck were shaken with water, of conductivity 1 >< 10—*, for some days in sealed tubes in order to remove all traces of soluble matters which might possibly still be present. The specimens, after filtration, were then dried for a week in vacuo over sulphuric acid. A few grams of each material were placed in steamed glass tubes, a few cc. of potash lye added and the tubes, which had long necks in order to avoid warming the liquids in sealing them, sealed up before the blowpipe. They were then shaken in the thermostat at 25°,0 for 14 days and nights in order to saturate the lye with HgO and bring about equilibrium. The cell was then put together and placed in the thermostat at 25°.0. In the following table the results obtained are given in the same way as in table IT. TABLE III. t (hours) FE (Millivolts). 0 0,686 24 0,685 70 0,685 96 0,685 120 0,685 168 0,685 The potential difference found here is therefore the same as in the first series of experiments, which proves that the materials were quite pure before they were shaken with water and that in the first experiment equilibrium was obtained (by diffusion). 10. Between the free energies of red and yellow mercuric oxides, therefore, a sensible difference exist, viz. 0,685 millivolt at 25°.0, a difference at least 700 times greater than the difference which I was able to detect with the apparatus used between red anil red or yellow and yellow oxide. OsTWALD’s statement, that the capillary electrometer employed, which was capable of detecting potential differences of 1 to 2 milli- volts, showed no deflection, agrees completely with my result that the difference of potential in question is only 0.685 millivolt. (OsTWALD does not state at what temperature MARK’s measurements were made.) ERNST COHEN, The Enantiotropy of Tin™(IID. BLOCK OF BANCA TIN WITH TINPLAGUE. Inoculated with grey tin; in solution of pink salt. 27 Sept.—13 Oct. 1899. Temp. —5e C. Enlargement 11/, lin, Proceedings Royal Acad. Amsterdam. Vol. I. ( 281 ) A second proof of the isomerism of the two oxides may be given by means of measurements of the temperature coefficient of the mercuric oxide cell. I shall shortly make a communication on this point. Summary of the resuits of the investigation. 1. There is a difference in the free energy of red and yellow mercuric oxides (0.685 millivolts at 25°). Contrary to Ost- WALD’s opinion, therefore, the substances are isomeric and not identical. 2. The measurements of GLAZEBROOK and SKINNER, according to which a difference of 7 millivolts at 12° exists between the E.M.F.’s of Gouy standard cells made with the two oxides, are incorrect. ‘I'he difference at 12° C. is less than 0.6 millivolt. Amsterdam, University Chemical Laboratory. November, 1899. Chemistry. — ‘The Enantiotropy of Tin” (III). By Dr. Ernst CouEeNn. (Communicated by Prof. H. W. Baknurs RoozEBoom.) 1. In continuation of the investigation of the two modifications of tin a large block of Banca tin, weighing about '/, kilo, was inoculated with grey tin, and subsequently submitted to a tempera- ture of — 5° C. for 3 weeks in contact with a solution of pink salt in order to observe the phenomenon on a larger scale. The accompanying figure, from a photograph, shows that the whole surface is covered with grey warts, between which the original silver- white colour of the metal is to be seen only in a few places. Once the change has begun the waste goes forward at the ordinary temperature. 2. It appears from the following communication, which I owe to Dr. VAN DER Puaats of Utrecht, that the phenomenon of the spontaneous change of white tin into the grey modification has oc- curred in this country also. In 1883 it was found that the water jn the water mains of Utrecht contained lead. Since that time tin lined lead tubes have been employed. At the beginning of 1884, Messrs. HAMBURGER of Utrecht, who made the tubes, stated that a number of blocks of Banca tin in their store had become grey and ( 282 ) brittle. On analysis Dr. v. D. Puaats found that the grey metal contained 99,9 pCt. of tin and therefore was to be regarded as pure tin. When remelted with borax and potassium cyanide a good re- gulus of ordinary tin was formed. The Messrs. HAMBURGER accord- ingly remelted the blocks of tin in this way, including, unfortu- nately, a quantity which Dr. v.p. Praavs had wished to investigate further. Of interest is further that when Dr. v. D. PLAatTs mentioned the phenomenon to Mr. CorneLis DE Groot, ex-chief of the mining department in the Dutch Indies, and one of the pioneers of the Biliton Company, he said that he was acquainted with the pheno- menon and added: “And it is easy to get rid of: we put such tin in the sun, the spots disappear in the light’’. That the heat-rays, and not the light, are the cause of the dis- appearance of the spots is at once evident from the facts now and previously communicated. 3. In the last paper?) (II) it was shown that the velocity of the reaction white tin — grey tin increases as the temperature rises from — 83° C., reaches a maximum at — 48° and finally becomes zero at + 20° C. As may be seen from the curve in that paper, the velocity between + 10° and + 20° is extremely small. In order to study the change in this interval of temperature it would be necessary to make observations lasting many years. On the other hand, if a piece of tin can be obtained which has been exposed to temperatures within that interval for a very long time, it is possible that it will have changed from the white into the grey modification. 4. Through the kindness of Dr. W. Rermprrs, at present resi- dent in London, and of Dr. Gownanp of London, a piece of an antique tin vessel, which had been dug up in England in the neighbourhood of Appleshaw in Hampshire, came into my possession. Regarding the objects found in the excavation of an old Roman 1) Proceedings Roy. Acad. Amsterdam. 1899. Vol. IL. p. 149. ( 283 ) villa at that place, ENG@Leneart!) says in a memoir dated Nov. 25, 1897: About the set of metal vessels from Appleshaw now exhibited, [ will say little, since they are submitted for the opinion of experts. It was my curious good fortune to hit upon them at once in a first experimental trench dug on the site already mentioned, one mile south of my house. They appeared to be designedly hidden in a pit sunk through a cement floor, 3 feet below the surface of the field. The smaller vessels were carefully covered by the larger dishes. One suggestion I may make with regard to their date. Lying at the floor below which they were buried was’a fragment of wall plaster bearing a peculiar pattern of red flower buds on a white ground, absolutely identical with plaster found in the Clanville Villa. Now the inscribed stone found in the latter proves that the house was inhabited in the year 284 a. D., while the coins cease with Decentius, 351 a. D. Therefore, on the not unreasonable suppositions (1) that the plas- ter as found represents the wall-decoration of the houses at the time of their destruction or abandonment, (2) that the identity of design shows a correspondence of dates, (3) that the vessels were concealed when the house was abandoned, we may assign the ves- sels to a period not by many years removed from 350 a. D. Dr. Gownanp*) adds the followmg notes regarding the vessel N°. 27, at present preserved in the British Museum at Londen. “27. Portion of low vase, probably of oval section; foot rim. Height 2'/, inches, diameter uncertain, about 8 inches. Composition : Tin Lead Tron Copper Oxygen, carbonic acid and loss 9. 35pCt 5.06 trace trace 0.59, The extraordinary molecular change which the metal of this ves- sel has undergone is of more interest to the physicist and metallur- gist than to the antiquary; a brief note respecting it, however, cannot be omitted here. The metal is not much oxydised, yet it is so ex- 1) On some Buildings of the Romano-British Period, discovered at Clanville, near Andover and on a Deposit of Pewter Vessels of the same Period, found at Ap- pleshaw, Hants, communicated to the Society of Antiquaries by the Rev. G. H. Engleheart, M. A., with appendixes by Charles H. Read Esq. Seeretary and William Gowland, Esq. F. 8. A. F. C. S., Associate R. S. M. *) Loc. cit. pag. 12 and 14. ( 284 ) ceedingly brittle that it can be easily broken with the fingers. The effect of time upon it has resulted in a complete alteration of its molecular structure, the mass of the alloy being converted into an agglomeration of crystals, and to this its brittleness is due. On melting and casting a small fragment I found that the cristalline structure disappeared and the metal regained its original toughness.” These observations agree so completely with the results so far obtained that it was decidedly worth while to investigate whether the plate described had been converted into the grey modification. 5. A dilatometer was filled with 4.8 grams of the material derived from the antique vessel. Petroleum was used as measuring liquid in the capillary. The dilatometer was placed in a bath, the temperature of which rose slowly. The change which occurred was shown by a considerable fall of the level of the petroleum in the capillary. The fall amounted to 537 mm. The white tin had therefore been converted into the grey modi- fication. The following caleulation shows that the change had taken place practically completely. Assuming the specific gravity of white tin to be 7.3 and that of grey tin 5.8 the volume of the 4.8 grams, containing according to GOWLAND’s analysis 94.35 percent of tin, should decrease, in consequence of the change from grey tin to white tin, by = = 0.16 ee. ted, 4.8 X 0.943 4.8 xX 0.943 8 The volume of 1 mm. of the dilatometer capillary tube was 0.00028 ecc.; a fall of 537 & 0.00028 ce. = 0.15 ce. If the white tin had been wholly converted into the grey modi- fication, therefore, the change of volume in the dilatometer experi- ment would have been 0.16 cc., that found bemg 0.15 ce. We may therefore conclude from this experiment that the white tin in the ancient vessel was practically completely converted into the grey modification. I have to thank Dr. vay per Praats of Utrecht for further information respecting the mean temperature of the place where the vessel was discovered. According to BarruoLomnw, Physical Atlas, Edinburgh, 1899, the mean temperature there is 10° C. The yearly variation of tem- perature at the surface is + 12°.2. Under ground it is of course 285 ) less. No secular variation is known. From these data it appears that the temperature to which the vessel was exposed for 22 centu- ries cannot, for any prolonged period, have been higher than 20° C. 6. In the last communication on the enantiotropy of tin, the velocity of the change white tin — grey tin was determined at different temperatures. It was found that the change grey tin — white tin (above + 20° C.) in absence of a solution of pink salt took place very slowly, so that it appeared possible to study the velocity also above the transition point. In all systems investigated up to the present, which have a transition temperature, the change takes place so rapidly above this temperature that determinations of the velocity are impossible. I filled a dilatometer with about 30 grams of grey tin and added water to serve as the measuring liquid. In this way the pure phe- nomenon may be studied. The dilatometer was placed in a thermostat the temperature of which could be maintained constant within 0.03° by means of an electric regulator. The position of the liquid was read from time to time on the porcelain millimeter scale placed behind the capillary ; the corresponding times were measured by a chronometer to 1/; sec. In order to be able to regard the mass undergoing the change as the same at all temperatures, a very small quantity of tin was allowed to change at each temperature. Temperature ‘Time (i2 minutes Fall of the level of the Fall per hour. liquid in mm. 30°,0 60 7,2 7,2 30°,0 60 7,25 7,25 31°,0 40 13,0 19,50 32°,0 ol 30,0 35,0 33°,0 6 10,75 OGR OM me 90 7 = a m7 106,2 33°,0 6 10,5 LOS 0) 34°,0 6 17 A 99) ; ° . 180 34°,0 6 19 190 § 35°,0 3 25 500 35°,0 51 44 500 ( 286 ) 20° 25° Fig. 2. 30°31°32°33°34°35° At 40°,0 the velocity was so great that I could no longer measure it, In Fig. 2 the measurements are represented. The abscissae are temperatures, the ordinates ve- locities, I have also taken up the study of antimony which appears to undergo similar changes (explosive antimony, Gorg). Other metals too, such as aluminium, invite investigation. Amsterdam, University Chemical Laboratory. November, 1899. (December 20, 1899.) KONINKLUKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, PROCEEDINGS OF THE MEETING of Saturday December 30, 1899. 3G (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 30 December 1899 Dl. VIII). Conrents: “The resorption of Fat and Soap in the large and the small Intestine”. By Dr. H. J. Hampurcer, p. 287. — “Some Observations concerning an Asymmetrical Change of the Spectral Lines of Iron, radiating in a Magnetic Field”. By Dr. P. Zeeman, p- 298. — “Borev’s formulae for divergent series”. By Prof. J. C. Kruyver, p. 302. — “The Entropy of Radiation”. By J. D. van DER Waats Jr. (Communicated by Prof. J. D. yan per Waats), p. 308. — “On some special cases of Monce’s Differential Equation” (Supplement). By Prof. W. Kapreyy, p. 326. — “A new graphic System of Craniology”. By Dr. P. H. Eykman (Communicated by Prof. C. WinkiErR) (with 4 plates), p. 327. — ‘“Pomus in Pomo”. By Miss T. Taxes (Communicated by Prof. J. W. Motz), p. 331. — “On the Theory of the Transition Cell of the third kind” (First part). By Dr. Ernst Conen (Communicated by Prof. H. W. Bakuurs RoozEBoom), p- 834. — “On the Nitration of Dimethylaniline dissolved in Concentrated Sulphuric Acid”. By Dr. P. van RompurcuH (Communicated by Prof. A. P. N. Francurmonr), p- 842. — “On the Formation of Indigo from Indigofera’s an from Marsdenia tinc- toria”’. By Dr. P. van Rompereu (Communicated by Prof. A. P. N. Prancurmont), p- 344. — “The Hatt-effect and the increase of resistance of Bismuth in the Magnetic Field at very low Temperatures” I (continued). By Dr. E. van Everpincen Jr. (Communicated by Prof. H. KaxertincH Onnes), p. 348 (with one plate). The following pay crs were read: Physiology. — “The resorption of fat and soap in the large and the small intestine”. By Dr. H. J. Hampurcer. (Read November 25, 1899.) Introduction. While investigating the distribution of fat in the bloodcorpuscles and plasma under the influence of respiratory gas exchanges, I tried some experiments which may be said to prove that the large in- testine probably possesses the power of resorbing fatty matter by al Proceedings Royal Acad, Amsterdam, Vol. LI. ( 288 ) means of its blood vessels '). I have thought it necessary still further to pursue these preliminary experiments, as they touch ona question which, both from a theoretical and a practical point of view, seems to be of the greatest importance. From a theoretical point of view, because some light may, at the same time, be thrown on our present, in many respects, very inadequate knowledge of the resorption of fat in the more complicated smal] intestine; from a practical point of view, because the problem of rectal nutrition with fat has not yet been satisfactorily solved. In this domain, indeed, there has hitherto been but little investi- gation. In 1874 Czerny and LarscHENBERGER ”) tried two experi- ments on a man to whom an anus praeternaturalis had been applied. They brought into the fistula a known quantity of some fat emulsion, then by rinsing out the contents after some time and ascertaining how much fat they contained, they determined how much emulsion had been absorbed. In 1891 Munk and Rosenstern *) administered some rectal injections of oil emulsion to a girl who had chyle fistula on her leg, and by quantitative determination of the fat in the issuing chyle ascertained how much fat had been absorbed. They found, as CzprNY and LATsCHENBERGER had also done, that the resorption was insignificant. Devucuer *) and PLANTENGA °) injected into persons with a normal intestine a clysma consisting of the yolk of an egg and milk; here too fat appeared to be resorbed, but the resorption was insignificant. Though these experiments of Munk and Rosenster have un- questionably shown that from a clysma fat may be resorbed, it has not yet been proved that this resorption takes place in the large intestine. What proof has there been afforded that, in the above mentioned experiments, a part of the clysma has not passed the valvula Bauhini? And as for the experiments of Czerny and LATSCHENBERGER, 1) Verhand. d. Koninkl. Akad. v. Wetensch. Dl. IIL NO 10. 1894, p, 31. 2) Czprny und Latscuensercer, Physiologische Untersuchungen iiber die Verdauung und Resorption im Dickdarm. Vircnow’s Archiv B. 59, 1874. 8. 179. 3) Munk und Rosrnsrri, Zur Lehre von der Resorption im Darm, nach Untersu- chungen an einer Chylustistel beim Menschen. Vrrcnow’s Archiv B. 129, 1891. S. 230 en 284. 1) Devcuer, Ueber die Resorption des Fettes aus Klystieren. Deutsches Archiv f. Klin. Medizin. B. 58. 1896. S. 260. °) Puanrenca, Der Werth der Nihrklystiere. Diss. Freiburg 1/B. 1898. ( 289 ) they were only two in number, and, from more than one point of view, they are questionable. If we consider that, as yet, no hypothesis even has been formed as to the way in which the fat is resorbed in the large intestine, an investigation of this subject will not be deemed superfluous. In the first place we wish to know with certainty whether the large intestine is indeed able to resorb fat. I. Does the large intestine possess the power of resorbing fat? A loop is taken out of the large intestine of a dog in a state of narcosis, is cleancd out inside, and by means of strings tied round it is divided into three equal parts a, 6 and c. An emulsion of lipanine (olive oil with 6.4°/, of oleic acid) in a solution Nag CO; of !/.°/p is then introduced into the middle part 6; nothing is introduced into the exterior parts a and c. The intestine is then replaced, the central cavity closed, and four hours later the intestine is removed and by administering more chloroform the animal is killed. The mucosa of the central part 5, which contains no more fluid is prepared and cut into small pieces. As a means of control the mucosae of the two outer pieces are also cut into small pieces, placed in two small receptacles, and as much emulsion added as was injected into d at the beginning of the experiment. The fat in the three receptacles is then with the utmost precaution determined. EXPERIMENT I. Length of the pieces of intestine a, 4 and ¢ 9 eM. Into 4 12.5 ce of a 5 pCts. lipanine emulsion in Na,CO, of */.°/ is injected. Four hours later the intestine is eliminated. Isolation of the mucosae, cutting into pieces. To the mass a@ and ¢ 12.5 ce of the emulsion is added. After it has been dried the extract of ether yields the following results: Ether residu of intestine a (mucosa + emulsion) = 0.635 Gr. ” mon ” a(C 7 Hh )==0.659 Gr. Mean... = 0.649 Gr. Ether residu of intestine 4 (mucosa + not resorbed fat = 0.499 Gr. This proves that 0.649—0.499 =0.180 Gr. of fat has been absorbed out of the intestine 4 during these four hours. Another experiment on another animal resulted in a resorption of @.482 er. of fat in four hours. These two experiments and many others of which we shall speak 21% 2 ( 290 ) later (ef. page 293), have decisively proved that the large intestine does really possess the power of resorbing fat. It was remarkable that the piece b, on being opened, proved to be nearly empty, and that big drops of fat clung to the mucous membrane. This gave rise to the suggestion that the Naz COs solu- tion had probably been rapidly resorbed and the emulsion thus destroyed; the fat had got into a condition in which it could not be absorbed at all, or but very slightly. This agrees with the views of Munk and RosENsTEIN, viz., that of an emulsion of 15 gr. lipanine in a NaCl solution of 0.4 pCt., in 74—9 hours, 0.55 gr. of fat issues from the chyle fistula, but that the quantity amounted to 1.1, that is to say about double as much, when emulgent fluid Nay CO; was used. Now it is known that with a Na,COs solution fat remains suspended much longer than with a NaCl solution. It appeared then that on using NagCO, the lipanine remained longer in an emulgent state in the intestine than on the application of Na Cl. Having obtained this result, which was confirmed by further experiments, we thought it of importance to empioy, instead of the Nag COs solution, a fluid in which the emulsion would remain still longer existing in the intestine. It had therefore, to be a fluid of great emulgent power and moreover not rapidly absorbed in the wall of the intestine. For years clysmata of the yolks of eggs, of cream, and of milk have been used for these purposes. As these are compound mixtures these forms of emulsion seemed to me less fit; it is especially the albuminous investment of the fatglobules by which new factors are introduced into the problem of the resorption of fat. jesides DeucHeR and PLaNnTENGA had already shown that the quantity of fat which a man resorbs from such emulsions amounts but to about 10 gr. per 24 hours. It now occurred to me to try a fluid which also in the small intestine exercises an important influence on the physiological emul- gent, viz. a solution of soap. After a preliminary experiment had shown that in a solution of sapo medicatus, the lipanine forms an emulsion which remains long in the intestine, and from which in the long run much fat is resorbed, we wished to determine the influence of soap on the large intestine. Such a research in itself seemed to us not destitute of importance, as under normal circumstances no inconsiderable quantities of soap oceur in the contents of the large intestine and we are unacquainted with its functions in this part of the tractus intestinalis. ( 29) II. Resorption of soap in the large intestine. In order to ascertain whether soap is resorbed in the large intestine we pursued three methods. 1st. Into a loop of the large intestine tied in two places we introduced a solution of soap. The loop having been replaced in the ventral cavity, it is left to itself for a few hours. From the quantity of soap still present we infer how much has been resorbed '). 2nd, From a dog in a state of narcosis a loop of the large intestine is ligatured at one end, and at the other furnished with a tube which is connected with a funnel that may be adjusted at different heights. A solution of sapo medicatus is introduced into the funnel and the intestine filled. From time to time it is now necessary by replenishing, to raise to its original height the level of the fluid descending in consequence of resorption. At the end of the experiment the contents of the funnel, con- necting tube and intestine are rinsed out, and the quantity of soap contained in this and in the mucosa is determined. If we deduct this quantity from the whole of the soap solution used, what has been resorbed remains. 3d, The large intestine is cut through close to the coecum. The free ends are attached to the ventral wall *). After a cure has been effected we dispose of a separate piece of the large intestine. Into this large quantities of a solution of soap are now introduced through the rectum. By ascertaining how much seap, after a limited time, still remains in this portion of the intestine, we can determine how much has been resorbed. All the three methods agree in showing unanimously that the large intestine possesses in a large measure the power of resorbing soap. Ill. What happens to the soap resorbed? The researches of J. Munk *) and of J. Munk and A. Rosen- sTEIN*) have shown that the fatty acids taken into the body are ‘) We cannot enter into particulars here; they will be found in a paper which will appear in the Archiv f. Anat. u. Physiol. Physiol. Abth. *) Dr. Foumer, surgeon, was so kind as to attach this intestine fistula for me. *) J. Munk, Zur Kenntniss der Bedeutung des Fettes und seiner Componenten fiir den Stoflwechsel. Virenow’s Arch. B. 80. 1880 S, 10. DMG Ge ( 292 ) éonverted into fat, and as such appear for a great part in the chylevessels. The last is opportune; for as Munk first observed, the presence of relatively small quantities of soap in the blood circuit is dangerous to life; an intravenous injection of 0.12 gr. of soap per kilogr. of the weights of the rabbit already caused death. These experiments made it highly probable that already in the mucosa of the small intestine the fatty acids combine!) with gly- cerine into fat. And the preliminary experiments of Ewa.p?*) with finely minced mucosa of the small intestine have confirmed this hypothesis. Now as there is no ground for assuming that the soap which is absorbed in the large intestine passes without injury into the blood it seemed to me not too hazardous to conjecture that the oleic acid in the large intestine is also converted into fat. To test this hypothesis by observation, we made experiments in three directions. 1st We examined whether the mucosa of a loop of intestine which has been some time filled with a solution of soap shows an increase of fat. (As is known, some fat can always be extracted from the normal mucosa). 2nd We examined whether the formation of fat stated under 1* does indeed continue after the intestine has been taken out of the body and is left to itself at the temperature of the body. 3"¢ We inquired whether the fresh and still warm mucosa of the intestine, after having been minced fine and then saturated with a solution of soap in which was a little glycerine, was still able to convert soap into fat. This proved to be really the case. The conversion, however, could no longer be observed when the mucosa had previously been heated to 80°. Hence this suggests fermentation. There can be no doubt, then, that soap resorbed in the large intestine is, partially at least, converted into fat in the mucosa. lV. Resorption of fat from lipanine-soap emulsion. 1 It having thus been established what happens to the soap resorbed in the large intestine, we went back to our point ef departure and inquired whether, according to our theory, laid down at page 290, 1) The origin of the glycerine is still uncertain. 2) C. A. Ewaup. Uber Fettbildung durch die tiberlebende Darmschleimhaut. Archiv. f. Anat. und Physiol. Abth. 1883. Supplem. S. 302. ( 293) more fat is resorbed from emulsions with solutions of soap ther from emulsions with Na, COs. In order to answer this question, a loop was produced from the large intestine and by means of a string tied round it, divided into three parts, of equal length. Into the central part 6b a lipanine-Na, COs;-emulsion was introduced, into @ lipanine-soap- emulsion. The two emulsions contain 20 cc lipanine to 80 ce emulgent fluid (soapsolution 5 °/) and Na, COs-solution !/, °/o). The piece of intestine c¢ serves as a control and does not contain anything. Five hours afterwards the intestine is eliminated. On opening } there is no trace of emulsion to be observed; this section is empty, but a mass of fat is found lying against the mucosa. In @ there is still a fine emulsion present; of a fatty mass or of drops of fat against the mucosa there is no trace. The contents and mucosa of the two sections are taken in hand for the quantative examination of the fat still present. The mucosa is also removed from the controlling section ¢ and its fatcontents determined; but before proceeding to the last, we add, in order as much as possible to avoid mistakes the same quantity of lipanine-soap-emulsion as was injected into @ in this case, thus, 20) ec. The first experiment showed that from the lipanine-soap-emulsion 0.558 Gr. of fat had been resorbed, whereas, in the same time, only 0.456 Gr. of fat had been resorbed from the lipanine-Nay COs- emulsion. Further experiments yielded the same results. Though it had hereby become certain that more fat is resorbed from lipanine-soap-emulsions than from lipanine-Nay CO;-emulsions and the power of the large intestine to resorb fat has hitherto been rated too low, yet, in order to form an idea of the resorbing power of the large intestine, it seemed desirable to compare it with that of the small intestine. In making this comparison, the necessity of reducing the extent of the resorption to equal surfaces of mucous membrane, presents no little difficulty. If, however, in preparing the mucosa we make a circular incision which penetrates to the mucosa, and then strip off serosa with muscle from the mucous membrane, it is very easy to ascertain the surface of the mucosae of the two pieces of intestine to be compared. The experiments have now shown that, for fat, the resorptive ( 294 ) power of the large intestine is, under the given circumstances, not inferior to that of the small intestine. I say: “the resorptivepower,’ by which I do not mean, of course, that in normal life the large intestine resorbs as much, per unit, of the surface of the mucous membrane, as the small intestine. Nor is that the case. For the fat is supplied to the small intestine in a pulpy, sometimes almost liquid mass, whereas the large intestine must absorb the fat from a more solid condition, which is, of ‘ourse, done with less facility. Moreover, on reaching the large intestine, the contents have already rejected the greater part of the fat, and consequently what, in 1ormal life, the large intestine absorbs 1 fat will amount to less than what the small intestine resorbs. What our experiments teach us is this: that when the lipanine- soap-emulsion is supplied to the unit of the surface of the mucous membrane, an almost equal quantity of fat is resorbed. Besides in detached pieces of the intestine, we have now also studied the resorption of fat in a fistula of the large intestine. In somewhat over a day we saw from a lipanine-soap-emulsion about 10 gram of fat arrive at resorption in 12 hours. If we consider that this quantity is about the same that PLANTENGA in the course of twenty-four hours could bring in maximo to resorption in a human being whose large intestine possesses a much larger surface of mucous membrane than that of the dog, it then becomes highly probable that also in man, if we also employ lipanine-soap-emulsions we shall be able to bring about a much more considerable resorption of fat than we have hitherto obtained with other emulsions, The emulsion with soap selution yields another practical advan- tage, viz. that resorbed soap contributes as such to the absorption of fat, for, as we have seen, the soap is converted into fat. From a practical point of view it would be of importance system- atically to examine what will be the most favorable proportion of lipanine and soap-solution, and also what concentration must be given to the soap-solution in order to make the resorption as great as possible. We shall have further to discover how much the extent of the resorption depends on the volume of injected emulsion and, therefore also on the respective times of injection. We have, however, not pursued the subject further in this direction. ( 295 j We have occupied ourselves with another problem, viz. what path does the fat take in the mucosa. V. What way does the fat take in the mucosa ? We may a priori assume that the particles of fat after leaving the epithelial layer of the Lieberkiihns glands and entering the lymphduets, will, for a part at least, be carried off with the current of lymph. The remaining fat would then have to follow the path of the blood capillaries situated in the lymphducts, and seeing that in the mucosa of the large intestine the system of lymphatic vessels is relatively only slightly developed, it would not even be improbable that the blood capillaries form the principal channel of conveyance. Meanwhile the question might be raised: has a transition from fat into blood capillaries ever been observed in other places? And this then suggests in the first place, the smal] intestine. That a great part of the fat there follows the way of the lymphatic vessels, few will question; but whether the blood capillaries are also responsible for a part of the transport has not hitherto been decided. According to Craupr Bernarp the serum of the v. porta in mammalia during digestion looks as white as milk. On the other hand, comparative investigation of the blood of the v. porta and of the a. carotis, undertaken by Bornstein ') at the instance of Hemennain showed that the fat contents of the portal-blood are less than those of the a. carotis. The experiments of ZawiLski*) also seem to argue against a direct absorption of fat by the blood capillaries. Eighteen hours and a half after partaking of a rich meal, while the resorption of fat was still in active operation, the contents of the ductus thora- cicus where drawn outside so that the blood no longer received any chyle. The fat contents of the blood amounted only to 0 05 °/,; to no more, then, than in a stato of hunger. Over against the results obtained by ZAwILsKkr and Bornsrein we must set those of von WALTHER’) and of Franx*). Von 1) Herpennatn, Beitrige zur Histologie und Physiologie der Dtinndarmschleimhaut. Pruiicger’s Archiv Suppl. 1888. 8. 95. 2) Zawiiskt, Die Abfuhrwege des Fettes. Arbeiten aus der physiologischen Anstalt m Leipzig. Jahre. XL. 1876. ‘) von Warner, Zur Lehre von der Fettrescrption, Du Bois-Rryvonv’s Archiv. 1890. p. 328. ‘) Frank, Die Resorption der Fettsiiuren der Nahrungsfette, mit Umgehung des Brustganges. Ibid. 1892. p. 497. Derselbe, Zur Lehre der Iettresorption. Ibid. 1894. p. 297. ( 296 J Water showed that only a very small portion of the whole quantity from 40 to 50 gr. of the resorbed fat is transported through the ductus thoracicus. And FRANK observed that, after ligaturing the ductus thoracius, the resorption of faity acids in the small intestine was considerable. ,,These observations’, HAMMARSTEN says rightly in his textbook on physiological Chemistry, hardly seem, however, under normal circumstances, capable of being trans- ferred to the resorption of neutral fats in man”. Munk and Rosen- STEIN in their investigations on a girl who had a lymphfistula in the leg, could find again in the chyle scareely more than 60°/, of the fat administered per os. It will be seen that there is still little agreement with respect to the direct transition of fat into the blood capillaries. It appears to me that I have succeeded in showing with certainty that cm the small intestine of the dog the blood capillaries have a considerable share in the resorption of yat. The experiment was as follows. In a large dog in a state of profound narcosis a loop of the small intestine was produced by means of an incision in the linea alba. In consequence of a rich meal (bread with a great deal of lard) which the dog had received the night before the chyle vessels were splendidly injected. At distances of 17 cM. strings are thrust through the mesenterium, close to the attachment of the intestine. By means of these strings pieces of the intestine will be shortly alterwards detached. The chyle vessels of the central piece of the intestine 6 are carefully bound together. Those of the adjoining parts @ and ¢ are not. The whole loop is then well rinsed with a tepid sojution of Na Cl-solution of 0.9°%). The strings are then tightened and the loop divided into three equal parts. Into each of the three parts is injected 25 c.c. of a lipanine-soap-emulsion, con- sisting of 200 cc. sapo medicatus of 5°), +50 ee. lipanine. When from the side of a@ and e two pieces a’ and c' had after rinsing been untied, everything was again restored to the ventral cavity, which was then closed. Five hours later the intestine was removed from the animal, which was still in a state of nareosis and was now killed. The determination of the percentage of the fat of the contents of the loop inclusive of the mucosae showed that in b, where the chylevessels were bound together, still 0.419 gr. was resorbed; whereas in a and e, that is to say in chyle-vessels not bound ( 297 ) together, 0.714 gr. and 0.697 gr. respectively of fat were absorbed. Three more experiments yielded the same result. There can be no doubt, then, that the blood capillaries possess in a large measure the power of resorbing fat. This result agrees with that of Munk’s and ROsENSTEIN’s expe- riments, which showed that only about 60 "/, of the fat resorbed flows out through the chyle vessels. With respect, now, to the experiments of other investigators who deny that the blood vessels have a direct share in the resorption, it seems to me, that considering the present state of our knowledge, those of ZAwitskt are no longer conclusive. Of later years it has been shown that in the blood ferments occur (lipolytie ferment of ConnsTEIN and Muicnaiinis, lipase of Hanrior) which possess the power of converting fat. When Zawiskt finds that on the effluence of chyle the blood does not contain more fat than about what is found in a state of hunger, this does not exclude the absorption of fat through the blood capillaries; owing to the slow resorption the fat always undergoes, what had passed into the blood-cireulation could be regularly analyzed. On the same grounds, comparative determinations in different sorts of blood, such as were made by BornsTEIN cannot be decisive in this question. Moreover in these experiments no notice has been taken of the significance of the relative volume of blood corpuscles and plasma in the composition of the total of blood in the two cases. It may now be further asked whether the fatglobules as such are absorbed in the blood capillaria, or not until they have first perhaps, been converted into a soluble combination. CLAUDE BrrNaRp’s experiments suggests, indeed, the first hypo- thesis, but it does not exclude the second. On this question I hope soon to make some communications. It has already been shown that the blood capillaria take a direct part in the resorption of fat in the small intestine ; and may also most probably do so in the large intestine. Summary. 1. It may now be considered as proved that the large intestine of the dog has the power of resorbing fat. 2. Contrary to the opinion hitherto held, this power is consider- able, and is not inferior even to that of the small intestine, ( 298 j Ww In order to bring about a resorption so considerable, it is necessary to take an emulsion that can stay a long time in the intestine. The usual Na, CO, is not well adapted for the preparation of such an emulsion and the NaCl still less so, because both are rapidly resorbed and with them the emulsion neu- tralized. A solution of sapo medicatus, however, seems to answer the requirement. 4. As to the soap solution itself, it appears that this is resorbed, though much more slowly than the Na, CO,, and during the resorption is, at least for a part, converted into fat already in the mucosa. This conversion continues in the intestine that has been cut out; nay it is effected even when the mucosa has been minced fine. Heating to 80°, however, neutralizes the said property. 9. As to the path taken by the fat in its resorption in the large intestine, it is highly probable that a part of it is transported through the blood capillaria. The experiments described above have at least shown with certainty that this is the case in the small intestine. Physics. — ‘Some Observations concerning an Asymmetrical Change of the Spectral Lines of Iron, radiating ina Magnetic Field”. By Dr. P. Zeeman. 1. In observing spectral lines resolved into triplets by the action of the magnetic field, one is certainly struck by the symmetrical position and the equal intensity of the outer components of these triplets. There are especially in the case of iron not a few of the stronger lines, which seem to represent ideal cases of triplets, as originally predicted by Lorenrz’s theory. It is only after more attentive inspection that several faint triplets are seen in which one of the outer components is apparently more intense than the other. On a former occasion!) I pointed out that there were reasons for expecting triplets with a more intense lateral component toward the —— 1) Proceedings Royal Academy of Sciences Amsterdam, June 1898. Astrophysical Journal, Vol. 9. Jan. 1899. ( 299 ) red. In strong fields I noticed a few. I could show however that most of these asymmetrical triplets were due to superpositions and T concluded that we had no evidence of a directing influence of the magnetic field on the orbits of the light-ions. No more was done upon this subject. 2. Some time ago Prof. Vorer of Gottingen kindly communicated to me that he had deduced from theory that normal triplets must show in weak magnetic fields a remarkable asymmetry viz. the outer component teward the red has the greater intensity, the outer com- ponent toward the violet has the greater distance from the original line. In low fields these asymmetries will preponderate, disappearing however in strong fields 1). It has given me much pleasure to undertake at Prof. Voret’s request a testing of this result of his theory. I made these observations the more willingly now I was in possession of a beautiful concave grating, which Prof. RowLanp with kind courtesy has examined and selected for me. The grating is, like the one lent from the Leyden laboratory, ruled with 14438 lines to the inch and has a radius of about 3 M. The resolving power of the present grating is however superior to that of the one formerly used. Negatives now were taken generally in the second order. 3. I tried to study by eye observation, using the spectrum of the first order, the inequality of the outer components. Iron termi- nals (all following facts relate to this substance) were used. A Nicou’s prism was placed before the slit with its plane of vibration vertical, in order that the outer components of the triplet only were visible. But notwithstanding the lateral components were but slightly separated and therefore the circumstances, and as to intensity of the field and as to facility of comparison, very favourable, I could not conclude to an indubitable mequality of the outer components. It may be that the flickerg of the spark interferes rather infavour- able with these observations. 4. I had more success with the photographs taken. I studied the spectrum of the second and third orders; between 3400 and 1) Vorer’s paper will be published shortly in Wiedemann Ann. under title ; “Dis- symmetrie der ZeEMAN’schen Triplets”. ( 309 ) 3960 tenth metres in the second and a somewhat smaller part in the third order. ' I did not introduce a Nico between the spark and the slit. The strength of the field may be roughly characterized by the state- ment that about two thirds of the more intense lines were resolved into triplets or quadruplets (showing with the field used for the greater part as doublets). It was now possible to look for inequality of intensities and at the same for asymmetry of the distances. Excluding the Jines where the before mentioned perturbations interfered '), I have found several lines, which showed the asymmetries predicted by VoreT; it is true, in a very small degree. Some lines showed the asymmetry of the intensities only or of the distances only, but other lines the two asymmetries at the same time, The phenomenon is however extremely small. The difference of the distances between the components toward red and toward violet and the original line never exceeds a few percent. For the moment I will not communicate the amount of the asym- metries of different lines. Either both or one of the asymmetries are shown by the following lines: 3498.00, 3687.60, 3709.40, 3735.01, 3763.91, 3878.71 2). 5. As the outer components of quadruplets behave in a normal manner I have looked for an inequality of intensity between these components. The field used was somewhat stronger than the one mentioned in § 4. There was a difference in the expected sense in the case of the lines: 3466.01, 3475.61, 3705.73, 3722.73, 3872.65. Moreover 3466.01 and 3705.73 showed a displacement toward the violet of the mean of ihe outer components relatively to the mean of the inner ones. This result is confirmed, at least for 3466.01, by an observation of Reese: “but the most careful measurements that I could make indicated a possibility that in the case of 3466.0 the mean of the inner pair is a trifle further toward the red than that of the outer pair*).” Vorar’s developments ') Proceedings Royal Academy Amsterdam, June 1898. Astrophys. Journal. Vol. 9. Jan. 1899. *) The wave-lengths of the spare-spectrum according to Exnpr and Hascuek, 8) Notes on the Zerman-Effect. Johns Hopkins Un. Circular. June 1899, N°. 140. Phil. Mag. Sept. 1899. ( 301 ) only refer to triplets, but, I think, we may consider also these observations concerning quadruplets as indications in favour of the theory. 6. The line 3733.46 is so modified as to be a triplet, the com- ponent toward the violet being at a smaller distance from the original line than the component toward the red. There seemed to be no inequality of intensity of the outer components. Of the triplet 3824.58 the component toward the violet is apparently more intense than the component toward the red. It does not seem to me very probable that in the last mentioned case there is some perturbation by the presence of the air-line 3824.4 (Nrovius), because the component is tar from hazy and the air-line very faint. It is invisible upon a negative taken with a very low field but with a time of exposition equal to that used in taking the negative with the more intense component toward the violet. It must remain for further inquiry to decide whether these obser- vations must be explained by an extension of theory or by some perturbating cause not yet taken into account. 7. From the mentioned observations we may draw, I think, the conclusion that the observed asymmetries are very probably real. The extreme minuteness of the asymmetry makes it desirable however to establish further its reality. I hope to do this in a future paper. Finally it is to be observed, as was remarked to the author by Prof. Vorer, that my observation does not decide between his theory and that of Lorentz, but confirms the common basis of both theories !). | Addition of Jan. 15. I have lately found that in the case of the triplet and quadruplet of cadmium 4678 and 4800, and the triplet and quadruplet of zinc 4680 and 4722, the outer components toward red are decidedly more intense than the components toward violet. Measurements of the distances were not yet made. The line 3733 mentioned in § 6 happens to be one of the lines showing “reversed polarisation.” Probably this deviation from the normal polarisation will account also for the reversed asymmetry of the distances. i I doubt however at the possibility of the suggested explanation in the case of a few other lines, lately examined, and which appar- ently exhibit the behaviour mentioned in the beginning of § 6.] ') The relation between these theories is exposed by Lorentz. Physik. Zeitschrift d. Riecke u. Simon. 8. 39. 1899, ( 302 ) Mathematics. — ‘Bore.’s formulae for divergent series’. By Prof. J. C. KLUYVER. In his memoir on divergent series (Ann. se. de Ecole norm., t. 16, p. 77, foot-note) BorEL suggested that in his “adjoint integer function” Un a” yy E (a/e — Py 0 nl ! perhaps the factor a,:n/ might be advantageously replaced by se p _f{ ” : oe A Oe Ball (es 1), where p is a positive integer. In the present communication the truth of this remark will be shown. It will appear that this slight alteration in E (az) leads to a “region of summability’’, identical to those found by Boren him- self, and also by Servant (Ann. de Toulouse, 2° série, t. 1, p. 152), when they considered other modifications of the adjoint integer function. Starting with the function f(z) and its expansion Dm DR DY fe\ a Se eSS [@Q=2;,.22 = Unis 0 which expansion we assume to have a finite radius of convergence, we consider the adjoint integer function E ca Cn =” al i, (a/z) = > — — 2 0 n E+) P The integer p is arbitrary; if p be taken equal to unity, the function 2; (a/z) becomes the function (az) of Bore. In the first place it will be necessary to express Ep (a/z) by means of a definite integral. A suitable path of integration W is obtained in the following manner. In the complex x-plane we draw a curve nearly in the shape of a cardioid, the cusp at «= 0 pointing in the direction of «= —o, and the curve itself enclosing the origin. We suppose that the path W begins at 2 =0 and that, along the cardioid, it goes in a positive direction round the origin, ending again at «= 0, ( 303 ) With this assumption about W we have immediately 1 x 1 mt 1 1 2 me ae = i= (a! go dae, wv P n a Wp 1 ne 4 als Cn 22 a € = au s= - | ee o(ee 2 ee eda, n CATE ac x r\(\—-+ 1) Ww P and finally, provided J#| remains small enough, ze 1 e eed ? erin E, (a/z) = ani itn (er Ze ye de , ~ a. av 0 W or a 1 ren 1 xt é eae Saw Ey (a/z) = ian ee (a? Et ti) eho a a « W The latter equation however conveys no definite meaning, unless 3) 1 ami during the integration the value of f(«” ze °) can be fixed without ambiguity. This requires that the region bounded by W contains 1 mt none of the singular points ¢ of f(#? ze ”). We will assume that in the <- plane /(z) can be continued across DR the circle of convergence of the series Se, 2” and that it has outside 0 this circle a set of singular points a = Ac, Then, takingz=¢ e's, 1 me ol . n }? . . . . the function f(7” ze ”) has in the z-plane a similar set of singular points ¢, given by 1 P p aaa < cos p(O—) —i > sin p(O—/?) « In order to exclude the points ¢ from the region delimited by the cardioid, we confine the point ¢ in the 2-plane to an area, con- a) ot ed Proceedings Royal Acad. Amsterdam. Vol. LL. ( 304 ) structed as follows. Each of the points e=Aei? determines a curve whose equation written in polar coordinates is ) i cos p (O—f) ’ and the totality of these curves divides the --plane into a system of curvilinear polygons. In one of these polygons, which we shall designate by G,, the origin and the circle of convergence of the nD series = ¢, 2” are contained. We suppose now that the point < never 0 Jeaves the interior of this polygon Gy . In that case we constantly have a sp ve cos p (O— P<: and consequently real part of iS +757) 10 In other words, we may affirm that the points ¢ in the «-plane are situated outside the circle with diameter 1+ ¢ and centre «= —}(1+¢). Moreover, since necessarily we must suppose |< | to remain finite, there is a non-evanescent minimum value of |¢], so that it must be possible to draw the loop W in such a manner, that all the points ¢ remain outside, the loop thereby enclosing at the same time the cirele with diameter 1 and centre «= — }. The latter condition is imposed on the path W in order that during the integration we shall constantly have real part of ee 4) 0 With the thus constructed loop W as path of integration the equation a x s sok 1 é a seis F, (aje)= 5 — | 7 f(a ze Pede Ww retains its signification, even when the point 2 passes beyond the circle of convergence far: only it remains within G . ( 305 ) The first property of the function £, («/z) is now proved at once, Multiplying by e-« we have 1 xi 1 1 p Hip. . —a (+ +1) Lim e* Ey (w/z) =- = f(@ cq ° ) Lim e x de a—+o QC tir. wv a=t+o W and hence, as —a V4] Lim e a ==), a=+o ah é 2 Cn 2” a? Tym e-¢ E, (a/z) = Line e-% = ——— ==1 0) inten GL) a=+4+o a=+o 0 r(* a 1) P Secondly we find _ 5 1 1 xi ao 1 Aa rs a te pa | e—* EB, (a/z) da = aa {2 mio ze! yi en (3 ') dieas 0 W 0 1 ] 1 mt aL D ae Se tat aati) 2ntJ «+1 W In the latter integral the only infinity of the subject of integration within the loop W being «= —1=e7?, the loop can be contracted into a small circle round this point and there results i 2) f Hs (al2\idai=—ae) 02) «os 6 os) (IE) 0 This equation may serve to evaluate f(z) for any given point z within the region G, , therefore we must regard G, as the region of summability associated with the function Z, (a/z). Meanwhile Boren indicated still a different way to calculate 7(z). Supposing p = 1, and 2 lying within the polygon G), he proved that we have [ © g an im e- a en alee a+ 0 nr ! bho bo * where h=n ee ch ee > Uh h=0 The question remains whether the function am = 8 a P Pp (a/2) = = - Ov aye ee ate 1) ie may be similarly used for any point - within the region G), this is indeed the case we prove as follows. It is easy to see that we can write . That n = (2 — 8n—p) a” da au r(=) : P if we only agree to take u, = 0 and s,=0 as soon ash< 0. Replacing sp — s,—, by 1 Ipy k=p—1 Un Up—1 + upg f+ 2 ee) Mr—pt1 = > Un—k » k—0 we get n k= 1 2= igus dpy ae ae 1 d LP Unk 2" a — fy = = - = da fp k=0 ck da n=O G ari 2 ) and oO ey dpy a=o e—@ — Pp }da= le fp (a/2) | = . a= i x k=p—1 n=O yp 7 2k a’ ja=a — ee S ——_. k—0 ak | n=0 n a—0 a r(i-+i1 Pp n v2) k ? k—pi— 1" Pali - n=" y, 72k a +- = [ows eS dare k—0 ok : ee) ( 307) Now, always supposing < to lie inside the region G), it is evident that E, (a/z) is related to f(z) in the same manner as ney 2k BO) = = n= n rey D is related to now AG AC) — PS. Drea eae n—0 hence we may apply equations I and IT and conclude that Lim e-2 B™ (az) =0., a=+o0 P | e-4@ E® (ajz) da = zk f(z). 0 So it apjears that we have [ 29» (ale) | = — + Ps) or ee Sn ae Tmt Sf (2) TD) a=+o 0 r(= ab 1) P an equation wholly equivalent to the original formula of Boren. Cases may occur in which the formulae I, II and III established in the foregoing have some importance. For, in asking for the value of f(z) in a given point z, it may happen that this point lies outside Borex’s region of summability G, and that we are able by a proper selection of the integer p to find a region Gp, wherein 2 is contained. In that case we can replace BoreEL’s equations by the formulae II and III, the application of which presents scarcely more difficulties than that of the formulae for the region G,. Finally we may remark that equations I and II still hold if p is an arbitrarily assigned positive number. For rational non-integer values of p however, the extent of the region of summability G, is considerably reduced, and for irrational values of p the region G, ulti- mately coincides with the circle of convergence, so that the summation- formula II is no longer of any use. ( 308 ) Physics. — “The Entropy of Radiation’. By J. D. VAN DER Waats Jr. (Communicated by Prof. J.D. VAN DER WAALS.) The entropy principle may be formulated in different ways. hain P ) ; Strictly speaking, nothing follows from the examination of the cyclic process of Carnot but: tq aQ . ar ; ; skies i ~ is a total differential, if the process is reversible. 2nd. If we pass from state A to state B in a not reversible way, dQ. , ; Ie is smaller than when the process is reversible. The second formulation is: The entropy tends to a maximum, i.e. the entropy always increases; and if the other conditions to which the system is subjected, allow different processes, that one in which the increase of the entropy is greatest, will take place. As we may consider every slight change as “the process’, we may also say, that the fluction of the entropy is always a maximum. To derive the second formulation from the first, we must gene- ralize the idea entropy. We must then also attribute entropy to substances which are not in equilibrium. It being however imposs- ible, that in a reversible way a substance is brought to a state which is not a state of equilibrium, the definition: entropy is be for a reversible process, cannot be applied here. It has really been attempted to find a conception of entropy which also appiies to substances which are not in a state of equilibrium. In order that the second formulation of the principle be correct, the original conception must be extended still in another way. An entropy of radiation must be introduced. Whether a deviation from the law of Carnor might be obtained by radiation, has repeatedly been made the subject of an investigation. BarToLi!) imagined a cycle in which apparently a deviation occurred. Prof. BoLTZMANN *) proved however, that this contradiction may be avoided by taking into account the pressure exercised by luminous rays on a body by which they are absorbed or reflected. In this they tried to solve only this question: Can we obtain by means of radiation a process, in which the substances yield quantities of heat, which have another ratio than would follow from 1) Barvont, Sopra i movimenti prodotti dalla luce e dal calore, Firenze, Le Monnter 1876, *) Wied. Ann. XXI[ 1 Anno 1884. No, 5. Page 31. ( 309 ) the law of Carnor? Wien has first introduced an “entropy of radiation” !). He thinks it a matter of course, that radiation which can be in equilibrium with radiating bodies, and which possesses energy, must also possess entropy. He derives his arguments exclusively from the examination of reversible processes. He defines as “tem- perature of radiation” the temperature of a perfectly black body, which is in equilibrium with this radiation. In reversible processes, however, the quantity of heat yielded by the walls is the same as that communicated to the ether. As further according to the defini- tion the temperatures of the walls and of the radiation are the same, it comes to the same thing whether the law of Carnot be applied to the ether, as Wien did, or to the walls, als BoLTzMANN 7 ception “entropy of radiation” can therefore never be concluded from reversible processes. KE. Wrepemann had already pointed out the necessity of that conception for phosphorescence- and fluorescence phenomena *). Yet it is clear that if the entropy principle is expressed in the second formulation, every irreversible radiation phenomenon is in contradiction with the entropy principle, if we do not attribute en- tropy to radiation. Every body which radiates heat into a vacuum, which heat is not at the same time absorbed by another body, would lose entropy without that at the same time at least an equal amount of entropy was gained elsewhere. Therefore the entropy principle requires, that the ether participating in the movement of radiation, is assumed to have at least as great an amount of entropy, as the radiating body has lost. Whether it is possible to find such an entropy function for radiation, cannot in my opinion, be doubted. This extension of the entropy principle is l:ss hazardous than that in which the second formulation is derived from the first. Yet nobody will doubt whether the second formulation is correct, pro- vided that we follow BoLTzMANN in considering the entropy prin- ciple not as an exact law but as a principle of probability. Win derives, inter alia, from his considerations, the theoretical reliability of the law of SrepHAN and the relative intensity of the different wave-lengths in the light emitted by black bodies. Another advantage of his introduction of the idea of “entropy of did: | is identical in both cases. The necessity of the con- 1) Wied. Ann. 52,1. Anno 1894, No, 5. P. 182 sequ. 2) Wied. Ann. 38,3. Anno 1889, No. 11, P. 485, (7310) radiation” is, that we ean aseribe a continuous existence to the entropy: when a body loses entropy by means of radiation and ancther gains entropy, we need not say, that in one place at least as much is created, as is lost in another place, but that the entropy has moved continuously through space from one place to another. The question about the localization of the entropy is, however, not of so much importance, as that about the localization of the energy. The constancy of this second quantity induces us to think of an identical continuance of existence, so that we postulate a perfectly continuous way of moving. This is not the case with the entropy and as the entropy of a point depends on the condition of the points round it, the entropy of a molecule may be modified by modifying its sur- roundings, there being no question of a continuous propagation. For if we assume the formula of BourzMann: H = | Flog (fF) da the amount which every molecule contributes to the entropy is —log(F’), as — H represents the entropy. This quantity is changed momentaneously for every molecule of the group /’, when one or more molecules are added to that group, there being no question of propagation. It is remarkable that if the entropy in a volume element increases in consequence of shocks, the amount with which the entropy increases must be ascribed exclusively to the molecules which have collided. For in the quantity // both F and log(/) change. The change may be represented by: {2 F log (£) da a d log (Lf) do. The first term is the increase of the entropy of the molecules which have collided, the second term that of the other molecules. The second term, however, appears to be 0, for: 1 [Peateg B) do = [5a Pdo = d F do. This represents the change in the total number of molecules. This number is however, not changed by collisions, and the second term is 01). If however, the entropy of the volume elements as a whole 1) See BotrzMaNn, Vorlesungen iiber Gastheorie, Iste Theil p. 35. ( 3165 is considered, and not that of every one of the molecules separately, we may say in consequence of the entropy of radiation, introduced by Wien: the entropy is never lost, and it propagates continuously through space. In what follows I hope to prove: Entropy originates only, when collisions (or their analogue in radiation) occur, and the new entropy is then to be found at that place where the collision has taken place. Though much might be Jearned from considerations like those of Wien, I prefer to make an attempt to obtain an insight into the nature of the entropy of radiation by considerations analogous to those of BottzMaNN for the entropy of substances. re When writing the preceding chapter, the treatises of Prof. PLaNcK entitled: “Ueber irreversible Stralungsvorgiinge” and his debate with Prof. BottzMaANN in “Die Sitzungsberichte der Akademie der Wissen- schaften zu Berlin, 1897, 1898 and 1899”, were unknown to me. My attention was afterwards drawn to them. I found that several of the observations which I have made already occur in Prof. PLANCK’s treatises. However, as my opinion differs in many respects from that of Prof. Prancx, I think that I ought to publish the following paper, though I can oppose against the elaborate system of Prof. Pniayck only a beginning of a system according to my views. ‘lo make clear the course of my thoughts, I have left the preceding chapter unchanged. In the first place I shall have to vindicate, why I do not follow the method of treatment of Prof. Puancx, but follow the considerations of Prof. BoLrzMaNN on the molecular thermal movement also for the ethereal movement of ra- diation. For this purpose I shall put the views of the entropy principle of Prof. BottzMann and Prof. PLanck in sharp contrast ; or at least what seems to me to be the view of Prof. PLANCK, for he does not expressively state his opinion. Prof. PLANCK’s meaning seems to me to be the following: The basis of his considerations is that the entropy principle is correct, that is to say that the entropy can only increase. Now many processes which occur in nature, are not elementary e.g. all thermal phenomena can only be treated adequately by applying strict mechanic laws to the separate molecules. In order to find an exact law of nature, it will be necessary to consider an elementary process which is ruled by strict mechanic laws. Now the entropy can change in one direction only, the cause of which ( 312 ) must be found in an elementary process, which can take place in one direction only. In this way quite a different idea of reversibility is introduced as that which was originally deduced from the cycle of Carnor. The reversibility according to CaARNOT means, if we consider more closely the mechanism of the movement of heat, that all states, through which the system has passed, are states of equilibrium. These states of equilibrium now, are nothing but a particular kind of stationary states, namely such as can exist, without continual change taking place necessarily anywhere outside the system. So e. g. a gas between two plates, one kept at 100° by means of steam and the other at 0° by means of melting ice, is in a perfectly stationary state, which however is no state of equilibrium, as on one plate steam is continually condensing and on the other ice melting. It is easy to see that this idea has little in common with the idea of irreversibility of Prof. PLANCK. Many processes are irreversible according to Carnot, reversible according to Prof. PLANCK, e. g. thermal processes which are brought about by the movement of the molecules. In these processes Prof. PLANCK grants the rever- sibility according to his definition. As these processes however, increase the entropy, it seems to me, that Prof. PLanck ought not to have tried to find a process, which is irreversible according to his definitions but an explanation, why processes, which are irre- versible according to CaRNOT can only cause increase of entropy. This observation of mine would scem fallacious only to him who wanted to explain all thermal processes not by molecular motion and collisions, but either by radiation or by an elementary strictly irre- versible process of which we have as yet not the least idea. Now we shall investigate the question whether there is really an elemen- tary strictly irreversible process. Prof. BottzMANN denies this positively. As well in the ordinary mechanics (provided heat and other internal movement be introduced as kinetic energy) as in all ether phenomena no process occurs that could not take place in an opposite direction. If a movement fulfils the equations of LAGRANGE and those of MAXWELL, the same applies to a movement which arises from the former by reversing all velocities and all magnetic forces. This observation seems to me to be quite decisive. Yet the con- sideration of all processes is not equally justified. The movement of a Hervrz’s vibrator, which is damped because of the emission of radiation, may be thought to take place in opposite direction, so ( 318 that a wave converges from the infinite space where it has every- where the same phasis, exactly into the same point. Yet we are not justified in assuming, that this second movement occurs in nature. On this Prof. PLANcK’s considerations are based. He thinks that he has found his perfectly irreversible process in radiation which falls on a resonator. He makes this process really irreversible by excluding a certain number of movements as not occurring. In reality Prof. PLANcK’s ideas differ less from those of Prof. Bourz- MANN than he thinks. For the latter calls a great many movements possible, but very improbable, and assumes justly, that such improb- able movements may occur both in phenomena of molecular move- ment and in phenomena of radiation. Prof. BoLTZMANN’s considerations seem to be chiefly as foliows. As basis of his considerations he takes the reversibility of all processes, as well mechanical as electrical and magnetical ones. From this follows that a process, in which the entropy increases, might also take place in the opposite direction, so that the entropy decreased. Apparently this is i contradiction with the experiment which teaches us, that only those processes occur, in which the entropy increases. To explain this apparent contradiction, Prof. BOLTZMANN argues as follows: If we know exactly the initial conditions of a system with n degrees of freedom, i.e. the x generalised coordinates and their fluctions at a given moment, and if we know the laws of all the forces, acting on the system, we can caleulate the state of the system at any moment. If however we know at a given moment only »— 1 of the coordinates and their fluctions, we can in general calculate nothing for a later moment. The want of knowledge of one of the 2 » necessary data, makes not only that one coordinate indetermined for the future, but ajl the coordinates. If we consider ¢ gas as a system with many degrees of freedom, the condition would be exactly determined only then, if at a given moment we know exictly the coordinates and their fluctions for every molecule sepa- rately. As we however never know them, we can never say how the condition in the next moment will be. Perfectly general laws for movement of heat can therefore not be drawn up. By varying the coordinates of the separate molecules, we can however obtain a great number of systerss, all of which fulfil the conditions, which are required to call the system in question a gas or a solid substance with a certain temperature and under a certain pressure and which differ only in the coordinates of the separate molecules. The number of these systems is infinite. Now Prof. ( 314 ) BoLtzMANN has proved that for the vast majority of those systems, the state after a given time is of course not perfectly determined, but yet fulfils certain conditions, that uamely the mean density and the mean kinetic energy in every volume clement will be such that we may speak again of a solid or a gas of a certain tempera- ture and under a certain pressure. Of course this is not proved for the great majority of all systems ocewrring in nature, but for all imaginable systems which answer to our idea “substance of a certain temperature and under a certain pressure”. If we suppose all these different systems to be equally probavle, we may say that it is highly improbable that we meet with a phenomenon, in which the entropy increases with a measurable amount. The supposition of Prof. BoLtzMaNN thet these systems are equally probable, is not new. Every one who has written on kinetic gas theory could not but make this supposition though in a somewhat different formula- tion, in order to calculate the mean number of collisions and such like quantities. The fact that observations show that the entropy always increases, justifies the assumption that this supposition agrees with reality. Convinced of the correctness of these considerations of Prof. Bottzmann, I wanted to treat the entropy of radiation in a similar way. The H theorem of Prof. BoLTzMann is closely connected with the distribution of velocities according to MAXWELL. Therefore I thought that I had in the first place to find the analogue of it for the distribution of the electric forces in a space, in which a great number of radiating molecules are to be found. This distribution will be treated in the following chapter. First some observations on an, in my opinion, essentiel conse- quence of the considerations of Prof. BoLTzMANN, viz that the entropy increases only in consequence of collisions. To show this we take the following process into conside- ration: The walls inclosing a quantity of gas are suddenly removed at the moment ¢, so that the gas spreads in an infinite vacuum. We leave the molecular attraction out of account. If we take the gas at a high degree of rarefaction and if the volume in which it was enclosed is supposed to be not too large, many molecules will move away without any collision. In order that we may apply Borrz- MANN’s H theorem, we must have a large quantity of molecules, The assumption that after the moment ¢ not a single molecule col- lides, may be in opposition to this requirement. Yet we may examine what might be the consequence of the assumption that all molecu- les moved away with the velocity which they had at the moment ( 315 ) #, without changing it by collisions. It is casy to show, that the entropy would then remain constant. Let us first think the gas enclosed in a small cube with a centre O, the axes being taken parallel to the sides. We get jie uf a 4 hi J ik F log (F) dev dy dz d& dy df & » © representing the components of the velocities of the mole- cules. The first three integrals for « y and 2 must be taken between the limits — 4aand + 3a, where a represents the edge of the cube, and the other three for § 7 and € between — om and + om. If the volume of the cube was 0, the velocity of the molecules which had reached after one second the point P(#'y'2') at a distance r from O would also be r and their density a? J7(a'y’ z'), By assuming this density as being the real one, we shall make a slight error. For the velocity we must however take into account that the velocity of molecules, which reach P after one second, starting from different points of the cube, is different. The probability that the components of the velocity ofa molecule which has reached point P, are enclosed between the limits: we + 27>’ and 2 +2+de=— 4 di’ y ty=n7! and y' + y+ dy=7! + dr 2a+tz2e=C' and 2? t2+dz=0'4+ de! “, y and < representing the coordinates of the point of the cube, from which the molecule has started, is: de dydz — d&' dy! dé a? a? we find for # after one second: J . 1 1 Hig | fe I’ — log (a i —) div’ dy' dz' d&' dy! at! Wale : a a®, ={( [Tf E" log (") da! dy! dz' d&! dy! dt! /” is obtained, as we have seen, by substituting r in / for the velo- city; 7 represents the distance from an arbitrary point to the origin, ( 316 ) The integrals with respect to 2, y and z must here be taken between — amen +o, those with respect to & 7 and ¢ between — ta and + 4a. Therefore H’ is equal to H, the only difference is that the coordinates have been interchanged with the velocities. The unity of time being arbitrary 4 will remain also constant after an arbitrary time. 4 changes only if the molecules which are moving away, cannot reach infinity, but come in collision with a new wall and are arranging themselves into a state of stationary movement in the new volume. The great importance which I think ought to be attached to the collisions, made me look for its analogue in radiation. For this purpose I have had to make a supposition on the nature of radia- ting molecules. 1 have namely imagined them as Hertz’s vibrators all of the same period. In this case the emitted radiation also has everywhere the same period. Its amplitude varies from point to point and changes with the time. As collision of a special kind I consider the action of an alternating electric force of a determinate direction, intensity) and phasis on a molecule, which is in a vibra- tion, the direction, amplitude and phasis of which are also deter- minate. According to this, every molecule is always in collision. This view agrees with an observation of Prof. PLaNck, who says more generally !): »Dureh die Strahlungsvorgiinge im freien Felde kann also keine Entropieiinderung des Systems hervor gerufen werden. Dagegen bewirkt jeder Resonator im allgemeinen eine Entropieiinderung der ihm treffenden Strahlenbiindel.” LE Law of the distribution of Electrical forces. Concerning the nature of radiating molecules there are principally two conceptions. The first is that a source of light has a periodical movement, which gives rise to more or less regular vibrations in the ether. The other conception is that the molecules bring about perfectly irregular disturbances of the ether, which get a seeming periodicity from the apparatus by means of which we observe. Possibly both these suppositions are partly true and in some sources ’) Berliner Sitzungsberichte XXV 18 Mai 1899 pag. 467. ( 317 ) of light the regular, in others the irregular ways of movement are more prominent. As my considerations will be simplest for a gas, and we are there most inclined to think of vibrations in the mole- cules, I have chosen the first conception; and that in very simplified suppositions, hoping that these may be extended for processes such as really occur in nature. I imagine namely a great number of molecules spread in space which I suppose as vibrating, all with exactly the same period. I leave out of account the change of the period caused by the Dorper effect. I suppose that for those mole- cules vibrations in the direction of the , y and z-axis are on an average equally represented, while also all phases equally probable. These suppositions are sufficient for finding something about the distribution of the forces, without our having to determine whether or no all molecules have the same amplitude; and if not, how the distribution of the amplitudes will be. Let us now consider a volume element dr. The action of it at a certain distance will be only determined by its electrical moment and the way in which that changes, and not by the way in which that moment is spread over the element. If the moments of the molecules now had the most probable distri- bution, i.e. if all directions and phases were exactly equally repre- sented, the moment of the element would be always 0 and no radiation would take place. The most probable distribution, however, is itself highly improbable, and generally a deviation will be found. This deviation is the cause of radiation. Let us assume that the unity of volume contains » molecules. Let us represent the components of ther vibration by: 27t . 2 Gz = Az) COs. - + azg sin. - 2nt » amet dy = ay) Cos. T + aye sin. - Q7t , 276t dz = Az) 608. — + azo sin. — | of and let us call the number of the molecules per unity of volume, the amplitudes of which are contained between the limits: xl) Gx2) Ayly Gy2) M1 and azo and dri + dari, 422, day2, ayi + dayi, ayo + day, az, + daz, and a.9 + dazo, Flag, ax2 Ay \ Ay2 Uz a29) day, day day, day2 daz, da-. or Ida, ( 318 ) The group, the amplitudes of which have the same values, but all the opposite sign, will be about as numerous. These two groups together contain + 2¥d@ molecules. If the most probable distribution prevailed, these two groups would have exactly the same number of molecules and would furnish together a moment 0. If we have an event, which may take place in two directions, the probability for one direction being p and that for ihe other ¢ (where p + ¢=1) and if this event occurs a very great number (n) of times, the calculus of probabilities teaches that the chance, that of these » events the number which occurs in one direction is between np + v and np + v + dr, is represented by: 1 v? = e C dy. Vals In this C is equal to Y2npg and is called modulus. lf we apply this to the 2/dmdr molecules, then p=g = 3. The probability that the deviation, which one of the groups shows from the most probable value, lies between vy and v + dy, is: where 2? =F da dr. Of the 2 dw molecules one group has a deviation of + 7, so that it amounts to Fdw-+-y, the other group has a deviation of — vy and amounts to fdw—y. The difference between the two eyoups is then 2 y and the amount they contribute to the moment of the volume element is [2 vez]. If we put: (2 vax = nz in which the brackets indicate that also a corresponding expression : _ Qt for the y and = components and for the coefficients of sin is meant, then we may represent the probability that the two groups in consideration contribute to the moment of the volume element an amount, the amplitudes of which lie between [mz] and [mz + dmg] by v 2 1 —% mene y2 dmx v\ / 0 where Now we are going to seek the probability that the total moment M of the volume element i.e., the sum of the amounts contributed by the separately considered groups of molecules, has amplitudes which lie between: [Ma] and [My + dai]. According to the calculus of probabilities the probability for such a sum is again represented by a function of the same form as the separate terms, while the modulus is the root of the sum of the squares of the moduli of the separate terms. So: o= Va {J I] 4a’, Fdwdr, If we take the integrals between the limits —o and + ™, the factor 4 must not be omitted, because we have to take only half of all the groups: for if we take a group with definite amplitudes, that one with equal amplitudes, but of opposite sign has been taken into account at the same time. For the other quantities 4,2, Mi, Myo, M1 and M22 of course the same formula holds good. Now we have still to prove that the chances for these quantities are independent of one another. To this purpose we draw vectors from point O, which have the quantities 4.1, My, and M.; as components. Along the axes the density of the final points of these vectors is the same as in the distribution of velocities of MaxwerLu. If a large 4), was probably accompanied by a large M/,,, the distribution in space would not be that of Maxwenn. The choice of the axis is however perfectly arbitrary, and the distribution along every line passing through 0, must be the same as along the z-axis. From this follows that the distribution is really the same, as that which Maxwetr found for the velocities, ic. that the chances of the quantities Mai, My: and M., are independent of each other. In a corresponding way we may prove this for Mz; en Vj., My: and Myz, Mr and Mzs. nie If we represent the mean of the squares of all quantities a1 2 , rat « by ai,, we get: O ==} Jon. Y az, and Proceedings Royal Acad. Amsterdam, Vol. LI. The electrie and the magnetic forees of the ether vibrations, emitted by the element are proportionate to [4¥z1.]. The emitted energy is therefore proportionate to |43,|. This energy proves to be on an average the sum of the quantities of the energy, which every molecule would emit, if it were alone in space. Let us now examine what would be the distribution of the electric and the magnetic forces, the components of which we represent by: 27t 27t esi COBs 7 + fg sn: —— 2nt ve , ant — COS. Io . g AEE D9 is ah 20t he Qt el POOLE pot tS es 2nt 2nt L = Iy cos — + Ly sin. — Ti 2mt 2mt M = M, cos.—— + Mg sin Tr 2ut Lh NaN COs Tr + No sin. — For this we apply the following formula '): Oye Oxy | 0? xz) 02x ee le y 82 J joer eh aaayat casi oe and Oxy 0°72) ee oe Lee ldzde dyadt) 1 7 MM, =—- — dt; 7y= — —dr xe IgV?) ope dae V2 ae — ays 5 where J represents the moment of a volume-element at the moment t— =, so that: 1) Lorentz Arch. Neerl. XXV 5. 1892 pag. 429. ( 321 ) 1 1 = {ae Re we hay Pay ani , ) : ps he Suber Vi; xl COS 7 eae 7) + 44 z2 Sin. a rie Gk a on ae ‘ CS alae | Ma COs. ple =) ++ M29 sin. “AC ole Cal 2 a r ) 8 z( , )} 5 oe = M,> a (5 Waray r pen SEN may + Myo sin 7 =) bi Aes al) Qa pie a 22) ene (t= ay 3) ioe ane = he a ordz rl LE ae stn 7 =) iy gaat : Me a Vv? Oe | Mas peat: (« = 9) + Mig sin. — (« _ =) dt In this the influence of absorption has been neglected. In a complete theory we should have to caleulate it by examining to what influence the vibration of every molecule is subjected by the radiation of every other molecule. Then it would be necessary to take into account the influence of the damping, which the vibrating molecules experience, and the quite unknown influence of the colli- sions. Here I shall confine myself to assume that the distur- bances, when they have propagated over the unity of length, are anced to e of their original amount. Then we have to multiply with e~*" every term under the integral sign in the expression for f. For points for which r is great compared with the wave length, we may write by approximation: 1 723 = | 20 r 20 ry jx? (| 08 (t=) Myo st Fli-S) = f Ge). rh saat vy) ae, vr) Var » 9 ; : a cn | ae a gene Fea ail i yl ; yf} V Ye Tp V/S v2 2% r 27 r\) rz 08. ——— M.9 sit ale — 2) ee = Re i 7) + Rae aE V/\7 — eaten, aa ey a de. So the modulus for the probability, that [A] lies between the limits [fj] and [/,+-¢/,], becomes: QQ* so ( 322 ) si! Me 7 ie : Ny. ( *y y 4 (2) las = a ee hens In the same way we find for L: 9 _ 42 | 2; : 20 r ares =| maa : Me cos ¢ (« = =) + M29 sin ? (« = = oy ot r | Cee a 2% r CAEL r\) == Rae VE pen cos - ai (¢ — >) 4- M2 sin r (: — =) dv or by approximation: 2% 2% (e—ur y ( 27 / r 200 r\) L=— ee | eee |e 0s ——{ § — = 39 8 ——| it — =) WD Vs) E jr ta 2 ie ine ( v/s : { M, t *) M, z if ih ee 1), cos — eee -. 9 = = f c 1 yl cos ( y sin 7( )\ and for the modulus of the corresponding chance: n=() eA Bice — dv. The reasoning, according to which these formulae have been derived, is correct only when we may choose volume elements, which contain many molecules and which are yet small compared with a wave-length and with v. It does not hold for the immediate sur- roundings of a point. Yet the not approximated formulae for [/ } and [Z,] hold also for the immediate surroundings, provided we neglect the volume of the molecules. If we imagine an element dx dy dz or dr at the distance 7 from the point P, then the proha- bility that we should tind a molecule in it, is » dr. The chance, that we should find a molecule in it with az: lying between az and ax. + day, is Ly (ax1) dari nm de. If we imagine a region Av Ay Az, which contains many (p) ele- ments dr and which is yet small compared with the wave-length and r, then the chance, that this region has a moment [ Mz J is the sum of the chances of the different ways, in which that moment ( 393 ) may be brought about. The chance, that the volume element dr contains no molecule is the chance, that all the molecules of the unity of volume lie outside the element. For one molecule this change is 1—dr, so for the » molecules (1—dzr)". Now the moment 4» may be brought about by the fact that in g elements dr we have no molecule, in p—q—1 we have a molecule, every one of which has an arbitrary amplitude az: and in the last element with the amplitude ,a71 = Mz — Sar. The chance of being brought about in this way, is: (1-—.’r)"9 (ndr)P—4 Fy (yaz1) Fy (gaz1) «A Gp - q—"a1) Fy (My21—= az) d (yar1) d(g4z1) +++ d (p—q—@e1) d Mz). We find the total change for an amplitude between J/,, and M,, +4M,, by first integrating with respect to yagi , 221. «)—g—1421 between the limits —o and + ©, and by adding the results for all values of 4. As we have to do this for the case in which p=o, we execute this addition by multiplying with dg and by then integrating with respect to g between the limits 0 and «©. These formulae hold always, independent of the size of A» 4y Az, andas we have found for it for a region with many molecules 2 1 at Mal 4 ova” “= where d = //3n Aa. Ay. Az. this formula will also hold if Az Ay Az is so small that the chance that it contains a molecule, is slight. , In this we have assumed, that the fact, that at a certain point P a definite moment [4/71] prevails, has no influence on the chance for the moment of the immediately surrounding points. This would be true only if the molecules themselves had no extension. If how- ever point P lies in a molecule, which has extension, the surrounding points will also have moments of the same direction and the same phasis as P. If this circumstance however, causes a deviation from the here derived law of probability, it will probably be very small for gases. Our resuit shows that in the unity of volume the total region in which /; is contained between the limits f, and fy, + df; is: ible 1 rit iige df; and that the changes for /\, /: gi, go; ’ and hy are independent of one another. This does not completely determine the condition: it is left un- settled, how the total region is spread over the unity of volume; whether it probably consists of comparatively few regions which are not so very small, or of a great many very small regions. In order to find something about this, we should have to calculate the pro- bable value of [3] . In the same way we might also try to find the probable value of [4]. Whereas kal may be deduced from the suppositions which we have already made, new suppositions d necessary, to make suppositions about the causes of change of [¢.1]. The significance of these quantities will appear from the following chapter. At first I had thought that the name ‘entropy of the ether” would be preferable to that of “entropy of radiation.” The name introduced by WIEN “entropy of radiation,’ seems however, prefer- able to me. At the absolute zeropoint matter has an entropy — @. Now both the formulae, that of Wien and that of PLANK, give for space without radiation 0 as the quantity of entropy; and this result seems correct to me. In order to maintain the analogy between the two kinds of entropy, it seems best to me, to ascribe the entropy not to the ether but to the radiation. A space, where no radiation takes place, can consequently not contain entropy of radiation. If we speak of entropy of the ether, it would probably have a orm like the following: would be necessary, in order to find 4}. It would be namely f PAD bo # ah Probably however the entropy will be represented by a form like the following: [ead PULAD boy @P). [aA in which @ represents the density, i.e. it has the same function as n in the formula of BoLTzMann : (325 ) n -— H= { Fog (do where : ae ee Possibly this is nothing but the energy per unity of volume, which quantity we are most inclined to call “density of radiation.” For the distribution of the magnetic forces the entropy will consist of another term formed in a similar way. Possibly however we shall have to find the entropy not from the electric and the magnetic forces separately, but from the vectors of Poyntina. We find therefore the analogue of matter at the absolute 0-point not in a space without radiation, but in absolutely regular movement, e.g. in a plain wave of monochromatic light, everywhere with the same amplitude. Let us represent this wave by: ashe 20 y J=So cos. (t= £) 105 e102 Here we must take into consideration, that in this case f, and /, are not independent of each other, so that we cannot simply add the entropy for these two terms. Probably we have to diminish the amplitude everywhere with: 2 2 So €08. = and fy sin. = and we have to take for # the chance that the remaining amplitude lies between certain limits, i.e. 1 = —e cy a jae ae a ! 2ny ce” where c= 0 and f'} = fy — f, cos. — . r F This is analogous to the way, in which we prove for a gas of 0°, which moves as a whole, that the quantity 4 of BonrzMann becomes o. If we put for g the mean energy, we find: 12 ; +o il = fi = te H=|4 Piet e So the entropy is — ~, 2 | -_—_ —le—tL la — df|' ne *) ( 326 ) Mathematics. — Prof. W. Kapreyn presents a supplement to his communication of the Meeting of November 25, 1899: “On some special cases of Monan’s differential equation”. In my last communication was mentioned sub I that the equation 7—s=0 possesses two intermediate integrals, if 4 is given by the relation (— W (p) q—vyp)’ in which supposition these intermediate integrals were deduced. However a closer examination shows that this result represents only . 1 a particular case. In the most general one “= sa presents itself in the form aU aU Fax: ‘ Salt ey sre Eee du+W fe = 9a erage ea fee oat = =) c+ W(p,y)s where Y= U(upy) and W(p,y} denote arbitrary functions of u, p, y and p, y respectively, whilst u stands for z—pze. The corresponding intermediate integrals are UQU ; geU + fe aaa W (p. y) dp =f (y) HOLA BI we -— fe ape +f WC) ap ye) By putting dp dp W—e [io eu) w(p)’ Y (Pp) the first mentioned case reappears, as is easily demonstrated. C327) Anthropology. — “A new graphic system of craniology” by Dr. P. H. Eykman, at Scheveningen. (Communicated by Prof. C. WINKLER.) For a rough comparison of skulls, we often use three measure- ments, viz.: length, breadth and height. Because the review of these three is still too difficult, Scamp, at Leipsic, proposed using the relative instead of the absolute meas- 300 : ra eeaeaT The sum of the relative becomes thus constant; that is: 300; and he then really only works with two instead of three respectively independent proportions, because the third is always equal to 300 minus the other two relative measurements. If two are known, then the third is also definite and in an ordinary diagram, you could, by one point, find out the relative proportions of the skull. For practice this method is insufficient, because the third meas- urement, although it can be calculated, is not shown in the diagram and so escapes our notice. I have discovered a method, giving a graphic representation ina plane, showing three measurements that suffice, to denote that their sum is constant, and at the same time indicated by one point. We start from a trihedral angle (fig. 1), of which the ribs PQ, PR and PS represent a triple ordinate-system. ures, which he obtained by multiplying the last with By a single point ¢@ in space, we can in this manner show three absolute measurements at the same time. Suppose now we draw a plane, that crosses the three ribs at the same length, going through such a graphic point d, it would be easy to prove, that the sum of the three absolute measurements is equal to the length of one rib; viz.: Be -— Po | Pb = PR:=P2Q'= PS. If we suppose the rib to be 300, then this secant plane, that has the form of an equilateral triangle, will be the geometrical place of all graphic points, of which the sum of the three ordinates = 300; viz.: all points of the formula of Scumipr are in this triangle. Supposing there were planes parallel to the three sides of the tri- hedral angle, you could call them planes of measurement, and then these planes would show on the equilateral triangle, systems of ( 398 ) smaller equilateral triangles, that in their turn could serve for deter- mining the measurement, so that we could do without the trihe- dral angle itself. Fig. 2 represents the equilateral triangle with omission of the trihedral angle. As soon as you eliminate one of the three measurements (Length, Breadth and Height), the stereometrical ordinate-system will of course alter into a diagram in a plane. Instead of the three ordinates: Pbi(= iad); Pe\(=cd), and» Po\(— ad); ic. the three perpendiculars, let down from the graphic point d to the sides of the trihedral angle, now come the perpendicular lines dj, dl and dk, let down from the same point to the sides of the equilateral triangle QRS. This will present no difficulty; for the sum of these perpendicu- lars is constant (or = the height of the triangle) and in future we will reckon this as 300, instead of the rib of the trihedral angle. This triangular diagram has this advantage over the rectangular, that all the three relative measurements are represented on it; by means of which the eye can compare them better, as all three come out equally right. HetmnHo.tz in his Physiologische Optik, just refers to the trian- gular diagram, in connection with LamBert’s Farbenpyramide : ,veder Schnittpunkt einer dieser Linién mit der Ebene des Dreiecks, wiirde den Ort der entsprechenden Farben in diesen anzeigen, und zwar wiirde die Vertheilung der einzelnen Farben darin genau der durch Schwerpunktsconstructionen herstellbaren Ordnung entsprechen. In jeder solche Ebene wiirden aber nur Farben gewisser Helligkeit angeordnet sein, welche durch die Summe der Werthe («+ 4+ 2) gegeben ist.” Let the perpendicular dj, drawn on the basis QS, signify the relative height; the perpendicular dk the relative breadth, and di the relative length; then we shall be more conversant with the subject by the following: all points, drawn in a line parallel to the basis, have the same relative height ; all points, in a line parallel to Q2 (resp. /S.) have equal relative breadth (resp. rel. length); (7329) if there be a point in the perpendicular 2, drawn on the basis QS, the length and breadth are equal to each other. Mutatis mutan- dis the same also concerns the perpendiculars, drawn from Qand S on the opposite sides. if there were a point in the intersection of the three perpendicu- lars, all three of the measurements would be mutually equal. Fora skull this would signify a mathematical roundhead, but this does not occur in reality. if we draw lines, that we will call radii, from / to the basis, we sha!l see in each radius the points, of which the proportion of the Breadth and Length is constant ; eg. by Apis BY L—9 11 Ret By = 2s Skulls, that, seen from above, are conformable, lie in the same radius of R; a radius, drawn from S to QR, combines the points, of which the proportion of the height to the length is constant; eg. by Ss is H:D=9:i1 20 Sr j2 Ai 2h: 3. Skulls, that, seen from the side, are comformable, lie in the same radius of S; by a radius, drawn from Q to RS, the proportion of the height to the breadth is constant ; eg. by Qt is H:B=9:11 » Qu > Be: B22) 3. Skulls, that, seen from the back, are conformable, lie in the same radius of Q. To draw a graphic point in the diagram, is very simple. For a skull rel. 2 = 120; rel. B= 90 and rel. H=90, we find the point by taking the intersection of the lines 120 Z and 90 B, which is then naturally the intersection for 90 #, If we draw in the figure the five skulls, which ToprnarD de- scribes as differing most in form: ( 330 ) rel. LL. rel. B. rel. H. A Parisian 116.1 93.6 90.3 A Savoyard 111.4 101.3 87.3 Amelander 193.2 96.6 80.2 N. Caledonian 1O25 82.9 94.6 Soudanese Negro 126.6 81.8 91.6 we see (fig. 2), as was to be expected, that they are all rather near to each other, and that the greater part of the figure remains unused. The place that the skulls occupy, is shown in the figure by a broad outline; the rest of the triangle we omit, and draw the place itself with larger measurements; this was the case in fig. 3. Here we see in an equilateral triangle at regular spaces from each other, 38 lines parallel to the basis. The basis is marked with 75 H; each of the lines with a higher number and the top with 115 4; these are the measuring lines for the height. We draw lines parallel to Q” for the relative breadth, marked 80 B to 120 B; in a similar way we draw lines for the relative length parallel to RS, marked 105 ZL to 145 JL, To facilitate this matter, the same radii given in fig. 2 are also given in fig. 3. The lines of this figure can serve for a great num- ber of skulls. On a rather large scale I applied this method for the first time on: »Hine anthropologisch-historische Studie dber siebenhundert Schidel aus den elsissischen Ossuarién von Dr. Med. EpmMunpD Burp.” Of the 701 skulis, that this list contains, 164 were deducted, because by all these, the three measurements were not shown. Of the remaining 537 the relative measurements were calculated accu- rately to a decimal and the points were indicated, as is shown in fig. 4; these are printed on transparent paper and agree with the lines, shown in fig. 3. The points are drawn in their exact place, but so, that, where two points come partly or wholly together, this is avoided, by the points being drawn next to one another. On consideration, we soon notice, that there is a certain centre of accumulation perceptible, limited by 84 H — 89 H and 96 B—99 B, round which the points, slightly running out in all directions, are grouped. It is also my intention to draw diagrams of other large groups of skulls and to subject them to a similar comparison. Scheveningen, Dec. 99. ( 331 ) Botanics. — Prof. J. W. Moun presents a communication of Miss T. Tames at Groningen, entitled: ,Pomus in Pomo’’. By Professor C. A. J. A. OUDEMANS a monstrous apple was given to the Botanical Laboratory of the University of Groningen. This apple is originary from Dr. A. C. OUDEMANS, who got it acciden- tally in 1894. Within the apple is a second, quite loose from the external. In an added writing of Maxwett T. Masters he tells us, that he has often seen similar apples, but always the inner one joined to the external. In the literature of teratology we meet now and then with descriptions of cases where within a fruit a smaller one is found, The greater number of these cases relates to the genus Citrus; but the abnormality occurs with other plants also. So mention is made of some Cruciferae '), where the pod contains internally a smaller one; further, of so called fructus in fructu of Gentiana lutea *), Carica Papaya®), Passiflora alata), Passiflora Alpinia °) and Piper nigrum *). Usually the communication ig limited to one or mostly two cases; with the Citrus-species ®) on the contrary, the phenomenon is by no means rare. It seems to occur so often in this genus that double oranges are known in the Canaries by the name of ,Narangas pregnadas” °); whilst also at Nizza such fruits can be bought as ,oranges doubles” *). The descriptions of the internal fruit are not always in accordance with one another. In some cases the internal fruit has seeds, in others not. It is also described with and without a fruit-wall ; the phenomenon seems not always to be quite the same and of its explication relatively very little is known, The described apple is in alkohol and is here figured, in natural 1) The Gard. Chron. 1882. Part [. p. 10 and p. 601. 2) Bull. Soe, Botan. de France. 1878. p. 252. *) Flora Jahrg. 73, 1890. p. 382. 4) B. Torr, B. C., vol. 18. New-York, 1891. p. 151. ®) Jiicer, Ueber die Missbildungen der Gewachse 1814. p. 222, und Verh. Natur- hist. Ver. Rheinlande, 1860. p. 376. °) Hanausek, Z. Oest. Apoth. 1888, No. 16. *) Levende Natuur 1899-1900. No. 2. size, in longitudinal section. The apple is composed of an envelope, which, probably at the cutting, has fallen into three parts, and an inner apple, cut longitudinally and of which the halves are quite loose from the envelope. The thickness of the layer of the outer apple differs from a few m.m. to about 1 cm. The inner- side of it cannot be distinguished by the naked eyefrom the common fruit-flesh. On the top are in the usual way fragments of the calyx; but at the base no peduncle is to be found. When fitting the parts together an opening remains at that spot. The internal apple is flat globular, the section from base to apex is + 41/, cm. long, the vertical section + 6 c.m. This apple has no separate peel. The fruit-flesh seems to differ from that of the external one; for in the alkohol-material it is softer and of lighter colour. This portion, also, wears on its summit a dried, hard, dark-coloured part, which in everything resembles the apex of a normal apple. The whole apple being cut through longitudinally the core is visible. This core is of normal structure. At the base it passes in the usual way into the peduncle a which here, as is the case with many apples and pears, is continued in the interior of the apple till near the core, rather markedly separated from the fruit-Hesh. The peduncle does not stick out of the fruit-flesh of the inner apple, yet, it must have been somewhat longer, as through the envelope, it must have been united with the branch. Microscopically the external apple presents at the outside an epidermis with thick cuticle, under which some layers of cells with rather thick walls. The parenchyma, which follows inwardly is a very luose tissue with great intercellular spaces. The cells are more ( 333 ) or Jess isodiametrical, whilst the walls are thin and, in accordance with the jodine-sulphuric-acid reaction, consist of cellulose. The inside of this envelope shows no separate differentiation; the paren- chyma extends unchanged until this inside. The structure of the inner apple accords in so far with that of the envelope, that it is also composed of a loose parenchyma of about isodiametrical cells, whose thin walls show cellulose reaction. The whole tissue is however filled up with a mycelium, the hyphae of which are in some places so numerous that in the glycerine- preparation the parenchyma cells can only be found with much trouble. The cellulose reaction, in which the hyphae are coloured yellow by jodine-kaliumjodine whilst the parenchyma cells grow dark blue, renders the latter distinctly visible. The mycelium is not everywhere equally compact. At the outside the hyphae are much more numerous than more inwardly; they form by their conglomeration at the surface a kind of layer which, on nearer view, is even visible to the naked eye. In all portions of the core, even in the seeds, the hyphae are to be found. In the interior of the endocarp the myce- lium is also very compact and there the hyphae are of a stronger structure than in the surrounding fruit-flesh. As follows from the above description this apple not only deviates from the normal one by its monstrous structure, it moreover presents another curiosity: the presence of a fungus in the inner part, and the absence of it in the envelope. To my opinion this fact explains the monstrosity. I think that the fungus has grown at first in the interior of the quite normal apple, and using some constituents of it as food, has more and more extended itself. The portion sucked out by the fungus has had a disposition for shrivelling and the tension between the healthy and the sick part of the fruit-flesh has finally become so strong that on the limit of both a splitting has originated, so that the apple was divided into two parts; an outer normal part and an inner one full of hyphae. The greater accumulation of hyphae at the surface of the inner portion of the apple has then probably taken place after the division, as the fungus will by preference develop there, where, in consequence of the splitt- ing, a space filled with air was present. With this explanation the following facts perfectly agree. The remains of the calyx and other flower-parts at the top of the inner apple fit precisely in the opening which exists between the dry fragments of the outer portion when these fragments are joined together. These remains have evidently formed one whole, so that there can be here no question of a flower within another, The longitudinal seetion of a normal apple shows ( 334 ) clearly that it is quite well possible that the dried part at the apex might divide itself into two concentric portions; the inner member of which, wearing chiefly the stamens, would belong to the central body of the apple and the circular exterior to the envelope. On a nearer inspection of the different portions of the described apple it is evident that such has undoubtedly been the case here, and it is, moreover, to be observed in the figure. At the top of the envelope there are only fragments which remind of the calyx, whilst, the top of the inner apple wears, besides a few remnants of the calyx, the whole cirele of dried stamens. How the fungus has entered the apple; from whence the growth of the mycelium has begun; when the severing of the two parts has taken place, — these are questions not to be answered with the help of this one object. But the case appeared to me remark- able enough to describe it in short, whilst it will be of importance henceforth in the appearance of similar monstrosities, to pay atten- tion to the presence of fungi. Chemistry. — “On the Theory of the Transition Cell of the third kind”. By Dr. Ernsr Conen. (First part.) (Communicated by Prof. H. W. Baknurs Roozenoom.) 1. The theory of the transition cell of the third kind, to which van "rt Hore!) first drew attention, has not yet been considered. In a former paper”) I have pointed out that it may be verified by means of JAEGER’s °) measurements, but that a number of expe- rimental data needed for the complete calculation are still lacking. In what follows I propose to develop in the first place the thermo- dynamic theory of these elements, then to describe the experiments which have been made for the determination of the quantities re- quired in the calculations, whilst, finally, the results of theory and experiment will be compared with one another. ') van “2 Horr, Vorlesungen iiber die Bildung und Spaltung von Doppelsalzen, Leipzig (1897), 5. 29. Also: Vorlesungen iiber theoretische und physikalische Chemie, Erstes Heft. 5. 179. — Erxst Contn, Veber cine neue (vierte) Art Umwandlungs- elemente, Zeitschr. fiir phys. Chemie, 25 (1898) 300. *) Zeitschrift fiir phys. Chemie 25 (1898), 300. — Maandblad voor Natuurweten- schappen, 22 (1898) 17. ’) Wiepemann’s Annalen, Bd. 63 (Jubelband) (1897) 354. ( 335 ) The elements considered consist of two ceils, coupled in opposition, and constructed as follows: Saturated solution of a salt Electrode, reversible with Electrode, reversible with Sin contact with the stadle respect to the anion. respect to the kathion, solid phase of the salt. and Saturated solution of the salt Electrode, reversible with Electrode, reversible with S in contact with the meéa- respect to the anion. respect to the kathion. stable solid phase of the salt. 2. The temperature coefficient of the transition element will first be calculated at the transition temperature itself, on the supposition that the salt in the element is zine sulphate (Zn SO,.7H.O and Zn SO, . 6 H20). We will set out from the equation !) al Where £ is the E. M. F. of the element in calories, g the heat evolved by the change which gives rise to the current, P the abso- lute transition temperature of the change which occurs in the ele- ment and 7 the temperature of the element. Differentiating (1) with respect to 7 we find: di gq 2 LT ae We Pp) . . ° . . . ° . (2) At the transition temperature, the change which takes place in the element during the passage of 96540 coulombs may be repre- sented by the equation : a a Zn SO,.6 H,0 + ———__—_ Zn SO,.aU,0 = FG ee iat i 73 (=) (a—7) ne ah none ‘i = ABNOR 1G 6) Go (G)) a—l In this equation « is the number of molecules of water associated ') van “t Horr-Conen, Studien zur chemischen Dynamik (1896), S. 247 u. 260. 24 Proceedings Royal Acad, Amsterdam, Vol, IL. ( 336 ) with one molecule of ZnSO, in the saturated solution of ZnSO,.6 HO at the temperature P+). The value of g in equation (2) is therefore to be taken as the heat of transformation of ZnSO,. 7 H,O. 3. To determine « the solubility of Zn SO,. 6 H,0 (or Zn SO,. 7 HO) at the transition temperature must be known. We shall also find that the solubilities of the two salts at other temperatures (below the transition temperature) are required in order to calculate the E.M.F. of the transition-element at these temperatures. I therefore give at once the results of the determinations, which will be used in subsequent calculations. The zine sulphate employed was obtained from Merck; it was quite neutral to congo-red paper. Its purity was attested by the fact that CLark-cells set up with it gave exactly the same E.M.F. as the standards of the Physikalisch-Technische Reichsanstalt at the same temperature. Determinations of the solubility of Zn SO,.7H.0O (the stable system below 39°) and of ZnSO,.6H;0 (the metastable system) were made in the usual way by means of the shaking apparatus of Noyes”). By taking special precautions which I have described elsewhere *) it was possible to determine the solubility of the meta- stable system down to — 5°. In the following table (1) the results obtained are given, along with the figures found by CaLLeNDAR and Baryes*) for tne solu- bility of the salt with seven molecules of water of crystallisation which agree very well with my own. That the determinations of PoGGiALE, MubLprer, Roscore and ScHORLEMMER, Erarp and other authors are faulty is thus confirmed °). The saturated solutions were evaporated in shallow platinum dishes on the water-bath. Zn SO,.1H,0 is formed, its composition remaining unchanged even after prolonged heating. CaLLENDAR and Barnes have also adopted this method. Since however they say in their paper: “They were then evaporated to dryness at 100° C., and the percentage of ZnSO, in each case was 1) At the transition temperature the saturated solutions of the two salts Zn SO, . 6 H,O and ZnSO,.7 1,0 have the same concentration! 2) Zeitschrift fiir phys. Chemie, 9 (1892) 606. 5) Zeitschrift fiir phys. Chemie, 31 (1899). Jubelband S. 169. 4) Proceedings Royal Society, 62, 147. 5) See Comey, A dictionnary of chemical solubilities (1896, London, Macmillan and Co.), p. 458. ee ( 337 ) saleulated, assuming the residue to be the monohydrate”, without proving that this was really the case by separate experiments | first made sure of this point. a. Of a solution containing 57.20 grams of ZnSO, to 100 grams of water, 59390 grams were evaporated. The weight of the residue after 24 hours was 2.3986 grams. Assuming that the composition of the residue was ZnSO,.1 H,0 the original solution must have contained 57.20 grams Zn SO, to 100 grams of water. _ After remaining seven days and nights on the water bath the Zn SO,. 1 HO lost 3,8 mgrms., or '/, pCt. of its weight. b. Of a solution containing 65.84 grams of Zn SO, to 100 grams of water, 6.9124 grams were evaporated. After 16 hours the residue weighed 3.0506 grams. From this 65.84 grams Zn SO, to 100 grams water is calculated. After remaining for eight days and nights on the water-bath the residue had lost 4 mgrms. or 1/7 pCt. of its weight. The method adopted is therefore quite trustworthy. All the measurements were made with the temperatures rising, that is to say the salt and water were maintained for a long time at a lower temperature than that at which the solubility was to be determined. This was necessary since I had observed that the very viscid solutions readily remain in a supersaturated condition. AON oh br ey ag Solubility of Zn SO,.7 H,0. || Solubility of Zn SO, .6H,0. —__—_— | ——__- Ist Deter- | 2nd Deter-| _ Ee s Li Ist Deter- 2nd Deter-) _ 5 A Pa Temp. | 28 | acy | aa | 2cy mination. | mination. | £5 | 328 mination. | mination. s 6 | as & SY NN Beh 5) O;s 4 iS) | ee ee ee — 5° 39.33 39.27 | 39.30, — 47.08 — 47.08) — 0°.1 41. 94. 41.92 41.93} 41.85 49.53 49 . 44. 49.48) — ei 47.11 47 07 47.09} 46,96 —_ 54.20 54.20) — 152.0 50.83 50.94 50.88} 50.74 57-09 57.20 57.15} — 25°.0 57.94 57.87 57.90) 57.95 63.74 — | 63.74) 63.74 39° .0 -- -- - 61.92 65.80 65.84 65.82) 65.65* | 35°.0 66.59 66.63 66.61) 66.61 67.99 = 67.99) 67.94" 39°.0 70.00 70 09 | 70.05) 70.05 — 70.08 70.08) 70.02 1 if | All the figures are grams of Zn SO, in 100 grams of water. D4* ( 338 ) Between — 5° and the transition point the solubility of Zn SO,. 7H, O is well represented by the equation: Ly = 41.80 + 0.522 ¢ + 0.00496 22 whilst the equation which I have deduced from the determinations of CALLENDAR and Barnes between 39°.9 and 50°.2, viz.: L, = 59.34 + 0.0054 ¢ + 0.00695 2? holds good, according to my determinations, to 25°. The figures, marked in the table with asterisks are calculated from this expression. From the above interpolation formulae the following table (ID), which will be used subsequently, is obtained. In it A is the number of molecules of water to one molecule of Zn SO, in the saturated solution of the system Zn SO, . 7H, 0, whilst a@ is the same quantity for the system Zn SO, . 6 H,0. Ar BS oe ae Temperature A a 39°.0 12.79 12.79 35°.0 13.54 13.18 30°.0 14.47 13.65 25°.0 15.46 14.16 15°.0 17.65 15.67 Ogu 19.08 16.53 0°.1 21.43 18.11 . al % ee z 4. The calculation of aa (equation 2) and also of / requires a a knowledge of the value of ¢. At the transition temperature, q is the heat of fusion of Zn SO,. 7 H,O. This quantity may be determined in two ways, a. By extrapolation from THOMSEN’s figures. b, Experimentally. ( 339 ) a. Determination of q by extrapolation. The change undergone by Zn SO,. 7 H,O at 39° may be repre- sented by equation (5) on p. 3535. According to the solubility determinations in table II, the value to @ at 39° is 12.79. Equation (3) therefore becomes: L.1 Zn SOy. 7 Hy O=0.941 Zn S04. 6 Hy O 40.162 Zn S04. 12.79 Hy O. According to THOMSEN !): The heat of solution Zn SO,.7 H,0 — Zn SO, 400 H,0 = — 4260 cal. The heat of solution Zn SO,. 6 H,0 — Zn SO,.400 H,0 = — 843 eal. Heat of dilution Zn SO,. 20 H,0 — Zn SO,. 200 H,0 = + 390 eal. -(THomsEn |. c¢. p. 37). Heat of dilution Zn SO,. 20 H,0 — Zn SO. 50 Hy0 = + 3818 eal. From the last figures we find by extrapolation : Heat of dilution Zn S04. 12.79 H,0 — Zn SO,. 20 HO = 318 30 (20 — 12.79) = + 76.8 eal. Therefore heat of dilution Zn SO,.12.79 HO — Zn SO,. 200 H, O= 390 + 76.3 = + 466.3'cal. Since further, the heat of dilution Zn SO. 200 HyO — Zn SO, 400 HO = + 10 cal. (THoMsEN, ].c. p. 91). we find: Heat of dilution Zn SO,. 12.79 H,O — Zn SO,. 400 H,O = +- 476 cal The heat evolved by the change represented by equation (3) is therefore: — 1.1 X 4260 + 0.941 x 843 — 0.162 X 476 = — 3970 cal. 1) Thermochemische Untersuchungen, III, 138, ( 340 ) The heat evolved by the fusion of one molecule of ZnSO,.7H0, q, 1S — — 3609 calories. b. Bxperimental determination of q. To determine g, the heat of solution of Zn SO,.7H,O in 393 mol. H,0 (final concentration therefore Zn SO, .400 HO) was first determined just below 39°, and then the heat of solution of the system which jis formed from Zn SO,.7H.O above 39° in the same quantity of water. The difference between these quantities of heat is the value of g required. In order to keep the water in the calorimeter at 39° it was sur- rounded with a metallic mantle with double walls which in its turn was wrapped in felt. Water at about 60° was poured into this mantle. The Zn SO,.7 H.2O was weighed out in thin walled flasks which were then sealed up and kept for some days in a thermostat at 39°.0. From this they were transferred immediately to the ealori- meter. When the heat of solution of the system (0.941 Zn SO,.6 H,O + 0.162 Zn SO, 12.79 HO) was to be determined the flasks, filled with Zn SO,.7 H20, were placed in a thermostat at 42° for 14 days and nights after which they were kept in a thermostat at 39°.1 for some days. Asa control other flasks were treated in the same way for a shorter time; both evolved the same amount of heat when dissolved, a proof that the desired condition had been attained. a. Determination of the heat of solution of Zn SO,.7 H.,0 — ZnSO0,.400H,O at 39°. Zn SO,.7H20 used = 20.333 or. Water value of calorimeter ete. = 530 er. t; — 13.699 ty = 13.120 At= — 0.579. 097.44 [Heat of solution = ———— XX 530 &K — 0.579 & 0,970 = — 4219 cal. 20.333 The specific heat of the final solution was 0 970. | ( 341 ) The second determination gave — 4212 cal. _As the mean of the two experiments we will take — 4215 eal. (at 39°) whilst THOMSEN gives — 4260 cal. (at 18°) (?. Determination of the heat of solution of the system formed from Zn SO,.7H,O — ZnSO, . 400 HO (at 39°). Zn $O,.7 H.O used = 20.366 er. Water value of calorimeter ete. — 530 er. t; = 16.301 ty = 16.232 At = — 0.069 ee ee f f Heat of solution = SOE x 5380 K — 0.069 & 0.970 = — 500 eal. A second determination gave — 516 eal. As mean we will take — 508 eal. From the determinations described under @ and /? that heat of fusion of ZnSO,.7H,O is therefore —3752 cal. (39°), whilst from THOMSEN’s figures we obtained, by extrapolation, — 3609 cal. (18°). The agreement is satisfactory when it is considered that similar and even greater differences exist between the direct determinations of the heat of solution of simple substances made by BerruELor and THomsen, the cause of which it is not easy to conceive !), As the mean value of g we will take — 3680 cal. 5. Introducing the values found into the equation dE a q akan P and expressing them in electrical units, we find ; — 0.51 Millivolits. dT/s9° 28.09 312 eae 3680 1 39° 1) As one of the many examples which might be advanced in support of this, 1 take here the heat of solution of Pb(NO,), which is, according to Bertiretor, —4..Lk., according to THhomsry, — 3.8 k. ( 342 ) The following table of the E.M.F.’s of Crark-cells containing solid ZnSO,.7H,O or Zn50,.6H,O is given by JakaER!) in his memoir. In the last column | have added the EK. M. F.’s of our transition element. TeAsB L EH aT | E.M.F. E.M.F. E.M.F. ‘Temperature. in millivolts. | iniillivolts. | ‘Transition cell | ZnSO,.7H,0 | ZrSO,.6H,O | — in millivolts. oe 1449 1434. 15 | 10° 1439 | 1427 12 20° | 1427 1418 9 30° | 1414 1409 5 | 390 | 14000 | 1400 | 0 From these figures the temperature coefficient is ad 2 0,55 millivolt = —— = — 0,55 millivolt Gus 9 / , whiist the thermodynamic calculation gave — 0,51 millivolt ; the agreement is, thus, very satisfactory. In a subsequent paper IT shall show that the E.M.E. of our transition cell at other temperatures may be calculated by thermo- dynamics. Amsterdam, University Chemical Laboratory. December 1899. Chemistry. — “On the nitration of dimethylaniline dissolved in concentrated sulphuric acid”. By Dr. P. vAN Romburen. (Communicated by Prof. A. P. N. FRANCHIMONT.) Some years ago”) I had the honour of communicating to the Academy the results of an investigation of two new dinitro-deriva- tives of dimethylaniline obtained by dissolving this base (1 mol.) in 1) Wigpemann’s Annalen 63 (1897), p. 356, 2» ) Zittinosverslag 23 Februari 1895. ( 343 ) twenty times its weight of concentrated sulphuric acid, and allowing 2 mols. of nitric acid, also dissolved in sulphuric acid, to act on the solution so obtained at a low temperature and pouring the mixture onto ice. Different observations made during the often re- peated nitrations led me to doubt whether the dinitration really took place in the concentrated sulphuric acid solution, or whether, more probably, the reaction leading to the formation of the two nitropro- ducts teok place in the mixture of acids when diluted with ice water. Further investigation of the course of the reaction actually brought to light that the nitration in concentrated sulphuric acid solution, even in presence of excess of nitric acid, does not go further than the formation of the mononitro-compound. If a cooled mixture of 104 gr. nitric acid of 50 pCt., or 60 gr. of 86 pCt., and 300 gr. sulphuric acid be added in small quantities to a solution of 60 gr. dimethylaniline in 1 kg. of concentrated sulphuric acid, cooled to 0°, the temperature of the mixture rises at first with each addition. When half of the nitric acid has been added, however, no further rise of temperature is observed on adding the remaining half. When all the nitric acid has been added it is clear from the smell of the mixture that it contains free nitric acid. If, after half an hour, the half of the liquid is poured into 1'/, kg. of ice water (a mixture of equal parts of Bass and ice) the tempera- ture at the end of the experiment is 30° C., a yellow crystalline product (the dinitro-compound melting at ay ) is obtained and after addition of soda to the filtered acid liquid the red isomeric compound (melting point 112°). If a cooled solution of 25 grams of dimethyl- aniline in 1/, kg. of sulphuric acid is added to the other half of the nitration liquid the rise of temperature is again clearly obser- yable. On pouring the mass, after some time, into 2!/, litres of ice water a mixture of para-and metanitrodimethylaniline with a little of Mr. Mertens’ 1. 2.4. dinitrodimethylaniline is obtained, such as is also produced according to GRott ') when dimethylaniline dissolved in concentrated sulphuric acid is nitrated with one molecule of nitric acid. When the nitration mixture containing one molecule of dimethyl- aniline and two molecules of nitric acid is poured into a mixture of ice and soda, dinitro-compounds are formed only in very small quantity or not at all. From these experiments it may be concluded that, in the solu- 1) Berl, Ber. 19. 198, ( 344 ) tion in concentrated sulphuric acid the nitration does not go further than the metamononitrocompound, so that the entry of the second nitro group must occur after the admixture of water. I pointed out previously (loc. cit) that the two dinitrocompounds may also be prepared by dissolving the metanitrocompound in an excess of very dilute nitrie acid. I now found that by dissolving 1 gram of metanitrodimethyl- aniline in a mixture of 26 grams of sulphuric acid and 50° grams of water, cooled to 30°, and adding 0.85 grams nitrie acid of 50 pCt, a paste of the yellow dinitro-compound melting at 176° is obtained whilst, by means of sodium carbonate, the red isomeric is separated from the filtrate. These relative quantities are exactly those found in the liquid obtained by pouring the nitration mixture into the quantity of water prescribed. The small quantity of the dinitrodimethylaniline of Mertens which is produced shows that in nitrating dimethylaniline by the method of GRoLL the meta-compound is formed almost exclusively in the con- centrated sulphuric acid solution and that the para-compound is most probably formed in the liquid after dilution with water by the action of unused nitric acid on dimethylaniline which has escaped nitration. When para-nitrodimethylaniline (1 mol.) is dissolved in concen- trated sulphuric acid and 1 mol. of nitric acid is added to the solution, the dinitro-compound of Merrnys is found alone after pouring the mixture into water; no nitro-group has taken up the meta position with regard to the amino-group. Chemistry — ‘On the formation of Indigo from Intigoferas and from Marsdenia tinctoria’. By Dr. P. vAN Rompuren. (Communicated by Prof. A. P. N. FRaNcHIMONT). The interesting communication which Prof. Beyertnck made to the meeting of Sept. 30th last, from which it appears that the indigo yielding plants belong to two, physiologically quite distinct groups induce me to invite attention to some observations which I made some years ago during an investigation of indigo-yielding Indigoferas and of Marsdenia tinctoria which was published in the ‘Verslagen van ’s Lands Plantentuin”. I would add one remark. Owing to my other affairs I was unable to devote as much time to these resear- ches as I could have wished and they are therefore of a more or less preliminary nature. When I found, on the occasion of a meeting with Mr. Hazewinket, Director of the Indigo Experimental Station ( 345 ) at Klaten, that our researches were tending in many ways in the same direction, I terminated mine for the time being and I am post- poning the publication of various results until Mr. Hazewinken shall have ended his researches, which are in many respects of impor- tance, and published the results of them. In the “Verslag” for 1891/2 it is stated that preliminary investi- gations into the preparation of indigo showed that the extraction of the leaves with water at the temperature prevailing here is not accompanied by evolution of gas during the time which in Java is considered needful to extract the constituents which yield the colour- ing matter from the plant viz: 6—7 hours. Later, for example in a day, this does occur. The gas evolved consists of carbon dioxyde and a gas which burns with a colourless flame, very probably hydrogen. What compound exists in the aqueous extract of the indigoleaves is not yet made out with certainty. It had a distinctly acid reaction ') and shows the so ealled indicanreaction very beautifully when it is shaken with hydrochloric acid, chloroform and air. The filtrate obtained after treating the extract with excess of lead acetate gives a yellow precipitate *) with ammonia, stated by ScnuNck to be characteristic of mdican. Since indigowhite is said to be insoluble in acid liquids, it is not very probable that this substance is present im the aqueous extract of the indigoleaves. A dilute solution of indigowhite in lime water behaves also in many respects quite differently from the extract. If the indigoleaves are extracted with dilute acetic acid (1 pCt.) instead of with water, the extract yields indigoblue abundantly when shaken with air, especially if ammonia is added.” According to Mr. v. Lookerpn CampaGNe *) the liquid produced by the so called fermentation is alkaline and contains indigowhite in solution. In the “Jaarverslag van ’s Lands Plantentuin” for 1893, the following is to be found: “The solution obtained by extracting indigoleaves with water for 7 hours has again been the subject of an investigation, a few of the results of which will be indicated here. The liquid contained free 1) That the extract of the indigo-leaves in acid is very easily shown by running it into a solution of potash coloured red by phenolphthalein. The reaction is also suc- cessful with a solution of blue litmus. (Note of 1892). 2) [ have found, subsequently, that an extract of the leaves of Zndigofera galegoides, which contains a substances resembling amygdalin, also gives a yellow coloured pre- cipitate in which, however, the glucoside has no part. 3) Verslag omtrent onderzoekingen over Indigo, 1895, L6. ( 346 ) or very loosely combined carbon dioxide!) in very large quantity, which may be driven out not only by warming but also by a current of gas free from oxygen *). The substance which yields indigoblue on oxidation may be extracted from the solution by means of chloroform either with or without addition of acetic acid. When the chloroform solution, which has a light greenish yellow colour, is evaporated by blowing a current of air into it, a greenish coloured residue is obtained which is partially soluble in water. The aqueous solution, which possesses a splendid fluorescence, gives indigoblue at onee when shaken with air and ammonia ; indigoblue is also formed by exposure to the air, and very rapidly when warmed. An extract of the leaves of Marsdenia tinctoria, which is also very distinctly acid to litmus, behaves in a similar way. It has not yet been possibie to obtain the substance which yields the indigoblue in a state fit for analysis, nor to prepare erystallized derivatives of it.” The fact that the indigo-yielding substance is formed from the leaves by dilute organic acids was confirmed by Messrs. vAN LOOKEREN CAMPAGNE and VAN DER VEEN in 1895 %); notwithstanding the inso- lubility in acids it is still taken for indigowhite. The solubility of the indigowhite in the extract is explained, by these investigators, by the formation of an unstable compound with substances which yield indigored and indigorubin on oxidation. The ready oxydation of the substance which is extracted by chloroform, in presence of mineral acids or of alkaline carbonates, shows, according to the same authors, that we are not dealing with indoxyl. In 1897 I again took up my researches, and in the “Verslag” for that year the following is to be found: “If Indigoleaves (Guatemala or Natal) or leaves of Marsdenia tinctoria are placed in an atmosphere of chloroform or carbondioxide they retain their green colour. If, after some time, they are brought in contact with the air, they quickly become bluish, proving that the indican in the dead leaves, which had probably escaped from the cells in the form of a solution, had been decomposed. 1) If carbon dioxide is passed into a solution of indigowhite in lime water until the lime is converted into bicarbonate, the whole of the indigo is precipitated and no indigoblue can be obtained from the filtrate by means of air and ammonia. (Note of 1893.). *) If the current of gas is passed through the liquid for a long time, it is well to mix it with chloroform vapour in order to render living organisms, which might give rise to carbon dioxide during the experiment, inactive. ‘) Landwirtsch. Versuchsstationen. XLVI, 249, = ( 347 ) The presence of a soluble enzyme, capable of decomposing the glucoside, has not so far been proved with certainty 1). The many attempts which have been made to separate such a soluble compound have so far given no result. On the other hand it was possible to show that the leaves contain, either a substance of this kind which is so firmly retained that it may be regarded as practically insoluble, or else they carry an insoluble substance which has the power of decomposing a solution of indican so that the sub- stance which on oxidation yields indigo, is set free. If indigoleaves are steeped in water for 7 hours and the sherry: coloured liquid, which contains the decompositionproduct which yields indigo on oxydation, is then displaced by distilled water con- taining chloroform, it is found that after several repetitions of this treatment, the displaced liquid yields no more indigo. The dried leaves are again washed several times with water containing chloro- form and then placed in contact with a solution of indican *) to which chloroform is added; after two hours this gives, when shaken with air, an abundant separation of indigo. If the leaves are now again thoroughly washed, they are still able to decompose a sterili- zed solution of indican. This may be repeated several times with the same leaves, even when they have been in contact with chloro- form water for more than a month. The washed leaves may be dried over sulphuric acid without losing this property. The property of decomposing a solution of indican in an hour is retained after extracting the fresh leaves with ether, alcohol, acetone or chloroform. By treating the leaves, dried in this way, with dilute acids or bases or with glycerine, it has not sofar been possible to obtain ) Van Looxerrnn Campaone, Verslag omtrent onderzoekingen over Indigo, p. 13. contented himself with a reductio ad absurdum, «a kind of proof which is somewhat unusual in researches of this nature. *) Such a solution of indican is prepared, according to Antvarez (C. R. 105, 287) by placing indigoleayes in small quantities at a time in boiling water. Quantitative ceterminations show that the decomposition of indican is very small when the time of contact is short. Mr. Loumayy, assistent for the examination of tea, found that such a solution of indican yields indigo in contact with emulsin and air; this agrees with older, vague statements that indican is decomposed by enzymes. The specimens of emulsin in the laboratory were insoluble in water. In the mean time it appeared from a publication of the Indigo-experimental-s tation at Klaten that Mr. Hazewinknn was experimenting with soluble enzymes in the preparation of indigo, this observation was therefore not followed further. (Note of 1897). ( 348 ) a solution of the substance which decomposes the indican. The dried leaves of Indigofera galegoides, as also some other kinds of leaves with which experiments were made, were incapable of producing the decomposition, so that it appears to be a specific property of some indigo yielding plants. These researches, which proceed slowly, will be continued, as also those on the substance which on oxidation gives rise to indigo; this substance may also be extracted by carbon tetrachloride.” Finally in the recent ‘Verslag’’ for 1898: “Investigations on the composition and properties of a red com- pound, which is obtained by evaporation of the chloroform soiution of the liquid decompositionproduct of indican from Indigoferas which yields indigo, progress but little owing to lack of time. MARCHLEWSKI and RapcLiFFE (Chem. Centralbl. 1898, II, 204), consider indican to be the glucoside of indoxyi. The properties of the decomposition product which yields indigo on oxidation, and which has already been shown here not to be identical with indigowhite, agree, to some extent, well with those of indoxyl. Since Mr. Hazewiket, Director of the Experimental Station at Klaten is occupied with this matter, I have not followed it further.” Physics. — Dr. E. van Everpincen Jr.: “The Hawt-effect and the increase of resistance of bismuth in the magnetic field at very iow temperatures” 1 (continued). (Communication N°. 53 (cont.) from the Physical Laboratory at Leiden, by Prof. H. Kamer- LINGH ONNES.) 5. In the Proceedings of October 28, 1899, p. 221, I expressed the hope that the measurement of the Haw-effect at the boiling-point of liquid oxygen would yield a more decisive answer to the question as to whether or no this phenomenon has a maximum at low tem- peratures. This measurement has now been made, though as yet only for one strength of field, and the answer is certainly a decided negative, as will appear from § 7. 6. The liquid oxygen bath. For pouring out the liquid oxygen we used the vessel without a vacuum-wall, described and drawn in § 2 of this communication, but somewhat altered for this purpose after the manner of Prof. KaMertincu Onnes’ cryostat !). Besides ‘) See Communication N°. 51, Proc. 30 Sept. °99. p. 126. Comm. Phys. Lab. Leiden N°. 51, p. 2. E. VAN EVERDINGEN Jr. The HALL-effect and the increase of resistance of bismuth in the magnetic field at very low temperatures. (I) continued. Proceedings Royal Acad. Amsterdam. Vol. LL. oa) ( 349 ) lengthening the wooden receptacle a and the glass tube d, a double jacket was added to lead off the cold vapours, which in this manner largely screen the liquid from heat. Moreover observing-glasses were used to watch the liquid streaming out. The whole apparatus is drawn in fig. 2, whilst fig. 1 may serve to further elucidate it. The lengthened wooden receptacle a, the paper vessel l, the caoutchoue-ring c, the glass-tube ¢, the T-piece e, the caoutchouc-tube f and the plate carrier / were meutioned in § 2 of this paper. The steel capillary tube & is now introduced into the T-piece through the oblique side tube w, from which it is wholly insulated by means of wood and caoutchouc, the horizontal side- tube now leading towards a safety-tube immersed in mercury. The supply of liquid oxygen from the oxygen-spiral in the ethylene boiling flask!) ean be shut off by the cock”) <, by means ofa long wooden stem; before entering the capillary tube the liquid passes through a small filter. The tube 4 ends in front of the observing- tubes *) 0, which are fastened by means of a copper case and sealing- wax to the tube d; the jet of liquid meets a jet-catcher *) p suspended by means of fiddle strings to d, and spreads out in a fan over this tube. In order to indicate the level of liquid in a, a float g with a stem was used, which latter ends at the level of the observing-glasses. The cold vapours leave a through the holes r, six in number, and stream downwards in the annular space between a and b on one side and the jacket s;—ss on the other side. s, is a cireular eylinder of compressed paper, fastened to the border of a, s. a wooden bottom with an oval hole, into which an oval cylinder of paper s, has been glued; the minor axis of this is only a little wider than b, but sufficient space is left along the major axis for the vapour to escape °). The latter then rises in the space limited by the jacket t)...t;. ¢, is a copper rim, joined to the case of the ob- serving-tubes and fitting on the glass-cylinder &, to which it is fastened by means of a caoutchouc-tube and brass tightening bands. ts; is a wooden cylinder with holes provided with flanges to admit the pole-pieces; a tight fit is obtained here by means of a leather washer, screwed on by the wooden nuts t. ¢ is again a glass- eylinder and ¢; a cork stopper. In order to prevent the cold vapours 1) Proc. 29 Dec. 94, p. 172. Comm. N°. 14, p. 17. *) See Communication N’. 51. Proc. 30 Sept. 799, p. 129, Comm. N°. 51, p. 9. 3) ib. p. 130. Comm. N”. 51, p. 10. 4) ib. p. 127, glass C. Comm. N?. 51, -p. 5. *) See transverse section, drawn in the figure on the right hand side of e. from flowing immediately to the bottom and to diminish the con- duction of heat from below, another little vessel u of compressed paper with a wooden bottom has been placed under and around sz. The space left beneath the pole pieces has been filled up with wool. In the rim 4 six holes have been made, connected with the copper tubes v, four of which lead off the gaseous oxygen, whilst two have been shut with a stopper and serve as a safety arrangement. In order to obtain the room wanted for these jackets between the coils of the electromagnet, it was necessary to considerably lengthen the pole-pieces. For weak currents this did not much diminish the strength of the field; for strong currents the loss was considerable. During the experiment all parts of the apparatus except the observing-glasses were wrapped in wool. The receptacle @ was com- pletely filled with liquid oxygen, and as an additional precaution liquid was even allowed to flow out until a considerable quantity had passed through the holes 7 and had collected inv. The apparatus stood this well; especially the compressed paper, which appears to be a very suitable material for this work. i. The Hauu-effect at the boiling point of liquid oxygen. For the Hat coefficient & in a magnetic field of 4400 C.G.5S. units the value 41,4 was found. Hence the product RM is 182000. Before, at a temperature of 10°C., & was found to be 11,0. This does not wholly agree with the value 10,15, which may be obtained by interpolation from the table given in § 3 of this paper for the field 4400 and the temperature 10° C. Recently Perrot!) has noticed, that the thermo-electric constants of crystalline bismuth showed irregular variations with time, which he at first was inclined to ascribe to the influence of repeated heating and cooling; this however appeared later *) not to be the case. In order to see whether perhaps something of that kind really happened in consequence of the strong coolmg in my experiments, I repeated the deter- mination of the HaL-coefficient & at 10°C. shortly after the experi- ment in liquid oxygen, and found 11,1. The difference from the value of #& 11,0, determined immediately before the experiment is too small to be worth attention. As formerly I have also not noticed continuous variations with time in electrolytic bismuth, I think we 1) Arch. d. Se. phys. et nat. (4) 6 p. 105 and 229, 1898. Wy 1 yu oui (4) 7 p. 149, 1899. ( 351 ) must rather describe the difference between the values found now and formerly to an uncertainty in the knowledge of the resistance in the circuit of the Hatt-current*), which is required for the calculation of R. For, as the variations of this resistance appeared only after some time, the resistance was not measured during the experiments of the first determinations in § 3. With the determina- tions now published the resistance was measured twice during the experiment and was found to be constant. Therefore we retain the value 11,0 for 10° C. The value at — 90° C. for a magnetic field of 4400 is found by interpolation to be 17,1 and is for the same reason not quite certain. C oH Birnie R - Cr 283 11,0 11,0 11,0 183 il 7igal 17,0 12,7 91 41,4 34,2 22,2 EEE EP 50 Joo SSO 200 250 $00 Fig. 3. 5) See § 3. bo Ot Proceedings Royal Acad, Ams‘erdam. Vol. IL. ( 352 ) This however interferes little with the value of the following. in which for the sake of comparison besides the absolute temperatures : : C T and the corresponding values of & the values pr are also given, where C has been chosen so as to make the value at 10° C. equal to 11,0. Further in the values C'r, where 7 represents the resistance of electrolytic bismuth in a field of 4400 C.G.S. units, taken from observations by Friemine and Dewar!), C’' is likewise chosen to make the value 11,0 at 10° C. Fig. 3. gives a graphical representation of these numbers. It is evident that the HaLt-coefficient increases much more rapidly than a C : the resistance and a little more rapidly than Tar Hence no evidence of an approach towards a maximum can be found. In order to give a clearer view of the meaning of a Haut- coefficient 41,4 we will calculate the tangent of the angle through which the equipotential lines were turned in this experiment. For this it is necessary to know the resistance of the bismuth at — 182° C. in the magnetic field. As this resistance has not yet been measured for the plate, we take as a preliminary value 2,46.10°, taken from FLeminG and Dewar. We then find for the tangent the value 0,740. For the sake of comparison a list is appended of the values of this tangent for some of the metals with the largest HALL-coefficients, all of them for a magnetic field of 4400. Bismuth — 0,740 Nickel — 0,083 Antimony + 0,021 Tellurium + 0,017 Tron + 0,004 As it may safely be assumed, that the Hatt phenomenon has never been observed in a field of greater intensity, higher than 20.000 C.G.S. units, it appears that the value 0,740 is the largest ever obtained. 1) Proc. Roy. Soc. 60 p. 73, 1896. (January 24, 1900.) KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TH AMSTERDAM, PROCEEDINGS OF THE MERTING of Saturday January 27, 1900. $= t0ce— —_ —_ (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 27 Januari 1900 Dl. VIII). Contents: “The determination of the Apex of the Solar motion”, By Prof. J. C. Kaprryn, p- 353. — “On twisted quintics of genus unity”. By Prof. Jan pe Vries, p. 374. — “The cooling of a current of gas by sudden change of pressure”. By Prof. J. D. van pER WAALS, p. 379. + “The direct deduction of the capillary constant o as a surface tension”. By H. Hurspor (Communicated by Prof. J. D. van per Waats), p. 389.— “Determination of the latitude of Ambriz and of San Salvador (Portuguese West- Africa)”. By C. Sanpers (Communicated by Dr. E. F. van pe Sanpe Baxk- HUYZEN), p. 398. — “Methods and Apparatus used in the Cryogenic Laboratory. JI. Mercury pump for compressing pure and costly gases under high pressure”. 3y Prof. H. Kameriincu Onnes, p. 406. — “hLipolytic ferment in human ascitic fluid’. By Dr. H. J. Hampurcer, p. 406. — “The action of strong nitric acid upon the three isomeric chloro-benzoic acids and some of their derivatives. By Dr. P. J. MonraGne (Communicated by Prof. A. P. N. Francurmont), p. 407. — “The alleged identity of red and yellow mercure oxide” (IT). By Dr. Erxsr Conren (Communicated by Prof. H. W. Baxuurs Roozenoom), p. 407. — “Determination of the decrease of the vapour tension of solutions by determining the rise of the boiling point”. By Dr. A. Smirs (Communicated by Prof. H. W. Bakuvis RoozeBoom), p. 407. — Erratum, p. 408. The following papers were read : Astronomy. — ‘The determination of the Apex of the Solar motion.” By Prof. J. C. Kapreyn. 1. Fundamental hypothesis. It is usually taken for granted that the best known determinations of the direction of the solar motion in space are based on the following hypothesis : Hypothesis H, The peculiar proper motions of the fixed stars have no preference for any particular direction. In reality however this is not quite correct; at a closer investi- 26 Proceodings Royal Acad. Amsterdam. Vol. LI. ( 354 ) gation we find that neither the method of Arry, nor that of ARanr- LANDER is entirely based on this hypothesis, and yet these two were almost without exception used in all modern determinations of the position of the Apex. Finding the distribution of the proper motions in regard to the great circles drawn through the position of the Apex as determined by these methods unsatisfactory, KosoLp concludes that we must drop the hypothesis 4, as not agreeing sufficiently with the facts. Such a conclusion however cannot be accepted until at least one compu- tation has been made, which is completely founded on this hypothesis. This has given rise to the following investigation, in which I have tried to develop a method satisfying this condition. After having explained the method I shall give a short criticism of those of Airy, ARGELANDER and Kosoup, which criticism however Jays no claim whatever to being complete. 2. Meaning of the letters and simple relations. BP Antapex Fig. 1, O the Apex; P the Pole of the Equator; S an arbitrary Star ; A and PD the coordinates of the Apex 0; a and 0 the coordinates of the Star S; 4 = OS = the angular distance of the Star to the Apex; je Sye the observed motion of S; SQ the direction towards the Antapex = direction of the paral- lactic proper motion ; ( 355 ) y = PSw=angle made by the total proper motion « with the declination circle ; Z==PSQ=angle made by parallactic proper motion with th e declination circle ; v =component of total proper motion in direction SQ; r=component at right angles to the former (sign same as that of sin(y—y)); Q) p=7—w=4SQ=angle made by « with the parallactic proper motion ; h = linear motion of the solar system in space ; vy = distance of the star to the solar system. We have: (2) — sinh = parallactic proper motion of star S; Vv Moreover let : y (fig. 2) = peculiar proper motion of S; a’ the angle made by this peculiar proper motion with the parallactic. We then have the following relations : (3) v= fecos(y—w) = fe cos p (4) roeusin(y—yw) = “sin p (j@aaou Ox = = —T (5) 0A 0A du mys OD gD QA a “oA or 0x OD oD | | | ieee BOLE | 5 (6 3. Stars in a very limited part of the sky. First we consider only a group of stars lying so close together that we can practically assume that they are all at the same point of the sky. 26* We have to express that these stars satisfy the hypothesis /. The very first condition, the one which I shall here use exclusively, resulting from this hypothesis is this, that the sum of the projections of the peculiar proper motions on any direction is equal to zero. This can also be expressed as follows: the resultant of the pecu- liar proper motions must be. equal to zero. If we project the proper motion y (fig. 2) on C A S A sind B G o Fig. 2. the direction SG to the Antapex and at right angles to it, this condition is expressed by the equations : (7) 2 v'cos a’ = 0 sine 0c Now along with the peculiar proper motion each star has a paral- : . A : lactic motion — sin A, in the direction of SG to the Antapex. Con- (g sequently the entire proper motion « of each star has for components ' h . * t VU=vVcos @ + — sin X CSV sn @& v so that if we take the sum for ali the stars of the group we obtain, according to the conditions (7). / (8) Sv=snhz=— Ps Q The resultant of all the total proper motions @ is directed along SG, from which we conclude at once that the sum of the projections of the motions « on this direction is greater than on any other. If therefore the direction in which the Antapex is situated as seen from the group of stars under consideration is unknown, it can be derived from the observed proper motions by the fact that for this direction (357) (9) 2v must be maximum. It is easy to see that for a group of stars as that here consi- dered, this condition is equivalent to the second condition of (8) (10) Sr=0 This latter however is not so easily extended to all parts of the sky. 4. Influence of the different distances of the stars. For a group of stars at one point of the sky it is easy to derive from condition (9) or (10) the direction to the Antapex. We can arrive at a result however, at least theoretically more accurate, by modifying that condition (without throwing up the principle). It is easy to sce at once that if we have stars of greatly differing distances to the sun, the stars whose distance is very large (and whose proper motion is therefore as a rule very small) will influence the result much less than stars at a smaller distance (and with as a rule greater proper motion). If we start from the principle that one and the same irregularity in the distribution of the linear, peculiar proper motions must have the same effect on the accuracy of the direction to the Ant- apex for stars at a greater distance and for those at a smaller distance, it is easy to show that not the condition (9) but (11) gv maximum. must be satisfied. This one would certainly be preferable to (9), if the distances of the stars were known. This being however the case for so very few objects we are forced to adhere to the theoretically less valuable condition (9). Fortunately however the objection, arising from the predominating influence of the stars nearest to the sun, may be met to a great extent. 5. Grouping according to amount of proper motion. This may be done by grouping the stars into classes included between pretty narrow, determined limits of the proper motion. The separate results for these groups will finally be combined into a single one, taking due account of their probable errors. We will first have to show however that for such groups of stars the condi- tion (9) is still satisfied, for from considerations as were given in Astr. Nachr. N°. 3487 Page 100 ete. (and which for the sake of brevity we must omit here) follows, that, for groups as are meant here, the distribution of the peculiar proper motions will certainly no longer satisfy Hypothesis H. ( 358 ) This is easily done. For it is seen at once that, whereas the former of the conditions (7) ceases in general to be satisfied by such groups, the condition os Vv sin a’ = 0 will still hold. We immediately conclude to this from reasons of symmetry. Now as vsine@'=7, we shall also still have=7=0 and the condition (9) will be satisfied which is equivalent to it. Consequently there can be no objection to the grouping in classes of determined proper motions. With this the only advantage which condition (11) might have over (9) disappears in a great measure. In what follows we shall therefore entirely neglect the conditions (11). 6. Stars scattered about the whole sky or any considerable part of i. So every region of the sky gives a condition of the form (9). These might all be combined to one condition (12) Sv maximum where the sum is to be extended to the stars available in all parts of the sky. In that way however not the most accurate determination of the position of the Apex will be obtained: To arrive at a more advantageous combination the following problem is to be solved: Given that for the various parts of the sky the accidental devia- tions from Hypothesis 47 are equal, to combine the conditions (12), which hold for the separate zones of constant 4, in such a way that the effect of those deviations on the coordinates of the Apex which have to be determined, be a minimum. The solution of this problem which gives rise to no particular difficulties, shows that the + v of each region must be multiplied by its corresponding value of sin 4, before they are combined into a single sum. Consequently for the whole sky we shall not have to satisfy the condition (12), but (I) 2wusind, maximum. «, Second form of the method. As has already been remarked the objection, that by using (1) the large proper motions exercise a very predominant influence, may ( 359 ) be avoided by a grouping into classes of different proper motion. This can be done in still another way. By substituting the value (3) for v in (I) it becomes > cos p sin hy Maximum. As this holds also for stars whose proper motion is included between determined limits, it also holds for stars with absolutely the same proper motion “== 4). For such a group the condition becomes (I) cos p sin Ay maximum -and as each value of the proper motion leads to such a condition, it must also be satisfied by all the stars together. The equations for the coordinates of the Apex, obtained in this way contain only the directions and are entirely independent of the amount of the proper motion. It seems to me however that the condition (I), at least if it is applied to stars whose proper motions are included between pretty narrow limits, is preferable to (II) especially for this reason, that the former is a more direct consequence of hypothesis H on which the investigation is based. 8. Derivation of the Apex from the condition (1). To determine the coordinates of the Apex in such a way that condition (I) is satisfied, the differential quotients in regard to A and D of Zvusindy must disappear. Consequently we have with the aid of (5) ed (13) Oa) sin hy = 0 Site A= 0 oD which for stars at one point of the sky is reduced to the single equation =r = 0, as of course was to be expected. Let A, and Do be approximate values of A and D and dd, dD the required corrections of these, All the quantities computed with the aid of these approximate values will be distinguished by means of an appended . So vw, and t, will represent the projections of the proper motion “ on the great circle through the star and the approximate position of the Apex and at right angles to it. We thus have in the equation (13) ( 360) Pam h (4). aA + (5) a= Sst » (54) a4 sagt (34). dD at = (54) 4 (FA) eat Grapy ca Evidently these equations hold only as long as we do not approach the Apex or the Antapex within distances of the order of dA and dD where the terms of a higher order may not be neglected. It will be best therefore to exclude entirely the stars close to the approximate position of the Apex. This cannot cause any considerable loss of weight. I find e. g. that of the stars of BRapLEy only a fourteenth part have sind < 0.40 and less than one eighth part have sink < 0.50, The first of the equations (13) now becomes 2a gait (gas) fet + + dD = he (£4) (f) 40 (5545). f sinh) = —- = ra( ain A, The quantities + must be in all parts of the sky as often positive as negative. According to what we have discussed this is an immediate consequence of the hypothesis H (compare form. (10) ). dA Sot (G2) will already disappear for limited parts of the sky. fia Wd 0 The same holds @ fortiori? for the sum extended over the whole sky. Py. ; ; PTR (<4) differs from the preceding sum only in the quanti- CAG ties « being computed with an approximate Apex, the coordinates of which need still the corrections dA and dD, This quantity will thus be of the order of dA and dD and may be neglected in the coefficient of dA. The same holds for all quantities containing 7) in the coefficients of dA and dD. So_the above equation is reduced to the former of the two following ones, in which the sums are indicated with’ the notation used in the theory of least squares: [vosindy (2). Jest [eosin @ a () |e=- [roinda(52) | ewind 52), (G5) 24+ [evn sh), ] 2=— [rent 3)) (14) ( 361 ) The second of these equations is derived in quite the same way as the first. 9. Derivation of the Apex from condition (II). The maximum conditions are: aOR 4 Esinp sin, % = 0 E sinp sin ky A =0 in which we put: 03 sinp = sinpo -+ Cos po € a ah dA + cos py ( ap)? = (8), +8), e44 Ge) The first of the equations thus becomes: 3 frp ante AE) vn osent(24) 14 4205 ryan) (24) i ti = — J sin po sinh, ae Here again, for quite similar reasons as in the equations of the preceding article, the terms with sin po in the coefficient of dA and dD may be neglected, they being of the order of dA and dD. The equation is thus reduced to the former of the two following ones (the second is found in the same way as the first) : | |eo=po sind (22). |e + jer" Pa sin nee a aa of) \av= —|sin po sin in(54) | f) ( | [eos po sino (34). (34), Je Js |e08 po sin (4) Jav= —|sing sin 1n(55) | 10. Arry’s method. In his derivation of the position of the Apex and the amount of the linear proper motion of the sun, Arry starts from the idea, that the peculiar proper motions having no preference for any particular directions, may be treated entirely as errors of observation. (15) 362 ) ; Hence each star gives two equations of condition between h, A and D, expressing that the observed proper motions projected on two mutually perpendicular directions are equal to the projections on those same directions of the parallactic proper motions. AIRY chooses for the two directions the parallel and the declination circle. To get a clear insight into the character of Atry’s solution it is preferable however to choose for these directions the direction of the star towards the Antapex and the great circle through the star at right angles to the former. Doing this his equations of condition get the form (16) r=0 and h = (17) w= —aends Q So we can say that by Airy’s method A, D and h are deter- mined in such a way that all the equations (16) and (17) are satisfied in the best way possible. Now as Arry and every one who has applied his method, have solved these equations by least squares, this determination comes in reality to the choosing of 4, D and * in such a way that both (18) 2? minimum 9 I 2 (19) = = sin i—v) minimum. Q The former of these does not contain the unknown quantity 4 and only leads to a determination of A and D. The second gives the three unknown quantities, so that we arrive at two independent determinations of A and D and one of 4. I will here discuss the two conditions (18) and (19) separately. 11. The condition = t* minimum. The minimum conditions are (with the aid of (6)): 4 (20) Srv =i) Api eae (21) Srva5=0. For stars all situated at the same point of the sky, they are reduced to this one (22) Srv=0 ( 365 ) differing from the condition 25 GS which we have found as a necessary consequence of hypothesis /. This proves sufficiently that in reality Arry’s method (at least if his equations of condition are treated with least squares) does not agree with hypothesis H. A few examples will show this still more clearly and will at the same time prove that the application of conditions (9) and (18) may lead to very considerably different solutions. 1st example (see fig. 3). In each of the two points of the celestial 0. : (Airy) Fig. 3. sphere S and S' we find two stars. The proper motions SA and SB of the two stars in S are equal and we will begin by assuming that their directions form an obtuse angle. The same holds for the stars in S', ( 364 ) We see at once that the direction which causes the Yr!) of the proper motions of the stars in S§ to disappear is the bisectrix SO of the angle ASB, Likewise the line which in S' makes © 7 = 0 will be the bisectrix S'O of A'S'B’, From the given proper motion we conclude therefore, according to the method proposed by me, to a position O of the Apex. On the other hand the direction which makes minimum the = 7? of the proper motions of the stars in S is evidently the line SO' at right angles to the bisectrix; likwise in S' the line satisfying this condition is the line §'O' at right angles to S'O, According to the condition ~ 7* min. of Army we conclude there- fore to a position for the Apex (or Antapex) in 0’, If we leave the angle ASB unchanged, but reduce B'S'A' in such a way, that the bisectrix does not change place, then in the moment that that angle passes through 90° the Apex (Antapex) according to Arry’s determination, will suddenly leap over from 0' to O", where it remains when the angle S'S'A'is still more reduced. If the angle B's'A' had retained its original value (> 90°) and angle ASB had been reduced in the above stated way, the Apex would have leaped from 0O' to O'. If then again we had reduced A'S'B', at the moment of this angle passing through 90°, the Apex (Antapex) would have leaped from 0" to 0. In the nature of the problem there seems to be no reason whatever for such leaping *®) and in our determination the Apex remains where it is notwithstanding the changes introduced. Moreover it seems very little plausible indeed to assume for the Apex one of the positions O', 0", 0". The place determined according to both methods coincides evidently only when both angles are acute. 9nd example (see fig. 4). For stars in the region § let the line Antaper ) According to the statement in §3 the condition for stars at one point of the sky is equivalent to 2 r= 0. i 2) There are still many other cases in which the condition (18) leads to discontinuous changes in the Apex for continuous changes of the data of the problem. ( 365 ) to the Apex be determined by a number of proper motions (not shown in the figure) which, to avoid complication, we shall suppose to be all direct. If now one more star be added, whose proper motion SA makes an acute angle with the line towards the Apex (which therefore is retrograde) we easily see that according to the condition =v? min. (Arry) the line S& towards the Apex will have to be turned somewhat more into the direction AV, whilst the con- dition (10) demands a movement in the direction RW'!), 9 2 h Super: 12. The condition (— sini — v) minimum. Q The equations of condition are of the form I (23) —sink =v ‘ They contain the distances which are as a rule unknown. This is certainly the chief objection to the use of these equations. They seem therefore much more suitable to give information about mean parallaxes of definite groups of stars when once the Apex is known, than to assist in determining the position of the Apex itself. For the calculations according to ArRy’s method different ways have been followed to escape the difficulty arising from the unknown distances. One of the commonest practices (STUMPE, PORTER, etc.) is to divide the stars into groups included between narrower or wider limits of proper motion and then to assume the distance of the stars of each group to the sun to be the same. If this be true in the mean of great numbers of stars for diffe- rent parts of the sky, it might seem for a moment that we might really derive trustworty values of dA, dD and the mean value of h ; — from a treatment of the equations (23). Meanwhile we must Q bear in mind that at all events a new hypothesis has been introduced, viz., that the mean parallax of stars with equal proper motion in different parts of the sky, is the same. If this is not the case the position obtained for the Apex too will be in general erroneous. However there is another and decisive objection to the use of equations (23) if we have grouped the stars according to their proper 1) A practical advantage of our method over Arry’s may still be mentioned here: In Arry’s method the large proper motions have a much more predominant influence on the results even than in ours; This is easy to see from the normal equations to be given in art. 15, ( 366 ) motions, viz: that these equations for groups of stars included between determined, arbitrary limits of the proper motion, howsoever nume- rous the stars may be, are certainly in general not true’). This is evident from the argument given in Astron. Nachr. N°. 3487, pages 100—102, to which we must refer here. The error committed will certainly be different in general for regions with different 4 even in the case that the proper motions are equal. So not only do derivations such as those of SruMPE (Astron. Nachr. N°. 3000) and many others, give entirely illusory determinations for the secular parallax of the stars (as I already tried to show in Astr. Nachr. N°. 3487) but neither can the determination of the position of the Apex be defended. It may even be anticipated with great probability that the error must change systematically with the amount of the proper motion, so that the regular change found by Stumpy in the declination of the Apex for his various groups has nothing particularly surprising. Other writers as i. a. L. SrRuveE attribute determined parallaxes to stars of determined magnitude. The last decisive objection dis- appears here, but not the first. It rans as follows: we assume that at least the mean parallax of the stars of determined magnitude is everywhere in the sky the same. For the galaxy and outside it I have already tried to show, some years ago, (Verslag Kon. Akad. Jan. 1893) that this is probably not the case. To sum up, according to the preceding, AIRy’s method comes to the determination of the coordinates of the Apex and the linear motion of the sun in such a way that the conditions (18) and (19) are satisfied. The first condition does not contain the distances but does not in general satisfy the conditions Sr —=0 for stars in one and the same part of the sky, which must be considered as the principal condition derivable from the hypothesis H. The second condition contains the distances which are in general unknown. ‘This causes the introduction of hypotheses which are more or less probable, and which may easily exercise an injurious influence on the deter- mination of A and D. Particularly the grouping according to proper motion must be absolutely objevted to in the application of Arry’s method, because implicit suppositions are introduced which are certainly not realized. 1) It is even not permissable to exclude stars with very small proper motion. ( 367 ) 13. Method of ARGELANDER. In this method each star gives an equation of condition of the form @t) p= 0 (weight six? A,) They are treated with least squares. So in reality A and D are determined by the condition (25) Sp? sin? Ay minimum, giving the minimum conditions ral 0. JA (26) = psin®d, > p sin? d on 0 aD << s For a single region of the sky the two are reduced to this one (211) ap "0; so that here neither the condition furnished by hypothesis 4 is satisfied. The objection to the method of ARGELANDER consists chiefly in this that the retrograde proper motions have too great an influence. Let for instance the proper motions (4 f “3 44 (belonging to stars in the same region of the sky) make with an assumed direction towards the Antapex angles of +-20°, 10°, —10°,—20°. As long as we know only these proper motions the assumed direction towards the Antapex, both according to my method and to that of ARGELANDER, will be the most probable. If however a_ proper motion «; is added, making with the assumed direction towards the Antapex an angle of 170°, this direction, according to ARGE- LANDER’s method will have to be corrected by 34°, whereas according to our method that correction will be only 2°.1 in the same. direction. Since long it has been remarked moreover that in ARGELANDER’s method too, discontinuous changes in the place of the Apex may be caused by continuous changes of the proper motions, The following example will prove this clearly. In a definite region of the sky there are stars whose proper motion is in perfectly the same direction. This common direction is assumed as the approximate direction towards the Antapex. We now add one star, making with that direction the angle Py = 180 — @ ( 368 ) where @ is a very small quantity. If this is neglected, it follows from (27) that the direction towards the Antapex has to be correeted by 180° n+1- If however for the added star we had Po = 180 + wo = — (180 — a then we should have found for that correction F 3 So there is a leap of ——~. 7 There is again no foundation for such a leap in the nature of the problem, and it does not appear in our solution. 14. Method of Kosoup (Bessel). I need but say a few words of this method, as Koxsonp himself clearly states that his method is not based on hypothesis H. He determines the Apex of the motion of the sun in such a way that the great circle of which the Apex is the pole, approaches as closely as possible to the pole of the proper motions of all the stars. To satisfy this condition he makes = cos? Q minimum, where Q represents the distance from the Apex of the pole of a proper motion. Expressed in the quantities used by us, the condition is (28) J sin? d sin® p minimum. This is satisfied if we write down for each star an equation of condition (29) sind sinp = 0 and then solve the whole of these equations with least squares. This method cannot be tested by the condition (10). It is namely a peculiarity of this method, that whereas, according to the other methods, from stars of one part of the sky, only a direction can be derived, in which the Apex must be situated, we find by Koporp’s method a complete determination of the position of that point. ( 369 ) Its position is no other than that of the group of stars itself. In the choice of the position of the Apex each region votes as it were for itself. Every line passing through this region thus passes through the Apex too, so that at the same time the condition (10) is satis- fied and it is not. This peculiarity of the method together with this second (which exists for stars of one part as well as for stars of all parts of the sky) that for the direction of the motion of an arbitrary number of stars we may substitute a diametrically opposite metion without the slightest effect on the coordinates of the Apex, appears to me sufficient to declare the method unsuitable for the determination of the direction of the motion of the sun. 15. Abridged calculation. It is a very common practice in the derivation of the coordinates of the Apex, to abridge the work of computation by taking the mean of the proper motions of a greater or smaller number of stars situated close together. I wish to point out that in this way the result, derived by means of the various methods, will approach in general to those which will be found by the method proposed here. So, far from having been more or less impaired by this abridged calculation, the results must have gained considerably in accuracy. It must be borne in mind however that m this way, in all methods except in that proposed by me, the principle is sacrificed, at least in part. The proof of what has been advanced here will be best given by writing out in full and in a similar form for the variyus methods, the equations of condifion and the normal equations ensuing from these. I begin by giving them. a. Method of Aiky (as modified). I leave out of consideration condition (19), this being the only one dependent on the distances. As T=T+ (=) dA + (55), =t +) (54) a + U% (54) an ) the equations (16) become Ox 0x 30) w (5%) a4 + 9 (<*) ap = — ( : = 0 aa “0 0D 0 ¥o which, treated with least squares, give the normal equations: 27 Proceedings Royal Acad. Amsterdam. Vol. IT. ( 370 ) ((38),) “4 + 14,032), (¢5),]= —[ (G5), (54, (55),)¢4 + [(55)} = — Lr (55) | 0 They ave of course identical with the equations (20) and (21) if in the (31) xe reduction of these we treat the quantities _— as quantities of the 1) order of dA and dD, b. Method of ARGELANDER. If we reduce to unity of weight, the equations of condition (24) may be writen (32) psind=0 or by writing ram (at aan t aa () (33) sin Ag (£4) dA + sinkg (2 aa dD = — po sinh, , th / 0 which lead to the normal equations: et 22) oa (2) (22) Jun =— a2) 1 (34) | [nal 22) (22) Janae 24) r= fn(%4) which again will be identical with (26), if we treat the quantities po as of the order of dA and dD, ce. Method of Kopoup. By introducing A r sinh = sin A, + cos hy eI dA + cosh, =) dD 0 0 sin p = sin py + cos po (4). dA + cos Po (4) ap the equations of condition (29) become ( 371 ) OA ox _ (0a ox\ | pire Oey (35) feosacsinn (G5 )-tsinavcone ( ) 4st jon sinn( Sp )-tsinascoan( <7) {aD sinng sinpy 0 C which give the normal equations : [feast rt) '] et + {fir 2a 2) ern 2) ihm) ] = [|n( id von) at a \ / a - | cosysinn (54) bsindarona( 4) | coesinpo(o) sindoroapa( $2) / dA + (36) a [he 0sAysinpo (5) 4 sink COSPy (34). ‘i ‘lop ' =— [\eostasinno (SF )-+sindcspe (5%) {sindsino| Let us now assume, as was supposed above, that we take the mean of the proper motions of the stars situated closely together and continue working with these as if they were real proper motions. The effect of thus taking means of a considerable number of motions will of course be, that the peculiar motion, which takes place in various directions, is eliminated for the greater part, so that the mean proper motion found will, with some approximation, represent the mean parallactic motion for the region under consideration. If we distinguish the values obtained by taking means by dashes over the letters, then we will evidently have for the various regions, with greater or smaller approximation (ef. (8)): and consequently If first we take only zones of constant A, and if farthermore ln. ’ é we assume that the mean secular parallax — is, with some approxi- 0 2T# ( 372 ) mation, the same for stars in various parts of the sky, we shall see at once that the effect of taking the mean for various parts of the sky in such a zone of constant A,, is this, that the different v’s will become equal with some approximation, whilst moreover for such a zone, as indeed for the whole sky, + and p become small quantities. If therefore we introduce into the equations (31) of Arry: A = constant Uy = v = constant (37) | To—T ~dy they will become 4 * (ga) 4+ (Ge =— Fe o Blere[ GS) joe ob These equations are identically the same as those into which our equations (14) are transformed, if in these too we introduce the values (37). So zones of the same 4 will furnish approximately the same results if treated according to both methods. Hence the combination of all these partial solutions will certainly not lead to strongly deviating results. A still closer correspondence may be expected between the results of ARGELANDER’s method and the results of the second form of that proposed by us, when by taking means, all the angles are first made small. For if we neglect quantities of the order. p aA ap? dD yp we may write in the second member of the equations (34) py = sin po, so that those equations become, if here again we take a zone of constant Ap, sin? hy (ey | dA + sin? ie a dD = — sin* ho Ea ax) sin? AG a i) dA + sin? A, (Cue eee, Q S | | a Sk 22 aia A $s ~ os} INI a) (373 ) which equations are identical with (15) if we introduce in them the same suppositions. So, here again we find, that zones of identical 4, wil] lcad to approximately the same results in the two methods. What hoids for each of the zones separately, must also hold with some approx- imation for the final results. For Kosonp’s method the approximation will be sormewhat less satisfactory. For here we must neglect terms of the order pdA, pdD, p* to gain our end. If we do this, the equations (36) will become 9 sin? Ap (ey HAO sed Ee | dD = — 2 sin®), [airp 2 2 sin? Ox Ox) on IVa Se eee * | aA dA + 2 sin? Ko (54) dD = — 2 sin” Ay sin p 4 which are again identical with our equations (15) if we introduce in them the same suppositions. Zones of identical 4 treated according to both methods giving approximately identical results, this must lead here also to pretty nearly the same final results. The calculations of KoboLp (Astr. Nachr. N°. 3592) confirm this conclusion. The solution which he makes with mean proper motions is the only one which is in a somewhat tolerable agreement with what others have found, calculating with other methods but also with mean values of the proper motions. Koso.up finds A= 26228 D= + 16°.5 ‘ L. Srevve finds A= 273°.3 D273 After all that has been said the conclusion is pretty obvious that what, perhaps more than anything else, must hinder us in accepting the methods used until now for the derivation ot the direction of the solar motion is this: that quantities are treated as small ones, which in reality are not small), ?) From an utterance of Prof. Newcoms I conelude that he too ascribes the deviating result of Kosoxtp to the reason here stated. 16. Values of the differential quotients used in the preceding articles, ah ; ; a : The following formulae may serve for the various differential quotients used in the preceding equations. (lor the meaning of the letters see fig. 1). 0% cos D cos O JA sinh 0% cos 0 sing, 0D cos D sina OA Y si — = — cos 0 sin oA oA D = — cos O where %, 4 and O are to be computed by sinh sin ¥ = sin (a@ — A) cos D sin A cos 4 = cos (@ — A) cos D sin 0 — sin D cos 0 sin A sin O = sin(a@ — A) cos 0 sin A cos O = — cos (a@ — A) cos 0 sin D + sin 0 cos D. A few observations of Prof. JAN DE Vries and Prof. J. A. C. OuDEMANS were answered by the lecturer. Mathematics. — “On twisted quintics of genus unity.” By Prof. JAN DE VRIES. 1. By central projection a twisted curve of order five and genus unity can be transformed into a plane curve of order five with five nedes. Consequently in each point of space meet five chords or bisecants of the twisted curve &;. If the centre of projection is taken on R; a curve of order four with two nodes is obtained. From this ensues that through each point of Rk; two trisecants may pass. 2. The bisecants that meet a given right line / form a surface ee ( 375 ) A, on which J is a fivefold line. Ten chords lying in every plane through J the scroll .4 is of order fifteen. Besides the fourfold curve FR; the scroll _/ contains a double curve of which we shall determine the order. If the points 4; (¢=1, 2, 3, 4, 5) lie in a plane with 7 then the fifteen points B =(4;4;, 4,4,,) belong to the above mentioned curve. In order to find how many poinis B are lying on / we assign the point common to / and 4; 4; to the points common to / and the right lines AjAm, Am4An and Andi; hereby we create a corre- spondence (15,15) between the points of 7. Two corresponding points only then coincide when a point B lies on J. In the correspondence there are still thirteen other points which differ from B agreeing with such a point; so & represents fo coincidences. Hence / con- tains fifteen points & and the above mentioned double curve is of order thirty. 3. If 2 has a point-S in common with R; then 4; breaks up into the quartic cone, with centre S, standing on /, and into a surface 4,, on which &; is a threefold curve, / remaining a fivefold line. Moreover by a very simple deduction it is shown that now the double curve is of order eight. 4. If J becomes a bisecant b the surface 4; contains two quartic cones. The remaining scroll 4; has the fourfold line 6 and the double curve &;. The double curve (#2) disappears here. By assigning each of the three pomts of &; lying with / in the same plane to the chord connecting the other two, the chords of the scroll 4; are brought into projective relation with the points of &;. So any plane section of 4; is, just as R;, of genus unity and must have fourteen nodes or an equivalent set of singularities. This curve has five double points on #; and a fourfold point on 6, Evidently the missing three double points can only be represented by a threefold point derived from a threefold generator of 47, 1.e. from the trisecant of the twisted curve. So a bisecant will be cut only by one trisecant. 5. As 2 meets in each of its points of intersection with the curve two trisecants, the trisecants of Rh; forma scroll T; of order five of which #; is a double curve. Evidently 7; can have no other double curve, so this surface is also of genus unity. ( 376 ) Two bisecants meet a trisecant ¢ in each of its points whilst each plane through ¢ contains a chord. All these bisecants form a cubie seroll 4, with double director t. The single director u is evidently a unisecant of /;. On the scroll .%; determined by w of course ¢ is a part of the above mentioned double curve. Each of the double points of the involution determined on u, by the generators of 4, procures coinciding chords; consequently w is the section of two double tangent planes. 6. A conic Q) having five points in common with &; is not intersected by a trisecant in a point not lying on &,, for in its points of intersection with 7; it has ten points in common with 7;. The surface J” formed by the conics @., the planes of which pass through the line c, is intersected by each trisecant in three points; so I’ is a cubic surface. The right line ¢ meets five trisecants lying on J's, hence also five bisecants belonging to this surface. As e¢ is intersected by the conic Q: of J in an involution, there are two conics Q, touching it. When ¢ becomes a unisecant then its point S on P, is a double point of J°;. Besides ¢ still five right lines of 1; pass through 4, two of which are trisecants; the remaining three must be bisecants completed to degenerated conics Q, by the other trisecants resting on e. If ¢ becomes a chord, J; has two double points, each of which supports two bisecants belonging to J, and two trisecants also lying on the surface. If finally ¢ is a trisecant, 7°; becomes the above mentioned surface 3. So: All conics Wg intersecting two times a given right line form a cubic surface. 7. The conics Qg passing through any given point P form a cubic surface Il, with double point P. For only one conic Q, passes through P and the point S on &;, as PS is a single line on the cubic surface 1; determined by PS, From this ensues that R; is a single curve of the surface J/;, so that this is intersected by a trisecant in three points. And as a right line through P has in general with only one conie Q) two points in common, one of which is lying in P, P is a double point of J/s, On this surface lie the five bisecants meeting in P, moreover the five trisecants by which they are completed to conics. The quadratic cone determined by these five chords intersects 77; in a right line p, on which the mentioned trisecants rest; so p has no point in ( 377 ) common with &;. Moreover any given right line through P deter- mining only one conic Q» of J/;, the planes of the conics @: on 7), must form a pencil; the planes of the above mentioned degen- erated conic @, pass through p, so p is the axis of the pencil. The remaining ten right lines of //; are evidently unisecants of 75. 8. The axis p determined by P cannot belong to a second sur- face J/,, for the five trisecants resting on p determine together with p the bisecants intersecting each other in P. If P lies on R,, p is quite undeterminate. The point P being taken on a trisecant t, through that point two bisecants pass forming with ¢ conics Q:; the axis p coincides with t, which follows as a matter of course from this, that //; becomes the surface ./; belonging to ¢. 9. If P describes the right line a,, the locus of the axis p is a cubic scroll Q;, of which a, is the linear director. For if P' and P" are the points common to a and Q,, then this conic lies on the surface J/;' and 17," belonging to P' and P"; so its plane contains the corresponding axes p’ and p". To Ag evidently belong the five trisecants resting on a; in the points common to #; and these trisecants ?; is cut by As. They moreover meet the double director ay of Az. These trisecants lie at the same time on the scroll As’ having ag as linear director; on this surface a; is the double director. The right lines a, and ag correspond mutually to one another. If a, is itself an axis, each plane through this right line contains only one axis p differing from a. In that case the surface A, be- comes a scroll of CayLey and a, coincides with a). In the correspondence (a), a) each axis is consequently assigned to itself. This also relates to all trisecants, as each of these must be regarded as an axis of each of its points. 10. The five trisecants cut by a, and by ag also lie on the surface J’, determined by ¢,; so this contains the right line ay as well. Therefore both axes p' and p” lying with a, in a plane w cut each other in the point 9 common to ag and the conic Q, deter- mined by @. From the mutual correspondence between a, and a, we conclude that I, also contains all the conics Q,, the planes of which pass through a. Five bisecants belonging to I, rest on ag. If according to a well known annotation we call the five tri- secants consecutively 3, by, 65, ¥¢ and cj, then the five bisecants resting on a are indicated by ¢y3, ¢14) ¢j5, ¢ig ANd Dy, and ay meets the bisecants ¢g3. ¢24) ¢25, Cag and Dy. It is easy to sce that the remaining ten right lines of 1, viz. 31 Ay. As, AG, C34y C51 C3gs 459 C4o. sg have each one point in common with R,. 11. Let P be any point of the conic @Q, meeting a in P' and P", Now the axes p and p' must intersect each other on Q); so p will pass through the point O common to p' and p". Consequently the axes p lying in a plane @ pass through a point O of conic QQ, determined by o. As 9 has been found to describe the line ay if w revolves about a, O and w are focus and focal plane in relation to a linear com- ? plex of rays of which a, and ag are conjugate lines, the axes p and the trisecants ¢ being rays. 12. The conics Q) which cut R; in P and P' forming a cubic surface, a right line / having @ points in common with 2; meets the (3—«) conics @: through P and P’. So R; is a (8—e@)-fold curve of the surface 7, containing the conics Q: which pass through F and rest on /. As a trisecant can meet none of those conics in a point not on 2, @ is a surface of order 3 (8—a@), Of the 3 (8—e«) points common to @ and the /-secant m 2 (3—a) lie on &;. The remaining (8 — a@) (3—/2) points of inter- section determine as many conies Q, resting on / and on m and passing through P as well. From this we conclude again that all the conics Q) cut by / and m will form a surface ¥, on which 2; is a (83—@) (8—/?)-fold curve. Then however “ must be a surface of order 3 (3—a) (3—/2). If we now notice that a y-secant x is cut by ¥ in (8—a) (83—/)y points lying on #;, thus in (8—a) (—/) (3—y)-points not lying on this curve, it is evident that three right lines having respectively a, 2 and y points common with R; determine (3—e) (3—/?) (3—7) conics Qs resting on these lines. So any three bisecants meet one conic Qs only. 13. Let C, be a conic having xo point in common with &;. The surface J/;, with its duuble point P on C,, cuts this curve still in four points P’; consequently C, is a fourfold curve of the locus = of the conics Q., each having two points in common with C3. The conic @ lying in the plane @ of C, belongs six times to the section of = and @. Moreover as each bisecant of FR; lying in @ determines a conic Q, of =, this surface is of order 4 xX 2+ 6x 2+4+10= 30. Through the point Sz of R; lying in ® ten conics Q. of yo, pass, viz. the four conics determined by the chords S; S; and the conic @, to be counted six times containing all the points Sz. So A; is a tenfold curve. If C, breaks up into two right lines / and m intersecting each other in YP the locus consists of the cubic surface //; belonging to P and the surface 9; formed by the conics @: resting on / and m, And now according to 12. the curve R; is a ninefold curve of 77 and according to 7. a single curve on //;; so in accordance with what was mentioned above it is a tenfold curve of 23, = Wo, + 113. As Cy and Rk; have @ points in common, we find in a similar way that the conics Q, which meet Cy in two points not situated on #; form a surface of order °/,(4—@)(5—«), where &; isa curve of multiplicity 1/.(4—«)(5—@), C, being a (4—«)-fold line. 14. We shall still determine the number of conics Q) resting on the @-conic Cy, the f-conic D, and the y-conic £4. The surface 7’; of the conics Qs, cutting R; in P and P', and Cy have (6—@) points in common. So &; is a (6—a)-fold curve of the locus of the conic Q:, passing through P and meeting C,; so this surface is of order 3 (6—a), Of its sections with D, a number of (6—«@) (6—/) are not situated on &;, which proves that R; is a (6—a@)(6—/)-fold curve of the surface of the conics Q) resting on Cy and P,; so this latter surface is of order 3(6—a) (6—/). Consequently there are (6—a)(6—/)(6—y) conics Q, having a point in common with each of the conics Cy, Dy, Ep. In particular any three conics Q, are cut by one conic Qs only. Physics. — “The cooling of a current of gas by sudden change of pressure.” By Prof. J. D. VAN DER WAALS. If a gas stream under a constant high pressure is conducted through a tube, so wide that we may neglect the internal friction, and this stream is suddenly brought under a smaller pressure, either by means of a tap with a fine aperture, or, as in the experiments of Lord Kenvin and JouLe by means of a porous plug, the ( 380 ) temperature of the gas falls. For a small difference in pressure of the gas before the tap and the gas behind the tap the amount has been determined by the experiments of Ketyin and Joutn. They represent the cooling 7,—7 for air in the empirie formula: oye P\—P2 if ara 1 — h: ~— l ” LT? By means of the equation of state we calculate for this cooling !), again on the supposition that p, and po are small: 7p pee ae 273 2a ») ( ) 1 ere ey Gece a ) Pi—P2 In this formula p,; and p, are expressed in atmospheres, m is the molecular weight, c, the specific heat at a constant pressure for the gas in a rarefied state. If in the equation of state a is a function of the temperature, ; ey and is to be represented by a me ie should find, if 7; and 7, do not differ much, and p,; and pg are small: 9 2 io 273 \2 ; L—-f, == = E a( = ) — o| (rp ) m ep T; 5 It is still doubtful, which of those two formulae better represents the observations of KeLyin and JouLe. It is-remarkable how dif- ferent a value we find for this cooling, as for everything which relates to quantities of heat, if a is a function of the temperature. The accurate knowledge of this process has of late proved to be more necessary than before, as Linpg has applied this process for obtaining very low temperatures and as in Linpp’s apparatus this way of expansion is made use of to obtain liquid air. Let us represent the energy per unity of weight of the gas under the pressure p, by ¢,. Let the specific volume be v, and the tem- perature 7,. For the gas under the pressure p, we represent these quantities by &, 2, 72. Then the process is represented by the formula: & + pi —Pr2 = & eS i Ome ee WY) or 1) Die Continuitit etc., Ite Auflage Seite 123. ( 381 ) & + pir) = & + po % With the symbol 7 =«-+ pv chosen by GIBBS, we may represent the process shortly by YR SFR} 0 The vis viva of the progressive motion may be neglected, if the velocity of the motion is small. Moreover the section of the tube before- and after the tap may be chosen in such a way, that the velocity may be considered as invariable. We may therefore represent by ¢ the thermodynamic energy of a gas, being in equilibrium. de {4 ae From the equation: (=) Sl (<7) —p we find, if we assume v/T Aa) RT a f(T) as equation of state: p= - —- : v—b v c= 9(N—“~[f@y—Ty(2)) . U Vv The meaning of g(Z) we find from ¢, = (=) from which ar tg } follows: a Es ORO) a aay Vv The meaning of g'(7) is therefore the value of the specific heat at v=, which we shall represent by ¢_) . If we think the substance in a very rarefied state to consist of molecules, which do not change with the temperature, we may put ¢ == pn (i) = . v=o constant and sv p(Z’)== Te_ . The quantity « is: a 6 Leo == [s(2)— TPE) ; v q If we write: aD a pu = RT + RT —_ — —_ f(T) , v—b vo” the value of 7 becomes as follows: ( 382 ) ary mest’ ah b 2f(1)— Tf (2) + RA [ v—b oe a v6 — (ee -{- h) — = v or v—h ; l gar re [24 = rf'(2)| 4 ORT ae p=0 DAL Making use of this value of 7, we deduce from 7; = 7 the following formula: : af (2) — rf (2)| = 1 = vj —b \ \ a >) PY ry Yorn = is (264) — Ty J (1)|— ae lv, ‘ Vg If we want to keep a and }b at the value which they have in the equation of state, in which the pressure of one atmosphere is chosen as the unity of pressure and the volume which the unity of weight of the gas occupies under that pressure and at 0° as unity of volume, this last formula assumes the following form: ryy Ty 2 (2 € A Ae Bl ia al a Ag RTMb | ep (TT) = 278 | [2 f(D) — HS (T)] —— — m (ry vj—b { 2 973 (2 Tes Tr) Vote RT ob ) - 3} [2s — Br) |— 5 RT, b Let us think. vg so great that the quantities = gn as Stor Vo V9 — (1 + a) (1 — 0) (1 + ety) b ‘ 2 Us 6S Ss co) may be neglected, then the cooling is Ug = b ; : : i RTb determined by the value which oe [va 4 | — 5 possess- v7) oT es. If at given 7, we make the value of v; pass through all the values from v) =o to v= 6, and if we think 7, chosen in such a way that: «2 — AFM] > A+ 9-H +an)2, the value of the expression : al RTb vy roar b lercn) = Ay ea) = Cal ( 383 ) will begin with zero; then this expression will obtain a positive value, which rises to a maximum; after which it will diminish again and after having passed through zero, it may even become negative. It appears from this remark, that at a given value of 7, we may give to %, and so also to p,; such a value that the cooling has its maximum value; or in other words there is a most advanta- geous value for p; in Linps’s apparatus. The existence of such a most advantageous value follows of course by no means from the approximated empiric formula of Lord Ketviy and JouLe, which is generally used to explain the Lrypg-process. Yet the existence of a most advantageous way of working has been observed, but it is ascribed to a quite different cause. So we read in , La liquéfaction des gaz. J. Cauro, pag. 33” about this what follows: ,Comme yla production frigorifique de l’appareil dépend de la différence de »pression p;— Pp, avant et apres |’écoulement et que, d’un autre ,coté, le travail de compression est fonction du quotient de ces m 3 Pi ‘ ‘ 9 * at ; ,mémes pressions eo il est clair, que lavantage est d’ avoir une ygrande différence de pression, mais en méme temps un rapport ,yaussi faible que possible entre ces mémes pressions.” In this phrase very great importance is attached to the quantity of heat, which is developed when the gas, returning under the pressure py, 18 again compressed to its original pressure p, — and this heat is in fact, considerable, and the more considerable the smaller pg is at given p). It is even greater than the heat which is annihilated when the pressure is lowered to p:. But in the appa- ratus of Linde the arrangement is such, that the developed heat is given out in quite a different part of the apparatus, from that where the cold is produced; and the gas heated by compression loses this heat before it reaches the cooling-spiral, so for instance by passing through the cooling mixture, which serves to dry the gas. And if this, were not sufficient for taking away the heat which is pro- duced by compression, it would not be difficult to find more effica- cious means. But in the quoted phrase the usual mistake has been made, against which I will warn here, viz. to put the cooling proportional to (pi—p2) —— or to expect at any rate that the cooling will always inerease with the increase of p, — po. In order to find the condition which must be fulfilled that the cooling be maximum, we may consider 7; as function of 7) and p, and Zg as function of 7; and po. The value of 7) we think ag ( 384 ) being given; also the value of p:. We get from: RA = 72 07 0X2 eS dp, = ee) dT," Opi 77, 073 /p, If 7, is to be a minimum and therefore the cooling a maximum, Ae ae then (4) and therefore also () must be 0. opi 77, du, 7 7, Pi Gat C= Therefore: or g Vy CF SU fp | RT ee ED ad es fel (ED) nee (1) ial 4 (, — 0)? If a is thought to be constant, this equation becomes: 2¢ = Mo ee ee) vn (v, — 6)? ; 273 If, however, @ is taken as a Spee CLaAusius does for CO, we find : 3a ae + a)(1—)d) (1+ at,)? ye (x, — 6) In order to avoid needless calculations, I shall in what follows oaly examine the consequences if @ is put constant. Then we find: 2a PAC tbe v} 2 ran 2 i 48 Le (a 15a) (1 =) leat) ee If we had sought the value of », for which the value of pv is a minimum, we had obtained ; From this appears that the value +, for which a maximum value is obtained, is the same as that for which pe has a minimum value at a temperature equal to half 7}. ( 385 ) If we had calculated the value of » for which the cooling is 0, a b always on the supposition that — and ia may be neglected, ; Uo oh we should have found: v7} 2a OH od her P= ea ead aah). 2 Ts while we obtain for the value 2, for which pv, has again the limiting value /7;: v! a Die as 7 he (2c). Shae 4. T Here again we arrive at the result, that the value of 7, for which the cooling == 0, is the same as that for which pv has again SS slab eerie , 1 the limiting value at a temperature of —. Through this remark we are able to conclude also to the cireum- stances of the discussed cooling, if we know the course of pv. Thus we find both the minimum product of pu and the value of 27 Dui ele ta by som 7 == = T, — and we find the maximum cool- ing and the cooling = 0 also if v=o at a temperature which has twice this value. This means for the product pv that it is found greater than #7 for every finite value of v and for the cooling ; 27 that it is negative for every value of v. At Nr — 7, the conse- quence of the process, in which 7; = Za, will be ha the oe sis heated when it flows out. As for ena we may put T= 40°, the gas will be heated at 7 > 270°, so this must have been the case in the experiment of Lord Krtyvin and JouLe!). As the experiment was made at t= 17° or 7= 290°, only a slight increase of temperature may have been observed, if we have determined the ‘imits of the temperature correctly. If @ is considered as a function of the tem- perature, these limits are rendered by other ratios. But the existence of such a limit of the temperature is beyond doubt. When 7 is lowered, the value of » becomes smaller, as well for the maximum cooling, as for the limit between cooling and heating. 1) See also KaMERLINGH ONNeES, Verslag Kon, Akad. Febr. 1895. Proceedings Royal Acad. Amsterdam. Vol. LI. ( 386 ) If we put eg. 7 =27,, which is the case for air that is cooled somewhat below 0° centigrade, we find for the value of v for the maximum cooling 2,26, and for the value of v for a cooling = 0 7 an amount = 76 b. For 72 =T, these values have decreased to 27 /5b and b. By elimination of 7 we find for the locus of the points of maxi- mum cooling in the p,v diagram: 1 If we put —=g (density), we find the parabola: 5 a F z p=— (20—3b¢"), eal x which yields p=90 for g=090 and for g= mig The maximum ‘ : i eae a value of p, which is found for as equal to spo to 9p,. For air (which we treat here for simplicity’s sake as a single substance) this minimum pressure amounts to 9 & 39 = 351 atmospheres. ; To the existence of such a parabola for the points, where pv has a minimum value, has been concluded by Betrrami from the obser- vations concerning pe of AMAGAT. For the points, for which the cooling = 0, we find: or a 9 9° j= 5 (2 v—b y*). So also a parabola in the p, g diagram. By elimination of +; we get a relation between p, and 7), which has the following form : pi = 27 pb — ee [3 a ae (387 ) We find the maximum value of p,; at T= 3 L,, and as has been mentioned before, it is equal to 9 p,. So for air 9X 39 = 351. For T=2 7, we find p; = 304 atmospheres, and for ih — eel Pp, = 100 z The constant value which has been chosen in the apparatus of LINDE, may be considered as an arithmetical mean of the most ad- vantageous pressure at the beginming and that at the end of the process. But at the same time we may conclude from the circumstance that p; is a function of 7, that an apparatus, whieh would work theoretically perfectly, should be able to regulate the pressure p; according to the temperature which reigns in the inner spiral. The numeric values of the pressure, and the limits of the tem- perature which have been found, will be different according to the equation of state which is used. But though we cannot warrant the absolute accuracy of the numeric values in consequence of the in- accuracies of the equation of state, yet we may prove, that from every equation of state, which properly accounts for the course of the product pv, as found experimentally, the existence of a pressure, for which the cooling is equal to 0, follows, and so also the existence of a pressure, for which the cooling has a maximum value. For as long as p,%) << pet, the resulting external work will promote cooling. This influence is greatest for a pressure, at which pyr, has a minimum value. If p, 7) is again equal to p2 v2, the cooling has the same value as it has in case of perfectly free expansion, But if the pressure is still higher, ») 7 rises above po v), and approaches infinitely to a limiting value which is «©, so that every cooling which would be the immediate result of free expansion, may be neutralized by that of p, v7) — pp %,. Only if we should assume also an infinite value for the cooling caused by free expansion, the above reasoning would not be convincing. But then, nobody will assume this. We may represent the maximum cooling in the following simple form : Qe tae ela b\?2 1,—-1, = ( ) m Cp b v} or ee eet 2) Vaal 2 an Cp EK Bey kM) or = f a) ALE, ( Va 4 Te 1, = — a fs 5 mie ( 388 ) From this we find at 7; = 27, the value 55°. Properly speaking we ought to subtract a certain amount from this 55°, because the opposed py may not be neglected. Let us put it at 0,265 x 20. Then we may at 7;=2 Ty put the cooling at 50°, if the opposed pressure amounts to 20 atm. and p, has the most advantageous value. According to the approximating formula we should find somewhat more than 75°. For decreasing values of 7, the maximum value increases, as Se | Ni aes ay increases with 7). Ty. ASOT aT) ipa Che ep Diiely { : T,—T ; - 2 it appears that if ~~ hes the same value, ——— has also the same x “4 value for all gases for which me, has the same value, and this is the case for all those whose molecules contain two atoms. If we write: m Cy (T;—T,) __ 27 f ith | Ape T, 2/ 27 Ty, S D we conclude, that at the same value of = the heat annihilated by x the expansion is for all substances an equal fraction of 7, of 7), and so of the vis viva of the progressive motion. It need scarcely be observed that if the expansion could have taken place in an adiabatic way, the cooling would have been much more considerable. From the equation of state: a : \ Tul : (p a 5) (v0 ) i fils follows for the course of the isentropic line: (45) (=e. : ; op Re rie : in which z represents the value of & at infinite rarefaction. Cy By elimination of p we find 7(v— b)*#7I=C,, ( 389 ) If we take 7,;= 27; and for v, the value for the greatest cooling according to the process 7%; = %, SO %; = 2,26, and for v a value, which corresponds to pg = 20 atm., then even by this one expansion the air wouid have been cooled already far below the critical point. Lord RAYLEIGH has already pointed out, that the process of LrypE might be improved by causing the expanding gas to perform more work. It remains therefore desirable to find an arrangement, by which the expansion approaches more nearly an isentropic process than is the case in the apparatus of Lrnpr. Physics. — Prof. J. D. van pER WAALS presents for the proceed- ings a communication of Mr. H. Huxsnor at Delft, on: “The direct deduction of the capillary constant 6 as a surface- tension.” The amount of the capillary tension and the capillary energy, as found by Prof. van DER Waats in his Théorie Thermodynamique de la capillarité, may also be determined directly. The existence of capillary tension is undoubtedly the consequence of molecular attrac- tion. Therefore we shall have to examiae the influence of molecular attraction in the capillary layer, i.e. we shall have to determin > the value of the molecular pressure for an arbitrary point of the capillary layer. The equation of state gives ag? for the value of the molecular pressure; the equation of state, however, comprises only those cases, in which the distribution of matter is homogeneous. As the molecular pressure is the direct consequence of the attraction, which the particles exercise on one another and is therefore deter- mined in a point by the condition of the surroundings, it may be expected that for not homogeneous distribution of matter the molecular pressure in different directions will have different values. The existence of capillary tension is to be ascribed to the fact, that in the capillary layer the molecular pressure in the direction of the surface of the liquid is different from that in the direction normal to the surface. When the matter is homogeneously distributed the molecular pressure per surface element do is equal to the foree with which all the matter on one side of the plane in which do is situated, attracts in the direction towards this plane the materia! cylinder with do as base, situated on the other side of the plane. In the capillary layer we can also define the molecular pressure in the same way. (390 ) Therefore we shall determine the molecular pressure in a point 4 of the capillary layer: a. in the direction normal to the surface of the liquid; b. in the direction parallel to the surface. a. Through A we lay a plane parallel to the surface of the liquid. The foree with which the layer of a thickness du, parallel to the separating layer, at a distance « below the plane laid through A, attracts the unity of mass /, 2;¢M above this plane, is: —dy(u+h), on the supposition that the examined layer has the .unity of density. The density in a layer parallel to the surface of the liquid is the same every- where. We give there- - fore, the density asa function of the dis- a tance from the plane en laid through A. If we call the normal / and take as positive direction that one turned towards the vapour phasis, so that 4 = 0 is situated in the homo- geneous liquid phasis, the density of the layer with a thickness du will be: do u? dy g—u -—- — ete: dh 1.2 dh* dg dg : ahd ‘ where vg, —, — have the values which these quantities have in dh? dh? point A. For all layers below the plane through it, the attraction is: ue 2 2, do ue do } - C i se =) eral u=0 Let us imagine in f/ not the unity of mass, but let us consider there a volume-element with a thickness of dh, and for the sake of simplicity with a base of 1 em.? instead of do. The density of this volume-element being: ( 391 ) = h,? d’o Eee ett: Cabin! goa the attraction which is to be calculated may be represented by: - j do h,? =) i ai oe ue do ; ; (¢ eh ny a sed AD) at Can Lavan? 2) ee aaly 0 “= 0 = odw(u+ hh) = ew (hy) uv—0 u—o —" dg rs dyw(uth)= ee —w(u+h) m)| — — ae (u + hy) du ‘ L uo ie u—Q The integrated term is zero for the two limits. uo ie “a do j u ~~ 12 dh? +h) = |-; sae ve A] + YH 0) u=0 Hie: a w(u + hy) udu u=0 The integrated term is here also zero for the two limits. The integral becomes therefore: do hye a ; (¢ +h, — FF + 12 Ae dhy le wy (hy) — — ore + hy) du +- 0 (1) (2) (3) qa’) 0 (2!) Po a de. wy (u +h) u au| SO (3) 2) f eme w (hy) = ¢? [wd ahy = ag? Seateueee. ==; - GL) aCls) 0 0 ( 392 ) ~| g dh, — a yw (wu +- hy) du = — yt a as y(u + hy) du = 0 uO v= '0 4 2 ‘fm f antes Moe re 104) (C2 u=0 We put yw (uv) du = — da (uv) and suppose, as is usually done that m( co) is equal to zero. The latter expression may be transformed into: do —o Th fa (1) dh, = = 0 aca) —— yt fi w (h,) dh, 0 0 0 The integrated term is zero for the two limits. fem ae 8 fe (u + h)udu= — wa fe fee d. mt (u +- hy) = u=0 u=0 =—¢ ae fim E a (u + i,)| + ¢ oo Be (ai ee (uth)du...(1)(3) dh* a) u=O0 0) u=—O0 Here too the integrated term is zero for the two limits. We put (7) de=— dy(x) and suppose as usuai that 7 (0) = 0. The latter expression may. be transformed into : u—— © D u—@& do i‘ Ooi. 5 0 Tie. a i, fa ZAtuthy=—eo Tie. dh, |x (u + i,)| = o 0 u—= 0 0 i u=0 2 do do —— 0) The. (hy) dh, = 0 0 a €li, 94 (i)| a ua mc fh 7m (hy) dhy. (Lhi~ 0 The integrated term is zero for the two limits; so the expression becomes: 2 = h,? Po h,* i “ha? Lo 4 ¢ 4 ae oot fauna. va aly ole @ay “ly ¢ el w (hy) thy 0 0 0 ( 393 ) The integrated form is again zero for the two limits. + d dg © ; fia = ow(h;)dhi=¢@ % fi wi(h})dh,. - . (2)(1) 0 0 y= un (ge es = hy as E fiv(uph)du=— (\ sy | J finan, fit) te = u=0 0 u—0 uo u— 2 d. = (zi) Son fe a (uth) = (2) ium |z@+h)] = = ic (} u—0 u—0 dg do \2 . h,2 — (28 fi ah 2 y= — (ST) J (id. += 0) 0 sey Lae (se) (a wana .. 2) 0 0 The integrated form is zero for the two limits. fo) “hy? tO do “hy ie Sy Os ON aaa = ()(0) 1.2 dh? dh? 2, ° 0 w uo uo ; dy * ode a yaa dy d v ] 1 ( ] ; ara = — u udu — j du .(2)(: fa Fi; ai de” ‘ ee A eaTe fi i fe (u--hy) udu . (2)(3) 0 u—0 0 u—0 D This expression has the dimension f tab a Gad at and will be 0 neglected by us as well as (3) (2') and (3) (8’). For the molecular pressure in the direction normal to the surface of the liquid we find therefore : do 7h BP 2 — oF a yw (h) dhy + GE — aah L w(hy)dhy ao poe fi w(h,) dh, — dh . dh? J 2 ~ dh 0 0 0 a 1'~ do “hy? 2g hy? -(#2) (> > Wy) hy + 0 a5 ie w (hy) dhy 0 0 or ( 394 ) Fi TO ~ do 2 “hy? ag -+-¢@ me fae y (h,) dh, — (=*) \ ns wy (1,) dh, 0 0 We put ff w (h,) dh; = c, and es w (h,) dh, = eg, therefore the ex- 0 ° pression for the molecular pressure is transformed into : P do? oe! + ees — 3a) 2 \dh If we add to this molecular pressure the external pressure p,, we may equate this sum to pag’, if p represents the pressure, which belongs to a homogeneous phasis with the density go. I y if ta pit ag? + eek ~S(2) =p + ay! Lh? dh do Cy & i Pi AP ae igs mera a This relation is the same as has been deduced by Prof. vAN DER WAALS. b. We shall now calculate the molecular pressure in the direction of the surface of the liquid. For this purpose we suppose a plane laid through A, normal to the capillary layer, and in A a cylinder with a thickness do normal to that plane. The matter in the cylinder has everywhere the same density. The unity of mass in ¢ acts on the unity of mass in S with a force (7), if r represents the distance Sc. The component of this force in the direction normal to PQ dr . is p(r) cos Sca or —p(r) = if we — dz Fig. 2. call the direction ab the direction z. The material cylinder ab 1 PQ, with a thickness do’ and with a ( 395 ) unity of density acts therefore on the unity of mass in S with a force, of which the component in the direction L PQ is: r—@ DR ir : 4 w' fy (r) . dz = do! yv (vr) dr = do'C (7), az 4 ra where we assume that d.C(r) = — p(r)dr and C(a)=0. Let us now imagine in the plane PQ a system of polar coordi- nates with A as origin and the line L to the paper as fixed axis. We take as surface element y dy dp. Let the density in A be 9, then in an arbitrary point of the plane PQ the density is: by x do ld... ( — Y Sin @g— — — YY” 8inrn~ | sutehrel ve OUT td © heap al EO yey od Ra SS : ; dQ ss : It is easy to see that if the terms g + an Ue g alone existed, ah the attraction which the substance right of PQ would exercise on the unity of mass in the direction £ PQ, would be the same as in case of a homogeneous density 9 and therefore : gw (W) We have still to add to this attraction: eed Ou ey. 5 - x aie y? sin® py dy dp f(r). 27 [sve gpdp=—n 0 and so the expression becomes: 1 de “ x 1 hy os 9 9 7 we fe (r) wy? dy = aro 2 0 € (r) (r?—u*) vr dr 0 r=4& for 2 = w+ y*? and so rdr=ydy. For this latter expression we may also write : ( 396 ) lL” .do fr } =F aa (r2—u?) d w(r) = r=u r= r=— Be: 70 ee 1 @&e = [-4 Bevo] + 5 Fb fvore. r—u 4 This. integrated term is zero for the two limits. D So we find for the component of the attraction LP.Q: ‘~~ 1 @& ew (uw) + £e Fy) dr and therefore for the attraction of the cylinder: DR do | oO du | 0 gy (u) oS “3 ae (r) rar] u and for the molecular pressure in the direction of the capillary layer: Pn 1 @ { o du le w (uw) + Bt aie { wi(r)r ar| 2 . a A ¢ “ 0 u This expression becomes : a0 (u) d Ye fi fe 7 e 2 (= = / dma (r Oo fv 1) du ae ae. sia rd (r) i) u“ 0 The latter term may be transformed into: Lao ; (x) *: 1 aay (- eye — — 0 7 | en 7 — au TN?) ar = ott Fn 2 ae) JS 0 u 0 u 1 @e fe (u) iG Pos gv - (u) d —i — uw) du => U = 5 0 a, uw 7 (1) dere li u) da 0 0 i ee eee oe Le a 7 = — 09 — u) du - A 0 die. ut (1 3 FA 2] + — 3 ¢ dee um (u) du 0 0 0 C307 } The integrated term is zero for the two limits and so we keep: D ao azo. 1 d20 = bow C. ke Gs ) mall 2um (u)du= ls 0 “a u? mw (w) | -+ Sy Q “5 | uw (u) du. 0 0 fn) Also this integrated term is zero for the two limits. We find therefore for the molecular pressure in the direction of the capillary layer: ; Po + Q° fv (u) du + 3¢@ x ss fe w (wu) du age ae aha 0 A or oe Cons 2 eens A Sane The pressure in consequence of the attraction has therefore an- other value in the direction of the capillary layer than in the diree- tion normal to this layer. In the direction of the capillary layer a surplus of molecular pressure will exist in consequence of the attraction. This surplus will amount to: 24 2 do -. d*o Co (2 i IS LS SE Sa CT teh Gee 7 Ua PRN eNO or Cope G20) €y (do? 9 © dh? F 2 Ce ; This surplus of pressure taken over a surface L to the bordering layer whose length in the direction of the capillary layer is 1 em. and whose breadth is equal to the thickness of the capillary layer, furnishes the value of the capillary tension : ( CoO C9 ( do y Liye aes Siecle fe 2 o dh? 20 on any) which integral is to be taken over the whole thickness of the capillary layer. We may make also another representation to ourselves of the capillary tension. Let us bear in mind that the thermal pressure des Ak i = — yim any point has the same value in all directions. If now ———{!) in consequence of the molecular attraction the molecular pressure ( 398 ) has different values in different directions, the condition, which is thereby brought about, may be compared with a condition where the pressure has a different value in different directions. If we call the quantity which is to be considered as the pressure in the diree- tion | to the capillary layer, p, and that in the direction of the capillary layer, the following formula would hold: 9 dy 2 ee I? i) Lo pra ag? sete ze (4 9 © aie dh2 2 dh or cae Gor CaO C9 ey Pha — 9 ae Oe an)” This difference in pressure taken over a surface normal to the bordering layer, with a length of 1 cm. and a breadth equal to the thickness of the capillary layer, furnishes the value of the capillary tension : [(r-py dh . The work which is to be performed for enlarging the surface with 1 em.?, the temperature remaining constant, so the capillary energy is: ‘ 29, P 9 i 2 = [ (rp) a= | eae oa aeae ss (<2) ! dh . ’ . J ( Qeradh? 2\dah/ $ With the aid of this latter consideration we can easily show that the capillary energy is equal to the amount with which the thermo- dynamic potential of the bordering layer, taken over a cylinder whose section is | em.? and whose height is equal to the thickness of the capillary layer, exceeds the thermodynamic potential of the same mass in the homogeneous vapour- or liquid-phasis. Astronomy. — “Determination of the latitude of Ambriz and of San Salvador (Portuguese West-Africa).” By C. SANDERS (Communicated by Dr. E. F. vAN DE SANDE BAKHUYZEN). During a several years’ residence on the West coast of Africa I spent as much as I could of my leisure in making observations for determining geographical positions. Till now, besides a rather ( 399 ) inaccurate theodolite, which did not allow to read beyond full minutes, I had at my disposal only a sextant. Recently however, after consulting with Dr. E. F. vAN pe Sanpbe BakauiwzeEN who for a long time already has rendered me valuable assistance in my endeavours to obtain useful results, I have bought a portable uni- versal instrument, by means of which I hope that my future obser- vations will attain a higher degree of accuracy. Yet, among the earlier observations there are already some, of which the publication may prove desirable, with a view to the great uncertainty which still exists about the exact position of several places on the South-West coast of Africa. I will here communicate my observations for the determination of the latitude of Ambriz and of San Salvador, both in Portuguese West-Africa. I. Determination of the latitude of Ambriz. The observations were made with a sextant of WEGENER with vernier on which can be read 10", and an artificial horizon ; besides I used a mean time chronometer. Observations referred to the sea- horizon, together with some made by means of the small theodolite mentioned above, are not communicated, because they are far less accurate. The errors of graduation of the sextant were determined by Dr. Katser at Leiden as follows: at 10° 0"0 at 70° + 225 10 + 5.5 80 + 23.5 20 + 9.5 90 + 24.0 30 + 13.0 100 + 24.5 40 + 16.0 110 + 24.5 50 + 18.7 120 + 24,5 60 + 21.0 Before each set of observations I tested the adjustment of the mirrors and the telescope. If smal! deviations were found, they were imme- diately corrected. The index error was always determined before the observations by 4 till 6 pointings on the direct images; in the case of solar obseryations they were equally distributed over both limbs. This determination was often repeated in the same manner after the observations. I assumed for the eastern longitude 13° 8' or expressed in time 52 m. 32 sec. This value. was deduced from determinations of ( 400 ) the time (measurements of 8 till 10. altitudes near the prime vertical) and a comparison of the so found local time with that of Greenwich, as given by the chronometers on board several ships that touched at this port. The English Admiralty-chart (corrected up to 1897) gives also 13°38’ for the Eastern longitude of Ambriz. As provisional value of the latitude I assumed 7°50’ south. The observations were made before the old factory cf the ,Nieuwe Afrikaansche Handelsvennootschap” and consist of the three fol- lowing series: 1. Circummeridian altitudes of the sun on May 10, 1893. For the reduction of the observations I used the following formula: J cosp cos 2 sin®ht ~—cos® gw cos? 0 0 p—do—z = 22 5 SS — aa Colg (0' —.¢—)——- P a sin(O — p) sin 1" sin?(0 — ) PI in 1" 2sin' kt z represents the northern zenith distance, whereas southern latitude is regarded negative. The term depending on 2 sixn®4¢ could be neglected, as its influence, even in the case of the greatest hour angles, was too small. The following corrections and daily rates of the chronometer were found: March 18 1893 + 4.6m 56s 50 — 0824 April 12 + 46 50.40 — 0.23 May 3 » + 46 45.48 — 0.39 June 3 + 46 33.26 That I might use a constant value for the declination of the sun, the hour-angles were reckoned from the instant of the maximum altitude, computed from the formula: do : tp = 0.255 ab (tang — tango) € in which ¢,, the hour-angle of the maximum altitude, is expressed .. do ray . in seconds of time and a stands for the variation of the sun’s : declination in one hour, expressed in seconds of are. The observed altitudes were corrected for refraction, parallax and semidiameter. The places of the sun ete. were taken from the Con- naissance des Temps. ( 401 ) For the time of the observations and we find: Corr. chronometer to mean loc. time Indexcorrection sextant Corr. for error of graduation Temperature Barometer Mean loc. time of transit of sun, 7’ Hour-angle of maximum altitude, ¢ Declination of the sun for 7'-++ 4, The separate observations and_ their the used part of the sextant + 46m 4354 — 1'55" + 25" 21x: 760 ra.M,. 1156m 13s — 485 + 17° 4414315 results are given in the following table, which needs no further comment. Limb Chron. time. Hour-angle. Reading Sext. Latitude. l | ons3m4os | — 15m 45s1 197° 45°40" | — 7° 50! 3N6 u | 54 55 14 30.1 128 54 50 49 53.2 | 56 14 iets lil eal 127 56 20 49 59.1 u bf. alo 12 23.6 129 2 30 50 4 4 | GH BYE Re) ll 47.6 128 110 50) 223 u 58 20 ii seven 129 7 30 49 45.4: ] bys NOM=23.2 128 5 30 50 5.5 ul 59 40 9 45.1 129) 11-90 49 48.8 l OR A 9 766 128 § 50 50 10.3 u ate ge 8 18.6 2G bn 5: 49 47.7 Hence: Latitude from lower limb y ” upper limb Mean value Difference upper limb—lower limb — 7° 50' 4N2 49 51.9 — 7° 491580 + 19"3 Examining these results and also those of the 2"¢ series given below, it appears clearly that there is a perceptible constant personal error in esteeming the contact of the two images 0 as deduced from the two series is 5'.3 results for this amount, we obtain as me Proceedings Royal Acad. Amsterdam. Vol. IL. f the sun, and its mean value If we correct the separate » . e . . an error of a single pointing 29 ( 402 ) ° + 5'".8 and as mean error of the final result £1".8. We must also take into account however the error made in determining the index correction, which influences all the observations equally. If we assume that for this determination 5 pointings were made (compare above) and accordingly take the mean value of its error to be + 5.8 & //}/; = + 2".6, the total mean error of the result becomes + 3".2. Moreover, as the observations are not arranged symmetrically with respect to the meridian, an error in the correction of the chrono- meter also influences the final result. Probably this error is not large, as the rate of the chronometer was pretty regular in the period considered. Also the results from the first and the last pair of observations, viz. 58".3 and 58".6, agree well inter se. An error in the chronometer correction of 28 would resuit in a variation of 3”.5 in the latitude. . 2. Circummeridian altitudes of the sun on May 14, 1894. The observations were reduced in the same way as those of May 10, 1893. The sun’s places ete. were now taken from the Nautical Almanac; they are based on the same elements and values as those of the Conn. d. T. The following corrections and daily rates of the chronometer were found: Jan. 12 1894 + 43m 44576 — 0s 80 April 26 , + 42 21.30 — 0.99 May 22. + 41 55.60 — 2.01 July 138 ow + 40 11.20 For the time of the observations and the used part of the sextant we find: . . Corr. of the chronometer + 42m 356 Index correction sextant — 1/50" Correction for error of graduation -+- 25” Temperature 27° Barometer 760 mM. Mean loc. time of transit of sun, 7' 11h 56m 9s4. Hour angle of maximum altitude, 4, — 454 e Declination of the sun for 7+-¢, + 18° 41/16"1 ( 403 ) The separate observations and their results follow here: il Limb. Chron. time. 1 11h Qm 4]s u ore a0) 10 | ately ; 9 u ye alts) 8 | 6 9 7 u 6 54 7 1 7 42 6 u 8 24 5) l Or a5 4. u 9 42 4 1 Tees + 7 uw 21 42 7 | 22 16 8 u 22 50 8 | 23) 2:9 i) u Qh 45 10 1 25 33 ll u 2650-9 12 | 26 46 12 uw 27 26 13 Hence : Latitude from lower limb Difference upper limb—lower limb upper» Mean result Hour angle. == [ifm 20 s%4 Reading Sext. 126° 10! 20" — 7° 50! +805 49 59.25 — 7° 50! 36 + 8/8 Latitude. — 7° 50! 50 50 49 The value now found for the personal contact error agrees fairly well with that found from the first series. If again we correct the separate results for the mean value of this error, viz. 5".3, we now get as mean error of one pointing + 8".3 ( 404 ) and for the mean of all + 1.9. If we add to this as mean error of the index correction + 8".3 & /1/,; = + 3".7, the total mean error becomes + 4".1. The uncertainty in the correction of the chronometer may be perhaps a little larger than for May 10, 1893, although the acceleration found after May 22 has probably not begun before that date, about which time the colder season began. But at any rate, through the symmetrical arrangement of the observations, an error of this kind will influence only very slightly the final result. In reality the observations for imdex error will as a rule be preciser than the altitude determinations with the mercurial horizon and, if on the other hand we take into consideration the possible uncertainty of the chronometer correction, then I don’t think the precision of my observations is overrated, if we assume + 5" as mean error both of the result of May 10 1893 and of that of May 14,1894. 3. Meridian altitudes of the sun and of @ Crucis. In the third place I measured several times the greatest altitude of the sun and once that of @ Crucis. The observations on the sun were always made on the lower limb, as in this way the maximum altitude from the mercurial horizon is easiest and most accurately measured; the images of the lower limb namely are separating before the culmination. Ilere follow the observations and their results. The column ,Corr.”” gives the sum of the index correction and the correction for errors of graduation. The declinations and the semidiameter and parallax of the sun were taken for 1893 from the Connaissance des Temps, for 1894 from the Nautical Almanac. Date. Object. | Reading. Corr. Temp. | Barom. | Latitude. ae | May 7 1893 Sun L. L. | 129° 5650") — 1'30" | 99° 1595 |—= "7° 150) G7) ” 8 ou ’ ” 129 24 20 | 1 30 29 758 50 4.4 naonty wi) THDOTHM TOR! 59 GOI B7 so'MII298 759 50 4.2 u 10 «2 ” ” 2S 2 es 05) SO) yoy 760 50, 125 (ie ae 119 90.15 | al S227. cele 76 50 1.1 May 19 1394 | » Crucis. 70 42 0 | eats} 95.5 760.4 50 946 w 4 a Sun L. LL. 126 28 20 | 1 30 27 760 49 57.0 The results from the altitudes of the sun still remain to be eor- ( 405 ) rected for the personal error; applying for this the value found previously, we obtain as final results : May 7 1893 — 7° 50! 1"4 Tt a) ” 49 59.1 Peete) ” 49 58.9 v lO ” 49 56.2 June 2 " 49 55.8 May 10 1894 50 9.6 ” 14 ” 49 51.7 Mean — 7° 49/59" As it is difficult to form an opinion about the relative precision of the observation of @ Crucis and those of the sun, the same weight is given to all of them. The mean error of an observation is then found to be + 5".6, that of the mean + 2".1. The results from the 3 series now must be combined. Although for the last series a smaller mean error was found, it did not seem advis- able to assign to it a greater weight than to the others. For it is possible that for this kind of solar observations the personal error differs perceptibly from that in the determination of circum- meridian altitudes. So we have : Series I — 7° 49' 58"0 Pp) AL 63.6 wo UT 59.0 Mean — 7° 50! 0''2 The three series agree fairly well inter se, and as final result for the latitude of the place of observation we may take : — 7° 50’ 0” which value will probably be exact within a few seconds. The reduction of the latitude to that of the harbour light amounts, according to the map of “Port Ambriz” on the English Admiralty chart: “Cape-Lopez-bay to St. Paul de Loanda’’, to + 12" + 2" (the map is not graduated), and so the latitude of the harbour light is found to be: — 7° 49' 48” The value given on the Admiralty chart is: — 7°52'9" and accordingly 2'21" too much south. ( 406 ) II. Determination of the latitude of S. Salvador do Congo. A few observations have been obtained about the latitude of San Salvador, the old capital of the former kingdom of Congo. They were made before the factory of the “N. Afrik, Handelsvenn.”, situated about 1 K.M. north of the centre of the hill on which the town is built (562 m. above the sea-level). Only the following meridian altitudes were observed. Date. Object. Reading. | Corr. | Temp. Bar. Latitude. | | May 8 18957} Sun L. L. | 132° 49'10"| — 1'10"5) 927° 714 |— 6° 15/182 » 10 4» 3 131 45 20 116 27.5 714 15.3 ieee, z Crucis. 67 31 50 | 1 13 22 713.5 26.1 If to the results from the observations of the sun we apply the cor- rection + 5.38, the mean result for the latitude becomes : —6° 15' 16" with an uncertainty of perhaps 10" or still more. Dr. CHavanne (Map of Justus Prrtnes 1886) found for the latitude of San Salvador (the hill extends over a few kilometers only) — 6° 20' 10” and for the longitude 14° 47'18" East of Greenwich. Very probably there is also an error in the longitude of more than 20', the true eastern longitude being smaller. Physics. — ‘Methods and Apparatus used in the Cryogenic Labo- ratory. II. Mercury pump for compressing pure and costly gases under high pressure”. By Prof. H. KAMERLINGH ONNES. (Will be published in the Proceedings of the next meeting). Physiology. — ‘Lipolytic ferment in human ascitic fluid”. By Dr. H. J. HaMBuRGER. (Will be published in the Proceedings of the next meeting.) ( 407 ) Chemistry. — Prof. A. P. N. FRancuiMont presented to the library the dissertation of Dr. P. J. Monraane, entitled: “The action of strong nitric acid upon the three isomeric chloro-benzoic acides and some of their derivates”. (Will be published in the Proceedings of the next meeting.) Chemistry. — ‘The aileged identity of red and yellow mercure oxide” (II). By Dr. Ernst Conrn (Communicated by Prof, H. W. Bakuvurs Roozenoom). (Will be published in the Proceedings of the next mecting.) Chemistry. — ‘Determination of the decrease of the vapour tension of solutions by determining the rise of the boiling point”. By Dr. A. Smits (Communicated by Prof. H. W. Bakuuts RoozeBoom). (Will be published in-the Proceedings of the next meeting.) (February 21, 1900.) ( 408 ) ERRATU M. Page 103 formula 2, 3 read as follow: 1+(p+P)(a) (and + (p P’) (Fr («— TE ep eae oi ae BO oe eee YS oe 5 ae 22 3 ; (273.2 ; ruse + (pi + Pi) (=) (a 1 373) a fg C2) led ooo) tor on (ota Page 104 Table I read as follow: = —_—_—_—_— x B 3 B, (I —w)+ Bo av a 0 | 1.8328 | 4.3238 0.2082 1.3057 1.3019 1.3075 0.2135 0.30001)| 1.2052 | 1.2024 1.2112 0.3084 0.4192 1.0826 1.0809 1.0862 | 0.4243 0.5077 0.9884 0.9877 0.9934 0.5131 0.6498 0.8399 0.8398 O. 8444 0.6541 0.7085 0.7799 0.7802 0.7828 0.7110 1 0.4765 0.4774 KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday February 24, 1900. IEG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 24 Februari 1900 DI. VIII). Contents: “A simple and rapid method for preparing neutral Pikro-carmine”. By Prof. J. W. van Wine, p. 409. — “The Entropy of Radiation” (Il). By J.D. van per WAats Jr. fCommunicaied by Prof. H. G. van DE Sanpg Baxkuvyzen), p. 413. — “On rational twisted Curves”. By Prof. P. H. Scroure, p. 421. — “Lipolytic ferment in Ascites-liquid of man”. By Dr. H. J. Hampurcer, p. 428. — “Methods and Apparatus used in the Cryogenic Laboratory. If: Mercury pump for compressing pure and costly gases under high pressure”. By Prof. H. KaAMERLINGH Onnys (with 7 plates), p. 437. — “The alleged identity of red and yellow mercuric oxide” (Part II). By Dr. Ernst Conen (Commu- nicated by Prof. H. W. Baxuuis Roozesoom), p. 458. — Prof. A. P. N. Francurmonr presents Dr. P. J. MonraGne’s dissertation: “The action of hydrogen nitrate upon the three isomeric chloro-benzoic acids and some of their derivatives”, p. 461. — “The Enantiotropy of Tin” (IV). By Dr. Dr. Ernst Conen (Communicated by Prof. H. W. Baknuis RoozEBoom), p. 464 (with one plate). — “On Phenomena on the sun con- sidered in connection with anomalous dispersion of light”. By Prof. W. H. Jurius, p- 467. — “On the formation of trisubstituents of benzol form disubstituents”. By Prof. A. F. Horteman (Communicated by Prof. C. A. Lopry pe Bruyn), p. 468. — “Enquiries into the system Tl1NO,;+AgNO,”. By Dr. C. van Eyx (Communicated by Prof. H. W. Bakuuis RoozeBoom), p. 468. The following papers were read: Anatomy. — Prof. J. W. van WisHE describes: “A simple and rapid method for preparing neutral Pikro-carmine’’. By many it will no doubt be deemed unnecessary trouble to add another to the manifold prescriptions for the preparation of pikro- carmine. Most investigators who use it, will be content with one of the well-known methods of preparation which they have been in the habit of following, as was also the case with me, until, about a year ago, the stain disappointed me. This happened during the study of young embryonic tissue, which had been blackened by osmic acid and had afterwards been bleached. 30 Proceedings Royal Acad. Amsterdam, Vol. II. ( 410 ) The ordinary means to tinge nuclei: haematoxylin, alum-carmine and different aniline-stains produced a diffuse colouring, whereas only after having been for about fourteen days in pikro-carmine the nuclei became visible. Then however the protoplasm of the cells had disappeared; it could not be otherwise than dissolved in the alkaline pikro-carmine, and it seemed only natural rather to take a neutral solution of this tincture. I tried different prescriptions, but I was not successful in finding a neutral solution: a moist red litmuspaper hung in the bottle above the liquid, was tinged blue after a few hours. PauL MAYER in his article: “Ueber Pikrocarmin” ') says not to believe that: “Carmin in einer ganz neutralen Fliissigkeit, die noch dazu eine relativ grosse Menge pikrinsauren Salzes enthiilt, gelost bleiben kann” (1. ¢., p. 19). He examined pikro-carmine from the anatomical laboratory at Munich and from the College de France, moreover liquid and solid samples of Grt&BLER and different solid samples of MeERcK. The pikro-carmine is a solution of two solids: picrate of ammo- nium and ammoniumearmine — the discoverer RANVIER believed it to be a chemical combination, but this is an assertio gratuita — and now it is (leaving the alkaline reaction out of the question), a deficiency of most prescriptions that they cannot specify the relative proportion of these elements and leave it to the inconstancy of chance. This is the case with all prescriptions in which bacteria from the air are called to aid, according to the method followed in the Collége de France *), moreover the preparation then lasts several months, and, as experience has taught me, there is considerable danger of obtaining a totally useless product. : Because of the difficulties just mentioned and others besides, PAUL MayYER says at the end of his article (l.c., p. 28): ,Das Facit wire also: das Pikro-carmin gehért zu den Firbmitteln, die eine bewegte Vergangenheit hinter sich haben, und yon denen man méglichst wenig Aufhebens mehr machen sollte.” Pikro-carmine can however not yet be considered out of date as a stain in microscopical technics, and I have been successful in preparing in a simple way a liquid, which may practically be called neutral, at the same time containing fully known quantities of picrate of ammonium and ammoniumearmine. The method can ‘) Paut Mayer, “Ueber Pikrocarmin”, Zeitschrift fiir wissenschaftliche Mikroskopie und mikroskopische Technik. Bd. 14, 1897. *) See A. Bounes Ler, The Microtomist’s Vademecum, fourth Ed. 1896, p. 153. ( 411 ) partly be considered as a modification and simplification of HoyeEr’s prescription ') running thus: Take 25 ec.*) of an old strong *) solution of carmine in ammonia and pour it carefully in 100 cc. of strong alcohol (of circa 96 pCt.), a voluminous precipitate of ammeniumecarmine now forms itself. Filter after half an hour or longer, rinse the precipitate on the filtrum with 100 ce. strong alcohol and dry it for 24 hours in a thermo- state of 40—45° C. *). Tf the solution was old enough a dark red, nearly black crumbled mass is obtained, which is easily rubbed down to a powder tho- roughly and clearly soluble in distilled water or in picrate of ammonium of whatever strength. If picrie acid is added to the solution, a precipitate is immediately formed; the picrate of ammonium may therefore not contain free picric-acid which was the case with a certain quantity which I received from MERCK °). The relative proportion of ammoniumearmine and picrate of am- monium, which, as a rule, seemed to me most favourable for staining was as 1: 2. In order to obtain a liquid, which would at the same time fix the tissues to some extent (as pikrocarmine is ex- pected to bring about), I took a 1 pCt. solution of picrate of am- monium, — i.e. a nearly concentrated solution °) and added thereto 1/9 pCt. ammoniumearmine. 1) Hover, Beitriige zur histologischen Technik, Biologisches Centralblatt, Bd. 2, 1882. Following the somewhat lengthy prescription of Hover, I was not successful in obtaining a powder quite soluble in water. Besides a good deal of carmine is lost. The ‘“Pikrocarmin nach Hoyer” of Griibner must, according to the List of Prices, be dissolved with ammonia, and could therefore not be used for my purpose. 2) These and other quantities are of course taken ad libitum, the statement is for the convenience of those who may want to follow the prescription. 4) At first I dissolved 30 er. carmine in 100 ec. not diluted ammonia of circa 10 pCt. Afterwards I found out that the carmine dissolves better in ammonia diluted with the double quantity of distilled water. 4) The filtered liquid is thrown away. After evaporation a tough red substance is obtained, which, when thoroughly dried forms a coherent, hard mass, soluble in alcohol as well as in water. With alcohol the watery solution gives no precipitate. In the same manner it appears that the solution of carminic acid in ammonia con- sists of two kinds of ammoniumearmine, one of which can be precipitated by strong alcohol, but the other cannot. 5) A sample, which I received from Grisier was excellent on the contrary, Picrate of ammonium can easily be prepared. For instance 9 gr. picric-acid are dissolved in 100 ce. alcohol of circa 96 pCt. adding 15 cc. ammonia and evapo- rating on the thermostate at about 60°. °) In winter erystals are formed in the 1 pCt. solution of picrate of ammonium. To prevent the stain from crystallising in winter, it can be diluted with half the quantity .of distilled water. 30* ( 412 ) The solution was not neutral however, although both ingredients were perfectly dry. Although they were dried for a whole week in a temperature of 45°, a moist red litmuspaper hung in the bottle above the liquid, turned blue after some time. Probably free am- monia clung to the dry powders. To get rid of it a solution was boiled in a glass receiver for some time, until a red litmuspaper did not turn blue in the vapour. This was the case after boiling from a quarter to half an hour. After cooling down, the liquid looked slightly unclear, which was easily amended by filtering. The loss of volume was restored with distilled water. The tincture was now ready; to keep it free of mould, it was needful to add an antiseptic; 1 pCt. chloral, recommended by Hoyer, proved efficient. This pikrocarmine !) is practically neutral, for a moist red litmus- paper hung in the closed bottle above the surface of the liquid, was not yet tinged blue after four months. The tincture *) contains 1/9 pCt. ammoniumearmine and 1 pCt. picrate of ammonium, for the loss of weight in consequence of the unclearness after boiling, is so insignificant, that it cannot be taken into consideration. The preparation is finished in two days; should time be short it could even be done in one day; in which ease the drying is left undone, and after a preliminary experiment, the quantity can be calculated which must be taken from the moist precipitate. The insignificant quantity of alcohol, which it contains, is of no consequence, and is moreover dispersed by boiling. A difficulty with this method is that an o/d carmine solution in ammonia must be used. Mine was two years old. Fresh solutions, and such as well which were half a year old, produced, instead of a black, a more or less clear red ammoniumearmine powder, which was only partly and unclearly soluble in water. The carmine-solution must therefore “ripen”, how long, I have not been able to ascertain; but two years is not too much. The question now is wherein this ripening consists and if it cannot take place at once. It is well-known that a ripe solution (from which the superfluous ammonia has been allowed to evaporate as much as possible), stains the tissues better than a fresh one, and this is very generally — amongst others by GieRKE*) — ascribed to the for- 1) To be obtained at the address of Dr. G. Grisuer, Leipzig. 2) One drop of the tincture on the filtering-paper gives, after being dried, a brown- yellow stain with red edge. This edge is much broader with the boiled, than with the unboiled liquid. 8) H. Grerke, Firberei zu mikroskopischen Zwecken, 1885, p. 14 and 16. ( 413 ) mation of ammonium-carbonate, the carbonic acid being resorbed from the air. There is no doubt that this resorption takes place; and expecting that the salt mentioned might cause the ripening, I added 10 pCt. carbonate of ammonium to the solution. However without the desired result, even after the solution was several months old. I then took into consideration whether the carmine might perhaps resorb oxygen from the air, and would need to be oxygenated; and this proved to be case. When putting together: 10 gr. carmine powder, 10 ce. ammonia, 20 ec. hydrogenperoxyd, the mixture boiled for a short time in a glass receiver, then cooled down (for instance by letting the receiver float in water in a half- filled cylinderglass), a ripe carmine solution is obtained in a few minutes, which, treated in the above-mentioned way, produces fully 9 gr.}) of an almost black ammoniumcarmine, which is entirely, sometimes a little unclearly, soluble in water. Instead of boiling with hydrogen-peroxyd an equal quantity of a 1 pCt. solution of kaliumpermanganate can be taken as well, although in this case the oxygenation is easily carried too far. Physics. — “The entropy of radiation” (Il). By J. D. VAN DER Waats JR. (Communicated by Prof. H. G. vaAN DE SANDE BaAKHUYZEN). VE Distribution of the vibrations of the molecules. In the second part of his “Vorlesungen iiber Gastheorie” Prof. BoLTZMANN discusses the way in which the intramolecular energy is distributed over the different molecules. He finds that the chance 1) If dry carmine has been used. But carmine as it is sold, frequently contains 10 pCt. or more water, though it may seem to be dry, (414 ) that a molecule belongs to a certain group, may be represented by : A, 2h; dp, dpg . » « dpydgq,dqg ... dq. In this 4; and % are constants, 2, ihe energy of the intramole- cular motion, p; - + + pz the coordinates, which determine that motion and q, - ++ 9. the momenta corresponding to those coordinates. From this would follow, that the chance that the amplitude an of the vibration of a molecule is contained within certain limits, is represented by: BYn- However we cannot accept this result without further proof. The motion, which we are considering, and which is the cause of radi- ation, is necessarily damped, so that between two collisions a mo- lecule has lost part of its intramolecular energy; moreover the molecule has absorbed energy from the field. For such a motion the proof of Prof. BotrzMann does no longer hold. In order to find the distribution of the amplitudes we shall have to take into consideration two causes of change: the collisions and the electric forces. First I shall examine the influence of the electric forces, and then inquire whether the collisions of the molecules will modify the distribution brought about by the electric forces. I shall make the same assumptions about the construction of a molecule as Prof. Lorentz did’), i.e.: a. I assume every molecule to contain an ion charged with electricity. b. That ion has a position of equilibrium in the molecule, from which it can move in all directions, and to which it is driven back with a force, proportional to the deviation. c. The mass of the ion is so small compared to that of the rest of the molecule, that when the molecule is vibrating, the ion alone may be considered to move. d. ‘The remaining part of the molecule is charged opposite to the charge of the ion and that in such a way that, when the ion is in its position of equilibrium, the electric forces, exercised by 1) Arch, Neerl. XXV, 5, 1892. (415 ) the ion, are entirely destroyed by the remaining part of ihe mole- cule. From these assumptions we find for the equation of motion of an ion !): dx CHEE TR e dx # m ee eet ee Se feo adi Fee ul 2 ef + dy dz ——\ it) : rie G ; dt Here m represents the mass of the ion, f a constant factor, « the coordinate of the ion, 7, that of the position of equilibrium of the ion, e the electric charge. The term —f(#— 2) is due to the fact that an ion has a po- sition of equilibrium, towards which it is driven back. The second and third term of the right hand side indicate the influence of the electric forces exercised by the molecule itself. The second term may be transferred with the negative sign to the left hand side; it is evident that it gives then an apparent change of the mass of the ion. If we represent by m the mass of the ion, modified in such a way, we may leave this term further out of account. The third term has always the sign opposite to that of the velocity and explains the damping, which a vibrating particle experiences in consequence of the fact that part of the energy is radiated into space. The three last terms express the forces exercised by the surrounding molecules on the ion. Prof. Lorentz has pointed out that the fourth term is great compared to the fifth and sixth. For f/ we shall take the electric force, as it is in the position of equilibrium of the ion. The force 42 V?ef, which we take then into consideration, acts on the ion and on the rest of the molecule with the same amount but in an opposite direction, and has therefore only influence on the vibration of the molecule. On the other hand, the forces which we neglect : df dy dz Aw V2e ——(«#— — N — — mt) ‘ 4 dx Carne ( dt dt would also give a progessive motion to the centre of gravity of the molecule. Afterwards I hope to discuss the influence of these forces. For the external force / we shall write: 1) Lorentz, loc. cit. equation T § 90 in connection with equations 111 and 112. and we shall take constants for f; and fy. As a molecule is actually subjected to an alternating electric force, the amplitude and the phasis of which vary with the time, we get in this way a solution which will hold with approximation for a short time only ; but which will yet be sufficient to conclude from the condition at a given moment to that of a short time At after. The equation which we have to solve, is therefore reduced to: Ba . 2 mt m— =— f(@# Teste V de 447 Vi (fi aoa a + Sasin ==) dt? or if we put a, =e («—a): d?a e dea 2 mt 2 at m = = — fia, —- 7 at +42 Ve Gi cos eee sin a) The solution of this is: 2 nt gut 2) ag = (a' a ASE ie =- Q' x9 sin ne e—kt -|- bey phe ae Rca bx sin = ’ ete 2 a : By substituting in the equation for m —- this value of a» and by equating the coefficients of i 2 at aie 2 nt 2 at a 2 nt e—*t cos —— Ee —*" sin — cos —— and sin —— Te Pe P. li separately to zero, we find the following four equations : A 7? Bs e 20 Ay) mM Se — i?) — fay + yu e k8 + FE) 4 Bemmbon a oL 4n? e 4 7? 20 Qzg mM Ge — i?) — f azo +> Azo (—e4 30% — 2an mk, te 9 ra rime ee] =0 (417) 4? e /22\3 ba me — fin —ba G(G) +4 Ve fi =0 4 n? e /27\3 “a Dro m T?2 {betta G(G) $4 epao. From the first and tie second equations follows : 4 72 & 4m? Pek \\ EE Bee (ee ao Fs) ae" nm (=-#) f+5( B+ 38k ae e 4 x? 2 mk + 7 (3#— aa = 0 from which 7 and & may be calculated. az, and a'z2 are constants which may be arbitrarily chosen. The quantities 4,1 and 0,2 are not arbitrary, but are determined from the third and the fourth equations as follows: 4n Ve? [(m oo = iA =r = (=) a in = - (EG) 4n V2 é| Sola ats (m 7a ‘Al 22 — 3 ; ("a — ae. We shall represent this by: bi =phAt+qhe bra = — Qf t+Phe The quantity 6 depends therefore only on the accidental value of the amplitude of the electric force on the point where it happens to be, and not on the accidental value of the amplitude of the vibration of the molecule. Bin + bia = (p? + 9?) (fi + fo) - The amplitude of 4, is therefore Vp? + g? times or 4 Ve? times ( 418 ) the amplitude of /. Moreover the phasis of be is f. As however all phases occur equally frequently the distribution of the quantities [b.| will be the same as that of the quantities [/,], so that the chance that %: is contained within certain limits may be repres- ented by: 2 Fat TG he alas Fagen —e dby, where C=4nV%e@?¢ : bya In order to find the distribution of the vibrations we may reason as follows. Starting from a certain initial condition the molecules will entirely lose their original vibrations by radiation. The vibrations in the direction of the X-axis, which they absorb from the field, are dependent on the /-component of the vibrations of the ether, and not on the g- and /-component. As the /-, g- and /-compo- nents are independent of each other, also ar, ay and az, caused by them, must be independent of each other, and as all directions occur with the same frequency, the distribution of the a’s must also be that of Maxwexu. The chance that the quantity an is contained within given limits, may therefore be represented by: In order to arrive at this result the solution of the differential equation for a, is not necessary. In this way however the condition is not yet perfectly determined. From the value found for az appears that if a molecule were exposed to an electric wave of constant intensity, it would have assumed the amplitude bd after an infinite time. If a molecule is placed in a region where the amplitude of the electric force has a definite value, it will have been for some, though it be a short, time in a region, where the amplitude of the electric force did not differ much from that definite value. So it will have already assumed part of the amplitude b. The probability of the action of a force f on a molecule with a vibration a, cannot be simply represented by: e © df; dfy dam daz , 1) Proc. Roy. Acad., Dec. 1899. Pag. 322. ( 419 ) as would be the case if electric force and vibration were indepen- dent of each cther; but these quantities are dependent on one another. If the above expression held true for the probability of the action, the way of motion would satisfy conditions, exactly cor- responding to those which Prof. BoLTzMANN assumes for the case of molecular thermal motion, in order that the motion may be called “molecular-irregulated.” ') In reality however, the way of motion is here molecular-regulated or as I would call it partially regulated. Totally regulated the condition would be, if the a; was entirely determined by /; if e.g. a had everywhere assumed the value bx. The way of motion will be regulated in a higher degree as the quantity eS of, de of; dy afi de dt ot | dxdt dy dt 2 zal af ; is smaller. Here a represents the fluction of /, in a point which d does not move from its place, a the total fluction of the quantity J, for a molecule which moves with a velocity, the components of which are sed ; fy and ae dt dt dt I have however not yet succeeded in finding the law according to which the motion is regulated. At first sight it may seem strange that the condition of maximum- entropy should possess a certain order, whereas for the case of the molecular thermal motion of a gas we consider the total irregularity as condition for the maximum-entropy. In order to solve this seeming contradiction we must take notice of the fact that we are here concerned with the action of forces. Now we know that the action of external forces which varies so slowly from point to point that they may be thought constant throughout regions which though small, are still measurable and contain many molecules (e.g. gravity), causes the density to be not everywhere the same in the condition of maximum-entropy, so that we have ,molar regulation.” But then it is not to be wondered at that the electric forces of radiation, which cannot be thought constant throughout regions of measurable dimensions, should cause a “molecular-regulation”’. yen though we had succeeded in determining the regulation in con- 1) /Molekular-ungeordnet.” BourzMann, Gastheorie I. Pag. 21. ( 420 ) sequence of the electric forces, we should not have found the true con- dition. The influence of the collisions may probably not be neglected. If the mutual collisions of the molecules took place in a perfectly irregular way, they would undoubtedly lessen the degree of regula- tion, and render the condition nearer irregular. The way of motion is however not only partially regulated with regard to the action of the electric forces on the molecules, but also with regard to the mutual collisions of the molecules. In order to explain this we consider two molecules which have come very near to each other. The forces exercised by the surrounding molecules will be about the same for both, and will tend to bring their internal motion more and more into syntony. Moreover each of the molecules absorbs part of the energy emitted by the other. On account of these two causes a partial regulation is brought about in the collisions of the mole- cules, of which it seems impossible to me to determine the influence without special hypotheses on the mechanism and even the form of the molecules, for which as yet all data are wanting. There is however another difficulty which makes me doubt whether the considerations of Prof. BourzMann on the internal motion are applicable to the motion which causes radiation. For according to Prof. BottzmMann the internal energy would increase in proportion to that of the progressive motion of the mo- lecules, i.e. with the temperature. According to the law of Sreran the emitted energy is proportional to the fourth power of the tem- perature. These two results can only be brought into harmony by assuming that the absorption decreases strongly with the rise of the. temperature. Properly speaking the law of Sreraw holds good for the total quantity of emitted light and may perhaps only be applied for cases where a continuous spectrum is emitted. The wavelength, which has the greatest intensity depends however for a continuous spectrum on the temperature, so that for the light of a fixed wave-length the law of Sreran does not hold good. The displacement of the predominating wave-length is however not so great, that the law of Steran could not be applied with approximation. Let us assume that actually the internal energy increases propor- tional with the temperature, and so the quantity 0+) with the root of the temperature. Let us represent two temperatures by 7) and T,, the intensities of light emitted at that temperature by J, and 7, and *) Proc, Royal Acad, of Sciences, Dec, 1899. Pag. 319. ( 421 ) the corresponding quantities 0 and «¢ ') by 0, and 0, and by & é,, then we haye, neglecting the molecules which surround a point immediately : eae iP y Ags 4 mui tA nes I, &° re Te PCa ECT a, Beal Any ol a é SS ye oe of J a dt e 7 or Peta y? 22 wo : —— ———— r* dr sin p dp dO ae “ar dp N 9” r? dani bi 8 etre Me F703 ae — I Ts maa, y2 + 22 eae ap [we = r? dr sin ~p dp dO 2 eae Prof. Lorentz?) has deduced, that w (his quantity @) is inver- sively proportional to the root of the temperature. And though both the way in which I have arrived at the conclusion that the ab- sorption is inversely proportional to the third power of the tempe- rature, and that in which Prof. Lorentz found that it is inversely proportional to the root of the temperature, are but rough approxi- mations yet these results differ too much, to attribute this only to the neglections. Therefore an incorrect assumption must have been made some- where. And if so I should doubt in the first place the correctness of the assumption, that for all internal motions the increase of the energy must be proportional to the energy of the progressive motion. I should therefore suppose that in collisions there are influences felt which cause the energy of the internal motions, which bring about radiation, to increase more at a rise of the temperature than the energy of the progressive motion of the molecules. Mathematics. — ‘On rational twisted curves”. By Prof. P. H. Scnoure. 1. Let Pi, Po, P3, 24, ... be successive points of a given twisted curve &; then we may consider the centre of circle P, P: P; lying in plane P; P,P; as well as that of sphere P, P, P; P,. When the 1) Proc. Royal Acad. of Sciences, Nec. 1899. Pag. 322. ®) Versl, Kon. Akad. y. Wet. April 1898, DI. VI, blz, 559. points taken on the curve coincide in a same point P, the limit of the first point is the centre C, of the circle of curvature, that of the second point the centre S, of the sphere of curvature, i.e. the centre of spherical curvature of R in P. If P describes the given curve , then C, and S, describe twisted curves related to R, of which the latter is also the cuspidal edge of the developable enve- loped by the normal planes of #; this locus of centres S, of spherical curvature may be indicated by the symbol FR, . From the wellknown theorem according to which the line of inter- section ¢ of two planes «, /?, perpendicular to the intersecting lines a and b, is a normal to the plane y of these lines a and 0, ensues that reversely the osculating planes of & are also perpendicular to the corresponding tangents of ,. These osculating planes of & however, not passing at the same time through the points of con- tact of the corresponding tangents of R,, are not normal planes of R, and so the relation between the curves & and &, is generally not reciprocal. A wellknown striking example derived from trans- cendent twisted curves, where this reciprocity really exists, is the helix or curve formed by the thread of a screw; moreover for this curve the two loci of the points C, and S, coincide. Let us go a step farther and suppose that P,, P,, P3, Py, P;,.- are successive points of a given curve #, which is contained in a four-dimensional space, but not in a three-dimensional one, which curve we therefore call a “wrung curve”; then besides the centres of the circle and sphere of curvature the centre H, of the hyper- sphere of curvature appears, which is the limit of the hypersphere P, P,P; Py P;, when the five determining points coincide in point P of the given curve. A third locus has then to be dealt with, and so we can extend these considerations to a space with any given number of dimensions. In the following pages we wish to deduce the characteristics of the locus /;, of the centre of hyperspherical curvature of the highest e . . . t/ rank in relation with the general rational wrung curve R; of degree », which ¢s contained in a space with s dimensions but not in a space with s—1 dimensions. 2. “The row of characteristic numbers from class to degree of “the locus “, of the centres of hyperspherical curve of the highest . . . n . “rank belonging to the general rational wrung curve in Rs is “3n—2, 2(8n—3), 3(8n—4),... s(8n—s—1).” ( 423 ) To prove this we represent R? by the equations fa a (oS ig oto)! 26" oa ae ao coe CL) on rectangular axes, where the symbols @, @,... @s and v in- dicate polynomia of degree » in a parameter ¢. If the equations represent the result of the division of the s polynomia @; by v, where the s quantities a; are independent of ¢ and the s new polynomia (7; contain ¢t in the degree n—7 at most, then it is clear that the transformation of the system of coordinates to parallel axes corres- ponding to the formulae Ppa ioie as, (G5 Chae ah 2) simplifies the original representation (1) of R: into eles (3 ah pct 3 OD) Be coe uot vo dow AC) vy We repeat that this simplification consists in the fact that the s polynomia /?; ascend only to the degree »—7 in t. If moreover /7'; and v' represent the differential-coefficients of /7; and vy according to ¢, then v = (py — fiiv')&= > (pi vy — [3; v’) eee ees. CD) represents the normal space with s—1 dimensions of /: in the point (2) with the value ¢ of the parameter. This equation is of degree 3n—2 in t, which proves what was asserted. For the envelope of a space of s—/ dimensions, the equation of which contains a parameter to the degree &, has for character- istic numbers: he OF RS 3) ae ie a sd): ( 424 ) By means of the general theorem now proved we find from n= 2 to n= 10 the following table for the general rational twisted curve of minimum order: 3 s=n= 4... 10, 18, 24, 28, s—n= 5... 13, 24, 383, 40, 45, s=n=6... 16, 30, 42, 52, 60, 66, s=n=7... 19, 36, 51, 64, 75, 84, 91, s=n=8 22, 42, GO, 76, 90, 102, 112, 120, s=n= 9... 25, 48, 69, 88, 105, 120, 133, 144, 158, s=n=10... 28, 54, 78, 100, 120, 138, 154, 168, 180, 190. The first line of this table says that the evolute of a general conic is a curve of class four and order six, the second that the locus Rs of the general skew cubic R3 is a twisted curve of class seven, rank twelve and order fifteen, ete. If as usual we consider the coefficients 1, wo, vw... . us of the equation = 6; = 0,(¢= 1,2,...s) as the tangential coordinates of the space with s—/ dimensions represented by that equation, we find from (3) for the normal space v (Biv — Biv’) - si) calicnd, Os oars ae) = fi(Biv— fir’) | us — which representation of &,; in space of s dimensions is dualistically opposite to that given for 2; . We write it in the abridged form: uf = OS Gao ae a) eee eC) 3. The degree of the equation (3) or that of the forms z of (5), all in ¢, can lower itself in particular circumstances. These, appa- rently of five kinds, can be reduced to the following two cases: a). The equation y =0 has equal roots. b). The equations 7; = 9, ((=1,2,... 8) have common equal roots, We shall now consider the influence of each of those suppesitions on the class of the locus 2). 3¢, Ift=t, is a k-fold root of y=90, this value is at the same time a £—1-fold root of y'=0 and each of the forms 7 of (5), and so (3) too, is divisible by (¢—#,)*—!. The curve £;, is then of class 5n—k— 1. . bake: 1 By the substitution of ¢— t= ai the case of the £-fold root t, of y =O assumes an apparently different form. It transforms the equations (2) into ie ENGINE et) ats ace) where the s forms 7; represent polynomia of degree ~ in ¢’ without constant term, whilst 4 contains ¢’ to the degree n—é only ; so i it leads to the case that «= 0, considered as an equation of degree n, possesses a k-fold root =o. Then the s forms Ti, (i = 1,2, ... 8) of (5) become polynomia of degree 3n— 2k — 1 in t', whilst 7) ascends to degree 3n—k—1 in t'. Then the cor- responding equation (3) is also of degree 3n—k— 1 in #’ and so Ry remains of class 3n—k— 7 as it should do. In passing we draw attention to the fact that the degree of 4 being lower than » it will be impossible to lower at the same time the degree of all the s polynomia y; by a transformation of coordinates to parallel axes, as this would include at the same time the possi- bility to lower the order of > . The particular case treated here refers to the position of the points of 2; at infinity. If y is divisible by (¢—,)' the point at infinity of the curve belonging to ¢ will count & times among the n points of intersection of the curve with the space at infinity with s—1 dimensions containing all points at infimty of the space with s dimensions. So we find fors=n=3: “The class of the locus &, of a skew ellipse or a skew hyperbola is seven, whilst this number passes into six with the parabolic hyperbola and into five with the skew parabola.” What we find here agrees with the wellknown results for s=n= 2. Although through any point P of the plane of an ellipse or hyperbola four normals of this curve pass, we can fall from this 31 Proceedings Royal Acad. Amsterdam, Vol. II. ( 426 ) point three normals only on the parabola, as the line connecting P with the point P, at infinity of the parabola must be consi- dered as an improper normal. Any point P of space is situated in seven normal planes of a skew ellipse or skew hyperbola, but only in six normal planes of a parabolic hyperbola and in five normal planes of a skew parabola, as the plane through the connecting line PP, of P with the point of contact P, at infinity with the plane V, at infinity, perpendicular to the tangent p, of the curve in P,, represents one improper normal plane for the last but one, and the coincidence of two improper normal planes for the Jast. Of course the particularity treated here can appear more than once. If »=0 contains the roots ¢,, %,..... t) respectively hy, ky, . + + ky times, where each of the p quantities & exceeds unity, ; PB the class of /, is represented by 3+ p— 2— a es J= 3. If t= is a common é-fold root of the s equations 7; = 0, then this value is at the same time a common 4—1-fold root of the s equations /?;=90 and the s forms of 7; (5) are divisible by (t—t,)/*—!, whilst 7, contains the factor (¢—#,)2*—1; then again (3) is divisible by (¢—t,)*—! and the curve /, is of class 3n —k— 1. 7 . . , By the substitution of t—t,= i the case treated here presents itself in an apparently different form. It leads to the equations (6°, where now the s forms 7; represent polynomia of degree » — k + / in ¢ without constant term and is a general form of degree x in ¢, Regarded as equations of degree n in t’, the s equations y;= 0 contain the common —/-fold root ¢ = om and the common simple root z'=0O. The s terms z;,(@= 4, 2, .... 8) become polynomia. of degree 3n—k—1 in t', whilst zr, ascends only to degree 3n—2k—1 in ¢’. The corresponding equation (3) is then as above of degree 3n—k— 1. Apparently besides the eases treated up till now where the equation (3) lowers its degree, another entirely new case can be pointed out, namely that where the s+ / equations ?;'=0, v'=0 have a common f-fold root t=. It is easy to see however that this apparent new case forms but a special case of what was treated above. If we start from the equations (1), because after all we shall directly have to transform the coordinates to parallel axes, then we have a = (t= Hy) pe Po = 1, 2). 88) jo SSF Por—*-) , ( 427 ) when the s symbols p—*—) and y—-*—)_ represent polynomia of degree n—k—1 in t. From this ensues by integration = (t—t,)F+} pim—k-l) 1, (G12) ares ha (t—t, e+} wyr—*k-1) + bo, in which the quantities ); and 4, denote constants. So the trans- formation of coordinates to parallel axes characterized by the formulae finally gives (t—t,)k 11 ym-k—-1) i ; — - = p05 hoe an Vv et by which we alight on the case that the s equations «i= 0 be- longing to (1) have a common & + I-fold root 4, whilst v moreover after being diminished by a constant quantity 6, is divisible by (t— t))k+1, The particularity treated here appears only in the case when 7m . . a A the curve Rs has singular points of a definite character. So the simplest case of a common double root t; of the s equations (;:=0 implies that the origin of each of the spaces of coordinates Po » - . . . 2 . &:=0 represents two of the ~ pvuints of intersection with A, , which with a view to the equality of the values of the parameter belonging . n . to those points only then takes place when “s shows a cusp in this point. We see at the same time that we have not generally enough enunciated the case sub 3°). For from this appears that the particularity will come in as soon as /} has a cusp anywhere. So the case sub 3%) ought to run: “The equations @; = 0, (= 1, 2,...8) have common equal roots or a transformation of coordinates to parallel axes can call forth this particularity.” Of course the case may present itself that ¢ 1s a common equal root of the s equations /7i= 0, but that the degree of multiplicity in relation to those equations differs. If 4 is a 4-fold root of (7; = 0, a ky fold root of /?77= 90, ete, then for & we must take the smallest nuinber 4;. If it happens p times that a transformation of coordinates to parallel axes implies the particularity indicated here, and if hy, kgy++-h, are the smallest numbers & for each of the correspond- 3l* ( 428 ) ing values t), 49, ... t of ¢, then 3n+4+p—?2 — & fk; will indicate i—1 the class of Ry,. 4. In the preceding number we have dealt with the class of Rk, only, without taking the other characteristic numbers into consideration. We now immediately add that the rule according to which the envelope of a space with s—Z/ dimensions, the equation of which contains a parameter to degree /, is characterized by the numbers ibe 2(k—1), Bi (Ka 2 )igr a eae se) 181 ——csih in general needs some modifications as soon as one of the above- mentioned particular cases appears. In the very simplest case of the parabola we find e.g. for the characteristic numbers, class and order, of the evolute 3 and 3, but not 3 and 4 as might be expected for k == 3, So in general in each of the particular cases treated here the numbers &, 2 (4 -- 1), 3 (4 — 2), ete. must be treated as upper limits. In a following paper we shall revert to this Jast point. Physiology. — ‘ Lipolytic ferment in ascites-liquid of man”. (Remarks on the resorption of fat and on the lipolytic function of the blood). By Dr. H. J. Hampurcer. (Read January 27, 1900.) In an essay published in the year 1880 Casn!) has contradicted the opinion that the emulsion of fat already takes place in the intestinal lumen. For he was never successful in separating an emulsion from the contents of the intestines by centrifugal force. And he did not much wonder at this: for the small intestine has an acid reaction, and with acid reaction no fat-emulsion can be produced. This opinion of Casi does not seem quite correct to me. Giving to animals a meal containing much fat, HerpeNnain has found 2), and so have I myself many a time, that a creamy surface can be taken off the mucosa of the small intestine, which, examined microscopically, contains small fat-globules. Nevertheless this layer 1) Archiv f. Physiol. 1880. S. 323. 2) Prriianr’s Archiv. 1888, supplement, 8. 93, has an acid reaction, That acid reaction can be coexistent with exquisite emulsions, has been proved by J. Munk, who obtained emulsions by mixing pure fatty acid with a little Nay COs;-solution. Another question is however whether the emulsion is already found so finely divided in the intestinal lumen as Jater on in the chyle-vessels. This now is certainly not the case. Even in the epithetium-cells and in the adenoid tissue of the villi relatively large globules of fat are found, and it is only in the chyle that it appears in its peculiar dust-shape. It can scarcely be doubted that in the lymph of the villi a cause must exist which brings about the transition of fat to the form of dust. In order to test this supposition it would be well to gather chyle, undo it by means of a CHAMBERLAND’s candle of particles of fat and afterwards shake the clear liquid with fat. It is however scarcely possible to obtain the necessary quantities of chyle for the purpose. I happened to learn that in the Hospital of the Utrecht University a patient was treated, whose abdomen contained a large quantity of aseites-lquid, which had the appearance of chyle. Professor TALMA kindly put it at my disposal. Upon close microscopical investigation however the liquid showed not a single particle of fat and it soon appeared that the observed opalescence proceeded from a mucoid substance which was. first described by HamMarsryn !) and the existence of which was later on confirmed by different medical men *). As regards its composition, the liquid contained 1.939 pCt. solids, consequently less than normal lymph; in which, as is well known, cirea 4 pCt. solids are present. It contained 1.715 pCt. albumen, 0.0808 pCt fat, and 0.0564 pCt. soap. The extraordinary insignificant quantity of fat proved that this was not a case of real chylous ascites, as one could have believed at first sight. 1) O. Hammarsren. Ueber das Vorkommen van Mucoidsubstanzen in Ascitestliissio- keiten, Autoreferat in Maly’s Jahresber. f. Thierchemie, iiber das Jahr 1890. S. 417. 2) 8. und A, L, Payxun. Beitriige zur Kenntniss der Chemie der serésen Exsu- date, Ref. Jahresber. f. Thierchemie, iiber das Jahr 1892. S. 558. G, Taoxn. Communication dun cas Vaseite laiteuse ou chyleuse. Arch. de méd. expériment. 1894, p. 826. Crcont, Ueber einen Fall milchig getriibten nicht fetthaltigen Ascites. Ltaliaansch in Riforma mediche, 1897, no 51. Ref. Maly’s Jahresber. f. Thierchemie, itber das Jahr 1897. 8. 190, ( 430 ) It was proved by laparatomy that the patient was suffering from cirrhosis hepatis and slight chronic peritonitis. Although the liquid was not chylous, we have nevertheless examined it in the proposed direction, because lymph from other parts of the body seems likewise to have the property to divide fat into the smallest grains. Think of Gimpert’s!) experiments; he repeatedly injected into the human body, not only without harm, but with favourable influence on the general condition 25—30 gr. olive—oil with 1:15 creosote. The experiments of Leuspe should also be remembered *). He was encouraged by the experience made with respeet the human body, that subcutaneous injections of cam- phorated oil applied even in large quantities, can be borne without disad vantage, and consequently tried subcutaneous injections of fat on dogs and thus obtained a considerable deposit of fat in different parts of the body. Finally I quote the experiments of J. L. Priivosr *) according to which the ot] injected into the lymphbag of frogs lobe] appears as tiny globules in the circulation. It must be taken for granted that the fat can undergo a minute division in the tissue spaces; otherwise mortal emboli, for instance in the lung-capillaries, would undoubtedly have followed these experiments. With regard to this it is interesting on the other hand that Daremperc ') by subeutaneous injections on rabbits and Guinea pigs, caused death. Furthermore 50 ce. of the ascites-liquid with 5 ce. of lipanine were shaken together. In this manner an emulsion was formed, which, by standing motionless and also by centrifugalizing separated itself into two Jayers. The upper layer examined microscopically, showed large fatglobules; the lower one, particles as tiny as dust, similar to those that are found in chyle and also in milk, the cream having been taken off by centrifugalizing. After that the lower layer was removed and once more centrifugalized. It remained however equally untransparent. Why had the emulsion separated itself into two layers? Is it because the oil contained two different kinds of fat, of which the one gives an emulsion as fine as dust, but not the other ) Compt. rend, de la Soc. de Biol. T. 40, 1889, p. 733. *) Sitzungsber. der physik. med. Gesellsch. zu Wiirzburg. 1895, 8. 1 no. 5. ®) Travaux du laboratoire de thérap. expérim. de PUnivers. de Genéve, IL. 1896, p. 44. *) Compt. rend. de la Soc. de Biol, ‘T.40, 1889, p. 702. ( 431 ) one? Or were the conditions not favourable for a thorough dust- emulsion of the whole mass of fat? In order to decide this question the uppermost layer (large drops of fat) was taken off by means of a pipette and shaken anew with fresh ascites-liquid. Centrifugal force was again applied and once more a separation into two lavers was visible. Both layers contained fat; now the undermost Jayer even contained more fat than at the beginning of the experiment and the microscope only showed the dustshape. From this it was evident, that the part of the fat, which, with the first experiment was separated in the shape of globules into an uppermost layer, had been transformed into fat in the shape of dust by shaking with fresh ascites-liquid. That which had not passed into dust was shaken again with fresh ascites-liquid, and now at length all the fat had been turned into the shape of dust. That with the first shaking-experiment the fat only partly passed into dustform, does not find its cause in an eventual difference in the relative condition of the different kinds of fat in the oil, but ean be explained from the conditions of the experiment. It has in- deed been proved that a perfect dust-shaped emulsion can be obtained at once, if only the shaking is continued for a long time and with a relatively large quantity of ascitesliquid. I have further considered whether a peculiar quality of the ascites- liquid must account for this. Therefore the experiment was repeated with another albuminous liquid, viz. with bloodserum. 30 ce. horse- serum were mixed with 5 ec. lipanine and the mixture strongly shaken for one hour. The emulsion was next centrifugalized, and thereby divided itself into two layers, a lower one with fat in dust- shape, an upper one with tiny fatglobules. The latter was removed, vigorously shaken with 30 ce. of the fresh serum and after that centrifugalized again; once more two layers were obtained; the lower one however now contained much more fat than with the first shaking. After having been shaken third time with 30 ce. serum, all the fat was brought into the form of dust. Shaking 150 ec. serum with 5 cc. lipanine for four hours, brought about the perfect dust-shaped emulsion. This emuision could now no more be divided into two layers by centrifugalizing. We thus did not find any specifie quality in our aseites-liquid with regard to the dispersion of the fat, for the same oceurred with the blood-serum, Transferring these facts to normal life — which does not seem too hazardous in this case — it ean be imagined, that the lymph ( 432 ) of the villi in its motion, causes the little fatglobules, already in a state of thorough division, to pass into the shape of dust. Surely this lymph-current works slowly, but it should be considered, that the time at its disposal is not short; 30 hours after a rich meal has been taken the chyle still carries away fat. As is well known Connsrem and Micnaiiis have pointed out in two interesting publications !), that, when blood has been mixed with chyle-fat and air is then carried through the mixture, the fat disappears, and a combination dissoluble in water takes its place. We were interested to know, when blood is mixed with our artificial chyle (dust-shaped emulsion of lipanine in ascites-liquid) and a current of air was made to pass through, whether a disappearance of fat would likewise be observed. To this purpose 240 ce. of the ascites-liquid with 15 cc. lipanine were shaken for 11. hour. After centrifugalizing, the undermost of the two layers is removed, which contains the fat exclusively in dust-form. Of the artificial chyle attained in this manner: (1) 75 ec. was mixed with 25 ec. horse-blood rich in erythrocytes *). lor 23 hours a current of air is allowed to pass through under a temperature of + 16° C. (2) 75 ee. of the artifical chyle are mixed with 25 ce. blood. No current of air is allowed to pass through. The liquids (2) are mixed just before drying takes place. At the same time exactly the same experiments are performed with dust-shaped lipanine-serwm-emulsion, consequently : (8) 75 ce. of a dust-shaped lipanine-serum-emulsion are mixed with 25 ee. horse-blood, and through this mixture air is allowed to pass through for 23 hours (the same current of air as under (1). (4) 75 ce. of the dust-shaped lipanine-serum-emulsion are mixed with 25 ce. of blood. No current of air passes through. The liquids (4) are mixed just before drying takes place. (1), (2), (3) and (4) are placed into two small receptacles, mixed with 20 gr, of pure sand and being stirred, dried in a temperature of 80°, After having been pulveriged, extraction with ether, free of water, in a Soxhlet apparatus for 48 hours. From (1)....... . 0,244 or. ether residu Haye (2) ie merbsnen ses «2 O75 or. ow " were be obtained. ') Sitzungsber. der Preussischen Akademie der Wissensch. 1896. S. 1713 more cir- cumstantially in Peniiegr’s Archiv. B. 65, 1897 S. 76; B. 69, 1897, S. 473. *) Such blood is obtained by leaving defibrinated horse-blood to itself and by pipetting off the serum after the red blood-corpuscles have settled down, ( 433 ) By this we have proved, that by letting the air stream through the mixture of blood and lipanine-aseites-emulsion a considerable trans- formation of fat takes place. From (8) 0.371 gr, Ether residu is obtained y (4) 0 283 or. " y uw " From these two numbers it is evident that by letting a current of air pass through a mixture of blood and dust-shaped lipanine- serum-emuision, no transformation of fat takes place. These numbers even rather tend in the opposite direction. After all these experiments it must be taken for granted, that the lipolytic ferment was not present in the blood, nor in the serum, but existed in the ascites-liquid. The question could now be examined, whether the presence of blood is really required for the transformation of fat and whether it is not suf- fic:ent to pass air through the lipanine-ascites-emulsion. To reply to this question, 80 cc. of a lipanine-ascites-emulsion (75 ce. ascites-liquid ++ 5 cc. lipanine) were shaken for 3 hours and submitted to a current of air for 20 hours. After that the fat- contents were determined, which took place at the same time with a portion of the same emulsion, not having been treated with a current of air. 80 es. lipanine ascites-emuision treated with air contained 4.300 er. of fat 80 ec, ” ” " not " y " uw OLSON ne hiie® B77 The pavsng through of air only, has consequently not given cause to transformation of fat. This result agrees with that of ConnsTrer and Micuainis. These investigators also found in their experiments with true chyle, that without the presence of red blood-corpuseles, the passing through of a current of air was not able to cause a transformation of fat. Repetition of the experiment. This experiment was performed in the same manner as the fore- going; the only difference being that instead of 24 hours, the current of air was only allowed to pass for 12'/, hours, under room-tem- perature, and instead of horse-blood, ox-blood was used, (1) 75 ce. of dust-shaped lipanine-aseites-emulsion + 25 ce. ox-blood. Current of air for 121/, hours; after that the liquid is mixed with sand, dried an extracted with ether. Kther-extract 0.064 gr. ( 434 ) (2) 75 ce. of the dust-shaped lipanine-ascites-emulsion are mixed with 25 ee. ox-blood, although nof before a current of air has been Jed through the mix- ture (1) during 12'/. hours. After intermixing, the liquid is treated at the same time and in the same way as in (1). Only here, as has been mentioned, no air is allowed to pass through, Ether-extract 0.186 gr. (3) 75 cc. of the dust-shaped lipanine-aseites-emulsion produce an ether-extract of 0.219 er. (4) 75 ec. of dust-shaped lipanine-serviu-emulsion are mixed with 25 ce. ox- blood. Current of air for 121/, hours. Dried with sand, extracted with ether. Kither-extract 0.359 er. (5) The same as experiment (+), however without the current of air. Ether- extract 0.364 gr, (6) 75 ce. of the dust-shaped lipanine-serum-emulsion. Ether-extract 0.569 gr. It appears from (1) and (2), that in passing air through the mixture of blood and dust-shaped lpanine-ascites-emulsion (artifical chyle), fat disappears. On comparing (2) with (3) it appears that also when a current of air is not passed through, a little fat is analysed. As the experiments of Counsrern and Micua®iis have pointed out, and we have been able to confirm, this transformation takes place in conse- quence of the drying of the emulsion in presence of blood and air. It appears from (4) and (5), that the passage of air through the mixture of dust-shaped lipanine-serwm-emulsion and blood, causes no transformation of fat, which is confirmed by the result of (6). Two repetitions of the experiment. Ox-blood was now again taken; duration of the passage of air 28 and 18 hours. Room-temperature. (1) 75 ec. dust-shaped lipanine-ascites-emulsion + 25 ce. ox-blood. Passage of a eurrent of air through the mixture for 18 hours, After that dried with sand and extracted with ether. Ether-extract in the two experiments 0.215 Gr. and 0.114 Gr. (2) 75 ce. of the dust-shaped lipanine-ascites-emulsion are mixed with 25 ec. ox-blood, after air has been conducted through the former mixture for 18 hours; after mixture the whole mass is treated instantaneously, consequently at the same time with (1), for the determination of fat. This experiment is therefore similar to (1); with the exception that no air is conducted through. Ether-extract 0.498 and 0.288 Gr. (3) 75 ce. of the dust-shaped lipanine-ascites-emulsion give from 0.562 and 0.315 Gr, (4) 75 cc. of the dust-shaped lipanine-serum-emulsion are mixed with 25 ce. oxen-blood. Passage of air for 18 hours. Drying with sand, extraction by means of ether, free of water. Ether-extract 0.401 and 0.512 Gr. (5) Same experiment (4), but without passage of air. Ether-extract 0.394 and 0.321 Gr. (6) Passage of air through 75 ce. of the dust-shaped lipanine-ascites-emulsion, Ether-extract 0.567 Gr. On comparing (1) and (2) it appears again, that by passing air through the mixture of blood and dust-shaped lipanine-ascites- emulsion, disappearance of fat takes place. On comparing (2) and (3) it appears that by non-conduction of air, some fat is transformed as well. ‘This transformation occurs whilst the drying is going on, as long as the temperature still remains below the transformation-temperature of the ferment. (4) and (5) show, that conduction of air through the mixture of blood and dust-shaped lipanine-sevwm-emulsion, causes no transfor- mation of fat, which is confirmed by the results drawn from (6). Finally the comparison of (6) and (3) proves, that without the aid of blood, the passing through of air is not efficient to make the fet disappear. Considering the results of the different experiments, there is no doubt, that in the examined ascites-liquid a substance exists which appears able to transform fat, and which, with the aid of bloodeorpuseles and with acecss of oxygen, performs the change. CounxsTein and Micnainis are of opinion that this substance, with which they obtained such a transformation of the chyle-fat, is contained in the blood which was used by them. Closely considering their experiments it strikes us that they have no right to maintain this conclusion. For when they observe that after mixing blood with chyle, fat disappears from the latter, it is notwithstanding possible, that the ferment is not present in the blood, but in the chyle. It must seem strange that the authors have not considered this possibility, because no fat disappeared from the mixtures of m7/i: and blood and from cod/iver-oil-emulsions with blood. The authors have tried to explain this latter fact by taking for granted, that the fat would be present in the chyle in a more finely divided condition. Meanwhile this explanation does not seem satisfactory to the investigators themselves, and it cannot be correct, for as was mentioned above, fat also appears in milk in dust-shape. The fat of the so-called undermilk (the undermost of the two layers im which the milk is separated when contrifugalized), consists ex- clusively of dust-particles; it amounts to about !/.) of the total quantity of fat. Also from emulsions of codliver-oil with Na, CO, a portion can always, by centrifugalizing, be separated as emulsion in dust shape. It would perhaps be possible — also in connection with what we found in our ascites-liquid — to find the explanation of their negative result with milk and codliver-oil, in the fact, that neither in milk and codliver-oil, nor in blood a lipolytic ferment was present, - ( 486 ) but that it was present in the chyle; hence the transformation of fat in a mixture of blood and chyle. To my regret I was obliged to cut short my investigation on this subject. Although L am fully aware that these results are in- complete in many ways, it seemed expedient to me to publish them at present, as for some time I shall not have the opportunity to pursue this subject, and I wished to stir up other inquirers to the use of ascites-liquid for the study of the lipolytic ferment. The mucoid aseites-liquid can be had in such abundance (repeatedly more than 8 Liter of liquid were removed from the abdominal cavity of the patient), that it will afford a better and mure extensive oppor- tunity for the study of the nature and the effects of the lipolytic ferment, than most other animal ferments. The above mentioned researches have given the following results : 1. It is possible to make from lipanine (acid olive oil) a perfect dust-shaped emulsion. This has not only been successfully performed with the aid of the examined mucoid ascites-liquid, but also with ordinary horse-blood-serum. 9. This fact seems to indicate, that during life, the transition into dust-shape of the small fat globules, which still exist in the adenoid tissue of the villi, is caused by the continuous motion of the lymph of the vill. 3. The opalescent, non-fatcontaining, mucoid ascites-liquid exa- mined by us, contains a lipolytic ferment, which possesses the power to transform dust-shaped fat. For this transformation the presence of bloodcorpuseles and also access of air is necessary. 4. The contention of ConnsTEIN and Micnabiis, that the lipolytic ferment discovered by them, originates from the blood, has not been proved. Their and my experiments rather show, that the ferment is a constituent of the chyle. ( 437 ) Physics. — Communication N°. 54 from the Physical Laboratory at Leiden by Prof. H. Kamerninan Onnes: “Methods and Apparatus used in the Cryogenic Laboratory IL: Mercury pump for compressing pure and costly gases under high pressure”, (Read January 27, 1900.) § 1. At the meeting of January 25, 1896 I read the description of a compressor which has been repeatedly used for researches in the Physical Laboratory. As the reproduction of the drawings be- longing to this description was very expensive I had to delay their publication. To the description of the cryogenic laboratory by Prof. Maruras!) a diagram was added which could serve as a preliminary illustration to § 3 of Comm. 14 (Dec. °94). Of late only I had the opportunity to prepare the complete set of drawings for zincogra- phical reproduction. These enable me to now describe more fully the way in which I have availed myself of CaILLeret’s lappy idea of a mercury pump in order to obtain a compressor of great use in researches with compressed gas. The compression with mercury has two advantages. If a liquid is brought into the pump cylinder of a compressor, we may thereby eliminate the clearancespace, if the gas does not dissolve perceptibly in this fluid under high pressure. For in this case, the gas which is formed during exhaustion from the residual liquid in the pump-cylinder will partly fill the latter and its clisturbing influence will be greater or Jess, as the difference between the exhaustion and forcing pressures is greater or less. Therefore with most liquids only small differences of pressure between the sucking and com- pression sides will be permissible, and if a higher degree of pressure is required we shall have to apply compressions in successive pump- eylinders as in the BrorprRHoop compressor (Comp. Comm. N°. 51 § 3). If however mercury is used, there is no objection to raising the gas at onee from its normal or even its exhausted condition to more than 100 atmospheres, if desired *). 1) BE. Marutas, Le laboratoire eryog¢ne de Leyde. Rey. Gen. de Sciences, 1896, pag. 381. *) The sudden compression causes a great generation of heat (as in the case of the fire pump) notwithstanding the considerable cooling by the walls and the mercury. A mixture which is easily exploded should not be compressed by the pump, as it might be ignited by the heating. This occurred once, when methane and oxygen became mixed by accident. The manometer was smashed and flung away, a flash of fire burst from one of the outlets, and on opening the pump, several parts were found to be burned. The explosion fortunately oceurred without any personal accident. ( 438 ) In the second place the gas enclosed between pure mereury and steel cannot become contaminated by volatile substances which it might otherwise absorb from the liquid in the pump-cylinder or from the lubricant used for this cylinder. These advantages are of especial importance if we must compress moderately large quantities of pure or costly gases, and for this pur- pose an apparatus of the same dimensions as that of CAILLETET is indispensable in a laboratory. That the compressor (to be described below) answers its purpose in all respects, may be proved by the fact that it has been frequently used during the last eight years, without having undergone the slightest change, or giving the least trouble. The improvements made upon the original CAILLETEY pump in former years (especially in ’88) were rendered necessary by repeated disappointments, which so often disagreeably interrupted the progress of my work that I almost despaired of evcr obtaining a mercury pump easily handled and perfectly trustworthy. In considering the apparatus we must bear in mind that it has grown by gradual improvement from the CAILLETEY-pump, and also that traces of less successful modifications have remained. It would be possible to design now a prior’ a compressor that from the point of view of mechanical design would be of better shape and construction owing to the greater harmony of its dimensions. I hope that a mechanical engineer will feel himself drawn to the solution of this problem. J. was satisfied in having an apparatus which worked well from a physicist’s point of view, and, in the same manner and after this design every other CAILLETET-pump can be successfully modified. § 2. Fig. 1 Pl. I. shows CatLuerer’s original compressor so that we may compare the two compressors together. Fig. 1 is a section, figs. 2 and 3 show the manner in which the gas to be compressed is admitted through the sucking-cock 4 into the pump-cylinder. Pl. HL is a diagramatic representation of the new compressor with the accessories belonging to it. The purpose of this plate is to explain the way in which the different parts work, These are for the greater part drawn on the same scale in a simplified but yet recognizable manner, while the connections are entirely diagra- matical. The real form of these parts, so far as they are not suf- ficiently represented in this plate, may be seen on Pls. IV, V and VI figs. 1 and 2, while figs. 1, 3 and 2 of Pl. II show the actual arrangement of the different parts of the foremost and the hind- ( 439 ) most halves in front elevation, and of the whole in side elevation !). We now come to a more complete explanation of the desirability of the most important changes”). A survey of these has been given in § 3 Comm. No. 14 (Dec. 94), to which a reference should be made in the first place. a1. It was necessary to arrange that air can not get into the pump tube through the packing (comp. 0, Pl. I fig. 1). 42. The piston can not be damaged through insufficient lubri- cation and hence cause the packing to fail to give adequate closure. 43. The mercury can not be soiled by the lubricant. When the latter occurs the scum which gathers near the foreing- valve, keeps back the high pressure gas below this and enables mereury and then gas to leak back from the reservoir under high pressure, Therefore it is of the greatest importance that the mercury remains quite clean. My principal desire in most of the changes was to enable me to accomplish this. Tt was possible to attain all these requirements by transferring the plunger, which by moving upwards in CaILLETger’s compressor causes the compression of the gas (comp. @ fig. 1, Pl. I) toa separate compression tube C' Pl. IIL. From this through a wide connecting tube d, as shown in the diagram, it moves the mercury in the pump- cylinder ¢ up and down. The lubricant used was glycerine, which gives a sufficient lubrication and yet as is the case with vaseline and more especially oils, does not unite with mercury by agitation to a butterlike substance (see especially % 35). Contact of the mercury with the packing is wholly avoided by introducing a Jayer of glycerine above the mercury, which can be done now that the packing is above and not under the mereury. The stuffing box & is entirely immersed in glycerine, so that the pump can only suck in glycerine, if the packing does not fit tightly; should however air enter if might cause the pump to stop working but could not mix with the experimental gas. This could only take place if the mercury and the glycerine were entirely forced ") The resemblance of the forms makes it easy to find our way on the drawings, moreover the letters have been chosen so that the letter itself indicates a distinet part of the apparatus, the annexed numeral a certain detail of that part, and followine numerals details of that detail. *) Some of the newly added pieces were constructed with much care by Mr. J. W. Ginvay (formerly Kipp & Sons); to Messrs. Kouw and Curvers, mechanics at the laboratory I owe my best thanks for the extreme care with whieh they have assisted ine in these alterations, ( 440 ) over to the sucking-side but against this the necessary precautions have been taken. B. 1. If the packing of the plunger is to produce no difficulties it is necessary that it should give a good closure with little frict- ion, for which reason I have replaced CarLLerer’s packing by a collar packing. B. 2. It is also necessary that the plunger should remain per- fect!y smooth (comp. %. 2), which can only be obtained in the long run when a perfectly rectilinear motion independent of the packing is secured. This is facilitated by the use of guides and rods and by modifying the beam accordingly. %. 3. The moving of the mercury should be slow only, (from 20 to 60 up and down movements per minute); to obtain this and also to allow the pump to be regularly worked by hand, the crank is connected to the shaft which makes 60 revolutions per minutes (with an clectromotor up to 90) by means of chain gearing. &. During compression, the pump-cylinder must always be enti- rely filled with mercury, so that the high pressure gas remaining behind in the clearance space, shall not make exhaustion impossible when the mercury recedes. Each time that the mercury presses the gas through the forcing valve into the reservoir of compressed gas, the gas takes some mereury with it. In CaILLerer’s pump to make up for this loss, some mercury is admitted into the sucking chamber from the reser- voir above v (PI. 1 fig. 2). But after some time there is an uncer- tainty about the quantity of mercury in the high-pressure reservoir of the pump, more especially in consequence of the leakage of mercury from the apparatus, which is unavoidable with the con- struction of this pump. If too much mercury is admitted into this reservoir, it would overflow into the apparatus in which the compressed gas is forced. In the newly constructed pump the quantity of mercury to be used is measured precisely once for all and is not lable to diminish. Moreover a capillary connection has been contrived between the reservoir of compressed gas and the pump-cylinder, through which a quantity of mereury which can be exactly regulated, can flow back from the former into the pump body, so that during every com- pression there is a small excess of mercury in the latter, ®. 1. A perfectly rectilinear up and down motion is desirable in order to ensure a satisfactory fit of the forcing valve, which separates the pump reservoir from the pump cylinder. D. 2. In finishing the upper end of the pump chamber we must ( 441 ) bear in mind that compressed gas must not remain behind in scratches, holes or other irregularities of the walls, as this could have the same influence as any air-bubbles which might be kept back by dirt gathered near the pressing valve, if we had not taken the necessary precautions to prevent this as described in %. 3. For it is not unusual for all the gas from the pump cylinder to be compressed to less than 1 c.c. when forced through the pressing- valve. In addition all the parts must remain free from rust, and hence only perfectly dry gas can be admitted into the pump. By means of the precautions taken (comp. also S 1 and % 1) it is possible to obtain a vacuum, which in the pump cylinder is a primary necessity if the exhaust is to be satisfactory. ®. 3. Into this vacuum again the gas must be so admitted during the exhaust, that no air can possibly enter, that the mercury cannot be contaminated, and that the inflow of the gas is not hindered, while even under the highest pressure nothing must leak back from the pump-cylinder towards the exhaust-side. In CaAILLETET’s original pump this is attained by a cock, which is opened and shut at the right moments by means of levers moved by blocks (comp. Pl. I) fastened to a disk on the shaft of the pump. Such a cock cannot work without being lubricated and a little of the lubricant might come on to the surface of the mercury, and the pump could then no longer be used (comp. % 3). We cannot be certain that the cock will remain properly lubricated after some time, and in lubricating air might come in which could contaminatie the gas. Besides it is difficult to keep the cock channel free from the lubricant and therefore large enough. And yet CaILLeter had good reason for using this cock. For an ordinary valve will generally give either an insufficient closure with the various pressures, at which a good closure is required, or it will stick at the highest pressure, so that it does not admit gas into the pump-cylinder during the next exhaust. In order therefore to replace that cock by a valve, which would avoid this lubrication, we had to contrive (as remarked in Comm. N°. 14) a special construction which would satisfy the above men- tioned requirements without being liable to the difficulties offered by ordinary valves. The valve described in § 3 enables us at least as far as it is concerned, to work with the pump uninterrupt- edly, for as long as is required. It is only rarely that the exhaustion fails, and then it suffices to let the pump rest a few moments in the exhaust position in order that the valve may again become loosened. 32 Proceedings Royal Acad. Amsterdam, Vol, IL, ( 442 ) €. 1. We must always expect the possibility of the mercury returning, or what sometimes could be worse, of the already com- pressed gas returning into the apparatus, from which it is taken, in consequence of leakage along forcing and suction valves, espe- cially when the working of the pump is interrupted for some time for one reason or other. This returning of the mercury might cause great disturbances and even accidents. In CartLueret’s original pump a feeding valve (« Pl]. I fig. 1) has sometimes been used but afterwards this has been again removed. When this small ebonite valve came into use, and was closed ty a pressure of for instance 100 atmospheres, it thereby stuck and the pump was stopped working. It could not then be started again without very complicated opera- tions, if we did not wish to lose gas or to have it contaminated with air. Moreover this valve was an obstruction to the easy entrance of the gas into the cylinder. In the newly constructed compressor a safety-feeding-valve (comp. gio Pl. If) has been constructed which in ordinary circumstances lies loosely under its support but is raised and pressed against this by the mercury, as soon as this forces its way towards the exhaust side, while the valve can be loosencd from the support from the outside, after having been pressed against it by high pressure, with- out opening the pump. € 2. At the same time we can avail ourselves of this valve for closing the pump at the exhaust-side, and this is always done as soon as we stop the working of the pump. When started again after an interruption or stoppage with the valve closed, the pump begins to exhaust the sucking-chamber as far as the valve, and then by opening this we can again make the connection with the exhaust-tube, €. 3. As with the least contamination of the mereury (and especially when small splinters of iron or other particles of hard material are in the pump) the valves cease to be perfectly closed, part of the mercury may flow over to the exhaust-side. In order to prevent this from getting into the apparatus, from which the was is taken, an antechamber gg (Pl. IIT) is made, which if neces- sary can contain the whole quantity of mercury which is above the exhaust-valve in the pump cylinder. %. The compressed gas must be entirely freed from mercury. The spreading of the gas jet in the dome shaped reservoir, in which (in CAILLETET’s pump) it is compressed before it is admitted into the outflow pipe is partly useful to this end. ( 443 ) &. 1. It appeared however an advantage to add a spray catcher and separating plate. 8. 2. Further separation is promoted by passage through a small cylinder *,; (Pl. III) in which the current of gas is once more forced to change its direction, while 6 3. the last traces of mercury are removed by a mereury-filter ks (Pl. IIT) in which the mereury is brought into contact with copper and gold-leaf. ©. In order to be warned when the mereury passes over into either the chamber gy, or into the overflowvessel £,, and to observe the position of the mercury in the compression tube C’, insulated contacts are taken through the steel wails, of which those ing, and k, are permanently connected with an electric bell, while that in ¢ only makes contact through a control switch. §. The above indicates what is necessary for sucking in the pure gas at the exhaust-side and for forcing it out at the pressure- side under high pressure and free from mercury. In order to be able to work regularly with the pump we must still contrive some additional apparatus. Among these are: §. 1. A number of cocks, several of which are united together on a cock-board, which also gives §. 2. an opportunity for measuring not only the tension in the reservoir of the pump (as in CaILLerer’s pump), but also that in the apparatus in which the gas is being compressed. §. 3. A safety-valve, which bursts whenever the pressure be- comes high enough to endanger one of the pieces of apparatus which are under pressure and joined on to the pump. . 4. a safety-tube on the exhaust-side, for protecting the appa- ratus to be connected with it, . 5. a connection with the air-pump so that the compressor and all the accessories can be exhausted before pure gas is admitted into them. The operations which are made with the pump, may be arranged under three different heads, which we can find for ourselves from the diagram if we connect I, IT and IIL with the exhaust-tube of the pump. But before treating of these three operations we will first describe the pump itself more in detail. § 3. @. Packing of the compression-tube (see Pl. IV). The piston-rod or plunger 4’; moves in a lignum vitae coating ds fitting in a cavity turned in the compression-tube C'). Before working the oO x OG ( 444 ) wood it is thoroughly soaked in glycerine'). On this coating rests a leather collar 0,,;, which has been made by pressing it, when moist, into a mould made specially for it. When the pressure below the leather collar increases, the inner part of this is pressed against the steel rod, and hence the higher the pressure the better the closure. If however the plunger moves upwards and the vacuum oecurs in the compression-tube, which vacuum with closed suction- valve can amount to 10cm. of mercury (comp. Pl. III), the closure would be prevented owing to the pressure from without; therefore the leather ring must be pressed artificially against the piston-rod (comp. § 2 U1). For this purpose we have placed in the leather collar an india-rubber ring l,,, which presses the collar against the plunger, when the packing-ring is tightened. The packing-compressor b), with the lining l:) is pressed down by the nut J, screwed on to the forcing-cylinder. In this nut also a wooden lining ?3; is screwed, through which the plunger runs. In order to keep the packing entirely under the glycerine (comp. § 2 % 1) a small cup Jj, is placed on the nut 0, which is entirely filled with glycerine and which communicates by two tubes )3 and and 0), and grooves bs, in the nut with the space between the nut and the cylinder 0,; and also with the space between the packing- compressor and the plunger. The air in this space can escape through the longer tube while the space is being filled by the glycerine through the other tube. The screw-threads 0,; between the cylinder-wall C, and the nut }, are filled with wax in order to prevent the glycerine from leaking away along them. If ‘the apparatus is out of use for some time, the glycerine is removed to prevent it from attracting water and hence causing rust, while thegwooden linings are kept in glycerine. In screwing off the nut the glycerine which flows out is caught in the cup Vj, fitting on the support Vj). The glycerine is removed from the compression cylinder by means of a pipette and blotting paper. The mercury (7 KG.) is left in the pump. For the preparation of the apparatus exactly measured quantities of glycerine are poured into the forcing cylinder (70 c.c.) and into the cup bj. To introduce the glycerine into the closed pump the packing is 1) It is first immersed in glycerine and turned nearly to its proper dimensions, it is again soaked for some time in glycerine and then turned to its correct size. Reserve pieces are kept in stock, ( 445 ) loosened under decreased pressure, while to remove the glycerine one of the contacts is loosened a little under pressure. If the exact quantity of glycerine is present, and if during the exhaust the switch belonging to the contact C’, is pressed down (§2 ©), the bell is not heard, if the same is done with the switch belonging to C’, the bell must always be heard, but with the switch belonging to C’, the bell is only heard for a moment. Pl. V fig. 2 shows a high-pressure- proof contact with platinum-point. (3. Up and down motion of the plunger. The plunger 4’, together with the cross-arm 4’, (comp. also PJ. II fig. 3) and the rod A which is directed upwards are forged of one piece of steel. The rod moves through a guide block V., (comp. § 2 %. 2) which con- sists of two parts V2; and Vy. screwed upon each other and is connected to the frame V, through the arm V4. The lubricating oil which flows from the guide-block is caught in the cup 4’, which fits loosely on the cross-piece, and so cannot soil the glycerine (comp. § 2 2. 3). The side arms of the cross piece A's are moved up and down by drawing rods S,. These are coupled to a ring Ss sliding round the smooth cylinder C’, (comp. §2 %. 2); the levers S; in moving up and down can turn on the bolts S,, with which they are fastened to the ring Ss. The beam consists of two symmetrical curved levers being wider towards the side of the compression-tube, and enclosing it (comp. Fig. 3 Pl. IL and Pl. IV to the left, upper view of the ring), while the two parts where they are coupled to the connecting rod or with the hinge Sg, fit immediately against the smooth sides of the rods S,). The piece ‘3, consisting of the halves $3; and S,, screwed against each other (comp. upper view Pl. IV) leaves room when moving up and down for the contact-screws C’; C', C',. For greater security it is covered with a small plate $3) in which is a small lubrication- hole leading to the lubrication-canals $,; and S35. y. Transferring of the motion, gearing. In this connection fig. 1, 2 and 3, of Pl. IL must be consulted, on which no letters are placed for the sake of clearness. The connecting rod ¢, Pl. IV is moved by the crank Uy, Uj2 Vis on which is a ratchet wheel with ratchet and ratchetsupport to render a backward movement impossible. This improvement is especially useful when the pressure-valvye ( 446 )j leaks, but also when we stop the pump and put the plunger in the lowest position in order to reduce the possibility of leakage as much as possible. The fly-wheel is connected on one side of the crank with, a pin, on the other side a toothed wheel is fastened which receives the motion by a chain from a second toothed wheel on the shaft proper. This shaft runs in a supporting piece fixed tightly by means of strong screws to the frame and strengthened by a separate oblique stay. The wheel is drawn in the figures of Pl. II on the shaft over which the leather belt runs to an additional shaft worked by a steam engine. In the Leiden laboratory this latter shaft is on the wall opposite the pump. Instead of the steam engine we can also employ an electromotor of 1 TI. P. (75 K.G.M. per sec.) by means of a large and lightly built wheel of 1 meter diameter and the same additional shaft. Finally there is an arrangement for placing a handle on the shaft of the pump, so that one or two men can turn this at the proper speed (§ 2 3 5). 0. Compression tube and the communication of the mercury of the compression tube and the pump cylinder. The thick-walled for- cing cylinder C’) rests with its base C's, on the frame V, screwed on to it tightly with four bolts Cz the exact position being determined by four pins C's. A direct connection with the pumpeylinder was made impossible owing to the frame and the crank. Therefore, a little above the bottom of the cylinder a bored tap with screw-thread C'; is forged on, on which the thick-walled bent connection-tube dd: (see Pl. II, VI fig. 1 and Pl. II) is fastened by the nut d,. The T-piece ¢, forms a junction between the elbow dy and the double bent tube ¢;, which is fastened with the nut d, on the pump proper es) (Pl. V) this being itself provided with a screw-thread. The nut ¢; rests on the tube by means of a collar dos forged on to d), and a closure is obtained by the washer d;. The fastening of the nut ¢, was a little more complicated. On the tube 3, is screwed a ring ds, above which is plaeed an india-rubber ring dg and a plate ds, which can be pushed over the screw-thread of d3,, this being slightly rounded off towards the upper end by the addition of a rounded ring ¢3,. The india-rubber ring is thus completely en- closed and in tightening the nut d, this india-rubber gives a perfect closure. ( 447 ) The T-piece dy, (Pl. VI fig. 1) is screwed on the two tubes % and ds, so that the bend of the former becomes of the required form, the proper thickness is then given to the leather packings d-, and dg, the closure being obtained by securing nuts dy, and do». The passage for the mercury, is interrupted in the T-piece by two bends dy, and do2, opening into a space dyo3, which space is closed by a tap provided with packing d,3 and also with an opening with its screw d,, and accompanying packing. It is used during the cleaning of the pump to ran off mercury, for which purpose the T-piece is held downwards ; moreover drops of glycerine if they are carried along by the mercury can gather in dg and be drawn off through day. It is seldom necessary to dismount the double bent tube. A great convenience of the above mentioned arrangements is that the mercury can always remain in the pump and hence the introduction of dust or splinters is not to be feared. e. The pump body e with its water circulation eg (PI. IIL and V) is in the main the same as CaILLeTet’s. Here also the head ey is hermetically fitted on the pump body by means of a leather ring while a layer of mercury renders the closure of this packing perfect !). The iron basin e, is arranged to prevent the mercury being spilt *). £. Connection of pump-cylinder and pressure-reservoir. The steel capillary < is fixed at both ends in the cocks 7, and 7,. The latter is adjusted at the height of the suction-valve. At first the commu- nication was made for convenience along do,, but it is evident that the leaking of gas into the pump-cylinder, whenever the cock is not shut in time, may cause great inconvenience. The cocks ¢, ‘2 are constructed according to the Leiden model of high pressure cocks. In order that they should work satisfactorily it is most important that everything should be very accurately prepared on the lathe, so that the point of the pin i,9, which is hardened, fits quite centrally into the conical hole 7,. When the pivot is loosened, the gas must be able to move freely along ¢g3,;, and there- fore the space left should not be too small. The screw-thread 939 must not cut the packing when the cock is entirely open, and hence the pivot %33 must have the full thickness out of which the screw is 1) The packing is tightened by means of a key with a very long handle, *) The floor in the neighbourhood of the pump is arranged so that any mercury spilt can be easily collected, 5 ( 448 ) cut and fit precisely in the small ring 7,;. A little below the washer ‘ase the serew-thread must end in a cylindrical boring corresponding with the part of %:3 projecting outside the packing. The packing itself is pressed into a conical space and care must be taken that new layers of leather (or cork) are always added in time, before the packing-compressor 7, is screwed too far down by the nut é2;. On placing the cock in the apparatus, care must be taken that the point is directed towards that side, where the removal of the pack- ing, which these cocks especially permit, could offer difficulties. To show that the position of the cock may not be altered the handle is taken away from the head of the pin. As usual the capillary 7) is fastened into the overpipes with screw-threads and marine-glue. When the cock 7, is open the boring 7;,; communicates with the eock 7. In the boring 7, of this cock is a filter consisting of closely packed platinum-wires 7,,, enclosed in a small case with sieve-shaped bottom 75; and with a rim and washer 7) 9 resting on the cock itself. The satisfactory working of the filter depends on the pump being thoroughly cleaned, an operation which is rarely necessary with my construction, and which therefore can be done with the utmost care. With one of the cocks 7 we regulate, with the other we shut entirely, a thing which should not be forgotten if the work is stopped for a moment. Moreover these two cocks are required for removing the capillary from the pump when necessary without inter- rupting the work. If everything goes well we can see the capillary moving regularly between two positions (like a Bourdon spring) under the influence of the alternating pressure. The boring 7; communicates with the boring i. in the pump body. To adjust the cock 7% to this so that the packing can be tightened while the cock remains perfectly stationary (which the space at our disposal renders necessary in view of the capil- lary connected with it) a cylinder shaped lengthening piece 7), with flange is forged on 7). It is fastened in the boring ej. by means of a bored conical joint with a thread 7,,, which is in two pieces, held together by pegs. In the boring egg an ebonite cap eg with packing is fastened, so that, when as much mercury as possible has run through 7, a layer remains to assist the closure of ey in e,. n. Forcing-valve with accessories. The steel pressure-valve (Pl. V fig. 1) rests on the support e. which is screwed in the upper-end ne ( 449 ) of the boring in the pump-body. This upper-end is provided with a very finely finished serew-thread in which the thread on the valve support fits very tightly (comp. § 2 D 2). The lower end of the boring in this steel support is turned out smooth and trumpet shaped, so that during compression bubbles of gas cannot remain behind (comp. § 2 D 2). The support fits on the pump body with the help of the enclosed washers ego. The conical part of the valve-pin e;; is ground with the utmost care on the support ¢3, when it is moved it is guided (comp. § 2 D 1) by a cylinder es. sliding up and down in the cylindrical opening ¢g,, in which cylinder pieces are cut away along the lines of movement. The spring ez; and the pin e;, prevent the lengthening piece é33 from moving too much upwards. Moreover a slightly bent asbestos plate e,, may be screwed in the valve between es; and e33;, which in some cases secures a better closure, but this means is not always applied. The upper part of the spray-catcher ez) is supported by the eylinder e7;; screwed on to eg. The superabundant mercury pressed through the forcing-valve rises in this cylinder. The gas escapes through the openings e;,2 and is directed downwards by the second cylinder ej, (comp. § 2 8 1). The plate ¢;; prevents the penetration of mercury into the upper part of the dome (comp. § 2 §. 1). After applying the second jacket no mercury drops were ever found on the plate. The outlet tubes e; and es for the gas from the head are, as in the case of CAILLETET’s apparatus, provided at their upper extremities with flat ends in order to screw them on the washers in the bottom. The cock e,; through which we can allow the gas to flow out, without using the tubes e, and e;, is not now used because of the troublesome mercury-mist, which is produced on opening at high pressure. 6. Exhaust-valve. (For the different sections and details of the valve-box and accessories see Pl. V fig. 1.) The steel valve- box f is fixed against the flat side of the pump body (comp. Pl. II]), in which the boring coincides with the boring f; in the valve-box. They are fastened together by bolts, running through the holes f, and screwed in the holes e,, in the pump body. Be- tween the flat sides of the exhaust valve-box and of the pump-body india-rubber sheeting (45 mg. per cm*.) is laid over the grooves fo; which are useful in making a good closure. The support of the suction-valve f,; is screwed in the piece f, while the closure takes place at the packing f;. The valve support is provided with nu- ( 450 ) merous fine holes f;. The valve-pin f; which is carefully ground on the valve-support, is guided in it by means of the cylindrical rod fs, while the conical part f;,; closes the openings in the valve-support. The valve-pin is constantly pressed against the valve- support by the small spring f,; and the small pin 755. The valve- support can be screwed out by means of the doubly interrupted ring /s;, Which is turned out of it. An india-rubber plate f5, is fas- tened on the valve-pin by means of the screw f52; a four-armed stecl spring f,, presses the edges of the india-rubber plate lightly 5 pressure on the forcing-side to press the steel valve tightly on to the valve support. Should this happen at high pressure the india-rubber sheet rests simply on a flat surface formed by the upper part of the valve-cone and the upper-side of the valve-support. The screw stopper or valve-box-lid /; with the packing fs allow us to test whether the valve works well and to remove the valve-support with its valve from the yalve-box. e. Safety feeding-valve. 'The valve-box and the exhaust-box fy, adja- cent to it are formed of one piece of forged steel ; the boring f, forms the communication between the exhausted space f,; and fj), the space left between the ring fs; and the valve-box-wall, and the suction-chamber fy, in which the gas enters from the sucking-tube Jio, if the valve gy is not closed (comp. § 2 € 2). A small cylinder ggg provided with two notches is connected to this valve by a rol gs., and peg gzi9, on which rod is cuta screw- thread with which it can be serewed up and down through the packing gz3 by a thread in the screwhead gg9. This screwhead is provided on its innerside with a thread. If the small peg gsi9 is held, then the smal] rod must, by the rotating motion of qq, slide up and down without turnig as is necessary in order to loosen it (comp. § 2 € 1). The screwhead is turned by means of the disc Ysa. Of Joo- The lowerside of the tube gj) ag presses is rounded towards the inner side (comp. gj,) to ensure a vetter closure of the valve. The coating ga, of india-rubber mixed with much zine white is tightly foreed into the conical cup gy) and requires only little pressure to assure the closure. As a rule the valve lies on three ridges gy;, made on a supporting ring ainst which the safety-valve ) Additional valves are turned on the lathe to the correct size and kept in stock, against the valve support. It requires then some excess of ( 451) G1. (which encloses also the packing of g,), so that the gas can always stream freely from gj) to fy:, for which purpose also grooves have been cut in the tube gj. The stem gs;, is usually also screwed back a few turns and the valve may still, without being hindered by the peg, be raised so far by the mercury rising suddenly that it closes the opening 41 9)- Tt will be remarked that the connection between the several parts of g and f is a little more complicated than is required; this will also appear to be the case for g itself, which is explained by the remark at the end of § 1; the detailed drawing may be useful for those who wish to change a CAILLETET-pump into a compressor of the Leiden pattern. The nut g, (Pl. VI fig. 2) presses 9) closely against g;;. In the same way as CAILLETET we use the pointed screw g;, to let mercury flow out into the tube g;, from the mercury reservoir g;~ through the hole g,; and the opening g;,, from there it is received in the exhaust-chamber and from there again in the pump cylinder, provided these spaces are under no pressure. This screw-cock is only opened at the commencement or in the case of leakage. Gene- rally the pump sucks gas through g;,; from the cavity gs. and the chamber g, (see Pl. IIL). The latter (comp. § 2 €. 3) is made from a gun barrel, provided with the necessary steel mountings (see Pl. VI fig. 2). The gas is admitted into it by the tube g-;. On the joint g-, connected with it, several conducting tubes (J, II, and IIT) with nuts and packing can be screwed. At the lower end this chamber is provided with a cock 9, to Jet out any mercury that might have run over. The upward ‘bent tube g,,, which can be screwed off, must give a tight joint by a mercury layer. Even if a small quantity of mercury begins to overflow into the tube by insufficient closure of the valves the contact ge; gives warning immediately (comp. § 2 ©), while the contact gg, indicates that more mercury has run over than was contained in the pump cylinder above the suction-valve (sce PI. III), and hence that something is wrong with the compression. tube C'5. z. The transference of the compressed gas. 'The compressed gas can escape (see PI. III) from the reservoir through the conducting tubes k and J. If this is done slowly, very little mercury usually will be carried along. Therefore the cocks are always opened very carefully and except in urgent cases the gas is let out as slowly as it is admitted by the regular working of the pump. ( 452 ) The flange 4, (sec Pl. III and Pl. V fig. 3) is fastened to the bent tube 44, of the main conduit by marine-glue, it is closed by means of the packing 4,5, which is screwed on to the overflow vessel &, by means of the nut 43. The contact k,, whieh inmedia- tely gives warning when mercury passes over into this vessel, is constructed like C’,; (see Pl. V fig. 2). The joint 4; on which the outlet tube f., fits with a nut and packing, is forged on to the side of the steel vessel %,; which is fastened to the frame (see Pl. II fig. 2 en 1). The steel high-pressure point-cock f,,; (see Pl. III) which closes the forcing side of the pump is constructed in the manner explained in detail for 7 and i, like %, it is fastened to the frame. The bent tube 7g) which is more especially intended to enable the pressure in the head to be read on the manometer is provided with a (smaller) overflow vessel J,; its bottom can be screwed off, but as we need hardly fear any mercury on this side, no connections to an electric bell were made. From this vessel (not shown on Pl. II as it is not fastened to the pump itself) the pressure is brought to the bronze high-pressure point-cock /) on the cock-board and can be transferred to the manometer Jy, along J. The steel filter-box %, Pl. III, whither the gas passes from the overflow-vessel, consists (PI. V fig. 4) of a hollow cylinder /3,, on the joints of which the overpipes of the inlets and outlets %,; can be connected by nuts. The overpipes are bored trumpetshape on the side turned towards the filter-box. This contains, enclosed by rirgs and perforated supporting plates 433, thicker brass-wires packed closely together %3,;, secondly thinner brass-wires in &,,,, and finally between two plates with fine sieve-holes, gold-leaf /,,, is placed in order to remove the last traces of the mercury (comp. § 2 §%. 3). This filter-box is fastened to the frame of the pump (see Pl. II, fig. 2 and 1). The cocks, tubes or apparatus in which the gas is admitted after having traversed this filter need not be made exclus- ively of steel or other material, unattacked by mercury, nor need all soldering work be avoided, as was the case with the preceding. But then they must be placed at such a distance from the pump itself, that no contact with mercury is to be feared, which would be the case if they were in the immediate neighbourhood. The tubes connecting the pump to the cock-board, for instance, are made of iron or steel. '). 1) The bell wires are either made of iroti coated by india-tubber of are protected by iron tubes, ( 453 ) 2. The safety-cap (ks Pl. III) consists of a small chamber 4,,, on the rim of which a carefully rolled thin plate of hard brass is screwed by means of a nut 4. and a washer. Thickness and mani- pulation are so arranged that explosion will occur at a given pressure, while leakage which easily occurs with the usual safety- valves is excluded. we. The cockboard. The tube *; (Pl. III) conducts the compressed gas to the main tube 9 of the cock-board, carrying the arms nj), my, and ns, so that the gas can be drawn off by four ways. Generally the cock 7, admits the gas into the apparatus in which it is to be kept or used for researches, while a reservoir p is con- nected to the tube ,, which reservoir in many cases serves to maintain the pressure, when the apparatus is fastened on to the cock 73. The cock n,, serves to conduct the compressed gas to another apparatus or to be sampled for analysis. The cock 7%. allows the tension of the compressed gas to be measured on the manometer. With cocks /,; and ly closed we can also measure on the manometer the tension of the apparatus connected to my4 Or m3, and also with cock 72 closed and cock /, opened the tension of the gas in the dome of the pump. As an example: we may wish to test if the pump is working regularly (especially with the operations IT and ITI). By means of the cock gz the pump with accessories is connected with the sucking-apparatus (comp. § 47) consisting, among other things of a tube leading to an airpump and to an open bottle with a safety-tube immersed in mercury. Moreover 32 is used to permit gas brought under pressure, to flow back to the exhaust-side of the pump (e.g. a gas-holder) (comp. § 4 7). § 4. The accessories described above may be considered as im- mediately belonging to the pump, now we have still to consider what is further required for the operations mentioned in § 2 and indicated on PI. III by I, II, IIL. I. To suck gas from a space under ordinary or less than atmospheric pressure. An instance of this is the frequently occuring sucking from a gas-holder. To this end the sucking-tube gz; of the pump is con- nected to the: ( 454 ) v. Exhaust apparatus for ordinary pressure. (Comp. I Pl. IIT.) This consists entirely of glass pieces of apparatus, to which the iron sucking-tube is connected by means of india-rubber. The gas from the gasholder is filtered through cotton wool and drawn through the tube Os Pl. ILL; if the cock O; is in the position shown here, the gas flows immediately to the pump along Qj) and through the olasswool, phosphoric anhydride and fused sodiumhydrate in the tube Os. If we turn the cock 0; through 180° into its usual position, the gas passes through the washbottles O;, usually filled with pure sulphuric acid (comp. § 2-9. 2). In both cases the wide safety-tube 0, is connected, in which the mercury rises to barometric height during evacuation. The double washbottles are made so!) that they work in the same way with either direction of the gas-current. The bubbling of the gas through the sulphuric acid, which must remain perfectly clear, allows us, like the rising of the mercury in 0; to test very accurately whether the suction-valve works well and also if the pamp-cylinder is properly exhausted. The pump-cylinder is filled with gas of less pressure than that in the apparatus from which it flows; we can reckon to take in from 100 to 125 liters of normal gag in an hour. sal Any spray from the sulphuric acid is received in the bulbs 0) and 0Os,; moreover the tubes are arranged so that the liquid flows back to the bottles; very fine drops that might be carried along, are retained in Oy). If the compression is stopped, the gas still left in the dome ey is caused to flow back through the cock 3 along OQg9 and O; to Ox. The mercury-pump and accessories are exhausted through O,. The three-way stopeock must then be so turned that the drying tubes communicate on both sides with the air-pump. For the exhaustion of the tubing of the apparatus (e.g. gas-holder) up to O; we can use O;. Il. To force compressed gas from a space of lower into one of higher pressure. As an instance of this we may consider the transference of gas from one cylinder to another (e.g. from an almost empty one into one not quite full, a case which often occurs when we wish to raise the pressure in the latter or to have the former at our disposal). With a view to this operation the chamber gs is made so that it can resist if necessary the full pressure of the pump. Fig. III (Pl. IIT) 1) Compare EH. C, De Vares. ‘Thesis for the Doctorate. Leiden 1893. ( 455 ) indicates the connection through a high pressure cock g with a reservoir gs, in which the pressure is read on the manometer 5 to be closed by the cock qy,. In this reservoir the gas from the cylinder g, which is to be forced through the regulating-cock q5 is generally admitted so that the tension in gg does not rise above 10 atmospheres. With higher pressures at the beginning or at the end the pump might begin to work too heavily and the pump-cylinder become warm. Generally before commencing to force over the gas, the pump and the reservoir are exhausted through Nyy and O,. If the apparatus on the exhaust-side is strong enough, a safety-valve may be applied, which conducts gas when the pressure is too high on the forcing-side back to the exhaust-side (comp. § 5 C55). Because the working of the mercury-pump requires constant attention, we may however trust to being warned in time by the manometer whilst the safety-cap gives final security. If. To work in conjunction with a pump which delivers gas under pressure. With regard to the mercury-pump itself, the conditions are the same as if compressed gas were admitted from a cylinder through q, and it is obvious that we may often avail ourselves of the usefulness of my compressor for this purpose. As an example of this I will consider here only the case when the auxiliary compressor is espe- cially constructed to work together with the mercury-pump, i.e. when it transmits exactly so much gas at the highest pressure (admitted on the exhaust side of the mercury-pump), as the latter can take up. If in such a compressor the gas were also forced by means of rmercury we would actually have obtained a mercury com- pressor with two degrees of pressure and tenfold power. With a mercury-pump after the present pattern buth on a somewhat larger scale and with a proportionate auxiliary compressor at my disposal, I should be able to bring about the long wished for circulation of liquid hydrogen in the cryogenic laboratory. In the mean time many researches do not involve the great requirements of this last problem, nor do they admit the use of a BroraerRHoop compressor, arranged for the compression of large quantities of pure gas as described Comm. N°. § 3. For a commencement I found it sufficient to build an auxiliary compressor, which in contradistinction to the BorneRHoop is meant to be exhausted and in which the gas is compressed by a minimum of glycerine. Thereby in contrast with the mereury-pump the auxiliary compressor, destined to work with it could be made ( 456 ) to run fast (at 150 revolutions per minute), and could hence be of small dimensions and inexpensive. With pressures up to 10 atmospheres the disadvantages of the lubricant used, in connection with a drying apparatus presently to be described (in g) are so unimportant that I hope before long to obtain by means of this apparatus liquid hydrogen. The vacuum pump which I considered necessary for this in Comm. N° 23 § 5 will soon be in regular work. The connection, whenever the mercury pump and the auxiliary compressor work together, is shown by II (Pl. IIl). The mereury pump and auxiliary compressor are regularly used for the oxygen- circulation of the cryogenic Jaboratory (comp. comm. N°. 14) }), in the manner described. The gas from the auxiliary compressor passes first through the ge. drying tower for gas under high pressure. This is a steel bottle 7 (see Pl. IIL and Pl. VI, fig. 3. Htbyer and STROMEYER first obtained the 6 aji7390 1, 2. 4 acid by this process and later on | Ciaus and HALBERSTADT working on a larger i5 al co quantity of material isolated the 1, 3, 4 acid : A which is no doubt formed to a smaller extent. \4y ; NO, In the nitration of chloro-benzene at 0° a semi-solid crystalline mass is obtained; if care is taken to collect together all the products formed in the reaction this mass after being fused solidifies at 58°.9. It is known that ortho- and para-chloro-nitrobenzene are formed in this nitration; whether the meta compound is also formed in small quan- titicts remains to be seen; at all events its presence in the nitrated mass is not stated in the literature. Since p- chloronitrobenzene melts at 82° and the ortho compound at 32°, it is evident from the soli- difying point that the para compound strongly predominates, so that the relation will be: ortho little, meta traces, para very much. This, and the relation in which the three nitrobenzoic acids are formed, proves that in the nitration of ortho-chloro-benzoic acid, the acid 1: 2:5 (CO, H = 1) ought to be formed in large predominating quantity toge- ther with small quantities of the acid 1:2:3,; in the nitration of m-chlorobenzoic acid the acid 1:3:6 should be chiefly formed, the acid 1:3:2 occurring only in small and the other isomers in very trifling quantities; in the nitration of p- chlorobenzoic acid the acid 1:4:3 should be almost exclusively formed. This quite confirms the recent research of MONTAGNE '). In the literature, nothing much is said about the relative quan- tities of the isomers formed in the nitration of benzene derivatives ; as a rule the writers confine themselves to such statements as “chief product”, or ,much” of this ,little’ of the other isomer. With the aid of such statements it is possible to ascertain whether the above rule is of general application. This seems indeed to be the case. !) Dissertation, Leiden 1899. ( 480 ) This does not only apply to nitrations, but also in cases of the intro- duction of bromine and chlorine. I have met with many instances in which it was possible to predict which of the possible isomers would be the chief product. The question now arises whether the relative quantities in which the isomeric trisubstituted derivatives are generated corresponds to the relation shown by the above mentioned products, or in other words whether the phenomena observed in the formation of trisub- stituted derivatives may be explained quantitatively in this manner. Researches in this direction are in progress in my laboratory. Chemistry. — Prof. H. W. Bakuuis Roozezoom presents in the name of Dr. C. van Eyk, of Breda, the following paper: * Porma- tion and transformation of the double salt of Silvernitrate and Thalliumnitrate.” (Read February 24, 1900.) 1. Silvernitrate and thalliumnitrate are rhombic at the ordinary temperature; at 159° and 142° respectively, they undergo a struc- tural change and become rhombohedric. No records exist as to the formation of mixed crystals. Reraers (Zeit. phys. Chem. 5, 451) mentions the existence of a double salt without mentioning however whether he has obtained this from the aqueous solution or from the fused mixture. The object of this investigation was to see what kind of crystals are deposited from fused mixtures of various con- centrations (varying from 100 per cent of silvernitrate to 100 per cent of thaliiumnitrate) and to study the possible changes which these crystals undergo at lower temperatures. 2. Determination of the meltingpoint line. The solidifying points of mixtures of Tl NO, and Ag NOs (varying from 0 to 100 percent) were observed and the course of the solidification was watched. Tt was found that the meltingpoint line, starting from either TINO; or Ag NOs, took a descending course with a short double salt line situated between the two branches. Mol. pCt. Ag NO. Commencement of Solidification. MOOS? <.' 3) 5° Ast ke: Bee AO OmO Oasis. 5 at es eee Oe CO Soe So ermora cas Be dekh) Biiee, say > cielo? bom ( 481 ) Mol. pCt. Ag NOs. Commencement of Solidification. SOME n tn bees are Lei (Stommee oo eres ose LOLs (eODie ase. ay oe Sent 4 OF Oe) Sg pe oe oy aioe GQk Sate hoes p VLTGE FAae ica ehcr septs) LOLS Like Gee fase Oe, Ot oe Oe. ee Be GY io Bore ie ede oe tele o AO sho Bo ewe aloe eres AO emo Melee Mires se Ole A Ge a encase oO 41.5 ; 100°.6 40.5. 105° Sao nls 30.7 129° 22.5 149° VA pein eoe cal ee cludes.) Oe bse op ey 2062 The graphic illustration (see figure) gives a clearer view. The points of intersection C and D of the doublesalt line with the two descending branches of the meltingpoint line cannot be readily determined, as both the lines A C and B D continue far beyond those points. For instance, the mixture with 47 mol. per cent of Ag NO; commences to solidify at 85°, crystals being deposited which are heavier than the melt. On lowering the temperature to below 80°, the crystals continue to form until all at once a large quantity of double salt separates and the temperature rises to 82°.8. The temperature at which this sudden separation takes place is not the same in every experiment; sometimes this only commences at 68°. The same takes place with mixtures containing more than 50 mol. per cent of Ag NO;. From the mixture with 53 mol. per cent of Ag NO,, crystals begin to form at 83°.5; these are lighter than the melt. Sometimes the formation of them may continue down to 75° or lower until all at once a large quantity of doublesalt crystals is deposited and the temperature goes up to 82°.8. The mixture with 50 mol. per cent of Ag NOs; deposits, from the commencement, crystals different from the two first. The erystals are of about the same density as the melt. In this mixture the first erystals separate at $2°8, or if supercooling takes place the tempe- rature goes up to 82°8, which is the melting point of the double salt, as soon as crystals are deposited, - ( 482 ) 200° 180° 160° 14.09 120° 100° 80° 6L° NO, 10 20° 380 (40 501°! 60. 170") 604) 90) AgNO, Mol. pCt. The meltingpoint / and the two eutectic points for doublesalt + AgNO, and double salt + TINO, do not perceptibly differ. The short line C #& D of the doublesalt is, therefore, almost horizontal. As a consequence of the fact that the points C and D lie so close to 50 percent, the solidification trajectory that is the series of temperatures at which solidification takes place, is very prolonged for fused mixtures containing much Ag NO; or TI NOs. Even in the case of these mixtures, the lines A C and B D may pass the points C and D owing to superfusion of the doublesalt. Solidification was incomplete even at 80° in the case of mixtures containing 90 percent Ag NO, or 90 percent T] NOs. If the doublesalt did not form of its own accord, the eutectic point F where the melt solidifies to a conglomerate of Ag NO; + TINO; would be noticed at about 75°. 3. The course of the meltingpoint line admits of two possibilities as regards the nature of the crystals which separate from the melt . ( 483 ) containing from 0 to 48 mol. percent of AgNO; or from 52 to 100 mol. percent of AgNOs;: either the pure salts are deposited or else their mixed crystals. The fact that mixtures with a high percentage of either Ag NO; or TINO; are not quite solidified until close upon 80° proves that there can be only a very slight mixing in the solid phases. It is however, impossible to separate the crystals from the melt sufficiently completely to make it possible to decide, by means of an analysis of the separated crystals, whether a small intermixture oceurs or not. This may be more accurately found out by determining the transition points of the separated crystals. At the AgNO,— side, the rhombohedric crystals (whether consisting of pure AgNO; or mixed crystals) which are deposited from the melt at a high temperature, will change into the rhombic form when they are left in contact with the melt at a lower temperature; this change is accompanied by a retardation in the fall of the temperature. When the melt deposits pure Ag NOs th change takes place at 159°, but in the case of mixed crystals the temperature must be either higher or lower than 159°. The same is true of the crystals which deposite on the Tl NOs — side. On ebserving the course of the solidification the retardation always occurred at 152° in the case of mixtures at the AgNO; side, which solidified about 160° and consequently contained from 100 to about 80 percent at Ag NO,. At the TINO, side it always occurred at 142’. From this it follows that mixed crystals are not deposited on either side, or, at most, mixed crystals containing a very small admixture. 4. he solidified mixtures of different concentrations are, therefore, conglomerates of the doublesalt with AgNO; or TINOs. These, on a further decrease in temperature, undergo another change. When the mixtures are allowed to solidify on a glass slide and then exposed to a low temperature they gradually become opaque as may be noticed with the naked eye. The temperature at which the transformation takes place cannot be determined by optical or thermometric methode as the change proceeds too slowly, and therefore, the dilatometric process was applied. First of all, a comparative experiment was made to demonstrate that the change in the conglomerates is a change in the double salt and not of Ag NO; or TINOs alone, ( 484 ) Dilatometer Dilatometer Dilatometer Temperature Tl NO, Ag NO, 51 mol. pCt. Ag NO, 36°.6 24,1 22,5 57.8 Bout 31.9 28.3 52.3 31? 35.9 31.4 49.5 28°.6 40.8 35 46.1 These dilatometers were now cooled down to about 10°, left at that temperature for about 20 hours and then again heated to the original temperatures to see whether any change in volume had taken place. In this way the following numbers were obtained: 31° 35.9 31.4 34.4 TINO; and AgNO, have, therefore, undergone no alteration whilst the volume of the mixture has greatly diminished. The transition temperature of different mixtures was determined next. Rise of level with mixtures of Temperature. Time 40 pCt. 50 pCt. 60 pCi. 70 pCt. in hours. Ag NO, Ag NO, Ag NO, Ag NO, 34°.4 4 + 6.4 + 6.9 + 7.2 + 7.2 30°.9 4 + 1.4 + 1.9 + 1.3 + 1.5 27° 6 + 0.5 + 0.8 + 0.4 + 0.5 26° 6 — 0.35 — 0.4 — 0.2 — 0.3 24° 3 — 1.4 — 1.4 — 1.2 — 1.5 19° 1 — 14 — 2.0 — 18 — 1.6 With mixtures of 20 percent and of 80 percent of AgNO, it was possible to determine that the transition temperature lies between 24° and 29°. It, therefore, appears that all the mixtures have the transition temperature at 26°—27°. It will have to be proved by solubility experiments whether at this temperature, the double salt changes into another modification or breaks up into the components. The following groups of phases exist in the different regions in- dicated in the figure: I. T1NO, a -+ Melt. II. Ag NO, @ + Melt. III. TINO, /? -+ Melt. IV. AgNO, 7? -+ Melt. V. TINO, 2+ Double salt. VI. AgNO; + Double salt. Region VII will contain the group Tl NO; + Ag NO; /, or will have to be divided into two parts representing the conditions of existence of each of these salts with the new modification of the double salt. ( 485 ) Mathematics. — ‘On Orthogonal Comitants”. By Prof. Jan DE VRIES. If we regard #; and xy as the coordinates of any point P with respect to the rectangular axes OX, and OX,, the binary form n == —— n n—-l . yn—2 2 4 a) (a, 2 + ag £9) = ano 2) +N Gn—1,1 7, T2- (| )en—2,2 ty & 2 is represented by » lines through OQ, containing the points for which the form « disappears. x If §, and & are the coordinates of P with respect to the rectan- gular axes OZ, and O2, between the quantities 7), 72 and §), 3 exist relations of the form vy = 41,8 + Aye Sos $y = An % + Agi @9, ay = hy §) + Age Sos Eq = Aqg 2 + dog a. If by these substitutions the form a” is transformed into , we have Gp = Ay 8 $F ag ye = (4 Aq] FH Aq gq) Ey + (Gy Age + 42 Aga) Se, 80 ey = Ay ay + 91 a, l= Are ay -L oo ag - This proves that the symbolical coefficients a), a, and @,, as are transformed into each other by the same substitution as the variables 2,, v2 and &, &. 2. In order to obtain comitants, i.e. functions of a), a), 2, 25 that are invariant with respect to the indicated orthogonal transfor- mations, we can start from the covariants a si as and (@—y3)° + (*—y2)”, representing the square respectively of OP and of the mutual dis- tance of two points P and Q, being therefore absolute comitants. The second covariant can be replaced by 35 Proceedings Royal Acad, Amsierdam. Vol. II. ( 486 ) (22 $22) —2 (ey, + 20 yo) + (9? + 92 See — 2 ay + yy, whilst from the relation (#1 yo — %o yy)* = (a? + 22) (y? + 92) — (tig + 2040)? or (cy)? = rz Yy — ty Ye ensues that the covariant (zy) is related to the covariants «, and #= yz. Now from these three absolute comitants follows immediately the invariant character of the symbols an ay, and (ab). According to the above these absolute invariant symbols are con- nected by the relation (eb)? a7 by — ar. So for the construction of orthogonal comitants we can dispose of the symbols Gg, a), (ab), az, (ar), fz, Ty 4 (zy) . Evidently linear invariants can be generated only by the symbol a, and present themselves only in the study of forms of even degree. Consequently the form a" possesses the linear absolute invariant 1) eT at = dono + 2 A2n—2,2 * 2n—4,4 +++ + 140,20. 3. The quadratic form + 2 ayy % #2 + ao. 2 = ll = oO + a cS) g ow I Q ow S ip bo aro 7 + on S) 1) The existence of this invariant was proved by Mr. W. Manrex by means of an infinitesimal transformation (Wiskundige Opgaven, Dl. VIL, p. 148). ( 487 ) (ab)? = 2 (a9 ao9 — a?) united by the relation found above. Whilst (ab)? =0 points to the coinciding of the two lines indi- cated by a2 =0, aq disappears when those lines are at right angles. If ¢ is the tangent of the angle formed by the two lines, their angular coefficients satisfy the relation f my — Mo i 1 -+ my mg or 4 (499 42 — a) ++ ¢? (a9 + a2)? = 0, or 2 (ab)? + caghs = 0, or at last (c? + 2) (ab)? + ¢? a* Sic So the invariant a; disappears when c? = — 2. 4. By the interpretation of the substitution 7, = 9 or Yili) te Oe oi eee] follows immediately that the covariant (az)? disappears for two lines which are at right angles to the lines i 2 representing a® The covariant (az) az changes only its sign by the substitution z, = 0, So (az) az = 0 represents two orthogonal lines. Indeed the sum of the coefficients of #7 and 25 is equal to zero. If a}; = 0, so that the lines of a2 lie symmetrically with respect to the axes of coordinates, we have (ar) az = (499 — Ag) 2 ay - This proves that the covariant (ar) az furnishes the bisectors of the angles of the lines a2 = 0. ( 488 ) This result is confirmed by the following consideration : By the equations dz dy = 0 and ty = 0 the pairs of lines are indicated lying respectively harmonically with the lines «2? = 0 and with the isotropical lines 72 = 0. And now these two involutions have the pair of rays in common of which the equation is obtained by eliminating y between Q Ax yy + ag dx Yx = 0 and 19, + 74. =0. So the equation (ax) az == represents the orthogonal lines separating a2 = 0 harmonically. 5. If we put ay dz bx = g? , then with a view to the equivalence of the symbols a and 0, we have Ya Jy = 4 Az by ; and Gx (gx) = ay az (5x). But from the identical relation aq bz — bg az = (ab) (az) follows (92) Jr = Aq (bx) be — (ab) (ax) (bx). The second term of the right member disappearing identically and (ba) br = 0 representing the bisectors of the angles of the lines 2 = 0, the covariant ay az bz furnishes two lines having in common with the lines of a> the axes of symmetry. At the same time it is evident that the form ay az (bx) does not give a new covariant. ( 489 ) It is clear that a (ax) (be) represents the lines at right angles to Qi ani0s == 0: 9 6. To two quadratic forms «? and 7? belong the simultaneous invariants (af)? » ae ie ’ (af)ay. As is known the first disappears when the two pairs of lines separate each other harmonically. Under the condition (af) a7 = 0 the lines determined by (af) az fz=9 are perpendicular to one another. These right lines being the double rays of the involution a2+Af2=0, the equation (a/)«y= 0 indicates that the pair of lines a? = 0 and /2 = 0 have common axes of symmetry. This is confirmed by the following consideration. We have (af) af = (429 — 49) fr — 411 (420 — Soa) + If f1; = 9, the invariant disappears when at the same time a,=0 or foo = fog, i.e. When the two pairs of rays have common bisectors or when one pair of rays consists of the isotropical lines. From the expression found above for the tangent of the angles of a pair of lines follows readily that the invariant (wy 7,9, — Ua a, 6, disappears, when these pairs of lines can be brought to coincidence by the rotation of one of them. 7. When the equations 2 — as — a9 at -|- 2 ay) Vy v9 -|- 09 a2 == (1) ’ _—_ Bats wa w Sor * — 2 fir #1 % + Sao w= 0 have a root 7 : e, in common, one of the lines a2 = 0 is at right angles to a line of #2 =9. So the resultant of these equations must furnish a simultaneous invariant. 36 Proceedings Royal Acad, Amsterdam, Vol. LI. ( 490 ) By elimination of «+. we find (429 20 — 40202)” + 4 (420 fir + 411 Soa) (02 fir + 11 So0) = 9 - By a simple computation this expression is reduced to the sym- bolic form a be — 2 (ab) (/y) af by ===) (I) where a2 =0? and f2=¢”?. 7 a zx ae If in the preceding equations we put 4a, = 9, then we have foo=9 or a2, foo + 4 a2 an fi + 4a* fo = 0. In the former case a line of a? is at right angles to a line of /®. Inthe latter case the substitution a 9 = 27a), furnishes the condition — foo + 2tfir + foo = 9; from which ensues that one of the two isotropical lines belongs to each of the pairs; then again a line of a? is at right angles to a line of /? e ot Jeske The consideration of the orthogonal pair of rays of the involution f=) 2 Dyes, a -}- Like = 0 leads to a simultaneous covariant. This pair is indicated by ie at Ae cal Ws +as5)=9, or by da +a f= 9, so by er ge "2 — eee a f2=9. 8. It is a matter of course, that to the cubic form a? = 39 a f- 8 dy, a ay + 38 ayy xy 2? + ays 23 Z 2 2 belong only invariants with an even number of symbols, i. e. of even degree in the coefficients. 49m) Setting aside the forms (4d) a and (ab)? which disappear identi- cally, we have the invariants (ab)? ay = 2 (a5 412 — 4, — a, + 43 21)» at = a+ 35 + 3 a2, -+ ae. From the identity (ab)? + at = aa by evidently follows dg uy by == (ab)? ay + a8 5 For 439 = 0 and a 3 = 0 we have a’ = 3 (a2 + a?) and (ab)? a, = — 2(a3, + a1,); sO 2 a? + 3 (ab)? ay =2 (a3 + 3 dg9 yg + 8 ay3 aq, + a°.) = 0. Reciprocally the disappearing of this invariant indicates that two lines of a3 = 0 are at right angles to each other. For, if by a rotation of the axes of coordinates a3 is transformed into 3 Go) SF So +3 a; $) & + 53 which implies that one of the lines is represented by §: = 0, then the angular coefficients of the remaining lines are connected by the relation m m3 = 3 @,. The above named invariant being transformed into 3; + 1, its disappearing produces the relation mgm; + 1= 0, by which two perpendicular lines are indicated. 9. The comitant ay a2 == 0 determines the polar of a’ with respect to the line 4): ¥2 = 2): 9, or, what comes to the same thing, the double lines of the cubic involution of which («y)=0 is a threefold ray and a’ = 0 forms a group. For the double rays of the involution 36* are determined by or by ay, a2 = 0. ! y yy os In connection with this consideration the covariant of Hesse (a by? ar bz furnishes two lines forming the threefold elements of a eubie invo- lution of which a =0 is a group. The lines of Hesse are orthogonal, when the invariant (ab)? a, is equal to zero. The lines ay a2 =0 are orthogonal when the covariant aay dis- appears, i. e. when we have YL = Ya = 4g da - — A, da: By substitution into 6, 0 =0 we find that the pair of rays in question is indicated by (ab) aq b° = (); The lines of Hesse are the double elements of the involution (a b)? az by = 0. If 7:42 is replaced by ¢y cc: — ¢ ¢c, it is evident that the covariant (a b)? (be) ec ar determines the ray conjugate in this involution to the ray a ay = 0. Evidently the orthogonal pair of rays of this involution is indicated by (a b)? ar (bx) = 0. ( 493 ) So this must correspond with (a6) aq 2 0, which indicates according to the above the same pair of rays. By applying the identity (ab) (aa) = ag be — da ay, We find (ab)bz(av)=(a b) aq be — (ab) ba ax bz, where the third covariant disappears identically. 10. The biquadratie form i 4 2 5 2 472 5 ay ee 24 at = ayy #4 + 4 as, a ay + 6 agg at ae + 4 ay, a #3 + agg as has, beside the above mentioned invariant h = a2 = a49 Ee 2 a9 4 oa a and the well known invariants t=(ab)}* and j=(a b)? (ac)? (d c)’, the quadratie invariants mm of: a2 2 5 a2 2 2 m = at = a* + 4 Gate 0.625. 4 a? -f- a 4Q LES (a bY af) = 2 ago (a4q — 2 99 + Ao4) — 2 (31 — a3)? « In consequence of the identity (a)? + a? =aaby we have ~ =~ ES 4, 9 Dies — 1b)! + 2 (ab) a2 4 at = a2 b? so that we have also i+2l/tm=hR’. If we put a4, = 90 and a4 = 9, then h => 2 994 == 74((3} a, — 4 a3) a4), j == 6 (2 dg dog a}3—03,)s SO 325 =6ih+ 8j. ( 494 ) Consequently the invariant 8 (ab)? (ae)® (be)? +- 6 (ab)* Ci — Sarno tee disappears when the four lines af =0 contain two pairs at right angles. 11. Ternary forms can be represented by cones the top of which is situated in the origin of three axes of coordinates perpendicular to one another. Here too it is evident that by a rotation of the axes of coordi- nates the symbolical coefficients a; of the form at = (ay + ag 4 + ag 25) undergo the same substitution as the coordinates. So the comitants a? + ah + ae 1 4) + ty Yo + 3 Ys (71 Yo — #291) + (2 ¥3 — 73 Yo)? + (#31 — 7 Ys) furnish the invariant symbols Cas 7) (@ bg)? + (ag bg)? + (az 01)? and (abe). For quadratic cones we immediately find the orthogonal invariants ca — ay] + 99 + Ass ’ > (ay) 39 -—— as) and (abe)? — Sa Q)4 99 Ass . ( 495 j Bacteriology. — ‘On Indigo-fermentation”. By Prof. M. W. BEIJERINCK !), At a former occasion it was demonstrated *) that the indigo-plants may be brought to two physiologically different groups, viz. indoxyl- plants, to which the woad (satis tinctoria) belongs and indican- plants. Of the latter, which seem the most numerously represented, were examined Indigofera leptostachya, Polygonum tinctorium and Phajus grandiflorus*). The result was that they contain specific enzymes differing from one another, which split the indican into indoxyl and glucose, while in woad there is no such enzyme. Indican can moreover be decomposed by katabolism*), i.e. by the direct action of the living protoplasm, which has been observed in some indicanplants, beside enzyme-action. Various microbes, too, can decompose indican and here the decomposition is generally effected by katabolism only; some species, however, contain specific indigo- enzymes. Hence the word “indigo-fermentation” means two quite different processes: a katabolic and an enzymatic process, and the enzymes are of twofold origin, products of higher plants and pro- ducts of microbes. It is clear that in the formation of indigo from woad, in which no glucoside but free indoxyl occurs, there can be no question of ,indigo-fermentation”’. 1. Preparation of the Indican as used for the Experiments °), For the preparation of indican-solutions from indican-plants, a method was described (l.c. p. 122) the principle of which is so quickly to destroy the enzyme that the giucoside can be dissolved without decomposition °). This is best done for Indigofera and Po- lygonum by immersion in boiling water, by which an extract is obtained of 0.5 to 1 pCt. indican, which as such, or after mixing ') I am indebted to Mr. J. ¥. B. van Hassetr and Mr. A. van DELpeEN for as- sistance in the following study. *) “On Indigo-formation from the Woad (satis tinctoria)”. Proc. Royal Acad. of Sciences. Amsterdam, Sept. 30, 1899, p. 120, *) Received under this name from a horticultural institution. ‘) For this expression see: Centralbl. f. Bacteriologie 2e Abt. Bd. 6, p. 5, 1900. °) Further informations about the indican and the enzyme of Indigofera are found in the recently published interesting paper of Mr. J J. Hazewsnket, Maandelijksch Bulletin van het Proefstation voor Indigo, Klaten (Java). Aflevering I, Januari 1900, Samarane. *) For the production of many other glucosides the same method can be applied, ( 496 ) with gelatine or agar is fit for bacteriologie or enzyme experiments. The leaves of Phajus grandiflorus decompose the indican at high temperatures with so much energy, that the extraction by boiling does not produce indican but indoxyl, so that I first took Phajus for an indoxyl-plant. In this case, in order to perform the experi- ment at low temperature without indican decomposition, the prepar- ation should be effected in presence of an enzyme poison which does not act on indican. To this effect the leaves are rubbed down in caustic lime or baryta, then filtered and carbonic acid passed through; after filtering again a very pure indican-solution is ob- tained !). The leaves can also be boiled in diluted ammoniac and the superfluous ammoniac be removed by evaporation. Another method is to crush the leaves under alcohol by which the enzyme, though not destroyed, precipitates in the cells, while the indican dissolves in the alcohol and after evaporation of the latter can be taken up in water. By evaporating the solutions to dryness, the impure indican results as a brown mass, resembling sealing-wax, which can be powdered and, in dry condition, be kept unchanged an unlimited length of time. The crude, neutralized or feebly alkaline-solutions, when sterilized and preserved from the access of microbes, also remain unchanged for many months *). A purified indican-preparation is obtained from the decoctions by evaporating them to dryness with caustic lime or baryta, dissolving in little water, filtering, passing through carbonic acid or preci- pitating the baryta with aluminium sulphate, then again filtering and evaporating to dryness. The thus formed preparation contains fewer pigments and fewer proteids than the crude solutions. The impure or thus purified indican is fit for mixing with a solid medium destined for microbe-cultures. On such ‘indican agar” or “indican gelatine’ poured out to plates, colonies or streaks of microbes produce or do not produce indigo, according to the species. Of this later more. For our experiments we used the decoction or the crude indican prepared from it, either or not purified with lime, of Polygonum tinctorium and Indigofera leptostachya, cultivated partly in the garden of the Bacteriological Laboratory at Delft, partly at Wage- 1) The extraction with caustic lime has also been applied by Mr. Hazewinxen for Indigofera. 2) But after a very long time the amount of indican diminishes when air finds aceess. When air was excluded I could note no change in the solutions, ( 497 ) ningen, and kindly procured by Mr. van Looxeren Campaaye. | also received from Mr. HazewiNKeL of Klaten, Java, perfectly well preserved extracts of Indigofera in tins, together with crude enzyme prepared from this plant. 2. Preparation of the Enzymes. i For this preparation I followed the method pointed out before (l.c. pag. 124). The plants are rubbed fine in a mortar under alcohol and during the rubbing the alcohol is a few times renewed. In the beginning alcohol of 96 pCt. is taken, which is sufficiently diluted by the juice of the plant, but afterwards some water is added as otherwise the chlorophyll-pigment cannot be completely extracted from the granules. I suppose this must be explained by the strong water-attracting power of the alcohol, which produces from the protoplasm a proteid, impervious to the chlorophyll pigment and possibly to the alcohol itself, but which, by water, becomes again permeable. In this operation the indigo-enzyme is precipitated in the cells and this occurs so quickly that the indican, which is soluble in alcohol has disappeared before its decomposition can set in. As by this method the chlorophyll is completely extracted by alcohol, a colourless product is obtained, which, after drying, first at 37° C. and then at 55° C., is a snow-white powder, directly, or aiter further pulverising, fit for enzyme experiments. In stoppered bottles I have kept such preparations for months without observing any decrease of activity '). As, in the preparation of the indigo-enzyme from Polygonum tinctorium decomposition of the indican occurs much more easily than with Indigofera, it is necessary, in order to get colourless preparations from this plant, to proceed with greater precaution and to kill the protoplasm more quickly. This is done by taking only a small quantity of leaf substance at a time for the rubbing in the mortar so that the alcohol can penetrate in a few seconds, With Indigo- fera much larger quantities of leaves may be taken, without fear of obtaining preparations coloured by indigo. As I could not point out by the ammoniac-experiment, the presence of free indoxyl in Polygonum leaves, 1 thought at first that the ') The loss of activity in enzyme preparations may be compared to the loss of germinating power in plant-seeds. If they are kept in complete absence of water, both, the activity of enzymes and the germinating power of seeds, will last an unlimited length of time, ( 498 j difference was to be explained by admitting that the enzyme of Polygonum is more soluble in water than that of Indigofera and so, during the extraction could perhaps in higher concentration act on the indican. But the experiment showed that this is not the ease. Neither can the acid reaction of the juice of Polygonum, caused by kalium bioxalate, account for this difference, as the addition of this salt, kalium biphosphate, or of a little acid, to the materials used for the preparing of the enzyme from Indigofera, produces no change in the course of the phenomena. The addition of asparagine is likewise without effect. Nor is the explanation to be found in the relation of both enzymes to the temperature. I have so come to the conclusion that in Polygonum part of the indican is decomposed by the direct action of the living protoplasm itself. This part is however small, and by quickly immersing in boiling water the protoplasm is killed before it causes decomposition. In the preparation of indigo-enzyme from Phajus grandiflorus nothing particular is observed. But we saw before that the decoction method produces no indican but indoxyl from this plant. As the figure below shows that the enzyme of Phajus becomes inactive already at a lower temperature (67° C.) than that of Indigo- fera (75° C.), I must admit that also in the leaves of Phajus kata- bolism exists together with enzyme action and that, at the immer- sion in boiling water, simultaneously with the dying of the proto- plasm, this katabolism causes a vigorous indican decomposition !). Hence Polygonum and Phajus agree in so far as in both indigo- fermentation is caused by katabolism and by enzymes; but they differ in the fact that in Phajus the katabolism is quickened by high, in Polygonum by low temperature. In Indigofera katabolism seems not to occur at all and the decomposition of indican appears exclu- sively effected by the enzyme. From the preparations obtained in the way described, the enzyme itself can but be imperfectly extracted. In water it proves almost quite insoluble, somewhat better in glycerine and _ best of all in a 10 pCt. solution of common salt, as was already indicated by Mr. HazewinkeL, and in a 10 pCt. solution of calcium chloride. In these solutions only a small quantity of enzyme is soluble, for the remaining substance is nearly as strongly active as before the extraction. In the solutions themselves alechol produces hardly any precipitate, so that more active preparations cannot be procured in ) In § 3 p. 513, will be demonstrated that all the indican is loealised in the rotoplasm, ( 499 ) this way. Accordingly the best results in the enzyme experiments are obtained by crude enzyme finely powdered. 3. On the Distribution of Indican and the Indigo- enzymes in the Plants. By the examination of the different parts of indigo- and other plants in the two ways described, the distribution of the indican and the indigo-enzymes was established. It was thus made evident that both commonly occur or lack together. They are accumulated in the leafy organs, especially in the green leaves; in flowers and flower-buds they are in smaller quantity. In the seeds and germs they fail entirely. The roots and stems of Polygonum tinctorium and of Indigofera leptostachya are also quite or nearly quite devoid of indican and indigo-enzyme. Only in transverse sections of branches of the latter, kept for some days in strongly diluted indican solution, I could detect traces of indigo-blue particularly in the medulla and the medullary rays and in the bark, which shows that these parts contain some, but very little indigo-enzyme. The absence of enzyme and indican in the stem and roots of Polygonum tinctorium can be easily shown as the stems of this plant have a great disposition to form radiculae which are, as the stems, by their herbaceous nature and broad-celled structure, quite fit for such experiments. If the roots are allowed to die off in a chloroform-atmosphere they remain colourless; this is likewise the case when the dying is occasioned by immersion in mercury followed by treatment with ammoniac vapour. But from this follows only that indican and enzyme do not occur together; if but either of them is present it is not detected by this experiment), but may be demonstrated as follows. If indigo-enzyme is added to a decoction made from the stems or roots of Polygonum tinctorium, or if this decoction is boiled with hydrochloric acid and a little ferrichlorid to decompose the indican and oxidise the indoxyl, then no indigo appears; so, indican is absent. That in the said parts indigo-enzyme, too, is wanting follows from the fact that parts of stems and roots finely crushed in alcohol, after filtering off and drying, produce a powder quite inactive on indican- solution. Even the growing point and the region of growth of the ‘) This should be kept in view with regard to the ‘“alcohol-experiment” of Mr. Mouiscu, ( 500 ) roots contain no enzyme !), as thin slices killed in alcohol, remain quite colourless in indican-solution at 45°. The same is the case with entire roots which, after killing in aleohol, are put in indican- solution. From these facts seems to follow that the growth and development of indican-plants is not in inseparable relation to the presence of indican and enzyme. To this result we are also led concerning the relation between the development and the presence of indoxyl in the woad, though its distribution in this plant is somewhat different from that of the indican. In woad the indoxyl occurs, besides in the young leaves, and buds, also in the young rootperidermis, in the root-buds and in the growing root-ends*), The distribution of the indican agrees with that of the indoxyl in the fact that they are both completely wanting within the thicker stems and all the thicker roots. So there is in woad no indoxyl in the inner part of the stem organs of the leaf-rosettes in spring, when they are ready to elongate and push out the inflorescence which is then in the very period of the most intens- ive cell-partition and cell-elongation. Likewise, there is no indoxyl in the cambium and the secondary tissues of the woad-roots. Even the flower-buds are in an early period, and when still growing vigorously, free from indoxyl; likewise the embryos, seeds and fruits. First at the germination indoxyl can be pointed out in the seeds and other parts of the germinating plant. So it is very probable that neither indican nor indoxy] are necessarily related to the growth or development of the indigo-plants. But the possibility remains that in certain cases these substances originate as quickly as they dis- appear. So, in the young leaves of Indigofera leptostachya, when kept some days in the dark, a little indoxyl may be detected by means of the ammoniac-experiment, while the normal plant is in all its parts quite free from indoxyl, whence it seems possible, that in normal conditions, there is a continual splitting of indican, which is not observable only because the freed indoxyl directly forms indican again with freshly supplied sugar. For the rest, the woad, of which all full-grown parts are devoid of indoxyl, proves that this substance ean relatively quickly disappear. The appearance of indican, particularly in the peripheric parts of the aerial organs, and the bitter taste it gives them, might suggest }) While in the stem these parts are extremely rich as well in indican as enzyme. *) Which shows that the formation and accumulation of indoxyl is possible in the dark as well as in the light. ( 501 ) the idea that, like tannin, it serves as a defensive against insects and snails. But this supposition would explain only the function of the indican but not that of the splitting products and the indigo-enzyme. If a beneficient influence on the growth in general could be ascribed to indoxyl, then a useful action of this substance on the curing of hurt parts would become probable. And this would also spread more light on the function of the indican and the enzyme, for then it would be clear that the enzyme-action, which operates at the very dying off of the hurt cells, would promote the curing, not only by the formation of indoxyl but also by the production of glucose. As to the localisation in the cell, I found the leaves of Phajus grandiflorus by their broad-celled structure fit for demonstrating microchemically indican as well as indigo-enzyme. The indican can be precipitated as indigo-blue or indigo-red, and both ways point out that it is present in the protoplasm and wanting in the cell-walls, cell-nuclei, and cell-sap. To demonstrate this a not too thin microscopic transverse section of a leaf is put in living condition in a boiling mixture of strong hydrochloric acid and ferri- chloride. The indican is suddenly decomposed and the freed indoxyl as quickly oxidized into indigo-blue, which is easily detected under the microscope as a precipitate in the shape of small blue granules in the colourless protoplasm of the green parenchyma and_ the epidermis. I could not trace it with certainty in the chlorophyll- granules, If the sections, in living condition, are put in a boiling mixture of hydrochloric acid and isatine, the indican passes into indigo-red, which sets off in the protoplasm as very characteristic red crystal needles '). The enzyme, on the contrary, is exclusively accumulated in the chlorophyll-granules as is proved by the following. If living microscopic sections of leaves of Phajus are put in an indican-solution (e. g. in a decoct of Indigofera or Polygonum) they become blackish blue in a short time, which colour is exclusively caused by indigo-blue precipitated in the chlorophyll- granules. In the epidermis much indigo is precipitated only in 1) The presense of indoxyl in urine may be shown with much more certainty and exactness in the form of indigo-red than of indigo-blue. To this end the urine is boiled with hydrochloric acid and isatine by which the colour grows red. At cooling the indigo-red crystallises in characteristic microscopic needles. These are easily filtered and dissolve beautifwlly red in aleohol (best is to boil out the whole filter with alcohol), ( 502 ) the cells of the stomata, elsewhere none at all. If the microscopic sections are beforehand killed and extracted with alcohol, the enzyme spreads in the cell but remains confined within the cell-walls, so that, by putting them into an indican solution they become of a uniform intense blue, in which only the bast bundles remain colourless. The accumulation of enzyme in the chlorophyll-granules is perhaps connected with the formation of starch from the glucose of the indican, As to the localisation of indoxyl in the leaves of woad I have acquired no certainty, but I suppose that, like indican, it occurs only in the protoplasm. The hypothesis of Mr. Mortscn ') according to which indoxyl and indican should be in close relation to the decomposition of carbonic acid in the chlorophyll, appears contrary to the great accumulation of indoxyl in the root-peridermis, which is completely free from chlorophyll, and in the colourless root-buds of the woad, which seems unnoticed by Mr. Mouisca. Nor do I think his argu- ments and figures convincing for the occurrence of indoxy] and indican in the chlorophyll-granules; moreover was Mr. Moniscu unacquainted with the existence of indigo-enzymes and their local- isation, Elsewhere than in the indigo-plants indigo-enzymes seem but seldom to occur. Like Dr. vAN RomBurGu ”) I observed that emulsine of almonds decomposes indican, and in $6 the intensity of this action is graphically represented in connection with temperature. The said fact may serve to demonstrate in a simple way the localisation of emulsine in almonds. If thin sections of the seed- lobes are put in an indican-solution at 50° C., the vascular bundles will first take a deep blue colour, which shows that there the emuls- ine is the most accumulated. Then the parenchyma around them grows blue, and finally the more peripheric parenchyma. This points out that the emulsine is nowhere wholly absent but is accum- ulated about the confines of the central-cylinder, which becomes distinctly visible by this experiment °). A rather great number of other plants examined for indigo-enzymes have all given negative results *). 1) Berichte der deutschen Bot. Gesellschaft, Bd. 17, p. 230, 1899. 2) Communicated by Mr. Hazewinke, Maandelijksch Bulletin N® 1, pag. 8. 5) Nearly the same has been found by JoHaNNsEN, who examined the decomposi- tion of amygdaline with separate parts of the seedlobes. (Ann. Sci. Nat. Botan. Série 7, T. 6, p. 118, 1887). *) So I could not find indigo-enzymes in; Indigofera dosua, Polygonum persicaria, (503 ) Neither is indican decomposed by sections of branches or leaves of apricots, pears, apples, peaches, while in the kernels of the fruits of these species a feebly decomposing emulsine is found. Malt, malt-diastase, pancreas, papayotine, pepsine and saliva are inactive; likewise mustard-seed and myrosine prepared from T'opae- olum majus. Glucase, from maize dees not decompose indican, which is the more noteworthy as amygdaline is decomposed by it. 4. Decomposition of Indican by Microbes in general. Mr. Mouiscu has drawn attention to the fact, that various species of microbes give rise to indigo-formation from indican and that others do not, which may be rendered useful for differential diagnosis. He experimented with the decoct of Polygonum tinctorium or Indigo- fera mixed with agar or gelatine, pouring it out to plates and using these as a solid nutrient. Aerobics and temporary anaerobics from the soil or from canal water sown out on it will develop, and in and around the colonies which split the indican, indigo-blue will separate out in microscopic lumps or globules which often show crystal structure. The ,indican microbes” are in this way elegantly distinguished as pigment-microbes among the non-decomposers. ') The indican, as a powder, may be added in a percentage of 0.5 to 1 pCt. to solid or liquid nutrients, adapted for the examination of specific mikrobe groups. P. aviculare, P. fagopyrum, P. bistorta, P. sacchalinense, Trifolium repens, T. pratense, Medicago sativa, Lotus corniculata, Pisum sativum, Vicia faba, Robinia pseudoacacia, Baptisia australis, Melilotus caeruleus, Spiraea filipendula, S.ulmaria, Rubia tinctorium, Asperula odorata, Solanum tuberosum, Amsonia salicifolia, Asclepias cornuti, Scorzoneru hispanica, Linaria vulgaris, Stellaria holostea, Cochlearia armoracia, Brassieca oleracea, Isatis tinctoria, Iris germanica. 1) Sitz.ber. der Akad. d. Wiss, zu Wien. Math. Naturw.Classe, Bd. 107, p- 758, 1898. Mr. Mowtsch enumerates the following species as decomposing indican : Bacillus anthracis, B. prodigiosus, Streptothrix odorifera, 8. dichotoma, Sarcine lutea, Penicillium sp. and Mucor mucedo; as non-decomposing: Streptococcus pyogenes, Staphylo- coccus pyogenes aureus, Bacillus subtilis, B. coli communis, B. fluorescens liquefaciens, B. megatherium and pressed yeast. Mr. van Hasseur and I saw no decomposition with Acetobacter aceti, A. ranscens, Bacillus cyaneus, B. cyanoyenus, B. pyocyaneus, B. diastaticus, B. prodigiosus, B. pseudotuberculosis. Many spore-forming bacteria, such as B. subtilis, B. megatherium, B. pulcher, B. mesentericus and others sometimes decompose and sometimes do not. Further there is no indican splitting by beer- yeast (Saccharomyces cerevisiae), wine-yeast (S. edlipsoideus), pressed-yeast (S. panis), S. mycoderma, 8S. passularum, 8. uvarum, Schizosaccharomyes octosporus, S. pombe and by the following moulds; Aspergillus niger, A. oryzae, Ainylomyces rouvii, Mucor oryzae, Oidium lactis, Endomyces magnusii. ( 504 ) I found that some specics decompose indican with extraordinary facility. Especially the common ferment-bacteria of plant infusions, which of late I united in the genus Aérobacter!), decompose with so much intensity, that they may with some reason claim the name of ,indigobacteria”; they will later be discussed in particular. For the species which split with more difficulty this power depends on cireum- stances not yet quite clear to me. It may occur that in pure cultures colonies of one and the same origin, and separated from the common stock by a few generations only, behave quite differently, so that species, which for a long time I considered as non-decomposing, later proved vigorous indigo-producers. This I observed for instance in the photogenic bacteria of the Northsea. I suppose this fact to be connected with the influence of the sugar freed at the splitting of the indican, as other experiences prove that this influence is not constantly the same for all individuals of a species. That especially glucose acts vigorously on the life of some bacteria, and, even in small quantities, e.g. 0.05 pCt. to 0.1 pCt. may be a violent poison for some photogenic bacteria, I proved before, and this is noteworthy as still smaller quantities are favourable to the same species. That the different conditions of the bacteria may be of influence on their power for decomposition, follows for instance from the fact that Bacillus radicicola, from the tubercles of Pisum sativum and Trifolium, decomposes the indican, while this is not done by the bacteroids of the tubercles of these plauts. Closely allied species may also behave differently; thus, Bacillus ornithopodis, from the root- tubercles of Ornithopus sativus, does not decompose at all and, among lactic-acid ferments, I observed vigorous decomposition by the rod- shaped ferments used in the yeast-industry (Lactobacter longus), and no decomposition by the diplococci and streptococci (L. lactis) of the dairy industry. The ease with which this reaction is effected and its clear result recommend it for further research. The splitting of the indican by microbes is operated in the same way as in indigo-plants, either by katabolism, i. e. by direct ferment- action of the living protoplasm on the indican, or by specific indigo- enzymes. Consequently the forms belonging to the former group decompose the indican in living condition only *), those of the latter both living and dead. The experiment, demonstrating this, may be performed as follows. ") Centralbl. f. Bacteriologie, 2e Abth. Bd. 6, N° 7, pag. 193, 1900. 2) The optimum temperature of the decompositon by katabolism agrees, for the examined species, with that of the growth. (505 ) Of a culture, grown on a solid nutrient substratum with copious access of air, some material is put on a glass-slide and killed in such a way that eventually present enzyme remains unhurt. This may be done by immersing the material in strong alcohol, in which it should remain at least 24 hours to be quite sure that the microbes are killed, or by exposition to ether-, alcohol- or chloroform- vapour !). In the latter case the microbe-material is placed in a glass-box beside a vessel with chloroform, where ferments moulds, and most bacteria die after '/. to 1 hour already, while the enzymes in the ceils remain unhurt. If a small lump of killed microbes is put in an indican-solution, poured out to a thin layer in a white porcelain vessel floating on water of cirea 45° C., then only those microbes will become blue, which contain indigo-enzyme, while those, acting by katabolism, don’t cause decomposition. If in the latter case not all but only most of the microbes have been killed, there will at first be no manifest decomposition, but it will set in as soon as the living individuals have sufficiently multiplied, which is at the same time a good control of the experiment. The microbes containing enzymes can be dried and powdered after killing and such “crude enzymes’, when kept dry, preserve their activity very long. By the little dissolubility of the indigo-enzymes in water, glycerine and salt-solutions, it was not possible by extracting the crude enzymes and precipitating with alcohol, to obtain more active preparations from them. It has been proved that all examined bacteria, blastomycetes 2) and moulds, which decompose indican, do not effect this by enzymes but by katabolism, while among alcohol-ferments both cases occur. So indican is decomposed katabolically by Saccharomyces ludwigi and Monilia candida, while Saccharomyces sphaericus *), S. apicu- latus, S.muciparus*), S.tyrocola®) contain indigo-enzymes. One of 1) In aleohol vapour many microbes die sooner than in strong alcohol, this having water absorbing power and thus acting protectingly. *) Blastomycetes have the shape of yeast-cells but produce no alcohol. ‘lo these belong e.g. the red “yeasts” Blastomyces glutimis, B. roseus, B. granulosus (of which the last colours deep blue with jodine), and which all decompose indican vigorously. §) Under this name, given by NAcew, | united the various forms of aethyl-acetate yeast. (Verhandelingen 5e Natuur- en Geneeskundig Congres te Amsterdam, 1895, p. 301). ‘) This name I give to a saccharose-yeast, very common in pressed yeast and which does not ferment maltose. 5) §. tyrocola is a lactose-yeast, not rare in Edam cheese. Its cultures on wort- gelatine are sometimes rose-coloured. 37 Proceedings Royal Acad. Amsterdam. Vol. II. ( 506 ) these enzymes, that of S. sphaericus, which acts the most strongly of all, will be treated in § 6. Here I wish to remark that indigo-enzymes originate in the yeast-cells only then, when cultured on a solid medium e.g. on wort-gelatine, with abundant access of air. When cultured in nutrient liquids, even with a current of air passing through, they produce no or oply very little enzyme. The indigo-blue, formed by most moulds and yeast-species in the decomposition of indican, is for the greater part confined within the protoplasm, as was already described and figured by Mr. Motiscu (l.¢.); but in those cases when decomposition is very strong, as with many bacteria, the indoxyl streams out and also precipitates outside of the cell in granules of indigo-blue. 5. Indigo-fermentation by Aérobacter. When a decoction of Indigofera or Polygonum is infected with garden-soil, canal-water or mud, and placed at 28°C., there origin- ates, during a copious formation of indigo, a rich bacteria-flora in which the common gas-producing ferments, which I recently united ') in the genus Aérobacter, perform the chief part. The first who drew attention to this fact was ALVAREZ, but he went too far by admitting the existence of specific bacteria for indigo-fermentation *). By bring- ing a drop of the first crude fermentation into a second quantity of a decoction and so on, an accumulation, sometimes a pure culture of Aérobacter is obtained *). By sowing out an Aérobacter-fermentation on indican-gelatine, not only the Aérobacter-colonies, but also those of various other bacteria colour deeply blue by indigo. Commonly, however, the Aérobacter-species are recognised by their number. But the chief characteristic of Aéro- bacter is its fermenting power and its temporary anaerobiosis, by which the splitting of indican goes on even at temporary exclusion of air, which is not the case with the aerobics. On this characteristic is based the supplanting of the aerobics by Aérobacter in liquid cultures and the prevailing part which these bacteria have in the splitting ’) Centralblatt fiir Bacteriologie. 2e Abt. Bd. 6 N°. 7, 1900. 2) Comptes rendus, T. 105, pag. 287, 1887. 3) In several other plant-infusions, not from indigo-plants, quite the same is ob- served. The strongest 4érobacter-fermentations are obtained by mixing rye-flour with water to a thick pap and placing it at 28° C. After a few hours the development sets in of carbonic acid and hydrogen, caused by the dérodbacter-species, never wanting in flour, which in the beginning supplant all other bacteria. ( 507 ) of the indican in the spontaneous indigo-fermentations. In pure cultures this splitting can of course be as well effected by various common aerobics, albeit more slowly. The decomposition of indican by Aérobacter is operated katabol- ically, as in all other examined bacteria also, so that killed bacteria are inactive and indigo-enzyme cannot be separated out. The optimum temperature for the decomposition agrees with that of the growth and is, for instance, 28° C. for a variety of A. acrogones isolated from milk. The number of *) Indican is, therefore isomeric with Fiscner’s amygdonitril. Ber. D. Chem. Ges. XXVIII, 1508. ( 523 ) PCy He NOy tO, = Cis Hag Ny 0, 4-2 Cy Hy, Og or rather : Cy, Hy, NO, + H, O = Cy His O, + Cs H, NO 2 Cs H, NO + Og = 2 Hy, O + Cig Hig Ne Op but the experiment will have to be repeated on a larger scale so as to be able to judge of the purity of the indigo-blue and ascertain its percentage of indigo-red which also seems to be formed. We also wish to state that during this investigation not the least difference was noticed between the indican prepared from Indigofera leptostachya and that obtained from Polygonum tinctorium and we, therefore incline to the belicf that both plants contain the same indican. As soon as larger quantities of indican are again at our disposal, we hope to continue and extend the investigation of this important compound. The following results were obtained when subjecting indican to ultimate analysis. The sample was dried in vacuo over suiphuric acid. I. 0.2416 gram of indican (Indigofera) yielded on combustion with copperoxide in a current of oxygen 0.4960 gram of carbon dioxide and 0.1257 gram of water. II. 0.2397 gram yielded 0.4928 gram of carbon dioxide and 0.1244 gram of water. III. 0.1539 gram of the indican treated by the KseLpAuL- GUNNING process yielded 5.12 cc. of N/jy ammonia. IV. 0.6310 gram similarly treated yielded 20.60 ce. of Niji) ammonia. On comparing the percentages of carbon-hydrogen and nitrogen with those calculated from MarcuLewskt’s formula: Calculated for C'4 H'7 NOS, 16 Ii III. LYe © 56.0 pC 56.1 pt. — it 56.95 pCt H 5.8 pCt. 5.8 pCt. — -- 5.76 pCt. N we = 4.7 pCt. 4.7 pCt. 4.75 pCt. it is apparent that while the figures for the hydrogen and nitrogen practically agree, those of the carbon are somewhat too low. We, therefore, repeated the determination of carbon by means of the 38* MEssINGER-FRITSCcH!) moist combustion process so as to make more sure about the true percentage of carbon. We first tested the accuracy of the process by some blank experiments and some combustions of salicylamide. V. 0.1371 gram of indican (Indigofera) heated with sulphuric acid and potasium dichromate yielded 0.2341 gram of carbon dioxide = 56.5 percent of carbon. VI. 0.2169 gram of indican (Polygonum) yielded 0.4517 gram of carbon dioxide = 56.8 percent of carbon. If we now take take the mean of these two determinations the composition of indican is: 56.7 pCt. C 5.8 pCt..H 4.7 pCt. N which satisfactorily agrees with that calculated from MARCHLEWSKI’s formula. For the determination of the molecular weight the eryoseopie method was used, as indican is too little soluble in the liquids generally used in the process based on the increase of the boiling point. Two determinations were made: I. 0.1935 gram of indican (Polygonum) dissolved in 24.89 gram of water lowered the freezing point to the extent of 0.058%. TI. 0.8301 gram of indican dissolved in 24.89 gram of water lowered the freezing point to the extent of 0.208°, From these determinations the following figures are calculated for the molecular weight: I 248 en Il 297 which shows that it is not a multiple of 295. C),Hy;NO,; must be aecepted as the molecular formula of indican. The determinations of the water of crystallization were done with indican from Polygonum. I. 0.4149 gram of indican lost on drying in vacuo 0.0594 gram of water. IJ. 3.2262 gram lost 0.4943 gram. III. 0.2291 gram of the dried indican when exposed to the air until the weight was constant, absorbed 0.0393 gram of water *). 1) Lieb. Ann, 294. p. 79. *) The amount of water which is reabsorbed depends on the state of humidity of the air. ( 525 ) The percentage of water contained in crystallized indican is therefore : I 14.3 pCt. IE 15.4 pCt. Ill 17.2 pCt. the formula C,, Hy; NO, + 3 H.O requires 15.5 pCt. Chemical Laboratory of the Polytechnical School. Mathematics. — “A special case of the differential equation of Monee.” by Prof. W. Kapreyn. To the communications inserted in the Proceedings of Noy. 25th and Dec. 30% 1899 we here add the results of our investigation of a case where the equation of MoNGE consists of three terms. If the equation of Monce has the form stittu=—o this equation will admit of two intermediate integrals, only when 1 9 1 A=—=(petv) , w=—HA(pe+»), o og g where gy represents any function of «,y,2,¢, and the function vu satisfies the differential equation 1 dg de (1 Ee = A(g = q g 7 v at ) and #7 denotes the operation — + q— . dy! t02 Then one of the intermediate integrals is petv=f(), where f denotes an arbitrary function, the second being found by connecting the two integrals of the complete system Svecial cases : 1 Here «=— H(pe+v)= 9; therefore Q Hiej=0 and 2 @)=.0; whilst the differential equation for v reduces to du__ dg dz ow Let o be any function of 2, g, w=2—qy. We then find here 1 0G 26 2G 00 =~ |p (oe oq (22) ) . a me ow =| : du The differential equation s+ At=0 now possesses the two inter- mediate integrals Las do 00 mou je 2 = Oe where / represents an arbitrary function. These results are more general than those formerly communica- ted sub IV; we find these back by putting gQ=eSoad , v= — fev (q) dq yp («, g) dy. Tl. sw 0; Here 4 = a @ (po-+v)=0; therefore v 04 € 52) whilst the differential equation for v reduces to au _ 02 or. Let o be an arbitrary function of «, 4,2. We shail now find i; sdo ze) 00 ao = 5, | (5, AE Uk ace OBO a2 del oz The differential equation s-+ 4 = 0, for which may be written @o dr dy 7m possesses as intermediate integrals dx - 06 00 ana as sae a =f (#), do 0a 00 a aly 15, =fy), where f denotes an arbitrary function. These results differ in form only from those formerly communi- cated sub V. Mathematics. —- “On the locus of the centre of hyperspherical curvature for the normal curve of n-dimensional space”. By Prof. P. H. ScHoure. At the close of the preceding paper we have pointed out that the characteristic numbers of the locus of the centre of hyperspherical curvature are lowered if some of the points of the given rational curve lying at infinity coincide. At present we wish to trace fora special case the amount of those lower numbers, viz. for the case where . . ) nm u . . the given curve is the “normal curve’ N,, of the 2-dimensional space S,, in which it is situated. It is known that this curve is represented on rectangular coordinates by the equations Th tn a Come e 10)) 5 eee es 6 teu (Bt) ( 528) ) where ¢ is again the parametervalue of the “point ¢’ of the curve. The quintic » of the preceding paper being unity here, y =O considered as an equation of degree n has here n infinite roots, from which ensues that the » points at infinity of the curve coincide in a single point, the point at infinity of the «,-axis. As an introduction to the general case of an arbitrary », let us first however consider the case n= 3 of the skew parabola. 1. If to avoid indices we write for the rectangular coordinates of a point of S, as is customary 2, y, 2 instead of 2), 7, 73, the skew parabola is represented by mit AR eV ole er oy ay er (4) The equation of the normal plane in the point ¢ is a—t + 2t(y—t) + 3? (e—#)=9, or classified according to ¢ 8 4+ 208 — 32t% + (1-—2y)t —2#=0. . .« (3) This equation being of degree 5 in ¢, five normal planes of the skew parabola pass through any given point and so the locus Rs is of order five, as was formerly found. The equation of the developable enveloped by the series of normal planes is found by eliminating ¢ out of (3) and its differential coeffi- cient according to ¢. This is immediately reduced to the elimination of ¢ between the two cubic equations 413 —92 +4(1-2y)t —5x2=0 ) ’ 135 20+ 12 (10 y—7) 2+ 8 (25 x—8)t+4(1—-2y)=0 j by which is found by means of the wellknown method of elimination Al —92e , 4—8y , —5x2 , @) A 0 O.% Ah) = 98 |, 2 bye ba eno ie Ou ee 4.) $2 5 Seg eS 7 be Se 11952, 120y—84, 75u—24, 4-8y , 0. eo a (Oe = 13852 , 120y—84, 75x—-24, 4-—8y, 0 Os 0 , . 1852 , 120y—84, Wx—24, 4-8y (529 ) So the developable referred to is of degree six; so six is the rank of R, . By solving «, y, z out of (3) and its first and second differential coefficients according to ¢ we find c=28( 9+) from which ensues that the curve F, is of degree five. So, instead of 5, 2(5—1), 3(5—2) or 5, 8, 9, the characteristic numbers of R, are 5, 6, 5. In passing we can remark here, that the normal plane 282 —3tytaj=108t+147+S88+t . . 2 . 6) of the curve #, in the point ¢ is parallel, as it should be, to the plane of curvature B-—38Pxtdsty —z=0 of the skew parabola in the point ¢. The equation (5) being of degree seven in ¢, the locus #’;, belonging to R, as original curve, is of class seven. This agrees with the general result obtained in the pre- ceding paper. For the number 3x—2, here 13, must be diminished by four on account of the particularity sub“) and by two on account of the particularity sub’). For, » being a constant, the quintic equation y=0O has five cqual infinite roots; moreover the three equations @';=0, a',=—0, «';=90 have the factor 15t2+-7 in common, in connection with which the curve F’, proves to contain two conjugate complex cusps. 2. The method followed here for »=3 not being so easy to apply to the space S,, we shall try to find another way, where that drawback does not present itself. To do so we must recall in mind the proof of the theorem formerly used, according to which the envelope of a space with n—/ dimensions, of which the equa- tion, linear in the coordinates x; (i= 1, 2,... n), contains a para- meter ¢ to degree &, has the characteristic numbers k, 2(k—1), Sie — 2) ean tele od te (n—1) (k—n + 2), where it is taken for granted that & >n—2, as otherwise the last ( 530 } envelope contains either a morefold infinite number of points and is then not a curve, or — in case it really consists of a singly in- finite number of points — it is situated in a space S,-;. Ilere k is always 2n— 7. The indicated proof can be given by means of the two following considerations : a). The system. of s+ 7 equations consisting of the equation of degree k fO=atht+atit+....aqnitta= and its first, second.... st differential coefficients according to t may be replaced by a system of s+ 7 equations of degree —s in ¢, all ad- mitting coefficients that are linear forms of the coefficients of f(t) = O. b). The degree of the locus represented by s + 1 equations of degree k—s in t, of which the coefficients are linear forms in the coordina- tes aj(i= 1, 2,...n), 18 obtained by adding to the system n—s entirely arbitrary equations linear in the coordinates and by elimi- nating the n coordinates between the so formed system of x + 7 equa- tions of which n—s do not contain t. The degree of the resulting equation in ¢ is the order of the locus we were in search of. The proof of these two lemmae is very simple. The first is but an extension of a wellknown theorem of EuLer. If we transform the equation / (4) = 0 by the substitution ¢ = — into the homogeneous form g (u,v) = 0, the s+ 7 indicated equations are cp Ss osep asp eee 0), got ee ous dus—! dv And by following the method pointed out in the second lemma we find the number of points common to the locus of x—s dimen- sions, determined by the s+7/ equations of degree k—s and the space S,, being the intersection of any system of n—s spaces S,_1. If the condition is written down, that the eliminant of the system of n+7 equations, linear in the » coordinates, disappears, we obtain an equation of degree (s--1)(k—s) in ¢, which proves the theorem. 3. It goes without saying that the lowering, which the charac- teristic numbers of the locus R, belonging to the skew parabola undergo, is closely connected with the particular structure of the equation. First, this equation is not complet>, for ¢* is lacking ; secondly, not all existing terms contain the three coordinates «, y, < (531 ) in their coefficients. We shall first point out, that the latter pecu- liarity explains the lowering appearing here even then, if we neglect to avail ourselves of the simplification indicated in the lemma a); we shall then show that the first particularity has no effect here. By substituting in the eliminant of the system for each element the number indicating its degree in ¢ and by representing the places made vacant by differentiation by the symbol +, then in the three cases s= 9, 1, 2, appearing in the skew parabola, we have — inde- pendent of the lacking of ¢* in (3) — to deal with the three symbolic equations (9 eaiy ani? Nia 5) (t On pZh—- Qiee Ont ian 2st 0000 le Old 4 PLOVL 4 | = 0, =0, = 0, 0m 080" 0 Or oGr oO + +0 8 | 00 0 0| lo 00 0| 000 0 which really show that the corresponding equations in ¢ are respec- tively of degree 5, 6, 5. By substituting furthermore in the eliminant for each element the term of the highest degree in ¢, we then find omitting the first case, clear enough in itself, Gy) dam ds) Og Gir Capea: Gan | and now, taking the arbitrariness of the coefficients a, } of the equa- tions of the planes S, into consideration, it is clear that the terms of the highest degree [dp edn a8 ee he oe | | ccs lal | =Si(ay bs)t®, ay PL 2t° St! | = — 12a, 8 b, ba | | 2t 5t4 fe 2b 208 | ( 532 ) of these equations cannot be expelled by applying the method of the first lemma or by making use of the lacking of ¢* in (3), by which equations /(t)=0 etc. of still lower degree are obtained. For, these operations correspond with the diminishing of the elements of a row of the determinant indicated above by the corresponding elements of another now multiplied by a form in ¢, and by this method of transformation, much in use with determinants, the degree of the determinant in ¢ cannot be lowered. So it is only appa- rently that by applying the first lemma the degree of the general eliminant is lowered from _@k-) 64+ , Ck—*96+D ’ i(k =) ee See) in reality the eliminant of the equations i) =9, is already of degree (s + 1) (& —s), although judging by the form it seems to be of a higher degree. On the other hand in the case of the skew parabola 0 2 2.5 0212 8| Oo et Been ay see bak? § 0+ 9.4) F282 == (0 passes into =0 and 0, 0 0 O 0 | (0 0° 0 0 0710 “10 ‘4 f | | | 000 0| 00:0 0 00 0 Ol if in succession we make use of the method of the first lemma or of the two cubie equations used in the direct solution; so the deter- minant remains of degree six in t. 4. We are now able to treat the general case completely, where n and s << are arbitrary and & is equal to 2x — 7, If as is custo- mary we represent the analytical faculty Pipa) (p> 2 1) Pat) ry by p7” the equation under investigation appears in the form 5) t 2 Sok jn—s—1 jis, " ju—l {eu—1 | eee 2° .(n—s=Dies—* (nse)... 2 (n—1) ee? (2n—1) t2»—2 LT EE dey cf acide eT Shs ee cease Mell comics itch ikon ite Viele dias Res en lek cl 2) ate dest ctu cePerbe A cepts fen ttss lek fon eee te an Orsay). (2p —gyeltgen—s—1| 7 | 1 a2 GUS a 6 3 « Ola—s O,n—stl + + «© © Ayn (1, n41 d21 2,2 GIS se as os CORn—s C2,n—st1l - + © « An (12, n+1 o: Eros) Go aso one ° ie ol oO Ge d be | Cn—s1 Un—3,2 Un—s,3 + © + An—s,n—s On—s,n—st1 - «© «© An—syn Cn—s, n+1| ( 533 ) By multiplying the second row by ¢, the third by 7 ete. and the s+st by #, the first s+/ elements of each column assume the same power of ¢ From this ensues that (xn —s)+(n—s+i1) +...4- (w—21) 4 2n—1 diminished by 1+e+... +s or 2n—1-+s(r~—s— 1) indicates the degree of the equation, if the terms of the highest degree and the constant term do not disappear. The constant term is the product of the numbers 7, 2, 6, 24,..,and a determinant of coefficients a4; so this does not disappear. And taken together the terms of the highest degree 2x — 1+ s(~— s— 1) have as coefficient the product of a determinant of quantities aiz and ef i Savene I Z n— 8 Woe Gaton be amimal oe n—-7 2n—1 Pn Giksteten cont aise ck eet (n — s)*! \2n — 8)'11 which is reducible to ! ) 1 1 wi ie 1 / | if n—8 m= S87, 6 i ok MER 2n—-1 | (n — 8)? (i 8 DP aay caen gn eae le (2n—1)? .| } (nm — s)s (n — s-+ 1) (n — 1): (2n — 1) and this differs from zero, it being the product of all possible dif- ferences of the s+ numbers »—s, n—s+1,....n—d1, 2n—1 and no equal ones appearing among them. According to the final result obtaimed in this way the character- istic numbers of the locus of the centre of hyperspherical curva- ture 2, for the normal curve N;, are respectively 2n—1, 38n—8, 4n—7, On—18, Gn—21,.... 2a—d, from which ensues that they do not change if taken in reversed order. In particular we find for ree 3, Oo n= 8. Dy Ono n= 4. hs 29R OS 7. m= 9d. Gy elo, UL ne n= 6 cel PL LO) 17, a ileh eLOeLEL n= 7 > 18; 18, 21; 22, 21; 18, 13 n= 8.... 15, 21, 25, 27, 27, 25, 21, 15 n= 9.... 17, 24, 29, 32, 33, 82, 29, 24, 17 n=10.... 19, 27, 83, 87, 39, 89, 87, 33, 27, 19. With this the table inserted in the preceding paper referring to the general rational skew curve of minimum degree can be compared. Physics. — ‘kquations in which functions occur for different values of the independent variable”. By J. D. VAN DER WAALS JR. (Communicated by Prof. J. D. vAN DER WAALS.) § 1. Let us imagine an. electric vibrator at a distance r from a reflecting plane. If we wish to construe the equation of motion of that vibrator at the moment ¢ we shall have to take into consideration that forces act on the vibrator, which it has given out itseif and which have then been reflected by the plane. ,These forces are determined (a 2) by the condition of the vibrator at the moment ¢ at which the vibrations were given out, i.e. at the moment which precedes with . ” Us . . an interval of 2 — the moment, at which we want to know the way of motion. The equation of motion, which determines the motion of the vibrator, will therefore besides the electric moment of the vibrator and its fluctions at the moment ¢, contain the same quantities at the moment ¢’=t— 2 . : Similar problems of a more intricate kind may occur in great numbers. First we may want to examine the influence which diffe- rent vibrators exercise on each other, in which case a set of simul- taneous differential equations is to be solved which show the pecu- liarity which we are discussing. Further the different bodies in question may move, which makes r and therefore the difference of time between ¢ and ¢ variable. If we have e.g. a vibrator, which moves normally towards a reflecting plane, it will have been at the moment ¢#’ at a distance from the wall which we call 7’, so that: Now it may be that we want to examine the ponderomotoric actions, so that the quantity r, which occurs in ?¢' is at the same time the quantity, which is not given as function of t, but which we want to determine as function of ¢ by means of the differentia] equation. Similar problems are of course also found in the theory of sound. Though these problems are possibly not of so much importance, that it is worth while drawing up a complete theory of the equations in consideration, I will point out some particulars of the solutions, as they have never been discussed as far as I know. § 2. In the physical problems there occur always differential equations. I will however begin with the simpler case in which the equation to be solved does not contain any differential quotients. In general such an equation may be represented by : IORI cede a pe Up Here y' represents the value of y which is obtained by substi- ( 536 ) tuting « by «' in y=/(«). Now we must also know in what con- nection «’ is with the other quantities. In general this is done by giving: EM Opeperen cae) Pe The problem is therefore reduced to the solution of: Ey, y, oe) 0 and af)\(y,.9, 25.2) —0 where we must take into account, that the dependence of ¥’ on « and that of y on # is expressed by the same function. From these two eyuations we may think y' and 2’ as being solved: a = x) (2 y) y' = Z2(% Y)- Let us now assume an arbitrary value «= 2; and a perfectly arbitrary function y= w,(#). Let us now calculate y, = y (7) and t= 7) (#4). Then we can represent the quantity y between the limits # and a, by the perfectly arbitrary function. If we substitute in 7: (vy) and 7o(xy) the value yy (7) for y, we get #’ and y' both expressed in wz: By eliminating 2 from these two equations we get y' = yy («’'). If we then determine: Yo = Wa (et) and v3 = YZ (*2 Yo) we may represent the value y by 2 (v), When « ranges between the limits w, and 73. In exactly the same way we may determine functions 3 (x), Wy (x) ete., which will respectively be a solution for z be- tween wv; and «,, «4 and #; ete. With the aid of the integrals of FourieR we may write the solution as follows: % «=«@ y =() i sin (ua) sin (vw) yr, (v) dv du ++ Zi 20 vs wo +f a sin (ux) sin (vu) wy (v) dv du + ete. 2 0 In this way however we do not get a continuous curve as solution. In general the function will have two values at 2), %o, #3 etc., and it will then consist of two branches, which have no connection with each other. We have viz. not taken care, that the value y= yy; (2) with which the portion of the curve between x, and 9 ends, is the same as Y's = Wo (2) with which the portion between 7, and 23; begins. It is this last value for y , which we have to substitute for y' in Fy, ye, x)= 0 and Fy (y',y, 2,2) = 0, if we want to find out whether the data are fulfilled by taking the points (7), 4) and (7, yg) as points (7, y) and (2’, y’). By putting: Y= YW) (ici Coy ee oe Ger) in which ¢), ¢),..-. - ¢n—1 represent constants, which are still at our disposal, we find for ww; ete. also functions, which contain these same constants. If we put YQ = y¥'95 Ys = Y's se 2 Yn ==) 5 we may solve the c’s by means of these »—1 equations, By substituting the values of these c’s obtained in this way in y= YW (@,¢ «+ + Cn—1) we get between x) and #4, a curve as solu- tion, whose coordinates do no longer show any discontinuity. In ememene: : ; general however the quantity cm will vary discontinuously at the POmtsierg Most nea We must state here, that it is not necessary that 2 Wy << ts 0 a a time of oscillation of the order =o must exist. Moreover we shall find a series of overtones, as equation (3) has an infinite number of roots. Thus far we have occupied ourselves only with the function- solution. It is however easy to find also the general solution. ie If we represent between the moments ¢ and t ae the electric moment a, by 9 (t) and ag by y, (#), the equations (1) and (2) take the following forms: Pow tt =) du, (¢t—— Bay day va Ve tt YW) ( > eg A), a che ck 18 ere ana te a dt: dt ie 7 d (« 20. : ( V 2 + 4541 (t=) = 2 («— “2 d (= Bag dary ii Yi Ss v) a 9 — ge ot es Og = Ag oars at de geass) a(+-2 re AV, r) These equations can certainly be solved. ( 545 ) Let us represent the solution by: a = Fy \¢) and ay = We (t) then gs and y, are the solution of the problem between the moments 24 v9 0 t) + V and q + ay § 6. From a mathematical point of view perhaps the function- solutions only may be considered as genuine solutions of the problem. We seek namely a quantity y as function of 7, which is in a cer- tain relation to a quantity »', which represents the same function of x, but for a different value of z. If in the general solution y is equated to w(x), y' is represented by another function of «, namely wo(e). It is not essential that we take y, only between the limits v, and @,, W between the limits 2, and z,;: we might also have taken as a solution : y = YW) (®) + Ye (2) + ws (x) + ete. We must take care, however, that if for a given value of « we take y on a branch belonging to the curve y = w (2), we take y' on a branch of the curve y= Wn41 (2). From a physical point of view, however, the general solution with Fourter’s integrals is in fact the genuine solution. For let us imagine that we have only one system with n degrees of freedom which is made to move after a certain method, and which after the moment ¢ is suffered to move freely. The motion after the moment ¢ will then be determined only by the x generalized coor- dinates and their » fluctions. On the other hand, if we have two systems which act on each other with forces which propagate with finite velocity through a medium, and if we suffer these after the moment ¢ to move freely, the motion after the moment ¢ will depend not only on the x» coordinates and their fluctions, but also on the con- dition of the medium. The condition of the medium at the moment # gives an accurate image of what has happened with the systems during some time preceding the moment ¢, that is to say it gives an accurate idea of the way in which the systems are made to move. Let us for instance take the problem of Gaxirzin, and let us imagine that the molecules are set vibrating by the collisions, and . ; vr that a collision lasts a very short time 7, so that 0< mt Let ( 546 ) us now imagine that at the moment t, the molecule I collides with a” ay : the molecule III. Between 4; and t;-+ 7 the value sr will then dt? be very great. Afterwards that quantity will be reduced to an aver- Lo a age value; but at the moment ¢ + ay the wave emitted by mole- ; 5 : a? ag cule I will arrive at molecule II and will cause ae to have an dt 2 r abnormally great value between ¢,; + = and t; + : 4-0. Between Lo Ly a, the moments ¢, + 2 es and #+ es + 0 the value of -- will 9 be again abnormally great and so on. This solution is certainly not contained in the function-solution. Therefore before we assume the theory of GaLirzin of the broad- ening of the lines of the spectrum as proved, we should have to make a separate examination, in order to investigate in how far we may assume that the motion of the molecules may be represented approximately by the function-solution, and in how far the roots which GaLirzin has not found, have influence on the phenomenon. In this investigation we should have to start from the hypothesis about the way in which the molecules are made to vibrate. I shall however, not occupy myself further with this problem, but I shall try to solve the more intricate problem of vibrators which are in motion, in order to investigate, if a connection may be found between the ponderomotoric forces of radiation and the molecular forces. The solution of this problem I have had in view from the very beginning. Astronomy. — “The 14-monthly period of the motion of the pole of the earth from determinations of the azimuth of the meri- dian marks of the Leiden observatory from 1882 —1896”. By J. Weeder (Communicated by Prof. H. G. van peg SANDE BakuUYZEN). 1. From the motion of the poles of the earth over the earth’s surface results not only a variation of the geographical latitude of each place, but also a variation of the direction of the meridian; hence the azimuth of each direction varies accordingly. If in seconds of are 2 and y express the deyiations of the north pole (547 ) from its mean place in the direction of the meridian of Greenwich (2) and in the direction of 90° West of Greenwich (y), then we can repre- sent the azimuthal deviation A of a meridian with regard to its mean direction for a place at geographical longitude 4 (West of Greenwich) and latitude /?, in seconds of time by the formula: sec [P __ + (x sink — ycos h) AR tae A This formula represents also the variable part of each azimuth when these azimuths are taken so as to increase from North to West. 2. Prof. Tu. ALBRECHT!) has deduced from the variations of latitude of several places a continuous series of values for the co-ordinates x and y, beginning with 1890.0 ; these show that the path of the pole of the earth is geometrically rather intricate. In 1891 Dr.S. C. CHANDLER found a 14-monthly as well as a yearly pericd in the motion of the pole, but thought that two periodical terms of the periods mentioned would be insufficient to express the co-ordinates of this motion. Dr. EK. F. vy. D. SanDE Bakuuyzen on the contrary has contented himself with using these two periodical terms *). According to his computation the results derived with regard to the motion of the pole from observations after 1858 can be brought to agree fairly well with the supposition that each of the co-ordinates « and y consists of 2 singly- periodical terms one having a period of about 14 months, the other of exactly a year. It appears then that the terms of the 14-monthly period may also be the components of a circular motion of the pole. The most probable elements of this circular motion are according to Dr. E. F. v. D. SANDE BAKHUYZEN: Period 430.66 days Amplitude = 0."159 Epoch of the greatest latitude } Julian date 2408568 for Greenwich j or 1882 May 2 and the components for the Julian date ¢ corresponding to this: ¢ — 2408568 2 == +.0."159 cos. 2 2 Fa0566 ') Tu. Auprecut, Berichte iiber den Stand der Erforschung der Breitenvariation, in December 1897, 98, und 99, *) E, EF. van pg Saype Bakuuyzen, Sur le mouvement du pole terrestre, d’aprés les observations des années 1890—97, et les résultats des observations antérieures, Archiv. Neéerl. Série 2. 7. IL. (548 ) ee BANS GS yor 0."159 sin.2 a 430.66 From the terms of the yearly period follows a motion of the pole in an ellipse whose axes are 0."121 and 0."057; on September 28 the pole is in the major axis, in the meridian 19° East of Greenwich. 3. The following investigation intends to deduce the 14 monthly part of the motion of the pole from the results for the azimuth of the meridian marks of the Leiden observatory. The pier of the north mark was renewed in 1880, the pier of the south mark in 1882; the determinations of azimuth used for this research, were begun for the north mark only not until Juli 1882, for the mean azimuth of both marks in January 1884, and so in each case more than a year after the construction of the pier, when the masonry was for the greater part solidified. The period of the observations used here ends July 1896, and so includes 14 years or 12 14-monthly periods so that the variations of azimuth of the latter period could be deduced independently of the yearly period. The material consists of transits of « Ursae minoris in both culminations and without using the artificial horizon. The observers were E. F. vy. p. SANDE BakuuyzeN and J. H. WILTERDINK. The following tables I and II show, for both observers and cul- minations separately, the number of the observations made and their distribution over the years and the months. DAS Let July 1882 | 83 | 84 | 85 | 86 | 87 | 88 | 9 | 90 a1 | 92 | 93 | 94 | 95 | | ' daly 185 | 86 | Serer BB Ba) 0, PL as Shee |_| | | | Observer: E. F. v. p. S. BAKHUYZEN. | | | 1 j i i j | | Upp. | an | losal adit saul aetna @ Bee era one 1 30 | 28 | 26 | 23 |. 23 13) AB AG ese 412 6 3 Cali, es ee ele freee Nee | Tow. | 3, | 32! 39 | 97! 01! 9! 94] 10/12! 95| 99! 14! 9! 5 Culm. | } | | | | Observer: J. H. WILTERDINK. Ww i) ow | { | | } 11 | 87 | 19 | 35 | 98 | 20) 12 g| 9 aoe a ~ ; 23 |; 23 28) 1 ( 549 ) TA Bye all: es lige. | al Seay ae ee eee | Months, |) J. (R02 | Mi. | AS VME Jd de tA | S25) OL FN. | Dy] Lotal: | | je Se a Be eae Observer: KE. F. vy. p. 8S. BAKHUYZEN. Up | | | | | | (i= [an Guin 5 | 28 | 27 | 30 | 17 | DT Ba 26 | 30 | 28 | 24 19 256 canoe dla a ee ee ee oe a Gatan.s Je? || 201 3020 28 | 43°) 25 See fella UE AE We 3) | 9278 Observer: J. H. WILTERDINK. : i T 7 7 | ) | Upp. 2 : 2 7 Gal 16 | 36 | 32 | 42 | 33 | 10 9 | 13 | 22 | 27 | 20 | 14 274. Low. | eral [arate l Game pee ee ae ee es 986 4. The following remarks may help to form an opinion about the value of this material for the investigation of the motion of the pole: 1st. The mean value of the accidental error in the azimuth, de- duced from one transit-observation, is two or three times greater than the amplitude of the 14-monthly motion. 2nd, The directions of the marks in the horizontal plane are by no means absolutely stable, on the contrary their accidental varia- tions throughout the whole period have been greater than the variation of the direction of the meridian resulting from the motion of the pole. 34, In spite of the remarks 1 and 2, the number of the obser- vations and their distribution over a long period may lead us to expect a satisfactory determination of the periodical influences on the azimuth. Yet for an independent determination of the length of the period, the time during which the observations were made was too short. Therefore I had to content myself with a determination of the ampli- tude and the epoch. Besides the accidental variations the two directions of the marks are liable to systematic yearly-periodical motions in azimuth, as is clearly proved by the differences in azimuth of the two directions, which are of course independent of the motion of the pole. The graphi- eal representation of this periodical variation (Fig. 1) has been deduced from the readings of the marks from 1883 Aug. 10—1898 Aug. 10. Fig. 1 Seal oD of on nN on n a 7 aad + oD — Ce ae ee ee ee ee a ea iS < DB cs) be a = om = < a = 5 Tals =r Sue oa [aa =e 0 040 | : + + | Hail | | [ +0040 COPERREEE oe + — 4 an STS NN \ ae fom as = Bai es Wn — we) elas i a ea ieee DestesaT MERA ors for) wo foo) ive) ~ oa ~ ~ ~ o o wo a 4 foal ca nal 4 al fol al cq oa al Baol AO Re see. OSs ope yeh. ect emene me Res 3 Sr v 2 oS 2 w o oa =u oS 3 ac) One part of this periodical annual variation is caused by a motion of the direction of the north mark, another part by a similar motion in the direction of the south mark, and probably the mean azi- muth of the two directions is also influenced by the same motion- As communicated in § 3 the determinations of azimuth from 1882 July to the end of 1883 concerned the north mark only ; in order to be able to unite the azimuth of this period with those of the following years to a system as homogeneous as possible, the azimuths of the north mark before 1894 are diminished by half the difference in azimuth between the two directions from fig. 1; after having applied this correction, the remaining influence of the periodic motion on the azimuth of the north mark, is equal to that on the mean azimuth of both marks. In the azimuths this influence is combined with that of the periodic motion of the meridian direction, resulting from the yearly- periodical part of the motion of the pole; as we cannot compute the two influences separately, we cannot compare these determina- * (551) tions of azimuth with the elements of the yearly motion of the pole. As with regard to the 14-monthly motion of the pole there is no reason to expect changes of the same period in the directions of the marks, I have attributed the variation of azimuth to the me- ridian direction, and therefore to the motion of the pole only, and from the latter I have calculated, assuming a period of 430°/; days, the amplitude and epoch of the above-mentioned part of the motion of the pole. 5. About the reduction of the observations I will communicate as much as is required to understand the deduction of the numbers to be given below, and also their meaning with respect to the 14-monthly motion of the pole. The observed time of transit reduced to the middle thread, has been corrected for the inclination of the axis of rotation, the collimation constant, the clock-correction, and also partly for the azimuth of the telescope and the personal equa- tion of the observer. The azimuth constant of the transit instrument used for this reduct- ion is deduced from approximate values of the azimuth of the north mark up to 1884, further for the mean azimuth of both marks, which approximate values are derived from the results of preliminary calculations and are taken so as to vary with the time as regularly as possible. A few corrections have been applied to these values: 1°. In agreement with the idea mentioned above, half the differ- ence in azimuth of the north and south marks has been added to the azimuth of the north mark before 1884. 2°, periodical corrections have been applied to the azimuths over the whole period, which corrections result from a 14-monthly motion of the pole according to Dr. E. F. v. D. SANDE BakHUYZEN, and are expressed by the formula: A 03159) sec fur . 12408568 A = in (22 — ) 15 430.66 ? and 4 being the latitude and longitude (West of Greenwich) of the Leiden observatory. (Proc. Vol. I, p. 202). By applying the correction 2 for the periodic motion of the pole to the approximate values of the azimuth constant, the corrections of that constant deduced from the discussion of the whole series of observations are freed from the greater part of the influence of the 14-monthly periodic motion as proved by the results. By means of the azimuth-differences between the telescope and the north mark (before 1884) or the mean of the two marks (after 188-4) ( 552) as deduced from the micrometer readings on the marks, we have deduced the approximate values of the azimuth of the transit circle from those of the azimuths of the marks. The personal equations of the observers which have been applied here are the differences of the Right Ascension of Polaris according to their observations and the Right Ascension of this star according to the “Fundamental Catalog der Astronomische Gesellschaft.” 'These approximate values are deduced from former observations of Polaris, in the supposition that the personal equation for both culminations and under all circumstances is the same. 6. After the reduction mentioned in § 5 each time of transit o should represent, if the elements of reduction were exact, the apparent Right Ascension of Polaris ¢ as deduced for the moment of observation from the mean place of the Fundamental Catalog. The apparent Right Ascensions are borrowed from the ‘Berliner Jahrbuch” ; only in the years 1882—85 the mean Right Ascension of the “Jahrbuch” differs from that of the “Katolog” and then the apparent Right Ascension of the Jahrbuch have been reduced to the later system. The differences o—e of the observed and com- puted Right Ascensions further have served to determine the cor- rections of the personal equation and the instrumental errors and principally those of the assumed azimuths of the marks. 7. For the discussion of the quantities o—c the following course has been taken. First the mean of the values o—c for three successive months have been formed for each observer and for each culmination separately in order to determine that part of the values o—e which, independently of the influence of the accidental and systematical errors of the instrument, is the same for the two culminations. For tke deter- mination of this part the observations of the two observers at first have been treated separately. In so far as the two culminations were both observed during the same periods of three months half the sums of their mean results are taken; as it appeared that these values showed periodical annual variations, the periodic part has first been deduced and afterwards the annual means of the residuals are com- puted. It then appeared that the results for the two observers agreed fairly well, both with regard to the annual means and to the co-efficients of the periodic part. Therefore I have combined the corresponding results of the two observers in one system; and have represented graphically the annual means obtained in this way by a smooth curve. The sum of the ordinates of this curve and of the deviations resulting from the periodical annual variation form the part of the quantities o—c, common to both the culminations; ( 553 ) this part has been subtracted from them. Finally a constant cor- rection for personal equation, different for each observer has been applied to the o—e, in order to reduce the mean value of the cor- rected o—c for each observer to 0. 8. The quantities o—e corrected as explained in 7 consist of the accidental errors of observation and the influences of systematical errors in the adopted values for the inclination of the axis, the constant of collimation and the azimuth. The azimuth-corrections might have been determined with greater precision if the observations had been or could be made free from the influence of the firstmen- tioned systematical errors. The observations at my disposal do not contain any data from which to determine the systematical cor- rections of the inclinations adopted; some reflection-observations of Ponaris from 1882—84, made for this purpose, have not been considered as their number was too small for the determination of a satisfactory correction of the inclination. Somewhat different from this is the opportunity for correcting the constants of collima- tion from the observations themselves as they have been made in the two positions of the instrument. During the period of the obser- vations the transit circle has been reversed 24 times which divide the whole interval into 12 periods in which tie clamp was east and 11 during which it was west. The longest of these periods lasted 28 months, the shortest nearly 2 months. The influence of an error in the assumed amount of the constant of collimation on the azimuth-correction, calculated from the value of o—e, changes in sign by the reversal of the instrument; it can therefore be found when we compare the azimuth-corrections from observations of Polaris, immediately before and after the reversal, or, if that error proves to be constant during a longer time, when we compare the mean azimuth-corrections deduced from observations during a longer period before and after the reversal. It now appeared that the observations of Polaris immediately before and after the reversals were not numerous and that moreover one single observation is not accurate enough to betray a small syste- matie error. The graphical representation of the mean azimuth-cor- rections during long periods, on the contrary showed clearly the influence of a smali error in the assumed constant of collimation. These mean values during the same position of the instrument showed generally a regular variation; if however we would combine the means of all the periods in a regular chronological order, then the curve 40 Proceedings Royal Acad. Amsterdam, Vol II. ( 554 ) obtained disagreed for the greater part of the time with the idea of a regular variation of the azimuths of the marks. 9. That a small correction of the assumed constant of collimation for Polaris, which might give a regular variation of the azimuth during the whole period, is not impossible may be seen from what follows. This constant consists of two parts: the constant of collimation determined in the nadir by the reflection of the vertical thread on the horizontal mercury-surface, and the small correction for the flexure of the rotation axis axpressed by the for- mula )(1 + cosz). The first part, the constant of collimation in the nadir, is probably very exact (only in the period 1884—1885 the degree of precision may be a little less, the level being less reliable), but the value of the flexure found by determining from time to time the constant of collimation in the horizontal position of the telescope by pointing at the marks before and after a reversal is less trust- worthy, especially as it appeared that it varies distinctly, when the position of the cell of the object glass was altered. Therefore I thought myself justified in deducing from the Polaris- observations and the readings of the meridian marks small corrections to the constant of collimation, which rendered the variation of the azimuth-correction more regular, and which, with a few exceptions were constant in the periods during which the cell of the object glass was in the same position. In order to be able to judge in how far the motion of the pole in the 14-monthly period deduced from the observations is dependent on this correction, I have computed this motion supposing: 1st that the constant of collimation is left unchanged, 24 that the small correction mentioned has been applied to it. 10. The values of o—e, during 14 years (1882 July to 1896 July) corrected according to 7, for each observer separately, are divided according to the time of the observations into 12 groups, each enclosing 430 days (the assumed value of the period of the pole-motion) and each of these periods is subdivided into 43 periods of 10 days!). The mean values of o—c, during these 10 days for each culmination separately, were now formed and to each mean was given the weight 1, independent of the number of values. So we ebiined a series of numbers (at a maximum of 24), representing the values of o—e in both culminations belonging to one and the same ') In this computation the period is actually reduced to 4342/,, days, by causing a period of 430 days to sueceed two periods of 431 days. In the periods of 431 days one of the subdivisions consists of 11 days instead of 10 days. (555 ) phase of the pole-motion; after this the means of these values belonging to a same phase were taken, after changing the sign of o—c at lower culmination, because the influence of a variation of azimuth on o—e in both culminations has a different sign. Finally for each observer the deviations of these 43 numbers from their mean has been formed, which deviations after the reduction from differences in time of transit to differences in azimuth, represent the still remaining influence of a periodical change of the pole on the azimuth of the marks. A great part of that influence has been removed by applying to the azimuth, assumed in the reduction, the periodic corrections men- tioned in § 5 sub 2°, computed after the formula deduced for the 14-monthly motion of the pole by Dr. E. F. van pe Sanne BAKHUYZEN. In order to obtain the whole influence of this periodic motion, this correction of the azimuth has again been added to those 43 values for each observer. Of these values “,g and Uy for the two observers the mean has been taken independently of the number of the observations and these numbers are given in Table III. Deel i ner. 3 Before the correction 5 After the correction of the A of the 3 constant of collimation. 22 constant of collimation. 2) ee i) = ah Ae egirie | ae : Re i | | n | Yo(U_ +U y) 1/.(U3—Uy) | (Up +Uy) | Y2(¥g—VU iy) Obs.—Comp. 1 + 0.017 + 0.0138 + 0.010 + 12 + 0.003 2 +h 26 4 01 + 19 — 05 + 10 3 a 17 =f 07 + 17 + 06 + 07 4 + 12 + 01 + 14 = 08 + 02 5 00 4 04 + 03 + 04 — 10 6 — 12 + 10 — 07 07 — 21 7 — 02 = 02 + 06 00 — 08 8 + Sie e—— 03 4 22 — 3 a 07 9 + 13 = 04 + 16 00 4 01 10 25 4 ll + 29 + 06 a 15 11 =f 29 -- 03 + 32 + 01 + 18 12 — 05 08 + 07 + 06 — 06 13 + 16 04 + ll + 10 Ol z — ei Before the correction of the After the correction of the S constant of collimation constant of collimation. m | 5 (ie Urey |i 2( 0,—Uy) le(Uy + Uy) .(Uz—Uy) Obs.—Comp. _— 16 Sa 02 _ 30 1] + 06 _ 06 Se [ (557 ) The first column contains the ordinal numbers of each period of 10 days, the second and fourth columns contain the half sums of Up and Uy in the two suppositions: that the correction of the constant of collimation mentioned in $$8 and 9 has, or has not been applied. The degree of precision of these numbers can be derived from the values of half the differences }(Ug— Uj) which, if the observations are correct, must be equal to 0. I have formed the means from each set of three successive values of '/g (Us 4- Ujy) and have represented them graphically in Fig. 2. Fig. 2 Pos SPs FRR eH RE 1 ' ' (he eer) ' (eae ae ee eT ey ga Wea —+—— -9020 | | sal If we try to represent the numbers !'. (Ug + Uyr) of the 4th column by an ordinary sinusoid and, assuming that this formula is exact for the middle-epoch, we reckon the time ¢ in days from May 19th 1888, we obtain the following formula for the influence of the motion of the pole on the azimuth of the meridian marks at Leiden : a 360 U = 08,0148 Sin . Ea 19°.0) 430,66 Column 6 of table IIL gives the differences of the results accor- ding to this formula and the observed quantities in column 4. Accor- ding to this formula the influence of the motion of the pole on the azimuth is 0 on April 26th 1888; at that moment the latitude of Leiden resulting from that periodic variation attained its maximum. The amplitude a of the circular motion of the pole, is found from the amplitude of the variation of azimuth 0.0148 by means of the formula a= 15 X 0.0148 Cos mp = 0.136 in which y represents the latitude of Leiden, ( 558 ) If from this formula for the variation of latitude for Leyden we want to deduce that for the variation of latitude for Greenwich, we must only take for the date of the maximum latitude 5 days earlier i. e. April 21st 1888, so that the co-ordinates of the motion of the pole for Greenwich are : t— 2410749 430.65 w= + 0".136 cos 2 a t— 2410749 ee 0".136 sin 2 2% —— Met Es 430.66 in which ¢ represents the Julian date. 11. If we compare this epoch for the maximum latitude of Greenwich with that deduced by Dr. E. F. vy. p. S. Bakuuyzen, we see a difference of 2181 and after subtracting 5 periods or 2153 days, it appears that the epoch found by me occurs 28 days later than that according to Dr. E. F. v. p. S. Bakauyzen. In the Astronomische Nachrichten n°? 3207 A. Soxonorr has given the results of an investigation of the motion of the pole ina period of 430 days by means of the meridian marks of the transit- instrument in the observatory at Pulkowa. In order to compare his results with those found by me, I here give the results deduced by SoKoLorr from the observations from 1880—1887 made by WAGNER, Wirrram and Harzer. a. From 476 transits of @ Ursae-Minoris Amplitude = 0".172 Epoch for Greenwich = 2410743 i.e. 22 days later than according to E. F. v. p.S. B. b. From 288 transits of 0 Ursae-Minoris: Amplitude = 0".195 Epoch for Greenwich = 2410771 i.e. 50 days later than according to E. F. vy. p.S. B. e. From 226 transits of 51 H. Cephei: Amplitude = 0.156 Epoch for Greenwich = 2410759 i.e. 38 days later than according to E. F. v. p. S. B. In SoKoLorr’s computation the time of the period is assumed to be 429.7 days. The epoch of maximum latitude of Greenwich given above, has been reduced by me from the year 1884 to the year 1888 by using a period of 430.66 days. (559 ) Physics. — ‘Considerations on Gravitation”. By Prof. H. A. LORENTZ. § 1. After all we have learned in the last twenty or thirty years about the mechanism of electric and magnetic phenomena, it is natural to examine in how far it is possible to account for the force of gra- vitation by ascribing it to a certain state of the aether. A theory of universal attraction, founded on such an assumption, would take the simplest form if new hypotheses about the aether could be avoided, i.e. if the two states which exist in an electric and a magnetic field, and whose mutual connection is expressed by the well known elec- tromagnetic equations were found sufficient for the purpose. If further it be taken for granted that only electrically charged particles or ions, are directly acted on by the aether, one is led to the idea that every particle of ponderable matter might consist of two ions with equal opposite charges — or at least might contain two such ions — and that gravitation might be the result of the forces experienced by these ions. Now that so many phenomena have been explained by a theory of ions, this idea seems to be more admissible than it was ever before. As to the electromagnetic disturbances in the aether which migh possibly be the cause of gravitation, they must at all events be ol such a nature, that they are capable of penetrating all ponderable bodies without appreciably diminishing in intensity. Now, electric vibrations of extremely small wave-length possess this property; hence the question arises what action there would be between two ions if the aether were traversed in all directions by trains of electric waves of small wave-length. The above ideas are not new. Every physicist knows Le Sage’s theory in which innumerable small corpuscula are supposed to move with great velocities, producing gravitation by their impact against the coarser particles of ordinary ponderable matter. I shall not here discuss this theory which is not in harmony with modern phy- sical views. But, when it had been found that a pressure against a body may be produced as well by trains of electric waves, by rays of light e.g., as by moving projectiles and when the RéNTGEN-rays with their remarkable penetrating power had been discovered, it was natural to replace Ly Sage’s corpuscula by vibratory motions. Why should there not exist radiations, far more penetrating than even the X-rays, and which might therefore serve to account for a force which as far as we know, is independent of all intervening ponderable matter? I have deemed it worth while to put this idea to the test. In ( 560 ) what follows, before passing to considerations of a different order (§5), I shall explain the reasons for which this theory of rapid vibrations as a cause of gravitation can not be accepted. ore § 2. Let an ion carrying a charge e, and having a certain mass, be situated at the point P(z, y, 2); it may be subject or not to an elastic force, proportional to the displacement and driving it back to P, as soon as it has left this position. Next, let the aether be traversed by electromagnetic vibrations, the dielectric displacement being denoted by > , and the magnetic foree by §, then the ion will be acted on by a force 4nV2ed, whose direction changes continually, and whose components are Reta VA e0., YS 4a eb, a Ae eee) In these formulae V means the velocity of light. By the action of the force (1) the ion will be made to vibrate about its origial position P, the displacement (x, y, z) being deter- mined by well known differential equations. For the sake of simplicity we shall confine ourselves to simple harmonic vibrations with frequency ». All our formulae will then con- tain the factor cos xt or sin nt, and the forced vibrations of the ion may be represented by expressions of the form xX = ae dy — beds, y = ae dy —bedy, on eae ome 0 (4) z= aed, — ber, with certain constant coefficients @ and b. The terms with dx, dy and , have been introduced in order to indicate that the phase of the forced vibration differs from that of the force (X, Y,Z); this will be the case as soon as there is a resistance, proportional to the velocity, and the coefficient ’ may then be shown to be positive. One -cause of a resistance lies in the reaction of the aether, called forth by the radiation of which the vibrating ion itself becomes the eentre, a reaction which determines at the same time an apparent increase of the mass of the particle. We shall suppose however that we have kept in view this reaction in establishing the equations of motion, and in assigning their values to the coefficients @ and b, (561 ) Then, in what follows, we need only consider the forces due to the state of the aether, in so far as it not directly produced by the ion itself. Since the formulae (2) contain e as a factor, the coefficients a and & will be independent of the charge; their sign will be the same for a negative ion and for a positive one. Now, as soon as the ion has shifted from its position of equili- brium, new forces come into play. In the first place, the force 4a V?ebd will have changed a little, because, for the new position, > will be somewhat different from what it was at the point P. We may express this by saying that, in addition to the force (1), there will be a new one with the components 0 dx 0 dx 0 dx at ee ana cle a Giese tPA a) In the second place, in consequence of the velocity of vibration, there will be an electromagnetic force with the components Aye aie) eles wa eee a, & C4) If, as we shall suppose, the displacement of the ion be very small, compared with the wave-length, the forces (3) and (4) are much smaller than the force (1); since they are periodic — with the frequency 2, — they will give rise to new vibrations of the particle. We shall however omit the consideration of these slight vibrations, and examine only the mean values of the forces (3) and (4), calculated for a rather long lapse of time, or, what amounts to the same thing, for a full te 276 period J n § 3. It is immediately clear that this mean force will be 0 if the ion is alone in a field in which the propagation of waves takes place equally in all directions. It will be otherwise, as soon as a second ion @ has been placed in the neighbourhood of P; then, in consequence of the vibrations emitted by Q after it has heen itself put in motion, there may be a force on P, of course in the direction of the lne QP. In computing the value of this force, one finds a great number of terms, which depend in different ways on the distance rv. We shall retain those which are inversely proportional to ror7*, but we shall neglect all terms varying inversely as the higher powers of 7; indeed, the influence of these, compared with . ; : Ay that of the first mentioned terms will be of the order —, if A is the - ( 562 ) wave-length, and we shall suppose this to be a very small fraction. We shall also omit all terms containing such factors as r 7 r cos 2 m k— or sin 2 dary (t a moderate number). These reverse their signs by a very small change in 1; they will therefore disappear from the resultant foree, as soon as, instead of single particles P and @, we come to consider systems of particles with dimensions many times greater than the wave-length. From what has been said, we may deduce in the first place that, in applying the above formulae to the ion P, it is sufficient, to take for » and § the vectors that would exist if P were removed from the field. In each of these vectors two parts are to be distinguished, We shal) denote by >; and ; the parts existing independently of Q, and by >: and 2 the parts due to the vibrations of this ion. Let Q be taken as origin of coordinates, QP as axis of «, and let us begin with the terms in (2) having the coefficient a. To these corresponds a foree on P, whose first component is : dx Odx 0dx 9 ‘ x 5 +o) pO) +8 aby db). 4nV? ea (Ps Re Since we have only to deal with the mean values for a full period, we may write for the last term — a (dy Bz — de By), and if, in this expression, Hy and §, be replaced by d ‘a { b< “4 An V2 (2% _9 *) and 42”V2 dds =), v 2 Oy On (5) becomes d2 on Vig Sees, Ic ALE MI ota ee (0) On where > is the numerical value of the dielectric displacement. Now, »? will consist of three parts, the first being 5°, the second do? and the third depending on the combination of d, and 9. Evidently, the value of (6), corresponding to the first part, will be 0. As to the second part, it is to be remarked that the dielectric displacement, produced by Q, is a periodic function of the time. At : : : c “ae distant points the amplitade takes the form —, where ¢ is indepen- A prt > bite ( 563 ) oo dent of » The mean value of »? for a full period is 5 ibac and by Pe) differentiating this with regard to 2 or to 7, we should get? in the denominator. The terms in (6) which correspond to the part 2 (d1x dox a. diy Doy fe diz doz) in 2, may likewise be neglected. Indeed, if these terms are to r ihe contain no factors such as cos 2ak zo sin 2 1k re there must be between 0, and oy, either no phase-difference at all, or a difference which is independent of 7. This condition can only be fulfilled, if a system of waves, proceeding in the direction of QP, is combined with the vibrations excited by Q, in so far as this ion is put in motion by that system itself. Then, the two vectors d,; and », will have a common direction perpendicular to QP, say that of the axis of y, and they will be of the form diy = 7 cosn (7 a) c & Voy = — cos n (: — +8). 7 The mean value of diy dey is 1 ge Sie cos n (&| — £9) + 2 9 and its differential coefficient with regard to « has 7? in the denom- inator.. It ought therefore to be retained, were it not for the extremely small intensity of the systems of waves which give rise to such a result. In fact, by the restriction imposed on them as to their direction, these waves form no more than a very minute part of the whole motion. § 4. So, it is only the terms in (2), with the coefficient }, with which we are concerned. The corresponding forces are —4An V2 2b (6.2 + dy 2s +d: ts Pee (7) v y z. and OUD (S reste AD ERG) «speech ay As veges (8) ( 564 ) If Q were removed, these forces together would be 0, as has already been remarked. On the other hand, the foree (8), taken by itself, would then likewise be 0. Indeed, its value is ne? b (by 2 — 02 Hy), - - - « » -.~ (9) n? eb or, by PoyntTiNna’s theorem ae Sx, if Sx be the flow of energy in a direction parallel to the axis of «. Now, it is clear that, in the absence of Q, any plane must be traversed in the two directions by equal amounts of energy. In this way we come to the conclusion that the force (7), in so far as it depends on the part (,), is 0, and from this it follows that the total value of (7) will vanish, because the part arising from the combination of (d,) and (d,), as well as that which is solely due to the vibrations of Q, are 0. As to the first part, this may be shown by a reasoning similar to that used at the end of the pre- ceding §. For the second part, the proof is as follows. The vibrations excited by Q in any point A of the surrounding aether are represented by expressions of the form 1 9 r * ——"iC08 2000 —) —— é r ( V ) where # depends on the direction of the line QA, and r denotes the length of this line. If, in differentiating such expressions, we wish to avoid in the denominator powers of 7, higher than the first — and this is necessary, in order that (7) may remain free from 1 powers higher than the second — — and & have to be treated as Uh constants. Moreover, the factors # are such, that the vibrations are perpendicular to the line QA. If, now, A coincides with P, and QA with the axis of z, in the expression for 5, we shall have i= 0, and since this factor is not to be differentiated, all terms in (7) will vanish. Thus, the question reduces itself to (8) or (9). If, in this last expression, we take for > and their real values, modified as they are by the motion of Q, we may again write for the force n? e& b 2 Sx ; this time, however, we have to understand by S, the flow of energy as it is in the actual case, v ( 565 ) Now, it is clear that, by our assumptions, the flow of energy must be symmetrical all around Q; hence, if an amount Z of energy traverses, in the outward direction, a spherical surface described around Q as centre with radius 7, we shall have cure E ae face and the foree on P will be n? bE K—— 47 V2 92 It will have the direction of QP prolonged. In the space surrounding Q the state of the aether will be sta- tionary; hence, two spherical surfaces enclosing this particle must be traversed by equal quantities of energy. The quantity / will be independent of 7, and the force & inversely proportional to the square of the distance. If the vibrations of @ were opposed by no other resistance but that which results from radiation, the total amount of electro-mag- netic energy enclosed by a surface surrounding Q would remain constant; “ and K would then both be 0. If, on the contrary, in addition to the just mentioned resistance, there were a resistance of a different kind, the vibrations of @ would be accompanied by a continual loss of electro-magnetic energy; less energy would leave the space within one of the spherical surfaces than would enter that space. / would be negative, and, since b is positive, there would be attraction. It would be independent of the signs of the charges of P and Q. The circumstance however, that this attraction could only exist, if in some way or other electromagnetic energy were continually disappearing, is so serious a difficulty, that what has been said cannot be considered as furnishing an explanation of gravitation. Nor is this the only objection that can be raised. If the mechanism of gravitation consisted in vibrations which cross the aether with the velocity of light, the attraction ought to be medified by the motion of the celestial bodies to a much larger extent than astronomical observations make it possible to admit. § 5. Though the states of the aether, the existence and the laws of which have been deduced from electromagnetic phenomena, are found insufficient to account for universal attraction, yet one may try to establish a theory which is not wholly different from that of ( 566 ) electricity, but has some features in common with it. In order to obtain a theory of this kind, I shall start from an idea that has been suggested long ago by Mossortr and has been afterwards accepted by WiILNELM Weber and Z6OLLNER. According to these physicists, every particle of ponderable matter consists of two oppositely electrified particles. Thus, between two par- ticles of matter, there will be four electric forees, two attractions between the charges of different, and two repulsions between those of equal signs. Mossorrr supposes the attractions to be somewhat greater than the repulsions, the difference between the two being precisely what we call gravitation. It is easily seen that such a difference might exist in cases where an action of a specific electric nature is not exerted. Now, if the form of this theory is to be brought into harmony with the present state of electrical science, we must regard the four forees of Mossortr as the effect of certain states in the aether which are called forth by the positive and negative ions. A positive ion, as well as a negative one, is the centre of a dielectric displacement, and, in treating of electrical phenomena, these two displacements are considered as being of the same nature, so that, if m opposite directions and of equal magnitude, they wholly destroy each other. If gravitation is to be included in the theory, this view must be modified. Indeed, if the actions exerted by positive and negative ions depended on veector-quantities of the same kind, in such a way that all phenomena in the neighbourhood of a pair of ions with opposite charges were determined by the resulting vector, then electric actions could only be absent, if this resulting vector were 0, but, if such were the case, no other actions could exist; a gravi- tation, i.e. a force in the absence of an electric field) would be impossible. I shall therefore suppose that the two disturbances in the aether, produced by positive and negative ions, are of a somewhat different nature, so that, even if they are represented in a diagram by equal and opposite vectors, the state of the aether is not the natural one. This corresponds in a sense to Mossorri’s idea that positive and negative charges differ from each other to a larger extent, than may be expressed by the signs + and —. After having attributed to each of the two states an independent and separate existence, we may assume that, though both able to act on positive and negative ions, the one has more power over the positive particles and the other over the negative ones. This diffe- ( 567 ) rence will lead us to the same result that Mossorrr attained by means of the supposed inequality of the attractive and the repulsive forces. § 6. I shall suppose that each of the two disturbances of the acther is propagated with the velocity of light, and, taken by itself, obeys the ordinary laws of the electromagnetic field. These laws are expressed in the simplest form if, besides the dielectric displacement d, we consider the magnetic force , both together determining, as we shall now say, one state of the acther or one field. In aceor- dance with this, I shall introduce two pairs of vectors, the one d, belonging to the field that is produced by the positive ions, whereas the other pair ’, ' serve to indicate the state of the aether which is called into existence by the negative ions. I shall write down two sets of equations, one for >, 9, the other for 9’, 9’, and having the form which I have used in former papers ') for the equations of the electromagnetic field, and which is founded on the assumption that the ions are perfectly permeable to the aether and that they can be displaced without dragging the aether along with them. I shall immediately take this general case of moving particles. Let us further suppose the charges to be distributed with finite volume-density, and let the units in which these are expressed be chosen in such a way that, in a body which exerts no electrical actions, the total amount of the positive charges has the same nume- rical value as that of the negative charges. Let g be the density of the positive, and g' that of the negative charges, the first number being positive and the second negative. Let » (or v') be the velocity of an ion. Then the equations for the state (>, 9) are *) Die Or—F O \ Div = 0 Rot H=4na99+4nd 4 V2 Rot} = — 8; 1) Lorentz. La théorie Clectromagnétique de Maxwe.t et son application aux corps mouvants, Arch. Néerl. XXV, p. 363; Versuch einer Theorie der electrischen ? I ’ und optischen Krscheinungen in bewegten Kérpern. ddx ddy | ddz de | Oy dz Rot d is a vector, whose components are SN) IDS yr ddz = ddy — —, etc. dy dz ( 568 ) and those for the state (b', 9’) Dia. deo) Dis $= 0 PES Mo (( 1) Rot H' = 4ag0'y' +470! 4a V2 Rot ' = — In the ordinary theory of electromagnetism, the foree acting ona particle, moving with velocity y, is 4nV2o4[0. SI, per unit charge '). In the modified theory, we shall suppose that a positively electri- fied particle with charge e experiences a force haan VRE io ci OUiice oa ae eee nO) on account of the field (>, ), and a force ke = Pi4n V?d'-b [ou Dec. «eee ead) on account of the field (>’ 5'), the positive coefficients @ and 2 having slightly different values. For the forces, exerted on a negatively charged particle I shall write ky Bde VEDA BOUTS ae oe oe ee I) and k= 24a V2.0 biol. Dies. m6 sels) expressing by these formulae that e is acted on by (®, 9) in the same way as é’ by (0, 9’), and vice versa. § 7, Let us next consider the actions exerted by a pair of oppositely charged ions, placed close to each other, and remaining so during their motion. For convenience of mathematical treatment, we may even reason as if the two charges penetrated each other, so ibs ae, that, if they are equal, gy = — @. 1) [y. H} is the vector-product of » and J). (569 ) On the other hand »’= %; hence, by (1) and (ID), ’=—d and f=— Hh. Now let us put in the field, produced by the pair of ions, a similar pair with charges e and e'-=-—e, and moving with the common velocity ». Then, by (i10)—(13), 2 3 Cp ’ oars ’ eg vie The total foree on the positive particle will be 3 ky thy = hy (1 a _ a and that on the negative ion hy + hy = hy (1 = -) These forces being equal and having the same direction, there is no force tending to separate the two ions, as would be the case in an electric field. Nevertheless, the pair is acted on by a resultant force 2 hy (1 2 e ). If now / be somewhat larger than @, the factor 2 (1 — yin a have a certain negative value — «, and our result may be expressed as follows: If we wish to determine the action between two ponderable bo- dies, we may first consider the forces existing between the positive ions in the one and the positive ions in the other. We then have to reverse the direction of these forces, and to multiply them by the factor ¢. Of course, we are led in this way to Newron’s law of gravitation. The assumption that all ponderable matter is composed of posi- tive and negative ions is no essentiai part of the above theory. We might have confined ourselves to the supposition that the state of the aether which is the cause of gravitation is propagated in a similar way as that which exists in the electromagnetic field, 41 Proceedings Royal Acad. Amsterdam. Vol. IL. ( 570 ) Instead of introducing two pairs of vectors (b, ) and (d’, 6’), both of which come into play in the electromagnetic actions, as well as in the phenomenon of gravitation, we might have assumed one pair for the electromagnetic field and one for universal attraction. For these latter vectors, say >, 9, we should then have established the equations (I), gy being the density of ponderable matter, and for the force acting on unit mass, we should have put —nf4nV*d+4+[». H]}, where 7 is a certain positive coefficient. § 8. Every theory of gravitation has to deal with the problem of the influence, exerted on this force by the motion of the heavenly bodies. The solution is easily deduced from our equations; it takes the same form as the corresponding solution for the electromagnetic actions between charged particles '). I shall only treat the case of a body A, revolving around a cen- tral body 4, this latter having a given constant velocity p. Let r be the line MA, taken in the direction from / towards A, @, y, z the relative coordinates of A with respect to MW, w the velocity of A’s motion relatively to M, # the angle between w and p, finally pr the component of p in the direction of 7. Then, besides the attraction ote "eo BY ucla ees os eee nL) 2 wo which would exist if the bodies were both at rest, A will be sub- ject to the following actions. fst’): A foree Sngeee une Ce) bo N 2 2 io in the direction of 7, gud, A force whose components are ho 07x kOe ko dep: ae = ee >, —sar(4 hess ax (*) - (16) 2V20x\ r 2V20y\ r 2V20z\r ') See the second of the above cited papers. 3rd, A force i 1d a a9 D OR ae A (17) parallel to the velocity p. 4th, A force Ine 3 EO COST MG te be? ie) sy fe ee) (LO) Vieine in the direction of ». Of these, (15) and (16) depend only on the common velocity p, (17) and (18) on the contrary, on p and w conjointly. It is further to be remarked that the additional forees (15)—(18) are all of the second order with respect to the small quantities w and —. J In so far, the law expressed by the above formulae presents a certain analogy with the Jaws proposed by Weber, RIEMANN and Craustus for the electromagnetic actions, and applied by some astro- nomers to the motions of the planets. Like the formulae of CLaustus, our equations contain the absolute velocities, 1. e. the velocities, rela- tively to the aether. There is no doubt but that, in the present state of science, if we wish to try for gravitation a similar law as for electromagnetic forces, the law contained in (15)—(18) is to be preferred to the three other just mentioned laws. § 9. The forces (15)—(18) will give rise to small equalities in the elements of a planetary orbit; in computing these, we have to take for p the velocity of the Sun’s motion through space. I have caleu- lated the secular variations, using the formulae communicated by TISSERAND in his Mécanique céleste. Let a be the mean distance to the sun, e the eccentricity, y the inclination to the ecliptic, 0 the longitude of the ascending node, @ the longitude of perihelion, # the mean anomaly at time f= 9, in this sense that, if x (572 ) be the mean motion, as determined by a, the mean anomaly at time t is given by oe +f dt. 0 Further, let 2, « and y be the direction-cosines of the velocity o] ? ‘ d p with respect to: 1s. the radius vector of the perihelion, 2". a direction which is got by giving to that radius vector a rotation of 90°, in the direction of the planet’s revolution, 3". the normal to the ? ) plane of the orbit, drawn towards the side whence the planet is seen to revolve in the same direction as the hands of a watch. : na ‘ 4 : Put o=a—O, +. =o and spit a O' (na is the velocity in a circular orbit of radius a). Then I find for the variations during one revolution Na=0 —e)— 2y(l-—é YA / de he=tay I—e)li nee = e 2S EY) oe a aes Ag= Ly v4 [—A0?2 cos w-+-0 (ed'— 0) sina] pon A Laer ) + a Steincal V(l—e*) | e j SO — eure vy 1202 sina + 0 (e0' — 420) cos | — Bee Ss Vv (—e ) sin —p a) + «0? cos of Foe 7A Ga eer ee NS Kon Ge eye sa evi i ag py} ee oo a € eae vy \2 0? sin o-0 (¢0'—420) cos @] eae ) + «0° cos al Vv (le ) hn yee st Meee eet oe 2202? —2n p20? — e 1 — &) —-yu—é —2aud0' args al glee 2) (a9 § 10. I have worked out the case of the planet Mercury, taking 276° and + 34° for the right ascension and declination of the apex of the Sun’s motion. I have got the following results : ( 573 ) Aa=0 Ac= 0,018 02 + 1,38 0 0” Ap= 0,95 02 +.0,28 00" AO= 7,60 d2°— 4,26 00" Ao =—0,09 52+ 1,95 00’ Az' = — 6,82 302 — 1,93 0 o' Now, 0’=1,6 X10-* and, if we put 0=5,3 X 10-5, we get eee 7. Se 1010 ee Arne oie 1010: OH BT NGAGE. | ABie= 1625105105 Ae! = 355 sc:10=10) The changes that take place in a century are found from these numbers, if we multiply them by 415, and, if the variations of yp, @, @ and z' are to be expressed in seconds, we have to introduce the factor 2,06 x 10°. The result is, that the changes in ¢, 4, @ and z' amount to a few seconds, and that in e to 0,000005. Hence we conclude that our modification of Newron’s law can- not account for the observed inequality in the longitude of the perihelion — as WEBER’s law can to some extent do — but that, if we do not pretend to explain this inequality by an alteration of the law of attraction, there is nothing against the proposed formulae. Of course it will be necessary to apply them to other heavenly bodies, though it seems scarcely probable that there will be found any case in which the additional terms have an appreciable influence. The special form of these terms may perhaps be modified. Yet, what has been said is sufficient to show that gravitation may be attributed to actions which are propagated with no greater velocity than that of light. As is well known, Lapnace has been the first to discuss this question of the velocity of propagation of universal attraction, and later astronomers have often treated the same problem. Let a body B be attracted by a body A, moving with the velocity p. Then, if the action is propagated with a finite velocity V, the influence which reaches B at time ¢, will have been emitted by A at an anterior moment, say #—7t. Let A, be the position of the acting body at this moment, A, that at time ¢. It is an easy matter to calculate the distance between these positions. Now, if the action at time (574 ) tis calculated, as if A had continued to occupy the position A, one is led to an influence on the astronomical motions of the order ) p , . » 4° ois oi if V were equal to the velocity of light, this influence would be much greater than observations permit us to suppose. If, on the contrary, the terms with 4 are to have admissible values, V ought to be many millions of times as great as the velocity of light. From the considerations in this paper, it appears that this con- clusion can be avoided. Changes of state in the aether, satisfying equations of the form (I), are propagated with the velocity V; yet, ae Pp w no quantities of the first order 7 Sap (§ 8), but only terms con- 2 Ran ay w : me tainng — and ee appear in the results. This is brought about V2 y2 by the peculiar way — determined by the equations — in which moving matter changes the state of the aether ; in the above mentioned case the condition of the aether will not be what it would have been, if the acting body were at rest in the position A}. Physiology. — ‘On the power of resistance of the red blood cor- puscles”. By Dr. H. J. HamBureer. (Will be published in the Proceedings of the next meeting.) Physics. — ‘On the critical isotherm and the densities of saturated vapour and liquid in the case of isopentane and carbonic acid”. By Dr. J. E. Verscnarrert (Communicated by Prof. H. KAMERLINGH ONNEs). (Will be published in the Proceedings of the next meeting). (April 25, 1900.) KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM. PROCEEDINGS OF THE MEETING of Saturday April 21, 1900. ICG (Translated from: Verslag van de gewone vergadering der Wis- en Natuurkundige Afdeeling van Zaterdag 21 April 1900 Dl. VIII). Contents: ,,Solar Phenomena, considered in connection with Anomalous Dispersion of Light.” By Prof. W. H. Juxius, p. 575. — ,,On the critical Isothermal Line and the densities of Saturated vapour and Liquid in Isopentane and Carbon dioxide.” By Dr. J. E. Ver- SCHAFFELT (Communicated by Prof. H. Kamerztincu Onnes), p: 588 (With one plate). — ,,The theorem of Joacuimsruat of the Normal curves.” By Prof. P. H. Scuours, p- 593. — ,,Approximation formulae concerning the prime numbers not exceeding a given limit.” By Prof. J. C. Kiuyver, p. 599. — .,/Thermodynamics of Standard Cells (ist Part).” By Dr. Ernst Conen (Communicated by Prof. H.W. Bakuuis RooznBoom), p- 610. — ,,Studies on Inversion (Ist Part)’. By Dr. Ernst Conen (Communicated by Prof. H. W. Baxuvis RoozEegoom), p. 618. — ,,Determinations of the dimiaution of Vapour-pressure and of the elevation of the Boiling-point of dilute Solutions.” By Dr. A. Suits (Communicated by Prof. H. W. Bakuvis RoozeBoom), p. 635. — ,,Some reflexes on the Respiration in connection with Lasorpr’s method to restore, by rhyth- mical traction of the Tongue, the respiration suppressed in Narcosis.” By M. A. van Metie (Communicated by Prof. C. Winker). (With one plate), p. 640. — ,,Echinopsine, a new crystalline vegetable base.” By Dr. M. Gresnore (Communicated by Prof. A. P. N. Francuimonr), p. 645. — ,,The constitution of the vapourphase in the system: Water-Phenol, with one or two liquidphases.” By Dr. F. A. H. ScuremneMAKERS (Communicated by Prof. J. M. van BemMMeELeEn), p. 645. The following papers were read: Physics. — “Solar Phenomena, considered in connection with Ano- malous Dispersion of Light’. By Prof. W. H. Junius. (Read February 24, 1900.) The rule that the propagation of light is, in all directions, recti- linear, holds only for quite homogeneous media. If various consid- erations lead us to assume that the solar rays on their course penetrate media of unequal density, or of different composition, the rays must be curved, and the supposition that the observed light is emitted by objects situated in the direction of vision becomes untenable. Now, though no one doubts the unequal distribution of matter 42 Proceedings Royal Acad. Amsterdam, Vol. Ll. (576 ) in and near the sun, yet in theories concerning this celestial body hardly any attention has been paid to refraction. The study of atmospheric refraction had, long since, made us acquainted with the laws of curved rays +), but the first important attempt to investigate the influence which refraction in the sun itself must have had on the course of the rays, which reach our eye, and consequently on the optical image we get of it, was made by Dr. A. Scumipr. His paper ,Die Strahlenbrechung auf der Sonne; ein geometrischer Bei- trag zur Sonnenphysik” *) leads to very remarkable results, and at any rate urges the necessity of submitting the existing theories of the sun to a severe criticism from this point of view. Tf it is taken for granted that refraction in the solar atmosphere must be taken into account, we must also pay attention to those special cases in which extraordinary values — great or small — of the refractive index occur; in other words, the phenomenon of anomalous dispersion must be reckoned with. It is my purpose to show that many peculiarities, which have been observed at the border of the sun and in the spots, may easily be considered as caused by anomalous dispersion. It is not difficult to obtain the experimental evidence that the index of refraction of sodium vapour for light differing but slightly in wavelength from that for the J-lines, is very different from the index for the other rays of the spectrum. H. Brcqueret (C. R. 127, p. 399; and 128, p. 145) used for the study of the phenomenon Kunpt’s method of crossed prisms, in a slightly modified manner. The image of the crater of an are-light was projected on a horizontal slit, placed in the focus of a colli- mator-lens. The parallel beam next passed through a sodium flame, which BecqueREL had succeeded in giving the form of a prism with horizontal refracting edge, and was then, through a telescope lens, focussed into an image of the horizontal slit, falling exactly on the vertical slit of a spectroscope of rather great dispersion. As long as the sodium flame was absent, a continuous spectrum was seen in the spectroscope, the height of which naturally depended on the width of the horizontal slit. When the flame was introduced in its proper place, and good care was taken to limit the parallel beam by means of an easily adjusted diaphragm, in such a manner that only such light could penetrate into the telescope lens as had passed a properly prismatical part of the flame, the spectrum clearly ~ 1) The litterature on this subject is to be found i.a. ina dissertation by O. WIENER, Wied. Ann. 49, p. 105-149, 1893. 2) Stuttgart, Verlag von J. B. Merzter 1891. ~ (577 ) exhibited the anomalous dispersion. On either side of the two dark sodium lines the originally horizontal spectrum-band was boldly curved, so that for rays with wave-lengths, slightly larger than Ap, or Ap, the sodium vapour appeared to possess an index of refraction rapidly increasing in the neighbourhood of an absorption- line; whereas for rays of wave-lengths, slightly smaller than Ap, or Ap, the index of refraction rapidiy decreased when approaching the absorption-lines. The amount of the anomalous dispersion near Dg exceeded that near Dj. In repeating this experiment I obtained materially the same results. Moreover, I noticed a peculiarity in the phenomenon, not mentioned by Becqurret, and not exhibited in the diagrams accompanying his paper. BecquereL states, that when he introduced a flame, rich in sodium, the lines D, and D, appeared Pwen| CO as broad, dark bands, and that on either D side of both bands the spectrum was curved. According to his diagrams these displace- ments only refer to light, outside the bands; the rays inside this region, in the more immediate neighbourhood of the D-lines, are — totally wanting. Fig. 1 refers to a pris- zie Pe matic part of the flame, edge upwards; fig. 2, to a prismatic part, edge downwards. Both cases represent the image as seen in a telescope, so, reversed. Fig. 1 and 2. I myself, however, have observed the phenomenon in the form of i fig. 3. The dotted lines indicate the places of D, and D,. When the electric a light is intercepted by means of a screen intro- duced between the flame and the horizontal slit, the D-lines appear in those places as two faintly lumi- nous, sharply defined slit- images. The light is faint because the flame is placed at a distance of more than ton 70 cms. from the vertical Ms 2 slit, and its radiation is is oh all but intercepted by the 42* adjustable diaphragm, which allows only a beam of a cross-section of about 0.2 cm?. to enter the telescope lens. When next the are light is allowed to cross the flame, the spec- trum of fig. 3 appears with such intensity, that the bright sodium lines are undistinguishable in the centre of the dark bands. In the upper and lower parts of the field of vision however, they can yet be seen as continuations of the four bright arrows of light which are, as it were, flashed forth from the horizontal spectrum into the dark. By repeatedly intercepting and re-admitting the light of the main source, | have actually convinced myself that the intense arrow-light, with the dispersion used, gradually passes into the faint light of the emission-lines, both with respect to intensity and place in the spec- trum. A flat RowLANp grating with 47000 lines was used in the spectroscope; one spectrum of the first order being extremely brilliant. The crosswires of a micrometer eye-piece (65 divisons of which cor- responding to the distance of the D-lines in the first diffraction spec- trum) were repeatedly adjusted as close as possible to the extreme part that was yet distinctly visible of such an arrow, the so- dium lines of the flame being all but invisible. I next removed the diaphragm near the flame, intercepted the main light, so that the sodium lines now became clearly visible, and took a number of the readings of the emission line. The mean readings of two series of observations did not mutually differ by one division; the arrow, therefore, approached the -line to within 0.01 az. From the data furnished by Brcqueren (C. R. 128. p. 146) it can be inferred, that the distance between the D-lines and the most deflected parts of the arrows upon which, in his experiments, the cross-wires could still be adjusted, was on an average greater than Olan. I am not quite sure how this difference in the results must be accounted for; perhaps BecquEREL’s flame contained more sodium than mine; anyhow so much sodium is not wanted to produce strong anomalous dispersion. The following experiment convinced me how narrow was in reality the absorption-region of each of the sodium-tines. An additional lens of 20 cm focal distance was placed between the telescope lens and the vertical slit, in such a manner that on this slit was thrown the image of the prismatic part of the sodium flame, and not that of the horizontal slit, as before. In this image, therefore, all rays that had passed the flame and had been refracted in different direc- tions, must be found re-united. The absorption-lines were now actually ery narrow, the emission-lines in some places all but covering them. (579 ) The additional lens being removed, the light-arrows forthwith re-appeared above and below the rather broad dark bands in the curved spectrum. It appears therefore, from our observations that in spite of the considerable width of the dark bands in the main spectrum, the corresponding light is but very slightly absorbed by the sodium lines. The flame has allowed every kind of light to pass, even that of which the wavelength differed ever so little from that of the D-lines; but it has caused these rays to be deflected from the straight line much more forcibly than the other parts of the spectrum lying further removed from the absorption lines. Here, then, we have a case where the absorption spectrum of a vapour exhibits broad bands not deserving the name of absorption bands. The special manner in which the experiment was made, enabled us to see what had become of the light that had disappeared around the sodium lines; but very likely the broad bands would have been attributed entirely to absorption if somehow this abnormally refracted light had fallen outside the field of vision of the spectroscope. In studying the absorption spectra of gases and vapours, we should be careful to see — which is not always done — that the absorb- ing layer shall have equal density in all its parts and shall not act anywhere as a prism. It would be worth while investigating in how far the anomalous dispersion can have influenced cases in which broadening or reversal of absorption-lines have been observed. In my arrangement the absorption-lines were narrow, if the main light had passed through a pretty much homogeneous and non- prismatic part of the flame. The experiment, as described above, offers no opportunity for ob- taining reliable values of the refractive indices. A better method to arrive at more reliable results is now being investigated; for the present all we can say is that the deviation of rays whose wave- length is very near 4p, or Ap, is at least six or eight times greater than that which the remoter parts of the spectrum were subject to. BrCQUEREL says that the index for waves greater than Ap, and dp, may attain 1.0009; for waves on the other side of the absorption line the index falls considerably below unity. The line ?, produces in a much higher degree than DP, refractive indices smaller than unity '); the very high indices are represented in pretty much the same degree near D, and Dg. ‘) In the woodeut Fig. 3, pag. 577 the upper arrow near D, is spoiled and rather short compared with that near D,. ( 580 ) From all this we infer : 1. Where light emitted by a source that yields a continuous spectrum, traverses a space in which sodium vapour is unequally distributed, the rays in the neighbourhood of the D-lines will be much further deflected from their course than any others. Of all things this holds good of those rays whose wavelength differs so little from 2p, and Ap, that they can hardly be distinguished from sodium light. A pretty strong light, therefore, misleadingly resem- bling sodium light, but in reality owing its existence to other sources, may seem to proceed from a faintly luminous sodium vapour, in a direction deviating from that of the incident light. 2. C == 07,00") 0485 (see Comm. N®, 28 p. 12). In order to represent the interpola- tion-curve given by AMAGAT by my formula, it would in this region be necessary to raise the exponent of (L —m) in this formula from 0.367 to for instance 0.5, the value occurring in the formula vl — Qo = AY (1—m), which has been deduced theoretically by van DER WAALS, and given empirically by CAILLeTeT and Marutas. This deviation might as remarked in Communication N°. 28, be caused by the fact that AmaGaT, without giving a satisfactory experimental proof for it, has rounded off his interpolation-curve 1) Comm. from the Phys. Lab. at Leiden N°. 28, Dr. J. E. Verscuarreit. Measu- rements on the capillary ascension of liquefied carbon dioxide near the critical temperature. (589 ) towards the critical state with a parabola of the second degree. In the very accurate determinations of density by SypNey Youna, to which no corrections by interpolation have been applied and for which I have computed a formula of the same form as the one mentioned above viz. Cl — Oy = 0,11058 79,8434 the agreement between observation and calculation appears to exist even at the highest temperatures (t = 0°,4). A log (Qi—@v) G = 1°58 and 0°,8 still 0,344 bet Eee ewe ¢ = 0°,8 and 0°4 still 0,337 while, according to the law of the corresponding states we might predict already at r=1°,5 a distinct increase from the above-men- tioned deviation in the case of the interpolation-curve of carbon dioxide. Therefore for the time being no experimental proofs can be given for the supposition, that up to the immediate neighbourhood of the critical state @: — @y = A(1 — m)°544 would not hold instead of the theoretical formula ei — @, = A (1 — m)?. The table given here shows that my formula gives precisely the difference in density till about t= 60°, With lower temperatures the agreement diminishes. HAY Heparin ole T (Gi-@v) observ. (¢]—-@,) calculat. 0,4 0,0810 0,0807 0,8 0,1023 0,1024 1,8 0,1351 0,1353 2,8 0,1567 0,1575 4,8 0,1889 0,1895 7,8 0,2240 0,2239 11,8 0,2591 0,2581 17,8 0,2982 0.2972 27,8 0,38477 0,3464 37,8 0,3862 0,3849 47,8 0,4169 0,4173 57,8 0,4443 0,4454 67,8 0,4680 0,4705 2. The relation deduced by VAN DER WaAA.s between the surface- tension @ and the reduced temperature m ( 590 ) 6 = C(1 — m)'/s is intimately connected with the form of the isothermals near the critical point, by means of which also the formula for the densities of liquid and vapour (with the aid of the MaxwenLi-—Crausius theorem) must be determined. It now appears that in the place of the exponent !/) in the difference of liquid and vapour density a less simple fraction must be substituted. Hence as according to VAN DER WAALS’ simple supposition the isothermal is a curve of the third degree, I have investigated whether the critical isothermal could not be expressed in an analogous way by means of a fractional exponent. The result I arrived at, was that the observations of 8. YounG on the form of the critical isothermal of isopentane are well expressed by the formulae : Ve — b P = Pc — Pe € = ) » for v > % ve—b and ve — b a p= e+ pe( b —1), for v< tc} ye in which p.=82,92 atm., 1.=4,266 c.c. (specific volume), 5=0,518 c.c., and n= 4,259. The following table shows that these formulae are in good harmony with the observations: fT ArBot B, I. v p (observ.) p (caleul.) 19,41 19,99 20,06 16,91 21,95 21,99 14,40 24,13 24,27 1190 26,84 26,86 9,440 29,69 29,65 4,505 32,92 32,92 3,160 33,70 33,73 3,050 34,39 34,35 2,939 35,49 35,06 2,829 37,49 37,32 2,718 40,51 40,37 2,608 45,49 45,27 2,497 53,51 53,58 2,431 60,59 60,42 2,394 65,24 65,60 2,361 70,63 70,87 (591 ) From the formula given for v >», it follows that for very great volumes pu = 525,5, from which & = 1,140, in good harmony with the value 1,138 found by applying AvoGrapo’s law as holding for the limit !). In order to know whether my formulae give also a sufficient approximation for very high pressures, I have calculated the critical isothermal from AMAGAT’s system of isothermals for carbon dioxide. As critical temperature I found 31°,4 C., hence pe = 73,6 atm.; for v, I took the value 0.00424 (the normal volume being chosen as unit), computed from the critical density 0.464. The following table shows that if » = 4 and 6 = 0,00045, my formulae well represent the observations up to pressures of about 800 atm. The third column gives the pressures I have computed from the volumes observed, and the fourth column gives the volumes computed from the pressure observed. eeAG Bay, sBreealilele P v p (caleul.) » (calcul.) 1000 0,001752 1055 0,001764 950 1767 989 1776 900 1782 927 1789 850 LK99 S64 1803 800 1815 808 1817 750 1832 752 1835 700 1847 709 1850 650 1864 659 1868 600 1887 603 1888 550 1909 552 1910 500 1934 504 1936 450 1965 448,5 1964 400 1998 397,3 1996 350 2037 346,7 2034 300 2087 294,53 2081 275 2115 268,5 2108 250 2148 242,9 2139 225 2182 220,83 2175 200 2220 198,6 2217 1) Using the theoretical normal density for hydrogen 0,00008955 » 1.00059 — 0,0000896L and the molecular weight of C, H,, = 71.82 (Comp. Comm. from the Leiden laboratory N°. 47 page 12.) 43 Proceedings Royal Acad. Amsterdam. Vol. IL. p v p (calcul.) —-v (caleul.) 175 0,002263 177,6 0,002269 150 2333 151,0 2336 125 2432 124,6 2430 100 2600 98,7 2587 76,30 3090 76,25 3086 74,50 3283 74,57 3295 13500, 3573 73,76 3576 73,26 547 73,34 558 72,37 630 72,46 637 71,42 682 71,62 693 69,50 rec 69,76 782 67,57 850 67,83 361 64,63 968 64,72 972 59,71 0,01156 59,74 0,01157 54,77 1356 54,53 1359 49,81 1584 49,88 1588 44,84 1856 44,85 1856 39,86 2187 39,86 2186 3. The formulae I have found for the critical isothermals are purely empirical. I was led to using formulae of the form given above by the remark that it was possible to find such a value of 6 that the critical isothermal, drawn in a diagram with p as axis of ordinates and as axis of abscissae showed a centre of symmetry in the critical = point. In the annexed figure, representing the critical isothermals of isopentane, this symmetry is very conspicuous. The marks represent the observations, the line drawn represents my formula. It may be seen that only in a very forced way a division of the pressure into a thermodynamical and a cohesion pressure can be deduced from my formula, which division is the basis of VAN DER WAALS’ theory. If therefore my formulae have a theoretical meaning, this seems to be based on a principle somewhat different from VAN DER WAALS’ equation of state; I did however not succeed in deducing such a principle. J. E. VERSCHAFFELT, ,,On the critical isothermal line and the densities of saturated vapour and liquid in isopentane and carbon dioxide.” deeedings Royal Acad. Amsterdam. Vol. IT, (593 ) Mathematics. — “The theorem of JoacHIMsTHAL for the normal curves’, by Prof. P. H. ScHoUTE. The circle through the feet of the three normals, which we can let fall from any point of the plane of a parabola on this curve, passes through the vertex of the curve. In other words: “The circles of JOACHIMSTHAL presenting themselves for a para- “bola form a net with one basepoint, the vertex of the parabola”. And the relation between the point P through which the three normals pass, and the centre MZ of the corresponding circle of JOACHIMSTHAL can be expressed as follows: “If P describes the point-field of which the plane of the parabola “is the bearer, Mf generates in the same plane a point-field affinely “related to this.” We shall now investigate how far these theorems can be extended n é _ 2 : : to the normal curve NV, of the space S, with » dimensions, and we shall commence this investigation with the simple case » = of the skew parabola. 1. The spheres of JoacurmsrHan for the skew parabola. If the skew parabola is represented by the equations x=t, Yi, a— (3; then Sh1+28—szP4+U—-2yt—x=0 ...... (1) is the equation of the normal plane in point t. his equation in ¢ being of degree five, through any point P five normal planes pass; the feet of these normal planes we shal] call “conormal points” of the curve. These conormal points form on the curve an involution of degree five with three dimensions, for, if three points of such a qu'ntuple are taken arbitrarily, the point P in space through which the five normal planes must pass, and in this way likewise the supplementary pair of feet, is unequivocally determined. So there must exist two relations between the parametervalues ¢ of five conormal points. If in general Sm represents the sum of the products k,l L by / of & quantities m, we deduce immediately from (1) = 0; See oe ae = (2) 5,1 5,2 On the other hand the six points of intersection of the given curve with the sphere 43% ( 594 ) (vp)? + yg)? + one — = 0 are determined by the equation (tp)? + (Cg? + C1 — FP =, 4+ tf — 2ri8 4 (1—29)t? —2pt +p? +_4+r?—8 =0. (3) or These “conspherical points” form on the skew parabola an invo- lution of degree six with four dimensions; for, if four of the six points of intersection be chosen, the sphere is determined and together with it the supplementary pair of points of intersection, From (3) follows immediately that six conspherical points are connected by the two relations bi '0, Di i — i Be al) 6,1 between their parametervalues. We now prove the following theorems: “The spheres determined by the quadruples of points of the skew “parabola, conormal with a given point 4, intersect this curve still “in two fixed points, determined by the equation 8@—84t+71=05 so they form a net of which these two points are the basepoints. And the point ¢, describing the curve, these basepoints generate on it a quadratic involution of one dimension, of which the two points 1 ; Se Ble are the double points. If 7), 7) 73, 7, are four points conormal with 4, then according to (2) we have the relations 2 =t+i4=—90, =r+y ft r=— 4,1 4,2 4,1 3 If ty, 72) T3, T, are four points conspherical with ¢, ¢;, then according to (4) we have 2 a a 0; Zt + (to + te) ST + tats = 1 - (6) : 4,2 4,1 So from (5) and (6) follows immediately : 1 tjt+t,=t, Peters Rib Sect acon 8h (7) with which is proved what was asserted. For the spheres belonging ( 595 ) in the indicated way to the point 4, which we name the spheres of JOACHIMSTHAL of this point, pass through two fixed points tg, ts and their number is twofold infinite, it being possible to assume arbitrarily besides ¢, still two of the other four points t. 2. The affinely-related point-fields (P) and (M). If the point P, through which the five normal planes pass, describes the normal plane of point , and , as was assumed above, is always one of the five conormal points, the centre of the sphere of JOACHIMSTHAL passing through the four other points moves in the plane that bisects orthogonally the distance of the points to, ¢; belonging to t. Indicating the first plane by = and the second plane by “, we have the theorem: “The point-fields (P) and (JZ) in the planes z and y corresponding “with each other are affinely related.” From (3) ensues 2in== t, 1-2yn== t, 2en= = t, 6,5 6,4 6,3 where the sums refer to six conspherical points. If t:, ts appear among these and if we call the others again 7, To, T3, T4, We find 2 fn = tots [T+ (& + tz) ST \ 4,3 4,4 1—2 ym = ty tg Fo + (te + ts:) Pr + zr SEP SONS) 4,2 4,3 4,4 Qemmigtz PT + (to +t) ler + set 4,1 4,2 Asie) Moreover, if ¢ is conormal with 7, Tg. 73, 74, We obtain accord. ing to (1) i -f7=0 4,1 1 — 4,1 4,2 ) Zor+str=24 Wyo 6. fo 6 0 (Y) 42 4,3 4 Sr+ 2r=—7U—27 yw) 4,3 4,4 : 1 ty De Tt = iy a) ( 596 ) So in connection with (7) we find by elimination of the quantities = + the relations 18 tm = 3 (tp + 2p) —3 2 — 2t, 18.4n = 6 Yp +3 +4 oT att top Meer (ALO) 6 Zn = 3 zy eel proving what was asserted. However the two point-fields (P) and (J/) are not in perspective. For on the line of intersection of the planes z and w not a single point corresponds to itself. For the conditions a = am, yp) = Ym, 2» = 2m involve t) (3 t)? + 1) _ st? +4 _4 i 15 ‘ Ed an ee and this point is not situated in the normal plane of t. So the connecting lines PM of the corresponding points P and M of a and 4 form a system of rays (3, 1). 3. Relation between the spacial systems (P) and (M). To a point P taken arbitrarily five points / correspond. For, if P is given, the five conormal points, the normal planes of which intersect in P, are given and any point of this quintuple may be regarded as the above given point ¢. To investigate how many points P correspond to any point M, we deduce the equation of the plane z belonging to the normal plane a of the point ¢. The plane w& bisecting the distance of the points tg, ts; orthogonally, it is represented by the equation (xt)? + (y—12)? + (208)? = (tg)? + (y—2)? + (28) which reduces itself in connection with (7) to 36 — 8 —6224+2(1—8y)t 4 2(e—82)=0 .« (11) As t presents itself to degree five in this equation, any given point 7 is centre of five spheres of JOACHTMSTHAL and so a quintuple of points P corresponds to this point 4. So we find : “The relation of the spacial systems (P) and (J/) is a corres- pondence (5,5)”. ~ (597 ) Although it would not be difficult to trace by means of the equations (10) the complex of the connecting lines P 4/, we shall avoid this for brevity’s sake. 4. Cyclographic representation of the spheres of JOACHIMSTHAL, If we wish to extend FimpLer’s cyclographic representation of circles lying in a plane to spheres in space, we must suppose that the three-dimensional space containing the spheres forms part of a space S, with four dimensions. We represent in S,; a sphere lying in 43 and having M as centre and g as radius by the two points /;, M, of the normal in /@ on S, at a distance M1, = M M,=¢@ from WM. We shall now first investigate what is the representation of the net of the spheres of JOACHIMSTHAL passing through the points tg, ts of the skew parabola. If the ordinate in the direction perpendicular on S; is indicated by w, the equations ee meee” | Sor eee (i) @ 42 +y-AQ+e—r=w| will indicate the two quadratic hypercones forming successively the representation of all the spheres through ¢, and all the spheres through t;. By subtracting these equations from each other we find that the section of the two hypercones les in a three-dimensional space perpendicular to S; along the plane (11). So the locus of pairs of points M,, Mz, corresponding to this net of spheres of JOACHIMSTHAL is, as the section of a hypercone of revolution with a three-dimensional space parallel to the axis of the hypercone, a hyperboloid of revolution with two sheets, and tie orthogonal one. Passing on to the investigation of the curved space containing the pairs of images of all the spheres of JOACHIMSTHAL, we have to deal with a simple infinite number of orthogonal hyperboloids of reyo- lution with two sheets. ‘lo find the degree of that curved space we have but to observe that the point common to all the normals on 8, does not belong to the locus and that the number of points of that curved space situated on a definite one of those normals is double the number of planes (11) passing through the point (J/) where that normal meets S;. This number being five, the curved space must be of order ten. It is not difficult to deduce the equation of the locus; we have but to eliminate ft, and ts between the two equations i! (12) and tt = 3° To this end we give the equations (12) the form ( 598 ) Se tere 8 tinue ame eae / ye 9 ‘ ¢ fe ies Ty = + th 22+ (1—2y)8— 2244 °=0 where v® stands for a? + y? + 2? — w?. Reducing t;° T, — t® T, = O and #,? 7, — t.2 Tz =O by means of the relation 3t,#,—= 1, we find in ¢, as variable 3 (1 — 27 v7) te + 542t, + 270° 4+ 18y—T= "| ( ’ 943 O7 42 (9 a 3? + (1 — 27 e*)t, + 682 hes and so after elimination of ¢; we obtain the equation 3(1—27 v*), 542 , 27 v-+18 y—7, 0 f 0 @) , I(1—27 vr), 54 , 27 v+18 y—7, 0 0 ; 0 , 8 — 27v*) , 54% » 270-718 y—7| =0, 3 ; 0 5 1—270 , 6(8z2—2) , 0 O ; 3 ; 0 ; 1—27v? , 6(82—2) which is really of degree ten. For by developing we find - Bip ey ee a, Of this curved space the sphere, according to which the hyper- cone = + yg -+2,— w, = 29 intersects the space at infinity, is a fivefold surface, ete. In passing we remark that the plane (11) envelops the developable of which the rational skew curve of degree five represented by the equations Gx=t(18 th + 9 — 1) 2 — 34) = 30 (150? — 1) 2z2—=t(10 ? — 1) is the cuspidal edge; as follows from the common factor 30— 1 of the derivatives of «,y,2 according to ¢ this curve has two real cusps, etc. ~ n 5 . 5. The normal curve Nn of S*. If we represent the curve by the equations ( 599 ) teat ani he meee a © ifs 420), the following theorems are proved in an entirely similar way: “The hyperspheres H,-, with x—Z dimensions determined by “oroups of n+ 7 points of the curve NV, conormal with n—2 given “points t), to, .... t—2 of that curve, intersect the curve still in “n—1 fixed points s, sg, ... s,-1 and form therefore a net, of “which the hypersphere #,-3 determined by those n—Z points s is “the base. And if the system of the x—2 given points describes “the curve N;,, the groups of n—1 points s determine on Nj, an invo- “lution of degree »—1 with x—2 dimensions.’ “If the point P describes the plane a common to the normal “spaces of n—2 given points t, tj, +... t,—2, the centre M of the “corresponding hypersphere of JOACHIMSTHAL describes the plane yw, “which is the locus of the points at equal distance from the “n—1 points s depending in the indicated way on the n—2 given “points ¢; then ? and MM describe in the planes a and v affinely “related point-fields (P) and (4/).” “Between the spacial systems (P) and (WZ) with » dimensions “exists a correspondence (2n—1, 2n—1).” “The cyclographic representation of all the hyperspheres of “JOACHIMSTHAL demands the given space S, to be supposed to be “part of a Sn+i; it leads to a curved space of order 2 (2n—1) with “nx dimensions in this S,+1 as locus of the pairs of images, etc.” We believe we can suffice with these general indications; we only wish still to observe that the coefficients of the equation deter- mining the n—7 fixed points are connected in a simple way with the symmetrical functions > ¢ of the »—2 points ¢ taken arbitrarily. n—2,k Mathematics. — ‘Approximution formulae concerning the prime numbers not exceeding a given limit”. By Prof. J. C. Kuuyvur. RieManny’s method for determining the total number of the prime numbers p less than a given number ¢ is equally serviceable, when it is required to evaluate other arithmetic expressions involving these prime numbers, for example the sum = p~ of their (—s)"* powers, pve or the least common multiple M/(¢) of all integers less than ¢. The different results, thus deduced, constantly contain a set of terms depending on the complex zeros “ of the Rimmann ¢-function. The most important of these terms is always one and the same disconti- ( 600 ) nuous functions of ¢; the remaining ones are continuous and of less consequence. A direct evaluation of the discontinuous term is not to be thought of; if however we suppose given beforehand the number of the prime numbers Jess than ¢, we can eliminate the discontinuous term and we are enabled, as will be shown subsequently, to arrive at rather close approximations of other more or less symmetric functions of these prime numbers, In order to obtain the formulae we have in view, we must apply RieMANN’s method to the discontinuous integral atio Gs (c) = —-——, — loy (es (2 -|- 8) dz A the path of integration being a straight line parallel to the imaginary axis and on the positive side of it. By Evier’s equation we have, supposing z-+s > 1, n= log 6\(2--3) = = — 2 pe n=1 2 and by inserting this value in the integral we find rn=n 1 G30) = SS pt n=1 7% p™ [of ct du + a98.(0 cule. oY) ct x dx — eB p Ibs —Om en 4+—s 1 ct x du > WE B Va RR sin ¢ og ¢ + sin Vey =) —@ 2 cis sin (/? loge 1 gel ile = [= (/ ge) Cae 1 = (/ ogc) Los oge L p pP ; 22 = 33 P pe B jae loge g denoting a quantity the absolute value of which is less than Py) yee je ee I. | yi Nts | Dealing similarly with the integral ( 602 ) = dt lee (t2—1) log t ’ c it appears that we may replace it by 0 (2 + s) (e2—1)14+48 loge’ where @ is positive and less than unity. Hence the preceding equation for @s(c) can be written 0 Gs (e) = log | & (6) | +Li(e#) + ——_____. (2+8) (e&—1)'*#* log c 2ct—s 7 sin (f log c) 1 1 cos (/? log e) 1 ae Fea a 2 loge Lae p 2 loge / | pe B [2° and in particular we have for s—= 0 Go (¢) ! Aue pe eee c) = — log 2 + Li(e == = f : 2 (c? — 1) loge a 2h == (7 log ) | ( 1 ay In aS S cos (/3 log e) tess al log cl p i? 2 log c/ pp e [2% In these equations we have got expressed as trigonometrical series the terms the oceurrence of which makes it nearly impossible to arrive at a direct and complete determination of either Gs(¢) or G(c). All we know about these series, is that 31 = (2 we c) Be pas @ [(P a (3° converge unconditionally and that their values are rather small, because we have 1 1 =— = 0.023105, = — < 0.002. a (3° e (3° Further, that > sin (/? log c) A 2p is a discontinous function of ¢ suddenly changing its value, each ( 603 ) time its argument becomes equal to the first, second, third,... power of a prime number. This suggests that we eliminate the discontinuous function between the two equations and merely retain the relation |G (c) — log | § (s) | — Li (ess) | —it=S |G (c) + log 2 — Li (| — _ Bech cos (Plog) Ty peas rere log ¢ @ pe @ 7 ets log ¢ Whatever may be here the values of the coefficients A and B, from what precedes we may infer that they are finite and rather it small, so that for s > = and for tolerably large values of ¢ the right-hand side tends rapidly to zero. Regarding it as a vanishing quantity we are led to conclude that the relation [6 (¢) = eg 1 5 (6) | — Lie) = 0-5 [Go (e) + toy 2 — Livo| furnishes approximatively the value of Gs(¢) as soon as @ (ce) be given, that is, as soon as we know how many prime numbers and powers of prime numbers are to be found among the integers not exceeding c. The last equation necessarily takes a slightly altered form when s is tending to unity. In that case we must make use of the expansions log | & (s) | = — log (s —1) + (8s —1) PF, (s — 1), Ti (c—8¥1) = C + log log es—! + (s — 1) Py (s — 1), from which we have ultimately Lim tog | € (s) | + Li (e-s#1 | = C+ log loge. ‘s—! Hence the value of G, (¢) may be derived approximately from |@ (Cy Oe en loa (| ye & (ea Ts (|. Moreover it is evident that a relation similar to that between ( 604 ) Gs(c) and Gj (c) exists between two integrals @s(¢) and Gi(¢), and 1 that for s >t and s > = we may write [Gs (0) boy | £ (8) | Lie) = = ett [a (c) — log | £(t) | — Le (et | Lastly, we may remark that it is perfectly admissible to differen- tiate with respect to s the equation connecting @s(¢) and Gy (¢). Remembering that is equal to the logarithm of the least common multiple Mf (c) of all integers less than c, and that ¢'(0):¢(0)=Jlog2a, we find, by putting s equal to zero after the performance of the differentiation, [eed M (c) + log 2% — | — loge |G (c) + log 2 — Li (0)| = B' oor 2ch = cos (3 log ¢) «3 log ¢* 1 = = A p ie 1 ef 5| 1 Now although the second member increases as e¢ increases, it remains relatively small with respect to ¢ and log M(c); therefore we may expect the relation log ¢ [eg M (c) + log 2 a — (| = loge |“ (c) + log 2 — Li (| to furnish approximately the value of log M(c). r y 1 , + »~gqaa « ‘ r bs The following test-cases abundantly show, that already for a c of moderate magnitude the approximation is very close. L c= &= 7.389, Ge (c) = 0.45277, Gz (c) = 0.18077. [Gs (c) — log £ (8) — Li (e*)] = 0.00082, e—2 [Gg (c) — log § (2) — Li (e-*)] = 000054. Il. cae = 20.086, G, (c) = 1.69330, Gy (c) = 0.48456. [Gq (c) — log f (2) — Li (e—*)] = 0.00089, e—® [G, (c) — C — log 3] = 0.00088. . cine fe «> ( 605 ) TH. c=e= 148.413, G, (c) = 38.50953, — G, (c) = 2,18005, log M (c) = 141.66097. [G, (ce) — C — log 5] = — 0.00661, é—* [G, (c) + log 2 — Li (e°)] = — 0.00662. [log M (c) + log 2m — e®] = — 4.914, log e® [Go (c) + log 2 — Li (e°)] = — 4.913. IV. c= el = 1096.633, G,(c) = 191.79563, Gy (c) = 2.52401. [G, (ce) — C — log 7] = 0.00088, e—7 [G, (c) + log 2 — Li (e7)] = 0.00090. If we have s>1, it is fairly evident that for large values of c¢ already the expression [Gs (c) — log & (s) — Lt (c~s*1)] itself may be considered as evanescent, and that by equating it to zero we are sure to obtain, quite independent of the value of G (c), a result for Gs(c) that involves only a very small error. 1 But if we had s=1, or even > 1 and consider again the relation Ore log & (s) = = — Tape yy — Dy. From it we have conversely h=an (— ])eh : = ps = SF —— log E (hs) 5), h=1 h where / denotes the successive terms of the infinite sequence 1, 2, 8-5, 6 278i pie 8h iw ig formed by writing in, ascending order the integers not admitting multiple factors, and 4; stands for the number of prime factors of h (this number 4 itself, if prime, included). Thus making s tend to unity we have simultancously = n==0 J] Lim |= ps — log S (5) =— = —p", s=l : nm—2 f h=o (—1)rh ; ‘Lim =P ® — log £()|= S <= log § (t) = — 0.31572, SL : li—? u and at once find n=0 1] = = fj p-* = 0.31572, n—2 7 so that finally an |= p-! — log log (| — C — 0.31572 = 0.26150. c=0 pce We mentioned this result in order to compare it with a similar 1) From this formula it is readily seen: 1st that Lp—* is an analytic function J (s) of s, we may affirm to exist in the right half-plane; 2"4 that the band between the parallels s =t+i and s=0+7, is dotted with an infinity of logarithmic discontinuities of f(s); 3'¢ that these discontinuities grow more and more dense as we approach the axis of imaginaries, so as to prevent / (s) effectually from being continued into the left half-plane. i ( 607 ) though wholly empirical formula communicated by LEGENDRE '). According to LEGENDRE we shall have = p—! = log (loge — 0.08366) — 0.22150, pce but LrEGENDRE not taking 2 for a prime number, as we did, 0,5 should be added to his result, so that we must read S p-! = log (log ¢ — 0.08366) ++ 0.27850, poe or ultimately for «= Lim Dias a log log (| = 0.27850. c=oa pce Thus it appears that the error in LeGEenpRe’s formula for ¢ = amounts to 0.017, this error diminishing somewhat, when the for- mula is used for large though finite values of e. In the preceding we have considered almost exclusively the inte- grals Gs(e); we now proceed to show that we may deal similarly with the sum = p-*, though by so doimg the formulae lose in aoe p G(r. h=h’s h Obviously we may write also lea ee Gis (c*) — log s)| —L oo = [Gwe son Et — ate H, (0) = and, from what has been proved before, we infer that Hs (c) approxi- mately obeys the relation H; (¢) = c-* Hp (c)< Tt is by means of this equation that we are able to find = p-* as soon as = p® be given. pce pce The choice of /' and 4" is quite arbitrary. If desired we may take h' = h'"; in general it will be advisable to determine 4” by the con- i dition that ch’ is just a little less than 5, in order to avoid the J application of the approximation formula for Gis (¢ *) in cases where Bs c* is too small a number. It will be seen from the following examples that the formula may be relied on, if a not too close approximation is required. I oS 148-418) Sep 04) ee pie — al oe 0: pce pce pay I 5) Teal 1 5 H, (c) = 84 — [— log 2 + Li(e*)] + oi [— log 2 + Li(e2)] + f ] 1 1 ie [—log2-+ Li (e3)] + 7+ | 01+ 7H) = — 1.08524. deh cual ( 609 ) Hy (= E pt — [C+ og5]+>[o9@ + EH] + pce 1 a pel hyp al ipa inal a peg [doakt8) + Lite =)| Ts l=: 7 le ++ = [= = Se eas ps The relation Ey (c) See (ce) gives 2 De OOO, Av. 0200010; pisaic ee — 2 — 1096-633, 2) pul oom S| pha. 2)2239- pce p< Hy (2) = 188 — [— log 2 + Lie?) | + “ [tog 2+ Li 02)]+ + [—log2++ Lite3)| tes [245] == 2 ]+ ap ski [1 | = 0.88308. B7 Sx PaatO HT, (¢) wen. — lc ++ log 7| = tog €(2)+ ft (¢ “7)| = meg C Hera) (setae a “ale oer gal + Ler] ~qalgs) = 227 — 22010 The relation H, (c) = e-7 H, (c) gives = pi) = 2.21248, A = 0.00004. pase Il. C= —=04,0085) a pe 105, pe — O.L0e7 2. p| leg 6 (6) + Lie] + p, (A) If this representation were correct, then when 2 % 95640 Cou- lombs have passed through the cell and consequently 1 gram-atom of zine has passed into solution, the heat-effect “. would be repre- 1) Wimp. Ann. 28, S. 21 en 491 (1886); ibid 68, S. 44 (1897). ( 612 ) sented by the difference of the heats of formation of Zn SO, and He, SO,. It must be at onee pointed out that under the ordinary conditions in which the cell is used, namely below 39°, the ZnSO, generated by the current will take up 7 H,O, which action is accompanied by evolution of heat. One would thus be inclined to replace the equation A by: Zn + Hg, 80, + aq. = 2Hg+2n80,7H,0 . . . (A’) But even this representation of the matter is incomplete and gives totally wrong results if a calculation is based on it. I, here, refer to the article of Mac-Inrosu in the Journal of Physical Chemistry, Vol. 2. p. 185 (1898), in which this erroneous view forms the starting point. He investigated a cell of the CLarK-type in which the Zn and Zn SO,.7H,0 had been replaced by Cu and CuSO,.5 H,0. The difference of the heats of formation of CuSO, .5 H.O and Hg» SO, in accordance with the equation : Cu + Hg, SO, + ay. =. 2 Ay + CuS0,.5 0,0. . . (B) is regarded as the heat evolved by the reaction taking place in the cell. From the measured E.M.F., 0,3613 volts, of this cell at T= 290°, and the temperature-coefficient ao —0,0006 volts at that tempe- rature, he calculates (taking the heat of formation of CuSO,.5 H,0 as 201000 calories) the heat of formation of HggSO, to be 175000 calories. With the aid of this figure and the heat of formation of Zn 8O0,.7H,0 (253000 calories) he calculates, starting from the equation A’ the E.M.F. of the Cuarx-cell at 17°,0 to be 1.427 volts, whilst KAHLE has found it to be 1.4304 at 17°,0. We will see later on that the difference of 2,6 millivolts is due to the wrong principle on which the calculation is based. 4. I will now in the first place calculate E, for the CLARK-cell with the aid of the data given by the electrical measurements of KAHLE, JAEGER, WACHSMUTH, CaLLENDAR and Barnes. ‘The calculations will all be worked out for 7 = 291°, as the calorimetric determi- nations of THoMsEN, which we shall use later on are made at that temperature. CF ( 613 ) The E.M.F. of the Crark-cell at # may, according to Kane, be represented by: E, = E,, — 0,00119, @—15) — 0,000007 @—15)? . . (2) CALLENDAR and BaRNEs give as the result of their measurements: E, = Ey; — 0,001200 (¢—15) — 0.000062 @—15)? . . (3) From (2) follows : dE T, = — 0,00119 — 0,0000140 15). . « . (2a) € From (3): dE j= — 0100120 — 0,0000124 (15)... . (Ba) a According to Jaraer and Kanun, the E.MF. of the Crark-cell at 15°,0 C. is 1,4328 volt. If we now calculate the temperature-coefficient at 18°C. (7=291) we find: According to (2a) iB; e — — 0,001232 Volt. T—291 According to (3a) di G = — 0,001237 Volt. dt O91 For the E.M.F. of the Cuark-cell- at 18°C. (Z7= 291) we find: Ey, = 1.4291 Volt. If these values are introduced into equation (1) p. 611 and everything expressed in caloric measure, 1 volt-coulomb being taken, in accordance with the measurements of JAHN ') as being equal to 0,2362 cal. we obtain: E.= 2 & 40745 = $1490 calories. ‘). Wiep. Ann, 25, 8. 49 (1885), Zeitschr. fiir phys. Chemie 26.585 (1898). ( 614 ) 5. If we now calculate this heating effect, by means of the incorrect equation A on pag. 611 we find: i, = Heat of formation ZnSO, — Heat of formation Hg, SO,. The heat of formation of ZnSO, has been determined by Tose ') as 230090 calories, that of Hg, SO, determined by Varer*) some years ago in two totally different ways as 175000 calories. sy the calorimetric way we therefore find: E., = 230090 — 175000 = 55090 ealories a value differing no less than 26000 calories from that obtained by the electrical method. If with Mac-Inrosu, we take into consideration the fact that Zn SO,.7 He O is formed, and allow, according to THomsEN, 22690 calories for the heat of hydration of Zn SO, to Zn S8O,4. 7 Tig O we find : i, = 252780 — 175000 = 77780 calories a figure which still differs considerably from that calculated (81490 cal.). 6. Having now demonstrated that the prevailing ideas as to the reactions taking place in the Cuark-cell lead to great differences, we may investigate what really occurs in the cell when the current is closed. Suppose 2 X 96540 Coulombs have passed; 1 gram-atom of zinc will have dissolved and this will have combined with an equivalent quantity of SO, from the Hg, SOx, to form Zn SOx. This ZnSO, will now immediately abstract water from the satur- ated solution of ZnSOs.7H.O contained in the cell in order to form ZnSOs,.7H,0. This abstraction of water will take place according to the equation: 7 : A Zn 80, + 4, (dn SO, A 0) = 7 Zn $04.7 H,0 . . . (©) where A represents the number of mols. of water which are present in the saturated solution alung with 1 mol. of ZnSO, at the temperature 7’ of the cell. ') Thermochem. Untersuchungen ILI, 8. 275 en II 8. 245. *), Ann. de chimie et physique, VIII (7) (1896). See also Bertuetor, Thermochimie II p. 360 (1897). i ( 615 ) The ZnSO,.7H,O formed will be deposited from the saturated solution contained in the cell and be added to the crystals already present. The heating effect 2. in the cell is now equal to the difference of the heats of formation of ZnSO, and Hgs SO, plus the heat effect W of the change represented by equation (C) which may be caleuiated from thermochemical data. The value of 4 may be calculated from the solubility determinat- ions made by CaLLenDAR and Barnes') and Conen*). Their results, which agree perfectly, lead to the equation: L = 41.80 + 0.522 ¢ + 0.00496 ¢? where L represents the number of grams of ZnSO, which are soluble in 100 grams of water at ¢°. From this equation it is found that at 18° C. A=16.81 so that at that temperature the equation (C) assumes the following form: Zn SO, ++ 0.718 (Zn SO, . 16.81 H,O) = 1.713 Zn SO, . 7 H,0... (C}) The heat effect accompanying this change may be found by supposing the systems on the left and on the right hand side of the equation to be dissolved in water so that both shall have the final-concentration Zn SO, . 400 H,0. We then find: Heat of solution Zn SO,— Zn SO, . 400 H,O = + 18430 calories Tuomsen, Thermochem. Untersuchungen III, $. 275. The heat of dilution of (ZnSO. 16,81 H,O0 — Zn SOq. 400 H,0) is calculated as follows: The heat of dilution ZnSO, . 20H,O — ZnSO, . 50 H,O = + 318 calories THomsEN |. ¢. p. 90. therefore, heat of dilution ZnSO. . 16,81 H,O — Zn SO. 20 H.0 318 x j — 30 (20 — 16.81) = + 338 calories. Since now, the heat of dilution Zn SOx. 20 HJO—Zn SO,. 200 H.0 = + 390 calories THoMSEN |.c. p. 37 and the heat of dilution Zn SO4 . 200 H,O — Zn SOs. 400 H,O = + 10 calories THOMSEN l. ec. p. 91. 1) Proc. Roy, Soc. 62. 117. *) Proc. Roy. Acad. Amsterdam. Vol. [Lf 1900, p. 337. ( 616 ) the heat of dilution required, ZnSO, . 16,81 HO — Zn SO, . 400 H,O = 33.8 + 390 4- 10 = 433.8 calories. The heat of solution of ZnSO,.7H,O — ZnSO,. 400 H,O = — 4260 calories THOMSEN, 1. c. p. 275 Equation (C) now gives: W = 18430 + 0.713 X 433.8 + 1.713 X 4260 = + 26037 calories. The total heat-effect in the cell now becomes: E, = (230090 + 26037) — 175000 = S429 calories while the calculation based on the electrical measurements gave us $1490 which is a very satisfactory agreement. We can, of course, express this result in a different manner and calculate the temperature-coefficient at 18° C. from the thermochemical data and compare it with that found experimentally. The calculation gives: — 0.001203 Volt, eS i 8006 \ dt 291° 22782 | 18° whilst 0.008235 Volt. was found experimentally. Fi i. Thus far we have only considered cells such as are used in practice, that is to say cells which contain a large excess of undissolved Zn SO,. 7 H.O. If the cell has a higher temperature than 39°, which is the tran- sition point of the salt with 7 mols. of water of crystallisation, or when it has come down to a lower temperature after the complete change of the solid salt, the cell will contain undissolved ZnSO,4.6H,0 !). Similar considerations then lead to the following equation for the change which occurs during the passage of the current: a a—6 6 dn 80, + ——; Zn 80, « H; 0 = ZnS0,.6H,O. . (D) am For this cell we can also calculate Z, from JAEGER’s electrical measurements and compare it with the value found by the calori- metric method. ‘) See Cattenpar and Barnes, Proc. Roy. Soc. 62, 117. Jarcer, Wiep. Ann. 63, 354. Conen, Zeitschrift fiir phys. Chemie 25, 300 (1898). Barnes, Journal of physical Chemistry 4, 1 (1900). rape ~ ( 617 ) We will, for instance, make the calculation for 15°C.; a is ') than 15,67 and the equation (Y) becomes: Zn SO, +- 0,620 Zn SO, 15.67 H,O = 1,620 ZnS0,.6H,0 . (D’) Caleuiating as before and using THOMSEN’s figures we find: W = 18430 + 0,620 x 441 + 1,620 X 843 = + 20069 calories and for the total heat evolved in the cell: E, = (23090 +. 20069) — 175000 = $5859 calories . According to JAEGER’s measurements, for a cell containing un- dissolved ZnSO, . 6 H,0: E, = 1,400 — 0,00102 (e—39) — 0,000004 (t—39)? . . (A) therefore Ey, == 1,4225 Volts. It further follows from (4) that IE (— = — 0,00102 + 48 X 0,000004 = — 0,000828 Volt at therefore EE. = 2 (1,4225 + 288 0,000828) 22782 = $56%9% calories whilst caloric determinations gave 2, = 44459 calories an almost perfect agreement. Results of the research. 1. The accepted views respecting the mechanism of the action of standard celis are incorrect, because insufficient attention has been paid to the actual phases of the substances which take part in the reactions going on in the cells. 2. The representation of the reaction in the CLAaRK-normal cell by the equation: Zn -++- Hg,SO, = 2 Hg + Zn80, as given for instance by Nernst, must be replaced by the equations : ‘) Proceedings Royal Acad. Amsterdam. Vol. IL, p. 338. ( 618 ) fd 7 : A p Zn + ——(ZnS80O,. AH,O) + Hg,50, = 2 He + ‘ar Zn SO,. 7 H, O. liquid solid and 6 = Fn iSO, 10 HO a—bv dn +, (ZnSO, a H,0) + Hg, $0, 2 2 Cc g liquid solid in which 3 2 1 ( 620 ) 2. If it be supposed that both cane-sugar and the products obtained by inversion d-glucose and d-fructose are of an acidic nature, then the qualitative action in the experiments of RayMAN and Suc may be explained by assuming that the produced invert-sugar is a stronger acid than the originally present saccharose. It was now my object to experimentally prove in the first place the correctness of that assumption. If it is correct then it must be assumed that by the action of pure water on saccharose two (stronger) acids are formed which as their amounts increase will accelerate the inversion. That cane-sugar behaves like an acid is shown by the researches of C. KunLiGren in ARRHENIUS’ laboratory. He determined the influence exercised by different non-electrolytes on the saponification-velocity of ethyl acetate by sodium hydroxide at 20°.7 C. His results are represented graphically in fig. 1. The abscissae a otal ss) = ia le laren le “ ile ead se ra | leet [ f : i Hail ae f HH | leah ita | Ae CI peeai (eal 4 8 12°16 20), 94 28'- 32 "36" 40; “44° 9°48 352° 56 60 (64° = 68 Percentages by volume. —> Wiese: represent the concentrations of the added non-electrolytes (in per- centage by volume). Curve I relates to the experiments with acetone. +) {1 ”? 33 39 » » ethyl alcohol. ob UME Fl ven) R y s ;, methyl alcohol. NEY ES) Foley 5 » glycerol. ee NE ey ene ” sy Saccharose. the ordinates the saponification-velocities at 20°.7 C. From this representation we see at once that glycerol and parti- 72 ( 621 ) cularly saccharose enormously diminish the saponification velocity. Now, these are just the substances which form salts with Na OH according to the scheme: Cio Hoo Or, +- Na OH = Cre Ho, On Na -- HO. KULLGREN attributes the influence exercised by glycerol and saccharose to a chemical change in the above sense, showing plainly the acidie nature of cane-sugar. If, on the strength of this view, the influence exercised by the addition of saccharose on the electrical conductive power of N./4o NaOH solutions is calculated, a satisfactory agreement appears to exist between the calculation and the experiment as shown by the following table taken from KULUGREN. TABLE II. Relative Percentage by volume — Conductivity (at 209.7 C.) Se saccharose, found. calculated. 0 4.04 — 0.538 3.06 3.32 1.058 2.79 2.36 2.11 2.12 2.33 4.20 1.63 1.78 7.00 1.26 1.31 15.87 0.78 0.73 3. I have now studied the influence which cane-sugar invert-sugar, d-glucose, d-fructose and finally mannitol exercise on the saponifi- eation-velocity of N./4o ethylacetate by N./y NaOH. 25° was chosen as the temperature of the experiments. Mannitol was also investigated in order to show once more that substances which do not yield salts exercise an influence of a quite different kind than those who do form such compounds. The different solutions were mixed together in the well-known manner in 100 cc. flasks made of Jena-glass which were previously steamed. In every case the concentration of the ethyl acetate and of the lye was N./,o. The flasks were suspended in a thermostat the temperature of which was constant within 0,03° (toluene-regulator and powerful stirring by means of HeinRict hot air-motor). From time to time ( 622 ) (the chronometer showed a fifth of a second) 10 ce. were pipetted from the flasks and added to 10 ee. of standardised acid; the excess of acid was then titrated with N./4) NaOH using phenolphthalein as indicator. The standard liquids were kept in large bottles and duly protected from the carbon dioxide of the air 3), The preparation of lye free from CO, is generally done by allowing metallic sodium to liquefy under a jar in which a basin of water is placed. By following this method*) the prepar- ation of, say, 1 litre of N. soda takes many days. I have, therefore, con- structed a simple little apparatus which enables us to dissolve in a few hours 50 grams of sodium out of contact with the air. The apparatus may be put together by means of materials which are found in every laboratory *). (Fig. 2). B is a jar (bottomless bottle) closed by a trebly-perforated cork. Through the hole in the centre passes a soda-lime tube G. Through both the other holes a thin copper tube enters (or leaves) the jar, which runs alongside the walls and is rolled circularly at the bottom (3 windings). Within the circle is placed a silver dish filled with metallic sodium cut up into smal] pieces. The jar with the dish is then placed into a crystallizing basin containing a little water so that the lower edge of the jar dips a few c.m. into the water. From a boiling-flask with a safety tube steam is passed through the copper tube the other end of which is connected with a water- airpump to remove condensed water. Soon the jar gets filled with water vapour, hydrogen escapes through the soda-line tube and after a few hours, the sodium is completely liquefied and dissolved. Traces of carbon dioxide which may be present in the solution were removed by boiling the solution with a little Ba (OH)s. 1) Compare Spour, Zeitschrift fiir phys. Chemie 2, S. 194 (1888). 2) Osrwatp, Hand- und Hiilfsbuch zur Ausfithrung physiko-chemischer Messungen, 8. 281. 3) Compare Rosenretp, Journ. fiir pract. Chemie N. F, 48 (1893) 599. ( 623 ) A. Experiments with saccharose. 4. Pure sugar candy was dissolved in water !), precipitated with alcohol (96 vol. proc.), washed with ether and then dried in vacuo °). The ethyl acetate used in these and subsequent experiments was thrice redistilled and afterwards a N./;, solution was made of it. I investigated the influence of N./;, N./9, N-/o9, N./y. and N./so sugar solutions on the saponification-velocity. These were prepared by means of N./2!/, stock solution which was preserved with camphor to prevent fungoid growth. In these as in all subsequent experiments the solutions were always prepared quite independently of each other whilst for each solution the velocity-constant was determined 5 (or more) times. The mean of the two series thus obtained will be taken as the end figure. When calculating the constant (4), the concentration at the first observation was considered as the initial concentration, so that the influence of the first errors becomes trifling. The constant follows from the equation *): — Q ama ~ C) Cn (tn — ty)” Before giving the results obtained on saponifying solutions to which saccharose had been added, I will first give some determinations made with purely aqueous sclutions. In all the following tables, ¢ represents the time required for saponification in minutes, C, the concentration cf the lye (expressed in N./y) NaOH); the third column contains the value & C,. TPeASBaLeky Shi. N./,9 ethyl acetate + N./,, NaOu. First series. Second series t Cn kC, t Cn kC, 2 7.29 9 —-— 2 7.20 —-— 4 5.82 0.126 4. 5.75 0.126 Guppe4e90) 05123. k= 6,85 6 4.81 0.124 8 4.18 0.124 eh eBatl0) 0.121 k=6,88 10. = 33..68 0.126 12 3.18 0.126 12 3.23 0.125 15 2.73 0.123 average 0 195 average 0 124 ') The water used in the experiments was distilled with particular care and freed from carbon dioxide by passing a current of air (free from CO,) for 6 hours. 2) See E. O. von Lrepmann, die Chemie der Zuckerarten (1895), S. 59. 3) See van “¢ Horr-Conrn, Studien zur chemischen Dynamik (1896), S. 18; ArruENtIvs, Zeitschrift fiir phys. Chemie 1. 112 (1887). 45 Proceedings Royal Acad. Amsterdam. Vol Il. ( 624 ) As the average of both series we, therefore, find k= 6,86 at 25°. By way of comparison we may put the figures of ARRHENIUS and SpouRr side by side: ARRHENIUS') found at 24°.7(N./,, ethyl acetate + N / NaOH) 6.45 and 6.59 aver. 6.52 SProHR *) found at 25°.0 (N./,, ethyl acetate +- N./,, NaOH) 6.51 The found figure 6.86 at 25°.0 agrees very well with ARRHENIUS’ figure 6.52 at 24°.7, if we consider that a difference in temperature of 0°.3 already influences the velocity of the reaction to the extent of about 6 pCt. °). TA BaL oH Ay: N./4 ethyl acetate -+ N/,, NaOH + N./; saccharose. First serie. Second series. t Cu kC, t Cn kC, 10 6.43 — 10 6.45 — 15 5.51 0.0333 15 5.55 0.0324 200 4.85 326 k=2,03 20 4.90 316 k=1,99 25 4,30 330 25 4.38 315 35 3.58 318 35 3.53 330 average 0.0327 average 0.0321 — TAS Beale Ne N./,9 ethyl acetate + N./,, Na Ol + N./\9 saccharose. First series. Second series. t Cn kC, t Cn kC, 5 6.91 — 5 6.81 — 10 5.45 0.0535 10 5.40 0.0525 15 4.47 545 k= 314 15 4,45 530 k=—3,10 20 3.81 542 20 3.78 534 25 3.30 547 25 3.33 522 average 0.0542 average 0.0528 ') Arruentius, Zeitschrift fiir phys. Chemie 1. 112 (1887). *) Spour, ibid 2. 19+ (1888). *) Studien zur chemischen Dynamik S. 129. ( 625 ) Dy ABest vl, N./j ethyl acetate + N./jo NaOH -+- N./,, saccharose. First Series. Second series. t Cn kC, t Cn kC, 3 7.20 _ 6 5.81 —_ 7 Seog Osa 9 4.90 0.0619 9 4.91 13 4.02 635 k= 4,82 13 4.08 764 k=4,26 Wf 3.40 630 17 3.48 763 average 0.0766 average 0.0628 To Belekioe VEE N./,, ethyl acetate + N./jy NaOH + N./,) saccharose. First series. Second series. t Cy kC, t Cn kC, 3 6.91 — 3 6.93 - 6 5.43 0.0908 6 5.48 0.0882 9 4.48 903 k=5,22 9 4.50 900 k=5,15 12 3.82 901 12 3.85 888 15 3.33 $96 15 3.37 880 average 0.0902 average 0.0887 AB hehe vrit: N./4) ethyl acetate + N./,, NaOH -+ N./,, saccharose. First series. Second series. t Ch kC, t Cn kC, 2 7.40 _— 2 7.30 4. 6.08 0.108 k= 5,84 4 6.00 108 k=5,92 6 5.12 106 6 5.05 Ma 9 4,21 108 12 3.52 107 12 3.55 108 average 0.108 average 0. 10S B. Experiments with invert-sugar. A N.2!/, solution of invert-sugar was prepared by inverting a N.21, solution of cane-sugar by means of a little acid at 60° C. A weighed quantity of saccharose was dissolved in a little water 45* ( 626 ) contained in a measuring flask, 20 ec. of N./., HNO; were added and the whole kept for 24 hours at 60°. The acid was then neutralized with lye and the liquid was diluted to the mark. I made sure about the completeness of the inversion by a polar- iscopic test. Operating in this manner, the liquid contains but little Na NOs; the presence of salts should be avoided as, according to SPoHR’s experiments they exercise a great influence on the saponification- velocity of ethyl acetate by Na OH. To be more sure, I inverted a second solution with a trace of oxalic acid: the figures which I obtained afterwards on saponification were identical with those given by the solution inverted with H NOs. Both the solutions were, therefore, used in the further saponification experiments. I have studied closer an additional phenomenon which might have been of influence on the experiments where invert-sugar or d-glucose and d-fructose were used. Lopry De Bruyn and ALBERDA VAN EKENSTEIN ') when studying the action of dilute alkalis on carbohydrates have found that d-glu- cose and d-fructose undergo decomposition even by dilute solutions of NaOH. A portion of the added NaOH disappears as it gets neutralized by the organic acids which are formed. The decompo- sition was very plainly observable at 63° after a short time, when N./s;, NaOH was used. It, therefore, became necessary to ascertain in how far a similar secondary reaction may interfere here at 25° C. during the time my observations lasted. For that purpose, I mixed in a flask: 50 ec. N.2!/, invert-sugar, 25 ec. of water and 25 cc. of N./;9 NaOH and kept the mixture in a thermostat at 25° C. From time to time, the alkalinity was determined by titrating 10 ce. with N./,) acid. After 80 minutes 0.2 ec. of N./,, NaOH were assumed. 250 wy, 0:3 eta y Nia eNa Oe ‘ » 1320 pelt cose SNe. ” ” As in our case the experiments are finished within 150 minutes, the secondary action is not likely to influence the general result. ') Rec. des Tray. chim. des Pays-Bas. 14, 156, 203 (1895). ( 627} UR BO EEX 2 N./49 ethyl acetate + N./,, NaOH -++ N./, invert-sugar. t Ca kC, 30 7.52 - 50 6.59 0.00705 Si)) 5.51 729 k=0.879 1100 4.79 712 average 0.00715 AR (A.B eh yeeXe. N. 4 ethyl acetate -+ N./,, NaOH -+ N./,, invert-sugar. First: series. Second series. t Cn kC, t Ca kC, 15 7.78 — 15 7.75 _— 30 6.50 0.0131 30 6.50 0.01381 50 «5.35 129 k = 0.68 50 «45.88 127 k = 0.66 73 4.35 131 75 4.39 128 | 105 3.59 142 105 3.55 132 average 0,0133 average 0.0139 TSA Be Tay Hi oxXel N./4 ethyl acetate ++ N./,. NaOH -+- N./9 invert-sugar. First series. Second series, t Ca kC, t Cn kC, 10 7.44 — 10 7.40 = 20 6.10 0.0219 20 6.05 0.0223 30 5.20 WMsk = 11S 30 5.13 921 ke — 118 45 4.28 211 45 4,21 216 65 3.40 216 65 3.42 212 average 0.0215 average 0.0218 AG Bei Boxe kl. N.J,o ethyl acetate + N./,. NaOH +- N./,9 invert-sugar. First series. Second series. t Cn kC, t Cn kC, 5 Weep: — 5 7.50 — 10 6.32 0.0376 15 5.42 0.0383 15 5.41 $88 k=2.01 20 4.78 379 k=2.04 20 4.80 376 30 3.81 387 30 3.90 370 average 0.0377 average 0.0383 ( 628 ) TA. BL, Bi eee N./., ethyl acetate +- N./, NaOH -+- N./,, invert-sugar. First series, Second series. t Cn kC, t Ch kC, 3 7.60 — 3 7.52 _ 6 6.36 0.0650 k=3.39 6 6.32 0.0633 9 5.48 644 9 5.42 645 k=3.86 12 4.82 641 12 4.80 629 _ 17 4.0] _ 625 average 0.0644 average 0.0633 ©. Experiments with d-glucose. For these experiments [| made use of a preparation sold by Merck as *Traubenzucker purissimum, wasserfrei’. By polarisation and a water determination, the article, however, appeared to contain about 6 pCt. of water. A second preparation in beautiful crystals was kindly offered to me by Prof. RinpELL of Helsingfors. Both specimens gave the same figures in the saponification experiments and were used side by side, LA Bab Cw Ske N.j,9 ethyl acetate + N./,, NaOH + N./, d-glucose First series. Second series. t Cn kC, t Ch kC, 15 7.32 —_ 15 7.82 -- 30. 6.07 = 0.0137 30 =©6.02 =—0..0148 45 5.13 142 45 5.14 142 60 4.41 146 k=0.79 60 4.41 146 k=0.79 80 3.72 148 80 3.72 148 1105 3-05 See 1103.05 147 average 0.0144 average 0.0145 DY A BSE exe Ve/yo ethyl acetate + N./,. NaOH + N./,, d-glucose. First series. Second series. t Cn kC, t Ca kC, 10 7.04 —_ 10 7.04 = 20 5.68 0.0239 20 5.68 0.0239 30 4.70 948 k=1.36 30 4.70 248 45 3.83 239 45 3.83 939) ek — 1-38 60 3.20 240 60 3.18 24.2 75 2.80 233 73 2.70 247 average 0.0240 average U 0243 ——_ oe ae ( 629 y ep Ate Bey N./4) ethyl acetate +- N./,,) NaOH + N./,, d-glucose. First series. Second series. Cn kC, t Cn kC, 7.39 — 5 7.32 — 6.08 0.0430 k=—2,31 10 6.08 0.04.27 5.18 426 15 511 432 4.50 428 20 4.48 422 25 3.98 419 30 3.55 4.24 average 0.0428 average 0.0425 PAS Birla; Bye: N./4o ethyl acetate -+ N./,) NaOH + N./,. d-glucose. First series. Second series. Cn kC, t Cn kC, 6.96 — 4 6.89 — 5.81 0.0659 7 5.80 0.0626 5.02 644 k= 3,72 10 4.99 634 4.40 646 13 4.40 628 3.80 639 17 3.78 633 average 0.0647 average 0,0630 TP ACB Lh BE XV i: N./4) ethyl acetate ++ N./,, NaOH ++ N./,, d-glucose. First series. Second series. Cn kC, t Cn kC, 7.02 — 3 6.92 —_ 5.60 0.0845 6 5.52 0.0845 4.61 871 k=4.79 12 3.98 818 4.50 839 15 3.47 828 3.53 824 18 3.10 821 3.13 828 average 0.0841 average 0.0828 c= 2,82 k=3,66 ee Sart) ( 630 ) D. Experiments with d-Fructose. Two specimens of this substance were in my possession. A small quantity of erystallised d-fructose from Merck of Darmstadt and a larger quantity which Mr. ALBeERDA VAN EkensteErN, director of the Government sugar laboratory of Amsterdam, had been kind enough to prepare and recrystallize for me. I will not neglect to express here my particular thanks for the great kindness with which Mr. AtBerDa has obliged me with this expensive preparation as this alone has rendered it possible for me to do the experiments with d-fructose on a somewhat larger scale. Both preparations gave the same figures as will be noticed from the tables. TAB Ley XX, N./,) ethyl acetate -- N./,.) NaOH -++ N./, d-fructose. First series Second series (ALBERDA’s preparation.) (MeRcK’s preparation.) t Ch kC, t Cn kC, 30 6.73 — 30 6.60 _ 45 5.82 0.0104: 45 5.80 0.0092 60 5.21 097 k=0,59 60 5.10 98 k=0,59 80 4,52 098 80 4.40 100 11 3.73 099 110 3.63 102 145 3.07 104 145 3.03 102 average 0.0100 average 0.00988 TY Ay Bobi EB) xX, N.J49 ethyl acetate +- N./,, NaOH + N./,9 d-fructose. Virst series. Second series. t Cn kC, t Ch kC, ll 7.48 _- 10 7 53 — 20 6.38 0.0191 20 6.38 0.0180 30 5.49 190 k=1,08 33 5.44 192 k=1,01 45 4.51 198 45 4.50 192 60 3.85 192 60 3.82 194. SO 3.22 191 80 3.15 198 100 2.76 192 average 0.0192 average 0.0191 EE ( 631 ) yA: Bi Ly, Ee ext. N./4 ethyl acetate + N./,, NaOH ++ N./,, d-fructose. First series. Second series. t Cn kC, t Cn kC, 5 7.68 _- 5 7.60 _ 10 6.50 0.0363 10 6.39 0.0378 15 5.64 363 k=1.89 15 5.60 357 20 4.92 373 20 4.90 367 k=1.87 average 0.03631) 30 4.10 341 40 3.42 349 50 3.00 340 average 0.0355 TAB LR) Xa: N./4) ethyl acetate + N./,, NaOH + N./,, d-fructose. First series, Second series. Cn kC, t Cn kC, ES feel — Ay, 220 — 8 5.90 0.0555 8 5.90 0.0550 12 5.00 552 12 4.99 553 16 4.38 5388 k= 3.02 16 4.33 552 k=3.05 20 3.87 539 20 3.82 553 24 83.46 541 average 0.0552 28 3.13 544. average 0.0545. AAG ey dG Be). ©. Hs N./,9 ethyl acetate ++ N./,, NaOH + N./,9 d-fructose. First series. Second series. t Cn kC, t Cn kC, 3 7.12 — 3 tale — 9 4.87 0.0770 9 4.87 0.0770 12 4.22 763 k=—4,29 12 4.95 750 k=4,24 15 3.71 766 15 3.71 766 20 3.11 758 20 3.11 758 25 2.65 766 25 2.71 739 average 0.0764 average 0.0756 ') As I find in my notes that the figure 4.92 is decidedly too low I have disregarded the value 0.0373 when calculating the average. ( 632 ) KE. Kaxperiments with Mannitol. The preparation obtained from KanLBaUM was sharply dried and then used for making the solutions. PA Ba Ey XSXTVe N./,) ethyl acetate ++ N./,. NaOH + N./, mannitol. First series. Second series. t Cn kC, t Cn kC, 3 7.23 ne 3 {fake = 9 4.68 0.0907 k=5,13 6 5.61 0.0938 12 3.92 938 9 4.60 988 k=5,20 7 3.12 940 12 3.90 937 alZgerm ial 937 average 6.0928 average 0.0938 PAB WG) XSX Ve N./,9 ethyl acetate +- N./,) NaOH -++ N./,) mannitol. First series. Second series. t Ch kC, t Ch kC, 2 7.53 _— 2 7.49 — 4 6.19 0.109 4 6:17 03107 6 5.2) lll k=5,88 6 5.20 110 k=5,87 8 4.50 112 8 4.52 109 LL 3.80 109 11 3.70 113 average 0.110 average 0.110 — TA YBa, Eo oer N./4o ethyl acetate ++ N./,, NaOH -+ N./.9 mannitol. First series. Second series. t Cn kC, t Ca kC, 2 7.32 _ 2 7.80 4 6.01 0.109 4 5.97 0.111 Cios Ol WS k= (6,17 6 4.99 115 k=6,19 8 4.33 115 8 4,31 115 10 = -3..80 115 10) 3580 lll average 0.113 average 0. is ia ( 633 ) TA Bil, Ey xOxe WIT. N./4 ethyl acetate + N./,) NaOH + N./, mannitol. First series. Second series. t Co kC, t Cu kC, 2 7.20 — 2 7.23 — 4 5.84 0.116 4. 5.84 0.119 6 4.98 lll k=6,83 6 4.98 112 k=6,47 8 4.22 117 8 4,23 118 10 Bint Ka) 114 10 By Al 118 average 0.114 average 0.117 Ty AB hg RiepexevenhT. N./4) ethyl acetate ++ N./,. NaOH + N./,) mannitol. Tirst series, Second series. tt Ca kC, t Co : kC, 2 7.20 — 2 7.12 — 4 5.79 0.121 4 Gia A2) 0.119 6 4.80 124 k=6.88 6 4.80 1200 k= 6.74 8 4.10 126 10 3.60 122 10 3.62 124 average 0.124 average 0.120 Summary of results obtained. If we now take the mean of the figures obtained in the above tables as end-figure we get the following summary: T A BOL oR XX Saponification-velocity of N./,, ethyl acetate ++ N./,, NaOH at 25°.0 C. In: N./; N./.0 N./eo Hiro N./s9 | Water 6.86 Saccharose 2 01 3.12 4.29 5.19 5.88 | Tuvert-sugar 0.38 0.67 alfaly/ 2.03 3.38 d-Glucose 0.79 1eay/ 9.32 3.69 4.79 d-Fructose 0.59 1.02 1.88 3.04 4.97 Mannitol 5.17 5.85 6.18 6.40 6.81 Fig. 3 gives a graphic representation of the results; the abscissae representent the concentrations and the ordinates, the velocities +). 1) It must be observed that in fig. 1 which gives KuLteren’s results the abscissae represent percentages by volume, whilst here normalities have been used for calcu- lation. In KuLLGReEn’s case, this representation would have caused difficulties in con- nection with the great concentrations of several of the non-electrolytes used by him, in view of the scale to be used. —s ( 634 ) W Seen He aK | a ay i, MeN Hie | ES) NON Sd 3 \ = 5, \ e|_AN g B cK 0 Wifes Niven NYG Nifio Nils Concentration —> Fig. 3. Curve I relates to saccharose. Curve IL , , imvert-sugar. Curve III » 9: d-glucose Curve IV, _—,,_ d-fructose. Curve V » » Mannitol. These curves must, of course, intersect in one point (W). A glance at the figure shows at once that the saponification- velocity is considerably retarted by saccharose ; still more so by invert- sugar. The result showing that the influence exercised by d-glucose and d-fructose is different, is of importance as d-fructose retards the saponification to a much larger extent than d-glucose. Mannitol, however, exercises but little influence even in the strongest solutions and thus behaves like ethyl and methyl alcohol. In connection with what has been said at the commencement about KULLGRENS researches, we see that saccharose, d-glucose, d-fructose and invert-sugar behave like acids. Invert-sugar is stronger than cane-sugar, d-fructose stronger than d-glucose. The remarkable behaviour of cane sugar solutions observed by Ra¥man and Sutc may be easily explained after these results. In a following communication the results obtamed will be sub- jected to calculation. Stockholm, University physical Laboratory. Aug. 1899. as eee ( 635 ) Chemistry. — ‘Determinations of the diminution of vapourpres- sure and of the elevation of the boiling point of dilute solutions”, by Dr. A. Smirs (Communicated by Prof. H. W. Bakuutis Roozesoom). Introduction. In a former article ') the apparatus has been described, which has enabled me to ascertain the decrease of the vapourpressure and the elevation of the boiling point of dilute solutions. The method of experimenting when determining the diminution of vapourpressure is already described there, so that it is only neces- sary to say here that in determining the elevation of the boiling point, the manostat is always set at the same pressure; the thermo- meter, which remains continuously in the boiling water, controls the action of the manostat, since a small change of pressure in the apparatus is immediately betrayed by a change of temperature. Regarding the accuracy of the two methods, the preference must be given to the determination of the increase in the boiling point. Tf, in the method for determining the diminution of vapourpressure, the decrease in the vapourpressure of the solution is to be caleu- lated from the observed fall in the boilmg point of pure water, it is necessary to use the table constructed by Regnaunr®) for the maximum pressure of watervapour, which gives the differences for each 0.1°. It is plain that errors are committed here; in the first place because the table is not quite correct and secondly because interpolation must be resorted to. The value of < obtained from the value of the decrease in the vapourpressure thus calculated can, therefore, not be very accurate. In the determination of 7 from the elevation of the boiling point, it is only necessary to divide by a constant factor; in this method the values of ¢ can only be affected by a constant error. J have, therefore, applied the two methods to the same solutions of NaCl, but in the case of the other salts, the elevation of the boiling points only has been determined. The results, which I have obtained with solutions of NaCl, K Cl and K NOs are included in the following tables. Between each of the different series of obser- vations of the NaCl-solutions, the manostat was set at a different pressure. ') Proceeding Royal Acad. Jan. 27, 1900, p. 471. ») Mémoires de Acad. T. XXI, p. 632. ( 636 ) Re Sar lt 3: NaCl. Calculated dimi- Concentration Observed decrease of tj fF thevanour in the boiling point of the paeine eo adag ade’ i er. mols, per 1000 ers. of H,O. pure water. a Ey Ee 5 ; A in mm, of He. 0.0500 0.048 1.27 1.89 0.0730 | 0.073 | 1.94 | 4.93 0.10014 0.093 2.47 | 1.84 0.5001 | 0.408 | 12.41 | 1.85 1.0000 | 0.965 | 25.37 | 1.89 NaCl. Boiling point of the pure water = 99.424° ¢— 5.18 !). Concentration in | Elevation of the boiling | Molecular elevation | er. mols, per 1000 grs. of H,O.| point of the solution. jof the boiling point. rn | ~ An | 0.0500 0.050 | 10.00 1.93 0.0750 0.075 3899 1.93 | 0.1001 | 0.096 9.60 1.85 | 0.5004 0.471 9.42 1.82 1.0000 0.968 9.68 1.869 2.0798 2.120 10,20 1.969 NaCl. Boiling point of the pure water = 99.793° ¢ = 5.19. aS | Concentration in | Elevation in the boiling | Molecular elevation | i er. mols. per 1000 cc. of HO. | point of the solution. of the boiling point. —_—_— rT ’ 0.0800 0.049 9.81 | 1.89 | | 0.1000 0.095 9.50 1.83 0.5000 | 0.472 9.44 1 82 U.TA9T | 0.717 9.36 | 4.84 1 0000 | 0.970 9.70 1.869 ') ¢=molecular elevation of the boiling point calewlated from van “2 Hore’s for- 0,02 7? . : : mulae é= ————.. _N.B. Although very few of the solutions are weak enough to ww warrant the calewlation of ¢@; this has been done for all concentrations to facilitate the comparison with previous results. ie ole, ee ( 637 ) NaCl. Boiling point of the pure water = 99.61° += 5.19°. Concentration in Elevation of the boiling | Molecular elevation | i gr. mols. per 1000 grs. of H,O. point of the solution. of the boiling point. | | | 0.0560 0.049 | 9.68 | 24287 | 9 10115 0.096 9.48 | 1.83 0.50566 )) 479 9.47 1.82 1.0112 0.979 9.68 1.865 KeCH: Boiling point cf the pure water = 99.695° ¢= 5.19. Concentration in | Elevation of the boiling | Moleculor elevation i gr. mols. per 1000 grs. of H,O.| point of the solution. jof the boiling point. 0.0504 0.050 9.93 1.914 0.1008 0.091 9.03 1.74 0.5037 0.455 9.03 1.74 1.0074 0.926 9.19 i evyet K N03. Boiling point of the pure water = 99.691° ¢= 5,19. Concentration in | Elevation of the boiling | Molecular elevation | gr. mols. per 1000 grs. of H,O.| point of the solution. jof the boiling point.| 0.0499 0.054 10.21 1.97 0.0898 0.095 9.52 1.83 0.4991 0.430 9.02 1.74 0.7486 0.648 8.65 1.67 0.9981 0.858 8.57 1.651 I From these tables it is apparent, that in the case of NaCl 7 reaches a minimum value at about 0.1 gr. mol. per L000 grs. of water when the diminution of the vapourpressure is determined, and at about 0.5 gr. mol., when the elevation of the boiling point is deter- cn ( 638 ) mined. In the case of KCl, 7 also reaches a minimum between the concentrations 0.1 and 0.5 gr. mol. From 0.5 gr. mol. upwards a rise of 7 is observed as the concentration increases. Above 0.5 gr. mol. the results are therefore, qualitatively, the same as with the micromanometer. Below this concentration 7 seems to increase again with the dilution. In the case of K NO, 7 increases proportionally with the dilution just as I have observed with the micromanometer. Both at 100° and at 0° a solution of K NO, seems to behave differently to solutions of K Cl and Na Cl. As regards the accuracy of the results, I may say that the greatest error of each thermometer was 0,002°. If these errors of the two thermometers have opposite signs, the error of observation amounts to 0,004°. As, however, each determination lasted 15 minutes, a reading being taken every 5 minutes, the average error must have been really less than 0,004° which is confirmed by the thorough agreement of the results obtained in the three series of observations on the Na Cl solutions. Earlier observations. W. LAnpsperGer!) has already found in 1898 that more con- eentrated solutions of Na Cl show a rise in the molecular increase of the boiling point when the concentration increases. From his molecular weight determinations, I have calculated the following values for the molecular increase of the boiling point and for 7, NaCl. iG — alice Concentration in Elevation of the Molecular Mol. elereaon i gr. mols per 1000 grs. of H,0.| boiling point. |weight found.| boiling saint 0.7145 | 0.676 32.2 | 9.46 | 1.82 1.0581 1.026 | 31.4 9.70 | 1.87 1.0872 1.080 | 30.7 9.93 state) | 1.1077 4.067 31.6 9.63 1.85 1.2427 1.285 30.6 9.94 |} 4.94 2.0735 DQ Aai 29.0 10.50 | 2.02 2.0855 2.186 29.0 10.50 2.20 1) Zeitschr. f. Anorg. Chem. XVL 452. (1898). ( 639 ) Excepting the value of ¢ for the concentration 1.1077 gr. mol., which is very probably too small on account of an experimental error, we also notice here a perciptible increase of 7 with increasing concentration. LANDSBERGER says regarding the results: »Die angefiihrten Zahlen fiir Natriumchlorid lehren, das die Disso- ziation in wisseriger Lésung mit steigender Konzentration fortschreitet.” Although this conclusion seems to me to be erroneous I have quoted it in order to show that LANDSBERGER regards the observed changes as essential. For concentrated solutions of NaCl and K Cl, Learanp !) has already noticed the same phenomenon as I have now done for the more diluted ones. From the following table this progressive change is plainly visible. Number of grams | Number of grams Number of grams | Increase of NaCl of KCl of K NO, | in the per 100 grs. of H,O. | per 100 grs. of HO. | per 100 grs. of H,O. boiling point. } Teatlh 9.0 12.2 1° 13.4 ties 26.4 Q° 18.3 24.5 42.2 3° 23.4 31.4 59.6 4° 27.4 37.8 78.3 3° We see from this table that with NaCl and KCl the elevation of the boiling point increases more rapidly than the concentration, whilst with KNO, the reverse is the case. At greater concentrations the molecular elevation of the boiling point of solutions of Na Cl and KCl seems to increase with the concentration, whilst for solu- tion of KNO; it steadily declines. Summary of the results. The result is, therefore, that the progressive change observed with concentrated solutions of KNOs also oceurs with dilute solutions, whilst with concentrated solutions of NaCl and KCl it ends at a concentration of 0.5 gr. mol. where it takes another direction. In my determinations of vapourpressure with the micromano- 1) Ann. de Chim. et de Phys. T. LILI. Poggend. Ann. Bd. XXXVI. 46 Proceedings Royal Acad. Amsterdam. Vol. II. ( 640 ) meter, I did not notice a minimum of the molecular diminution of vapourpressure; it is possible that the cause of this is as follows: At about 100°, I observed a minimum at the concentration of 0.5 gr. mol.; should the position of this minimum alter with the temperature which is quite possible, it may occur that at lower temperatures it is displaced in the direction of still more dilute so- lutions and that at 0° it may fall below the concentrations with which I was able to make sufficiently accurate observations. To decide whether there really is a minimum which changes its position with the temperature, I propose to make further measure- ments of the diminution of *vapourpressure of solutions at tempe- ratures between 0° and 100°. Amsterdam, University Chem, Laboratory. April 1900. Physiology. — “Some reflexes on the respiration in connection with Laporpe’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in narcosis”. By M. A. van Metue (Communicated by Prof. C. WiInKLER). In the Weekblad van het Nederlandsch Tijdschrift voor Genees- kunde, March 31, 1900. Dr. WeNCKEBACH inserts a note on LABORDE’s communications in the Académie de Médecine, which are published in the Bulletins de V Académie de Médecine, N°. 45 1899 en N°. 2, 4, 5, 6. 1900 and with slight modifications in the Comptes Rendus de la Societé de Biologie: 1899. N°. 39 and N°. 2, 4, 5. 1900. In this communication LABORDE gives fuller details about a method in which rhythmical traction of the tongue is used to restore the paralyzed respiration. An explanation is to be found for this phenomenon, as it cannot be considered as anything but a re- flectory action, originating from the sensible nerves of the first air- passages on the so-called centres of respiration. LABORDE thinks, that according to his experiments the refiectory action depends on the Nn. laryngei superiores, the electrical and mechanical excitation of which brings about an ‘arrest’ during the active respiration, whereas it restores the respiration when the latter was suppressed. In the laboratory of Prof. WiyktLeR, under whose guidance im- portant investigations on the mechanism of the respiration have been ( 641 ) made !), I have tried to find further data about the effect on the respiration of the excitation of some periferic nerves. I have to return thanks to Mr. van Caxtcar and Mr. H. Jager for their valuable assistance. Since the impulse to this investigation which MarsHati Hatu’s “Treatise of the Nervous System” gave in 1840, many experiments have been made on this subject, but on the whole the results do not agree very well. The difference of animals experimented on, of the conditions under which the expe- riment was made, of the nature of the excitation used, is so difficult to bring under simple points of view, that I thought it desirable to make a new attempt under conditions as much the same as possible, For want of time I could make only a beginning with this very interesting study of the automatism of respiration, the knowledge of which is of the highest importance both from a physiological and a clinical point of view. Nevertheless it seems to me, specially with a view to LABorDE’s opinion, that I am justified in communicating some of the obtained results. The animals experimented on were dogs, almost all of the same species. The experiments were made in narcosis of pure chloroform, In the beginning this gave difficulties as it is a well-known fact, that dogs which are not morphinized, react very violently on the inhalation of chloroformvapours and therefore often succumb of the narcosis. On purpose I did not make use of the mixed morphia-chloroform narcosis, because morphia introduces a factor, by no means to be neglected in the mechanism of respiration (as proved by the well-known morphia-sigh) which indicates over-irritability of inspiration-centres, The chloroform also introduces an unknown factor, but this seemed to me a peremptory demand of humanity. Moreover if dogs are not narcotized there is also an unknown factor acting, because pain makes the respiration strongly irregular. When the narcosis with pure chloroform has become complete, it gives a fine regular respiration, which changes as long as active stimulation lasts, but generally returns immediately to the normal condition. The explanation of the violent reaction, which takes place in the beginning of narcosis, is not found, as we should be inclined to assume, in the disagreeable irritating action of the chloroform on ') Proc. Roy. Acad. Amsterdam Oct. 29, 1898 and March 25, 1899. Dr. Wrarpt Beckman. Diss. Inaug. 1899. Amsterdam, De invloed yan de schors der yoorhoofds- hersenen op de ademhaling. ( 642 ) the olfactory mucous membrane, for I found the same reaction with one of the dogs, narcotized through the trachea after tracheotomy. This occurred, when I wanted to stimulate the fila olfactoria by means of electricity and therefore would not paralyze them before- hand by chloroformyapours. This violent reaction, when found with dogs which had been first tied, may cause the dogs to succumb; if however, we leave a_ possibility of free movement, which is best done by tying the dogs in a bag leaving only the head and the legs free, and the bag with the dog suspended in the air, the asphyxia is generally not found, and the further narcosis remains very calm and regular. The chloroform was administered by means of CURSCHMANN’s inhalator. The narcosis being deep enough, tracheotomy was performed and the chloroform was administered through the tracheal canula. The registration took place with the pneumograph of Maney, The sensible nerves were stimulated with a moderately strong in- duction current. Generally, differences in the strength of the current had little influence, except that a certain minimum had to be exceeded. Under these circumstances, i which the results show much uniformity and constancy, it appeared that the stimulation of those periferic nerves, which are exclusively composed of sympathic nerve-fibres or contain many of them, brought about an arrest of the respiration and generally, as has been found already by Harney and HaMBuRGER, in its expiratory position. So do the N.splanchnicus and the N. vago-syinpathicus. I succeeded sometimes by mechanic stimulation of, the N. splanchnicus (by traction of the entrails) in arresting the respiration for 65 seconds, as long as the stimulation lasted, while before and after the stimulation the respi- ration was perfectly regular. By electrical stimulation of the N. splanchnicus the same result was obtained. This proves that no centre has been disturbed by shock. The same thing is seen when the N. vago-sympathicus is stimulated (see fig. I—-LY). The excitation of the N. laryngeus superior gives also an arrest in the expiratory position, but has generally, in the same way as the sensible branches of the N. trigeminus, an after-effect of long duration. Some time passes before the dog breathes again calmly, and there is a tendency to get out of the narcosis. If the narcosis is very deep the effect is simple retardation (see fig. V). That of the N. glossopharyngeus always gives a deep inspiratory position, as is never reached in simple breathing, but only with deep sighs. Strong currents bring about a forced deep inspiration lasting ( 643 ) as long as the current lasts, weak currents at the same time accel- eration (see fig. VII—XI). That of the N.lingualis N.trigemini always gives, just as the N. laryng. sup. an arrest in expiratory position, but with accelerated super- ficial breathings and long continued after-effects (see fig, XITI—-XV). The stimulation of the N. hypoglossus, the N. accessorius and the N. facialis proved to have no influence on the respiration. The stimulation of the fila oifactoria appeared to be exceedingly dangerous as there was a great chance of sudden death, but, gave in some cases a curve analogous to that of the stimulation of the N. sympathicus (see fig. VI and fig. XII). Under the given circumstances, i.e. chloroformnarcosis and mode- rately strong induction current (we cannot lay too much stress on this), all sensible nerves of the tractus intestinalis and of the airpassages proved to have a retarding influence, with the exception of N. trigeminus, which may be considered as being in secondary connection with the deeper organs, being primarily a sensible nerve of the outward cover of the body. The arrest is a position of rest when the N. Splanchnicus, N. Vagus and the N. olfactorius are stimulated and the arrest is a forced inspiratory position when the N. Glossopharyngeus is stimulated. This result agrees on the whole with what others, under different circumstances, have found. Yet there are important deviations in some points. PHILIP KNOLL states in the ,Sitzwngsberichte der Wiener Akademie” Ba. 86. p: 483 and Bd. 92. p. 315, that the ramus lingualis N. trigemini belongs to the nerves, the excitation of which always gives inspiratory effects, whereas experimenting on five dogs with numerous stimulations, I have never found an inspiratory effect, but constantly an expiratcry effect with acceleration of respiration. This is of importance because the statement of the author that there is no real difference in the working of the sensible stimulation for narcotized, not narcotized or brainless animals, proves not to be exact in all cases. But these results are also of importance with a view to the theoretical considerations of LABORDE and this is in fact what gave rise to this communication. LABORDE passes the N. glossopharyngeus over in a few words, which prove, that he does not pay sufficient attention to what is known about this nerve. He says about it: ,Grace & un des résultats nouveaux de mes recherches personnelles ce nerf (c. a. s. N. Laryngé supérieur) n’est pas le seul qui puisse intervenir efficacement dans la réalisation fonctionelle dont il s’agit. ( 644 ) Le nerf glossopharyngien considéré jusqu’’ présent dans sa fonction essentielle comme un agent de sensibilité spéciale (sensibilité gustative), prend aussi une part réelle et active a titre de nerf sensitif de départ réflexe au fonctionnement respiratoire.” In 1883 Knox considered the N. Glossopharyngeus as belonging to those nerves which have always an inspiratory reflex-action on the respiration and several physiologists deny the gustative signifi- cation of the N. glossopharyngeus altogether or consider it at least of Jittle importance. For the action of the rhythmical tongue-tractions we have to think of three sensible nerves, viz.: 1. N. laryngeus superior. 2. N. glossopharyngeus. 3. Ram. lingualis N. trigemini. The first is of little importance to our purpose because on account of the distribution of its branches, it has the smallest chance of being really stimulated in LaBorpr’s method. Moreover it gives regularly a suspension of expiration under my experiment-conditions, and the results arrived at by means of pure chloroformnarcosis have some more value in this case, because the method will find its most important application in the chloroform-asphyxia. Yet it is not impossible that the N. laryng. sup. under certain conditions may restore the arrested respiration. LaBORDE brought about suffocation of his animals, by closing the air passages completely. The respiration curve changes its character completely, it begins to resemble a normal curve, held upside down. Instead of expiratory we get inspiratory positions of rest (see curve XVII). It is not easy to explain this phenomenon, as it would be more likely that the air-resorption in lungs where the air cannot enter, would give mechanically an expiratory position. The craving for air (comp. the subjoined curve XVI) does not explain it satis- factorily either, as a double pneumothorax gives long positions of rest in expiration, interrupted by energetical inspirations. The sti- mulation of the N. laryngeus superior gives an arrest, generally in a strongly pronounced expiratory position. The fact is that the electric excitation of the N. laryngeus superior has an opposite effect, which favours expiratory positions and in connection with the forced inspirations may bring about rhythmical in- and expiration. Therefore it does not seem probable to me, that on account of the experiment of LaBorDE, about which no sufficient information ( 645 ) is to be had, we may hold the N. laryng. sup. answerable for the usual action of the method, as it will most likely never be applied except for experiments on animals, when complete closure of the air passages has brought about cessation of respiraton. For it is exactly the experimental closure which modifies the usual type of respiration greatly, and which introduces unknown factors in the mechanism of respiration. It is quite a different thing for the N. glossopharyngeus and the ram. ling. N. V. They must necessarily be stimulated by every traction of the tongue. The N. glossopharyngeus appears to have an exceedingly strong effect on the inspiration, an arrest with strong stimulations, an acceleration with weaker stimulations. As well according to the investigations of KNoLi of 1883, as to my investigations in Prof. WINKLER’s laboratory, and to LABorDE’s vague allusion, the 9th nerve of the brain has this strong reflex-action. It is therefore not very ratioual, not to look first of all to this nerve, in trying to find _the explanation of the respiratory mechanism in LABorpDg’s method. The excitation of the N. trigeminus may also produce inspiratory effects under the experimental conditions introduced by KNouu (unknown to me); a pure chloroformnarcosis however, cannot have any or but a very small effect. Chemistry. — ‘EHchinopsine, a new crystalline vegetable base”. By Dr. M. GresHorr (Communicated by Prof. A. P. N, FRANCHIMONT). (Will be published in the Proceedings of the next meeting). Chemics. — ,7Vhe constitution of the Vapowr-phase in the System Water-Phenol, with one or two Liquid-phases.” By Dr. F. A. H. SCHREINEMAKERS (Communicated by Prof. J. M. van BEMMELEN. (Will be published in the Proceedings of the next meeting.) (June 20, 1900.) : U HBA yy Me ae) wi | Nl iP ean ( ur ins fact 4 fue) 7 7 ° A it a CON] Ree Ds. ACETONE (On the system: water- phenol-). 1. — and ether (The determination of the refractivity as a method for the investi- gation of the composition of co-existing phases in mixtures of). 101. ALBERDA VAN EKESTEIN (w.) and C. A. Losey pre Bruyn. ,On d sorbinose and l-sorbinose (p-tagatose) and their configurations”. 268, AMBRIZ (Determination of the latitude of) and of San Salvador (Portuguese West- Africa), 398. Anatomy. J. W. van Wiue: vA simple and rapid method for preparing neutral Pikrocarmine”, 409. ANOMALOUS DISPERSION of light (Solar phenomena, considered in connection with). 467. 575. Anthropology. P. H. Exyxman: /A new graphic system of Craniology” (communicated by Prof. C. Winker). 327. ApEX of the solar motion (The determination of the). 343. — of the solar motion in space (On the systematic corrections of the proper mo- tions of the stars, contained in AuWeExrs-Brapiey-Catalogue, and the coordinates of the). 262. apparatus (Methods and) used in the Cryogenic Laboratory, L. 129, IL. 406. 437, APPROXIMATION FORMULAE concerning the prime numbers not exceeding a given limit. 599. AROMATIC NITRO-coMPOUNDS (On the action of sodium mono- and -disulphides on), 271, ASCITES LIQUID of man (Lipolytic ferment in). 406, 428. Astronomy. H. J. Zwiurs: /The system of Sirius according to the latest observations” (communicated by Prof. H. G. van DB Sanne Bakituyzey). 6. — H. G. van pp Sanpr Bakuuyzen: »On the finding back of the comet of Hot- Mes according to the computations of H. J. Zwrers.” 69. — S8. L. Veenstra: »On the systematic corrections of the proper motions of the stars, contained in Auwers’-Brapipy-Catalogue, and the coordinates of the Apex of the solar motion in space” (communicated by Prof. J.C. Kaprryn). 262. — J. C. Kapreyy: /The determination of the Apex of the solar motion,” 353. — C. Sanpers: ,Determination of the latitude of Ambriz and of San Salvador 47 Proceedings Royal Acad, Amsterdam. Vol. LI. If GON T ENTS; (Portuguese West-Africa)” (communicated by Dr. KE. F. van be Sanne Bak HUYZEN). 398, Astronomy. J. Wereper: /The 14-monthly period of the motion of the pole of the earth from determinations of the azimuth of the meridian marks of the Leiden Observatory from 1882—-)$96” (communicated by Prof. H. G. van pE Sanpe BaknvyZzen). 546. ASYMMETRICAL CHANGE (Some observations concerning an) of the spectral lines of iron, radiating in a magnetic field. 298. azimutH (The 14-monthly period of the motion of the pole of the earth from deter- minations of the) of the meridian marks of the Leiden Observatory from 1$82 —1896. 546. Bacteriology. M. W. Beierinck: »On Jndigo-fermentation.” 495. BAKHUIS ROOZEBOOM (a. w.). An example of the conversion of mixed erystals into a compound. 23. 74. — presents a paper of Dr. Eanst Conen and C. van Eyx: On the Enantictropy of Tin.” 23. 77. IT. 81. 149. IIL. 281. IV. 464. — Mixed crystals of mercuric iodide and bromide. 81. 146. — presents a paper of Dr. Exnsr Conen: On a new kind of Transition elements (sixth kind).” 81. 153. — presents the dissertation of Dr. H. J. Hisstyx: »On mixed erystals of sodium nitrate with potassium nitrate and of sodium nitrate with silver nitrate.” 158. — The nature of inactive Carvoxime. !60. — presents a paper of Dr. Eunst Couen: »The alleged identity of red and yellow mercuric oxide.” I. 273. UL. 407. 458. — presents a paper of Dr. Kenst Conen: 7On the theory of the Transition Cell of the third kind.” (Part 1). 334. — presents a paper of Dr. A. Smers: ,Determination of the decrease in the vapour tension of solutions by means of determination of the increase in the boiling point”. 407. 469. — presents a paper of Dr. C. van Esk: /Formation and transformation of the double salt of Silvernitrate and Thalliumnitrate”. 468. 450, -— presents a paper of Dr. Exnsr Couen: ,Thermodynamics of Standard cells.’ (1st Part). GLO. — presents a paper of Dr. Ernst Cowen: Studies on Inversion.” (1st Part), 618. — presents a paper of Dr. A. Smits: /Determinations of the diminution of vapour- pressure and of the elevation of the boiling-point of dilute solutions.” 635. BAKNHUWZEN (E. F. VAN DE SANDE). See SanDE Bakuulzen (E. I. van pe), BAKHUIJZEN (H. G VAN DE SANDE), See SanpeE Baknouwzen (U. G. van pp). BAKKBR (G.). A remark on the molecular potentialfunction of Prof. van per Waals. 163. “gr i y . — The potentialfunction pg (7) = OEE ER nee (7) ee red) r ; r and the potential function of van per Waats. 247. BATAVIA (On spasms in the terrestrial magnetic force at). 141. 202. — (Iwo earth-quakes registered in Hurope aud at). 244, CyOUN TD EGNETSS: Tr BEHRENS (tH. H.). On isomorphous compounds of gold and mercury, 163. BEMMELEN (J. F. VAN). The results of a comparative investigation concerning the palatine-, orbital- and temporal regions of the Monotreme-skull. 81. BEMMELEN (J, M. VAN) presents a paper of Dr. F, A. H. ScHREINEMAKERS ; vOn the system: water, phenol, acetone.” 1. — presents a paper of Dr. F. A. H. Scurernemaxers: The constitution of the vapourphase in the system: Water-Phenol, with one or with two liquidphases.” 615. BEMMUELEN (w. VAN), Onspasms in the terrestrial magnetic force at Batavia, 141. 202, BENZENE (The formation of trisubstituted derivatives from disubstituted derivatives of), 468. 478. BENZOIC AcID (On the nitration of ) and its methylic and ethylic salts. 4. BES (K.). The formation of the resultant. 85. BEIJEKINCK (M. W.). On the formation of indigo from the Woad (Isatis tinctoe ria). 120. — On Indigo-fermentation, 495. BISMUTH (The Haxt-elfect and the increase of resistance of) in the magnetic field at very low temperatures. 228. 229, 348. BLANKSMA (J. J.). On the action of sodium mono- and -disulphides on aromatia nitrocompounds, 271. BLOODCORPUSCLES (On the power of resistance of the red), 574. BOILING-PoiNT (Determination of the decrease in the vapour tension of solutions by means of determination of the increase in the). 407. 469. — (Determinations of the diminution of vapour-pressure and of the elevation of the) of dilute solutions. 635. BOREL’s formulae for divergent series, 302. Botanics. M. W. Briertxcx: vOn the formation of indigo from the Woad (Isatis tinctoria). 120. — Miss T. Tammes: /Pomus in Pomo” (communicated by Prof. J. W. Mout). 331. BROMIDE (Mixed crystals of mercuric iodide and). $1. 146. BRUYN (Cc. 4. LOBRY DE). See Lopry bE Bruyn (C, A_). BRUYN (H. FE. De). On the relation between the mean sea-level and the height of half-tide. 189. BIJL (H. c.) and C. A. LosBry pe Bruyn. On isodialdane. 81. 143. CAPILLARY CONSTANT g (Lhe direct deduction of the) as a surface tension. 389. CAPILLARY ELECTROMETER (On the theory of LippMawn’s). 108. CARBON DIOXIDE (On the critical isothermal line and the densities of saturated vapour and liquid in isopentane and). 574. 588. CARDINAAL (J.) presents a paper of K. Bas: /On the formation of the resultant,” 85. — On an application of the involutions of higher order. 234. caRVOXIME (The nature of inactive). 160, Chemistry. I. A. H. Scureinemakers: vOn the system: water, phenol, acetone” (communicated by Prof. J. M. van Bemmepcey). 1. — A. F, Houteman: vOn the nitration of benzoie acid and its methylie and ethylic salts” (communicated by Prof. C. A, Losey pe Bruyn). 4. 47* Iv CONTENTS. Chemistry. C. A. Lopry pr Bruyn and A. Srecer: On the influence of water on the velocity of the formation of ether.” 23. 71. — H. W. Baxnuis RoozEsoom: /An example of the conversion of mixed crystals into a compound.” 23. 74, — Yrnsrv Conen and C. van Erk: On the Enantiotropy of Tin” (communicated by Prof. H. W. Bakuuis RoozEsoom). 23. 77. I. 81, 149. LUT. 281. IV. 464. — H.W.Baxkuuis Roozesoom: /Mixed crystals of mercuric iodide and bromide” 8i.146. — Ernst Conen: On a new kind of Transition elements (sixth kind)” (communi- cated by Prof. H. W. Baknurs Roozepoom). 81. 153. — ©. A. Losry pE Bruyn and H. C. Buu: vOn isodialdane’”. 81. 143. — A. Smits: Investigations with the micromanometer” (communicated by Prof, V. A. Jutus). 88. — U. W. Baxnuis RoozeBoom presents the dissertation of Dr. H. J. Hisstxk: 7On mixed crystals cf Sodiumnitrate with Potassiumnitrate and of Sodium nitrate with Silvernitrate ” 158. — H. W. Baxuurs Roozesoom: The nature of inactive Carvoxime.” 160. — Tu. H. Berens: ”On isomorphous compounds of gold and mercury.” 163. — ( A. Lospry pe Bruyn and W. ALBerpa van EKenstern: »d-Sorbinose and l-sorbinose ()-tagatose) and their configurations.” 268. — J. J. Buaxxsma: On the action of sodium mono- and -disulphides on aromatic- nitro-compounds” (communicated by Prof. C. A. Lopry pr Bruyy). 271. — Ernst Conen: «The alleged identity of red and yellow mercuric oxide” (commu- nicated by Prof. H. W. Bakuvrs Roozepoom). I. 273. II. 407. 458. — Ernst Conen: ,On the theory of the transition cell of the third kind” Part 1. (communicated by Prof UH. W. Bakuurs RoozeBoom). 534, — P. van Rompoureu: 7On the nitration of dimethylaniline dissolved in concentrated sulphuric acid’? (communicated by Prof. A. P. N. Francurmont). 342. — P. van RomBurcu: vOn the formation of indigo from Indigoferas and from Marsdenia tinctoria” (communicated by Prof. A. P. N. Francuimon'r). 344. — A. P. N. Francurmonr presents the dissertation of Dr. P. J. MonraGne: /Vhe action of hydrogen-nitrate upon the three isomeric chloro-benzoic acids and some of their derivatives.” 497. 461. —- A, Sirs: Determination of the decrease in the vapourtension of solutions by means of determination of the increase in the boiling-point” (communicated by Prof. H. W. Bakuuts Roozenoom). 407. 469. — A. F. Hotteman: The formation of trisubstituted derivatives from disubstituted derivatives of Benzene” (communicated by Prof. C. A. Lopry DE Bruyn). 468. 478. — ©. van Eryx: »Formation and transformation of the double sait of Silvernitrate and Thalliumnitrate.” 468. 480. — J. J. Hazewtnxet: Indican- its hydrolysis and the enzyme causing the same” (communicated by Prof. S. HooGewerrr). 512. — 8. Hoocrwerrr and H. ter Meunty: Contribution to the knowledge of Indican.” 520. — Ernst Conen: Thermodynamics of Standard cells” (1st Part) (communicated by Prof. H. W. Baxturs Roozesoom). 619. C ON T ENS T'S: Vv Chemistry. Ernst Conen: Studies on Inversion” (1st Part) (communicated by Prof. H. W. Bakuuis RoozeEBoom). 618. — A. Smirs: Determinations of the diminution of vapour-pressure and the elevation of the boiling-point of dilute solutions” (communicated by Prof. H. W. Baxnurs RoozeBoom). 635, — M. Gresnorr: /Echinopsine, a new crystalline vegetable base” (communicated by Prof. A. P. N. Francurmont). 645. — ¥. A. H. Scurernemaxers: »The constitution of the vapourphase in the system: Water-Phenol, with one or with two liquidphases” (communicated by Prof. J. M. van BemMMeE.en). 645. CHLORO-BENZOIC AcIDS (The action of hydrogennitrate wpon the three) and some of their derivatives. 407. 461. COHEN (ERNS87). On a new kind of Transition elements (sixth kind). $1. 153. — The alleged identity of red and yellow mercuric oxide. I. 273. If. 407. 458. — On the theory of the Transition cell of the third kind (1st Part). 334. — Thermodynamies of Standard cells (1st Part). 610. — Studies on Inversion (1st Part). 618. — and C. van Eyx: ,On the Enantiotropy of Tin.” 23. 77. IL. $1. 149, ILL. 281. IV. 464, comet of Holmes (On the finding back of the) according to the computations of H. J. Zwiers. 69. coMITANTS (On orthogonal). 485. CoMPouND (An example of the conversion of mixed crystals into a). 23. 74. CONVERSION (An example of the) of mixed erystals into a compound, 23. 74. COOLING (The) of a current of gas by sudden change of pressure. 379. coorDINatEs (On the systematic corrections of the proper motions of the stars, contained in Avwers’-BrapLey — Catalogue and the) of the Apex of the solar motion in space. 262. CRANIOLOGY (A new graphic system of). 327. CRYOGENIC LABORATORY (Methods and apparatus used in the). [. 129. IL. 406, 437. crysTaLs (An example of the conversion of mixed) into a compound. 23. 74. — (On mixed) of Sodiumnitrate with Potassiumnitrate and of Sodiumnitrate with Silvernitrate, 158. — (Mixed) of mercuric iodide and bromide. 81. 146. CUNAEUS (£. H. J.). The determination of the refractivity as a method for the investigation of the composition of co-existing phases in mixtures of acetone and ether. 101. curve (On the locus of the centre of hyperspherical curvature for the normal) of n-dimensional space. 527. curvEs (On rational twisted). 421. — (The theorem of JoacurmstHaL of the normal). 593. DEDUCTION (The direct) of the capillary constant ¢ as a surface tension. 389. DENSITIES (On the critical isothermalline and the) of saturated vapour and liquid in isopentane and carbon dioxide. 574, 588. DIELECTRIC COEFFICIENTS (The) of liquid nitrous oxide and oxygen. 140, 211. DIFFERENTIAL EQUATION (On some special cases of MonGo’s), 241. 326, 525, bad CrOl NID EGNeDss: DIMENSIONAL-SPACE (On the locus of the centre of hyperspherical curvature for the normal curve of v-). 527. DIMETHYLANILINE (On the nitration of) dissolved in concentrated sulphuric acid. 342. DISPERSION OF LIGHT (Solar Phenomena, considered in connection with anomalous). 487. 575. DISUBSTITUTED DERIVATIVES (The formation of trisubstituted derivatives from) of Benzene. 468. 478. DIVERGENT SERIES (BorEL’s formulae for). 302. FARTH (The 14-monthly period of the motion of the pole of the} from determinations of the azimuth of the meridian marks of the Leiden observatory from 1882 —1896. 546. FARTH-QUAKES (Two) registered in Europe and at Batavia, 244. ECHINOPSINE, a new crystalline vegetable base. 645. EINtTHOVEN (W,). On the theory of Lippmann’s capillary electrometer. 108. EKENSTEIN (W. ALBERDA VAN). See ALBERDA VAN ExensteIn (W.). ELECTROMETER (On the theory of Lipemann’s capillary). 108. ENANTIOTROPY of Tin (On the). 23. 77. If. 81. 149. IIL. 281. TV. 464. pxtropy of Radiation (The). I. 308. IL. 413. ENZYME (Indican- its hydrolysis and the) causing the same. 512. EQuavIons in which functions occur for different values of the independent variable. 534. ERRATUM. 141, 408. ETHER (The determination of the refractivity as a method for the investigation of the composition of co-existing phases in mixtures of acetone and). 101. — (On the influence of water on the velocity of the formation of). 23. 71. ®urope (Two earth-quakes registered in) and at Batavia. 244. EVERDINGEN JR, (BE. VAN). The Hatt-eflect and the increase of resistance of bismuth in the magnetic field at very low temperatures. 228, 229. 348. gyxk (c. VAN). Formation and transformation of the double salt of Silvernitrate and Thalliumnitrate. 468. 480, — and Ernst Conen: On the Enantiotropy of Tin”. 23. 77. UL. 81. 149. EYKMAN (Pp. H.j. A new graphic system of Craniology. 327. rat (The resorption of) and soap in the large and the small intestine. 234. 287. FORMATION (The) of the resultant. $5, FORMULAE (BorEL’s) for divergent series, 302. — (Approximation) concerning the prime numbers not exceeding a given limit. 599, FRANCHIMONT (A. P. N,) presents a paper of Dr. P. van RompurcH: /On the nitration of dimethylaniline dissolved in concentrated sulphuric acid.” 342, — presents a paper of Dr. P. van Rompurcu: /On the formation of indigo from Indigoferas and from Marsdenia tinctoria,” 344, — presents the dissertation of Dr. P. J. Monracne: The action of hydrogen-nitrate upon the three isomeric chloro-benzoie acids and some of their derivatives.” 407. 461. — presents a paper of Dr. M. Gresnorr: /Echinopsine, a new crystalline vegetable base.” 645. FUNCTION (The continuation of a one-valued) represented by a double series. 24. E50 Ni LB eNe IS. vil FuNcTIONS (Equations in which) occur for different values of the independent variable. 534. — C; (x) (New theorems on the roots of the). 196. Gas (The cooling of a current of) by sudden change of pressure. 379. Gases (Mereury pump for compressing pure and costly) under high pressure. 406. 437. GASMANOMETERS (Standard). 29. GEGENBAUBPR (z.). New theorems on the roots of the functions Cc" (a). 1986: GENUS UNITY (On twisted quinties of). 374. GOLD and mercury (On isomorphous compounds of). 163. GRAPHIC systEM (A new) of Craniology. 327. GRAVITATION (Considerations on). 559. GRresuHorr (m.). Echinopsine, a new crystalline vegetable base. 645. HALF-TIDE (On the relation between the mean sea-level and the height of). 189. HALL-EFFECT (The) and the increase of resistance of bismuth in the magnetic field at very low temperatures. 228. 229. 348. HAMBURGER (H. J.). The resorption of fat and soap in the large and the small intestine. 234. 287. — Lipolytie ferment in ascites-liquid of man. 406. 428. -— On the power of resistance of the red bloodcorpuscles. 574. HAZENOFHRL (FRITZ). The dielectric coefticients of liquid nitrous oxide and oxygen. 140. 211. HAZEWINKEL (J. J.). Indican-its hydrolysis and the enzyme causing the same. 512. HISSINK (H. J.). On mixed crystals of Sodium nitrate with Potassium nitrate and of Sodium nitrate with Silver nitrate. 158. HOLLEMAN (a. F.). On the nitration of benzoic acid and its methylic and ethylic salts. 4. — The formation of trisubstituted derivatives from disubstituted derivatives of Bens zene. 468. 478. wouMes (On the finding back of the comet of) according to the computations of H. J. Zwrers. 69. HOOGEWERFF (s,) presents a paper of J. J. Hazewrykei: /Indican-its hydrolysis and the enzyme causing the same.” 512. — and H. rer Mevten. Contribution to the knowledge of Indican. 520. HUBRECHT (A. A. W.) presents a paper of Dr. J. F. vay Bemmenen: The results of a comparative investigation concerning the palatine-, orbital- and temporal regions of the Monotreme-skull.” $1. HULSHOF (H.). The direct deduction of the capillary constant ¢ as a surface tension. 389. HYDROGEN-NITRATE (The action of) upon the three isomeric chloro-benzoie acids and some of their derivatives. 407. 461. Hydrography. J. P. van per Srok: /Tidal constants in the Lampong- and Sabang bay, Sumatra.” 178. — H. E, pp Bruyn: On the relation between the mean sea-level and the height of halftide.” 189. HYPERSPHERICAL CURVATURE (On the locus of the centre of) for the normal curve of v—dimensional space. 527. VII CONTENTS. IDENTITY (The alleged) of red and yellow mercuric oxide. J. 273. Il. 407. 458. INbIcAN-its hydrolysis and the enzyme causing the same. 512. — (Contribution to the knowledge of). 520, inp1Go (On the formation of) from the woad (Isatis tinctoria). 120. — (On the formation of) from Indigoferas and from Marsdenia tinctoria. 344. INDIGOFERAS (On the formation of indigo from) and from Marsdenia tinctoria. 344. INDIGO-PERMENTATION (On), 495. INTESTINE (‘he resorption of fat and soap in the large and the small). 234, 287. INVERSION (Studies on). 1st Part. 618. INVOLUTIONS of higher order (An application of the). 234. 10D1DE (Mixed crystals of mercuric) and bromide. 81. 146. tron (Some observations concerning an asymmetrical change of the spectral lines of) radiating in a magnetic field. 298. ISATIS TrNcrorTa (On the formation of indigo from the woad). 120. ISODIALDANE (On). SL. 143. ISOMORPHOUS COMPOUNDS (On) of gold and mercury. 163, ISOPENTANE and carbon dioxide (On the critical isothermal-line and the densities o saturated vapour and liquid in). 574. 588. ISOTHERMAL-LINE (On the critical) and the densities of saturated vapour and liquid in isopentane and carbon dioxide. 574. 588. ISOTHERMALS (The determination of) for mixtures of HCl and CH,. 40. JOACHIMSTHAL (The theorem of) of the normal curves. 593. JULIUS (Vv. A) presents a paper of Dr. A. Smits: Investigations with the micro- manometer.” 88. JULIUS (Ww. H.). Solar phenomena considered in connection with anomalous disper- sion of light. 467. 575. KAMERLINGH ONNES (H.) presets a paper of Dr. L. H. Srertsema: /Measure- ments on the magnetic rotation of the plane of polarisation in oxygen at different pressures.” 19. — Standard Gasmanometers. 29. — Methods and apparatus used in the Cryogenic Laboratory. I, 129, Il. 406. 437. — presents a paper of Dr. Fritz Hazexornri: /The dielectric coefficients of liquid nitrous oxide and oxygen.” 140. 211. = presents a paper of Dr. W. van BremMezen: On spasms in the terrestria magnetic force at Batavia.” 141. 202. — presents a paper of Dr. E. van EverDincen Jr,: The Hant-effect and the increase of resistance of bismuth in the magnetic field at very low temperatures.” 228. 229, 348. — presents a paper of Dr. J. E. Verscuarrett: /On the critical isothermal line and the densities of sattirated vapour and liquid in isopentane and carbon dioxide.” 574. 588. KAPTEYN (J. c) presents a paper of S. L, Vennsrra: ”On the systematic correc- tions of the proper motions of the stars, contained in AuwErs’-BrapLEy Catalogue and the coordinates of the Apex of the solar motion in space. 262. — The determination of the Apex of the solar motion, 353. KAPvTEYN (W.). On some special cases of Monan’s differential equation. 241, 326, 525, ClOUN 2 EONS: IX KLUYVER (J. c.). The continuation of a one-valued function represented by a double series. 24. — Boret’s formulae for divergent series. 302. — Approximation formulae ‘concerning the prime numbers not exceeding a given limit. 599. LABORDE’s method (Some reflexes on the respiration in connection with) to restore by rhythmical traction of the tongue, the respiration suppressed in narcosis. 640, LAMPONG- and Sabangbay, Sumatra (Tidal constants in the). 17S. LATITUDE (Determination of the) of Ambriz and of San Salvador (Portuguese West- Africa), 398. LicutT (Solar Phenomena considered in connection with anomalous dispersion of). 467. 575. LIPOLYTIC FERMENT in ascites-liquid of man. 406. 428. LIPPMANN’S capillary electrometer (On the theory of). 108. Liguip (On the critical isothermal tine and the densities of saturated vapour and) in isopentane and carbon dioxide. 574. 588. LiguipPHases (‘The constitution of the vapourphase in the system: Water-Phenol, with one or with two). 645. LOBRY DE BRUYN (C. A.) presents a paper of Prof. A. F. HoLteman: On the nitration of benzoic acid and its methylic and ethylic salts.” 4, — presents a paper of J. J. Buanksma: On the action of sodium mono- and -disulphides on aromatic nitro-compounds.” 271. — presents a paper of Prof. A, F. Honueman: The formation of trisubstituted derivatives from disubstituted derivatives of Benzene.” 468, 478, — and A. Srecer: vOn the influence of water on the velocity of the formation of ether.” 23. 71. — and H. C. Biz. On isodialdane. 81. 148. — and W. ALBerpa vAN EKENSTELN: /d-Sorbinose and /-sorbinose ()-tagatose) and their configurations.” 268. LORENTZ (H. A.). The elementary theory of the Zenman-effect. 52. — Considerations on Gravitation. 559. MAGNETIC FIELD (The Hatt-effect and the increase of resistance of bismuth in the) at very low temperatures, 228. 229. 348. — (Some observations concerning an asymmetrical change of the spectral lines of iron, radiating in a). 298. MAGNETIC ROTATION (Measurements on the) of the plane of polarisation in oxygen at different pressures. 19). Magnetism. W. van Bemmenen: /Spasms in the terrestrial magnetic force at Batavia” (communicated by Prof. H. Kameritincu Onngs). 141. 202. MARSDENIA TINCTORTA (On the formation of indigo from Indigoferas and from). 344. Mathematics. J. ©. Kiuyvyr: vThe continuation of a one-valued function, represented by a double series.” 24, — k. Bus: /On the formation of the resultant” (communicated by Prof. J.CarDINaaL). 85. — L. Graenpaurr: vNew theorems on the roots of the functions C* (a) (com- municated by Prof. Jan pe Vrigs). 196, xX CONTENTS. Mathematics. J. Carpinaat: /An application of the inyolutions of higher order.” 234. — W. Kapreyw: /On some special cases of Moner’s diflerential equation’’. 241. 326. 525. — J. C. Kivyver: /Boren’s formulae for divergent series”. 302. — Jan bE Vries: ,On twisted quintics of genus unity-”? 374. — P. H. Scuoure: /On rational twisted curves”. 421. — Jan be Vries: On orthogonal comitants.”” 485. — P. H. Scuoute: On the locus of the centre of hyperspherical curvature for the normal curve of ~-dimensional space.” 527. — P. H. Scuoure: The theorem of Joacuimsruan of the normal curves”. 593. — J. ©. Kuvyver: vApproximation formulae concerning the prime numbers not exceeding a given limit.” 599. MPASUREMENTS on the magnetic rotation of the plane of polarisation in oxygen at diferent pressures, 19. MELLB (M. A. VAN). Some reflexes on the respiration in connection with LaBorpE’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in narcosis. 640. MERCURIC IODIDE and bromide (Mixed crystals of). 81. 146. MERCURIC OXIDE (The alleged identity of red and yellow). [. 273. II. 407. 458. MERCURY (On isomorphous compounds of gold and). 163. MERCURY PUMP for compressing pure and costly gases under high pressure. 406. 437. METHOD (A simple and rapid) for preparing neutral Pikrocarmine. 409. — for the investigation (The determination of the refractivity as a) of the compo- sition of co-existing phases in mixtures of acetone and ether. 101. METHODS and apparatus used in the Cryogenic Laboratory. I. 129. IL. 406. 487. MEULEN (H. TEX) and 8S. HooGewerrr. Contribution to the knowledge of Indican. 520. MICROMANOMETER (Investigations with the). 88. MIXTURES of acetone and ether (The determination of the refractivity as a method for the investigation of the composition of co-existing phases in). 101. mixtures of HCl and C, H, (The determination of isothermals for). 40. MOLECULAR potential function (A remark on the) of Prof. vaN DER Waats. 163. MOLL (J. W.) presents a paper of Miss T. Tammes: »Pomus in Pomo.” 331. MONGE's differential equation (On some special cases of). 25]. 326. 525. MONOTREME-SKULL (The results of a comparative investigation concerning the palatine- orbital- and temporal regions of the). 81. MONTAGNE (pe. J.). The action of hydrogen-nitrate upon the three isomeric chloro- benzoic acids and some of their derivatives. £07. 461. motion of the pole of the earth (he 14-monthly period of the) from determinations of the azimuth of the meridian marks of the Leiden Observatory from 1882 — 1896. 546. narcosis (Some reflexes on the respiration in connection with LasorpE’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in). 640. niTRATION (On the) of benzoie acid and its methylic and ethylic salts. 4. — (On the) of dimethylaniline dissolved in concentrated sulphuric acid. 342. CONTENTS. XI NiTRoO-compounps (On the action of sodium mono- and -disulphides on aromatic). 271. NITROUS OXIDE and oxygen (The dielectric coefficients of liquid). 140. 211. ONNES (H. KAMERLINGH). See KamerLINGH Onnes (H.). orBITaL- and temporal regions of the Monotreme-skull (The results of a comparative investigation concerning the palatine-,). 81. ORTHOGONAL comitants (On). 485. OXYGEN (The dielectric coefficients of liquid nitrous oxide and). 140. 211. — (Measurements on the magnetic rotation of the plane of polarisation in) at different pressures. 19. PALATINU-, orbital- and temporal regions of the Monotreme-skull (The results of a comparative investigation concerning the), 81. pHasEs (The Cetermination of the refractivity as a method for the investigation of the composition of co-existing) in mixtures of acetone and ether. 101. PHENOL (The constitution of the vapourphase in the system: Water-), with one or with two liquidphases. 645. — Acetone (On the system: Water). 1. PHENOMENA (Solar) considered in connection with anomalous dispersion of light. 467. 575. Physical geography. J. P. van per Srox: »Two earth-quakes, registered in Europe and at Batavia’. 244. Physics. L. H. Srertsrema: »Measurements on the magnetic rotation of the plane of polarisation in oxygen at different pressures” (communicated by Prof. H. Kamertrnen Onngs). 19. — H. Kameriincu Onnes: Standard Gasmanometers.” 29. — N. Quint Gzn: The determination of isothermals for mixtures of HCl and CoH,” (communicated by Prof. J. D. van per Waats). 40. — H. A. Lorentz: vThe elementary theory of the ZEEMAN-effect.” 52. — FE. H. J. Cunarus: /The determination of the refractivity as a method for the investigation of the composition of co-existing phases in mixtures of acetone and ether” (communicated by Prof. J. D. van per Waats). LOI. — W. Erytuoven: vOn the theory of Lrppmann’s capillary electrometer” (com- municated by Prof. T, Zasyer), 108. — H. Kameruincu Onnes: /Methods and apparatus used in the Cryogenic Labo- ratory.” [. 129. IL. 406. 487. — Fritz Hazenornri: The dielectric coefficients of liquid nitrous oxite and oxygen” (communicated by Prof. H. Kampruincd Onnus). 140. 211. — G. Bakker: vA remark on the molecular potentialfunction of Prof. v. bp. Waats” (communicated by Prof. J. D. vax per Waats). 163. — BE. van Everpixcen Jr.: The Haxt-effect and the increase of resistance of bismuth in the magnetic field at very low temperatures” (communicated by Prof. H. KamerLincH Onnes). 228. 229. 348. Aev + Bear = sin (qr -+ 2) ; and ¢(7 2 — G. Bakker: ”The potentialfunction g (7) = ; and the potentialfunction of van per Waazs” (communicated by Prof. J. D. van der Waals). 247. x1 C ON TE Ni L's; Physics. P. Zeyman: Some observations concerning an asymmetrical change of the spectral lines of iron, radiating in a magnetic field.” 298. —J. D. van per Waats Jr.: Lhe Entropy of Radiation” (communicated by Prof. J. D. van per Waats). L. 308. IL. 413. — J. D. van per Waats: /The cooling of a current of gas by sudden change of pressure.” 379. — H. Hursnor: The direct deduction of the capillary constant ¢ as a surface- tension” (communicated by Prof. J. D. van DER Waals). 389. — W. H. Junius: Scolar Phenomena considered in connection with anomalous dispersion of iight.”” 467. 575. — J. D. van per Waats Jr. : Equations in which functions occur for different values of the independent variable” (communicated by Prof. J. D. van per Waats). 534. — H. A, Lorentz: /Considerations on Gravitation.” 559. J. E. Verscuarrett: 7On the critical isothermal line and the densities of satur- ated vapour and liquid in isopentane and carbon dioxide’ (communicated by Prof. H. Kampriinen Onnes). 574. 588. Physiology. H. J. Hamburcrr: The resorption of fat and soap in the large and the small intestine.” 234, 287, — H. J. Hampurcer: /Lipolytic ferment in ascites-liquid of man.” 406. 428. — H. J. Hampurcer: On the power of resistance of the red blood-corpuscles.” 574. — M. A. van MBLLE: /Some reflexes on the respiration in connection with LaBorDE’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in Nareosis” (communicated by Prof. C. WixkiEr). 640. PIEZOMETERS (Precision-) with variable volume for gases. 29. PIKRO-CARMINE (A simple and rapid method for preparing neutral). 409. POLARISATION (Measurements on the magnetic rotation of the plane of) in oxygen at different pressures, 19. POLE OF THE EARTH (The 14-monthly period of the motion of the) from determinations of the azimuth of the meridian marks of the Leiden observatory from 1882— 1896. 546. pomus in Pomo. 331. POTASSIUMNITRATE (On mixe+ crystals of Sodiumnitrate with) and of Sodiumnitrate with Silvernitrate, 158. POTENTIAL FUNCTION (A rema-k on the molecular) of Prof. vaN DER Waats. 163. — (The) g(r) = Ae BO and ¢(7) = aa and the potentialfunction of 7 Fs VAN DER WAALS. 247. PRESSURE (The cooling of a current of gas by sudden change of). 379. PRESSURES (Measurements on the magnetic rotation of the plane of polarisation in oxygen at different). 19. PRIME NUMBERS (Approximation formulae concerning the) not exceeding a given limit. 599. QUINT GZN. (N.). The determination of isothermals for mixtures of HCl and C,H,. 40. auintics (On twisted) of genus unity. 374. RADIATION (The Entropy of). I. 308. IL. 413. Rerractivity (The determination of the) as a method for the investigation of the composition of co-existing phases in mixtures of acetone and ether. 101, CONTENTS. XT REINDERS (w.). Mixed crystals of mercuric iodide and bromide. 81. 146. RESISTANCE (On the power of) of the red blood-corpuscles. 574. — (The Hatt-effect and the increase of) of bismuth in the magnetic field at very low temperatures. 228. 229. 348. RESPIRATION (Some reflexes on the) in connection with LaBorpe’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in narcosis. 640. RESORPTION (The) of fat and soap in the large and the small intestine. 234, 287, RESULTANT (The formation of the). 85. RHYTHMICAL TRACTION of the tongue (Some reflexes on the respiration in connection with Lasorpe’s method, to restore by), tke respiration suppressed in narcosis, 640, ROMBURGH (P. VAN). Qn the nitration of dimethylaniline dissolved in concen- trated sulphuric acid, 342. — On the formation of indigo from Indigoferas and from Marsdenia tinctoria. 344. roots (New theorems on the) of the functions CN(a). 196. ROOZEBOOM (H. W. BAKHUTS). See Bakaurts Roozesoom (H. W.). SABANG-BAY, Sumatra (Tidal constants in the Lampong- and). 178. saut (Formation and transformation of the double) of Silvernitrate and Thalliumnitrate. 468. 480. saLts (On the nitration of benzoic acid and its methylic and ethylic). 4. SANDE BAKHUYZE®N (8. F. VAN DE) presents a paper of C. Sanpers: Deter- mination of the latitude of Ambriz and of San Salvador (Portuguese West- Africa), 398. SANDE BAKHUYZEN (H. G VAN De) presents a paper of H. J. Zwiers vThe system of Sirius according to the latest observations.” 6. — On the finding back of the comet of Holmes according to the computations of H. J. Zwiers. 69. — presents a paper of J, Werrper: The 14-monthly period of the pole of the earth from determinations of the azimuth of the meridian marks of the Leiden Observatory from 1882—1896.” 546. SANDERS (c.). Determination of the latitude of Ambriz and of San Salvador (Por- tuguese West-Africa). 398. SAN SALVADOR (Portuguese West-Africa) (Determination of the latitude of Ambriz and of). 398. scHourer (Pv. 4). On rational twisted curves. 421. — On the locus of the centre of hyperspherical curvature for the normal curve of n-dimensional space, 527. — The theorem of JoacnimstuaL of the normal curves. 593. SCHREINEMAKERS (f. A. H.). On the system: water, phencl, acetone. L. — The constitution of the vapourphase in the system: Water-Phenol, with one or two liquidphases. 645, SBEA-LEVEL (On the relation between the mean) and the height of half-tide. 189. sERIES (The continuation of one-valued function represented by a double). 24. STERTSEMA (tL. H.), Measurements on the magnetic rotation of the plane of polari- sation in oxygen ab different pressures, 19. XIV C ON DE Nis: sIbverNiTRATE (Formation aud transformation of the double salt of) and Thallium- nitrate. 408. 480. — (On mixed crystals of Sodiumnitrate with Potassiumnitrate and of Sodiumnitrate with), 158. sirius (The system of) according to the latest observations. 6. smivs (a.). Investigations with the micromanometer, 88. — Determination of the decrease in the vapourtension of solutions by means of determination of the increase in the boiling point. 407. 409, — Determinations of the diminution of vapour-pressure and of the elevation of the boilingpoint of dilute solutions. 635. soap (The resorption of fat and) in the large and the small intestine. 234. 287. SODIUMMONO- AND -DISULPHIDES (On the action of) on aromatic nitro-compounds, 271. SODIUMNITRATE (On mixed crystals of) with potassiummitrate and of sodiumnitrate with silvernitrate. 158. SOLAR MOTION (The determination of the Apex of the). 353. — in space (On the systematic corrections of the proper motions of the stars, contained in Auwers’-Brapiey Catalogue, and the zoordinates of the Apex of the). 262. SOLAR PHENOMENA considered in connection with anomalous dispersion of light. 467.575. soLurions (Determination of the decrease in the vapourtension of) by means of deter- mination of the increase in the boilingpoint. 407. 469. — (Determinations of the diminution of vapour-pressure and of the elevation of the boilingpoint of dilute). 635. d-sorBinose and l-sorbinose (p-tagatose) aud their configurations. 268. spasms (On) in the terrestrial magnetic force at Batavia. 141. 202. SPECTRAL LINES of iron (Some observations concerning an asymmetrical change of the) radiating in a magnetic field. 298. STANDARD CELLS (Thermodynamics of). 1st Part. 610. STANDARD GASMANOMETERS. 29, stars (On the systematic corrections of the proper motions of the) contained in Auwers’-BrapDLEy-Catalogue and the coordinates of the Apex of the solar motion in space. 262. sTEGER (a.) and C. A. Losry pr Bruyn: 7On the influence of water on the velocity ‘of the formation of ether. 23, 71. stok (J. Pp VAN DER). Tidal constants in the Lampong- and Sabangbay, Sumatra, 178. — Two earth-quakes, registered in Europe and at Batavia. 244. uLeuuric acid (On the nitration of dimethylaniline dissolved in concentrated). 342. SURFACE-TENSION (The direct deduction of the capillary constant ¢ as a). 389. y-tacarosE (d-Sorbinose and |-sorbinose) and their configurations. 268. TAMMEsS (T.). Pomus in Pomo. 331. gemprratures (The IHauu-effect and the increase of resistance of bismuth in the magnetic field at very low). 228. 229. 348. TEMPORAL REGIONS of the Monotreme-skull (The results of a comparative investigation concerning the palatine-, orbital and), $1. CONTENTS. Xv TERRESTRIAL MAGNETIC PACE (On spasms in the) at Batavia. 141. 202. YHALLIUMNITRaTE (ormation and transformation of the double salt of Silvernitrate and). 468. 450. THEOREM of JoacuimstHaL (The) of the normaicurves. 593. THEOREMS (New) on the roots of the functions Os (x). 196. THEORY (On the) of LippmMann’s capillary electrometer. 108. — (On the) of the transition-cell of the third kind. (Part I), 334. — (The elementary) of the ZeErman-eflect. 52. THERMODYNAMICS of standard cells (lst Part). 610. TIDAL consrants in the Lampong- and Sabangbay, Sumatra. 178. tm (On the Enantiotropy of). 23. 77. IL $1. 149. ILL 281. IV. 464. TONGUE (Some reflexes on the respiration in connection with Laporpgr’s method, to restore by rhythmical traction of the), the respiration suppressed in narcosis. 640. TRANSITION CELL (On the theory of the) third kind. Part 1. 334, — ELEMENTs (sixth kind) (On a new kind of). 81. 153, TRISUBSTITUTED DERIVATIVES (The formation of) from disubstituted derivatives of Benzene. 468. 478. TWISTED CURVES (On rational). 421. vapour (Ou the critical isothermalline and the densities of saturated) and liquid in isopentane and carbon dioxide. 574. 588. vapourPHase (The constitution of the) in the system: Water-Phenol, with one or with two liquidphases. 645, VAPOUR-PRESSURE (Determination of the diminution of) and of the elevation of the boilingpoint of dilute solutions. 635, VAPOUR TENSION (Determination of the decrease in the) of solutions by means of deter- mination of the increase in the boilingpoint. 407. 469. VARIABLE (Equations in which functions occur for different values of the indepen- dent). 534. VEENSTRA (8. L.). On the systematic corrections of the proper motions of the stars, contained in Auwers’-Brabiey-Catalogue, and the coordinates of the Apex of the solar motion in space. 262. VEGETABLE BASE (Echinopsine, a new erystalline), 645, vetocity (On the influence of water on the) of the formation of ether, 23. 71. VERSCHAEFFELT (J. B.). On the critical isothermal line and the densities of saturated vapour and liquid in isopentane anil carbondioxide. 574. 588. VRIES (JAN DE) presents a paper of Prof. LL. Gearnpatrr: 7New theorems on : ea y ; the roots of the functions C; (7).” 196. — On twisted quinties of genus unity. 374. — On orthogonal comitants. 455. WAALS (J. D. VAN DER) presents a paper of N. Qurnv Gzy.: /The determination of isothermals for mixtures of HCl and CU.” 40. — preseats a paper of WU. H. J. Cunanus: 7fhe determination of the refractivity as a method for the investigation of the composition of co-existing phases in mixtures of acetone and ether.’ LOL, XVI CON TEN: T's. WAALS (J, D. VAN DER) presents ‘a paper of Dr. G. Bakker: vA remark on the molecular potential function of Prof. van per Waats.” 163. — presents a paper of Dr. G, Bakker: /'The potential function g(r) = Seed core . x. and g(”) = Asin (9rF2) ond the potential function of vaN DER Waats.” 247. ra — presents a paper of J. D. van per Waats Jr.: /The Entropy of Radiation.” L. 308. 11. 413. — The cooling of a current of gas by sudden change of pressure. 379. — presents a paper of H. Hunsuor: The direct deduction of capillary constant « as a surface-tension.” 389. — presents a paper of J. D. van per Waats Jr.: /Miquations in which functions occur for different values of the independent variable.” 534. WAALS JR. (J. D. VAN DER). The Entropy of Radiation. [. 308. IL. 413. — Equations in which functions occur for different values of the independent variable, 534. WA'TER-Phenol (The constitution of the vapourphase in the system), with one or with two liquidphases. 645. — Phenol, Acetone (On the system). 1. — (On the influence of) on the velocity of the formation of ether. 23. 71. WEEDER (J.). The 14-monthly period of the motion of the pole of the earth from determinations of the azimuth of the meridian marks of the Leiden Observatory from 1882—1896. 546. WINKLER (c.) presents a paper of Dr. P. H. Eykman: vA new graphic system of Craniology.” 327. — presents a paper of M. A. van MELLE: /Some reflexes on the respiration in connection with Lasorpsr’s method to restore, by rhythmical traction of the tongue, the respiration suppressed in narcosis.” 640. woab (lsatis tinctoria) (On the formation of indigo from the), 120. WIJHE (J. W. VAN). A simple and rapid method for preparing neutral Vikro carmine. 409. ZAAIJER (t.) presents a paper of Prof. W. ErntHoven : On the theory of LiprMann’s capillary electrometer.” 108. ZEEMAN-EFFECT (The elementary theory of the). 52. ZBREMAN (p.). Some observations concerning an asymmetrical change of the spectral lines of iron, radiating in a magnetic field. 298. Zoology. J. F. van BemMELen: /‘ihe results of a comparative investigation concerning” the palatine-, orbital- and temporal regions of the Monotreme skull” (communi- cated by Prof. A. 4. W. Huprecut). 81. ZWIERS (Hu. J.). The system of Sirius according to the latest observations: 6. — (On the finding back of the comet of Houmes according to the computations of). 69. Q Akademie van Wetenschappen, 5 a Amsterdam. Afdeeling voor ALS de Wis~ en Natuurkundige Wise Wetenschappen Physical & Proceedings of the Section pplied Sci: of Sciences PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET UNIVERSITY OF TORONTO LIBRARY 4 STORAGE ———